[1, 1, 1, 1, 1, 1, 1, 1, 1] => 1, 1, 1, 1, 1, 1, 1, 1, 1
[1, 1, 1, 1, 1, 1, 1, 1, 2] => 1, 1, 1, 1, 1, 1, 1, 1, 2
[1, 1, 1, 1, 1, 1, 1, 1, 3] => 1, 1, 1, 1, 1, 1, 1, 1, 3
[1, 1, 1, 1, 1, 1, 1, 2, 1] => 1, 1, 1, 1, 1, 1, 1, 2, 1
[1, 1, 1, 1, 1, 1, 1, 2, 2] => 1, 1, 1, 1, 1, 1, 1, 2, 2
[1, 1, 1, 1, 1, 1, 1, 2, 3] => 1, 1, 1, 1, 1, 1, 1, 2, 3
[1, 1, 1, 1, 1, 1, 1, 3, 1] => 1, 1, 1, 1, 1, 1, 1, 3, 1
[1, 1, 1, 1, 1, 1, 1, 3, 2] => 1, 1, 1, 1, 1, 1, 1, 3, 2
[1, 1, 1, 1, 1, 1, 1, 3, 3] => 1, 1, 1, 1, 1, 1, 1, 3, 3
[1, 1, 1, 1, 1, 1, 2, 1, 1] => 1, 1, 1, 1, 1, 1, 2, 1, 1
[1, 1, 1, 1, 1, 1, 2, 1, 2] => 1, 1, 1, 1, 1, 1, 2, 1, 2
[1, 1, 1, 1, 1, 1, 2, 1, 3] => 1, 1, 1, 1, 1, 1, 2, 1, 3
[1, 1, 1, 1, 1, 1, 2, 2, 1] => 1, 1, 1, 1, 1, 1, 2, 2, 1
[1, 1, 1, 1, 1, 1, 2, 2, 2] => 1, 1, 1, 1, 1, 1, 2, 2, 2
[1, 1, 1, 1, 1, 1, 2, 2, 3] => 1, 1, 1, 1, 1, 1, 2, 2, 3
[1, 1, 1, 1, 1, 1, 2, 3, 1] => 1, 1, 1, 1, 1, 1, 2, 3, 1
[1, 1, 1, 1, 1, 1, 2, 3, 2] => 1, 1, 1, 1, 1, 1, 2, 3, 2
[1, 1, 1, 1, 1, 1, 2, 3, 3] => 1, 1, 1, 1, 1, 1, 2, 3, 3
[1, 1, 1, 1, 1, 1, 3, 1, 1] => 1, 1, 1, 1, 1, 1, 3, 1, 1
[1, 1, 1, 1, 1, 1, 3, 1, 2] => 1, 1, 1, 1, 1, 1, 3, 1, 2
[1, 1, 1, 1, 1, 1, 3, 1, 3] => 1, 1, 1, 1, 1, 1, 3, 1, 3
[1, 1, 1, 1, 1, 1, 3, 2, 1] => 1, 1, 1, 1, 1, 1, 3, 2, 1
[1, 1, 1, 1, 1, 1, 3, 2, 2] => 1, 1, 1, 1, 1, 1, 3, 2, 2
[1, 1, 1, 1, 1, 1, 3, 2, 3] => 1, 1, 1, 1, 1, 1, 3, 2, 3
[1, 1, 1, 1, 1, 1, 3, 3, 1] => 1, 1, 1, 1, 1, 1, 3, 3, 1
[1, 1, 1, 1, 1, 1, 3, 3, 2] => 1, 1, 1, 1, 1, 1, 3, 3, 2
[1, 1, 1, 1, 1, 1, 3, 3, 3] => 1, 1, 1, 1, 1, 1, 3, 3, 3
[1, 1, 1, 1, 1, 2, 1, 1, 1] => 1, 1, 1, 1, 1, 2, 1, 1, 1
[1, 1, 1, 1, 1, 2, 1, 1, 2] => 1, 1, 1, 1, 1, 2, 1, 1, 2
[1, 1, 1, 1, 1, 2, 1, 1, 3] => 1, 1, 1, 1, 1, 2, 1, 1, 3
[1, 1, 1, 1, 1, 2, 1, 2, 1] => 1, 1, 1, 1, 1, 2, 1, 2, 1
[1, 1, 1, 1, 1, 2, 1, 2, 2] => 1, 1, 1, 1, 1, 2, 1, 2, 2
[1, 1, 1, 1, 1, 2, 1, 2, 3] => 1, 1, 1, 1, 1, 2, 1, 2, 3
[1, 1, 1, 1, 1, 2, 1, 3, 1] => 1, 1, 1, 1, 1, 2, 1, 3, 1
[1, 1, 1, 1, 1, 2, 1, 3, 2] => 1, 1, 1, 1, 1, 2, 1, 3, 2
[1, 1, 1, 1, 1, 2, 1, 3, 3] => 1, 1, 1, 1, 1, 2, 1, 3, 3
[1, 1, 1, 1, 1, 2, 2, 1, 1] => 1, 1, 1, 1, 1, 2, 2, 1, 1
[1, 1, 1, 1, 1, 2, 2, 1, 2] => 1, 1, 1, 1, 1, 2, 2, 1, 2
[1, 1, 1, 1, 1, 2, 2, 1, 3] => 1, 1, 1, 1, 1, 2, 2, 1, 3
[1, 1, 1, 1, 1, 2, 2, 2, 1] => 1, 1, 1, 1, 1, 2, 2, 2, 1
[1, 1, 1, 1, 1, 2, 2, 2, 2] => 1, 1, 1, 1, 1, 2, 2, 2, 2
[1, 1, 1, 1, 1, 2, 2, 2, 3] => 1, 1, 1, 1, 1, 2, 2, 2, 3
[1, 1, 1, 1, 1, 2, 2, 3, 1] => 1, 1, 1, 1, 1, 2, 2, 3, 1
[1, 1, 1, 1, 1, 2, 2, 3, 2] => 1, 1, 1, 1, 1, 2, 2, 3, 2
[1, 1, 1, 1, 1, 2, 2, 3, 3] => 1, 1, 1, 1, 1, 2, 2, 3, 3
[1, 1, 1, 1, 1, 2, 3, 1, 1] => 1, 1, 1, 1, 1, 2, 3, 1, 1
[1, 1, 1, 1, 1, 2, 3, 1, 2] => 1, 1, 1, 1, 1, 2, 3, 1, 2
[1, 1, 1, 1, 1, 2, 3, 1, 3] => 1, 1, 1, 1, 1, 2, 3, 1, 3
[1, 1, 1, 1, 1, 2, 3, 2, 1] => 1, 1, 1, 1, 1, 2, 3, 2, 1
[1, 1, 1, 1, 1, 2, 3, 2, 2] => 1, 1, 1, 1, 1, 2, 3, 2, 2
[1, 1, 1, 1, 1, 2, 3, 2, 3] => 1, 1, 1, 1, 1, 2, 3, 2, 3
[1, 1, 1, 1, 1, 2, 3, 3, 1] => 1, 1, 1, 1, 1, 2, 3, 3, 1
[1, 1, 1, 1, 1, 2, 3, 3, 2] => 1, 1, 1, 1, 1, 2, 3, 3, 2
[1, 1, 1, 1, 1, 2, 3, 3, 3] => 1, 1, 1, 1, 1, 2, 3, 3, 3
[1, 1, 1, 1, 1, 3, 1, 1, 1] => 1, 1, 1, 1, 1, 3, 1, 1, 1
[1, 1, 1, 1, 1, 3, 1, 1, 2] => 1, 1, 1, 1, 1, 3, 1, 1, 2
[1, 1, 1, 1, 1, 3, 1, 1, 3] => 1, 1, 1, 1, 1, 3, 1, 1, 3
[1, 1, 1, 1, 1, 3, 1, 2, 1] => 1, 1, 1, 1, 1, 3, 1, 2, 1
[1, 1, 1, 1, 1, 3, 1, 2, 2] => 1, 1, 1, 1, 1, 3, 1, 2, 2
[1, 1, 1, 1, 1, 3, 1, 2, 3] => 1, 1, 1, 1, 1, 3, 1, 2, 3
[1, 1, 1, 1, 1, 3, 1, 3, 1] => 1, 1, 1, 1, 1, 3, 1, 3, 1
[1, 1, 1, 1, 1, 3, 1, 3, 2] => 1, 1, 1, 1, 1, 3, 1, 3, 2
[1, 1, 1, 1, 1, 3, 1, 3, 3] => 1, 1, 1, 1, 1, 3, 1, 3, 3
[1, 1, 1, 1, 1, 3, 2, 1, 1] => 1, 1, 1, 1, 1, 3, 2, 1, 1
[1, 1, 1, 1, 1, 3, 2, 1, 2] => 1, 1, 1, 1, 1, 3, 2, 1, 2
[1, 1, 1, 1, 1, 3, 2, 1, 3] => 1, 1, 1, 1, 1, 3, 2, 1, 3
[1, 1, 1, 1, 1, 3, 2, 2, 1] => 1, 1, 1, 1, 1, 3, 2, 2, 1
[1, 1, 1, 1, 1, 3, 2, 2, 2] => 1, 1, 1, 1, 1, 3, 2, 2, 2
[1, 1, 1, 1, 1, 3, 2, 2, 3] => 1, 1, 1, 1, 1, 3, 2, 2, 3
[1, 1, 1, 1, 1, 3, 2, 3, 1] => 1, 1, 1, 1, 1, 3, 2, 3, 1
[1, 1, 1, 1, 1, 3, 2, 3, 2] => 1, 1, 1, 1, 1, 3, 2, 3, 2
[1, 1, 1, 1, 1, 3, 2, 3, 3] => 1, 1, 1, 1, 1, 3, 2, 3, 3
[1, 1, 1, 1, 1, 3, 3, 1, 1] => 1, 1, 1, 1, 1, 3, 3, 1, 1
[1, 1, 1, 1, 1, 3, 3, 1, 2] => 1, 1, 1, 1, 1, 3, 3, 1, 2
[1, 1, 1, 1, 1, 3, 3, 1, 3] => 1, 1, 1, 1, 1, 3, 3, 1, 3
[1, 1, 1, 1, 1, 3, 3, 2, 1] => 1, 1, 1, 1, 1, 3, 3, 2, 1
[1, 1, 1, 1, 1, 3, 3, 2, 2] => 1, 1, 1, 1, 1, 3, 3, 2, 2
[1, 1, 1, 1, 1, 3, 3, 2, 3] => 1, 1, 1, 1, 1, 3, 3, 2, 3
[1, 1, 1, 1, 1, 3, 3, 3, 1] => 1, 1, 1, 1, 1, 3, 3, 3, 1
[1, 1, 1, 1, 1, 3, 3, 3, 2] => 1, 1, 1, 1, 1, 3, 3, 3, 2
[1, 1, 1, 1, 1, 3, 3, 3, 3] => 1, 1, 1, 1, 1, 3, 3, 3, 3
[1, 1, 1, 1, 2, 1, 1, 1, 1] => 1, 1, 1, 1, 2, 1, 1, 1, 1
[1, 1, 1, 1, 2, 1, 1, 1, 2] => 1, 1, 1, 1, 2, 1, 1, 1, 2
[1, 1, 1, 1, 2, 1, 1, 1, 3] => 1, 1, 1, 1, 2, 1, 1, 1, 3
[1, 1, 1, 1, 2, 1, 1, 2, 1] => 1, 1, 1, 1, 2, 1, 1, 2, 1
[1, 1, 1, 1, 2, 1, 1, 2, 2] => 1, 1, 1, 1, 2, 1, 1, 2, 2
[1, 1, 1, 1, 2, 1, 1, 2, 3] => 1, 1, 1, 1, 2, 1, 1, 2, 3
[1, 1, 1, 1, 2, 1, 1, 3, 1] => 1, 1, 1, 1, 2, 1, 1, 3, 1
[1, 1, 1, 1, 2, 1, 1, 3, 2] => 1, 1, 1, 1, 2, 1, 1, 3, 2
[1, 1, 1, 1, 2, 1, 1, 3, 3] => 1, 1, 1, 1, 2, 1, 1, 3, 3
[1, 1, 1, 1, 2, 1, 2, 1, 1] => 1, 1, 1, 1, 2, 1, 2, 1, 1
[1, 1, 1, 1, 2, 1, 2, 1, 2] => 1, 1, 1, 1, 2, 1, 2, 1, 2
[1, 1, 1, 1, 2, 1, 2, 1, 3] => 1, 1, 1, 1, 2, 1, 2, 1, 3
[1, 1, 1, 1, 2, 1, 2, 2, 1] => 1, 1, 1, 1, 2, 1, 2, 2, 1
[1, 1, 1, 1, 2, 1, 2, 2, 2] => 1, 1, 1, 1, 2, 1, 2, 2, 2
[1, 1, 1, 1, 2, 1, 2, 2, 3] => 1, 1, 1, 1, 2, 1, 2, 2, 3
[1, 1, 1, 1, 2, 1, 2, 3, 1] => 1, 1, 1, 1, 2, 1, 2, 3, 1
[1, 1, 1, 1, 2, 1, 2, 3, 2] => 1, 1, 1, 1, 2, 1, 2, 3, 2
[1, 1, 1, 1, 2, 1, 2, 3, 3] => 1, 1, 1, 1, 2, 1, 2, 3, 3
[1, 1, 1, 1, 2, 1, 3, 1, 1] => 1, 1, 1, 1, 2, 1, 3, 1, 1
[1, 1, 1, 1, 2, 1, 3, 1, 2] => 1, 1, 1, 1, 2, 1, 3, 1, 2
[1, 1, 1, 1, 2, 1, 3, 1, 3] => 1, 1, 1, 1, 2, 1, 3, 1, 3
[1, 1, 1, 1, 2, 1, 3, 2, 1] => 1, 1, 1, 1, 2, 1, 3, 2, 1
[1, 1, 1, 1, 2, 1, 3, 2, 2] => 1, 1, 1, 1, 2, 1, 3, 2, 2
[1, 1, 1, 1, 2, 1, 3, 2, 3] => 1, 1, 1, 1, 2, 1, 3, 2, 3
[1, 1, 1, 1, 2, 1, 3, 3, 1] => 1, 1, 1, 1, 2, 1, 3, 3, 1
[1, 1, 1, 1, 2, 1, 3, 3, 2] => 1, 1, 1, 1, 2, 1, 3, 3, 2
[1, 1, 1, 1, 2, 1, 3, 3, 3] => 1, 1, 1, 1, 2, 1, 3, 3, 3
[1, 1, 1, 1, 2, 2, 1, 1, 1] => 1, 1, 1, 1, 2, 2, 1, 1, 1
[1, 1, 1, 1, 2, 2, 1, 1, 2] => 1, 1, 1, 1, 2, 2, 1, 1, 2
[1, 1, 1, 1, 2, 2, 1, 1, 3] => 1, 1, 1, 1, 2, 2, 1, 1, 3
[1, 1, 1, 1, 2, 2, 1, 2, 1] => 1, 1, 1, 1, 2, 2, 1, 2, 1
[1, 1, 1, 1, 2, 2, 1, 2, 2] => 1, 1, 1, 1, 2, 2, 1, 2, 2
[1, 1, 1, 1, 2, 2, 1, 2, 3] => 1, 1, 1, 1, 2, 2, 1, 2, 3
[1, 1, 1, 1, 2, 2, 1, 3, 1] => 1, 1, 1, 1, 2, 2, 1, 3, 1
[1, 1, 1, 1, 2, 2, 1, 3, 2] => 1, 1, 1, 1, 2, 2, 1, 3, 2
[1, 1, 1, 1, 2, 2, 1, 3, 3] => 1, 1, 1, 1, 2, 2, 1, 3, 3
[1, 1, 1, 1, 2, 2, 2, 1, 1] => 1, 1, 1, 1, 2, 2, 2, 1, 1
[1, 1, 1, 1, 2, 2, 2, 1, 2] => 1, 1, 1, 1, 2, 2, 2, 1, 2
[1, 1, 1, 1, 2, 2, 2, 1, 3] => 1, 1, 1, 1, 2, 2, 2, 1, 3
[1, 1, 1, 1, 2, 2, 2, 2, 1] => 1, 1, 1, 1, 2, 2, 2, 2, 1
[1, 1, 1, 1, 2, 2, 2, 2, 2] => 1, 1, 1, 1, 2, 2, 2, 2, 2
[1, 1, 1, 1, 2, 2, 2, 2, 3] => 1, 1, 1, 1, 2, 2, 2, 2, 3
[1, 1, 1, 1, 2, 2, 2, 3, 1] => 1, 1, 1, 1, 2, 2, 2, 3, 1
[1, 1, 1, 1, 2, 2, 2, 3, 2] => 1, 1, 1, 1, 2, 2, 2, 3, 2
[1, 1, 1, 1, 2, 2, 2, 3, 3] => 1, 1, 1, 1, 2, 2, 2, 3, 3
[1, 1, 1, 1, 2, 2, 3, 1, 1] => 1, 1, 1, 1, 2, 2, 3, 1, 1
[1, 1, 1, 1, 2, 2, 3, 1, 2] => 1, 1, 1, 1, 2, 2, 3, 1, 2
[1, 1, 1, 1, 2, 2, 3, 1, 3] => 1, 1, 1, 1, 2, 2, 3, 1, 3
[1, 1, 1, 1, 2, 2, 3, 2, 1] => 1, 1, 1, 1, 2, 2, 3, 2, 1
[1, 1, 1, 1, 2, 2, 3, 2, 2] => 1, 1, 1, 1, 2, 2, 3, 2, 2
[1, 1, 1, 1, 2, 2, 3, 2, 3] => 1, 1, 1, 1, 2, 2, 3, 2, 3
[1, 1, 1, 1, 2, 2, 3, 3, 1] => 1, 1, 1, 1, 2, 2, 3, 3, 1
[1, 1, 1, 1, 2, 2, 3, 3, 2] => 1, 1, 1, 1, 2, 2, 3, 3, 2
[1, 1, 1, 1, 2, 2, 3, 3, 3] => 1, 1, 1, 1, 2, 2, 3, 3, 3
[1, 1, 1, 1, 2, 3, 1, 1, 1] => 1, 1, 1, 1, 2, 3, 1, 1, 1
[1, 1, 1, 1, 2, 3, 1, 1, 2] => 1, 1, 1, 1, 2, 3, 1, 1, 2
[1, 1, 1, 1, 2, 3, 1, 1, 3] => 1, 1, 1, 1, 2, 3, 1, 1, 3
[1, 1, 1, 1, 2, 3, 1, 2, 1] => 1, 1, 1, 1, 2, 3, 1, 2, 1
[1, 1, 1, 1, 2, 3, 1, 2, 2] => 1, 1, 1, 1, 2, 3, 1, 2, 2
[1, 1, 1, 1, 2, 3, 1, 2, 3] => 1, 1, 1, 1, 2, 3, 1, 2, 3
[1, 1, 1, 1, 2, 3, 1, 3, 1] => 1, 1, 1, 1, 2, 3, 1, 3, 1
[1, 1, 1, 1, 2, 3, 1, 3, 2] => 1, 1, 1, 1, 2, 3, 1, 3, 2
[1, 1, 1, 1, 2, 3, 1, 3, 3] => 1, 1, 1, 1, 2, 3, 1, 3, 3
[1, 1, 1, 1, 2, 3, 2, 1, 1] => 1, 1, 1, 1, 2, 3, 2, 1, 1
[1, 1, 1, 1, 2, 3, 2, 1, 2] => 1, 1, 1, 1, 2, 3, 2, 1, 2
[1, 1, 1, 1, 2, 3, 2, 1, 3] => 1, 1, 1, 1, 2, 3, 2, 1, 3
[1, 1, 1, 1, 2, 3, 2, 2, 1] => 1, 1, 1, 1, 2, 3, 2, 2, 1
[1, 1, 1, 1, 2, 3, 2, 2, 2] => 1, 1, 1, 1, 2, 3, 2, 2, 2
[1, 1, 1, 1, 2, 3, 2, 2, 3] => 1, 1, 1, 1, 2, 3, 2, 2, 3
[1, 1, 1, 1, 2, 3, 2, 3, 1] => 1, 1, 1, 1, 2, 3, 2, 3, 1
[1, 1, 1, 1, 2, 3, 2, 3, 2] => 1, 1, 1, 1, 2, 3, 2, 3, 2
[1, 1, 1, 1, 2, 3, 2, 3, 3] => 1, 1, 1, 1, 2, 3, 2, 3, 3
[1, 1, 1, 1, 2, 3, 3, 1, 1] => 1, 1, 1, 1, 2, 3, 3, 1, 1
[1, 1, 1, 1, 2, 3, 3, 1, 2] => 1, 1, 1, 1, 2, 3, 3, 1, 2
[1, 1, 1, 1, 2, 3, 3, 1, 3] => 1, 1, 1, 1, 2, 3, 3, 1, 3
[1, 1, 1, 1, 2, 3, 3, 2, 1] => 1, 1, 1, 1, 2, 3, 3, 2, 1
[1, 1, 1, 1, 2, 3, 3, 2, 2] => 1, 1, 1, 1, 2, 3, 3, 2, 2
[1, 1, 1, 1, 2, 3, 3, 2, 3] => 1, 1, 1, 1, 2, 3, 3, 2, 3
[1, 1, 1, 1, 2, 3, 3, 3, 1] => 1, 1, 1, 1, 2, 3, 3, 3, 1
[1, 1, 1, 1, 2, 3, 3, 3, 2] => 1, 1, 1, 1, 2, 3, 3, 3, 2
[1, 1, 1, 1, 2, 3, 3, 3, 3] => 1, 1, 1, 1, 2, 3, 3, 3, 3
[1, 1, 1, 1, 3, 1, 1, 1, 1] => 1, 1, 1, 1, 3, 1, 1, 1, 1
[1, 1, 1, 1, 3, 1, 1, 1, 2] => 1, 1, 1, 1, 3, 1, 1, 1, 2
[1, 1, 1, 1, 3, 1, 1, 1, 3] => 1, 1, 1, 1, 3, 1, 1, 1, 3
[1, 1, 1, 1, 3, 1, 1, 2, 1] => 1, 1, 1, 1, 3, 1, 1, 2, 1
[1, 1, 1, 1, 3, 1, 1, 2, 2] => 1, 1, 1, 1, 3, 1, 1, 2, 2
[1, 1, 1, 1, 3, 1, 1, 2, 3] => 1, 1, 1, 1, 3, 1, 1, 2, 3
[1, 1, 1, 1, 3, 1, 1, 3, 1] => 1, 1, 1, 1, 3, 1, 1, 3, 1
[1, 1, 1, 1, 3, 1, 1, 3, 2] => 1, 1, 1, 1, 3, 1, 1, 3, 2
[1, 1, 1, 1, 3, 1, 1, 3, 3] => 1, 1, 1, 1, 3, 1, 1, 3, 3
[1, 1, 1, 1, 3, 1, 2, 1, 1] => 1, 1, 1, 1, 3, 1, 2, 1, 1
[1, 1, 1, 1, 3, 1, 2, 1, 2] => 1, 1, 1, 1, 3, 1, 2, 1, 2
[1, 1, 1, 1, 3, 1, 2, 1, 3] => 1, 1, 1, 1, 3, 1, 2, 1, 3
[1, 1, 1, 1, 3, 1, 2, 2, 1] => 1, 1, 1, 1, 3, 1, 2, 2, 1
[1, 1, 1, 1, 3, 1, 2, 2, 2] => 1, 1, 1, 1, 3, 1, 2, 2, 2
[1, 1, 1, 1, 3, 1, 2, 2, 3] => 1, 1, 1, 1, 3, 1, 2, 2, 3
[1, 1, 1, 1, 3, 1, 2, 3, 1] => 1, 1, 1, 1, 3, 1, 2, 3, 1
[1, 1, 1, 1, 3, 1, 2, 3, 2] => 1, 1, 1, 1, 3, 1, 2, 3, 2
[1, 1, 1, 1, 3, 1, 2, 3, 3] => 1, 1, 1, 1, 3, 1, 2, 3, 3
[1, 1, 1, 1, 3, 1, 3, 1, 1] => 1, 1, 1, 1, 3, 1, 3, 1, 1
[1, 1, 1, 1, 3, 1, 3, 1, 2] => 1, 1, 1, 1, 3, 1, 3, 1, 2
[1, 1, 1, 1, 3, 1, 3, 1, 3] => 1, 1, 1, 1, 3, 1, 3, 1, 3
[1, 1, 1, 1, 3, 1, 3, 2, 1] => 1, 1, 1, 1, 3, 1, 3, 2, 1
[1, 1, 1, 1, 3, 1, 3, 2, 2] => 1, 1, 1, 1, 3, 1, 3, 2, 2
[1, 1, 1, 1, 3, 1, 3, 2, 3] => 1, 1, 1, 1, 3, 1, 3, 2, 3
[1, 1, 1, 1, 3, 1, 3, 3, 1] => 1, 1, 1, 1, 3, 1, 3, 3, 1
[1, 1, 1, 1, 3, 1, 3, 3, 2] => 1, 1, 1, 1, 3, 1, 3, 3, 2
[1, 1, 1, 1, 3, 1, 3, 3, 3] => 1, 1, 1, 1, 3, 1, 3, 3, 3
[1, 1, 1, 1, 3, 2, 1, 1, 1] => 1, 1, 1, 1, 3, 2, 1, 1, 1
[1, 1, 1, 1, 3, 2, 1, 1, 2] => 1, 1, 1, 1, 3, 2, 1, 1, 2
[1, 1, 1, 1, 3, 2, 1, 1, 3] => 1, 1, 1, 1, 3, 2, 1, 1, 3
[1, 1, 1, 1, 3, 2, 1, 2, 1] => 1, 1, 1, 1, 3, 2, 1, 2, 1
[1, 1, 1, 1, 3, 2, 1, 2, 2] => 1, 1, 1, 1, 3, 2, 1, 2, 2
[1, 1, 1, 1, 3, 2, 1, 2, 3] => 1, 1, 1, 1, 3, 2, 1, 2, 3
[1, 1, 1, 1, 3, 2, 1, 3, 1] => 1, 1, 1, 1, 3, 2, 1, 3, 1
[1, 1, 1, 1, 3, 2, 1, 3, 2] => 1, 1, 1, 1, 3, 2, 1, 3, 2
[1, 1, 1, 1, 3, 2, 1, 3, 3] => 1, 1, 1, 1, 3, 2, 1, 3, 3
[1, 1, 1, 1, 3, 2, 2, 1, 1] => 1, 1, 1, 1, 3, 2, 2, 1, 1
[1, 1, 1, 1, 3, 2, 2, 1, 2] => 1, 1, 1, 1, 3, 2, 2, 1, 2
[1, 1, 1, 1, 3, 2, 2, 1, 3] => 1, 1, 1, 1, 3, 2, 2, 1, 3
[1, 1, 1, 1, 3, 2, 2, 2, 1] => 1, 1, 1, 1, 3, 2, 2, 2, 1
[1, 1, 1, 1, 3, 2, 2, 2, 2] => 1, 1, 1, 1, 3, 2, 2, 2, 2
[1, 1, 1, 1, 3, 2, 2, 2, 3] => 1, 1, 1, 1, 3, 2, 2, 2, 3
[1, 1, 1, 1, 3, 2, 2, 3, 1] => 1, 1, 1, 1, 3, 2, 2, 3, 1
[1, 1, 1, 1, 3, 2, 2, 3, 2] => 1, 1, 1, 1, 3, 2, 2, 3, 2
[1, 1, 1, 1, 3, 2, 2, 3, 3] => 1, 1, 1, 1, 3, 2, 2, 3, 3
[1, 1, 1, 1, 3, 2, 3, 1, 1] => 1, 1, 1, 1, 3, 2, 3, 1, 1
[1, 1, 1, 1, 3, 2, 3, 1, 2] => 1, 1, 1, 1, 3, 2, 3, 1, 2
[1, 1, 1, 1, 3, 2, 3, 1, 3] => 1, 1, 1, 1, 3, 2, 3, 1, 3
[1, 1, 1, 1, 3, 2, 3, 2, 1] => 1, 1, 1, 1, 3, 2, 3, 2, 1
[1, 1, 1, 1, 3, 2, 3, 2, 2] => 1, 1, 1, 1, 3, 2, 3, 2, 2
[1, 1, 1, 1, 3, 2, 3, 2, 3] => 1, 1, 1, 1, 3, 2, 3, 2, 3
[1, 1, 1, 1, 3, 2, 3, 3, 1] => 1, 1, 1, 1, 3, 2, 3, 3, 1
[1, 1, 1, 1, 3, 2, 3, 3, 2] => 1, 1, 1, 1, 3, 2, 3, 3, 2
[1, 1, 1, 1, 3, 2, 3, 3, 3] => 1, 1, 1, 1, 3, 2, 3, 3, 3
[1, 1, 1, 1, 3, 3, 1, 1, 1] => 1, 1, 1, 1, 3, 3, 1, 1, 1
[1, 1, 1, 1, 3, 3, 1, 1, 2] => 1, 1, 1, 1, 3, 3, 1, 1, 2
[1, 1, 1, 1, 3, 3, 1, 1, 3] => 1, 1, 1, 1, 3, 3, 1, 1, 3
[1, 1, 1, 1, 3, 3, 1, 2, 1] => 1, 1, 1, 1, 3, 3, 1, 2, 1
[1, 1, 1, 1, 3, 3, 1, 2, 2] => 1, 1, 1, 1, 3, 3, 1, 2, 2
[1, 1, 1, 1, 3, 3, 1, 2, 3] => 1, 1, 1, 1, 3, 3, 1, 2, 3
[1, 1, 1, 1, 3, 3, 1, 3, 1] => 1, 1, 1, 1, 3, 3, 1, 3, 1
[1, 1, 1, 1, 3, 3, 1, 3, 2] => 1, 1, 1, 1, 3, 3, 1, 3, 2
[1, 1, 1, 1, 3, 3, 1, 3, 3] => 1, 1, 1, 1, 3, 3, 1, 3, 3
[1, 1, 1, 1, 3, 3, 2, 1, 1] => 1, 1, 1, 1, 3, 3, 2, 1, 1
[1, 1, 1, 1, 3, 3, 2, 1, 2] => 1, 1, 1, 1, 3, 3, 2, 1, 2
[1, 1, 1, 1, 3, 3, 2, 1, 3] => 1, 1, 1, 1, 3, 3, 2, 1, 3
[1, 1, 1, 1, 3, 3, 2, 2, 1] => 1, 1, 1, 1, 3, 3, 2, 2, 1
[1, 1, 1, 1, 3, 3, 2, 2, 2] => 1, 1, 1, 1, 3, 3, 2, 2, 2
[1, 1, 1, 1, 3, 3, 2, 2, 3] => 1, 1, 1, 1, 3, 3, 2, 2, 3
[1, 1, 1, 1, 3, 3, 2, 3, 1] => 1, 1, 1, 1, 3, 3, 2, 3, 1
[1, 1, 1, 1, 3, 3, 2, 3, 2] => 1, 1, 1, 1, 3, 3, 2, 3, 2
[1, 1, 1, 1, 3, 3, 2, 3, 3] => 1, 1, 1, 1, 3, 3, 2, 3, 3
[1, 1, 1, 1, 3, 3, 3, 1, 1] => 1, 1, 1, 1, 3, 3, 3, 1, 1
[1, 1, 1, 1, 3, 3, 3, 1, 2] => 1, 1, 1, 1, 3, 3, 3, 1, 2
[1, 1, 1, 1, 3, 3, 3, 1, 3] => 1, 1, 1, 1, 3, 3, 3, 1, 3
[1, 1, 1, 1, 3, 3, 3, 2, 1] => 1, 1, 1, 1, 3, 3, 3, 2, 1
[1, 1, 1, 1, 3, 3, 3, 2, 2] => 1, 1, 1, 1, 3, 3, 3, 2, 2
[1, 1, 1, 1, 3, 3, 3, 2, 3] => 1, 1, 1, 1, 3, 3, 3, 2, 3
[1, 1, 1, 1, 3, 3, 3, 3, 1] => 1, 1, 1, 1, 3, 3, 3, 3, 1
[1, 1, 1, 1, 3, 3, 3, 3, 2] => 1, 1, 1, 1, 3, 3, 3, 3, 2
[1, 1, 1, 1, 3, 3, 3, 3, 3] => 1, 1, 1, 1, 3, 3, 3, 3, 3
[1, 1, 1, 2, 1, 1, 1, 1, 1] => 1, 1, 1, 2, 1, 1, 1, 1, 1
[1, 1, 1, 2, 1, 1, 1, 1, 2] => 1, 1, 1, 2, 1, 1, 1, 1, 2
[1, 1, 1, 2, 1, 1, 1, 1, 3] => 1, 1, 1, 2, 1, 1, 1, 1, 3
[1, 1, 1, 2, 1, 1, 1, 2, 1] => 1, 1, 1, 2, 1, 1, 1, 2, 1
[1, 1, 1, 2, 1, 1, 1, 2, 2] => 1, 1, 1, 2, 1, 1, 1, 2, 2
[1, 1, 1, 2, 1, 1, 1, 2, 3] => 1, 1, 1, 2, 1, 1, 1, 2, 3
[1, 1, 1, 2, 1, 1, 1, 3, 1] => 1, 1, 1, 2, 1, 1, 1, 3, 1
[1, 1, 1, 2, 1, 1, 1, 3, 2] => 1, 1, 1, 2, 1, 1, 1, 3, 2
[1, 1, 1, 2, 1, 1, 1, 3, 3] => 1, 1, 1, 2, 1, 1, 1, 3, 3
[1, 1, 1, 2, 1, 1, 2, 1, 1] => 1, 1, 1, 2, 1, 1, 2, 1, 1
[1, 1, 1, 2, 1, 1, 2, 1, 2] => 1, 1, 1, 2, 1, 1, 2, 1, 2
[1, 1, 1, 2, 1, 1, 2, 1, 3] => 1, 1, 1, 2, 1, 1, 2, 1, 3
[1, 1, 1, 2, 1, 1, 2, 2, 1] => 1, 1, 1, 2, 1, 1, 2, 2, 1
[1, 1, 1, 2, 1, 1, 2, 2, 2] => 1, 1, 1, 2, 1, 1, 2, 2, 2
[1, 1, 1, 2, 1, 1, 2, 2, 3] => 1, 1, 1, 2, 1, 1, 2, 2, 3
[1, 1, 1, 2, 1, 1, 2, 3, 1] => 1, 1, 1, 2, 1, 1, 2, 3, 1
[1, 1, 1, 2, 1, 1, 2, 3, 2] => 1, 1, 1, 2, 1, 1, 2, 3, 2
[1, 1, 1, 2, 1, 1, 2, 3, 3] => 1, 1, 1, 2, 1, 1, 2, 3, 3
[1, 1, 1, 2, 1, 1, 3, 1, 1] => 1, 1, 1, 2, 1, 1, 3, 1, 1
[1, 1, 1, 2, 1, 1, 3, 1, 2] => 1, 1, 1, 2, 1, 1, 3, 1, 2
[1, 1, 1, 2, 1, 1, 3, 1, 3] => 1, 1, 1, 2, 1, 1, 3, 1, 3
[1, 1, 1, 2, 1, 1, 3, 2, 1] => 1, 1, 1, 2, 1, 1, 3, 2, 1
[1, 1, 1, 2, 1, 1, 3, 2, 2] => 1, 1, 1, 2, 1, 1, 3, 2, 2
[1, 1, 1, 2, 1, 1, 3, 2, 3] => 1, 1, 1, 2, 1, 1, 3, 2, 3
[1, 1, 1, 2, 1, 1, 3, 3, 1] => 1, 1, 1, 2, 1, 1, 3, 3, 1
[1, 1, 1, 2, 1, 1, 3, 3, 2] => 1, 1, 1, 2, 1, 1, 3, 3, 2
[1, 1, 1, 2, 1, 1, 3, 3, 3] => 1, 1, 1, 2, 1, 1, 3, 3, 3
[1, 1, 1, 2, 1, 2, 1, 1, 1] => 1, 1, 1, 2, 1, 2, 1, 1, 1
[1, 1, 1, 2, 1, 2, 1, 1, 2] => 1, 1, 1, 2, 1, 2, 1, 1, 2
[1, 1, 1, 2, 1, 2, 1, 1, 3] => 1, 1, 1, 2, 1, 2, 1, 1, 3
[1, 1, 1, 2, 1, 2, 1, 2, 1] => 1, 1, 1, 2, 1, 2, 1, 2, 1
[1, 1, 1, 2, 1, 2, 1, 2, 2] => 1, 1, 1, 2, 1, 2, 1, 2, 2
[1, 1, 1, 2, 1, 2, 1, 2, 3] => 1, 1, 1, 2, 1, 2, 1, 2, 3
[1, 1, 1, 2, 1, 2, 1, 3, 1] => 1, 1, 1, 2, 1, 2, 1, 3, 1
[1, 1, 1, 2, 1, 2, 1, 3, 2] => 1, 1, 1, 2, 1, 2, 1, 3, 2
[1, 1, 1, 2, 1, 2, 1, 3, 3] => 1, 1, 1, 2, 1, 2, 1, 3, 3
[1, 1, 1, 2, 1, 2, 2, 1, 1] => 1, 1, 1, 2, 1, 2, 2, 1, 1
[1, 1, 1, 2, 1, 2, 2, 1, 2] => 1, 1, 1, 2, 1, 2, 2, 1, 2
[1, 1, 1, 2, 1, 2, 2, 1, 3] => 1, 1, 1, 2, 1, 2, 2, 1, 3
[1, 1, 1, 2, 1, 2, 2, 2, 1] => 1, 1, 1, 2, 1, 2, 2, 2, 1
[1, 1, 1, 2, 1, 2, 2, 2, 2] => 1, 1, 1, 2, 1, 2, 2, 2, 2
[1, 1, 1, 2, 1, 2, 2, 2, 3] => 1, 1, 1, 2, 1, 2, 2, 2, 3
[1, 1, 1, 2, 1, 2, 2, 3, 1] => 1, 1, 1, 2, 1, 2, 2, 3, 1
[1, 1, 1, 2, 1, 2, 2, 3, 2] => 1, 1, 1, 2, 1, 2, 2, 3, 2
[1, 1, 1, 2, 1, 2, 2, 3, 3] => 1, 1, 1, 2, 1, 2, 2, 3, 3
[1, 1, 1, 2, 1, 2, 3, 1, 1] => 1, 1, 1, 2, 1, 2, 3, 1, 1
[1, 1, 1, 2, 1, 2, 3, 1, 2] => 1, 1, 1, 2, 1, 2, 3, 1, 2
[1, 1, 1, 2, 1, 2, 3, 1, 3] => 1, 1, 1, 2, 1, 2, 3, 1, 3
[1, 1, 1, 2, 1, 2, 3, 2, 1] => 1, 1, 1, 2, 1, 2, 3, 2, 1
[1, 1, 1, 2, 1, 2, 3, 2, 2] => 1, 1, 1, 2, 1, 2, 3, 2, 2
[1, 1, 1, 2, 1, 2, 3, 2, 3] => 1, 1, 1, 2, 1, 2, 3, 2, 3
[1, 1, 1, 2, 1, 2, 3, 3, 1] => 1, 1, 1, 2, 1, 2, 3, 3, 1
[1, 1, 1, 2, 1, 2, 3, 3, 2] => 1, 1, 1, 2, 1, 2, 3, 3, 2
[1, 1, 1, 2, 1, 2, 3, 3, 3] => 1, 1, 1, 2, 1, 2, 3, 3, 3
[1, 1, 1, 2, 1, 3, 1, 1, 1] => 1, 1, 1, 2, 1, 3, 1, 1, 1
[1, 1, 1, 2, 1, 3, 1, 1, 2] => 1, 1, 1, 2, 1, 3, 1, 1, 2
[1, 1, 1, 2, 1, 3, 1, 1, 3] => 1, 1, 1, 2, 1, 3, 1, 1, 3
[1, 1, 1, 2, 1, 3, 1, 2, 1] => 1, 1, 1, 2, 1, 3, 1, 2, 1
[1, 1, 1, 2, 1, 3, 1, 2, 2] => 1, 1, 1, 2, 1, 3, 1, 2, 2
[1, 1, 1, 2, 1, 3, 1, 2, 3] => 1, 1, 1, 2, 1, 3, 1, 2, 3
[1, 1, 1, 2, 1, 3, 1, 3, 1] => 1, 1, 1, 2, 1, 3, 1, 3, 1
[1, 1, 1, 2, 1, 3, 1, 3, 2] => 1, 1, 1, 2, 1, 3, 1, 3, 2
[1, 1, 1, 2, 1, 3, 1, 3, 3] => 1, 1, 1, 2, 1, 3, 1, 3, 3
[1, 1, 1, 2, 1, 3, 2, 1, 1] => 1, 1, 1, 2, 1, 3, 2, 1, 1
[1, 1, 1, 2, 1, 3, 2, 1, 2] => 1, 1, 1, 2, 1, 3, 2, 1, 2
[1, 1, 1, 2, 1, 3, 2, 1, 3] => 1, 1, 1, 2, 1, 3, 2, 1, 3
[1, 1, 1, 2, 1, 3, 2, 2, 1] => 1, 1, 1, 2, 1, 3, 2, 2, 1
[1, 1, 1, 2, 1, 3, 2, 2, 2] => 1, 1, 1, 2, 1, 3, 2, 2, 2
[1, 1, 1, 2, 1, 3, 2, 2, 3] => 1, 1, 1, 2, 1, 3, 2, 2, 3
[1, 1, 1, 2, 1, 3, 2, 3, 1] => 1, 1, 1, 2, 1, 3, 2, 3, 1
[1, 1, 1, 2, 1, 3, 2, 3, 2] => 1, 1, 1, 2, 1, 3, 2, 3, 2
[1, 1, 1, 2, 1, 3, 2, 3, 3] => 1, 1, 1, 2, 1, 3, 2, 3, 3
[1, 1, 1, 2, 1, 3, 3, 1, 1] => 1, 1, 1, 2, 1, 3, 3, 1, 1
[1, 1, 1, 2, 1, 3, 3, 1, 2] => 1, 1, 1, 2, 1, 3, 3, 1, 2
[1, 1, 1, 2, 1, 3, 3, 1, 3] => 1, 1, 1, 2, 1, 3, 3, 1, 3
[1, 1, 1, 2, 1, 3, 3, 2, 1] => 1, 1, 1, 2, 1, 3, 3, 2, 1
[1, 1, 1, 2, 1, 3, 3, 2, 2] => 1, 1, 1, 2, 1, 3, 3, 2, 2
[1, 1, 1, 2, 1, 3, 3, 2, 3] => 1, 1, 1, 2, 1, 3, 3, 2, 3
[1, 1, 1, 2, 1, 3, 3, 3, 1] => 1, 1, 1, 2, 1, 3, 3, 3, 1
[1, 1, 1, 2, 1, 3, 3, 3, 2] => 1, 1, 1, 2, 1, 3, 3, 3, 2
[1, 1, 1, 2, 1, 3, 3, 3, 3] => 1, 1, 1, 2, 1, 3, 3, 3, 3
[1, 1, 1, 2, 2, 1, 1, 1, 1] => 1, 1, 1, 2, 2, 1, 1, 1, 1
[1, 1, 1, 2, 2, 1, 1, 1, 2] => 1, 1, 1, 2, 2, 1, 1, 1, 2
[1, 1, 1, 2, 2, 1, 1, 1, 3] => 1, 1, 1, 2, 2, 1, 1, 1, 3
[1, 1, 1, 2, 2, 1, 1, 2, 1] => 1, 1, 1, 2, 2, 1, 1, 2, 1
[1, 1, 1, 2, 2, 1, 1, 2, 2] => 1, 1, 1, 2, 2, 1, 1, 2, 2
[1, 1, 1, 2, 2, 1, 1, 2, 3] => 1, 1, 1, 2, 2, 1, 1, 2, 3
[1, 1, 1, 2, 2, 1, 1, 3, 1] => 1, 1, 1, 2, 2, 1, 1, 3, 1
[1, 1, 1, 2, 2, 1, 1, 3, 2] => 1, 1, 1, 2, 2, 1, 1, 3, 2
[1, 1, 1, 2, 2, 1, 1, 3, 3] => 1, 1, 1, 2, 2, 1, 1, 3, 3
[1, 1, 1, 2, 2, 1, 2, 1, 1] => 1, 1, 1, 2, 2, 1, 2, 1, 1
[1, 1, 1, 2, 2, 1, 2, 1, 2] => 1, 1, 1, 2, 2, 1, 2, 1, 2
[1, 1, 1, 2, 2, 1, 2, 1, 3] => 1, 1, 1, 2, 2, 1, 2, 1, 3
[1, 1, 1, 2, 2, 1, 2, 2, 1] => 1, 1, 1, 2, 2, 1, 2, 2, 1
[1, 1, 1, 2, 2, 1, 2, 2, 2] => 1, 1, 1, 2, 2, 1, 2, 2, 2
[1, 1, 1, 2, 2, 1, 2, 2, 3] => 1, 1, 1, 2, 2, 1, 2, 2, 3
[1, 1, 1, 2, 2, 1, 2, 3, 1] => 1, 1, 1, 2, 2, 1, 2, 3, 1
[1, 1, 1, 2, 2, 1, 2, 3, 2] => 1, 1, 1, 2, 2, 1, 2, 3, 2
[1, 1, 1, 2, 2, 1, 2, 3, 3] => 1, 1, 1, 2, 2, 1, 2, 3, 3
[1, 1, 1, 2, 2, 1, 3, 1, 1] => 1, 1, 1, 2, 2, 1, 3, 1, 1
[1, 1, 1, 2, 2, 1, 3, 1, 2] => 1, 1, 1, 2, 2, 1, 3, 1, 2
[1, 1, 1, 2, 2, 1, 3, 1, 3] => 1, 1, 1, 2, 2, 1, 3, 1, 3
[1, 1, 1, 2, 2, 1, 3, 2, 1] => 1, 1, 1, 2, 2, 1, 3, 2, 1
[1, 1, 1, 2, 2, 1, 3, 2, 2] => 1, 1, 1, 2, 2, 1, 3, 2, 2
[1, 1, 1, 2, 2, 1, 3, 2, 3] => 1, 1, 1, 2, 2, 1, 3, 2, 3
[1, 1, 1, 2, 2, 1, 3, 3, 1] => 1, 1, 1, 2, 2, 1, 3, 3, 1
[1, 1, 1, 2, 2, 1, 3, 3, 2] => 1, 1, 1, 2, 2, 1, 3, 3, 2
[1, 1, 1, 2, 2, 1, 3, 3, 3] => 1, 1, 1, 2, 2, 1, 3, 3, 3
[1, 1, 1, 2, 2, 2, 1, 1, 1] => 1, 1, 1, 2, 2, 2, 1, 1, 1
[1, 1, 1, 2, 2, 2, 1, 1, 2] => 1, 1, 1, 2, 2, 2, 1, 1, 2
[1, 1, 1, 2, 2, 2, 1, 1, 3] => 1, 1, 1, 2, 2, 2, 1, 1, 3
[1, 1, 1, 2, 2, 2, 1, 2, 1] => 1, 1, 1, 2, 2, 2, 1, 2, 1
[1, 1, 1, 2, 2, 2, 1, 2, 2] => 1, 1, 1, 2, 2, 2, 1, 2, 2
[1, 1, 1, 2, 2, 2, 1, 2, 3] => 1, 1, 1, 2, 2, 2, 1, 2, 3
[1, 1, 1, 2, 2, 2, 1, 3, 1] => 1, 1, 1, 2, 2, 2, 1, 3, 1
[1, 1, 1, 2, 2, 2, 1, 3, 2] => 1, 1, 1, 2, 2, 2, 1, 3, 2
[1, 1, 1, 2, 2, 2, 1, 3, 3] => 1, 1, 1, 2, 2, 2, 1, 3, 3
[1, 1, 1, 2, 2, 2, 2, 1, 1] => 1, 1, 1, 2, 2, 2, 2, 1, 1
[1, 1, 1, 2, 2, 2, 2, 1, 2] => 1, 1, 1, 2, 2, 2, 2, 1, 2
[1, 1, 1, 2, 2, 2, 2, 1, 3] => 1, 1, 1, 2, 2, 2, 2, 1, 3
[1, 1, 1, 2, 2, 2, 2, 2, 1] => 1, 1, 1, 2, 2, 2, 2, 2, 1
[1, 1, 1, 2, 2, 2, 2, 2, 2] => 1, 1, 1, 2, 2, 2, 2, 2, 2
[1, 1, 1, 2, 2, 2, 2, 2, 3] => 1, 1, 1, 2, 2, 2, 2, 2, 3
[1, 1, 1, 2, 2, 2, 2, 3, 1] => 1, 1, 1, 2, 2, 2, 2, 3, 1
[1, 1, 1, 2, 2, 2, 2, 3, 2] => 1, 1, 1, 2, 2, 2, 2, 3, 2
[1, 1, 1, 2, 2, 2, 2, 3, 3] => 1, 1, 1, 2, 2, 2, 2, 3, 3
[1, 1, 1, 2, 2, 2, 3, 1, 1] => 1, 1, 1, 2, 2, 2, 3, 1, 1
[1, 1, 1, 2, 2, 2, 3, 1, 2] => 1, 1, 1, 2, 2, 2, 3, 1, 2
[1, 1, 1, 2, 2, 2, 3, 1, 3] => 1, 1, 1, 2, 2, 2, 3, 1, 3
[1, 1, 1, 2, 2, 2, 3, 2, 1] => 1, 1, 1, 2, 2, 2, 3, 2, 1
[1, 1, 1, 2, 2, 2, 3, 2, 2] => 1, 1, 1, 2, 2, 2, 3, 2, 2
[1, 1, 1, 2, 2, 2, 3, 2, 3] => 1, 1, 1, 2, 2, 2, 3, 2, 3
[1, 1, 1, 2, 2, 2, 3, 3, 1] => 1, 1, 1, 2, 2, 2, 3, 3, 1
[1, 1, 1, 2, 2, 2, 3, 3, 2] => 1, 1, 1, 2, 2, 2, 3, 3, 2
[1, 1, 1, 2, 2, 2, 3, 3, 3] => 1, 1, 1, 2, 2, 2, 3, 3, 3
[1, 1, 1, 2, 2, 3, 1, 1, 1] => 1, 1, 1, 2, 2, 3, 1, 1, 1
[1, 1, 1, 2, 2, 3, 1, 1, 2] => 1, 1, 1, 2, 2, 3, 1, 1, 2
[1, 1, 1, 2, 2, 3, 1, 1, 3] => 1, 1, 1, 2, 2, 3, 1, 1, 3
[1, 1, 1, 2, 2, 3, 1, 2, 1] => 1, 1, 1, 2, 2, 3, 1, 2, 1
[1, 1, 1, 2, 2, 3, 1, 2, 2] => 1, 1, 1, 2, 2, 3, 1, 2, 2
[1, 1, 1, 2, 2, 3, 1, 2, 3] => 1, 1, 1, 2, 2, 3, 1, 2, 3
[1, 1, 1, 2, 2, 3, 1, 3, 1] => 1, 1, 1, 2, 2, 3, 1, 3, 1
[1, 1, 1, 2, 2, 3, 1, 3, 2] => 1, 1, 1, 2, 2, 3, 1, 3, 2
[1, 1, 1, 2, 2, 3, 1, 3, 3] => 1, 1, 1, 2, 2, 3, 1, 3, 3
[1, 1, 1, 2, 2, 3, 2, 1, 1] => 1, 1, 1, 2, 2, 3, 2, 1, 1
[1, 1, 1, 2, 2, 3, 2, 1, 2] => 1, 1, 1, 2, 2, 3, 2, 1, 2
[1, 1, 1, 2, 2, 3, 2, 1, 3] => 1, 1, 1, 2, 2, 3, 2, 1, 3
[1, 1, 1, 2, 2, 3, 2, 2, 1] => 1, 1, 1, 2, 2, 3, 2, 2, 1
[1, 1, 1, 2, 2, 3, 2, 2, 2] => 1, 1, 1, 2, 2, 3, 2, 2, 2
[1, 1, 1, 2, 2, 3, 2, 2, 3] => 1, 1, 1, 2, 2, 3, 2, 2, 3
[1, 1, 1, 2, 2, 3, 2, 3, 1] => 1, 1, 1, 2, 2, 3, 2, 3, 1
[1, 1, 1, 2, 2, 3, 2, 3, 2] => 1, 1, 1, 2, 2, 3, 2, 3, 2
[1, 1, 1, 2, 2, 3, 2, 3, 3] => 1, 1, 1, 2, 2, 3, 2, 3, 3
[1, 1, 1, 2, 2, 3, 3, 1, 1] => 1, 1, 1, 2, 2, 3, 3, 1, 1
[1, 1, 1, 2, 2, 3, 3, 1, 2] => 1, 1, 1, 2, 2, 3, 3, 1, 2
[1, 1, 1, 2, 2, 3, 3, 1, 3] => 1, 1, 1, 2, 2, 3, 3, 1, 3
[1, 1, 1, 2, 2, 3, 3, 2, 1] => 1, 1, 1, 2, 2, 3, 3, 2, 1
[1, 1, 1, 2, 2, 3, 3, 2, 2] => 1, 1, 1, 2, 2, 3, 3, 2, 2
[1, 1, 1, 2, 2, 3, 3, 2, 3] => 1, 1, 1, 2, 2, 3, 3, 2, 3
[1, 1, 1, 2, 2, 3, 3, 3, 1] => 1, 1, 1, 2, 2, 3, 3, 3, 1
[1, 1, 1, 2, 2, 3, 3, 3, 2] => 1, 1, 1, 2, 2, 3, 3, 3, 2
[1, 1, 1, 2, 2, 3, 3, 3, 3] => 1, 1, 1, 2, 2, 3, 3, 3, 3
[1, 1, 1, 2, 3, 1, 1, 1, 1] => 1, 1, 1, 2, 3, 1, 1, 1, 1
[1, 1, 1, 2, 3, 1, 1, 1, 2] => 1, 1, 1, 2, 3, 1, 1, 1, 2
[1, 1, 1, 2, 3, 1, 1, 1, 3] => 1, 1, 1, 2, 3, 1, 1, 1, 3
[1, 1, 1, 2, 3, 1, 1, 2, 1] => 1, 1, 1, 2, 3, 1, 1, 2, 1
[1, 1, 1, 2, 3, 1, 1, 2, 2] => 1, 1, 1, 2, 3, 1, 1, 2, 2
[1, 1, 1, 2, 3, 1, 1, 2, 3] => 1, 1, 1, 2, 3, 1, 1, 2, 3
[1, 1, 1, 2, 3, 1, 1, 3, 1] => 1, 1, 1, 2, 3, 1, 1, 3, 1
[1, 1, 1, 2, 3, 1, 1, 3, 2] => 1, 1, 1, 2, 3, 1, 1, 3, 2
[1, 1, 1, 2, 3, 1, 1, 3, 3] => 1, 1, 1, 2, 3, 1, 1, 3, 3
[1, 1, 1, 2, 3, 1, 2, 1, 1] => 1, 1, 1, 2, 3, 1, 2, 1, 1
[1, 1, 1, 2, 3, 1, 2, 1, 2] => 1, 1, 1, 2, 3, 1, 2, 1, 2
[1, 1, 1, 2, 3, 1, 2, 1, 3] => 1, 1, 1, 2, 3, 1, 2, 1, 3
[1, 1, 1, 2, 3, 1, 2, 2, 1] => 1, 1, 1, 2, 3, 1, 2, 2, 1
[1, 1, 1, 2, 3, 1, 2, 2, 2] => 1, 1, 1, 2, 3, 1, 2, 2, 2
[1, 1, 1, 2, 3, 1, 2, 2, 3] => 1, 1, 1, 2, 3, 1, 2, 2, 3
[1, 1, 1, 2, 3, 1, 2, 3, 1] => 1, 1, 1, 2, 3, 1, 2, 3, 1
[1, 1, 1, 2, 3, 1, 2, 3, 2] => 1, 1, 1, 2, 3, 1, 2, 3, 2
[1, 1, 1, 2, 3, 1, 2, 3, 3] => 1, 1, 1, 2, 3, 1, 2, 3, 3
[1, 1, 1, 2, 3, 1, 3, 1, 1] => 1, 1, 1, 2, 3, 1, 3, 1, 1
[1, 1, 1, 2, 3, 1, 3, 1, 2] => 1, 1, 1, 2, 3, 1, 3, 1, 2
[1, 1, 1, 2, 3, 1, 3, 1, 3] => 1, 1, 1, 2, 3, 1, 3, 1, 3
[1, 1, 1, 2, 3, 1, 3, 2, 1] => 1, 1, 1, 2, 3, 1, 3, 2, 1
[1, 1, 1, 2, 3, 1, 3, 2, 2] => 1, 1, 1, 2, 3, 1, 3, 2, 2
[1, 1, 1, 2, 3, 1, 3, 2, 3] => 1, 1, 1, 2, 3, 1, 3, 2, 3
[1, 1, 1, 2, 3, 1, 3, 3, 1] => 1, 1, 1, 2, 3, 1, 3, 3, 1
[1, 1, 1, 2, 3, 1, 3, 3, 2] => 1, 1, 1, 2, 3, 1, 3, 3, 2
[1, 1, 1, 2, 3, 1, 3, 3, 3] => 1, 1, 1, 2, 3, 1, 3, 3, 3
[1, 1, 1, 2, 3, 2, 1, 1, 1] => 1, 1, 1, 2, 3, 2, 1, 1, 1
[1, 1, 1, 2, 3, 2, 1, 1, 2] => 1, 1, 1, 2, 3, 2, 1, 1, 2
[1, 1, 1, 2, 3, 2, 1, 1, 3] => 1, 1, 1, 2, 3, 2, 1, 1, 3
[1, 1, 1, 2, 3, 2, 1, 2, 1] => 1, 1, 1, 2, 3, 2, 1, 2, 1
[1, 1, 1, 2, 3, 2, 1, 2, 2] => 1, 1, 1, 2, 3, 2, 1, 2, 2
[1, 1, 1, 2, 3, 2, 1, 2, 3] => 1, 1, 1, 2, 3, 2, 1, 2, 3
[1, 1, 1, 2, 3, 2, 1, 3, 1] => 1, 1, 1, 2, 3, 2, 1, 3, 1
[1, 1, 1, 2, 3, 2, 1, 3, 2] => 1, 1, 1, 2, 3, 2, 1, 3, 2
[1, 1, 1, 2, 3, 2, 1, 3, 3] => 1, 1, 1, 2, 3, 2, 1, 3, 3
[1, 1, 1, 2, 3, 2, 2, 1, 1] => 1, 1, 1, 2, 3, 2, 2, 1, 1
[1, 1, 1, 2, 3, 2, 2, 1, 2] => 1, 1, 1, 2, 3, 2, 2, 1, 2
[1, 1, 1, 2, 3, 2, 2, 1, 3] => 1, 1, 1, 2, 3, 2, 2, 1, 3
[1, 1, 1, 2, 3, 2, 2, 2, 1] => 1, 1, 1, 2, 3, 2, 2, 2, 1
[1, 1, 1, 2, 3, 2, 2, 2, 2] => 1, 1, 1, 2, 3, 2, 2, 2, 2
[1, 1, 1, 2, 3, 2, 2, 2, 3] => 1, 1, 1, 2, 3, 2, 2, 2, 3
[1, 1, 1, 2, 3, 2, 2, 3, 1] => 1, 1, 1, 2, 3, 2, 2, 3, 1
[1, 1, 1, 2, 3, 2, 2, 3, 2] => 1, 1, 1, 2, 3, 2, 2, 3, 2
[1, 1, 1, 2, 3, 2, 2, 3, 3] => 1, 1, 1, 2, 3, 2, 2, 3, 3
[1, 1, 1, 2, 3, 2, 3, 1, 1] => 1, 1, 1, 2, 3, 2, 3, 1, 1
[1, 1, 1, 2, 3, 2, 3, 1, 2] => 1, 1, 1, 2, 3, 2, 3, 1, 2
[1, 1, 1, 2, 3, 2, 3, 1, 3] => 1, 1, 1, 2, 3, 2, 3, 1, 3
[1, 1, 1, 2, 3, 2, 3, 2, 1] => 1, 1, 1, 2, 3, 2, 3, 2, 1
[1, 1, 1, 2, 3, 2, 3, 2, 2] => 1, 1, 1, 2, 3, 2, 3, 2, 2
[1, 1, 1, 2, 3, 2, 3, 2, 3] => 1, 1, 1, 2, 3, 2, 3, 2, 3
[1, 1, 1, 2, 3, 2, 3, 3, 1] => 1, 1, 1, 2, 3, 2, 3, 3, 1
[1, 1, 1, 2, 3, 2, 3, 3, 2] => 1, 1, 1, 2, 3, 2, 3, 3, 2
[1, 1, 1, 2, 3, 2, 3, 3, 3] => 1, 1, 1, 2, 3, 2, 3, 3, 3
[1, 1, 1, 2, 3, 3, 1, 1, 1] => 1, 1, 1, 2, 3, 3, 1, 1, 1
[1, 1, 1, 2, 3, 3, 1, 1, 2] => 1, 1, 1, 2, 3, 3, 1, 1, 2
[1, 1, 1, 2, 3, 3, 1, 1, 3] => 1, 1, 1, 2, 3, 3, 1, 1, 3
[1, 1, 1, 2, 3, 3, 1, 2, 1] => 1, 1, 1, 2, 3, 3, 1, 2, 1
[1, 1, 1, 2, 3, 3, 1, 2, 2] => 1, 1, 1, 2, 3, 3, 1, 2, 2
[1, 1, 1, 2, 3, 3, 1, 2, 3] => 1, 1, 1, 2, 3, 3, 1, 2, 3
[1, 1, 1, 2, 3, 3, 1, 3, 1] => 1, 1, 1, 2, 3, 3, 1, 3, 1
[1, 1, 1, 2, 3, 3, 1, 3, 2] => 1, 1, 1, 2, 3, 3, 1, 3, 2
[1, 1, 1, 2, 3, 3, 1, 3, 3] => 1, 1, 1, 2, 3, 3, 1, 3, 3
[1, 1, 1, 2, 3, 3, 2, 1, 1] => 1, 1, 1, 2, 3, 3, 2, 1, 1
[1, 1, 1, 2, 3, 3, 2, 1, 2] => 1, 1, 1, 2, 3, 3, 2, 1, 2
[1, 1, 1, 2, 3, 3, 2, 1, 3] => 1, 1, 1, 2, 3, 3, 2, 1, 3
[1, 1, 1, 2, 3, 3, 2, 2, 1] => 1, 1, 1, 2, 3, 3, 2, 2, 1
[1, 1, 1, 2, 3, 3, 2, 2, 2] => 1, 1, 1, 2, 3, 3, 2, 2, 2
[1, 1, 1, 2, 3, 3, 2, 2, 3] => 1, 1, 1, 2, 3, 3, 2, 2, 3
[1, 1, 1, 2, 3, 3, 2, 3, 1] => 1, 1, 1, 2, 3, 3, 2, 3, 1
[1, 1, 1, 2, 3, 3, 2, 3, 2] => 1, 1, 1, 2, 3, 3, 2, 3, 2
[1, 1, 1, 2, 3, 3, 2, 3, 3] => 1, 1, 1, 2, 3, 3, 2, 3, 3
[1, 1, 1, 2, 3, 3, 3, 1, 1] => 1, 1, 1, 2, 3, 3, 3, 1, 1
[1, 1, 1, 2, 3, 3, 3, 1, 2] => 1, 1, 1, 2, 3, 3, 3, 1, 2
[1, 1, 1, 2, 3, 3, 3, 1, 3] => 1, 1, 1, 2, 3, 3, 3, 1, 3
[1, 1, 1, 2, 3, 3, 3, 2, 1] => 1, 1, 1, 2, 3, 3, 3, 2, 1
[1, 1, 1, 2, 3, 3, 3, 2, 2] => 1, 1, 1, 2, 3, 3, 3, 2, 2
[1, 1, 1, 2, 3, 3, 3, 2, 3] => 1, 1, 1, 2, 3, 3, 3, 2, 3
[1, 1, 1, 2, 3, 3, 3, 3, 1] => 1, 1, 1, 2, 3, 3, 3, 3, 1
[1, 1, 1, 2, 3, 3, 3, 3, 2] => 1, 1, 1, 2, 3, 3, 3, 3, 2
[1, 1, 1, 2, 3, 3, 3, 3, 3] => 1, 1, 1, 2, 3, 3, 3, 3, 3
[1, 1, 1, 3, 1, 1, 1, 1, 1] => 1, 1, 1, 3, 1, 1, 1, 1, 1
[1, 1, 1, 3, 1, 1, 1, 1, 2] => 1, 1, 1, 3, 1, 1, 1, 1, 2
[1, 1, 1, 3, 1, 1, 1, 1, 3] => 1, 1, 1, 3, 1, 1, 1, 1, 3
[1, 1, 1, 3, 1, 1, 1, 2, 1] => 1, 1, 1, 3, 1, 1, 1, 2, 1
[1, 1, 1, 3, 1, 1, 1, 2, 2] => 1, 1, 1, 3, 1, 1, 1, 2, 2
[1, 1, 1, 3, 1, 1, 1, 2, 3] => 1, 1, 1, 3, 1, 1, 1, 2, 3
[1, 1, 1, 3, 1, 1, 1, 3, 1] => 1, 1, 1, 3, 1, 1, 1, 3, 1
[1, 1, 1, 3, 1, 1, 1, 3, 2] => 1, 1, 1, 3, 1, 1, 1, 3, 2
[1, 1, 1, 3, 1, 1, 1, 3, 3] => 1, 1, 1, 3, 1, 1, 1, 3, 3
[1, 1, 1, 3, 1, 1, 2, 1, 1] => 1, 1, 1, 3, 1, 1, 2, 1, 1
[1, 1, 1, 3, 1, 1, 2, 1, 2] => 1, 1, 1, 3, 1, 1, 2, 1, 2
[1, 1, 1, 3, 1, 1, 2, 1, 3] => 1, 1, 1, 3, 1, 1, 2, 1, 3
[1, 1, 1, 3, 1, 1, 2, 2, 1] => 1, 1, 1, 3, 1, 1, 2, 2, 1
[1, 1, 1, 3, 1, 1, 2, 2, 2] => 1, 1, 1, 3, 1, 1, 2, 2, 2
[1, 1, 1, 3, 1, 1, 2, 2, 3] => 1, 1, 1, 3, 1, 1, 2, 2, 3
[1, 1, 1, 3, 1, 1, 2, 3, 1] => 1, 1, 1, 3, 1, 1, 2, 3, 1
[1, 1, 1, 3, 1, 1, 2, 3, 2] => 1, 1, 1, 3, 1, 1, 2, 3, 2
[1, 1, 1, 3, 1, 1, 2, 3, 3] => 1, 1, 1, 3, 1, 1, 2, 3, 3
[1, 1, 1, 3, 1, 1, 3, 1, 1] => 1, 1, 1, 3, 1, 1, 3, 1, 1
[1, 1, 1, 3, 1, 1, 3, 1, 2] => 1, 1, 1, 3, 1, 1, 3, 1, 2
[1, 1, 1, 3, 1, 1, 3, 1, 3] => 1, 1, 1, 3, 1, 1, 3, 1, 3
[1, 1, 1, 3, 1, 1, 3, 2, 1] => 1, 1, 1, 3, 1, 1, 3, 2, 1
[1, 1, 1, 3, 1, 1, 3, 2, 2] => 1, 1, 1, 3, 1, 1, 3, 2, 2
[1, 1, 1, 3, 1, 1, 3, 2, 3] => 1, 1, 1, 3, 1, 1, 3, 2, 3
[1, 1, 1, 3, 1, 1, 3, 3, 1] => 1, 1, 1, 3, 1, 1, 3, 3, 1
[1, 1, 1, 3, 1, 1, 3, 3, 2] => 1, 1, 1, 3, 1, 1, 3, 3, 2
[1, 1, 1, 3, 1, 1, 3, 3, 3] => 1, 1, 1, 3, 1, 1, 3, 3, 3
[1, 1, 1, 3, 1, 2, 1, 1, 1] => 1, 1, 1, 3, 1, 2, 1, 1, 1
[1, 1, 1, 3, 1, 2, 1, 1, 2] => 1, 1, 1, 3, 1, 2, 1, 1, 2
[1, 1, 1, 3, 1, 2, 1, 1, 3] => 1, 1, 1, 3, 1, 2, 1, 1, 3
[1, 1, 1, 3, 1, 2, 1, 2, 1] => 1, 1, 1, 3, 1, 2, 1, 2, 1
[1, 1, 1, 3, 1, 2, 1, 2, 2] => 1, 1, 1, 3, 1, 2, 1, 2, 2
[1, 1, 1, 3, 1, 2, 1, 2, 3] => 1, 1, 1, 3, 1, 2, 1, 2, 3
[1, 1, 1, 3, 1, 2, 1, 3, 1] => 1, 1, 1, 3, 1, 2, 1, 3, 1
[1, 1, 1, 3, 1, 2, 1, 3, 2] => 1, 1, 1, 3, 1, 2, 1, 3, 2
[1, 1, 1, 3, 1, 2, 1, 3, 3] => 1, 1, 1, 3, 1, 2, 1, 3, 3
[1, 1, 1, 3, 1, 2, 2, 1, 1] => 1, 1, 1, 3, 1, 2, 2, 1, 1
[1, 1, 1, 3, 1, 2, 2, 1, 2] => 1, 1, 1, 3, 1, 2, 2, 1, 2
[1, 1, 1, 3, 1, 2, 2, 1, 3] => 1, 1, 1, 3, 1, 2, 2, 1, 3
[1, 1, 1, 3, 1, 2, 2, 2, 1] => 1, 1, 1, 3, 1, 2, 2, 2, 1
[1, 1, 1, 3, 1, 2, 2, 2, 2] => 1, 1, 1, 3, 1, 2, 2, 2, 2
[1, 1, 1, 3, 1, 2, 2, 2, 3] => 1, 1, 1, 3, 1, 2, 2, 2, 3
[1, 1, 1, 3, 1, 2, 2, 3, 1] => 1, 1, 1, 3, 1, 2, 2, 3, 1
[1, 1, 1, 3, 1, 2, 2, 3, 2] => 1, 1, 1, 3, 1, 2, 2, 3, 2
[1, 1, 1, 3, 1, 2, 2, 3, 3] => 1, 1, 1, 3, 1, 2, 2, 3, 3
[1, 1, 1, 3, 1, 2, 3, 1, 1] => 1, 1, 1, 3, 1, 2, 3, 1, 1
[1, 1, 1, 3, 1, 2, 3, 1, 2] => 1, 1, 1, 3, 1, 2, 3, 1, 2
[1, 1, 1, 3, 1, 2, 3, 1, 3] => 1, 1, 1, 3, 1, 2, 3, 1, 3
[1, 1, 1, 3, 1, 2, 3, 2, 1] => 1, 1, 1, 3, 1, 2, 3, 2, 1
[1, 1, 1, 3, 1, 2, 3, 2, 2] => 1, 1, 1, 3, 1, 2, 3, 2, 2
[1, 1, 1, 3, 1, 2, 3, 2, 3] => 1, 1, 1, 3, 1, 2, 3, 2, 3
[1, 1, 1, 3, 1, 2, 3, 3, 1] => 1, 1, 1, 3, 1, 2, 3, 3, 1
[1, 1, 1, 3, 1, 2, 3, 3, 2] => 1, 1, 1, 3, 1, 2, 3, 3, 2
[1, 1, 1, 3, 1, 2, 3, 3, 3] => 1, 1, 1, 3, 1, 2, 3, 3, 3
[1, 1, 1, 3, 1, 3, 1, 1, 1] => 1, 1, 1, 3, 1, 3, 1, 1, 1
[1, 1, 1, 3, 1, 3, 1, 1, 2] => 1, 1, 1, 3, 1, 3, 1, 1, 2
[1, 1, 1, 3, 1, 3, 1, 1, 3] => 1, 1, 1, 3, 1, 3, 1, 1, 3
[1, 1, 1, 3, 1, 3, 1, 2, 1] => 1, 1, 1, 3, 1, 3, 1, 2, 1
[1, 1, 1, 3, 1, 3, 1, 2, 2] => 1, 1, 1, 3, 1, 3, 1, 2, 2
[1, 1, 1, 3, 1, 3, 1, 2, 3] => 1, 1, 1, 3, 1, 3, 1, 2, 3
[1, 1, 1, 3, 1, 3, 1, 3, 1] => 1, 1, 1, 3, 1, 3, 1, 3, 1
[1, 1, 1, 3, 1, 3, 1, 3, 2] => 1, 1, 1, 3, 1, 3, 1, 3, 2
[1, 1, 1, 3, 1, 3, 1, 3, 3] => 1, 1, 1, 3, 1, 3, 1, 3, 3
[1, 1, 1, 3, 1, 3, 2, 1, 1] => 1, 1, 1, 3, 1, 3, 2, 1, 1
[1, 1, 1, 3, 1, 3, 2, 1, 2] => 1, 1, 1, 3, 1, 3, 2, 1, 2
[1, 1, 1, 3, 1, 3, 2, 1, 3] => 1, 1, 1, 3, 1, 3, 2, 1, 3
[1, 1, 1, 3, 1, 3, 2, 2, 1] => 1, 1, 1, 3, 1, 3, 2, 2, 1
[1, 1, 1, 3, 1, 3, 2, 2, 2] => 1, 1, 1, 3, 1, 3, 2, 2, 2
[1, 1, 1, 3, 1, 3, 2, 2, 3] => 1, 1, 1, 3, 1, 3, 2, 2, 3
[1, 1, 1, 3, 1, 3, 2, 3, 1] => 1, 1, 1, 3, 1, 3, 2, 3, 1
[1, 1, 1, 3, 1, 3, 2, 3, 2] => 1, 1, 1, 3, 1, 3, 2, 3, 2
[1, 1, 1, 3, 1, 3, 2, 3, 3] => 1, 1, 1, 3, 1, 3, 2, 3, 3
[1, 1, 1, 3, 1, 3, 3, 1, 1] => 1, 1, 1, 3, 1, 3, 3, 1, 1
[1, 1, 1, 3, 1, 3, 3, 1, 2] => 1, 1, 1, 3, 1, 3, 3, 1, 2
[1, 1, 1, 3, 1, 3, 3, 1, 3] => 1, 1, 1, 3, 1, 3, 3, 1, 3
[1, 1, 1, 3, 1, 3, 3, 2, 1] => 1, 1, 1, 3, 1, 3, 3, 2, 1
[1, 1, 1, 3, 1, 3, 3, 2, 2] => 1, 1, 1, 3, 1, 3, 3, 2, 2
[1, 1, 1, 3, 1, 3, 3, 2, 3] => 1, 1, 1, 3, 1, 3, 3, 2, 3
[1, 1, 1, 3, 1, 3, 3, 3, 1] => 1, 1, 1, 3, 1, 3, 3, 3, 1
[1, 1, 1, 3, 1, 3, 3, 3, 2] => 1, 1, 1, 3, 1, 3, 3, 3, 2
[1, 1, 1, 3, 1, 3, 3, 3, 3] => 1, 1, 1, 3, 1, 3, 3, 3, 3
[1, 1, 1, 3, 2, 1, 1, 1, 1] => 1, 1, 1, 3, 2, 1, 1, 1, 1
[1, 1, 1, 3, 2, 1, 1, 1, 2] => 1, 1, 1, 3, 2, 1, 1, 1, 2
[1, 1, 1, 3, 2, 1, 1, 1, 3] => 1, 1, 1, 3, 2, 1, 1, 1, 3
[1, 1, 1, 3, 2, 1, 1, 2, 1] => 1, 1, 1, 3, 2, 1, 1, 2, 1
[1, 1, 1, 3, 2, 1, 1, 2, 2] => 1, 1, 1, 3, 2, 1, 1, 2, 2
[1, 1, 1, 3, 2, 1, 1, 2, 3] => 1, 1, 1, 3, 2, 1, 1, 2, 3
[1, 1, 1, 3, 2, 1, 1, 3, 1] => 1, 1, 1, 3, 2, 1, 1, 3, 1
[1, 1, 1, 3, 2, 1, 1, 3, 2] => 1, 1, 1, 3, 2, 1, 1, 3, 2
[1, 1, 1, 3, 2, 1, 1, 3, 3] => 1, 1, 1, 3, 2, 1, 1, 3, 3
[1, 1, 1, 3, 2, 1, 2, 1, 1] => 1, 1, 1, 3, 2, 1, 2, 1, 1
[1, 1, 1, 3, 2, 1, 2, 1, 2] => 1, 1, 1, 3, 2, 1, 2, 1, 2
[1, 1, 1, 3, 2, 1, 2, 1, 3] => 1, 1, 1, 3, 2, 1, 2, 1, 3
[1, 1, 1, 3, 2, 1, 2, 2, 1] => 1, 1, 1, 3, 2, 1, 2, 2, 1
[1, 1, 1, 3, 2, 1, 2, 2, 2] => 1, 1, 1, 3, 2, 1, 2, 2, 2
[1, 1, 1, 3, 2, 1, 2, 2, 3] => 1, 1, 1, 3, 2, 1, 2, 2, 3
[1, 1, 1, 3, 2, 1, 2, 3, 1] => 1, 1, 1, 3, 2, 1, 2, 3, 1
[1, 1, 1, 3, 2, 1, 2, 3, 2] => 1, 1, 1, 3, 2, 1, 2, 3, 2
[1, 1, 1, 3, 2, 1, 2, 3, 3] => 1, 1, 1, 3, 2, 1, 2, 3, 3
[1, 1, 1, 3, 2, 1, 3, 1, 1] => 1, 1, 1, 3, 2, 1, 3, 1, 1
[1, 1, 1, 3, 2, 1, 3, 1, 2] => 1, 1, 1, 3, 2, 1, 3, 1, 2
[1, 1, 1, 3, 2, 1, 3, 1, 3] => 1, 1, 1, 3, 2, 1, 3, 1, 3
[1, 1, 1, 3, 2, 1, 3, 2, 1] => 1, 1, 1, 3, 2, 1, 3, 2, 1
[1, 1, 1, 3, 2, 1, 3, 2, 2] => 1, 1, 1, 3, 2, 1, 3, 2, 2
[1, 1, 1, 3, 2, 1, 3, 2, 3] => 1, 1, 1, 3, 2, 1, 3, 2, 3
[1, 1, 1, 3, 2, 1, 3, 3, 1] => 1, 1, 1, 3, 2, 1, 3, 3, 1
[1, 1, 1, 3, 2, 1, 3, 3, 2] => 1, 1, 1, 3, 2, 1, 3, 3, 2
[1, 1, 1, 3, 2, 1, 3, 3, 3] => 1, 1, 1, 3, 2, 1, 3, 3, 3
[1, 1, 1, 3, 2, 2, 1, 1, 1] => 1, 1, 1, 3, 2, 2, 1, 1, 1
[1, 1, 1, 3, 2, 2, 1, 1, 2] => 1, 1, 1, 3, 2, 2, 1, 1, 2
[1, 1, 1, 3, 2, 2, 1, 1, 3] => 1, 1, 1, 3, 2, 2, 1, 1, 3
[1, 1, 1, 3, 2, 2, 1, 2, 1] => 1, 1, 1, 3, 2, 2, 1, 2, 1
[1, 1, 1, 3, 2, 2, 1, 2, 2] => 1, 1, 1, 3, 2, 2, 1, 2, 2
[1, 1, 1, 3, 2, 2, 1, 2, 3] => 1, 1, 1, 3, 2, 2, 1, 2, 3
[1, 1, 1, 3, 2, 2, 1, 3, 1] => 1, 1, 1, 3, 2, 2, 1, 3, 1
[1, 1, 1, 3, 2, 2, 1, 3, 2] => 1, 1, 1, 3, 2, 2, 1, 3, 2
[1, 1, 1, 3, 2, 2, 1, 3, 3] => 1, 1, 1, 3, 2, 2, 1, 3, 3
[1, 1, 1, 3, 2, 2, 2, 1, 1] => 1, 1, 1, 3, 2, 2, 2, 1, 1
[1, 1, 1, 3, 2, 2, 2, 1, 2] => 1, 1, 1, 3, 2, 2, 2, 1, 2
[1, 1, 1, 3, 2, 2, 2, 1, 3] => 1, 1, 1, 3, 2, 2, 2, 1, 3
[1, 1, 1, 3, 2, 2, 2, 2, 1] => 1, 1, 1, 3, 2, 2, 2, 2, 1
[1, 1, 1, 3, 2, 2, 2, 2, 2] => 1, 1, 1, 3, 2, 2, 2, 2, 2
[1, 1, 1, 3, 2, 2, 2, 2, 3] => 1, 1, 1, 3, 2, 2, 2, 2, 3
[1, 1, 1, 3, 2, 2, 2, 3, 1] => 1, 1, 1, 3, 2, 2, 2, 3, 1
[1, 1, 1, 3, 2, 2, 2, 3, 2] => 1, 1, 1, 3, 2, 2, 2, 3, 2
[1, 1, 1, 3, 2, 2, 2, 3, 3] => 1, 1, 1, 3, 2, 2, 2, 3, 3
[1, 1, 1, 3, 2, 2, 3, 1, 1] => 1, 1, 1, 3, 2, 2, 3, 1, 1
[1, 1, 1, 3, 2, 2, 3, 1, 2] => 1, 1, 1, 3, 2, 2, 3, 1, 2
[1, 1, 1, 3, 2, 2, 3, 1, 3] => 1, 1, 1, 3, 2, 2, 3, 1, 3
[1, 1, 1, 3, 2, 2, 3, 2, 1] => 1, 1, 1, 3, 2, 2, 3, 2, 1
[1, 1, 1, 3, 2, 2, 3, 2, 2] => 1, 1, 1, 3, 2, 2, 3, 2, 2
[1, 1, 1, 3, 2, 2, 3, 2, 3] => 1, 1, 1, 3, 2, 2, 3, 2, 3
[1, 1, 1, 3, 2, 2, 3, 3, 1] => 1, 1, 1, 3, 2, 2, 3, 3, 1
[1, 1, 1, 3, 2, 2, 3, 3, 2] => 1, 1, 1, 3, 2, 2, 3, 3, 2
[1, 1, 1, 3, 2, 2, 3, 3, 3] => 1, 1, 1, 3, 2, 2, 3, 3, 3
[1, 1, 1, 3, 2, 3, 1, 1, 1] => 1, 1, 1, 3, 2, 3, 1, 1, 1
[1, 1, 1, 3, 2, 3, 1, 1, 2] => 1, 1, 1, 3, 2, 3, 1, 1, 2
[1, 1, 1, 3, 2, 3, 1, 1, 3] => 1, 1, 1, 3, 2, 3, 1, 1, 3
[1, 1, 1, 3, 2, 3, 1, 2, 1] => 1, 1, 1, 3, 2, 3, 1, 2, 1
[1, 1, 1, 3, 2, 3, 1, 2, 2] => 1, 1, 1, 3, 2, 3, 1, 2, 2
[1, 1, 1, 3, 2, 3, 1, 2, 3] => 1, 1, 1, 3, 2, 3, 1, 2, 3
[1, 1, 1, 3, 2, 3, 1, 3, 1] => 1, 1, 1, 3, 2, 3, 1, 3, 1
[1, 1, 1, 3, 2, 3, 1, 3, 2] => 1, 1, 1, 3, 2, 3, 1, 3, 2
[1, 1, 1, 3, 2, 3, 1, 3, 3] => 1, 1, 1, 3, 2, 3, 1, 3, 3
[1, 1, 1, 3, 2, 3, 2, 1, 1] => 1, 1, 1, 3, 2, 3, 2, 1, 1
[1, 1, 1, 3, 2, 3, 2, 1, 2] => 1, 1, 1, 3, 2, 3, 2, 1, 2
[1, 1, 1, 3, 2, 3, 2, 1, 3] => 1, 1, 1, 3, 2, 3, 2, 1, 3
[1, 1, 1, 3, 2, 3, 2, 2, 1] => 1, 1, 1, 3, 2, 3, 2, 2, 1
[1, 1, 1, 3, 2, 3, 2, 2, 2] => 1, 1, 1, 3, 2, 3, 2, 2, 2
[1, 1, 1, 3, 2, 3, 2, 2, 3] => 1, 1, 1, 3, 2, 3, 2, 2, 3
[1, 1, 1, 3, 2, 3, 2, 3, 1] => 1, 1, 1, 3, 2, 3, 2, 3, 1
[1, 1, 1, 3, 2, 3, 2, 3, 2] => 1, 1, 1, 3, 2, 3, 2, 3, 2
[1, 1, 1, 3, 2, 3, 2, 3, 3] => 1, 1, 1, 3, 2, 3, 2, 3, 3
[1, 1, 1, 3, 2, 3, 3, 1, 1] => 1, 1, 1, 3, 2, 3, 3, 1, 1
[1, 1, 1, 3, 2, 3, 3, 1, 2] => 1, 1, 1, 3, 2, 3, 3, 1, 2
[1, 1, 1, 3, 2, 3, 3, 1, 3] => 1, 1, 1, 3, 2, 3, 3, 1, 3
[1, 1, 1, 3, 2, 3, 3, 2, 1] => 1, 1, 1, 3, 2, 3, 3, 2, 1
[1, 1, 1, 3, 2, 3, 3, 2, 2] => 1, 1, 1, 3, 2, 3, 3, 2, 2
[1, 1, 1, 3, 2, 3, 3, 2, 3] => 1, 1, 1, 3, 2, 3, 3, 2, 3
[1, 1, 1, 3, 2, 3, 3, 3, 1] => 1, 1, 1, 3, 2, 3, 3, 3, 1
[1, 1, 1, 3, 2, 3, 3, 3, 2] => 1, 1, 1, 3, 2, 3, 3, 3, 2
[1, 1, 1, 3, 2, 3, 3, 3, 3] => 1, 1, 1, 3, 2, 3, 3, 3, 3
[1, 1, 1, 3, 3, 1, 1, 1, 1] => 1, 1, 1, 3, 3, 1, 1, 1, 1
[1, 1, 1, 3, 3, 1, 1, 1, 2] => 1, 1, 1, 3, 3, 1, 1, 1, 2
[1, 1, 1, 3, 3, 1, 1, 1, 3] => 1, 1, 1, 3, 3, 1, 1, 1, 3
[1, 1, 1, 3, 3, 1, 1, 2, 1] => 1, 1, 1, 3, 3, 1, 1, 2, 1
[1, 1, 1, 3, 3, 1, 1, 2, 2] => 1, 1, 1, 3, 3, 1, 1, 2, 2
[1, 1, 1, 3, 3, 1, 1, 2, 3] => 1, 1, 1, 3, 3, 1, 1, 2, 3
[1, 1, 1, 3, 3, 1, 1, 3, 1] => 1, 1, 1, 3, 3, 1, 1, 3, 1
[1, 1, 1, 3, 3, 1, 1, 3, 2] => 1, 1, 1, 3, 3, 1, 1, 3, 2
[1, 1, 1, 3, 3, 1, 1, 3, 3] => 1, 1, 1, 3, 3, 1, 1, 3, 3
[1, 1, 1, 3, 3, 1, 2, 1, 1] => 1, 1, 1, 3, 3, 1, 2, 1, 1
[1, 1, 1, 3, 3, 1, 2, 1, 2] => 1, 1, 1, 3, 3, 1, 2, 1, 2
[1, 1, 1, 3, 3, 1, 2, 1, 3] => 1, 1, 1, 3, 3, 1, 2, 1, 3
[1, 1, 1, 3, 3, 1, 2, 2, 1] => 1, 1, 1, 3, 3, 1, 2, 2, 1
[1, 1, 1, 3, 3, 1, 2, 2, 2] => 1, 1, 1, 3, 3, 1, 2, 2, 2
[1, 1, 1, 3, 3, 1, 2, 2, 3] => 1, 1, 1, 3, 3, 1, 2, 2, 3
[1, 1, 1, 3, 3, 1, 2, 3, 1] => 1, 1, 1, 3, 3, 1, 2, 3, 1
[1, 1, 1, 3, 3, 1, 2, 3, 2] => 1, 1, 1, 3, 3, 1, 2, 3, 2
[1, 1, 1, 3, 3, 1, 2, 3, 3] => 1, 1, 1, 3, 3, 1, 2, 3, 3
[1, 1, 1, 3, 3, 1, 3, 1, 1] => 1, 1, 1, 3, 3, 1, 3, 1, 1
[1, 1, 1, 3, 3, 1, 3, 1, 2] => 1, 1, 1, 3, 3, 1, 3, 1, 2
[1, 1, 1, 3, 3, 1, 3, 1, 3] => 1, 1, 1, 3, 3, 1, 3, 1, 3
[1, 1, 1, 3, 3, 1, 3, 2, 1] => 1, 1, 1, 3, 3, 1, 3, 2, 1
[1, 1, 1, 3, 3, 1, 3, 2, 2] => 1, 1, 1, 3, 3, 1, 3, 2, 2
[1, 1, 1, 3, 3, 1, 3, 2, 3] => 1, 1, 1, 3, 3, 1, 3, 2, 3
[1, 1, 1, 3, 3, 1, 3, 3, 1] => 1, 1, 1, 3, 3, 1, 3, 3, 1
[1, 1, 1, 3, 3, 1, 3, 3, 2] => 1, 1, 1, 3, 3, 1, 3, 3, 2
[1, 1, 1, 3, 3, 1, 3, 3, 3] => 1, 1, 1, 3, 3, 1, 3, 3, 3
[1, 1, 1, 3, 3, 2, 1, 1, 1] => 1, 1, 1, 3, 3, 2, 1, 1, 1
[1, 1, 1, 3, 3, 2, 1, 1, 2] => 1, 1, 1, 3, 3, 2, 1, 1, 2
[1, 1, 1, 3, 3, 2, 1, 1, 3] => 1, 1, 1, 3, 3, 2, 1, 1, 3
[1, 1, 1, 3, 3, 2, 1, 2, 1] => 1, 1, 1, 3, 3, 2, 1, 2, 1
[1, 1, 1, 3, 3, 2, 1, 2, 2] => 1, 1, 1, 3, 3, 2, 1, 2, 2
[1, 1, 1, 3, 3, 2, 1, 2, 3] => 1, 1, 1, 3, 3, 2, 1, 2, 3
[1, 1, 1, 3, 3, 2, 1, 3, 1] => 1, 1, 1, 3, 3, 2, 1, 3, 1
[1, 1, 1, 3, 3, 2, 1, 3, 2] => 1, 1, 1, 3, 3, 2, 1, 3, 2
[1, 1, 1, 3, 3, 2, 1, 3, 3] => 1, 1, 1, 3, 3, 2, 1, 3, 3
[1, 1, 1, 3, 3, 2, 2, 1, 1] => 1, 1, 1, 3, 3, 2, 2, 1, 1
[1, 1, 1, 3, 3, 2, 2, 1, 2] => 1, 1, 1, 3, 3, 2, 2, 1, 2
[1, 1, 1, 3, 3, 2, 2, 1, 3] => 1, 1, 1, 3, 3, 2, 2, 1, 3
[1, 1, 1, 3, 3, 2, 2, 2, 1] => 1, 1, 1, 3, 3, 2, 2, 2, 1
[1, 1, 1, 3, 3, 2, 2, 2, 2] => 1, 1, 1, 3, 3, 2, 2, 2, 2
[1, 1, 1, 3, 3, 2, 2, 2, 3] => 1, 1, 1, 3, 3, 2, 2, 2, 3
[1, 1, 1, 3, 3, 2, 2, 3, 1] => 1, 1, 1, 3, 3, 2, 2, 3, 1
[1, 1, 1, 3, 3, 2, 2, 3, 2] => 1, 1, 1, 3, 3, 2, 2, 3, 2
[1, 1, 1, 3, 3, 2, 2, 3, 3] => 1, 1, 1, 3, 3, 2, 2, 3, 3
[1, 1, 1, 3, 3, 2, 3, 1, 1] => 1, 1, 1, 3, 3, 2, 3, 1, 1
[1, 1, 1, 3, 3, 2, 3, 1, 2] => 1, 1, 1, 3, 3, 2, 3, 1, 2
[1, 1, 1, 3, 3, 2, 3, 1, 3] => 1, 1, 1, 3, 3, 2, 3, 1, 3
[1, 1, 1, 3, 3, 2, 3, 2, 1] => 1, 1, 1, 3, 3, 2, 3, 2, 1
[1, 1, 1, 3, 3, 2, 3, 2, 2] => 1, 1, 1, 3, 3, 2, 3, 2, 2
[1, 1, 1, 3, 3, 2, 3, 2, 3] => 1, 1, 1, 3, 3, 2, 3, 2, 3
[1, 1, 1, 3, 3, 2, 3, 3, 1] => 1, 1, 1, 3, 3, 2, 3, 3, 1
[1, 1, 1, 3, 3, 2, 3, 3, 2] => 1, 1, 1, 3, 3, 2, 3, 3, 2
[1, 1, 1, 3, 3, 2, 3, 3, 3] => 1, 1, 1, 3, 3, 2, 3, 3, 3
[1, 1, 1, 3, 3, 3, 1, 1, 1] => 1, 1, 1, 3, 3, 3, 1, 1, 1
[1, 1, 1, 3, 3, 3, 1, 1, 2] => 1, 1, 1, 3, 3, 3, 1, 1, 2
[1, 1, 1, 3, 3, 3, 1, 1, 3] => 1, 1, 1, 3, 3, 3, 1, 1, 3
[1, 1, 1, 3, 3, 3, 1, 2, 1] => 1, 1, 1, 3, 3, 3, 1, 2, 1
[1, 1, 1, 3, 3, 3, 1, 2, 2] => 1, 1, 1, 3, 3, 3, 1, 2, 2
[1, 1, 1, 3, 3, 3, 1, 2, 3] => 1, 1, 1, 3, 3, 3, 1, 2, 3
[1, 1, 1, 3, 3, 3, 1, 3, 1] => 1, 1, 1, 3, 3, 3, 1, 3, 1
[1, 1, 1, 3, 3, 3, 1, 3, 2] => 1, 1, 1, 3, 3, 3, 1, 3, 2
[1, 1, 1, 3, 3, 3, 1, 3, 3] => 1, 1, 1, 3, 3, 3, 1, 3, 3
[1, 1, 1, 3, 3, 3, 2, 1, 1] => 1, 1, 1, 3, 3, 3, 2, 1, 1
[1, 1, 1, 3, 3, 3, 2, 1, 2] => 1, 1, 1, 3, 3, 3, 2, 1, 2
[1, 1, 1, 3, 3, 3, 2, 1, 3] => 1, 1, 1, 3, 3, 3, 2, 1, 3
[1, 1, 1, 3, 3, 3, 2, 2, 1] => 1, 1, 1, 3, 3, 3, 2, 2, 1
[1, 1, 1, 3, 3, 3, 2, 2, 2] => 1, 1, 1, 3, 3, 3, 2, 2, 2
[1, 1, 1, 3, 3, 3, 2, 2, 3] => 1, 1, 1, 3, 3, 3, 2, 2, 3
[1, 1, 1, 3, 3, 3, 2, 3, 1] => 1, 1, 1, 3, 3, 3, 2, 3, 1
[1, 1, 1, 3, 3, 3, 2, 3, 2] => 1, 1, 1, 3, 3, 3, 2, 3, 2
[1, 1, 1, 3, 3, 3, 2, 3, 3] => 1, 1, 1, 3, 3, 3, 2, 3, 3
[1, 1, 1, 3, 3, 3, 3, 1, 1] => 1, 1, 1, 3, 3, 3, 3, 1, 1
[1, 1, 1, 3, 3, 3, 3, 1, 2] => 1, 1, 1, 3, 3, 3, 3, 1, 2
[1, 1, 1, 3, 3, 3, 3, 1, 3] => 1, 1, 1, 3, 3, 3, 3, 1, 3
[1, 1, 1, 3, 3, 3, 3, 2, 1] => 1, 1, 1, 3, 3, 3, 3, 2, 1
[1, 1, 1, 3, 3, 3, 3, 2, 2] => 1, 1, 1, 3, 3, 3, 3, 2, 2
[1, 1, 1, 3, 3, 3, 3, 2, 3] => 1, 1, 1, 3, 3, 3, 3, 2, 3
[1, 1, 1, 3, 3, 3, 3, 3, 1] => 1, 1, 1, 3, 3, 3, 3, 3, 1
[1, 1, 1, 3, 3, 3, 3, 3, 2] => 1, 1, 1, 3, 3, 3, 3, 3, 2
[1, 1, 1, 3, 3, 3, 3, 3, 3] => 1, 1, 1, 3, 3, 3, 3, 3, 3
[1, 1, 2, 1, 1, 1, 1, 1, 1] => 1, 1, 2, 1, 1, 1, 1, 1, 1
[1, 1, 2, 1, 1, 1, 1, 1, 2] => 1, 1, 2, 1, 1, 1, 1, 1, 2
[1, 1, 2, 1, 1, 1, 1, 1, 3] => 1, 1, 2, 1, 1, 1, 1, 1, 3
[1, 1, 2, 1, 1, 1, 1, 2, 1] => 1, 1, 2, 1, 1, 1, 1, 2, 1
[1, 1, 2, 1, 1, 1, 1, 2, 2] => 1, 1, 2, 1, 1, 1, 1, 2, 2
[1, 1, 2, 1, 1, 1, 1, 2, 3] => 1, 1, 2, 1, 1, 1, 1, 2, 3
[1, 1, 2, 1, 1, 1, 1, 3, 1] => 1, 1, 2, 1, 1, 1, 1, 3, 1
[1, 1, 2, 1, 1, 1, 1, 3, 2] => 1, 1, 2, 1, 1, 1, 1, 3, 2
[1, 1, 2, 1, 1, 1, 1, 3, 3] => 1, 1, 2, 1, 1, 1, 1, 3, 3
[1, 1, 2, 1, 1, 1, 2, 1, 1] => 1, 1, 2, 1, 1, 1, 2, 1, 1
[1, 1, 2, 1, 1, 1, 2, 1, 2] => 1, 1, 2, 1, 1, 1, 2, 1, 2
[1, 1, 2, 1, 1, 1, 2, 1, 3] => 1, 1, 2, 1, 1, 1, 2, 1, 3
[1, 1, 2, 1, 1, 1, 2, 2, 1] => 1, 1, 2, 1, 1, 1, 2, 2, 1
[1, 1, 2, 1, 1, 1, 2, 2, 2] => 1, 1, 2, 1, 1, 1, 2, 2, 2
[1, 1, 2, 1, 1, 1, 2, 2, 3] => 1, 1, 2, 1, 1, 1, 2, 2, 3
[1, 1, 2, 1, 1, 1, 2, 3, 1] => 1, 1, 2, 1, 1, 1, 2, 3, 1
[1, 1, 2, 1, 1, 1, 2, 3, 2] => 1, 1, 2, 1, 1, 1, 2, 3, 2
[1, 1, 2, 1, 1, 1, 2, 3, 3] => 1, 1, 2, 1, 1, 1, 2, 3, 3
[1, 1, 2, 1, 1, 1, 3, 1, 1] => 1, 1, 2, 1, 1, 1, 3, 1, 1
[1, 1, 2, 1, 1, 1, 3, 1, 2] => 1, 1, 2, 1, 1, 1, 3, 1, 2
[1, 1, 2, 1, 1, 1, 3, 1, 3] => 1, 1, 2, 1, 1, 1, 3, 1, 3
[1, 1, 2, 1, 1, 1, 3, 2, 1] => 1, 1, 2, 1, 1, 1, 3, 2, 1
[1, 1, 2, 1, 1, 1, 3, 2, 2] => 1, 1, 2, 1, 1, 1, 3, 2, 2
[1, 1, 2, 1, 1, 1, 3, 2, 3] => 1, 1, 2, 1, 1, 1, 3, 2, 3
[1, 1, 2, 1, 1, 1, 3, 3, 1] => 1, 1, 2, 1, 1, 1, 3, 3, 1
[1, 1, 2, 1, 1, 1, 3, 3, 2] => 1, 1, 2, 1, 1, 1, 3, 3, 2
[1, 1, 2, 1, 1, 1, 3, 3, 3] => 1, 1, 2, 1, 1, 1, 3, 3, 3
[1, 1, 2, 1, 1, 2, 1, 1, 1] => 1, 1, 2, 1, 1, 2, 1, 1, 1
[1, 1, 2, 1, 1, 2, 1, 1, 2] => 1, 1, 2, 1, 1, 2, 1, 1, 2
[1, 1, 2, 1, 1, 2, 1, 1, 3] => 1, 1, 2, 1, 1, 2, 1, 1, 3
[1, 1, 2, 1, 1, 2, 1, 2, 1] => 1, 1, 2, 1, 1, 2, 1, 2, 1
[1, 1, 2, 1, 1, 2, 1, 2, 2] => 1, 1, 2, 1, 1, 2, 1, 2, 2
[1, 1, 2, 1, 1, 2, 1, 2, 3] => 1, 1, 2, 1, 1, 2, 1, 2, 3
[1, 1, 2, 1, 1, 2, 1, 3, 1] => 1, 1, 2, 1, 1, 2, 1, 3, 1
[1, 1, 2, 1, 1, 2, 1, 3, 2] => 1, 1, 2, 1, 1, 2, 1, 3, 2
[1, 1, 2, 1, 1, 2, 1, 3, 3] => 1, 1, 2, 1, 1, 2, 1, 3, 3
[1, 1, 2, 1, 1, 2, 2, 1, 1] => 1, 1, 2, 1, 1, 2, 2, 1, 1
[1, 1, 2, 1, 1, 2, 2, 1, 2] => 1, 1, 2, 1, 1, 2, 2, 1, 2
[1, 1, 2, 1, 1, 2, 2, 1, 3] => 1, 1, 2, 1, 1, 2, 2, 1, 3
[1, 1, 2, 1, 1, 2, 2, 2, 1] => 1, 1, 2, 1, 1, 2, 2, 2, 1
[1, 1, 2, 1, 1, 2, 2, 2, 2] => 1, 1, 2, 1, 1, 2, 2, 2, 2
[1, 1, 2, 1, 1, 2, 2, 2, 3] => 1, 1, 2, 1, 1, 2, 2, 2, 3
[1, 1, 2, 1, 1, 2, 2, 3, 1] => 1, 1, 2, 1, 1, 2, 2, 3, 1
[1, 1, 2, 1, 1, 2, 2, 3, 2] => 1, 1, 2, 1, 1, 2, 2, 3, 2
[1, 1, 2, 1, 1, 2, 2, 3, 3] => 1, 1, 2, 1, 1, 2, 2, 3, 3
[1, 1, 2, 1, 1, 2, 3, 1, 1] => 1, 1, 2, 1, 1, 2, 3, 1, 1
[1, 1, 2, 1, 1, 2, 3, 1, 2] => 1, 1, 2, 1, 1, 2, 3, 1, 2
[1, 1, 2, 1, 1, 2, 3, 1, 3] => 1, 1, 2, 1, 1, 2, 3, 1, 3
[1, 1, 2, 1, 1, 2, 3, 2, 1] => 1, 1, 2, 1, 1, 2, 3, 2, 1
[1, 1, 2, 1, 1, 2, 3, 2, 2] => 1, 1, 2, 1, 1, 2, 3, 2, 2
[1, 1, 2, 1, 1, 2, 3, 2, 3] => 1, 1, 2, 1, 1, 2, 3, 2, 3
[1, 1, 2, 1, 1, 2, 3, 3, 1] => 1, 1, 2, 1, 1, 2, 3, 3, 1
[1, 1, 2, 1, 1, 2, 3, 3, 2] => 1, 1, 2, 1, 1, 2, 3, 3, 2
[1, 1, 2, 1, 1, 2, 3, 3, 3] => 1, 1, 2, 1, 1, 2, 3, 3, 3
[1, 1, 2, 1, 1, 3, 1, 1, 1] => 1, 1, 2, 1, 1, 3, 1, 1, 1
[1, 1, 2, 1, 1, 3, 1, 1, 2] => 1, 1, 2, 1, 1, 3, 1, 1, 2
[1, 1, 2, 1, 1, 3, 1, 1, 3] => 1, 1, 2, 1, 1, 3, 1, 1, 3
[1, 1, 2, 1, 1, 3, 1, 2, 1] => 1, 1, 2, 1, 1, 3, 1, 2, 1
[1, 1, 2, 1, 1, 3, 1, 2, 2] => 1, 1, 2, 1, 1, 3, 1, 2, 2
[1, 1, 2, 1, 1, 3, 1, 2, 3] => 1, 1, 2, 1, 1, 3, 1, 2, 3
[1, 1, 2, 1, 1, 3, 1, 3, 1] => 1, 1, 2, 1, 1, 3, 1, 3, 1
[1, 1, 2, 1, 1, 3, 1, 3, 2] => 1, 1, 2, 1, 1, 3, 1, 3, 2
[1, 1, 2, 1, 1, 3, 1, 3, 3] => 1, 1, 2, 1, 1, 3, 1, 3, 3
[1, 1, 2, 1, 1, 3, 2, 1, 1] => 1, 1, 2, 1, 1, 3, 2, 1, 1
[1, 1, 2, 1, 1, 3, 2, 1, 2] => 1, 1, 2, 1, 1, 3, 2, 1, 2
[1, 1, 2, 1, 1, 3, 2, 1, 3] => 1, 1, 2, 1, 1, 3, 2, 1, 3
[1, 1, 2, 1, 1, 3, 2, 2, 1] => 1, 1, 2, 1, 1, 3, 2, 2, 1
[1, 1, 2, 1, 1, 3, 2, 2, 2] => 1, 1, 2, 1, 1, 3, 2, 2, 2
[1, 1, 2, 1, 1, 3, 2, 2, 3] => 1, 1, 2, 1, 1, 3, 2, 2, 3
[1, 1, 2, 1, 1, 3, 2, 3, 1] => 1, 1, 2, 1, 1, 3, 2, 3, 1
[1, 1, 2, 1, 1, 3, 2, 3, 2] => 1, 1, 2, 1, 1, 3, 2, 3, 2
[1, 1, 2, 1, 1, 3, 2, 3, 3] => 1, 1, 2, 1, 1, 3, 2, 3, 3
[1, 1, 2, 1, 1, 3, 3, 1, 1] => 1, 1, 2, 1, 1, 3, 3, 1, 1
[1, 1, 2, 1, 1, 3, 3, 1, 2] => 1, 1, 2, 1, 1, 3, 3, 1, 2
[1, 1, 2, 1, 1, 3, 3, 1, 3] => 1, 1, 2, 1, 1, 3, 3, 1, 3
[1, 1, 2, 1, 1, 3, 3, 2, 1] => 1, 1, 2, 1, 1, 3, 3, 2, 1
[1, 1, 2, 1, 1, 3, 3, 2, 2] => 1, 1, 2, 1, 1, 3, 3, 2, 2
[1, 1, 2, 1, 1, 3, 3, 2, 3] => 1, 1, 2, 1, 1, 3, 3, 2, 3
[1, 1, 2, 1, 1, 3, 3, 3, 1] => 1, 1, 2, 1, 1, 3, 3, 3, 1
[1, 1, 2, 1, 1, 3, 3, 3, 2] => 1, 1, 2, 1, 1, 3, 3, 3, 2
[1, 1, 2, 1, 1, 3, 3, 3, 3] => 1, 1, 2, 1, 1, 3, 3, 3, 3
[1, 1, 2, 1, 2, 1, 1, 1, 1] => 1, 1, 2, 1, 2, 1, 1, 1, 1
[1, 1, 2, 1, 2, 1, 1, 1, 2] => 1, 1, 2, 1, 2, 1, 1, 1, 2
[1, 1, 2, 1, 2, 1, 1, 1, 3] => 1, 1, 2, 1, 2, 1, 1, 1, 3
[1, 1, 2, 1, 2, 1, 1, 2, 1] => 1, 1, 2, 1, 2, 1, 1, 2, 1
[1, 1, 2, 1, 2, 1, 1, 2, 2] => 1, 1, 2, 1, 2, 1, 1, 2, 2
[1, 1, 2, 1, 2, 1, 1, 2, 3] => 1, 1, 2, 1, 2, 1, 1, 2, 3
[1, 1, 2, 1, 2, 1, 1, 3, 1] => 1, 1, 2, 1, 2, 1, 1, 3, 1
[1, 1, 2, 1, 2, 1, 1, 3, 2] => 1, 1, 2, 1, 2, 1, 1, 3, 2
[1, 1, 2, 1, 2, 1, 1, 3, 3] => 1, 1, 2, 1, 2, 1, 1, 3, 3
[1, 1, 2, 1, 2, 1, 2, 1, 1] => 1, 1, 2, 1, 2, 1, 2, 1, 1
[1, 1, 2, 1, 2, 1, 2, 1, 2] => 1, 1, 2, 1, 2, 1, 2, 1, 2
[1, 1, 2, 1, 2, 1, 2, 1, 3] => 1, 1, 2, 1, 2, 1, 2, 1, 3
[1, 1, 2, 1, 2, 1, 2, 2, 1] => 1, 1, 2, 1, 2, 1, 2, 2, 1
[1, 1, 2, 1, 2, 1, 2, 2, 2] => 1, 1, 2, 1, 2, 1, 2, 2, 2
[1, 1, 2, 1, 2, 1, 2, 2, 3] => 1, 1, 2, 1, 2, 1, 2, 2, 3
[1, 1, 2, 1, 2, 1, 2, 3, 1] => 1, 1, 2, 1, 2, 1, 2, 3, 1
[1, 1, 2, 1, 2, 1, 2, 3, 2] => 1, 1, 2, 1, 2, 1, 2, 3, 2
[1, 1, 2, 1, 2, 1, 2, 3, 3] => 1, 1, 2, 1, 2, 1, 2, 3, 3
[1, 1, 2, 1, 2, 1, 3, 1, 1] => 1, 1, 2, 1, 2, 1, 3, 1, 1
[1, 1, 2, 1, 2, 1, 3, 1, 2] => 1, 1, 2, 1, 2, 1, 3, 1, 2
[1, 1, 2, 1, 2, 1, 3, 1, 3] => 1, 1, 2, 1, 2, 1, 3, 1, 3
[1, 1, 2, 1, 2, 1, 3, 2, 1] => 1, 1, 2, 1, 2, 1, 3, 2, 1
[1, 1, 2, 1, 2, 1, 3, 2, 2] => 1, 1, 2, 1, 2, 1, 3, 2, 2
[1, 1, 2, 1, 2, 1, 3, 2, 3] => 1, 1, 2, 1, 2, 1, 3, 2, 3
[1, 1, 2, 1, 2, 1, 3, 3, 1] => 1, 1, 2, 1, 2, 1, 3, 3, 1
[1, 1, 2, 1, 2, 1, 3, 3, 2] => 1, 1, 2, 1, 2, 1, 3, 3, 2
[1, 1, 2, 1, 2, 1, 3, 3, 3] => 1, 1, 2, 1, 2, 1, 3, 3, 3
[1, 1, 2, 1, 2, 2, 1, 1, 1] => 1, 1, 2, 1, 2, 2, 1, 1, 1
[1, 1, 2, 1, 2, 2, 1, 1, 2] => 1, 1, 2, 1, 2, 2, 1, 1, 2
[1, 1, 2, 1, 2, 2, 1, 1, 3] => 1, 1, 2, 1, 2, 2, 1, 1, 3
[1, 1, 2, 1, 2, 2, 1, 2, 1] => 1, 1, 2, 1, 2, 2, 1, 2, 1
[1, 1, 2, 1, 2, 2, 1, 2, 2] => 1, 1, 2, 1, 2, 2, 1, 2, 2
[1, 1, 2, 1, 2, 2, 1, 2, 3] => 1, 1, 2, 1, 2, 2, 1, 2, 3
[1, 1, 2, 1, 2, 2, 1, 3, 1] => 1, 1, 2, 1, 2, 2, 1, 3, 1
[1, 1, 2, 1, 2, 2, 1, 3, 2] => 1, 1, 2, 1, 2, 2, 1, 3, 2
[1, 1, 2, 1, 2, 2, 1, 3, 3] => 1, 1, 2, 1, 2, 2, 1, 3, 3
[1, 1, 2, 1, 2, 2, 2, 1, 1] => 1, 1, 2, 1, 2, 2, 2, 1, 1
[1, 1, 2, 1, 2, 2, 2, 1, 2] => 1, 1, 2, 1, 2, 2, 2, 1, 2
[1, 1, 2, 1, 2, 2, 2, 1, 3] => 1, 1, 2, 1, 2, 2, 2, 1, 3
[1, 1, 2, 1, 2, 2, 2, 2, 1] => 1, 1, 2, 1, 2, 2, 2, 2, 1
[1, 1, 2, 1, 2, 2, 2, 2, 2] => 1, 1, 2, 1, 2, 2, 2, 2, 2
[1, 1, 2, 1, 2, 2, 2, 2, 3] => 1, 1, 2, 1, 2, 2, 2, 2, 3
[1, 1, 2, 1, 2, 2, 2, 3, 1] => 1, 1, 2, 1, 2, 2, 2, 3, 1
[1, 1, 2, 1, 2, 2, 2, 3, 2] => 1, 1, 2, 1, 2, 2, 2, 3, 2
[1, 1, 2, 1, 2, 2, 2, 3, 3] => 1, 1, 2, 1, 2, 2, 2, 3, 3
[1, 1, 2, 1, 2, 2, 3, 1, 1] => 1, 1, 2, 1, 2, 2, 3, 1, 1
[1, 1, 2, 1, 2, 2, 3, 1, 2] => 1, 1, 2, 1, 2, 2, 3, 1, 2
[1, 1, 2, 1, 2, 2, 3, 1, 3] => 1, 1, 2, 1, 2, 2, 3, 1, 3
[1, 1, 2, 1, 2, 2, 3, 2, 1] => 1, 1, 2, 1, 2, 2, 3, 2, 1
[1, 1, 2, 1, 2, 2, 3, 2, 2] => 1, 1, 2, 1, 2, 2, 3, 2, 2
[1, 1, 2, 1, 2, 2, 3, 2, 3] => 1, 1, 2, 1, 2, 2, 3, 2, 3
[1, 1, 2, 1, 2, 2, 3, 3, 1] => 1, 1, 2, 1, 2, 2, 3, 3, 1
[1, 1, 2, 1, 2, 2, 3, 3, 2] => 1, 1, 2, 1, 2, 2, 3, 3, 2
[1, 1, 2, 1, 2, 2, 3, 3, 3] => 1, 1, 2, 1, 2, 2, 3, 3, 3
[1, 1, 2, 1, 2, 3, 1, 1, 1] => 1, 1, 2, 1, 2, 3, 1, 1, 1
[1, 1, 2, 1, 2, 3, 1, 1, 2] => 1, 1, 2, 1, 2, 3, 1, 1, 2
[1, 1, 2, 1, 2, 3, 1, 1, 3] => 1, 1, 2, 1, 2, 3, 1, 1, 3
[1, 1, 2, 1, 2, 3, 1, 2, 1] => 1, 1, 2, 1, 2, 3, 1, 2, 1
[1, 1, 2, 1, 2, 3, 1, 2, 2] => 1, 1, 2, 1, 2, 3, 1, 2, 2
[1, 1, 2, 1, 2, 3, 1, 2, 3] => 1, 1, 2, 1, 2, 3, 1, 2, 3
[1, 1, 2, 1, 2, 3, 1, 3, 1] => 1, 1, 2, 1, 2, 3, 1, 3, 1
[1, 1, 2, 1, 2, 3, 1, 3, 2] => 1, 1, 2, 1, 2, 3, 1, 3, 2
[1, 1, 2, 1, 2, 3, 1, 3, 3] => 1, 1, 2, 1, 2, 3, 1, 3, 3
[1, 1, 2, 1, 2, 3, 2, 1, 1] => 1, 1, 2, 1, 2, 3, 2, 1, 1
[1, 1, 2, 1, 2, 3, 2, 1, 2] => 1, 1, 2, 1, 2, 3, 2, 1, 2
[1, 1, 2, 1, 2, 3, 2, 1, 3] => 1, 1, 2, 1, 2, 3, 2, 1, 3
[1, 1, 2, 1, 2, 3, 2, 2, 1] => 1, 1, 2, 1, 2, 3, 2, 2, 1
[1, 1, 2, 1, 2, 3, 2, 2, 2] => 1, 1, 2, 1, 2, 3, 2, 2, 2
[1, 1, 2, 1, 2, 3, 2, 2, 3] => 1, 1, 2, 1, 2, 3, 2, 2, 3
[1, 1, 2, 1, 2, 3, 2, 3, 1] => 1, 1, 2, 1, 2, 3, 2, 3, 1
[1, 1, 2, 1, 2, 3, 2, 3, 2] => 1, 1, 2, 1, 2, 3, 2, 3, 2
[1, 1, 2, 1, 2, 3, 2, 3, 3] => 1, 1, 2, 1, 2, 3, 2, 3, 3
[1, 1, 2, 1, 2, 3, 3, 1, 1] => 1, 1, 2, 1, 2, 3, 3, 1, 1
[1, 1, 2, 1, 2, 3, 3, 1, 2] => 1, 1, 2, 1, 2, 3, 3, 1, 2
[1, 1, 2, 1, 2, 3, 3, 1, 3] => 1, 1, 2, 1, 2, 3, 3, 1, 3
[1, 1, 2, 1, 2, 3, 3, 2, 1] => 1, 1, 2, 1, 2, 3, 3, 2, 1
[1, 1, 2, 1, 2, 3, 3, 2, 2] => 1, 1, 2, 1, 2, 3, 3, 2, 2
[1, 1, 2, 1, 2, 3, 3, 2, 3] => 1, 1, 2, 1, 2, 3, 3, 2, 3
[1, 1, 2, 1, 2, 3, 3, 3, 1] => 1, 1, 2, 1, 2, 3, 3, 3, 1
[1, 1, 2, 1, 2, 3, 3, 3, 2] => 1, 1, 2, 1, 2, 3, 3, 3, 2
[1, 1, 2, 1, 2, 3, 3, 3, 3] => 1, 1, 2, 1, 2, 3, 3, 3, 3
[1, 1, 2, 1, 3, 1, 1, 1, 1] => 1, 1, 2, 1, 3, 1, 1, 1, 1
[1, 1, 2, 1, 3, 1, 1, 1, 2] => 1, 1, 2, 1, 3, 1, 1, 1, 2
[1, 1, 2, 1, 3, 1, 1, 1, 3] => 1, 1, 2, 1, 3, 1, 1, 1, 3
[1, 1, 2, 1, 3, 1, 1, 2, 1] => 1, 1, 2, 1, 3, 1, 1, 2, 1
[1, 1, 2, 1, 3, 1, 1, 2, 2] => 1, 1, 2, 1, 3, 1, 1, 2, 2
[1, 1, 2, 1, 3, 1, 1, 2, 3] => 1, 1, 2, 1, 3, 1, 1, 2, 3
[1, 1, 2, 1, 3, 1, 1, 3, 1] => 1, 1, 2, 1, 3, 1, 1, 3, 1
[1, 1, 2, 1, 3, 1, 1, 3, 2] => 1, 1, 2, 1, 3, 1, 1, 3, 2
[1, 1, 2, 1, 3, 1, 1, 3, 3] => 1, 1, 2, 1, 3, 1, 1, 3, 3
[1, 1, 2, 1, 3, 1, 2, 1, 1] => 1, 1, 2, 1, 3, 1, 2, 1, 1
[1, 1, 2, 1, 3, 1, 2, 1, 2] => 1, 1, 2, 1, 3, 1, 2, 1, 2
[1, 1, 2, 1, 3, 1, 2, 1, 3] => 1, 1, 2, 1, 3, 1, 2, 1, 3
[1, 1, 2, 1, 3, 1, 2, 2, 1] => 1, 1, 2, 1, 3, 1, 2, 2, 1
[1, 1, 2, 1, 3, 1, 2, 2, 2] => 1, 1, 2, 1, 3, 1, 2, 2, 2
[1, 1, 2, 1, 3, 1, 2, 2, 3] => 1, 1, 2, 1, 3, 1, 2, 2, 3
[1, 1, 2, 1, 3, 1, 2, 3, 1] => 1, 1, 2, 1, 3, 1, 2, 3, 1
[1, 1, 2, 1, 3, 1, 2, 3, 2] => 1, 1, 2, 1, 3, 1, 2, 3, 2
[1, 1, 2, 1, 3, 1, 2, 3, 3] => 1, 1, 2, 1, 3, 1, 2, 3, 3
[1, 1, 2, 1, 3, 1, 3, 1, 1] => 1, 1, 2, 1, 3, 1, 3, 1, 1
[1, 1, 2, 1, 3, 1, 3, 1, 2] => 1, 1, 2, 1, 3, 1, 3, 1, 2
[1, 1, 2, 1, 3, 1, 3, 1, 3] => 1, 1, 2, 1, 3, 1, 3, 1, 3
[1, 1, 2, 1, 3, 1, 3, 2, 1] => 1, 1, 2, 1, 3, 1, 3, 2, 1
[1, 1, 2, 1, 3, 1, 3, 2, 2] => 1, 1, 2, 1, 3, 1, 3, 2, 2
[1, 1, 2, 1, 3, 1, 3, 2, 3] => 1, 1, 2, 1, 3, 1, 3, 2, 3
[1, 1, 2, 1, 3, 1, 3, 3, 1] => 1, 1, 2, 1, 3, 1, 3, 3, 1
[1, 1, 2, 1, 3, 1, 3, 3, 2] => 1, 1, 2, 1, 3, 1, 3, 3, 2
[1, 1, 2, 1, 3, 1, 3, 3, 3] => 1, 1, 2, 1, 3, 1, 3, 3, 3
[1, 1, 2, 1, 3, 2, 1, 1, 1] => 1, 1, 2, 1, 3, 2, 1, 1, 1
[1, 1, 2, 1, 3, 2, 1, 1, 2] => 1, 1, 2, 1, 3, 2, 1, 1, 2
[1, 1, 2, 1, 3, 2, 1, 1, 3] => 1, 1, 2, 1, 3, 2, 1, 1, 3
[1, 1, 2, 1, 3, 2, 1, 2, 1] => 1, 1, 2, 1, 3, 2, 1, 2, 1
[1, 1, 2, 1, 3, 2, 1, 2, 2] => 1, 1, 2, 1, 3, 2, 1, 2, 2
[1, 1, 2, 1, 3, 2, 1, 2, 3] => 1, 1, 2, 1, 3, 2, 1, 2, 3
[1, 1, 2, 1, 3, 2, 1, 3, 1] => 1, 1, 2, 1, 3, 2, 1, 3, 1
[1, 1, 2, 1, 3, 2, 1, 3, 2] => 1, 1, 2, 1, 3, 2, 1, 3, 2
[1, 1, 2, 1, 3, 2, 1, 3, 3] => 1, 1, 2, 1, 3, 2, 1, 3, 3
[1, 1, 2, 1, 3, 2, 2, 1, 1] => 1, 1, 2, 1, 3, 2, 2, 1, 1
[1, 1, 2, 1, 3, 2, 2, 1, 2] => 1, 1, 2, 1, 3, 2, 2, 1, 2
[1, 1, 2, 1, 3, 2, 2, 1, 3] => 1, 1, 2, 1, 3, 2, 2, 1, 3
[1, 1, 2, 1, 3, 2, 2, 2, 1] => 1, 1, 2, 1, 3, 2, 2, 2, 1
[1, 1, 2, 1, 3, 2, 2, 2, 2] => 1, 1, 2, 1, 3, 2, 2, 2, 2
[1, 1, 2, 1, 3, 2, 2, 2, 3] => 1, 1, 2, 1, 3, 2, 2, 2, 3
[1, 1, 2, 1, 3, 2, 2, 3, 1] => 1, 1, 2, 1, 3, 2, 2, 3, 1
[1, 1, 2, 1, 3, 2, 2, 3, 2] => 1, 1, 2, 1, 3, 2, 2, 3, 2
[1, 1, 2, 1, 3, 2, 2, 3, 3] => 1, 1, 2, 1, 3, 2, 2, 3, 3
[1, 1, 2, 1, 3, 2, 3, 1, 1] => 1, 1, 2, 1, 3, 2, 3, 1, 1
[1, 1, 2, 1, 3, 2, 3, 1, 2] => 1, 1, 2, 1, 3, 2, 3, 1, 2
[1, 1, 2, 1, 3, 2, 3, 1, 3] => 1, 1, 2, 1, 3, 2, 3, 1, 3
[1, 1, 2, 1, 3, 2, 3, 2, 1] => 1, 1, 2, 1, 3, 2, 3, 2, 1
[1, 1, 2, 1, 3, 2, 3, 2, 2] => 1, 1, 2, 1, 3, 2, 3, 2, 2
[1, 1, 2, 1, 3, 2, 3, 2, 3] => 1, 1, 2, 1, 3, 2, 3, 2, 3
[1, 1, 2, 1, 3, 2, 3, 3, 1] => 1, 1, 2, 1, 3, 2, 3, 3, 1
[1, 1, 2, 1, 3, 2, 3, 3, 2] => 1, 1, 2, 1, 3, 2, 3, 3, 2
[1, 1, 2, 1, 3, 2, 3, 3, 3] => 1, 1, 2, 1, 3, 2, 3, 3, 3
[1, 1, 2, 1, 3, 3, 1, 1, 1] => 1, 1, 2, 1, 3, 3, 1, 1, 1
[1, 1, 2, 1, 3, 3, 1, 1, 2] => 1, 1, 2, 1, 3, 3, 1, 1, 2
[1, 1, 2, 1, 3, 3, 1, 1, 3] => 1, 1, 2, 1, 3, 3, 1, 1, 3
[1, 1, 2, 1, 3, 3, 1, 2, 1] => 1, 1, 2, 1, 3, 3, 1, 2, 1
[1, 1, 2, 1, 3, 3, 1, 2, 2] => 1, 1, 2, 1, 3, 3, 1, 2, 2
[1, 1, 2, 1, 3, 3, 1, 2, 3] => 1, 1, 2, 1, 3, 3, 1, 2, 3
[1, 1, 2, 1, 3, 3, 1, 3, 1] => 1, 1, 2, 1, 3, 3, 1, 3, 1
[1, 1, 2, 1, 3, 3, 1, 3, 2] => 1, 1, 2, 1, 3, 3, 1, 3, 2
[1, 1, 2, 1, 3, 3, 1, 3, 3] => 1, 1, 2, 1, 3, 3, 1, 3, 3
[1, 1, 2, 1, 3, 3, 2, 1, 1] => 1, 1, 2, 1, 3, 3, 2, 1, 1
[1, 1, 2, 1, 3, 3, 2, 1, 2] => 1, 1, 2, 1, 3, 3, 2, 1, 2
[1, 1, 2, 1, 3, 3, 2, 1, 3] => 1, 1, 2, 1, 3, 3, 2, 1, 3
[1, 1, 2, 1, 3, 3, 2, 2, 1] => 1, 1, 2, 1, 3, 3, 2, 2, 1
[1, 1, 2, 1, 3, 3, 2, 2, 2] => 1, 1, 2, 1, 3, 3, 2, 2, 2
[1, 1, 2, 1, 3, 3, 2, 2, 3] => 1, 1, 2, 1, 3, 3, 2, 2, 3
[1, 1, 2, 1, 3, 3, 2, 3, 1] => 1, 1, 2, 1, 3, 3, 2, 3, 1
[1, 1, 2, 1, 3, 3, 2, 3, 2] => 1, 1, 2, 1, 3, 3, 2, 3, 2
[1, 1, 2, 1, 3, 3, 2, 3, 3] => 1, 1, 2, 1, 3, 3, 2, 3, 3
[1, 1, 2, 1, 3, 3, 3, 1, 1] => 1, 1, 2, 1, 3, 3, 3, 1, 1
[1, 1, 2, 1, 3, 3, 3, 1, 2] => 1, 1, 2, 1, 3, 3, 3, 1, 2
[1, 1, 2, 1, 3, 3, 3, 1, 3] => 1, 1, 2, 1, 3, 3, 3, 1, 3
[1, 1, 2, 1, 3, 3, 3, 2, 1] => 1, 1, 2, 1, 3, 3, 3, 2, 1
[1, 1, 2, 1, 3, 3, 3, 2, 2] => 1, 1, 2, 1, 3, 3, 3, 2, 2
[1, 1, 2, 1, 3, 3, 3, 2, 3] => 1, 1, 2, 1, 3, 3, 3, 2, 3
[1, 1, 2, 1, 3, 3, 3, 3, 1] => 1, 1, 2, 1, 3, 3, 3, 3, 1
[1, 1, 2, 1, 3, 3, 3, 3, 2] => 1, 1, 2, 1, 3, 3, 3, 3, 2
[1, 1, 2, 1, 3, 3, 3, 3, 3] => 1, 1, 2, 1, 3, 3, 3, 3, 3
[1, 1, 2, 2, 1, 1, 1, 1, 1] => 1, 1, 2, 2, 1, 1, 1, 1, 1
[1, 1, 2, 2, 1, 1, 1, 1, 2] => 1, 1, 2, 2, 1, 1, 1, 1, 2
[1, 1, 2, 2, 1, 1, 1, 1, 3] => 1, 1, 2, 2, 1, 1, 1, 1, 3
[1, 1, 2, 2, 1, 1, 1, 2, 1] => 1, 1, 2, 2, 1, 1, 1, 2, 1
[1, 1, 2, 2, 1, 1, 1, 2, 2] => 1, 1, 2, 2, 1, 1, 1, 2, 2
[1, 1, 2, 2, 1, 1, 1, 2, 3] => 1, 1, 2, 2, 1, 1, 1, 2, 3
[1, 1, 2, 2, 1, 1, 1, 3, 1] => 1, 1, 2, 2, 1, 1, 1, 3, 1
[1, 1, 2, 2, 1, 1, 1, 3, 2] => 1, 1, 2, 2, 1, 1, 1, 3, 2
[1, 1, 2, 2, 1, 1, 1, 3, 3] => 1, 1, 2, 2, 1, 1, 1, 3, 3
[1, 1, 2, 2, 1, 1, 2, 1, 1] => 1, 1, 2, 2, 1, 1, 2, 1, 1
[1, 1, 2, 2, 1, 1, 2, 1, 2] => 1, 1, 2, 2, 1, 1, 2, 1, 2
[1, 1, 2, 2, 1, 1, 2, 1, 3] => 1, 1, 2, 2, 1, 1, 2, 1, 3
[1, 1, 2, 2, 1, 1, 2, 2, 1] => 1, 1, 2, 2, 1, 1, 2, 2, 1
[1, 1, 2, 2, 1, 1, 2, 2, 2] => 1, 1, 2, 2, 1, 1, 2, 2, 2
[1, 1, 2, 2, 1, 1, 2, 2, 3] => 1, 1, 2, 2, 1, 1, 2, 2, 3
[1, 1, 2, 2, 1, 1, 2, 3, 1] => 1, 1, 2, 2, 1, 1, 2, 3, 1
[1, 1, 2, 2, 1, 1, 2, 3, 2] => 1, 1, 2, 2, 1, 1, 2, 3, 2
[1, 1, 2, 2, 1, 1, 2, 3, 3] => 1, 1, 2, 2, 1, 1, 2, 3, 3
[1, 1, 2, 2, 1, 1, 3, 1, 1] => 1, 1, 2, 2, 1, 1, 3, 1, 1
[1, 1, 2, 2, 1, 1, 3, 1, 2] => 1, 1, 2, 2, 1, 1, 3, 1, 2
[1, 1, 2, 2, 1, 1, 3, 1, 3] => 1, 1, 2, 2, 1, 1, 3, 1, 3
[1, 1, 2, 2, 1, 1, 3, 2, 1] => 1, 1, 2, 2, 1, 1, 3, 2, 1
[1, 1, 2, 2, 1, 1, 3, 2, 2] => 1, 1, 2, 2, 1, 1, 3, 2, 2
[1, 1, 2, 2, 1, 1, 3, 2, 3] => 1, 1, 2, 2, 1, 1, 3, 2, 3
[1, 1, 2, 2, 1, 1, 3, 3, 1] => 1, 1, 2, 2, 1, 1, 3, 3, 1
[1, 1, 2, 2, 1, 1, 3, 3, 2] => 1, 1, 2, 2, 1, 1, 3, 3, 2
[1, 1, 2, 2, 1, 1, 3, 3, 3] => 1, 1, 2, 2, 1, 1, 3, 3, 3
[1, 1, 2, 2, 1, 2, 1, 1, 1] => 1, 1, 2, 2, 1, 2, 1, 1, 1
[1, 1, 2, 2, 1, 2, 1, 1, 2] => 1, 1, 2, 2, 1, 2, 1, 1, 2
[1, 1, 2, 2, 1, 2, 1, 1, 3] => 1, 1, 2, 2, 1, 2, 1, 1, 3
[1, 1, 2, 2, 1, 2, 1, 2, 1] => 1, 1, 2, 2, 1, 2, 1, 2, 1
[1, 1, 2, 2, 1, 2, 1, 2, 2] => 1, 1, 2, 2, 1, 2, 1, 2, 2
[1, 1, 2, 2, 1, 2, 1, 2, 3] => 1, 1, 2, 2, 1, 2, 1, 2, 3
[1, 1, 2, 2, 1, 2, 1, 3, 1] => 1, 1, 2, 2, 1, 2, 1, 3, 1
[1, 1, 2, 2, 1, 2, 1, 3, 2] => 1, 1, 2, 2, 1, 2, 1, 3, 2
[1, 1, 2, 2, 1, 2, 1, 3, 3] => 1, 1, 2, 2, 1, 2, 1, 3, 3
[1, 1, 2, 2, 1, 2, 2, 1, 1] => 1, 1, 2, 2, 1, 2, 2, 1, 1
[1, 1, 2, 2, 1, 2, 2, 1, 2] => 1, 1, 2, 2, 1, 2, 2, 1, 2
[1, 1, 2, 2, 1, 2, 2, 1, 3] => 1, 1, 2, 2, 1, 2, 2, 1, 3
[1, 1, 2, 2, 1, 2, 2, 2, 1] => 1, 1, 2, 2, 1, 2, 2, 2, 1
[1, 1, 2, 2, 1, 2, 2, 2, 2] => 1, 1, 2, 2, 1, 2, 2, 2, 2
[1, 1, 2, 2, 1, 2, 2, 2, 3] => 1, 1, 2, 2, 1, 2, 2, 2, 3
[1, 1, 2, 2, 1, 2, 2, 3, 1] => 1, 1, 2, 2, 1, 2, 2, 3, 1
[1, 1, 2, 2, 1, 2, 2, 3, 2] => 1, 1, 2, 2, 1, 2, 2, 3, 2
[1, 1, 2, 2, 1, 2, 2, 3, 3] => 1, 1, 2, 2, 1, 2, 2, 3, 3
[1, 1, 2, 2, 1, 2, 3, 1, 1] => 1, 1, 2, 2, 1, 2, 3, 1, 1
[1, 1, 2, 2, 1, 2, 3, 1, 2] => 1, 1, 2, 2, 1, 2, 3, 1, 2
[1, 1, 2, 2, 1, 2, 3, 1, 3] => 1, 1, 2, 2, 1, 2, 3, 1, 3
[1, 1, 2, 2, 1, 2, 3, 2, 1] => 1, 1, 2, 2, 1, 2, 3, 2, 1
[1, 1, 2, 2, 1, 2, 3, 2, 2] => 1, 1, 2, 2, 1, 2, 3, 2, 2
[1, 1, 2, 2, 1, 2, 3, 2, 3] => 1, 1, 2, 2, 1, 2, 3, 2, 3
[1, 1, 2, 2, 1, 2, 3, 3, 1] => 1, 1, 2, 2, 1, 2, 3, 3, 1
[1, 1, 2, 2, 1, 2, 3, 3, 2] => 1, 1, 2, 2, 1, 2, 3, 3, 2
[1, 1, 2, 2, 1, 2, 3, 3, 3] => 1, 1, 2, 2, 1, 2, 3, 3, 3
[1, 1, 2, 2, 1, 3, 1, 1, 1] => 1, 1, 2, 2, 1, 3, 1, 1, 1
[1, 1, 2, 2, 1, 3, 1, 1, 2] => 1, 1, 2, 2, 1, 3, 1, 1, 2
[1, 1, 2, 2, 1, 3, 1, 1, 3] => 1, 1, 2, 2, 1, 3, 1, 1, 3
[1, 1, 2, 2, 1, 3, 1, 2, 1] => 1, 1, 2, 2, 1, 3, 1, 2, 1
[1, 1, 2, 2, 1, 3, 1, 2, 2] => 1, 1, 2, 2, 1, 3, 1, 2, 2
[1, 1, 2, 2, 1, 3, 1, 2, 3] => 1, 1, 2, 2, 1, 3, 1, 2, 3
[1, 1, 2, 2, 1, 3, 1, 3, 1] => 1, 1, 2, 2, 1, 3, 1, 3, 1
[1, 1, 2, 2, 1, 3, 1, 3, 2] => 1, 1, 2, 2, 1, 3, 1, 3, 2
[1, 1, 2, 2, 1, 3, 1, 3, 3] => 1, 1, 2, 2, 1, 3, 1, 3, 3
[1, 1, 2, 2, 1, 3, 2, 1, 1] => 1, 1, 2, 2, 1, 3, 2, 1, 1
[1, 1, 2, 2, 1, 3, 2, 1, 2] => 1, 1, 2, 2, 1, 3, 2, 1, 2
[1, 1, 2, 2, 1, 3, 2, 1, 3] => 1, 1, 2, 2, 1, 3, 2, 1, 3
[1, 1, 2, 2, 1, 3, 2, 2, 1] => 1, 1, 2, 2, 1, 3, 2, 2, 1
[1, 1, 2, 2, 1, 3, 2, 2, 2] => 1, 1, 2, 2, 1, 3, 2, 2, 2
[1, 1, 2, 2, 1, 3, 2, 2, 3] => 1, 1, 2, 2, 1, 3, 2, 2, 3
[1, 1, 2, 2, 1, 3, 2, 3, 1] => 1, 1, 2, 2, 1, 3, 2, 3, 1
[1, 1, 2, 2, 1, 3, 2, 3, 2] => 1, 1, 2, 2, 1, 3, 2, 3, 2
[1, 1, 2, 2, 1, 3, 2, 3, 3] => 1, 1, 2, 2, 1, 3, 2, 3, 3
[1, 1, 2, 2, 1, 3, 3, 1, 1] => 1, 1, 2, 2, 1, 3, 3, 1, 1
[1, 1, 2, 2, 1, 3, 3, 1, 2] => 1, 1, 2, 2, 1, 3, 3, 1, 2
[1, 1, 2, 2, 1, 3, 3, 1, 3] => 1, 1, 2, 2, 1, 3, 3, 1, 3
[1, 1, 2, 2, 1, 3, 3, 2, 1] => 1, 1, 2, 2, 1, 3, 3, 2, 1
[1, 1, 2, 2, 1, 3, 3, 2, 2] => 1, 1, 2, 2, 1, 3, 3, 2, 2
[1, 1, 2, 2, 1, 3, 3, 2, 3] => 1, 1, 2, 2, 1, 3, 3, 2, 3
[1, 1, 2, 2, 1, 3, 3, 3, 1] => 1, 1, 2, 2, 1, 3, 3, 3, 1
[1, 1, 2, 2, 1, 3, 3, 3, 2] => 1, 1, 2, 2, 1, 3, 3, 3, 2
[1, 1, 2, 2, 1, 3, 3, 3, 3] => 1, 1, 2, 2, 1, 3, 3, 3, 3
[1, 1, 2, 2, 2, 1, 1, 1, 1] => 1, 1, 2, 2, 2, 1, 1, 1, 1
[1, 1, 2, 2, 2, 1, 1, 1, 2] => 1, 1, 2, 2, 2, 1, 1, 1, 2
[1, 1, 2, 2, 2, 1, 1, 1, 3] => 1, 1, 2, 2, 2, 1, 1, 1, 3
[1, 1, 2, 2, 2, 1, 1, 2, 1] => 1, 1, 2, 2, 2, 1, 1, 2, 1
[1, 1, 2, 2, 2, 1, 1, 2, 2] => 1, 1, 2, 2, 2, 1, 1, 2, 2
[1, 1, 2, 2, 2, 1, 1, 2, 3] => 1, 1, 2, 2, 2, 1, 1, 2, 3
[1, 1, 2, 2, 2, 1, 1, 3, 1] => 1, 1, 2, 2, 2, 1, 1, 3, 1
[1, 1, 2, 2, 2, 1, 1, 3, 2] => 1, 1, 2, 2, 2, 1, 1, 3, 2
[1, 1, 2, 2, 2, 1, 1, 3, 3] => 1, 1, 2, 2, 2, 1, 1, 3, 3
[1, 1, 2, 2, 2, 1, 2, 1, 1] => 1, 1, 2, 2, 2, 1, 2, 1, 1
[1, 1, 2, 2, 2, 1, 2, 1, 2] => 1, 1, 2, 2, 2, 1, 2, 1, 2
[1, 1, 2, 2, 2, 1, 2, 1, 3] => 1, 1, 2, 2, 2, 1, 2, 1, 3
[1, 1, 2, 2, 2, 1, 2, 2, 1] => 1, 1, 2, 2, 2, 1, 2, 2, 1
[1, 1, 2, 2, 2, 1, 2, 2, 2] => 1, 1, 2, 2, 2, 1, 2, 2, 2
[1, 1, 2, 2, 2, 1, 2, 2, 3] => 1, 1, 2, 2, 2, 1, 2, 2, 3
[1, 1, 2, 2, 2, 1, 2, 3, 1] => 1, 1, 2, 2, 2, 1, 2, 3, 1
[1, 1, 2, 2, 2, 1, 2, 3, 2] => 1, 1, 2, 2, 2, 1, 2, 3, 2
[1, 1, 2, 2, 2, 1, 2, 3, 3] => 1, 1, 2, 2, 2, 1, 2, 3, 3
[1, 1, 2, 2, 2, 1, 3, 1, 1] => 1, 1, 2, 2, 2, 1, 3, 1, 1
[1, 1, 2, 2, 2, 1, 3, 1, 2] => 1, 1, 2, 2, 2, 1, 3, 1, 2
[1, 1, 2, 2, 2, 1, 3, 1, 3] => 1, 1, 2, 2, 2, 1, 3, 1, 3
[1, 1, 2, 2, 2, 1, 3, 2, 1] => 1, 1, 2, 2, 2, 1, 3, 2, 1
[1, 1, 2, 2, 2, 1, 3, 2, 2] => 1, 1, 2, 2, 2, 1, 3, 2, 2
[1, 1, 2, 2, 2, 1, 3, 2, 3] => 1, 1, 2, 2, 2, 1, 3, 2, 3
[1, 1, 2, 2, 2, 1, 3, 3, 1] => 1, 1, 2, 2, 2, 1, 3, 3, 1
[1, 1, 2, 2, 2, 1, 3, 3, 2] => 1, 1, 2, 2, 2, 1, 3, 3, 2
[1, 1, 2, 2, 2, 1, 3, 3, 3] => 1, 1, 2, 2, 2, 1, 3, 3, 3
[1, 1, 2, 2, 2, 2, 1, 1, 1] => 1, 1, 2, 2, 2, 2, 1, 1, 1
[1, 1, 2, 2, 2, 2, 1, 1, 2] => 1, 1, 2, 2, 2, 2, 1, 1, 2
[1, 1, 2, 2, 2, 2, 1, 1, 3] => 1, 1, 2, 2, 2, 2, 1, 1, 3
[1, 1, 2, 2, 2, 2, 1, 2, 1] => 1, 1, 2, 2, 2, 2, 1, 2, 1
[1, 1, 2, 2, 2, 2, 1, 2, 2] => 1, 1, 2, 2, 2, 2, 1, 2, 2
[1, 1, 2, 2, 2, 2, 1, 2, 3] => 1, 1, 2, 2, 2, 2, 1, 2, 3
[1, 1, 2, 2, 2, 2, 1, 3, 1] => 1, 1, 2, 2, 2, 2, 1, 3, 1
[1, 1, 2, 2, 2, 2, 1, 3, 2] => 1, 1, 2, 2, 2, 2, 1, 3, 2
[1, 1, 2, 2, 2, 2, 1, 3, 3] => 1, 1, 2, 2, 2, 2, 1, 3, 3
[1, 1, 2, 2, 2, 2, 2, 1, 1] => 1, 1, 2, 2, 2, 2, 2, 1, 1
[1, 1, 2, 2, 2, 2, 2, 1, 2] => 1, 1, 2, 2, 2, 2, 2, 1, 2
[1, 1, 2, 2, 2, 2, 2, 1, 3] => 1, 1, 2, 2, 2, 2, 2, 1, 3
[1, 1, 2, 2, 2, 2, 2, 2, 1] => 1, 1, 2, 2, 2, 2, 2, 2, 1
[1, 1, 2, 2, 2, 2, 2, 2, 2] => 1, 1, 2, 2, 2, 2, 2, 2, 2
[1, 1, 2, 2, 2, 2, 2, 2, 3] => 1, 1, 2, 2, 2, 2, 2, 2, 3
[1, 1, 2, 2, 2, 2, 2, 3, 1] => 1, 1, 2, 2, 2, 2, 2, 3, 1
[1, 1, 2, 2, 2, 2, 2, 3, 2] => 1, 1, 2, 2, 2, 2, 2, 3, 2
[1, 1, 2, 2, 2, 2, 2, 3, 3] => 1, 1, 2, 2, 2, 2, 2, 3, 3
[1, 1, 2, 2, 2, 2, 3, 1, 1] => 1, 1, 2, 2, 2, 2, 3, 1, 1
[1, 1, 2, 2, 2, 2, 3, 1, 2] => 1, 1, 2, 2, 2, 2, 3, 1, 2
[1, 1, 2, 2, 2, 2, 3, 1, 3] => 1, 1, 2, 2, 2, 2, 3, 1, 3
[1, 1, 2, 2, 2, 2, 3, 2, 1] => 1, 1, 2, 2, 2, 2, 3, 2, 1
[1, 1, 2, 2, 2, 2, 3, 2, 2] => 1, 1, 2, 2, 2, 2, 3, 2, 2
[1, 1, 2, 2, 2, 2, 3, 2, 3] => 1, 1, 2, 2, 2, 2, 3, 2, 3
[1, 1, 2, 2, 2, 2, 3, 3, 1] => 1, 1, 2, 2, 2, 2, 3, 3, 1
[1, 1, 2, 2, 2, 2, 3, 3, 2] => 1, 1, 2, 2, 2, 2, 3, 3, 2
[1, 1, 2, 2, 2, 2, 3, 3, 3] => 1, 1, 2, 2, 2, 2, 3, 3, 3
[1, 1, 2, 2, 2, 3, 1, 1, 1] => 1, 1, 2, 2, 2, 3, 1, 1, 1
[1, 1, 2, 2, 2, 3, 1, 1, 2] => 1, 1, 2, 2, 2, 3, 1, 1, 2
[1, 1, 2, 2, 2, 3, 1, 1, 3] => 1, 1, 2, 2, 2, 3, 1, 1, 3
[1, 1, 2, 2, 2, 3, 1, 2, 1] => 1, 1, 2, 2, 2, 3, 1, 2, 1
[1, 1, 2, 2, 2, 3, 1, 2, 2] => 1, 1, 2, 2, 2, 3, 1, 2, 2
[1, 1, 2, 2, 2, 3, 1, 2, 3] => 1, 1, 2, 2, 2, 3, 1, 2, 3
[1, 1, 2, 2, 2, 3, 1, 3, 1] => 1, 1, 2, 2, 2, 3, 1, 3, 1
[1, 1, 2, 2, 2, 3, 1, 3, 2] => 1, 1, 2, 2, 2, 3, 1, 3, 2
[1, 1, 2, 2, 2, 3, 1, 3, 3] => 1, 1, 2, 2, 2, 3, 1, 3, 3
[1, 1, 2, 2, 2, 3, 2, 1, 1] => 1, 1, 2, 2, 2, 3, 2, 1, 1
[1, 1, 2, 2, 2, 3, 2, 1, 2] => 1, 1, 2, 2, 2, 3, 2, 1, 2
[1, 1, 2, 2, 2, 3, 2, 1, 3] => 1, 1, 2, 2, 2, 3, 2, 1, 3
[1, 1, 2, 2, 2, 3, 2, 2, 1] => 1, 1, 2, 2, 2, 3, 2, 2, 1
[1, 1, 2, 2, 2, 3, 2, 2, 2] => 1, 1, 2, 2, 2, 3, 2, 2, 2
[1, 1, 2, 2, 2, 3, 2, 2, 3] => 1, 1, 2, 2, 2, 3, 2, 2, 3
[1, 1, 2, 2, 2, 3, 2, 3, 1] => 1, 1, 2, 2, 2, 3, 2, 3, 1
[1, 1, 2, 2, 2, 3, 2, 3, 2] => 1, 1, 2, 2, 2, 3, 2, 3, 2
[1, 1, 2, 2, 2, 3, 2, 3, 3] => 1, 1, 2, 2, 2, 3, 2, 3, 3
[1, 1, 2, 2, 2, 3, 3, 1, 1] => 1, 1, 2, 2, 2, 3, 3, 1, 1
[1, 1, 2, 2, 2, 3, 3, 1, 2] => 1, 1, 2, 2, 2, 3, 3, 1, 2
[1, 1, 2, 2, 2, 3, 3, 1, 3] => 1, 1, 2, 2, 2, 3, 3, 1, 3
[1, 1, 2, 2, 2, 3, 3, 2, 1] => 1, 1, 2, 2, 2, 3, 3, 2, 1
[1, 1, 2, 2, 2, 3, 3, 2, 2] => 1, 1, 2, 2, 2, 3, 3, 2, 2
[1, 1, 2, 2, 2, 3, 3, 2, 3] => 1, 1, 2, 2, 2, 3, 3, 2, 3
[1, 1, 2, 2, 2, 3, 3, 3, 1] => 1, 1, 2, 2, 2, 3, 3, 3, 1
[1, 1, 2, 2, 2, 3, 3, 3, 2] => 1, 1, 2, 2, 2, 3, 3, 3, 2
[1, 1, 2, 2, 2, 3, 3, 3, 3] => 1, 1, 2, 2, 2, 3, 3, 3, 3
[1, 1, 2, 2, 3, 1, 1, 1, 1] => 1, 1, 2, 2, 3, 1, 1, 1, 1
[1, 1, 2, 2, 3, 1, 1, 1, 2] => 1, 1, 2, 2, 3, 1, 1, 1, 2
[1, 1, 2, 2, 3, 1, 1, 1, 3] => 1, 1, 2, 2, 3, 1, 1, 1, 3
[1, 1, 2, 2, 3, 1, 1, 2, 1] => 1, 1, 2, 2, 3, 1, 1, 2, 1
[1, 1, 2, 2, 3, 1, 1, 2, 2] => 1, 1, 2, 2, 3, 1, 1, 2, 2
[1, 1, 2, 2, 3, 1, 1, 2, 3] => 1, 1, 2, 2, 3, 1, 1, 2, 3
[1, 1, 2, 2, 3, 1, 1, 3, 1] => 1, 1, 2, 2, 3, 1, 1, 3, 1
[1, 1, 2, 2, 3, 1, 1, 3, 2] => 1, 1, 2, 2, 3, 1, 1, 3, 2
[1, 1, 2, 2, 3, 1, 1, 3, 3] => 1, 1, 2, 2, 3, 1, 1, 3, 3
[1, 1, 2, 2, 3, 1, 2, 1, 1] => 1, 1, 2, 2, 3, 1, 2, 1, 1
[1, 1, 2, 2, 3, 1, 2, 1, 2] => 1, 1, 2, 2, 3, 1, 2, 1, 2
[1, 1, 2, 2, 3, 1, 2, 1, 3] => 1, 1, 2, 2, 3, 1, 2, 1, 3
[1, 1, 2, 2, 3, 1, 2, 2, 1] => 1, 1, 2, 2, 3, 1, 2, 2, 1
[1, 1, 2, 2, 3, 1, 2, 2, 2] => 1, 1, 2, 2, 3, 1, 2, 2, 2
[1, 1, 2, 2, 3, 1, 2, 2, 3] => 1, 1, 2, 2, 3, 1, 2, 2, 3
[1, 1, 2, 2, 3, 1, 2, 3, 1] => 1, 1, 2, 2, 3, 1, 2, 3, 1
[1, 1, 2, 2, 3, 1, 2, 3, 2] => 1, 1, 2, 2, 3, 1, 2, 3, 2
[1, 1, 2, 2, 3, 1, 2, 3, 3] => 1, 1, 2, 2, 3, 1, 2, 3, 3
[1, 1, 2, 2, 3, 1, 3, 1, 1] => 1, 1, 2, 2, 3, 1, 3, 1, 1
[1, 1, 2, 2, 3, 1, 3, 1, 2] => 1, 1, 2, 2, 3, 1, 3, 1, 2
[1, 1, 2, 2, 3, 1, 3, 1, 3] => 1, 1, 2, 2, 3, 1, 3, 1, 3
[1, 1, 2, 2, 3, 1, 3, 2, 1] => 1, 1, 2, 2, 3, 1, 3, 2, 1
[1, 1, 2, 2, 3, 1, 3, 2, 2] => 1, 1, 2, 2, 3, 1, 3, 2, 2
[1, 1, 2, 2, 3, 1, 3, 2, 3] => 1, 1, 2, 2, 3, 1, 3, 2, 3
[1, 1, 2, 2, 3, 1, 3, 3, 1] => 1, 1, 2, 2, 3, 1, 3, 3, 1
[1, 1, 2, 2, 3, 1, 3, 3, 2] => 1, 1, 2, 2, 3, 1, 3, 3, 2
[1, 1, 2, 2, 3, 1, 3, 3, 3] => 1, 1, 2, 2, 3, 1, 3, 3, 3
[1, 1, 2, 2, 3, 2, 1, 1, 1] => 1, 1, 2, 2, 3, 2, 1, 1, 1
[1, 1, 2, 2, 3, 2, 1, 1, 2] => 1, 1, 2, 2, 3, 2, 1, 1, 2
[1, 1, 2, 2, 3, 2, 1, 1, 3] => 1, 1, 2, 2, 3, 2, 1, 1, 3
[1, 1, 2, 2, 3, 2, 1, 2, 1] => 1, 1, 2, 2, 3, 2, 1, 2, 1
[1, 1, 2, 2, 3, 2, 1, 2, 2] => 1, 1, 2, 2, 3, 2, 1, 2, 2
[1, 1, 2, 2, 3, 2, 1, 2, 3] => 1, 1, 2, 2, 3, 2, 1, 2, 3
[1, 1, 2, 2, 3, 2, 1, 3, 1] => 1, 1, 2, 2, 3, 2, 1, 3, 1
[1, 1, 2, 2, 3, 2, 1, 3, 2] => 1, 1, 2, 2, 3, 2, 1, 3, 2
[1, 1, 2, 2, 3, 2, 1, 3, 3] => 1, 1, 2, 2, 3, 2, 1, 3, 3
[1, 1, 2, 2, 3, 2, 2, 1, 1] => 1, 1, 2, 2, 3, 2, 2, 1, 1
[1, 1, 2, 2, 3, 2, 2, 1, 2] => 1, 1, 2, 2, 3, 2, 2, 1, 2
[1, 1, 2, 2, 3, 2, 2, 1, 3] => 1, 1, 2, 2, 3, 2, 2, 1, 3
[1, 1, 2, 2, 3, 2, 2, 2, 1] => 1, 1, 2, 2, 3, 2, 2, 2, 1
[1, 1, 2, 2, 3, 2, 2, 2, 2] => 1, 1, 2, 2, 3, 2, 2, 2, 2
[1, 1, 2, 2, 3, 2, 2, 2, 3] => 1, 1, 2, 2, 3, 2, 2, 2, 3
[1, 1, 2, 2, 3, 2, 2, 3, 1] => 1, 1, 2, 2, 3, 2, 2, 3, 1
[1, 1, 2, 2, 3, 2, 2, 3, 2] => 1, 1, 2, 2, 3, 2, 2, 3, 2
[1, 1, 2, 2, 3, 2, 2, 3, 3] => 1, 1, 2, 2, 3, 2, 2, 3, 3
[1, 1, 2, 2, 3, 2, 3, 1, 1] => 1, 1, 2, 2, 3, 2, 3, 1, 1
[1, 1, 2, 2, 3, 2, 3, 1, 2] => 1, 1, 2, 2, 3, 2, 3, 1, 2
[1, 1, 2, 2, 3, 2, 3, 1, 3] => 1, 1, 2, 2, 3, 2, 3, 1, 3
[1, 1, 2, 2, 3, 2, 3, 2, 1] => 1, 1, 2, 2, 3, 2, 3, 2, 1
[1, 1, 2, 2, 3, 2, 3, 2, 2] => 1, 1, 2, 2, 3, 2, 3, 2, 2
[1, 1, 2, 2, 3, 2, 3, 2, 3] => 1, 1, 2, 2, 3, 2, 3, 2, 3
[1, 1, 2, 2, 3, 2, 3, 3, 1] => 1, 1, 2, 2, 3, 2, 3, 3, 1
[1, 1, 2, 2, 3, 2, 3, 3, 2] => 1, 1, 2, 2, 3, 2, 3, 3, 2
[1, 1, 2, 2, 3, 2, 3, 3, 3] => 1, 1, 2, 2, 3, 2, 3, 3, 3
[1, 1, 2, 2, 3, 3, 1, 1, 1] => 1, 1, 2, 2, 3, 3, 1, 1, 1
[1, 1, 2, 2, 3, 3, 1, 1, 2] => 1, 1, 2, 2, 3, 3, 1, 1, 2
[1, 1, 2, 2, 3, 3, 1, 1, 3] => 1, 1, 2, 2, 3, 3, 1, 1, 3
[1, 1, 2, 2, 3, 3, 1, 2, 1] => 1, 1, 2, 2, 3, 3, 1, 2, 1
[1, 1, 2, 2, 3, 3, 1, 2, 2] => 1, 1, 2, 2, 3, 3, 1, 2, 2
[1, 1, 2, 2, 3, 3, 1, 2, 3] => 1, 1, 2, 2, 3, 3, 1, 2, 3
[1, 1, 2, 2, 3, 3, 1, 3, 1] => 1, 1, 2, 2, 3, 3, 1, 3, 1
[1, 1, 2, 2, 3, 3, 1, 3, 2] => 1, 1, 2, 2, 3, 3, 1, 3, 2
[1, 1, 2, 2, 3, 3, 1, 3, 3] => 1, 1, 2, 2, 3, 3, 1, 3, 3
[1, 1, 2, 2, 3, 3, 2, 1, 1] => 1, 1, 2, 2, 3, 3, 2, 1, 1
[1, 1, 2, 2, 3, 3, 2, 1, 2] => 1, 1, 2, 2, 3, 3, 2, 1, 2
[1, 1, 2, 2, 3, 3, 2, 1, 3] => 1, 1, 2, 2, 3, 3, 2, 1, 3
[1, 1, 2, 2, 3, 3, 2, 2, 1] => 1, 1, 2, 2, 3, 3, 2, 2, 1
[1, 1, 2, 2, 3, 3, 2, 2, 2] => 1, 1, 2, 2, 3, 3, 2, 2, 2
[1, 1, 2, 2, 3, 3, 2, 2, 3] => 1, 1, 2, 2, 3, 3, 2, 2, 3
[1, 1, 2, 2, 3, 3, 2, 3, 1] => 1, 1, 2, 2, 3, 3, 2, 3, 1
[1, 1, 2, 2, 3, 3, 2, 3, 2] => 1, 1, 2, 2, 3, 3, 2, 3, 2
[1, 1, 2, 2, 3, 3, 2, 3, 3] => 1, 1, 2, 2, 3, 3, 2, 3, 3
[1, 1, 2, 2, 3, 3, 3, 1, 1] => 1, 1, 2, 2, 3, 3, 3, 1, 1
[1, 1, 2, 2, 3, 3, 3, 1, 2] => 1, 1, 2, 2, 3, 3, 3, 1, 2
[1, 1, 2, 2, 3, 3, 3, 1, 3] => 1, 1, 2, 2, 3, 3, 3, 1, 3
[1, 1, 2, 2, 3, 3, 3, 2, 1] => 1, 1, 2, 2, 3, 3, 3, 2, 1
[1, 1, 2, 2, 3, 3, 3, 2, 2] => 1, 1, 2, 2, 3, 3, 3, 2, 2
[1, 1, 2, 2, 3, 3, 3, 2, 3] => 1, 1, 2, 2, 3, 3, 3, 2, 3
[1, 1, 2, 2, 3, 3, 3, 3, 1] => 1, 1, 2, 2, 3, 3, 3, 3, 1
[1, 1, 2, 2, 3, 3, 3, 3, 2] => 1, 1, 2, 2, 3, 3, 3, 3, 2
[1, 1, 2, 2, 3, 3, 3, 3, 3] => 1, 1, 2, 2, 3, 3, 3, 3, 3
[1, 1, 2, 3, 1, 1, 1, 1, 1] => 1, 1, 2, 3, 1, 1, 1, 1, 1
[1, 1, 2, 3, 1, 1, 1, 1, 2] => 1, 1, 2, 3, 1, 1, 1, 1, 2
[1, 1, 2, 3, 1, 1, 1, 1, 3] => 1, 1, 2, 3, 1, 1, 1, 1, 3
[1, 1, 2, 3, 1, 1, 1, 2, 1] => 1, 1, 2, 3, 1, 1, 1, 2, 1
[1, 1, 2, 3, 1, 1, 1, 2, 2] => 1, 1, 2, 3, 1, 1, 1, 2, 2
[1, 1, 2, 3, 1, 1, 1, 2, 3] => 1, 1, 2, 3, 1, 1, 1, 2, 3
[1, 1, 2, 3, 1, 1, 1, 3, 1] => 1, 1, 2, 3, 1, 1, 1, 3, 1
[1, 1, 2, 3, 1, 1, 1, 3, 2] => 1, 1, 2, 3, 1, 1, 1, 3, 2
[1, 1, 2, 3, 1, 1, 1, 3, 3] => 1, 1, 2, 3, 1, 1, 1, 3, 3
[1, 1, 2, 3, 1, 1, 2, 1, 1] => 1, 1, 2, 3, 1, 1, 2, 1, 1
[1, 1, 2, 3, 1, 1, 2, 1, 2] => 1, 1, 2, 3, 1, 1, 2, 1, 2
[1, 1, 2, 3, 1, 1, 2, 1, 3] => 1, 1, 2, 3, 1, 1, 2, 1, 3
[1, 1, 2, 3, 1, 1, 2, 2, 1] => 1, 1, 2, 3, 1, 1, 2, 2, 1
[1, 1, 2, 3, 1, 1, 2, 2, 2] => 1, 1, 2, 3, 1, 1, 2, 2, 2
[1, 1, 2, 3, 1, 1, 2, 2, 3] => 1, 1, 2, 3, 1, 1, 2, 2, 3
[1, 1, 2, 3, 1, 1, 2, 3, 1] => 1, 1, 2, 3, 1, 1, 2, 3, 1
[1, 1, 2, 3, 1, 1, 2, 3, 2] => 1, 1, 2, 3, 1, 1, 2, 3, 2
[1, 1, 2, 3, 1, 1, 2, 3, 3] => 1, 1, 2, 3, 1, 1, 2, 3, 3
[1, 1, 2, 3, 1, 1, 3, 1, 1] => 1, 1, 2, 3, 1, 1, 3, 1, 1
[1, 1, 2, 3, 1, 1, 3, 1, 2] => 1, 1, 2, 3, 1, 1, 3, 1, 2
[1, 1, 2, 3, 1, 1, 3, 1, 3] => 1, 1, 2, 3, 1, 1, 3, 1, 3
[1, 1, 2, 3, 1, 1, 3, 2, 1] => 1, 1, 2, 3, 1, 1, 3, 2, 1
[1, 1, 2, 3, 1, 1, 3, 2, 2] => 1, 1, 2, 3, 1, 1, 3, 2, 2
[1, 1, 2, 3, 1, 1, 3, 2, 3] => 1, 1, 2, 3, 1, 1, 3, 2, 3
[1, 1, 2, 3, 1, 1, 3, 3, 1] => 1, 1, 2, 3, 1, 1, 3, 3, 1
[1, 1, 2, 3, 1, 1, 3, 3, 2] => 1, 1, 2, 3, 1, 1, 3, 3, 2
[1, 1, 2, 3, 1, 1, 3, 3, 3] => 1, 1, 2, 3, 1, 1, 3, 3, 3
[1, 1, 2, 3, 1, 2, 1, 1, 1] => 1, 1, 2, 3, 1, 2, 1, 1, 1
[1, 1, 2, 3, 1, 2, 1, 1, 2] => 1, 1, 2, 3, 1, 2, 1, 1, 2
[1, 1, 2, 3, 1, 2, 1, 1, 3] => 1, 1, 2, 3, 1, 2, 1, 1, 3
[1, 1, 2, 3, 1, 2, 1, 2, 1] => 1, 1, 2, 3, 1, 2, 1, 2, 1
[1, 1, 2, 3, 1, 2, 1, 2, 2] => 1, 1, 2, 3, 1, 2, 1, 2, 2
[1, 1, 2, 3, 1, 2, 1, 2, 3] => 1, 1, 2, 3, 1, 2, 1, 2, 3
[1, 1, 2, 3, 1, 2, 1, 3, 1] => 1, 1, 2, 3, 1, 2, 1, 3, 1
[1, 1, 2, 3, 1, 2, 1, 3, 2] => 1, 1, 2, 3, 1, 2, 1, 3, 2
[1, 1, 2, 3, 1, 2, 1, 3, 3] => 1, 1, 2, 3, 1, 2, 1, 3, 3
[1, 1, 2, 3, 1, 2, 2, 1, 1] => 1, 1, 2, 3, 1, 2, 2, 1, 1
[1, 1, 2, 3, 1, 2, 2, 1, 2] => 1, 1, 2, 3, 1, 2, 2, 1, 2
[1, 1, 2, 3, 1, 2, 2, 1, 3] => 1, 1, 2, 3, 1, 2, 2, 1, 3
[1, 1, 2, 3, 1, 2, 2, 2, 1] => 1, 1, 2, 3, 1, 2, 2, 2, 1
[1, 1, 2, 3, 1, 2, 2, 2, 2] => 1, 1, 2, 3, 1, 2, 2, 2, 2
[1, 1, 2, 3, 1, 2, 2, 2, 3] => 1, 1, 2, 3, 1, 2, 2, 2, 3
[1, 1, 2, 3, 1, 2, 2, 3, 1] => 1, 1, 2, 3, 1, 2, 2, 3, 1
[1, 1, 2, 3, 1, 2, 2, 3, 2] => 1, 1, 2, 3, 1, 2, 2, 3, 2
[1, 1, 2, 3, 1, 2, 2, 3, 3] => 1, 1, 2, 3, 1, 2, 2, 3, 3
[1, 1, 2, 3, 1, 2, 3, 1, 1] => 1, 1, 2, 3, 1, 2, 3, 1, 1
[1, 1, 2, 3, 1, 2, 3, 1, 2] => 1, 1, 2, 3, 1, 2, 3, 1, 2
[1, 1, 2, 3, 1, 2, 3, 1, 3] => 1, 1, 2, 3, 1, 2, 3, 1, 3
[1, 1, 2, 3, 1, 2, 3, 2, 1] => 1, 1, 2, 3, 1, 2, 3, 2, 1
[1, 1, 2, 3, 1, 2, 3, 2, 2] => 1, 1, 2, 3, 1, 2, 3, 2, 2
[1, 1, 2, 3, 1, 2, 3, 2, 3] => 1, 1, 2, 3, 1, 2, 3, 2, 3
[1, 1, 2, 3, 1, 2, 3, 3, 1] => 1, 1, 2, 3, 1, 2, 3, 3, 1
[1, 1, 2, 3, 1, 2, 3, 3, 2] => 1, 1, 2, 3, 1, 2, 3, 3, 2
[1, 1, 2, 3, 1, 2, 3, 3, 3] => 1, 1, 2, 3, 1, 2, 3, 3, 3
[1, 1, 2, 3, 1, 3, 1, 1, 1] => 1, 1, 2, 3, 1, 3, 1, 1, 1
[1, 1, 2, 3, 1, 3, 1, 1, 2] => 1, 1, 2, 3, 1, 3, 1, 1, 2
[1, 1, 2, 3, 1, 3, 1, 1, 3] => 1, 1, 2, 3, 1, 3, 1, 1, 3
[1, 1, 2, 3, 1, 3, 1, 2, 1] => 1, 1, 2, 3, 1, 3, 1, 2, 1
[1, 1, 2, 3, 1, 3, 1, 2, 2] => 1, 1, 2, 3, 1, 3, 1, 2, 2
[1, 1, 2, 3, 1, 3, 1, 2, 3] => 1, 1, 2, 3, 1, 3, 1, 2, 3
[1, 1, 2, 3, 1, 3, 1, 3, 1] => 1, 1, 2, 3, 1, 3, 1, 3, 1
[1, 1, 2, 3, 1, 3, 1, 3, 2] => 1, 1, 2, 3, 1, 3, 1, 3, 2
[1, 1, 2, 3, 1, 3, 1, 3, 3] => 1, 1, 2, 3, 1, 3, 1, 3, 3
[1, 1, 2, 3, 1, 3, 2, 1, 1] => 1, 1, 2, 3, 1, 3, 2, 1, 1
[1, 1, 2, 3, 1, 3, 2, 1, 2] => 1, 1, 2, 3, 1, 3, 2, 1, 2
[1, 1, 2, 3, 1, 3, 2, 1, 3] => 1, 1, 2, 3, 1, 3, 2, 1, 3
[1, 1, 2, 3, 1, 3, 2, 2, 1] => 1, 1, 2, 3, 1, 3, 2, 2, 1
[1, 1, 2, 3, 1, 3, 2, 2, 2] => 1, 1, 2, 3, 1, 3, 2, 2, 2
[1, 1, 2, 3, 1, 3, 2, 2, 3] => 1, 1, 2, 3, 1, 3, 2, 2, 3
[1, 1, 2, 3, 1, 3, 2, 3, 1] => 1, 1, 2, 3, 1, 3, 2, 3, 1
[1, 1, 2, 3, 1, 3, 2, 3, 2] => 1, 1, 2, 3, 1, 3, 2, 3, 2
[1, 1, 2, 3, 1, 3, 2, 3, 3] => 1, 1, 2, 3, 1, 3, 2, 3, 3
[1, 1, 2, 3, 1, 3, 3, 1, 1] => 1, 1, 2, 3, 1, 3, 3, 1, 1
[1, 1, 2, 3, 1, 3, 3, 1, 2] => 1, 1, 2, 3, 1, 3, 3, 1, 2
[1, 1, 2, 3, 1, 3, 3, 1, 3] => 1, 1, 2, 3, 1, 3, 3, 1, 3
[1, 1, 2, 3, 1, 3, 3, 2, 1] => 1, 1, 2, 3, 1, 3, 3, 2, 1
[1, 1, 2, 3, 1, 3, 3, 2, 2] => 1, 1, 2, 3, 1, 3, 3, 2, 2
[1, 1, 2, 3, 1, 3, 3, 2, 3] => 1, 1, 2, 3, 1, 3, 3, 2, 3
[1, 1, 2, 3, 1, 3, 3, 3, 1] => 1, 1, 2, 3, 1, 3, 3, 3, 1
[1, 1, 2, 3, 1, 3, 3, 3, 2] => 1, 1, 2, 3, 1, 3, 3, 3, 2
[1, 1, 2, 3, 1, 3, 3, 3, 3] => 1, 1, 2, 3, 1, 3, 3, 3, 3
[1, 1, 2, 3, 2, 1, 1, 1, 1] => 1, 1, 2, 3, 2, 1, 1, 1, 1
[1, 1, 2, 3, 2, 1, 1, 1, 2] => 1, 1, 2, 3, 2, 1, 1, 1, 2
[1, 1, 2, 3, 2, 1, 1, 1, 3] => 1, 1, 2, 3, 2, 1, 1, 1, 3
[1, 1, 2, 3, 2, 1, 1, 2, 1] => 1, 1, 2, 3, 2, 1, 1, 2, 1
[1, 1, 2, 3, 2, 1, 1, 2, 2] => 1, 1, 2, 3, 2, 1, 1, 2, 2
[1, 1, 2, 3, 2, 1, 1, 2, 3] => 1, 1, 2, 3, 2, 1, 1, 2, 3
[1, 1, 2, 3, 2, 1, 1, 3, 1] => 1, 1, 2, 3, 2, 1, 1, 3, 1
[1, 1, 2, 3, 2, 1, 1, 3, 2] => 1, 1, 2, 3, 2, 1, 1, 3, 2
[1, 1, 2, 3, 2, 1, 1, 3, 3] => 1, 1, 2, 3, 2, 1, 1, 3, 3
[1, 1, 2, 3, 2, 1, 2, 1, 1] => 1, 1, 2, 3, 2, 1, 2, 1, 1
[1, 1, 2, 3, 2, 1, 2, 1, 2] => 1, 1, 2, 3, 2, 1, 2, 1, 2
[1, 1, 2, 3, 2, 1, 2, 1, 3] => 1, 1, 2, 3, 2, 1, 2, 1, 3
[1, 1, 2, 3, 2, 1, 2, 2, 1] => 1, 1, 2, 3, 2, 1, 2, 2, 1
[1, 1, 2, 3, 2, 1, 2, 2, 2] => 1, 1, 2, 3, 2, 1, 2, 2, 2
[1, 1, 2, 3, 2, 1, 2, 2, 3] => 1, 1, 2, 3, 2, 1, 2, 2, 3
[1, 1, 2, 3, 2, 1, 2, 3, 1] => 1, 1, 2, 3, 2, 1, 2, 3, 1
[1, 1, 2, 3, 2, 1, 2, 3, 2] => 1, 1, 2, 3, 2, 1, 2, 3, 2
[1, 1, 2, 3, 2, 1, 2, 3, 3] => 1, 1, 2, 3, 2, 1, 2, 3, 3
[1, 1, 2, 3, 2, 1, 3, 1, 1] => 1, 1, 2, 3, 2, 1, 3, 1, 1
[1, 1, 2, 3, 2, 1, 3, 1, 2] => 1, 1, 2, 3, 2, 1, 3, 1, 2
[1, 1, 2, 3, 2, 1, 3, 1, 3] => 1, 1, 2, 3, 2, 1, 3, 1, 3
[1, 1, 2, 3, 2, 1, 3, 2, 1] => 1, 1, 2, 3, 2, 1, 3, 2, 1
[1, 1, 2, 3, 2, 1, 3, 2, 2] => 1, 1, 2, 3, 2, 1, 3, 2, 2
[1, 1, 2, 3, 2, 1, 3, 2, 3] => 1, 1, 2, 3, 2, 1, 3, 2, 3
[1, 1, 2, 3, 2, 1, 3, 3, 1] => 1, 1, 2, 3, 2, 1, 3, 3, 1
[1, 1, 2, 3, 2, 1, 3, 3, 2] => 1, 1, 2, 3, 2, 1, 3, 3, 2
[1, 1, 2, 3, 2, 1, 3, 3, 3] => 1, 1, 2, 3, 2, 1, 3, 3, 3
[1, 1, 2, 3, 2, 2, 1, 1, 1] => 1, 1, 2, 3, 2, 2, 1, 1, 1
[1, 1, 2, 3, 2, 2, 1, 1, 2] => 1, 1, 2, 3, 2, 2, 1, 1, 2
[1, 1, 2, 3, 2, 2, 1, 1, 3] => 1, 1, 2, 3, 2, 2, 1, 1, 3
[1, 1, 2, 3, 2, 2, 1, 2, 1] => 1, 1, 2, 3, 2, 2, 1, 2, 1
[1, 1, 2, 3, 2, 2, 1, 2, 2] => 1, 1, 2, 3, 2, 2, 1, 2, 2
[1, 1, 2, 3, 2, 2, 1, 2, 3] => 1, 1, 2, 3, 2, 2, 1, 2, 3
[1, 1, 2, 3, 2, 2, 1, 3, 1] => 1, 1, 2, 3, 2, 2, 1, 3, 1
[1, 1, 2, 3, 2, 2, 1, 3, 2] => 1, 1, 2, 3, 2, 2, 1, 3, 2
[1, 1, 2, 3, 2, 2, 1, 3, 3] => 1, 1, 2, 3, 2, 2, 1, 3, 3
[1, 1, 2, 3, 2, 2, 2, 1, 1] => 1, 1, 2, 3, 2, 2, 2, 1, 1
[1, 1, 2, 3, 2, 2, 2, 1, 2] => 1, 1, 2, 3, 2, 2, 2, 1, 2
[1, 1, 2, 3, 2, 2, 2, 1, 3] => 1, 1, 2, 3, 2, 2, 2, 1, 3
[1, 1, 2, 3, 2, 2, 2, 2, 1] => 1, 1, 2, 3, 2, 2, 2, 2, 1
[1, 1, 2, 3, 2, 2, 2, 2, 2] => 1, 1, 2, 3, 2, 2, 2, 2, 2
[1, 1, 2, 3, 2, 2, 2, 2, 3] => 1, 1, 2, 3, 2, 2, 2, 2, 3
[1, 1, 2, 3, 2, 2, 2, 3, 1] => 1, 1, 2, 3, 2, 2, 2, 3, 1
[1, 1, 2, 3, 2, 2, 2, 3, 2] => 1, 1, 2, 3, 2, 2, 2, 3, 2
[1, 1, 2, 3, 2, 2, 2, 3, 3] => 1, 1, 2, 3, 2, 2, 2, 3, 3
[1, 1, 2, 3, 2, 2, 3, 1, 1] => 1, 1, 2, 3, 2, 2, 3, 1, 1
[1, 1, 2, 3, 2, 2, 3, 1, 2] => 1, 1, 2, 3, 2, 2, 3, 1, 2
[1, 1, 2, 3, 2, 2, 3, 1, 3] => 1, 1, 2, 3, 2, 2, 3, 1, 3
[1, 1, 2, 3, 2, 2, 3, 2, 1] => 1, 1, 2, 3, 2, 2, 3, 2, 1
[1, 1, 2, 3, 2, 2, 3, 2, 2] => 1, 1, 2, 3, 2, 2, 3, 2, 2
[1, 1, 2, 3, 2, 2, 3, 2, 3] => 1, 1, 2, 3, 2, 2, 3, 2, 3
[1, 1, 2, 3, 2, 2, 3, 3, 1] => 1, 1, 2, 3, 2, 2, 3, 3, 1
[1, 1, 2, 3, 2, 2, 3, 3, 2] => 1, 1, 2, 3, 2, 2, 3, 3, 2
[1, 1, 2, 3, 2, 2, 3, 3, 3] => 1, 1, 2, 3, 2, 2, 3, 3, 3
[1, 1, 2, 3, 2, 3, 1, 1, 1] => 1, 1, 2, 3, 2, 3, 1, 1, 1
[1, 1, 2, 3, 2, 3, 1, 1, 2] => 1, 1, 2, 3, 2, 3, 1, 1, 2
[1, 1, 2, 3, 2, 3, 1, 1, 3] => 1, 1, 2, 3, 2, 3, 1, 1, 3
[1, 1, 2, 3, 2, 3, 1, 2, 1] => 1, 1, 2, 3, 2, 3, 1, 2, 1
[1, 1, 2, 3, 2, 3, 1, 2, 2] => 1, 1, 2, 3, 2, 3, 1, 2, 2
[1, 1, 2, 3, 2, 3, 1, 2, 3] => 1, 1, 2, 3, 2, 3, 1, 2, 3
[1, 1, 2, 3, 2, 3, 1, 3, 1] => 1, 1, 2, 3, 2, 3, 1, 3, 1
[1, 1, 2, 3, 2, 3, 1, 3, 2] => 1, 1, 2, 3, 2, 3, 1, 3, 2
[1, 1, 2, 3, 2, 3, 1, 3, 3] => 1, 1, 2, 3, 2, 3, 1, 3, 3
[1, 1, 2, 3, 2, 3, 2, 1, 1] => 1, 1, 2, 3, 2, 3, 2, 1, 1
[1, 1, 2, 3, 2, 3, 2, 1, 2] => 1, 1, 2, 3, 2, 3, 2, 1, 2
[1, 1, 2, 3, 2, 3, 2, 1, 3] => 1, 1, 2, 3, 2, 3, 2, 1, 3
[1, 1, 2, 3, 2, 3, 2, 2, 1] => 1, 1, 2, 3, 2, 3, 2, 2, 1
[1, 1, 2, 3, 2, 3, 2, 2, 2] => 1, 1, 2, 3, 2, 3, 2, 2, 2
[1, 1, 2, 3, 2, 3, 2, 2, 3] => 1, 1, 2, 3, 2, 3, 2, 2, 3
[1, 1, 2, 3, 2, 3, 2, 3, 1] => 1, 1, 2, 3, 2, 3, 2, 3, 1
[1, 1, 2, 3, 2, 3, 2, 3, 2] => 1, 1, 2, 3, 2, 3, 2, 3, 2
[1, 1, 2, 3, 2, 3, 2, 3, 3] => 1, 1, 2, 3, 2, 3, 2, 3, 3
[1, 1, 2, 3, 2, 3, 3, 1, 1] => 1, 1, 2, 3, 2, 3, 3, 1, 1
[1, 1, 2, 3, 2, 3, 3, 1, 2] => 1, 1, 2, 3, 2, 3, 3, 1, 2
[1, 1, 2, 3, 2, 3, 3, 1, 3] => 1, 1, 2, 3, 2, 3, 3, 1, 3
[1, 1, 2, 3, 2, 3, 3, 2, 1] => 1, 1, 2, 3, 2, 3, 3, 2, 1
[1, 1, 2, 3, 2, 3, 3, 2, 2] => 1, 1, 2, 3, 2, 3, 3, 2, 2
[1, 1, 2, 3, 2, 3, 3, 2, 3] => 1, 1, 2, 3, 2, 3, 3, 2, 3
[1, 1, 2, 3, 2, 3, 3, 3, 1] => 1, 1, 2, 3, 2, 3, 3, 3, 1
[1, 1, 2, 3, 2, 3, 3, 3, 2] => 1, 1, 2, 3, 2, 3, 3, 3, 2
[1, 1, 2, 3, 2, 3, 3, 3, 3] => 1, 1, 2, 3, 2, 3, 3, 3, 3
[1, 1, 2, 3, 3, 1, 1, 1, 1] => 1, 1, 2, 3, 3, 1, 1, 1, 1
[1, 1, 2, 3, 3, 1, 1, 1, 2] => 1, 1, 2, 3, 3, 1, 1, 1, 2
[1, 1, 2, 3, 3, 1, 1, 1, 3] => 1, 1, 2, 3, 3, 1, 1, 1, 3
[1, 1, 2, 3, 3, 1, 1, 2, 1] => 1, 1, 2, 3, 3, 1, 1, 2, 1
[1, 1, 2, 3, 3, 1, 1, 2, 2] => 1, 1, 2, 3, 3, 1, 1, 2, 2
[1, 1, 2, 3, 3, 1, 1, 2, 3] => 1, 1, 2, 3, 3, 1, 1, 2, 3
[1, 1, 2, 3, 3, 1, 1, 3, 1] => 1, 1, 2, 3, 3, 1, 1, 3, 1
[1, 1, 2, 3, 3, 1, 1, 3, 2] => 1, 1, 2, 3, 3, 1, 1, 3, 2
[1, 1, 2, 3, 3, 1, 1, 3, 3] => 1, 1, 2, 3, 3, 1, 1, 3, 3
[1, 1, 2, 3, 3, 1, 2, 1, 1] => 1, 1, 2, 3, 3, 1, 2, 1, 1
[1, 1, 2, 3, 3, 1, 2, 1, 2] => 1, 1, 2, 3, 3, 1, 2, 1, 2
[1, 1, 2, 3, 3, 1, 2, 1, 3] => 1, 1, 2, 3, 3, 1, 2, 1, 3
[1, 1, 2, 3, 3, 1, 2, 2, 1] => 1, 1, 2, 3, 3, 1, 2, 2, 1
[1, 1, 2, 3, 3, 1, 2, 2, 2] => 1, 1, 2, 3, 3, 1, 2, 2, 2
[1, 1, 2, 3, 3, 1, 2, 2, 3] => 1, 1, 2, 3, 3, 1, 2, 2, 3
[1, 1, 2, 3, 3, 1, 2, 3, 1] => 1, 1, 2, 3, 3, 1, 2, 3, 1
[1, 1, 2, 3, 3, 1, 2, 3, 2] => 1, 1, 2, 3, 3, 1, 2, 3, 2
[1, 1, 2, 3, 3, 1, 2, 3, 3] => 1, 1, 2, 3, 3, 1, 2, 3, 3
[1, 1, 2, 3, 3, 1, 3, 1, 1] => 1, 1, 2, 3, 3, 1, 3, 1, 1
[1, 1, 2, 3, 3, 1, 3, 1, 2] => 1, 1, 2, 3, 3, 1, 3, 1, 2
[1, 1, 2, 3, 3, 1, 3, 1, 3] => 1, 1, 2, 3, 3, 1, 3, 1, 3
[1, 1, 2, 3, 3, 1, 3, 2, 1] => 1, 1, 2, 3, 3, 1, 3, 2, 1
[1, 1, 2, 3, 3, 1, 3, 2, 2] => 1, 1, 2, 3, 3, 1, 3, 2, 2
[1, 1, 2, 3, 3, 1, 3, 2, 3] => 1, 1, 2, 3, 3, 1, 3, 2, 3
[1, 1, 2, 3, 3, 1, 3, 3, 1] => 1, 1, 2, 3, 3, 1, 3, 3, 1
[1, 1, 2, 3, 3, 1, 3, 3, 2] => 1, 1, 2, 3, 3, 1, 3, 3, 2
[1, 1, 2, 3, 3, 1, 3, 3, 3] => 1, 1, 2, 3, 3, 1, 3, 3, 3
[1, 1, 2, 3, 3, 2, 1, 1, 1] => 1, 1, 2, 3, 3, 2, 1, 1, 1
[1, 1, 2, 3, 3, 2, 1, 1, 2] => 1, 1, 2, 3, 3, 2, 1, 1, 2
[1, 1, 2, 3, 3, 2, 1, 1, 3] => 1, 1, 2, 3, 3, 2, 1, 1, 3
[1, 1, 2, 3, 3, 2, 1, 2, 1] => 1, 1, 2, 3, 3, 2, 1, 2, 1
[1, 1, 2, 3, 3, 2, 1, 2, 2] => 1, 1, 2, 3, 3, 2, 1, 2, 2
[1, 1, 2, 3, 3, 2, 1, 2, 3] => 1, 1, 2, 3, 3, 2, 1, 2, 3
[1, 1, 2, 3, 3, 2, 1, 3, 1] => 1, 1, 2, 3, 3, 2, 1, 3, 1
[1, 1, 2, 3, 3, 2, 1, 3, 2] => 1, 1, 2, 3, 3, 2, 1, 3, 2
[1, 1, 2, 3, 3, 2, 1, 3, 3] => 1, 1, 2, 3, 3, 2, 1, 3, 3
[1, 1, 2, 3, 3, 2, 2, 1, 1] => 1, 1, 2, 3, 3, 2, 2, 1, 1
[1, 1, 2, 3, 3, 2, 2, 1, 2] => 1, 1, 2, 3, 3, 2, 2, 1, 2
[1, 1, 2, 3, 3, 2, 2, 1, 3] => 1, 1, 2, 3, 3, 2, 2, 1, 3
[1, 1, 2, 3, 3, 2, 2, 2, 1] => 1, 1, 2, 3, 3, 2, 2, 2, 1
[1, 1, 2, 3, 3, 2, 2, 2, 2] => 1, 1, 2, 3, 3, 2, 2, 2, 2
[1, 1, 2, 3, 3, 2, 2, 2, 3] => 1, 1, 2, 3, 3, 2, 2, 2, 3
[1, 1, 2, 3, 3, 2, 2, 3, 1] => 1, 1, 2, 3, 3, 2, 2, 3, 1
[1, 1, 2, 3, 3, 2, 2, 3, 2] => 1, 1, 2, 3, 3, 2, 2, 3, 2
[1, 1, 2, 3, 3, 2, 2, 3, 3] => 1, 1, 2, 3, 3, 2, 2, 3, 3
[1, 1, 2, 3, 3, 2, 3, 1, 1] => 1, 1, 2, 3, 3, 2, 3, 1, 1
[1, 1, 2, 3, 3, 2, 3, 1, 2] => 1, 1, 2, 3, 3, 2, 3, 1, 2
[1, 1, 2, 3, 3, 2, 3, 1, 3] => 1, 1, 2, 3, 3, 2, 3, 1, 3
[1, 1, 2, 3, 3, 2, 3, 2, 1] => 1, 1, 2, 3, 3, 2, 3, 2, 1
[1, 1, 2, 3, 3, 2, 3, 2, 2] => 1, 1, 2, 3, 3, 2, 3, 2, 2
[1, 1, 2, 3, 3, 2, 3, 2, 3] => 1, 1, 2, 3, 3, 2, 3, 2, 3
[1, 1, 2, 3, 3, 2, 3, 3, 1] => 1, 1, 2, 3, 3, 2, 3, 3, 1
[1, 1, 2, 3, 3, 2, 3, 3, 2] => 1, 1, 2, 3, 3, 2, 3, 3, 2
[1, 1, 2, 3, 3, 2, 3, 3, 3] => 1, 1, 2, 3, 3, 2, 3, 3, 3
[1, 1, 2, 3, 3, 3, 1, 1, 1] => 1, 1, 2, 3, 3, 3, 1, 1, 1
[1, 1, 2, 3, 3, 3, 1, 1, 2] => 1, 1, 2, 3, 3, 3, 1, 1, 2
[1, 1, 2, 3, 3, 3, 1, 1, 3] => 1, 1, 2, 3, 3, 3, 1, 1, 3
[1, 1, 2, 3, 3, 3, 1, 2, 1] => 1, 1, 2, 3, 3, 3, 1, 2, 1
[1, 1, 2, 3, 3, 3, 1, 2, 2] => 1, 1, 2, 3, 3, 3, 1, 2, 2
[1, 1, 2, 3, 3, 3, 1, 2, 3] => 1, 1, 2, 3, 3, 3, 1, 2, 3
[1, 1, 2, 3, 3, 3, 1, 3, 1] => 1, 1, 2, 3, 3, 3, 1, 3, 1
[1, 1, 2, 3, 3, 3, 1, 3, 2] => 1, 1, 2, 3, 3, 3, 1, 3, 2
[1, 1, 2, 3, 3, 3, 1, 3, 3] => 1, 1, 2, 3, 3, 3, 1, 3, 3
[1, 1, 2, 3, 3, 3, 2, 1, 1] => 1, 1, 2, 3, 3, 3, 2, 1, 1
[1, 1, 2, 3, 3, 3, 2, 1, 2] => 1, 1, 2, 3, 3, 3, 2, 1, 2
[1, 1, 2, 3, 3, 3, 2, 1, 3] => 1, 1, 2, 3, 3, 3, 2, 1, 3
[1, 1, 2, 3, 3, 3, 2, 2, 1] => 1, 1, 2, 3, 3, 3, 2, 2, 1
[1, 1, 2, 3, 3, 3, 2, 2, 2] => 1, 1, 2, 3, 3, 3, 2, 2, 2
[1, 1, 2, 3, 3, 3, 2, 2, 3] => 1, 1, 2, 3, 3, 3, 2, 2, 3
[1, 1, 2, 3, 3, 3, 2, 3, 1] => 1, 1, 2, 3, 3, 3, 2, 3, 1
[1, 1, 2, 3, 3, 3, 2, 3, 2] => 1, 1, 2, 3, 3, 3, 2, 3, 2
[1, 1, 2, 3, 3, 3, 2, 3, 3] => 1, 1, 2, 3, 3, 3, 2, 3, 3
[1, 1, 2, 3, 3, 3, 3, 1, 1] => 1, 1, 2, 3, 3, 3, 3, 1, 1
[1, 1, 2, 3, 3, 3, 3, 1, 2] => 1, 1, 2, 3, 3, 3, 3, 1, 2
[1, 1, 2, 3, 3, 3, 3, 1, 3] => 1, 1, 2, 3, 3, 3, 3, 1, 3
[1, 1, 2, 3, 3, 3, 3, 2, 1] => 1, 1, 2, 3, 3, 3, 3, 2, 1
[1, 1, 2, 3, 3, 3, 3, 2, 2] => 1, 1, 2, 3, 3, 3, 3, 2, 2
[1, 1, 2, 3, 3, 3, 3, 2, 3] => 1, 1, 2, 3, 3, 3, 3, 2, 3
[1, 1, 2, 3, 3, 3, 3, 3, 1] => 1, 1, 2, 3, 3, 3, 3, 3, 1
[1, 1, 2, 3, 3, 3, 3, 3, 2] => 1, 1, 2, 3, 3, 3, 3, 3, 2
[1, 1, 2, 3, 3, 3, 3, 3, 3] => 1, 1, 2, 3, 3, 3, 3, 3, 3
[1, 1, 3, 1, 1, 1, 1, 1, 1] => 1, 1, 3, 1, 1, 1, 1, 1, 1
[1, 1, 3, 1, 1, 1, 1, 1, 2] => 1, 1, 3, 1, 1, 1, 1, 1, 2
[1, 1, 3, 1, 1, 1, 1, 1, 3] => 1, 1, 3, 1, 1, 1, 1, 1, 3
[1, 1, 3, 1, 1, 1, 1, 2, 1] => 1, 1, 3, 1, 1, 1, 1, 2, 1
[1, 1, 3, 1, 1, 1, 1, 2, 2] => 1, 1, 3, 1, 1, 1, 1, 2, 2
[1, 1, 3, 1, 1, 1, 1, 2, 3] => 1, 1, 3, 1, 1, 1, 1, 2, 3
[1, 1, 3, 1, 1, 1, 1, 3, 1] => 1, 1, 3, 1, 1, 1, 1, 3, 1
[1, 1, 3, 1, 1, 1, 1, 3, 2] => 1, 1, 3, 1, 1, 1, 1, 3, 2
[1, 1, 3, 1, 1, 1, 1, 3, 3] => 1, 1, 3, 1, 1, 1, 1, 3, 3
[1, 1, 3, 1, 1, 1, 2, 1, 1] => 1, 1, 3, 1, 1, 1, 2, 1, 1
[1, 1, 3, 1, 1, 1, 2, 1, 2] => 1, 1, 3, 1, 1, 1, 2, 1, 2
[1, 1, 3, 1, 1, 1, 2, 1, 3] => 1, 1, 3, 1, 1, 1, 2, 1, 3
[1, 1, 3, 1, 1, 1, 2, 2, 1] => 1, 1, 3, 1, 1, 1, 2, 2, 1
[1, 1, 3, 1, 1, 1, 2, 2, 2] => 1, 1, 3, 1, 1, 1, 2, 2, 2
[1, 1, 3, 1, 1, 1, 2, 2, 3] => 1, 1, 3, 1, 1, 1, 2, 2, 3
[1, 1, 3, 1, 1, 1, 2, 3, 1] => 1, 1, 3, 1, 1, 1, 2, 3, 1
[1, 1, 3, 1, 1, 1, 2, 3, 2] => 1, 1, 3, 1, 1, 1, 2, 3, 2
[1, 1, 3, 1, 1, 1, 2, 3, 3] => 1, 1, 3, 1, 1, 1, 2, 3, 3
[1, 1, 3, 1, 1, 1, 3, 1, 1] => 1, 1, 3, 1, 1, 1, 3, 1, 1
[1, 1, 3, 1, 1, 1, 3, 1, 2] => 1, 1, 3, 1, 1, 1, 3, 1, 2
[1, 1, 3, 1, 1, 1, 3, 1, 3] => 1, 1, 3, 1, 1, 1, 3, 1, 3
[1, 1, 3, 1, 1, 1, 3, 2, 1] => 1, 1, 3, 1, 1, 1, 3, 2, 1
[1, 1, 3, 1, 1, 1, 3, 2, 2] => 1, 1, 3, 1, 1, 1, 3, 2, 2
[1, 1, 3, 1, 1, 1, 3, 2, 3] => 1, 1, 3, 1, 1, 1, 3, 2, 3
[1, 1, 3, 1, 1, 1, 3, 3, 1] => 1, 1, 3, 1, 1, 1, 3, 3, 1
[1, 1, 3, 1, 1, 1, 3, 3, 2] => 1, 1, 3, 1, 1, 1, 3, 3, 2
[1, 1, 3, 1, 1, 1, 3, 3, 3] => 1, 1, 3, 1, 1, 1, 3, 3, 3
[1, 1, 3, 1, 1, 2, 1, 1, 1] => 1, 1, 3, 1, 1, 2, 1, 1, 1
[1, 1, 3, 1, 1, 2, 1, 1, 2] => 1, 1, 3, 1, 1, 2, 1, 1, 2
[1, 1, 3, 1, 1, 2, 1, 1, 3] => 1, 1, 3, 1, 1, 2, 1, 1, 3
[1, 1, 3, 1, 1, 2, 1, 2, 1] => 1, 1, 3, 1, 1, 2, 1, 2, 1
[1, 1, 3, 1, 1, 2, 1, 2, 2] => 1, 1, 3, 1, 1, 2, 1, 2, 2
[1, 1, 3, 1, 1, 2, 1, 2, 3] => 1, 1, 3, 1, 1, 2, 1, 2, 3
[1, 1, 3, 1, 1, 2, 1, 3, 1] => 1, 1, 3, 1, 1, 2, 1, 3, 1
[1, 1, 3, 1, 1, 2, 1, 3, 2] => 1, 1, 3, 1, 1, 2, 1, 3, 2
[1, 1, 3, 1, 1, 2, 1, 3, 3] => 1, 1, 3, 1, 1, 2, 1, 3, 3
[1, 1, 3, 1, 1, 2, 2, 1, 1] => 1, 1, 3, 1, 1, 2, 2, 1, 1
[1, 1, 3, 1, 1, 2, 2, 1, 2] => 1, 1, 3, 1, 1, 2, 2, 1, 2
[1, 1, 3, 1, 1, 2, 2, 1, 3] => 1, 1, 3, 1, 1, 2, 2, 1, 3
[1, 1, 3, 1, 1, 2, 2, 2, 1] => 1, 1, 3, 1, 1, 2, 2, 2, 1
[1, 1, 3, 1, 1, 2, 2, 2, 2] => 1, 1, 3, 1, 1, 2, 2, 2, 2
[1, 1, 3, 1, 1, 2, 2, 2, 3] => 1, 1, 3, 1, 1, 2, 2, 2, 3
[1, 1, 3, 1, 1, 2, 2, 3, 1] => 1, 1, 3, 1, 1, 2, 2, 3, 1
[1, 1, 3, 1, 1, 2, 2, 3, 2] => 1, 1, 3, 1, 1, 2, 2, 3, 2
[1, 1, 3, 1, 1, 2, 2, 3, 3] => 1, 1, 3, 1, 1, 2, 2, 3, 3
[1, 1, 3, 1, 1, 2, 3, 1, 1] => 1, 1, 3, 1, 1, 2, 3, 1, 1
[1, 1, 3, 1, 1, 2, 3, 1, 2] => 1, 1, 3, 1, 1, 2, 3, 1, 2
[1, 1, 3, 1, 1, 2, 3, 1, 3] => 1, 1, 3, 1, 1, 2, 3, 1, 3
[1, 1, 3, 1, 1, 2, 3, 2, 1] => 1, 1, 3, 1, 1, 2, 3, 2, 1
[1, 1, 3, 1, 1, 2, 3, 2, 2] => 1, 1, 3, 1, 1, 2, 3, 2, 2
[1, 1, 3, 1, 1, 2, 3, 2, 3] => 1, 1, 3, 1, 1, 2, 3, 2, 3
[1, 1, 3, 1, 1, 2, 3, 3, 1] => 1, 1, 3, 1, 1, 2, 3, 3, 1
[1, 1, 3, 1, 1, 2, 3, 3, 2] => 1, 1, 3, 1, 1, 2, 3, 3, 2
[1, 1, 3, 1, 1, 2, 3, 3, 3] => 1, 1, 3, 1, 1, 2, 3, 3, 3
[1, 1, 3, 1, 1, 3, 1, 1, 1] => 1, 1, 3, 1, 1, 3, 1, 1, 1
[1, 1, 3, 1, 1, 3, 1, 1, 2] => 1, 1, 3, 1, 1, 3, 1, 1, 2
[1, 1, 3, 1, 1, 3, 1, 1, 3] => 1, 1, 3, 1, 1, 3, 1, 1, 3
[1, 1, 3, 1, 1, 3, 1, 2, 1] => 1, 1, 3, 1, 1, 3, 1, 2, 1
[1, 1, 3, 1, 1, 3, 1, 2, 2] => 1, 1, 3, 1, 1, 3, 1, 2, 2
[1, 1, 3, 1, 1, 3, 1, 2, 3] => 1, 1, 3, 1, 1, 3, 1, 2, 3
[1, 1, 3, 1, 1, 3, 1, 3, 1] => 1, 1, 3, 1, 1, 3, 1, 3, 1
[1, 1, 3, 1, 1, 3, 1, 3, 2] => 1, 1, 3, 1, 1, 3, 1, 3, 2
[1, 1, 3, 1, 1, 3, 1, 3, 3] => 1, 1, 3, 1, 1, 3, 1, 3, 3
[1, 1, 3, 1, 1, 3, 2, 1, 1] => 1, 1, 3, 1, 1, 3, 2, 1, 1
[1, 1, 3, 1, 1, 3, 2, 1, 2] => 1, 1, 3, 1, 1, 3, 2, 1, 2
[1, 1, 3, 1, 1, 3, 2, 1, 3] => 1, 1, 3, 1, 1, 3, 2, 1, 3
[1, 1, 3, 1, 1, 3, 2, 2, 1] => 1, 1, 3, 1, 1, 3, 2, 2, 1
[1, 1, 3, 1, 1, 3, 2, 2, 2] => 1, 1, 3, 1, 1, 3, 2, 2, 2
[1, 1, 3, 1, 1, 3, 2, 2, 3] => 1, 1, 3, 1, 1, 3, 2, 2, 3
[1, 1, 3, 1, 1, 3, 2, 3, 1] => 1, 1, 3, 1, 1, 3, 2, 3, 1
[1, 1, 3, 1, 1, 3, 2, 3, 2] => 1, 1, 3, 1, 1, 3, 2, 3, 2
[1, 1, 3, 1, 1, 3, 2, 3, 3] => 1, 1, 3, 1, 1, 3, 2, 3, 3
[1, 1, 3, 1, 1, 3, 3, 1, 1] => 1, 1, 3, 1, 1, 3, 3, 1, 1
[1, 1, 3, 1, 1, 3, 3, 1, 2] => 1, 1, 3, 1, 1, 3, 3, 1, 2
[1, 1, 3, 1, 1, 3, 3, 1, 3] => 1, 1, 3, 1, 1, 3, 3, 1, 3
[1, 1, 3, 1, 1, 3, 3, 2, 1] => 1, 1, 3, 1, 1, 3, 3, 2, 1
[1, 1, 3, 1, 1, 3, 3, 2, 2] => 1, 1, 3, 1, 1, 3, 3, 2, 2
[1, 1, 3, 1, 1, 3, 3, 2, 3] => 1, 1, 3, 1, 1, 3, 3, 2, 3
[1, 1, 3, 1, 1, 3, 3, 3, 1] => 1, 1, 3, 1, 1, 3, 3, 3, 1
[1, 1, 3, 1, 1, 3, 3, 3, 2] => 1, 1, 3, 1, 1, 3, 3, 3, 2
[1, 1, 3, 1, 1, 3, 3, 3, 3] => 1, 1, 3, 1, 1, 3, 3, 3, 3
[1, 1, 3, 1, 2, 1, 1, 1, 1] => 1, 1, 3, 1, 2, 1, 1, 1, 1
[1, 1, 3, 1, 2, 1, 1, 1, 2] => 1, 1, 3, 1, 2, 1, 1, 1, 2
[1, 1, 3, 1, 2, 1, 1, 1, 3] => 1, 1, 3, 1, 2, 1, 1, 1, 3
[1, 1, 3, 1, 2, 1, 1, 2, 1] => 1, 1, 3, 1, 2, 1, 1, 2, 1
[1, 1, 3, 1, 2, 1, 1, 2, 2] => 1, 1, 3, 1, 2, 1, 1, 2, 2
[1, 1, 3, 1, 2, 1, 1, 2, 3] => 1, 1, 3, 1, 2, 1, 1, 2, 3
[1, 1, 3, 1, 2, 1, 1, 3, 1] => 1, 1, 3, 1, 2, 1, 1, 3, 1
[1, 1, 3, 1, 2, 1, 1, 3, 2] => 1, 1, 3, 1, 2, 1, 1, 3, 2
[1, 1, 3, 1, 2, 1, 1, 3, 3] => 1, 1, 3, 1, 2, 1, 1, 3, 3
[1, 1, 3, 1, 2, 1, 2, 1, 1] => 1, 1, 3, 1, 2, 1, 2, 1, 1
[1, 1, 3, 1, 2, 1, 2, 1, 2] => 1, 1, 3, 1, 2, 1, 2, 1, 2
[1, 1, 3, 1, 2, 1, 2, 1, 3] => 1, 1, 3, 1, 2, 1, 2, 1, 3
[1, 1, 3, 1, 2, 1, 2, 2, 1] => 1, 1, 3, 1, 2, 1, 2, 2, 1
[1, 1, 3, 1, 2, 1, 2, 2, 2] => 1, 1, 3, 1, 2, 1, 2, 2, 2
[1, 1, 3, 1, 2, 1, 2, 2, 3] => 1, 1, 3, 1, 2, 1, 2, 2, 3
[1, 1, 3, 1, 2, 1, 2, 3, 1] => 1, 1, 3, 1, 2, 1, 2, 3, 1
[1, 1, 3, 1, 2, 1, 2, 3, 2] => 1, 1, 3, 1, 2, 1, 2, 3, 2
[1, 1, 3, 1, 2, 1, 2, 3, 3] => 1, 1, 3, 1, 2, 1, 2, 3, 3
[1, 1, 3, 1, 2, 1, 3, 1, 1] => 1, 1, 3, 1, 2, 1, 3, 1, 1
[1, 1, 3, 1, 2, 1, 3, 1, 2] => 1, 1, 3, 1, 2, 1, 3, 1, 2
[1, 1, 3, 1, 2, 1, 3, 1, 3] => 1, 1, 3, 1, 2, 1, 3, 1, 3
[1, 1, 3, 1, 2, 1, 3, 2, 1] => 1, 1, 3, 1, 2, 1, 3, 2, 1
[1, 1, 3, 1, 2, 1, 3, 2, 2] => 1, 1, 3, 1, 2, 1, 3, 2, 2
[1, 1, 3, 1, 2, 1, 3, 2, 3] => 1, 1, 3, 1, 2, 1, 3, 2, 3
[1, 1, 3, 1, 2, 1, 3, 3, 1] => 1, 1, 3, 1, 2, 1, 3, 3, 1
[1, 1, 3, 1, 2, 1, 3, 3, 2] => 1, 1, 3, 1, 2, 1, 3, 3, 2
[1, 1, 3, 1, 2, 1, 3, 3, 3] => 1, 1, 3, 1, 2, 1, 3, 3, 3
[1, 1, 3, 1, 2, 2, 1, 1, 1] => 1, 1, 3, 1, 2, 2, 1, 1, 1
[1, 1, 3, 1, 2, 2, 1, 1, 2] => 1, 1, 3, 1, 2, 2, 1, 1, 2
[1, 1, 3, 1, 2, 2, 1, 1, 3] => 1, 1, 3, 1, 2, 2, 1, 1, 3
[1, 1, 3, 1, 2, 2, 1, 2, 1] => 1, 1, 3, 1, 2, 2, 1, 2, 1
[1, 1, 3, 1, 2, 2, 1, 2, 2] => 1, 1, 3, 1, 2, 2, 1, 2, 2
[1, 1, 3, 1, 2, 2, 1, 2, 3] => 1, 1, 3, 1, 2, 2, 1, 2, 3
[1, 1, 3, 1, 2, 2, 1, 3, 1] => 1, 1, 3, 1, 2, 2, 1, 3, 1
[1, 1, 3, 1, 2, 2, 1, 3, 2] => 1, 1, 3, 1, 2, 2, 1, 3, 2
[1, 1, 3, 1, 2, 2, 1, 3, 3] => 1, 1, 3, 1, 2, 2, 1, 3, 3
[1, 1, 3, 1, 2, 2, 2, 1, 1] => 1, 1, 3, 1, 2, 2, 2, 1, 1
[1, 1, 3, 1, 2, 2, 2, 1, 2] => 1, 1, 3, 1, 2, 2, 2, 1, 2
[1, 1, 3, 1, 2, 2, 2, 1, 3] => 1, 1, 3, 1, 2, 2, 2, 1, 3
[1, 1, 3, 1, 2, 2, 2, 2, 1] => 1, 1, 3, 1, 2, 2, 2, 2, 1
[1, 1, 3, 1, 2, 2, 2, 2, 2] => 1, 1, 3, 1, 2, 2, 2, 2, 2
[1, 1, 3, 1, 2, 2, 2, 2, 3] => 1, 1, 3, 1, 2, 2, 2, 2, 3
[1, 1, 3, 1, 2, 2, 2, 3, 1] => 1, 1, 3, 1, 2, 2, 2, 3, 1
[1, 1, 3, 1, 2, 2, 2, 3, 2] => 1, 1, 3, 1, 2, 2, 2, 3, 2
[1, 1, 3, 1, 2, 2, 2, 3, 3] => 1, 1, 3, 1, 2, 2, 2, 3, 3
[1, 1, 3, 1, 2, 2, 3, 1, 1] => 1, 1, 3, 1, 2, 2, 3, 1, 1
[1, 1, 3, 1, 2, 2, 3, 1, 2] => 1, 1, 3, 1, 2, 2, 3, 1, 2
[1, 1, 3, 1, 2, 2, 3, 1, 3] => 1, 1, 3, 1, 2, 2, 3, 1, 3
[1, 1, 3, 1, 2, 2, 3, 2, 1] => 1, 1, 3, 1, 2, 2, 3, 2, 1
[1, 1, 3, 1, 2, 2, 3, 2, 2] => 1, 1, 3, 1, 2, 2, 3, 2, 2
[1, 1, 3, 1, 2, 2, 3, 2, 3] => 1, 1, 3, 1, 2, 2, 3, 2, 3
[1, 1, 3, 1, 2, 2, 3, 3, 1] => 1, 1, 3, 1, 2, 2, 3, 3, 1
[1, 1, 3, 1, 2, 2, 3, 3, 2] => 1, 1, 3, 1, 2, 2, 3, 3, 2
[1, 1, 3, 1, 2, 2, 3, 3, 3] => 1, 1, 3, 1, 2, 2, 3, 3, 3
[1, 1, 3, 1, 2, 3, 1, 1, 1] => 1, 1, 3, 1, 2, 3, 1, 1, 1
[1, 1, 3, 1, 2, 3, 1, 1, 2] => 1, 1, 3, 1, 2, 3, 1, 1, 2
[1, 1, 3, 1, 2, 3, 1, 1, 3] => 1, 1, 3, 1, 2, 3, 1, 1, 3
[1, 1, 3, 1, 2, 3, 1, 2, 1] => 1, 1, 3, 1, 2, 3, 1, 2, 1
[1, 1, 3, 1, 2, 3, 1, 2, 2] => 1, 1, 3, 1, 2, 3, 1, 2, 2
[1, 1, 3, 1, 2, 3, 1, 2, 3] => 1, 1, 3, 1, 2, 3, 1, 2, 3
[1, 1, 3, 1, 2, 3, 1, 3, 1] => 1, 1, 3, 1, 2, 3, 1, 3, 1
[1, 1, 3, 1, 2, 3, 1, 3, 2] => 1, 1, 3, 1, 2, 3, 1, 3, 2
[1, 1, 3, 1, 2, 3, 1, 3, 3] => 1, 1, 3, 1, 2, 3, 1, 3, 3
[1, 1, 3, 1, 2, 3, 2, 1, 1] => 1, 1, 3, 1, 2, 3, 2, 1, 1
[1, 1, 3, 1, 2, 3, 2, 1, 2] => 1, 1, 3, 1, 2, 3, 2, 1, 2
[1, 1, 3, 1, 2, 3, 2, 1, 3] => 1, 1, 3, 1, 2, 3, 2, 1, 3
[1, 1, 3, 1, 2, 3, 2, 2, 1] => 1, 1, 3, 1, 2, 3, 2, 2, 1
[1, 1, 3, 1, 2, 3, 2, 2, 2] => 1, 1, 3, 1, 2, 3, 2, 2, 2
[1, 1, 3, 1, 2, 3, 2, 2, 3] => 1, 1, 3, 1, 2, 3, 2, 2, 3
[1, 1, 3, 1, 2, 3, 2, 3, 1] => 1, 1, 3, 1, 2, 3, 2, 3, 1
[1, 1, 3, 1, 2, 3, 2, 3, 2] => 1, 1, 3, 1, 2, 3, 2, 3, 2
[1, 1, 3, 1, 2, 3, 2, 3, 3] => 1, 1, 3, 1, 2, 3, 2, 3, 3
[1, 1, 3, 1, 2, 3, 3, 1, 1] => 1, 1, 3, 1, 2, 3, 3, 1, 1
[1, 1, 3, 1, 2, 3, 3, 1, 2] => 1, 1, 3, 1, 2, 3, 3, 1, 2
[1, 1, 3, 1, 2, 3, 3, 1, 3] => 1, 1, 3, 1, 2, 3, 3, 1, 3
[1, 1, 3, 1, 2, 3, 3, 2, 1] => 1, 1, 3, 1, 2, 3, 3, 2, 1
[1, 1, 3, 1, 2, 3, 3, 2, 2] => 1, 1, 3, 1, 2, 3, 3, 2, 2
[1, 1, 3, 1, 2, 3, 3, 2, 3] => 1, 1, 3, 1, 2, 3, 3, 2, 3
[1, 1, 3, 1, 2, 3, 3, 3, 1] => 1, 1, 3, 1, 2, 3, 3, 3, 1
[1, 1, 3, 1, 2, 3, 3, 3, 2] => 1, 1, 3, 1, 2, 3, 3, 3, 2
[1, 1, 3, 1, 2, 3, 3, 3, 3] => 1, 1, 3, 1, 2, 3, 3, 3, 3
[1, 1, 3, 1, 3, 1, 1, 1, 1] => 1, 1, 3, 1, 3, 1, 1, 1, 1
[1, 1, 3, 1, 3, 1, 1, 1, 2] => 1, 1, 3, 1, 3, 1, 1, 1, 2
[1, 1, 3, 1, 3, 1, 1, 1, 3] => 1, 1, 3, 1, 3, 1, 1, 1, 3
[1, 1, 3, 1, 3, 1, 1, 2, 1] => 1, 1, 3, 1, 3, 1, 1, 2, 1
[1, 1, 3, 1, 3, 1, 1, 2, 2] => 1, 1, 3, 1, 3, 1, 1, 2, 2
[1, 1, 3, 1, 3, 1, 1, 2, 3] => 1, 1, 3, 1, 3, 1, 1, 2, 3
[1, 1, 3, 1, 3, 1, 1, 3, 1] => 1, 1, 3, 1, 3, 1, 1, 3, 1
[1, 1, 3, 1, 3, 1, 1, 3, 2] => 1, 1, 3, 1, 3, 1, 1, 3, 2
[1, 1, 3, 1, 3, 1, 1, 3, 3] => 1, 1, 3, 1, 3, 1, 1, 3, 3
[1, 1, 3, 1, 3, 1, 2, 1, 1] => 1, 1, 3, 1, 3, 1, 2, 1, 1
[1, 1, 3, 1, 3, 1, 2, 1, 2] => 1, 1, 3, 1, 3, 1, 2, 1, 2
[1, 1, 3, 1, 3, 1, 2, 1, 3] => 1, 1, 3, 1, 3, 1, 2, 1, 3
[1, 1, 3, 1, 3, 1, 2, 2, 1] => 1, 1, 3, 1, 3, 1, 2, 2, 1
[1, 1, 3, 1, 3, 1, 2, 2, 2] => 1, 1, 3, 1, 3, 1, 2, 2, 2
[1, 1, 3, 1, 3, 1, 2, 2, 3] => 1, 1, 3, 1, 3, 1, 2, 2, 3
[1, 1, 3, 1, 3, 1, 2, 3, 1] => 1, 1, 3, 1, 3, 1, 2, 3, 1
[1, 1, 3, 1, 3, 1, 2, 3, 2] => 1, 1, 3, 1, 3, 1, 2, 3, 2
[1, 1, 3, 1, 3, 1, 2, 3, 3] => 1, 1, 3, 1, 3, 1, 2, 3, 3
[1, 1, 3, 1, 3, 1, 3, 1, 1] => 1, 1, 3, 1, 3, 1, 3, 1, 1
[1, 1, 3, 1, 3, 1, 3, 1, 2] => 1, 1, 3, 1, 3, 1, 3, 1, 2
[1, 1, 3, 1, 3, 1, 3, 1, 3] => 1, 1, 3, 1, 3, 1, 3, 1, 3
[1, 1, 3, 1, 3, 1, 3, 2, 1] => 1, 1, 3, 1, 3, 1, 3, 2, 1
[1, 1, 3, 1, 3, 1, 3, 2, 2] => 1, 1, 3, 1, 3, 1, 3, 2, 2
[1, 1, 3, 1, 3, 1, 3, 2, 3] => 1, 1, 3, 1, 3, 1, 3, 2, 3
[1, 1, 3, 1, 3, 1, 3, 3, 1] => 1, 1, 3, 1, 3, 1, 3, 3, 1
[1, 1, 3, 1, 3, 1, 3, 3, 2] => 1, 1, 3, 1, 3, 1, 3, 3, 2
[1, 1, 3, 1, 3, 1, 3, 3, 3] => 1, 1, 3, 1, 3, 1, 3, 3, 3
[1, 1, 3, 1, 3, 2, 1, 1, 1] => 1, 1, 3, 1, 3, 2, 1, 1, 1
[1, 1, 3, 1, 3, 2, 1, 1, 2] => 1, 1, 3, 1, 3, 2, 1, 1, 2
[1, 1, 3, 1, 3, 2, 1, 1, 3] => 1, 1, 3, 1, 3, 2, 1, 1, 3
[1, 1, 3, 1, 3, 2, 1, 2, 1] => 1, 1, 3, 1, 3, 2, 1, 2, 1
[1, 1, 3, 1, 3, 2, 1, 2, 2] => 1, 1, 3, 1, 3, 2, 1, 2, 2
[1, 1, 3, 1, 3, 2, 1, 2, 3] => 1, 1, 3, 1, 3, 2, 1, 2, 3
[1, 1, 3, 1, 3, 2, 1, 3, 1] => 1, 1, 3, 1, 3, 2, 1, 3, 1
[1, 1, 3, 1, 3, 2, 1, 3, 2] => 1, 1, 3, 1, 3, 2, 1, 3, 2
[1, 1, 3, 1, 3, 2, 1, 3, 3] => 1, 1, 3, 1, 3, 2, 1, 3, 3
[1, 1, 3, 1, 3, 2, 2, 1, 1] => 1, 1, 3, 1, 3, 2, 2, 1, 1
[1, 1, 3, 1, 3, 2, 2, 1, 2] => 1, 1, 3, 1, 3, 2, 2, 1, 2
[1, 1, 3, 1, 3, 2, 2, 1, 3] => 1, 1, 3, 1, 3, 2, 2, 1, 3
[1, 1, 3, 1, 3, 2, 2, 2, 1] => 1, 1, 3, 1, 3, 2, 2, 2, 1
[1, 1, 3, 1, 3, 2, 2, 2, 2] => 1, 1, 3, 1, 3, 2, 2, 2, 2
[1, 1, 3, 1, 3, 2, 2, 2, 3] => 1, 1, 3, 1, 3, 2, 2, 2, 3
[1, 1, 3, 1, 3, 2, 2, 3, 1] => 1, 1, 3, 1, 3, 2, 2, 3, 1
[1, 1, 3, 1, 3, 2, 2, 3, 2] => 1, 1, 3, 1, 3, 2, 2, 3, 2
[1, 1, 3, 1, 3, 2, 2, 3, 3] => 1, 1, 3, 1, 3, 2, 2, 3, 3
[1, 1, 3, 1, 3, 2, 3, 1, 1] => 1, 1, 3, 1, 3, 2, 3, 1, 1
[1, 1, 3, 1, 3, 2, 3, 1, 2] => 1, 1, 3, 1, 3, 2, 3, 1, 2
[1, 1, 3, 1, 3, 2, 3, 1, 3] => 1, 1, 3, 1, 3, 2, 3, 1, 3
[1, 1, 3, 1, 3, 2, 3, 2, 1] => 1, 1, 3, 1, 3, 2, 3, 2, 1
[1, 1, 3, 1, 3, 2, 3, 2, 2] => 1, 1, 3, 1, 3, 2, 3, 2, 2
[1, 1, 3, 1, 3, 2, 3, 2, 3] => 1, 1, 3, 1, 3, 2, 3, 2, 3
[1, 1, 3, 1, 3, 2, 3, 3, 1] => 1, 1, 3, 1, 3, 2, 3, 3, 1
[1, 1, 3, 1, 3, 2, 3, 3, 2] => 1, 1, 3, 1, 3, 2, 3, 3, 2
[1, 1, 3, 1, 3, 2, 3, 3, 3] => 1, 1, 3, 1, 3, 2, 3, 3, 3
[1, 1, 3, 1, 3, 3, 1, 1, 1] => 1, 1, 3, 1, 3, 3, 1, 1, 1
[1, 1, 3, 1, 3, 3, 1, 1, 2] => 1, 1, 3, 1, 3, 3, 1, 1, 2
[1, 1, 3, 1, 3, 3, 1, 1, 3] => 1, 1, 3, 1, 3, 3, 1, 1, 3
[1, 1, 3, 1, 3, 3, 1, 2, 1] => 1, 1, 3, 1, 3, 3, 1, 2, 1
[1, 1, 3, 1, 3, 3, 1, 2, 2] => 1, 1, 3, 1, 3, 3, 1, 2, 2
[1, 1, 3, 1, 3, 3, 1, 2, 3] => 1, 1, 3, 1, 3, 3, 1, 2, 3
[1, 1, 3, 1, 3, 3, 1, 3, 1] => 1, 1, 3, 1, 3, 3, 1, 3, 1
[1, 1, 3, 1, 3, 3, 1, 3, 2] => 1, 1, 3, 1, 3, 3, 1, 3, 2
[1, 1, 3, 1, 3, 3, 1, 3, 3] => 1, 1, 3, 1, 3, 3, 1, 3, 3
[1, 1, 3, 1, 3, 3, 2, 1, 1] => 1, 1, 3, 1, 3, 3, 2, 1, 1
[1, 1, 3, 1, 3, 3, 2, 1, 2] => 1, 1, 3, 1, 3, 3, 2, 1, 2
[1, 1, 3, 1, 3, 3, 2, 1, 3] => 1, 1, 3, 1, 3, 3, 2, 1, 3
[1, 1, 3, 1, 3, 3, 2, 2, 1] => 1, 1, 3, 1, 3, 3, 2, 2, 1
[1, 1, 3, 1, 3, 3, 2, 2, 2] => 1, 1, 3, 1, 3, 3, 2, 2, 2
[1, 1, 3, 1, 3, 3, 2, 2, 3] => 1, 1, 3, 1, 3, 3, 2, 2, 3
[1, 1, 3, 1, 3, 3, 2, 3, 1] => 1, 1, 3, 1, 3, 3, 2, 3, 1
[1, 1, 3, 1, 3, 3, 2, 3, 2] => 1, 1, 3, 1, 3, 3, 2, 3, 2
[1, 1, 3, 1, 3, 3, 2, 3, 3] => 1, 1, 3, 1, 3, 3, 2, 3, 3
[1, 1, 3, 1, 3, 3, 3, 1, 1] => 1, 1, 3, 1, 3, 3, 3, 1, 1
[1, 1, 3, 1, 3, 3, 3, 1, 2] => 1, 1, 3, 1, 3, 3, 3, 1, 2
[1, 1, 3, 1, 3, 3, 3, 1, 3] => 1, 1, 3, 1, 3, 3, 3, 1, 3
[1, 1, 3, 1, 3, 3, 3, 2, 1] => 1, 1, 3, 1, 3, 3, 3, 2, 1
[1, 1, 3, 1, 3, 3, 3, 2, 2] => 1, 1, 3, 1, 3, 3, 3, 2, 2
[1, 1, 3, 1, 3, 3, 3, 2, 3] => 1, 1, 3, 1, 3, 3, 3, 2, 3
[1, 1, 3, 1, 3, 3, 3, 3, 1] => 1, 1, 3, 1, 3, 3, 3, 3, 1
[1, 1, 3, 1, 3, 3, 3, 3, 2] => 1, 1, 3, 1, 3, 3, 3, 3, 2
[1, 1, 3, 1, 3, 3, 3, 3, 3] => 1, 1, 3, 1, 3, 3, 3, 3, 3
[1, 1, 3, 2, 1, 1, 1, 1, 1] => 1, 1, 3, 2, 1, 1, 1, 1, 1
[1, 1, 3, 2, 1, 1, 1, 1, 2] => 1, 1, 3, 2, 1, 1, 1, 1, 2
[1, 1, 3, 2, 1, 1, 1, 1, 3] => 1, 1, 3, 2, 1, 1, 1, 1, 3
[1, 1, 3, 2, 1, 1, 1, 2, 1] => 1, 1, 3, 2, 1, 1, 1, 2, 1
[1, 1, 3, 2, 1, 1, 1, 2, 2] => 1, 1, 3, 2, 1, 1, 1, 2, 2
[1, 1, 3, 2, 1, 1, 1, 2, 3] => 1, 1, 3, 2, 1, 1, 1, 2, 3
[1, 1, 3, 2, 1, 1, 1, 3, 1] => 1, 1, 3, 2, 1, 1, 1, 3, 1
[1, 1, 3, 2, 1, 1, 1, 3, 2] => 1, 1, 3, 2, 1, 1, 1, 3, 2
[1, 1, 3, 2, 1, 1, 1, 3, 3] => 1, 1, 3, 2, 1, 1, 1, 3, 3
[1, 1, 3, 2, 1, 1, 2, 1, 1] => 1, 1, 3, 2, 1, 1, 2, 1, 1
[1, 1, 3, 2, 1, 1, 2, 1, 2] => 1, 1, 3, 2, 1, 1, 2, 1, 2
[1, 1, 3, 2, 1, 1, 2, 1, 3] => 1, 1, 3, 2, 1, 1, 2, 1, 3
[1, 1, 3, 2, 1, 1, 2, 2, 1] => 1, 1, 3, 2, 1, 1, 2, 2, 1
[1, 1, 3, 2, 1, 1, 2, 2, 2] => 1, 1, 3, 2, 1, 1, 2, 2, 2
[1, 1, 3, 2, 1, 1, 2, 2, 3] => 1, 1, 3, 2, 1, 1, 2, 2, 3
[1, 1, 3, 2, 1, 1, 2, 3, 1] => 1, 1, 3, 2, 1, 1, 2, 3, 1
[1, 1, 3, 2, 1, 1, 2, 3, 2] => 1, 1, 3, 2, 1, 1, 2, 3, 2
[1, 1, 3, 2, 1, 1, 2, 3, 3] => 1, 1, 3, 2, 1, 1, 2, 3, 3
[1, 1, 3, 2, 1, 1, 3, 1, 1] => 1, 1, 3, 2, 1, 1, 3, 1, 1
[1, 1, 3, 2, 1, 1, 3, 1, 2] => 1, 1, 3, 2, 1, 1, 3, 1, 2
[1, 1, 3, 2, 1, 1, 3, 1, 3] => 1, 1, 3, 2, 1, 1, 3, 1, 3
[1, 1, 3, 2, 1, 1, 3, 2, 1] => 1, 1, 3, 2, 1, 1, 3, 2, 1
[1, 1, 3, 2, 1, 1, 3, 2, 2] => 1, 1, 3, 2, 1, 1, 3, 2, 2
[1, 1, 3, 2, 1, 1, 3, 2, 3] => 1, 1, 3, 2, 1, 1, 3, 2, 3
[1, 1, 3, 2, 1, 1, 3, 3, 1] => 1, 1, 3, 2, 1, 1, 3, 3, 1
[1, 1, 3, 2, 1, 1, 3, 3, 2] => 1, 1, 3, 2, 1, 1, 3, 3, 2
[1, 1, 3, 2, 1, 1, 3, 3, 3] => 1, 1, 3, 2, 1, 1, 3, 3, 3
[1, 1, 3, 2, 1, 2, 1, 1, 1] => 1, 1, 3, 2, 1, 2, 1, 1, 1
[1, 1, 3, 2, 1, 2, 1, 1, 2] => 1, 1, 3, 2, 1, 2, 1, 1, 2
[1, 1, 3, 2, 1, 2, 1, 1, 3] => 1, 1, 3, 2, 1, 2, 1, 1, 3
[1, 1, 3, 2, 1, 2, 1, 2, 1] => 1, 1, 3, 2, 1, 2, 1, 2, 1
[1, 1, 3, 2, 1, 2, 1, 2, 2] => 1, 1, 3, 2, 1, 2, 1, 2, 2
[1, 1, 3, 2, 1, 2, 1, 2, 3] => 1, 1, 3, 2, 1, 2, 1, 2, 3
[1, 1, 3, 2, 1, 2, 1, 3, 1] => 1, 1, 3, 2, 1, 2, 1, 3, 1
[1, 1, 3, 2, 1, 2, 1, 3, 2] => 1, 1, 3, 2, 1, 2, 1, 3, 2
[1, 1, 3, 2, 1, 2, 1, 3, 3] => 1, 1, 3, 2, 1, 2, 1, 3, 3
[1, 1, 3, 2, 1, 2, 2, 1, 1] => 1, 1, 3, 2, 1, 2, 2, 1, 1
[1, 1, 3, 2, 1, 2, 2, 1, 2] => 1, 1, 3, 2, 1, 2, 2, 1, 2
[1, 1, 3, 2, 1, 2, 2, 1, 3] => 1, 1, 3, 2, 1, 2, 2, 1, 3
[1, 1, 3, 2, 1, 2, 2, 2, 1] => 1, 1, 3, 2, 1, 2, 2, 2, 1
[1, 1, 3, 2, 1, 2, 2, 2, 2] => 1, 1, 3, 2, 1, 2, 2, 2, 2
[1, 1, 3, 2, 1, 2, 2, 2, 3] => 1, 1, 3, 2, 1, 2, 2, 2, 3
[1, 1, 3, 2, 1, 2, 2, 3, 1] => 1, 1, 3, 2, 1, 2, 2, 3, 1
[1, 1, 3, 2, 1, 2, 2, 3, 2] => 1, 1, 3, 2, 1, 2, 2, 3, 2
[1, 1, 3, 2, 1, 2, 2, 3, 3] => 1, 1, 3, 2, 1, 2, 2, 3, 3
[1, 1, 3, 2, 1, 2, 3, 1, 1] => 1, 1, 3, 2, 1, 2, 3, 1, 1
[1, 1, 3, 2, 1, 2, 3, 1, 2] => 1, 1, 3, 2, 1, 2, 3, 1, 2
[1, 1, 3, 2, 1, 2, 3, 1, 3] => 1, 1, 3, 2, 1, 2, 3, 1, 3
[1, 1, 3, 2, 1, 2, 3, 2, 1] => 1, 1, 3, 2, 1, 2, 3, 2, 1
[1, 1, 3, 2, 1, 2, 3, 2, 2] => 1, 1, 3, 2, 1, 2, 3, 2, 2
[1, 1, 3, 2, 1, 2, 3, 2, 3] => 1, 1, 3, 2, 1, 2, 3, 2, 3
[1, 1, 3, 2, 1, 2, 3, 3, 1] => 1, 1, 3, 2, 1, 2, 3, 3, 1
[1, 1, 3, 2, 1, 2, 3, 3, 2] => 1, 1, 3, 2, 1, 2, 3, 3, 2
[1, 1, 3, 2, 1, 2, 3, 3, 3] => 1, 1, 3, 2, 1, 2, 3, 3, 3
[1, 1, 3, 2, 1, 3, 1, 1, 1] => 1, 1, 3, 2, 1, 3, 1, 1, 1
[1, 1, 3, 2, 1, 3, 1, 1, 2] => 1, 1, 3, 2, 1, 3, 1, 1, 2
[1, 1, 3, 2, 1, 3, 1, 1, 3] => 1, 1, 3, 2, 1, 3, 1, 1, 3
[1, 1, 3, 2, 1, 3, 1, 2, 1] => 1, 1, 3, 2, 1, 3, 1, 2, 1
[1, 1, 3, 2, 1, 3, 1, 2, 2] => 1, 1, 3, 2, 1, 3, 1, 2, 2
[1, 1, 3, 2, 1, 3, 1, 2, 3] => 1, 1, 3, 2, 1, 3, 1, 2, 3
[1, 1, 3, 2, 1, 3, 1, 3, 1] => 1, 1, 3, 2, 1, 3, 1, 3, 1
[1, 1, 3, 2, 1, 3, 1, 3, 2] => 1, 1, 3, 2, 1, 3, 1, 3, 2
[1, 1, 3, 2, 1, 3, 1, 3, 3] => 1, 1, 3, 2, 1, 3, 1, 3, 3
[1, 1, 3, 2, 1, 3, 2, 1, 1] => 1, 1, 3, 2, 1, 3, 2, 1, 1
[1, 1, 3, 2, 1, 3, 2, 1, 2] => 1, 1, 3, 2, 1, 3, 2, 1, 2
[1, 1, 3, 2, 1, 3, 2, 1, 3] => 1, 1, 3, 2, 1, 3, 2, 1, 3
[1, 1, 3, 2, 1, 3, 2, 2, 1] => 1, 1, 3, 2, 1, 3, 2, 2, 1
[1, 1, 3, 2, 1, 3, 2, 2, 2] => 1, 1, 3, 2, 1, 3, 2, 2, 2
[1, 1, 3, 2, 1, 3, 2, 2, 3] => 1, 1, 3, 2, 1, 3, 2, 2, 3
[1, 1, 3, 2, 1, 3, 2, 3, 1] => 1, 1, 3, 2, 1, 3, 2, 3, 1
[1, 1, 3, 2, 1, 3, 2, 3, 2] => 1, 1, 3, 2, 1, 3, 2, 3, 2
[1, 1, 3, 2, 1, 3, 2, 3, 3] => 1, 1, 3, 2, 1, 3, 2, 3, 3
[1, 1, 3, 2, 1, 3, 3, 1, 1] => 1, 1, 3, 2, 1, 3, 3, 1, 1
[1, 1, 3, 2, 1, 3, 3, 1, 2] => 1, 1, 3, 2, 1, 3, 3, 1, 2
[1, 1, 3, 2, 1, 3, 3, 1, 3] => 1, 1, 3, 2, 1, 3, 3, 1, 3
[1, 1, 3, 2, 1, 3, 3, 2, 1] => 1, 1, 3, 2, 1, 3, 3, 2, 1
[1, 1, 3, 2, 1, 3, 3, 2, 2] => 1, 1, 3, 2, 1, 3, 3, 2, 2
[1, 1, 3, 2, 1, 3, 3, 2, 3] => 1, 1, 3, 2, 1, 3, 3, 2, 3
[1, 1, 3, 2, 1, 3, 3, 3, 1] => 1, 1, 3, 2, 1, 3, 3, 3, 1
[1, 1, 3, 2, 1, 3, 3, 3, 2] => 1, 1, 3, 2, 1, 3, 3, 3, 2
[1, 1, 3, 2, 1, 3, 3, 3, 3] => 1, 1, 3, 2, 1, 3, 3, 3, 3
[1, 1, 3, 2, 2, 1, 1, 1, 1] => 1, 1, 3, 2, 2, 1, 1, 1, 1
[1, 1, 3, 2, 2, 1, 1, 1, 2] => 1, 1, 3, 2, 2, 1, 1, 1, 2
[1, 1, 3, 2, 2, 1, 1, 1, 3] => 1, 1, 3, 2, 2, 1, 1, 1, 3
[1, 1, 3, 2, 2, 1, 1, 2, 1] => 1, 1, 3, 2, 2, 1, 1, 2, 1
[1, 1, 3, 2, 2, 1, 1, 2, 2] => 1, 1, 3, 2, 2, 1, 1, 2, 2
[1, 1, 3, 2, 2, 1, 1, 2, 3] => 1, 1, 3, 2, 2, 1, 1, 2, 3
[1, 1, 3, 2, 2, 1, 1, 3, 1] => 1, 1, 3, 2, 2, 1, 1, 3, 1
[1, 1, 3, 2, 2, 1, 1, 3, 2] => 1, 1, 3, 2, 2, 1, 1, 3, 2
[1, 1, 3, 2, 2, 1, 1, 3, 3] => 1, 1, 3, 2, 2, 1, 1, 3, 3
[1, 1, 3, 2, 2, 1, 2, 1, 1] => 1, 1, 3, 2, 2, 1, 2, 1, 1
[1, 1, 3, 2, 2, 1, 2, 1, 2] => 1, 1, 3, 2, 2, 1, 2, 1, 2
[1, 1, 3, 2, 2, 1, 2, 1, 3] => 1, 1, 3, 2, 2, 1, 2, 1, 3
[1, 1, 3, 2, 2, 1, 2, 2, 1] => 1, 1, 3, 2, 2, 1, 2, 2, 1
[1, 1, 3, 2, 2, 1, 2, 2, 2] => 1, 1, 3, 2, 2, 1, 2, 2, 2
[1, 1, 3, 2, 2, 1, 2, 2, 3] => 1, 1, 3, 2, 2, 1, 2, 2, 3
[1, 1, 3, 2, 2, 1, 2, 3, 1] => 1, 1, 3, 2, 2, 1, 2, 3, 1
[1, 1, 3, 2, 2, 1, 2, 3, 2] => 1, 1, 3, 2, 2, 1, 2, 3, 2
[1, 1, 3, 2, 2, 1, 2, 3, 3] => 1, 1, 3, 2, 2, 1, 2, 3, 3
[1, 1, 3, 2, 2, 1, 3, 1, 1] => 1, 1, 3, 2, 2, 1, 3, 1, 1
[1, 1, 3, 2, 2, 1, 3, 1, 2] => 1, 1, 3, 2, 2, 1, 3, 1, 2
[1, 1, 3, 2, 2, 1, 3, 1, 3] => 1, 1, 3, 2, 2, 1, 3, 1, 3
[1, 1, 3, 2, 2, 1, 3, 2, 1] => 1, 1, 3, 2, 2, 1, 3, 2, 1
[1, 1, 3, 2, 2, 1, 3, 2, 2] => 1, 1, 3, 2, 2, 1, 3, 2, 2
[1, 1, 3, 2, 2, 1, 3, 2, 3] => 1, 1, 3, 2, 2, 1, 3, 2, 3
[1, 1, 3, 2, 2, 1, 3, 3, 1] => 1, 1, 3, 2, 2, 1, 3, 3, 1
[1, 1, 3, 2, 2, 1, 3, 3, 2] => 1, 1, 3, 2, 2, 1, 3, 3, 2
[1, 1, 3, 2, 2, 1, 3, 3, 3] => 1, 1, 3, 2, 2, 1, 3, 3, 3
[1, 1, 3, 2, 2, 2, 1, 1, 1] => 1, 1, 3, 2, 2, 2, 1, 1, 1
[1, 1, 3, 2, 2, 2, 1, 1, 2] => 1, 1, 3, 2, 2, 2, 1, 1, 2
[1, 1, 3, 2, 2, 2, 1, 1, 3] => 1, 1, 3, 2, 2, 2, 1, 1, 3
[1, 1, 3, 2, 2, 2, 1, 2, 1] => 1, 1, 3, 2, 2, 2, 1, 2, 1
[1, 1, 3, 2, 2, 2, 1, 2, 2] => 1, 1, 3, 2, 2, 2, 1, 2, 2
[1, 1, 3, 2, 2, 2, 1, 2, 3] => 1, 1, 3, 2, 2, 2, 1, 2, 3
[1, 1, 3, 2, 2, 2, 1, 3, 1] => 1, 1, 3, 2, 2, 2, 1, 3, 1
[1, 1, 3, 2, 2, 2, 1, 3, 2] => 1, 1, 3, 2, 2, 2, 1, 3, 2
[1, 1, 3, 2, 2, 2, 1, 3, 3] => 1, 1, 3, 2, 2, 2, 1, 3, 3
[1, 1, 3, 2, 2, 2, 2, 1, 1] => 1, 1, 3, 2, 2, 2, 2, 1, 1
[1, 1, 3, 2, 2, 2, 2, 1, 2] => 1, 1, 3, 2, 2, 2, 2, 1, 2
[1, 1, 3, 2, 2, 2, 2, 1, 3] => 1, 1, 3, 2, 2, 2, 2, 1, 3
[1, 1, 3, 2, 2, 2, 2, 2, 1] => 1, 1, 3, 2, 2, 2, 2, 2, 1
[1, 1, 3, 2, 2, 2, 2, 2, 2] => 1, 1, 3, 2, 2, 2, 2, 2, 2
[1, 1, 3, 2, 2, 2, 2, 2, 3] => 1, 1, 3, 2, 2, 2, 2, 2, 3
[1, 1, 3, 2, 2, 2, 2, 3, 1] => 1, 1, 3, 2, 2, 2, 2, 3, 1
[1, 1, 3, 2, 2, 2, 2, 3, 2] => 1, 1, 3, 2, 2, 2, 2, 3, 2
[1, 1, 3, 2, 2, 2, 2, 3, 3] => 1, 1, 3, 2, 2, 2, 2, 3, 3
[1, 1, 3, 2, 2, 2, 3, 1, 1] => 1, 1, 3, 2, 2, 2, 3, 1, 1
[1, 1, 3, 2, 2, 2, 3, 1, 2] => 1, 1, 3, 2, 2, 2, 3, 1, 2
[1, 1, 3, 2, 2, 2, 3, 1, 3] => 1, 1, 3, 2, 2, 2, 3, 1, 3
[1, 1, 3, 2, 2, 2, 3, 2, 1] => 1, 1, 3, 2, 2, 2, 3, 2, 1
[1, 1, 3, 2, 2, 2, 3, 2, 2] => 1, 1, 3, 2, 2, 2, 3, 2, 2
[1, 1, 3, 2, 2, 2, 3, 2, 3] => 1, 1, 3, 2, 2, 2, 3, 2, 3
[1, 1, 3, 2, 2, 2, 3, 3, 1] => 1, 1, 3, 2, 2, 2, 3, 3, 1
[1, 1, 3, 2, 2, 2, 3, 3, 2] => 1, 1, 3, 2, 2, 2, 3, 3, 2
[1, 1, 3, 2, 2, 2, 3, 3, 3] => 1, 1, 3, 2, 2, 2, 3, 3, 3
[1, 1, 3, 2, 2, 3, 1, 1, 1] => 1, 1, 3, 2, 2, 3, 1, 1, 1
[1, 1, 3, 2, 2, 3, 1, 1, 2] => 1, 1, 3, 2, 2, 3, 1, 1, 2
[1, 1, 3, 2, 2, 3, 1, 1, 3] => 1, 1, 3, 2, 2, 3, 1, 1, 3
[1, 1, 3, 2, 2, 3, 1, 2, 1] => 1, 1, 3, 2, 2, 3, 1, 2, 1
[1, 1, 3, 2, 2, 3, 1, 2, 2] => 1, 1, 3, 2, 2, 3, 1, 2, 2
[1, 1, 3, 2, 2, 3, 1, 2, 3] => 1, 1, 3, 2, 2, 3, 1, 2, 3
[1, 1, 3, 2, 2, 3, 1, 3, 1] => 1, 1, 3, 2, 2, 3, 1, 3, 1
[1, 1, 3, 2, 2, 3, 1, 3, 2] => 1, 1, 3, 2, 2, 3, 1, 3, 2
[1, 1, 3, 2, 2, 3, 1, 3, 3] => 1, 1, 3, 2, 2, 3, 1, 3, 3
[1, 1, 3, 2, 2, 3, 2, 1, 1] => 1, 1, 3, 2, 2, 3, 2, 1, 1
[1, 1, 3, 2, 2, 3, 2, 1, 2] => 1, 1, 3, 2, 2, 3, 2, 1, 2
[1, 1, 3, 2, 2, 3, 2, 1, 3] => 1, 1, 3, 2, 2, 3, 2, 1, 3
[1, 1, 3, 2, 2, 3, 2, 2, 1] => 1, 1, 3, 2, 2, 3, 2, 2, 1
[1, 1, 3, 2, 2, 3, 2, 2, 2] => 1, 1, 3, 2, 2, 3, 2, 2, 2
[1, 1, 3, 2, 2, 3, 2, 2, 3] => 1, 1, 3, 2, 2, 3, 2, 2, 3
[1, 1, 3, 2, 2, 3, 2, 3, 1] => 1, 1, 3, 2, 2, 3, 2, 3, 1
[1, 1, 3, 2, 2, 3, 2, 3, 2] => 1, 1, 3, 2, 2, 3, 2, 3, 2
[1, 1, 3, 2, 2, 3, 2, 3, 3] => 1, 1, 3, 2, 2, 3, 2, 3, 3
[1, 1, 3, 2, 2, 3, 3, 1, 1] => 1, 1, 3, 2, 2, 3, 3, 1, 1
[1, 1, 3, 2, 2, 3, 3, 1, 2] => 1, 1, 3, 2, 2, 3, 3, 1, 2
[1, 1, 3, 2, 2, 3, 3, 1, 3] => 1, 1, 3, 2, 2, 3, 3, 1, 3
[1, 1, 3, 2, 2, 3, 3, 2, 1] => 1, 1, 3, 2, 2, 3, 3, 2, 1
[1, 1, 3, 2, 2, 3, 3, 2, 2] => 1, 1, 3, 2, 2, 3, 3, 2, 2
[1, 1, 3, 2, 2, 3, 3, 2, 3] => 1, 1, 3, 2, 2, 3, 3, 2, 3
[1, 1, 3, 2, 2, 3, 3, 3, 1] => 1, 1, 3, 2, 2, 3, 3, 3, 1
[1, 1, 3, 2, 2, 3, 3, 3, 2] => 1, 1, 3, 2, 2, 3, 3, 3, 2
[1, 1, 3, 2, 2, 3, 3, 3, 3] => 1, 1, 3, 2, 2, 3, 3, 3, 3
[1, 1, 3, 2, 3, 1, 1, 1, 1] => 1, 1, 3, 2, 3, 1, 1, 1, 1
[1, 1, 3, 2, 3, 1, 1, 1, 2] => 1, 1, 3, 2, 3, 1, 1, 1, 2
[1, 1, 3, 2, 3, 1, 1, 1, 3] => 1, 1, 3, 2, 3, 1, 1, 1, 3
[1, 1, 3, 2, 3, 1, 1, 2, 1] => 1, 1, 3, 2, 3, 1, 1, 2, 1
[1, 1, 3, 2, 3, 1, 1, 2, 2] => 1, 1, 3, 2, 3, 1, 1, 2, 2
[1, 1, 3, 2, 3, 1, 1, 2, 3] => 1, 1, 3, 2, 3, 1, 1, 2, 3
[1, 1, 3, 2, 3, 1, 1, 3, 1] => 1, 1, 3, 2, 3, 1, 1, 3, 1
[1, 1, 3, 2, 3, 1, 1, 3, 2] => 1, 1, 3, 2, 3, 1, 1, 3, 2
[1, 1, 3, 2, 3, 1, 1, 3, 3] => 1, 1, 3, 2, 3, 1, 1, 3, 3
[1, 1, 3, 2, 3, 1, 2, 1, 1] => 1, 1, 3, 2, 3, 1, 2, 1, 1
[1, 1, 3, 2, 3, 1, 2, 1, 2] => 1, 1, 3, 2, 3, 1, 2, 1, 2
[1, 1, 3, 2, 3, 1, 2, 1, 3] => 1, 1, 3, 2, 3, 1, 2, 1, 3
[1, 1, 3, 2, 3, 1, 2, 2, 1] => 1, 1, 3, 2, 3, 1, 2, 2, 1
[1, 1, 3, 2, 3, 1, 2, 2, 2] => 1, 1, 3, 2, 3, 1, 2, 2, 2
[1, 1, 3, 2, 3, 1, 2, 2, 3] => 1, 1, 3, 2, 3, 1, 2, 2, 3
[1, 1, 3, 2, 3, 1, 2, 3, 1] => 1, 1, 3, 2, 3, 1, 2, 3, 1
[1, 1, 3, 2, 3, 1, 2, 3, 2] => 1, 1, 3, 2, 3, 1, 2, 3, 2
[1, 1, 3, 2, 3, 1, 2, 3, 3] => 1, 1, 3, 2, 3, 1, 2, 3, 3
[1, 1, 3, 2, 3, 1, 3, 1, 1] => 1, 1, 3, 2, 3, 1, 3, 1, 1
[1, 1, 3, 2, 3, 1, 3, 1, 2] => 1, 1, 3, 2, 3, 1, 3, 1, 2
[1, 1, 3, 2, 3, 1, 3, 1, 3] => 1, 1, 3, 2, 3, 1, 3, 1, 3
[1, 1, 3, 2, 3, 1, 3, 2, 1] => 1, 1, 3, 2, 3, 1, 3, 2, 1
[1, 1, 3, 2, 3, 1, 3, 2, 2] => 1, 1, 3, 2, 3, 1, 3, 2, 2
[1, 1, 3, 2, 3, 1, 3, 2, 3] => 1, 1, 3, 2, 3, 1, 3, 2, 3
[1, 1, 3, 2, 3, 1, 3, 3, 1] => 1, 1, 3, 2, 3, 1, 3, 3, 1
[1, 1, 3, 2, 3, 1, 3, 3, 2] => 1, 1, 3, 2, 3, 1, 3, 3, 2
[1, 1, 3, 2, 3, 1, 3, 3, 3] => 1, 1, 3, 2, 3, 1, 3, 3, 3
[1, 1, 3, 2, 3, 2, 1, 1, 1] => 1, 1, 3, 2, 3, 2, 1, 1, 1
[1, 1, 3, 2, 3, 2, 1, 1, 2] => 1, 1, 3, 2, 3, 2, 1, 1, 2
[1, 1, 3, 2, 3, 2, 1, 1, 3] => 1, 1, 3, 2, 3, 2, 1, 1, 3
[1, 1, 3, 2, 3, 2, 1, 2, 1] => 1, 1, 3, 2, 3, 2, 1, 2, 1
[1, 1, 3, 2, 3, 2, 1, 2, 2] => 1, 1, 3, 2, 3, 2, 1, 2, 2
[1, 1, 3, 2, 3, 2, 1, 2, 3] => 1, 1, 3, 2, 3, 2, 1, 2, 3
[1, 1, 3, 2, 3, 2, 1, 3, 1] => 1, 1, 3, 2, 3, 2, 1, 3, 1
[1, 1, 3, 2, 3, 2, 1, 3, 2] => 1, 1, 3, 2, 3, 2, 1, 3, 2
[1, 1, 3, 2, 3, 2, 1, 3, 3] => 1, 1, 3, 2, 3, 2, 1, 3, 3
[1, 1, 3, 2, 3, 2, 2, 1, 1] => 1, 1, 3, 2, 3, 2, 2, 1, 1
[1, 1, 3, 2, 3, 2, 2, 1, 2] => 1, 1, 3, 2, 3, 2, 2, 1, 2
[1, 1, 3, 2, 3, 2, 2, 1, 3] => 1, 1, 3, 2, 3, 2, 2, 1, 3
[1, 1, 3, 2, 3, 2, 2, 2, 1] => 1, 1, 3, 2, 3, 2, 2, 2, 1
[1, 1, 3, 2, 3, 2, 2, 2, 2] => 1, 1, 3, 2, 3, 2, 2, 2, 2
[1, 1, 3, 2, 3, 2, 2, 2, 3] => 1, 1, 3, 2, 3, 2, 2, 2, 3
[1, 1, 3, 2, 3, 2, 2, 3, 1] => 1, 1, 3, 2, 3, 2, 2, 3, 1
[1, 1, 3, 2, 3, 2, 2, 3, 2] => 1, 1, 3, 2, 3, 2, 2, 3, 2
[1, 1, 3, 2, 3, 2, 2, 3, 3] => 1, 1, 3, 2, 3, 2, 2, 3, 3
[1, 1, 3, 2, 3, 2, 3, 1, 1] => 1, 1, 3, 2, 3, 2, 3, 1, 1
[1, 1, 3, 2, 3, 2, 3, 1, 2] => 1, 1, 3, 2, 3, 2, 3, 1, 2
[1, 1, 3, 2, 3, 2, 3, 1, 3] => 1, 1, 3, 2, 3, 2, 3, 1, 3
[1, 1, 3, 2, 3, 2, 3, 2, 1] => 1, 1, 3, 2, 3, 2, 3, 2, 1
[1, 1, 3, 2, 3, 2, 3, 2, 2] => 1, 1, 3, 2, 3, 2, 3, 2, 2
[1, 1, 3, 2, 3, 2, 3, 2, 3] => 1, 1, 3, 2, 3, 2, 3, 2, 3
[1, 1, 3, 2, 3, 2, 3, 3, 1] => 1, 1, 3, 2, 3, 2, 3, 3, 1
[1, 1, 3, 2, 3, 2, 3, 3, 2] => 1, 1, 3, 2, 3, 2, 3, 3, 2
[1, 1, 3, 2, 3, 2, 3, 3, 3] => 1, 1, 3, 2, 3, 2, 3, 3, 3
[1, 1, 3, 2, 3, 3, 1, 1, 1] => 1, 1, 3, 2, 3, 3, 1, 1, 1
[1, 1, 3, 2, 3, 3, 1, 1, 2] => 1, 1, 3, 2, 3, 3, 1, 1, 2
[1, 1, 3, 2, 3, 3, 1, 1, 3] => 1, 1, 3, 2, 3, 3, 1, 1, 3
[1, 1, 3, 2, 3, 3, 1, 2, 1] => 1, 1, 3, 2, 3, 3, 1, 2, 1
[1, 1, 3, 2, 3, 3, 1, 2, 2] => 1, 1, 3, 2, 3, 3, 1, 2, 2
[1, 1, 3, 2, 3, 3, 1, 2, 3] => 1, 1, 3, 2, 3, 3, 1, 2, 3
[1, 1, 3, 2, 3, 3, 1, 3, 1] => 1, 1, 3, 2, 3, 3, 1, 3, 1
[1, 1, 3, 2, 3, 3, 1, 3, 2] => 1, 1, 3, 2, 3, 3, 1, 3, 2
[1, 1, 3, 2, 3, 3, 1, 3, 3] => 1, 1, 3, 2, 3, 3, 1, 3, 3
[1, 1, 3, 2, 3, 3, 2, 1, 1] => 1, 1, 3, 2, 3, 3, 2, 1, 1
[1, 1, 3, 2, 3, 3, 2, 1, 2] => 1, 1, 3, 2, 3, 3, 2, 1, 2
[1, 1, 3, 2, 3, 3, 2, 1, 3] => 1, 1, 3, 2, 3, 3, 2, 1, 3
[1, 1, 3, 2, 3, 3, 2, 2, 1] => 1, 1, 3, 2, 3, 3, 2, 2, 1
[1, 1, 3, 2, 3, 3, 2, 2, 2] => 1, 1, 3, 2, 3, 3, 2, 2, 2
[1, 1, 3, 2, 3, 3, 2, 2, 3] => 1, 1, 3, 2, 3, 3, 2, 2, 3
[1, 1, 3, 2, 3, 3, 2, 3, 1] => 1, 1, 3, 2, 3, 3, 2, 3, 1
[1, 1, 3, 2, 3, 3, 2, 3, 2] => 1, 1, 3, 2, 3, 3, 2, 3, 2
[1, 1, 3, 2, 3, 3, 2, 3, 3] => 1, 1, 3, 2, 3, 3, 2, 3, 3
[1, 1, 3, 2, 3, 3, 3, 1, 1] => 1, 1, 3, 2, 3, 3, 3, 1, 1
[1, 1, 3, 2, 3, 3, 3, 1, 2] => 1, 1, 3, 2, 3, 3, 3, 1, 2
[1, 1, 3, 2, 3, 3, 3, 1, 3] => 1, 1, 3, 2, 3, 3, 3, 1, 3
[1, 1, 3, 2, 3, 3, 3, 2, 1] => 1, 1, 3, 2, 3, 3, 3, 2, 1
[1, 1, 3, 2, 3, 3, 3, 2, 2] => 1, 1, 3, 2, 3, 3, 3, 2, 2
[1, 1, 3, 2, 3, 3, 3, 2, 3] => 1, 1, 3, 2, 3, 3, 3, 2, 3
[1, 1, 3, 2, 3, 3, 3, 3, 1] => 1, 1, 3, 2, 3, 3, 3, 3, 1
[1, 1, 3, 2, 3, 3, 3, 3, 2] => 1, 1, 3, 2, 3, 3, 3, 3, 2
[1, 1, 3, 2, 3, 3, 3, 3, 3] => 1, 1, 3, 2, 3, 3, 3, 3, 3
[1, 1, 3, 3, 1, 1, 1, 1, 1] => 1, 1, 3, 3, 1, 1, 1, 1, 1
[1, 1, 3, 3, 1, 1, 1, 1, 2] => 1, 1, 3, 3, 1, 1, 1, 1, 2
[1, 1, 3, 3, 1, 1, 1, 1, 3] => 1, 1, 3, 3, 1, 1, 1, 1, 3
[1, 1, 3, 3, 1, 1, 1, 2, 1] => 1, 1, 3, 3, 1, 1, 1, 2, 1
[1, 1, 3, 3, 1, 1, 1, 2, 2] => 1, 1, 3, 3, 1, 1, 1, 2, 2
[1, 1, 3, 3, 1, 1, 1, 2, 3] => 1, 1, 3, 3, 1, 1, 1, 2, 3
[1, 1, 3, 3, 1, 1, 1, 3, 1] => 1, 1, 3, 3, 1, 1, 1, 3, 1
[1, 1, 3, 3, 1, 1, 1, 3, 2] => 1, 1, 3, 3, 1, 1, 1, 3, 2
[1, 1, 3, 3, 1, 1, 1, 3, 3] => 1, 1, 3, 3, 1, 1, 1, 3, 3
[1, 1, 3, 3, 1, 1, 2, 1, 1] => 1, 1, 3, 3, 1, 1, 2, 1, 1
[1, 1, 3, 3, 1, 1, 2, 1, 2] => 1, 1, 3, 3, 1, 1, 2, 1, 2
[1, 1, 3, 3, 1, 1, 2, 1, 3] => 1, 1, 3, 3, 1, 1, 2, 1, 3
[1, 1, 3, 3, 1, 1, 2, 2, 1] => 1, 1, 3, 3, 1, 1, 2, 2, 1
[1, 1, 3, 3, 1, 1, 2, 2, 2] => 1, 1, 3, 3, 1, 1, 2, 2, 2
[1, 1, 3, 3, 1, 1, 2, 2, 3] => 1, 1, 3, 3, 1, 1, 2, 2, 3
[1, 1, 3, 3, 1, 1, 2, 3, 1] => 1, 1, 3, 3, 1, 1, 2, 3, 1
[1, 1, 3, 3, 1, 1, 2, 3, 2] => 1, 1, 3, 3, 1, 1, 2, 3, 2
[1, 1, 3, 3, 1, 1, 2, 3, 3] => 1, 1, 3, 3, 1, 1, 2, 3, 3
[1, 1, 3, 3, 1, 1, 3, 1, 1] => 1, 1, 3, 3, 1, 1, 3, 1, 1
[1, 1, 3, 3, 1, 1, 3, 1, 2] => 1, 1, 3, 3, 1, 1, 3, 1, 2
[1, 1, 3, 3, 1, 1, 3, 1, 3] => 1, 1, 3, 3, 1, 1, 3, 1, 3
[1, 1, 3, 3, 1, 1, 3, 2, 1] => 1, 1, 3, 3, 1, 1, 3, 2, 1
[1, 1, 3, 3, 1, 1, 3, 2, 2] => 1, 1, 3, 3, 1, 1, 3, 2, 2
[1, 1, 3, 3, 1, 1, 3, 2, 3] => 1, 1, 3, 3, 1, 1, 3, 2, 3
[1, 1, 3, 3, 1, 1, 3, 3, 1] => 1, 1, 3, 3, 1, 1, 3, 3, 1
[1, 1, 3, 3, 1, 1, 3, 3, 2] => 1, 1, 3, 3, 1, 1, 3, 3, 2
[1, 1, 3, 3, 1, 1, 3, 3, 3] => 1, 1, 3, 3, 1, 1, 3, 3, 3
[1, 1, 3, 3, 1, 2, 1, 1, 1] => 1, 1, 3, 3, 1, 2, 1, 1, 1
[1, 1, 3, 3, 1, 2, 1, 1, 2] => 1, 1, 3, 3, 1, 2, 1, 1, 2
[1, 1, 3, 3, 1, 2, 1, 1, 3] => 1, 1, 3, 3, 1, 2, 1, 1, 3
[1, 1, 3, 3, 1, 2, 1, 2, 1] => 1, 1, 3, 3, 1, 2, 1, 2, 1
[1, 1, 3, 3, 1, 2, 1, 2, 2] => 1, 1, 3, 3, 1, 2, 1, 2, 2
[1, 1, 3, 3, 1, 2, 1, 2, 3] => 1, 1, 3, 3, 1, 2, 1, 2, 3
[1, 1, 3, 3, 1, 2, 1, 3, 1] => 1, 1, 3, 3, 1, 2, 1, 3, 1
[1, 1, 3, 3, 1, 2, 1, 3, 2] => 1, 1, 3, 3, 1, 2, 1, 3, 2
[1, 1, 3, 3, 1, 2, 1, 3, 3] => 1, 1, 3, 3, 1, 2, 1, 3, 3
[1, 1, 3, 3, 1, 2, 2, 1, 1] => 1, 1, 3, 3, 1, 2, 2, 1, 1
[1, 1, 3, 3, 1, 2, 2, 1, 2] => 1, 1, 3, 3, 1, 2, 2, 1, 2
[1, 1, 3, 3, 1, 2, 2, 1, 3] => 1, 1, 3, 3, 1, 2, 2, 1, 3
[1, 1, 3, 3, 1, 2, 2, 2, 1] => 1, 1, 3, 3, 1, 2, 2, 2, 1
[1, 1, 3, 3, 1, 2, 2, 2, 2] => 1, 1, 3, 3, 1, 2, 2, 2, 2
[1, 1, 3, 3, 1, 2, 2, 2, 3] => 1, 1, 3, 3, 1, 2, 2, 2, 3
[1, 1, 3, 3, 1, 2, 2, 3, 1] => 1, 1, 3, 3, 1, 2, 2, 3, 1
[1, 1, 3, 3, 1, 2, 2, 3, 2] => 1, 1, 3, 3, 1, 2, 2, 3, 2
[1, 1, 3, 3, 1, 2, 2, 3, 3] => 1, 1, 3, 3, 1, 2, 2, 3, 3
[1, 1, 3, 3, 1, 2, 3, 1, 1] => 1, 1, 3, 3, 1, 2, 3, 1, 1
[1, 1, 3, 3, 1, 2, 3, 1, 2] => 1, 1, 3, 3, 1, 2, 3, 1, 2
[1, 1, 3, 3, 1, 2, 3, 1, 3] => 1, 1, 3, 3, 1, 2, 3, 1, 3
[1, 1, 3, 3, 1, 2, 3, 2, 1] => 1, 1, 3, 3, 1, 2, 3, 2, 1
[1, 1, 3, 3, 1, 2, 3, 2, 2] => 1, 1, 3, 3, 1, 2, 3, 2, 2
[1, 1, 3, 3, 1, 2, 3, 2, 3] => 1, 1, 3, 3, 1, 2, 3, 2, 3
[1, 1, 3, 3, 1, 2, 3, 3, 1] => 1, 1, 3, 3, 1, 2, 3, 3, 1
[1, 1, 3, 3, 1, 2, 3, 3, 2] => 1, 1, 3, 3, 1, 2, 3, 3, 2
[1, 1, 3, 3, 1, 2, 3, 3, 3] => 1, 1, 3, 3, 1, 2, 3, 3, 3
[1, 1, 3, 3, 1, 3, 1, 1, 1] => 1, 1, 3, 3, 1, 3, 1, 1, 1
[1, 1, 3, 3, 1, 3, 1, 1, 2] => 1, 1, 3, 3, 1, 3, 1, 1, 2
[1, 1, 3, 3, 1, 3, 1, 1, 3] => 1, 1, 3, 3, 1, 3, 1, 1, 3
[1, 1, 3, 3, 1, 3, 1, 2, 1] => 1, 1, 3, 3, 1, 3, 1, 2, 1
[1, 1, 3, 3, 1, 3, 1, 2, 2] => 1, 1, 3, 3, 1, 3, 1, 2, 2
[1, 1, 3, 3, 1, 3, 1, 2, 3] => 1, 1, 3, 3, 1, 3, 1, 2, 3
[1, 1, 3, 3, 1, 3, 1, 3, 1] => 1, 1, 3, 3, 1, 3, 1, 3, 1
[1, 1, 3, 3, 1, 3, 1, 3, 2] => 1, 1, 3, 3, 1, 3, 1, 3, 2
[1, 1, 3, 3, 1, 3, 1, 3, 3] => 1, 1, 3, 3, 1, 3, 1, 3, 3
[1, 1, 3, 3, 1, 3, 2, 1, 1] => 1, 1, 3, 3, 1, 3, 2, 1, 1
[1, 1, 3, 3, 1, 3, 2, 1, 2] => 1, 1, 3, 3, 1, 3, 2, 1, 2
[1, 1, 3, 3, 1, 3, 2, 1, 3] => 1, 1, 3, 3, 1, 3, 2, 1, 3
[1, 1, 3, 3, 1, 3, 2, 2, 1] => 1, 1, 3, 3, 1, 3, 2, 2, 1
[1, 1, 3, 3, 1, 3, 2, 2, 2] => 1, 1, 3, 3, 1, 3, 2, 2, 2
[1, 1, 3, 3, 1, 3, 2, 2, 3] => 1, 1, 3, 3, 1, 3, 2, 2, 3
[1, 1, 3, 3, 1, 3, 2, 3, 1] => 1, 1, 3, 3, 1, 3, 2, 3, 1
[1, 1, 3, 3, 1, 3, 2, 3, 2] => 1, 1, 3, 3, 1, 3, 2, 3, 2
[1, 1, 3, 3, 1, 3, 2, 3, 3] => 1, 1, 3, 3, 1, 3, 2, 3, 3
[1, 1, 3, 3, 1, 3, 3, 1, 1] => 1, 1, 3, 3, 1, 3, 3, 1, 1
[1, 1, 3, 3, 1, 3, 3, 1, 2] => 1, 1, 3, 3, 1, 3, 3, 1, 2
[1, 1, 3, 3, 1, 3, 3, 1, 3] => 1, 1, 3, 3, 1, 3, 3, 1, 3
[1, 1, 3, 3, 1, 3, 3, 2, 1] => 1, 1, 3, 3, 1, 3, 3, 2, 1
[1, 1, 3, 3, 1, 3, 3, 2, 2] => 1, 1, 3, 3, 1, 3, 3, 2, 2
[1, 1, 3, 3, 1, 3, 3, 2, 3] => 1, 1, 3, 3, 1, 3, 3, 2, 3
[1, 1, 3, 3, 1, 3, 3, 3, 1] => 1, 1, 3, 3, 1, 3, 3, 3, 1
[1, 1, 3, 3, 1, 3, 3, 3, 2] => 1, 1, 3, 3, 1, 3, 3, 3, 2
[1, 1, 3, 3, 1, 3, 3, 3, 3] => 1, 1, 3, 3, 1, 3, 3, 3, 3
[1, 1, 3, 3, 2, 1, 1, 1, 1] => 1, 1, 3, 3, 2, 1, 1, 1, 1
[1, 1, 3, 3, 2, 1, 1, 1, 2] => 1, 1, 3, 3, 2, 1, 1, 1, 2
[1, 1, 3, 3, 2, 1, 1, 1, 3] => 1, 1, 3, 3, 2, 1, 1, 1, 3
[1, 1, 3, 3, 2, 1, 1, 2, 1] => 1, 1, 3, 3, 2, 1, 1, 2, 1
[1, 1, 3, 3, 2, 1, 1, 2, 2] => 1, 1, 3, 3, 2, 1, 1, 2, 2
[1, 1, 3, 3, 2, 1, 1, 2, 3] => 1, 1, 3, 3, 2, 1, 1, 2, 3
[1, 1, 3, 3, 2, 1, 1, 3, 1] => 1, 1, 3, 3, 2, 1, 1, 3, 1
[1, 1, 3, 3, 2, 1, 1, 3, 2] => 1, 1, 3, 3, 2, 1, 1, 3, 2
[1, 1, 3, 3, 2, 1, 1, 3, 3] => 1, 1, 3, 3, 2, 1, 1, 3, 3
[1, 1, 3, 3, 2, 1, 2, 1, 1] => 1, 1, 3, 3, 2, 1, 2, 1, 1
[1, 1, 3, 3, 2, 1, 2, 1, 2] => 1, 1, 3, 3, 2, 1, 2, 1, 2
[1, 1, 3, 3, 2, 1, 2, 1, 3] => 1, 1, 3, 3, 2, 1, 2, 1, 3
[1, 1, 3, 3, 2, 1, 2, 2, 1] => 1, 1, 3, 3, 2, 1, 2, 2, 1
[1, 1, 3, 3, 2, 1, 2, 2, 2] => 1, 1, 3, 3, 2, 1, 2, 2, 2
[1, 1, 3, 3, 2, 1, 2, 2, 3] => 1, 1, 3, 3, 2, 1, 2, 2, 3
[1, 1, 3, 3, 2, 1, 2, 3, 1] => 1, 1, 3, 3, 2, 1, 2, 3, 1
[1, 1, 3, 3, 2, 1, 2, 3, 2] => 1, 1, 3, 3, 2, 1, 2, 3, 2
[1, 1, 3, 3, 2, 1, 2, 3, 3] => 1, 1, 3, 3, 2, 1, 2, 3, 3
[1, 1, 3, 3, 2, 1, 3, 1, 1] => 1, 1, 3, 3, 2, 1, 3, 1, 1
[1, 1, 3, 3, 2, 1, 3, 1, 2] => 1, 1, 3, 3, 2, 1, 3, 1, 2
[1, 1, 3, 3, 2, 1, 3, 1, 3] => 1, 1, 3, 3, 2, 1, 3, 1, 3
[1, 1, 3, 3, 2, 1, 3, 2, 1] => 1, 1, 3, 3, 2, 1, 3, 2, 1
[1, 1, 3, 3, 2, 1, 3, 2, 2] => 1, 1, 3, 3, 2, 1, 3, 2, 2
[1, 1, 3, 3, 2, 1, 3, 2, 3] => 1, 1, 3, 3, 2, 1, 3, 2, 3
[1, 1, 3, 3, 2, 1, 3, 3, 1] => 1, 1, 3, 3, 2, 1, 3, 3, 1
[1, 1, 3, 3, 2, 1, 3, 3, 2] => 1, 1, 3, 3, 2, 1, 3, 3, 2
[1, 1, 3, 3, 2, 1, 3, 3, 3] => 1, 1, 3, 3, 2, 1, 3, 3, 3
[1, 1, 3, 3, 2, 2, 1, 1, 1] => 1, 1, 3, 3, 2, 2, 1, 1, 1
[1, 1, 3, 3, 2, 2, 1, 1, 2] => 1, 1, 3, 3, 2, 2, 1, 1, 2
[1, 1, 3, 3, 2, 2, 1, 1, 3] => 1, 1, 3, 3, 2, 2, 1, 1, 3
[1, 1, 3, 3, 2, 2, 1, 2, 1] => 1, 1, 3, 3, 2, 2, 1, 2, 1
[1, 1, 3, 3, 2, 2, 1, 2, 2] => 1, 1, 3, 3, 2, 2, 1, 2, 2
[1, 1, 3, 3, 2, 2, 1, 2, 3] => 1, 1, 3, 3, 2, 2, 1, 2, 3
[1, 1, 3, 3, 2, 2, 1, 3, 1] => 1, 1, 3, 3, 2, 2, 1, 3, 1
[1, 1, 3, 3, 2, 2, 1, 3, 2] => 1, 1, 3, 3, 2, 2, 1, 3, 2
[1, 1, 3, 3, 2, 2, 1, 3, 3] => 1, 1, 3, 3, 2, 2, 1, 3, 3
[1, 1, 3, 3, 2, 2, 2, 1, 1] => 1, 1, 3, 3, 2, 2, 2, 1, 1
[1, 1, 3, 3, 2, 2, 2, 1, 2] => 1, 1, 3, 3, 2, 2, 2, 1, 2
[1, 1, 3, 3, 2, 2, 2, 1, 3] => 1, 1, 3, 3, 2, 2, 2, 1, 3
[1, 1, 3, 3, 2, 2, 2, 2, 1] => 1, 1, 3, 3, 2, 2, 2, 2, 1
[1, 1, 3, 3, 2, 2, 2, 2, 2] => 1, 1, 3, 3, 2, 2, 2, 2, 2
[1, 1, 3, 3, 2, 2, 2, 2, 3] => 1, 1, 3, 3, 2, 2, 2, 2, 3
[1, 1, 3, 3, 2, 2, 2, 3, 1] => 1, 1, 3, 3, 2, 2, 2, 3, 1
[1, 1, 3, 3, 2, 2, 2, 3, 2] => 1, 1, 3, 3, 2, 2, 2, 3, 2
[1, 1, 3, 3, 2, 2, 2, 3, 3] => 1, 1, 3, 3, 2, 2, 2, 3, 3
[1, 1, 3, 3, 2, 2, 3, 1, 1] => 1, 1, 3, 3, 2, 2, 3, 1, 1
[1, 1, 3, 3, 2, 2, 3, 1, 2] => 1, 1, 3, 3, 2, 2, 3, 1, 2
[1, 1, 3, 3, 2, 2, 3, 1, 3] => 1, 1, 3, 3, 2, 2, 3, 1, 3
[1, 1, 3, 3, 2, 2, 3, 2, 1] => 1, 1, 3, 3, 2, 2, 3, 2, 1
[1, 1, 3, 3, 2, 2, 3, 2, 2] => 1, 1, 3, 3, 2, 2, 3, 2, 2
[1, 1, 3, 3, 2, 2, 3, 2, 3] => 1, 1, 3, 3, 2, 2, 3, 2, 3
[1, 1, 3, 3, 2, 2, 3, 3, 1] => 1, 1, 3, 3, 2, 2, 3, 3, 1
[1, 1, 3, 3, 2, 2, 3, 3, 2] => 1, 1, 3, 3, 2, 2, 3, 3, 2
[1, 1, 3, 3, 2, 2, 3, 3, 3] => 1, 1, 3, 3, 2, 2, 3, 3, 3
[1, 1, 3, 3, 2, 3, 1, 1, 1] => 1, 1, 3, 3, 2, 3, 1, 1, 1
[1, 1, 3, 3, 2, 3, 1, 1, 2] => 1, 1, 3, 3, 2, 3, 1, 1, 2
[1, 1, 3, 3, 2, 3, 1, 1, 3] => 1, 1, 3, 3, 2, 3, 1, 1, 3
[1, 1, 3, 3, 2, 3, 1, 2, 1] => 1, 1, 3, 3, 2, 3, 1, 2, 1
[1, 1, 3, 3, 2, 3, 1, 2, 2] => 1, 1, 3, 3, 2, 3, 1, 2, 2
[1, 1, 3, 3, 2, 3, 1, 2, 3] => 1, 1, 3, 3, 2, 3, 1, 2, 3
[1, 1, 3, 3, 2, 3, 1, 3, 1] => 1, 1, 3, 3, 2, 3, 1, 3, 1
[1, 1, 3, 3, 2, 3, 1, 3, 2] => 1, 1, 3, 3, 2, 3, 1, 3, 2
[1, 1, 3, 3, 2, 3, 1, 3, 3] => 1, 1, 3, 3, 2, 3, 1, 3, 3
[1, 1, 3, 3, 2, 3, 2, 1, 1] => 1, 1, 3, 3, 2, 3, 2, 1, 1
[1, 1, 3, 3, 2, 3, 2, 1, 2] => 1, 1, 3, 3, 2, 3, 2, 1, 2
[1, 1, 3, 3, 2, 3, 2, 1, 3] => 1, 1, 3, 3, 2, 3, 2, 1, 3
[1, 1, 3, 3, 2, 3, 2, 2, 1] => 1, 1, 3, 3, 2, 3, 2, 2, 1
[1, 1, 3, 3, 2, 3, 2, 2, 2] => 1, 1, 3, 3, 2, 3, 2, 2, 2
[1, 1, 3, 3, 2, 3, 2, 2, 3] => 1, 1, 3, 3, 2, 3, 2, 2, 3
[1, 1, 3, 3, 2, 3, 2, 3, 1] => 1, 1, 3, 3, 2, 3, 2, 3, 1
[1, 1, 3, 3, 2, 3, 2, 3, 2] => 1, 1, 3, 3, 2, 3, 2, 3, 2
[1, 1, 3, 3, 2, 3, 2, 3, 3] => 1, 1, 3, 3, 2, 3, 2, 3, 3
[1, 1, 3, 3, 2, 3, 3, 1, 1] => 1, 1, 3, 3, 2, 3, 3, 1, 1
[1, 1, 3, 3, 2, 3, 3, 1, 2] => 1, 1, 3, 3, 2, 3, 3, 1, 2
[1, 1, 3, 3, 2, 3, 3, 1, 3] => 1, 1, 3, 3, 2, 3, 3, 1, 3
[1, 1, 3, 3, 2, 3, 3, 2, 1] => 1, 1, 3, 3, 2, 3, 3, 2, 1
[1, 1, 3, 3, 2, 3, 3, 2, 2] => 1, 1, 3, 3, 2, 3, 3, 2, 2
[1, 1, 3, 3, 2, 3, 3, 2, 3] => 1, 1, 3, 3, 2, 3, 3, 2, 3
[1, 1, 3, 3, 2, 3, 3, 3, 1] => 1, 1, 3, 3, 2, 3, 3, 3, 1
[1, 1, 3, 3, 2, 3, 3, 3, 2] => 1, 1, 3, 3, 2, 3, 3, 3, 2
[1, 1, 3, 3, 2, 3, 3, 3, 3] => 1, 1, 3, 3, 2, 3, 3, 3, 3
[1, 1, 3, 3, 3, 1, 1, 1, 1] => 1, 1, 3, 3, 3, 1, 1, 1, 1
[1, 1, 3, 3, 3, 1, 1, 1, 2] => 1, 1, 3, 3, 3, 1, 1, 1, 2
[1, 1, 3, 3, 3, 1, 1, 1, 3] => 1, 1, 3, 3, 3, 1, 1, 1, 3
[1, 1, 3, 3, 3, 1, 1, 2, 1] => 1, 1, 3, 3, 3, 1, 1, 2, 1
[1, 1, 3, 3, 3, 1, 1, 2, 2] => 1, 1, 3, 3, 3, 1, 1, 2, 2
[1, 1, 3, 3, 3, 1, 1, 2, 3] => 1, 1, 3, 3, 3, 1, 1, 2, 3
[1, 1, 3, 3, 3, 1, 1, 3, 1] => 1, 1, 3, 3, 3, 1, 1, 3, 1
[1, 1, 3, 3, 3, 1, 1, 3, 2] => 1, 1, 3, 3, 3, 1, 1, 3, 2
[1, 1, 3, 3, 3, 1, 1, 3, 3] => 1, 1, 3, 3, 3, 1, 1, 3, 3
[1, 1, 3, 3, 3, 1, 2, 1, 1] => 1, 1, 3, 3, 3, 1, 2, 1, 1
[1, 1, 3, 3, 3, 1, 2, 1, 2] => 1, 1, 3, 3, 3, 1, 2, 1, 2
[1, 1, 3, 3, 3, 1, 2, 1, 3] => 1, 1, 3, 3, 3, 1, 2, 1, 3
[1, 1, 3, 3, 3, 1, 2, 2, 1] => 1, 1, 3, 3, 3, 1, 2, 2, 1
[1, 1, 3, 3, 3, 1, 2, 2, 2] => 1, 1, 3, 3, 3, 1, 2, 2, 2
[1, 1, 3, 3, 3, 1, 2, 2, 3] => 1, 1, 3, 3, 3, 1, 2, 2, 3
[1, 1, 3, 3, 3, 1, 2, 3, 1] => 1, 1, 3, 3, 3, 1, 2, 3, 1
[1, 1, 3, 3, 3, 1, 2, 3, 2] => 1, 1, 3, 3, 3, 1, 2, 3, 2
[1, 1, 3, 3, 3, 1, 2, 3, 3] => 1, 1, 3, 3, 3, 1, 2, 3, 3
[1, 1, 3, 3, 3, 1, 3, 1, 1] => 1, 1, 3, 3, 3, 1, 3, 1, 1
[1, 1, 3, 3, 3, 1, 3, 1, 2] => 1, 1, 3, 3, 3, 1, 3, 1, 2
[1, 1, 3, 3, 3, 1, 3, 1, 3] => 1, 1, 3, 3, 3, 1, 3, 1, 3
[1, 1, 3, 3, 3, 1, 3, 2, 1] => 1, 1, 3, 3, 3, 1, 3, 2, 1
[1, 1, 3, 3, 3, 1, 3, 2, 2] => 1, 1, 3, 3, 3, 1, 3, 2, 2
[1, 1, 3, 3, 3, 1, 3, 2, 3] => 1, 1, 3, 3, 3, 1, 3, 2, 3
[1, 1, 3, 3, 3, 1, 3, 3, 1] => 1, 1, 3, 3, 3, 1, 3, 3, 1
[1, 1, 3, 3, 3, 1, 3, 3, 2] => 1, 1, 3, 3, 3, 1, 3, 3, 2
[1, 1, 3, 3, 3, 1, 3, 3, 3] => 1, 1, 3, 3, 3, 1, 3, 3, 3
[1, 1, 3, 3, 3, 2, 1, 1, 1] => 1, 1, 3, 3, 3, 2, 1, 1, 1
[1, 1, 3, 3, 3, 2, 1, 1, 2] => 1, 1, 3, 3, 3, 2, 1, 1, 2
[1, 1, 3, 3, 3, 2, 1, 1, 3] => 1, 1, 3, 3, 3, 2, 1, 1, 3
[1, 1, 3, 3, 3, 2, 1, 2, 1] => 1, 1, 3, 3, 3, 2, 1, 2, 1
[1, 1, 3, 3, 3, 2, 1, 2, 2] => 1, 1, 3, 3, 3, 2, 1, 2, 2
[1, 1, 3, 3, 3, 2, 1, 2, 3] => 1, 1, 3, 3, 3, 2, 1, 2, 3
[1, 1, 3, 3, 3, 2, 1, 3, 1] => 1, 1, 3, 3, 3, 2, 1, 3, 1
[1, 1, 3, 3, 3, 2, 1, 3, 2] => 1, 1, 3, 3, 3, 2, 1, 3, 2
[1, 1, 3, 3, 3, 2, 1, 3, 3] => 1, 1, 3, 3, 3, 2, 1, 3, 3
[1, 1, 3, 3, 3, 2, 2, 1, 1] => 1, 1, 3, 3, 3, 2, 2, 1, 1
[1, 1, 3, 3, 3, 2, 2, 1, 2] => 1, 1, 3, 3, 3, 2, 2, 1, 2
[1, 1, 3, 3, 3, 2, 2, 1, 3] => 1, 1, 3, 3, 3, 2, 2, 1, 3
[1, 1, 3, 3, 3, 2, 2, 2, 1] => 1, 1, 3, 3, 3, 2, 2, 2, 1
[1, 1, 3, 3, 3, 2, 2, 2, 2] => 1, 1, 3, 3, 3, 2, 2, 2, 2
[1, 1, 3, 3, 3, 2, 2, 2, 3] => 1, 1, 3, 3, 3, 2, 2, 2, 3
[1, 1, 3, 3, 3, 2, 2, 3, 1] => 1, 1, 3, 3, 3, 2, 2, 3, 1
[1, 1, 3, 3, 3, 2, 2, 3, 2] => 1, 1, 3, 3, 3, 2, 2, 3, 2
[1, 1, 3, 3, 3, 2, 2, 3, 3] => 1, 1, 3, 3, 3, 2, 2, 3, 3
[1, 1, 3, 3, 3, 2, 3, 1, 1] => 1, 1, 3, 3, 3, 2, 3, 1, 1
[1, 1, 3, 3, 3, 2, 3, 1, 2] => 1, 1, 3, 3, 3, 2, 3, 1, 2
[1, 1, 3, 3, 3, 2, 3, 1, 3] => 1, 1, 3, 3, 3, 2, 3, 1, 3
[1, 1, 3, 3, 3, 2, 3, 2, 1] => 1, 1, 3, 3, 3, 2, 3, 2, 1
[1, 1, 3, 3, 3, 2, 3, 2, 2] => 1, 1, 3, 3, 3, 2, 3, 2, 2
[1, 1, 3, 3, 3, 2, 3, 2, 3] => 1, 1, 3, 3, 3, 2, 3, 2, 3
[1, 1, 3, 3, 3, 2, 3, 3, 1] => 1, 1, 3, 3, 3, 2, 3, 3, 1
[1, 1, 3, 3, 3, 2, 3, 3, 2] => 1, 1, 3, 3, 3, 2, 3, 3, 2
[1, 1, 3, 3, 3, 2, 3, 3, 3] => 1, 1, 3, 3, 3, 2, 3, 3, 3
[1, 1, 3, 3, 3, 3, 1, 1, 1] => 1, 1, 3, 3, 3, 3, 1, 1, 1
[1, 1, 3, 3, 3, 3, 1, 1, 2] => 1, 1, 3, 3, 3, 3, 1, 1, 2
[1, 1, 3, 3, 3, 3, 1, 1, 3] => 1, 1, 3, 3, 3, 3, 1, 1, 3
[1, 1, 3, 3, 3, 3, 1, 2, 1] => 1, 1, 3, 3, 3, 3, 1, 2, 1
[1, 1, 3, 3, 3, 3, 1, 2, 2] => 1, 1, 3, 3, 3, 3, 1, 2, 2
[1, 1, 3, 3, 3, 3, 1, 2, 3] => 1, 1, 3, 3, 3, 3, 1, 2, 3
[1, 1, 3, 3, 3, 3, 1, 3, 1] => 1, 1, 3, 3, 3, 3, 1, 3, 1
[1, 1, 3, 3, 3, 3, 1, 3, 2] => 1, 1, 3, 3, 3, 3, 1, 3, 2
[1, 1, 3, 3, 3, 3, 1, 3, 3] => 1, 1, 3, 3, 3, 3, 1, 3, 3
[1, 1, 3, 3, 3, 3, 2, 1, 1] => 1, 1, 3, 3, 3, 3, 2, 1, 1
[1, 1, 3, 3, 3, 3, 2, 1, 2] => 1, 1, 3, 3, 3, 3, 2, 1, 2
[1, 1, 3, 3, 3, 3, 2, 1, 3] => 1, 1, 3, 3, 3, 3, 2, 1, 3
[1, 1, 3, 3, 3, 3, 2, 2, 1] => 1, 1, 3, 3, 3, 3, 2, 2, 1
[1, 1, 3, 3, 3, 3, 2, 2, 2] => 1, 1, 3, 3, 3, 3, 2, 2, 2
[1, 1, 3, 3, 3, 3, 2, 2, 3] => 1, 1, 3, 3, 3, 3, 2, 2, 3
[1, 1, 3, 3, 3, 3, 2, 3, 1] => 1, 1, 3, 3, 3, 3, 2, 3, 1
[1, 1, 3, 3, 3, 3, 2, 3, 2] => 1, 1, 3, 3, 3, 3, 2, 3, 2
[1, 1, 3, 3, 3, 3, 2, 3, 3] => 1, 1, 3, 3, 3, 3, 2, 3, 3
[1, 1, 3, 3, 3, 3, 3, 1, 1] => 1, 1, 3, 3, 3, 3, 3, 1, 1
[1, 1, 3, 3, 3, 3, 3, 1, 2] => 1, 1, 3, 3, 3, 3, 3, 1, 2
[1, 1, 3, 3, 3, 3, 3, 1, 3] => 1, 1, 3, 3, 3, 3, 3, 1, 3
[1, 1, 3, 3, 3, 3, 3, 2, 1] => 1, 1, 3, 3, 3, 3, 3, 2, 1
[1, 1, 3, 3, 3, 3, 3, 2, 2] => 1, 1, 3, 3, 3, 3, 3, 2, 2
[1, 1, 3, 3, 3, 3, 3, 2, 3] => 1, 1, 3, 3, 3, 3, 3, 2, 3
[1, 1, 3, 3, 3, 3, 3, 3, 1] => 1, 1, 3, 3, 3, 3, 3, 3, 1
[1, 1, 3, 3, 3, 3, 3, 3, 2] => 1, 1, 3, 3, 3, 3, 3, 3, 2
[1, 1, 3, 3, 3, 3, 3, 3, 3] => 1, 1, 3, 3, 3, 3, 3, 3, 3
[1, 2, 1, 1, 1, 1, 1, 1, 1] => 1, 2, 1, 1, 1, 1, 1, 1, 1
[1, 2, 1, 1, 1, 1, 1, 1, 2] => 1, 2, 1, 1, 1, 1, 1, 1, 2
[1, 2, 1, 1, 1, 1, 1, 1, 3] => 1, 2, 1, 1, 1, 1, 1, 1, 3
[1, 2, 1, 1, 1, 1, 1, 2, 1] => 1, 2, 1, 1, 1, 1, 1, 2, 1
[1, 2, 1, 1, 1, 1, 1, 2, 2] => 1, 2, 1, 1, 1, 1, 1, 2, 2
[1, 2, 1, 1, 1, 1, 1, 2, 3] => 1, 2, 1, 1, 1, 1, 1, 2, 3
[1, 2, 1, 1, 1, 1, 1, 3, 1] => 1, 2, 1, 1, 1, 1, 1, 3, 1
[1, 2, 1, 1, 1, 1, 1, 3, 2] => 1, 2, 1, 1, 1, 1, 1, 3, 2
[1, 2, 1, 1, 1, 1, 1, 3, 3] => 1, 2, 1, 1, 1, 1, 1, 3, 3
[1, 2, 1, 1, 1, 1, 2, 1, 1] => 1, 2, 1, 1, 1, 1, 2, 1, 1
[1, 2, 1, 1, 1, 1, 2, 1, 2] => 1, 2, 1, 1, 1, 1, 2, 1, 2
[1, 2, 1, 1, 1, 1, 2, 1, 3] => 1, 2, 1, 1, 1, 1, 2, 1, 3
[1, 2, 1, 1, 1, 1, 2, 2, 1] => 1, 2, 1, 1, 1, 1, 2, 2, 1
[1, 2, 1, 1, 1, 1, 2, 2, 2] => 1, 2, 1, 1, 1, 1, 2, 2, 2
[1, 2, 1, 1, 1, 1, 2, 2, 3] => 1, 2, 1, 1, 1, 1, 2, 2, 3
[1, 2, 1, 1, 1, 1, 2, 3, 1] => 1, 2, 1, 1, 1, 1, 2, 3, 1
[1, 2, 1, 1, 1, 1, 2, 3, 2] => 1, 2, 1, 1, 1, 1, 2, 3, 2
[1, 2, 1, 1, 1, 1, 2, 3, 3] => 1, 2, 1, 1, 1, 1, 2, 3, 3
[1, 2, 1, 1, 1, 1, 3, 1, 1] => 1, 2, 1, 1, 1, 1, 3, 1, 1
[1, 2, 1, 1, 1, 1, 3, 1, 2] => 1, 2, 1, 1, 1, 1, 3, 1, 2
[1, 2, 1, 1, 1, 1, 3, 1, 3] => 1, 2, 1, 1, 1, 1, 3, 1, 3
[1, 2, 1, 1, 1, 1, 3, 2, 1] => 1, 2, 1, 1, 1, 1, 3, 2, 1
[1, 2, 1, 1, 1, 1, 3, 2, 2] => 1, 2, 1, 1, 1, 1, 3, 2, 2
[1, 2, 1, 1, 1, 1, 3, 2, 3] => 1, 2, 1, 1, 1, 1, 3, 2, 3
[1, 2, 1, 1, 1, 1, 3, 3, 1] => 1, 2, 1, 1, 1, 1, 3, 3, 1
[1, 2, 1, 1, 1, 1, 3, 3, 2] => 1, 2, 1, 1, 1, 1, 3, 3, 2
[1, 2, 1, 1, 1, 1, 3, 3, 3] => 1, 2, 1, 1, 1, 1, 3, 3, 3
[1, 2, 1, 1, 1, 2, 1, 1, 1] => 1, 2, 1, 1, 1, 2, 1, 1, 1
[1, 2, 1, 1, 1, 2, 1, 1, 2] => 1, 2, 1, 1, 1, 2, 1, 1, 2
[1, 2, 1, 1, 1, 2, 1, 1, 3] => 1, 2, 1, 1, 1, 2, 1, 1, 3
[1, 2, 1, 1, 1, 2, 1, 2, 1] => 1, 2, 1, 1, 1, 2, 1, 2, 1
[1, 2, 1, 1, 1, 2, 1, 2, 2] => 1, 2, 1, 1, 1, 2, 1, 2, 2
[1, 2, 1, 1, 1, 2, 1, 2, 3] => 1, 2, 1, 1, 1, 2, 1, 2, 3
[1, 2, 1, 1, 1, 2, 1, 3, 1] => 1, 2, 1, 1, 1, 2, 1, 3, 1
[1, 2, 1, 1, 1, 2, 1, 3, 2] => 1, 2, 1, 1, 1, 2, 1, 3, 2
[1, 2, 1, 1, 1, 2, 1, 3, 3] => 1, 2, 1, 1, 1, 2, 1, 3, 3
[1, 2, 1, 1, 1, 2, 2, 1, 1] => 1, 2, 1, 1, 1, 2, 2, 1, 1
[1, 2, 1, 1, 1, 2, 2, 1, 2] => 1, 2, 1, 1, 1, 2, 2, 1, 2
[1, 2, 1, 1, 1, 2, 2, 1, 3] => 1, 2, 1, 1, 1, 2, 2, 1, 3
[1, 2, 1, 1, 1, 2, 2, 2, 1] => 1, 2, 1, 1, 1, 2, 2, 2, 1
[1, 2, 1, 1, 1, 2, 2, 2, 2] => 1, 2, 1, 1, 1, 2, 2, 2, 2
[1, 2, 1, 1, 1, 2, 2, 2, 3] => 1, 2, 1, 1, 1, 2, 2, 2, 3
[1, 2, 1, 1, 1, 2, 2, 3, 1] => 1, 2, 1, 1, 1, 2, 2, 3, 1
[1, 2, 1, 1, 1, 2, 2, 3, 2] => 1, 2, 1, 1, 1, 2, 2, 3, 2
[1, 2, 1, 1, 1, 2, 2, 3, 3] => 1, 2, 1, 1, 1, 2, 2, 3, 3
[1, 2, 1, 1, 1, 2, 3, 1, 1] => 1, 2, 1, 1, 1, 2, 3, 1, 1
[1, 2, 1, 1, 1, 2, 3, 1, 2] => 1, 2, 1, 1, 1, 2, 3, 1, 2
[1, 2, 1, 1, 1, 2, 3, 1, 3] => 1, 2, 1, 1, 1, 2, 3, 1, 3
[1, 2, 1, 1, 1, 2, 3, 2, 1] => 1, 2, 1, 1, 1, 2, 3, 2, 1
[1, 2, 1, 1, 1, 2, 3, 2, 2] => 1, 2, 1, 1, 1, 2, 3, 2, 2
[1, 2, 1, 1, 1, 2, 3, 2, 3] => 1, 2, 1, 1, 1, 2, 3, 2, 3
[1, 2, 1, 1, 1, 2, 3, 3, 1] => 1, 2, 1, 1, 1, 2, 3, 3, 1
[1, 2, 1, 1, 1, 2, 3, 3, 2] => 1, 2, 1, 1, 1, 2, 3, 3, 2
[1, 2, 1, 1, 1, 2, 3, 3, 3] => 1, 2, 1, 1, 1, 2, 3, 3, 3
[1, 2, 1, 1, 1, 3, 1, 1, 1] => 1, 2, 1, 1, 1, 3, 1, 1, 1
[1, 2, 1, 1, 1, 3, 1, 1, 2] => 1, 2, 1, 1, 1, 3, 1, 1, 2
[1, 2, 1, 1, 1, 3, 1, 1, 3] => 1, 2, 1, 1, 1, 3, 1, 1, 3
[1, 2, 1, 1, 1, 3, 1, 2, 1] => 1, 2, 1, 1, 1, 3, 1, 2, 1
[1, 2, 1, 1, 1, 3, 1, 2, 2] => 1, 2, 1, 1, 1, 3, 1, 2, 2
[1, 2, 1, 1, 1, 3, 1, 2, 3] => 1, 2, 1, 1, 1, 3, 1, 2, 3
[1, 2, 1, 1, 1, 3, 1, 3, 1] => 1, 2, 1, 1, 1, 3, 1, 3, 1
[1, 2, 1, 1, 1, 3, 1, 3, 2] => 1, 2, 1, 1, 1, 3, 1, 3, 2
[1, 2, 1, 1, 1, 3, 1, 3, 3] => 1, 2, 1, 1, 1, 3, 1, 3, 3
[1, 2, 1, 1, 1, 3, 2, 1, 1] => 1, 2, 1, 1, 1, 3, 2, 1, 1
[1, 2, 1, 1, 1, 3, 2, 1, 2] => 1, 2, 1, 1, 1, 3, 2, 1, 2
[1, 2, 1, 1, 1, 3, 2, 1, 3] => 1, 2, 1, 1, 1, 3, 2, 1, 3
[1, 2, 1, 1, 1, 3, 2, 2, 1] => 1, 2, 1, 1, 1, 3, 2, 2, 1
[1, 2, 1, 1, 1, 3, 2, 2, 2] => 1, 2, 1, 1, 1, 3, 2, 2, 2
[1, 2, 1, 1, 1, 3, 2, 2, 3] => 1, 2, 1, 1, 1, 3, 2, 2, 3
[1, 2, 1, 1, 1, 3, 2, 3, 1] => 1, 2, 1, 1, 1, 3, 2, 3, 1
[1, 2, 1, 1, 1, 3, 2, 3, 2] => 1, 2, 1, 1, 1, 3, 2, 3, 2
[1, 2, 1, 1, 1, 3, 2, 3, 3] => 1, 2, 1, 1, 1, 3, 2, 3, 3
[1, 2, 1, 1, 1, 3, 3, 1, 1] => 1, 2, 1, 1, 1, 3, 3, 1, 1
[1, 2, 1, 1, 1, 3, 3, 1, 2] => 1, 2, 1, 1, 1, 3, 3, 1, 2
[1, 2, 1, 1, 1, 3, 3, 1, 3] => 1, 2, 1, 1, 1, 3, 3, 1, 3
[1, 2, 1, 1, 1, 3, 3, 2, 1] => 1, 2, 1, 1, 1, 3, 3, 2, 1
[1, 2, 1, 1, 1, 3, 3, 2, 2] => 1, 2, 1, 1, 1, 3, 3, 2, 2
[1, 2, 1, 1, 1, 3, 3, 2, 3] => 1, 2, 1, 1, 1, 3, 3, 2, 3
[1, 2, 1, 1, 1, 3, 3, 3, 1] => 1, 2, 1, 1, 1, 3, 3, 3, 1
[1, 2, 1, 1, 1, 3, 3, 3, 2] => 1, 2, 1, 1, 1, 3, 3, 3, 2
[1, 2, 1, 1, 1, 3, 3, 3, 3] => 1, 2, 1, 1, 1, 3, 3, 3, 3
[1, 2, 1, 1, 2, 1, 1, 1, 1] => 1, 2, 1, 1, 2, 1, 1, 1, 1
[1, 2, 1, 1, 2, 1, 1, 1, 2] => 1, 2, 1, 1, 2, 1, 1, 1, 2
[1, 2, 1, 1, 2, 1, 1, 1, 3] => 1, 2, 1, 1, 2, 1, 1, 1, 3
[1, 2, 1, 1, 2, 1, 1, 2, 1] => 1, 2, 1, 1, 2, 1, 1, 2, 1
[1, 2, 1, 1, 2, 1, 1, 2, 2] => 1, 2, 1, 1, 2, 1, 1, 2, 2
[1, 2, 1, 1, 2, 1, 1, 2, 3] => 1, 2, 1, 1, 2, 1, 1, 2, 3
[1, 2, 1, 1, 2, 1, 1, 3, 1] => 1, 2, 1, 1, 2, 1, 1, 3, 1
[1, 2, 1, 1, 2, 1, 1, 3, 2] => 1, 2, 1, 1, 2, 1, 1, 3, 2
[1, 2, 1, 1, 2, 1, 1, 3, 3] => 1, 2, 1, 1, 2, 1, 1, 3, 3
[1, 2, 1, 1, 2, 1, 2, 1, 1] => 1, 2, 1, 1, 2, 1, 2, 1, 1
[1, 2, 1, 1, 2, 1, 2, 1, 2] => 1, 2, 1, 1, 2, 1, 2, 1, 2
[1, 2, 1, 1, 2, 1, 2, 1, 3] => 1, 2, 1, 1, 2, 1, 2, 1, 3
[1, 2, 1, 1, 2, 1, 2, 2, 1] => 1, 2, 1, 1, 2, 1, 2, 2, 1
[1, 2, 1, 1, 2, 1, 2, 2, 2] => 1, 2, 1, 1, 2, 1, 2, 2, 2
[1, 2, 1, 1, 2, 1, 2, 2, 3] => 1, 2, 1, 1, 2, 1, 2, 2, 3
[1, 2, 1, 1, 2, 1, 2, 3, 1] => 1, 2, 1, 1, 2, 1, 2, 3, 1
[1, 2, 1, 1, 2, 1, 2, 3, 2] => 1, 2, 1, 1, 2, 1, 2, 3, 2
[1, 2, 1, 1, 2, 1, 2, 3, 3] => 1, 2, 1, 1, 2, 1, 2, 3, 3
[1, 2, 1, 1, 2, 1, 3, 1, 1] => 1, 2, 1, 1, 2, 1, 3, 1, 1
[1, 2, 1, 1, 2, 1, 3, 1, 2] => 1, 2, 1, 1, 2, 1, 3, 1, 2
[1, 2, 1, 1, 2, 1, 3, 1, 3] => 1, 2, 1, 1, 2, 1, 3, 1, 3
[1, 2, 1, 1, 2, 1, 3, 2, 1] => 1, 2, 1, 1, 2, 1, 3, 2, 1
[1, 2, 1, 1, 2, 1, 3, 2, 2] => 1, 2, 1, 1, 2, 1, 3, 2, 2
[1, 2, 1, 1, 2, 1, 3, 2, 3] => 1, 2, 1, 1, 2, 1, 3, 2, 3
[1, 2, 1, 1, 2, 1, 3, 3, 1] => 1, 2, 1, 1, 2, 1, 3, 3, 1
[1, 2, 1, 1, 2, 1, 3, 3, 2] => 1, 2, 1, 1, 2, 1, 3, 3, 2
[1, 2, 1, 1, 2, 1, 3, 3, 3] => 1, 2, 1, 1, 2, 1, 3, 3, 3
[1, 2, 1, 1, 2, 2, 1, 1, 1] => 1, 2, 1, 1, 2, 2, 1, 1, 1
[1, 2, 1, 1, 2, 2, 1, 1, 2] => 1, 2, 1, 1, 2, 2, 1, 1, 2
[1, 2, 1, 1, 2, 2, 1, 1, 3] => 1, 2, 1, 1, 2, 2, 1, 1, 3
[1, 2, 1, 1, 2, 2, 1, 2, 1] => 1, 2, 1, 1, 2, 2, 1, 2, 1
[1, 2, 1, 1, 2, 2, 1, 2, 2] => 1, 2, 1, 1, 2, 2, 1, 2, 2
[1, 2, 1, 1, 2, 2, 1, 2, 3] => 1, 2, 1, 1, 2, 2, 1, 2, 3
[1, 2, 1, 1, 2, 2, 1, 3, 1] => 1, 2, 1, 1, 2, 2, 1, 3, 1
[1, 2, 1, 1, 2, 2, 1, 3, 2] => 1, 2, 1, 1, 2, 2, 1, 3, 2
[1, 2, 1, 1, 2, 2, 1, 3, 3] => 1, 2, 1, 1, 2, 2, 1, 3, 3
[1, 2, 1, 1, 2, 2, 2, 1, 1] => 1, 2, 1, 1, 2, 2, 2, 1, 1
[1, 2, 1, 1, 2, 2, 2, 1, 2] => 1, 2, 1, 1, 2, 2, 2, 1, 2
[1, 2, 1, 1, 2, 2, 2, 1, 3] => 1, 2, 1, 1, 2, 2, 2, 1, 3
[1, 2, 1, 1, 2, 2, 2, 2, 1] => 1, 2, 1, 1, 2, 2, 2, 2, 1
[1, 2, 1, 1, 2, 2, 2, 2, 2] => 1, 2, 1, 1, 2, 2, 2, 2, 2
[1, 2, 1, 1, 2, 2, 2, 2, 3] => 1, 2, 1, 1, 2, 2, 2, 2, 3
[1, 2, 1, 1, 2, 2, 2, 3, 1] => 1, 2, 1, 1, 2, 2, 2, 3, 1
[1, 2, 1, 1, 2, 2, 2, 3, 2] => 1, 2, 1, 1, 2, 2, 2, 3, 2
[1, 2, 1, 1, 2, 2, 2, 3, 3] => 1, 2, 1, 1, 2, 2, 2, 3, 3
[1, 2, 1, 1, 2, 2, 3, 1, 1] => 1, 2, 1, 1, 2, 2, 3, 1, 1
[1, 2, 1, 1, 2, 2, 3, 1, 2] => 1, 2, 1, 1, 2, 2, 3, 1, 2
[1, 2, 1, 1, 2, 2, 3, 1, 3] => 1, 2, 1, 1, 2, 2, 3, 1, 3
[1, 2, 1, 1, 2, 2, 3, 2, 1] => 1, 2, 1, 1, 2, 2, 3, 2, 1
[1, 2, 1, 1, 2, 2, 3, 2, 2] => 1, 2, 1, 1, 2, 2, 3, 2, 2
[1, 2, 1, 1, 2, 2, 3, 2, 3] => 1, 2, 1, 1, 2, 2, 3, 2, 3
[1, 2, 1, 1, 2, 2, 3, 3, 1] => 1, 2, 1, 1, 2, 2, 3, 3, 1
[1, 2, 1, 1, 2, 2, 3, 3, 2] => 1, 2, 1, 1, 2, 2, 3, 3, 2
[1, 2, 1, 1, 2, 2, 3, 3, 3] => 1, 2, 1, 1, 2, 2, 3, 3, 3
[1, 2, 1, 1, 2, 3, 1, 1, 1] => 1, 2, 1, 1, 2, 3, 1, 1, 1
[1, 2, 1, 1, 2, 3, 1, 1, 2] => 1, 2, 1, 1, 2, 3, 1, 1, 2
[1, 2, 1, 1, 2, 3, 1, 1, 3] => 1, 2, 1, 1, 2, 3, 1, 1, 3
[1, 2, 1, 1, 2, 3, 1, 2, 1] => 1, 2, 1, 1, 2, 3, 1, 2, 1
[1, 2, 1, 1, 2, 3, 1, 2, 2] => 1, 2, 1, 1, 2, 3, 1, 2, 2
[1, 2, 1, 1, 2, 3, 1, 2, 3] => 1, 2, 1, 1, 2, 3, 1, 2, 3
[1, 2, 1, 1, 2, 3, 1, 3, 1] => 1, 2, 1, 1, 2, 3, 1, 3, 1
[1, 2, 1, 1, 2, 3, 1, 3, 2] => 1, 2, 1, 1, 2, 3, 1, 3, 2
[1, 2, 1, 1, 2, 3, 1, 3, 3] => 1, 2, 1, 1, 2, 3, 1, 3, 3
[1, 2, 1, 1, 2, 3, 2, 1, 1] => 1, 2, 1, 1, 2, 3, 2, 1, 1
[1, 2, 1, 1, 2, 3, 2, 1, 2] => 1, 2, 1, 1, 2, 3, 2, 1, 2
[1, 2, 1, 1, 2, 3, 2, 1, 3] => 1, 2, 1, 1, 2, 3, 2, 1, 3
[1, 2, 1, 1, 2, 3, 2, 2, 1] => 1, 2, 1, 1, 2, 3, 2, 2, 1
[1, 2, 1, 1, 2, 3, 2, 2, 2] => 1, 2, 1, 1, 2, 3, 2, 2, 2
[1, 2, 1, 1, 2, 3, 2, 2, 3] => 1, 2, 1, 1, 2, 3, 2, 2, 3
[1, 2, 1, 1, 2, 3, 2, 3, 1] => 1, 2, 1, 1, 2, 3, 2, 3, 1
[1, 2, 1, 1, 2, 3, 2, 3, 2] => 1, 2, 1, 1, 2, 3, 2, 3, 2
[1, 2, 1, 1, 2, 3, 2, 3, 3] => 1, 2, 1, 1, 2, 3, 2, 3, 3
[1, 2, 1, 1, 2, 3, 3, 1, 1] => 1, 2, 1, 1, 2, 3, 3, 1, 1
[1, 2, 1, 1, 2, 3, 3, 1, 2] => 1, 2, 1, 1, 2, 3, 3, 1, 2
[1, 2, 1, 1, 2, 3, 3, 1, 3] => 1, 2, 1, 1, 2, 3, 3, 1, 3
[1, 2, 1, 1, 2, 3, 3, 2, 1] => 1, 2, 1, 1, 2, 3, 3, 2, 1
[1, 2, 1, 1, 2, 3, 3, 2, 2] => 1, 2, 1, 1, 2, 3, 3, 2, 2
[1, 2, 1, 1, 2, 3, 3, 2, 3] => 1, 2, 1, 1, 2, 3, 3, 2, 3
[1, 2, 1, 1, 2, 3, 3, 3, 1] => 1, 2, 1, 1, 2, 3, 3, 3, 1
[1, 2, 1, 1, 2, 3, 3, 3, 2] => 1, 2, 1, 1, 2, 3, 3, 3, 2
[1, 2, 1, 1, 2, 3, 3, 3, 3] => 1, 2, 1, 1, 2, 3, 3, 3, 3
[1, 2, 1, 1, 3, 1, 1, 1, 1] => 1, 2, 1, 1, 3, 1, 1, 1, 1
[1, 2, 1, 1, 3, 1, 1, 1, 2] => 1, 2, 1, 1, 3, 1, 1, 1, 2
[1, 2, 1, 1, 3, 1, 1, 1, 3] => 1, 2, 1, 1, 3, 1, 1, 1, 3
[1, 2, 1, 1, 3, 1, 1, 2, 1] => 1, 2, 1, 1, 3, 1, 1, 2, 1
[1, 2, 1, 1, 3, 1, 1, 2, 2] => 1, 2, 1, 1, 3, 1, 1, 2, 2
[1, 2, 1, 1, 3, 1, 1, 2, 3] => 1, 2, 1, 1, 3, 1, 1, 2, 3
[1, 2, 1, 1, 3, 1, 1, 3, 1] => 1, 2, 1, 1, 3, 1, 1, 3, 1
[1, 2, 1, 1, 3, 1, 1, 3, 2] => 1, 2, 1, 1, 3, 1, 1, 3, 2
[1, 2, 1, 1, 3, 1, 1, 3, 3] => 1, 2, 1, 1, 3, 1, 1, 3, 3
[1, 2, 1, 1, 3, 1, 2, 1, 1] => 1, 2, 1, 1, 3, 1, 2, 1, 1
[1, 2, 1, 1, 3, 1, 2, 1, 2] => 1, 2, 1, 1, 3, 1, 2, 1, 2
[1, 2, 1, 1, 3, 1, 2, 1, 3] => 1, 2, 1, 1, 3, 1, 2, 1, 3
[1, 2, 1, 1, 3, 1, 2, 2, 1] => 1, 2, 1, 1, 3, 1, 2, 2, 1
[1, 2, 1, 1, 3, 1, 2, 2, 2] => 1, 2, 1, 1, 3, 1, 2, 2, 2
[1, 2, 1, 1, 3, 1, 2, 2, 3] => 1, 2, 1, 1, 3, 1, 2, 2, 3
[1, 2, 1, 1, 3, 1, 2, 3, 1] => 1, 2, 1, 1, 3, 1, 2, 3, 1
[1, 2, 1, 1, 3, 1, 2, 3, 2] => 1, 2, 1, 1, 3, 1, 2, 3, 2
[1, 2, 1, 1, 3, 1, 2, 3, 3] => 1, 2, 1, 1, 3, 1, 2, 3, 3
[1, 2, 1, 1, 3, 1, 3, 1, 1] => 1, 2, 1, 1, 3, 1, 3, 1, 1
[1, 2, 1, 1, 3, 1, 3, 1, 2] => 1, 2, 1, 1, 3, 1, 3, 1, 2
[1, 2, 1, 1, 3, 1, 3, 1, 3] => 1, 2, 1, 1, 3, 1, 3, 1, 3
[1, 2, 1, 1, 3, 1, 3, 2, 1] => 1, 2, 1, 1, 3, 1, 3, 2, 1
[1, 2, 1, 1, 3, 1, 3, 2, 2] => 1, 2, 1, 1, 3, 1, 3, 2, 2
[1, 2, 1, 1, 3, 1, 3, 2, 3] => 1, 2, 1, 1, 3, 1, 3, 2, 3
[1, 2, 1, 1, 3, 1, 3, 3, 1] => 1, 2, 1, 1, 3, 1, 3, 3, 1
[1, 2, 1, 1, 3, 1, 3, 3, 2] => 1, 2, 1, 1, 3, 1, 3, 3, 2
[1, 2, 1, 1, 3, 1, 3, 3, 3] => 1, 2, 1, 1, 3, 1, 3, 3, 3
[1, 2, 1, 1, 3, 2, 1, 1, 1] => 1, 2, 1, 1, 3, 2, 1, 1, 1
[1, 2, 1, 1, 3, 2, 1, 1, 2] => 1, 2, 1, 1, 3, 2, 1, 1, 2
[1, 2, 1, 1, 3, 2, 1, 1, 3] => 1, 2, 1, 1, 3, 2, 1, 1, 3
[1, 2, 1, 1, 3, 2, 1, 2, 1] => 1, 2, 1, 1, 3, 2, 1, 2, 1
[1, 2, 1, 1, 3, 2, 1, 2, 2] => 1, 2, 1, 1, 3, 2, 1, 2, 2
[1, 2, 1, 1, 3, 2, 1, 2, 3] => 1, 2, 1, 1, 3, 2, 1, 2, 3
[1, 2, 1, 1, 3, 2, 1, 3, 1] => 1, 2, 1, 1, 3, 2, 1, 3, 1
[1, 2, 1, 1, 3, 2, 1, 3, 2] => 1, 2, 1, 1, 3, 2, 1, 3, 2
[1, 2, 1, 1, 3, 2, 1, 3, 3] => 1, 2, 1, 1, 3, 2, 1, 3, 3
[1, 2, 1, 1, 3, 2, 2, 1, 1] => 1, 2, 1, 1, 3, 2, 2, 1, 1
[1, 2, 1, 1, 3, 2, 2, 1, 2] => 1, 2, 1, 1, 3, 2, 2, 1, 2
[1, 2, 1, 1, 3, 2, 2, 1, 3] => 1, 2, 1, 1, 3, 2, 2, 1, 3
[1, 2, 1, 1, 3, 2, 2, 2, 1] => 1, 2, 1, 1, 3, 2, 2, 2, 1
[1, 2, 1, 1, 3, 2, 2, 2, 2] => 1, 2, 1, 1, 3, 2, 2, 2, 2
[1, 2, 1, 1, 3, 2, 2, 2, 3] => 1, 2, 1, 1, 3, 2, 2, 2, 3
[1, 2, 1, 1, 3, 2, 2, 3, 1] => 1, 2, 1, 1, 3, 2, 2, 3, 1
[1, 2, 1, 1, 3, 2, 2, 3, 2] => 1, 2, 1, 1, 3, 2, 2, 3, 2
[1, 2, 1, 1, 3, 2, 2, 3, 3] => 1, 2, 1, 1, 3, 2, 2, 3, 3
[1, 2, 1, 1, 3, 2, 3, 1, 1] => 1, 2, 1, 1, 3, 2, 3, 1, 1
[1, 2, 1, 1, 3, 2, 3, 1, 2] => 1, 2, 1, 1, 3, 2, 3, 1, 2
[1, 2, 1, 1, 3, 2, 3, 1, 3] => 1, 2, 1, 1, 3, 2, 3, 1, 3
[1, 2, 1, 1, 3, 2, 3, 2, 1] => 1, 2, 1, 1, 3, 2, 3, 2, 1
[1, 2, 1, 1, 3, 2, 3, 2, 2] => 1, 2, 1, 1, 3, 2, 3, 2, 2
[1, 2, 1, 1, 3, 2, 3, 2, 3] => 1, 2, 1, 1, 3, 2, 3, 2, 3
[1, 2, 1, 1, 3, 2, 3, 3, 1] => 1, 2, 1, 1, 3, 2, 3, 3, 1
[1, 2, 1, 1, 3, 2, 3, 3, 2] => 1, 2, 1, 1, 3, 2, 3, 3, 2
[1, 2, 1, 1, 3, 2, 3, 3, 3] => 1, 2, 1, 1, 3, 2, 3, 3, 3
[1, 2, 1, 1, 3, 3, 1, 1, 1] => 1, 2, 1, 1, 3, 3, 1, 1, 1
[1, 2, 1, 1, 3, 3, 1, 1, 2] => 1, 2, 1, 1, 3, 3, 1, 1, 2
[1, 2, 1, 1, 3, 3, 1, 1, 3] => 1, 2, 1, 1, 3, 3, 1, 1, 3
[1, 2, 1, 1, 3, 3, 1, 2, 1] => 1, 2, 1, 1, 3, 3, 1, 2, 1
[1, 2, 1, 1, 3, 3, 1, 2, 2] => 1, 2, 1, 1, 3, 3, 1, 2, 2
[1, 2, 1, 1, 3, 3, 1, 2, 3] => 1, 2, 1, 1, 3, 3, 1, 2, 3
[1, 2, 1, 1, 3, 3, 1, 3, 1] => 1, 2, 1, 1, 3, 3, 1, 3, 1
[1, 2, 1, 1, 3, 3, 1, 3, 2] => 1, 2, 1, 1, 3, 3, 1, 3, 2
[1, 2, 1, 1, 3, 3, 1, 3, 3] => 1, 2, 1, 1, 3, 3, 1, 3, 3
[1, 2, 1, 1, 3, 3, 2, 1, 1] => 1, 2, 1, 1, 3, 3, 2, 1, 1
[1, 2, 1, 1, 3, 3, 2, 1, 2] => 1, 2, 1, 1, 3, 3, 2, 1, 2
[1, 2, 1, 1, 3, 3, 2, 1, 3] => 1, 2, 1, 1, 3, 3, 2, 1, 3
[1, 2, 1, 1, 3, 3, 2, 2, 1] => 1, 2, 1, 1, 3, 3, 2, 2, 1
[1, 2, 1, 1, 3, 3, 2, 2, 2] => 1, 2, 1, 1, 3, 3, 2, 2, 2
[1, 2, 1, 1, 3, 3, 2, 2, 3] => 1, 2, 1, 1, 3, 3, 2, 2, 3
[1, 2, 1, 1, 3, 3, 2, 3, 1] => 1, 2, 1, 1, 3, 3, 2, 3, 1
[1, 2, 1, 1, 3, 3, 2, 3, 2] => 1, 2, 1, 1, 3, 3, 2, 3, 2
[1, 2, 1, 1, 3, 3, 2, 3, 3] => 1, 2, 1, 1, 3, 3, 2, 3, 3
[1, 2, 1, 1, 3, 3, 3, 1, 1] => 1, 2, 1, 1, 3, 3, 3, 1, 1
[1, 2, 1, 1, 3, 3, 3, 1, 2] => 1, 2, 1, 1, 3, 3, 3, 1, 2
[1, 2, 1, 1, 3, 3, 3, 1, 3] => 1, 2, 1, 1, 3, 3, 3, 1, 3
[1, 2, 1, 1, 3, 3, 3, 2, 1] => 1, 2, 1, 1, 3, 3, 3, 2, 1
[1, 2, 1, 1, 3, 3, 3, 2, 2] => 1, 2, 1, 1, 3, 3, 3, 2, 2
[1, 2, 1, 1, 3, 3, 3, 2, 3] => 1, 2, 1, 1, 3, 3, 3, 2, 3
[1, 2, 1, 1, 3, 3, 3, 3, 1] => 1, 2, 1, 1, 3, 3, 3, 3, 1
[1, 2, 1, 1, 3, 3, 3, 3, 2] => 1, 2, 1, 1, 3, 3, 3, 3, 2
[1, 2, 1, 1, 3, 3, 3, 3, 3] => 1, 2, 1, 1, 3, 3, 3, 3, 3
[1, 2, 1, 2, 1, 1, 1, 1, 1] => 1, 2, 1, 2, 1, 1, 1, 1, 1
[1, 2, 1, 2, 1, 1, 1, 1, 2] => 1, 2, 1, 2, 1, 1, 1, 1, 2
[1, 2, 1, 2, 1, 1, 1, 1, 3] => 1, 2, 1, 2, 1, 1, 1, 1, 3
[1, 2, 1, 2, 1, 1, 1, 2, 1] => 1, 2, 1, 2, 1, 1, 1, 2, 1
[1, 2, 1, 2, 1, 1, 1, 2, 2] => 1, 2, 1, 2, 1, 1, 1, 2, 2
[1, 2, 1, 2, 1, 1, 1, 2, 3] => 1, 2, 1, 2, 1, 1, 1, 2, 3
[1, 2, 1, 2, 1, 1, 1, 3, 1] => 1, 2, 1, 2, 1, 1, 1, 3, 1
[1, 2, 1, 2, 1, 1, 1, 3, 2] => 1, 2, 1, 2, 1, 1, 1, 3, 2
[1, 2, 1, 2, 1, 1, 1, 3, 3] => 1, 2, 1, 2, 1, 1, 1, 3, 3
[1, 2, 1, 2, 1, 1, 2, 1, 1] => 1, 2, 1, 2, 1, 1, 2, 1, 1
[1, 2, 1, 2, 1, 1, 2, 1, 2] => 1, 2, 1, 2, 1, 1, 2, 1, 2
[1, 2, 1, 2, 1, 1, 2, 1, 3] => 1, 2, 1, 2, 1, 1, 2, 1, 3
[1, 2, 1, 2, 1, 1, 2, 2, 1] => 1, 2, 1, 2, 1, 1, 2, 2, 1
[1, 2, 1, 2, 1, 1, 2, 2, 2] => 1, 2, 1, 2, 1, 1, 2, 2, 2
[1, 2, 1, 2, 1, 1, 2, 2, 3] => 1, 2, 1, 2, 1, 1, 2, 2, 3
[1, 2, 1, 2, 1, 1, 2, 3, 1] => 1, 2, 1, 2, 1, 1, 2, 3, 1
[1, 2, 1, 2, 1, 1, 2, 3, 2] => 1, 2, 1, 2, 1, 1, 2, 3, 2
[1, 2, 1, 2, 1, 1, 2, 3, 3] => 1, 2, 1, 2, 1, 1, 2, 3, 3
[1, 2, 1, 2, 1, 1, 3, 1, 1] => 1, 2, 1, 2, 1, 1, 3, 1, 1
[1, 2, 1, 2, 1, 1, 3, 1, 2] => 1, 2, 1, 2, 1, 1, 3, 1, 2
[1, 2, 1, 2, 1, 1, 3, 1, 3] => 1, 2, 1, 2, 1, 1, 3, 1, 3
[1, 2, 1, 2, 1, 1, 3, 2, 1] => 1, 2, 1, 2, 1, 1, 3, 2, 1
[1, 2, 1, 2, 1, 1, 3, 2, 2] => 1, 2, 1, 2, 1, 1, 3, 2, 2
[1, 2, 1, 2, 1, 1, 3, 2, 3] => 1, 2, 1, 2, 1, 1, 3, 2, 3
[1, 2, 1, 2, 1, 1, 3, 3, 1] => 1, 2, 1, 2, 1, 1, 3, 3, 1
[1, 2, 1, 2, 1, 1, 3, 3, 2] => 1, 2, 1, 2, 1, 1, 3, 3, 2
[1, 2, 1, 2, 1, 1, 3, 3, 3] => 1, 2, 1, 2, 1, 1, 3, 3, 3
[1, 2, 1, 2, 1, 2, 1, 1, 1] => 1, 2, 1, 2, 1, 2, 1, 1, 1
[1, 2, 1, 2, 1, 2, 1, 1, 2] => 1, 2, 1, 2, 1, 2, 1, 1, 2
[1, 2, 1, 2, 1, 2, 1, 1, 3] => 1, 2, 1, 2, 1, 2, 1, 1, 3
[1, 2, 1, 2, 1, 2, 1, 2, 1] => 1, 2, 1, 2, 1, 2, 1, 2, 1
[1, 2, 1, 2, 1, 2, 1, 2, 2] => 1, 2, 1, 2, 1, 2, 1, 2, 2
[1, 2, 1, 2, 1, 2, 1, 2, 3] => 1, 2, 1, 2, 1, 2, 1, 2, 3
[1, 2, 1, 2, 1, 2, 1, 3, 1] => 1, 2, 1, 2, 1, 2, 1, 3, 1
[1, 2, 1, 2, 1, 2, 1, 3, 2] => 1, 2, 1, 2, 1, 2, 1, 3, 2
[1, 2, 1, 2, 1, 2, 1, 3, 3] => 1, 2, 1, 2, 1, 2, 1, 3, 3
[1, 2, 1, 2, 1, 2, 2, 1, 1] => 1, 2, 1, 2, 1, 2, 2, 1, 1
[1, 2, 1, 2, 1, 2, 2, 1, 2] => 1, 2, 1, 2, 1, 2, 2, 1, 2
[1, 2, 1, 2, 1, 2, 2, 1, 3] => 1, 2, 1, 2, 1, 2, 2, 1, 3
[1, 2, 1, 2, 1, 2, 2, 2, 1] => 1, 2, 1, 2, 1, 2, 2, 2, 1
[1, 2, 1, 2, 1, 2, 2, 2, 2] => 1, 2, 1, 2, 1, 2, 2, 2, 2
[1, 2, 1, 2, 1, 2, 2, 2, 3] => 1, 2, 1, 2, 1, 2, 2, 2, 3
[1, 2, 1, 2, 1, 2, 2, 3, 1] => 1, 2, 1, 2, 1, 2, 2, 3, 1
[1, 2, 1, 2, 1, 2, 2, 3, 2] => 1, 2, 1, 2, 1, 2, 2, 3, 2
[1, 2, 1, 2, 1, 2, 2, 3, 3] => 1, 2, 1, 2, 1, 2, 2, 3, 3
[1, 2, 1, 2, 1, 2, 3, 1, 1] => 1, 2, 1, 2, 1, 2, 3, 1, 1
[1, 2, 1, 2, 1, 2, 3, 1, 2] => 1, 2, 1, 2, 1, 2, 3, 1, 2
[1, 2, 1, 2, 1, 2, 3, 1, 3] => 1, 2, 1, 2, 1, 2, 3, 1, 3
[1, 2, 1, 2, 1, 2, 3, 2, 1] => 1, 2, 1, 2, 1, 2, 3, 2, 1
[1, 2, 1, 2, 1, 2, 3, 2, 2] => 1, 2, 1, 2, 1, 2, 3, 2, 2
[1, 2, 1, 2, 1, 2, 3, 2, 3] => 1, 2, 1, 2, 1, 2, 3, 2, 3
[1, 2, 1, 2, 1, 2, 3, 3, 1] => 1, 2, 1, 2, 1, 2, 3, 3, 1
[1, 2, 1, 2, 1, 2, 3, 3, 2] => 1, 2, 1, 2, 1, 2, 3, 3, 2
[1, 2, 1, 2, 1, 2, 3, 3, 3] => 1, 2, 1, 2, 1, 2, 3, 3, 3
[1, 2, 1, 2, 1, 3, 1, 1, 1] => 1, 2, 1, 2, 1, 3, 1, 1, 1
[1, 2, 1, 2, 1, 3, 1, 1, 2] => 1, 2, 1, 2, 1, 3, 1, 1, 2
[1, 2, 1, 2, 1, 3, 1, 1, 3] => 1, 2, 1, 2, 1, 3, 1, 1, 3
[1, 2, 1, 2, 1, 3, 1, 2, 1] => 1, 2, 1, 2, 1, 3, 1, 2, 1
[1, 2, 1, 2, 1, 3, 1, 2, 2] => 1, 2, 1, 2, 1, 3, 1, 2, 2
[1, 2, 1, 2, 1, 3, 1, 2, 3] => 1, 2, 1, 2, 1, 3, 1, 2, 3
[1, 2, 1, 2, 1, 3, 1, 3, 1] => 1, 2, 1, 2, 1, 3, 1, 3, 1
[1, 2, 1, 2, 1, 3, 1, 3, 2] => 1, 2, 1, 2, 1, 3, 1, 3, 2
[1, 2, 1, 2, 1, 3, 1, 3, 3] => 1, 2, 1, 2, 1, 3, 1, 3, 3
[1, 2, 1, 2, 1, 3, 2, 1, 1] => 1, 2, 1, 2, 1, 3, 2, 1, 1
[1, 2, 1, 2, 1, 3, 2, 1, 2] => 1, 2, 1, 2, 1, 3, 2, 1, 2
[1, 2, 1, 2, 1, 3, 2, 1, 3] => 1, 2, 1, 2, 1, 3, 2, 1, 3
[1, 2, 1, 2, 1, 3, 2, 2, 1] => 1, 2, 1, 2, 1, 3, 2, 2, 1
[1, 2, 1, 2, 1, 3, 2, 2, 2] => 1, 2, 1, 2, 1, 3, 2, 2, 2
[1, 2, 1, 2, 1, 3, 2, 2, 3] => 1, 2, 1, 2, 1, 3, 2, 2, 3
[1, 2, 1, 2, 1, 3, 2, 3, 1] => 1, 2, 1, 2, 1, 3, 2, 3, 1
[1, 2, 1, 2, 1, 3, 2, 3, 2] => 1, 2, 1, 2, 1, 3, 2, 3, 2
[1, 2, 1, 2, 1, 3, 2, 3, 3] => 1, 2, 1, 2, 1, 3, 2, 3, 3
[1, 2, 1, 2, 1, 3, 3, 1, 1] => 1, 2, 1, 2, 1, 3, 3, 1, 1
[1, 2, 1, 2, 1, 3, 3, 1, 2] => 1, 2, 1, 2, 1, 3, 3, 1, 2
[1, 2, 1, 2, 1, 3, 3, 1, 3] => 1, 2, 1, 2, 1, 3, 3, 1, 3
[1, 2, 1, 2, 1, 3, 3, 2, 1] => 1, 2, 1, 2, 1, 3, 3, 2, 1
[1, 2, 1, 2, 1, 3, 3, 2, 2] => 1, 2, 1, 2, 1, 3, 3, 2, 2
[1, 2, 1, 2, 1, 3, 3, 2, 3] => 1, 2, 1, 2, 1, 3, 3, 2, 3
[1, 2, 1, 2, 1, 3, 3, 3, 1] => 1, 2, 1, 2, 1, 3, 3, 3, 1
[1, 2, 1, 2, 1, 3, 3, 3, 2] => 1, 2, 1, 2, 1, 3, 3, 3, 2
[1, 2, 1, 2, 1, 3, 3, 3, 3] => 1, 2, 1, 2, 1, 3, 3, 3, 3
[1, 2, 1, 2, 2, 1, 1, 1, 1] => 1, 2, 1, 2, 2, 1, 1, 1, 1
[1, 2, 1, 2, 2, 1, 1, 1, 2] => 1, 2, 1, 2, 2, 1, 1, 1, 2
[1, 2, 1, 2, 2, 1, 1, 1, 3] => 1, 2, 1, 2, 2, 1, 1, 1, 3
[1, 2, 1, 2, 2, 1, 1, 2, 1] => 1, 2, 1, 2, 2, 1, 1, 2, 1
[1, 2, 1, 2, 2, 1, 1, 2, 2] => 1, 2, 1, 2, 2, 1, 1, 2, 2
[1, 2, 1, 2, 2, 1, 1, 2, 3] => 1, 2, 1, 2, 2, 1, 1, 2, 3
[1, 2, 1, 2, 2, 1, 1, 3, 1] => 1, 2, 1, 2, 2, 1, 1, 3, 1
[1, 2, 1, 2, 2, 1, 1, 3, 2] => 1, 2, 1, 2, 2, 1, 1, 3, 2
[1, 2, 1, 2, 2, 1, 1, 3, 3] => 1, 2, 1, 2, 2, 1, 1, 3, 3
[1, 2, 1, 2, 2, 1, 2, 1, 1] => 1, 2, 1, 2, 2, 1, 2, 1, 1
[1, 2, 1, 2, 2, 1, 2, 1, 2] => 1, 2, 1, 2, 2, 1, 2, 1, 2
[1, 2, 1, 2, 2, 1, 2, 1, 3] => 1, 2, 1, 2, 2, 1, 2, 1, 3
[1, 2, 1, 2, 2, 1, 2, 2, 1] => 1, 2, 1, 2, 2, 1, 2, 2, 1
[1, 2, 1, 2, 2, 1, 2, 2, 2] => 1, 2, 1, 2, 2, 1, 2, 2, 2
[1, 2, 1, 2, 2, 1, 2, 2, 3] => 1, 2, 1, 2, 2, 1, 2, 2, 3
[1, 2, 1, 2, 2, 1, 2, 3, 1] => 1, 2, 1, 2, 2, 1, 2, 3, 1
[1, 2, 1, 2, 2, 1, 2, 3, 2] => 1, 2, 1, 2, 2, 1, 2, 3, 2
[1, 2, 1, 2, 2, 1, 2, 3, 3] => 1, 2, 1, 2, 2, 1, 2, 3, 3
[1, 2, 1, 2, 2, 1, 3, 1, 1] => 1, 2, 1, 2, 2, 1, 3, 1, 1
[1, 2, 1, 2, 2, 1, 3, 1, 2] => 1, 2, 1, 2, 2, 1, 3, 1, 2
[1, 2, 1, 2, 2, 1, 3, 1, 3] => 1, 2, 1, 2, 2, 1, 3, 1, 3
[1, 2, 1, 2, 2, 1, 3, 2, 1] => 1, 2, 1, 2, 2, 1, 3, 2, 1
[1, 2, 1, 2, 2, 1, 3, 2, 2] => 1, 2, 1, 2, 2, 1, 3, 2, 2
[1, 2, 1, 2, 2, 1, 3, 2, 3] => 1, 2, 1, 2, 2, 1, 3, 2, 3
[1, 2, 1, 2, 2, 1, 3, 3, 1] => 1, 2, 1, 2, 2, 1, 3, 3, 1
[1, 2, 1, 2, 2, 1, 3, 3, 2] => 1, 2, 1, 2, 2, 1, 3, 3, 2
[1, 2, 1, 2, 2, 1, 3, 3, 3] => 1, 2, 1, 2, 2, 1, 3, 3, 3
[1, 2, 1, 2, 2, 2, 1, 1, 1] => 1, 2, 1, 2, 2, 2, 1, 1, 1
[1, 2, 1, 2, 2, 2, 1, 1, 2] => 1, 2, 1, 2, 2, 2, 1, 1, 2
[1, 2, 1, 2, 2, 2, 1, 1, 3] => 1, 2, 1, 2, 2, 2, 1, 1, 3
[1, 2, 1, 2, 2, 2, 1, 2, 1] => 1, 2, 1, 2, 2, 2, 1, 2, 1
[1, 2, 1, 2, 2, 2, 1, 2, 2] => 1, 2, 1, 2, 2, 2, 1, 2, 2
[1, 2, 1, 2, 2, 2, 1, 2, 3] => 1, 2, 1, 2, 2, 2, 1, 2, 3
[1, 2, 1, 2, 2, 2, 1, 3, 1] => 1, 2, 1, 2, 2, 2, 1, 3, 1
[1, 2, 1, 2, 2, 2, 1, 3, 2] => 1, 2, 1, 2, 2, 2, 1, 3, 2
[1, 2, 1, 2, 2, 2, 1, 3, 3] => 1, 2, 1, 2, 2, 2, 1, 3, 3
[1, 2, 1, 2, 2, 2, 2, 1, 1] => 1, 2, 1, 2, 2, 2, 2, 1, 1
[1, 2, 1, 2, 2, 2, 2, 1, 2] => 1, 2, 1, 2, 2, 2, 2, 1, 2
[1, 2, 1, 2, 2, 2, 2, 1, 3] => 1, 2, 1, 2, 2, 2, 2, 1, 3
[1, 2, 1, 2, 2, 2, 2, 2, 1] => 1, 2, 1, 2, 2, 2, 2, 2, 1
[1, 2, 1, 2, 2, 2, 2, 2, 2] => 1, 2, 1, 2, 2, 2, 2, 2, 2
[1, 2, 1, 2, 2, 2, 2, 2, 3] => 1, 2, 1, 2, 2, 2, 2, 2, 3
[1, 2, 1, 2, 2, 2, 2, 3, 1] => 1, 2, 1, 2, 2, 2, 2, 3, 1
[1, 2, 1, 2, 2, 2, 2, 3, 2] => 1, 2, 1, 2, 2, 2, 2, 3, 2
[1, 2, 1, 2, 2, 2, 2, 3, 3] => 1, 2, 1, 2, 2, 2, 2, 3, 3
[1, 2, 1, 2, 2, 2, 3, 1, 1] => 1, 2, 1, 2, 2, 2, 3, 1, 1
[1, 2, 1, 2, 2, 2, 3, 1, 2] => 1, 2, 1, 2, 2, 2, 3, 1, 2
[1, 2, 1, 2, 2, 2, 3, 1, 3] => 1, 2, 1, 2, 2, 2, 3, 1, 3
[1, 2, 1, 2, 2, 2, 3, 2, 1] => 1, 2, 1, 2, 2, 2, 3, 2, 1
[1, 2, 1, 2, 2, 2, 3, 2, 2] => 1, 2, 1, 2, 2, 2, 3, 2, 2
[1, 2, 1, 2, 2, 2, 3, 2, 3] => 1, 2, 1, 2, 2, 2, 3, 2, 3
[1, 2, 1, 2, 2, 2, 3, 3, 1] => 1, 2, 1, 2, 2, 2, 3, 3, 1
[1, 2, 1, 2, 2, 2, 3, 3, 2] => 1, 2, 1, 2, 2, 2, 3, 3, 2
[1, 2, 1, 2, 2, 2, 3, 3, 3] => 1, 2, 1, 2, 2, 2, 3, 3, 3
[1, 2, 1, 2, 2, 3, 1, 1, 1] => 1, 2, 1, 2, 2, 3, 1, 1, 1
[1, 2, 1, 2, 2, 3, 1, 1, 2] => 1, 2, 1, 2, 2, 3, 1, 1, 2
[1, 2, 1, 2, 2, 3, 1, 1, 3] => 1, 2, 1, 2, 2, 3, 1, 1, 3
[1, 2, 1, 2, 2, 3, 1, 2, 1] => 1, 2, 1, 2, 2, 3, 1, 2, 1
[1, 2, 1, 2, 2, 3, 1, 2, 2] => 1, 2, 1, 2, 2, 3, 1, 2, 2
[1, 2, 1, 2, 2, 3, 1, 2, 3] => 1, 2, 1, 2, 2, 3, 1, 2, 3
[1, 2, 1, 2, 2, 3, 1, 3, 1] => 1, 2, 1, 2, 2, 3, 1, 3, 1
[1, 2, 1, 2, 2, 3, 1, 3, 2] => 1, 2, 1, 2, 2, 3, 1, 3, 2
[1, 2, 1, 2, 2, 3, 1, 3, 3] => 1, 2, 1, 2, 2, 3, 1, 3, 3
[1, 2, 1, 2, 2, 3, 2, 1, 1] => 1, 2, 1, 2, 2, 3, 2, 1, 1
[1, 2, 1, 2, 2, 3, 2, 1, 2] => 1, 2, 1, 2, 2, 3, 2, 1, 2
[1, 2, 1, 2, 2, 3, 2, 1, 3] => 1, 2, 1, 2, 2, 3, 2, 1, 3
[1, 2, 1, 2, 2, 3, 2, 2, 1] => 1, 2, 1, 2, 2, 3, 2, 2, 1
[1, 2, 1, 2, 2, 3, 2, 2, 2] => 1, 2, 1, 2, 2, 3, 2, 2, 2
[1, 2, 1, 2, 2, 3, 2, 2, 3] => 1, 2, 1, 2, 2, 3, 2, 2, 3
[1, 2, 1, 2, 2, 3, 2, 3, 1] => 1, 2, 1, 2, 2, 3, 2, 3, 1
[1, 2, 1, 2, 2, 3, 2, 3, 2] => 1, 2, 1, 2, 2, 3, 2, 3, 2
[1, 2, 1, 2, 2, 3, 2, 3, 3] => 1, 2, 1, 2, 2, 3, 2, 3, 3
[1, 2, 1, 2, 2, 3, 3, 1, 1] => 1, 2, 1, 2, 2, 3, 3, 1, 1
[1, 2, 1, 2, 2, 3, 3, 1, 2] => 1, 2, 1, 2, 2, 3, 3, 1, 2
[1, 2, 1, 2, 2, 3, 3, 1, 3] => 1, 2, 1, 2, 2, 3, 3, 1, 3
[1, 2, 1, 2, 2, 3, 3, 2, 1] => 1, 2, 1, 2, 2, 3, 3, 2, 1
[1, 2, 1, 2, 2, 3, 3, 2, 2] => 1, 2, 1, 2, 2, 3, 3, 2, 2
[1, 2, 1, 2, 2, 3, 3, 2, 3] => 1, 2, 1, 2, 2, 3, 3, 2, 3
[1, 2, 1, 2, 2, 3, 3, 3, 1] => 1, 2, 1, 2, 2, 3, 3, 3, 1
[1, 2, 1, 2, 2, 3, 3, 3, 2] => 1, 2, 1, 2, 2, 3, 3, 3, 2
[1, 2, 1, 2, 2, 3, 3, 3, 3] => 1, 2, 1, 2, 2, 3, 3, 3, 3
[1, 2, 1, 2, 3, 1, 1, 1, 1] => 1, 2, 1, 2, 3, 1, 1, 1, 1
[1, 2, 1, 2, 3, 1, 1, 1, 2] => 1, 2, 1, 2, 3, 1, 1, 1, 2
[1, 2, 1, 2, 3, 1, 1, 1, 3] => 1, 2, 1, 2, 3, 1, 1, 1, 3
[1, 2, 1, 2, 3, 1, 1, 2, 1] => 1, 2, 1, 2, 3, 1, 1, 2, 1
[1, 2, 1, 2, 3, 1, 1, 2, 2] => 1, 2, 1, 2, 3, 1, 1, 2, 2
[1, 2, 1, 2, 3, 1, 1, 2, 3] => 1, 2, 1, 2, 3, 1, 1, 2, 3
[1, 2, 1, 2, 3, 1, 1, 3, 1] => 1, 2, 1, 2, 3, 1, 1, 3, 1
[1, 2, 1, 2, 3, 1, 1, 3, 2] => 1, 2, 1, 2, 3, 1, 1, 3, 2
[1, 2, 1, 2, 3, 1, 1, 3, 3] => 1, 2, 1, 2, 3, 1, 1, 3, 3
[1, 2, 1, 2, 3, 1, 2, 1, 1] => 1, 2, 1, 2, 3, 1, 2, 1, 1
[1, 2, 1, 2, 3, 1, 2, 1, 2] => 1, 2, 1, 2, 3, 1, 2, 1, 2
[1, 2, 1, 2, 3, 1, 2, 1, 3] => 1, 2, 1, 2, 3, 1, 2, 1, 3
[1, 2, 1, 2, 3, 1, 2, 2, 1] => 1, 2, 1, 2, 3, 1, 2, 2, 1
[1, 2, 1, 2, 3, 1, 2, 2, 2] => 1, 2, 1, 2, 3, 1, 2, 2, 2
[1, 2, 1, 2, 3, 1, 2, 2, 3] => 1, 2, 1, 2, 3, 1, 2, 2, 3
[1, 2, 1, 2, 3, 1, 2, 3, 1] => 1, 2, 1, 2, 3, 1, 2, 3, 1
[1, 2, 1, 2, 3, 1, 2, 3, 2] => 1, 2, 1, 2, 3, 1, 2, 3, 2
[1, 2, 1, 2, 3, 1, 2, 3, 3] => 1, 2, 1, 2, 3, 1, 2, 3, 3
[1, 2, 1, 2, 3, 1, 3, 1, 1] => 1, 2, 1, 2, 3, 1, 3, 1, 1
[1, 2, 1, 2, 3, 1, 3, 1, 2] => 1, 2, 1, 2, 3, 1, 3, 1, 2
[1, 2, 1, 2, 3, 1, 3, 1, 3] => 1, 2, 1, 2, 3, 1, 3, 1, 3
[1, 2, 1, 2, 3, 1, 3, 2, 1] => 1, 2, 1, 2, 3, 1, 3, 2, 1
[1, 2, 1, 2, 3, 1, 3, 2, 2] => 1, 2, 1, 2, 3, 1, 3, 2, 2
[1, 2, 1, 2, 3, 1, 3, 2, 3] => 1, 2, 1, 2, 3, 1, 3, 2, 3
[1, 2, 1, 2, 3, 1, 3, 3, 1] => 1, 2, 1, 2, 3, 1, 3, 3, 1
[1, 2, 1, 2, 3, 1, 3, 3, 2] => 1, 2, 1, 2, 3, 1, 3, 3, 2
[1, 2, 1, 2, 3, 1, 3, 3, 3] => 1, 2, 1, 2, 3, 1, 3, 3, 3
[1, 2, 1, 2, 3, 2, 1, 1, 1] => 1, 2, 1, 2, 3, 2, 1, 1, 1
[1, 2, 1, 2, 3, 2, 1, 1, 2] => 1, 2, 1, 2, 3, 2, 1, 1, 2
[1, 2, 1, 2, 3, 2, 1, 1, 3] => 1, 2, 1, 2, 3, 2, 1, 1, 3
[1, 2, 1, 2, 3, 2, 1, 2, 1] => 1, 2, 1, 2, 3, 2, 1, 2, 1
[1, 2, 1, 2, 3, 2, 1, 2, 2] => 1, 2, 1, 2, 3, 2, 1, 2, 2
[1, 2, 1, 2, 3, 2, 1, 2, 3] => 1, 2, 1, 2, 3, 2, 1, 2, 3
[1, 2, 1, 2, 3, 2, 1, 3, 1] => 1, 2, 1, 2, 3, 2, 1, 3, 1
[1, 2, 1, 2, 3, 2, 1, 3, 2] => 1, 2, 1, 2, 3, 2, 1, 3, 2
[1, 2, 1, 2, 3, 2, 1, 3, 3] => 1, 2, 1, 2, 3, 2, 1, 3, 3
[1, 2, 1, 2, 3, 2, 2, 1, 1] => 1, 2, 1, 2, 3, 2, 2, 1, 1
[1, 2, 1, 2, 3, 2, 2, 1, 2] => 1, 2, 1, 2, 3, 2, 2, 1, 2
[1, 2, 1, 2, 3, 2, 2, 1, 3] => 1, 2, 1, 2, 3, 2, 2, 1, 3
[1, 2, 1, 2, 3, 2, 2, 2, 1] => 1, 2, 1, 2, 3, 2, 2, 2, 1
[1, 2, 1, 2, 3, 2, 2, 2, 2] => 1, 2, 1, 2, 3, 2, 2, 2, 2
[1, 2, 1, 2, 3, 2, 2, 2, 3] => 1, 2, 1, 2, 3, 2, 2, 2, 3
[1, 2, 1, 2, 3, 2, 2, 3, 1] => 1, 2, 1, 2, 3, 2, 2, 3, 1
[1, 2, 1, 2, 3, 2, 2, 3, 2] => 1, 2, 1, 2, 3, 2, 2, 3, 2
[1, 2, 1, 2, 3, 2, 2, 3, 3] => 1, 2, 1, 2, 3, 2, 2, 3, 3
[1, 2, 1, 2, 3, 2, 3, 1, 1] => 1, 2, 1, 2, 3, 2, 3, 1, 1
[1, 2, 1, 2, 3, 2, 3, 1, 2] => 1, 2, 1, 2, 3, 2, 3, 1, 2
[1, 2, 1, 2, 3, 2, 3, 1, 3] => 1, 2, 1, 2, 3, 2, 3, 1, 3
[1, 2, 1, 2, 3, 2, 3, 2, 1] => 1, 2, 1, 2, 3, 2, 3, 2, 1
[1, 2, 1, 2, 3, 2, 3, 2, 2] => 1, 2, 1, 2, 3, 2, 3, 2, 2
[1, 2, 1, 2, 3, 2, 3, 2, 3] => 1, 2, 1, 2, 3, 2, 3, 2, 3
[1, 2, 1, 2, 3, 2, 3, 3, 1] => 1, 2, 1, 2, 3, 2, 3, 3, 1
[1, 2, 1, 2, 3, 2, 3, 3, 2] => 1, 2, 1, 2, 3, 2, 3, 3, 2
[1, 2, 1, 2, 3, 2, 3, 3, 3] => 1, 2, 1, 2, 3, 2, 3, 3, 3
[1, 2, 1, 2, 3, 3, 1, 1, 1] => 1, 2, 1, 2, 3, 3, 1, 1, 1
[1, 2, 1, 2, 3, 3, 1, 1, 2] => 1, 2, 1, 2, 3, 3, 1, 1, 2
[1, 2, 1, 2, 3, 3, 1, 1, 3] => 1, 2, 1, 2, 3, 3, 1, 1, 3
[1, 2, 1, 2, 3, 3, 1, 2, 1] => 1, 2, 1, 2, 3, 3, 1, 2, 1
[1, 2, 1, 2, 3, 3, 1, 2, 2] => 1, 2, 1, 2, 3, 3, 1, 2, 2
[1, 2, 1, 2, 3, 3, 1, 2, 3] => 1, 2, 1, 2, 3, 3, 1, 2, 3
[1, 2, 1, 2, 3, 3, 1, 3, 1] => 1, 2, 1, 2, 3, 3, 1, 3, 1
[1, 2, 1, 2, 3, 3, 1, 3, 2] => 1, 2, 1, 2, 3, 3, 1, 3, 2
[1, 2, 1, 2, 3, 3, 1, 3, 3] => 1, 2, 1, 2, 3, 3, 1, 3, 3
[1, 2, 1, 2, 3, 3, 2, 1, 1] => 1, 2, 1, 2, 3, 3, 2, 1, 1
[1, 2, 1, 2, 3, 3, 2, 1, 2] => 1, 2, 1, 2, 3, 3, 2, 1, 2
[1, 2, 1, 2, 3, 3, 2, 1, 3] => 1, 2, 1, 2, 3, 3, 2, 1, 3
[1, 2, 1, 2, 3, 3, 2, 2, 1] => 1, 2, 1, 2, 3, 3, 2, 2, 1
[1, 2, 1, 2, 3, 3, 2, 2, 2] => 1, 2, 1, 2, 3, 3, 2, 2, 2
[1, 2, 1, 2, 3, 3, 2, 2, 3] => 1, 2, 1, 2, 3, 3, 2, 2, 3
[1, 2, 1, 2, 3, 3, 2, 3, 1] => 1, 2, 1, 2, 3, 3, 2, 3, 1
[1, 2, 1, 2, 3, 3, 2, 3, 2] => 1, 2, 1, 2, 3, 3, 2, 3, 2
[1, 2, 1, 2, 3, 3, 2, 3, 3] => 1, 2, 1, 2, 3, 3, 2, 3, 3
[1, 2, 1, 2, 3, 3, 3, 1, 1] => 1, 2, 1, 2, 3, 3, 3, 1, 1
[1, 2, 1, 2, 3, 3, 3, 1, 2] => 1, 2, 1, 2, 3, 3, 3, 1, 2
[1, 2, 1, 2, 3, 3, 3, 1, 3] => 1, 2, 1, 2, 3, 3, 3, 1, 3
[1, 2, 1, 2, 3, 3, 3, 2, 1] => 1, 2, 1, 2, 3, 3, 3, 2, 1
[1, 2, 1, 2, 3, 3, 3, 2, 2] => 1, 2, 1, 2, 3, 3, 3, 2, 2
[1, 2, 1, 2, 3, 3, 3, 2, 3] => 1, 2, 1, 2, 3, 3, 3, 2, 3
[1, 2, 1, 2, 3, 3, 3, 3, 1] => 1, 2, 1, 2, 3, 3, 3, 3, 1
[1, 2, 1, 2, 3, 3, 3, 3, 2] => 1, 2, 1, 2, 3, 3, 3, 3, 2
[1, 2, 1, 2, 3, 3, 3, 3, 3] => 1, 2, 1, 2, 3, 3, 3, 3, 3
[1, 2, 1, 3, 1, 1, 1, 1, 1] => 1, 2, 1, 3, 1, 1, 1, 1, 1
[1, 2, 1, 3, 1, 1, 1, 1, 2] => 1, 2, 1, 3, 1, 1, 1, 1, 2
[1, 2, 1, 3, 1, 1, 1, 1, 3] => 1, 2, 1, 3, 1, 1, 1, 1, 3
[1, 2, 1, 3, 1, 1, 1, 2, 1] => 1, 2, 1, 3, 1, 1, 1, 2, 1
[1, 2, 1, 3, 1, 1, 1, 2, 2] => 1, 2, 1, 3, 1, 1, 1, 2, 2
[1, 2, 1, 3, 1, 1, 1, 2, 3] => 1, 2, 1, 3, 1, 1, 1, 2, 3
[1, 2, 1, 3, 1, 1, 1, 3, 1] => 1, 2, 1, 3, 1, 1, 1, 3, 1
[1, 2, 1, 3, 1, 1, 1, 3, 2] => 1, 2, 1, 3, 1, 1, 1, 3, 2
[1, 2, 1, 3, 1, 1, 1, 3, 3] => 1, 2, 1, 3, 1, 1, 1, 3, 3
[1, 2, 1, 3, 1, 1, 2, 1, 1] => 1, 2, 1, 3, 1, 1, 2, 1, 1
[1, 2, 1, 3, 1, 1, 2, 1, 2] => 1, 2, 1, 3, 1, 1, 2, 1, 2
[1, 2, 1, 3, 1, 1, 2, 1, 3] => 1, 2, 1, 3, 1, 1, 2, 1, 3
[1, 2, 1, 3, 1, 1, 2, 2, 1] => 1, 2, 1, 3, 1, 1, 2, 2, 1
[1, 2, 1, 3, 1, 1, 2, 2, 2] => 1, 2, 1, 3, 1, 1, 2, 2, 2
[1, 2, 1, 3, 1, 1, 2, 2, 3] => 1, 2, 1, 3, 1, 1, 2, 2, 3
[1, 2, 1, 3, 1, 1, 2, 3, 1] => 1, 2, 1, 3, 1, 1, 2, 3, 1
[1, 2, 1, 3, 1, 1, 2, 3, 2] => 1, 2, 1, 3, 1, 1, 2, 3, 2
[1, 2, 1, 3, 1, 1, 2, 3, 3] => 1, 2, 1, 3, 1, 1, 2, 3, 3
[1, 2, 1, 3, 1, 1, 3, 1, 1] => 1, 2, 1, 3, 1, 1, 3, 1, 1
[1, 2, 1, 3, 1, 1, 3, 1, 2] => 1, 2, 1, 3, 1, 1, 3, 1, 2
[1, 2, 1, 3, 1, 1, 3, 1, 3] => 1, 2, 1, 3, 1, 1, 3, 1, 3
[1, 2, 1, 3, 1, 1, 3, 2, 1] => 1, 2, 1, 3, 1, 1, 3, 2, 1
[1, 2, 1, 3, 1, 1, 3, 2, 2] => 1, 2, 1, 3, 1, 1, 3, 2, 2
[1, 2, 1, 3, 1, 1, 3, 2, 3] => 1, 2, 1, 3, 1, 1, 3, 2, 3
[1, 2, 1, 3, 1, 1, 3, 3, 1] => 1, 2, 1, 3, 1, 1, 3, 3, 1
[1, 2, 1, 3, 1, 1, 3, 3, 2] => 1, 2, 1, 3, 1, 1, 3, 3, 2
[1, 2, 1, 3, 1, 1, 3, 3, 3] => 1, 2, 1, 3, 1, 1, 3, 3, 3
[1, 2, 1, 3, 1, 2, 1, 1, 1] => 1, 2, 1, 3, 1, 2, 1, 1, 1
[1, 2, 1, 3, 1, 2, 1, 1, 2] => 1, 2, 1, 3, 1, 2, 1, 1, 2
[1, 2, 1, 3, 1, 2, 1, 1, 3] => 1, 2, 1, 3, 1, 2, 1, 1, 3
[1, 2, 1, 3, 1, 2, 1, 2, 1] => 1, 2, 1, 3, 1, 2, 1, 2, 1
[1, 2, 1, 3, 1, 2, 1, 2, 2] => 1, 2, 1, 3, 1, 2, 1, 2, 2
[1, 2, 1, 3, 1, 2, 1, 2, 3] => 1, 2, 1, 3, 1, 2, 1, 2, 3
[1, 2, 1, 3, 1, 2, 1, 3, 1] => 1, 2, 1, 3, 1, 2, 1, 3, 1
[1, 2, 1, 3, 1, 2, 1, 3, 2] => 1, 2, 1, 3, 1, 2, 1, 3, 2
[1, 2, 1, 3, 1, 2, 1, 3, 3] => 1, 2, 1, 3, 1, 2, 1, 3, 3
[1, 2, 1, 3, 1, 2, 2, 1, 1] => 1, 2, 1, 3, 1, 2, 2, 1, 1
[1, 2, 1, 3, 1, 2, 2, 1, 2] => 1, 2, 1, 3, 1, 2, 2, 1, 2
[1, 2, 1, 3, 1, 2, 2, 1, 3] => 1, 2, 1, 3, 1, 2, 2, 1, 3
[1, 2, 1, 3, 1, 2, 2, 2, 1] => 1, 2, 1, 3, 1, 2, 2, 2, 1
[1, 2, 1, 3, 1, 2, 2, 2, 2] => 1, 2, 1, 3, 1, 2, 2, 2, 2
[1, 2, 1, 3, 1, 2, 2, 2, 3] => 1, 2, 1, 3, 1, 2, 2, 2, 3
[1, 2, 1, 3, 1, 2, 2, 3, 1] => 1, 2, 1, 3, 1, 2, 2, 3, 1
[1, 2, 1, 3, 1, 2, 2, 3, 2] => 1, 2, 1, 3, 1, 2, 2, 3, 2
[1, 2, 1, 3, 1, 2, 2, 3, 3] => 1, 2, 1, 3, 1, 2, 2, 3, 3
[1, 2, 1, 3, 1, 2, 3, 1, 1] => 1, 2, 1, 3, 1, 2, 3, 1, 1
[1, 2, 1, 3, 1, 2, 3, 1, 2] => 1, 2, 1, 3, 1, 2, 3, 1, 2
[1, 2, 1, 3, 1, 2, 3, 1, 3] => 1, 2, 1, 3, 1, 2, 3, 1, 3
[1, 2, 1, 3, 1, 2, 3, 2, 1] => 1, 2, 1, 3, 1, 2, 3, 2, 1
[1, 2, 1, 3, 1, 2, 3, 2, 2] => 1, 2, 1, 3, 1, 2, 3, 2, 2
[1, 2, 1, 3, 1, 2, 3, 2, 3] => 1, 2, 1, 3, 1, 2, 3, 2, 3
[1, 2, 1, 3, 1, 2, 3, 3, 1] => 1, 2, 1, 3, 1, 2, 3, 3, 1
[1, 2, 1, 3, 1, 2, 3, 3, 2] => 1, 2, 1, 3, 1, 2, 3, 3, 2
[1, 2, 1, 3, 1, 2, 3, 3, 3] => 1, 2, 1, 3, 1, 2, 3, 3, 3
[1, 2, 1, 3, 1, 3, 1, 1, 1] => 1, 2, 1, 3, 1, 3, 1, 1, 1
[1, 2, 1, 3, 1, 3, 1, 1, 2] => 1, 2, 1, 3, 1, 3, 1, 1, 2
[1, 2, 1, 3, 1, 3, 1, 1, 3] => 1, 2, 1, 3, 1, 3, 1, 1, 3
[1, 2, 1, 3, 1, 3, 1, 2, 1] => 1, 2, 1, 3, 1, 3, 1, 2, 1
[1, 2, 1, 3, 1, 3, 1, 2, 2] => 1, 2, 1, 3, 1, 3, 1, 2, 2
[1, 2, 1, 3, 1, 3, 1, 2, 3] => 1, 2, 1, 3, 1, 3, 1, 2, 3
[1, 2, 1, 3, 1, 3, 1, 3, 1] => 1, 2, 1, 3, 1, 3, 1, 3, 1
[1, 2, 1, 3, 1, 3, 1, 3, 2] => 1, 2, 1, 3, 1, 3, 1, 3, 2
[1, 2, 1, 3, 1, 3, 1, 3, 3] => 1, 2, 1, 3, 1, 3, 1, 3, 3
[1, 2, 1, 3, 1, 3, 2, 1, 1] => 1, 2, 1, 3, 1, 3, 2, 1, 1
[1, 2, 1, 3, 1, 3, 2, 1, 2] => 1, 2, 1, 3, 1, 3, 2, 1, 2
[1, 2, 1, 3, 1, 3, 2, 1, 3] => 1, 2, 1, 3, 1, 3, 2, 1, 3
[1, 2, 1, 3, 1, 3, 2, 2, 1] => 1, 2, 1, 3, 1, 3, 2, 2, 1
[1, 2, 1, 3, 1, 3, 2, 2, 2] => 1, 2, 1, 3, 1, 3, 2, 2, 2
[1, 2, 1, 3, 1, 3, 2, 2, 3] => 1, 2, 1, 3, 1, 3, 2, 2, 3
[1, 2, 1, 3, 1, 3, 2, 3, 1] => 1, 2, 1, 3, 1, 3, 2, 3, 1
[1, 2, 1, 3, 1, 3, 2, 3, 2] => 1, 2, 1, 3, 1, 3, 2, 3, 2
[1, 2, 1, 3, 1, 3, 2, 3, 3] => 1, 2, 1, 3, 1, 3, 2, 3, 3
[1, 2, 1, 3, 1, 3, 3, 1, 1] => 1, 2, 1, 3, 1, 3, 3, 1, 1
[1, 2, 1, 3, 1, 3, 3, 1, 2] => 1, 2, 1, 3, 1, 3, 3, 1, 2
[1, 2, 1, 3, 1, 3, 3, 1, 3] => 1, 2, 1, 3, 1, 3, 3, 1, 3
[1, 2, 1, 3, 1, 3, 3, 2, 1] => 1, 2, 1, 3, 1, 3, 3, 2, 1
[1, 2, 1, 3, 1, 3, 3, 2, 2] => 1, 2, 1, 3, 1, 3, 3, 2, 2
[1, 2, 1, 3, 1, 3, 3, 2, 3] => 1, 2, 1, 3, 1, 3, 3, 2, 3
[1, 2, 1, 3, 1, 3, 3, 3, 1] => 1, 2, 1, 3, 1, 3, 3, 3, 1
[1, 2, 1, 3, 1, 3, 3, 3, 2] => 1, 2, 1, 3, 1, 3, 3, 3, 2
[1, 2, 1, 3, 1, 3, 3, 3, 3] => 1, 2, 1, 3, 1, 3, 3, 3, 3
[1, 2, 1, 3, 2, 1, 1, 1, 1] => 1, 2, 1, 3, 2, 1, 1, 1, 1
[1, 2, 1, 3, 2, 1, 1, 1, 2] => 1, 2, 1, 3, 2, 1, 1, 1, 2
[1, 2, 1, 3, 2, 1, 1, 1, 3] => 1, 2, 1, 3, 2, 1, 1, 1, 3
[1, 2, 1, 3, 2, 1, 1, 2, 1] => 1, 2, 1, 3, 2, 1, 1, 2, 1
[1, 2, 1, 3, 2, 1, 1, 2, 2] => 1, 2, 1, 3, 2, 1, 1, 2, 2
[1, 2, 1, 3, 2, 1, 1, 2, 3] => 1, 2, 1, 3, 2, 1, 1, 2, 3
[1, 2, 1, 3, 2, 1, 1, 3, 1] => 1, 2, 1, 3, 2, 1, 1, 3, 1
[1, 2, 1, 3, 2, 1, 1, 3, 2] => 1, 2, 1, 3, 2, 1, 1, 3, 2
[1, 2, 1, 3, 2, 1, 1, 3, 3] => 1, 2, 1, 3, 2, 1, 1, 3, 3
[1, 2, 1, 3, 2, 1, 2, 1, 1] => 1, 2, 1, 3, 2, 1, 2, 1, 1
[1, 2, 1, 3, 2, 1, 2, 1, 2] => 1, 2, 1, 3, 2, 1, 2, 1, 2
[1, 2, 1, 3, 2, 1, 2, 1, 3] => 1, 2, 1, 3, 2, 1, 2, 1, 3
[1, 2, 1, 3, 2, 1, 2, 2, 1] => 1, 2, 1, 3, 2, 1, 2, 2, 1
[1, 2, 1, 3, 2, 1, 2, 2, 2] => 1, 2, 1, 3, 2, 1, 2, 2, 2
[1, 2, 1, 3, 2, 1, 2, 2, 3] => 1, 2, 1, 3, 2, 1, 2, 2, 3
[1, 2, 1, 3, 2, 1, 2, 3, 1] => 1, 2, 1, 3, 2, 1, 2, 3, 1
[1, 2, 1, 3, 2, 1, 2, 3, 2] => 1, 2, 1, 3, 2, 1, 2, 3, 2
[1, 2, 1, 3, 2, 1, 2, 3, 3] => 1, 2, 1, 3, 2, 1, 2, 3, 3
[1, 2, 1, 3, 2, 1, 3, 1, 1] => 1, 2, 1, 3, 2, 1, 3, 1, 1
[1, 2, 1, 3, 2, 1, 3, 1, 2] => 1, 2, 1, 3, 2, 1, 3, 1, 2
[1, 2, 1, 3, 2, 1, 3, 1, 3] => 1, 2, 1, 3, 2, 1, 3, 1, 3
[1, 2, 1, 3, 2, 1, 3, 2, 1] => 1, 2, 1, 3, 2, 1, 3, 2, 1
[1, 2, 1, 3, 2, 1, 3, 2, 2] => 1, 2, 1, 3, 2, 1, 3, 2, 2
[1, 2, 1, 3, 2, 1, 3, 2, 3] => 1, 2, 1, 3, 2, 1, 3, 2, 3
[1, 2, 1, 3, 2, 1, 3, 3, 1] => 1, 2, 1, 3, 2, 1, 3, 3, 1
[1, 2, 1, 3, 2, 1, 3, 3, 2] => 1, 2, 1, 3, 2, 1, 3, 3, 2
[1, 2, 1, 3, 2, 1, 3, 3, 3] => 1, 2, 1, 3, 2, 1, 3, 3, 3
[1, 2, 1, 3, 2, 2, 1, 1, 1] => 1, 2, 1, 3, 2, 2, 1, 1, 1
[1, 2, 1, 3, 2, 2, 1, 1, 2] => 1, 2, 1, 3, 2, 2, 1, 1, 2
[1, 2, 1, 3, 2, 2, 1, 1, 3] => 1, 2, 1, 3, 2, 2, 1, 1, 3
[1, 2, 1, 3, 2, 2, 1, 2, 1] => 1, 2, 1, 3, 2, 2, 1, 2, 1
[1, 2, 1, 3, 2, 2, 1, 2, 2] => 1, 2, 1, 3, 2, 2, 1, 2, 2
[1, 2, 1, 3, 2, 2, 1, 2, 3] => 1, 2, 1, 3, 2, 2, 1, 2, 3
[1, 2, 1, 3, 2, 2, 1, 3, 1] => 1, 2, 1, 3, 2, 2, 1, 3, 1
[1, 2, 1, 3, 2, 2, 1, 3, 2] => 1, 2, 1, 3, 2, 2, 1, 3, 2
[1, 2, 1, 3, 2, 2, 1, 3, 3] => 1, 2, 1, 3, 2, 2, 1, 3, 3
[1, 2, 1, 3, 2, 2, 2, 1, 1] => 1, 2, 1, 3, 2, 2, 2, 1, 1
[1, 2, 1, 3, 2, 2, 2, 1, 2] => 1, 2, 1, 3, 2, 2, 2, 1, 2
[1, 2, 1, 3, 2, 2, 2, 1, 3] => 1, 2, 1, 3, 2, 2, 2, 1, 3
[1, 2, 1, 3, 2, 2, 2, 2, 1] => 1, 2, 1, 3, 2, 2, 2, 2, 1
[1, 2, 1, 3, 2, 2, 2, 2, 2] => 1, 2, 1, 3, 2, 2, 2, 2, 2
[1, 2, 1, 3, 2, 2, 2, 2, 3] => 1, 2, 1, 3, 2, 2, 2, 2, 3
[1, 2, 1, 3, 2, 2, 2, 3, 1] => 1, 2, 1, 3, 2, 2, 2, 3, 1
[1, 2, 1, 3, 2, 2, 2, 3, 2] => 1, 2, 1, 3, 2, 2, 2, 3, 2
[1, 2, 1, 3, 2, 2, 2, 3, 3] => 1, 2, 1, 3, 2, 2, 2, 3, 3
[1, 2, 1, 3, 2, 2, 3, 1, 1] => 1, 2, 1, 3, 2, 2, 3, 1, 1
[1, 2, 1, 3, 2, 2, 3, 1, 2] => 1, 2, 1, 3, 2, 2, 3, 1, 2
[1, 2, 1, 3, 2, 2, 3, 1, 3] => 1, 2, 1, 3, 2, 2, 3, 1, 3
[1, 2, 1, 3, 2, 2, 3, 2, 1] => 1, 2, 1, 3, 2, 2, 3, 2, 1
[1, 2, 1, 3, 2, 2, 3, 2, 2] => 1, 2, 1, 3, 2, 2, 3, 2, 2
[1, 2, 1, 3, 2, 2, 3, 2, 3] => 1, 2, 1, 3, 2, 2, 3, 2, 3
[1, 2, 1, 3, 2, 2, 3, 3, 1] => 1, 2, 1, 3, 2, 2, 3, 3, 1
[1, 2, 1, 3, 2, 2, 3, 3, 2] => 1, 2, 1, 3, 2, 2, 3, 3, 2
[1, 2, 1, 3, 2, 2, 3, 3, 3] => 1, 2, 1, 3, 2, 2, 3, 3, 3
[1, 2, 1, 3, 2, 3, 1, 1, 1] => 1, 2, 1, 3, 2, 3, 1, 1, 1
[1, 2, 1, 3, 2, 3, 1, 1, 2] => 1, 2, 1, 3, 2, 3, 1, 1, 2
[1, 2, 1, 3, 2, 3, 1, 1, 3] => 1, 2, 1, 3, 2, 3, 1, 1, 3
[1, 2, 1, 3, 2, 3, 1, 2, 1] => 1, 2, 1, 3, 2, 3, 1, 2, 1
[1, 2, 1, 3, 2, 3, 1, 2, 2] => 1, 2, 1, 3, 2, 3, 1, 2, 2
[1, 2, 1, 3, 2, 3, 1, 2, 3] => 1, 2, 1, 3, 2, 3, 1, 2, 3
[1, 2, 1, 3, 2, 3, 1, 3, 1] => 1, 2, 1, 3, 2, 3, 1, 3, 1
[1, 2, 1, 3, 2, 3, 1, 3, 2] => 1, 2, 1, 3, 2, 3, 1, 3, 2
[1, 2, 1, 3, 2, 3, 1, 3, 3] => 1, 2, 1, 3, 2, 3, 1, 3, 3
[1, 2, 1, 3, 2, 3, 2, 1, 1] => 1, 2, 1, 3, 2, 3, 2, 1, 1
[1, 2, 1, 3, 2, 3, 2, 1, 2] => 1, 2, 1, 3, 2, 3, 2, 1, 2
[1, 2, 1, 3, 2, 3, 2, 1, 3] => 1, 2, 1, 3, 2, 3, 2, 1, 3
[1, 2, 1, 3, 2, 3, 2, 2, 1] => 1, 2, 1, 3, 2, 3, 2, 2, 1
[1, 2, 1, 3, 2, 3, 2, 2, 2] => 1, 2, 1, 3, 2, 3, 2, 2, 2
[1, 2, 1, 3, 2, 3, 2, 2, 3] => 1, 2, 1, 3, 2, 3, 2, 2, 3
[1, 2, 1, 3, 2, 3, 2, 3, 1] => 1, 2, 1, 3, 2, 3, 2, 3, 1
[1, 2, 1, 3, 2, 3, 2, 3, 2] => 1, 2, 1, 3, 2, 3, 2, 3, 2
[1, 2, 1, 3, 2, 3, 2, 3, 3] => 1, 2, 1, 3, 2, 3, 2, 3, 3
[1, 2, 1, 3, 2, 3, 3, 1, 1] => 1, 2, 1, 3, 2, 3, 3, 1, 1
[1, 2, 1, 3, 2, 3, 3, 1, 2] => 1, 2, 1, 3, 2, 3, 3, 1, 2
[1, 2, 1, 3, 2, 3, 3, 1, 3] => 1, 2, 1, 3, 2, 3, 3, 1, 3
[1, 2, 1, 3, 2, 3, 3, 2, 1] => 1, 2, 1, 3, 2, 3, 3, 2, 1
[1, 2, 1, 3, 2, 3, 3, 2, 2] => 1, 2, 1, 3, 2, 3, 3, 2, 2
[1, 2, 1, 3, 2, 3, 3, 2, 3] => 1, 2, 1, 3, 2, 3, 3, 2, 3
[1, 2, 1, 3, 2, 3, 3, 3, 1] => 1, 2, 1, 3, 2, 3, 3, 3, 1
[1, 2, 1, 3, 2, 3, 3, 3, 2] => 1, 2, 1, 3, 2, 3, 3, 3, 2
[1, 2, 1, 3, 2, 3, 3, 3, 3] => 1, 2, 1, 3, 2, 3, 3, 3, 3
[1, 2, 1, 3, 3, 1, 1, 1, 1] => 1, 2, 1, 3, 3, 1, 1, 1, 1
[1, 2, 1, 3, 3, 1, 1, 1, 2] => 1, 2, 1, 3, 3, 1, 1, 1, 2
[1, 2, 1, 3, 3, 1, 1, 1, 3] => 1, 2, 1, 3, 3, 1, 1, 1, 3
[1, 2, 1, 3, 3, 1, 1, 2, 1] => 1, 2, 1, 3, 3, 1, 1, 2, 1
[1, 2, 1, 3, 3, 1, 1, 2, 2] => 1, 2, 1, 3, 3, 1, 1, 2, 2
[1, 2, 1, 3, 3, 1, 1, 2, 3] => 1, 2, 1, 3, 3, 1, 1, 2, 3
[1, 2, 1, 3, 3, 1, 1, 3, 1] => 1, 2, 1, 3, 3, 1, 1, 3, 1
[1, 2, 1, 3, 3, 1, 1, 3, 2] => 1, 2, 1, 3, 3, 1, 1, 3, 2
[1, 2, 1, 3, 3, 1, 1, 3, 3] => 1, 2, 1, 3, 3, 1, 1, 3, 3
[1, 2, 1, 3, 3, 1, 2, 1, 1] => 1, 2, 1, 3, 3, 1, 2, 1, 1
[1, 2, 1, 3, 3, 1, 2, 1, 2] => 1, 2, 1, 3, 3, 1, 2, 1, 2
[1, 2, 1, 3, 3, 1, 2, 1, 3] => 1, 2, 1, 3, 3, 1, 2, 1, 3
[1, 2, 1, 3, 3, 1, 2, 2, 1] => 1, 2, 1, 3, 3, 1, 2, 2, 1
[1, 2, 1, 3, 3, 1, 2, 2, 2] => 1, 2, 1, 3, 3, 1, 2, 2, 2
[1, 2, 1, 3, 3, 1, 2, 2, 3] => 1, 2, 1, 3, 3, 1, 2, 2, 3
[1, 2, 1, 3, 3, 1, 2, 3, 1] => 1, 2, 1, 3, 3, 1, 2, 3, 1
[1, 2, 1, 3, 3, 1, 2, 3, 2] => 1, 2, 1, 3, 3, 1, 2, 3, 2
[1, 2, 1, 3, 3, 1, 2, 3, 3] => 1, 2, 1, 3, 3, 1, 2, 3, 3
[1, 2, 1, 3, 3, 1, 3, 1, 1] => 1, 2, 1, 3, 3, 1, 3, 1, 1
[1, 2, 1, 3, 3, 1, 3, 1, 2] => 1, 2, 1, 3, 3, 1, 3, 1, 2
[1, 2, 1, 3, 3, 1, 3, 1, 3] => 1, 2, 1, 3, 3, 1, 3, 1, 3
[1, 2, 1, 3, 3, 1, 3, 2, 1] => 1, 2, 1, 3, 3, 1, 3, 2, 1
[1, 2, 1, 3, 3, 1, 3, 2, 2] => 1, 2, 1, 3, 3, 1, 3, 2, 2
[1, 2, 1, 3, 3, 1, 3, 2, 3] => 1, 2, 1, 3, 3, 1, 3, 2, 3
[1, 2, 1, 3, 3, 1, 3, 3, 1] => 1, 2, 1, 3, 3, 1, 3, 3, 1
[1, 2, 1, 3, 3, 1, 3, 3, 2] => 1, 2, 1, 3, 3, 1, 3, 3, 2
[1, 2, 1, 3, 3, 1, 3, 3, 3] => 1, 2, 1, 3, 3, 1, 3, 3, 3
[1, 2, 1, 3, 3, 2, 1, 1, 1] => 1, 2, 1, 3, 3, 2, 1, 1, 1
[1, 2, 1, 3, 3, 2, 1, 1, 2] => 1, 2, 1, 3, 3, 2, 1, 1, 2
[1, 2, 1, 3, 3, 2, 1, 1, 3] => 1, 2, 1, 3, 3, 2, 1, 1, 3
[1, 2, 1, 3, 3, 2, 1, 2, 1] => 1, 2, 1, 3, 3, 2, 1, 2, 1
[1, 2, 1, 3, 3, 2, 1, 2, 2] => 1, 2, 1, 3, 3, 2, 1, 2, 2
[1, 2, 1, 3, 3, 2, 1, 2, 3] => 1, 2, 1, 3, 3, 2, 1, 2, 3
[1, 2, 1, 3, 3, 2, 1, 3, 1] => 1, 2, 1, 3, 3, 2, 1, 3, 1
[1, 2, 1, 3, 3, 2, 1, 3, 2] => 1, 2, 1, 3, 3, 2, 1, 3, 2
[1, 2, 1, 3, 3, 2, 1, 3, 3] => 1, 2, 1, 3, 3, 2, 1, 3, 3
[1, 2, 1, 3, 3, 2, 2, 1, 1] => 1, 2, 1, 3, 3, 2, 2, 1, 1
[1, 2, 1, 3, 3, 2, 2, 1, 2] => 1, 2, 1, 3, 3, 2, 2, 1, 2
[1, 2, 1, 3, 3, 2, 2, 1, 3] => 1, 2, 1, 3, 3, 2, 2, 1, 3
[1, 2, 1, 3, 3, 2, 2, 2, 1] => 1, 2, 1, 3, 3, 2, 2, 2, 1
[1, 2, 1, 3, 3, 2, 2, 2, 2] => 1, 2, 1, 3, 3, 2, 2, 2, 2
[1, 2, 1, 3, 3, 2, 2, 2, 3] => 1, 2, 1, 3, 3, 2, 2, 2, 3
[1, 2, 1, 3, 3, 2, 2, 3, 1] => 1, 2, 1, 3, 3, 2, 2, 3, 1
[1, 2, 1, 3, 3, 2, 2, 3, 2] => 1, 2, 1, 3, 3, 2, 2, 3, 2
[1, 2, 1, 3, 3, 2, 2, 3, 3] => 1, 2, 1, 3, 3, 2, 2, 3, 3
[1, 2, 1, 3, 3, 2, 3, 1, 1] => 1, 2, 1, 3, 3, 2, 3, 1, 1
[1, 2, 1, 3, 3, 2, 3, 1, 2] => 1, 2, 1, 3, 3, 2, 3, 1, 2
[1, 2, 1, 3, 3, 2, 3, 1, 3] => 1, 2, 1, 3, 3, 2, 3, 1, 3
[1, 2, 1, 3, 3, 2, 3, 2, 1] => 1, 2, 1, 3, 3, 2, 3, 2, 1
[1, 2, 1, 3, 3, 2, 3, 2, 2] => 1, 2, 1, 3, 3, 2, 3, 2, 2
[1, 2, 1, 3, 3, 2, 3, 2, 3] => 1, 2, 1, 3, 3, 2, 3, 2, 3
[1, 2, 1, 3, 3, 2, 3, 3, 1] => 1, 2, 1, 3, 3, 2, 3, 3, 1
[1, 2, 1, 3, 3, 2, 3, 3, 2] => 1, 2, 1, 3, 3, 2, 3, 3, 2
[1, 2, 1, 3, 3, 2, 3, 3, 3] => 1, 2, 1, 3, 3, 2, 3, 3, 3
[1, 2, 1, 3, 3, 3, 1, 1, 1] => 1, 2, 1, 3, 3, 3, 1, 1, 1
[1, 2, 1, 3, 3, 3, 1, 1, 2] => 1, 2, 1, 3, 3, 3, 1, 1, 2
[1, 2, 1, 3, 3, 3, 1, 1, 3] => 1, 2, 1, 3, 3, 3, 1, 1, 3
[1, 2, 1, 3, 3, 3, 1, 2, 1] => 1, 2, 1, 3, 3, 3, 1, 2, 1
[1, 2, 1, 3, 3, 3, 1, 2, 2] => 1, 2, 1, 3, 3, 3, 1, 2, 2
[1, 2, 1, 3, 3, 3, 1, 2, 3] => 1, 2, 1, 3, 3, 3, 1, 2, 3
[1, 2, 1, 3, 3, 3, 1, 3, 1] => 1, 2, 1, 3, 3, 3, 1, 3, 1
[1, 2, 1, 3, 3, 3, 1, 3, 2] => 1, 2, 1, 3, 3, 3, 1, 3, 2
[1, 2, 1, 3, 3, 3, 1, 3, 3] => 1, 2, 1, 3, 3, 3, 1, 3, 3
[1, 2, 1, 3, 3, 3, 2, 1, 1] => 1, 2, 1, 3, 3, 3, 2, 1, 1
[1, 2, 1, 3, 3, 3, 2, 1, 2] => 1, 2, 1, 3, 3, 3, 2, 1, 2
[1, 2, 1, 3, 3, 3, 2, 1, 3] => 1, 2, 1, 3, 3, 3, 2, 1, 3
[1, 2, 1, 3, 3, 3, 2, 2, 1] => 1, 2, 1, 3, 3, 3, 2, 2, 1
[1, 2, 1, 3, 3, 3, 2, 2, 2] => 1, 2, 1, 3, 3, 3, 2, 2, 2
[1, 2, 1, 3, 3, 3, 2, 2, 3] => 1, 2, 1, 3, 3, 3, 2, 2, 3
[1, 2, 1, 3, 3, 3, 2, 3, 1] => 1, 2, 1, 3, 3, 3, 2, 3, 1
[1, 2, 1, 3, 3, 3, 2, 3, 2] => 1, 2, 1, 3, 3, 3, 2, 3, 2
[1, 2, 1, 3, 3, 3, 2, 3, 3] => 1, 2, 1, 3, 3, 3, 2, 3, 3
[1, 2, 1, 3, 3, 3, 3, 1, 1] => 1, 2, 1, 3, 3, 3, 3, 1, 1
[1, 2, 1, 3, 3, 3, 3, 1, 2] => 1, 2, 1, 3, 3, 3, 3, 1, 2
[1, 2, 1, 3, 3, 3, 3, 1, 3] => 1, 2, 1, 3, 3, 3, 3, 1, 3
[1, 2, 1, 3, 3, 3, 3, 2, 1] => 1, 2, 1, 3, 3, 3, 3, 2, 1
[1, 2, 1, 3, 3, 3, 3, 2, 2] => 1, 2, 1, 3, 3, 3, 3, 2, 2
[1, 2, 1, 3, 3, 3, 3, 2, 3] => 1, 2, 1, 3, 3, 3, 3, 2, 3
[1, 2, 1, 3, 3, 3, 3, 3, 1] => 1, 2, 1, 3, 3, 3, 3, 3, 1
[1, 2, 1, 3, 3, 3, 3, 3, 2] => 1, 2, 1, 3, 3, 3, 3, 3, 2
[1, 2, 1, 3, 3, 3, 3, 3, 3] => 1, 2, 1, 3, 3, 3, 3, 3, 3
[1, 2, 2, 1, 1, 1, 1, 1, 1] => 1, 2, 2, 1, 1, 1, 1, 1, 1
[1, 2, 2, 1, 1, 1, 1, 1, 2] => 1, 2, 2, 1, 1, 1, 1, 1, 2
[1, 2, 2, 1, 1, 1, 1, 1, 3] => 1, 2, 2, 1, 1, 1, 1, 1, 3
[1, 2, 2, 1, 1, 1, 1, 2, 1] => 1, 2, 2, 1, 1, 1, 1, 2, 1
[1, 2, 2, 1, 1, 1, 1, 2, 2] => 1, 2, 2, 1, 1, 1, 1, 2, 2
[1, 2, 2, 1, 1, 1, 1, 2, 3] => 1, 2, 2, 1, 1, 1, 1, 2, 3
[1, 2, 2, 1, 1, 1, 1, 3, 1] => 1, 2, 2, 1, 1, 1, 1, 3, 1
[1, 2, 2, 1, 1, 1, 1, 3, 2] => 1, 2, 2, 1, 1, 1, 1, 3, 2
[1, 2, 2, 1, 1, 1, 1, 3, 3] => 1, 2, 2, 1, 1, 1, 1, 3, 3
[1, 2, 2, 1, 1, 1, 2, 1, 1] => 1, 2, 2, 1, 1, 1, 2, 1, 1
[1, 2, 2, 1, 1, 1, 2, 1, 2] => 1, 2, 2, 1, 1, 1, 2, 1, 2
[1, 2, 2, 1, 1, 1, 2, 1, 3] => 1, 2, 2, 1, 1, 1, 2, 1, 3
[1, 2, 2, 1, 1, 1, 2, 2, 1] => 1, 2, 2, 1, 1, 1, 2, 2, 1
[1, 2, 2, 1, 1, 1, 2, 2, 2] => 1, 2, 2, 1, 1, 1, 2, 2, 2
[1, 2, 2, 1, 1, 1, 2, 2, 3] => 1, 2, 2, 1, 1, 1, 2, 2, 3
[1, 2, 2, 1, 1, 1, 2, 3, 1] => 1, 2, 2, 1, 1, 1, 2, 3, 1
[1, 2, 2, 1, 1, 1, 2, 3, 2] => 1, 2, 2, 1, 1, 1, 2, 3, 2
[1, 2, 2, 1, 1, 1, 2, 3, 3] => 1, 2, 2, 1, 1, 1, 2, 3, 3
[1, 2, 2, 1, 1, 1, 3, 1, 1] => 1, 2, 2, 1, 1, 1, 3, 1, 1
[1, 2, 2, 1, 1, 1, 3, 1, 2] => 1, 2, 2, 1, 1, 1, 3, 1, 2
[1, 2, 2, 1, 1, 1, 3, 1, 3] => 1, 2, 2, 1, 1, 1, 3, 1, 3
[1, 2, 2, 1, 1, 1, 3, 2, 1] => 1, 2, 2, 1, 1, 1, 3, 2, 1
[1, 2, 2, 1, 1, 1, 3, 2, 2] => 1, 2, 2, 1, 1, 1, 3, 2, 2
[1, 2, 2, 1, 1, 1, 3, 2, 3] => 1, 2, 2, 1, 1, 1, 3, 2, 3
[1, 2, 2, 1, 1, 1, 3, 3, 1] => 1, 2, 2, 1, 1, 1, 3, 3, 1
[1, 2, 2, 1, 1, 1, 3, 3, 2] => 1, 2, 2, 1, 1, 1, 3, 3, 2
[1, 2, 2, 1, 1, 1, 3, 3, 3] => 1, 2, 2, 1, 1, 1, 3, 3, 3
[1, 2, 2, 1, 1, 2, 1, 1, 1] => 1, 2, 2, 1, 1, 2, 1, 1, 1
[1, 2, 2, 1, 1, 2, 1, 1, 2] => 1, 2, 2, 1, 1, 2, 1, 1, 2
[1, 2, 2, 1, 1, 2, 1, 1, 3] => 1, 2, 2, 1, 1, 2, 1, 1, 3
[1, 2, 2, 1, 1, 2, 1, 2, 1] => 1, 2, 2, 1, 1, 2, 1, 2, 1
[1, 2, 2, 1, 1, 2, 1, 2, 2] => 1, 2, 2, 1, 1, 2, 1, 2, 2
[1, 2, 2, 1, 1, 2, 1, 2, 3] => 1, 2, 2, 1, 1, 2, 1, 2, 3
[1, 2, 2, 1, 1, 2, 1, 3, 1] => 1, 2, 2, 1, 1, 2, 1, 3, 1
[1, 2, 2, 1, 1, 2, 1, 3, 2] => 1, 2, 2, 1, 1, 2, 1, 3, 2
[1, 2, 2, 1, 1, 2, 1, 3, 3] => 1, 2, 2, 1, 1, 2, 1, 3, 3
[1, 2, 2, 1, 1, 2, 2, 1, 1] => 1, 2, 2, 1, 1, 2, 2, 1, 1
[1, 2, 2, 1, 1, 2, 2, 1, 2] => 1, 2, 2, 1, 1, 2, 2, 1, 2
[1, 2, 2, 1, 1, 2, 2, 1, 3] => 1, 2, 2, 1, 1, 2, 2, 1, 3
[1, 2, 2, 1, 1, 2, 2, 2, 1] => 1, 2, 2, 1, 1, 2, 2, 2, 1
[1, 2, 2, 1, 1, 2, 2, 2, 2] => 1, 2, 2, 1, 1, 2, 2, 2, 2
[1, 2, 2, 1, 1, 2, 2, 2, 3] => 1, 2, 2, 1, 1, 2, 2, 2, 3
[1, 2, 2, 1, 1, 2, 2, 3, 1] => 1, 2, 2, 1, 1, 2, 2, 3, 1
[1, 2, 2, 1, 1, 2, 2, 3, 2] => 1, 2, 2, 1, 1, 2, 2, 3, 2
[1, 2, 2, 1, 1, 2, 2, 3, 3] => 1, 2, 2, 1, 1, 2, 2, 3, 3
[1, 2, 2, 1, 1, 2, 3, 1, 1] => 1, 2, 2, 1, 1, 2, 3, 1, 1
[1, 2, 2, 1, 1, 2, 3, 1, 2] => 1, 2, 2, 1, 1, 2, 3, 1, 2
[1, 2, 2, 1, 1, 2, 3, 1, 3] => 1, 2, 2, 1, 1, 2, 3, 1, 3
[1, 2, 2, 1, 1, 2, 3, 2, 1] => 1, 2, 2, 1, 1, 2, 3, 2, 1
[1, 2, 2, 1, 1, 2, 3, 2, 2] => 1, 2, 2, 1, 1, 2, 3, 2, 2
[1, 2, 2, 1, 1, 2, 3, 2, 3] => 1, 2, 2, 1, 1, 2, 3, 2, 3
[1, 2, 2, 1, 1, 2, 3, 3, 1] => 1, 2, 2, 1, 1, 2, 3, 3, 1
[1, 2, 2, 1, 1, 2, 3, 3, 2] => 1, 2, 2, 1, 1, 2, 3, 3, 2
[1, 2, 2, 1, 1, 2, 3, 3, 3] => 1, 2, 2, 1, 1, 2, 3, 3, 3
[1, 2, 2, 1, 1, 3, 1, 1, 1] => 1, 2, 2, 1, 1, 3, 1, 1, 1
[1, 2, 2, 1, 1, 3, 1, 1, 2] => 1, 2, 2, 1, 1, 3, 1, 1, 2
[1, 2, 2, 1, 1, 3, 1, 1, 3] => 1, 2, 2, 1, 1, 3, 1, 1, 3
[1, 2, 2, 1, 1, 3, 1, 2, 1] => 1, 2, 2, 1, 1, 3, 1, 2, 1
[1, 2, 2, 1, 1, 3, 1, 2, 2] => 1, 2, 2, 1, 1, 3, 1, 2, 2
[1, 2, 2, 1, 1, 3, 1, 2, 3] => 1, 2, 2, 1, 1, 3, 1, 2, 3
[1, 2, 2, 1, 1, 3, 1, 3, 1] => 1, 2, 2, 1, 1, 3, 1, 3, 1
[1, 2, 2, 1, 1, 3, 1, 3, 2] => 1, 2, 2, 1, 1, 3, 1, 3, 2
[1, 2, 2, 1, 1, 3, 1, 3, 3] => 1, 2, 2, 1, 1, 3, 1, 3, 3
[1, 2, 2, 1, 1, 3, 2, 1, 1] => 1, 2, 2, 1, 1, 3, 2, 1, 1
[1, 2, 2, 1, 1, 3, 2, 1, 2] => 1, 2, 2, 1, 1, 3, 2, 1, 2
[1, 2, 2, 1, 1, 3, 2, 1, 3] => 1, 2, 2, 1, 1, 3, 2, 1, 3
[1, 2, 2, 1, 1, 3, 2, 2, 1] => 1, 2, 2, 1, 1, 3, 2, 2, 1
[1, 2, 2, 1, 1, 3, 2, 2, 2] => 1, 2, 2, 1, 1, 3, 2, 2, 2
[1, 2, 2, 1, 1, 3, 2, 2, 3] => 1, 2, 2, 1, 1, 3, 2, 2, 3
[1, 2, 2, 1, 1, 3, 2, 3, 1] => 1, 2, 2, 1, 1, 3, 2, 3, 1
[1, 2, 2, 1, 1, 3, 2, 3, 2] => 1, 2, 2, 1, 1, 3, 2, 3, 2
[1, 2, 2, 1, 1, 3, 2, 3, 3] => 1, 2, 2, 1, 1, 3, 2, 3, 3
[1, 2, 2, 1, 1, 3, 3, 1, 1] => 1, 2, 2, 1, 1, 3, 3, 1, 1
[1, 2, 2, 1, 1, 3, 3, 1, 2] => 1, 2, 2, 1, 1, 3, 3, 1, 2
[1, 2, 2, 1, 1, 3, 3, 1, 3] => 1, 2, 2, 1, 1, 3, 3, 1, 3
[1, 2, 2, 1, 1, 3, 3, 2, 1] => 1, 2, 2, 1, 1, 3, 3, 2, 1
[1, 2, 2, 1, 1, 3, 3, 2, 2] => 1, 2, 2, 1, 1, 3, 3, 2, 2
[1, 2, 2, 1, 1, 3, 3, 2, 3] => 1, 2, 2, 1, 1, 3, 3, 2, 3
[1, 2, 2, 1, 1, 3, 3, 3, 1] => 1, 2, 2, 1, 1, 3, 3, 3, 1
[1, 2, 2, 1, 1, 3, 3, 3, 2] => 1, 2, 2, 1, 1, 3, 3, 3, 2
[1, 2, 2, 1, 1, 3, 3, 3, 3] => 1, 2, 2, 1, 1, 3, 3, 3, 3
[1, 2, 2, 1, 2, 1, 1, 1, 1] => 1, 2, 2, 1, 2, 1, 1, 1, 1
[1, 2, 2, 1, 2, 1, 1, 1, 2] => 1, 2, 2, 1, 2, 1, 1, 1, 2
[1, 2, 2, 1, 2, 1, 1, 1, 3] => 1, 2, 2, 1, 2, 1, 1, 1, 3
[1, 2, 2, 1, 2, 1, 1, 2, 1] => 1, 2, 2, 1, 2, 1, 1, 2, 1
[1, 2, 2, 1, 2, 1, 1, 2, 2] => 1, 2, 2, 1, 2, 1, 1, 2, 2
[1, 2, 2, 1, 2, 1, 1, 2, 3] => 1, 2, 2, 1, 2, 1, 1, 2, 3
[1, 2, 2, 1, 2, 1, 1, 3, 1] => 1, 2, 2, 1, 2, 1, 1, 3, 1
[1, 2, 2, 1, 2, 1, 1, 3, 2] => 1, 2, 2, 1, 2, 1, 1, 3, 2
[1, 2, 2, 1, 2, 1, 1, 3, 3] => 1, 2, 2, 1, 2, 1, 1, 3, 3
[1, 2, 2, 1, 2, 1, 2, 1, 1] => 1, 2, 2, 1, 2, 1, 2, 1, 1
[1, 2, 2, 1, 2, 1, 2, 1, 2] => 1, 2, 2, 1, 2, 1, 2, 1, 2
[1, 2, 2, 1, 2, 1, 2, 1, 3] => 1, 2, 2, 1, 2, 1, 2, 1, 3
[1, 2, 2, 1, 2, 1, 2, 2, 1] => 1, 2, 2, 1, 2, 1, 2, 2, 1
[1, 2, 2, 1, 2, 1, 2, 2, 2] => 1, 2, 2, 1, 2, 1, 2, 2, 2
[1, 2, 2, 1, 2, 1, 2, 2, 3] => 1, 2, 2, 1, 2, 1, 2, 2, 3
[1, 2, 2, 1, 2, 1, 2, 3, 1] => 1, 2, 2, 1, 2, 1, 2, 3, 1
[1, 2, 2, 1, 2, 1, 2, 3, 2] => 1, 2, 2, 1, 2, 1, 2, 3, 2
[1, 2, 2, 1, 2, 1, 2, 3, 3] => 1, 2, 2, 1, 2, 1, 2, 3, 3
[1, 2, 2, 1, 2, 1, 3, 1, 1] => 1, 2, 2, 1, 2, 1, 3, 1, 1
[1, 2, 2, 1, 2, 1, 3, 1, 2] => 1, 2, 2, 1, 2, 1, 3, 1, 2
[1, 2, 2, 1, 2, 1, 3, 1, 3] => 1, 2, 2, 1, 2, 1, 3, 1, 3
[1, 2, 2, 1, 2, 1, 3, 2, 1] => 1, 2, 2, 1, 2, 1, 3, 2, 1
[1, 2, 2, 1, 2, 1, 3, 2, 2] => 1, 2, 2, 1, 2, 1, 3, 2, 2
[1, 2, 2, 1, 2, 1, 3, 2, 3] => 1, 2, 2, 1, 2, 1, 3, 2, 3
[1, 2, 2, 1, 2, 1, 3, 3, 1] => 1, 2, 2, 1, 2, 1, 3, 3, 1
[1, 2, 2, 1, 2, 1, 3, 3, 2] => 1, 2, 2, 1, 2, 1, 3, 3, 2
[1, 2, 2, 1, 2, 1, 3, 3, 3] => 1, 2, 2, 1, 2, 1, 3, 3, 3
[1, 2, 2, 1, 2, 2, 1, 1, 1] => 1, 2, 2, 1, 2, 2, 1, 1, 1
[1, 2, 2, 1, 2, 2, 1, 1, 2] => 1, 2, 2, 1, 2, 2, 1, 1, 2
[1, 2, 2, 1, 2, 2, 1, 1, 3] => 1, 2, 2, 1, 2, 2, 1, 1, 3
[1, 2, 2, 1, 2, 2, 1, 2, 1] => 1, 2, 2, 1, 2, 2, 1, 2, 1
[1, 2, 2, 1, 2, 2, 1, 2, 2] => 1, 2, 2, 1, 2, 2, 1, 2, 2
[1, 2, 2, 1, 2, 2, 1, 2, 3] => 1, 2, 2, 1, 2, 2, 1, 2, 3
[1, 2, 2, 1, 2, 2, 1, 3, 1] => 1, 2, 2, 1, 2, 2, 1, 3, 1
[1, 2, 2, 1, 2, 2, 1, 3, 2] => 1, 2, 2, 1, 2, 2, 1, 3, 2
[1, 2, 2, 1, 2, 2, 1, 3, 3] => 1, 2, 2, 1, 2, 2, 1, 3, 3
[1, 2, 2, 1, 2, 2, 2, 1, 1] => 1, 2, 2, 1, 2, 2, 2, 1, 1
[1, 2, 2, 1, 2, 2, 2, 1, 2] => 1, 2, 2, 1, 2, 2, 2, 1, 2
[1, 2, 2, 1, 2, 2, 2, 1, 3] => 1, 2, 2, 1, 2, 2, 2, 1, 3
[1, 2, 2, 1, 2, 2, 2, 2, 1] => 1, 2, 2, 1, 2, 2, 2, 2, 1
[1, 2, 2, 1, 2, 2, 2, 2, 2] => 1, 2, 2, 1, 2, 2, 2, 2, 2
[1, 2, 2, 1, 2, 2, 2, 2, 3] => 1, 2, 2, 1, 2, 2, 2, 2, 3
[1, 2, 2, 1, 2, 2, 2, 3, 1] => 1, 2, 2, 1, 2, 2, 2, 3, 1
[1, 2, 2, 1, 2, 2, 2, 3, 2] => 1, 2, 2, 1, 2, 2, 2, 3, 2
[1, 2, 2, 1, 2, 2, 2, 3, 3] => 1, 2, 2, 1, 2, 2, 2, 3, 3
[1, 2, 2, 1, 2, 2, 3, 1, 1] => 1, 2, 2, 1, 2, 2, 3, 1, 1
[1, 2, 2, 1, 2, 2, 3, 1, 2] => 1, 2, 2, 1, 2, 2, 3, 1, 2
[1, 2, 2, 1, 2, 2, 3, 1, 3] => 1, 2, 2, 1, 2, 2, 3, 1, 3
[1, 2, 2, 1, 2, 2, 3, 2, 1] => 1, 2, 2, 1, 2, 2, 3, 2, 1
[1, 2, 2, 1, 2, 2, 3, 2, 2] => 1, 2, 2, 1, 2, 2, 3, 2, 2
[1, 2, 2, 1, 2, 2, 3, 2, 3] => 1, 2, 2, 1, 2, 2, 3, 2, 3
[1, 2, 2, 1, 2, 2, 3, 3, 1] => 1, 2, 2, 1, 2, 2, 3, 3, 1
[1, 2, 2, 1, 2, 2, 3, 3, 2] => 1, 2, 2, 1, 2, 2, 3, 3, 2
[1, 2, 2, 1, 2, 2, 3, 3, 3] => 1, 2, 2, 1, 2, 2, 3, 3, 3
[1, 2, 2, 1, 2, 3, 1, 1, 1] => 1, 2, 2, 1, 2, 3, 1, 1, 1
[1, 2, 2, 1, 2, 3, 1, 1, 2] => 1, 2, 2, 1, 2, 3, 1, 1, 2
[1, 2, 2, 1, 2, 3, 1, 1, 3] => 1, 2, 2, 1, 2, 3, 1, 1, 3
[1, 2, 2, 1, 2, 3, 1, 2, 1] => 1, 2, 2, 1, 2, 3, 1, 2, 1
[1, 2, 2, 1, 2, 3, 1, 2, 2] => 1, 2, 2, 1, 2, 3, 1, 2, 2
[1, 2, 2, 1, 2, 3, 1, 2, 3] => 1, 2, 2, 1, 2, 3, 1, 2, 3
[1, 2, 2, 1, 2, 3, 1, 3, 1] => 1, 2, 2, 1, 2, 3, 1, 3, 1
[1, 2, 2, 1, 2, 3, 1, 3, 2] => 1, 2, 2, 1, 2, 3, 1, 3, 2
[1, 2, 2, 1, 2, 3, 1, 3, 3] => 1, 2, 2, 1, 2, 3, 1, 3, 3
[1, 2, 2, 1, 2, 3, 2, 1, 1] => 1, 2, 2, 1, 2, 3, 2, 1, 1
[1, 2, 2, 1, 2, 3, 2, 1, 2] => 1, 2, 2, 1, 2, 3, 2, 1, 2
[1, 2, 2, 1, 2, 3, 2, 1, 3] => 1, 2, 2, 1, 2, 3, 2, 1, 3
[1, 2, 2, 1, 2, 3, 2, 2, 1] => 1, 2, 2, 1, 2, 3, 2, 2, 1
[1, 2, 2, 1, 2, 3, 2, 2, 2] => 1, 2, 2, 1, 2, 3, 2, 2, 2
[1, 2, 2, 1, 2, 3, 2, 2, 3] => 1, 2, 2, 1, 2, 3, 2, 2, 3
[1, 2, 2, 1, 2, 3, 2, 3, 1] => 1, 2, 2, 1, 2, 3, 2, 3, 1
[1, 2, 2, 1, 2, 3, 2, 3, 2] => 1, 2, 2, 1, 2, 3, 2, 3, 2
[1, 2, 2, 1, 2, 3, 2, 3, 3] => 1, 2, 2, 1, 2, 3, 2, 3, 3
[1, 2, 2, 1, 2, 3, 3, 1, 1] => 1, 2, 2, 1, 2, 3, 3, 1, 1
[1, 2, 2, 1, 2, 3, 3, 1, 2] => 1, 2, 2, 1, 2, 3, 3, 1, 2
[1, 2, 2, 1, 2, 3, 3, 1, 3] => 1, 2, 2, 1, 2, 3, 3, 1, 3
[1, 2, 2, 1, 2, 3, 3, 2, 1] => 1, 2, 2, 1, 2, 3, 3, 2, 1
[1, 2, 2, 1, 2, 3, 3, 2, 2] => 1, 2, 2, 1, 2, 3, 3, 2, 2
[1, 2, 2, 1, 2, 3, 3, 2, 3] => 1, 2, 2, 1, 2, 3, 3, 2, 3
[1, 2, 2, 1, 2, 3, 3, 3, 1] => 1, 2, 2, 1, 2, 3, 3, 3, 1
[1, 2, 2, 1, 2, 3, 3, 3, 2] => 1, 2, 2, 1, 2, 3, 3, 3, 2
[1, 2, 2, 1, 2, 3, 3, 3, 3] => 1, 2, 2, 1, 2, 3, 3, 3, 3
[1, 2, 2, 1, 3, 1, 1, 1, 1] => 1, 2, 2, 1, 3, 1, 1, 1, 1
[1, 2, 2, 1, 3, 1, 1, 1, 2] => 1, 2, 2, 1, 3, 1, 1, 1, 2
[1, 2, 2, 1, 3, 1, 1, 1, 3] => 1, 2, 2, 1, 3, 1, 1, 1, 3
[1, 2, 2, 1, 3, 1, 1, 2, 1] => 1, 2, 2, 1, 3, 1, 1, 2, 1
[1, 2, 2, 1, 3, 1, 1, 2, 2] => 1, 2, 2, 1, 3, 1, 1, 2, 2
[1, 2, 2, 1, 3, 1, 1, 2, 3] => 1, 2, 2, 1, 3, 1, 1, 2, 3
[1, 2, 2, 1, 3, 1, 1, 3, 1] => 1, 2, 2, 1, 3, 1, 1, 3, 1
[1, 2, 2, 1, 3, 1, 1, 3, 2] => 1, 2, 2, 1, 3, 1, 1, 3, 2
[1, 2, 2, 1, 3, 1, 1, 3, 3] => 1, 2, 2, 1, 3, 1, 1, 3, 3
[1, 2, 2, 1, 3, 1, 2, 1, 1] => 1, 2, 2, 1, 3, 1, 2, 1, 1
[1, 2, 2, 1, 3, 1, 2, 1, 2] => 1, 2, 2, 1, 3, 1, 2, 1, 2
[1, 2, 2, 1, 3, 1, 2, 1, 3] => 1, 2, 2, 1, 3, 1, 2, 1, 3
[1, 2, 2, 1, 3, 1, 2, 2, 1] => 1, 2, 2, 1, 3, 1, 2, 2, 1
[1, 2, 2, 1, 3, 1, 2, 2, 2] => 1, 2, 2, 1, 3, 1, 2, 2, 2
[1, 2, 2, 1, 3, 1, 2, 2, 3] => 1, 2, 2, 1, 3, 1, 2, 2, 3
[1, 2, 2, 1, 3, 1, 2, 3, 1] => 1, 2, 2, 1, 3, 1, 2, 3, 1
[1, 2, 2, 1, 3, 1, 2, 3, 2] => 1, 2, 2, 1, 3, 1, 2, 3, 2
[1, 2, 2, 1, 3, 1, 2, 3, 3] => 1, 2, 2, 1, 3, 1, 2, 3, 3
[1, 2, 2, 1, 3, 1, 3, 1, 1] => 1, 2, 2, 1, 3, 1, 3, 1, 1
[1, 2, 2, 1, 3, 1, 3, 1, 2] => 1, 2, 2, 1, 3, 1, 3, 1, 2
[1, 2, 2, 1, 3, 1, 3, 1, 3] => 1, 2, 2, 1, 3, 1, 3, 1, 3
[1, 2, 2, 1, 3, 1, 3, 2, 1] => 1, 2, 2, 1, 3, 1, 3, 2, 1
[1, 2, 2, 1, 3, 1, 3, 2, 2] => 1, 2, 2, 1, 3, 1, 3, 2, 2
[1, 2, 2, 1, 3, 1, 3, 2, 3] => 1, 2, 2, 1, 3, 1, 3, 2, 3
[1, 2, 2, 1, 3, 1, 3, 3, 1] => 1, 2, 2, 1, 3, 1, 3, 3, 1
[1, 2, 2, 1, 3, 1, 3, 3, 2] => 1, 2, 2, 1, 3, 1, 3, 3, 2
[1, 2, 2, 1, 3, 1, 3, 3, 3] => 1, 2, 2, 1, 3, 1, 3, 3, 3
[1, 2, 2, 1, 3, 2, 1, 1, 1] => 1, 2, 2, 1, 3, 2, 1, 1, 1
[1, 2, 2, 1, 3, 2, 1, 1, 2] => 1, 2, 2, 1, 3, 2, 1, 1, 2
[1, 2, 2, 1, 3, 2, 1, 1, 3] => 1, 2, 2, 1, 3, 2, 1, 1, 3
[1, 2, 2, 1, 3, 2, 1, 2, 1] => 1, 2, 2, 1, 3, 2, 1, 2, 1
[1, 2, 2, 1, 3, 2, 1, 2, 2] => 1, 2, 2, 1, 3, 2, 1, 2, 2
[1, 2, 2, 1, 3, 2, 1, 2, 3] => 1, 2, 2, 1, 3, 2, 1, 2, 3
[1, 2, 2, 1, 3, 2, 1, 3, 1] => 1, 2, 2, 1, 3, 2, 1, 3, 1
[1, 2, 2, 1, 3, 2, 1, 3, 2] => 1, 2, 2, 1, 3, 2, 1, 3, 2
[1, 2, 2, 1, 3, 2, 1, 3, 3] => 1, 2, 2, 1, 3, 2, 1, 3, 3
[1, 2, 2, 1, 3, 2, 2, 1, 1] => 1, 2, 2, 1, 3, 2, 2, 1, 1
[1, 2, 2, 1, 3, 2, 2, 1, 2] => 1, 2, 2, 1, 3, 2, 2, 1, 2
[1, 2, 2, 1, 3, 2, 2, 1, 3] => 1, 2, 2, 1, 3, 2, 2, 1, 3
[1, 2, 2, 1, 3, 2, 2, 2, 1] => 1, 2, 2, 1, 3, 2, 2, 2, 1
[1, 2, 2, 1, 3, 2, 2, 2, 2] => 1, 2, 2, 1, 3, 2, 2, 2, 2
[1, 2, 2, 1, 3, 2, 2, 2, 3] => 1, 2, 2, 1, 3, 2, 2, 2, 3
[1, 2, 2, 1, 3, 2, 2, 3, 1] => 1, 2, 2, 1, 3, 2, 2, 3, 1
[1, 2, 2, 1, 3, 2, 2, 3, 2] => 1, 2, 2, 1, 3, 2, 2, 3, 2
[1, 2, 2, 1, 3, 2, 2, 3, 3] => 1, 2, 2, 1, 3, 2, 2, 3, 3
[1, 2, 2, 1, 3, 2, 3, 1, 1] => 1, 2, 2, 1, 3, 2, 3, 1, 1
[1, 2, 2, 1, 3, 2, 3, 1, 2] => 1, 2, 2, 1, 3, 2, 3, 1, 2
[1, 2, 2, 1, 3, 2, 3, 1, 3] => 1, 2, 2, 1, 3, 2, 3, 1, 3
[1, 2, 2, 1, 3, 2, 3, 2, 1] => 1, 2, 2, 1, 3, 2, 3, 2, 1
[1, 2, 2, 1, 3, 2, 3, 2, 2] => 1, 2, 2, 1, 3, 2, 3, 2, 2
[1, 2, 2, 1, 3, 2, 3, 2, 3] => 1, 2, 2, 1, 3, 2, 3, 2, 3
[1, 2, 2, 1, 3, 2, 3, 3, 1] => 1, 2, 2, 1, 3, 2, 3, 3, 1
[1, 2, 2, 1, 3, 2, 3, 3, 2] => 1, 2, 2, 1, 3, 2, 3, 3, 2
[1, 2, 2, 1, 3, 2, 3, 3, 3] => 1, 2, 2, 1, 3, 2, 3, 3, 3
[1, 2, 2, 1, 3, 3, 1, 1, 1] => 1, 2, 2, 1, 3, 3, 1, 1, 1
[1, 2, 2, 1, 3, 3, 1, 1, 2] => 1, 2, 2, 1, 3, 3, 1, 1, 2
[1, 2, 2, 1, 3, 3, 1, 1, 3] => 1, 2, 2, 1, 3, 3, 1, 1, 3
[1, 2, 2, 1, 3, 3, 1, 2, 1] => 1, 2, 2, 1, 3, 3, 1, 2, 1
[1, 2, 2, 1, 3, 3, 1, 2, 2] => 1, 2, 2, 1, 3, 3, 1, 2, 2
[1, 2, 2, 1, 3, 3, 1, 2, 3] => 1, 2, 2, 1, 3, 3, 1, 2, 3
[1, 2, 2, 1, 3, 3, 1, 3, 1] => 1, 2, 2, 1, 3, 3, 1, 3, 1
[1, 2, 2, 1, 3, 3, 1, 3, 2] => 1, 2, 2, 1, 3, 3, 1, 3, 2
[1, 2, 2, 1, 3, 3, 1, 3, 3] => 1, 2, 2, 1, 3, 3, 1, 3, 3
[1, 2, 2, 1, 3, 3, 2, 1, 1] => 1, 2, 2, 1, 3, 3, 2, 1, 1
[1, 2, 2, 1, 3, 3, 2, 1, 2] => 1, 2, 2, 1, 3, 3, 2, 1, 2
[1, 2, 2, 1, 3, 3, 2, 1, 3] => 1, 2, 2, 1, 3, 3, 2, 1, 3
[1, 2, 2, 1, 3, 3, 2, 2, 1] => 1, 2, 2, 1, 3, 3, 2, 2, 1
[1, 2, 2, 1, 3, 3, 2, 2, 2] => 1, 2, 2, 1, 3, 3, 2, 2, 2
[1, 2, 2, 1, 3, 3, 2, 2, 3] => 1, 2, 2, 1, 3, 3, 2, 2, 3
[1, 2, 2, 1, 3, 3, 2, 3, 1] => 1, 2, 2, 1, 3, 3, 2, 3, 1
[1, 2, 2, 1, 3, 3, 2, 3, 2] => 1, 2, 2, 1, 3, 3, 2, 3, 2
[1, 2, 2, 1, 3, 3, 2, 3, 3] => 1, 2, 2, 1, 3, 3, 2, 3, 3
[1, 2, 2, 1, 3, 3, 3, 1, 1] => 1, 2, 2, 1, 3, 3, 3, 1, 1
[1, 2, 2, 1, 3, 3, 3, 1, 2] => 1, 2, 2, 1, 3, 3, 3, 1, 2
[1, 2, 2, 1, 3, 3, 3, 1, 3] => 1, 2, 2, 1, 3, 3, 3, 1, 3
[1, 2, 2, 1, 3, 3, 3, 2, 1] => 1, 2, 2, 1, 3, 3, 3, 2, 1
[1, 2, 2, 1, 3, 3, 3, 2, 2] => 1, 2, 2, 1, 3, 3, 3, 2, 2
[1, 2, 2, 1, 3, 3, 3, 2, 3] => 1, 2, 2, 1, 3, 3, 3, 2, 3
[1, 2, 2, 1, 3, 3, 3, 3, 1] => 1, 2, 2, 1, 3, 3, 3, 3, 1
[1, 2, 2, 1, 3, 3, 3, 3, 2] => 1, 2, 2, 1, 3, 3, 3, 3, 2
[1, 2, 2, 1, 3, 3, 3, 3, 3] => 1, 2, 2, 1, 3, 3, 3, 3, 3
[1, 2, 2, 2, 1, 1, 1, 1, 1] => 1, 2, 2, 2, 1, 1, 1, 1, 1
[1, 2, 2, 2, 1, 1, 1, 1, 2] => 1, 2, 2, 2, 1, 1, 1, 1, 2
[1, 2, 2, 2, 1, 1, 1, 1, 3] => 1, 2, 2, 2, 1, 1, 1, 1, 3
[1, 2, 2, 2, 1, 1, 1, 2, 1] => 1, 2, 2, 2, 1, 1, 1, 2, 1
[1, 2, 2, 2, 1, 1, 1, 2, 2] => 1, 2, 2, 2, 1, 1, 1, 2, 2
[1, 2, 2, 2, 1, 1, 1, 2, 3] => 1, 2, 2, 2, 1, 1, 1, 2, 3
[1, 2, 2, 2, 1, 1, 1, 3, 1] => 1, 2, 2, 2, 1, 1, 1, 3, 1
[1, 2, 2, 2, 1, 1, 1, 3, 2] => 1, 2, 2, 2, 1, 1, 1, 3, 2
[1, 2, 2, 2, 1, 1, 1, 3, 3] => 1, 2, 2, 2, 1, 1, 1, 3, 3
[1, 2, 2, 2, 1, 1, 2, 1, 1] => 1, 2, 2, 2, 1, 1, 2, 1, 1
[1, 2, 2, 2, 1, 1, 2, 1, 2] => 1, 2, 2, 2, 1, 1, 2, 1, 2
[1, 2, 2, 2, 1, 1, 2, 1, 3] => 1, 2, 2, 2, 1, 1, 2, 1, 3
[1, 2, 2, 2, 1, 1, 2, 2, 1] => 1, 2, 2, 2, 1, 1, 2, 2, 1
[1, 2, 2, 2, 1, 1, 2, 2, 2] => 1, 2, 2, 2, 1, 1, 2, 2, 2
[1, 2, 2, 2, 1, 1, 2, 2, 3] => 1, 2, 2, 2, 1, 1, 2, 2, 3
[1, 2, 2, 2, 1, 1, 2, 3, 1] => 1, 2, 2, 2, 1, 1, 2, 3, 1
[1, 2, 2, 2, 1, 1, 2, 3, 2] => 1, 2, 2, 2, 1, 1, 2, 3, 2
[1, 2, 2, 2, 1, 1, 2, 3, 3] => 1, 2, 2, 2, 1, 1, 2, 3, 3
[1, 2, 2, 2, 1, 1, 3, 1, 1] => 1, 2, 2, 2, 1, 1, 3, 1, 1
[1, 2, 2, 2, 1, 1, 3, 1, 2] => 1, 2, 2, 2, 1, 1, 3, 1, 2
[1, 2, 2, 2, 1, 1, 3, 1, 3] => 1, 2, 2, 2, 1, 1, 3, 1, 3
[1, 2, 2, 2, 1, 1, 3, 2, 1] => 1, 2, 2, 2, 1, 1, 3, 2, 1
[1, 2, 2, 2, 1, 1, 3, 2, 2] => 1, 2, 2, 2, 1, 1, 3, 2, 2
[1, 2, 2, 2, 1, 1, 3, 2, 3] => 1, 2, 2, 2, 1, 1, 3, 2, 3
[1, 2, 2, 2, 1, 1, 3, 3, 1] => 1, 2, 2, 2, 1, 1, 3, 3, 1
[1, 2, 2, 2, 1, 1, 3, 3, 2] => 1, 2, 2, 2, 1, 1, 3, 3, 2
[1, 2, 2, 2, 1, 1, 3, 3, 3] => 1, 2, 2, 2, 1, 1, 3, 3, 3
[1, 2, 2, 2, 1, 2, 1, 1, 1] => 1, 2, 2, 2, 1, 2, 1, 1, 1
[1, 2, 2, 2, 1, 2, 1, 1, 2] => 1, 2, 2, 2, 1, 2, 1, 1, 2
[1, 2, 2, 2, 1, 2, 1, 1, 3] => 1, 2, 2, 2, 1, 2, 1, 1, 3
[1, 2, 2, 2, 1, 2, 1, 2, 1] => 1, 2, 2, 2, 1, 2, 1, 2, 1
[1, 2, 2, 2, 1, 2, 1, 2, 2] => 1, 2, 2, 2, 1, 2, 1, 2, 2
[1, 2, 2, 2, 1, 2, 1, 2, 3] => 1, 2, 2, 2, 1, 2, 1, 2, 3
[1, 2, 2, 2, 1, 2, 1, 3, 1] => 1, 2, 2, 2, 1, 2, 1, 3, 1
[1, 2, 2, 2, 1, 2, 1, 3, 2] => 1, 2, 2, 2, 1, 2, 1, 3, 2
[1, 2, 2, 2, 1, 2, 1, 3, 3] => 1, 2, 2, 2, 1, 2, 1, 3, 3
[1, 2, 2, 2, 1, 2, 2, 1, 1] => 1, 2, 2, 2, 1, 2, 2, 1, 1
[1, 2, 2, 2, 1, 2, 2, 1, 2] => 1, 2, 2, 2, 1, 2, 2, 1, 2
[1, 2, 2, 2, 1, 2, 2, 1, 3] => 1, 2, 2, 2, 1, 2, 2, 1, 3
[1, 2, 2, 2, 1, 2, 2, 2, 1] => 1, 2, 2, 2, 1, 2, 2, 2, 1
[1, 2, 2, 2, 1, 2, 2, 2, 2] => 1, 2, 2, 2, 1, 2, 2, 2, 2
[1, 2, 2, 2, 1, 2, 2, 2, 3] => 1, 2, 2, 2, 1, 2, 2, 2, 3
[1, 2, 2, 2, 1, 2, 2, 3, 1] => 1, 2, 2, 2, 1, 2, 2, 3, 1
[1, 2, 2, 2, 1, 2, 2, 3, 2] => 1, 2, 2, 2, 1, 2, 2, 3, 2
[1, 2, 2, 2, 1, 2, 2, 3, 3] => 1, 2, 2, 2, 1, 2, 2, 3, 3
[1, 2, 2, 2, 1, 2, 3, 1, 1] => 1, 2, 2, 2, 1, 2, 3, 1, 1
[1, 2, 2, 2, 1, 2, 3, 1, 2] => 1, 2, 2, 2, 1, 2, 3, 1, 2
[1, 2, 2, 2, 1, 2, 3, 1, 3] => 1, 2, 2, 2, 1, 2, 3, 1, 3
[1, 2, 2, 2, 1, 2, 3, 2, 1] => 1, 2, 2, 2, 1, 2, 3, 2, 1
[1, 2, 2, 2, 1, 2, 3, 2, 2] => 1, 2, 2, 2, 1, 2, 3, 2, 2
[1, 2, 2, 2, 1, 2, 3, 2, 3] => 1, 2, 2, 2, 1, 2, 3, 2, 3
[1, 2, 2, 2, 1, 2, 3, 3, 1] => 1, 2, 2, 2, 1, 2, 3, 3, 1
[1, 2, 2, 2, 1, 2, 3, 3, 2] => 1, 2, 2, 2, 1, 2, 3, 3, 2
[1, 2, 2, 2, 1, 2, 3, 3, 3] => 1, 2, 2, 2, 1, 2, 3, 3, 3
[1, 2, 2, 2, 1, 3, 1, 1, 1] => 1, 2, 2, 2, 1, 3, 1, 1, 1
[1, 2, 2, 2, 1, 3, 1, 1, 2] => 1, 2, 2, 2, 1, 3, 1, 1, 2
[1, 2, 2, 2, 1, 3, 1, 1, 3] => 1, 2, 2, 2, 1, 3, 1, 1, 3
[1, 2, 2, 2, 1, 3, 1, 2, 1] => 1, 2, 2, 2, 1, 3, 1, 2, 1
[1, 2, 2, 2, 1, 3, 1, 2, 2] => 1, 2, 2, 2, 1, 3, 1, 2, 2
[1, 2, 2, 2, 1, 3, 1, 2, 3] => 1, 2, 2, 2, 1, 3, 1, 2, 3
[1, 2, 2, 2, 1, 3, 1, 3, 1] => 1, 2, 2, 2, 1, 3, 1, 3, 1
[1, 2, 2, 2, 1, 3, 1, 3, 2] => 1, 2, 2, 2, 1, 3, 1, 3, 2
[1, 2, 2, 2, 1, 3, 1, 3, 3] => 1, 2, 2, 2, 1, 3, 1, 3, 3
[1, 2, 2, 2, 1, 3, 2, 1, 1] => 1, 2, 2, 2, 1, 3, 2, 1, 1
[1, 2, 2, 2, 1, 3, 2, 1, 2] => 1, 2, 2, 2, 1, 3, 2, 1, 2
[1, 2, 2, 2, 1, 3, 2, 1, 3] => 1, 2, 2, 2, 1, 3, 2, 1, 3
[1, 2, 2, 2, 1, 3, 2, 2, 1] => 1, 2, 2, 2, 1, 3, 2, 2, 1
[1, 2, 2, 2, 1, 3, 2, 2, 2] => 1, 2, 2, 2, 1, 3, 2, 2, 2
[1, 2, 2, 2, 1, 3, 2, 2, 3] => 1, 2, 2, 2, 1, 3, 2, 2, 3
[1, 2, 2, 2, 1, 3, 2, 3, 1] => 1, 2, 2, 2, 1, 3, 2, 3, 1
[1, 2, 2, 2, 1, 3, 2, 3, 2] => 1, 2, 2, 2, 1, 3, 2, 3, 2
[1, 2, 2, 2, 1, 3, 2, 3, 3] => 1, 2, 2, 2, 1, 3, 2, 3, 3
[1, 2, 2, 2, 1, 3, 3, 1, 1] => 1, 2, 2, 2, 1, 3, 3, 1, 1
[1, 2, 2, 2, 1, 3, 3, 1, 2] => 1, 2, 2, 2, 1, 3, 3, 1, 2
[1, 2, 2, 2, 1, 3, 3, 1, 3] => 1, 2, 2, 2, 1, 3, 3, 1, 3
[1, 2, 2, 2, 1, 3, 3, 2, 1] => 1, 2, 2, 2, 1, 3, 3, 2, 1
[1, 2, 2, 2, 1, 3, 3, 2, 2] => 1, 2, 2, 2, 1, 3, 3, 2, 2
[1, 2, 2, 2, 1, 3, 3, 2, 3] => 1, 2, 2, 2, 1, 3, 3, 2, 3
[1, 2, 2, 2, 1, 3, 3, 3, 1] => 1, 2, 2, 2, 1, 3, 3, 3, 1
[1, 2, 2, 2, 1, 3, 3, 3, 2] => 1, 2, 2, 2, 1, 3, 3, 3, 2
[1, 2, 2, 2, 1, 3, 3, 3, 3] => 1, 2, 2, 2, 1, 3, 3, 3, 3
[1, 2, 2, 2, 2, 1, 1, 1, 1] => 1, 2, 2, 2, 2, 1, 1, 1, 1
[1, 2, 2, 2, 2, 1, 1, 1, 2] => 1, 2, 2, 2, 2, 1, 1, 1, 2
[1, 2, 2, 2, 2, 1, 1, 1, 3] => 1, 2, 2, 2, 2, 1, 1, 1, 3
[1, 2, 2, 2, 2, 1, 1, 2, 1] => 1, 2, 2, 2, 2, 1, 1, 2, 1
[1, 2, 2, 2, 2, 1, 1, 2, 2] => 1, 2, 2, 2, 2, 1, 1, 2, 2
[1, 2, 2, 2, 2, 1, 1, 2, 3] => 1, 2, 2, 2, 2, 1, 1, 2, 3
[1, 2, 2, 2, 2, 1, 1, 3, 1] => 1, 2, 2, 2, 2, 1, 1, 3, 1
[1, 2, 2, 2, 2, 1, 1, 3, 2] => 1, 2, 2, 2, 2, 1, 1, 3, 2
[1, 2, 2, 2, 2, 1, 1, 3, 3] => 1, 2, 2, 2, 2, 1, 1, 3, 3
[1, 2, 2, 2, 2, 1, 2, 1, 1] => 1, 2, 2, 2, 2, 1, 2, 1, 1
[1, 2, 2, 2, 2, 1, 2, 1, 2] => 1, 2, 2, 2, 2, 1, 2, 1, 2
[1, 2, 2, 2, 2, 1, 2, 1, 3] => 1, 2, 2, 2, 2, 1, 2, 1, 3
[1, 2, 2, 2, 2, 1, 2, 2, 1] => 1, 2, 2, 2, 2, 1, 2, 2, 1
[1, 2, 2, 2, 2, 1, 2, 2, 2] => 1, 2, 2, 2, 2, 1, 2, 2, 2
[1, 2, 2, 2, 2, 1, 2, 2, 3] => 1, 2, 2, 2, 2, 1, 2, 2, 3
[1, 2, 2, 2, 2, 1, 2, 3, 1] => 1, 2, 2, 2, 2, 1, 2, 3, 1
[1, 2, 2, 2, 2, 1, 2, 3, 2] => 1, 2, 2, 2, 2, 1, 2, 3, 2
[1, 2, 2, 2, 2, 1, 2, 3, 3] => 1, 2, 2, 2, 2, 1, 2, 3, 3
[1, 2, 2, 2, 2, 1, 3, 1, 1] => 1, 2, 2, 2, 2, 1, 3, 1, 1
[1, 2, 2, 2, 2, 1, 3, 1, 2] => 1, 2, 2, 2, 2, 1, 3, 1, 2
[1, 2, 2, 2, 2, 1, 3, 1, 3] => 1, 2, 2, 2, 2, 1, 3, 1, 3
[1, 2, 2, 2, 2, 1, 3, 2, 1] => 1, 2, 2, 2, 2, 1, 3, 2, 1
[1, 2, 2, 2, 2, 1, 3, 2, 2] => 1, 2, 2, 2, 2, 1, 3, 2, 2
[1, 2, 2, 2, 2, 1, 3, 2, 3] => 1, 2, 2, 2, 2, 1, 3, 2, 3
[1, 2, 2, 2, 2, 1, 3, 3, 1] => 1, 2, 2, 2, 2, 1, 3, 3, 1
[1, 2, 2, 2, 2, 1, 3, 3, 2] => 1, 2, 2, 2, 2, 1, 3, 3, 2
[1, 2, 2, 2, 2, 1, 3, 3, 3] => 1, 2, 2, 2, 2, 1, 3, 3, 3
[1, 2, 2, 2, 2, 2, 1, 1, 1] => 1, 2, 2, 2, 2, 2, 1, 1, 1
[1, 2, 2, 2, 2, 2, 1, 1, 2] => 1, 2, 2, 2, 2, 2, 1, 1, 2
[1, 2, 2, 2, 2, 2, 1, 1, 3] => 1, 2, 2, 2, 2, 2, 1, 1, 3
[1, 2, 2, 2, 2, 2, 1, 2, 1] => 1, 2, 2, 2, 2, 2, 1, 2, 1
[1, 2, 2, 2, 2, 2, 1, 2, 2] => 1, 2, 2, 2, 2, 2, 1, 2, 2
[1, 2, 2, 2, 2, 2, 1, 2, 3] => 1, 2, 2, 2, 2, 2, 1, 2, 3
[1, 2, 2, 2, 2, 2, 1, 3, 1] => 1, 2, 2, 2, 2, 2, 1, 3, 1
[1, 2, 2, 2, 2, 2, 1, 3, 2] => 1, 2, 2, 2, 2, 2, 1, 3, 2
[1, 2, 2, 2, 2, 2, 1, 3, 3] => 1, 2, 2, 2, 2, 2, 1, 3, 3
[1, 2, 2, 2, 2, 2, 2, 1, 1] => 1, 2, 2, 2, 2, 2, 2, 1, 1
[1, 2, 2, 2, 2, 2, 2, 1, 2] => 1, 2, 2, 2, 2, 2, 2, 1, 2
[1, 2, 2, 2, 2, 2, 2, 1, 3] => 1, 2, 2, 2, 2, 2, 2, 1, 3
[1, 2, 2, 2, 2, 2, 2, 2, 1] => 1, 2, 2, 2, 2, 2, 2, 2, 1
[1, 2, 2, 2, 2, 2, 2, 2, 2] => 1, 2, 2, 2, 2, 2, 2, 2, 2
[1, 2, 2, 2, 2, 2, 2, 2, 3] => 1, 2, 2, 2, 2, 2, 2, 2, 3
[1, 2, 2, 2, 2, 2, 2, 3, 1] => 1, 2, 2, 2, 2, 2, 2, 3, 1
[1, 2, 2, 2, 2, 2, 2, 3, 2] => 1, 2, 2, 2, 2, 2, 2, 3, 2
[1, 2, 2, 2, 2, 2, 2, 3, 3] => 1, 2, 2, 2, 2, 2, 2, 3, 3
[1, 2, 2, 2, 2, 2, 3, 1, 1] => 1, 2, 2, 2, 2, 2, 3, 1, 1
[1, 2, 2, 2, 2, 2, 3, 1, 2] => 1, 2, 2, 2, 2, 2, 3, 1, 2
[1, 2, 2, 2, 2, 2, 3, 1, 3] => 1, 2, 2, 2, 2, 2, 3, 1, 3
[1, 2, 2, 2, 2, 2, 3, 2, 1] => 1, 2, 2, 2, 2, 2, 3, 2, 1
[1, 2, 2, 2, 2, 2, 3, 2, 2] => 1, 2, 2, 2, 2, 2, 3, 2, 2
[1, 2, 2, 2, 2, 2, 3, 2, 3] => 1, 2, 2, 2, 2, 2, 3, 2, 3
[1, 2, 2, 2, 2, 2, 3, 3, 1] => 1, 2, 2, 2, 2, 2, 3, 3, 1
[1, 2, 2, 2, 2, 2, 3, 3, 2] => 1, 2, 2, 2, 2, 2, 3, 3, 2
[1, 2, 2, 2, 2, 2, 3, 3, 3] => 1, 2, 2, 2, 2, 2, 3, 3, 3
[1, 2, 2, 2, 2, 3, 1, 1, 1] => 1, 2, 2, 2, 2, 3, 1, 1, 1
[1, 2, 2, 2, 2, 3, 1, 1, 2] => 1, 2, 2, 2, 2, 3, 1, 1, 2
[1, 2, 2, 2, 2, 3, 1, 1, 3] => 1, 2, 2, 2, 2, 3, 1, 1, 3
[1, 2, 2, 2, 2, 3, 1, 2, 1] => 1, 2, 2, 2, 2, 3, 1, 2, 1
[1, 2, 2, 2, 2, 3, 1, 2, 2] => 1, 2, 2, 2, 2, 3, 1, 2, 2
[1, 2, 2, 2, 2, 3, 1, 2, 3] => 1, 2, 2, 2, 2, 3, 1, 2, 3
[1, 2, 2, 2, 2, 3, 1, 3, 1] => 1, 2, 2, 2, 2, 3, 1, 3, 1
[1, 2, 2, 2, 2, 3, 1, 3, 2] => 1, 2, 2, 2, 2, 3, 1, 3, 2
[1, 2, 2, 2, 2, 3, 1, 3, 3] => 1, 2, 2, 2, 2, 3, 1, 3, 3
[1, 2, 2, 2, 2, 3, 2, 1, 1] => 1, 2, 2, 2, 2, 3, 2, 1, 1
[1, 2, 2, 2, 2, 3, 2, 1, 2] => 1, 2, 2, 2, 2, 3, 2, 1, 2
[1, 2, 2, 2, 2, 3, 2, 1, 3] => 1, 2, 2, 2, 2, 3, 2, 1, 3
[1, 2, 2, 2, 2, 3, 2, 2, 1] => 1, 2, 2, 2, 2, 3, 2, 2, 1
[1, 2, 2, 2, 2, 3, 2, 2, 2] => 1, 2, 2, 2, 2, 3, 2, 2, 2
[1, 2, 2, 2, 2, 3, 2, 2, 3] => 1, 2, 2, 2, 2, 3, 2, 2, 3
[1, 2, 2, 2, 2, 3, 2, 3, 1] => 1, 2, 2, 2, 2, 3, 2, 3, 1
[1, 2, 2, 2, 2, 3, 2, 3, 2] => 1, 2, 2, 2, 2, 3, 2, 3, 2
[1, 2, 2, 2, 2, 3, 2, 3, 3] => 1, 2, 2, 2, 2, 3, 2, 3, 3
[1, 2, 2, 2, 2, 3, 3, 1, 1] => 1, 2, 2, 2, 2, 3, 3, 1, 1
[1, 2, 2, 2, 2, 3, 3, 1, 2] => 1, 2, 2, 2, 2, 3, 3, 1, 2
[1, 2, 2, 2, 2, 3, 3, 1, 3] => 1, 2, 2, 2, 2, 3, 3, 1, 3
[1, 2, 2, 2, 2, 3, 3, 2, 1] => 1, 2, 2, 2, 2, 3, 3, 2, 1
[1, 2, 2, 2, 2, 3, 3, 2, 2] => 1, 2, 2, 2, 2, 3, 3, 2, 2
[1, 2, 2, 2, 2, 3, 3, 2, 3] => 1, 2, 2, 2, 2, 3, 3, 2, 3
[1, 2, 2, 2, 2, 3, 3, 3, 1] => 1, 2, 2, 2, 2, 3, 3, 3, 1
[1, 2, 2, 2, 2, 3, 3, 3, 2] => 1, 2, 2, 2, 2, 3, 3, 3, 2
[1, 2, 2, 2, 2, 3, 3, 3, 3] => 1, 2, 2, 2, 2, 3, 3, 3, 3
[1, 2, 2, 2, 3, 1, 1, 1, 1] => 1, 2, 2, 2, 3, 1, 1, 1, 1
[1, 2, 2, 2, 3, 1, 1, 1, 2] => 1, 2, 2, 2, 3, 1, 1, 1, 2
[1, 2, 2, 2, 3, 1, 1, 1, 3] => 1, 2, 2, 2, 3, 1, 1, 1, 3
[1, 2, 2, 2, 3, 1, 1, 2, 1] => 1, 2, 2, 2, 3, 1, 1, 2, 1
[1, 2, 2, 2, 3, 1, 1, 2, 2] => 1, 2, 2, 2, 3, 1, 1, 2, 2
[1, 2, 2, 2, 3, 1, 1, 2, 3] => 1, 2, 2, 2, 3, 1, 1, 2, 3
[1, 2, 2, 2, 3, 1, 1, 3, 1] => 1, 2, 2, 2, 3, 1, 1, 3, 1
[1, 2, 2, 2, 3, 1, 1, 3, 2] => 1, 2, 2, 2, 3, 1, 1, 3, 2
[1, 2, 2, 2, 3, 1, 1, 3, 3] => 1, 2, 2, 2, 3, 1, 1, 3, 3
[1, 2, 2, 2, 3, 1, 2, 1, 1] => 1, 2, 2, 2, 3, 1, 2, 1, 1
[1, 2, 2, 2, 3, 1, 2, 1, 2] => 1, 2, 2, 2, 3, 1, 2, 1, 2
[1, 2, 2, 2, 3, 1, 2, 1, 3] => 1, 2, 2, 2, 3, 1, 2, 1, 3
[1, 2, 2, 2, 3, 1, 2, 2, 1] => 1, 2, 2, 2, 3, 1, 2, 2, 1
[1, 2, 2, 2, 3, 1, 2, 2, 2] => 1, 2, 2, 2, 3, 1, 2, 2, 2
[1, 2, 2, 2, 3, 1, 2, 2, 3] => 1, 2, 2, 2, 3, 1, 2, 2, 3
[1, 2, 2, 2, 3, 1, 2, 3, 1] => 1, 2, 2, 2, 3, 1, 2, 3, 1
[1, 2, 2, 2, 3, 1, 2, 3, 2] => 1, 2, 2, 2, 3, 1, 2, 3, 2
[1, 2, 2, 2, 3, 1, 2, 3, 3] => 1, 2, 2, 2, 3, 1, 2, 3, 3
[1, 2, 2, 2, 3, 1, 3, 1, 1] => 1, 2, 2, 2, 3, 1, 3, 1, 1
[1, 2, 2, 2, 3, 1, 3, 1, 2] => 1, 2, 2, 2, 3, 1, 3, 1, 2
[1, 2, 2, 2, 3, 1, 3, 1, 3] => 1, 2, 2, 2, 3, 1, 3, 1, 3
[1, 2, 2, 2, 3, 1, 3, 2, 1] => 1, 2, 2, 2, 3, 1, 3, 2, 1
[1, 2, 2, 2, 3, 1, 3, 2, 2] => 1, 2, 2, 2, 3, 1, 3, 2, 2
[1, 2, 2, 2, 3, 1, 3, 2, 3] => 1, 2, 2, 2, 3, 1, 3, 2, 3
[1, 2, 2, 2, 3, 1, 3, 3, 1] => 1, 2, 2, 2, 3, 1, 3, 3, 1
[1, 2, 2, 2, 3, 1, 3, 3, 2] => 1, 2, 2, 2, 3, 1, 3, 3, 2
[1, 2, 2, 2, 3, 1, 3, 3, 3] => 1, 2, 2, 2, 3, 1, 3, 3, 3
[1, 2, 2, 2, 3, 2, 1, 1, 1] => 1, 2, 2, 2, 3, 2, 1, 1, 1
[1, 2, 2, 2, 3, 2, 1, 1, 2] => 1, 2, 2, 2, 3, 2, 1, 1, 2
[1, 2, 2, 2, 3, 2, 1, 1, 3] => 1, 2, 2, 2, 3, 2, 1, 1, 3
[1, 2, 2, 2, 3, 2, 1, 2, 1] => 1, 2, 2, 2, 3, 2, 1, 2, 1
[1, 2, 2, 2, 3, 2, 1, 2, 2] => 1, 2, 2, 2, 3, 2, 1, 2, 2
[1, 2, 2, 2, 3, 2, 1, 2, 3] => 1, 2, 2, 2, 3, 2, 1, 2, 3
[1, 2, 2, 2, 3, 2, 1, 3, 1] => 1, 2, 2, 2, 3, 2, 1, 3, 1
[1, 2, 2, 2, 3, 2, 1, 3, 2] => 1, 2, 2, 2, 3, 2, 1, 3, 2
[1, 2, 2, 2, 3, 2, 1, 3, 3] => 1, 2, 2, 2, 3, 2, 1, 3, 3
[1, 2, 2, 2, 3, 2, 2, 1, 1] => 1, 2, 2, 2, 3, 2, 2, 1, 1
[1, 2, 2, 2, 3, 2, 2, 1, 2] => 1, 2, 2, 2, 3, 2, 2, 1, 2
[1, 2, 2, 2, 3, 2, 2, 1, 3] => 1, 2, 2, 2, 3, 2, 2, 1, 3
[1, 2, 2, 2, 3, 2, 2, 2, 1] => 1, 2, 2, 2, 3, 2, 2, 2, 1
[1, 2, 2, 2, 3, 2, 2, 2, 2] => 1, 2, 2, 2, 3, 2, 2, 2, 2
[1, 2, 2, 2, 3, 2, 2, 2, 3] => 1, 2, 2, 2, 3, 2, 2, 2, 3
[1, 2, 2, 2, 3, 2, 2, 3, 1] => 1, 2, 2, 2, 3, 2, 2, 3, 1
[1, 2, 2, 2, 3, 2, 2, 3, 2] => 1, 2, 2, 2, 3, 2, 2, 3, 2
[1, 2, 2, 2, 3, 2, 2, 3, 3] => 1, 2, 2, 2, 3, 2, 2, 3, 3
[1, 2, 2, 2, 3, 2, 3, 1, 1] => 1, 2, 2, 2, 3, 2, 3, 1, 1
[1, 2, 2, 2, 3, 2, 3, 1, 2] => 1, 2, 2, 2, 3, 2, 3, 1, 2
[1, 2, 2, 2, 3, 2, 3, 1, 3] => 1, 2, 2, 2, 3, 2, 3, 1, 3
[1, 2, 2, 2, 3, 2, 3, 2, 1] => 1, 2, 2, 2, 3, 2, 3, 2, 1
[1, 2, 2, 2, 3, 2, 3, 2, 2] => 1, 2, 2, 2, 3, 2, 3, 2, 2
[1, 2, 2, 2, 3, 2, 3, 2, 3] => 1, 2, 2, 2, 3, 2, 3, 2, 3
[1, 2, 2, 2, 3, 2, 3, 3, 1] => 1, 2, 2, 2, 3, 2, 3, 3, 1
[1, 2, 2, 2, 3, 2, 3, 3, 2] => 1, 2, 2, 2, 3, 2, 3, 3, 2
[1, 2, 2, 2, 3, 2, 3, 3, 3] => 1, 2, 2, 2, 3, 2, 3, 3, 3
[1, 2, 2, 2, 3, 3, 1, 1, 1] => 1, 2, 2, 2, 3, 3, 1, 1, 1
[1, 2, 2, 2, 3, 3, 1, 1, 2] => 1, 2, 2, 2, 3, 3, 1, 1, 2
[1, 2, 2, 2, 3, 3, 1, 1, 3] => 1, 2, 2, 2, 3, 3, 1, 1, 3
[1, 2, 2, 2, 3, 3, 1, 2, 1] => 1, 2, 2, 2, 3, 3, 1, 2, 1
[1, 2, 2, 2, 3, 3, 1, 2, 2] => 1, 2, 2, 2, 3, 3, 1, 2, 2
[1, 2, 2, 2, 3, 3, 1, 2, 3] => 1, 2, 2, 2, 3, 3, 1, 2, 3
[1, 2, 2, 2, 3, 3, 1, 3, 1] => 1, 2, 2, 2, 3, 3, 1, 3, 1
[1, 2, 2, 2, 3, 3, 1, 3, 2] => 1, 2, 2, 2, 3, 3, 1, 3, 2
[1, 2, 2, 2, 3, 3, 1, 3, 3] => 1, 2, 2, 2, 3, 3, 1, 3, 3
[1, 2, 2, 2, 3, 3, 2, 1, 1] => 1, 2, 2, 2, 3, 3, 2, 1, 1
[1, 2, 2, 2, 3, 3, 2, 1, 2] => 1, 2, 2, 2, 3, 3, 2, 1, 2
[1, 2, 2, 2, 3, 3, 2, 1, 3] => 1, 2, 2, 2, 3, 3, 2, 1, 3
[1, 2, 2, 2, 3, 3, 2, 2, 1] => 1, 2, 2, 2, 3, 3, 2, 2, 1
[1, 2, 2, 2, 3, 3, 2, 2, 2] => 1, 2, 2, 2, 3, 3, 2, 2, 2
[1, 2, 2, 2, 3, 3, 2, 2, 3] => 1, 2, 2, 2, 3, 3, 2, 2, 3
[1, 2, 2, 2, 3, 3, 2, 3, 1] => 1, 2, 2, 2, 3, 3, 2, 3, 1
[1, 2, 2, 2, 3, 3, 2, 3, 2] => 1, 2, 2, 2, 3, 3, 2, 3, 2
[1, 2, 2, 2, 3, 3, 2, 3, 3] => 1, 2, 2, 2, 3, 3, 2, 3, 3
[1, 2, 2, 2, 3, 3, 3, 1, 1] => 1, 2, 2, 2, 3, 3, 3, 1, 1
[1, 2, 2, 2, 3, 3, 3, 1, 2] => 1, 2, 2, 2, 3, 3, 3, 1, 2
[1, 2, 2, 2, 3, 3, 3, 1, 3] => 1, 2, 2, 2, 3, 3, 3, 1, 3
[1, 2, 2, 2, 3, 3, 3, 2, 1] => 1, 2, 2, 2, 3, 3, 3, 2, 1
[1, 2, 2, 2, 3, 3, 3, 2, 2] => 1, 2, 2, 2, 3, 3, 3, 2, 2
[1, 2, 2, 2, 3, 3, 3, 2, 3] => 1, 2, 2, 2, 3, 3, 3, 2, 3
[1, 2, 2, 2, 3, 3, 3, 3, 1] => 1, 2, 2, 2, 3, 3, 3, 3, 1
[1, 2, 2, 2, 3, 3, 3, 3, 2] => 1, 2, 2, 2, 3, 3, 3, 3, 2
[1, 2, 2, 2, 3, 3, 3, 3, 3] => 1, 2, 2, 2, 3, 3, 3, 3, 3
[1, 2, 2, 3, 1, 1, 1, 1, 1] => 1, 2, 2, 3, 1, 1, 1, 1, 1
[1, 2, 2, 3, 1, 1, 1, 1, 2] => 1, 2, 2, 3, 1, 1, 1, 1, 2
[1, 2, 2, 3, 1, 1, 1, 1, 3] => 1, 2, 2, 3, 1, 1, 1, 1, 3
[1, 2, 2, 3, 1, 1, 1, 2, 1] => 1, 2, 2, 3, 1, 1, 1, 2, 1
[1, 2, 2, 3, 1, 1, 1, 2, 2] => 1, 2, 2, 3, 1, 1, 1, 2, 2
[1, 2, 2, 3, 1, 1, 1, 2, 3] => 1, 2, 2, 3, 1, 1, 1, 2, 3
[1, 2, 2, 3, 1, 1, 1, 3, 1] => 1, 2, 2, 3, 1, 1, 1, 3, 1
[1, 2, 2, 3, 1, 1, 1, 3, 2] => 1, 2, 2, 3, 1, 1, 1, 3, 2
[1, 2, 2, 3, 1, 1, 1, 3, 3] => 1, 2, 2, 3, 1, 1, 1, 3, 3
[1, 2, 2, 3, 1, 1, 2, 1, 1] => 1, 2, 2, 3, 1, 1, 2, 1, 1
[1, 2, 2, 3, 1, 1, 2, 1, 2] => 1, 2, 2, 3, 1, 1, 2, 1, 2
[1, 2, 2, 3, 1, 1, 2, 1, 3] => 1, 2, 2, 3, 1, 1, 2, 1, 3
[1, 2, 2, 3, 1, 1, 2, 2, 1] => 1, 2, 2, 3, 1, 1, 2, 2, 1
[1, 2, 2, 3, 1, 1, 2, 2, 2] => 1, 2, 2, 3, 1, 1, 2, 2, 2
[1, 2, 2, 3, 1, 1, 2, 2, 3] => 1, 2, 2, 3, 1, 1, 2, 2, 3
[1, 2, 2, 3, 1, 1, 2, 3, 1] => 1, 2, 2, 3, 1, 1, 2, 3, 1
[1, 2, 2, 3, 1, 1, 2, 3, 2] => 1, 2, 2, 3, 1, 1, 2, 3, 2
[1, 2, 2, 3, 1, 1, 2, 3, 3] => 1, 2, 2, 3, 1, 1, 2, 3, 3
[1, 2, 2, 3, 1, 1, 3, 1, 1] => 1, 2, 2, 3, 1, 1, 3, 1, 1
[1, 2, 2, 3, 1, 1, 3, 1, 2] => 1, 2, 2, 3, 1, 1, 3, 1, 2
[1, 2, 2, 3, 1, 1, 3, 1, 3] => 1, 2, 2, 3, 1, 1, 3, 1, 3
[1, 2, 2, 3, 1, 1, 3, 2, 1] => 1, 2, 2, 3, 1, 1, 3, 2, 1
[1, 2, 2, 3, 1, 1, 3, 2, 2] => 1, 2, 2, 3, 1, 1, 3, 2, 2
[1, 2, 2, 3, 1, 1, 3, 2, 3] => 1, 2, 2, 3, 1, 1, 3, 2, 3
[1, 2, 2, 3, 1, 1, 3, 3, 1] => 1, 2, 2, 3, 1, 1, 3, 3, 1
[1, 2, 2, 3, 1, 1, 3, 3, 2] => 1, 2, 2, 3, 1, 1, 3, 3, 2
[1, 2, 2, 3, 1, 1, 3, 3, 3] => 1, 2, 2, 3, 1, 1, 3, 3, 3
[1, 2, 2, 3, 1, 2, 1, 1, 1] => 1, 2, 2, 3, 1, 2, 1, 1, 1
[1, 2, 2, 3, 1, 2, 1, 1, 2] => 1, 2, 2, 3, 1, 2, 1, 1, 2
[1, 2, 2, 3, 1, 2, 1, 1, 3] => 1, 2, 2, 3, 1, 2, 1, 1, 3
[1, 2, 2, 3, 1, 2, 1, 2, 1] => 1, 2, 2, 3, 1, 2, 1, 2, 1
[1, 2, 2, 3, 1, 2, 1, 2, 2] => 1, 2, 2, 3, 1, 2, 1, 2, 2
[1, 2, 2, 3, 1, 2, 1, 2, 3] => 1, 2, 2, 3, 1, 2, 1, 2, 3
[1, 2, 2, 3, 1, 2, 1, 3, 1] => 1, 2, 2, 3, 1, 2, 1, 3, 1
[1, 2, 2, 3, 1, 2, 1, 3, 2] => 1, 2, 2, 3, 1, 2, 1, 3, 2
[1, 2, 2, 3, 1, 2, 1, 3, 3] => 1, 2, 2, 3, 1, 2, 1, 3, 3
[1, 2, 2, 3, 1, 2, 2, 1, 1] => 1, 2, 2, 3, 1, 2, 2, 1, 1
[1, 2, 2, 3, 1, 2, 2, 1, 2] => 1, 2, 2, 3, 1, 2, 2, 1, 2
[1, 2, 2, 3, 1, 2, 2, 1, 3] => 1, 2, 2, 3, 1, 2, 2, 1, 3
[1, 2, 2, 3, 1, 2, 2, 2, 1] => 1, 2, 2, 3, 1, 2, 2, 2, 1
[1, 2, 2, 3, 1, 2, 2, 2, 2] => 1, 2, 2, 3, 1, 2, 2, 2, 2
[1, 2, 2, 3, 1, 2, 2, 2, 3] => 1, 2, 2, 3, 1, 2, 2, 2, 3
[1, 2, 2, 3, 1, 2, 2, 3, 1] => 1, 2, 2, 3, 1, 2, 2, 3, 1
[1, 2, 2, 3, 1, 2, 2, 3, 2] => 1, 2, 2, 3, 1, 2, 2, 3, 2
[1, 2, 2, 3, 1, 2, 2, 3, 3] => 1, 2, 2, 3, 1, 2, 2, 3, 3
[1, 2, 2, 3, 1, 2, 3, 1, 1] => 1, 2, 2, 3, 1, 2, 3, 1, 1
[1, 2, 2, 3, 1, 2, 3, 1, 2] => 1, 2, 2, 3, 1, 2, 3, 1, 2
[1, 2, 2, 3, 1, 2, 3, 1, 3] => 1, 2, 2, 3, 1, 2, 3, 1, 3
[1, 2, 2, 3, 1, 2, 3, 2, 1] => 1, 2, 2, 3, 1, 2, 3, 2, 1
[1, 2, 2, 3, 1, 2, 3, 2, 2] => 1, 2, 2, 3, 1, 2, 3, 2, 2
[1, 2, 2, 3, 1, 2, 3, 2, 3] => 1, 2, 2, 3, 1, 2, 3, 2, 3
[1, 2, 2, 3, 1, 2, 3, 3, 1] => 1, 2, 2, 3, 1, 2, 3, 3, 1
[1, 2, 2, 3, 1, 2, 3, 3, 2] => 1, 2, 2, 3, 1, 2, 3, 3, 2
[1, 2, 2, 3, 1, 2, 3, 3, 3] => 1, 2, 2, 3, 1, 2, 3, 3, 3
[1, 2, 2, 3, 1, 3, 1, 1, 1] => 1, 2, 2, 3, 1, 3, 1, 1, 1
[1, 2, 2, 3, 1, 3, 1, 1, 2] => 1, 2, 2, 3, 1, 3, 1, 1, 2
[1, 2, 2, 3, 1, 3, 1, 1, 3] => 1, 2, 2, 3, 1, 3, 1, 1, 3
[1, 2, 2, 3, 1, 3, 1, 2, 1] => 1, 2, 2, 3, 1, 3, 1, 2, 1
[1, 2, 2, 3, 1, 3, 1, 2, 2] => 1, 2, 2, 3, 1, 3, 1, 2, 2
[1, 2, 2, 3, 1, 3, 1, 2, 3] => 1, 2, 2, 3, 1, 3, 1, 2, 3
[1, 2, 2, 3, 1, 3, 1, 3, 1] => 1, 2, 2, 3, 1, 3, 1, 3, 1
[1, 2, 2, 3, 1, 3, 1, 3, 2] => 1, 2, 2, 3, 1, 3, 1, 3, 2
[1, 2, 2, 3, 1, 3, 1, 3, 3] => 1, 2, 2, 3, 1, 3, 1, 3, 3
[1, 2, 2, 3, 1, 3, 2, 1, 1] => 1, 2, 2, 3, 1, 3, 2, 1, 1
[1, 2, 2, 3, 1, 3, 2, 1, 2] => 1, 2, 2, 3, 1, 3, 2, 1, 2
[1, 2, 2, 3, 1, 3, 2, 1, 3] => 1, 2, 2, 3, 1, 3, 2, 1, 3
[1, 2, 2, 3, 1, 3, 2, 2, 1] => 1, 2, 2, 3, 1, 3, 2, 2, 1
[1, 2, 2, 3, 1, 3, 2, 2, 2] => 1, 2, 2, 3, 1, 3, 2, 2, 2
[1, 2, 2, 3, 1, 3, 2, 2, 3] => 1, 2, 2, 3, 1, 3, 2, 2, 3
[1, 2, 2, 3, 1, 3, 2, 3, 1] => 1, 2, 2, 3, 1, 3, 2, 3, 1
[1, 2, 2, 3, 1, 3, 2, 3, 2] => 1, 2, 2, 3, 1, 3, 2, 3, 2
[1, 2, 2, 3, 1, 3, 2, 3, 3] => 1, 2, 2, 3, 1, 3, 2, 3, 3
[1, 2, 2, 3, 1, 3, 3, 1, 1] => 1, 2, 2, 3, 1, 3, 3, 1, 1
[1, 2, 2, 3, 1, 3, 3, 1, 2] => 1, 2, 2, 3, 1, 3, 3, 1, 2
[1, 2, 2, 3, 1, 3, 3, 1, 3] => 1, 2, 2, 3, 1, 3, 3, 1, 3
[1, 2, 2, 3, 1, 3, 3, 2, 1] => 1, 2, 2, 3, 1, 3, 3, 2, 1
[1, 2, 2, 3, 1, 3, 3, 2, 2] => 1, 2, 2, 3, 1, 3, 3, 2, 2
[1, 2, 2, 3, 1, 3, 3, 2, 3] => 1, 2, 2, 3, 1, 3, 3, 2, 3
[1, 2, 2, 3, 1, 3, 3, 3, 1] => 1, 2, 2, 3, 1, 3, 3, 3, 1
[1, 2, 2, 3, 1, 3, 3, 3, 2] => 1, 2, 2, 3, 1, 3, 3, 3, 2
[1, 2, 2, 3, 1, 3, 3, 3, 3] => 1, 2, 2, 3, 1, 3, 3, 3, 3
[1, 2, 2, 3, 2, 1, 1, 1, 1] => 1, 2, 2, 3, 2, 1, 1, 1, 1
[1, 2, 2, 3, 2, 1, 1, 1, 2] => 1, 2, 2, 3, 2, 1, 1, 1, 2
[1, 2, 2, 3, 2, 1, 1, 1, 3] => 1, 2, 2, 3, 2, 1, 1, 1, 3
[1, 2, 2, 3, 2, 1, 1, 2, 1] => 1, 2, 2, 3, 2, 1, 1, 2, 1
[1, 2, 2, 3, 2, 1, 1, 2, 2] => 1, 2, 2, 3, 2, 1, 1, 2, 2
[1, 2, 2, 3, 2, 1, 1, 2, 3] => 1, 2, 2, 3, 2, 1, 1, 2, 3
[1, 2, 2, 3, 2, 1, 1, 3, 1] => 1, 2, 2, 3, 2, 1, 1, 3, 1
[1, 2, 2, 3, 2, 1, 1, 3, 2] => 1, 2, 2, 3, 2, 1, 1, 3, 2
[1, 2, 2, 3, 2, 1, 1, 3, 3] => 1, 2, 2, 3, 2, 1, 1, 3, 3
[1, 2, 2, 3, 2, 1, 2, 1, 1] => 1, 2, 2, 3, 2, 1, 2, 1, 1
[1, 2, 2, 3, 2, 1, 2, 1, 2] => 1, 2, 2, 3, 2, 1, 2, 1, 2
[1, 2, 2, 3, 2, 1, 2, 1, 3] => 1, 2, 2, 3, 2, 1, 2, 1, 3
[1, 2, 2, 3, 2, 1, 2, 2, 1] => 1, 2, 2, 3, 2, 1, 2, 2, 1
[1, 2, 2, 3, 2, 1, 2, 2, 2] => 1, 2, 2, 3, 2, 1, 2, 2, 2
[1, 2, 2, 3, 2, 1, 2, 2, 3] => 1, 2, 2, 3, 2, 1, 2, 2, 3
[1, 2, 2, 3, 2, 1, 2, 3, 1] => 1, 2, 2, 3, 2, 1, 2, 3, 1
[1, 2, 2, 3, 2, 1, 2, 3, 2] => 1, 2, 2, 3, 2, 1, 2, 3, 2
[1, 2, 2, 3, 2, 1, 2, 3, 3] => 1, 2, 2, 3, 2, 1, 2, 3, 3
[1, 2, 2, 3, 2, 1, 3, 1, 1] => 1, 2, 2, 3, 2, 1, 3, 1, 1
[1, 2, 2, 3, 2, 1, 3, 1, 2] => 1, 2, 2, 3, 2, 1, 3, 1, 2
[1, 2, 2, 3, 2, 1, 3, 1, 3] => 1, 2, 2, 3, 2, 1, 3, 1, 3
[1, 2, 2, 3, 2, 1, 3, 2, 1] => 1, 2, 2, 3, 2, 1, 3, 2, 1
[1, 2, 2, 3, 2, 1, 3, 2, 2] => 1, 2, 2, 3, 2, 1, 3, 2, 2
[1, 2, 2, 3, 2, 1, 3, 2, 3] => 1, 2, 2, 3, 2, 1, 3, 2, 3
[1, 2, 2, 3, 2, 1, 3, 3, 1] => 1, 2, 2, 3, 2, 1, 3, 3, 1
[1, 2, 2, 3, 2, 1, 3, 3, 2] => 1, 2, 2, 3, 2, 1, 3, 3, 2
[1, 2, 2, 3, 2, 1, 3, 3, 3] => 1, 2, 2, 3, 2, 1, 3, 3, 3
[1, 2, 2, 3, 2, 2, 1, 1, 1] => 1, 2, 2, 3, 2, 2, 1, 1, 1
[1, 2, 2, 3, 2, 2, 1, 1, 2] => 1, 2, 2, 3, 2, 2, 1, 1, 2
[1, 2, 2, 3, 2, 2, 1, 1, 3] => 1, 2, 2, 3, 2, 2, 1, 1, 3
[1, 2, 2, 3, 2, 2, 1, 2, 1] => 1, 2, 2, 3, 2, 2, 1, 2, 1
[1, 2, 2, 3, 2, 2, 1, 2, 2] => 1, 2, 2, 3, 2, 2, 1, 2, 2
[1, 2, 2, 3, 2, 2, 1, 2, 3] => 1, 2, 2, 3, 2, 2, 1, 2, 3
[1, 2, 2, 3, 2, 2, 1, 3, 1] => 1, 2, 2, 3, 2, 2, 1, 3, 1
[1, 2, 2, 3, 2, 2, 1, 3, 2] => 1, 2, 2, 3, 2, 2, 1, 3, 2
[1, 2, 2, 3, 2, 2, 1, 3, 3] => 1, 2, 2, 3, 2, 2, 1, 3, 3
[1, 2, 2, 3, 2, 2, 2, 1, 1] => 1, 2, 2, 3, 2, 2, 2, 1, 1
[1, 2, 2, 3, 2, 2, 2, 1, 2] => 1, 2, 2, 3, 2, 2, 2, 1, 2
[1, 2, 2, 3, 2, 2, 2, 1, 3] => 1, 2, 2, 3, 2, 2, 2, 1, 3
[1, 2, 2, 3, 2, 2, 2, 2, 1] => 1, 2, 2, 3, 2, 2, 2, 2, 1
[1, 2, 2, 3, 2, 2, 2, 2, 2] => 1, 2, 2, 3, 2, 2, 2, 2, 2
[1, 2, 2, 3, 2, 2, 2, 2, 3] => 1, 2, 2, 3, 2, 2, 2, 2, 3
[1, 2, 2, 3, 2, 2, 2, 3, 1] => 1, 2, 2, 3, 2, 2, 2, 3, 1
[1, 2, 2, 3, 2, 2, 2, 3, 2] => 1, 2, 2, 3, 2, 2, 2, 3, 2
[1, 2, 2, 3, 2, 2, 2, 3, 3] => 1, 2, 2, 3, 2, 2, 2, 3, 3
[1, 2, 2, 3, 2, 2, 3, 1, 1] => 1, 2, 2, 3, 2, 2, 3, 1, 1
[1, 2, 2, 3, 2, 2, 3, 1, 2] => 1, 2, 2, 3, 2, 2, 3, 1, 2
[1, 2, 2, 3, 2, 2, 3, 1, 3] => 1, 2, 2, 3, 2, 2, 3, 1, 3
[1, 2, 2, 3, 2, 2, 3, 2, 1] => 1, 2, 2, 3, 2, 2, 3, 2, 1
[1, 2, 2, 3, 2, 2, 3, 2, 2] => 1, 2, 2, 3, 2, 2, 3, 2, 2
[1, 2, 2, 3, 2, 2, 3, 2, 3] => 1, 2, 2, 3, 2, 2, 3, 2, 3
[1, 2, 2, 3, 2, 2, 3, 3, 1] => 1, 2, 2, 3, 2, 2, 3, 3, 1
[1, 2, 2, 3, 2, 2, 3, 3, 2] => 1, 2, 2, 3, 2, 2, 3, 3, 2
[1, 2, 2, 3, 2, 2, 3, 3, 3] => 1, 2, 2, 3, 2, 2, 3, 3, 3
[1, 2, 2, 3, 2, 3, 1, 1, 1] => 1, 2, 2, 3, 2, 3, 1, 1, 1
[1, 2, 2, 3, 2, 3, 1, 1, 2] => 1, 2, 2, 3, 2, 3, 1, 1, 2
[1, 2, 2, 3, 2, 3, 1, 1, 3] => 1, 2, 2, 3, 2, 3, 1, 1, 3
[1, 2, 2, 3, 2, 3, 1, 2, 1] => 1, 2, 2, 3, 2, 3, 1, 2, 1
[1, 2, 2, 3, 2, 3, 1, 2, 2] => 1, 2, 2, 3, 2, 3, 1, 2, 2
[1, 2, 2, 3, 2, 3, 1, 2, 3] => 1, 2, 2, 3, 2, 3, 1, 2, 3
[1, 2, 2, 3, 2, 3, 1, 3, 1] => 1, 2, 2, 3, 2, 3, 1, 3, 1
[1, 2, 2, 3, 2, 3, 1, 3, 2] => 1, 2, 2, 3, 2, 3, 1, 3, 2
[1, 2, 2, 3, 2, 3, 1, 3, 3] => 1, 2, 2, 3, 2, 3, 1, 3, 3
[1, 2, 2, 3, 2, 3, 2, 1, 1] => 1, 2, 2, 3, 2, 3, 2, 1, 1
[1, 2, 2, 3, 2, 3, 2, 1, 2] => 1, 2, 2, 3, 2, 3, 2, 1, 2
[1, 2, 2, 3, 2, 3, 2, 1, 3] => 1, 2, 2, 3, 2, 3, 2, 1, 3
[1, 2, 2, 3, 2, 3, 2, 2, 1] => 1, 2, 2, 3, 2, 3, 2, 2, 1
[1, 2, 2, 3, 2, 3, 2, 2, 2] => 1, 2, 2, 3, 2, 3, 2, 2, 2
[1, 2, 2, 3, 2, 3, 2, 2, 3] => 1, 2, 2, 3, 2, 3, 2, 2, 3
[1, 2, 2, 3, 2, 3, 2, 3, 1] => 1, 2, 2, 3, 2, 3, 2, 3, 1
[1, 2, 2, 3, 2, 3, 2, 3, 2] => 1, 2, 2, 3, 2, 3, 2, 3, 2
[1, 2, 2, 3, 2, 3, 2, 3, 3] => 1, 2, 2, 3, 2, 3, 2, 3, 3
[1, 2, 2, 3, 2, 3, 3, 1, 1] => 1, 2, 2, 3, 2, 3, 3, 1, 1
[1, 2, 2, 3, 2, 3, 3, 1, 2] => 1, 2, 2, 3, 2, 3, 3, 1, 2
[1, 2, 2, 3, 2, 3, 3, 1, 3] => 1, 2, 2, 3, 2, 3, 3, 1, 3
[1, 2, 2, 3, 2, 3, 3, 2, 1] => 1, 2, 2, 3, 2, 3, 3, 2, 1
[1, 2, 2, 3, 2, 3, 3, 2, 2] => 1, 2, 2, 3, 2, 3, 3, 2, 2
[1, 2, 2, 3, 2, 3, 3, 2, 3] => 1, 2, 2, 3, 2, 3, 3, 2, 3
[1, 2, 2, 3, 2, 3, 3, 3, 1] => 1, 2, 2, 3, 2, 3, 3, 3, 1
[1, 2, 2, 3, 2, 3, 3, 3, 2] => 1, 2, 2, 3, 2, 3, 3, 3, 2
[1, 2, 2, 3, 2, 3, 3, 3, 3] => 1, 2, 2, 3, 2, 3, 3, 3, 3
[1, 2, 2, 3, 3, 1, 1, 1, 1] => 1, 2, 2, 3, 3, 1, 1, 1, 1
[1, 2, 2, 3, 3, 1, 1, 1, 2] => 1, 2, 2, 3, 3, 1, 1, 1, 2
[1, 2, 2, 3, 3, 1, 1, 1, 3] => 1, 2, 2, 3, 3, 1, 1, 1, 3
[1, 2, 2, 3, 3, 1, 1, 2, 1] => 1, 2, 2, 3, 3, 1, 1, 2, 1
[1, 2, 2, 3, 3, 1, 1, 2, 2] => 1, 2, 2, 3, 3, 1, 1, 2, 2
[1, 2, 2, 3, 3, 1, 1, 2, 3] => 1, 2, 2, 3, 3, 1, 1, 2, 3
[1, 2, 2, 3, 3, 1, 1, 3, 1] => 1, 2, 2, 3, 3, 1, 1, 3, 1
[1, 2, 2, 3, 3, 1, 1, 3, 2] => 1, 2, 2, 3, 3, 1, 1, 3, 2
[1, 2, 2, 3, 3, 1, 1, 3, 3] => 1, 2, 2, 3, 3, 1, 1, 3, 3
[1, 2, 2, 3, 3, 1, 2, 1, 1] => 1, 2, 2, 3, 3, 1, 2, 1, 1
[1, 2, 2, 3, 3, 1, 2, 1, 2] => 1, 2, 2, 3, 3, 1, 2, 1, 2
[1, 2, 2, 3, 3, 1, 2, 1, 3] => 1, 2, 2, 3, 3, 1, 2, 1, 3
[1, 2, 2, 3, 3, 1, 2, 2, 1] => 1, 2, 2, 3, 3, 1, 2, 2, 1
[1, 2, 2, 3, 3, 1, 2, 2, 2] => 1, 2, 2, 3, 3, 1, 2, 2, 2
[1, 2, 2, 3, 3, 1, 2, 2, 3] => 1, 2, 2, 3, 3, 1, 2, 2, 3
[1, 2, 2, 3, 3, 1, 2, 3, 1] => 1, 2, 2, 3, 3, 1, 2, 3, 1
[1, 2, 2, 3, 3, 1, 2, 3, 2] => 1, 2, 2, 3, 3, 1, 2, 3, 2
[1, 2, 2, 3, 3, 1, 2, 3, 3] => 1, 2, 2, 3, 3, 1, 2, 3, 3
[1, 2, 2, 3, 3, 1, 3, 1, 1] => 1, 2, 2, 3, 3, 1, 3, 1, 1
[1, 2, 2, 3, 3, 1, 3, 1, 2] => 1, 2, 2, 3, 3, 1, 3, 1, 2
[1, 2, 2, 3, 3, 1, 3, 1, 3] => 1, 2, 2, 3, 3, 1, 3, 1, 3
[1, 2, 2, 3, 3, 1, 3, 2, 1] => 1, 2, 2, 3, 3, 1, 3, 2, 1
[1, 2, 2, 3, 3, 1, 3, 2, 2] => 1, 2, 2, 3, 3, 1, 3, 2, 2
[1, 2, 2, 3, 3, 1, 3, 2, 3] => 1, 2, 2, 3, 3, 1, 3, 2, 3
[1, 2, 2, 3, 3, 1, 3, 3, 1] => 1, 2, 2, 3, 3, 1, 3, 3, 1
[1, 2, 2, 3, 3, 1, 3, 3, 2] => 1, 2, 2, 3, 3, 1, 3, 3, 2
[1, 2, 2, 3, 3, 1, 3, 3, 3] => 1, 2, 2, 3, 3, 1, 3, 3, 3
[1, 2, 2, 3, 3, 2, 1, 1, 1] => 1, 2, 2, 3, 3, 2, 1, 1, 1
[1, 2, 2, 3, 3, 2, 1, 1, 2] => 1, 2, 2, 3, 3, 2, 1, 1, 2
[1, 2, 2, 3, 3, 2, 1, 1, 3] => 1, 2, 2, 3, 3, 2, 1, 1, 3
[1, 2, 2, 3, 3, 2, 1, 2, 1] => 1, 2, 2, 3, 3, 2, 1, 2, 1
[1, 2, 2, 3, 3, 2, 1, 2, 2] => 1, 2, 2, 3, 3, 2, 1, 2, 2
[1, 2, 2, 3, 3, 2, 1, 2, 3] => 1, 2, 2, 3, 3, 2, 1, 2, 3
[1, 2, 2, 3, 3, 2, 1, 3, 1] => 1, 2, 2, 3, 3, 2, 1, 3, 1
[1, 2, 2, 3, 3, 2, 1, 3, 2] => 1, 2, 2, 3, 3, 2, 1, 3, 2
[1, 2, 2, 3, 3, 2, 1, 3, 3] => 1, 2, 2, 3, 3, 2, 1, 3, 3
[1, 2, 2, 3, 3, 2, 2, 1, 1] => 1, 2, 2, 3, 3, 2, 2, 1, 1
[1, 2, 2, 3, 3, 2, 2, 1, 2] => 1, 2, 2, 3, 3, 2, 2, 1, 2
[1, 2, 2, 3, 3, 2, 2, 1, 3] => 1, 2, 2, 3, 3, 2, 2, 1, 3
[1, 2, 2, 3, 3, 2, 2, 2, 1] => 1, 2, 2, 3, 3, 2, 2, 2, 1
[1, 2, 2, 3, 3, 2, 2, 2, 2] => 1, 2, 2, 3, 3, 2, 2, 2, 2
[1, 2, 2, 3, 3, 2, 2, 2, 3] => 1, 2, 2, 3, 3, 2, 2, 2, 3
[1, 2, 2, 3, 3, 2, 2, 3, 1] => 1, 2, 2, 3, 3, 2, 2, 3, 1
[1, 2, 2, 3, 3, 2, 2, 3, 2] => 1, 2, 2, 3, 3, 2, 2, 3, 2
[1, 2, 2, 3, 3, 2, 2, 3, 3] => 1, 2, 2, 3, 3, 2, 2, 3, 3
[1, 2, 2, 3, 3, 2, 3, 1, 1] => 1, 2, 2, 3, 3, 2, 3, 1, 1
[1, 2, 2, 3, 3, 2, 3, 1, 2] => 1, 2, 2, 3, 3, 2, 3, 1, 2
[1, 2, 2, 3, 3, 2, 3, 1, 3] => 1, 2, 2, 3, 3, 2, 3, 1, 3
[1, 2, 2, 3, 3, 2, 3, 2, 1] => 1, 2, 2, 3, 3, 2, 3, 2, 1
[1, 2, 2, 3, 3, 2, 3, 2, 2] => 1, 2, 2, 3, 3, 2, 3, 2, 2
[1, 2, 2, 3, 3, 2, 3, 2, 3] => 1, 2, 2, 3, 3, 2, 3, 2, 3
[1, 2, 2, 3, 3, 2, 3, 3, 1] => 1, 2, 2, 3, 3, 2, 3, 3, 1
[1, 2, 2, 3, 3, 2, 3, 3, 2] => 1, 2, 2, 3, 3, 2, 3, 3, 2
[1, 2, 2, 3, 3, 2, 3, 3, 3] => 1, 2, 2, 3, 3, 2, 3, 3, 3
[1, 2, 2, 3, 3, 3, 1, 1, 1] => 1, 2, 2, 3, 3, 3, 1, 1, 1
[1, 2, 2, 3, 3, 3, 1, 1, 2] => 1, 2, 2, 3, 3, 3, 1, 1, 2
[1, 2, 2, 3, 3, 3, 1, 1, 3] => 1, 2, 2, 3, 3, 3, 1, 1, 3
[1, 2, 2, 3, 3, 3, 1, 2, 1] => 1, 2, 2, 3, 3, 3, 1, 2, 1
[1, 2, 2, 3, 3, 3, 1, 2, 2] => 1, 2, 2, 3, 3, 3, 1, 2, 2
[1, 2, 2, 3, 3, 3, 1, 2, 3] => 1, 2, 2, 3, 3, 3, 1, 2, 3
[1, 2, 2, 3, 3, 3, 1, 3, 1] => 1, 2, 2, 3, 3, 3, 1, 3, 1
[1, 2, 2, 3, 3, 3, 1, 3, 2] => 1, 2, 2, 3, 3, 3, 1, 3, 2
[1, 2, 2, 3, 3, 3, 1, 3, 3] => 1, 2, 2, 3, 3, 3, 1, 3, 3
[1, 2, 2, 3, 3, 3, 2, 1, 1] => 1, 2, 2, 3, 3, 3, 2, 1, 1
[1, 2, 2, 3, 3, 3, 2, 1, 2] => 1, 2, 2, 3, 3, 3, 2, 1, 2
[1, 2, 2, 3, 3, 3, 2, 1, 3] => 1, 2, 2, 3, 3, 3, 2, 1, 3
[1, 2, 2, 3, 3, 3, 2, 2, 1] => 1, 2, 2, 3, 3, 3, 2, 2, 1
[1, 2, 2, 3, 3, 3, 2, 2, 2] => 1, 2, 2, 3, 3, 3, 2, 2, 2
[1, 2, 2, 3, 3, 3, 2, 2, 3] => 1, 2, 2, 3, 3, 3, 2, 2, 3
[1, 2, 2, 3, 3, 3, 2, 3, 1] => 1, 2, 2, 3, 3, 3, 2, 3, 1
[1, 2, 2, 3, 3, 3, 2, 3, 2] => 1, 2, 2, 3, 3, 3, 2, 3, 2
[1, 2, 2, 3, 3, 3, 2, 3, 3] => 1, 2, 2, 3, 3, 3, 2, 3, 3
[1, 2, 2, 3, 3, 3, 3, 1, 1] => 1, 2, 2, 3, 3, 3, 3, 1, 1
[1, 2, 2, 3, 3, 3, 3, 1, 2] => 1, 2, 2, 3, 3, 3, 3, 1, 2
[1, 2, 2, 3, 3, 3, 3, 1, 3] => 1, 2, 2, 3, 3, 3, 3, 1, 3
[1, 2, 2, 3, 3, 3, 3, 2, 1] => 1, 2, 2, 3, 3, 3, 3, 2, 1
[1, 2, 2, 3, 3, 3, 3, 2, 2] => 1, 2, 2, 3, 3, 3, 3, 2, 2
[1, 2, 2, 3, 3, 3, 3, 2, 3] => 1, 2, 2, 3, 3, 3, 3, 2, 3
[1, 2, 2, 3, 3, 3, 3, 3, 1] => 1, 2, 2, 3, 3, 3, 3, 3, 1
[1, 2, 2, 3, 3, 3, 3, 3, 2] => 1, 2, 2, 3, 3, 3, 3, 3, 2
[1, 2, 2, 3, 3, 3, 3, 3, 3] => 1, 2, 2, 3, 3, 3, 3, 3, 3
[1, 2, 3, 1, 1, 1, 1, 1, 1] => 1, 2, 3, 1, 1, 1, 1, 1, 1
[1, 2, 3, 1, 1, 1, 1, 1, 2] => 1, 2, 3, 1, 1, 1, 1, 1, 2
[1, 2, 3, 1, 1, 1, 1, 1, 3] => 1, 2, 3, 1, 1, 1, 1, 1, 3
[1, 2, 3, 1, 1, 1, 1, 2, 1] => 1, 2, 3, 1, 1, 1, 1, 2, 1
[1, 2, 3, 1, 1, 1, 1, 2, 2] => 1, 2, 3, 1, 1, 1, 1, 2, 2
[1, 2, 3, 1, 1, 1, 1, 2, 3] => 1, 2, 3, 1, 1, 1, 1, 2, 3
[1, 2, 3, 1, 1, 1, 1, 3, 1] => 1, 2, 3, 1, 1, 1, 1, 3, 1
[1, 2, 3, 1, 1, 1, 1, 3, 2] => 1, 2, 3, 1, 1, 1, 1, 3, 2
[1, 2, 3, 1, 1, 1, 1, 3, 3] => 1, 2, 3, 1, 1, 1, 1, 3, 3
[1, 2, 3, 1, 1, 1, 2, 1, 1] => 1, 2, 3, 1, 1, 1, 2, 1, 1
[1, 2, 3, 1, 1, 1, 2, 1, 2] => 1, 2, 3, 1, 1, 1, 2, 1, 2
[1, 2, 3, 1, 1, 1, 2, 1, 3] => 1, 2, 3, 1, 1, 1, 2, 1, 3
[1, 2, 3, 1, 1, 1, 2, 2, 1] => 1, 2, 3, 1, 1, 1, 2, 2, 1
[1, 2, 3, 1, 1, 1, 2, 2, 2] => 1, 2, 3, 1, 1, 1, 2, 2, 2
[1, 2, 3, 1, 1, 1, 2, 2, 3] => 1, 2, 3, 1, 1, 1, 2, 2, 3
[1, 2, 3, 1, 1, 1, 2, 3, 1] => 1, 2, 3, 1, 1, 1, 2, 3, 1
[1, 2, 3, 1, 1, 1, 2, 3, 2] => 1, 2, 3, 1, 1, 1, 2, 3, 2
[1, 2, 3, 1, 1, 1, 2, 3, 3] => 1, 2, 3, 1, 1, 1, 2, 3, 3
[1, 2, 3, 1, 1, 1, 3, 1, 1] => 1, 2, 3, 1, 1, 1, 3, 1, 1
[1, 2, 3, 1, 1, 1, 3, 1, 2] => 1, 2, 3, 1, 1, 1, 3, 1, 2
[1, 2, 3, 1, 1, 1, 3, 1, 3] => 1, 2, 3, 1, 1, 1, 3, 1, 3
[1, 2, 3, 1, 1, 1, 3, 2, 1] => 1, 2, 3, 1, 1, 1, 3, 2, 1
[1, 2, 3, 1, 1, 1, 3, 2, 2] => 1, 2, 3, 1, 1, 1, 3, 2, 2
[1, 2, 3, 1, 1, 1, 3, 2, 3] => 1, 2, 3, 1, 1, 1, 3, 2, 3
[1, 2, 3, 1, 1, 1, 3, 3, 1] => 1, 2, 3, 1, 1, 1, 3, 3, 1
[1, 2, 3, 1, 1, 1, 3, 3, 2] => 1, 2, 3, 1, 1, 1, 3, 3, 2
[1, 2, 3, 1, 1, 1, 3, 3, 3] => 1, 2, 3, 1, 1, 1, 3, 3, 3
[1, 2, 3, 1, 1, 2, 1, 1, 1] => 1, 2, 3, 1, 1, 2, 1, 1, 1
[1, 2, 3, 1, 1, 2, 1, 1, 2] => 1, 2, 3, 1, 1, 2, 1, 1, 2
[1, 2, 3, 1, 1, 2, 1, 1, 3] => 1, 2, 3, 1, 1, 2, 1, 1, 3
[1, 2, 3, 1, 1, 2, 1, 2, 1] => 1, 2, 3, 1, 1, 2, 1, 2, 1
[1, 2, 3, 1, 1, 2, 1, 2, 2] => 1, 2, 3, 1, 1, 2, 1, 2, 2
[1, 2, 3, 1, 1, 2, 1, 2, 3] => 1, 2, 3, 1, 1, 2, 1, 2, 3
[1, 2, 3, 1, 1, 2, 1, 3, 1] => 1, 2, 3, 1, 1, 2, 1, 3, 1
[1, 2, 3, 1, 1, 2, 1, 3, 2] => 1, 2, 3, 1, 1, 2, 1, 3, 2
[1, 2, 3, 1, 1, 2, 1, 3, 3] => 1, 2, 3, 1, 1, 2, 1, 3, 3
[1, 2, 3, 1, 1, 2, 2, 1, 1] => 1, 2, 3, 1, 1, 2, 2, 1, 1
[1, 2, 3, 1, 1, 2, 2, 1, 2] => 1, 2, 3, 1, 1, 2, 2, 1, 2
[1, 2, 3, 1, 1, 2, 2, 1, 3] => 1, 2, 3, 1, 1, 2, 2, 1, 3
[1, 2, 3, 1, 1, 2, 2, 2, 1] => 1, 2, 3, 1, 1, 2, 2, 2, 1
[1, 2, 3, 1, 1, 2, 2, 2, 2] => 1, 2, 3, 1, 1, 2, 2, 2, 2
[1, 2, 3, 1, 1, 2, 2, 2, 3] => 1, 2, 3, 1, 1, 2, 2, 2, 3
[1, 2, 3, 1, 1, 2, 2, 3, 1] => 1, 2, 3, 1, 1, 2, 2, 3, 1
[1, 2, 3, 1, 1, 2, 2, 3, 2] => 1, 2, 3, 1, 1, 2, 2, 3, 2
[1, 2, 3, 1, 1, 2, 2, 3, 3] => 1, 2, 3, 1, 1, 2, 2, 3, 3
[1, 2, 3, 1, 1, 2, 3, 1, 1] => 1, 2, 3, 1, 1, 2, 3, 1, 1
[1, 2, 3, 1, 1, 2, 3, 1, 2] => 1, 2, 3, 1, 1, 2, 3, 1, 2
[1, 2, 3, 1, 1, 2, 3, 1, 3] => 1, 2, 3, 1, 1, 2, 3, 1, 3
[1, 2, 3, 1, 1, 2, 3, 2, 1] => 1, 2, 3, 1, 1, 2, 3, 2, 1
[1, 2, 3, 1, 1, 2, 3, 2, 2] => 1, 2, 3, 1, 1, 2, 3, 2, 2
[1, 2, 3, 1, 1, 2, 3, 2, 3] => 1, 2, 3, 1, 1, 2, 3, 2, 3
[1, 2, 3, 1, 1, 2, 3, 3, 1] => 1, 2, 3, 1, 1, 2, 3, 3, 1
[1, 2, 3, 1, 1, 2, 3, 3, 2] => 1, 2, 3, 1, 1, 2, 3, 3, 2
[1, 2, 3, 1, 1, 2, 3, 3, 3] => 1, 2, 3, 1, 1, 2, 3, 3, 3
[1, 2, 3, 1, 1, 3, 1, 1, 1] => 1, 2, 3, 1, 1, 3, 1, 1, 1
[1, 2, 3, 1, 1, 3, 1, 1, 2] => 1, 2, 3, 1, 1, 3, 1, 1, 2
[1, 2, 3, 1, 1, 3, 1, 1, 3] => 1, 2, 3, 1, 1, 3, 1, 1, 3
[1, 2, 3, 1, 1, 3, 1, 2, 1] => 1, 2, 3, 1, 1, 3, 1, 2, 1
[1, 2, 3, 1, 1, 3, 1, 2, 2] => 1, 2, 3, 1, 1, 3, 1, 2, 2
[1, 2, 3, 1, 1, 3, 1, 2, 3] => 1, 2, 3, 1, 1, 3, 1, 2, 3
[1, 2, 3, 1, 1, 3, 1, 3, 1] => 1, 2, 3, 1, 1, 3, 1, 3, 1
[1, 2, 3, 1, 1, 3, 1, 3, 2] => 1, 2, 3, 1, 1, 3, 1, 3, 2
[1, 2, 3, 1, 1, 3, 1, 3, 3] => 1, 2, 3, 1, 1, 3, 1, 3, 3
[1, 2, 3, 1, 1, 3, 2, 1, 1] => 1, 2, 3, 1, 1, 3, 2, 1, 1
[1, 2, 3, 1, 1, 3, 2, 1, 2] => 1, 2, 3, 1, 1, 3, 2, 1, 2
[1, 2, 3, 1, 1, 3, 2, 1, 3] => 1, 2, 3, 1, 1, 3, 2, 1, 3
[1, 2, 3, 1, 1, 3, 2, 2, 1] => 1, 2, 3, 1, 1, 3, 2, 2, 1
[1, 2, 3, 1, 1, 3, 2, 2, 2] => 1, 2, 3, 1, 1, 3, 2, 2, 2
[1, 2, 3, 1, 1, 3, 2, 2, 3] => 1, 2, 3, 1, 1, 3, 2, 2, 3
[1, 2, 3, 1, 1, 3, 2, 3, 1] => 1, 2, 3, 1, 1, 3, 2, 3, 1
[1, 2, 3, 1, 1, 3, 2, 3, 2] => 1, 2, 3, 1, 1, 3, 2, 3, 2
[1, 2, 3, 1, 1, 3, 2, 3, 3] => 1, 2, 3, 1, 1, 3, 2, 3, 3
[1, 2, 3, 1, 1, 3, 3, 1, 1] => 1, 2, 3, 1, 1, 3, 3, 1, 1
[1, 2, 3, 1, 1, 3, 3, 1, 2] => 1, 2, 3, 1, 1, 3, 3, 1, 2
[1, 2, 3, 1, 1, 3, 3, 1, 3] => 1, 2, 3, 1, 1, 3, 3, 1, 3
[1, 2, 3, 1, 1, 3, 3, 2, 1] => 1, 2, 3, 1, 1, 3, 3, 2, 1
[1, 2, 3, 1, 1, 3, 3, 2, 2] => 1, 2, 3, 1, 1, 3, 3, 2, 2
[1, 2, 3, 1, 1, 3, 3, 2, 3] => 1, 2, 3, 1, 1, 3, 3, 2, 3
[1, 2, 3, 1, 1, 3, 3, 3, 1] => 1, 2, 3, 1, 1, 3, 3, 3, 1
[1, 2, 3, 1, 1, 3, 3, 3, 2] => 1, 2, 3, 1, 1, 3, 3, 3, 2
[1, 2, 3, 1, 1, 3, 3, 3, 3] => 1, 2, 3, 1, 1, 3, 3, 3, 3
[1, 2, 3, 1, 2, 1, 1, 1, 1] => 1, 2, 3, 1, 2, 1, 1, 1, 1
[1, 2, 3, 1, 2, 1, 1, 1, 2] => 1, 2, 3, 1, 2, 1, 1, 1, 2
[1, 2, 3, 1, 2, 1, 1, 1, 3] => 1, 2, 3, 1, 2, 1, 1, 1, 3
[1, 2, 3, 1, 2, 1, 1, 2, 1] => 1, 2, 3, 1, 2, 1, 1, 2, 1
[1, 2, 3, 1, 2, 1, 1, 2, 2] => 1, 2, 3, 1, 2, 1, 1, 2, 2
[1, 2, 3, 1, 2, 1, 1, 2, 3] => 1, 2, 3, 1, 2, 1, 1, 2, 3
[1, 2, 3, 1, 2, 1, 1, 3, 1] => 1, 2, 3, 1, 2, 1, 1, 3, 1
[1, 2, 3, 1, 2, 1, 1, 3, 2] => 1, 2, 3, 1, 2, 1, 1, 3, 2
[1, 2, 3, 1, 2, 1, 1, 3, 3] => 1, 2, 3, 1, 2, 1, 1, 3, 3
[1, 2, 3, 1, 2, 1, 2, 1, 1] => 1, 2, 3, 1, 2, 1, 2, 1, 1
[1, 2, 3, 1, 2, 1, 2, 1, 2] => 1, 2, 3, 1, 2, 1, 2, 1, 2
[1, 2, 3, 1, 2, 1, 2, 1, 3] => 1, 2, 3, 1, 2, 1, 2, 1, 3
[1, 2, 3, 1, 2, 1, 2, 2, 1] => 1, 2, 3, 1, 2, 1, 2, 2, 1
[1, 2, 3, 1, 2, 1, 2, 2, 2] => 1, 2, 3, 1, 2, 1, 2, 2, 2
[1, 2, 3, 1, 2, 1, 2, 2, 3] => 1, 2, 3, 1, 2, 1, 2, 2, 3
[1, 2, 3, 1, 2, 1, 2, 3, 1] => 1, 2, 3, 1, 2, 1, 2, 3, 1
[1, 2, 3, 1, 2, 1, 2, 3, 2] => 1, 2, 3, 1, 2, 1, 2, 3, 2
[1, 2, 3, 1, 2, 1, 2, 3, 3] => 1, 2, 3, 1, 2, 1, 2, 3, 3
[1, 2, 3, 1, 2, 1, 3, 1, 1] => 1, 2, 3, 1, 2, 1, 3, 1, 1
[1, 2, 3, 1, 2, 1, 3, 1, 2] => 1, 2, 3, 1, 2, 1, 3, 1, 2
[1, 2, 3, 1, 2, 1, 3, 1, 3] => 1, 2, 3, 1, 2, 1, 3, 1, 3
[1, 2, 3, 1, 2, 1, 3, 2, 1] => 1, 2, 3, 1, 2, 1, 3, 2, 1
[1, 2, 3, 1, 2, 1, 3, 2, 2] => 1, 2, 3, 1, 2, 1, 3, 2, 2
[1, 2, 3, 1, 2, 1, 3, 2, 3] => 1, 2, 3, 1, 2, 1, 3, 2, 3
[1, 2, 3, 1, 2, 1, 3, 3, 1] => 1, 2, 3, 1, 2, 1, 3, 3, 1
[1, 2, 3, 1, 2, 1, 3, 3, 2] => 1, 2, 3, 1, 2, 1, 3, 3, 2
[1, 2, 3, 1, 2, 1, 3, 3, 3] => 1, 2, 3, 1, 2, 1, 3, 3, 3
[1, 2, 3, 1, 2, 2, 1, 1, 1] => 1, 2, 3, 1, 2, 2, 1, 1, 1
[1, 2, 3, 1, 2, 2, 1, 1, 2] => 1, 2, 3, 1, 2, 2, 1, 1, 2
[1, 2, 3, 1, 2, 2, 1, 1, 3] => 1, 2, 3, 1, 2, 2, 1, 1, 3
[1, 2, 3, 1, 2, 2, 1, 2, 1] => 1, 2, 3, 1, 2, 2, 1, 2, 1
[1, 2, 3, 1, 2, 2, 1, 2, 2] => 1, 2, 3, 1, 2, 2, 1, 2, 2
[1, 2, 3, 1, 2, 2, 1, 2, 3] => 1, 2, 3, 1, 2, 2, 1, 2, 3
[1, 2, 3, 1, 2, 2, 1, 3, 1] => 1, 2, 3, 1, 2, 2, 1, 3, 1
[1, 2, 3, 1, 2, 2, 1, 3, 2] => 1, 2, 3, 1, 2, 2, 1, 3, 2
[1, 2, 3, 1, 2, 2, 1, 3, 3] => 1, 2, 3, 1, 2, 2, 1, 3, 3
[1, 2, 3, 1, 2, 2, 2, 1, 1] => 1, 2, 3, 1, 2, 2, 2, 1, 1
[1, 2, 3, 1, 2, 2, 2, 1, 2] => 1, 2, 3, 1, 2, 2, 2, 1, 2
[1, 2, 3, 1, 2, 2, 2, 1, 3] => 1, 2, 3, 1, 2, 2, 2, 1, 3
[1, 2, 3, 1, 2, 2, 2, 2, 1] => 1, 2, 3, 1, 2, 2, 2, 2, 1
[1, 2, 3, 1, 2, 2, 2, 2, 2] => 1, 2, 3, 1, 2, 2, 2, 2, 2
[1, 2, 3, 1, 2, 2, 2, 2, 3] => 1, 2, 3, 1, 2, 2, 2, 2, 3
[1, 2, 3, 1, 2, 2, 2, 3, 1] => 1, 2, 3, 1, 2, 2, 2, 3, 1
[1, 2, 3, 1, 2, 2, 2, 3, 2] => 1, 2, 3, 1, 2, 2, 2, 3, 2
[1, 2, 3, 1, 2, 2, 2, 3, 3] => 1, 2, 3, 1, 2, 2, 2, 3, 3
[1, 2, 3, 1, 2, 2, 3, 1, 1] => 1, 2, 3, 1, 2, 2, 3, 1, 1
[1, 2, 3, 1, 2, 2, 3, 1, 2] => 1, 2, 3, 1, 2, 2, 3, 1, 2
[1, 2, 3, 1, 2, 2, 3, 1, 3] => 1, 2, 3, 1, 2, 2, 3, 1, 3
[1, 2, 3, 1, 2, 2, 3, 2, 1] => 1, 2, 3, 1, 2, 2, 3, 2, 1
[1, 2, 3, 1, 2, 2, 3, 2, 2] => 1, 2, 3, 1, 2, 2, 3, 2, 2
[1, 2, 3, 1, 2, 2, 3, 2, 3] => 1, 2, 3, 1, 2, 2, 3, 2, 3
[1, 2, 3, 1, 2, 2, 3, 3, 1] => 1, 2, 3, 1, 2, 2, 3, 3, 1
[1, 2, 3, 1, 2, 2, 3, 3, 2] => 1, 2, 3, 1, 2, 2, 3, 3, 2
[1, 2, 3, 1, 2, 2, 3, 3, 3] => 1, 2, 3, 1, 2, 2, 3, 3, 3
[1, 2, 3, 1, 2, 3, 1, 1, 1] => 1, 2, 3, 1, 2, 3, 1, 1, 1
[1, 2, 3, 1, 2, 3, 1, 1, 2] => 1, 2, 3, 1, 2, 3, 1, 1, 2
[1, 2, 3, 1, 2, 3, 1, 1, 3] => 1, 2, 3, 1, 2, 3, 1, 1, 3
[1, 2, 3, 1, 2, 3, 1, 2, 1] => 1, 2, 3, 1, 2, 3, 1, 2, 1
[1, 2, 3, 1, 2, 3, 1, 2, 2] => 1, 2, 3, 1, 2, 3, 1, 2, 2
[1, 2, 3, 1, 2, 3, 1, 2, 3] => 1, 2, 3, 1, 2, 3, 1, 2, 3
[1, 2, 3, 1, 2, 3, 1, 3, 1] => 1, 2, 3, 1, 2, 3, 1, 3, 1
[1, 2, 3, 1, 2, 3, 1, 3, 2] => 1, 2, 3, 1, 2, 3, 1, 3, 2
[1, 2, 3, 1, 2, 3, 1, 3, 3] => 1, 2, 3, 1, 2, 3, 1, 3, 3
[1, 2, 3, 1, 2, 3, 2, 1, 1] => 1, 2, 3, 1, 2, 3, 2, 1, 1
[1, 2, 3, 1, 2, 3, 2, 1, 2] => 1, 2, 3, 1, 2, 3, 2, 1, 2
[1, 2, 3, 1, 2, 3, 2, 1, 3] => 1, 2, 3, 1, 2, 3, 2, 1, 3
[1, 2, 3, 1, 2, 3, 2, 2, 1] => 1, 2, 3, 1, 2, 3, 2, 2, 1
[1, 2, 3, 1, 2, 3, 2, 2, 2] => 1, 2, 3, 1, 2, 3, 2, 2, 2
[1, 2, 3, 1, 2, 3, 2, 2, 3] => 1, 2, 3, 1, 2, 3, 2, 2, 3
[1, 2, 3, 1, 2, 3, 2, 3, 1] => 1, 2, 3, 1, 2, 3, 2, 3, 1
[1, 2, 3, 1, 2, 3, 2, 3, 2] => 1, 2, 3, 1, 2, 3, 2, 3, 2
[1, 2, 3, 1, 2, 3, 2, 3, 3] => 1, 2, 3, 1, 2, 3, 2, 3, 3
[1, 2, 3, 1, 2, 3, 3, 1, 1] => 1, 2, 3, 1, 2, 3, 3, 1, 1
[1, 2, 3, 1, 2, 3, 3, 1, 2] => 1, 2, 3, 1, 2, 3, 3, 1, 2
[1, 2, 3, 1, 2, 3, 3, 1, 3] => 1, 2, 3, 1, 2, 3, 3, 1, 3
[1, 2, 3, 1, 2, 3, 3, 2, 1] => 1, 2, 3, 1, 2, 3, 3, 2, 1
[1, 2, 3, 1, 2, 3, 3, 2, 2] => 1, 2, 3, 1, 2, 3, 3, 2, 2
[1, 2, 3, 1, 2, 3, 3, 2, 3] => 1, 2, 3, 1, 2, 3, 3, 2, 3
[1, 2, 3, 1, 2, 3, 3, 3, 1] => 1, 2, 3, 1, 2, 3, 3, 3, 1
[1, 2, 3, 1, 2, 3, 3, 3, 2] => 1, 2, 3, 1, 2, 3, 3, 3, 2
[1, 2, 3, 1, 2, 3, 3, 3, 3] => 1, 2, 3, 1, 2, 3, 3, 3, 3
[1, 2, 3, 1, 3, 1, 1, 1, 1] => 1, 2, 3, 1, 3, 1, 1, 1, 1
[1, 2, 3, 1, 3, 1, 1, 1, 2] => 1, 2, 3, 1, 3, 1, 1, 1, 2
[1, 2, 3, 1, 3, 1, 1, 1, 3] => 1, 2, 3, 1, 3, 1, 1, 1, 3
[1, 2, 3, 1, 3, 1, 1, 2, 1] => 1, 2, 3, 1, 3, 1, 1, 2, 1
[1, 2, 3, 1, 3, 1, 1, 2, 2] => 1, 2, 3, 1, 3, 1, 1, 2, 2
[1, 2, 3, 1, 3, 1, 1, 2, 3] => 1, 2, 3, 1, 3, 1, 1, 2, 3
[1, 2, 3, 1, 3, 1, 1, 3, 1] => 1, 2, 3, 1, 3, 1, 1, 3, 1
[1, 2, 3, 1, 3, 1, 1, 3, 2] => 1, 2, 3, 1, 3, 1, 1, 3, 2
[1, 2, 3, 1, 3, 1, 1, 3, 3] => 1, 2, 3, 1, 3, 1, 1, 3, 3
[1, 2, 3, 1, 3, 1, 2, 1, 1] => 1, 2, 3, 1, 3, 1, 2, 1, 1
[1, 2, 3, 1, 3, 1, 2, 1, 2] => 1, 2, 3, 1, 3, 1, 2, 1, 2
[1, 2, 3, 1, 3, 1, 2, 1, 3] => 1, 2, 3, 1, 3, 1, 2, 1, 3
[1, 2, 3, 1, 3, 1, 2, 2, 1] => 1, 2, 3, 1, 3, 1, 2, 2, 1
[1, 2, 3, 1, 3, 1, 2, 2, 2] => 1, 2, 3, 1, 3, 1, 2, 2, 2
[1, 2, 3, 1, 3, 1, 2, 2, 3] => 1, 2, 3, 1, 3, 1, 2, 2, 3
[1, 2, 3, 1, 3, 1, 2, 3, 1] => 1, 2, 3, 1, 3, 1, 2, 3, 1
[1, 2, 3, 1, 3, 1, 2, 3, 2] => 1, 2, 3, 1, 3, 1, 2, 3, 2
[1, 2, 3, 1, 3, 1, 2, 3, 3] => 1, 2, 3, 1, 3, 1, 2, 3, 3
[1, 2, 3, 1, 3, 1, 3, 1, 1] => 1, 2, 3, 1, 3, 1, 3, 1, 1
[1, 2, 3, 1, 3, 1, 3, 1, 2] => 1, 2, 3, 1, 3, 1, 3, 1, 2
[1, 2, 3, 1, 3, 1, 3, 1, 3] => 1, 2, 3, 1, 3, 1, 3, 1, 3
[1, 2, 3, 1, 3, 1, 3, 2, 1] => 1, 2, 3, 1, 3, 1, 3, 2, 1
[1, 2, 3, 1, 3, 1, 3, 2, 2] => 1, 2, 3, 1, 3, 1, 3, 2, 2
[1, 2, 3, 1, 3, 1, 3, 2, 3] => 1, 2, 3, 1, 3, 1, 3, 2, 3
[1, 2, 3, 1, 3, 1, 3, 3, 1] => 1, 2, 3, 1, 3, 1, 3, 3, 1
[1, 2, 3, 1, 3, 1, 3, 3, 2] => 1, 2, 3, 1, 3, 1, 3, 3, 2
[1, 2, 3, 1, 3, 1, 3, 3, 3] => 1, 2, 3, 1, 3, 1, 3, 3, 3
[1, 2, 3, 1, 3, 2, 1, 1, 1] => 1, 2, 3, 1, 3, 2, 1, 1, 1
[1, 2, 3, 1, 3, 2, 1, 1, 2] => 1, 2, 3, 1, 3, 2, 1, 1, 2
[1, 2, 3, 1, 3, 2, 1, 1, 3] => 1, 2, 3, 1, 3, 2, 1, 1, 3
[1, 2, 3, 1, 3, 2, 1, 2, 1] => 1, 2, 3, 1, 3, 2, 1, 2, 1
[1, 2, 3, 1, 3, 2, 1, 2, 2] => 1, 2, 3, 1, 3, 2, 1, 2, 2
[1, 2, 3, 1, 3, 2, 1, 2, 3] => 1, 2, 3, 1, 3, 2, 1, 2, 3
[1, 2, 3, 1, 3, 2, 1, 3, 1] => 1, 2, 3, 1, 3, 2, 1, 3, 1
[1, 2, 3, 1, 3, 2, 1, 3, 2] => 1, 2, 3, 1, 3, 2, 1, 3, 2
[1, 2, 3, 1, 3, 2, 1, 3, 3] => 1, 2, 3, 1, 3, 2, 1, 3, 3
[1, 2, 3, 1, 3, 2, 2, 1, 1] => 1, 2, 3, 1, 3, 2, 2, 1, 1
[1, 2, 3, 1, 3, 2, 2, 1, 2] => 1, 2, 3, 1, 3, 2, 2, 1, 2
[1, 2, 3, 1, 3, 2, 2, 1, 3] => 1, 2, 3, 1, 3, 2, 2, 1, 3
[1, 2, 3, 1, 3, 2, 2, 2, 1] => 1, 2, 3, 1, 3, 2, 2, 2, 1
[1, 2, 3, 1, 3, 2, 2, 2, 2] => 1, 2, 3, 1, 3, 2, 2, 2, 2
[1, 2, 3, 1, 3, 2, 2, 2, 3] => 1, 2, 3, 1, 3, 2, 2, 2, 3
[1, 2, 3, 1, 3, 2, 2, 3, 1] => 1, 2, 3, 1, 3, 2, 2, 3, 1
[1, 2, 3, 1, 3, 2, 2, 3, 2] => 1, 2, 3, 1, 3, 2, 2, 3, 2
[1, 2, 3, 1, 3, 2, 2, 3, 3] => 1, 2, 3, 1, 3, 2, 2, 3, 3
[1, 2, 3, 1, 3, 2, 3, 1, 1] => 1, 2, 3, 1, 3, 2, 3, 1, 1
[1, 2, 3, 1, 3, 2, 3, 1, 2] => 1, 2, 3, 1, 3, 2, 3, 1, 2
[1, 2, 3, 1, 3, 2, 3, 1, 3] => 1, 2, 3, 1, 3, 2, 3, 1, 3
[1, 2, 3, 1, 3, 2, 3, 2, 1] => 1, 2, 3, 1, 3, 2, 3, 2, 1
[1, 2, 3, 1, 3, 2, 3, 2, 2] => 1, 2, 3, 1, 3, 2, 3, 2, 2
[1, 2, 3, 1, 3, 2, 3, 2, 3] => 1, 2, 3, 1, 3, 2, 3, 2, 3
[1, 2, 3, 1, 3, 2, 3, 3, 1] => 1, 2, 3, 1, 3, 2, 3, 3, 1
[1, 2, 3, 1, 3, 2, 3, 3, 2] => 1, 2, 3, 1, 3, 2, 3, 3, 2
[1, 2, 3, 1, 3, 2, 3, 3, 3] => 1, 2, 3, 1, 3, 2, 3, 3, 3
[1, 2, 3, 1, 3, 3, 1, 1, 1] => 1, 2, 3, 1, 3, 3, 1, 1, 1
[1, 2, 3, 1, 3, 3, 1, 1, 2] => 1, 2, 3, 1, 3, 3, 1, 1, 2
[1, 2, 3, 1, 3, 3, 1, 1, 3] => 1, 2, 3, 1, 3, 3, 1, 1, 3
[1, 2, 3, 1, 3, 3, 1, 2, 1] => 1, 2, 3, 1, 3, 3, 1, 2, 1
[1, 2, 3, 1, 3, 3, 1, 2, 2] => 1, 2, 3, 1, 3, 3, 1, 2, 2
[1, 2, 3, 1, 3, 3, 1, 2, 3] => 1, 2, 3, 1, 3, 3, 1, 2, 3
[1, 2, 3, 1, 3, 3, 1, 3, 1] => 1, 2, 3, 1, 3, 3, 1, 3, 1
[1, 2, 3, 1, 3, 3, 1, 3, 2] => 1, 2, 3, 1, 3, 3, 1, 3, 2
[1, 2, 3, 1, 3, 3, 1, 3, 3] => 1, 2, 3, 1, 3, 3, 1, 3, 3
[1, 2, 3, 1, 3, 3, 2, 1, 1] => 1, 2, 3, 1, 3, 3, 2, 1, 1
[1, 2, 3, 1, 3, 3, 2, 1, 2] => 1, 2, 3, 1, 3, 3, 2, 1, 2
[1, 2, 3, 1, 3, 3, 2, 1, 3] => 1, 2, 3, 1, 3, 3, 2, 1, 3
[1, 2, 3, 1, 3, 3, 2, 2, 1] => 1, 2, 3, 1, 3, 3, 2, 2, 1
[1, 2, 3, 1, 3, 3, 2, 2, 2] => 1, 2, 3, 1, 3, 3, 2, 2, 2
[1, 2, 3, 1, 3, 3, 2, 2, 3] => 1, 2, 3, 1, 3, 3, 2, 2, 3
[1, 2, 3, 1, 3, 3, 2, 3, 1] => 1, 2, 3, 1, 3, 3, 2, 3, 1
[1, 2, 3, 1, 3, 3, 2, 3, 2] => 1, 2, 3, 1, 3, 3, 2, 3, 2
[1, 2, 3, 1, 3, 3, 2, 3, 3] => 1, 2, 3, 1, 3, 3, 2, 3, 3
[1, 2, 3, 1, 3, 3, 3, 1, 1] => 1, 2, 3, 1, 3, 3, 3, 1, 1
[1, 2, 3, 1, 3, 3, 3, 1, 2] => 1, 2, 3, 1, 3, 3, 3, 1, 2
[1, 2, 3, 1, 3, 3, 3, 1, 3] => 1, 2, 3, 1, 3, 3, 3, 1, 3
[1, 2, 3, 1, 3, 3, 3, 2, 1] => 1, 2, 3, 1, 3, 3, 3, 2, 1
[1, 2, 3, 1, 3, 3, 3, 2, 2] => 1, 2, 3, 1, 3, 3, 3, 2, 2
[1, 2, 3, 1, 3, 3, 3, 2, 3] => 1, 2, 3, 1, 3, 3, 3, 2, 3
[1, 2, 3, 1, 3, 3, 3, 3, 1] => 1, 2, 3, 1, 3, 3, 3, 3, 1
[1, 2, 3, 1, 3, 3, 3, 3, 2] => 1, 2, 3, 1, 3, 3, 3, 3, 2
[1, 2, 3, 1, 3, 3, 3, 3, 3] => 1, 2, 3, 1, 3, 3, 3, 3, 3
[1, 2, 3, 2, 1, 1, 1, 1, 1] => 1, 2, 3, 2, 1, 1, 1, 1, 1
[1, 2, 3, 2, 1, 1, 1, 1, 2] => 1, 2, 3, 2, 1, 1, 1, 1, 2
[1, 2, 3, 2, 1, 1, 1, 1, 3] => 1, 2, 3, 2, 1, 1, 1, 1, 3
[1, 2, 3, 2, 1, 1, 1, 2, 1] => 1, 2, 3, 2, 1, 1, 1, 2, 1
[1, 2, 3, 2, 1, 1, 1, 2, 2] => 1, 2, 3, 2, 1, 1, 1, 2, 2
[1, 2, 3, 2, 1, 1, 1, 2, 3] => 1, 2, 3, 2, 1, 1, 1, 2, 3
[1, 2, 3, 2, 1, 1, 1, 3, 1] => 1, 2, 3, 2, 1, 1, 1, 3, 1
[1, 2, 3, 2, 1, 1, 1, 3, 2] => 1, 2, 3, 2, 1, 1, 1, 3, 2
[1, 2, 3, 2, 1, 1, 1, 3, 3] => 1, 2, 3, 2, 1, 1, 1, 3, 3
[1, 2, 3, 2, 1, 1, 2, 1, 1] => 1, 2, 3, 2, 1, 1, 2, 1, 1
[1, 2, 3, 2, 1, 1, 2, 1, 2] => 1, 2, 3, 2, 1, 1, 2, 1, 2
[1, 2, 3, 2, 1, 1, 2, 1, 3] => 1, 2, 3, 2, 1, 1, 2, 1, 3
[1, 2, 3, 2, 1, 1, 2, 2, 1] => 1, 2, 3, 2, 1, 1, 2, 2, 1
[1, 2, 3, 2, 1, 1, 2, 2, 2] => 1, 2, 3, 2, 1, 1, 2, 2, 2
[1, 2, 3, 2, 1, 1, 2, 2, 3] => 1, 2, 3, 2, 1, 1, 2, 2, 3
[1, 2, 3, 2, 1, 1, 2, 3, 1] => 1, 2, 3, 2, 1, 1, 2, 3, 1
[1, 2, 3, 2, 1, 1, 2, 3, 2] => 1, 2, 3, 2, 1, 1, 2, 3, 2
[1, 2, 3, 2, 1, 1, 2, 3, 3] => 1, 2, 3, 2, 1, 1, 2, 3, 3
[1, 2, 3, 2, 1, 1, 3, 1, 1] => 1, 2, 3, 2, 1, 1, 3, 1, 1
[1, 2, 3, 2, 1, 1, 3, 1, 2] => 1, 2, 3, 2, 1, 1, 3, 1, 2
[1, 2, 3, 2, 1, 1, 3, 1, 3] => 1, 2, 3, 2, 1, 1, 3, 1, 3
[1, 2, 3, 2, 1, 1, 3, 2, 1] => 1, 2, 3, 2, 1, 1, 3, 2, 1
[1, 2, 3, 2, 1, 1, 3, 2, 2] => 1, 2, 3, 2, 1, 1, 3, 2, 2
[1, 2, 3, 2, 1, 1, 3, 2, 3] => 1, 2, 3, 2, 1, 1, 3, 2, 3
[1, 2, 3, 2, 1, 1, 3, 3, 1] => 1, 2, 3, 2, 1, 1, 3, 3, 1
[1, 2, 3, 2, 1, 1, 3, 3, 2] => 1, 2, 3, 2, 1, 1, 3, 3, 2
[1, 2, 3, 2, 1, 1, 3, 3, 3] => 1, 2, 3, 2, 1, 1, 3, 3, 3
[1, 2, 3, 2, 1, 2, 1, 1, 1] => 1, 2, 3, 2, 1, 2, 1, 1, 1
[1, 2, 3, 2, 1, 2, 1, 1, 2] => 1, 2, 3, 2, 1, 2, 1, 1, 2
[1, 2, 3, 2, 1, 2, 1, 1, 3] => 1, 2, 3, 2, 1, 2, 1, 1, 3
[1, 2, 3, 2, 1, 2, 1, 2, 1] => 1, 2, 3, 2, 1, 2, 1, 2, 1
[1, 2, 3, 2, 1, 2, 1, 2, 2] => 1, 2, 3, 2, 1, 2, 1, 2, 2
[1, 2, 3, 2, 1, 2, 1, 2, 3] => 1, 2, 3, 2, 1, 2, 1, 2, 3
[1, 2, 3, 2, 1, 2, 1, 3, 1] => 1, 2, 3, 2, 1, 2, 1, 3, 1
[1, 2, 3, 2, 1, 2, 1, 3, 2] => 1, 2, 3, 2, 1, 2, 1, 3, 2
[1, 2, 3, 2, 1, 2, 1, 3, 3] => 1, 2, 3, 2, 1, 2, 1, 3, 3
[1, 2, 3, 2, 1, 2, 2, 1, 1] => 1, 2, 3, 2, 1, 2, 2, 1, 1
[1, 2, 3, 2, 1, 2, 2, 1, 2] => 1, 2, 3, 2, 1, 2, 2, 1, 2
[1, 2, 3, 2, 1, 2, 2, 1, 3] => 1, 2, 3, 2, 1, 2, 2, 1, 3
[1, 2, 3, 2, 1, 2, 2, 2, 1] => 1, 2, 3, 2, 1, 2, 2, 2, 1
[1, 2, 3, 2, 1, 2, 2, 2, 2] => 1, 2, 3, 2, 1, 2, 2, 2, 2
[1, 2, 3, 2, 1, 2, 2, 2, 3] => 1, 2, 3, 2, 1, 2, 2, 2, 3
[1, 2, 3, 2, 1, 2, 2, 3, 1] => 1, 2, 3, 2, 1, 2, 2, 3, 1
[1, 2, 3, 2, 1, 2, 2, 3, 2] => 1, 2, 3, 2, 1, 2, 2, 3, 2
[1, 2, 3, 2, 1, 2, 2, 3, 3] => 1, 2, 3, 2, 1, 2, 2, 3, 3
[1, 2, 3, 2, 1, 2, 3, 1, 1] => 1, 2, 3, 2, 1, 2, 3, 1, 1
[1, 2, 3, 2, 1, 2, 3, 1, 2] => 1, 2, 3, 2, 1, 2, 3, 1, 2
[1, 2, 3, 2, 1, 2, 3, 1, 3] => 1, 2, 3, 2, 1, 2, 3, 1, 3
[1, 2, 3, 2, 1, 2, 3, 2, 1] => 1, 2, 3, 2, 1, 2, 3, 2, 1
[1, 2, 3, 2, 1, 2, 3, 2, 2] => 1, 2, 3, 2, 1, 2, 3, 2, 2
[1, 2, 3, 2, 1, 2, 3, 2, 3] => 1, 2, 3, 2, 1, 2, 3, 2, 3
[1, 2, 3, 2, 1, 2, 3, 3, 1] => 1, 2, 3, 2, 1, 2, 3, 3, 1
[1, 2, 3, 2, 1, 2, 3, 3, 2] => 1, 2, 3, 2, 1, 2, 3, 3, 2
[1, 2, 3, 2, 1, 2, 3, 3, 3] => 1, 2, 3, 2, 1, 2, 3, 3, 3
[1, 2, 3, 2, 1, 3, 1, 1, 1] => 1, 2, 3, 2, 1, 3, 1, 1, 1
[1, 2, 3, 2, 1, 3, 1, 1, 2] => 1, 2, 3, 2, 1, 3, 1, 1, 2
[1, 2, 3, 2, 1, 3, 1, 1, 3] => 1, 2, 3, 2, 1, 3, 1, 1, 3
[1, 2, 3, 2, 1, 3, 1, 2, 1] => 1, 2, 3, 2, 1, 3, 1, 2, 1
[1, 2, 3, 2, 1, 3, 1, 2, 2] => 1, 2, 3, 2, 1, 3, 1, 2, 2
[1, 2, 3, 2, 1, 3, 1, 2, 3] => 1, 2, 3, 2, 1, 3, 1, 2, 3
[1, 2, 3, 2, 1, 3, 1, 3, 1] => 1, 2, 3, 2, 1, 3, 1, 3, 1
[1, 2, 3, 2, 1, 3, 1, 3, 2] => 1, 2, 3, 2, 1, 3, 1, 3, 2
[1, 2, 3, 2, 1, 3, 1, 3, 3] => 1, 2, 3, 2, 1, 3, 1, 3, 3
[1, 2, 3, 2, 1, 3, 2, 1, 1] => 1, 2, 3, 2, 1, 3, 2, 1, 1
[1, 2, 3, 2, 1, 3, 2, 1, 2] => 1, 2, 3, 2, 1, 3, 2, 1, 2
[1, 2, 3, 2, 1, 3, 2, 1, 3] => 1, 2, 3, 2, 1, 3, 2, 1, 3
[1, 2, 3, 2, 1, 3, 2, 2, 1] => 1, 2, 3, 2, 1, 3, 2, 2, 1
[1, 2, 3, 2, 1, 3, 2, 2, 2] => 1, 2, 3, 2, 1, 3, 2, 2, 2
[1, 2, 3, 2, 1, 3, 2, 2, 3] => 1, 2, 3, 2, 1, 3, 2, 2, 3
[1, 2, 3, 2, 1, 3, 2, 3, 1] => 1, 2, 3, 2, 1, 3, 2, 3, 1
[1, 2, 3, 2, 1, 3, 2, 3, 2] => 1, 2, 3, 2, 1, 3, 2, 3, 2
[1, 2, 3, 2, 1, 3, 2, 3, 3] => 1, 2, 3, 2, 1, 3, 2, 3, 3
[1, 2, 3, 2, 1, 3, 3, 1, 1] => 1, 2, 3, 2, 1, 3, 3, 1, 1
[1, 2, 3, 2, 1, 3, 3, 1, 2] => 1, 2, 3, 2, 1, 3, 3, 1, 2
[1, 2, 3, 2, 1, 3, 3, 1, 3] => 1, 2, 3, 2, 1, 3, 3, 1, 3
[1, 2, 3, 2, 1, 3, 3, 2, 1] => 1, 2, 3, 2, 1, 3, 3, 2, 1
[1, 2, 3, 2, 1, 3, 3, 2, 2] => 1, 2, 3, 2, 1, 3, 3, 2, 2
[1, 2, 3, 2, 1, 3, 3, 2, 3] => 1, 2, 3, 2, 1, 3, 3, 2, 3
[1, 2, 3, 2, 1, 3, 3, 3, 1] => 1, 2, 3, 2, 1, 3, 3, 3, 1
[1, 2, 3, 2, 1, 3, 3, 3, 2] => 1, 2, 3, 2, 1, 3, 3, 3, 2
[1, 2, 3, 2, 1, 3, 3, 3, 3] => 1, 2, 3, 2, 1, 3, 3, 3, 3
[1, 2, 3, 2, 2, 1, 1, 1, 1] => 1, 2, 3, 2, 2, 1, 1, 1, 1
[1, 2, 3, 2, 2, 1, 1, 1, 2] => 1, 2, 3, 2, 2, 1, 1, 1, 2
[1, 2, 3, 2, 2, 1, 1, 1, 3] => 1, 2, 3, 2, 2, 1, 1, 1, 3
[1, 2, 3, 2, 2, 1, 1, 2, 1] => 1, 2, 3, 2, 2, 1, 1, 2, 1
[1, 2, 3, 2, 2, 1, 1, 2, 2] => 1, 2, 3, 2, 2, 1, 1, 2, 2
[1, 2, 3, 2, 2, 1, 1, 2, 3] => 1, 2, 3, 2, 2, 1, 1, 2, 3
[1, 2, 3, 2, 2, 1, 1, 3, 1] => 1, 2, 3, 2, 2, 1, 1, 3, 1
[1, 2, 3, 2, 2, 1, 1, 3, 2] => 1, 2, 3, 2, 2, 1, 1, 3, 2
[1, 2, 3, 2, 2, 1, 1, 3, 3] => 1, 2, 3, 2, 2, 1, 1, 3, 3
[1, 2, 3, 2, 2, 1, 2, 1, 1] => 1, 2, 3, 2, 2, 1, 2, 1, 1
[1, 2, 3, 2, 2, 1, 2, 1, 2] => 1, 2, 3, 2, 2, 1, 2, 1, 2
[1, 2, 3, 2, 2, 1, 2, 1, 3] => 1, 2, 3, 2, 2, 1, 2, 1, 3
[1, 2, 3, 2, 2, 1, 2, 2, 1] => 1, 2, 3, 2, 2, 1, 2, 2, 1
[1, 2, 3, 2, 2, 1, 2, 2, 2] => 1, 2, 3, 2, 2, 1, 2, 2, 2
[1, 2, 3, 2, 2, 1, 2, 2, 3] => 1, 2, 3, 2, 2, 1, 2, 2, 3
[1, 2, 3, 2, 2, 1, 2, 3, 1] => 1, 2, 3, 2, 2, 1, 2, 3, 1
[1, 2, 3, 2, 2, 1, 2, 3, 2] => 1, 2, 3, 2, 2, 1, 2, 3, 2
[1, 2, 3, 2, 2, 1, 2, 3, 3] => 1, 2, 3, 2, 2, 1, 2, 3, 3
[1, 2, 3, 2, 2, 1, 3, 1, 1] => 1, 2, 3, 2, 2, 1, 3, 1, 1
[1, 2, 3, 2, 2, 1, 3, 1, 2] => 1, 2, 3, 2, 2, 1, 3, 1, 2
[1, 2, 3, 2, 2, 1, 3, 1, 3] => 1, 2, 3, 2, 2, 1, 3, 1, 3
[1, 2, 3, 2, 2, 1, 3, 2, 1] => 1, 2, 3, 2, 2, 1, 3, 2, 1
[1, 2, 3, 2, 2, 1, 3, 2, 2] => 1, 2, 3, 2, 2, 1, 3, 2, 2
[1, 2, 3, 2, 2, 1, 3, 2, 3] => 1, 2, 3, 2, 2, 1, 3, 2, 3
[1, 2, 3, 2, 2, 1, 3, 3, 1] => 1, 2, 3, 2, 2, 1, 3, 3, 1
[1, 2, 3, 2, 2, 1, 3, 3, 2] => 1, 2, 3, 2, 2, 1, 3, 3, 2
[1, 2, 3, 2, 2, 1, 3, 3, 3] => 1, 2, 3, 2, 2, 1, 3, 3, 3
[1, 2, 3, 2, 2, 2, 1, 1, 1] => 1, 2, 3, 2, 2, 2, 1, 1, 1
[1, 2, 3, 2, 2, 2, 1, 1, 2] => 1, 2, 3, 2, 2, 2, 1, 1, 2
[1, 2, 3, 2, 2, 2, 1, 1, 3] => 1, 2, 3, 2, 2, 2, 1, 1, 3
[1, 2, 3, 2, 2, 2, 1, 2, 1] => 1, 2, 3, 2, 2, 2, 1, 2, 1
[1, 2, 3, 2, 2, 2, 1, 2, 2] => 1, 2, 3, 2, 2, 2, 1, 2, 2
[1, 2, 3, 2, 2, 2, 1, 2, 3] => 1, 2, 3, 2, 2, 2, 1, 2, 3
[1, 2, 3, 2, 2, 2, 1, 3, 1] => 1, 2, 3, 2, 2, 2, 1, 3, 1
[1, 2, 3, 2, 2, 2, 1, 3, 2] => 1, 2, 3, 2, 2, 2, 1, 3, 2
[1, 2, 3, 2, 2, 2, 1, 3, 3] => 1, 2, 3, 2, 2, 2, 1, 3, 3
[1, 2, 3, 2, 2, 2, 2, 1, 1] => 1, 2, 3, 2, 2, 2, 2, 1, 1
[1, 2, 3, 2, 2, 2, 2, 1, 2] => 1, 2, 3, 2, 2, 2, 2, 1, 2
[1, 2, 3, 2, 2, 2, 2, 1, 3] => 1, 2, 3, 2, 2, 2, 2, 1, 3
[1, 2, 3, 2, 2, 2, 2, 2, 1] => 1, 2, 3, 2, 2, 2, 2, 2, 1
[1, 2, 3, 2, 2, 2, 2, 2, 2] => 1, 2, 3, 2, 2, 2, 2, 2, 2
[1, 2, 3, 2, 2, 2, 2, 2, 3] => 1, 2, 3, 2, 2, 2, 2, 2, 3
[1, 2, 3, 2, 2, 2, 2, 3, 1] => 1, 2, 3, 2, 2, 2, 2, 3, 1
[1, 2, 3, 2, 2, 2, 2, 3, 2] => 1, 2, 3, 2, 2, 2, 2, 3, 2
[1, 2, 3, 2, 2, 2, 2, 3, 3] => 1, 2, 3, 2, 2, 2, 2, 3, 3
[1, 2, 3, 2, 2, 2, 3, 1, 1] => 1, 2, 3, 2, 2, 2, 3, 1, 1
[1, 2, 3, 2, 2, 2, 3, 1, 2] => 1, 2, 3, 2, 2, 2, 3, 1, 2
[1, 2, 3, 2, 2, 2, 3, 1, 3] => 1, 2, 3, 2, 2, 2, 3, 1, 3
[1, 2, 3, 2, 2, 2, 3, 2, 1] => 1, 2, 3, 2, 2, 2, 3, 2, 1
[1, 2, 3, 2, 2, 2, 3, 2, 2] => 1, 2, 3, 2, 2, 2, 3, 2, 2
[1, 2, 3, 2, 2, 2, 3, 2, 3] => 1, 2, 3, 2, 2, 2, 3, 2, 3
[1, 2, 3, 2, 2, 2, 3, 3, 1] => 1, 2, 3, 2, 2, 2, 3, 3, 1
[1, 2, 3, 2, 2, 2, 3, 3, 2] => 1, 2, 3, 2, 2, 2, 3, 3, 2
[1, 2, 3, 2, 2, 2, 3, 3, 3] => 1, 2, 3, 2, 2, 2, 3, 3, 3
[1, 2, 3, 2, 2, 3, 1, 1, 1] => 1, 2, 3, 2, 2, 3, 1, 1, 1
[1, 2, 3, 2, 2, 3, 1, 1, 2] => 1, 2, 3, 2, 2, 3, 1, 1, 2
[1, 2, 3, 2, 2, 3, 1, 1, 3] => 1, 2, 3, 2, 2, 3, 1, 1, 3
[1, 2, 3, 2, 2, 3, 1, 2, 1] => 1, 2, 3, 2, 2, 3, 1, 2, 1
[1, 2, 3, 2, 2, 3, 1, 2, 2] => 1, 2, 3, 2, 2, 3, 1, 2, 2
[1, 2, 3, 2, 2, 3, 1, 2, 3] => 1, 2, 3, 2, 2, 3, 1, 2, 3
[1, 2, 3, 2, 2, 3, 1, 3, 1] => 1, 2, 3, 2, 2, 3, 1, 3, 1
[1, 2, 3, 2, 2, 3, 1, 3, 2] => 1, 2, 3, 2, 2, 3, 1, 3, 2
[1, 2, 3, 2, 2, 3, 1, 3, 3] => 1, 2, 3, 2, 2, 3, 1, 3, 3
[1, 2, 3, 2, 2, 3, 2, 1, 1] => 1, 2, 3, 2, 2, 3, 2, 1, 1
[1, 2, 3, 2, 2, 3, 2, 1, 2] => 1, 2, 3, 2, 2, 3, 2, 1, 2
[1, 2, 3, 2, 2, 3, 2, 1, 3] => 1, 2, 3, 2, 2, 3, 2, 1, 3
[1, 2, 3, 2, 2, 3, 2, 2, 1] => 1, 2, 3, 2, 2, 3, 2, 2, 1
[1, 2, 3, 2, 2, 3, 2, 2, 2] => 1, 2, 3, 2, 2, 3, 2, 2, 2
[1, 2, 3, 2, 2, 3, 2, 2, 3] => 1, 2, 3, 2, 2, 3, 2, 2, 3
[1, 2, 3, 2, 2, 3, 2, 3, 1] => 1, 2, 3, 2, 2, 3, 2, 3, 1
[1, 2, 3, 2, 2, 3, 2, 3, 2] => 1, 2, 3, 2, 2, 3, 2, 3, 2
[1, 2, 3, 2, 2, 3, 2, 3, 3] => 1, 2, 3, 2, 2, 3, 2, 3, 3
[1, 2, 3, 2, 2, 3, 3, 1, 1] => 1, 2, 3, 2, 2, 3, 3, 1, 1
[1, 2, 3, 2, 2, 3, 3, 1, 2] => 1, 2, 3, 2, 2, 3, 3, 1, 2
[1, 2, 3, 2, 2, 3, 3, 1, 3] => 1, 2, 3, 2, 2, 3, 3, 1, 3
[1, 2, 3, 2, 2, 3, 3, 2, 1] => 1, 2, 3, 2, 2, 3, 3, 2, 1
[1, 2, 3, 2, 2, 3, 3, 2, 2] => 1, 2, 3, 2, 2, 3, 3, 2, 2
[1, 2, 3, 2, 2, 3, 3, 2, 3] => 1, 2, 3, 2, 2, 3, 3, 2, 3
[1, 2, 3, 2, 2, 3, 3, 3, 1] => 1, 2, 3, 2, 2, 3, 3, 3, 1
[1, 2, 3, 2, 2, 3, 3, 3, 2] => 1, 2, 3, 2, 2, 3, 3, 3, 2
[1, 2, 3, 2, 2, 3, 3, 3, 3] => 1, 2, 3, 2, 2, 3, 3, 3, 3
[1, 2, 3, 2, 3, 1, 1, 1, 1] => 1, 2, 3, 2, 3, 1, 1, 1, 1
[1, 2, 3, 2, 3, 1, 1, 1, 2] => 1, 2, 3, 2, 3, 1, 1, 1, 2
[1, 2, 3, 2, 3, 1, 1, 1, 3] => 1, 2, 3, 2, 3, 1, 1, 1, 3
[1, 2, 3, 2, 3, 1, 1, 2, 1] => 1, 2, 3, 2, 3, 1, 1, 2, 1
[1, 2, 3, 2, 3, 1, 1, 2, 2] => 1, 2, 3, 2, 3, 1, 1, 2, 2
[1, 2, 3, 2, 3, 1, 1, 2, 3] => 1, 2, 3, 2, 3, 1, 1, 2, 3
[1, 2, 3, 2, 3, 1, 1, 3, 1] => 1, 2, 3, 2, 3, 1, 1, 3, 1
[1, 2, 3, 2, 3, 1, 1, 3, 2] => 1, 2, 3, 2, 3, 1, 1, 3, 2
[1, 2, 3, 2, 3, 1, 1, 3, 3] => 1, 2, 3, 2, 3, 1, 1, 3, 3
[1, 2, 3, 2, 3, 1, 2, 1, 1] => 1, 2, 3, 2, 3, 1, 2, 1, 1
[1, 2, 3, 2, 3, 1, 2, 1, 2] => 1, 2, 3, 2, 3, 1, 2, 1, 2
[1, 2, 3, 2, 3, 1, 2, 1, 3] => 1, 2, 3, 2, 3, 1, 2, 1, 3
[1, 2, 3, 2, 3, 1, 2, 2, 1] => 1, 2, 3, 2, 3, 1, 2, 2, 1
[1, 2, 3, 2, 3, 1, 2, 2, 2] => 1, 2, 3, 2, 3, 1, 2, 2, 2
[1, 2, 3, 2, 3, 1, 2, 2, 3] => 1, 2, 3, 2, 3, 1, 2, 2, 3
[1, 2, 3, 2, 3, 1, 2, 3, 1] => 1, 2, 3, 2, 3, 1, 2, 3, 1
[1, 2, 3, 2, 3, 1, 2, 3, 2] => 1, 2, 3, 2, 3, 1, 2, 3, 2
[1, 2, 3, 2, 3, 1, 2, 3, 3] => 1, 2, 3, 2, 3, 1, 2, 3, 3
[1, 2, 3, 2, 3, 1, 3, 1, 1] => 1, 2, 3, 2, 3, 1, 3, 1, 1
[1, 2, 3, 2, 3, 1, 3, 1, 2] => 1, 2, 3, 2, 3, 1, 3, 1, 2
[1, 2, 3, 2, 3, 1, 3, 1, 3] => 1, 2, 3, 2, 3, 1, 3, 1, 3
[1, 2, 3, 2, 3, 1, 3, 2, 1] => 1, 2, 3, 2, 3, 1, 3, 2, 1
[1, 2, 3, 2, 3, 1, 3, 2, 2] => 1, 2, 3, 2, 3, 1, 3, 2, 2
[1, 2, 3, 2, 3, 1, 3, 2, 3] => 1, 2, 3, 2, 3, 1, 3, 2, 3
[1, 2, 3, 2, 3, 1, 3, 3, 1] => 1, 2, 3, 2, 3, 1, 3, 3, 1
[1, 2, 3, 2, 3, 1, 3, 3, 2] => 1, 2, 3, 2, 3, 1, 3, 3, 2
[1, 2, 3, 2, 3, 1, 3, 3, 3] => 1, 2, 3, 2, 3, 1, 3, 3, 3
[1, 2, 3, 2, 3, 2, 1, 1, 1] => 1, 2, 3, 2, 3, 2, 1, 1, 1
[1, 2, 3, 2, 3, 2, 1, 1, 2] => 1, 2, 3, 2, 3, 2, 1, 1, 2
[1, 2, 3, 2, 3, 2, 1, 1, 3] => 1, 2, 3, 2, 3, 2, 1, 1, 3
[1, 2, 3, 2, 3, 2, 1, 2, 1] => 1, 2, 3, 2, 3, 2, 1, 2, 1
[1, 2, 3, 2, 3, 2, 1, 2, 2] => 1, 2, 3, 2, 3, 2, 1, 2, 2
[1, 2, 3, 2, 3, 2, 1, 2, 3] => 1, 2, 3, 2, 3, 2, 1, 2, 3
[1, 2, 3, 2, 3, 2, 1, 3, 1] => 1, 2, 3, 2, 3, 2, 1, 3, 1
[1, 2, 3, 2, 3, 2, 1, 3, 2] => 1, 2, 3, 2, 3, 2, 1, 3, 2
[1, 2, 3, 2, 3, 2, 1, 3, 3] => 1, 2, 3, 2, 3, 2, 1, 3, 3
[1, 2, 3, 2, 3, 2, 2, 1, 1] => 1, 2, 3, 2, 3, 2, 2, 1, 1
[1, 2, 3, 2, 3, 2, 2, 1, 2] => 1, 2, 3, 2, 3, 2, 2, 1, 2
[1, 2, 3, 2, 3, 2, 2, 1, 3] => 1, 2, 3, 2, 3, 2, 2, 1, 3
[1, 2, 3, 2, 3, 2, 2, 2, 1] => 1, 2, 3, 2, 3, 2, 2, 2, 1
[1, 2, 3, 2, 3, 2, 2, 2, 2] => 1, 2, 3, 2, 3, 2, 2, 2, 2
[1, 2, 3, 2, 3, 2, 2, 2, 3] => 1, 2, 3, 2, 3, 2, 2, 2, 3
[1, 2, 3, 2, 3, 2, 2, 3, 1] => 1, 2, 3, 2, 3, 2, 2, 3, 1
[1, 2, 3, 2, 3, 2, 2, 3, 2] => 1, 2, 3, 2, 3, 2, 2, 3, 2
[1, 2, 3, 2, 3, 2, 2, 3, 3] => 1, 2, 3, 2, 3, 2, 2, 3, 3
[1, 2, 3, 2, 3, 2, 3, 1, 1] => 1, 2, 3, 2, 3, 2, 3, 1, 1
[1, 2, 3, 2, 3, 2, 3, 1, 2] => 1, 2, 3, 2, 3, 2, 3, 1, 2
[1, 2, 3, 2, 3, 2, 3, 1, 3] => 1, 2, 3, 2, 3, 2, 3, 1, 3
[1, 2, 3, 2, 3, 2, 3, 2, 1] => 1, 2, 3, 2, 3, 2, 3, 2, 1
[1, 2, 3, 2, 3, 2, 3, 2, 2] => 1, 2, 3, 2, 3, 2, 3, 2, 2
[1, 2, 3, 2, 3, 2, 3, 2, 3] => 1, 2, 3, 2, 3, 2, 3, 2, 3
[1, 2, 3, 2, 3, 2, 3, 3, 1] => 1, 2, 3, 2, 3, 2, 3, 3, 1
[1, 2, 3, 2, 3, 2, 3, 3, 2] => 1, 2, 3, 2, 3, 2, 3, 3, 2
[1, 2, 3, 2, 3, 2, 3, 3, 3] => 1, 2, 3, 2, 3, 2, 3, 3, 3
[1, 2, 3, 2, 3, 3, 1, 1, 1] => 1, 2, 3, 2, 3, 3, 1, 1, 1
[1, 2, 3, 2, 3, 3, 1, 1, 2] => 1, 2, 3, 2, 3, 3, 1, 1, 2
[1, 2, 3, 2, 3, 3, 1, 1, 3] => 1, 2, 3, 2, 3, 3, 1, 1, 3
[1, 2, 3, 2, 3, 3, 1, 2, 1] => 1, 2, 3, 2, 3, 3, 1, 2, 1
[1, 2, 3, 2, 3, 3, 1, 2, 2] => 1, 2, 3, 2, 3, 3, 1, 2, 2
[1, 2, 3, 2, 3, 3, 1, 2, 3] => 1, 2, 3, 2, 3, 3, 1, 2, 3
[1, 2, 3, 2, 3, 3, 1, 3, 1] => 1, 2, 3, 2, 3, 3, 1, 3, 1
[1, 2, 3, 2, 3, 3, 1, 3, 2] => 1, 2, 3, 2, 3, 3, 1, 3, 2
[1, 2, 3, 2, 3, 3, 1, 3, 3] => 1, 2, 3, 2, 3, 3, 1, 3, 3
[1, 2, 3, 2, 3, 3, 2, 1, 1] => 1, 2, 3, 2, 3, 3, 2, 1, 1
[1, 2, 3, 2, 3, 3, 2, 1, 2] => 1, 2, 3, 2, 3, 3, 2, 1, 2
[1, 2, 3, 2, 3, 3, 2, 1, 3] => 1, 2, 3, 2, 3, 3, 2, 1, 3
[1, 2, 3, 2, 3, 3, 2, 2, 1] => 1, 2, 3, 2, 3, 3, 2, 2, 1
[1, 2, 3, 2, 3, 3, 2, 2, 2] => 1, 2, 3, 2, 3, 3, 2, 2, 2
[1, 2, 3, 2, 3, 3, 2, 2, 3] => 1, 2, 3, 2, 3, 3, 2, 2, 3
[1, 2, 3, 2, 3, 3, 2, 3, 1] => 1, 2, 3, 2, 3, 3, 2, 3, 1
[1, 2, 3, 2, 3, 3, 2, 3, 2] => 1, 2, 3, 2, 3, 3, 2, 3, 2
[1, 2, 3, 2, 3, 3, 2, 3, 3] => 1, 2, 3, 2, 3, 3, 2, 3, 3
[1, 2, 3, 2, 3, 3, 3, 1, 1] => 1, 2, 3, 2, 3, 3, 3, 1, 1
[1, 2, 3, 2, 3, 3, 3, 1, 2] => 1, 2, 3, 2, 3, 3, 3, 1, 2
[1, 2, 3, 2, 3, 3, 3, 1, 3] => 1, 2, 3, 2, 3, 3, 3, 1, 3
[1, 2, 3, 2, 3, 3, 3, 2, 1] => 1, 2, 3, 2, 3, 3, 3, 2, 1
[1, 2, 3, 2, 3, 3, 3, 2, 2] => 1, 2, 3, 2, 3, 3, 3, 2, 2
[1, 2, 3, 2, 3, 3, 3, 2, 3] => 1, 2, 3, 2, 3, 3, 3, 2, 3
[1, 2, 3, 2, 3, 3, 3, 3, 1] => 1, 2, 3, 2, 3, 3, 3, 3, 1
[1, 2, 3, 2, 3, 3, 3, 3, 2] => 1, 2, 3, 2, 3, 3, 3, 3, 2
[1, 2, 3, 2, 3, 3, 3, 3, 3] => 1, 2, 3, 2, 3, 3, 3, 3, 3
[1, 2, 3, 3, 1, 1, 1, 1, 1] => 1, 2, 3, 3, 1, 1, 1, 1, 1
[1, 2, 3, 3, 1, 1, 1, 1, 2] => 1, 2, 3, 3, 1, 1, 1, 1, 2
[1, 2, 3, 3, 1, 1, 1, 1, 3] => 1, 2, 3, 3, 1, 1, 1, 1, 3
[1, 2, 3, 3, 1, 1, 1, 2, 1] => 1, 2, 3, 3, 1, 1, 1, 2, 1
[1, 2, 3, 3, 1, 1, 1, 2, 2] => 1, 2, 3, 3, 1, 1, 1, 2, 2
[1, 2, 3, 3, 1, 1, 1, 2, 3] => 1, 2, 3, 3, 1, 1, 1, 2, 3
[1, 2, 3, 3, 1, 1, 1, 3, 1] => 1, 2, 3, 3, 1, 1, 1, 3, 1
[1, 2, 3, 3, 1, 1, 1, 3, 2] => 1, 2, 3, 3, 1, 1, 1, 3, 2
[1, 2, 3, 3, 1, 1, 1, 3, 3] => 1, 2, 3, 3, 1, 1, 1, 3, 3
[1, 2, 3, 3, 1, 1, 2, 1, 1] => 1, 2, 3, 3, 1, 1, 2, 1, 1
[1, 2, 3, 3, 1, 1, 2, 1, 2] => 1, 2, 3, 3, 1, 1, 2, 1, 2
[1, 2, 3, 3, 1, 1, 2, 1, 3] => 1, 2, 3, 3, 1, 1, 2, 1, 3
[1, 2, 3, 3, 1, 1, 2, 2, 1] => 1, 2, 3, 3, 1, 1, 2, 2, 1
[1, 2, 3, 3, 1, 1, 2, 2, 2] => 1, 2, 3, 3, 1, 1, 2, 2, 2
[1, 2, 3, 3, 1, 1, 2, 2, 3] => 1, 2, 3, 3, 1, 1, 2, 2, 3
[1, 2, 3, 3, 1, 1, 2, 3, 1] => 1, 2, 3, 3, 1, 1, 2, 3, 1
[1, 2, 3, 3, 1, 1, 2, 3, 2] => 1, 2, 3, 3, 1, 1, 2, 3, 2
[1, 2, 3, 3, 1, 1, 2, 3, 3] => 1, 2, 3, 3, 1, 1, 2, 3, 3
[1, 2, 3, 3, 1, 1, 3, 1, 1] => 1, 2, 3, 3, 1, 1, 3, 1, 1
[1, 2, 3, 3, 1, 1, 3, 1, 2] => 1, 2, 3, 3, 1, 1, 3, 1, 2
[1, 2, 3, 3, 1, 1, 3, 1, 3] => 1, 2, 3, 3, 1, 1, 3, 1, 3
[1, 2, 3, 3, 1, 1, 3, 2, 1] => 1, 2, 3, 3, 1, 1, 3, 2, 1
[1, 2, 3, 3, 1, 1, 3, 2, 2] => 1, 2, 3, 3, 1, 1, 3, 2, 2
[1, 2, 3, 3, 1, 1, 3, 2, 3] => 1, 2, 3, 3, 1, 1, 3, 2, 3
[1, 2, 3, 3, 1, 1, 3, 3, 1] => 1, 2, 3, 3, 1, 1, 3, 3, 1
[1, 2, 3, 3, 1, 1, 3, 3, 2] => 1, 2, 3, 3, 1, 1, 3, 3, 2
[1, 2, 3, 3, 1, 1, 3, 3, 3] => 1, 2, 3, 3, 1, 1, 3, 3, 3
[1, 2, 3, 3, 1, 2, 1, 1, 1] => 1, 2, 3, 3, 1, 2, 1, 1, 1
[1, 2, 3, 3, 1, 2, 1, 1, 2] => 1, 2, 3, 3, 1, 2, 1, 1, 2
[1, 2, 3, 3, 1, 2, 1, 1, 3] => 1, 2, 3, 3, 1, 2, 1, 1, 3
[1, 2, 3, 3, 1, 2, 1, 2, 1] => 1, 2, 3, 3, 1, 2, 1, 2, 1
[1, 2, 3, 3, 1, 2, 1, 2, 2] => 1, 2, 3, 3, 1, 2, 1, 2, 2
[1, 2, 3, 3, 1, 2, 1, 2, 3] => 1, 2, 3, 3, 1, 2, 1, 2, 3
[1, 2, 3, 3, 1, 2, 1, 3, 1] => 1, 2, 3, 3, 1, 2, 1, 3, 1
[1, 2, 3, 3, 1, 2, 1, 3, 2] => 1, 2, 3, 3, 1, 2, 1, 3, 2
[1, 2, 3, 3, 1, 2, 1, 3, 3] => 1, 2, 3, 3, 1, 2, 1, 3, 3
[1, 2, 3, 3, 1, 2, 2, 1, 1] => 1, 2, 3, 3, 1, 2, 2, 1, 1
[1, 2, 3, 3, 1, 2, 2, 1, 2] => 1, 2, 3, 3, 1, 2, 2, 1, 2
[1, 2, 3, 3, 1, 2, 2, 1, 3] => 1, 2, 3, 3, 1, 2, 2, 1, 3
[1, 2, 3, 3, 1, 2, 2, 2, 1] => 1, 2, 3, 3, 1, 2, 2, 2, 1
[1, 2, 3, 3, 1, 2, 2, 2, 2] => 1, 2, 3, 3, 1, 2, 2, 2, 2
[1, 2, 3, 3, 1, 2, 2, 2, 3] => 1, 2, 3, 3, 1, 2, 2, 2, 3
[1, 2, 3, 3, 1, 2, 2, 3, 1] => 1, 2, 3, 3, 1, 2, 2, 3, 1
[1, 2, 3, 3, 1, 2, 2, 3, 2] => 1, 2, 3, 3, 1, 2, 2, 3, 2
[1, 2, 3, 3, 1, 2, 2, 3, 3] => 1, 2, 3, 3, 1, 2, 2, 3, 3
[1, 2, 3, 3, 1, 2, 3, 1, 1] => 1, 2, 3, 3, 1, 2, 3, 1, 1
[1, 2, 3, 3, 1, 2, 3, 1, 2] => 1, 2, 3, 3, 1, 2, 3, 1, 2
[1, 2, 3, 3, 1, 2, 3, 1, 3] => 1, 2, 3, 3, 1, 2, 3, 1, 3
[1, 2, 3, 3, 1, 2, 3, 2, 1] => 1, 2, 3, 3, 1, 2, 3, 2, 1
[1, 2, 3, 3, 1, 2, 3, 2, 2] => 1, 2, 3, 3, 1, 2, 3, 2, 2
[1, 2, 3, 3, 1, 2, 3, 2, 3] => 1, 2, 3, 3, 1, 2, 3, 2, 3
[1, 2, 3, 3, 1, 2, 3, 3, 1] => 1, 2, 3, 3, 1, 2, 3, 3, 1
[1, 2, 3, 3, 1, 2, 3, 3, 2] => 1, 2, 3, 3, 1, 2, 3, 3, 2
[1, 2, 3, 3, 1, 2, 3, 3, 3] => 1, 2, 3, 3, 1, 2, 3, 3, 3
[1, 2, 3, 3, 1, 3, 1, 1, 1] => 1, 2, 3, 3, 1, 3, 1, 1, 1
[1, 2, 3, 3, 1, 3, 1, 1, 2] => 1, 2, 3, 3, 1, 3, 1, 1, 2
[1, 2, 3, 3, 1, 3, 1, 1, 3] => 1, 2, 3, 3, 1, 3, 1, 1, 3
[1, 2, 3, 3, 1, 3, 1, 2, 1] => 1, 2, 3, 3, 1, 3, 1, 2, 1
[1, 2, 3, 3, 1, 3, 1, 2, 2] => 1, 2, 3, 3, 1, 3, 1, 2, 2
[1, 2, 3, 3, 1, 3, 1, 2, 3] => 1, 2, 3, 3, 1, 3, 1, 2, 3
[1, 2, 3, 3, 1, 3, 1, 3, 1] => 1, 2, 3, 3, 1, 3, 1, 3, 1
[1, 2, 3, 3, 1, 3, 1, 3, 2] => 1, 2, 3, 3, 1, 3, 1, 3, 2
[1, 2, 3, 3, 1, 3, 1, 3, 3] => 1, 2, 3, 3, 1, 3, 1, 3, 3
[1, 2, 3, 3, 1, 3, 2, 1, 1] => 1, 2, 3, 3, 1, 3, 2, 1, 1
[1, 2, 3, 3, 1, 3, 2, 1, 2] => 1, 2, 3, 3, 1, 3, 2, 1, 2
[1, 2, 3, 3, 1, 3, 2, 1, 3] => 1, 2, 3, 3, 1, 3, 2, 1, 3
[1, 2, 3, 3, 1, 3, 2, 2, 1] => 1, 2, 3, 3, 1, 3, 2, 2, 1
[1, 2, 3, 3, 1, 3, 2, 2, 2] => 1, 2, 3, 3, 1, 3, 2, 2, 2
[1, 2, 3, 3, 1, 3, 2, 2, 3] => 1, 2, 3, 3, 1, 3, 2, 2, 3
[1, 2, 3, 3, 1, 3, 2, 3, 1] => 1, 2, 3, 3, 1, 3, 2, 3, 1
[1, 2, 3, 3, 1, 3, 2, 3, 2] => 1, 2, 3, 3, 1, 3, 2, 3, 2
[1, 2, 3, 3, 1, 3, 2, 3, 3] => 1, 2, 3, 3, 1, 3, 2, 3, 3
[1, 2, 3, 3, 1, 3, 3, 1, 1] => 1, 2, 3, 3, 1, 3, 3, 1, 1
[1, 2, 3, 3, 1, 3, 3, 1, 2] => 1, 2, 3, 3, 1, 3, 3, 1, 2
[1, 2, 3, 3, 1, 3, 3, 1, 3] => 1, 2, 3, 3, 1, 3, 3, 1, 3
[1, 2, 3, 3, 1, 3, 3, 2, 1] => 1, 2, 3, 3, 1, 3, 3, 2, 1
[1, 2, 3, 3, 1, 3, 3, 2, 2] => 1, 2, 3, 3, 1, 3, 3, 2, 2
[1, 2, 3, 3, 1, 3, 3, 2, 3] => 1, 2, 3, 3, 1, 3, 3, 2, 3
[1, 2, 3, 3, 1, 3, 3, 3, 1] => 1, 2, 3, 3, 1, 3, 3, 3, 1
[1, 2, 3, 3, 1, 3, 3, 3, 2] => 1, 2, 3, 3, 1, 3, 3, 3, 2
[1, 2, 3, 3, 1, 3, 3, 3, 3] => 1, 2, 3, 3, 1, 3, 3, 3, 3
[1, 2, 3, 3, 2, 1, 1, 1, 1] => 1, 2, 3, 3, 2, 1, 1, 1, 1
[1, 2, 3, 3, 2, 1, 1, 1, 2] => 1, 2, 3, 3, 2, 1, 1, 1, 2
[1, 2, 3, 3, 2, 1, 1, 1, 3] => 1, 2, 3, 3, 2, 1, 1, 1, 3
[1, 2, 3, 3, 2, 1, 1, 2, 1] => 1, 2, 3, 3, 2, 1, 1, 2, 1
[1, 2, 3, 3, 2, 1, 1, 2, 2] => 1, 2, 3, 3, 2, 1, 1, 2, 2
[1, 2, 3, 3, 2, 1, 1, 2, 3] => 1, 2, 3, 3, 2, 1, 1, 2, 3
[1, 2, 3, 3, 2, 1, 1, 3, 1] => 1, 2, 3, 3, 2, 1, 1, 3, 1
[1, 2, 3, 3, 2, 1, 1, 3, 2] => 1, 2, 3, 3, 2, 1, 1, 3, 2
[1, 2, 3, 3, 2, 1, 1, 3, 3] => 1, 2, 3, 3, 2, 1, 1, 3, 3
[1, 2, 3, 3, 2, 1, 2, 1, 1] => 1, 2, 3, 3, 2, 1, 2, 1, 1
[1, 2, 3, 3, 2, 1, 2, 1, 2] => 1, 2, 3, 3, 2, 1, 2, 1, 2
[1, 2, 3, 3, 2, 1, 2, 1, 3] => 1, 2, 3, 3, 2, 1, 2, 1, 3
[1, 2, 3, 3, 2, 1, 2, 2, 1] => 1, 2, 3, 3, 2, 1, 2, 2, 1
[1, 2, 3, 3, 2, 1, 2, 2, 2] => 1, 2, 3, 3, 2, 1, 2, 2, 2
[1, 2, 3, 3, 2, 1, 2, 2, 3] => 1, 2, 3, 3, 2, 1, 2, 2, 3
[1, 2, 3, 3, 2, 1, 2, 3, 1] => 1, 2, 3, 3, 2, 1, 2, 3, 1
[1, 2, 3, 3, 2, 1, 2, 3, 2] => 1, 2, 3, 3, 2, 1, 2, 3, 2
[1, 2, 3, 3, 2, 1, 2, 3, 3] => 1, 2, 3, 3, 2, 1, 2, 3, 3
[1, 2, 3, 3, 2, 1, 3, 1, 1] => 1, 2, 3, 3, 2, 1, 3, 1, 1
[1, 2, 3, 3, 2, 1, 3, 1, 2] => 1, 2, 3, 3, 2, 1, 3, 1, 2
[1, 2, 3, 3, 2, 1, 3, 1, 3] => 1, 2, 3, 3, 2, 1, 3, 1, 3
[1, 2, 3, 3, 2, 1, 3, 2, 1] => 1, 2, 3, 3, 2, 1, 3, 2, 1
[1, 2, 3, 3, 2, 1, 3, 2, 2] => 1, 2, 3, 3, 2, 1, 3, 2, 2
[1, 2, 3, 3, 2, 1, 3, 2, 3] => 1, 2, 3, 3, 2, 1, 3, 2, 3
[1, 2, 3, 3, 2, 1, 3, 3, 1] => 1, 2, 3, 3, 2, 1, 3, 3, 1
[1, 2, 3, 3, 2, 1, 3, 3, 2] => 1, 2, 3, 3, 2, 1, 3, 3, 2
[1, 2, 3, 3, 2, 1, 3, 3, 3] => 1, 2, 3, 3, 2, 1, 3, 3, 3
[1, 2, 3, 3, 2, 2, 1, 1, 1] => 1, 2, 3, 3, 2, 2, 1, 1, 1
[1, 2, 3, 3, 2, 2, 1, 1, 2] => 1, 2, 3, 3, 2, 2, 1, 1, 2
[1, 2, 3, 3, 2, 2, 1, 1, 3] => 1, 2, 3, 3, 2, 2, 1, 1, 3
[1, 2, 3, 3, 2, 2, 1, 2, 1] => 1, 2, 3, 3, 2, 2, 1, 2, 1
[1, 2, 3, 3, 2, 2, 1, 2, 2] => 1, 2, 3, 3, 2, 2, 1, 2, 2
[1, 2, 3, 3, 2, 2, 1, 2, 3] => 1, 2, 3, 3, 2, 2, 1, 2, 3
[1, 2, 3, 3, 2, 2, 1, 3, 1] => 1, 2, 3, 3, 2, 2, 1, 3, 1
[1, 2, 3, 3, 2, 2, 1, 3, 2] => 1, 2, 3, 3, 2, 2, 1, 3, 2
[1, 2, 3, 3, 2, 2, 1, 3, 3] => 1, 2, 3, 3, 2, 2, 1, 3, 3
[1, 2, 3, 3, 2, 2, 2, 1, 1] => 1, 2, 3, 3, 2, 2, 2, 1, 1
[1, 2, 3, 3, 2, 2, 2, 1, 2] => 1, 2, 3, 3, 2, 2, 2, 1, 2
[1, 2, 3, 3, 2, 2, 2, 1, 3] => 1, 2, 3, 3, 2, 2, 2, 1, 3
[1, 2, 3, 3, 2, 2, 2, 2, 1] => 1, 2, 3, 3, 2, 2, 2, 2, 1
[1, 2, 3, 3, 2, 2, 2, 2, 2] => 1, 2, 3, 3, 2, 2, 2, 2, 2
[1, 2, 3, 3, 2, 2, 2, 2, 3] => 1, 2, 3, 3, 2, 2, 2, 2, 3
[1, 2, 3, 3, 2, 2, 2, 3, 1] => 1, 2, 3, 3, 2, 2, 2, 3, 1
[1, 2, 3, 3, 2, 2, 2, 3, 2] => 1, 2, 3, 3, 2, 2, 2, 3, 2
[1, 2, 3, 3, 2, 2, 2, 3, 3] => 1, 2, 3, 3, 2, 2, 2, 3, 3
[1, 2, 3, 3, 2, 2, 3, 1, 1] => 1, 2, 3, 3, 2, 2, 3, 1, 1
[1, 2, 3, 3, 2, 2, 3, 1, 2] => 1, 2, 3, 3, 2, 2, 3, 1, 2
[1, 2, 3, 3, 2, 2, 3, 1, 3] => 1, 2, 3, 3, 2, 2, 3, 1, 3
[1, 2, 3, 3, 2, 2, 3, 2, 1] => 1, 2, 3, 3, 2, 2, 3, 2, 1
[1, 2, 3, 3, 2, 2, 3, 2, 2] => 1, 2, 3, 3, 2, 2, 3, 2, 2
[1, 2, 3, 3, 2, 2, 3, 2, 3] => 1, 2, 3, 3, 2, 2, 3, 2, 3
[1, 2, 3, 3, 2, 2, 3, 3, 1] => 1, 2, 3, 3, 2, 2, 3, 3, 1
[1, 2, 3, 3, 2, 2, 3, 3, 2] => 1, 2, 3, 3, 2, 2, 3, 3, 2
[1, 2, 3, 3, 2, 2, 3, 3, 3] => 1, 2, 3, 3, 2, 2, 3, 3, 3
[1, 2, 3, 3, 2, 3, 1, 1, 1] => 1, 2, 3, 3, 2, 3, 1, 1, 1
[1, 2, 3, 3, 2, 3, 1, 1, 2] => 1, 2, 3, 3, 2, 3, 1, 1, 2
[1, 2, 3, 3, 2, 3, 1, 1, 3] => 1, 2, 3, 3, 2, 3, 1, 1, 3
[1, 2, 3, 3, 2, 3, 1, 2, 1] => 1, 2, 3, 3, 2, 3, 1, 2, 1
[1, 2, 3, 3, 2, 3, 1, 2, 2] => 1, 2, 3, 3, 2, 3, 1, 2, 2
[1, 2, 3, 3, 2, 3, 1, 2, 3] => 1, 2, 3, 3, 2, 3, 1, 2, 3
[1, 2, 3, 3, 2, 3, 1, 3, 1] => 1, 2, 3, 3, 2, 3, 1, 3, 1
[1, 2, 3, 3, 2, 3, 1, 3, 2] => 1, 2, 3, 3, 2, 3, 1, 3, 2
[1, 2, 3, 3, 2, 3, 1, 3, 3] => 1, 2, 3, 3, 2, 3, 1, 3, 3
[1, 2, 3, 3, 2, 3, 2, 1, 1] => 1, 2, 3, 3, 2, 3, 2, 1, 1
[1, 2, 3, 3, 2, 3, 2, 1, 2] => 1, 2, 3, 3, 2, 3, 2, 1, 2
[1, 2, 3, 3, 2, 3, 2, 1, 3] => 1, 2, 3, 3, 2, 3, 2, 1, 3
[1, 2, 3, 3, 2, 3, 2, 2, 1] => 1, 2, 3, 3, 2, 3, 2, 2, 1
[1, 2, 3, 3, 2, 3, 2, 2, 2] => 1, 2, 3, 3, 2, 3, 2, 2, 2
[1, 2, 3, 3, 2, 3, 2, 2, 3] => 1, 2, 3, 3, 2, 3, 2, 2, 3
[1, 2, 3, 3, 2, 3, 2, 3, 1] => 1, 2, 3, 3, 2, 3, 2, 3, 1
[1, 2, 3, 3, 2, 3, 2, 3, 2] => 1, 2, 3, 3, 2, 3, 2, 3, 2
[1, 2, 3, 3, 2, 3, 2, 3, 3] => 1, 2, 3, 3, 2, 3, 2, 3, 3
[1, 2, 3, 3, 2, 3, 3, 1, 1] => 1, 2, 3, 3, 2, 3, 3, 1, 1
[1, 2, 3, 3, 2, 3, 3, 1, 2] => 1, 2, 3, 3, 2, 3, 3, 1, 2
[1, 2, 3, 3, 2, 3, 3, 1, 3] => 1, 2, 3, 3, 2, 3, 3, 1, 3
[1, 2, 3, 3, 2, 3, 3, 2, 1] => 1, 2, 3, 3, 2, 3, 3, 2, 1
[1, 2, 3, 3, 2, 3, 3, 2, 2] => 1, 2, 3, 3, 2, 3, 3, 2, 2
[1, 2, 3, 3, 2, 3, 3, 2, 3] => 1, 2, 3, 3, 2, 3, 3, 2, 3
[1, 2, 3, 3, 2, 3, 3, 3, 1] => 1, 2, 3, 3, 2, 3, 3, 3, 1
[1, 2, 3, 3, 2, 3, 3, 3, 2] => 1, 2, 3, 3, 2, 3, 3, 3, 2
[1, 2, 3, 3, 2, 3, 3, 3, 3] => 1, 2, 3, 3, 2, 3, 3, 3, 3
[1, 2, 3, 3, 3, 1, 1, 1, 1] => 1, 2, 3, 3, 3, 1, 1, 1, 1
[1, 2, 3, 3, 3, 1, 1, 1, 2] => 1, 2, 3, 3, 3, 1, 1, 1, 2
[1, 2, 3, 3, 3, 1, 1, 1, 3] => 1, 2, 3, 3, 3, 1, 1, 1, 3
[1, 2, 3, 3, 3, 1, 1, 2, 1] => 1, 2, 3, 3, 3, 1, 1, 2, 1
[1, 2, 3, 3, 3, 1, 1, 2, 2] => 1, 2, 3, 3, 3, 1, 1, 2, 2
[1, 2, 3, 3, 3, 1, 1, 2, 3] => 1, 2, 3, 3, 3, 1, 1, 2, 3
[1, 2, 3, 3, 3, 1, 1, 3, 1] => 1, 2, 3, 3, 3, 1, 1, 3, 1
[1, 2, 3, 3, 3, 1, 1, 3, 2] => 1, 2, 3, 3, 3, 1, 1, 3, 2
[1, 2, 3, 3, 3, 1, 1, 3, 3] => 1, 2, 3, 3, 3, 1, 1, 3, 3
[1, 2, 3, 3, 3, 1, 2, 1, 1] => 1, 2, 3, 3, 3, 1, 2, 1, 1
[1, 2, 3, 3, 3, 1, 2, 1, 2] => 1, 2, 3, 3, 3, 1, 2, 1, 2
[1, 2, 3, 3, 3, 1, 2, 1, 3] => 1, 2, 3, 3, 3, 1, 2, 1, 3
[1, 2, 3, 3, 3, 1, 2, 2, 1] => 1, 2, 3, 3, 3, 1, 2, 2, 1
[1, 2, 3, 3, 3, 1, 2, 2, 2] => 1, 2, 3, 3, 3, 1, 2, 2, 2
[1, 2, 3, 3, 3, 1, 2, 2, 3] => 1, 2, 3, 3, 3, 1, 2, 2, 3
[1, 2, 3, 3, 3, 1, 2, 3, 1] => 1, 2, 3, 3, 3, 1, 2, 3, 1
[1, 2, 3, 3, 3, 1, 2, 3, 2] => 1, 2, 3, 3, 3, 1, 2, 3, 2
[1, 2, 3, 3, 3, 1, 2, 3, 3] => 1, 2, 3, 3, 3, 1, 2, 3, 3
[1, 2, 3, 3, 3, 1, 3, 1, 1] => 1, 2, 3, 3, 3, 1, 3, 1, 1
[1, 2, 3, 3, 3, 1, 3, 1, 2] => 1, 2, 3, 3, 3, 1, 3, 1, 2
[1, 2, 3, 3, 3, 1, 3, 1, 3] => 1, 2, 3, 3, 3, 1, 3, 1, 3
[1, 2, 3, 3, 3, 1, 3, 2, 1] => 1, 2, 3, 3, 3, 1, 3, 2, 1
[1, 2, 3, 3, 3, 1, 3, 2, 2] => 1, 2, 3, 3, 3, 1, 3, 2, 2
[1, 2, 3, 3, 3, 1, 3, 2, 3] => 1, 2, 3, 3, 3, 1, 3, 2, 3
[1, 2, 3, 3, 3, 1, 3, 3, 1] => 1, 2, 3, 3, 3, 1, 3, 3, 1
[1, 2, 3, 3, 3, 1, 3, 3, 2] => 1, 2, 3, 3, 3, 1, 3, 3, 2
[1, 2, 3, 3, 3, 1, 3, 3, 3] => 1, 2, 3, 3, 3, 1, 3, 3, 3
[1, 2, 3, 3, 3, 2, 1, 1, 1] => 1, 2, 3, 3, 3, 2, 1, 1, 1
[1, 2, 3, 3, 3, 2, 1, 1, 2] => 1, 2, 3, 3, 3, 2, 1, 1, 2
[1, 2, 3, 3, 3, 2, 1, 1, 3] => 1, 2, 3, 3, 3, 2, 1, 1, 3
[1, 2, 3, 3, 3, 2, 1, 2, 1] => 1, 2, 3, 3, 3, 2, 1, 2, 1
[1, 2, 3, 3, 3, 2, 1, 2, 2] => 1, 2, 3, 3, 3, 2, 1, 2, 2
[1, 2, 3, 3, 3, 2, 1, 2, 3] => 1, 2, 3, 3, 3, 2, 1, 2, 3
[1, 2, 3, 3, 3, 2, 1, 3, 1] => 1, 2, 3, 3, 3, 2, 1, 3, 1
[1, 2, 3, 3, 3, 2, 1, 3, 2] => 1, 2, 3, 3, 3, 2, 1, 3, 2
[1, 2, 3, 3, 3, 2, 1, 3, 3] => 1, 2, 3, 3, 3, 2, 1, 3, 3
[1, 2, 3, 3, 3, 2, 2, 1, 1] => 1, 2, 3, 3, 3, 2, 2, 1, 1
[1, 2, 3, 3, 3, 2, 2, 1, 2] => 1, 2, 3, 3, 3, 2, 2, 1, 2
[1, 2, 3, 3, 3, 2, 2, 1, 3] => 1, 2, 3, 3, 3, 2, 2, 1, 3
[1, 2, 3, 3, 3, 2, 2, 2, 1] => 1, 2, 3, 3, 3, 2, 2, 2, 1
[1, 2, 3, 3, 3, 2, 2, 2, 2] => 1, 2, 3, 3, 3, 2, 2, 2, 2
[1, 2, 3, 3, 3, 2, 2, 2, 3] => 1, 2, 3, 3, 3, 2, 2, 2, 3
[1, 2, 3, 3, 3, 2, 2, 3, 1] => 1, 2, 3, 3, 3, 2, 2, 3, 1
[1, 2, 3, 3, 3, 2, 2, 3, 2] => 1, 2, 3, 3, 3, 2, 2, 3, 2
[1, 2, 3, 3, 3, 2, 2, 3, 3] => 1, 2, 3, 3, 3, 2, 2, 3, 3
[1, 2, 3, 3, 3, 2, 3, 1, 1] => 1, 2, 3, 3, 3, 2, 3, 1, 1
[1, 2, 3, 3, 3, 2, 3, 1, 2] => 1, 2, 3, 3, 3, 2, 3, 1, 2
[1, 2, 3, 3, 3, 2, 3, 1, 3] => 1, 2, 3, 3, 3, 2, 3, 1, 3
[1, 2, 3, 3, 3, 2, 3, 2, 1] => 1, 2, 3, 3, 3, 2, 3, 2, 1
[1, 2, 3, 3, 3, 2, 3, 2, 2] => 1, 2, 3, 3, 3, 2, 3, 2, 2
[1, 2, 3, 3, 3, 2, 3, 2, 3] => 1, 2, 3, 3, 3, 2, 3, 2, 3
[1, 2, 3, 3, 3, 2, 3, 3, 1] => 1, 2, 3, 3, 3, 2, 3, 3, 1
[1, 2, 3, 3, 3, 2, 3, 3, 2] => 1, 2, 3, 3, 3, 2, 3, 3, 2
[1, 2, 3, 3, 3, 2, 3, 3, 3] => 1, 2, 3, 3, 3, 2, 3, 3, 3
[1, 2, 3, 3, 3, 3, 1, 1, 1] => 1, 2, 3, 3, 3, 3, 1, 1, 1
[1, 2, 3, 3, 3, 3, 1, 1, 2] => 1, 2, 3, 3, 3, 3, 1, 1, 2
[1, 2, 3, 3, 3, 3, 1, 1, 3] => 1, 2, 3, 3, 3, 3, 1, 1, 3
[1, 2, 3, 3, 3, 3, 1, 2, 1] => 1, 2, 3, 3, 3, 3, 1, 2, 1
[1, 2, 3, 3, 3, 3, 1, 2, 2] => 1, 2, 3, 3, 3, 3, 1, 2, 2
[1, 2, 3, 3, 3, 3, 1, 2, 3] => 1, 2, 3, 3, 3, 3, 1, 2, 3
[1, 2, 3, 3, 3, 3, 1, 3, 1] => 1, 2, 3, 3, 3, 3, 1, 3, 1
[1, 2, 3, 3, 3, 3, 1, 3, 2] => 1, 2, 3, 3, 3, 3, 1, 3, 2
[1, 2, 3, 3, 3, 3, 1, 3, 3] => 1, 2, 3, 3, 3, 3, 1, 3, 3
[1, 2, 3, 3, 3, 3, 2, 1, 1] => 1, 2, 3, 3, 3, 3, 2, 1, 1
[1, 2, 3, 3, 3, 3, 2, 1, 2] => 1, 2, 3, 3, 3, 3, 2, 1, 2
[1, 2, 3, 3, 3, 3, 2, 1, 3] => 1, 2, 3, 3, 3, 3, 2, 1, 3
[1, 2, 3, 3, 3, 3, 2, 2, 1] => 1, 2, 3, 3, 3, 3, 2, 2, 1
[1, 2, 3, 3, 3, 3, 2, 2, 2] => 1, 2, 3, 3, 3, 3, 2, 2, 2
[1, 2, 3, 3, 3, 3, 2, 2, 3] => 1, 2, 3, 3, 3, 3, 2, 2, 3
[1, 2, 3, 3, 3, 3, 2, 3, 1] => 1, 2, 3, 3, 3, 3, 2, 3, 1
[1, 2, 3, 3, 3, 3, 2, 3, 2] => 1, 2, 3, 3, 3, 3, 2, 3, 2
[1, 2, 3, 3, 3, 3, 2, 3, 3] => 1, 2, 3, 3, 3, 3, 2, 3, 3
[1, 2, 3, 3, 3, 3, 3, 1, 1] => 1, 2, 3, 3, 3, 3, 3, 1, 1
[1, 2, 3, 3, 3, 3, 3, 1, 2] => 1, 2, 3, 3, 3, 3, 3, 1, 2
[1, 2, 3, 3, 3, 3, 3, 1, 3] => 1, 2, 3, 3, 3, 3, 3, 1, 3
[1, 2, 3, 3, 3, 3, 3, 2, 1] => 1, 2, 3, 3, 3, 3, 3, 2, 1
[1, 2, 3, 3, 3, 3, 3, 2, 2] => 1, 2, 3, 3, 3, 3, 3, 2, 2
[1, 2, 3, 3, 3, 3, 3, 2, 3] => 1, 2, 3, 3, 3, 3, 3, 2, 3
[1, 2, 3, 3, 3, 3, 3, 3, 1] => 1, 2, 3, 3, 3, 3, 3, 3, 1
[1, 2, 3, 3, 3, 3, 3, 3, 2] => 1, 2, 3, 3, 3, 3, 3, 3, 2
[1, 2, 3, 3, 3, 3, 3, 3, 3] => 1, 2, 3, 3, 3, 3, 3, 3, 3
[1, 3, 1, 1, 1, 1, 1, 1, 1] => 1, 3, 1, 1, 1, 1, 1, 1, 1
[1, 3, 1, 1, 1, 1, 1, 1, 2] => 1, 3, 1, 1, 1, 1, 1, 1, 2
[1, 3, 1, 1, 1, 1, 1, 1, 3] => 1, 3, 1, 1, 1, 1, 1, 1, 3
[1, 3, 1, 1, 1, 1, 1, 2, 1] => 1, 3, 1, 1, 1, 1, 1, 2, 1
[1, 3, 1, 1, 1, 1, 1, 2, 2] => 1, 3, 1, 1, 1, 1, 1, 2, 2
[1, 3, 1, 1, 1, 1, 1, 2, 3] => 1, 3, 1, 1, 1, 1, 1, 2, 3
[1, 3, 1, 1, 1, 1, 1, 3, 1] => 1, 3, 1, 1, 1, 1, 1, 3, 1
[1, 3, 1, 1, 1, 1, 1, 3, 2] => 1, 3, 1, 1, 1, 1, 1, 3, 2
[1, 3, 1, 1, 1, 1, 1, 3, 3] => 1, 3, 1, 1, 1, 1, 1, 3, 3
[1, 3, 1, 1, 1, 1, 2, 1, 1] => 1, 3, 1, 1, 1, 1, 2, 1, 1
[1, 3, 1, 1, 1, 1, 2, 1, 2] => 1, 3, 1, 1, 1, 1, 2, 1, 2
[1, 3, 1, 1, 1, 1, 2, 1, 3] => 1, 3, 1, 1, 1, 1, 2, 1, 3
[1, 3, 1, 1, 1, 1, 2, 2, 1] => 1, 3, 1, 1, 1, 1, 2, 2, 1
[1, 3, 1, 1, 1, 1, 2, 2, 2] => 1, 3, 1, 1, 1, 1, 2, 2, 2
[1, 3, 1, 1, 1, 1, 2, 2, 3] => 1, 3, 1, 1, 1, 1, 2, 2, 3
[1, 3, 1, 1, 1, 1, 2, 3, 1] => 1, 3, 1, 1, 1, 1, 2, 3, 1
[1, 3, 1, 1, 1, 1, 2, 3, 2] => 1, 3, 1, 1, 1, 1, 2, 3, 2
[1, 3, 1, 1, 1, 1, 2, 3, 3] => 1, 3, 1, 1, 1, 1, 2, 3, 3
[1, 3, 1, 1, 1, 1, 3, 1, 1] => 1, 3, 1, 1, 1, 1, 3, 1, 1
[1, 3, 1, 1, 1, 1, 3, 1, 2] => 1, 3, 1, 1, 1, 1, 3, 1, 2
[1, 3, 1, 1, 1, 1, 3, 1, 3] => 1, 3, 1, 1, 1, 1, 3, 1, 3
[1, 3, 1, 1, 1, 1, 3, 2, 1] => 1, 3, 1, 1, 1, 1, 3, 2, 1
[1, 3, 1, 1, 1, 1, 3, 2, 2] => 1, 3, 1, 1, 1, 1, 3, 2, 2
[1, 3, 1, 1, 1, 1, 3, 2, 3] => 1, 3, 1, 1, 1, 1, 3, 2, 3
[1, 3, 1, 1, 1, 1, 3, 3, 1] => 1, 3, 1, 1, 1, 1, 3, 3, 1
[1, 3, 1, 1, 1, 1, 3, 3, 2] => 1, 3, 1, 1, 1, 1, 3, 3, 2
[1, 3, 1, 1, 1, 1, 3, 3, 3] => 1, 3, 1, 1, 1, 1, 3, 3, 3
[1, 3, 1, 1, 1, 2, 1, 1, 1] => 1, 3, 1, 1, 1, 2, 1, 1, 1
[1, 3, 1, 1, 1, 2, 1, 1, 2] => 1, 3, 1, 1, 1, 2, 1, 1, 2
[1, 3, 1, 1, 1, 2, 1, 1, 3] => 1, 3, 1, 1, 1, 2, 1, 1, 3
[1, 3, 1, 1, 1, 2, 1, 2, 1] => 1, 3, 1, 1, 1, 2, 1, 2, 1
[1, 3, 1, 1, 1, 2, 1, 2, 2] => 1, 3, 1, 1, 1, 2, 1, 2, 2
[1, 3, 1, 1, 1, 2, 1, 2, 3] => 1, 3, 1, 1, 1, 2, 1, 2, 3
[1, 3, 1, 1, 1, 2, 1, 3, 1] => 1, 3, 1, 1, 1, 2, 1, 3, 1
[1, 3, 1, 1, 1, 2, 1, 3, 2] => 1, 3, 1, 1, 1, 2, 1, 3, 2
[1, 3, 1, 1, 1, 2, 1, 3, 3] => 1, 3, 1, 1, 1, 2, 1, 3, 3
[1, 3, 1, 1, 1, 2, 2, 1, 1] => 1, 3, 1, 1, 1, 2, 2, 1, 1
[1, 3, 1, 1, 1, 2, 2, 1, 2] => 1, 3, 1, 1, 1, 2, 2, 1, 2
[1, 3, 1, 1, 1, 2, 2, 1, 3] => 1, 3, 1, 1, 1, 2, 2, 1, 3
[1, 3, 1, 1, 1, 2, 2, 2, 1] => 1, 3, 1, 1, 1, 2, 2, 2, 1
[1, 3, 1, 1, 1, 2, 2, 2, 2] => 1, 3, 1, 1, 1, 2, 2, 2, 2
[1, 3, 1, 1, 1, 2, 2, 2, 3] => 1, 3, 1, 1, 1, 2, 2, 2, 3
[1, 3, 1, 1, 1, 2, 2, 3, 1] => 1, 3, 1, 1, 1, 2, 2, 3, 1
[1, 3, 1, 1, 1, 2, 2, 3, 2] => 1, 3, 1, 1, 1, 2, 2, 3, 2
[1, 3, 1, 1, 1, 2, 2, 3, 3] => 1, 3, 1, 1, 1, 2, 2, 3, 3
[1, 3, 1, 1, 1, 2, 3, 1, 1] => 1, 3, 1, 1, 1, 2, 3, 1, 1
[1, 3, 1, 1, 1, 2, 3, 1, 2] => 1, 3, 1, 1, 1, 2, 3, 1, 2
[1, 3, 1, 1, 1, 2, 3, 1, 3] => 1, 3, 1, 1, 1, 2, 3, 1, 3
[1, 3, 1, 1, 1, 2, 3, 2, 1] => 1, 3, 1, 1, 1, 2, 3, 2, 1
[1, 3, 1, 1, 1, 2, 3, 2, 2] => 1, 3, 1, 1, 1, 2, 3, 2, 2
[1, 3, 1, 1, 1, 2, 3, 2, 3] => 1, 3, 1, 1, 1, 2, 3, 2, 3
[1, 3, 1, 1, 1, 2, 3, 3, 1] => 1, 3, 1, 1, 1, 2, 3, 3, 1
[1, 3, 1, 1, 1, 2, 3, 3, 2] => 1, 3, 1, 1, 1, 2, 3, 3, 2
[1, 3, 1, 1, 1, 2, 3, 3, 3] => 1, 3, 1, 1, 1, 2, 3, 3, 3
[1, 3, 1, 1, 1, 3, 1, 1, 1] => 1, 3, 1, 1, 1, 3, 1, 1, 1
[1, 3, 1, 1, 1, 3, 1, 1, 2] => 1, 3, 1, 1, 1, 3, 1, 1, 2
[1, 3, 1, 1, 1, 3, 1, 1, 3] => 1, 3, 1, 1, 1, 3, 1, 1, 3
[1, 3, 1, 1, 1, 3, 1, 2, 1] => 1, 3, 1, 1, 1, 3, 1, 2, 1
[1, 3, 1, 1, 1, 3, 1, 2, 2] => 1, 3, 1, 1, 1, 3, 1, 2, 2
[1, 3, 1, 1, 1, 3, 1, 2, 3] => 1, 3, 1, 1, 1, 3, 1, 2, 3
[1, 3, 1, 1, 1, 3, 1, 3, 1] => 1, 3, 1, 1, 1, 3, 1, 3, 1
[1, 3, 1, 1, 1, 3, 1, 3, 2] => 1, 3, 1, 1, 1, 3, 1, 3, 2
[1, 3, 1, 1, 1, 3, 1, 3, 3] => 1, 3, 1, 1, 1, 3, 1, 3, 3
[1, 3, 1, 1, 1, 3, 2, 1, 1] => 1, 3, 1, 1, 1, 3, 2, 1, 1
[1, 3, 1, 1, 1, 3, 2, 1, 2] => 1, 3, 1, 1, 1, 3, 2, 1, 2
[1, 3, 1, 1, 1, 3, 2, 1, 3] => 1, 3, 1, 1, 1, 3, 2, 1, 3
[1, 3, 1, 1, 1, 3, 2, 2, 1] => 1, 3, 1, 1, 1, 3, 2, 2, 1
[1, 3, 1, 1, 1, 3, 2, 2, 2] => 1, 3, 1, 1, 1, 3, 2, 2, 2
[1, 3, 1, 1, 1, 3, 2, 2, 3] => 1, 3, 1, 1, 1, 3, 2, 2, 3
[1, 3, 1, 1, 1, 3, 2, 3, 1] => 1, 3, 1, 1, 1, 3, 2, 3, 1
[1, 3, 1, 1, 1, 3, 2, 3, 2] => 1, 3, 1, 1, 1, 3, 2, 3, 2
[1, 3, 1, 1, 1, 3, 2, 3, 3] => 1, 3, 1, 1, 1, 3, 2, 3, 3
[1, 3, 1, 1, 1, 3, 3, 1, 1] => 1, 3, 1, 1, 1, 3, 3, 1, 1
[1, 3, 1, 1, 1, 3, 3, 1, 2] => 1, 3, 1, 1, 1, 3, 3, 1, 2
[1, 3, 1, 1, 1, 3, 3, 1, 3] => 1, 3, 1, 1, 1, 3, 3, 1, 3
[1, 3, 1, 1, 1, 3, 3, 2, 1] => 1, 3, 1, 1, 1, 3, 3, 2, 1
[1, 3, 1, 1, 1, 3, 3, 2, 2] => 1, 3, 1, 1, 1, 3, 3, 2, 2
[1, 3, 1, 1, 1, 3, 3, 2, 3] => 1, 3, 1, 1, 1, 3, 3, 2, 3
[1, 3, 1, 1, 1, 3, 3, 3, 1] => 1, 3, 1, 1, 1, 3, 3, 3, 1
[1, 3, 1, 1, 1, 3, 3, 3, 2] => 1, 3, 1, 1, 1, 3, 3, 3, 2
[1, 3, 1, 1, 1, 3, 3, 3, 3] => 1, 3, 1, 1, 1, 3, 3, 3, 3
[1, 3, 1, 1, 2, 1, 1, 1, 1] => 1, 3, 1, 1, 2, 1, 1, 1, 1
[1, 3, 1, 1, 2, 1, 1, 1, 2] => 1, 3, 1, 1, 2, 1, 1, 1, 2
[1, 3, 1, 1, 2, 1, 1, 1, 3] => 1, 3, 1, 1, 2, 1, 1, 1, 3
[1, 3, 1, 1, 2, 1, 1, 2, 1] => 1, 3, 1, 1, 2, 1, 1, 2, 1
[1, 3, 1, 1, 2, 1, 1, 2, 2] => 1, 3, 1, 1, 2, 1, 1, 2, 2
[1, 3, 1, 1, 2, 1, 1, 2, 3] => 1, 3, 1, 1, 2, 1, 1, 2, 3
[1, 3, 1, 1, 2, 1, 1, 3, 1] => 1, 3, 1, 1, 2, 1, 1, 3, 1
[1, 3, 1, 1, 2, 1, 1, 3, 2] => 1, 3, 1, 1, 2, 1, 1, 3, 2
[1, 3, 1, 1, 2, 1, 1, 3, 3] => 1, 3, 1, 1, 2, 1, 1, 3, 3
[1, 3, 1, 1, 2, 1, 2, 1, 1] => 1, 3, 1, 1, 2, 1, 2, 1, 1
[1, 3, 1, 1, 2, 1, 2, 1, 2] => 1, 3, 1, 1, 2, 1, 2, 1, 2
[1, 3, 1, 1, 2, 1, 2, 1, 3] => 1, 3, 1, 1, 2, 1, 2, 1, 3
[1, 3, 1, 1, 2, 1, 2, 2, 1] => 1, 3, 1, 1, 2, 1, 2, 2, 1
[1, 3, 1, 1, 2, 1, 2, 2, 2] => 1, 3, 1, 1, 2, 1, 2, 2, 2
[1, 3, 1, 1, 2, 1, 2, 2, 3] => 1, 3, 1, 1, 2, 1, 2, 2, 3
[1, 3, 1, 1, 2, 1, 2, 3, 1] => 1, 3, 1, 1, 2, 1, 2, 3, 1
[1, 3, 1, 1, 2, 1, 2, 3, 2] => 1, 3, 1, 1, 2, 1, 2, 3, 2
[1, 3, 1, 1, 2, 1, 2, 3, 3] => 1, 3, 1, 1, 2, 1, 2, 3, 3
[1, 3, 1, 1, 2, 1, 3, 1, 1] => 1, 3, 1, 1, 2, 1, 3, 1, 1
[1, 3, 1, 1, 2, 1, 3, 1, 2] => 1, 3, 1, 1, 2, 1, 3, 1, 2
[1, 3, 1, 1, 2, 1, 3, 1, 3] => 1, 3, 1, 1, 2, 1, 3, 1, 3
[1, 3, 1, 1, 2, 1, 3, 2, 1] => 1, 3, 1, 1, 2, 1, 3, 2, 1
[1, 3, 1, 1, 2, 1, 3, 2, 2] => 1, 3, 1, 1, 2, 1, 3, 2, 2
[1, 3, 1, 1, 2, 1, 3, 2, 3] => 1, 3, 1, 1, 2, 1, 3, 2, 3
[1, 3, 1, 1, 2, 1, 3, 3, 1] => 1, 3, 1, 1, 2, 1, 3, 3, 1
[1, 3, 1, 1, 2, 1, 3, 3, 2] => 1, 3, 1, 1, 2, 1, 3, 3, 2
[1, 3, 1, 1, 2, 1, 3, 3, 3] => 1, 3, 1, 1, 2, 1, 3, 3, 3
[1, 3, 1, 1, 2, 2, 1, 1, 1] => 1, 3, 1, 1, 2, 2, 1, 1, 1
[1, 3, 1, 1, 2, 2, 1, 1, 2] => 1, 3, 1, 1, 2, 2, 1, 1, 2
[1, 3, 1, 1, 2, 2, 1, 1, 3] => 1, 3, 1, 1, 2, 2, 1, 1, 3
[1, 3, 1, 1, 2, 2, 1, 2, 1] => 1, 3, 1, 1, 2, 2, 1, 2, 1
[1, 3, 1, 1, 2, 2, 1, 2, 2] => 1, 3, 1, 1, 2, 2, 1, 2, 2
[1, 3, 1, 1, 2, 2, 1, 2, 3] => 1, 3, 1, 1, 2, 2, 1, 2, 3
[1, 3, 1, 1, 2, 2, 1, 3, 1] => 1, 3, 1, 1, 2, 2, 1, 3, 1
[1, 3, 1, 1, 2, 2, 1, 3, 2] => 1, 3, 1, 1, 2, 2, 1, 3, 2
[1, 3, 1, 1, 2, 2, 1, 3, 3] => 1, 3, 1, 1, 2, 2, 1, 3, 3
[1, 3, 1, 1, 2, 2, 2, 1, 1] => 1, 3, 1, 1, 2, 2, 2, 1, 1
[1, 3, 1, 1, 2, 2, 2, 1, 2] => 1, 3, 1, 1, 2, 2, 2, 1, 2
[1, 3, 1, 1, 2, 2, 2, 1, 3] => 1, 3, 1, 1, 2, 2, 2, 1, 3
[1, 3, 1, 1, 2, 2, 2, 2, 1] => 1, 3, 1, 1, 2, 2, 2, 2, 1
[1, 3, 1, 1, 2, 2, 2, 2, 2] => 1, 3, 1, 1, 2, 2, 2, 2, 2
[1, 3, 1, 1, 2, 2, 2, 2, 3] => 1, 3, 1, 1, 2, 2, 2, 2, 3
[1, 3, 1, 1, 2, 2, 2, 3, 1] => 1, 3, 1, 1, 2, 2, 2, 3, 1
[1, 3, 1, 1, 2, 2, 2, 3, 2] => 1, 3, 1, 1, 2, 2, 2, 3, 2
[1, 3, 1, 1, 2, 2, 2, 3, 3] => 1, 3, 1, 1, 2, 2, 2, 3, 3
[1, 3, 1, 1, 2, 2, 3, 1, 1] => 1, 3, 1, 1, 2, 2, 3, 1, 1
[1, 3, 1, 1, 2, 2, 3, 1, 2] => 1, 3, 1, 1, 2, 2, 3, 1, 2
[1, 3, 1, 1, 2, 2, 3, 1, 3] => 1, 3, 1, 1, 2, 2, 3, 1, 3
[1, 3, 1, 1, 2, 2, 3, 2, 1] => 1, 3, 1, 1, 2, 2, 3, 2, 1
[1, 3, 1, 1, 2, 2, 3, 2, 2] => 1, 3, 1, 1, 2, 2, 3, 2, 2
[1, 3, 1, 1, 2, 2, 3, 2, 3] => 1, 3, 1, 1, 2, 2, 3, 2, 3
[1, 3, 1, 1, 2, 2, 3, 3, 1] => 1, 3, 1, 1, 2, 2, 3, 3, 1
[1, 3, 1, 1, 2, 2, 3, 3, 2] => 1, 3, 1, 1, 2, 2, 3, 3, 2
[1, 3, 1, 1, 2, 2, 3, 3, 3] => 1, 3, 1, 1, 2, 2, 3, 3, 3
[1, 3, 1, 1, 2, 3, 1, 1, 1] => 1, 3, 1, 1, 2, 3, 1, 1, 1
[1, 3, 1, 1, 2, 3, 1, 1, 2] => 1, 3, 1, 1, 2, 3, 1, 1, 2
[1, 3, 1, 1, 2, 3, 1, 1, 3] => 1, 3, 1, 1, 2, 3, 1, 1, 3
[1, 3, 1, 1, 2, 3, 1, 2, 1] => 1, 3, 1, 1, 2, 3, 1, 2, 1
[1, 3, 1, 1, 2, 3, 1, 2, 2] => 1, 3, 1, 1, 2, 3, 1, 2, 2
[1, 3, 1, 1, 2, 3, 1, 2, 3] => 1, 3, 1, 1, 2, 3, 1, 2, 3
[1, 3, 1, 1, 2, 3, 1, 3, 1] => 1, 3, 1, 1, 2, 3, 1, 3, 1
[1, 3, 1, 1, 2, 3, 1, 3, 2] => 1, 3, 1, 1, 2, 3, 1, 3, 2
[1, 3, 1, 1, 2, 3, 1, 3, 3] => 1, 3, 1, 1, 2, 3, 1, 3, 3
[1, 3, 1, 1, 2, 3, 2, 1, 1] => 1, 3, 1, 1, 2, 3, 2, 1, 1
[1, 3, 1, 1, 2, 3, 2, 1, 2] => 1, 3, 1, 1, 2, 3, 2, 1, 2
[1, 3, 1, 1, 2, 3, 2, 1, 3] => 1, 3, 1, 1, 2, 3, 2, 1, 3
[1, 3, 1, 1, 2, 3, 2, 2, 1] => 1, 3, 1, 1, 2, 3, 2, 2, 1
[1, 3, 1, 1, 2, 3, 2, 2, 2] => 1, 3, 1, 1, 2, 3, 2, 2, 2
[1, 3, 1, 1, 2, 3, 2, 2, 3] => 1, 3, 1, 1, 2, 3, 2, 2, 3
[1, 3, 1, 1, 2, 3, 2, 3, 1] => 1, 3, 1, 1, 2, 3, 2, 3, 1
[1, 3, 1, 1, 2, 3, 2, 3, 2] => 1, 3, 1, 1, 2, 3, 2, 3, 2
[1, 3, 1, 1, 2, 3, 2, 3, 3] => 1, 3, 1, 1, 2, 3, 2, 3, 3
[1, 3, 1, 1, 2, 3, 3, 1, 1] => 1, 3, 1, 1, 2, 3, 3, 1, 1
[1, 3, 1, 1, 2, 3, 3, 1, 2] => 1, 3, 1, 1, 2, 3, 3, 1, 2
[1, 3, 1, 1, 2, 3, 3, 1, 3] => 1, 3, 1, 1, 2, 3, 3, 1, 3
[1, 3, 1, 1, 2, 3, 3, 2, 1] => 1, 3, 1, 1, 2, 3, 3, 2, 1
[1, 3, 1, 1, 2, 3, 3, 2, 2] => 1, 3, 1, 1, 2, 3, 3, 2, 2
[1, 3, 1, 1, 2, 3, 3, 2, 3] => 1, 3, 1, 1, 2, 3, 3, 2, 3
[1, 3, 1, 1, 2, 3, 3, 3, 1] => 1, 3, 1, 1, 2, 3, 3, 3, 1
[1, 3, 1, 1, 2, 3, 3, 3, 2] => 1, 3, 1, 1, 2, 3, 3, 3, 2
[1, 3, 1, 1, 2, 3, 3, 3, 3] => 1, 3, 1, 1, 2, 3, 3, 3, 3
[1, 3, 1, 1, 3, 1, 1, 1, 1] => 1, 3, 1, 1, 3, 1, 1, 1, 1
[1, 3, 1, 1, 3, 1, 1, 1, 2] => 1, 3, 1, 1, 3, 1, 1, 1, 2
[1, 3, 1, 1, 3, 1, 1, 1, 3] => 1, 3, 1, 1, 3, 1, 1, 1, 3
[1, 3, 1, 1, 3, 1, 1, 2, 1] => 1, 3, 1, 1, 3, 1, 1, 2, 1
[1, 3, 1, 1, 3, 1, 1, 2, 2] => 1, 3, 1, 1, 3, 1, 1, 2, 2
[1, 3, 1, 1, 3, 1, 1, 2, 3] => 1, 3, 1, 1, 3, 1, 1, 2, 3
[1, 3, 1, 1, 3, 1, 1, 3, 1] => 1, 3, 1, 1, 3, 1, 1, 3, 1
[1, 3, 1, 1, 3, 1, 1, 3, 2] => 1, 3, 1, 1, 3, 1, 1, 3, 2
[1, 3, 1, 1, 3, 1, 1, 3, 3] => 1, 3, 1, 1, 3, 1, 1, 3, 3
[1, 3, 1, 1, 3, 1, 2, 1, 1] => 1, 3, 1, 1, 3, 1, 2, 1, 1
[1, 3, 1, 1, 3, 1, 2, 1, 2] => 1, 3, 1, 1, 3, 1, 2, 1, 2
[1, 3, 1, 1, 3, 1, 2, 1, 3] => 1, 3, 1, 1, 3, 1, 2, 1, 3
[1, 3, 1, 1, 3, 1, 2, 2, 1] => 1, 3, 1, 1, 3, 1, 2, 2, 1
[1, 3, 1, 1, 3, 1, 2, 2, 2] => 1, 3, 1, 1, 3, 1, 2, 2, 2
[1, 3, 1, 1, 3, 1, 2, 2, 3] => 1, 3, 1, 1, 3, 1, 2, 2, 3
[1, 3, 1, 1, 3, 1, 2, 3, 1] => 1, 3, 1, 1, 3, 1, 2, 3, 1
[1, 3, 1, 1, 3, 1, 2, 3, 2] => 1, 3, 1, 1, 3, 1, 2, 3, 2
[1, 3, 1, 1, 3, 1, 2, 3, 3] => 1, 3, 1, 1, 3, 1, 2, 3, 3
[1, 3, 1, 1, 3, 1, 3, 1, 1] => 1, 3, 1, 1, 3, 1, 3, 1, 1
[1, 3, 1, 1, 3, 1, 3, 1, 2] => 1, 3, 1, 1, 3, 1, 3, 1, 2
[1, 3, 1, 1, 3, 1, 3, 1, 3] => 1, 3, 1, 1, 3, 1, 3, 1, 3
[1, 3, 1, 1, 3, 1, 3, 2, 1] => 1, 3, 1, 1, 3, 1, 3, 2, 1
[1, 3, 1, 1, 3, 1, 3, 2, 2] => 1, 3, 1, 1, 3, 1, 3, 2, 2
[1, 3, 1, 1, 3, 1, 3, 2, 3] => 1, 3, 1, 1, 3, 1, 3, 2, 3
[1, 3, 1, 1, 3, 1, 3, 3, 1] => 1, 3, 1, 1, 3, 1, 3, 3, 1
[1, 3, 1, 1, 3, 1, 3, 3, 2] => 1, 3, 1, 1, 3, 1, 3, 3, 2
[1, 3, 1, 1, 3, 1, 3, 3, 3] => 1, 3, 1, 1, 3, 1, 3, 3, 3
[1, 3, 1, 1, 3, 2, 1, 1, 1] => 1, 3, 1, 1, 3, 2, 1, 1, 1
[1, 3, 1, 1, 3, 2, 1, 1, 2] => 1, 3, 1, 1, 3, 2, 1, 1, 2
[1, 3, 1, 1, 3, 2, 1, 1, 3] => 1, 3, 1, 1, 3, 2, 1, 1, 3
[1, 3, 1, 1, 3, 2, 1, 2, 1] => 1, 3, 1, 1, 3, 2, 1, 2, 1
[1, 3, 1, 1, 3, 2, 1, 2, 2] => 1, 3, 1, 1, 3, 2, 1, 2, 2
[1, 3, 1, 1, 3, 2, 1, 2, 3] => 1, 3, 1, 1, 3, 2, 1, 2, 3
[1, 3, 1, 1, 3, 2, 1, 3, 1] => 1, 3, 1, 1, 3, 2, 1, 3, 1
[1, 3, 1, 1, 3, 2, 1, 3, 2] => 1, 3, 1, 1, 3, 2, 1, 3, 2
[1, 3, 1, 1, 3, 2, 1, 3, 3] => 1, 3, 1, 1, 3, 2, 1, 3, 3
[1, 3, 1, 1, 3, 2, 2, 1, 1] => 1, 3, 1, 1, 3, 2, 2, 1, 1
[1, 3, 1, 1, 3, 2, 2, 1, 2] => 1, 3, 1, 1, 3, 2, 2, 1, 2
[1, 3, 1, 1, 3, 2, 2, 1, 3] => 1, 3, 1, 1, 3, 2, 2, 1, 3
[1, 3, 1, 1, 3, 2, 2, 2, 1] => 1, 3, 1, 1, 3, 2, 2, 2, 1
[1, 3, 1, 1, 3, 2, 2, 2, 2] => 1, 3, 1, 1, 3, 2, 2, 2, 2
[1, 3, 1, 1, 3, 2, 2, 2, 3] => 1, 3, 1, 1, 3, 2, 2, 2, 3
[1, 3, 1, 1, 3, 2, 2, 3, 1] => 1, 3, 1, 1, 3, 2, 2, 3, 1
[1, 3, 1, 1, 3, 2, 2, 3, 2] => 1, 3, 1, 1, 3, 2, 2, 3, 2
[1, 3, 1, 1, 3, 2, 2, 3, 3] => 1, 3, 1, 1, 3, 2, 2, 3, 3
[1, 3, 1, 1, 3, 2, 3, 1, 1] => 1, 3, 1, 1, 3, 2, 3, 1, 1
[1, 3, 1, 1, 3, 2, 3, 1, 2] => 1, 3, 1, 1, 3, 2, 3, 1, 2
[1, 3, 1, 1, 3, 2, 3, 1, 3] => 1, 3, 1, 1, 3, 2, 3, 1, 3
[1, 3, 1, 1, 3, 2, 3, 2, 1] => 1, 3, 1, 1, 3, 2, 3, 2, 1
[1, 3, 1, 1, 3, 2, 3, 2, 2] => 1, 3, 1, 1, 3, 2, 3, 2, 2
[1, 3, 1, 1, 3, 2, 3, 2, 3] => 1, 3, 1, 1, 3, 2, 3, 2, 3
[1, 3, 1, 1, 3, 2, 3, 3, 1] => 1, 3, 1, 1, 3, 2, 3, 3, 1
[1, 3, 1, 1, 3, 2, 3, 3, 2] => 1, 3, 1, 1, 3, 2, 3, 3, 2
[1, 3, 1, 1, 3, 2, 3, 3, 3] => 1, 3, 1, 1, 3, 2, 3, 3, 3
[1, 3, 1, 1, 3, 3, 1, 1, 1] => 1, 3, 1, 1, 3, 3, 1, 1, 1
[1, 3, 1, 1, 3, 3, 1, 1, 2] => 1, 3, 1, 1, 3, 3, 1, 1, 2
[1, 3, 1, 1, 3, 3, 1, 1, 3] => 1, 3, 1, 1, 3, 3, 1, 1, 3
[1, 3, 1, 1, 3, 3, 1, 2, 1] => 1, 3, 1, 1, 3, 3, 1, 2, 1
[1, 3, 1, 1, 3, 3, 1, 2, 2] => 1, 3, 1, 1, 3, 3, 1, 2, 2
[1, 3, 1, 1, 3, 3, 1, 2, 3] => 1, 3, 1, 1, 3, 3, 1, 2, 3
[1, 3, 1, 1, 3, 3, 1, 3, 1] => 1, 3, 1, 1, 3, 3, 1, 3, 1
[1, 3, 1, 1, 3, 3, 1, 3, 2] => 1, 3, 1, 1, 3, 3, 1, 3, 2
[1, 3, 1, 1, 3, 3, 1, 3, 3] => 1, 3, 1, 1, 3, 3, 1, 3, 3
[1, 3, 1, 1, 3, 3, 2, 1, 1] => 1, 3, 1, 1, 3, 3, 2, 1, 1
[1, 3, 1, 1, 3, 3, 2, 1, 2] => 1, 3, 1, 1, 3, 3, 2, 1, 2
[1, 3, 1, 1, 3, 3, 2, 1, 3] => 1, 3, 1, 1, 3, 3, 2, 1, 3
[1, 3, 1, 1, 3, 3, 2, 2, 1] => 1, 3, 1, 1, 3, 3, 2, 2, 1
[1, 3, 1, 1, 3, 3, 2, 2, 2] => 1, 3, 1, 1, 3, 3, 2, 2, 2
[1, 3, 1, 1, 3, 3, 2, 2, 3] => 1, 3, 1, 1, 3, 3, 2, 2, 3
[1, 3, 1, 1, 3, 3, 2, 3, 1] => 1, 3, 1, 1, 3, 3, 2, 3, 1
[1, 3, 1, 1, 3, 3, 2, 3, 2] => 1, 3, 1, 1, 3, 3, 2, 3, 2
[1, 3, 1, 1, 3, 3, 2, 3, 3] => 1, 3, 1, 1, 3, 3, 2, 3, 3
[1, 3, 1, 1, 3, 3, 3, 1, 1] => 1, 3, 1, 1, 3, 3, 3, 1, 1
[1, 3, 1, 1, 3, 3, 3, 1, 2] => 1, 3, 1, 1, 3, 3, 3, 1, 2
[1, 3, 1, 1, 3, 3, 3, 1, 3] => 1, 3, 1, 1, 3, 3, 3, 1, 3
[1, 3, 1, 1, 3, 3, 3, 2, 1] => 1, 3, 1, 1, 3, 3, 3, 2, 1
[1, 3, 1, 1, 3, 3, 3, 2, 2] => 1, 3, 1, 1, 3, 3, 3, 2, 2
[1, 3, 1, 1, 3, 3, 3, 2, 3] => 1, 3, 1, 1, 3, 3, 3, 2, 3
[1, 3, 1, 1, 3, 3, 3, 3, 1] => 1, 3, 1, 1, 3, 3, 3, 3, 1
[1, 3, 1, 1, 3, 3, 3, 3, 2] => 1, 3, 1, 1, 3, 3, 3, 3, 2
[1, 3, 1, 1, 3, 3, 3, 3, 3] => 1, 3, 1, 1, 3, 3, 3, 3, 3
[1, 3, 1, 2, 1, 1, 1, 1, 1] => 1, 3, 1, 2, 1, 1, 1, 1, 1
[1, 3, 1, 2, 1, 1, 1, 1, 2] => 1, 3, 1, 2, 1, 1, 1, 1, 2
[1, 3, 1, 2, 1, 1, 1, 1, 3] => 1, 3, 1, 2, 1, 1, 1, 1, 3
[1, 3, 1, 2, 1, 1, 1, 2, 1] => 1, 3, 1, 2, 1, 1, 1, 2, 1
[1, 3, 1, 2, 1, 1, 1, 2, 2] => 1, 3, 1, 2, 1, 1, 1, 2, 2
[1, 3, 1, 2, 1, 1, 1, 2, 3] => 1, 3, 1, 2, 1, 1, 1, 2, 3
[1, 3, 1, 2, 1, 1, 1, 3, 1] => 1, 3, 1, 2, 1, 1, 1, 3, 1
[1, 3, 1, 2, 1, 1, 1, 3, 2] => 1, 3, 1, 2, 1, 1, 1, 3, 2
[1, 3, 1, 2, 1, 1, 1, 3, 3] => 1, 3, 1, 2, 1, 1, 1, 3, 3
[1, 3, 1, 2, 1, 1, 2, 1, 1] => 1, 3, 1, 2, 1, 1, 2, 1, 1
[1, 3, 1, 2, 1, 1, 2, 1, 2] => 1, 3, 1, 2, 1, 1, 2, 1, 2
[1, 3, 1, 2, 1, 1, 2, 1, 3] => 1, 3, 1, 2, 1, 1, 2, 1, 3
[1, 3, 1, 2, 1, 1, 2, 2, 1] => 1, 3, 1, 2, 1, 1, 2, 2, 1
[1, 3, 1, 2, 1, 1, 2, 2, 2] => 1, 3, 1, 2, 1, 1, 2, 2, 2
[1, 3, 1, 2, 1, 1, 2, 2, 3] => 1, 3, 1, 2, 1, 1, 2, 2, 3
[1, 3, 1, 2, 1, 1, 2, 3, 1] => 1, 3, 1, 2, 1, 1, 2, 3, 1
[1, 3, 1, 2, 1, 1, 2, 3, 2] => 1, 3, 1, 2, 1, 1, 2, 3, 2
[1, 3, 1, 2, 1, 1, 2, 3, 3] => 1, 3, 1, 2, 1, 1, 2, 3, 3
[1, 3, 1, 2, 1, 1, 3, 1, 1] => 1, 3, 1, 2, 1, 1, 3, 1, 1
[1, 3, 1, 2, 1, 1, 3, 1, 2] => 1, 3, 1, 2, 1, 1, 3, 1, 2
[1, 3, 1, 2, 1, 1, 3, 1, 3] => 1, 3, 1, 2, 1, 1, 3, 1, 3
[1, 3, 1, 2, 1, 1, 3, 2, 1] => 1, 3, 1, 2, 1, 1, 3, 2, 1
[1, 3, 1, 2, 1, 1, 3, 2, 2] => 1, 3, 1, 2, 1, 1, 3, 2, 2
[1, 3, 1, 2, 1, 1, 3, 2, 3] => 1, 3, 1, 2, 1, 1, 3, 2, 3
[1, 3, 1, 2, 1, 1, 3, 3, 1] => 1, 3, 1, 2, 1, 1, 3, 3, 1
[1, 3, 1, 2, 1, 1, 3, 3, 2] => 1, 3, 1, 2, 1, 1, 3, 3, 2
[1, 3, 1, 2, 1, 1, 3, 3, 3] => 1, 3, 1, 2, 1, 1, 3, 3, 3
[1, 3, 1, 2, 1, 2, 1, 1, 1] => 1, 3, 1, 2, 1, 2, 1, 1, 1
[1, 3, 1, 2, 1, 2, 1, 1, 2] => 1, 3, 1, 2, 1, 2, 1, 1, 2
[1, 3, 1, 2, 1, 2, 1, 1, 3] => 1, 3, 1, 2, 1, 2, 1, 1, 3
[1, 3, 1, 2, 1, 2, 1, 2, 1] => 1, 3, 1, 2, 1, 2, 1, 2, 1
[1, 3, 1, 2, 1, 2, 1, 2, 2] => 1, 3, 1, 2, 1, 2, 1, 2, 2
[1, 3, 1, 2, 1, 2, 1, 2, 3] => 1, 3, 1, 2, 1, 2, 1, 2, 3
[1, 3, 1, 2, 1, 2, 1, 3, 1] => 1, 3, 1, 2, 1, 2, 1, 3, 1
[1, 3, 1, 2, 1, 2, 1, 3, 2] => 1, 3, 1, 2, 1, 2, 1, 3, 2
[1, 3, 1, 2, 1, 2, 1, 3, 3] => 1, 3, 1, 2, 1, 2, 1, 3, 3
[1, 3, 1, 2, 1, 2, 2, 1, 1] => 1, 3, 1, 2, 1, 2, 2, 1, 1
[1, 3, 1, 2, 1, 2, 2, 1, 2] => 1, 3, 1, 2, 1, 2, 2, 1, 2
[1, 3, 1, 2, 1, 2, 2, 1, 3] => 1, 3, 1, 2, 1, 2, 2, 1, 3
[1, 3, 1, 2, 1, 2, 2, 2, 1] => 1, 3, 1, 2, 1, 2, 2, 2, 1
[1, 3, 1, 2, 1, 2, 2, 2, 2] => 1, 3, 1, 2, 1, 2, 2, 2, 2
[1, 3, 1, 2, 1, 2, 2, 2, 3] => 1, 3, 1, 2, 1, 2, 2, 2, 3
[1, 3, 1, 2, 1, 2, 2, 3, 1] => 1, 3, 1, 2, 1, 2, 2, 3, 1
[1, 3, 1, 2, 1, 2, 2, 3, 2] => 1, 3, 1, 2, 1, 2, 2, 3, 2
[1, 3, 1, 2, 1, 2, 2, 3, 3] => 1, 3, 1, 2, 1, 2, 2, 3, 3
[1, 3, 1, 2, 1, 2, 3, 1, 1] => 1, 3, 1, 2, 1, 2, 3, 1, 1
[1, 3, 1, 2, 1, 2, 3, 1, 2] => 1, 3, 1, 2, 1, 2, 3, 1, 2
[1, 3, 1, 2, 1, 2, 3, 1, 3] => 1, 3, 1, 2, 1, 2, 3, 1, 3
[1, 3, 1, 2, 1, 2, 3, 2, 1] => 1, 3, 1, 2, 1, 2, 3, 2, 1
[1, 3, 1, 2, 1, 2, 3, 2, 2] => 1, 3, 1, 2, 1, 2, 3, 2, 2
[1, 3, 1, 2, 1, 2, 3, 2, 3] => 1, 3, 1, 2, 1, 2, 3, 2, 3
[1, 3, 1, 2, 1, 2, 3, 3, 1] => 1, 3, 1, 2, 1, 2, 3, 3, 1
[1, 3, 1, 2, 1, 2, 3, 3, 2] => 1, 3, 1, 2, 1, 2, 3, 3, 2
[1, 3, 1, 2, 1, 2, 3, 3, 3] => 1, 3, 1, 2, 1, 2, 3, 3, 3
[1, 3, 1, 2, 1, 3, 1, 1, 1] => 1, 3, 1, 2, 1, 3, 1, 1, 1
[1, 3, 1, 2, 1, 3, 1, 1, 2] => 1, 3, 1, 2, 1, 3, 1, 1, 2
[1, 3, 1, 2, 1, 3, 1, 1, 3] => 1, 3, 1, 2, 1, 3, 1, 1, 3
[1, 3, 1, 2, 1, 3, 1, 2, 1] => 1, 3, 1, 2, 1, 3, 1, 2, 1
[1, 3, 1, 2, 1, 3, 1, 2, 2] => 1, 3, 1, 2, 1, 3, 1, 2, 2
[1, 3, 1, 2, 1, 3, 1, 2, 3] => 1, 3, 1, 2, 1, 3, 1, 2, 3
[1, 3, 1, 2, 1, 3, 1, 3, 1] => 1, 3, 1, 2, 1, 3, 1, 3, 1
[1, 3, 1, 2, 1, 3, 1, 3, 2] => 1, 3, 1, 2, 1, 3, 1, 3, 2
[1, 3, 1, 2, 1, 3, 1, 3, 3] => 1, 3, 1, 2, 1, 3, 1, 3, 3
[1, 3, 1, 2, 1, 3, 2, 1, 1] => 1, 3, 1, 2, 1, 3, 2, 1, 1
[1, 3, 1, 2, 1, 3, 2, 1, 2] => 1, 3, 1, 2, 1, 3, 2, 1, 2
[1, 3, 1, 2, 1, 3, 2, 1, 3] => 1, 3, 1, 2, 1, 3, 2, 1, 3
[1, 3, 1, 2, 1, 3, 2, 2, 1] => 1, 3, 1, 2, 1, 3, 2, 2, 1
[1, 3, 1, 2, 1, 3, 2, 2, 2] => 1, 3, 1, 2, 1, 3, 2, 2, 2
[1, 3, 1, 2, 1, 3, 2, 2, 3] => 1, 3, 1, 2, 1, 3, 2, 2, 3
[1, 3, 1, 2, 1, 3, 2, 3, 1] => 1, 3, 1, 2, 1, 3, 2, 3, 1
[1, 3, 1, 2, 1, 3, 2, 3, 2] => 1, 3, 1, 2, 1, 3, 2, 3, 2
[1, 3, 1, 2, 1, 3, 2, 3, 3] => 1, 3, 1, 2, 1, 3, 2, 3, 3
[1, 3, 1, 2, 1, 3, 3, 1, 1] => 1, 3, 1, 2, 1, 3, 3, 1, 1
[1, 3, 1, 2, 1, 3, 3, 1, 2] => 1, 3, 1, 2, 1, 3, 3, 1, 2
[1, 3, 1, 2, 1, 3, 3, 1, 3] => 1, 3, 1, 2, 1, 3, 3, 1, 3
[1, 3, 1, 2, 1, 3, 3, 2, 1] => 1, 3, 1, 2, 1, 3, 3, 2, 1
[1, 3, 1, 2, 1, 3, 3, 2, 2] => 1, 3, 1, 2, 1, 3, 3, 2, 2
[1, 3, 1, 2, 1, 3, 3, 2, 3] => 1, 3, 1, 2, 1, 3, 3, 2, 3
[1, 3, 1, 2, 1, 3, 3, 3, 1] => 1, 3, 1, 2, 1, 3, 3, 3, 1
[1, 3, 1, 2, 1, 3, 3, 3, 2] => 1, 3, 1, 2, 1, 3, 3, 3, 2
[1, 3, 1, 2, 1, 3, 3, 3, 3] => 1, 3, 1, 2, 1, 3, 3, 3, 3
[1, 3, 1, 2, 2, 1, 1, 1, 1] => 1, 3, 1, 2, 2, 1, 1, 1, 1
[1, 3, 1, 2, 2, 1, 1, 1, 2] => 1, 3, 1, 2, 2, 1, 1, 1, 2
[1, 3, 1, 2, 2, 1, 1, 1, 3] => 1, 3, 1, 2, 2, 1, 1, 1, 3
[1, 3, 1, 2, 2, 1, 1, 2, 1] => 1, 3, 1, 2, 2, 1, 1, 2, 1
[1, 3, 1, 2, 2, 1, 1, 2, 2] => 1, 3, 1, 2, 2, 1, 1, 2, 2
[1, 3, 1, 2, 2, 1, 1, 2, 3] => 1, 3, 1, 2, 2, 1, 1, 2, 3
[1, 3, 1, 2, 2, 1, 1, 3, 1] => 1, 3, 1, 2, 2, 1, 1, 3, 1
[1, 3, 1, 2, 2, 1, 1, 3, 2] => 1, 3, 1, 2, 2, 1, 1, 3, 2
[1, 3, 1, 2, 2, 1, 1, 3, 3] => 1, 3, 1, 2, 2, 1, 1, 3, 3
[1, 3, 1, 2, 2, 1, 2, 1, 1] => 1, 3, 1, 2, 2, 1, 2, 1, 1
[1, 3, 1, 2, 2, 1, 2, 1, 2] => 1, 3, 1, 2, 2, 1, 2, 1, 2
[1, 3, 1, 2, 2, 1, 2, 1, 3] => 1, 3, 1, 2, 2, 1, 2, 1, 3
[1, 3, 1, 2, 2, 1, 2, 2, 1] => 1, 3, 1, 2, 2, 1, 2, 2, 1
[1, 3, 1, 2, 2, 1, 2, 2, 2] => 1, 3, 1, 2, 2, 1, 2, 2, 2
[1, 3, 1, 2, 2, 1, 2, 2, 3] => 1, 3, 1, 2, 2, 1, 2, 2, 3
[1, 3, 1, 2, 2, 1, 2, 3, 1] => 1, 3, 1, 2, 2, 1, 2, 3, 1
[1, 3, 1, 2, 2, 1, 2, 3, 2] => 1, 3, 1, 2, 2, 1, 2, 3, 2
[1, 3, 1, 2, 2, 1, 2, 3, 3] => 1, 3, 1, 2, 2, 1, 2, 3, 3
[1, 3, 1, 2, 2, 1, 3, 1, 1] => 1, 3, 1, 2, 2, 1, 3, 1, 1
[1, 3, 1, 2, 2, 1, 3, 1, 2] => 1, 3, 1, 2, 2, 1, 3, 1, 2
[1, 3, 1, 2, 2, 1, 3, 1, 3] => 1, 3, 1, 2, 2, 1, 3, 1, 3
[1, 3, 1, 2, 2, 1, 3, 2, 1] => 1, 3, 1, 2, 2, 1, 3, 2, 1
[1, 3, 1, 2, 2, 1, 3, 2, 2] => 1, 3, 1, 2, 2, 1, 3, 2, 2
[1, 3, 1, 2, 2, 1, 3, 2, 3] => 1, 3, 1, 2, 2, 1, 3, 2, 3
[1, 3, 1, 2, 2, 1, 3, 3, 1] => 1, 3, 1, 2, 2, 1, 3, 3, 1
[1, 3, 1, 2, 2, 1, 3, 3, 2] => 1, 3, 1, 2, 2, 1, 3, 3, 2
[1, 3, 1, 2, 2, 1, 3, 3, 3] => 1, 3, 1, 2, 2, 1, 3, 3, 3
[1, 3, 1, 2, 2, 2, 1, 1, 1] => 1, 3, 1, 2, 2, 2, 1, 1, 1
[1, 3, 1, 2, 2, 2, 1, 1, 2] => 1, 3, 1, 2, 2, 2, 1, 1, 2
[1, 3, 1, 2, 2, 2, 1, 1, 3] => 1, 3, 1, 2, 2, 2, 1, 1, 3
[1, 3, 1, 2, 2, 2, 1, 2, 1] => 1, 3, 1, 2, 2, 2, 1, 2, 1
[1, 3, 1, 2, 2, 2, 1, 2, 2] => 1, 3, 1, 2, 2, 2, 1, 2, 2
[1, 3, 1, 2, 2, 2, 1, 2, 3] => 1, 3, 1, 2, 2, 2, 1, 2, 3
[1, 3, 1, 2, 2, 2, 1, 3, 1] => 1, 3, 1, 2, 2, 2, 1, 3, 1
[1, 3, 1, 2, 2, 2, 1, 3, 2] => 1, 3, 1, 2, 2, 2, 1, 3, 2
[1, 3, 1, 2, 2, 2, 1, 3, 3] => 1, 3, 1, 2, 2, 2, 1, 3, 3
[1, 3, 1, 2, 2, 2, 2, 1, 1] => 1, 3, 1, 2, 2, 2, 2, 1, 1
[1, 3, 1, 2, 2, 2, 2, 1, 2] => 1, 3, 1, 2, 2, 2, 2, 1, 2
[1, 3, 1, 2, 2, 2, 2, 1, 3] => 1, 3, 1, 2, 2, 2, 2, 1, 3
[1, 3, 1, 2, 2, 2, 2, 2, 1] => 1, 3, 1, 2, 2, 2, 2, 2, 1
[1, 3, 1, 2, 2, 2, 2, 2, 2] => 1, 3, 1, 2, 2, 2, 2, 2, 2
[1, 3, 1, 2, 2, 2, 2, 2, 3] => 1, 3, 1, 2, 2, 2, 2, 2, 3
[1, 3, 1, 2, 2, 2, 2, 3, 1] => 1, 3, 1, 2, 2, 2, 2, 3, 1
[1, 3, 1, 2, 2, 2, 2, 3, 2] => 1, 3, 1, 2, 2, 2, 2, 3, 2
[1, 3, 1, 2, 2, 2, 2, 3, 3] => 1, 3, 1, 2, 2, 2, 2, 3, 3
[1, 3, 1, 2, 2, 2, 3, 1, 1] => 1, 3, 1, 2, 2, 2, 3, 1, 1
[1, 3, 1, 2, 2, 2, 3, 1, 2] => 1, 3, 1, 2, 2, 2, 3, 1, 2
[1, 3, 1, 2, 2, 2, 3, 1, 3] => 1, 3, 1, 2, 2, 2, 3, 1, 3
[1, 3, 1, 2, 2, 2, 3, 2, 1] => 1, 3, 1, 2, 2, 2, 3, 2, 1
[1, 3, 1, 2, 2, 2, 3, 2, 2] => 1, 3, 1, 2, 2, 2, 3, 2, 2
[1, 3, 1, 2, 2, 2, 3, 2, 3] => 1, 3, 1, 2, 2, 2, 3, 2, 3
[1, 3, 1, 2, 2, 2, 3, 3, 1] => 1, 3, 1, 2, 2, 2, 3, 3, 1
[1, 3, 1, 2, 2, 2, 3, 3, 2] => 1, 3, 1, 2, 2, 2, 3, 3, 2
[1, 3, 1, 2, 2, 2, 3, 3, 3] => 1, 3, 1, 2, 2, 2, 3, 3, 3
[1, 3, 1, 2, 2, 3, 1, 1, 1] => 1, 3, 1, 2, 2, 3, 1, 1, 1
[1, 3, 1, 2, 2, 3, 1, 1, 2] => 1, 3, 1, 2, 2, 3, 1, 1, 2
[1, 3, 1, 2, 2, 3, 1, 1, 3] => 1, 3, 1, 2, 2, 3, 1, 1, 3
[1, 3, 1, 2, 2, 3, 1, 2, 1] => 1, 3, 1, 2, 2, 3, 1, 2, 1
[1, 3, 1, 2, 2, 3, 1, 2, 2] => 1, 3, 1, 2, 2, 3, 1, 2, 2
[1, 3, 1, 2, 2, 3, 1, 2, 3] => 1, 3, 1, 2, 2, 3, 1, 2, 3
[1, 3, 1, 2, 2, 3, 1, 3, 1] => 1, 3, 1, 2, 2, 3, 1, 3, 1
[1, 3, 1, 2, 2, 3, 1, 3, 2] => 1, 3, 1, 2, 2, 3, 1, 3, 2
[1, 3, 1, 2, 2, 3, 1, 3, 3] => 1, 3, 1, 2, 2, 3, 1, 3, 3
[1, 3, 1, 2, 2, 3, 2, 1, 1] => 1, 3, 1, 2, 2, 3, 2, 1, 1
[1, 3, 1, 2, 2, 3, 2, 1, 2] => 1, 3, 1, 2, 2, 3, 2, 1, 2
[1, 3, 1, 2, 2, 3, 2, 1, 3] => 1, 3, 1, 2, 2, 3, 2, 1, 3
[1, 3, 1, 2, 2, 3, 2, 2, 1] => 1, 3, 1, 2, 2, 3, 2, 2, 1
[1, 3, 1, 2, 2, 3, 2, 2, 2] => 1, 3, 1, 2, 2, 3, 2, 2, 2
[1, 3, 1, 2, 2, 3, 2, 2, 3] => 1, 3, 1, 2, 2, 3, 2, 2, 3
[1, 3, 1, 2, 2, 3, 2, 3, 1] => 1, 3, 1, 2, 2, 3, 2, 3, 1
[1, 3, 1, 2, 2, 3, 2, 3, 2] => 1, 3, 1, 2, 2, 3, 2, 3, 2
[1, 3, 1, 2, 2, 3, 2, 3, 3] => 1, 3, 1, 2, 2, 3, 2, 3, 3
[1, 3, 1, 2, 2, 3, 3, 1, 1] => 1, 3, 1, 2, 2, 3, 3, 1, 1
[1, 3, 1, 2, 2, 3, 3, 1, 2] => 1, 3, 1, 2, 2, 3, 3, 1, 2
[1, 3, 1, 2, 2, 3, 3, 1, 3] => 1, 3, 1, 2, 2, 3, 3, 1, 3
[1, 3, 1, 2, 2, 3, 3, 2, 1] => 1, 3, 1, 2, 2, 3, 3, 2, 1
[1, 3, 1, 2, 2, 3, 3, 2, 2] => 1, 3, 1, 2, 2, 3, 3, 2, 2
[1, 3, 1, 2, 2, 3, 3, 2, 3] => 1, 3, 1, 2, 2, 3, 3, 2, 3
[1, 3, 1, 2, 2, 3, 3, 3, 1] => 1, 3, 1, 2, 2, 3, 3, 3, 1
[1, 3, 1, 2, 2, 3, 3, 3, 2] => 1, 3, 1, 2, 2, 3, 3, 3, 2
[1, 3, 1, 2, 2, 3, 3, 3, 3] => 1, 3, 1, 2, 2, 3, 3, 3, 3
[1, 3, 1, 2, 3, 1, 1, 1, 1] => 1, 3, 1, 2, 3, 1, 1, 1, 1
[1, 3, 1, 2, 3, 1, 1, 1, 2] => 1, 3, 1, 2, 3, 1, 1, 1, 2
[1, 3, 1, 2, 3, 1, 1, 1, 3] => 1, 3, 1, 2, 3, 1, 1, 1, 3
[1, 3, 1, 2, 3, 1, 1, 2, 1] => 1, 3, 1, 2, 3, 1, 1, 2, 1
[1, 3, 1, 2, 3, 1, 1, 2, 2] => 1, 3, 1, 2, 3, 1, 1, 2, 2
[1, 3, 1, 2, 3, 1, 1, 2, 3] => 1, 3, 1, 2, 3, 1, 1, 2, 3
[1, 3, 1, 2, 3, 1, 1, 3, 1] => 1, 3, 1, 2, 3, 1, 1, 3, 1
[1, 3, 1, 2, 3, 1, 1, 3, 2] => 1, 3, 1, 2, 3, 1, 1, 3, 2
[1, 3, 1, 2, 3, 1, 1, 3, 3] => 1, 3, 1, 2, 3, 1, 1, 3, 3
[1, 3, 1, 2, 3, 1, 2, 1, 1] => 1, 3, 1, 2, 3, 1, 2, 1, 1
[1, 3, 1, 2, 3, 1, 2, 1, 2] => 1, 3, 1, 2, 3, 1, 2, 1, 2
[1, 3, 1, 2, 3, 1, 2, 1, 3] => 1, 3, 1, 2, 3, 1, 2, 1, 3
[1, 3, 1, 2, 3, 1, 2, 2, 1] => 1, 3, 1, 2, 3, 1, 2, 2, 1
[1, 3, 1, 2, 3, 1, 2, 2, 2] => 1, 3, 1, 2, 3, 1, 2, 2, 2
[1, 3, 1, 2, 3, 1, 2, 2, 3] => 1, 3, 1, 2, 3, 1, 2, 2, 3
[1, 3, 1, 2, 3, 1, 2, 3, 1] => 1, 3, 1, 2, 3, 1, 2, 3, 1
[1, 3, 1, 2, 3, 1, 2, 3, 2] => 1, 3, 1, 2, 3, 1, 2, 3, 2
[1, 3, 1, 2, 3, 1, 2, 3, 3] => 1, 3, 1, 2, 3, 1, 2, 3, 3
[1, 3, 1, 2, 3, 1, 3, 1, 1] => 1, 3, 1, 2, 3, 1, 3, 1, 1
[1, 3, 1, 2, 3, 1, 3, 1, 2] => 1, 3, 1, 2, 3, 1, 3, 1, 2
[1, 3, 1, 2, 3, 1, 3, 1, 3] => 1, 3, 1, 2, 3, 1, 3, 1, 3
[1, 3, 1, 2, 3, 1, 3, 2, 1] => 1, 3, 1, 2, 3, 1, 3, 2, 1
[1, 3, 1, 2, 3, 1, 3, 2, 2] => 1, 3, 1, 2, 3, 1, 3, 2, 2
[1, 3, 1, 2, 3, 1, 3, 2, 3] => 1, 3, 1, 2, 3, 1, 3, 2, 3
[1, 3, 1, 2, 3, 1, 3, 3, 1] => 1, 3, 1, 2, 3, 1, 3, 3, 1
[1, 3, 1, 2, 3, 1, 3, 3, 2] => 1, 3, 1, 2, 3, 1, 3, 3, 2
[1, 3, 1, 2, 3, 1, 3, 3, 3] => 1, 3, 1, 2, 3, 1, 3, 3, 3
[1, 3, 1, 2, 3, 2, 1, 1, 1] => 1, 3, 1, 2, 3, 2, 1, 1, 1
[1, 3, 1, 2, 3, 2, 1, 1, 2] => 1, 3, 1, 2, 3, 2, 1, 1, 2
[1, 3, 1, 2, 3, 2, 1, 1, 3] => 1, 3, 1, 2, 3, 2, 1, 1, 3
[1, 3, 1, 2, 3, 2, 1, 2, 1] => 1, 3, 1, 2, 3, 2, 1, 2, 1
[1, 3, 1, 2, 3, 2, 1, 2, 2] => 1, 3, 1, 2, 3, 2, 1, 2, 2
[1, 3, 1, 2, 3, 2, 1, 2, 3] => 1, 3, 1, 2, 3, 2, 1, 2, 3
[1, 3, 1, 2, 3, 2, 1, 3, 1] => 1, 3, 1, 2, 3, 2, 1, 3, 1
[1, 3, 1, 2, 3, 2, 1, 3, 2] => 1, 3, 1, 2, 3, 2, 1, 3, 2
[1, 3, 1, 2, 3, 2, 1, 3, 3] => 1, 3, 1, 2, 3, 2, 1, 3, 3
[1, 3, 1, 2, 3, 2, 2, 1, 1] => 1, 3, 1, 2, 3, 2, 2, 1, 1
[1, 3, 1, 2, 3, 2, 2, 1, 2] => 1, 3, 1, 2, 3, 2, 2, 1, 2
[1, 3, 1, 2, 3, 2, 2, 1, 3] => 1, 3, 1, 2, 3, 2, 2, 1, 3
[1, 3, 1, 2, 3, 2, 2, 2, 1] => 1, 3, 1, 2, 3, 2, 2, 2, 1
[1, 3, 1, 2, 3, 2, 2, 2, 2] => 1, 3, 1, 2, 3, 2, 2, 2, 2
[1, 3, 1, 2, 3, 2, 2, 2, 3] => 1, 3, 1, 2, 3, 2, 2, 2, 3
[1, 3, 1, 2, 3, 2, 2, 3, 1] => 1, 3, 1, 2, 3, 2, 2, 3, 1
[1, 3, 1, 2, 3, 2, 2, 3, 2] => 1, 3, 1, 2, 3, 2, 2, 3, 2
[1, 3, 1, 2, 3, 2, 2, 3, 3] => 1, 3, 1, 2, 3, 2, 2, 3, 3
[1, 3, 1, 2, 3, 2, 3, 1, 1] => 1, 3, 1, 2, 3, 2, 3, 1, 1
[1, 3, 1, 2, 3, 2, 3, 1, 2] => 1, 3, 1, 2, 3, 2, 3, 1, 2
[1, 3, 1, 2, 3, 2, 3, 1, 3] => 1, 3, 1, 2, 3, 2, 3, 1, 3
[1, 3, 1, 2, 3, 2, 3, 2, 1] => 1, 3, 1, 2, 3, 2, 3, 2, 1
[1, 3, 1, 2, 3, 2, 3, 2, 2] => 1, 3, 1, 2, 3, 2, 3, 2, 2
[1, 3, 1, 2, 3, 2, 3, 2, 3] => 1, 3, 1, 2, 3, 2, 3, 2, 3
[1, 3, 1, 2, 3, 2, 3, 3, 1] => 1, 3, 1, 2, 3, 2, 3, 3, 1
[1, 3, 1, 2, 3, 2, 3, 3, 2] => 1, 3, 1, 2, 3, 2, 3, 3, 2
[1, 3, 1, 2, 3, 2, 3, 3, 3] => 1, 3, 1, 2, 3, 2, 3, 3, 3
[1, 3, 1, 2, 3, 3, 1, 1, 1] => 1, 3, 1, 2, 3, 3, 1, 1, 1
[1, 3, 1, 2, 3, 3, 1, 1, 2] => 1, 3, 1, 2, 3, 3, 1, 1, 2
[1, 3, 1, 2, 3, 3, 1, 1, 3] => 1, 3, 1, 2, 3, 3, 1, 1, 3
[1, 3, 1, 2, 3, 3, 1, 2, 1] => 1, 3, 1, 2, 3, 3, 1, 2, 1
[1, 3, 1, 2, 3, 3, 1, 2, 2] => 1, 3, 1, 2, 3, 3, 1, 2, 2
[1, 3, 1, 2, 3, 3, 1, 2, 3] => 1, 3, 1, 2, 3, 3, 1, 2, 3
[1, 3, 1, 2, 3, 3, 1, 3, 1] => 1, 3, 1, 2, 3, 3, 1, 3, 1
[1, 3, 1, 2, 3, 3, 1, 3, 2] => 1, 3, 1, 2, 3, 3, 1, 3, 2
[1, 3, 1, 2, 3, 3, 1, 3, 3] => 1, 3, 1, 2, 3, 3, 1, 3, 3
[1, 3, 1, 2, 3, 3, 2, 1, 1] => 1, 3, 1, 2, 3, 3, 2, 1, 1
[1, 3, 1, 2, 3, 3, 2, 1, 2] => 1, 3, 1, 2, 3, 3, 2, 1, 2
[1, 3, 1, 2, 3, 3, 2, 1, 3] => 1, 3, 1, 2, 3, 3, 2, 1, 3
[1, 3, 1, 2, 3, 3, 2, 2, 1] => 1, 3, 1, 2, 3, 3, 2, 2, 1
[1, 3, 1, 2, 3, 3, 2, 2, 2] => 1, 3, 1, 2, 3, 3, 2, 2, 2
[1, 3, 1, 2, 3, 3, 2, 2, 3] => 1, 3, 1, 2, 3, 3, 2, 2, 3
[1, 3, 1, 2, 3, 3, 2, 3, 1] => 1, 3, 1, 2, 3, 3, 2, 3, 1
[1, 3, 1, 2, 3, 3, 2, 3, 2] => 1, 3, 1, 2, 3, 3, 2, 3, 2
[1, 3, 1, 2, 3, 3, 2, 3, 3] => 1, 3, 1, 2, 3, 3, 2, 3, 3
[1, 3, 1, 2, 3, 3, 3, 1, 1] => 1, 3, 1, 2, 3, 3, 3, 1, 1
[1, 3, 1, 2, 3, 3, 3, 1, 2] => 1, 3, 1, 2, 3, 3, 3, 1, 2
[1, 3, 1, 2, 3, 3, 3, 1, 3] => 1, 3, 1, 2, 3, 3, 3, 1, 3
[1, 3, 1, 2, 3, 3, 3, 2, 1] => 1, 3, 1, 2, 3, 3, 3, 2, 1
[1, 3, 1, 2, 3, 3, 3, 2, 2] => 1, 3, 1, 2, 3, 3, 3, 2, 2
[1, 3, 1, 2, 3, 3, 3, 2, 3] => 1, 3, 1, 2, 3, 3, 3, 2, 3
[1, 3, 1, 2, 3, 3, 3, 3, 1] => 1, 3, 1, 2, 3, 3, 3, 3, 1
[1, 3, 1, 2, 3, 3, 3, 3, 2] => 1, 3, 1, 2, 3, 3, 3, 3, 2
[1, 3, 1, 2, 3, 3, 3, 3, 3] => 1, 3, 1, 2, 3, 3, 3, 3, 3
[1, 3, 1, 3, 1, 1, 1, 1, 1] => 1, 3, 1, 3, 1, 1, 1, 1, 1
[1, 3, 1, 3, 1, 1, 1, 1, 2] => 1, 3, 1, 3, 1, 1, 1, 1, 2
[1, 3, 1, 3, 1, 1, 1, 1, 3] => 1, 3, 1, 3, 1, 1, 1, 1, 3
[1, 3, 1, 3, 1, 1, 1, 2, 1] => 1, 3, 1, 3, 1, 1, 1, 2, 1
[1, 3, 1, 3, 1, 1, 1, 2, 2] => 1, 3, 1, 3, 1, 1, 1, 2, 2
[1, 3, 1, 3, 1, 1, 1, 2, 3] => 1, 3, 1, 3, 1, 1, 1, 2, 3
[1, 3, 1, 3, 1, 1, 1, 3, 1] => 1, 3, 1, 3, 1, 1, 1, 3, 1
[1, 3, 1, 3, 1, 1, 1, 3, 2] => 1, 3, 1, 3, 1, 1, 1, 3, 2
[1, 3, 1, 3, 1, 1, 1, 3, 3] => 1, 3, 1, 3, 1, 1, 1, 3, 3
[1, 3, 1, 3, 1, 1, 2, 1, 1] => 1, 3, 1, 3, 1, 1, 2, 1, 1
[1, 3, 1, 3, 1, 1, 2, 1, 2] => 1, 3, 1, 3, 1, 1, 2, 1, 2
[1, 3, 1, 3, 1, 1, 2, 1, 3] => 1, 3, 1, 3, 1, 1, 2, 1, 3
[1, 3, 1, 3, 1, 1, 2, 2, 1] => 1, 3, 1, 3, 1, 1, 2, 2, 1
[1, 3, 1, 3, 1, 1, 2, 2, 2] => 1, 3, 1, 3, 1, 1, 2, 2, 2
[1, 3, 1, 3, 1, 1, 2, 2, 3] => 1, 3, 1, 3, 1, 1, 2, 2, 3
[1, 3, 1, 3, 1, 1, 2, 3, 1] => 1, 3, 1, 3, 1, 1, 2, 3, 1
[1, 3, 1, 3, 1, 1, 2, 3, 2] => 1, 3, 1, 3, 1, 1, 2, 3, 2
[1, 3, 1, 3, 1, 1, 2, 3, 3] => 1, 3, 1, 3, 1, 1, 2, 3, 3
[1, 3, 1, 3, 1, 1, 3, 1, 1] => 1, 3, 1, 3, 1, 1, 3, 1, 1
[1, 3, 1, 3, 1, 1, 3, 1, 2] => 1, 3, 1, 3, 1, 1, 3, 1, 2
[1, 3, 1, 3, 1, 1, 3, 1, 3] => 1, 3, 1, 3, 1, 1, 3, 1, 3
[1, 3, 1, 3, 1, 1, 3, 2, 1] => 1, 3, 1, 3, 1, 1, 3, 2, 1
[1, 3, 1, 3, 1, 1, 3, 2, 2] => 1, 3, 1, 3, 1, 1, 3, 2, 2
[1, 3, 1, 3, 1, 1, 3, 2, 3] => 1, 3, 1, 3, 1, 1, 3, 2, 3
[1, 3, 1, 3, 1, 1, 3, 3, 1] => 1, 3, 1, 3, 1, 1, 3, 3, 1
[1, 3, 1, 3, 1, 1, 3, 3, 2] => 1, 3, 1, 3, 1, 1, 3, 3, 2
[1, 3, 1, 3, 1, 1, 3, 3, 3] => 1, 3, 1, 3, 1, 1, 3, 3, 3
[1, 3, 1, 3, 1, 2, 1, 1, 1] => 1, 3, 1, 3, 1, 2, 1, 1, 1
[1, 3, 1, 3, 1, 2, 1, 1, 2] => 1, 3, 1, 3, 1, 2, 1, 1, 2
[1, 3, 1, 3, 1, 2, 1, 1, 3] => 1, 3, 1, 3, 1, 2, 1, 1, 3
[1, 3, 1, 3, 1, 2, 1, 2, 1] => 1, 3, 1, 3, 1, 2, 1, 2, 1
[1, 3, 1, 3, 1, 2, 1, 2, 2] => 1, 3, 1, 3, 1, 2, 1, 2, 2
[1, 3, 1, 3, 1, 2, 1, 2, 3] => 1, 3, 1, 3, 1, 2, 1, 2, 3
[1, 3, 1, 3, 1, 2, 1, 3, 1] => 1, 3, 1, 3, 1, 2, 1, 3, 1
[1, 3, 1, 3, 1, 2, 1, 3, 2] => 1, 3, 1, 3, 1, 2, 1, 3, 2
[1, 3, 1, 3, 1, 2, 1, 3, 3] => 1, 3, 1, 3, 1, 2, 1, 3, 3
[1, 3, 1, 3, 1, 2, 2, 1, 1] => 1, 3, 1, 3, 1, 2, 2, 1, 1
[1, 3, 1, 3, 1, 2, 2, 1, 2] => 1, 3, 1, 3, 1, 2, 2, 1, 2
[1, 3, 1, 3, 1, 2, 2, 1, 3] => 1, 3, 1, 3, 1, 2, 2, 1, 3
[1, 3, 1, 3, 1, 2, 2, 2, 1] => 1, 3, 1, 3, 1, 2, 2, 2, 1
[1, 3, 1, 3, 1, 2, 2, 2, 2] => 1, 3, 1, 3, 1, 2, 2, 2, 2
[1, 3, 1, 3, 1, 2, 2, 2, 3] => 1, 3, 1, 3, 1, 2, 2, 2, 3
[1, 3, 1, 3, 1, 2, 2, 3, 1] => 1, 3, 1, 3, 1, 2, 2, 3, 1
[1, 3, 1, 3, 1, 2, 2, 3, 2] => 1, 3, 1, 3, 1, 2, 2, 3, 2
[1, 3, 1, 3, 1, 2, 2, 3, 3] => 1, 3, 1, 3, 1, 2, 2, 3, 3
[1, 3, 1, 3, 1, 2, 3, 1, 1] => 1, 3, 1, 3, 1, 2, 3, 1, 1
[1, 3, 1, 3, 1, 2, 3, 1, 2] => 1, 3, 1, 3, 1, 2, 3, 1, 2
[1, 3, 1, 3, 1, 2, 3, 1, 3] => 1, 3, 1, 3, 1, 2, 3, 1, 3
[1, 3, 1, 3, 1, 2, 3, 2, 1] => 1, 3, 1, 3, 1, 2, 3, 2, 1
[1, 3, 1, 3, 1, 2, 3, 2, 2] => 1, 3, 1, 3, 1, 2, 3, 2, 2
[1, 3, 1, 3, 1, 2, 3, 2, 3] => 1, 3, 1, 3, 1, 2, 3, 2, 3
[1, 3, 1, 3, 1, 2, 3, 3, 1] => 1, 3, 1, 3, 1, 2, 3, 3, 1
[1, 3, 1, 3, 1, 2, 3, 3, 2] => 1, 3, 1, 3, 1, 2, 3, 3, 2
[1, 3, 1, 3, 1, 2, 3, 3, 3] => 1, 3, 1, 3, 1, 2, 3, 3, 3
[1, 3, 1, 3, 1, 3, 1, 1, 1] => 1, 3, 1, 3, 1, 3, 1, 1, 1
[1, 3, 1, 3, 1, 3, 1, 1, 2] => 1, 3, 1, 3, 1, 3, 1, 1, 2
[1, 3, 1, 3, 1, 3, 1, 1, 3] => 1, 3, 1, 3, 1, 3, 1, 1, 3
[1, 3, 1, 3, 1, 3, 1, 2, 1] => 1, 3, 1, 3, 1, 3, 1, 2, 1
[1, 3, 1, 3, 1, 3, 1, 2, 2] => 1, 3, 1, 3, 1, 3, 1, 2, 2
[1, 3, 1, 3, 1, 3, 1, 2, 3] => 1, 3, 1, 3, 1, 3, 1, 2, 3
[1, 3, 1, 3, 1, 3, 1, 3, 1] => 1, 3, 1, 3, 1, 3, 1, 3, 1
[1, 3, 1, 3, 1, 3, 1, 3, 2] => 1, 3, 1, 3, 1, 3, 1, 3, 2
[1, 3, 1, 3, 1, 3, 1, 3, 3] => 1, 3, 1, 3, 1, 3, 1, 3, 3
[1, 3, 1, 3, 1, 3, 2, 1, 1] => 1, 3, 1, 3, 1, 3, 2, 1, 1
[1, 3, 1, 3, 1, 3, 2, 1, 2] => 1, 3, 1, 3, 1, 3, 2, 1, 2
[1, 3, 1, 3, 1, 3, 2, 1, 3] => 1, 3, 1, 3, 1, 3, 2, 1, 3
[1, 3, 1, 3, 1, 3, 2, 2, 1] => 1, 3, 1, 3, 1, 3, 2, 2, 1
[1, 3, 1, 3, 1, 3, 2, 2, 2] => 1, 3, 1, 3, 1, 3, 2, 2, 2
[1, 3, 1, 3, 1, 3, 2, 2, 3] => 1, 3, 1, 3, 1, 3, 2, 2, 3
[1, 3, 1, 3, 1, 3, 2, 3, 1] => 1, 3, 1, 3, 1, 3, 2, 3, 1
[1, 3, 1, 3, 1, 3, 2, 3, 2] => 1, 3, 1, 3, 1, 3, 2, 3, 2
[1, 3, 1, 3, 1, 3, 2, 3, 3] => 1, 3, 1, 3, 1, 3, 2, 3, 3
[1, 3, 1, 3, 1, 3, 3, 1, 1] => 1, 3, 1, 3, 1, 3, 3, 1, 1
[1, 3, 1, 3, 1, 3, 3, 1, 2] => 1, 3, 1, 3, 1, 3, 3, 1, 2
[1, 3, 1, 3, 1, 3, 3, 1, 3] => 1, 3, 1, 3, 1, 3, 3, 1, 3
[1, 3, 1, 3, 1, 3, 3, 2, 1] => 1, 3, 1, 3, 1, 3, 3, 2, 1
[1, 3, 1, 3, 1, 3, 3, 2, 2] => 1, 3, 1, 3, 1, 3, 3, 2, 2
[1, 3, 1, 3, 1, 3, 3, 2, 3] => 1, 3, 1, 3, 1, 3, 3, 2, 3
[1, 3, 1, 3, 1, 3, 3, 3, 1] => 1, 3, 1, 3, 1, 3, 3, 3, 1
[1, 3, 1, 3, 1, 3, 3, 3, 2] => 1, 3, 1, 3, 1, 3, 3, 3, 2
[1, 3, 1, 3, 1, 3, 3, 3, 3] => 1, 3, 1, 3, 1, 3, 3, 3, 3
[1, 3, 1, 3, 2, 1, 1, 1, 1] => 1, 3, 1, 3, 2, 1, 1, 1, 1
[1, 3, 1, 3, 2, 1, 1, 1, 2] => 1, 3, 1, 3, 2, 1, 1, 1, 2
[1, 3, 1, 3, 2, 1, 1, 1, 3] => 1, 3, 1, 3, 2, 1, 1, 1, 3
[1, 3, 1, 3, 2, 1, 1, 2, 1] => 1, 3, 1, 3, 2, 1, 1, 2, 1
[1, 3, 1, 3, 2, 1, 1, 2, 2] => 1, 3, 1, 3, 2, 1, 1, 2, 2
[1, 3, 1, 3, 2, 1, 1, 2, 3] => 1, 3, 1, 3, 2, 1, 1, 2, 3
[1, 3, 1, 3, 2, 1, 1, 3, 1] => 1, 3, 1, 3, 2, 1, 1, 3, 1
[1, 3, 1, 3, 2, 1, 1, 3, 2] => 1, 3, 1, 3, 2, 1, 1, 3, 2
[1, 3, 1, 3, 2, 1, 1, 3, 3] => 1, 3, 1, 3, 2, 1, 1, 3, 3
[1, 3, 1, 3, 2, 1, 2, 1, 1] => 1, 3, 1, 3, 2, 1, 2, 1, 1
[1, 3, 1, 3, 2, 1, 2, 1, 2] => 1, 3, 1, 3, 2, 1, 2, 1, 2
[1, 3, 1, 3, 2, 1, 2, 1, 3] => 1, 3, 1, 3, 2, 1, 2, 1, 3
[1, 3, 1, 3, 2, 1, 2, 2, 1] => 1, 3, 1, 3, 2, 1, 2, 2, 1
[1, 3, 1, 3, 2, 1, 2, 2, 2] => 1, 3, 1, 3, 2, 1, 2, 2, 2
[1, 3, 1, 3, 2, 1, 2, 2, 3] => 1, 3, 1, 3, 2, 1, 2, 2, 3
[1, 3, 1, 3, 2, 1, 2, 3, 1] => 1, 3, 1, 3, 2, 1, 2, 3, 1
[1, 3, 1, 3, 2, 1, 2, 3, 2] => 1, 3, 1, 3, 2, 1, 2, 3, 2
[1, 3, 1, 3, 2, 1, 2, 3, 3] => 1, 3, 1, 3, 2, 1, 2, 3, 3
[1, 3, 1, 3, 2, 1, 3, 1, 1] => 1, 3, 1, 3, 2, 1, 3, 1, 1
[1, 3, 1, 3, 2, 1, 3, 1, 2] => 1, 3, 1, 3, 2, 1, 3, 1, 2
[1, 3, 1, 3, 2, 1, 3, 1, 3] => 1, 3, 1, 3, 2, 1, 3, 1, 3
[1, 3, 1, 3, 2, 1, 3, 2, 1] => 1, 3, 1, 3, 2, 1, 3, 2, 1
[1, 3, 1, 3, 2, 1, 3, 2, 2] => 1, 3, 1, 3, 2, 1, 3, 2, 2
[1, 3, 1, 3, 2, 1, 3, 2, 3] => 1, 3, 1, 3, 2, 1, 3, 2, 3
[1, 3, 1, 3, 2, 1, 3, 3, 1] => 1, 3, 1, 3, 2, 1, 3, 3, 1
[1, 3, 1, 3, 2, 1, 3, 3, 2] => 1, 3, 1, 3, 2, 1, 3, 3, 2
[1, 3, 1, 3, 2, 1, 3, 3, 3] => 1, 3, 1, 3, 2, 1, 3, 3, 3
[1, 3, 1, 3, 2, 2, 1, 1, 1] => 1, 3, 1, 3, 2, 2, 1, 1, 1
[1, 3, 1, 3, 2, 2, 1, 1, 2] => 1, 3, 1, 3, 2, 2, 1, 1, 2
[1, 3, 1, 3, 2, 2, 1, 1, 3] => 1, 3, 1, 3, 2, 2, 1, 1, 3
[1, 3, 1, 3, 2, 2, 1, 2, 1] => 1, 3, 1, 3, 2, 2, 1, 2, 1
[1, 3, 1, 3, 2, 2, 1, 2, 2] => 1, 3, 1, 3, 2, 2, 1, 2, 2
[1, 3, 1, 3, 2, 2, 1, 2, 3] => 1, 3, 1, 3, 2, 2, 1, 2, 3
[1, 3, 1, 3, 2, 2, 1, 3, 1] => 1, 3, 1, 3, 2, 2, 1, 3, 1
[1, 3, 1, 3, 2, 2, 1, 3, 2] => 1, 3, 1, 3, 2, 2, 1, 3, 2
[1, 3, 1, 3, 2, 2, 1, 3, 3] => 1, 3, 1, 3, 2, 2, 1, 3, 3
[1, 3, 1, 3, 2, 2, 2, 1, 1] => 1, 3, 1, 3, 2, 2, 2, 1, 1
[1, 3, 1, 3, 2, 2, 2, 1, 2] => 1, 3, 1, 3, 2, 2, 2, 1, 2
[1, 3, 1, 3, 2, 2, 2, 1, 3] => 1, 3, 1, 3, 2, 2, 2, 1, 3
[1, 3, 1, 3, 2, 2, 2, 2, 1] => 1, 3, 1, 3, 2, 2, 2, 2, 1
[1, 3, 1, 3, 2, 2, 2, 2, 2] => 1, 3, 1, 3, 2, 2, 2, 2, 2
[1, 3, 1, 3, 2, 2, 2, 2, 3] => 1, 3, 1, 3, 2, 2, 2, 2, 3
[1, 3, 1, 3, 2, 2, 2, 3, 1] => 1, 3, 1, 3, 2, 2, 2, 3, 1
[1, 3, 1, 3, 2, 2, 2, 3, 2] => 1, 3, 1, 3, 2, 2, 2, 3, 2
[1, 3, 1, 3, 2, 2, 2, 3, 3] => 1, 3, 1, 3, 2, 2, 2, 3, 3
[1, 3, 1, 3, 2, 2, 3, 1, 1] => 1, 3, 1, 3, 2, 2, 3, 1, 1
[1, 3, 1, 3, 2, 2, 3, 1, 2] => 1, 3, 1, 3, 2, 2, 3, 1, 2
[1, 3, 1, 3, 2, 2, 3, 1, 3] => 1, 3, 1, 3, 2, 2, 3, 1, 3
[1, 3, 1, 3, 2, 2, 3, 2, 1] => 1, 3, 1, 3, 2, 2, 3, 2, 1
[1, 3, 1, 3, 2, 2, 3, 2, 2] => 1, 3, 1, 3, 2, 2, 3, 2, 2
[1, 3, 1, 3, 2, 2, 3, 2, 3] => 1, 3, 1, 3, 2, 2, 3, 2, 3
[1, 3, 1, 3, 2, 2, 3, 3, 1] => 1, 3, 1, 3, 2, 2, 3, 3, 1
[1, 3, 1, 3, 2, 2, 3, 3, 2] => 1, 3, 1, 3, 2, 2, 3, 3, 2
[1, 3, 1, 3, 2, 2, 3, 3, 3] => 1, 3, 1, 3, 2, 2, 3, 3, 3
[1, 3, 1, 3, 2, 3, 1, 1, 1] => 1, 3, 1, 3, 2, 3, 1, 1, 1
[1, 3, 1, 3, 2, 3, 1, 1, 2] => 1, 3, 1, 3, 2, 3, 1, 1, 2
[1, 3, 1, 3, 2, 3, 1, 1, 3] => 1, 3, 1, 3, 2, 3, 1, 1, 3
[1, 3, 1, 3, 2, 3, 1, 2, 1] => 1, 3, 1, 3, 2, 3, 1, 2, 1
[1, 3, 1, 3, 2, 3, 1, 2, 2] => 1, 3, 1, 3, 2, 3, 1, 2, 2
[1, 3, 1, 3, 2, 3, 1, 2, 3] => 1, 3, 1, 3, 2, 3, 1, 2, 3
[1, 3, 1, 3, 2, 3, 1, 3, 1] => 1, 3, 1, 3, 2, 3, 1, 3, 1
[1, 3, 1, 3, 2, 3, 1, 3, 2] => 1, 3, 1, 3, 2, 3, 1, 3, 2
[1, 3, 1, 3, 2, 3, 1, 3, 3] => 1, 3, 1, 3, 2, 3, 1, 3, 3
[1, 3, 1, 3, 2, 3, 2, 1, 1] => 1, 3, 1, 3, 2, 3, 2, 1, 1
[1, 3, 1, 3, 2, 3, 2, 1, 2] => 1, 3, 1, 3, 2, 3, 2, 1, 2
[1, 3, 1, 3, 2, 3, 2, 1, 3] => 1, 3, 1, 3, 2, 3, 2, 1, 3
[1, 3, 1, 3, 2, 3, 2, 2, 1] => 1, 3, 1, 3, 2, 3, 2, 2, 1
[1, 3, 1, 3, 2, 3, 2, 2, 2] => 1, 3, 1, 3, 2, 3, 2, 2, 2
[1, 3, 1, 3, 2, 3, 2, 2, 3] => 1, 3, 1, 3, 2, 3, 2, 2, 3
[1, 3, 1, 3, 2, 3, 2, 3, 1] => 1, 3, 1, 3, 2, 3, 2, 3, 1
[1, 3, 1, 3, 2, 3, 2, 3, 2] => 1, 3, 1, 3, 2, 3, 2, 3, 2
[1, 3, 1, 3, 2, 3, 2, 3, 3] => 1, 3, 1, 3, 2, 3, 2, 3, 3
[1, 3, 1, 3, 2, 3, 3, 1, 1] => 1, 3, 1, 3, 2, 3, 3, 1, 1
[1, 3, 1, 3, 2, 3, 3, 1, 2] => 1, 3, 1, 3, 2, 3, 3, 1, 2
[1, 3, 1, 3, 2, 3, 3, 1, 3] => 1, 3, 1, 3, 2, 3, 3, 1, 3
[1, 3, 1, 3, 2, 3, 3, 2, 1] => 1, 3, 1, 3, 2, 3, 3, 2, 1
[1, 3, 1, 3, 2, 3, 3, 2, 2] => 1, 3, 1, 3, 2, 3, 3, 2, 2
[1, 3, 1, 3, 2, 3, 3, 2, 3] => 1, 3, 1, 3, 2, 3, 3, 2, 3
[1, 3, 1, 3, 2, 3, 3, 3, 1] => 1, 3, 1, 3, 2, 3, 3, 3, 1
[1, 3, 1, 3, 2, 3, 3, 3, 2] => 1, 3, 1, 3, 2, 3, 3, 3, 2
[1, 3, 1, 3, 2, 3, 3, 3, 3] => 1, 3, 1, 3, 2, 3, 3, 3, 3
[1, 3, 1, 3, 3, 1, 1, 1, 1] => 1, 3, 1, 3, 3, 1, 1, 1, 1
[1, 3, 1, 3, 3, 1, 1, 1, 2] => 1, 3, 1, 3, 3, 1, 1, 1, 2
[1, 3, 1, 3, 3, 1, 1, 1, 3] => 1, 3, 1, 3, 3, 1, 1, 1, 3
[1, 3, 1, 3, 3, 1, 1, 2, 1] => 1, 3, 1, 3, 3, 1, 1, 2, 1
[1, 3, 1, 3, 3, 1, 1, 2, 2] => 1, 3, 1, 3, 3, 1, 1, 2, 2
[1, 3, 1, 3, 3, 1, 1, 2, 3] => 1, 3, 1, 3, 3, 1, 1, 2, 3
[1, 3, 1, 3, 3, 1, 1, 3, 1] => 1, 3, 1, 3, 3, 1, 1, 3, 1
[1, 3, 1, 3, 3, 1, 1, 3, 2] => 1, 3, 1, 3, 3, 1, 1, 3, 2
[1, 3, 1, 3, 3, 1, 1, 3, 3] => 1, 3, 1, 3, 3, 1, 1, 3, 3
[1, 3, 1, 3, 3, 1, 2, 1, 1] => 1, 3, 1, 3, 3, 1, 2, 1, 1
[1, 3, 1, 3, 3, 1, 2, 1, 2] => 1, 3, 1, 3, 3, 1, 2, 1, 2
[1, 3, 1, 3, 3, 1, 2, 1, 3] => 1, 3, 1, 3, 3, 1, 2, 1, 3
[1, 3, 1, 3, 3, 1, 2, 2, 1] => 1, 3, 1, 3, 3, 1, 2, 2, 1
[1, 3, 1, 3, 3, 1, 2, 2, 2] => 1, 3, 1, 3, 3, 1, 2, 2, 2
[1, 3, 1, 3, 3, 1, 2, 2, 3] => 1, 3, 1, 3, 3, 1, 2, 2, 3
[1, 3, 1, 3, 3, 1, 2, 3, 1] => 1, 3, 1, 3, 3, 1, 2, 3, 1
[1, 3, 1, 3, 3, 1, 2, 3, 2] => 1, 3, 1, 3, 3, 1, 2, 3, 2
[1, 3, 1, 3, 3, 1, 2, 3, 3] => 1, 3, 1, 3, 3, 1, 2, 3, 3
[1, 3, 1, 3, 3, 1, 3, 1, 1] => 1, 3, 1, 3, 3, 1, 3, 1, 1
[1, 3, 1, 3, 3, 1, 3, 1, 2] => 1, 3, 1, 3, 3, 1, 3, 1, 2
[1, 3, 1, 3, 3, 1, 3, 1, 3] => 1, 3, 1, 3, 3, 1, 3, 1, 3
[1, 3, 1, 3, 3, 1, 3, 2, 1] => 1, 3, 1, 3, 3, 1, 3, 2, 1
[1, 3, 1, 3, 3, 1, 3, 2, 2] => 1, 3, 1, 3, 3, 1, 3, 2, 2
[1, 3, 1, 3, 3, 1, 3, 2, 3] => 1, 3, 1, 3, 3, 1, 3, 2, 3
[1, 3, 1, 3, 3, 1, 3, 3, 1] => 1, 3, 1, 3, 3, 1, 3, 3, 1
[1, 3, 1, 3, 3, 1, 3, 3, 2] => 1, 3, 1, 3, 3, 1, 3, 3, 2
[1, 3, 1, 3, 3, 1, 3, 3, 3] => 1, 3, 1, 3, 3, 1, 3, 3, 3
[1, 3, 1, 3, 3, 2, 1, 1, 1] => 1, 3, 1, 3, 3, 2, 1, 1, 1
[1, 3, 1, 3, 3, 2, 1, 1, 2] => 1, 3, 1, 3, 3, 2, 1, 1, 2
[1, 3, 1, 3, 3, 2, 1, 1, 3] => 1, 3, 1, 3, 3, 2, 1, 1, 3
[1, 3, 1, 3, 3, 2, 1, 2, 1] => 1, 3, 1, 3, 3, 2, 1, 2, 1
[1, 3, 1, 3, 3, 2, 1, 2, 2] => 1, 3, 1, 3, 3, 2, 1, 2, 2
[1, 3, 1, 3, 3, 2, 1, 2, 3] => 1, 3, 1, 3, 3, 2, 1, 2, 3
[1, 3, 1, 3, 3, 2, 1, 3, 1] => 1, 3, 1, 3, 3, 2, 1, 3, 1
[1, 3, 1, 3, 3, 2, 1, 3, 2] => 1, 3, 1, 3, 3, 2, 1, 3, 2
[1, 3, 1, 3, 3, 2, 1, 3, 3] => 1, 3, 1, 3, 3, 2, 1, 3, 3
[1, 3, 1, 3, 3, 2, 2, 1, 1] => 1, 3, 1, 3, 3, 2, 2, 1, 1
[1, 3, 1, 3, 3, 2, 2, 1, 2] => 1, 3, 1, 3, 3, 2, 2, 1, 2
[1, 3, 1, 3, 3, 2, 2, 1, 3] => 1, 3, 1, 3, 3, 2, 2, 1, 3
[1, 3, 1, 3, 3, 2, 2, 2, 1] => 1, 3, 1, 3, 3, 2, 2, 2, 1
[1, 3, 1, 3, 3, 2, 2, 2, 2] => 1, 3, 1, 3, 3, 2, 2, 2, 2
[1, 3, 1, 3, 3, 2, 2, 2, 3] => 1, 3, 1, 3, 3, 2, 2, 2, 3
[1, 3, 1, 3, 3, 2, 2, 3, 1] => 1, 3, 1, 3, 3, 2, 2, 3, 1
[1, 3, 1, 3, 3, 2, 2, 3, 2] => 1, 3, 1, 3, 3, 2, 2, 3, 2
[1, 3, 1, 3, 3, 2, 2, 3, 3] => 1, 3, 1, 3, 3, 2, 2, 3, 3
[1, 3, 1, 3, 3, 2, 3, 1, 1] => 1, 3, 1, 3, 3, 2, 3, 1, 1
[1, 3, 1, 3, 3, 2, 3, 1, 2] => 1, 3, 1, 3, 3, 2, 3, 1, 2
[1, 3, 1, 3, 3, 2, 3, 1, 3] => 1, 3, 1, 3, 3, 2, 3, 1, 3
[1, 3, 1, 3, 3, 2, 3, 2, 1] => 1, 3, 1, 3, 3, 2, 3, 2, 1
[1, 3, 1, 3, 3, 2, 3, 2, 2] => 1, 3, 1, 3, 3, 2, 3, 2, 2
[1, 3, 1, 3, 3, 2, 3, 2, 3] => 1, 3, 1, 3, 3, 2, 3, 2, 3
[1, 3, 1, 3, 3, 2, 3, 3, 1] => 1, 3, 1, 3, 3, 2, 3, 3, 1
[1, 3, 1, 3, 3, 2, 3, 3, 2] => 1, 3, 1, 3, 3, 2, 3, 3, 2
[1, 3, 1, 3, 3, 2, 3, 3, 3] => 1, 3, 1, 3, 3, 2, 3, 3, 3
[1, 3, 1, 3, 3, 3, 1, 1, 1] => 1, 3, 1, 3, 3, 3, 1, 1, 1
[1, 3, 1, 3, 3, 3, 1, 1, 2] => 1, 3, 1, 3, 3, 3, 1, 1, 2
[1, 3, 1, 3, 3, 3, 1, 1, 3] => 1, 3, 1, 3, 3, 3, 1, 1, 3
[1, 3, 1, 3, 3, 3, 1, 2, 1] => 1, 3, 1, 3, 3, 3, 1, 2, 1
[1, 3, 1, 3, 3, 3, 1, 2, 2] => 1, 3, 1, 3, 3, 3, 1, 2, 2
[1, 3, 1, 3, 3, 3, 1, 2, 3] => 1, 3, 1, 3, 3, 3, 1, 2, 3
[1, 3, 1, 3, 3, 3, 1, 3, 1] => 1, 3, 1, 3, 3, 3, 1, 3, 1
[1, 3, 1, 3, 3, 3, 1, 3, 2] => 1, 3, 1, 3, 3, 3, 1, 3, 2
[1, 3, 1, 3, 3, 3, 1, 3, 3] => 1, 3, 1, 3, 3, 3, 1, 3, 3
[1, 3, 1, 3, 3, 3, 2, 1, 1] => 1, 3, 1, 3, 3, 3, 2, 1, 1
[1, 3, 1, 3, 3, 3, 2, 1, 2] => 1, 3, 1, 3, 3, 3, 2, 1, 2
[1, 3, 1, 3, 3, 3, 2, 1, 3] => 1, 3, 1, 3, 3, 3, 2, 1, 3
[1, 3, 1, 3, 3, 3, 2, 2, 1] => 1, 3, 1, 3, 3, 3, 2, 2, 1
[1, 3, 1, 3, 3, 3, 2, 2, 2] => 1, 3, 1, 3, 3, 3, 2, 2, 2
[1, 3, 1, 3, 3, 3, 2, 2, 3] => 1, 3, 1, 3, 3, 3, 2, 2, 3
[1, 3, 1, 3, 3, 3, 2, 3, 1] => 1, 3, 1, 3, 3, 3, 2, 3, 1
[1, 3, 1, 3, 3, 3, 2, 3, 2] => 1, 3, 1, 3, 3, 3, 2, 3, 2
[1, 3, 1, 3, 3, 3, 2, 3, 3] => 1, 3, 1, 3, 3, 3, 2, 3, 3
[1, 3, 1, 3, 3, 3, 3, 1, 1] => 1, 3, 1, 3, 3, 3, 3, 1, 1
[1, 3, 1, 3, 3, 3, 3, 1, 2] => 1, 3, 1, 3, 3, 3, 3, 1, 2
[1, 3, 1, 3, 3, 3, 3, 1, 3] => 1, 3, 1, 3, 3, 3, 3, 1, 3
[1, 3, 1, 3, 3, 3, 3, 2, 1] => 1, 3, 1, 3, 3, 3, 3, 2, 1
[1, 3, 1, 3, 3, 3, 3, 2, 2] => 1, 3, 1, 3, 3, 3, 3, 2, 2
[1, 3, 1, 3, 3, 3, 3, 2, 3] => 1, 3, 1, 3, 3, 3, 3, 2, 3
[1, 3, 1, 3, 3, 3, 3, 3, 1] => 1, 3, 1, 3, 3, 3, 3, 3, 1
[1, 3, 1, 3, 3, 3, 3, 3, 2] => 1, 3, 1, 3, 3, 3, 3, 3, 2
[1, 3, 1, 3, 3, 3, 3, 3, 3] => 1, 3, 1, 3, 3, 3, 3, 3, 3
[1, 3, 2, 1, 1, 1, 1, 1, 1] => 1, 3, 2, 1, 1, 1, 1, 1, 1
[1, 3, 2, 1, 1, 1, 1, 1, 2] => 1, 3, 2, 1, 1, 1, 1, 1, 2
[1, 3, 2, 1, 1, 1, 1, 1, 3] => 1, 3, 2, 1, 1, 1, 1, 1, 3
[1, 3, 2, 1, 1, 1, 1, 2, 1] => 1, 3, 2, 1, 1, 1, 1, 2, 1
[1, 3, 2, 1, 1, 1, 1, 2, 2] => 1, 3, 2, 1, 1, 1, 1, 2, 2
[1, 3, 2, 1, 1, 1, 1, 2, 3] => 1, 3, 2, 1, 1, 1, 1, 2, 3
[1, 3, 2, 1, 1, 1, 1, 3, 1] => 1, 3, 2, 1, 1, 1, 1, 3, 1
[1, 3, 2, 1, 1, 1, 1, 3, 2] => 1, 3, 2, 1, 1, 1, 1, 3, 2
[1, 3, 2, 1, 1, 1, 1, 3, 3] => 1, 3, 2, 1, 1, 1, 1, 3, 3
[1, 3, 2, 1, 1, 1, 2, 1, 1] => 1, 3, 2, 1, 1, 1, 2, 1, 1
[1, 3, 2, 1, 1, 1, 2, 1, 2] => 1, 3, 2, 1, 1, 1, 2, 1, 2
[1, 3, 2, 1, 1, 1, 2, 1, 3] => 1, 3, 2, 1, 1, 1, 2, 1, 3
[1, 3, 2, 1, 1, 1, 2, 2, 1] => 1, 3, 2, 1, 1, 1, 2, 2, 1
[1, 3, 2, 1, 1, 1, 2, 2, 2] => 1, 3, 2, 1, 1, 1, 2, 2, 2
[1, 3, 2, 1, 1, 1, 2, 2, 3] => 1, 3, 2, 1, 1, 1, 2, 2, 3
[1, 3, 2, 1, 1, 1, 2, 3, 1] => 1, 3, 2, 1, 1, 1, 2, 3, 1
[1, 3, 2, 1, 1, 1, 2, 3, 2] => 1, 3, 2, 1, 1, 1, 2, 3, 2
[1, 3, 2, 1, 1, 1, 2, 3, 3] => 1, 3, 2, 1, 1, 1, 2, 3, 3
[1, 3, 2, 1, 1, 1, 3, 1, 1] => 1, 3, 2, 1, 1, 1, 3, 1, 1
[1, 3, 2, 1, 1, 1, 3, 1, 2] => 1, 3, 2, 1, 1, 1, 3, 1, 2
[1, 3, 2, 1, 1, 1, 3, 1, 3] => 1, 3, 2, 1, 1, 1, 3, 1, 3
[1, 3, 2, 1, 1, 1, 3, 2, 1] => 1, 3, 2, 1, 1, 1, 3, 2, 1
[1, 3, 2, 1, 1, 1, 3, 2, 2] => 1, 3, 2, 1, 1, 1, 3, 2, 2
[1, 3, 2, 1, 1, 1, 3, 2, 3] => 1, 3, 2, 1, 1, 1, 3, 2, 3
[1, 3, 2, 1, 1, 1, 3, 3, 1] => 1, 3, 2, 1, 1, 1, 3, 3, 1
[1, 3, 2, 1, 1, 1, 3, 3, 2] => 1, 3, 2, 1, 1, 1, 3, 3, 2
[1, 3, 2, 1, 1, 1, 3, 3, 3] => 1, 3, 2, 1, 1, 1, 3, 3, 3
[1, 3, 2, 1, 1, 2, 1, 1, 1] => 1, 3, 2, 1, 1, 2, 1, 1, 1
[1, 3, 2, 1, 1, 2, 1, 1, 2] => 1, 3, 2, 1, 1, 2, 1, 1, 2
[1, 3, 2, 1, 1, 2, 1, 1, 3] => 1, 3, 2, 1, 1, 2, 1, 1, 3
[1, 3, 2, 1, 1, 2, 1, 2, 1] => 1, 3, 2, 1, 1, 2, 1, 2, 1
[1, 3, 2, 1, 1, 2, 1, 2, 2] => 1, 3, 2, 1, 1, 2, 1, 2, 2
[1, 3, 2, 1, 1, 2, 1, 2, 3] => 1, 3, 2, 1, 1, 2, 1, 2, 3
[1, 3, 2, 1, 1, 2, 1, 3, 1] => 1, 3, 2, 1, 1, 2, 1, 3, 1
[1, 3, 2, 1, 1, 2, 1, 3, 2] => 1, 3, 2, 1, 1, 2, 1, 3, 2
[1, 3, 2, 1, 1, 2, 1, 3, 3] => 1, 3, 2, 1, 1, 2, 1, 3, 3
[1, 3, 2, 1, 1, 2, 2, 1, 1] => 1, 3, 2, 1, 1, 2, 2, 1, 1
[1, 3, 2, 1, 1, 2, 2, 1, 2] => 1, 3, 2, 1, 1, 2, 2, 1, 2
[1, 3, 2, 1, 1, 2, 2, 1, 3] => 1, 3, 2, 1, 1, 2, 2, 1, 3
[1, 3, 2, 1, 1, 2, 2, 2, 1] => 1, 3, 2, 1, 1, 2, 2, 2, 1
[1, 3, 2, 1, 1, 2, 2, 2, 2] => 1, 3, 2, 1, 1, 2, 2, 2, 2
[1, 3, 2, 1, 1, 2, 2, 2, 3] => 1, 3, 2, 1, 1, 2, 2, 2, 3
[1, 3, 2, 1, 1, 2, 2, 3, 1] => 1, 3, 2, 1, 1, 2, 2, 3, 1
[1, 3, 2, 1, 1, 2, 2, 3, 2] => 1, 3, 2, 1, 1, 2, 2, 3, 2
[1, 3, 2, 1, 1, 2, 2, 3, 3] => 1, 3, 2, 1, 1, 2, 2, 3, 3
[1, 3, 2, 1, 1, 2, 3, 1, 1] => 1, 3, 2, 1, 1, 2, 3, 1, 1
[1, 3, 2, 1, 1, 2, 3, 1, 2] => 1, 3, 2, 1, 1, 2, 3, 1, 2
[1, 3, 2, 1, 1, 2, 3, 1, 3] => 1, 3, 2, 1, 1, 2, 3, 1, 3
[1, 3, 2, 1, 1, 2, 3, 2, 1] => 1, 3, 2, 1, 1, 2, 3, 2, 1
[1, 3, 2, 1, 1, 2, 3, 2, 2] => 1, 3, 2, 1, 1, 2, 3, 2, 2
[1, 3, 2, 1, 1, 2, 3, 2, 3] => 1, 3, 2, 1, 1, 2, 3, 2, 3
[1, 3, 2, 1, 1, 2, 3, 3, 1] => 1, 3, 2, 1, 1, 2, 3, 3, 1
[1, 3, 2, 1, 1, 2, 3, 3, 2] => 1, 3, 2, 1, 1, 2, 3, 3, 2
[1, 3, 2, 1, 1, 2, 3, 3, 3] => 1, 3, 2, 1, 1, 2, 3, 3, 3
[1, 3, 2, 1, 1, 3, 1, 1, 1] => 1, 3, 2, 1, 1, 3, 1, 1, 1
[1, 3, 2, 1, 1, 3, 1, 1, 2] => 1, 3, 2, 1, 1, 3, 1, 1, 2
[1, 3, 2, 1, 1, 3, 1, 1, 3] => 1, 3, 2, 1, 1, 3, 1, 1, 3
[1, 3, 2, 1, 1, 3, 1, 2, 1] => 1, 3, 2, 1, 1, 3, 1, 2, 1
[1, 3, 2, 1, 1, 3, 1, 2, 2] => 1, 3, 2, 1, 1, 3, 1, 2, 2
[1, 3, 2, 1, 1, 3, 1, 2, 3] => 1, 3, 2, 1, 1, 3, 1, 2, 3
[1, 3, 2, 1, 1, 3, 1, 3, 1] => 1, 3, 2, 1, 1, 3, 1, 3, 1
[1, 3, 2, 1, 1, 3, 1, 3, 2] => 1, 3, 2, 1, 1, 3, 1, 3, 2
[1, 3, 2, 1, 1, 3, 1, 3, 3] => 1, 3, 2, 1, 1, 3, 1, 3, 3
[1, 3, 2, 1, 1, 3, 2, 1, 1] => 1, 3, 2, 1, 1, 3, 2, 1, 1
[1, 3, 2, 1, 1, 3, 2, 1, 2] => 1, 3, 2, 1, 1, 3, 2, 1, 2
[1, 3, 2, 1, 1, 3, 2, 1, 3] => 1, 3, 2, 1, 1, 3, 2, 1, 3
[1, 3, 2, 1, 1, 3, 2, 2, 1] => 1, 3, 2, 1, 1, 3, 2, 2, 1
[1, 3, 2, 1, 1, 3, 2, 2, 2] => 1, 3, 2, 1, 1, 3, 2, 2, 2
[1, 3, 2, 1, 1, 3, 2, 2, 3] => 1, 3, 2, 1, 1, 3, 2, 2, 3
[1, 3, 2, 1, 1, 3, 2, 3, 1] => 1, 3, 2, 1, 1, 3, 2, 3, 1
[1, 3, 2, 1, 1, 3, 2, 3, 2] => 1, 3, 2, 1, 1, 3, 2, 3, 2
[1, 3, 2, 1, 1, 3, 2, 3, 3] => 1, 3, 2, 1, 1, 3, 2, 3, 3
[1, 3, 2, 1, 1, 3, 3, 1, 1] => 1, 3, 2, 1, 1, 3, 3, 1, 1
[1, 3, 2, 1, 1, 3, 3, 1, 2] => 1, 3, 2, 1, 1, 3, 3, 1, 2
[1, 3, 2, 1, 1, 3, 3, 1, 3] => 1, 3, 2, 1, 1, 3, 3, 1, 3
[1, 3, 2, 1, 1, 3, 3, 2, 1] => 1, 3, 2, 1, 1, 3, 3, 2, 1
[1, 3, 2, 1, 1, 3, 3, 2, 2] => 1, 3, 2, 1, 1, 3, 3, 2, 2
[1, 3, 2, 1, 1, 3, 3, 2, 3] => 1, 3, 2, 1, 1, 3, 3, 2, 3
[1, 3, 2, 1, 1, 3, 3, 3, 1] => 1, 3, 2, 1, 1, 3, 3, 3, 1
[1, 3, 2, 1, 1, 3, 3, 3, 2] => 1, 3, 2, 1, 1, 3, 3, 3, 2
[1, 3, 2, 1, 1, 3, 3, 3, 3] => 1, 3, 2, 1, 1, 3, 3, 3, 3
[1, 3, 2, 1, 2, 1, 1, 1, 1] => 1, 3, 2, 1, 2, 1, 1, 1, 1
[1, 3, 2, 1, 2, 1, 1, 1, 2] => 1, 3, 2, 1, 2, 1, 1, 1, 2
[1, 3, 2, 1, 2, 1, 1, 1, 3] => 1, 3, 2, 1, 2, 1, 1, 1, 3
[1, 3, 2, 1, 2, 1, 1, 2, 1] => 1, 3, 2, 1, 2, 1, 1, 2, 1
[1, 3, 2, 1, 2, 1, 1, 2, 2] => 1, 3, 2, 1, 2, 1, 1, 2, 2
[1, 3, 2, 1, 2, 1, 1, 2, 3] => 1, 3, 2, 1, 2, 1, 1, 2, 3
[1, 3, 2, 1, 2, 1, 1, 3, 1] => 1, 3, 2, 1, 2, 1, 1, 3, 1
[1, 3, 2, 1, 2, 1, 1, 3, 2] => 1, 3, 2, 1, 2, 1, 1, 3, 2
[1, 3, 2, 1, 2, 1, 1, 3, 3] => 1, 3, 2, 1, 2, 1, 1, 3, 3
[1, 3, 2, 1, 2, 1, 2, 1, 1] => 1, 3, 2, 1, 2, 1, 2, 1, 1
[1, 3, 2, 1, 2, 1, 2, 1, 2] => 1, 3, 2, 1, 2, 1, 2, 1, 2
[1, 3, 2, 1, 2, 1, 2, 1, 3] => 1, 3, 2, 1, 2, 1, 2, 1, 3
[1, 3, 2, 1, 2, 1, 2, 2, 1] => 1, 3, 2, 1, 2, 1, 2, 2, 1
[1, 3, 2, 1, 2, 1, 2, 2, 2] => 1, 3, 2, 1, 2, 1, 2, 2, 2
[1, 3, 2, 1, 2, 1, 2, 2, 3] => 1, 3, 2, 1, 2, 1, 2, 2, 3
[1, 3, 2, 1, 2, 1, 2, 3, 1] => 1, 3, 2, 1, 2, 1, 2, 3, 1
[1, 3, 2, 1, 2, 1, 2, 3, 2] => 1, 3, 2, 1, 2, 1, 2, 3, 2
[1, 3, 2, 1, 2, 1, 2, 3, 3] => 1, 3, 2, 1, 2, 1, 2, 3, 3
[1, 3, 2, 1, 2, 1, 3, 1, 1] => 1, 3, 2, 1, 2, 1, 3, 1, 1
[1, 3, 2, 1, 2, 1, 3, 1, 2] => 1, 3, 2, 1, 2, 1, 3, 1, 2
[1, 3, 2, 1, 2, 1, 3, 1, 3] => 1, 3, 2, 1, 2, 1, 3, 1, 3
[1, 3, 2, 1, 2, 1, 3, 2, 1] => 1, 3, 2, 1, 2, 1, 3, 2, 1
[1, 3, 2, 1, 2, 1, 3, 2, 2] => 1, 3, 2, 1, 2, 1, 3, 2, 2
[1, 3, 2, 1, 2, 1, 3, 2, 3] => 1, 3, 2, 1, 2, 1, 3, 2, 3
[1, 3, 2, 1, 2, 1, 3, 3, 1] => 1, 3, 2, 1, 2, 1, 3, 3, 1
[1, 3, 2, 1, 2, 1, 3, 3, 2] => 1, 3, 2, 1, 2, 1, 3, 3, 2
[1, 3, 2, 1, 2, 1, 3, 3, 3] => 1, 3, 2, 1, 2, 1, 3, 3, 3
[1, 3, 2, 1, 2, 2, 1, 1, 1] => 1, 3, 2, 1, 2, 2, 1, 1, 1
[1, 3, 2, 1, 2, 2, 1, 1, 2] => 1, 3, 2, 1, 2, 2, 1, 1, 2
[1, 3, 2, 1, 2, 2, 1, 1, 3] => 1, 3, 2, 1, 2, 2, 1, 1, 3
[1, 3, 2, 1, 2, 2, 1, 2, 1] => 1, 3, 2, 1, 2, 2, 1, 2, 1
[1, 3, 2, 1, 2, 2, 1, 2, 2] => 1, 3, 2, 1, 2, 2, 1, 2, 2
[1, 3, 2, 1, 2, 2, 1, 2, 3] => 1, 3, 2, 1, 2, 2, 1, 2, 3
[1, 3, 2, 1, 2, 2, 1, 3, 1] => 1, 3, 2, 1, 2, 2, 1, 3, 1
[1, 3, 2, 1, 2, 2, 1, 3, 2] => 1, 3, 2, 1, 2, 2, 1, 3, 2
[1, 3, 2, 1, 2, 2, 1, 3, 3] => 1, 3, 2, 1, 2, 2, 1, 3, 3
[1, 3, 2, 1, 2, 2, 2, 1, 1] => 1, 3, 2, 1, 2, 2, 2, 1, 1
[1, 3, 2, 1, 2, 2, 2, 1, 2] => 1, 3, 2, 1, 2, 2, 2, 1, 2
[1, 3, 2, 1, 2, 2, 2, 1, 3] => 1, 3, 2, 1, 2, 2, 2, 1, 3
[1, 3, 2, 1, 2, 2, 2, 2, 1] => 1, 3, 2, 1, 2, 2, 2, 2, 1
[1, 3, 2, 1, 2, 2, 2, 2, 2] => 1, 3, 2, 1, 2, 2, 2, 2, 2
[1, 3, 2, 1, 2, 2, 2, 2, 3] => 1, 3, 2, 1, 2, 2, 2, 2, 3
[1, 3, 2, 1, 2, 2, 2, 3, 1] => 1, 3, 2, 1, 2, 2, 2, 3, 1
[1, 3, 2, 1, 2, 2, 2, 3, 2] => 1, 3, 2, 1, 2, 2, 2, 3, 2
[1, 3, 2, 1, 2, 2, 2, 3, 3] => 1, 3, 2, 1, 2, 2, 2, 3, 3
[1, 3, 2, 1, 2, 2, 3, 1, 1] => 1, 3, 2, 1, 2, 2, 3, 1, 1
[1, 3, 2, 1, 2, 2, 3, 1, 2] => 1, 3, 2, 1, 2, 2, 3, 1, 2
[1, 3, 2, 1, 2, 2, 3, 1, 3] => 1, 3, 2, 1, 2, 2, 3, 1, 3
[1, 3, 2, 1, 2, 2, 3, 2, 1] => 1, 3, 2, 1, 2, 2, 3, 2, 1
[1, 3, 2, 1, 2, 2, 3, 2, 2] => 1, 3, 2, 1, 2, 2, 3, 2, 2
[1, 3, 2, 1, 2, 2, 3, 2, 3] => 1, 3, 2, 1, 2, 2, 3, 2, 3
[1, 3, 2, 1, 2, 2, 3, 3, 1] => 1, 3, 2, 1, 2, 2, 3, 3, 1
[1, 3, 2, 1, 2, 2, 3, 3, 2] => 1, 3, 2, 1, 2, 2, 3, 3, 2
[1, 3, 2, 1, 2, 2, 3, 3, 3] => 1, 3, 2, 1, 2, 2, 3, 3, 3
[1, 3, 2, 1, 2, 3, 1, 1, 1] => 1, 3, 2, 1, 2, 3, 1, 1, 1
[1, 3, 2, 1, 2, 3, 1, 1, 2] => 1, 3, 2, 1, 2, 3, 1, 1, 2
[1, 3, 2, 1, 2, 3, 1, 1, 3] => 1, 3, 2, 1, 2, 3, 1, 1, 3
[1, 3, 2, 1, 2, 3, 1, 2, 1] => 1, 3, 2, 1, 2, 3, 1, 2, 1
[1, 3, 2, 1, 2, 3, 1, 2, 2] => 1, 3, 2, 1, 2, 3, 1, 2, 2
[1, 3, 2, 1, 2, 3, 1, 2, 3] => 1, 3, 2, 1, 2, 3, 1, 2, 3
[1, 3, 2, 1, 2, 3, 1, 3, 1] => 1, 3, 2, 1, 2, 3, 1, 3, 1
[1, 3, 2, 1, 2, 3, 1, 3, 2] => 1, 3, 2, 1, 2, 3, 1, 3, 2
[1, 3, 2, 1, 2, 3, 1, 3, 3] => 1, 3, 2, 1, 2, 3, 1, 3, 3
[1, 3, 2, 1, 2, 3, 2, 1, 1] => 1, 3, 2, 1, 2, 3, 2, 1, 1
[1, 3, 2, 1, 2, 3, 2, 1, 2] => 1, 3, 2, 1, 2, 3, 2, 1, 2
[1, 3, 2, 1, 2, 3, 2, 1, 3] => 1, 3, 2, 1, 2, 3, 2, 1, 3
[1, 3, 2, 1, 2, 3, 2, 2, 1] => 1, 3, 2, 1, 2, 3, 2, 2, 1
[1, 3, 2, 1, 2, 3, 2, 2, 2] => 1, 3, 2, 1, 2, 3, 2, 2, 2
[1, 3, 2, 1, 2, 3, 2, 2, 3] => 1, 3, 2, 1, 2, 3, 2, 2, 3
[1, 3, 2, 1, 2, 3, 2, 3, 1] => 1, 3, 2, 1, 2, 3, 2, 3, 1
[1, 3, 2, 1, 2, 3, 2, 3, 2] => 1, 3, 2, 1, 2, 3, 2, 3, 2
[1, 3, 2, 1, 2, 3, 2, 3, 3] => 1, 3, 2, 1, 2, 3, 2, 3, 3
[1, 3, 2, 1, 2, 3, 3, 1, 1] => 1, 3, 2, 1, 2, 3, 3, 1, 1
[1, 3, 2, 1, 2, 3, 3, 1, 2] => 1, 3, 2, 1, 2, 3, 3, 1, 2
[1, 3, 2, 1, 2, 3, 3, 1, 3] => 1, 3, 2, 1, 2, 3, 3, 1, 3
[1, 3, 2, 1, 2, 3, 3, 2, 1] => 1, 3, 2, 1, 2, 3, 3, 2, 1
[1, 3, 2, 1, 2, 3, 3, 2, 2] => 1, 3, 2, 1, 2, 3, 3, 2, 2
[1, 3, 2, 1, 2, 3, 3, 2, 3] => 1, 3, 2, 1, 2, 3, 3, 2, 3
[1, 3, 2, 1, 2, 3, 3, 3, 1] => 1, 3, 2, 1, 2, 3, 3, 3, 1
[1, 3, 2, 1, 2, 3, 3, 3, 2] => 1, 3, 2, 1, 2, 3, 3, 3, 2
[1, 3, 2, 1, 2, 3, 3, 3, 3] => 1, 3, 2, 1, 2, 3, 3, 3, 3
[1, 3, 2, 1, 3, 1, 1, 1, 1] => 1, 3, 2, 1, 3, 1, 1, 1, 1
[1, 3, 2, 1, 3, 1, 1, 1, 2] => 1, 3, 2, 1, 3, 1, 1, 1, 2
[1, 3, 2, 1, 3, 1, 1, 1, 3] => 1, 3, 2, 1, 3, 1, 1, 1, 3
[1, 3, 2, 1, 3, 1, 1, 2, 1] => 1, 3, 2, 1, 3, 1, 1, 2, 1
[1, 3, 2, 1, 3, 1, 1, 2, 2] => 1, 3, 2, 1, 3, 1, 1, 2, 2
[1, 3, 2, 1, 3, 1, 1, 2, 3] => 1, 3, 2, 1, 3, 1, 1, 2, 3
[1, 3, 2, 1, 3, 1, 1, 3, 1] => 1, 3, 2, 1, 3, 1, 1, 3, 1
[1, 3, 2, 1, 3, 1, 1, 3, 2] => 1, 3, 2, 1, 3, 1, 1, 3, 2
[1, 3, 2, 1, 3, 1, 1, 3, 3] => 1, 3, 2, 1, 3, 1, 1, 3, 3
[1, 3, 2, 1, 3, 1, 2, 1, 1] => 1, 3, 2, 1, 3, 1, 2, 1, 1
[1, 3, 2, 1, 3, 1, 2, 1, 2] => 1, 3, 2, 1, 3, 1, 2, 1, 2
[1, 3, 2, 1, 3, 1, 2, 1, 3] => 1, 3, 2, 1, 3, 1, 2, 1, 3
[1, 3, 2, 1, 3, 1, 2, 2, 1] => 1, 3, 2, 1, 3, 1, 2, 2, 1
[1, 3, 2, 1, 3, 1, 2, 2, 2] => 1, 3, 2, 1, 3, 1, 2, 2, 2
[1, 3, 2, 1, 3, 1, 2, 2, 3] => 1, 3, 2, 1, 3, 1, 2, 2, 3
[1, 3, 2, 1, 3, 1, 2, 3, 1] => 1, 3, 2, 1, 3, 1, 2, 3, 1
[1, 3, 2, 1, 3, 1, 2, 3, 2] => 1, 3, 2, 1, 3, 1, 2, 3, 2
[1, 3, 2, 1, 3, 1, 2, 3, 3] => 1, 3, 2, 1, 3, 1, 2, 3, 3
[1, 3, 2, 1, 3, 1, 3, 1, 1] => 1, 3, 2, 1, 3, 1, 3, 1, 1
[1, 3, 2, 1, 3, 1, 3, 1, 2] => 1, 3, 2, 1, 3, 1, 3, 1, 2
[1, 3, 2, 1, 3, 1, 3, 1, 3] => 1, 3, 2, 1, 3, 1, 3, 1, 3
[1, 3, 2, 1, 3, 1, 3, 2, 1] => 1, 3, 2, 1, 3, 1, 3, 2, 1
[1, 3, 2, 1, 3, 1, 3, 2, 2] => 1, 3, 2, 1, 3, 1, 3, 2, 2
[1, 3, 2, 1, 3, 1, 3, 2, 3] => 1, 3, 2, 1, 3, 1, 3, 2, 3
[1, 3, 2, 1, 3, 1, 3, 3, 1] => 1, 3, 2, 1, 3, 1, 3, 3, 1
[1, 3, 2, 1, 3, 1, 3, 3, 2] => 1, 3, 2, 1, 3, 1, 3, 3, 2
[1, 3, 2, 1, 3, 1, 3, 3, 3] => 1, 3, 2, 1, 3, 1, 3, 3, 3
[1, 3, 2, 1, 3, 2, 1, 1, 1] => 1, 3, 2, 1, 3, 2, 1, 1, 1
[1, 3, 2, 1, 3, 2, 1, 1, 2] => 1, 3, 2, 1, 3, 2, 1, 1, 2
[1, 3, 2, 1, 3, 2, 1, 1, 3] => 1, 3, 2, 1, 3, 2, 1, 1, 3
[1, 3, 2, 1, 3, 2, 1, 2, 1] => 1, 3, 2, 1, 3, 2, 1, 2, 1
[1, 3, 2, 1, 3, 2, 1, 2, 2] => 1, 3, 2, 1, 3, 2, 1, 2, 2
[1, 3, 2, 1, 3, 2, 1, 2, 3] => 1, 3, 2, 1, 3, 2, 1, 2, 3
[1, 3, 2, 1, 3, 2, 1, 3, 1] => 1, 3, 2, 1, 3, 2, 1, 3, 1
[1, 3, 2, 1, 3, 2, 1, 3, 2] => 1, 3, 2, 1, 3, 2, 1, 3, 2
[1, 3, 2, 1, 3, 2, 1, 3, 3] => 1, 3, 2, 1, 3, 2, 1, 3, 3
[1, 3, 2, 1, 3, 2, 2, 1, 1] => 1, 3, 2, 1, 3, 2, 2, 1, 1
[1, 3, 2, 1, 3, 2, 2, 1, 2] => 1, 3, 2, 1, 3, 2, 2, 1, 2
[1, 3, 2, 1, 3, 2, 2, 1, 3] => 1, 3, 2, 1, 3, 2, 2, 1, 3
[1, 3, 2, 1, 3, 2, 2, 2, 1] => 1, 3, 2, 1, 3, 2, 2, 2, 1
[1, 3, 2, 1, 3, 2, 2, 2, 2] => 1, 3, 2, 1, 3, 2, 2, 2, 2
[1, 3, 2, 1, 3, 2, 2, 2, 3] => 1, 3, 2, 1, 3, 2, 2, 2, 3
[1, 3, 2, 1, 3, 2, 2, 3, 1] => 1, 3, 2, 1, 3, 2, 2, 3, 1
[1, 3, 2, 1, 3, 2, 2, 3, 2] => 1, 3, 2, 1, 3, 2, 2, 3, 2
[1, 3, 2, 1, 3, 2, 2, 3, 3] => 1, 3, 2, 1, 3, 2, 2, 3, 3
[1, 3, 2, 1, 3, 2, 3, 1, 1] => 1, 3, 2, 1, 3, 2, 3, 1, 1
[1, 3, 2, 1, 3, 2, 3, 1, 2] => 1, 3, 2, 1, 3, 2, 3, 1, 2
[1, 3, 2, 1, 3, 2, 3, 1, 3] => 1, 3, 2, 1, 3, 2, 3, 1, 3
[1, 3, 2, 1, 3, 2, 3, 2, 1] => 1, 3, 2, 1, 3, 2, 3, 2, 1
[1, 3, 2, 1, 3, 2, 3, 2, 2] => 1, 3, 2, 1, 3, 2, 3, 2, 2
[1, 3, 2, 1, 3, 2, 3, 2, 3] => 1, 3, 2, 1, 3, 2, 3, 2, 3
[1, 3, 2, 1, 3, 2, 3, 3, 1] => 1, 3, 2, 1, 3, 2, 3, 3, 1
[1, 3, 2, 1, 3, 2, 3, 3, 2] => 1, 3, 2, 1, 3, 2, 3, 3, 2
[1, 3, 2, 1, 3, 2, 3, 3, 3] => 1, 3, 2, 1, 3, 2, 3, 3, 3
[1, 3, 2, 1, 3, 3, 1, 1, 1] => 1, 3, 2, 1, 3, 3, 1, 1, 1
[1, 3, 2, 1, 3, 3, 1, 1, 2] => 1, 3, 2, 1, 3, 3, 1, 1, 2
[1, 3, 2, 1, 3, 3, 1, 1, 3] => 1, 3, 2, 1, 3, 3, 1, 1, 3
[1, 3, 2, 1, 3, 3, 1, 2, 1] => 1, 3, 2, 1, 3, 3, 1, 2, 1
[1, 3, 2, 1, 3, 3, 1, 2, 2] => 1, 3, 2, 1, 3, 3, 1, 2, 2
[1, 3, 2, 1, 3, 3, 1, 2, 3] => 1, 3, 2, 1, 3, 3, 1, 2, 3
[1, 3, 2, 1, 3, 3, 1, 3, 1] => 1, 3, 2, 1, 3, 3, 1, 3, 1
[1, 3, 2, 1, 3, 3, 1, 3, 2] => 1, 3, 2, 1, 3, 3, 1, 3, 2
[1, 3, 2, 1, 3, 3, 1, 3, 3] => 1, 3, 2, 1, 3, 3, 1, 3, 3
[1, 3, 2, 1, 3, 3, 2, 1, 1] => 1, 3, 2, 1, 3, 3, 2, 1, 1
[1, 3, 2, 1, 3, 3, 2, 1, 2] => 1, 3, 2, 1, 3, 3, 2, 1, 2
[1, 3, 2, 1, 3, 3, 2, 1, 3] => 1, 3, 2, 1, 3, 3, 2, 1, 3
[1, 3, 2, 1, 3, 3, 2, 2, 1] => 1, 3, 2, 1, 3, 3, 2, 2, 1
[1, 3, 2, 1, 3, 3, 2, 2, 2] => 1, 3, 2, 1, 3, 3, 2, 2, 2
[1, 3, 2, 1, 3, 3, 2, 2, 3] => 1, 3, 2, 1, 3, 3, 2, 2, 3
[1, 3, 2, 1, 3, 3, 2, 3, 1] => 1, 3, 2, 1, 3, 3, 2, 3, 1
[1, 3, 2, 1, 3, 3, 2, 3, 2] => 1, 3, 2, 1, 3, 3, 2, 3, 2
[1, 3, 2, 1, 3, 3, 2, 3, 3] => 1, 3, 2, 1, 3, 3, 2, 3, 3
[1, 3, 2, 1, 3, 3, 3, 1, 1] => 1, 3, 2, 1, 3, 3, 3, 1, 1
[1, 3, 2, 1, 3, 3, 3, 1, 2] => 1, 3, 2, 1, 3, 3, 3, 1, 2
[1, 3, 2, 1, 3, 3, 3, 1, 3] => 1, 3, 2, 1, 3, 3, 3, 1, 3
[1, 3, 2, 1, 3, 3, 3, 2, 1] => 1, 3, 2, 1, 3, 3, 3, 2, 1
[1, 3, 2, 1, 3, 3, 3, 2, 2] => 1, 3, 2, 1, 3, 3, 3, 2, 2
[1, 3, 2, 1, 3, 3, 3, 2, 3] => 1, 3, 2, 1, 3, 3, 3, 2, 3
[1, 3, 2, 1, 3, 3, 3, 3, 1] => 1, 3, 2, 1, 3, 3, 3, 3, 1
[1, 3, 2, 1, 3, 3, 3, 3, 2] => 1, 3, 2, 1, 3, 3, 3, 3, 2
[1, 3, 2, 1, 3, 3, 3, 3, 3] => 1, 3, 2, 1, 3, 3, 3, 3, 3
[1, 3, 2, 2, 1, 1, 1, 1, 1] => 1, 3, 2, 2, 1, 1, 1, 1, 1
[1, 3, 2, 2, 1, 1, 1, 1, 2] => 1, 3, 2, 2, 1, 1, 1, 1, 2
[1, 3, 2, 2, 1, 1, 1, 1, 3] => 1, 3, 2, 2, 1, 1, 1, 1, 3
[1, 3, 2, 2, 1, 1, 1, 2, 1] => 1, 3, 2, 2, 1, 1, 1, 2, 1
[1, 3, 2, 2, 1, 1, 1, 2, 2] => 1, 3, 2, 2, 1, 1, 1, 2, 2
[1, 3, 2, 2, 1, 1, 1, 2, 3] => 1, 3, 2, 2, 1, 1, 1, 2, 3
[1, 3, 2, 2, 1, 1, 1, 3, 1] => 1, 3, 2, 2, 1, 1, 1, 3, 1
[1, 3, 2, 2, 1, 1, 1, 3, 2] => 1, 3, 2, 2, 1, 1, 1, 3, 2
[1, 3, 2, 2, 1, 1, 1, 3, 3] => 1, 3, 2, 2, 1, 1, 1, 3, 3
[1, 3, 2, 2, 1, 1, 2, 1, 1] => 1, 3, 2, 2, 1, 1, 2, 1, 1
[1, 3, 2, 2, 1, 1, 2, 1, 2] => 1, 3, 2, 2, 1, 1, 2, 1, 2
[1, 3, 2, 2, 1, 1, 2, 1, 3] => 1, 3, 2, 2, 1, 1, 2, 1, 3
[1, 3, 2, 2, 1, 1, 2, 2, 1] => 1, 3, 2, 2, 1, 1, 2, 2, 1
[1, 3, 2, 2, 1, 1, 2, 2, 2] => 1, 3, 2, 2, 1, 1, 2, 2, 2
[1, 3, 2, 2, 1, 1, 2, 2, 3] => 1, 3, 2, 2, 1, 1, 2, 2, 3
[1, 3, 2, 2, 1, 1, 2, 3, 1] => 1, 3, 2, 2, 1, 1, 2, 3, 1
[1, 3, 2, 2, 1, 1, 2, 3, 2] => 1, 3, 2, 2, 1, 1, 2, 3, 2
[1, 3, 2, 2, 1, 1, 2, 3, 3] => 1, 3, 2, 2, 1, 1, 2, 3, 3
[1, 3, 2, 2, 1, 1, 3, 1, 1] => 1, 3, 2, 2, 1, 1, 3, 1, 1
[1, 3, 2, 2, 1, 1, 3, 1, 2] => 1, 3, 2, 2, 1, 1, 3, 1, 2
[1, 3, 2, 2, 1, 1, 3, 1, 3] => 1, 3, 2, 2, 1, 1, 3, 1, 3
[1, 3, 2, 2, 1, 1, 3, 2, 1] => 1, 3, 2, 2, 1, 1, 3, 2, 1
[1, 3, 2, 2, 1, 1, 3, 2, 2] => 1, 3, 2, 2, 1, 1, 3, 2, 2
[1, 3, 2, 2, 1, 1, 3, 2, 3] => 1, 3, 2, 2, 1, 1, 3, 2, 3
[1, 3, 2, 2, 1, 1, 3, 3, 1] => 1, 3, 2, 2, 1, 1, 3, 3, 1
[1, 3, 2, 2, 1, 1, 3, 3, 2] => 1, 3, 2, 2, 1, 1, 3, 3, 2
[1, 3, 2, 2, 1, 1, 3, 3, 3] => 1, 3, 2, 2, 1, 1, 3, 3, 3
[1, 3, 2, 2, 1, 2, 1, 1, 1] => 1, 3, 2, 2, 1, 2, 1, 1, 1
[1, 3, 2, 2, 1, 2, 1, 1, 2] => 1, 3, 2, 2, 1, 2, 1, 1, 2
[1, 3, 2, 2, 1, 2, 1, 1, 3] => 1, 3, 2, 2, 1, 2, 1, 1, 3
[1, 3, 2, 2, 1, 2, 1, 2, 1] => 1, 3, 2, 2, 1, 2, 1, 2, 1
[1, 3, 2, 2, 1, 2, 1, 2, 2] => 1, 3, 2, 2, 1, 2, 1, 2, 2
[1, 3, 2, 2, 1, 2, 1, 2, 3] => 1, 3, 2, 2, 1, 2, 1, 2, 3
[1, 3, 2, 2, 1, 2, 1, 3, 1] => 1, 3, 2, 2, 1, 2, 1, 3, 1
[1, 3, 2, 2, 1, 2, 1, 3, 2] => 1, 3, 2, 2, 1, 2, 1, 3, 2
[1, 3, 2, 2, 1, 2, 1, 3, 3] => 1, 3, 2, 2, 1, 2, 1, 3, 3
[1, 3, 2, 2, 1, 2, 2, 1, 1] => 1, 3, 2, 2, 1, 2, 2, 1, 1
[1, 3, 2, 2, 1, 2, 2, 1, 2] => 1, 3, 2, 2, 1, 2, 2, 1, 2
[1, 3, 2, 2, 1, 2, 2, 1, 3] => 1, 3, 2, 2, 1, 2, 2, 1, 3
[1, 3, 2, 2, 1, 2, 2, 2, 1] => 1, 3, 2, 2, 1, 2, 2, 2, 1
[1, 3, 2, 2, 1, 2, 2, 2, 2] => 1, 3, 2, 2, 1, 2, 2, 2, 2
[1, 3, 2, 2, 1, 2, 2, 2, 3] => 1, 3, 2, 2, 1, 2, 2, 2, 3
[1, 3, 2, 2, 1, 2, 2, 3, 1] => 1, 3, 2, 2, 1, 2, 2, 3, 1
[1, 3, 2, 2, 1, 2, 2, 3, 2] => 1, 3, 2, 2, 1, 2, 2, 3, 2
[1, 3, 2, 2, 1, 2, 2, 3, 3] => 1, 3, 2, 2, 1, 2, 2, 3, 3
[1, 3, 2, 2, 1, 2, 3, 1, 1] => 1, 3, 2, 2, 1, 2, 3, 1, 1
[1, 3, 2, 2, 1, 2, 3, 1, 2] => 1, 3, 2, 2, 1, 2, 3, 1, 2
[1, 3, 2, 2, 1, 2, 3, 1, 3] => 1, 3, 2, 2, 1, 2, 3, 1, 3
[1, 3, 2, 2, 1, 2, 3, 2, 1] => 1, 3, 2, 2, 1, 2, 3, 2, 1
[1, 3, 2, 2, 1, 2, 3, 2, 2] => 1, 3, 2, 2, 1, 2, 3, 2, 2
[1, 3, 2, 2, 1, 2, 3, 2, 3] => 1, 3, 2, 2, 1, 2, 3, 2, 3
[1, 3, 2, 2, 1, 2, 3, 3, 1] => 1, 3, 2, 2, 1, 2, 3, 3, 1
[1, 3, 2, 2, 1, 2, 3, 3, 2] => 1, 3, 2, 2, 1, 2, 3, 3, 2
[1, 3, 2, 2, 1, 2, 3, 3, 3] => 1, 3, 2, 2, 1, 2, 3, 3, 3
[1, 3, 2, 2, 1, 3, 1, 1, 1] => 1, 3, 2, 2, 1, 3, 1, 1, 1
[1, 3, 2, 2, 1, 3, 1, 1, 2] => 1, 3, 2, 2, 1, 3, 1, 1, 2
[1, 3, 2, 2, 1, 3, 1, 1, 3] => 1, 3, 2, 2, 1, 3, 1, 1, 3
[1, 3, 2, 2, 1, 3, 1, 2, 1] => 1, 3, 2, 2, 1, 3, 1, 2, 1
[1, 3, 2, 2, 1, 3, 1, 2, 2] => 1, 3, 2, 2, 1, 3, 1, 2, 2
[1, 3, 2, 2, 1, 3, 1, 2, 3] => 1, 3, 2, 2, 1, 3, 1, 2, 3
[1, 3, 2, 2, 1, 3, 1, 3, 1] => 1, 3, 2, 2, 1, 3, 1, 3, 1
[1, 3, 2, 2, 1, 3, 1, 3, 2] => 1, 3, 2, 2, 1, 3, 1, 3, 2
[1, 3, 2, 2, 1, 3, 1, 3, 3] => 1, 3, 2, 2, 1, 3, 1, 3, 3
[1, 3, 2, 2, 1, 3, 2, 1, 1] => 1, 3, 2, 2, 1, 3, 2, 1, 1
[1, 3, 2, 2, 1, 3, 2, 1, 2] => 1, 3, 2, 2, 1, 3, 2, 1, 2
[1, 3, 2, 2, 1, 3, 2, 1, 3] => 1, 3, 2, 2, 1, 3, 2, 1, 3
[1, 3, 2, 2, 1, 3, 2, 2, 1] => 1, 3, 2, 2, 1, 3, 2, 2, 1
[1, 3, 2, 2, 1, 3, 2, 2, 2] => 1, 3, 2, 2, 1, 3, 2, 2, 2
[1, 3, 2, 2, 1, 3, 2, 2, 3] => 1, 3, 2, 2, 1, 3, 2, 2, 3
[1, 3, 2, 2, 1, 3, 2, 3, 1] => 1, 3, 2, 2, 1, 3, 2, 3, 1
[1, 3, 2, 2, 1, 3, 2, 3, 2] => 1, 3, 2, 2, 1, 3, 2, 3, 2
[1, 3, 2, 2, 1, 3, 2, 3, 3] => 1, 3, 2, 2, 1, 3, 2, 3, 3
[1, 3, 2, 2, 1, 3, 3, 1, 1] => 1, 3, 2, 2, 1, 3, 3, 1, 1
[1, 3, 2, 2, 1, 3, 3, 1, 2] => 1, 3, 2, 2, 1, 3, 3, 1, 2
[1, 3, 2, 2, 1, 3, 3, 1, 3] => 1, 3, 2, 2, 1, 3, 3, 1, 3
[1, 3, 2, 2, 1, 3, 3, 2, 1] => 1, 3, 2, 2, 1, 3, 3, 2, 1
[1, 3, 2, 2, 1, 3, 3, 2, 2] => 1, 3, 2, 2, 1, 3, 3, 2, 2
[1, 3, 2, 2, 1, 3, 3, 2, 3] => 1, 3, 2, 2, 1, 3, 3, 2, 3
[1, 3, 2, 2, 1, 3, 3, 3, 1] => 1, 3, 2, 2, 1, 3, 3, 3, 1
[1, 3, 2, 2, 1, 3, 3, 3, 2] => 1, 3, 2, 2, 1, 3, 3, 3, 2
[1, 3, 2, 2, 1, 3, 3, 3, 3] => 1, 3, 2, 2, 1, 3, 3, 3, 3
[1, 3, 2, 2, 2, 1, 1, 1, 1] => 1, 3, 2, 2, 2, 1, 1, 1, 1
[1, 3, 2, 2, 2, 1, 1, 1, 2] => 1, 3, 2, 2, 2, 1, 1, 1, 2
[1, 3, 2, 2, 2, 1, 1, 1, 3] => 1, 3, 2, 2, 2, 1, 1, 1, 3
[1, 3, 2, 2, 2, 1, 1, 2, 1] => 1, 3, 2, 2, 2, 1, 1, 2, 1
[1, 3, 2, 2, 2, 1, 1, 2, 2] => 1, 3, 2, 2, 2, 1, 1, 2, 2
[1, 3, 2, 2, 2, 1, 1, 2, 3] => 1, 3, 2, 2, 2, 1, 1, 2, 3
[1, 3, 2, 2, 2, 1, 1, 3, 1] => 1, 3, 2, 2, 2, 1, 1, 3, 1
[1, 3, 2, 2, 2, 1, 1, 3, 2] => 1, 3, 2, 2, 2, 1, 1, 3, 2
[1, 3, 2, 2, 2, 1, 1, 3, 3] => 1, 3, 2, 2, 2, 1, 1, 3, 3
[1, 3, 2, 2, 2, 1, 2, 1, 1] => 1, 3, 2, 2, 2, 1, 2, 1, 1
[1, 3, 2, 2, 2, 1, 2, 1, 2] => 1, 3, 2, 2, 2, 1, 2, 1, 2
[1, 3, 2, 2, 2, 1, 2, 1, 3] => 1, 3, 2, 2, 2, 1, 2, 1, 3
[1, 3, 2, 2, 2, 1, 2, 2, 1] => 1, 3, 2, 2, 2, 1, 2, 2, 1
[1, 3, 2, 2, 2, 1, 2, 2, 2] => 1, 3, 2, 2, 2, 1, 2, 2, 2
[1, 3, 2, 2, 2, 1, 2, 2, 3] => 1, 3, 2, 2, 2, 1, 2, 2, 3
[1, 3, 2, 2, 2, 1, 2, 3, 1] => 1, 3, 2, 2, 2, 1, 2, 3, 1
[1, 3, 2, 2, 2, 1, 2, 3, 2] => 1, 3, 2, 2, 2, 1, 2, 3, 2
[1, 3, 2, 2, 2, 1, 2, 3, 3] => 1, 3, 2, 2, 2, 1, 2, 3, 3
[1, 3, 2, 2, 2, 1, 3, 1, 1] => 1, 3, 2, 2, 2, 1, 3, 1, 1
[1, 3, 2, 2, 2, 1, 3, 1, 2] => 1, 3, 2, 2, 2, 1, 3, 1, 2
[1, 3, 2, 2, 2, 1, 3, 1, 3] => 1, 3, 2, 2, 2, 1, 3, 1, 3
[1, 3, 2, 2, 2, 1, 3, 2, 1] => 1, 3, 2, 2, 2, 1, 3, 2, 1
[1, 3, 2, 2, 2, 1, 3, 2, 2] => 1, 3, 2, 2, 2, 1, 3, 2, 2
[1, 3, 2, 2, 2, 1, 3, 2, 3] => 1, 3, 2, 2, 2, 1, 3, 2, 3
[1, 3, 2, 2, 2, 1, 3, 3, 1] => 1, 3, 2, 2, 2, 1, 3, 3, 1
[1, 3, 2, 2, 2, 1, 3, 3, 2] => 1, 3, 2, 2, 2, 1, 3, 3, 2
[1, 3, 2, 2, 2, 1, 3, 3, 3] => 1, 3, 2, 2, 2, 1, 3, 3, 3
[1, 3, 2, 2, 2, 2, 1, 1, 1] => 1, 3, 2, 2, 2, 2, 1, 1, 1
[1, 3, 2, 2, 2, 2, 1, 1, 2] => 1, 3, 2, 2, 2, 2, 1, 1, 2
[1, 3, 2, 2, 2, 2, 1, 1, 3] => 1, 3, 2, 2, 2, 2, 1, 1, 3
[1, 3, 2, 2, 2, 2, 1, 2, 1] => 1, 3, 2, 2, 2, 2, 1, 2, 1
[1, 3, 2, 2, 2, 2, 1, 2, 2] => 1, 3, 2, 2, 2, 2, 1, 2, 2
[1, 3, 2, 2, 2, 2, 1, 2, 3] => 1, 3, 2, 2, 2, 2, 1, 2, 3
[1, 3, 2, 2, 2, 2, 1, 3, 1] => 1, 3, 2, 2, 2, 2, 1, 3, 1
[1, 3, 2, 2, 2, 2, 1, 3, 2] => 1, 3, 2, 2, 2, 2, 1, 3, 2
[1, 3, 2, 2, 2, 2, 1, 3, 3] => 1, 3, 2, 2, 2, 2, 1, 3, 3
[1, 3, 2, 2, 2, 2, 2, 1, 1] => 1, 3, 2, 2, 2, 2, 2, 1, 1
[1, 3, 2, 2, 2, 2, 2, 1, 2] => 1, 3, 2, 2, 2, 2, 2, 1, 2
[1, 3, 2, 2, 2, 2, 2, 1, 3] => 1, 3, 2, 2, 2, 2, 2, 1, 3
[1, 3, 2, 2, 2, 2, 2, 2, 1] => 1, 3, 2, 2, 2, 2, 2, 2, 1
[1, 3, 2, 2, 2, 2, 2, 2, 2] => 1, 3, 2, 2, 2, 2, 2, 2, 2
[1, 3, 2, 2, 2, 2, 2, 2, 3] => 1, 3, 2, 2, 2, 2, 2, 2, 3
[1, 3, 2, 2, 2, 2, 2, 3, 1] => 1, 3, 2, 2, 2, 2, 2, 3, 1
[1, 3, 2, 2, 2, 2, 2, 3, 2] => 1, 3, 2, 2, 2, 2, 2, 3, 2
[1, 3, 2, 2, 2, 2, 2, 3, 3] => 1, 3, 2, 2, 2, 2, 2, 3, 3
[1, 3, 2, 2, 2, 2, 3, 1, 1] => 1, 3, 2, 2, 2, 2, 3, 1, 1
[1, 3, 2, 2, 2, 2, 3, 1, 2] => 1, 3, 2, 2, 2, 2, 3, 1, 2
[1, 3, 2, 2, 2, 2, 3, 1, 3] => 1, 3, 2, 2, 2, 2, 3, 1, 3
[1, 3, 2, 2, 2, 2, 3, 2, 1] => 1, 3, 2, 2, 2, 2, 3, 2, 1
[1, 3, 2, 2, 2, 2, 3, 2, 2] => 1, 3, 2, 2, 2, 2, 3, 2, 2
[1, 3, 2, 2, 2, 2, 3, 2, 3] => 1, 3, 2, 2, 2, 2, 3, 2, 3
[1, 3, 2, 2, 2, 2, 3, 3, 1] => 1, 3, 2, 2, 2, 2, 3, 3, 1
[1, 3, 2, 2, 2, 2, 3, 3, 2] => 1, 3, 2, 2, 2, 2, 3, 3, 2
[1, 3, 2, 2, 2, 2, 3, 3, 3] => 1, 3, 2, 2, 2, 2, 3, 3, 3
[1, 3, 2, 2, 2, 3, 1, 1, 1] => 1, 3, 2, 2, 2, 3, 1, 1, 1
[1, 3, 2, 2, 2, 3, 1, 1, 2] => 1, 3, 2, 2, 2, 3, 1, 1, 2
[1, 3, 2, 2, 2, 3, 1, 1, 3] => 1, 3, 2, 2, 2, 3, 1, 1, 3
[1, 3, 2, 2, 2, 3, 1, 2, 1] => 1, 3, 2, 2, 2, 3, 1, 2, 1
[1, 3, 2, 2, 2, 3, 1, 2, 2] => 1, 3, 2, 2, 2, 3, 1, 2, 2
[1, 3, 2, 2, 2, 3, 1, 2, 3] => 1, 3, 2, 2, 2, 3, 1, 2, 3
[1, 3, 2, 2, 2, 3, 1, 3, 1] => 1, 3, 2, 2, 2, 3, 1, 3, 1
[1, 3, 2, 2, 2, 3, 1, 3, 2] => 1, 3, 2, 2, 2, 3, 1, 3, 2
[1, 3, 2, 2, 2, 3, 1, 3, 3] => 1, 3, 2, 2, 2, 3, 1, 3, 3
[1, 3, 2, 2, 2, 3, 2, 1, 1] => 1, 3, 2, 2, 2, 3, 2, 1, 1
[1, 3, 2, 2, 2, 3, 2, 1, 2] => 1, 3, 2, 2, 2, 3, 2, 1, 2
[1, 3, 2, 2, 2, 3, 2, 1, 3] => 1, 3, 2, 2, 2, 3, 2, 1, 3
[1, 3, 2, 2, 2, 3, 2, 2, 1] => 1, 3, 2, 2, 2, 3, 2, 2, 1
[1, 3, 2, 2, 2, 3, 2, 2, 2] => 1, 3, 2, 2, 2, 3, 2, 2, 2
[1, 3, 2, 2, 2, 3, 2, 2, 3] => 1, 3, 2, 2, 2, 3, 2, 2, 3
[1, 3, 2, 2, 2, 3, 2, 3, 1] => 1, 3, 2, 2, 2, 3, 2, 3, 1
[1, 3, 2, 2, 2, 3, 2, 3, 2] => 1, 3, 2, 2, 2, 3, 2, 3, 2
[1, 3, 2, 2, 2, 3, 2, 3, 3] => 1, 3, 2, 2, 2, 3, 2, 3, 3
[1, 3, 2, 2, 2, 3, 3, 1, 1] => 1, 3, 2, 2, 2, 3, 3, 1, 1
[1, 3, 2, 2, 2, 3, 3, 1, 2] => 1, 3, 2, 2, 2, 3, 3, 1, 2
[1, 3, 2, 2, 2, 3, 3, 1, 3] => 1, 3, 2, 2, 2, 3, 3, 1, 3
[1, 3, 2, 2, 2, 3, 3, 2, 1] => 1, 3, 2, 2, 2, 3, 3, 2, 1
[1, 3, 2, 2, 2, 3, 3, 2, 2] => 1, 3, 2, 2, 2, 3, 3, 2, 2
[1, 3, 2, 2, 2, 3, 3, 2, 3] => 1, 3, 2, 2, 2, 3, 3, 2, 3
[1, 3, 2, 2, 2, 3, 3, 3, 1] => 1, 3, 2, 2, 2, 3, 3, 3, 1
[1, 3, 2, 2, 2, 3, 3, 3, 2] => 1, 3, 2, 2, 2, 3, 3, 3, 2
[1, 3, 2, 2, 2, 3, 3, 3, 3] => 1, 3, 2, 2, 2, 3, 3, 3, 3
[1, 3, 2, 2, 3, 1, 1, 1, 1] => 1, 3, 2, 2, 3, 1, 1, 1, 1
[1, 3, 2, 2, 3, 1, 1, 1, 2] => 1, 3, 2, 2, 3, 1, 1, 1, 2
[1, 3, 2, 2, 3, 1, 1, 1, 3] => 1, 3, 2, 2, 3, 1, 1, 1, 3
[1, 3, 2, 2, 3, 1, 1, 2, 1] => 1, 3, 2, 2, 3, 1, 1, 2, 1
[1, 3, 2, 2, 3, 1, 1, 2, 2] => 1, 3, 2, 2, 3, 1, 1, 2, 2
[1, 3, 2, 2, 3, 1, 1, 2, 3] => 1, 3, 2, 2, 3, 1, 1, 2, 3
[1, 3, 2, 2, 3, 1, 1, 3, 1] => 1, 3, 2, 2, 3, 1, 1, 3, 1
[1, 3, 2, 2, 3, 1, 1, 3, 2] => 1, 3, 2, 2, 3, 1, 1, 3, 2
[1, 3, 2, 2, 3, 1, 1, 3, 3] => 1, 3, 2, 2, 3, 1, 1, 3, 3
[1, 3, 2, 2, 3, 1, 2, 1, 1] => 1, 3, 2, 2, 3, 1, 2, 1, 1
[1, 3, 2, 2, 3, 1, 2, 1, 2] => 1, 3, 2, 2, 3, 1, 2, 1, 2
[1, 3, 2, 2, 3, 1, 2, 1, 3] => 1, 3, 2, 2, 3, 1, 2, 1, 3
[1, 3, 2, 2, 3, 1, 2, 2, 1] => 1, 3, 2, 2, 3, 1, 2, 2, 1
[1, 3, 2, 2, 3, 1, 2, 2, 2] => 1, 3, 2, 2, 3, 1, 2, 2, 2
[1, 3, 2, 2, 3, 1, 2, 2, 3] => 1, 3, 2, 2, 3, 1, 2, 2, 3
[1, 3, 2, 2, 3, 1, 2, 3, 1] => 1, 3, 2, 2, 3, 1, 2, 3, 1
[1, 3, 2, 2, 3, 1, 2, 3, 2] => 1, 3, 2, 2, 3, 1, 2, 3, 2
[1, 3, 2, 2, 3, 1, 2, 3, 3] => 1, 3, 2, 2, 3, 1, 2, 3, 3
[1, 3, 2, 2, 3, 1, 3, 1, 1] => 1, 3, 2, 2, 3, 1, 3, 1, 1
[1, 3, 2, 2, 3, 1, 3, 1, 2] => 1, 3, 2, 2, 3, 1, 3, 1, 2
[1, 3, 2, 2, 3, 1, 3, 1, 3] => 1, 3, 2, 2, 3, 1, 3, 1, 3
[1, 3, 2, 2, 3, 1, 3, 2, 1] => 1, 3, 2, 2, 3, 1, 3, 2, 1
[1, 3, 2, 2, 3, 1, 3, 2, 2] => 1, 3, 2, 2, 3, 1, 3, 2, 2
[1, 3, 2, 2, 3, 1, 3, 2, 3] => 1, 3, 2, 2, 3, 1, 3, 2, 3
[1, 3, 2, 2, 3, 1, 3, 3, 1] => 1, 3, 2, 2, 3, 1, 3, 3, 1
[1, 3, 2, 2, 3, 1, 3, 3, 2] => 1, 3, 2, 2, 3, 1, 3, 3, 2
[1, 3, 2, 2, 3, 1, 3, 3, 3] => 1, 3, 2, 2, 3, 1, 3, 3, 3
[1, 3, 2, 2, 3, 2, 1, 1, 1] => 1, 3, 2, 2, 3, 2, 1, 1, 1
[1, 3, 2, 2, 3, 2, 1, 1, 2] => 1, 3, 2, 2, 3, 2, 1, 1, 2
[1, 3, 2, 2, 3, 2, 1, 1, 3] => 1, 3, 2, 2, 3, 2, 1, 1, 3
[1, 3, 2, 2, 3, 2, 1, 2, 1] => 1, 3, 2, 2, 3, 2, 1, 2, 1
[1, 3, 2, 2, 3, 2, 1, 2, 2] => 1, 3, 2, 2, 3, 2, 1, 2, 2
[1, 3, 2, 2, 3, 2, 1, 2, 3] => 1, 3, 2, 2, 3, 2, 1, 2, 3
[1, 3, 2, 2, 3, 2, 1, 3, 1] => 1, 3, 2, 2, 3, 2, 1, 3, 1
[1, 3, 2, 2, 3, 2, 1, 3, 2] => 1, 3, 2, 2, 3, 2, 1, 3, 2
[1, 3, 2, 2, 3, 2, 1, 3, 3] => 1, 3, 2, 2, 3, 2, 1, 3, 3
[1, 3, 2, 2, 3, 2, 2, 1, 1] => 1, 3, 2, 2, 3, 2, 2, 1, 1
[1, 3, 2, 2, 3, 2, 2, 1, 2] => 1, 3, 2, 2, 3, 2, 2, 1, 2
[1, 3, 2, 2, 3, 2, 2, 1, 3] => 1, 3, 2, 2, 3, 2, 2, 1, 3
[1, 3, 2, 2, 3, 2, 2, 2, 1] => 1, 3, 2, 2, 3, 2, 2, 2, 1
[1, 3, 2, 2, 3, 2, 2, 2, 2] => 1, 3, 2, 2, 3, 2, 2, 2, 2
[1, 3, 2, 2, 3, 2, 2, 2, 3] => 1, 3, 2, 2, 3, 2, 2, 2, 3
[1, 3, 2, 2, 3, 2, 2, 3, 1] => 1, 3, 2, 2, 3, 2, 2, 3, 1
[1, 3, 2, 2, 3, 2, 2, 3, 2] => 1, 3, 2, 2, 3, 2, 2, 3, 2
[1, 3, 2, 2, 3, 2, 2, 3, 3] => 1, 3, 2, 2, 3, 2, 2, 3, 3
[1, 3, 2, 2, 3, 2, 3, 1, 1] => 1, 3, 2, 2, 3, 2, 3, 1, 1
[1, 3, 2, 2, 3, 2, 3, 1, 2] => 1, 3, 2, 2, 3, 2, 3, 1, 2
[1, 3, 2, 2, 3, 2, 3, 1, 3] => 1, 3, 2, 2, 3, 2, 3, 1, 3
[1, 3, 2, 2, 3, 2, 3, 2, 1] => 1, 3, 2, 2, 3, 2, 3, 2, 1
[1, 3, 2, 2, 3, 2, 3, 2, 2] => 1, 3, 2, 2, 3, 2, 3, 2, 2
[1, 3, 2, 2, 3, 2, 3, 2, 3] => 1, 3, 2, 2, 3, 2, 3, 2, 3
[1, 3, 2, 2, 3, 2, 3, 3, 1] => 1, 3, 2, 2, 3, 2, 3, 3, 1
[1, 3, 2, 2, 3, 2, 3, 3, 2] => 1, 3, 2, 2, 3, 2, 3, 3, 2
[1, 3, 2, 2, 3, 2, 3, 3, 3] => 1, 3, 2, 2, 3, 2, 3, 3, 3
[1, 3, 2, 2, 3, 3, 1, 1, 1] => 1, 3, 2, 2, 3, 3, 1, 1, 1
[1, 3, 2, 2, 3, 3, 1, 1, 2] => 1, 3, 2, 2, 3, 3, 1, 1, 2
[1, 3, 2, 2, 3, 3, 1, 1, 3] => 1, 3, 2, 2, 3, 3, 1, 1, 3
[1, 3, 2, 2, 3, 3, 1, 2, 1] => 1, 3, 2, 2, 3, 3, 1, 2, 1
[1, 3, 2, 2, 3, 3, 1, 2, 2] => 1, 3, 2, 2, 3, 3, 1, 2, 2
[1, 3, 2, 2, 3, 3, 1, 2, 3] => 1, 3, 2, 2, 3, 3, 1, 2, 3
[1, 3, 2, 2, 3, 3, 1, 3, 1] => 1, 3, 2, 2, 3, 3, 1, 3, 1
[1, 3, 2, 2, 3, 3, 1, 3, 2] => 1, 3, 2, 2, 3, 3, 1, 3, 2
[1, 3, 2, 2, 3, 3, 1, 3, 3] => 1, 3, 2, 2, 3, 3, 1, 3, 3
[1, 3, 2, 2, 3, 3, 2, 1, 1] => 1, 3, 2, 2, 3, 3, 2, 1, 1
[1, 3, 2, 2, 3, 3, 2, 1, 2] => 1, 3, 2, 2, 3, 3, 2, 1, 2
[1, 3, 2, 2, 3, 3, 2, 1, 3] => 1, 3, 2, 2, 3, 3, 2, 1, 3
[1, 3, 2, 2, 3, 3, 2, 2, 1] => 1, 3, 2, 2, 3, 3, 2, 2, 1
[1, 3, 2, 2, 3, 3, 2, 2, 2] => 1, 3, 2, 2, 3, 3, 2, 2, 2
[1, 3, 2, 2, 3, 3, 2, 2, 3] => 1, 3, 2, 2, 3, 3, 2, 2, 3
[1, 3, 2, 2, 3, 3, 2, 3, 1] => 1, 3, 2, 2, 3, 3, 2, 3, 1
[1, 3, 2, 2, 3, 3, 2, 3, 2] => 1, 3, 2, 2, 3, 3, 2, 3, 2
[1, 3, 2, 2, 3, 3, 2, 3, 3] => 1, 3, 2, 2, 3, 3, 2, 3, 3
[1, 3, 2, 2, 3, 3, 3, 1, 1] => 1, 3, 2, 2, 3, 3, 3, 1, 1
[1, 3, 2, 2, 3, 3, 3, 1, 2] => 1, 3, 2, 2, 3, 3, 3, 1, 2
[1, 3, 2, 2, 3, 3, 3, 1, 3] => 1, 3, 2, 2, 3, 3, 3, 1, 3
[1, 3, 2, 2, 3, 3, 3, 2, 1] => 1, 3, 2, 2, 3, 3, 3, 2, 1
[1, 3, 2, 2, 3, 3, 3, 2, 2] => 1, 3, 2, 2, 3, 3, 3, 2, 2
[1, 3, 2, 2, 3, 3, 3, 2, 3] => 1, 3, 2, 2, 3, 3, 3, 2, 3
[1, 3, 2, 2, 3, 3, 3, 3, 1] => 1, 3, 2, 2, 3, 3, 3, 3, 1
[1, 3, 2, 2, 3, 3, 3, 3, 2] => 1, 3, 2, 2, 3, 3, 3, 3, 2
[1, 3, 2, 2, 3, 3, 3, 3, 3] => 1, 3, 2, 2, 3, 3, 3, 3, 3
[1, 3, 2, 3, 1, 1, 1, 1, 1] => 1, 3, 2, 3, 1, 1, 1, 1, 1
[1, 3, 2, 3, 1, 1, 1, 1, 2] => 1, 3, 2, 3, 1, 1, 1, 1, 2
[1, 3, 2, 3, 1, 1, 1, 1, 3] => 1, 3, 2, 3, 1, 1, 1, 1, 3
[1, 3, 2, 3, 1, 1, 1, 2, 1] => 1, 3, 2, 3, 1, 1, 1, 2, 1
[1, 3, 2, 3, 1, 1, 1, 2, 2] => 1, 3, 2, 3, 1, 1, 1, 2, 2
[1, 3, 2, 3, 1, 1, 1, 2, 3] => 1, 3, 2, 3, 1, 1, 1, 2, 3
[1, 3, 2, 3, 1, 1, 1, 3, 1] => 1, 3, 2, 3, 1, 1, 1, 3, 1
[1, 3, 2, 3, 1, 1, 1, 3, 2] => 1, 3, 2, 3, 1, 1, 1, 3, 2
[1, 3, 2, 3, 1, 1, 1, 3, 3] => 1, 3, 2, 3, 1, 1, 1, 3, 3
[1, 3, 2, 3, 1, 1, 2, 1, 1] => 1, 3, 2, 3, 1, 1, 2, 1, 1
[1, 3, 2, 3, 1, 1, 2, 1, 2] => 1, 3, 2, 3, 1, 1, 2, 1, 2
[1, 3, 2, 3, 1, 1, 2, 1, 3] => 1, 3, 2, 3, 1, 1, 2, 1, 3
[1, 3, 2, 3, 1, 1, 2, 2, 1] => 1, 3, 2, 3, 1, 1, 2, 2, 1
[1, 3, 2, 3, 1, 1, 2, 2, 2] => 1, 3, 2, 3, 1, 1, 2, 2, 2
[1, 3, 2, 3, 1, 1, 2, 2, 3] => 1, 3, 2, 3, 1, 1, 2, 2, 3
[1, 3, 2, 3, 1, 1, 2, 3, 1] => 1, 3, 2, 3, 1, 1, 2, 3, 1
[1, 3, 2, 3, 1, 1, 2, 3, 2] => 1, 3, 2, 3, 1, 1, 2, 3, 2
[1, 3, 2, 3, 1, 1, 2, 3, 3] => 1, 3, 2, 3, 1, 1, 2, 3, 3
[1, 3, 2, 3, 1, 1, 3, 1, 1] => 1, 3, 2, 3, 1, 1, 3, 1, 1
[1, 3, 2, 3, 1, 1, 3, 1, 2] => 1, 3, 2, 3, 1, 1, 3, 1, 2
[1, 3, 2, 3, 1, 1, 3, 1, 3] => 1, 3, 2, 3, 1, 1, 3, 1, 3
[1, 3, 2, 3, 1, 1, 3, 2, 1] => 1, 3, 2, 3, 1, 1, 3, 2, 1
[1, 3, 2, 3, 1, 1, 3, 2, 2] => 1, 3, 2, 3, 1, 1, 3, 2, 2
[1, 3, 2, 3, 1, 1, 3, 2, 3] => 1, 3, 2, 3, 1, 1, 3, 2, 3
[1, 3, 2, 3, 1, 1, 3, 3, 1] => 1, 3, 2, 3, 1, 1, 3, 3, 1
[1, 3, 2, 3, 1, 1, 3, 3, 2] => 1, 3, 2, 3, 1, 1, 3, 3, 2
[1, 3, 2, 3, 1, 1, 3, 3, 3] => 1, 3, 2, 3, 1, 1, 3, 3, 3
[1, 3, 2, 3, 1, 2, 1, 1, 1] => 1, 3, 2, 3, 1, 2, 1, 1, 1
[1, 3, 2, 3, 1, 2, 1, 1, 2] => 1, 3, 2, 3, 1, 2, 1, 1, 2
[1, 3, 2, 3, 1, 2, 1, 1, 3] => 1, 3, 2, 3, 1, 2, 1, 1, 3
[1, 3, 2, 3, 1, 2, 1, 2, 1] => 1, 3, 2, 3, 1, 2, 1, 2, 1
[1, 3, 2, 3, 1, 2, 1, 2, 2] => 1, 3, 2, 3, 1, 2, 1, 2, 2
[1, 3, 2, 3, 1, 2, 1, 2, 3] => 1, 3, 2, 3, 1, 2, 1, 2, 3
[1, 3, 2, 3, 1, 2, 1, 3, 1] => 1, 3, 2, 3, 1, 2, 1, 3, 1
[1, 3, 2, 3, 1, 2, 1, 3, 2] => 1, 3, 2, 3, 1, 2, 1, 3, 2
[1, 3, 2, 3, 1, 2, 1, 3, 3] => 1, 3, 2, 3, 1, 2, 1, 3, 3
[1, 3, 2, 3, 1, 2, 2, 1, 1] => 1, 3, 2, 3, 1, 2, 2, 1, 1
[1, 3, 2, 3, 1, 2, 2, 1, 2] => 1, 3, 2, 3, 1, 2, 2, 1, 2
[1, 3, 2, 3, 1, 2, 2, 1, 3] => 1, 3, 2, 3, 1, 2, 2, 1, 3
[1, 3, 2, 3, 1, 2, 2, 2, 1] => 1, 3, 2, 3, 1, 2, 2, 2, 1
[1, 3, 2, 3, 1, 2, 2, 2, 2] => 1, 3, 2, 3, 1, 2, 2, 2, 2
[1, 3, 2, 3, 1, 2, 2, 2, 3] => 1, 3, 2, 3, 1, 2, 2, 2, 3
[1, 3, 2, 3, 1, 2, 2, 3, 1] => 1, 3, 2, 3, 1, 2, 2, 3, 1
[1, 3, 2, 3, 1, 2, 2, 3, 2] => 1, 3, 2, 3, 1, 2, 2, 3, 2
[1, 3, 2, 3, 1, 2, 2, 3, 3] => 1, 3, 2, 3, 1, 2, 2, 3, 3
[1, 3, 2, 3, 1, 2, 3, 1, 1] => 1, 3, 2, 3, 1, 2, 3, 1, 1
[1, 3, 2, 3, 1, 2, 3, 1, 2] => 1, 3, 2, 3, 1, 2, 3, 1, 2
[1, 3, 2, 3, 1, 2, 3, 1, 3] => 1, 3, 2, 3, 1, 2, 3, 1, 3
[1, 3, 2, 3, 1, 2, 3, 2, 1] => 1, 3, 2, 3, 1, 2, 3, 2, 1
[1, 3, 2, 3, 1, 2, 3, 2, 2] => 1, 3, 2, 3, 1, 2, 3, 2, 2
[1, 3, 2, 3, 1, 2, 3, 2, 3] => 1, 3, 2, 3, 1, 2, 3, 2, 3
[1, 3, 2, 3, 1, 2, 3, 3, 1] => 1, 3, 2, 3, 1, 2, 3, 3, 1
[1, 3, 2, 3, 1, 2, 3, 3, 2] => 1, 3, 2, 3, 1, 2, 3, 3, 2
[1, 3, 2, 3, 1, 2, 3, 3, 3] => 1, 3, 2, 3, 1, 2, 3, 3, 3
[1, 3, 2, 3, 1, 3, 1, 1, 1] => 1, 3, 2, 3, 1, 3, 1, 1, 1
[1, 3, 2, 3, 1, 3, 1, 1, 2] => 1, 3, 2, 3, 1, 3, 1, 1, 2
[1, 3, 2, 3, 1, 3, 1, 1, 3] => 1, 3, 2, 3, 1, 3, 1, 1, 3
[1, 3, 2, 3, 1, 3, 1, 2, 1] => 1, 3, 2, 3, 1, 3, 1, 2, 1
[1, 3, 2, 3, 1, 3, 1, 2, 2] => 1, 3, 2, 3, 1, 3, 1, 2, 2
[1, 3, 2, 3, 1, 3, 1, 2, 3] => 1, 3, 2, 3, 1, 3, 1, 2, 3
[1, 3, 2, 3, 1, 3, 1, 3, 1] => 1, 3, 2, 3, 1, 3, 1, 3, 1
[1, 3, 2, 3, 1, 3, 1, 3, 2] => 1, 3, 2, 3, 1, 3, 1, 3, 2
[1, 3, 2, 3, 1, 3, 1, 3, 3] => 1, 3, 2, 3, 1, 3, 1, 3, 3
[1, 3, 2, 3, 1, 3, 2, 1, 1] => 1, 3, 2, 3, 1, 3, 2, 1, 1
[1, 3, 2, 3, 1, 3, 2, 1, 2] => 1, 3, 2, 3, 1, 3, 2, 1, 2
[1, 3, 2, 3, 1, 3, 2, 1, 3] => 1, 3, 2, 3, 1, 3, 2, 1, 3
[1, 3, 2, 3, 1, 3, 2, 2, 1] => 1, 3, 2, 3, 1, 3, 2, 2, 1
[1, 3, 2, 3, 1, 3, 2, 2, 2] => 1, 3, 2, 3, 1, 3, 2, 2, 2
[1, 3, 2, 3, 1, 3, 2, 2, 3] => 1, 3, 2, 3, 1, 3, 2, 2, 3
[1, 3, 2, 3, 1, 3, 2, 3, 1] => 1, 3, 2, 3, 1, 3, 2, 3, 1
[1, 3, 2, 3, 1, 3, 2, 3, 2] => 1, 3, 2, 3, 1, 3, 2, 3, 2
[1, 3, 2, 3, 1, 3, 2, 3, 3] => 1, 3, 2, 3, 1, 3, 2, 3, 3
[1, 3, 2, 3, 1, 3, 3, 1, 1] => 1, 3, 2, 3, 1, 3, 3, 1, 1
[1, 3, 2, 3, 1, 3, 3, 1, 2] => 1, 3, 2, 3, 1, 3, 3, 1, 2
[1, 3, 2, 3, 1, 3, 3, 1, 3] => 1, 3, 2, 3, 1, 3, 3, 1, 3
[1, 3, 2, 3, 1, 3, 3, 2, 1] => 1, 3, 2, 3, 1, 3, 3, 2, 1
[1, 3, 2, 3, 1, 3, 3, 2, 2] => 1, 3, 2, 3, 1, 3, 3, 2, 2
[1, 3, 2, 3, 1, 3, 3, 2, 3] => 1, 3, 2, 3, 1, 3, 3, 2, 3
[1, 3, 2, 3, 1, 3, 3, 3, 1] => 1, 3, 2, 3, 1, 3, 3, 3, 1
[1, 3, 2, 3, 1, 3, 3, 3, 2] => 1, 3, 2, 3, 1, 3, 3, 3, 2
[1, 3, 2, 3, 1, 3, 3, 3, 3] => 1, 3, 2, 3, 1, 3, 3, 3, 3
[1, 3, 2, 3, 2, 1, 1, 1, 1] => 1, 3, 2, 3, 2, 1, 1, 1, 1
[1, 3, 2, 3, 2, 1, 1, 1, 2] => 1, 3, 2, 3, 2, 1, 1, 1, 2
[1, 3, 2, 3, 2, 1, 1, 1, 3] => 1, 3, 2, 3, 2, 1, 1, 1, 3
[1, 3, 2, 3, 2, 1, 1, 2, 1] => 1, 3, 2, 3, 2, 1, 1, 2, 1
[1, 3, 2, 3, 2, 1, 1, 2, 2] => 1, 3, 2, 3, 2, 1, 1, 2, 2
[1, 3, 2, 3, 2, 1, 1, 2, 3] => 1, 3, 2, 3, 2, 1, 1, 2, 3
[1, 3, 2, 3, 2, 1, 1, 3, 1] => 1, 3, 2, 3, 2, 1, 1, 3, 1
[1, 3, 2, 3, 2, 1, 1, 3, 2] => 1, 3, 2, 3, 2, 1, 1, 3, 2
[1, 3, 2, 3, 2, 1, 1, 3, 3] => 1, 3, 2, 3, 2, 1, 1, 3, 3
[1, 3, 2, 3, 2, 1, 2, 1, 1] => 1, 3, 2, 3, 2, 1, 2, 1, 1
[1, 3, 2, 3, 2, 1, 2, 1, 2] => 1, 3, 2, 3, 2, 1, 2, 1, 2
[1, 3, 2, 3, 2, 1, 2, 1, 3] => 1, 3, 2, 3, 2, 1, 2, 1, 3
[1, 3, 2, 3, 2, 1, 2, 2, 1] => 1, 3, 2, 3, 2, 1, 2, 2, 1
[1, 3, 2, 3, 2, 1, 2, 2, 2] => 1, 3, 2, 3, 2, 1, 2, 2, 2
[1, 3, 2, 3, 2, 1, 2, 2, 3] => 1, 3, 2, 3, 2, 1, 2, 2, 3
[1, 3, 2, 3, 2, 1, 2, 3, 1] => 1, 3, 2, 3, 2, 1, 2, 3, 1
[1, 3, 2, 3, 2, 1, 2, 3, 2] => 1, 3, 2, 3, 2, 1, 2, 3, 2
[1, 3, 2, 3, 2, 1, 2, 3, 3] => 1, 3, 2, 3, 2, 1, 2, 3, 3
[1, 3, 2, 3, 2, 1, 3, 1, 1] => 1, 3, 2, 3, 2, 1, 3, 1, 1
[1, 3, 2, 3, 2, 1, 3, 1, 2] => 1, 3, 2, 3, 2, 1, 3, 1, 2
[1, 3, 2, 3, 2, 1, 3, 1, 3] => 1, 3, 2, 3, 2, 1, 3, 1, 3
[1, 3, 2, 3, 2, 1, 3, 2, 1] => 1, 3, 2, 3, 2, 1, 3, 2, 1
[1, 3, 2, 3, 2, 1, 3, 2, 2] => 1, 3, 2, 3, 2, 1, 3, 2, 2
[1, 3, 2, 3, 2, 1, 3, 2, 3] => 1, 3, 2, 3, 2, 1, 3, 2, 3
[1, 3, 2, 3, 2, 1, 3, 3, 1] => 1, 3, 2, 3, 2, 1, 3, 3, 1
[1, 3, 2, 3, 2, 1, 3, 3, 2] => 1, 3, 2, 3, 2, 1, 3, 3, 2
[1, 3, 2, 3, 2, 1, 3, 3, 3] => 1, 3, 2, 3, 2, 1, 3, 3, 3
[1, 3, 2, 3, 2, 2, 1, 1, 1] => 1, 3, 2, 3, 2, 2, 1, 1, 1
[1, 3, 2, 3, 2, 2, 1, 1, 2] => 1, 3, 2, 3, 2, 2, 1, 1, 2
[1, 3, 2, 3, 2, 2, 1, 1, 3] => 1, 3, 2, 3, 2, 2, 1, 1, 3
[1, 3, 2, 3, 2, 2, 1, 2, 1] => 1, 3, 2, 3, 2, 2, 1, 2, 1
[1, 3, 2, 3, 2, 2, 1, 2, 2] => 1, 3, 2, 3, 2, 2, 1, 2, 2
[1, 3, 2, 3, 2, 2, 1, 2, 3] => 1, 3, 2, 3, 2, 2, 1, 2, 3
[1, 3, 2, 3, 2, 2, 1, 3, 1] => 1, 3, 2, 3, 2, 2, 1, 3, 1
[1, 3, 2, 3, 2, 2, 1, 3, 2] => 1, 3, 2, 3, 2, 2, 1, 3, 2
[1, 3, 2, 3, 2, 2, 1, 3, 3] => 1, 3, 2, 3, 2, 2, 1, 3, 3
[1, 3, 2, 3, 2, 2, 2, 1, 1] => 1, 3, 2, 3, 2, 2, 2, 1, 1
[1, 3, 2, 3, 2, 2, 2, 1, 2] => 1, 3, 2, 3, 2, 2, 2, 1, 2
[1, 3, 2, 3, 2, 2, 2, 1, 3] => 1, 3, 2, 3, 2, 2, 2, 1, 3
[1, 3, 2, 3, 2, 2, 2, 2, 1] => 1, 3, 2, 3, 2, 2, 2, 2, 1
[1, 3, 2, 3, 2, 2, 2, 2, 2] => 1, 3, 2, 3, 2, 2, 2, 2, 2
[1, 3, 2, 3, 2, 2, 2, 2, 3] => 1, 3, 2, 3, 2, 2, 2, 2, 3
[1, 3, 2, 3, 2, 2, 2, 3, 1] => 1, 3, 2, 3, 2, 2, 2, 3, 1
[1, 3, 2, 3, 2, 2, 2, 3, 2] => 1, 3, 2, 3, 2, 2, 2, 3, 2
[1, 3, 2, 3, 2, 2, 2, 3, 3] => 1, 3, 2, 3, 2, 2, 2, 3, 3
[1, 3, 2, 3, 2, 2, 3, 1, 1] => 1, 3, 2, 3, 2, 2, 3, 1, 1
[1, 3, 2, 3, 2, 2, 3, 1, 2] => 1, 3, 2, 3, 2, 2, 3, 1, 2
[1, 3, 2, 3, 2, 2, 3, 1, 3] => 1, 3, 2, 3, 2, 2, 3, 1, 3
[1, 3, 2, 3, 2, 2, 3, 2, 1] => 1, 3, 2, 3, 2, 2, 3, 2, 1
[1, 3, 2, 3, 2, 2, 3, 2, 2] => 1, 3, 2, 3, 2, 2, 3, 2, 2
[1, 3, 2, 3, 2, 2, 3, 2, 3] => 1, 3, 2, 3, 2, 2, 3, 2, 3
[1, 3, 2, 3, 2, 2, 3, 3, 1] => 1, 3, 2, 3, 2, 2, 3, 3, 1
[1, 3, 2, 3, 2, 2, 3, 3, 2] => 1, 3, 2, 3, 2, 2, 3, 3, 2
[1, 3, 2, 3, 2, 2, 3, 3, 3] => 1, 3, 2, 3, 2, 2, 3, 3, 3
[1, 3, 2, 3, 2, 3, 1, 1, 1] => 1, 3, 2, 3, 2, 3, 1, 1, 1
[1, 3, 2, 3, 2, 3, 1, 1, 2] => 1, 3, 2, 3, 2, 3, 1, 1, 2
[1, 3, 2, 3, 2, 3, 1, 1, 3] => 1, 3, 2, 3, 2, 3, 1, 1, 3
[1, 3, 2, 3, 2, 3, 1, 2, 1] => 1, 3, 2, 3, 2, 3, 1, 2, 1
[1, 3, 2, 3, 2, 3, 1, 2, 2] => 1, 3, 2, 3, 2, 3, 1, 2, 2
[1, 3, 2, 3, 2, 3, 1, 2, 3] => 1, 3, 2, 3, 2, 3, 1, 2, 3
[1, 3, 2, 3, 2, 3, 1, 3, 1] => 1, 3, 2, 3, 2, 3, 1, 3, 1
[1, 3, 2, 3, 2, 3, 1, 3, 2] => 1, 3, 2, 3, 2, 3, 1, 3, 2
[1, 3, 2, 3, 2, 3, 1, 3, 3] => 1, 3, 2, 3, 2, 3, 1, 3, 3
[1, 3, 2, 3, 2, 3, 2, 1, 1] => 1, 3, 2, 3, 2, 3, 2, 1, 1
[1, 3, 2, 3, 2, 3, 2, 1, 2] => 1, 3, 2, 3, 2, 3, 2, 1, 2
[1, 3, 2, 3, 2, 3, 2, 1, 3] => 1, 3, 2, 3, 2, 3, 2, 1, 3
[1, 3, 2, 3, 2, 3, 2, 2, 1] => 1, 3, 2, 3, 2, 3, 2, 2, 1
[1, 3, 2, 3, 2, 3, 2, 2, 2] => 1, 3, 2, 3, 2, 3, 2, 2, 2
[1, 3, 2, 3, 2, 3, 2, 2, 3] => 1, 3, 2, 3, 2, 3, 2, 2, 3
[1, 3, 2, 3, 2, 3, 2, 3, 1] => 1, 3, 2, 3, 2, 3, 2, 3, 1
[1, 3, 2, 3, 2, 3, 2, 3, 2] => 1, 3, 2, 3, 2, 3, 2, 3, 2
[1, 3, 2, 3, 2, 3, 2, 3, 3] => 1, 3, 2, 3, 2, 3, 2, 3, 3
[1, 3, 2, 3, 2, 3, 3, 1, 1] => 1, 3, 2, 3, 2, 3, 3, 1, 1
[1, 3, 2, 3, 2, 3, 3, 1, 2] => 1, 3, 2, 3, 2, 3, 3, 1, 2
[1, 3, 2, 3, 2, 3, 3, 1, 3] => 1, 3, 2, 3, 2, 3, 3, 1, 3
[1, 3, 2, 3, 2, 3, 3, 2, 1] => 1, 3, 2, 3, 2, 3, 3, 2, 1
[1, 3, 2, 3, 2, 3, 3, 2, 2] => 1, 3, 2, 3, 2, 3, 3, 2, 2
[1, 3, 2, 3, 2, 3, 3, 2, 3] => 1, 3, 2, 3, 2, 3, 3, 2, 3
[1, 3, 2, 3, 2, 3, 3, 3, 1] => 1, 3, 2, 3, 2, 3, 3, 3, 1
[1, 3, 2, 3, 2, 3, 3, 3, 2] => 1, 3, 2, 3, 2, 3, 3, 3, 2
[1, 3, 2, 3, 2, 3, 3, 3, 3] => 1, 3, 2, 3, 2, 3, 3, 3, 3
[1, 3, 2, 3, 3, 1, 1, 1, 1] => 1, 3, 2, 3, 3, 1, 1, 1, 1
[1, 3, 2, 3, 3, 1, 1, 1, 2] => 1, 3, 2, 3, 3, 1, 1, 1, 2
[1, 3, 2, 3, 3, 1, 1, 1, 3] => 1, 3, 2, 3, 3, 1, 1, 1, 3
[1, 3, 2, 3, 3, 1, 1, 2, 1] => 1, 3, 2, 3, 3, 1, 1, 2, 1
[1, 3, 2, 3, 3, 1, 1, 2, 2] => 1, 3, 2, 3, 3, 1, 1, 2, 2
[1, 3, 2, 3, 3, 1, 1, 2, 3] => 1, 3, 2, 3, 3, 1, 1, 2, 3
[1, 3, 2, 3, 3, 1, 1, 3, 1] => 1, 3, 2, 3, 3, 1, 1, 3, 1
[1, 3, 2, 3, 3, 1, 1, 3, 2] => 1, 3, 2, 3, 3, 1, 1, 3, 2
[1, 3, 2, 3, 3, 1, 1, 3, 3] => 1, 3, 2, 3, 3, 1, 1, 3, 3
[1, 3, 2, 3, 3, 1, 2, 1, 1] => 1, 3, 2, 3, 3, 1, 2, 1, 1
[1, 3, 2, 3, 3, 1, 2, 1, 2] => 1, 3, 2, 3, 3, 1, 2, 1, 2
[1, 3, 2, 3, 3, 1, 2, 1, 3] => 1, 3, 2, 3, 3, 1, 2, 1, 3
[1, 3, 2, 3, 3, 1, 2, 2, 1] => 1, 3, 2, 3, 3, 1, 2, 2, 1
[1, 3, 2, 3, 3, 1, 2, 2, 2] => 1, 3, 2, 3, 3, 1, 2, 2, 2
[1, 3, 2, 3, 3, 1, 2, 2, 3] => 1, 3, 2, 3, 3, 1, 2, 2, 3
[1, 3, 2, 3, 3, 1, 2, 3, 1] => 1, 3, 2, 3, 3, 1, 2, 3, 1
[1, 3, 2, 3, 3, 1, 2, 3, 2] => 1, 3, 2, 3, 3, 1, 2, 3, 2
[1, 3, 2, 3, 3, 1, 2, 3, 3] => 1, 3, 2, 3, 3, 1, 2, 3, 3
[1, 3, 2, 3, 3, 1, 3, 1, 1] => 1, 3, 2, 3, 3, 1, 3, 1, 1
[1, 3, 2, 3, 3, 1, 3, 1, 2] => 1, 3, 2, 3, 3, 1, 3, 1, 2
[1, 3, 2, 3, 3, 1, 3, 1, 3] => 1, 3, 2, 3, 3, 1, 3, 1, 3
[1, 3, 2, 3, 3, 1, 3, 2, 1] => 1, 3, 2, 3, 3, 1, 3, 2, 1
[1, 3, 2, 3, 3, 1, 3, 2, 2] => 1, 3, 2, 3, 3, 1, 3, 2, 2
[1, 3, 2, 3, 3, 1, 3, 2, 3] => 1, 3, 2, 3, 3, 1, 3, 2, 3
[1, 3, 2, 3, 3, 1, 3, 3, 1] => 1, 3, 2, 3, 3, 1, 3, 3, 1
[1, 3, 2, 3, 3, 1, 3, 3, 2] => 1, 3, 2, 3, 3, 1, 3, 3, 2
[1, 3, 2, 3, 3, 1, 3, 3, 3] => 1, 3, 2, 3, 3, 1, 3, 3, 3
[1, 3, 2, 3, 3, 2, 1, 1, 1] => 1, 3, 2, 3, 3, 2, 1, 1, 1
[1, 3, 2, 3, 3, 2, 1, 1, 2] => 1, 3, 2, 3, 3, 2, 1, 1, 2
[1, 3, 2, 3, 3, 2, 1, 1, 3] => 1, 3, 2, 3, 3, 2, 1, 1, 3
[1, 3, 2, 3, 3, 2, 1, 2, 1] => 1, 3, 2, 3, 3, 2, 1, 2, 1
[1, 3, 2, 3, 3, 2, 1, 2, 2] => 1, 3, 2, 3, 3, 2, 1, 2, 2
[1, 3, 2, 3, 3, 2, 1, 2, 3] => 1, 3, 2, 3, 3, 2, 1, 2, 3
[1, 3, 2, 3, 3, 2, 1, 3, 1] => 1, 3, 2, 3, 3, 2, 1, 3, 1
[1, 3, 2, 3, 3, 2, 1, 3, 2] => 1, 3, 2, 3, 3, 2, 1, 3, 2
[1, 3, 2, 3, 3, 2, 1, 3, 3] => 1, 3, 2, 3, 3, 2, 1, 3, 3
[1, 3, 2, 3, 3, 2, 2, 1, 1] => 1, 3, 2, 3, 3, 2, 2, 1, 1
[1, 3, 2, 3, 3, 2, 2, 1, 2] => 1, 3, 2, 3, 3, 2, 2, 1, 2
[1, 3, 2, 3, 3, 2, 2, 1, 3] => 1, 3, 2, 3, 3, 2, 2, 1, 3
[1, 3, 2, 3, 3, 2, 2, 2, 1] => 1, 3, 2, 3, 3, 2, 2, 2, 1
[1, 3, 2, 3, 3, 2, 2, 2, 2] => 1, 3, 2, 3, 3, 2, 2, 2, 2
[1, 3, 2, 3, 3, 2, 2, 2, 3] => 1, 3, 2, 3, 3, 2, 2, 2, 3
[1, 3, 2, 3, 3, 2, 2, 3, 1] => 1, 3, 2, 3, 3, 2, 2, 3, 1
[1, 3, 2, 3, 3, 2, 2, 3, 2] => 1, 3, 2, 3, 3, 2, 2, 3, 2
[1, 3, 2, 3, 3, 2, 2, 3, 3] => 1, 3, 2, 3, 3, 2, 2, 3, 3
[1, 3, 2, 3, 3, 2, 3, 1, 1] => 1, 3, 2, 3, 3, 2, 3, 1, 1
[1, 3, 2, 3, 3, 2, 3, 1, 2] => 1, 3, 2, 3, 3, 2, 3, 1, 2
[1, 3, 2, 3, 3, 2, 3, 1, 3] => 1, 3, 2, 3, 3, 2, 3, 1, 3
[1, 3, 2, 3, 3, 2, 3, 2, 1] => 1, 3, 2, 3, 3, 2, 3, 2, 1
[1, 3, 2, 3, 3, 2, 3, 2, 2] => 1, 3, 2, 3, 3, 2, 3, 2, 2
[1, 3, 2, 3, 3, 2, 3, 2, 3] => 1, 3, 2, 3, 3, 2, 3, 2, 3
[1, 3, 2, 3, 3, 2, 3, 3, 1] => 1, 3, 2, 3, 3, 2, 3, 3, 1
[1, 3, 2, 3, 3, 2, 3, 3, 2] => 1, 3, 2, 3, 3, 2, 3, 3, 2
[1, 3, 2, 3, 3, 2, 3, 3, 3] => 1, 3, 2, 3, 3, 2, 3, 3, 3
[1, 3, 2, 3, 3, 3, 1, 1, 1] => 1, 3, 2, 3, 3, 3, 1, 1, 1
[1, 3, 2, 3, 3, 3, 1, 1, 2] => 1, 3, 2, 3, 3, 3, 1, 1, 2
[1, 3, 2, 3, 3, 3, 1, 1, 3] => 1, 3, 2, 3, 3, 3, 1, 1, 3
[1, 3, 2, 3, 3, 3, 1, 2, 1] => 1, 3, 2, 3, 3, 3, 1, 2, 1
[1, 3, 2, 3, 3, 3, 1, 2, 2] => 1, 3, 2, 3, 3, 3, 1, 2, 2
[1, 3, 2, 3, 3, 3, 1, 2, 3] => 1, 3, 2, 3, 3, 3, 1, 2, 3
[1, 3, 2, 3, 3, 3, 1, 3, 1] => 1, 3, 2, 3, 3, 3, 1, 3, 1
[1, 3, 2, 3, 3, 3, 1, 3, 2] => 1, 3, 2, 3, 3, 3, 1, 3, 2
[1, 3, 2, 3, 3, 3, 1, 3, 3] => 1, 3, 2, 3, 3, 3, 1, 3, 3
[1, 3, 2, 3, 3, 3, 2, 1, 1] => 1, 3, 2, 3, 3, 3, 2, 1, 1
[1, 3, 2, 3, 3, 3, 2, 1, 2] => 1, 3, 2, 3, 3, 3, 2, 1, 2
[1, 3, 2, 3, 3, 3, 2, 1, 3] => 1, 3, 2, 3, 3, 3, 2, 1, 3
[1, 3, 2, 3, 3, 3, 2, 2, 1] => 1, 3, 2, 3, 3, 3, 2, 2, 1
[1, 3, 2, 3, 3, 3, 2, 2, 2] => 1, 3, 2, 3, 3, 3, 2, 2, 2
[1, 3, 2, 3, 3, 3, 2, 2, 3] => 1, 3, 2, 3, 3, 3, 2, 2, 3
[1, 3, 2, 3, 3, 3, 2, 3, 1] => 1, 3, 2, 3, 3, 3, 2, 3, 1
[1, 3, 2, 3, 3, 3, 2, 3, 2] => 1, 3, 2, 3, 3, 3, 2, 3, 2
[1, 3, 2, 3, 3, 3, 2, 3, 3] => 1, 3, 2, 3, 3, 3, 2, 3, 3
[1, 3, 2, 3, 3, 3, 3, 1, 1] => 1, 3, 2, 3, 3, 3, 3, 1, 1
[1, 3, 2, 3, 3, 3, 3, 1, 2] => 1, 3, 2, 3, 3, 3, 3, 1, 2
[1, 3, 2, 3, 3, 3, 3, 1, 3] => 1, 3, 2, 3, 3, 3, 3, 1, 3
[1, 3, 2, 3, 3, 3, 3, 2, 1] => 1, 3, 2, 3, 3, 3, 3, 2, 1
[1, 3, 2, 3, 3, 3, 3, 2, 2] => 1, 3, 2, 3, 3, 3, 3, 2, 2
[1, 3, 2, 3, 3, 3, 3, 2, 3] => 1, 3, 2, 3, 3, 3, 3, 2, 3
[1, 3, 2, 3, 3, 3, 3, 3, 1] => 1, 3, 2, 3, 3, 3, 3, 3, 1
[1, 3, 2, 3, 3, 3, 3, 3, 2] => 1, 3, 2, 3, 3, 3, 3, 3, 2
[1, 3, 2, 3, 3, 3, 3, 3, 3] => 1, 3, 2, 3, 3, 3, 3, 3, 3
[1, 3, 3, 1, 1, 1, 1, 1, 1] => 1, 3, 3, 1, 1, 1, 1, 1, 1
[1, 3, 3, 1, 1, 1, 1, 1, 2] => 1, 3, 3, 1, 1, 1, 1, 1, 2
[1, 3, 3, 1, 1, 1, 1, 1, 3] => 1, 3, 3, 1, 1, 1, 1, 1, 3
[1, 3, 3, 1, 1, 1, 1, 2, 1] => 1, 3, 3, 1, 1, 1, 1, 2, 1
[1, 3, 3, 1, 1, 1, 1, 2, 2] => 1, 3, 3, 1, 1, 1, 1, 2, 2
[1, 3, 3, 1, 1, 1, 1, 2, 3] => 1, 3, 3, 1, 1, 1, 1, 2, 3
[1, 3, 3, 1, 1, 1, 1, 3, 1] => 1, 3, 3, 1, 1, 1, 1, 3, 1
[1, 3, 3, 1, 1, 1, 1, 3, 2] => 1, 3, 3, 1, 1, 1, 1, 3, 2
[1, 3, 3, 1, 1, 1, 1, 3, 3] => 1, 3, 3, 1, 1, 1, 1, 3, 3
[1, 3, 3, 1, 1, 1, 2, 1, 1] => 1, 3, 3, 1, 1, 1, 2, 1, 1
[1, 3, 3, 1, 1, 1, 2, 1, 2] => 1, 3, 3, 1, 1, 1, 2, 1, 2
[1, 3, 3, 1, 1, 1, 2, 1, 3] => 1, 3, 3, 1, 1, 1, 2, 1, 3
[1, 3, 3, 1, 1, 1, 2, 2, 1] => 1, 3, 3, 1, 1, 1, 2, 2, 1
[1, 3, 3, 1, 1, 1, 2, 2, 2] => 1, 3, 3, 1, 1, 1, 2, 2, 2
[1, 3, 3, 1, 1, 1, 2, 2, 3] => 1, 3, 3, 1, 1, 1, 2, 2, 3
[1, 3, 3, 1, 1, 1, 2, 3, 1] => 1, 3, 3, 1, 1, 1, 2, 3, 1
[1, 3, 3, 1, 1, 1, 2, 3, 2] => 1, 3, 3, 1, 1, 1, 2, 3, 2
[1, 3, 3, 1, 1, 1, 2, 3, 3] => 1, 3, 3, 1, 1, 1, 2, 3, 3
[1, 3, 3, 1, 1, 1, 3, 1, 1] => 1, 3, 3, 1, 1, 1, 3, 1, 1
[1, 3, 3, 1, 1, 1, 3, 1, 2] => 1, 3, 3, 1, 1, 1, 3, 1, 2
[1, 3, 3, 1, 1, 1, 3, 1, 3] => 1, 3, 3, 1, 1, 1, 3, 1, 3
[1, 3, 3, 1, 1, 1, 3, 2, 1] => 1, 3, 3, 1, 1, 1, 3, 2, 1
[1, 3, 3, 1, 1, 1, 3, 2, 2] => 1, 3, 3, 1, 1, 1, 3, 2, 2
[1, 3, 3, 1, 1, 1, 3, 2, 3] => 1, 3, 3, 1, 1, 1, 3, 2, 3
[1, 3, 3, 1, 1, 1, 3, 3, 1] => 1, 3, 3, 1, 1, 1, 3, 3, 1
[1, 3, 3, 1, 1, 1, 3, 3, 2] => 1, 3, 3, 1, 1, 1, 3, 3, 2
[1, 3, 3, 1, 1, 1, 3, 3, 3] => 1, 3, 3, 1, 1, 1, 3, 3, 3
[1, 3, 3, 1, 1, 2, 1, 1, 1] => 1, 3, 3, 1, 1, 2, 1, 1, 1
[1, 3, 3, 1, 1, 2, 1, 1, 2] => 1, 3, 3, 1, 1, 2, 1, 1, 2
[1, 3, 3, 1, 1, 2, 1, 1, 3] => 1, 3, 3, 1, 1, 2, 1, 1, 3
[1, 3, 3, 1, 1, 2, 1, 2, 1] => 1, 3, 3, 1, 1, 2, 1, 2, 1
[1, 3, 3, 1, 1, 2, 1, 2, 2] => 1, 3, 3, 1, 1, 2, 1, 2, 2
[1, 3, 3, 1, 1, 2, 1, 2, 3] => 1, 3, 3, 1, 1, 2, 1, 2, 3
[1, 3, 3, 1, 1, 2, 1, 3, 1] => 1, 3, 3, 1, 1, 2, 1, 3, 1
[1, 3, 3, 1, 1, 2, 1, 3, 2] => 1, 3, 3, 1, 1, 2, 1, 3, 2
[1, 3, 3, 1, 1, 2, 1, 3, 3] => 1, 3, 3, 1, 1, 2, 1, 3, 3
[1, 3, 3, 1, 1, 2, 2, 1, 1] => 1, 3, 3, 1, 1, 2, 2, 1, 1
[1, 3, 3, 1, 1, 2, 2, 1, 2] => 1, 3, 3, 1, 1, 2, 2, 1, 2
[1, 3, 3, 1, 1, 2, 2, 1, 3] => 1, 3, 3, 1, 1, 2, 2, 1, 3
[1, 3, 3, 1, 1, 2, 2, 2, 1] => 1, 3, 3, 1, 1, 2, 2, 2, 1
[1, 3, 3, 1, 1, 2, 2, 2, 2] => 1, 3, 3, 1, 1, 2, 2, 2, 2
[1, 3, 3, 1, 1, 2, 2, 2, 3] => 1, 3, 3, 1, 1, 2, 2, 2, 3
[1, 3, 3, 1, 1, 2, 2, 3, 1] => 1, 3, 3, 1, 1, 2, 2, 3, 1
[1, 3, 3, 1, 1, 2, 2, 3, 2] => 1, 3, 3, 1, 1, 2, 2, 3, 2
[1, 3, 3, 1, 1, 2, 2, 3, 3] => 1, 3, 3, 1, 1, 2, 2, 3, 3
[1, 3, 3, 1, 1, 2, 3, 1, 1] => 1, 3, 3, 1, 1, 2, 3, 1, 1
[1, 3, 3, 1, 1, 2, 3, 1, 2] => 1, 3, 3, 1, 1, 2, 3, 1, 2
[1, 3, 3, 1, 1, 2, 3, 1, 3] => 1, 3, 3, 1, 1, 2, 3, 1, 3
[1, 3, 3, 1, 1, 2, 3, 2, 1] => 1, 3, 3, 1, 1, 2, 3, 2, 1
[1, 3, 3, 1, 1, 2, 3, 2, 2] => 1, 3, 3, 1, 1, 2, 3, 2, 2
[1, 3, 3, 1, 1, 2, 3, 2, 3] => 1, 3, 3, 1, 1, 2, 3, 2, 3
[1, 3, 3, 1, 1, 2, 3, 3, 1] => 1, 3, 3, 1, 1, 2, 3, 3, 1
[1, 3, 3, 1, 1, 2, 3, 3, 2] => 1, 3, 3, 1, 1, 2, 3, 3, 2
[1, 3, 3, 1, 1, 2, 3, 3, 3] => 1, 3, 3, 1, 1, 2, 3, 3, 3
[1, 3, 3, 1, 1, 3, 1, 1, 1] => 1, 3, 3, 1, 1, 3, 1, 1, 1
[1, 3, 3, 1, 1, 3, 1, 1, 2] => 1, 3, 3, 1, 1, 3, 1, 1, 2
[1, 3, 3, 1, 1, 3, 1, 1, 3] => 1, 3, 3, 1, 1, 3, 1, 1, 3
[1, 3, 3, 1, 1, 3, 1, 2, 1] => 1, 3, 3, 1, 1, 3, 1, 2, 1
[1, 3, 3, 1, 1, 3, 1, 2, 2] => 1, 3, 3, 1, 1, 3, 1, 2, 2
[1, 3, 3, 1, 1, 3, 1, 2, 3] => 1, 3, 3, 1, 1, 3, 1, 2, 3
[1, 3, 3, 1, 1, 3, 1, 3, 1] => 1, 3, 3, 1, 1, 3, 1, 3, 1
[1, 3, 3, 1, 1, 3, 1, 3, 2] => 1, 3, 3, 1, 1, 3, 1, 3, 2
[1, 3, 3, 1, 1, 3, 1, 3, 3] => 1, 3, 3, 1, 1, 3, 1, 3, 3
[1, 3, 3, 1, 1, 3, 2, 1, 1] => 1, 3, 3, 1, 1, 3, 2, 1, 1
[1, 3, 3, 1, 1, 3, 2, 1, 2] => 1, 3, 3, 1, 1, 3, 2, 1, 2
[1, 3, 3, 1, 1, 3, 2, 1, 3] => 1, 3, 3, 1, 1, 3, 2, 1, 3
[1, 3, 3, 1, 1, 3, 2, 2, 1] => 1, 3, 3, 1, 1, 3, 2, 2, 1
[1, 3, 3, 1, 1, 3, 2, 2, 2] => 1, 3, 3, 1, 1, 3, 2, 2, 2
[1, 3, 3, 1, 1, 3, 2, 2, 3] => 1, 3, 3, 1, 1, 3, 2, 2, 3
[1, 3, 3, 1, 1, 3, 2, 3, 1] => 1, 3, 3, 1, 1, 3, 2, 3, 1
[1, 3, 3, 1, 1, 3, 2, 3, 2] => 1, 3, 3, 1, 1, 3, 2, 3, 2
[1, 3, 3, 1, 1, 3, 2, 3, 3] => 1, 3, 3, 1, 1, 3, 2, 3, 3
[1, 3, 3, 1, 1, 3, 3, 1, 1] => 1, 3, 3, 1, 1, 3, 3, 1, 1
[1, 3, 3, 1, 1, 3, 3, 1, 2] => 1, 3, 3, 1, 1, 3, 3, 1, 2
[1, 3, 3, 1, 1, 3, 3, 1, 3] => 1, 3, 3, 1, 1, 3, 3, 1, 3
[1, 3, 3, 1, 1, 3, 3, 2, 1] => 1, 3, 3, 1, 1, 3, 3, 2, 1
[1, 3, 3, 1, 1, 3, 3, 2, 2] => 1, 3, 3, 1, 1, 3, 3, 2, 2
[1, 3, 3, 1, 1, 3, 3, 2, 3] => 1, 3, 3, 1, 1, 3, 3, 2, 3
[1, 3, 3, 1, 1, 3, 3, 3, 1] => 1, 3, 3, 1, 1, 3, 3, 3, 1
[1, 3, 3, 1, 1, 3, 3, 3, 2] => 1, 3, 3, 1, 1, 3, 3, 3, 2
[1, 3, 3, 1, 1, 3, 3, 3, 3] => 1, 3, 3, 1, 1, 3, 3, 3, 3
[1, 3, 3, 1, 2, 1, 1, 1, 1] => 1, 3, 3, 1, 2, 1, 1, 1, 1
[1, 3, 3, 1, 2, 1, 1, 1, 2] => 1, 3, 3, 1, 2, 1, 1, 1, 2
[1, 3, 3, 1, 2, 1, 1, 1, 3] => 1, 3, 3, 1, 2, 1, 1, 1, 3
[1, 3, 3, 1, 2, 1, 1, 2, 1] => 1, 3, 3, 1, 2, 1, 1, 2, 1
[1, 3, 3, 1, 2, 1, 1, 2, 2] => 1, 3, 3, 1, 2, 1, 1, 2, 2
[1, 3, 3, 1, 2, 1, 1, 2, 3] => 1, 3, 3, 1, 2, 1, 1, 2, 3
[1, 3, 3, 1, 2, 1, 1, 3, 1] => 1, 3, 3, 1, 2, 1, 1, 3, 1
[1, 3, 3, 1, 2, 1, 1, 3, 2] => 1, 3, 3, 1, 2, 1, 1, 3, 2
[1, 3, 3, 1, 2, 1, 1, 3, 3] => 1, 3, 3, 1, 2, 1, 1, 3, 3
[1, 3, 3, 1, 2, 1, 2, 1, 1] => 1, 3, 3, 1, 2, 1, 2, 1, 1
[1, 3, 3, 1, 2, 1, 2, 1, 2] => 1, 3, 3, 1, 2, 1, 2, 1, 2
[1, 3, 3, 1, 2, 1, 2, 1, 3] => 1, 3, 3, 1, 2, 1, 2, 1, 3
[1, 3, 3, 1, 2, 1, 2, 2, 1] => 1, 3, 3, 1, 2, 1, 2, 2, 1
[1, 3, 3, 1, 2, 1, 2, 2, 2] => 1, 3, 3, 1, 2, 1, 2, 2, 2
[1, 3, 3, 1, 2, 1, 2, 2, 3] => 1, 3, 3, 1, 2, 1, 2, 2, 3
[1, 3, 3, 1, 2, 1, 2, 3, 1] => 1, 3, 3, 1, 2, 1, 2, 3, 1
[1, 3, 3, 1, 2, 1, 2, 3, 2] => 1, 3, 3, 1, 2, 1, 2, 3, 2
[1, 3, 3, 1, 2, 1, 2, 3, 3] => 1, 3, 3, 1, 2, 1, 2, 3, 3
[1, 3, 3, 1, 2, 1, 3, 1, 1] => 1, 3, 3, 1, 2, 1, 3, 1, 1
[1, 3, 3, 1, 2, 1, 3, 1, 2] => 1, 3, 3, 1, 2, 1, 3, 1, 2
[1, 3, 3, 1, 2, 1, 3, 1, 3] => 1, 3, 3, 1, 2, 1, 3, 1, 3
[1, 3, 3, 1, 2, 1, 3, 2, 1] => 1, 3, 3, 1, 2, 1, 3, 2, 1
[1, 3, 3, 1, 2, 1, 3, 2, 2] => 1, 3, 3, 1, 2, 1, 3, 2, 2
[1, 3, 3, 1, 2, 1, 3, 2, 3] => 1, 3, 3, 1, 2, 1, 3, 2, 3
[1, 3, 3, 1, 2, 1, 3, 3, 1] => 1, 3, 3, 1, 2, 1, 3, 3, 1
[1, 3, 3, 1, 2, 1, 3, 3, 2] => 1, 3, 3, 1, 2, 1, 3, 3, 2
[1, 3, 3, 1, 2, 1, 3, 3, 3] => 1, 3, 3, 1, 2, 1, 3, 3, 3
[1, 3, 3, 1, 2, 2, 1, 1, 1] => 1, 3, 3, 1, 2, 2, 1, 1, 1
[1, 3, 3, 1, 2, 2, 1, 1, 2] => 1, 3, 3, 1, 2, 2, 1, 1, 2
[1, 3, 3, 1, 2, 2, 1, 1, 3] => 1, 3, 3, 1, 2, 2, 1, 1, 3
[1, 3, 3, 1, 2, 2, 1, 2, 1] => 1, 3, 3, 1, 2, 2, 1, 2, 1
[1, 3, 3, 1, 2, 2, 1, 2, 2] => 1, 3, 3, 1, 2, 2, 1, 2, 2
[1, 3, 3, 1, 2, 2, 1, 2, 3] => 1, 3, 3, 1, 2, 2, 1, 2, 3
[1, 3, 3, 1, 2, 2, 1, 3, 1] => 1, 3, 3, 1, 2, 2, 1, 3, 1
[1, 3, 3, 1, 2, 2, 1, 3, 2] => 1, 3, 3, 1, 2, 2, 1, 3, 2
[1, 3, 3, 1, 2, 2, 1, 3, 3] => 1, 3, 3, 1, 2, 2, 1, 3, 3
[1, 3, 3, 1, 2, 2, 2, 1, 1] => 1, 3, 3, 1, 2, 2, 2, 1, 1
[1, 3, 3, 1, 2, 2, 2, 1, 2] => 1, 3, 3, 1, 2, 2, 2, 1, 2
[1, 3, 3, 1, 2, 2, 2, 1, 3] => 1, 3, 3, 1, 2, 2, 2, 1, 3
[1, 3, 3, 1, 2, 2, 2, 2, 1] => 1, 3, 3, 1, 2, 2, 2, 2, 1
[1, 3, 3, 1, 2, 2, 2, 2, 2] => 1, 3, 3, 1, 2, 2, 2, 2, 2
[1, 3, 3, 1, 2, 2, 2, 2, 3] => 1, 3, 3, 1, 2, 2, 2, 2, 3
[1, 3, 3, 1, 2, 2, 2, 3, 1] => 1, 3, 3, 1, 2, 2, 2, 3, 1
[1, 3, 3, 1, 2, 2, 2, 3, 2] => 1, 3, 3, 1, 2, 2, 2, 3, 2
[1, 3, 3, 1, 2, 2, 2, 3, 3] => 1, 3, 3, 1, 2, 2, 2, 3, 3
[1, 3, 3, 1, 2, 2, 3, 1, 1] => 1, 3, 3, 1, 2, 2, 3, 1, 1
[1, 3, 3, 1, 2, 2, 3, 1, 2] => 1, 3, 3, 1, 2, 2, 3, 1, 2
[1, 3, 3, 1, 2, 2, 3, 1, 3] => 1, 3, 3, 1, 2, 2, 3, 1, 3
[1, 3, 3, 1, 2, 2, 3, 2, 1] => 1, 3, 3, 1, 2, 2, 3, 2, 1
[1, 3, 3, 1, 2, 2, 3, 2, 2] => 1, 3, 3, 1, 2, 2, 3, 2, 2
[1, 3, 3, 1, 2, 2, 3, 2, 3] => 1, 3, 3, 1, 2, 2, 3, 2, 3
[1, 3, 3, 1, 2, 2, 3, 3, 1] => 1, 3, 3, 1, 2, 2, 3, 3, 1
[1, 3, 3, 1, 2, 2, 3, 3, 2] => 1, 3, 3, 1, 2, 2, 3, 3, 2
[1, 3, 3, 1, 2, 2, 3, 3, 3] => 1, 3, 3, 1, 2, 2, 3, 3, 3
[1, 3, 3, 1, 2, 3, 1, 1, 1] => 1, 3, 3, 1, 2, 3, 1, 1, 1
[1, 3, 3, 1, 2, 3, 1, 1, 2] => 1, 3, 3, 1, 2, 3, 1, 1, 2
[1, 3, 3, 1, 2, 3, 1, 1, 3] => 1, 3, 3, 1, 2, 3, 1, 1, 3
[1, 3, 3, 1, 2, 3, 1, 2, 1] => 1, 3, 3, 1, 2, 3, 1, 2, 1
[1, 3, 3, 1, 2, 3, 1, 2, 2] => 1, 3, 3, 1, 2, 3, 1, 2, 2
[1, 3, 3, 1, 2, 3, 1, 2, 3] => 1, 3, 3, 1, 2, 3, 1, 2, 3
[1, 3, 3, 1, 2, 3, 1, 3, 1] => 1, 3, 3, 1, 2, 3, 1, 3, 1
[1, 3, 3, 1, 2, 3, 1, 3, 2] => 1, 3, 3, 1, 2, 3, 1, 3, 2
[1, 3, 3, 1, 2, 3, 1, 3, 3] => 1, 3, 3, 1, 2, 3, 1, 3, 3
[1, 3, 3, 1, 2, 3, 2, 1, 1] => 1, 3, 3, 1, 2, 3, 2, 1, 1
[1, 3, 3, 1, 2, 3, 2, 1, 2] => 1, 3, 3, 1, 2, 3, 2, 1, 2
[1, 3, 3, 1, 2, 3, 2, 1, 3] => 1, 3, 3, 1, 2, 3, 2, 1, 3
[1, 3, 3, 1, 2, 3, 2, 2, 1] => 1, 3, 3, 1, 2, 3, 2, 2, 1
[1, 3, 3, 1, 2, 3, 2, 2, 2] => 1, 3, 3, 1, 2, 3, 2, 2, 2
[1, 3, 3, 1, 2, 3, 2, 2, 3] => 1, 3, 3, 1, 2, 3, 2, 2, 3
[1, 3, 3, 1, 2, 3, 2, 3, 1] => 1, 3, 3, 1, 2, 3, 2, 3, 1
[1, 3, 3, 1, 2, 3, 2, 3, 2] => 1, 3, 3, 1, 2, 3, 2, 3, 2
[1, 3, 3, 1, 2, 3, 2, 3, 3] => 1, 3, 3, 1, 2, 3, 2, 3, 3
[1, 3, 3, 1, 2, 3, 3, 1, 1] => 1, 3, 3, 1, 2, 3, 3, 1, 1
[1, 3, 3, 1, 2, 3, 3, 1, 2] => 1, 3, 3, 1, 2, 3, 3, 1, 2
[1, 3, 3, 1, 2, 3, 3, 1, 3] => 1, 3, 3, 1, 2, 3, 3, 1, 3
[1, 3, 3, 1, 2, 3, 3, 2, 1] => 1, 3, 3, 1, 2, 3, 3, 2, 1
[1, 3, 3, 1, 2, 3, 3, 2, 2] => 1, 3, 3, 1, 2, 3, 3, 2, 2
[1, 3, 3, 1, 2, 3, 3, 2, 3] => 1, 3, 3, 1, 2, 3, 3, 2, 3
[1, 3, 3, 1, 2, 3, 3, 3, 1] => 1, 3, 3, 1, 2, 3, 3, 3, 1
[1, 3, 3, 1, 2, 3, 3, 3, 2] => 1, 3, 3, 1, 2, 3, 3, 3, 2
[1, 3, 3, 1, 2, 3, 3, 3, 3] => 1, 3, 3, 1, 2, 3, 3, 3, 3
[1, 3, 3, 1, 3, 1, 1, 1, 1] => 1, 3, 3, 1, 3, 1, 1, 1, 1
[1, 3, 3, 1, 3, 1, 1, 1, 2] => 1, 3, 3, 1, 3, 1, 1, 1, 2
[1, 3, 3, 1, 3, 1, 1, 1, 3] => 1, 3, 3, 1, 3, 1, 1, 1, 3
[1, 3, 3, 1, 3, 1, 1, 2, 1] => 1, 3, 3, 1, 3, 1, 1, 2, 1
[1, 3, 3, 1, 3, 1, 1, 2, 2] => 1, 3, 3, 1, 3, 1, 1, 2, 2
[1, 3, 3, 1, 3, 1, 1, 2, 3] => 1, 3, 3, 1, 3, 1, 1, 2, 3
[1, 3, 3, 1, 3, 1, 1, 3, 1] => 1, 3, 3, 1, 3, 1, 1, 3, 1
[1, 3, 3, 1, 3, 1, 1, 3, 2] => 1, 3, 3, 1, 3, 1, 1, 3, 2
[1, 3, 3, 1, 3, 1, 1, 3, 3] => 1, 3, 3, 1, 3, 1, 1, 3, 3
[1, 3, 3, 1, 3, 1, 2, 1, 1] => 1, 3, 3, 1, 3, 1, 2, 1, 1
[1, 3, 3, 1, 3, 1, 2, 1, 2] => 1, 3, 3, 1, 3, 1, 2, 1, 2
[1, 3, 3, 1, 3, 1, 2, 1, 3] => 1, 3, 3, 1, 3, 1, 2, 1, 3
[1, 3, 3, 1, 3, 1, 2, 2, 1] => 1, 3, 3, 1, 3, 1, 2, 2, 1
[1, 3, 3, 1, 3, 1, 2, 2, 2] => 1, 3, 3, 1, 3, 1, 2, 2, 2
[1, 3, 3, 1, 3, 1, 2, 2, 3] => 1, 3, 3, 1, 3, 1, 2, 2, 3
[1, 3, 3, 1, 3, 1, 2, 3, 1] => 1, 3, 3, 1, 3, 1, 2, 3, 1
[1, 3, 3, 1, 3, 1, 2, 3, 2] => 1, 3, 3, 1, 3, 1, 2, 3, 2
[1, 3, 3, 1, 3, 1, 2, 3, 3] => 1, 3, 3, 1, 3, 1, 2, 3, 3
[1, 3, 3, 1, 3, 1, 3, 1, 1] => 1, 3, 3, 1, 3, 1, 3, 1, 1
[1, 3, 3, 1, 3, 1, 3, 1, 2] => 1, 3, 3, 1, 3, 1, 3, 1, 2
[1, 3, 3, 1, 3, 1, 3, 1, 3] => 1, 3, 3, 1, 3, 1, 3, 1, 3
[1, 3, 3, 1, 3, 1, 3, 2, 1] => 1, 3, 3, 1, 3, 1, 3, 2, 1
[1, 3, 3, 1, 3, 1, 3, 2, 2] => 1, 3, 3, 1, 3, 1, 3, 2, 2
[1, 3, 3, 1, 3, 1, 3, 2, 3] => 1, 3, 3, 1, 3, 1, 3, 2, 3
[1, 3, 3, 1, 3, 1, 3, 3, 1] => 1, 3, 3, 1, 3, 1, 3, 3, 1
[1, 3, 3, 1, 3, 1, 3, 3, 2] => 1, 3, 3, 1, 3, 1, 3, 3, 2
[1, 3, 3, 1, 3, 1, 3, 3, 3] => 1, 3, 3, 1, 3, 1, 3, 3, 3
[1, 3, 3, 1, 3, 2, 1, 1, 1] => 1, 3, 3, 1, 3, 2, 1, 1, 1
[1, 3, 3, 1, 3, 2, 1, 1, 2] => 1, 3, 3, 1, 3, 2, 1, 1, 2
[1, 3, 3, 1, 3, 2, 1, 1, 3] => 1, 3, 3, 1, 3, 2, 1, 1, 3
[1, 3, 3, 1, 3, 2, 1, 2, 1] => 1, 3, 3, 1, 3, 2, 1, 2, 1
[1, 3, 3, 1, 3, 2, 1, 2, 2] => 1, 3, 3, 1, 3, 2, 1, 2, 2
[1, 3, 3, 1, 3, 2, 1, 2, 3] => 1, 3, 3, 1, 3, 2, 1, 2, 3
[1, 3, 3, 1, 3, 2, 1, 3, 1] => 1, 3, 3, 1, 3, 2, 1, 3, 1
[1, 3, 3, 1, 3, 2, 1, 3, 2] => 1, 3, 3, 1, 3, 2, 1, 3, 2
[1, 3, 3, 1, 3, 2, 1, 3, 3] => 1, 3, 3, 1, 3, 2, 1, 3, 3
[1, 3, 3, 1, 3, 2, 2, 1, 1] => 1, 3, 3, 1, 3, 2, 2, 1, 1
[1, 3, 3, 1, 3, 2, 2, 1, 2] => 1, 3, 3, 1, 3, 2, 2, 1, 2
[1, 3, 3, 1, 3, 2, 2, 1, 3] => 1, 3, 3, 1, 3, 2, 2, 1, 3
[1, 3, 3, 1, 3, 2, 2, 2, 1] => 1, 3, 3, 1, 3, 2, 2, 2, 1
[1, 3, 3, 1, 3, 2, 2, 2, 2] => 1, 3, 3, 1, 3, 2, 2, 2, 2
[1, 3, 3, 1, 3, 2, 2, 2, 3] => 1, 3, 3, 1, 3, 2, 2, 2, 3
[1, 3, 3, 1, 3, 2, 2, 3, 1] => 1, 3, 3, 1, 3, 2, 2, 3, 1
[1, 3, 3, 1, 3, 2, 2, 3, 2] => 1, 3, 3, 1, 3, 2, 2, 3, 2
[1, 3, 3, 1, 3, 2, 2, 3, 3] => 1, 3, 3, 1, 3, 2, 2, 3, 3
[1, 3, 3, 1, 3, 2, 3, 1, 1] => 1, 3, 3, 1, 3, 2, 3, 1, 1
[1, 3, 3, 1, 3, 2, 3, 1, 2] => 1, 3, 3, 1, 3, 2, 3, 1, 2
[1, 3, 3, 1, 3, 2, 3, 1, 3] => 1, 3, 3, 1, 3, 2, 3, 1, 3
[1, 3, 3, 1, 3, 2, 3, 2, 1] => 1, 3, 3, 1, 3, 2, 3, 2, 1
[1, 3, 3, 1, 3, 2, 3, 2, 2] => 1, 3, 3, 1, 3, 2, 3, 2, 2
[1, 3, 3, 1, 3, 2, 3, 2, 3] => 1, 3, 3, 1, 3, 2, 3, 2, 3
[1, 3, 3, 1, 3, 2, 3, 3, 1] => 1, 3, 3, 1, 3, 2, 3, 3, 1
[1, 3, 3, 1, 3, 2, 3, 3, 2] => 1, 3, 3, 1, 3, 2, 3, 3, 2
[1, 3, 3, 1, 3, 2, 3, 3, 3] => 1, 3, 3, 1, 3, 2, 3, 3, 3
[1, 3, 3, 1, 3, 3, 1, 1, 1] => 1, 3, 3, 1, 3, 3, 1, 1, 1
[1, 3, 3, 1, 3, 3, 1, 1, 2] => 1, 3, 3, 1, 3, 3, 1, 1, 2
[1, 3, 3, 1, 3, 3, 1, 1, 3] => 1, 3, 3, 1, 3, 3, 1, 1, 3
[1, 3, 3, 1, 3, 3, 1, 2, 1] => 1, 3, 3, 1, 3, 3, 1, 2, 1
[1, 3, 3, 1, 3, 3, 1, 2, 2] => 1, 3, 3, 1, 3, 3, 1, 2, 2
[1, 3, 3, 1, 3, 3, 1, 2, 3] => 1, 3, 3, 1, 3, 3, 1, 2, 3
[1, 3, 3, 1, 3, 3, 1, 3, 1] => 1, 3, 3, 1, 3, 3, 1, 3, 1
[1, 3, 3, 1, 3, 3, 1, 3, 2] => 1, 3, 3, 1, 3, 3, 1, 3, 2
[1, 3, 3, 1, 3, 3, 1, 3, 3] => 1, 3, 3, 1, 3, 3, 1, 3, 3
[1, 3, 3, 1, 3, 3, 2, 1, 1] => 1, 3, 3, 1, 3, 3, 2, 1, 1
[1, 3, 3, 1, 3, 3, 2, 1, 2] => 1, 3, 3, 1, 3, 3, 2, 1, 2
[1, 3, 3, 1, 3, 3, 2, 1, 3] => 1, 3, 3, 1, 3, 3, 2, 1, 3
[1, 3, 3, 1, 3, 3, 2, 2, 1] => 1, 3, 3, 1, 3, 3, 2, 2, 1
[1, 3, 3, 1, 3, 3, 2, 2, 2] => 1, 3, 3, 1, 3, 3, 2, 2, 2
[1, 3, 3, 1, 3, 3, 2, 2, 3] => 1, 3, 3, 1, 3, 3, 2, 2, 3
[1, 3, 3, 1, 3, 3, 2, 3, 1] => 1, 3, 3, 1, 3, 3, 2, 3, 1
[1, 3, 3, 1, 3, 3, 2, 3, 2] => 1, 3, 3, 1, 3, 3, 2, 3, 2
[1, 3, 3, 1, 3, 3, 2, 3, 3] => 1, 3, 3, 1, 3, 3, 2, 3, 3
[1, 3, 3, 1, 3, 3, 3, 1, 1] => 1, 3, 3, 1, 3, 3, 3, 1, 1
[1, 3, 3, 1, 3, 3, 3, 1, 2] => 1, 3, 3, 1, 3, 3, 3, 1, 2
[1, 3, 3, 1, 3, 3, 3, 1, 3] => 1, 3, 3, 1, 3, 3, 3, 1, 3
[1, 3, 3, 1, 3, 3, 3, 2, 1] => 1, 3, 3, 1, 3, 3, 3, 2, 1
[1, 3, 3, 1, 3, 3, 3, 2, 2] => 1, 3, 3, 1, 3, 3, 3, 2, 2
[1, 3, 3, 1, 3, 3, 3, 2, 3] => 1, 3, 3, 1, 3, 3, 3, 2, 3
[1, 3, 3, 1, 3, 3, 3, 3, 1] => 1, 3, 3, 1, 3, 3, 3, 3, 1
[1, 3, 3, 1, 3, 3, 3, 3, 2] => 1, 3, 3, 1, 3, 3, 3, 3, 2
[1, 3, 3, 1, 3, 3, 3, 3, 3] => 1, 3, 3, 1, 3, 3, 3, 3, 3
[1, 3, 3, 2, 1, 1, 1, 1, 1] => 1, 3, 3, 2, 1, 1, 1, 1, 1
[1, 3, 3, 2, 1, 1, 1, 1, 2] => 1, 3, 3, 2, 1, 1, 1, 1, 2
[1, 3, 3, 2, 1, 1, 1, 1, 3] => 1, 3, 3, 2, 1, 1, 1, 1, 3
[1, 3, 3, 2, 1, 1, 1, 2, 1] => 1, 3, 3, 2, 1, 1, 1, 2, 1
[1, 3, 3, 2, 1, 1, 1, 2, 2] => 1, 3, 3, 2, 1, 1, 1, 2, 2
[1, 3, 3, 2, 1, 1, 1, 2, 3] => 1, 3, 3, 2, 1, 1, 1, 2, 3
[1, 3, 3, 2, 1, 1, 1, 3, 1] => 1, 3, 3, 2, 1, 1, 1, 3, 1
[1, 3, 3, 2, 1, 1, 1, 3, 2] => 1, 3, 3, 2, 1, 1, 1, 3, 2
[1, 3, 3, 2, 1, 1, 1, 3, 3] => 1, 3, 3, 2, 1, 1, 1, 3, 3
[1, 3, 3, 2, 1, 1, 2, 1, 1] => 1, 3, 3, 2, 1, 1, 2, 1, 1
[1, 3, 3, 2, 1, 1, 2, 1, 2] => 1, 3, 3, 2, 1, 1, 2, 1, 2
[1, 3, 3, 2, 1, 1, 2, 1, 3] => 1, 3, 3, 2, 1, 1, 2, 1, 3
[1, 3, 3, 2, 1, 1, 2, 2, 1] => 1, 3, 3, 2, 1, 1, 2, 2, 1
[1, 3, 3, 2, 1, 1, 2, 2, 2] => 1, 3, 3, 2, 1, 1, 2, 2, 2
[1, 3, 3, 2, 1, 1, 2, 2, 3] => 1, 3, 3, 2, 1, 1, 2, 2, 3
[1, 3, 3, 2, 1, 1, 2, 3, 1] => 1, 3, 3, 2, 1, 1, 2, 3, 1
[1, 3, 3, 2, 1, 1, 2, 3, 2] => 1, 3, 3, 2, 1, 1, 2, 3, 2
[1, 3, 3, 2, 1, 1, 2, 3, 3] => 1, 3, 3, 2, 1, 1, 2, 3, 3
[1, 3, 3, 2, 1, 1, 3, 1, 1] => 1, 3, 3, 2, 1, 1, 3, 1, 1
[1, 3, 3, 2, 1, 1, 3, 1, 2] => 1, 3, 3, 2, 1, 1, 3, 1, 2
[1, 3, 3, 2, 1, 1, 3, 1, 3] => 1, 3, 3, 2, 1, 1, 3, 1, 3
[1, 3, 3, 2, 1, 1, 3, 2, 1] => 1, 3, 3, 2, 1, 1, 3, 2, 1
[1, 3, 3, 2, 1, 1, 3, 2, 2] => 1, 3, 3, 2, 1, 1, 3, 2, 2
[1, 3, 3, 2, 1, 1, 3, 2, 3] => 1, 3, 3, 2, 1, 1, 3, 2, 3
[1, 3, 3, 2, 1, 1, 3, 3, 1] => 1, 3, 3, 2, 1, 1, 3, 3, 1
[1, 3, 3, 2, 1, 1, 3, 3, 2] => 1, 3, 3, 2, 1, 1, 3, 3, 2
[1, 3, 3, 2, 1, 1, 3, 3, 3] => 1, 3, 3, 2, 1, 1, 3, 3, 3
[1, 3, 3, 2, 1, 2, 1, 1, 1] => 1, 3, 3, 2, 1, 2, 1, 1, 1
[1, 3, 3, 2, 1, 2, 1, 1, 2] => 1, 3, 3, 2, 1, 2, 1, 1, 2
[1, 3, 3, 2, 1, 2, 1, 1, 3] => 1, 3, 3, 2, 1, 2, 1, 1, 3
[1, 3, 3, 2, 1, 2, 1, 2, 1] => 1, 3, 3, 2, 1, 2, 1, 2, 1
[1, 3, 3, 2, 1, 2, 1, 2, 2] => 1, 3, 3, 2, 1, 2, 1, 2, 2
[1, 3, 3, 2, 1, 2, 1, 2, 3] => 1, 3, 3, 2, 1, 2, 1, 2, 3
[1, 3, 3, 2, 1, 2, 1, 3, 1] => 1, 3, 3, 2, 1, 2, 1, 3, 1
[1, 3, 3, 2, 1, 2, 1, 3, 2] => 1, 3, 3, 2, 1, 2, 1, 3, 2
[1, 3, 3, 2, 1, 2, 1, 3, 3] => 1, 3, 3, 2, 1, 2, 1, 3, 3
[1, 3, 3, 2, 1, 2, 2, 1, 1] => 1, 3, 3, 2, 1, 2, 2, 1, 1
[1, 3, 3, 2, 1, 2, 2, 1, 2] => 1, 3, 3, 2, 1, 2, 2, 1, 2
[1, 3, 3, 2, 1, 2, 2, 1, 3] => 1, 3, 3, 2, 1, 2, 2, 1, 3
[1, 3, 3, 2, 1, 2, 2, 2, 1] => 1, 3, 3, 2, 1, 2, 2, 2, 1
[1, 3, 3, 2, 1, 2, 2, 2, 2] => 1, 3, 3, 2, 1, 2, 2, 2, 2
[1, 3, 3, 2, 1, 2, 2, 2, 3] => 1, 3, 3, 2, 1, 2, 2, 2, 3
[1, 3, 3, 2, 1, 2, 2, 3, 1] => 1, 3, 3, 2, 1, 2, 2, 3, 1
[1, 3, 3, 2, 1, 2, 2, 3, 2] => 1, 3, 3, 2, 1, 2, 2, 3, 2
[1, 3, 3, 2, 1, 2, 2, 3, 3] => 1, 3, 3, 2, 1, 2, 2, 3, 3
[1, 3, 3, 2, 1, 2, 3, 1, 1] => 1, 3, 3, 2, 1, 2, 3, 1, 1
[1, 3, 3, 2, 1, 2, 3, 1, 2] => 1, 3, 3, 2, 1, 2, 3, 1, 2
[1, 3, 3, 2, 1, 2, 3, 1, 3] => 1, 3, 3, 2, 1, 2, 3, 1, 3
[1, 3, 3, 2, 1, 2, 3, 2, 1] => 1, 3, 3, 2, 1, 2, 3, 2, 1
[1, 3, 3, 2, 1, 2, 3, 2, 2] => 1, 3, 3, 2, 1, 2, 3, 2, 2
[1, 3, 3, 2, 1, 2, 3, 2, 3] => 1, 3, 3, 2, 1, 2, 3, 2, 3
[1, 3, 3, 2, 1, 2, 3, 3, 1] => 1, 3, 3, 2, 1, 2, 3, 3, 1
[1, 3, 3, 2, 1, 2, 3, 3, 2] => 1, 3, 3, 2, 1, 2, 3, 3, 2
[1, 3, 3, 2, 1, 2, 3, 3, 3] => 1, 3, 3, 2, 1, 2, 3, 3, 3
[1, 3, 3, 2, 1, 3, 1, 1, 1] => 1, 3, 3, 2, 1, 3, 1, 1, 1
[1, 3, 3, 2, 1, 3, 1, 1, 2] => 1, 3, 3, 2, 1, 3, 1, 1, 2
[1, 3, 3, 2, 1, 3, 1, 1, 3] => 1, 3, 3, 2, 1, 3, 1, 1, 3
[1, 3, 3, 2, 1, 3, 1, 2, 1] => 1, 3, 3, 2, 1, 3, 1, 2, 1
[1, 3, 3, 2, 1, 3, 1, 2, 2] => 1, 3, 3, 2, 1, 3, 1, 2, 2
[1, 3, 3, 2, 1, 3, 1, 2, 3] => 1, 3, 3, 2, 1, 3, 1, 2, 3
[1, 3, 3, 2, 1, 3, 1, 3, 1] => 1, 3, 3, 2, 1, 3, 1, 3, 1
[1, 3, 3, 2, 1, 3, 1, 3, 2] => 1, 3, 3, 2, 1, 3, 1, 3, 2
[1, 3, 3, 2, 1, 3, 1, 3, 3] => 1, 3, 3, 2, 1, 3, 1, 3, 3
[1, 3, 3, 2, 1, 3, 2, 1, 1] => 1, 3, 3, 2, 1, 3, 2, 1, 1
[1, 3, 3, 2, 1, 3, 2, 1, 2] => 1, 3, 3, 2, 1, 3, 2, 1, 2
[1, 3, 3, 2, 1, 3, 2, 1, 3] => 1, 3, 3, 2, 1, 3, 2, 1, 3
[1, 3, 3, 2, 1, 3, 2, 2, 1] => 1, 3, 3, 2, 1, 3, 2, 2, 1
[1, 3, 3, 2, 1, 3, 2, 2, 2] => 1, 3, 3, 2, 1, 3, 2, 2, 2
[1, 3, 3, 2, 1, 3, 2, 2, 3] => 1, 3, 3, 2, 1, 3, 2, 2, 3
[1, 3, 3, 2, 1, 3, 2, 3, 1] => 1, 3, 3, 2, 1, 3, 2, 3, 1
[1, 3, 3, 2, 1, 3, 2, 3, 2] => 1, 3, 3, 2, 1, 3, 2, 3, 2
[1, 3, 3, 2, 1, 3, 2, 3, 3] => 1, 3, 3, 2, 1, 3, 2, 3, 3
[1, 3, 3, 2, 1, 3, 3, 1, 1] => 1, 3, 3, 2, 1, 3, 3, 1, 1
[1, 3, 3, 2, 1, 3, 3, 1, 2] => 1, 3, 3, 2, 1, 3, 3, 1, 2
[1, 3, 3, 2, 1, 3, 3, 1, 3] => 1, 3, 3, 2, 1, 3, 3, 1, 3
[1, 3, 3, 2, 1, 3, 3, 2, 1] => 1, 3, 3, 2, 1, 3, 3, 2, 1
[1, 3, 3, 2, 1, 3, 3, 2, 2] => 1, 3, 3, 2, 1, 3, 3, 2, 2
[1, 3, 3, 2, 1, 3, 3, 2, 3] => 1, 3, 3, 2, 1, 3, 3, 2, 3
[1, 3, 3, 2, 1, 3, 3, 3, 1] => 1, 3, 3, 2, 1, 3, 3, 3, 1
[1, 3, 3, 2, 1, 3, 3, 3, 2] => 1, 3, 3, 2, 1, 3, 3, 3, 2
[1, 3, 3, 2, 1, 3, 3, 3, 3] => 1, 3, 3, 2, 1, 3, 3, 3, 3
[1, 3, 3, 2, 2, 1, 1, 1, 1] => 1, 3, 3, 2, 2, 1, 1, 1, 1
[1, 3, 3, 2, 2, 1, 1, 1, 2] => 1, 3, 3, 2, 2, 1, 1, 1, 2
[1, 3, 3, 2, 2, 1, 1, 1, 3] => 1, 3, 3, 2, 2, 1, 1, 1, 3
[1, 3, 3, 2, 2, 1, 1, 2, 1] => 1, 3, 3, 2, 2, 1, 1, 2, 1
[1, 3, 3, 2, 2, 1, 1, 2, 2] => 1, 3, 3, 2, 2, 1, 1, 2, 2
[1, 3, 3, 2, 2, 1, 1, 2, 3] => 1, 3, 3, 2, 2, 1, 1, 2, 3
[1, 3, 3, 2, 2, 1, 1, 3, 1] => 1, 3, 3, 2, 2, 1, 1, 3, 1
[1, 3, 3, 2, 2, 1, 1, 3, 2] => 1, 3, 3, 2, 2, 1, 1, 3, 2
[1, 3, 3, 2, 2, 1, 1, 3, 3] => 1, 3, 3, 2, 2, 1, 1, 3, 3
[1, 3, 3, 2, 2, 1, 2, 1, 1] => 1, 3, 3, 2, 2, 1, 2, 1, 1
[1, 3, 3, 2, 2, 1, 2, 1, 2] => 1, 3, 3, 2, 2, 1, 2, 1, 2
[1, 3, 3, 2, 2, 1, 2, 1, 3] => 1, 3, 3, 2, 2, 1, 2, 1, 3
[1, 3, 3, 2, 2, 1, 2, 2, 1] => 1, 3, 3, 2, 2, 1, 2, 2, 1
[1, 3, 3, 2, 2, 1, 2, 2, 2] => 1, 3, 3, 2, 2, 1, 2, 2, 2
[1, 3, 3, 2, 2, 1, 2, 2, 3] => 1, 3, 3, 2, 2, 1, 2, 2, 3
[1, 3, 3, 2, 2, 1, 2, 3, 1] => 1, 3, 3, 2, 2, 1, 2, 3, 1
[1, 3, 3, 2, 2, 1, 2, 3, 2] => 1, 3, 3, 2, 2, 1, 2, 3, 2
[1, 3, 3, 2, 2, 1, 2, 3, 3] => 1, 3, 3, 2, 2, 1, 2, 3, 3
[1, 3, 3, 2, 2, 1, 3, 1, 1] => 1, 3, 3, 2, 2, 1, 3, 1, 1
[1, 3, 3, 2, 2, 1, 3, 1, 2] => 1, 3, 3, 2, 2, 1, 3, 1, 2
[1, 3, 3, 2, 2, 1, 3, 1, 3] => 1, 3, 3, 2, 2, 1, 3, 1, 3
[1, 3, 3, 2, 2, 1, 3, 2, 1] => 1, 3, 3, 2, 2, 1, 3, 2, 1
[1, 3, 3, 2, 2, 1, 3, 2, 2] => 1, 3, 3, 2, 2, 1, 3, 2, 2
[1, 3, 3, 2, 2, 1, 3, 2, 3] => 1, 3, 3, 2, 2, 1, 3, 2, 3
[1, 3, 3, 2, 2, 1, 3, 3, 1] => 1, 3, 3, 2, 2, 1, 3, 3, 1
[1, 3, 3, 2, 2, 1, 3, 3, 2] => 1, 3, 3, 2, 2, 1, 3, 3, 2
[1, 3, 3, 2, 2, 1, 3, 3, 3] => 1, 3, 3, 2, 2, 1, 3, 3, 3
[1, 3, 3, 2, 2, 2, 1, 1, 1] => 1, 3, 3, 2, 2, 2, 1, 1, 1
[1, 3, 3, 2, 2, 2, 1, 1, 2] => 1, 3, 3, 2, 2, 2, 1, 1, 2
[1, 3, 3, 2, 2, 2, 1, 1, 3] => 1, 3, 3, 2, 2, 2, 1, 1, 3
[1, 3, 3, 2, 2, 2, 1, 2, 1] => 1, 3, 3, 2, 2, 2, 1, 2, 1
[1, 3, 3, 2, 2, 2, 1, 2, 2] => 1, 3, 3, 2, 2, 2, 1, 2, 2
[1, 3, 3, 2, 2, 2, 1, 2, 3] => 1, 3, 3, 2, 2, 2, 1, 2, 3
[1, 3, 3, 2, 2, 2, 1, 3, 1] => 1, 3, 3, 2, 2, 2, 1, 3, 1
[1, 3, 3, 2, 2, 2, 1, 3, 2] => 1, 3, 3, 2, 2, 2, 1, 3, 2
[1, 3, 3, 2, 2, 2, 1, 3, 3] => 1, 3, 3, 2, 2, 2, 1, 3, 3
[1, 3, 3, 2, 2, 2, 2, 1, 1] => 1, 3, 3, 2, 2, 2, 2, 1, 1
[1, 3, 3, 2, 2, 2, 2, 1, 2] => 1, 3, 3, 2, 2, 2, 2, 1, 2
[1, 3, 3, 2, 2, 2, 2, 1, 3] => 1, 3, 3, 2, 2, 2, 2, 1, 3
[1, 3, 3, 2, 2, 2, 2, 2, 1] => 1, 3, 3, 2, 2, 2, 2, 2, 1
[1, 3, 3, 2, 2, 2, 2, 2, 2] => 1, 3, 3, 2, 2, 2, 2, 2, 2
[1, 3, 3, 2, 2, 2, 2, 2, 3] => 1, 3, 3, 2, 2, 2, 2, 2, 3
[1, 3, 3, 2, 2, 2, 2, 3, 1] => 1, 3, 3, 2, 2, 2, 2, 3, 1
[1, 3, 3, 2, 2, 2, 2, 3, 2] => 1, 3, 3, 2, 2, 2, 2, 3, 2
[1, 3, 3, 2, 2, 2, 2, 3, 3] => 1, 3, 3, 2, 2, 2, 2, 3, 3
[1, 3, 3, 2, 2, 2, 3, 1, 1] => 1, 3, 3, 2, 2, 2, 3, 1, 1
[1, 3, 3, 2, 2, 2, 3, 1, 2] => 1, 3, 3, 2, 2, 2, 3, 1, 2
[1, 3, 3, 2, 2, 2, 3, 1, 3] => 1, 3, 3, 2, 2, 2, 3, 1, 3
[1, 3, 3, 2, 2, 2, 3, 2, 1] => 1, 3, 3, 2, 2, 2, 3, 2, 1
[1, 3, 3, 2, 2, 2, 3, 2, 2] => 1, 3, 3, 2, 2, 2, 3, 2, 2
[1, 3, 3, 2, 2, 2, 3, 2, 3] => 1, 3, 3, 2, 2, 2, 3, 2, 3
[1, 3, 3, 2, 2, 2, 3, 3, 1] => 1, 3, 3, 2, 2, 2, 3, 3, 1
[1, 3, 3, 2, 2, 2, 3, 3, 2] => 1, 3, 3, 2, 2, 2, 3, 3, 2
[1, 3, 3, 2, 2, 2, 3, 3, 3] => 1, 3, 3, 2, 2, 2, 3, 3, 3
[1, 3, 3, 2, 2, 3, 1, 1, 1] => 1, 3, 3, 2, 2, 3, 1, 1, 1
[1, 3, 3, 2, 2, 3, 1, 1, 2] => 1, 3, 3, 2, 2, 3, 1, 1, 2
[1, 3, 3, 2, 2, 3, 1, 1, 3] => 1, 3, 3, 2, 2, 3, 1, 1, 3
[1, 3, 3, 2, 2, 3, 1, 2, 1] => 1, 3, 3, 2, 2, 3, 1, 2, 1
[1, 3, 3, 2, 2, 3, 1, 2, 2] => 1, 3, 3, 2, 2, 3, 1, 2, 2
[1, 3, 3, 2, 2, 3, 1, 2, 3] => 1, 3, 3, 2, 2, 3, 1, 2, 3
[1, 3, 3, 2, 2, 3, 1, 3, 1] => 1, 3, 3, 2, 2, 3, 1, 3, 1
[1, 3, 3, 2, 2, 3, 1, 3, 2] => 1, 3, 3, 2, 2, 3, 1, 3, 2
[1, 3, 3, 2, 2, 3, 1, 3, 3] => 1, 3, 3, 2, 2, 3, 1, 3, 3
[1, 3, 3, 2, 2, 3, 2, 1, 1] => 1, 3, 3, 2, 2, 3, 2, 1, 1
[1, 3, 3, 2, 2, 3, 2, 1, 2] => 1, 3, 3, 2, 2, 3, 2, 1, 2
[1, 3, 3, 2, 2, 3, 2, 1, 3] => 1, 3, 3, 2, 2, 3, 2, 1, 3
[1, 3, 3, 2, 2, 3, 2, 2, 1] => 1, 3, 3, 2, 2, 3, 2, 2, 1
[1, 3, 3, 2, 2, 3, 2, 2, 2] => 1, 3, 3, 2, 2, 3, 2, 2, 2
[1, 3, 3, 2, 2, 3, 2, 2, 3] => 1, 3, 3, 2, 2, 3, 2, 2, 3
[1, 3, 3, 2, 2, 3, 2, 3, 1] => 1, 3, 3, 2, 2, 3, 2, 3, 1
[1, 3, 3, 2, 2, 3, 2, 3, 2] => 1, 3, 3, 2, 2, 3, 2, 3, 2
[1, 3, 3, 2, 2, 3, 2, 3, 3] => 1, 3, 3, 2, 2, 3, 2, 3, 3
[1, 3, 3, 2, 2, 3, 3, 1, 1] => 1, 3, 3, 2, 2, 3, 3, 1, 1
[1, 3, 3, 2, 2, 3, 3, 1, 2] => 1, 3, 3, 2, 2, 3, 3, 1, 2
[1, 3, 3, 2, 2, 3, 3, 1, 3] => 1, 3, 3, 2, 2, 3, 3, 1, 3
[1, 3, 3, 2, 2, 3, 3, 2, 1] => 1, 3, 3, 2, 2, 3, 3, 2, 1
[1, 3, 3, 2, 2, 3, 3, 2, 2] => 1, 3, 3, 2, 2, 3, 3, 2, 2
[1, 3, 3, 2, 2, 3, 3, 2, 3] => 1, 3, 3, 2, 2, 3, 3, 2, 3
[1, 3, 3, 2, 2, 3, 3, 3, 1] => 1, 3, 3, 2, 2, 3, 3, 3, 1
[1, 3, 3, 2, 2, 3, 3, 3, 2] => 1, 3, 3, 2, 2, 3, 3, 3, 2
[1, 3, 3, 2, 2, 3, 3, 3, 3] => 1, 3, 3, 2, 2, 3, 3, 3, 3
[1, 3, 3, 2, 3, 1, 1, 1, 1] => 1, 3, 3, 2, 3, 1, 1, 1, 1
[1, 3, 3, 2, 3, 1, 1, 1, 2] => 1, 3, 3, 2, 3, 1, 1, 1, 2
[1, 3, 3, 2, 3, 1, 1, 1, 3] => 1, 3, 3, 2, 3, 1, 1, 1, 3
[1, 3, 3, 2, 3, 1, 1, 2, 1] => 1, 3, 3, 2, 3, 1, 1, 2, 1
[1, 3, 3, 2, 3, 1, 1, 2, 2] => 1, 3, 3, 2, 3, 1, 1, 2, 2
[1, 3, 3, 2, 3, 1, 1, 2, 3] => 1, 3, 3, 2, 3, 1, 1, 2, 3
[1, 3, 3, 2, 3, 1, 1, 3, 1] => 1, 3, 3, 2, 3, 1, 1, 3, 1
[1, 3, 3, 2, 3, 1, 1, 3, 2] => 1, 3, 3, 2, 3, 1, 1, 3, 2
[1, 3, 3, 2, 3, 1, 1, 3, 3] => 1, 3, 3, 2, 3, 1, 1, 3, 3
[1, 3, 3, 2, 3, 1, 2, 1, 1] => 1, 3, 3, 2, 3, 1, 2, 1, 1
[1, 3, 3, 2, 3, 1, 2, 1, 2] => 1, 3, 3, 2, 3, 1, 2, 1, 2
[1, 3, 3, 2, 3, 1, 2, 1, 3] => 1, 3, 3, 2, 3, 1, 2, 1, 3
[1, 3, 3, 2, 3, 1, 2, 2, 1] => 1, 3, 3, 2, 3, 1, 2, 2, 1
[1, 3, 3, 2, 3, 1, 2, 2, 2] => 1, 3, 3, 2, 3, 1, 2, 2, 2
[1, 3, 3, 2, 3, 1, 2, 2, 3] => 1, 3, 3, 2, 3, 1, 2, 2, 3
[1, 3, 3, 2, 3, 1, 2, 3, 1] => 1, 3, 3, 2, 3, 1, 2, 3, 1
[1, 3, 3, 2, 3, 1, 2, 3, 2] => 1, 3, 3, 2, 3, 1, 2, 3, 2
[1, 3, 3, 2, 3, 1, 2, 3, 3] => 1, 3, 3, 2, 3, 1, 2, 3, 3
[1, 3, 3, 2, 3, 1, 3, 1, 1] => 1, 3, 3, 2, 3, 1, 3, 1, 1
[1, 3, 3, 2, 3, 1, 3, 1, 2] => 1, 3, 3, 2, 3, 1, 3, 1, 2
[1, 3, 3, 2, 3, 1, 3, 1, 3] => 1, 3, 3, 2, 3, 1, 3, 1, 3
[1, 3, 3, 2, 3, 1, 3, 2, 1] => 1, 3, 3, 2, 3, 1, 3, 2, 1
[1, 3, 3, 2, 3, 1, 3, 2, 2] => 1, 3, 3, 2, 3, 1, 3, 2, 2
[1, 3, 3, 2, 3, 1, 3, 2, 3] => 1, 3, 3, 2, 3, 1, 3, 2, 3
[1, 3, 3, 2, 3, 1, 3, 3, 1] => 1, 3, 3, 2, 3, 1, 3, 3, 1
[1, 3, 3, 2, 3, 1, 3, 3, 2] => 1, 3, 3, 2, 3, 1, 3, 3, 2
[1, 3, 3, 2, 3, 1, 3, 3, 3] => 1, 3, 3, 2, 3, 1, 3, 3, 3
[1, 3, 3, 2, 3, 2, 1, 1, 1] => 1, 3, 3, 2, 3, 2, 1, 1, 1
[1, 3, 3, 2, 3, 2, 1, 1, 2] => 1, 3, 3, 2, 3, 2, 1, 1, 2
[1, 3, 3, 2, 3, 2, 1, 1, 3] => 1, 3, 3, 2, 3, 2, 1, 1, 3
[1, 3, 3, 2, 3, 2, 1, 2, 1] => 1, 3, 3, 2, 3, 2, 1, 2, 1
[1, 3, 3, 2, 3, 2, 1, 2, 2] => 1, 3, 3, 2, 3, 2, 1, 2, 2
[1, 3, 3, 2, 3, 2, 1, 2, 3] => 1, 3, 3, 2, 3, 2, 1, 2, 3
[1, 3, 3, 2, 3, 2, 1, 3, 1] => 1, 3, 3, 2, 3, 2, 1, 3, 1
[1, 3, 3, 2, 3, 2, 1, 3, 2] => 1, 3, 3, 2, 3, 2, 1, 3, 2
[1, 3, 3, 2, 3, 2, 1, 3, 3] => 1, 3, 3, 2, 3, 2, 1, 3, 3
[1, 3, 3, 2, 3, 2, 2, 1, 1] => 1, 3, 3, 2, 3, 2, 2, 1, 1
[1, 3, 3, 2, 3, 2, 2, 1, 2] => 1, 3, 3, 2, 3, 2, 2, 1, 2
[1, 3, 3, 2, 3, 2, 2, 1, 3] => 1, 3, 3, 2, 3, 2, 2, 1, 3
[1, 3, 3, 2, 3, 2, 2, 2, 1] => 1, 3, 3, 2, 3, 2, 2, 2, 1
[1, 3, 3, 2, 3, 2, 2, 2, 2] => 1, 3, 3, 2, 3, 2, 2, 2, 2
[1, 3, 3, 2, 3, 2, 2, 2, 3] => 1, 3, 3, 2, 3, 2, 2, 2, 3
[1, 3, 3, 2, 3, 2, 2, 3, 1] => 1, 3, 3, 2, 3, 2, 2, 3, 1
[1, 3, 3, 2, 3, 2, 2, 3, 2] => 1, 3, 3, 2, 3, 2, 2, 3, 2
[1, 3, 3, 2, 3, 2, 2, 3, 3] => 1, 3, 3, 2, 3, 2, 2, 3, 3
[1, 3, 3, 2, 3, 2, 3, 1, 1] => 1, 3, 3, 2, 3, 2, 3, 1, 1
[1, 3, 3, 2, 3, 2, 3, 1, 2] => 1, 3, 3, 2, 3, 2, 3, 1, 2
[1, 3, 3, 2, 3, 2, 3, 1, 3] => 1, 3, 3, 2, 3, 2, 3, 1, 3
[1, 3, 3, 2, 3, 2, 3, 2, 1] => 1, 3, 3, 2, 3, 2, 3, 2, 1
[1, 3, 3, 2, 3, 2, 3, 2, 2] => 1, 3, 3, 2, 3, 2, 3, 2, 2
[1, 3, 3, 2, 3, 2, 3, 2, 3] => 1, 3, 3, 2, 3, 2, 3, 2, 3
[1, 3, 3, 2, 3, 2, 3, 3, 1] => 1, 3, 3, 2, 3, 2, 3, 3, 1
[1, 3, 3, 2, 3, 2, 3, 3, 2] => 1, 3, 3, 2, 3, 2, 3, 3, 2
[1, 3, 3, 2, 3, 2, 3, 3, 3] => 1, 3, 3, 2, 3, 2, 3, 3, 3
[1, 3, 3, 2, 3, 3, 1, 1, 1] => 1, 3, 3, 2, 3, 3, 1, 1, 1
[1, 3, 3, 2, 3, 3, 1, 1, 2] => 1, 3, 3, 2, 3, 3, 1, 1, 2
[1, 3, 3, 2, 3, 3, 1, 1, 3] => 1, 3, 3, 2, 3, 3, 1, 1, 3
[1, 3, 3, 2, 3, 3, 1, 2, 1] => 1, 3, 3, 2, 3, 3, 1, 2, 1
[1, 3, 3, 2, 3, 3, 1, 2, 2] => 1, 3, 3, 2, 3, 3, 1, 2, 2
[1, 3, 3, 2, 3, 3, 1, 2, 3] => 1, 3, 3, 2, 3, 3, 1, 2, 3
[1, 3, 3, 2, 3, 3, 1, 3, 1] => 1, 3, 3, 2, 3, 3, 1, 3, 1
[1, 3, 3, 2, 3, 3, 1, 3, 2] => 1, 3, 3, 2, 3, 3, 1, 3, 2
[1, 3, 3, 2, 3, 3, 1, 3, 3] => 1, 3, 3, 2, 3, 3, 1, 3, 3
[1, 3, 3, 2, 3, 3, 2, 1, 1] => 1, 3, 3, 2, 3, 3, 2, 1, 1
[1, 3, 3, 2, 3, 3, 2, 1, 2] => 1, 3, 3, 2, 3, 3, 2, 1, 2
[1, 3, 3, 2, 3, 3, 2, 1, 3] => 1, 3, 3, 2, 3, 3, 2, 1, 3
[1, 3, 3, 2, 3, 3, 2, 2, 1] => 1, 3, 3, 2, 3, 3, 2, 2, 1
[1, 3, 3, 2, 3, 3, 2, 2, 2] => 1, 3, 3, 2, 3, 3, 2, 2, 2
[1, 3, 3, 2, 3, 3, 2, 2, 3] => 1, 3, 3, 2, 3, 3, 2, 2, 3
[1, 3, 3, 2, 3, 3, 2, 3, 1] => 1, 3, 3, 2, 3, 3, 2, 3, 1
[1, 3, 3, 2, 3, 3, 2, 3, 2] => 1, 3, 3, 2, 3, 3, 2, 3, 2
[1, 3, 3, 2, 3, 3, 2, 3, 3] => 1, 3, 3, 2, 3, 3, 2, 3, 3
[1, 3, 3, 2, 3, 3, 3, 1, 1] => 1, 3, 3, 2, 3, 3, 3, 1, 1
[1, 3, 3, 2, 3, 3, 3, 1, 2] => 1, 3, 3, 2, 3, 3, 3, 1, 2
[1, 3, 3, 2, 3, 3, 3, 1, 3] => 1, 3, 3, 2, 3, 3, 3, 1, 3
[1, 3, 3, 2, 3, 3, 3, 2, 1] => 1, 3, 3, 2, 3, 3, 3, 2, 1
[1, 3, 3, 2, 3, 3, 3, 2, 2] => 1, 3, 3, 2, 3, 3, 3, 2, 2
[1, 3, 3, 2, 3, 3, 3, 2, 3] => 1, 3, 3, 2, 3, 3, 3, 2, 3
[1, 3, 3, 2, 3, 3, 3, 3, 1] => 1, 3, 3, 2, 3, 3, 3, 3, 1
[1, 3, 3, 2, 3, 3, 3, 3, 2] => 1, 3, 3, 2, 3, 3, 3, 3, 2
[1, 3, 3, 2, 3, 3, 3, 3, 3] => 1, 3, 3, 2, 3, 3, 3, 3, 3
[1, 3, 3, 3, 1, 1, 1, 1, 1] => 1, 3, 3, 3, 1, 1, 1, 1, 1
[1, 3, 3, 3, 1, 1, 1, 1, 2] => 1, 3, 3, 3, 1, 1, 1, 1, 2
[1, 3, 3, 3, 1, 1, 1, 1, 3] => 1, 3, 3, 3, 1, 1, 1, 1, 3
[1, 3, 3, 3, 1, 1, 1, 2, 1] => 1, 3, 3, 3, 1, 1, 1, 2, 1
[1, 3, 3, 3, 1, 1, 1, 2, 2] => 1, 3, 3, 3, 1, 1, 1, 2, 2
[1, 3, 3, 3, 1, 1, 1, 2, 3] => 1, 3, 3, 3, 1, 1, 1, 2, 3
[1, 3, 3, 3, 1, 1, 1, 3, 1] => 1, 3, 3, 3, 1, 1, 1, 3, 1
[1, 3, 3, 3, 1, 1, 1, 3, 2] => 1, 3, 3, 3, 1, 1, 1, 3, 2
[1, 3, 3, 3, 1, 1, 1, 3, 3] => 1, 3, 3, 3, 1, 1, 1, 3, 3
[1, 3, 3, 3, 1, 1, 2, 1, 1] => 1, 3, 3, 3, 1, 1, 2, 1, 1
[1, 3, 3, 3, 1, 1, 2, 1, 2] => 1, 3, 3, 3, 1, 1, 2, 1, 2
[1, 3, 3, 3, 1, 1, 2, 1, 3] => 1, 3, 3, 3, 1, 1, 2, 1, 3
[1, 3, 3, 3, 1, 1, 2, 2, 1] => 1, 3, 3, 3, 1, 1, 2, 2, 1
[1, 3, 3, 3, 1, 1, 2, 2, 2] => 1, 3, 3, 3, 1, 1, 2, 2, 2
[1, 3, 3, 3, 1, 1, 2, 2, 3] => 1, 3, 3, 3, 1, 1, 2, 2, 3
[1, 3, 3, 3, 1, 1, 2, 3, 1] => 1, 3, 3, 3, 1, 1, 2, 3, 1
[1, 3, 3, 3, 1, 1, 2, 3, 2] => 1, 3, 3, 3, 1, 1, 2, 3, 2
[1, 3, 3, 3, 1, 1, 2, 3, 3] => 1, 3, 3, 3, 1, 1, 2, 3, 3
[1, 3, 3, 3, 1, 1, 3, 1, 1] => 1, 3, 3, 3, 1, 1, 3, 1, 1
[1, 3, 3, 3, 1, 1, 3, 1, 2] => 1, 3, 3, 3, 1, 1, 3, 1, 2
[1, 3, 3, 3, 1, 1, 3, 1, 3] => 1, 3, 3, 3, 1, 1, 3, 1, 3
[1, 3, 3, 3, 1, 1, 3, 2, 1] => 1, 3, 3, 3, 1, 1, 3, 2, 1
[1, 3, 3, 3, 1, 1, 3, 2, 2] => 1, 3, 3, 3, 1, 1, 3, 2, 2
[1, 3, 3, 3, 1, 1, 3, 2, 3] => 1, 3, 3, 3, 1, 1, 3, 2, 3
[1, 3, 3, 3, 1, 1, 3, 3, 1] => 1, 3, 3, 3, 1, 1, 3, 3, 1
[1, 3, 3, 3, 1, 1, 3, 3, 2] => 1, 3, 3, 3, 1, 1, 3, 3, 2
[1, 3, 3, 3, 1, 1, 3, 3, 3] => 1, 3, 3, 3, 1, 1, 3, 3, 3
[1, 3, 3, 3, 1, 2, 1, 1, 1] => 1, 3, 3, 3, 1, 2, 1, 1, 1
[1, 3, 3, 3, 1, 2, 1, 1, 2] => 1, 3, 3, 3, 1, 2, 1, 1, 2
[1, 3, 3, 3, 1, 2, 1, 1, 3] => 1, 3, 3, 3, 1, 2, 1, 1, 3
[1, 3, 3, 3, 1, 2, 1, 2, 1] => 1, 3, 3, 3, 1, 2, 1, 2, 1
[1, 3, 3, 3, 1, 2, 1, 2, 2] => 1, 3, 3, 3, 1, 2, 1, 2, 2
[1, 3, 3, 3, 1, 2, 1, 2, 3] => 1, 3, 3, 3, 1, 2, 1, 2, 3
[1, 3, 3, 3, 1, 2, 1, 3, 1] => 1, 3, 3, 3, 1, 2, 1, 3, 1
[1, 3, 3, 3, 1, 2, 1, 3, 2] => 1, 3, 3, 3, 1, 2, 1, 3, 2
[1, 3, 3, 3, 1, 2, 1, 3, 3] => 1, 3, 3, 3, 1, 2, 1, 3, 3
[1, 3, 3, 3, 1, 2, 2, 1, 1] => 1, 3, 3, 3, 1, 2, 2, 1, 1
[1, 3, 3, 3, 1, 2, 2, 1, 2] => 1, 3, 3, 3, 1, 2, 2, 1, 2
[1, 3, 3, 3, 1, 2, 2, 1, 3] => 1, 3, 3, 3, 1, 2, 2, 1, 3
[1, 3, 3, 3, 1, 2, 2, 2, 1] => 1, 3, 3, 3, 1, 2, 2, 2, 1
[1, 3, 3, 3, 1, 2, 2, 2, 2] => 1, 3, 3, 3, 1, 2, 2, 2, 2
[1, 3, 3, 3, 1, 2, 2, 2, 3] => 1, 3, 3, 3, 1, 2, 2, 2, 3
[1, 3, 3, 3, 1, 2, 2, 3, 1] => 1, 3, 3, 3, 1, 2, 2, 3, 1
[1, 3, 3, 3, 1, 2, 2, 3, 2] => 1, 3, 3, 3, 1, 2, 2, 3, 2
[1, 3, 3, 3, 1, 2, 2, 3, 3] => 1, 3, 3, 3, 1, 2, 2, 3, 3
[1, 3, 3, 3, 1, 2, 3, 1, 1] => 1, 3, 3, 3, 1, 2, 3, 1, 1
[1, 3, 3, 3, 1, 2, 3, 1, 2] => 1, 3, 3, 3, 1, 2, 3, 1, 2
[1, 3, 3, 3, 1, 2, 3, 1, 3] => 1, 3, 3, 3, 1, 2, 3, 1, 3
[1, 3, 3, 3, 1, 2, 3, 2, 1] => 1, 3, 3, 3, 1, 2, 3, 2, 1
[1, 3, 3, 3, 1, 2, 3, 2, 2] => 1, 3, 3, 3, 1, 2, 3, 2, 2
[1, 3, 3, 3, 1, 2, 3, 2, 3] => 1, 3, 3, 3, 1, 2, 3, 2, 3
[1, 3, 3, 3, 1, 2, 3, 3, 1] => 1, 3, 3, 3, 1, 2, 3, 3, 1
[1, 3, 3, 3, 1, 2, 3, 3, 2] => 1, 3, 3, 3, 1, 2, 3, 3, 2
[1, 3, 3, 3, 1, 2, 3, 3, 3] => 1, 3, 3, 3, 1, 2, 3, 3, 3
[1, 3, 3, 3, 1, 3, 1, 1, 1] => 1, 3, 3, 3, 1, 3, 1, 1, 1
[1, 3, 3, 3, 1, 3, 1, 1, 2] => 1, 3, 3, 3, 1, 3, 1, 1, 2
[1, 3, 3, 3, 1, 3, 1, 1, 3] => 1, 3, 3, 3, 1, 3, 1, 1, 3
[1, 3, 3, 3, 1, 3, 1, 2, 1] => 1, 3, 3, 3, 1, 3, 1, 2, 1
[1, 3, 3, 3, 1, 3, 1, 2, 2] => 1, 3, 3, 3, 1, 3, 1, 2, 2
[1, 3, 3, 3, 1, 3, 1, 2, 3] => 1, 3, 3, 3, 1, 3, 1, 2, 3
[1, 3, 3, 3, 1, 3, 1, 3, 1] => 1, 3, 3, 3, 1, 3, 1, 3, 1
[1, 3, 3, 3, 1, 3, 1, 3, 2] => 1, 3, 3, 3, 1, 3, 1, 3, 2
[1, 3, 3, 3, 1, 3, 1, 3, 3] => 1, 3, 3, 3, 1, 3, 1, 3, 3
[1, 3, 3, 3, 1, 3, 2, 1, 1] => 1, 3, 3, 3, 1, 3, 2, 1, 1
[1, 3, 3, 3, 1, 3, 2, 1, 2] => 1, 3, 3, 3, 1, 3, 2, 1, 2
[1, 3, 3, 3, 1, 3, 2, 1, 3] => 1, 3, 3, 3, 1, 3, 2, 1, 3
[1, 3, 3, 3, 1, 3, 2, 2, 1] => 1, 3, 3, 3, 1, 3, 2, 2, 1
[1, 3, 3, 3, 1, 3, 2, 2, 2] => 1, 3, 3, 3, 1, 3, 2, 2, 2
[1, 3, 3, 3, 1, 3, 2, 2, 3] => 1, 3, 3, 3, 1, 3, 2, 2, 3
[1, 3, 3, 3, 1, 3, 2, 3, 1] => 1, 3, 3, 3, 1, 3, 2, 3, 1
[1, 3, 3, 3, 1, 3, 2, 3, 2] => 1, 3, 3, 3, 1, 3, 2, 3, 2
[1, 3, 3, 3, 1, 3, 2, 3, 3] => 1, 3, 3, 3, 1, 3, 2, 3, 3
[1, 3, 3, 3, 1, 3, 3, 1, 1] => 1, 3, 3, 3, 1, 3, 3, 1, 1
[1, 3, 3, 3, 1, 3, 3, 1, 2] => 1, 3, 3, 3, 1, 3, 3, 1, 2
[1, 3, 3, 3, 1, 3, 3, 1, 3] => 1, 3, 3, 3, 1, 3, 3, 1, 3
[1, 3, 3, 3, 1, 3, 3, 2, 1] => 1, 3, 3, 3, 1, 3, 3, 2, 1
[1, 3, 3, 3, 1, 3, 3, 2, 2] => 1, 3, 3, 3, 1, 3, 3, 2, 2
[1, 3, 3, 3, 1, 3, 3, 2, 3] => 1, 3, 3, 3, 1, 3, 3, 2, 3
[1, 3, 3, 3, 1, 3, 3, 3, 1] => 1, 3, 3, 3, 1, 3, 3, 3, 1
[1, 3, 3, 3, 1, 3, 3, 3, 2] => 1, 3, 3, 3, 1, 3, 3, 3, 2
[1, 3, 3, 3, 1, 3, 3, 3, 3] => 1, 3, 3, 3, 1, 3, 3, 3, 3
[1, 3, 3, 3, 2, 1, 1, 1, 1] => 1, 3, 3, 3, 2, 1, 1, 1, 1
[1, 3, 3, 3, 2, 1, 1, 1, 2] => 1, 3, 3, 3, 2, 1, 1, 1, 2
[1, 3, 3, 3, 2, 1, 1, 1, 3] => 1, 3, 3, 3, 2, 1, 1, 1, 3
[1, 3, 3, 3, 2, 1, 1, 2, 1] => 1, 3, 3, 3, 2, 1, 1, 2, 1
[1, 3, 3, 3, 2, 1, 1, 2, 2] => 1, 3, 3, 3, 2, 1, 1, 2, 2
[1, 3, 3, 3, 2, 1, 1, 2, 3] => 1, 3, 3, 3, 2, 1, 1, 2, 3
[1, 3, 3, 3, 2, 1, 1, 3, 1] => 1, 3, 3, 3, 2, 1, 1, 3, 1
[1, 3, 3, 3, 2, 1, 1, 3, 2] => 1, 3, 3, 3, 2, 1, 1, 3, 2
[1, 3, 3, 3, 2, 1, 1, 3, 3] => 1, 3, 3, 3, 2, 1, 1, 3, 3
[1, 3, 3, 3, 2, 1, 2, 1, 1] => 1, 3, 3, 3, 2, 1, 2, 1, 1
[1, 3, 3, 3, 2, 1, 2, 1, 2] => 1, 3, 3, 3, 2, 1, 2, 1, 2
[1, 3, 3, 3, 2, 1, 2, 1, 3] => 1, 3, 3, 3, 2, 1, 2, 1, 3
[1, 3, 3, 3, 2, 1, 2, 2, 1] => 1, 3, 3, 3, 2, 1, 2, 2, 1
[1, 3, 3, 3, 2, 1, 2, 2, 2] => 1, 3, 3, 3, 2, 1, 2, 2, 2
[1, 3, 3, 3, 2, 1, 2, 2, 3] => 1, 3, 3, 3, 2, 1, 2, 2, 3
[1, 3, 3, 3, 2, 1, 2, 3, 1] => 1, 3, 3, 3, 2, 1, 2, 3, 1
[1, 3, 3, 3, 2, 1, 2, 3, 2] => 1, 3, 3, 3, 2, 1, 2, 3, 2
[1, 3, 3, 3, 2, 1, 2, 3, 3] => 1, 3, 3, 3, 2, 1, 2, 3, 3
[1, 3, 3, 3, 2, 1, 3, 1, 1] => 1, 3, 3, 3, 2, 1, 3, 1, 1
[1, 3, 3, 3, 2, 1, 3, 1, 2] => 1, 3, 3, 3, 2, 1, 3, 1, 2
[1, 3, 3, 3, 2, 1, 3, 1, 3] => 1, 3, 3, 3, 2, 1, 3, 1, 3
[1, 3, 3, 3, 2, 1, 3, 2, 1] => 1, 3, 3, 3, 2, 1, 3, 2, 1
[1, 3, 3, 3, 2, 1, 3, 2, 2] => 1, 3, 3, 3, 2, 1, 3, 2, 2
[1, 3, 3, 3, 2, 1, 3, 2, 3] => 1, 3, 3, 3, 2, 1, 3, 2, 3
[1, 3, 3, 3, 2, 1, 3, 3, 1] => 1, 3, 3, 3, 2, 1, 3, 3, 1
[1, 3, 3, 3, 2, 1, 3, 3, 2] => 1, 3, 3, 3, 2, 1, 3, 3, 2
[1, 3, 3, 3, 2, 1, 3, 3, 3] => 1, 3, 3, 3, 2, 1, 3, 3, 3
[1, 3, 3, 3, 2, 2, 1, 1, 1] => 1, 3, 3, 3, 2, 2, 1, 1, 1
[1, 3, 3, 3, 2, 2, 1, 1, 2] => 1, 3, 3, 3, 2, 2, 1, 1, 2
[1, 3, 3, 3, 2, 2, 1, 1, 3] => 1, 3, 3, 3, 2, 2, 1, 1, 3
[1, 3, 3, 3, 2, 2, 1, 2, 1] => 1, 3, 3, 3, 2, 2, 1, 2, 1
[1, 3, 3, 3, 2, 2, 1, 2, 2] => 1, 3, 3, 3, 2, 2, 1, 2, 2
[1, 3, 3, 3, 2, 2, 1, 2, 3] => 1, 3, 3, 3, 2, 2, 1, 2, 3
[1, 3, 3, 3, 2, 2, 1, 3, 1] => 1, 3, 3, 3, 2, 2, 1, 3, 1
[1, 3, 3, 3, 2, 2, 1, 3, 2] => 1, 3, 3, 3, 2, 2, 1, 3, 2
[1, 3, 3, 3, 2, 2, 1, 3, 3] => 1, 3, 3, 3, 2, 2, 1, 3, 3
[1, 3, 3, 3, 2, 2, 2, 1, 1] => 1, 3, 3, 3, 2, 2, 2, 1, 1
[1, 3, 3, 3, 2, 2, 2, 1, 2] => 1, 3, 3, 3, 2, 2, 2, 1, 2
[1, 3, 3, 3, 2, 2, 2, 1, 3] => 1, 3, 3, 3, 2, 2, 2, 1, 3
[1, 3, 3, 3, 2, 2, 2, 2, 1] => 1, 3, 3, 3, 2, 2, 2, 2, 1
[1, 3, 3, 3, 2, 2, 2, 2, 2] => 1, 3, 3, 3, 2, 2, 2, 2, 2
[1, 3, 3, 3, 2, 2, 2, 2, 3] => 1, 3, 3, 3, 2, 2, 2, 2, 3
[1, 3, 3, 3, 2, 2, 2, 3, 1] => 1, 3, 3, 3, 2, 2, 2, 3, 1
[1, 3, 3, 3, 2, 2, 2, 3, 2] => 1, 3, 3, 3, 2, 2, 2, 3, 2
[1, 3, 3, 3, 2, 2, 2, 3, 3] => 1, 3, 3, 3, 2, 2, 2, 3, 3
[1, 3, 3, 3, 2, 2, 3, 1, 1] => 1, 3, 3, 3, 2, 2, 3, 1, 1
[1, 3, 3, 3, 2, 2, 3, 1, 2] => 1, 3, 3, 3, 2, 2, 3, 1, 2
[1, 3, 3, 3, 2, 2, 3, 1, 3] => 1, 3, 3, 3, 2, 2, 3, 1, 3
[1, 3, 3, 3, 2, 2, 3, 2, 1] => 1, 3, 3, 3, 2, 2, 3, 2, 1
[1, 3, 3, 3, 2, 2, 3, 2, 2] => 1, 3, 3, 3, 2, 2, 3, 2, 2
[1, 3, 3, 3, 2, 2, 3, 2, 3] => 1, 3, 3, 3, 2, 2, 3, 2, 3
[1, 3, 3, 3, 2, 2, 3, 3, 1] => 1, 3, 3, 3, 2, 2, 3, 3, 1
[1, 3, 3, 3, 2, 2, 3, 3, 2] => 1, 3, 3, 3, 2, 2, 3, 3, 2
[1, 3, 3, 3, 2, 2, 3, 3, 3] => 1, 3, 3, 3, 2, 2, 3, 3, 3
[1, 3, 3, 3, 2, 3, 1, 1, 1] => 1, 3, 3, 3, 2, 3, 1, 1, 1
[1, 3, 3, 3, 2, 3, 1, 1, 2] => 1, 3, 3, 3, 2, 3, 1, 1, 2
[1, 3, 3, 3, 2, 3, 1, 1, 3] => 1, 3, 3, 3, 2, 3, 1, 1, 3
[1, 3, 3, 3, 2, 3, 1, 2, 1] => 1, 3, 3, 3, 2, 3, 1, 2, 1
[1, 3, 3, 3, 2, 3, 1, 2, 2] => 1, 3, 3, 3, 2, 3, 1, 2, 2
[1, 3, 3, 3, 2, 3, 1, 2, 3] => 1, 3, 3, 3, 2, 3, 1, 2, 3
[1, 3, 3, 3, 2, 3, 1, 3, 1] => 1, 3, 3, 3, 2, 3, 1, 3, 1
[1, 3, 3, 3, 2, 3, 1, 3, 2] => 1, 3, 3, 3, 2, 3, 1, 3, 2
[1, 3, 3, 3, 2, 3, 1, 3, 3] => 1, 3, 3, 3, 2, 3, 1, 3, 3
[1, 3, 3, 3, 2, 3, 2, 1, 1] => 1, 3, 3, 3, 2, 3, 2, 1, 1
[1, 3, 3, 3, 2, 3, 2, 1, 2] => 1, 3, 3, 3, 2, 3, 2, 1, 2
[1, 3, 3, 3, 2, 3, 2, 1, 3] => 1, 3, 3, 3, 2, 3, 2, 1, 3
[1, 3, 3, 3, 2, 3, 2, 2, 1] => 1, 3, 3, 3, 2, 3, 2, 2, 1
[1, 3, 3, 3, 2, 3, 2, 2, 2] => 1, 3, 3, 3, 2, 3, 2, 2, 2
[1, 3, 3, 3, 2, 3, 2, 2, 3] => 1, 3, 3, 3, 2, 3, 2, 2, 3
[1, 3, 3, 3, 2, 3, 2, 3, 1] => 1, 3, 3, 3, 2, 3, 2, 3, 1
[1, 3, 3, 3, 2, 3, 2, 3, 2] => 1, 3, 3, 3, 2, 3, 2, 3, 2
[1, 3, 3, 3, 2, 3, 2, 3, 3] => 1, 3, 3, 3, 2, 3, 2, 3, 3
[1, 3, 3, 3, 2, 3, 3, 1, 1] => 1, 3, 3, 3, 2, 3, 3, 1, 1
[1, 3, 3, 3, 2, 3, 3, 1, 2] => 1, 3, 3, 3, 2, 3, 3, 1, 2
[1, 3, 3, 3, 2, 3, 3, 1, 3] => 1, 3, 3, 3, 2, 3, 3, 1, 3
[1, 3, 3, 3, 2, 3, 3, 2, 1] => 1, 3, 3, 3, 2, 3, 3, 2, 1
[1, 3, 3, 3, 2, 3, 3, 2, 2] => 1, 3, 3, 3, 2, 3, 3, 2, 2
[1, 3, 3, 3, 2, 3, 3, 2, 3] => 1, 3, 3, 3, 2, 3, 3, 2, 3
[1, 3, 3, 3, 2, 3, 3, 3, 1] => 1, 3, 3, 3, 2, 3, 3, 3, 1
[1, 3, 3, 3, 2, 3, 3, 3, 2] => 1, 3, 3, 3, 2, 3, 3, 3, 2
[1, 3, 3, 3, 2, 3, 3, 3, 3] => 1, 3, 3, 3, 2, 3, 3, 3, 3
[1, 3, 3, 3, 3, 1, 1, 1, 1] => 1, 3, 3, 3, 3, 1, 1, 1, 1
[1, 3, 3, 3, 3, 1, 1, 1, 2] => 1, 3, 3, 3, 3, 1, 1, 1, 2
[1, 3, 3, 3, 3, 1, 1, 1, 3] => 1, 3, 3, 3, 3, 1, 1, 1, 3
[1, 3, 3, 3, 3, 1, 1, 2, 1] => 1, 3, 3, 3, 3, 1, 1, 2, 1
[1, 3, 3, 3, 3, 1, 1, 2, 2] => 1, 3, 3, 3, 3, 1, 1, 2, 2
[1, 3, 3, 3, 3, 1, 1, 2, 3] => 1, 3, 3, 3, 3, 1, 1, 2, 3
[1, 3, 3, 3, 3, 1, 1, 3, 1] => 1, 3, 3, 3, 3, 1, 1, 3, 1
[1, 3, 3, 3, 3, 1, 1, 3, 2] => 1, 3, 3, 3, 3, 1, 1, 3, 2
[1, 3, 3, 3, 3, 1, 1, 3, 3] => 1, 3, 3, 3, 3, 1, 1, 3, 3
[1, 3, 3, 3, 3, 1, 2, 1, 1] => 1, 3, 3, 3, 3, 1, 2, 1, 1
[1, 3, 3, 3, 3, 1, 2, 1, 2] => 1, 3, 3, 3, 3, 1, 2, 1, 2
[1, 3, 3, 3, 3, 1, 2, 1, 3] => 1, 3, 3, 3, 3, 1, 2, 1, 3
[1, 3, 3, 3, 3, 1, 2, 2, 1] => 1, 3, 3, 3, 3, 1, 2, 2, 1
[1, 3, 3, 3, 3, 1, 2, 2, 2] => 1, 3, 3, 3, 3, 1, 2, 2, 2
[1, 3, 3, 3, 3, 1, 2, 2, 3] => 1, 3, 3, 3, 3, 1, 2, 2, 3
[1, 3, 3, 3, 3, 1, 2, 3, 1] => 1, 3, 3, 3, 3, 1, 2, 3, 1
[1, 3, 3, 3, 3, 1, 2, 3, 2] => 1, 3, 3, 3, 3, 1, 2, 3, 2
[1, 3, 3, 3, 3, 1, 2, 3, 3] => 1, 3, 3, 3, 3, 1, 2, 3, 3
[1, 3, 3, 3, 3, 1, 3, 1, 1] => 1, 3, 3, 3, 3, 1, 3, 1, 1
[1, 3, 3, 3, 3, 1, 3, 1, 2] => 1, 3, 3, 3, 3, 1, 3, 1, 2
[1, 3, 3, 3, 3, 1, 3, 1, 3] => 1, 3, 3, 3, 3, 1, 3, 1, 3
[1, 3, 3, 3, 3, 1, 3, 2, 1] => 1, 3, 3, 3, 3, 1, 3, 2, 1
[1, 3, 3, 3, 3, 1, 3, 2, 2] => 1, 3, 3, 3, 3, 1, 3, 2, 2
[1, 3, 3, 3, 3, 1, 3, 2, 3] => 1, 3, 3, 3, 3, 1, 3, 2, 3
[1, 3, 3, 3, 3, 1, 3, 3, 1] => 1, 3, 3, 3, 3, 1, 3, 3, 1
[1, 3, 3, 3, 3, 1, 3, 3, 2] => 1, 3, 3, 3, 3, 1, 3, 3, 2
[1, 3, 3, 3, 3, 1, 3, 3, 3] => 1, 3, 3, 3, 3, 1, 3, 3, 3
[1, 3, 3, 3, 3, 2, 1, 1, 1] => 1, 3, 3, 3, 3, 2, 1, 1, 1
[1, 3, 3, 3, 3, 2, 1, 1, 2] => 1, 3, 3, 3, 3, 2, 1, 1, 2
[1, 3, 3, 3, 3, 2, 1, 1, 3] => 1, 3, 3, 3, 3, 2, 1, 1, 3
[1, 3, 3, 3, 3, 2, 1, 2, 1] => 1, 3, 3, 3, 3, 2, 1, 2, 1
[1, 3, 3, 3, 3, 2, 1, 2, 2] => 1, 3, 3, 3, 3, 2, 1, 2, 2
[1, 3, 3, 3, 3, 2, 1, 2, 3] => 1, 3, 3, 3, 3, 2, 1, 2, 3
[1, 3, 3, 3, 3, 2, 1, 3, 1] => 1, 3, 3, 3, 3, 2, 1, 3, 1
[1, 3, 3, 3, 3, 2, 1, 3, 2] => 1, 3, 3, 3, 3, 2, 1, 3, 2
[1, 3, 3, 3, 3, 2, 1, 3, 3] => 1, 3, 3, 3, 3, 2, 1, 3, 3
[1, 3, 3, 3, 3, 2, 2, 1, 1] => 1, 3, 3, 3, 3, 2, 2, 1, 1
[1, 3, 3, 3, 3, 2, 2, 1, 2] => 1, 3, 3, 3, 3, 2, 2, 1, 2
[1, 3, 3, 3, 3, 2, 2, 1, 3] => 1, 3, 3, 3, 3, 2, 2, 1, 3
[1, 3, 3, 3, 3, 2, 2, 2, 1] => 1, 3, 3, 3, 3, 2, 2, 2, 1
[1, 3, 3, 3, 3, 2, 2, 2, 2] => 1, 3, 3, 3, 3, 2, 2, 2, 2
[1, 3, 3, 3, 3, 2, 2, 2, 3] => 1, 3, 3, 3, 3, 2, 2, 2, 3
[1, 3, 3, 3, 3, 2, 2, 3, 1] => 1, 3, 3, 3, 3, 2, 2, 3, 1
[1, 3, 3, 3, 3, 2, 2, 3, 2] => 1, 3, 3, 3, 3, 2, 2, 3, 2
[1, 3, 3, 3, 3, 2, 2, 3, 3] => 1, 3, 3, 3, 3, 2, 2, 3, 3
[1, 3, 3, 3, 3, 2, 3, 1, 1] => 1, 3, 3, 3, 3, 2, 3, 1, 1
[1, 3, 3, 3, 3, 2, 3, 1, 2] => 1, 3, 3, 3, 3, 2, 3, 1, 2
[1, 3, 3, 3, 3, 2, 3, 1, 3] => 1, 3, 3, 3, 3, 2, 3, 1, 3
[1, 3, 3, 3, 3, 2, 3, 2, 1] => 1, 3, 3, 3, 3, 2, 3, 2, 1
[1, 3, 3, 3, 3, 2, 3, 2, 2] => 1, 3, 3, 3, 3, 2, 3, 2, 2
[1, 3, 3, 3, 3, 2, 3, 2, 3] => 1, 3, 3, 3, 3, 2, 3, 2, 3
[1, 3, 3, 3, 3, 2, 3, 3, 1] => 1, 3, 3, 3, 3, 2, 3, 3, 1
[1, 3, 3, 3, 3, 2, 3, 3, 2] => 1, 3, 3, 3, 3, 2, 3, 3, 2
[1, 3, 3, 3, 3, 2, 3, 3, 3] => 1, 3, 3, 3, 3, 2, 3, 3, 3
[1, 3, 3, 3, 3, 3, 1, 1, 1] => 1, 3, 3, 3, 3, 3, 1, 1, 1
[1, 3, 3, 3, 3, 3, 1, 1, 2] => 1, 3, 3, 3, 3, 3, 1, 1, 2
[1, 3, 3, 3, 3, 3, 1, 1, 3] => 1, 3, 3, 3, 3, 3, 1, 1, 3
[1, 3, 3, 3, 3, 3, 1, 2, 1] => 1, 3, 3, 3, 3, 3, 1, 2, 1
[1, 3, 3, 3, 3, 3, 1, 2, 2] => 1, 3, 3, 3, 3, 3, 1, 2, 2
[1, 3, 3, 3, 3, 3, 1, 2, 3] => 1, 3, 3, 3, 3, 3, 1, 2, 3
[1, 3, 3, 3, 3, 3, 1, 3, 1] => 1, 3, 3, 3, 3, 3, 1, 3, 1
[1, 3, 3, 3, 3, 3, 1, 3, 2] => 1, 3, 3, 3, 3, 3, 1, 3, 2
[1, 3, 3, 3, 3, 3, 1, 3, 3] => 1, 3, 3, 3, 3, 3, 1, 3, 3
[1, 3, 3, 3, 3, 3, 2, 1, 1] => 1, 3, 3, 3, 3, 3, 2, 1, 1
[1, 3, 3, 3, 3, 3, 2, 1, 2] => 1, 3, 3, 3, 3, 3, 2, 1, 2
[1, 3, 3, 3, 3, 3, 2, 1, 3] => 1, 3, 3, 3, 3, 3, 2, 1, 3
[1, 3, 3, 3, 3, 3, 2, 2, 1] => 1, 3, 3, 3, 3, 3, 2, 2, 1
[1, 3, 3, 3, 3, 3, 2, 2, 2] => 1, 3, 3, 3, 3, 3, 2, 2, 2
[1, 3, 3, 3, 3, 3, 2, 2, 3] => 1, 3, 3, 3, 3, 3, 2, 2, 3
[1, 3, 3, 3, 3, 3, 2, 3, 1] => 1, 3, 3, 3, 3, 3, 2, 3, 1
[1, 3, 3, 3, 3, 3, 2, 3, 2] => 1, 3, 3, 3, 3, 3, 2, 3, 2
[1, 3, 3, 3, 3, 3, 2, 3, 3] => 1, 3, 3, 3, 3, 3, 2, 3, 3
[1, 3, 3, 3, 3, 3, 3, 1, 1] => 1, 3, 3, 3, 3, 3, 3, 1, 1
[1, 3, 3, 3, 3, 3, 3, 1, 2] => 1, 3, 3, 3, 3, 3, 3, 1, 2
[1, 3, 3, 3, 3, 3, 3, 1, 3] => 1, 3, 3, 3, 3, 3, 3, 1, 3
[1, 3, 3, 3, 3, 3, 3, 2, 1] => 1, 3, 3, 3, 3, 3, 3, 2, 1
[1, 3, 3, 3, 3, 3, 3, 2, 2] => 1, 3, 3, 3, 3, 3, 3, 2, 2
[1, 3, 3, 3, 3, 3, 3, 2, 3] => 1, 3, 3, 3, 3, 3, 3, 2, 3
[1, 3, 3, 3, 3, 3, 3, 3, 1] => 1, 3, 3, 3, 3, 3, 3, 3, 1
[1, 3, 3, 3, 3, 3, 3, 3, 2] => 1, 3, 3, 3, 3, 3, 3, 3, 2
[1, 3, 3, 3, 3, 3, 3, 3, 3] => 1, 3, 3, 3, 3, 3, 3, 3, 3
[2, 1, 1, 1, 1, 1, 1, 1, 1] => 2, 1, 1, 1, 1, 1, 1, 1, 1
[2, 1, 1, 1, 1, 1, 1, 1, 2] => 2, 1, 1, 1, 1, 1, 1, 1, 2
[2, 1, 1, 1, 1, 1, 1, 1, 3] => 2, 1, 1, 1, 1, 1, 1, 1, 3
[2, 1, 1, 1, 1, 1, 1, 2, 1] => 2, 1, 1, 1, 1, 1, 1, 2, 1
[2, 1, 1, 1, 1, 1, 1, 2, 2] => 2, 1, 1, 1, 1, 1, 1, 2, 2
[2, 1, 1, 1, 1, 1, 1, 2, 3] => 2, 1, 1, 1, 1, 1, 1, 2, 3
[2, 1, 1, 1, 1, 1, 1, 3, 1] => 2, 1, 1, 1, 1, 1, 1, 3, 1
[2, 1, 1, 1, 1, 1, 1, 3, 2] => 2, 1, 1, 1, 1, 1, 1, 3, 2
[2, 1, 1, 1, 1, 1, 1, 3, 3] => 2, 1, 1, 1, 1, 1, 1, 3, 3
[2, 1, 1, 1, 1, 1, 2, 1, 1] => 2, 1, 1, 1, 1, 1, 2, 1, 1
[2, 1, 1, 1, 1, 1, 2, 1, 2] => 2, 1, 1, 1, 1, 1, 2, 1, 2
[2, 1, 1, 1, 1, 1, 2, 1, 3] => 2, 1, 1, 1, 1, 1, 2, 1, 3
[2, 1, 1, 1, 1, 1, 2, 2, 1] => 2, 1, 1, 1, 1, 1, 2, 2, 1
[2, 1, 1, 1, 1, 1, 2, 2, 2] => 2, 1, 1, 1, 1, 1, 2, 2, 2
[2, 1, 1, 1, 1, 1, 2, 2, 3] => 2, 1, 1, 1, 1, 1, 2, 2, 3
[2, 1, 1, 1, 1, 1, 2, 3, 1] => 2, 1, 1, 1, 1, 1, 2, 3, 1
[2, 1, 1, 1, 1, 1, 2, 3, 2] => 2, 1, 1, 1, 1, 1, 2, 3, 2
[2, 1, 1, 1, 1, 1, 2, 3, 3] => 2, 1, 1, 1, 1, 1, 2, 3, 3
[2, 1, 1, 1, 1, 1, 3, 1, 1] => 2, 1, 1, 1, 1, 1, 3, 1, 1
[2, 1, 1, 1, 1, 1, 3, 1, 2] => 2, 1, 1, 1, 1, 1, 3, 1, 2
[2, 1, 1, 1, 1, 1, 3, 1, 3] => 2, 1, 1, 1, 1, 1, 3, 1, 3
[2, 1, 1, 1, 1, 1, 3, 2, 1] => 2, 1, 1, 1, 1, 1, 3, 2, 1
[2, 1, 1, 1, 1, 1, 3, 2, 2] => 2, 1, 1, 1, 1, 1, 3, 2, 2
[2, 1, 1, 1, 1, 1, 3, 2, 3] => 2, 1, 1, 1, 1, 1, 3, 2, 3
[2, 1, 1, 1, 1, 1, 3, 3, 1] => 2, 1, 1, 1, 1, 1, 3, 3, 1
[2, 1, 1, 1, 1, 1, 3, 3, 2] => 2, 1, 1, 1, 1, 1, 3, 3, 2
[2, 1, 1, 1, 1, 1, 3, 3, 3] => 2, 1, 1, 1, 1, 1, 3, 3, 3
[2, 1, 1, 1, 1, 2, 1, 1, 1] => 2, 1, 1, 1, 1, 2, 1, 1, 1
[2, 1, 1, 1, 1, 2, 1, 1, 2] => 2, 1, 1, 1, 1, 2, 1, 1, 2
[2, 1, 1, 1, 1, 2, 1, 1, 3] => 2, 1, 1, 1, 1, 2, 1, 1, 3
[2, 1, 1, 1, 1, 2, 1, 2, 1] => 2, 1, 1, 1, 1, 2, 1, 2, 1
[2, 1, 1, 1, 1, 2, 1, 2, 2] => 2, 1, 1, 1, 1, 2, 1, 2, 2
[2, 1, 1, 1, 1, 2, 1, 2, 3] => 2, 1, 1, 1, 1, 2, 1, 2, 3
[2, 1, 1, 1, 1, 2, 1, 3, 1] => 2, 1, 1, 1, 1, 2, 1, 3, 1
[2, 1, 1, 1, 1, 2, 1, 3, 2] => 2, 1, 1, 1, 1, 2, 1, 3, 2
[2, 1, 1, 1, 1, 2, 1, 3, 3] => 2, 1, 1, 1, 1, 2, 1, 3, 3
[2, 1, 1, 1, 1, 2, 2, 1, 1] => 2, 1, 1, 1, 1, 2, 2, 1, 1
[2, 1, 1, 1, 1, 2, 2, 1, 2] => 2, 1, 1, 1, 1, 2, 2, 1, 2
[2, 1, 1, 1, 1, 2, 2, 1, 3] => 2, 1, 1, 1, 1, 2, 2, 1, 3
[2, 1, 1, 1, 1, 2, 2, 2, 1] => 2, 1, 1, 1, 1, 2, 2, 2, 1
[2, 1, 1, 1, 1, 2, 2, 2, 2] => 2, 1, 1, 1, 1, 2, 2, 2, 2
[2, 1, 1, 1, 1, 2, 2, 2, 3] => 2, 1, 1, 1, 1, 2, 2, 2, 3
[2, 1, 1, 1, 1, 2, 2, 3, 1] => 2, 1, 1, 1, 1, 2, 2, 3, 1
[2, 1, 1, 1, 1, 2, 2, 3, 2] => 2, 1, 1, 1, 1, 2, 2, 3, 2
[2, 1, 1, 1, 1, 2, 2, 3, 3] => 2, 1, 1, 1, 1, 2, 2, 3, 3
[2, 1, 1, 1, 1, 2, 3, 1, 1] => 2, 1, 1, 1, 1, 2, 3, 1, 1
[2, 1, 1, 1, 1, 2, 3, 1, 2] => 2, 1, 1, 1, 1, 2, 3, 1, 2
[2, 1, 1, 1, 1, 2, 3, 1, 3] => 2, 1, 1, 1, 1, 2, 3, 1, 3
[2, 1, 1, 1, 1, 2, 3, 2, 1] => 2, 1, 1, 1, 1, 2, 3, 2, 1
[2, 1, 1, 1, 1, 2, 3, 2, 2] => 2, 1, 1, 1, 1, 2, 3, 2, 2
[2, 1, 1, 1, 1, 2, 3, 2, 3] => 2, 1, 1, 1, 1, 2, 3, 2, 3
[2, 1, 1, 1, 1, 2, 3, 3, 1] => 2, 1, 1, 1, 1, 2, 3, 3, 1
[2, 1, 1, 1, 1, 2, 3, 3, 2] => 2, 1, 1, 1, 1, 2, 3, 3, 2
[2, 1, 1, 1, 1, 2, 3, 3, 3] => 2, 1, 1, 1, 1, 2, 3, 3, 3
[2, 1, 1, 1, 1, 3, 1, 1, 1] => 2, 1, 1, 1, 1, 3, 1, 1, 1
[2, 1, 1, 1, 1, 3, 1, 1, 2] => 2, 1, 1, 1, 1, 3, 1, 1, 2
[2, 1, 1, 1, 1, 3, 1, 1, 3] => 2, 1, 1, 1, 1, 3, 1, 1, 3
[2, 1, 1, 1, 1, 3, 1, 2, 1] => 2, 1, 1, 1, 1, 3, 1, 2, 1
[2, 1, 1, 1, 1, 3, 1, 2, 2] => 2, 1, 1, 1, 1, 3, 1, 2, 2
[2, 1, 1, 1, 1, 3, 1, 2, 3] => 2, 1, 1, 1, 1, 3, 1, 2, 3
[2, 1, 1, 1, 1, 3, 1, 3, 1] => 2, 1, 1, 1, 1, 3, 1, 3, 1
[2, 1, 1, 1, 1, 3, 1, 3, 2] => 2, 1, 1, 1, 1, 3, 1, 3, 2
[2, 1, 1, 1, 1, 3, 1, 3, 3] => 2, 1, 1, 1, 1, 3, 1, 3, 3
[2, 1, 1, 1, 1, 3, 2, 1, 1] => 2, 1, 1, 1, 1, 3, 2, 1, 1
[2, 1, 1, 1, 1, 3, 2, 1, 2] => 2, 1, 1, 1, 1, 3, 2, 1, 2
[2, 1, 1, 1, 1, 3, 2, 1, 3] => 2, 1, 1, 1, 1, 3, 2, 1, 3
[2, 1, 1, 1, 1, 3, 2, 2, 1] => 2, 1, 1, 1, 1, 3, 2, 2, 1
[2, 1, 1, 1, 1, 3, 2, 2, 2] => 2, 1, 1, 1, 1, 3, 2, 2, 2
[2, 1, 1, 1, 1, 3, 2, 2, 3] => 2, 1, 1, 1, 1, 3, 2, 2, 3
[2, 1, 1, 1, 1, 3, 2, 3, 1] => 2, 1, 1, 1, 1, 3, 2, 3, 1
[2, 1, 1, 1, 1, 3, 2, 3, 2] => 2, 1, 1, 1, 1, 3, 2, 3, 2
[2, 1, 1, 1, 1, 3, 2, 3, 3] => 2, 1, 1, 1, 1, 3, 2, 3, 3
[2, 1, 1, 1, 1, 3, 3, 1, 1] => 2, 1, 1, 1, 1, 3, 3, 1, 1
[2, 1, 1, 1, 1, 3, 3, 1, 2] => 2, 1, 1, 1, 1, 3, 3, 1, 2
[2, 1, 1, 1, 1, 3, 3, 1, 3] => 2, 1, 1, 1, 1, 3, 3, 1, 3
[2, 1, 1, 1, 1, 3, 3, 2, 1] => 2, 1, 1, 1, 1, 3, 3, 2, 1
[2, 1, 1, 1, 1, 3, 3, 2, 2] => 2, 1, 1, 1, 1, 3, 3, 2, 2
[2, 1, 1, 1, 1, 3, 3, 2, 3] => 2, 1, 1, 1, 1, 3, 3, 2, 3
[2, 1, 1, 1, 1, 3, 3, 3, 1] => 2, 1, 1, 1, 1, 3, 3, 3, 1
[2, 1, 1, 1, 1, 3, 3, 3, 2] => 2, 1, 1, 1, 1, 3, 3, 3, 2
[2, 1, 1, 1, 1, 3, 3, 3, 3] => 2, 1, 1, 1, 1, 3, 3, 3, 3
[2, 1, 1, 1, 2, 1, 1, 1, 1] => 2, 1, 1, 1, 2, 1, 1, 1, 1
[2, 1, 1, 1, 2, 1, 1, 1, 2] => 2, 1, 1, 1, 2, 1, 1, 1, 2
[2, 1, 1, 1, 2, 1, 1, 1, 3] => 2, 1, 1, 1, 2, 1, 1, 1, 3
[2, 1, 1, 1, 2, 1, 1, 2, 1] => 2, 1, 1, 1, 2, 1, 1, 2, 1
[2, 1, 1, 1, 2, 1, 1, 2, 2] => 2, 1, 1, 1, 2, 1, 1, 2, 2
[2, 1, 1, 1, 2, 1, 1, 2, 3] => 2, 1, 1, 1, 2, 1, 1, 2, 3
[2, 1, 1, 1, 2, 1, 1, 3, 1] => 2, 1, 1, 1, 2, 1, 1, 3, 1
[2, 1, 1, 1, 2, 1, 1, 3, 2] => 2, 1, 1, 1, 2, 1, 1, 3, 2
[2, 1, 1, 1, 2, 1, 1, 3, 3] => 2, 1, 1, 1, 2, 1, 1, 3, 3
[2, 1, 1, 1, 2, 1, 2, 1, 1] => 2, 1, 1, 1, 2, 1, 2, 1, 1
[2, 1, 1, 1, 2, 1, 2, 1, 2] => 2, 1, 1, 1, 2, 1, 2, 1, 2
[2, 1, 1, 1, 2, 1, 2, 1, 3] => 2, 1, 1, 1, 2, 1, 2, 1, 3
[2, 1, 1, 1, 2, 1, 2, 2, 1] => 2, 1, 1, 1, 2, 1, 2, 2, 1
[2, 1, 1, 1, 2, 1, 2, 2, 2] => 2, 1, 1, 1, 2, 1, 2, 2, 2
[2, 1, 1, 1, 2, 1, 2, 2, 3] => 2, 1, 1, 1, 2, 1, 2, 2, 3
[2, 1, 1, 1, 2, 1, 2, 3, 1] => 2, 1, 1, 1, 2, 1, 2, 3, 1
[2, 1, 1, 1, 2, 1, 2, 3, 2] => 2, 1, 1, 1, 2, 1, 2, 3, 2
[2, 1, 1, 1, 2, 1, 2, 3, 3] => 2, 1, 1, 1, 2, 1, 2, 3, 3
[2, 1, 1, 1, 2, 1, 3, 1, 1] => 2, 1, 1, 1, 2, 1, 3, 1, 1
[2, 1, 1, 1, 2, 1, 3, 1, 2] => 2, 1, 1, 1, 2, 1, 3, 1, 2
[2, 1, 1, 1, 2, 1, 3, 1, 3] => 2, 1, 1, 1, 2, 1, 3, 1, 3
[2, 1, 1, 1, 2, 1, 3, 2, 1] => 2, 1, 1, 1, 2, 1, 3, 2, 1
[2, 1, 1, 1, 2, 1, 3, 2, 2] => 2, 1, 1, 1, 2, 1, 3, 2, 2
[2, 1, 1, 1, 2, 1, 3, 2, 3] => 2, 1, 1, 1, 2, 1, 3, 2, 3
[2, 1, 1, 1, 2, 1, 3, 3, 1] => 2, 1, 1, 1, 2, 1, 3, 3, 1
[2, 1, 1, 1, 2, 1, 3, 3, 2] => 2, 1, 1, 1, 2, 1, 3, 3, 2
[2, 1, 1, 1, 2, 1, 3, 3, 3] => 2, 1, 1, 1, 2, 1, 3, 3, 3
[2, 1, 1, 1, 2, 2, 1, 1, 1] => 2, 1, 1, 1, 2, 2, 1, 1, 1
[2, 1, 1, 1, 2, 2, 1, 1, 2] => 2, 1, 1, 1, 2, 2, 1, 1, 2
[2, 1, 1, 1, 2, 2, 1, 1, 3] => 2, 1, 1, 1, 2, 2, 1, 1, 3
[2, 1, 1, 1, 2, 2, 1, 2, 1] => 2, 1, 1, 1, 2, 2, 1, 2, 1
[2, 1, 1, 1, 2, 2, 1, 2, 2] => 2, 1, 1, 1, 2, 2, 1, 2, 2
[2, 1, 1, 1, 2, 2, 1, 2, 3] => 2, 1, 1, 1, 2, 2, 1, 2, 3
[2, 1, 1, 1, 2, 2, 1, 3, 1] => 2, 1, 1, 1, 2, 2, 1, 3, 1
[2, 1, 1, 1, 2, 2, 1, 3, 2] => 2, 1, 1, 1, 2, 2, 1, 3, 2
[2, 1, 1, 1, 2, 2, 1, 3, 3] => 2, 1, 1, 1, 2, 2, 1, 3, 3
[2, 1, 1, 1, 2, 2, 2, 1, 1] => 2, 1, 1, 1, 2, 2, 2, 1, 1
[2, 1, 1, 1, 2, 2, 2, 1, 2] => 2, 1, 1, 1, 2, 2, 2, 1, 2
[2, 1, 1, 1, 2, 2, 2, 1, 3] => 2, 1, 1, 1, 2, 2, 2, 1, 3
[2, 1, 1, 1, 2, 2, 2, 2, 1] => 2, 1, 1, 1, 2, 2, 2, 2, 1
[2, 1, 1, 1, 2, 2, 2, 2, 2] => 2, 1, 1, 1, 2, 2, 2, 2, 2
[2, 1, 1, 1, 2, 2, 2, 2, 3] => 2, 1, 1, 1, 2, 2, 2, 2, 3
[2, 1, 1, 1, 2, 2, 2, 3, 1] => 2, 1, 1, 1, 2, 2, 2, 3, 1
[2, 1, 1, 1, 2, 2, 2, 3, 2] => 2, 1, 1, 1, 2, 2, 2, 3, 2
[2, 1, 1, 1, 2, 2, 2, 3, 3] => 2, 1, 1, 1, 2, 2, 2, 3, 3
[2, 1, 1, 1, 2, 2, 3, 1, 1] => 2, 1, 1, 1, 2, 2, 3, 1, 1
[2, 1, 1, 1, 2, 2, 3, 1, 2] => 2, 1, 1, 1, 2, 2, 3, 1, 2
[2, 1, 1, 1, 2, 2, 3, 1, 3] => 2, 1, 1, 1, 2, 2, 3, 1, 3
[2, 1, 1, 1, 2, 2, 3, 2, 1] => 2, 1, 1, 1, 2, 2, 3, 2, 1
[2, 1, 1, 1, 2, 2, 3, 2, 2] => 2, 1, 1, 1, 2, 2, 3, 2, 2
[2, 1, 1, 1, 2, 2, 3, 2, 3] => 2, 1, 1, 1, 2, 2, 3, 2, 3
[2, 1, 1, 1, 2, 2, 3, 3, 1] => 2, 1, 1, 1, 2, 2, 3, 3, 1
[2, 1, 1, 1, 2, 2, 3, 3, 2] => 2, 1, 1, 1, 2, 2, 3, 3, 2
[2, 1, 1, 1, 2, 2, 3, 3, 3] => 2, 1, 1, 1, 2, 2, 3, 3, 3
[2, 1, 1, 1, 2, 3, 1, 1, 1] => 2, 1, 1, 1, 2, 3, 1, 1, 1
[2, 1, 1, 1, 2, 3, 1, 1, 2] => 2, 1, 1, 1, 2, 3, 1, 1, 2
[2, 1, 1, 1, 2, 3, 1, 1, 3] => 2, 1, 1, 1, 2, 3, 1, 1, 3
[2, 1, 1, 1, 2, 3, 1, 2, 1] => 2, 1, 1, 1, 2, 3, 1, 2, 1
[2, 1, 1, 1, 2, 3, 1, 2, 2] => 2, 1, 1, 1, 2, 3, 1, 2, 2
[2, 1, 1, 1, 2, 3, 1, 2, 3] => 2, 1, 1, 1, 2, 3, 1, 2, 3
[2, 1, 1, 1, 2, 3, 1, 3, 1] => 2, 1, 1, 1, 2, 3, 1, 3, 1
[2, 1, 1, 1, 2, 3, 1, 3, 2] => 2, 1, 1, 1, 2, 3, 1, 3, 2
[2, 1, 1, 1, 2, 3, 1, 3, 3] => 2, 1, 1, 1, 2, 3, 1, 3, 3
[2, 1, 1, 1, 2, 3, 2, 1, 1] => 2, 1, 1, 1, 2, 3, 2, 1, 1
[2, 1, 1, 1, 2, 3, 2, 1, 2] => 2, 1, 1, 1, 2, 3, 2, 1, 2
[2, 1, 1, 1, 2, 3, 2, 1, 3] => 2, 1, 1, 1, 2, 3, 2, 1, 3
[2, 1, 1, 1, 2, 3, 2, 2, 1] => 2, 1, 1, 1, 2, 3, 2, 2, 1
[2, 1, 1, 1, 2, 3, 2, 2, 2] => 2, 1, 1, 1, 2, 3, 2, 2, 2
[2, 1, 1, 1, 2, 3, 2, 2, 3] => 2, 1, 1, 1, 2, 3, 2, 2, 3
[2, 1, 1, 1, 2, 3, 2, 3, 1] => 2, 1, 1, 1, 2, 3, 2, 3, 1
[2, 1, 1, 1, 2, 3, 2, 3, 2] => 2, 1, 1, 1, 2, 3, 2, 3, 2
[2, 1, 1, 1, 2, 3, 2, 3, 3] => 2, 1, 1, 1, 2, 3, 2, 3, 3
[2, 1, 1, 1, 2, 3, 3, 1, 1] => 2, 1, 1, 1, 2, 3, 3, 1, 1
[2, 1, 1, 1, 2, 3, 3, 1, 2] => 2, 1, 1, 1, 2, 3, 3, 1, 2
[2, 1, 1, 1, 2, 3, 3, 1, 3] => 2, 1, 1, 1, 2, 3, 3, 1, 3
[2, 1, 1, 1, 2, 3, 3, 2, 1] => 2, 1, 1, 1, 2, 3, 3, 2, 1
[2, 1, 1, 1, 2, 3, 3, 2, 2] => 2, 1, 1, 1, 2, 3, 3, 2, 2
[2, 1, 1, 1, 2, 3, 3, 2, 3] => 2, 1, 1, 1, 2, 3, 3, 2, 3
[2, 1, 1, 1, 2, 3, 3, 3, 1] => 2, 1, 1, 1, 2, 3, 3, 3, 1
[2, 1, 1, 1, 2, 3, 3, 3, 2] => 2, 1, 1, 1, 2, 3, 3, 3, 2
[2, 1, 1, 1, 2, 3, 3, 3, 3] => 2, 1, 1, 1, 2, 3, 3, 3, 3
[2, 1, 1, 1, 3, 1, 1, 1, 1] => 2, 1, 1, 1, 3, 1, 1, 1, 1
[2, 1, 1, 1, 3, 1, 1, 1, 2] => 2, 1, 1, 1, 3, 1, 1, 1, 2
[2, 1, 1, 1, 3, 1, 1, 1, 3] => 2, 1, 1, 1, 3, 1, 1, 1, 3
[2, 1, 1, 1, 3, 1, 1, 2, 1] => 2, 1, 1, 1, 3, 1, 1, 2, 1
[2, 1, 1, 1, 3, 1, 1, 2, 2] => 2, 1, 1, 1, 3, 1, 1, 2, 2
[2, 1, 1, 1, 3, 1, 1, 2, 3] => 2, 1, 1, 1, 3, 1, 1, 2, 3
[2, 1, 1, 1, 3, 1, 1, 3, 1] => 2, 1, 1, 1, 3, 1, 1, 3, 1
[2, 1, 1, 1, 3, 1, 1, 3, 2] => 2, 1, 1, 1, 3, 1, 1, 3, 2
[2, 1, 1, 1, 3, 1, 1, 3, 3] => 2, 1, 1, 1, 3, 1, 1, 3, 3
[2, 1, 1, 1, 3, 1, 2, 1, 1] => 2, 1, 1, 1, 3, 1, 2, 1, 1
[2, 1, 1, 1, 3, 1, 2, 1, 2] => 2, 1, 1, 1, 3, 1, 2, 1, 2
[2, 1, 1, 1, 3, 1, 2, 1, 3] => 2, 1, 1, 1, 3, 1, 2, 1, 3
[2, 1, 1, 1, 3, 1, 2, 2, 1] => 2, 1, 1, 1, 3, 1, 2, 2, 1
[2, 1, 1, 1, 3, 1, 2, 2, 2] => 2, 1, 1, 1, 3, 1, 2, 2, 2
[2, 1, 1, 1, 3, 1, 2, 2, 3] => 2, 1, 1, 1, 3, 1, 2, 2, 3
[2, 1, 1, 1, 3, 1, 2, 3, 1] => 2, 1, 1, 1, 3, 1, 2, 3, 1
[2, 1, 1, 1, 3, 1, 2, 3, 2] => 2, 1, 1, 1, 3, 1, 2, 3, 2
[2, 1, 1, 1, 3, 1, 2, 3, 3] => 2, 1, 1, 1, 3, 1, 2, 3, 3
[2, 1, 1, 1, 3, 1, 3, 1, 1] => 2, 1, 1, 1, 3, 1, 3, 1, 1
[2, 1, 1, 1, 3, 1, 3, 1, 2] => 2, 1, 1, 1, 3, 1, 3, 1, 2
[2, 1, 1, 1, 3, 1, 3, 1, 3] => 2, 1, 1, 1, 3, 1, 3, 1, 3
[2, 1, 1, 1, 3, 1, 3, 2, 1] => 2, 1, 1, 1, 3, 1, 3, 2, 1
[2, 1, 1, 1, 3, 1, 3, 2, 2] => 2, 1, 1, 1, 3, 1, 3, 2, 2
[2, 1, 1, 1, 3, 1, 3, 2, 3] => 2, 1, 1, 1, 3, 1, 3, 2, 3
[2, 1, 1, 1, 3, 1, 3, 3, 1] => 2, 1, 1, 1, 3, 1, 3, 3, 1
[2, 1, 1, 1, 3, 1, 3, 3, 2] => 2, 1, 1, 1, 3, 1, 3, 3, 2
[2, 1, 1, 1, 3, 1, 3, 3, 3] => 2, 1, 1, 1, 3, 1, 3, 3, 3
[2, 1, 1, 1, 3, 2, 1, 1, 1] => 2, 1, 1, 1, 3, 2, 1, 1, 1
[2, 1, 1, 1, 3, 2, 1, 1, 2] => 2, 1, 1, 1, 3, 2, 1, 1, 2
[2, 1, 1, 1, 3, 2, 1, 1, 3] => 2, 1, 1, 1, 3, 2, 1, 1, 3
[2, 1, 1, 1, 3, 2, 1, 2, 1] => 2, 1, 1, 1, 3, 2, 1, 2, 1
[2, 1, 1, 1, 3, 2, 1, 2, 2] => 2, 1, 1, 1, 3, 2, 1, 2, 2
[2, 1, 1, 1, 3, 2, 1, 2, 3] => 2, 1, 1, 1, 3, 2, 1, 2, 3
[2, 1, 1, 1, 3, 2, 1, 3, 1] => 2, 1, 1, 1, 3, 2, 1, 3, 1
[2, 1, 1, 1, 3, 2, 1, 3, 2] => 2, 1, 1, 1, 3, 2, 1, 3, 2
[2, 1, 1, 1, 3, 2, 1, 3, 3] => 2, 1, 1, 1, 3, 2, 1, 3, 3
[2, 1, 1, 1, 3, 2, 2, 1, 1] => 2, 1, 1, 1, 3, 2, 2, 1, 1
[2, 1, 1, 1, 3, 2, 2, 1, 2] => 2, 1, 1, 1, 3, 2, 2, 1, 2
[2, 1, 1, 1, 3, 2, 2, 1, 3] => 2, 1, 1, 1, 3, 2, 2, 1, 3
[2, 1, 1, 1, 3, 2, 2, 2, 1] => 2, 1, 1, 1, 3, 2, 2, 2, 1
[2, 1, 1, 1, 3, 2, 2, 2, 2] => 2, 1, 1, 1, 3, 2, 2, 2, 2
[2, 1, 1, 1, 3, 2, 2, 2, 3] => 2, 1, 1, 1, 3, 2, 2, 2, 3
[2, 1, 1, 1, 3, 2, 2, 3, 1] => 2, 1, 1, 1, 3, 2, 2, 3, 1
[2, 1, 1, 1, 3, 2, 2, 3, 2] => 2, 1, 1, 1, 3, 2, 2, 3, 2
[2, 1, 1, 1, 3, 2, 2, 3, 3] => 2, 1, 1, 1, 3, 2, 2, 3, 3
[2, 1, 1, 1, 3, 2, 3, 1, 1] => 2, 1, 1, 1, 3, 2, 3, 1, 1
[2, 1, 1, 1, 3, 2, 3, 1, 2] => 2, 1, 1, 1, 3, 2, 3, 1, 2
[2, 1, 1, 1, 3, 2, 3, 1, 3] => 2, 1, 1, 1, 3, 2, 3, 1, 3
[2, 1, 1, 1, 3, 2, 3, 2, 1] => 2, 1, 1, 1, 3, 2, 3, 2, 1
[2, 1, 1, 1, 3, 2, 3, 2, 2] => 2, 1, 1, 1, 3, 2, 3, 2, 2
[2, 1, 1, 1, 3, 2, 3, 2, 3] => 2, 1, 1, 1, 3, 2, 3, 2, 3
[2, 1, 1, 1, 3, 2, 3, 3, 1] => 2, 1, 1, 1, 3, 2, 3, 3, 1
[2, 1, 1, 1, 3, 2, 3, 3, 2] => 2, 1, 1, 1, 3, 2, 3, 3, 2
[2, 1, 1, 1, 3, 2, 3, 3, 3] => 2, 1, 1, 1, 3, 2, 3, 3, 3
[2, 1, 1, 1, 3, 3, 1, 1, 1] => 2, 1, 1, 1, 3, 3, 1, 1, 1
[2, 1, 1, 1, 3, 3, 1, 1, 2] => 2, 1, 1, 1, 3, 3, 1, 1, 2
[2, 1, 1, 1, 3, 3, 1, 1, 3] => 2, 1, 1, 1, 3, 3, 1, 1, 3
[2, 1, 1, 1, 3, 3, 1, 2, 1] => 2, 1, 1, 1, 3, 3, 1, 2, 1
[2, 1, 1, 1, 3, 3, 1, 2, 2] => 2, 1, 1, 1, 3, 3, 1, 2, 2
[2, 1, 1, 1, 3, 3, 1, 2, 3] => 2, 1, 1, 1, 3, 3, 1, 2, 3
[2, 1, 1, 1, 3, 3, 1, 3, 1] => 2, 1, 1, 1, 3, 3, 1, 3, 1
[2, 1, 1, 1, 3, 3, 1, 3, 2] => 2, 1, 1, 1, 3, 3, 1, 3, 2
[2, 1, 1, 1, 3, 3, 1, 3, 3] => 2, 1, 1, 1, 3, 3, 1, 3, 3
[2, 1, 1, 1, 3, 3, 2, 1, 1] => 2, 1, 1, 1, 3, 3, 2, 1, 1
[2, 1, 1, 1, 3, 3, 2, 1, 2] => 2, 1, 1, 1, 3, 3, 2, 1, 2
[2, 1, 1, 1, 3, 3, 2, 1, 3] => 2, 1, 1, 1, 3, 3, 2, 1, 3
[2, 1, 1, 1, 3, 3, 2, 2, 1] => 2, 1, 1, 1, 3, 3, 2, 2, 1
[2, 1, 1, 1, 3, 3, 2, 2, 2] => 2, 1, 1, 1, 3, 3, 2, 2, 2
[2, 1, 1, 1, 3, 3, 2, 2, 3] => 2, 1, 1, 1, 3, 3, 2, 2, 3
[2, 1, 1, 1, 3, 3, 2, 3, 1] => 2, 1, 1, 1, 3, 3, 2, 3, 1
[2, 1, 1, 1, 3, 3, 2, 3, 2] => 2, 1, 1, 1, 3, 3, 2, 3, 2
[2, 1, 1, 1, 3, 3, 2, 3, 3] => 2, 1, 1, 1, 3, 3, 2, 3, 3
[2, 1, 1, 1, 3, 3, 3, 1, 1] => 2, 1, 1, 1, 3, 3, 3, 1, 1
[2, 1, 1, 1, 3, 3, 3, 1, 2] => 2, 1, 1, 1, 3, 3, 3, 1, 2
[2, 1, 1, 1, 3, 3, 3, 1, 3] => 2, 1, 1, 1, 3, 3, 3, 1, 3
[2, 1, 1, 1, 3, 3, 3, 2, 1] => 2, 1, 1, 1, 3, 3, 3, 2, 1
[2, 1, 1, 1, 3, 3, 3, 2, 2] => 2, 1, 1, 1, 3, 3, 3, 2, 2
[2, 1, 1, 1, 3, 3, 3, 2, 3] => 2, 1, 1, 1, 3, 3, 3, 2, 3
[2, 1, 1, 1, 3, 3, 3, 3, 1] => 2, 1, 1, 1, 3, 3, 3, 3, 1
[2, 1, 1, 1, 3, 3, 3, 3, 2] => 2, 1, 1, 1, 3, 3, 3, 3, 2
[2, 1, 1, 1, 3, 3, 3, 3, 3] => 2, 1, 1, 1, 3, 3, 3, 3, 3
[2, 1, 1, 2, 1, 1, 1, 1, 1] => 2, 1, 1, 2, 1, 1, 1, 1, 1
[2, 1, 1, 2, 1, 1, 1, 1, 2] => 2, 1, 1, 2, 1, 1, 1, 1, 2
[2, 1, 1, 2, 1, 1, 1, 1, 3] => 2, 1, 1, 2, 1, 1, 1, 1, 3
[2, 1, 1, 2, 1, 1, 1, 2, 1] => 2, 1, 1, 2, 1, 1, 1, 2, 1
[2, 1, 1, 2, 1, 1, 1, 2, 2] => 2, 1, 1, 2, 1, 1, 1, 2, 2
[2, 1, 1, 2, 1, 1, 1, 2, 3] => 2, 1, 1, 2, 1, 1, 1, 2, 3
[2, 1, 1, 2, 1, 1, 1, 3, 1] => 2, 1, 1, 2, 1, 1, 1, 3, 1
[2, 1, 1, 2, 1, 1, 1, 3, 2] => 2, 1, 1, 2, 1, 1, 1, 3, 2
[2, 1, 1, 2, 1, 1, 1, 3, 3] => 2, 1, 1, 2, 1, 1, 1, 3, 3
[2, 1, 1, 2, 1, 1, 2, 1, 1] => 2, 1, 1, 2, 1, 1, 2, 1, 1
[2, 1, 1, 2, 1, 1, 2, 1, 2] => 2, 1, 1, 2, 1, 1, 2, 1, 2
[2, 1, 1, 2, 1, 1, 2, 1, 3] => 2, 1, 1, 2, 1, 1, 2, 1, 3
[2, 1, 1, 2, 1, 1, 2, 2, 1] => 2, 1, 1, 2, 1, 1, 2, 2, 1
[2, 1, 1, 2, 1, 1, 2, 2, 2] => 2, 1, 1, 2, 1, 1, 2, 2, 2
[2, 1, 1, 2, 1, 1, 2, 2, 3] => 2, 1, 1, 2, 1, 1, 2, 2, 3
[2, 1, 1, 2, 1, 1, 2, 3, 1] => 2, 1, 1, 2, 1, 1, 2, 3, 1
[2, 1, 1, 2, 1, 1, 2, 3, 2] => 2, 1, 1, 2, 1, 1, 2, 3, 2
[2, 1, 1, 2, 1, 1, 2, 3, 3] => 2, 1, 1, 2, 1, 1, 2, 3, 3
[2, 1, 1, 2, 1, 1, 3, 1, 1] => 2, 1, 1, 2, 1, 1, 3, 1, 1
[2, 1, 1, 2, 1, 1, 3, 1, 2] => 2, 1, 1, 2, 1, 1, 3, 1, 2
[2, 1, 1, 2, 1, 1, 3, 1, 3] => 2, 1, 1, 2, 1, 1, 3, 1, 3
[2, 1, 1, 2, 1, 1, 3, 2, 1] => 2, 1, 1, 2, 1, 1, 3, 2, 1
[2, 1, 1, 2, 1, 1, 3, 2, 2] => 2, 1, 1, 2, 1, 1, 3, 2, 2
[2, 1, 1, 2, 1, 1, 3, 2, 3] => 2, 1, 1, 2, 1, 1, 3, 2, 3
[2, 1, 1, 2, 1, 1, 3, 3, 1] => 2, 1, 1, 2, 1, 1, 3, 3, 1
[2, 1, 1, 2, 1, 1, 3, 3, 2] => 2, 1, 1, 2, 1, 1, 3, 3, 2
[2, 1, 1, 2, 1, 1, 3, 3, 3] => 2, 1, 1, 2, 1, 1, 3, 3, 3
[2, 1, 1, 2, 1, 2, 1, 1, 1] => 2, 1, 1, 2, 1, 2, 1, 1, 1
[2, 1, 1, 2, 1, 2, 1, 1, 2] => 2, 1, 1, 2, 1, 2, 1, 1, 2
[2, 1, 1, 2, 1, 2, 1, 1, 3] => 2, 1, 1, 2, 1, 2, 1, 1, 3
[2, 1, 1, 2, 1, 2, 1, 2, 1] => 2, 1, 1, 2, 1, 2, 1, 2, 1
[2, 1, 1, 2, 1, 2, 1, 2, 2] => 2, 1, 1, 2, 1, 2, 1, 2, 2
[2, 1, 1, 2, 1, 2, 1, 2, 3] => 2, 1, 1, 2, 1, 2, 1, 2, 3
[2, 1, 1, 2, 1, 2, 1, 3, 1] => 2, 1, 1, 2, 1, 2, 1, 3, 1
[2, 1, 1, 2, 1, 2, 1, 3, 2] => 2, 1, 1, 2, 1, 2, 1, 3, 2
[2, 1, 1, 2, 1, 2, 1, 3, 3] => 2, 1, 1, 2, 1, 2, 1, 3, 3
[2, 1, 1, 2, 1, 2, 2, 1, 1] => 2, 1, 1, 2, 1, 2, 2, 1, 1
[2, 1, 1, 2, 1, 2, 2, 1, 2] => 2, 1, 1, 2, 1, 2, 2, 1, 2
[2, 1, 1, 2, 1, 2, 2, 1, 3] => 2, 1, 1, 2, 1, 2, 2, 1, 3
[2, 1, 1, 2, 1, 2, 2, 2, 1] => 2, 1, 1, 2, 1, 2, 2, 2, 1
[2, 1, 1, 2, 1, 2, 2, 2, 2] => 2, 1, 1, 2, 1, 2, 2, 2, 2
[2, 1, 1, 2, 1, 2, 2, 2, 3] => 2, 1, 1, 2, 1, 2, 2, 2, 3
[2, 1, 1, 2, 1, 2, 2, 3, 1] => 2, 1, 1, 2, 1, 2, 2, 3, 1
[2, 1, 1, 2, 1, 2, 2, 3, 2] => 2, 1, 1, 2, 1, 2, 2, 3, 2
[2, 1, 1, 2, 1, 2, 2, 3, 3] => 2, 1, 1, 2, 1, 2, 2, 3, 3
[2, 1, 1, 2, 1, 2, 3, 1, 1] => 2, 1, 1, 2, 1, 2, 3, 1, 1
[2, 1, 1, 2, 1, 2, 3, 1, 2] => 2, 1, 1, 2, 1, 2, 3, 1, 2
[2, 1, 1, 2, 1, 2, 3, 1, 3] => 2, 1, 1, 2, 1, 2, 3, 1, 3
[2, 1, 1, 2, 1, 2, 3, 2, 1] => 2, 1, 1, 2, 1, 2, 3, 2, 1
[2, 1, 1, 2, 1, 2, 3, 2, 2] => 2, 1, 1, 2, 1, 2, 3, 2, 2
[2, 1, 1, 2, 1, 2, 3, 2, 3] => 2, 1, 1, 2, 1, 2, 3, 2, 3
[2, 1, 1, 2, 1, 2, 3, 3, 1] => 2, 1, 1, 2, 1, 2, 3, 3, 1
[2, 1, 1, 2, 1, 2, 3, 3, 2] => 2, 1, 1, 2, 1, 2, 3, 3, 2
[2, 1, 1, 2, 1, 2, 3, 3, 3] => 2, 1, 1, 2, 1, 2, 3, 3, 3
[2, 1, 1, 2, 1, 3, 1, 1, 1] => 2, 1, 1, 2, 1, 3, 1, 1, 1
[2, 1, 1, 2, 1, 3, 1, 1, 2] => 2, 1, 1, 2, 1, 3, 1, 1, 2
[2, 1, 1, 2, 1, 3, 1, 1, 3] => 2, 1, 1, 2, 1, 3, 1, 1, 3
[2, 1, 1, 2, 1, 3, 1, 2, 1] => 2, 1, 1, 2, 1, 3, 1, 2, 1
[2, 1, 1, 2, 1, 3, 1, 2, 2] => 2, 1, 1, 2, 1, 3, 1, 2, 2
[2, 1, 1, 2, 1, 3, 1, 2, 3] => 2, 1, 1, 2, 1, 3, 1, 2, 3
[2, 1, 1, 2, 1, 3, 1, 3, 1] => 2, 1, 1, 2, 1, 3, 1, 3, 1
[2, 1, 1, 2, 1, 3, 1, 3, 2] => 2, 1, 1, 2, 1, 3, 1, 3, 2
[2, 1, 1, 2, 1, 3, 1, 3, 3] => 2, 1, 1, 2, 1, 3, 1, 3, 3
[2, 1, 1, 2, 1, 3, 2, 1, 1] => 2, 1, 1, 2, 1, 3, 2, 1, 1
[2, 1, 1, 2, 1, 3, 2, 1, 2] => 2, 1, 1, 2, 1, 3, 2, 1, 2
[2, 1, 1, 2, 1, 3, 2, 1, 3] => 2, 1, 1, 2, 1, 3, 2, 1, 3
[2, 1, 1, 2, 1, 3, 2, 2, 1] => 2, 1, 1, 2, 1, 3, 2, 2, 1
[2, 1, 1, 2, 1, 3, 2, 2, 2] => 2, 1, 1, 2, 1, 3, 2, 2, 2
[2, 1, 1, 2, 1, 3, 2, 2, 3] => 2, 1, 1, 2, 1, 3, 2, 2, 3
[2, 1, 1, 2, 1, 3, 2, 3, 1] => 2, 1, 1, 2, 1, 3, 2, 3, 1
[2, 1, 1, 2, 1, 3, 2, 3, 2] => 2, 1, 1, 2, 1, 3, 2, 3, 2
[2, 1, 1, 2, 1, 3, 2, 3, 3] => 2, 1, 1, 2, 1, 3, 2, 3, 3
[2, 1, 1, 2, 1, 3, 3, 1, 1] => 2, 1, 1, 2, 1, 3, 3, 1, 1
[2, 1, 1, 2, 1, 3, 3, 1, 2] => 2, 1, 1, 2, 1, 3, 3, 1, 2
[2, 1, 1, 2, 1, 3, 3, 1, 3] => 2, 1, 1, 2, 1, 3, 3, 1, 3
[2, 1, 1, 2, 1, 3, 3, 2, 1] => 2, 1, 1, 2, 1, 3, 3, 2, 1
[2, 1, 1, 2, 1, 3, 3, 2, 2] => 2, 1, 1, 2, 1, 3, 3, 2, 2
[2, 1, 1, 2, 1, 3, 3, 2, 3] => 2, 1, 1, 2, 1, 3, 3, 2, 3
[2, 1, 1, 2, 1, 3, 3, 3, 1] => 2, 1, 1, 2, 1, 3, 3, 3, 1
[2, 1, 1, 2, 1, 3, 3, 3, 2] => 2, 1, 1, 2, 1, 3, 3, 3, 2
[2, 1, 1, 2, 1, 3, 3, 3, 3] => 2, 1, 1, 2, 1, 3, 3, 3, 3
[2, 1, 1, 2, 2, 1, 1, 1, 1] => 2, 1, 1, 2, 2, 1, 1, 1, 1
[2, 1, 1, 2, 2, 1, 1, 1, 2] => 2, 1, 1, 2, 2, 1, 1, 1, 2
[2, 1, 1, 2, 2, 1, 1, 1, 3] => 2, 1, 1, 2, 2, 1, 1, 1, 3
[2, 1, 1, 2, 2, 1, 1, 2, 1] => 2, 1, 1, 2, 2, 1, 1, 2, 1
[2, 1, 1, 2, 2, 1, 1, 2, 2] => 2, 1, 1, 2, 2, 1, 1, 2, 2
[2, 1, 1, 2, 2, 1, 1, 2, 3] => 2, 1, 1, 2, 2, 1, 1, 2, 3
[2, 1, 1, 2, 2, 1, 1, 3, 1] => 2, 1, 1, 2, 2, 1, 1, 3, 1
[2, 1, 1, 2, 2, 1, 1, 3, 2] => 2, 1, 1, 2, 2, 1, 1, 3, 2
[2, 1, 1, 2, 2, 1, 1, 3, 3] => 2, 1, 1, 2, 2, 1, 1, 3, 3
[2, 1, 1, 2, 2, 1, 2, 1, 1] => 2, 1, 1, 2, 2, 1, 2, 1, 1
[2, 1, 1, 2, 2, 1, 2, 1, 2] => 2, 1, 1, 2, 2, 1, 2, 1, 2
[2, 1, 1, 2, 2, 1, 2, 1, 3] => 2, 1, 1, 2, 2, 1, 2, 1, 3
[2, 1, 1, 2, 2, 1, 2, 2, 1] => 2, 1, 1, 2, 2, 1, 2, 2, 1
[2, 1, 1, 2, 2, 1, 2, 2, 2] => 2, 1, 1, 2, 2, 1, 2, 2, 2
[2, 1, 1, 2, 2, 1, 2, 2, 3] => 2, 1, 1, 2, 2, 1, 2, 2, 3
[2, 1, 1, 2, 2, 1, 2, 3, 1] => 2, 1, 1, 2, 2, 1, 2, 3, 1
[2, 1, 1, 2, 2, 1, 2, 3, 2] => 2, 1, 1, 2, 2, 1, 2, 3, 2
[2, 1, 1, 2, 2, 1, 2, 3, 3] => 2, 1, 1, 2, 2, 1, 2, 3, 3
[2, 1, 1, 2, 2, 1, 3, 1, 1] => 2, 1, 1, 2, 2, 1, 3, 1, 1
[2, 1, 1, 2, 2, 1, 3, 1, 2] => 2, 1, 1, 2, 2, 1, 3, 1, 2
[2, 1, 1, 2, 2, 1, 3, 1, 3] => 2, 1, 1, 2, 2, 1, 3, 1, 3
[2, 1, 1, 2, 2, 1, 3, 2, 1] => 2, 1, 1, 2, 2, 1, 3, 2, 1
[2, 1, 1, 2, 2, 1, 3, 2, 2] => 2, 1, 1, 2, 2, 1, 3, 2, 2
[2, 1, 1, 2, 2, 1, 3, 2, 3] => 2, 1, 1, 2, 2, 1, 3, 2, 3
[2, 1, 1, 2, 2, 1, 3, 3, 1] => 2, 1, 1, 2, 2, 1, 3, 3, 1
[2, 1, 1, 2, 2, 1, 3, 3, 2] => 2, 1, 1, 2, 2, 1, 3, 3, 2
[2, 1, 1, 2, 2, 1, 3, 3, 3] => 2, 1, 1, 2, 2, 1, 3, 3, 3
[2, 1, 1, 2, 2, 2, 1, 1, 1] => 2, 1, 1, 2, 2, 2, 1, 1, 1
[2, 1, 1, 2, 2, 2, 1, 1, 2] => 2, 1, 1, 2, 2, 2, 1, 1, 2
[2, 1, 1, 2, 2, 2, 1, 1, 3] => 2, 1, 1, 2, 2, 2, 1, 1, 3
[2, 1, 1, 2, 2, 2, 1, 2, 1] => 2, 1, 1, 2, 2, 2, 1, 2, 1
[2, 1, 1, 2, 2, 2, 1, 2, 2] => 2, 1, 1, 2, 2, 2, 1, 2, 2
[2, 1, 1, 2, 2, 2, 1, 2, 3] => 2, 1, 1, 2, 2, 2, 1, 2, 3
[2, 1, 1, 2, 2, 2, 1, 3, 1] => 2, 1, 1, 2, 2, 2, 1, 3, 1
[2, 1, 1, 2, 2, 2, 1, 3, 2] => 2, 1, 1, 2, 2, 2, 1, 3, 2
[2, 1, 1, 2, 2, 2, 1, 3, 3] => 2, 1, 1, 2, 2, 2, 1, 3, 3
[2, 1, 1, 2, 2, 2, 2, 1, 1] => 2, 1, 1, 2, 2, 2, 2, 1, 1
[2, 1, 1, 2, 2, 2, 2, 1, 2] => 2, 1, 1, 2, 2, 2, 2, 1, 2
[2, 1, 1, 2, 2, 2, 2, 1, 3] => 2, 1, 1, 2, 2, 2, 2, 1, 3
[2, 1, 1, 2, 2, 2, 2, 2, 1] => 2, 1, 1, 2, 2, 2, 2, 2, 1
[2, 1, 1, 2, 2, 2, 2, 2, 2] => 2, 1, 1, 2, 2, 2, 2, 2, 2
[2, 1, 1, 2, 2, 2, 2, 2, 3] => 2, 1, 1, 2, 2, 2, 2, 2, 3
[2, 1, 1, 2, 2, 2, 2, 3, 1] => 2, 1, 1, 2, 2, 2, 2, 3, 1
[2, 1, 1, 2, 2, 2, 2, 3, 2] => 2, 1, 1, 2, 2, 2, 2, 3, 2
[2, 1, 1, 2, 2, 2, 2, 3, 3] => 2, 1, 1, 2, 2, 2, 2, 3, 3
[2, 1, 1, 2, 2, 2, 3, 1, 1] => 2, 1, 1, 2, 2, 2, 3, 1, 1
[2, 1, 1, 2, 2, 2, 3, 1, 2] => 2, 1, 1, 2, 2, 2, 3, 1, 2
[2, 1, 1, 2, 2, 2, 3, 1, 3] => 2, 1, 1, 2, 2, 2, 3, 1, 3
[2, 1, 1, 2, 2, 2, 3, 2, 1] => 2, 1, 1, 2, 2, 2, 3, 2, 1
[2, 1, 1, 2, 2, 2, 3, 2, 2] => 2, 1, 1, 2, 2, 2, 3, 2, 2
[2, 1, 1, 2, 2, 2, 3, 2, 3] => 2, 1, 1, 2, 2, 2, 3, 2, 3
[2, 1, 1, 2, 2, 2, 3, 3, 1] => 2, 1, 1, 2, 2, 2, 3, 3, 1
[2, 1, 1, 2, 2, 2, 3, 3, 2] => 2, 1, 1, 2, 2, 2, 3, 3, 2
[2, 1, 1, 2, 2, 2, 3, 3, 3] => 2, 1, 1, 2, 2, 2, 3, 3, 3
[2, 1, 1, 2, 2, 3, 1, 1, 1] => 2, 1, 1, 2, 2, 3, 1, 1, 1
[2, 1, 1, 2, 2, 3, 1, 1, 2] => 2, 1, 1, 2, 2, 3, 1, 1, 2
[2, 1, 1, 2, 2, 3, 1, 1, 3] => 2, 1, 1, 2, 2, 3, 1, 1, 3
[2, 1, 1, 2, 2, 3, 1, 2, 1] => 2, 1, 1, 2, 2, 3, 1, 2, 1
[2, 1, 1, 2, 2, 3, 1, 2, 2] => 2, 1, 1, 2, 2, 3, 1, 2, 2
[2, 1, 1, 2, 2, 3, 1, 2, 3] => 2, 1, 1, 2, 2, 3, 1, 2, 3
[2, 1, 1, 2, 2, 3, 1, 3, 1] => 2, 1, 1, 2, 2, 3, 1, 3, 1
[2, 1, 1, 2, 2, 3, 1, 3, 2] => 2, 1, 1, 2, 2, 3, 1, 3, 2
[2, 1, 1, 2, 2, 3, 1, 3, 3] => 2, 1, 1, 2, 2, 3, 1, 3, 3
[2, 1, 1, 2, 2, 3, 2, 1, 1] => 2, 1, 1, 2, 2, 3, 2, 1, 1
[2, 1, 1, 2, 2, 3, 2, 1, 2] => 2, 1, 1, 2, 2, 3, 2, 1, 2
[2, 1, 1, 2, 2, 3, 2, 1, 3] => 2, 1, 1, 2, 2, 3, 2, 1, 3
[2, 1, 1, 2, 2, 3, 2, 2, 1] => 2, 1, 1, 2, 2, 3, 2, 2, 1
[2, 1, 1, 2, 2, 3, 2, 2, 2] => 2, 1, 1, 2, 2, 3, 2, 2, 2
[2, 1, 1, 2, 2, 3, 2, 2, 3] => 2, 1, 1, 2, 2, 3, 2, 2, 3
[2, 1, 1, 2, 2, 3, 2, 3, 1] => 2, 1, 1, 2, 2, 3, 2, 3, 1
[2, 1, 1, 2, 2, 3, 2, 3, 2] => 2, 1, 1, 2, 2, 3, 2, 3, 2
[2, 1, 1, 2, 2, 3, 2, 3, 3] => 2, 1, 1, 2, 2, 3, 2, 3, 3
[2, 1, 1, 2, 2, 3, 3, 1, 1] => 2, 1, 1, 2, 2, 3, 3, 1, 1
[2, 1, 1, 2, 2, 3, 3, 1, 2] => 2, 1, 1, 2, 2, 3, 3, 1, 2
[2, 1, 1, 2, 2, 3, 3, 1, 3] => 2, 1, 1, 2, 2, 3, 3, 1, 3
[2, 1, 1, 2, 2, 3, 3, 2, 1] => 2, 1, 1, 2, 2, 3, 3, 2, 1
[2, 1, 1, 2, 2, 3, 3, 2, 2] => 2, 1, 1, 2, 2, 3, 3, 2, 2
[2, 1, 1, 2, 2, 3, 3, 2, 3] => 2, 1, 1, 2, 2, 3, 3, 2, 3
[2, 1, 1, 2, 2, 3, 3, 3, 1] => 2, 1, 1, 2, 2, 3, 3, 3, 1
[2, 1, 1, 2, 2, 3, 3, 3, 2] => 2, 1, 1, 2, 2, 3, 3, 3, 2
[2, 1, 1, 2, 2, 3, 3, 3, 3] => 2, 1, 1, 2, 2, 3, 3, 3, 3
[2, 1, 1, 2, 3, 1, 1, 1, 1] => 2, 1, 1, 2, 3, 1, 1, 1, 1
[2, 1, 1, 2, 3, 1, 1, 1, 2] => 2, 1, 1, 2, 3, 1, 1, 1, 2
[2, 1, 1, 2, 3, 1, 1, 1, 3] => 2, 1, 1, 2, 3, 1, 1, 1, 3
[2, 1, 1, 2, 3, 1, 1, 2, 1] => 2, 1, 1, 2, 3, 1, 1, 2, 1
[2, 1, 1, 2, 3, 1, 1, 2, 2] => 2, 1, 1, 2, 3, 1, 1, 2, 2
[2, 1, 1, 2, 3, 1, 1, 2, 3] => 2, 1, 1, 2, 3, 1, 1, 2, 3
[2, 1, 1, 2, 3, 1, 1, 3, 1] => 2, 1, 1, 2, 3, 1, 1, 3, 1
[2, 1, 1, 2, 3, 1, 1, 3, 2] => 2, 1, 1, 2, 3, 1, 1, 3, 2
[2, 1, 1, 2, 3, 1, 1, 3, 3] => 2, 1, 1, 2, 3, 1, 1, 3, 3
[2, 1, 1, 2, 3, 1, 2, 1, 1] => 2, 1, 1, 2, 3, 1, 2, 1, 1
[2, 1, 1, 2, 3, 1, 2, 1, 2] => 2, 1, 1, 2, 3, 1, 2, 1, 2
[2, 1, 1, 2, 3, 1, 2, 1, 3] => 2, 1, 1, 2, 3, 1, 2, 1, 3
[2, 1, 1, 2, 3, 1, 2, 2, 1] => 2, 1, 1, 2, 3, 1, 2, 2, 1
[2, 1, 1, 2, 3, 1, 2, 2, 2] => 2, 1, 1, 2, 3, 1, 2, 2, 2
[2, 1, 1, 2, 3, 1, 2, 2, 3] => 2, 1, 1, 2, 3, 1, 2, 2, 3
[2, 1, 1, 2, 3, 1, 2, 3, 1] => 2, 1, 1, 2, 3, 1, 2, 3, 1
[2, 1, 1, 2, 3, 1, 2, 3, 2] => 2, 1, 1, 2, 3, 1, 2, 3, 2
[2, 1, 1, 2, 3, 1, 2, 3, 3] => 2, 1, 1, 2, 3, 1, 2, 3, 3
[2, 1, 1, 2, 3, 1, 3, 1, 1] => 2, 1, 1, 2, 3, 1, 3, 1, 1
[2, 1, 1, 2, 3, 1, 3, 1, 2] => 2, 1, 1, 2, 3, 1, 3, 1, 2
[2, 1, 1, 2, 3, 1, 3, 1, 3] => 2, 1, 1, 2, 3, 1, 3, 1, 3
[2, 1, 1, 2, 3, 1, 3, 2, 1] => 2, 1, 1, 2, 3, 1, 3, 2, 1
[2, 1, 1, 2, 3, 1, 3, 2, 2] => 2, 1, 1, 2, 3, 1, 3, 2, 2
[2, 1, 1, 2, 3, 1, 3, 2, 3] => 2, 1, 1, 2, 3, 1, 3, 2, 3
[2, 1, 1, 2, 3, 1, 3, 3, 1] => 2, 1, 1, 2, 3, 1, 3, 3, 1
[2, 1, 1, 2, 3, 1, 3, 3, 2] => 2, 1, 1, 2, 3, 1, 3, 3, 2
[2, 1, 1, 2, 3, 1, 3, 3, 3] => 2, 1, 1, 2, 3, 1, 3, 3, 3
[2, 1, 1, 2, 3, 2, 1, 1, 1] => 2, 1, 1, 2, 3, 2, 1, 1, 1
[2, 1, 1, 2, 3, 2, 1, 1, 2] => 2, 1, 1, 2, 3, 2, 1, 1, 2
[2, 1, 1, 2, 3, 2, 1, 1, 3] => 2, 1, 1, 2, 3, 2, 1, 1, 3
[2, 1, 1, 2, 3, 2, 1, 2, 1] => 2, 1, 1, 2, 3, 2, 1, 2, 1
[2, 1, 1, 2, 3, 2, 1, 2, 2] => 2, 1, 1, 2, 3, 2, 1, 2, 2
[2, 1, 1, 2, 3, 2, 1, 2, 3] => 2, 1, 1, 2, 3, 2, 1, 2, 3
[2, 1, 1, 2, 3, 2, 1, 3, 1] => 2, 1, 1, 2, 3, 2, 1, 3, 1
[2, 1, 1, 2, 3, 2, 1, 3, 2] => 2, 1, 1, 2, 3, 2, 1, 3, 2
[2, 1, 1, 2, 3, 2, 1, 3, 3] => 2, 1, 1, 2, 3, 2, 1, 3, 3
[2, 1, 1, 2, 3, 2, 2, 1, 1] => 2, 1, 1, 2, 3, 2, 2, 1, 1
[2, 1, 1, 2, 3, 2, 2, 1, 2] => 2, 1, 1, 2, 3, 2, 2, 1, 2
[2, 1, 1, 2, 3, 2, 2, 1, 3] => 2, 1, 1, 2, 3, 2, 2, 1, 3
[2, 1, 1, 2, 3, 2, 2, 2, 1] => 2, 1, 1, 2, 3, 2, 2, 2, 1
[2, 1, 1, 2, 3, 2, 2, 2, 2] => 2, 1, 1, 2, 3, 2, 2, 2, 2
[2, 1, 1, 2, 3, 2, 2, 2, 3] => 2, 1, 1, 2, 3, 2, 2, 2, 3
[2, 1, 1, 2, 3, 2, 2, 3, 1] => 2, 1, 1, 2, 3, 2, 2, 3, 1
[2, 1, 1, 2, 3, 2, 2, 3, 2] => 2, 1, 1, 2, 3, 2, 2, 3, 2
[2, 1, 1, 2, 3, 2, 2, 3, 3] => 2, 1, 1, 2, 3, 2, 2, 3, 3
[2, 1, 1, 2, 3, 2, 3, 1, 1] => 2, 1, 1, 2, 3, 2, 3, 1, 1
[2, 1, 1, 2, 3, 2, 3, 1, 2] => 2, 1, 1, 2, 3, 2, 3, 1, 2
[2, 1, 1, 2, 3, 2, 3, 1, 3] => 2, 1, 1, 2, 3, 2, 3, 1, 3
[2, 1, 1, 2, 3, 2, 3, 2, 1] => 2, 1, 1, 2, 3, 2, 3, 2, 1
[2, 1, 1, 2, 3, 2, 3, 2, 2] => 2, 1, 1, 2, 3, 2, 3, 2, 2
[2, 1, 1, 2, 3, 2, 3, 2, 3] => 2, 1, 1, 2, 3, 2, 3, 2, 3
[2, 1, 1, 2, 3, 2, 3, 3, 1] => 2, 1, 1, 2, 3, 2, 3, 3, 1
[2, 1, 1, 2, 3, 2, 3, 3, 2] => 2, 1, 1, 2, 3, 2, 3, 3, 2
[2, 1, 1, 2, 3, 2, 3, 3, 3] => 2, 1, 1, 2, 3, 2, 3, 3, 3
[2, 1, 1, 2, 3, 3, 1, 1, 1] => 2, 1, 1, 2, 3, 3, 1, 1, 1
[2, 1, 1, 2, 3, 3, 1, 1, 2] => 2, 1, 1, 2, 3, 3, 1, 1, 2
[2, 1, 1, 2, 3, 3, 1, 1, 3] => 2, 1, 1, 2, 3, 3, 1, 1, 3
[2, 1, 1, 2, 3, 3, 1, 2, 1] => 2, 1, 1, 2, 3, 3, 1, 2, 1
[2, 1, 1, 2, 3, 3, 1, 2, 2] => 2, 1, 1, 2, 3, 3, 1, 2, 2
[2, 1, 1, 2, 3, 3, 1, 2, 3] => 2, 1, 1, 2, 3, 3, 1, 2, 3
[2, 1, 1, 2, 3, 3, 1, 3, 1] => 2, 1, 1, 2, 3, 3, 1, 3, 1
[2, 1, 1, 2, 3, 3, 1, 3, 2] => 2, 1, 1, 2, 3, 3, 1, 3, 2
[2, 1, 1, 2, 3, 3, 1, 3, 3] => 2, 1, 1, 2, 3, 3, 1, 3, 3
[2, 1, 1, 2, 3, 3, 2, 1, 1] => 2, 1, 1, 2, 3, 3, 2, 1, 1
[2, 1, 1, 2, 3, 3, 2, 1, 2] => 2, 1, 1, 2, 3, 3, 2, 1, 2
[2, 1, 1, 2, 3, 3, 2, 1, 3] => 2, 1, 1, 2, 3, 3, 2, 1, 3
[2, 1, 1, 2, 3, 3, 2, 2, 1] => 2, 1, 1, 2, 3, 3, 2, 2, 1
[2, 1, 1, 2, 3, 3, 2, 2, 2] => 2, 1, 1, 2, 3, 3, 2, 2, 2
[2, 1, 1, 2, 3, 3, 2, 2, 3] => 2, 1, 1, 2, 3, 3, 2, 2, 3
[2, 1, 1, 2, 3, 3, 2, 3, 1] => 2, 1, 1, 2, 3, 3, 2, 3, 1
[2, 1, 1, 2, 3, 3, 2, 3, 2] => 2, 1, 1, 2, 3, 3, 2, 3, 2
[2, 1, 1, 2, 3, 3, 2, 3, 3] => 2, 1, 1, 2, 3, 3, 2, 3, 3
[2, 1, 1, 2, 3, 3, 3, 1, 1] => 2, 1, 1, 2, 3, 3, 3, 1, 1
[2, 1, 1, 2, 3, 3, 3, 1, 2] => 2, 1, 1, 2, 3, 3, 3, 1, 2
[2, 1, 1, 2, 3, 3, 3, 1, 3] => 2, 1, 1, 2, 3, 3, 3, 1, 3
[2, 1, 1, 2, 3, 3, 3, 2, 1] => 2, 1, 1, 2, 3, 3, 3, 2, 1
[2, 1, 1, 2, 3, 3, 3, 2, 2] => 2, 1, 1, 2, 3, 3, 3, 2, 2
[2, 1, 1, 2, 3, 3, 3, 2, 3] => 2, 1, 1, 2, 3, 3, 3, 2, 3
[2, 1, 1, 2, 3, 3, 3, 3, 1] => 2, 1, 1, 2, 3, 3, 3, 3, 1
[2, 1, 1, 2, 3, 3, 3, 3, 2] => 2, 1, 1, 2, 3, 3, 3, 3, 2
[2, 1, 1, 2, 3, 3, 3, 3, 3] => 2, 1, 1, 2, 3, 3, 3, 3, 3
[2, 1, 1, 3, 1, 1, 1, 1, 1] => 2, 1, 1, 3, 1, 1, 1, 1, 1
[2, 1, 1, 3, 1, 1, 1, 1, 2] => 2, 1, 1, 3, 1, 1, 1, 1, 2
[2, 1, 1, 3, 1, 1, 1, 1, 3] => 2, 1, 1, 3, 1, 1, 1, 1, 3
[2, 1, 1, 3, 1, 1, 1, 2, 1] => 2, 1, 1, 3, 1, 1, 1, 2, 1
[2, 1, 1, 3, 1, 1, 1, 2, 2] => 2, 1, 1, 3, 1, 1, 1, 2, 2
[2, 1, 1, 3, 1, 1, 1, 2, 3] => 2, 1, 1, 3, 1, 1, 1, 2, 3
[2, 1, 1, 3, 1, 1, 1, 3, 1] => 2, 1, 1, 3, 1, 1, 1, 3, 1
[2, 1, 1, 3, 1, 1, 1, 3, 2] => 2, 1, 1, 3, 1, 1, 1, 3, 2
[2, 1, 1, 3, 1, 1, 1, 3, 3] => 2, 1, 1, 3, 1, 1, 1, 3, 3
[2, 1, 1, 3, 1, 1, 2, 1, 1] => 2, 1, 1, 3, 1, 1, 2, 1, 1
[2, 1, 1, 3, 1, 1, 2, 1, 2] => 2, 1, 1, 3, 1, 1, 2, 1, 2
[2, 1, 1, 3, 1, 1, 2, 1, 3] => 2, 1, 1, 3, 1, 1, 2, 1, 3
[2, 1, 1, 3, 1, 1, 2, 2, 1] => 2, 1, 1, 3, 1, 1, 2, 2, 1
[2, 1, 1, 3, 1, 1, 2, 2, 2] => 2, 1, 1, 3, 1, 1, 2, 2, 2
[2, 1, 1, 3, 1, 1, 2, 2, 3] => 2, 1, 1, 3, 1, 1, 2, 2, 3
[2, 1, 1, 3, 1, 1, 2, 3, 1] => 2, 1, 1, 3, 1, 1, 2, 3, 1
[2, 1, 1, 3, 1, 1, 2, 3, 2] => 2, 1, 1, 3, 1, 1, 2, 3, 2
[2, 1, 1, 3, 1, 1, 2, 3, 3] => 2, 1, 1, 3, 1, 1, 2, 3, 3
[2, 1, 1, 3, 1, 1, 3, 1, 1] => 2, 1, 1, 3, 1, 1, 3, 1, 1
[2, 1, 1, 3, 1, 1, 3, 1, 2] => 2, 1, 1, 3, 1, 1, 3, 1, 2
[2, 1, 1, 3, 1, 1, 3, 1, 3] => 2, 1, 1, 3, 1, 1, 3, 1, 3
[2, 1, 1, 3, 1, 1, 3, 2, 1] => 2, 1, 1, 3, 1, 1, 3, 2, 1
[2, 1, 1, 3, 1, 1, 3, 2, 2] => 2, 1, 1, 3, 1, 1, 3, 2, 2
[2, 1, 1, 3, 1, 1, 3, 2, 3] => 2, 1, 1, 3, 1, 1, 3, 2, 3
[2, 1, 1, 3, 1, 1, 3, 3, 1] => 2, 1, 1, 3, 1, 1, 3, 3, 1
[2, 1, 1, 3, 1, 1, 3, 3, 2] => 2, 1, 1, 3, 1, 1, 3, 3, 2
[2, 1, 1, 3, 1, 1, 3, 3, 3] => 2, 1, 1, 3, 1, 1, 3, 3, 3
[2, 1, 1, 3, 1, 2, 1, 1, 1] => 2, 1, 1, 3, 1, 2, 1, 1, 1
[2, 1, 1, 3, 1, 2, 1, 1, 2] => 2, 1, 1, 3, 1, 2, 1, 1, 2
[2, 1, 1, 3, 1, 2, 1, 1, 3] => 2, 1, 1, 3, 1, 2, 1, 1, 3
[2, 1, 1, 3, 1, 2, 1, 2, 1] => 2, 1, 1, 3, 1, 2, 1, 2, 1
[2, 1, 1, 3, 1, 2, 1, 2, 2] => 2, 1, 1, 3, 1, 2, 1, 2, 2
[2, 1, 1, 3, 1, 2, 1, 2, 3] => 2, 1, 1, 3, 1, 2, 1, 2, 3
[2, 1, 1, 3, 1, 2, 1, 3, 1] => 2, 1, 1, 3, 1, 2, 1, 3, 1
[2, 1, 1, 3, 1, 2, 1, 3, 2] => 2, 1, 1, 3, 1, 2, 1, 3, 2
[2, 1, 1, 3, 1, 2, 1, 3, 3] => 2, 1, 1, 3, 1, 2, 1, 3, 3
[2, 1, 1, 3, 1, 2, 2, 1, 1] => 2, 1, 1, 3, 1, 2, 2, 1, 1
[2, 1, 1, 3, 1, 2, 2, 1, 2] => 2, 1, 1, 3, 1, 2, 2, 1, 2
[2, 1, 1, 3, 1, 2, 2, 1, 3] => 2, 1, 1, 3, 1, 2, 2, 1, 3
[2, 1, 1, 3, 1, 2, 2, 2, 1] => 2, 1, 1, 3, 1, 2, 2, 2, 1
[2, 1, 1, 3, 1, 2, 2, 2, 2] => 2, 1, 1, 3, 1, 2, 2, 2, 2
[2, 1, 1, 3, 1, 2, 2, 2, 3] => 2, 1, 1, 3, 1, 2, 2, 2, 3
[2, 1, 1, 3, 1, 2, 2, 3, 1] => 2, 1, 1, 3, 1, 2, 2, 3, 1
[2, 1, 1, 3, 1, 2, 2, 3, 2] => 2, 1, 1, 3, 1, 2, 2, 3, 2
[2, 1, 1, 3, 1, 2, 2, 3, 3] => 2, 1, 1, 3, 1, 2, 2, 3, 3
[2, 1, 1, 3, 1, 2, 3, 1, 1] => 2, 1, 1, 3, 1, 2, 3, 1, 1
[2, 1, 1, 3, 1, 2, 3, 1, 2] => 2, 1, 1, 3, 1, 2, 3, 1, 2
[2, 1, 1, 3, 1, 2, 3, 1, 3] => 2, 1, 1, 3, 1, 2, 3, 1, 3
[2, 1, 1, 3, 1, 2, 3, 2, 1] => 2, 1, 1, 3, 1, 2, 3, 2, 1
[2, 1, 1, 3, 1, 2, 3, 2, 2] => 2, 1, 1, 3, 1, 2, 3, 2, 2
[2, 1, 1, 3, 1, 2, 3, 2, 3] => 2, 1, 1, 3, 1, 2, 3, 2, 3
[2, 1, 1, 3, 1, 2, 3, 3, 1] => 2, 1, 1, 3, 1, 2, 3, 3, 1
[2, 1, 1, 3, 1, 2, 3, 3, 2] => 2, 1, 1, 3, 1, 2, 3, 3, 2
[2, 1, 1, 3, 1, 2, 3, 3, 3] => 2, 1, 1, 3, 1, 2, 3, 3, 3
[2, 1, 1, 3, 1, 3, 1, 1, 1] => 2, 1, 1, 3, 1, 3, 1, 1, 1
[2, 1, 1, 3, 1, 3, 1, 1, 2] => 2, 1, 1, 3, 1, 3, 1, 1, 2
[2, 1, 1, 3, 1, 3, 1, 1, 3] => 2, 1, 1, 3, 1, 3, 1, 1, 3
[2, 1, 1, 3, 1, 3, 1, 2, 1] => 2, 1, 1, 3, 1, 3, 1, 2, 1
[2, 1, 1, 3, 1, 3, 1, 2, 2] => 2, 1, 1, 3, 1, 3, 1, 2, 2
[2, 1, 1, 3, 1, 3, 1, 2, 3] => 2, 1, 1, 3, 1, 3, 1, 2, 3
[2, 1, 1, 3, 1, 3, 1, 3, 1] => 2, 1, 1, 3, 1, 3, 1, 3, 1
[2, 1, 1, 3, 1, 3, 1, 3, 2] => 2, 1, 1, 3, 1, 3, 1, 3, 2
[2, 1, 1, 3, 1, 3, 1, 3, 3] => 2, 1, 1, 3, 1, 3, 1, 3, 3
[2, 1, 1, 3, 1, 3, 2, 1, 1] => 2, 1, 1, 3, 1, 3, 2, 1, 1
[2, 1, 1, 3, 1, 3, 2, 1, 2] => 2, 1, 1, 3, 1, 3, 2, 1, 2
[2, 1, 1, 3, 1, 3, 2, 1, 3] => 2, 1, 1, 3, 1, 3, 2, 1, 3
[2, 1, 1, 3, 1, 3, 2, 2, 1] => 2, 1, 1, 3, 1, 3, 2, 2, 1
[2, 1, 1, 3, 1, 3, 2, 2, 2] => 2, 1, 1, 3, 1, 3, 2, 2, 2
[2, 1, 1, 3, 1, 3, 2, 2, 3] => 2, 1, 1, 3, 1, 3, 2, 2, 3
[2, 1, 1, 3, 1, 3, 2, 3, 1] => 2, 1, 1, 3, 1, 3, 2, 3, 1
[2, 1, 1, 3, 1, 3, 2, 3, 2] => 2, 1, 1, 3, 1, 3, 2, 3, 2
[2, 1, 1, 3, 1, 3, 2, 3, 3] => 2, 1, 1, 3, 1, 3, 2, 3, 3
[2, 1, 1, 3, 1, 3, 3, 1, 1] => 2, 1, 1, 3, 1, 3, 3, 1, 1
[2, 1, 1, 3, 1, 3, 3, 1, 2] => 2, 1, 1, 3, 1, 3, 3, 1, 2
[2, 1, 1, 3, 1, 3, 3, 1, 3] => 2, 1, 1, 3, 1, 3, 3, 1, 3
[2, 1, 1, 3, 1, 3, 3, 2, 1] => 2, 1, 1, 3, 1, 3, 3, 2, 1
[2, 1, 1, 3, 1, 3, 3, 2, 2] => 2, 1, 1, 3, 1, 3, 3, 2, 2
[2, 1, 1, 3, 1, 3, 3, 2, 3] => 2, 1, 1, 3, 1, 3, 3, 2, 3
[2, 1, 1, 3, 1, 3, 3, 3, 1] => 2, 1, 1, 3, 1, 3, 3, 3, 1
[2, 1, 1, 3, 1, 3, 3, 3, 2] => 2, 1, 1, 3, 1, 3, 3, 3, 2
[2, 1, 1, 3, 1, 3, 3, 3, 3] => 2, 1, 1, 3, 1, 3, 3, 3, 3
[2, 1, 1, 3, 2, 1, 1, 1, 1] => 2, 1, 1, 3, 2, 1, 1, 1, 1
[2, 1, 1, 3, 2, 1, 1, 1, 2] => 2, 1, 1, 3, 2, 1, 1, 1, 2
[2, 1, 1, 3, 2, 1, 1, 1, 3] => 2, 1, 1, 3, 2, 1, 1, 1, 3
[2, 1, 1, 3, 2, 1, 1, 2, 1] => 2, 1, 1, 3, 2, 1, 1, 2, 1
[2, 1, 1, 3, 2, 1, 1, 2, 2] => 2, 1, 1, 3, 2, 1, 1, 2, 2
[2, 1, 1, 3, 2, 1, 1, 2, 3] => 2, 1, 1, 3, 2, 1, 1, 2, 3
[2, 1, 1, 3, 2, 1, 1, 3, 1] => 2, 1, 1, 3, 2, 1, 1, 3, 1
[2, 1, 1, 3, 2, 1, 1, 3, 2] => 2, 1, 1, 3, 2, 1, 1, 3, 2
[2, 1, 1, 3, 2, 1, 1, 3, 3] => 2, 1, 1, 3, 2, 1, 1, 3, 3
[2, 1, 1, 3, 2, 1, 2, 1, 1] => 2, 1, 1, 3, 2, 1, 2, 1, 1
[2, 1, 1, 3, 2, 1, 2, 1, 2] => 2, 1, 1, 3, 2, 1, 2, 1, 2
[2, 1, 1, 3, 2, 1, 2, 1, 3] => 2, 1, 1, 3, 2, 1, 2, 1, 3
[2, 1, 1, 3, 2, 1, 2, 2, 1] => 2, 1, 1, 3, 2, 1, 2, 2, 1
[2, 1, 1, 3, 2, 1, 2, 2, 2] => 2, 1, 1, 3, 2, 1, 2, 2, 2
[2, 1, 1, 3, 2, 1, 2, 2, 3] => 2, 1, 1, 3, 2, 1, 2, 2, 3
[2, 1, 1, 3, 2, 1, 2, 3, 1] => 2, 1, 1, 3, 2, 1, 2, 3, 1
[2, 1, 1, 3, 2, 1, 2, 3, 2] => 2, 1, 1, 3, 2, 1, 2, 3, 2
[2, 1, 1, 3, 2, 1, 2, 3, 3] => 2, 1, 1, 3, 2, 1, 2, 3, 3
[2, 1, 1, 3, 2, 1, 3, 1, 1] => 2, 1, 1, 3, 2, 1, 3, 1, 1
[2, 1, 1, 3, 2, 1, 3, 1, 2] => 2, 1, 1, 3, 2, 1, 3, 1, 2
[2, 1, 1, 3, 2, 1, 3, 1, 3] => 2, 1, 1, 3, 2, 1, 3, 1, 3
[2, 1, 1, 3, 2, 1, 3, 2, 1] => 2, 1, 1, 3, 2, 1, 3, 2, 1
[2, 1, 1, 3, 2, 1, 3, 2, 2] => 2, 1, 1, 3, 2, 1, 3, 2, 2
[2, 1, 1, 3, 2, 1, 3, 2, 3] => 2, 1, 1, 3, 2, 1, 3, 2, 3
[2, 1, 1, 3, 2, 1, 3, 3, 1] => 2, 1, 1, 3, 2, 1, 3, 3, 1
[2, 1, 1, 3, 2, 1, 3, 3, 2] => 2, 1, 1, 3, 2, 1, 3, 3, 2
[2, 1, 1, 3, 2, 1, 3, 3, 3] => 2, 1, 1, 3, 2, 1, 3, 3, 3
[2, 1, 1, 3, 2, 2, 1, 1, 1] => 2, 1, 1, 3, 2, 2, 1, 1, 1
[2, 1, 1, 3, 2, 2, 1, 1, 2] => 2, 1, 1, 3, 2, 2, 1, 1, 2
[2, 1, 1, 3, 2, 2, 1, 1, 3] => 2, 1, 1, 3, 2, 2, 1, 1, 3
[2, 1, 1, 3, 2, 2, 1, 2, 1] => 2, 1, 1, 3, 2, 2, 1, 2, 1
[2, 1, 1, 3, 2, 2, 1, 2, 2] => 2, 1, 1, 3, 2, 2, 1, 2, 2
[2, 1, 1, 3, 2, 2, 1, 2, 3] => 2, 1, 1, 3, 2, 2, 1, 2, 3
[2, 1, 1, 3, 2, 2, 1, 3, 1] => 2, 1, 1, 3, 2, 2, 1, 3, 1
[2, 1, 1, 3, 2, 2, 1, 3, 2] => 2, 1, 1, 3, 2, 2, 1, 3, 2
[2, 1, 1, 3, 2, 2, 1, 3, 3] => 2, 1, 1, 3, 2, 2, 1, 3, 3
[2, 1, 1, 3, 2, 2, 2, 1, 1] => 2, 1, 1, 3, 2, 2, 2, 1, 1
[2, 1, 1, 3, 2, 2, 2, 1, 2] => 2, 1, 1, 3, 2, 2, 2, 1, 2
[2, 1, 1, 3, 2, 2, 2, 1, 3] => 2, 1, 1, 3, 2, 2, 2, 1, 3
[2, 1, 1, 3, 2, 2, 2, 2, 1] => 2, 1, 1, 3, 2, 2, 2, 2, 1
[2, 1, 1, 3, 2, 2, 2, 2, 2] => 2, 1, 1, 3, 2, 2, 2, 2, 2
[2, 1, 1, 3, 2, 2, 2, 2, 3] => 2, 1, 1, 3, 2, 2, 2, 2, 3
[2, 1, 1, 3, 2, 2, 2, 3, 1] => 2, 1, 1, 3, 2, 2, 2, 3, 1
[2, 1, 1, 3, 2, 2, 2, 3, 2] => 2, 1, 1, 3, 2, 2, 2, 3, 2
[2, 1, 1, 3, 2, 2, 2, 3, 3] => 2, 1, 1, 3, 2, 2, 2, 3, 3
[2, 1, 1, 3, 2, 2, 3, 1, 1] => 2, 1, 1, 3, 2, 2, 3, 1, 1
[2, 1, 1, 3, 2, 2, 3, 1, 2] => 2, 1, 1, 3, 2, 2, 3, 1, 2
[2, 1, 1, 3, 2, 2, 3, 1, 3] => 2, 1, 1, 3, 2, 2, 3, 1, 3
[2, 1, 1, 3, 2, 2, 3, 2, 1] => 2, 1, 1, 3, 2, 2, 3, 2, 1
[2, 1, 1, 3, 2, 2, 3, 2, 2] => 2, 1, 1, 3, 2, 2, 3, 2, 2
[2, 1, 1, 3, 2, 2, 3, 2, 3] => 2, 1, 1, 3, 2, 2, 3, 2, 3
[2, 1, 1, 3, 2, 2, 3, 3, 1] => 2, 1, 1, 3, 2, 2, 3, 3, 1
[2, 1, 1, 3, 2, 2, 3, 3, 2] => 2, 1, 1, 3, 2, 2, 3, 3, 2
[2, 1, 1, 3, 2, 2, 3, 3, 3] => 2, 1, 1, 3, 2, 2, 3, 3, 3
[2, 1, 1, 3, 2, 3, 1, 1, 1] => 2, 1, 1, 3, 2, 3, 1, 1, 1
[2, 1, 1, 3, 2, 3, 1, 1, 2] => 2, 1, 1, 3, 2, 3, 1, 1, 2
[2, 1, 1, 3, 2, 3, 1, 1, 3] => 2, 1, 1, 3, 2, 3, 1, 1, 3
[2, 1, 1, 3, 2, 3, 1, 2, 1] => 2, 1, 1, 3, 2, 3, 1, 2, 1
[2, 1, 1, 3, 2, 3, 1, 2, 2] => 2, 1, 1, 3, 2, 3, 1, 2, 2
[2, 1, 1, 3, 2, 3, 1, 2, 3] => 2, 1, 1, 3, 2, 3, 1, 2, 3
[2, 1, 1, 3, 2, 3, 1, 3, 1] => 2, 1, 1, 3, 2, 3, 1, 3, 1
[2, 1, 1, 3, 2, 3, 1, 3, 2] => 2, 1, 1, 3, 2, 3, 1, 3, 2
[2, 1, 1, 3, 2, 3, 1, 3, 3] => 2, 1, 1, 3, 2, 3, 1, 3, 3
[2, 1, 1, 3, 2, 3, 2, 1, 1] => 2, 1, 1, 3, 2, 3, 2, 1, 1
[2, 1, 1, 3, 2, 3, 2, 1, 2] => 2, 1, 1, 3, 2, 3, 2, 1, 2
[2, 1, 1, 3, 2, 3, 2, 1, 3] => 2, 1, 1, 3, 2, 3, 2, 1, 3
[2, 1, 1, 3, 2, 3, 2, 2, 1] => 2, 1, 1, 3, 2, 3, 2, 2, 1
[2, 1, 1, 3, 2, 3, 2, 2, 2] => 2, 1, 1, 3, 2, 3, 2, 2, 2
[2, 1, 1, 3, 2, 3, 2, 2, 3] => 2, 1, 1, 3, 2, 3, 2, 2, 3
[2, 1, 1, 3, 2, 3, 2, 3, 1] => 2, 1, 1, 3, 2, 3, 2, 3, 1
[2, 1, 1, 3, 2, 3, 2, 3, 2] => 2, 1, 1, 3, 2, 3, 2, 3, 2
[2, 1, 1, 3, 2, 3, 2, 3, 3] => 2, 1, 1, 3, 2, 3, 2, 3, 3
[2, 1, 1, 3, 2, 3, 3, 1, 1] => 2, 1, 1, 3, 2, 3, 3, 1, 1
[2, 1, 1, 3, 2, 3, 3, 1, 2] => 2, 1, 1, 3, 2, 3, 3, 1, 2
[2, 1, 1, 3, 2, 3, 3, 1, 3] => 2, 1, 1, 3, 2, 3, 3, 1, 3
[2, 1, 1, 3, 2, 3, 3, 2, 1] => 2, 1, 1, 3, 2, 3, 3, 2, 1
[2, 1, 1, 3, 2, 3, 3, 2, 2] => 2, 1, 1, 3, 2, 3, 3, 2, 2
[2, 1, 1, 3, 2, 3, 3, 2, 3] => 2, 1, 1, 3, 2, 3, 3, 2, 3
[2, 1, 1, 3, 2, 3, 3, 3, 1] => 2, 1, 1, 3, 2, 3, 3, 3, 1
[2, 1, 1, 3, 2, 3, 3, 3, 2] => 2, 1, 1, 3, 2, 3, 3, 3, 2
[2, 1, 1, 3, 2, 3, 3, 3, 3] => 2, 1, 1, 3, 2, 3, 3, 3, 3
[2, 1, 1, 3, 3, 1, 1, 1, 1] => 2, 1, 1, 3, 3, 1, 1, 1, 1
[2, 1, 1, 3, 3, 1, 1, 1, 2] => 2, 1, 1, 3, 3, 1, 1, 1, 2
[2, 1, 1, 3, 3, 1, 1, 1, 3] => 2, 1, 1, 3, 3, 1, 1, 1, 3
[2, 1, 1, 3, 3, 1, 1, 2, 1] => 2, 1, 1, 3, 3, 1, 1, 2, 1
[2, 1, 1, 3, 3, 1, 1, 2, 2] => 2, 1, 1, 3, 3, 1, 1, 2, 2
[2, 1, 1, 3, 3, 1, 1, 2, 3] => 2, 1, 1, 3, 3, 1, 1, 2, 3
[2, 1, 1, 3, 3, 1, 1, 3, 1] => 2, 1, 1, 3, 3, 1, 1, 3, 1
[2, 1, 1, 3, 3, 1, 1, 3, 2] => 2, 1, 1, 3, 3, 1, 1, 3, 2
[2, 1, 1, 3, 3, 1, 1, 3, 3] => 2, 1, 1, 3, 3, 1, 1, 3, 3
[2, 1, 1, 3, 3, 1, 2, 1, 1] => 2, 1, 1, 3, 3, 1, 2, 1, 1
[2, 1, 1, 3, 3, 1, 2, 1, 2] => 2, 1, 1, 3, 3, 1, 2, 1, 2
[2, 1, 1, 3, 3, 1, 2, 1, 3] => 2, 1, 1, 3, 3, 1, 2, 1, 3
[2, 1, 1, 3, 3, 1, 2, 2, 1] => 2, 1, 1, 3, 3, 1, 2, 2, 1
[2, 1, 1, 3, 3, 1, 2, 2, 2] => 2, 1, 1, 3, 3, 1, 2, 2, 2
[2, 1, 1, 3, 3, 1, 2, 2, 3] => 2, 1, 1, 3, 3, 1, 2, 2, 3
[2, 1, 1, 3, 3, 1, 2, 3, 1] => 2, 1, 1, 3, 3, 1, 2, 3, 1
[2, 1, 1, 3, 3, 1, 2, 3, 2] => 2, 1, 1, 3, 3, 1, 2, 3, 2
[2, 1, 1, 3, 3, 1, 2, 3, 3] => 2, 1, 1, 3, 3, 1, 2, 3, 3
[2, 1, 1, 3, 3, 1, 3, 1, 1] => 2, 1, 1, 3, 3, 1, 3, 1, 1
[2, 1, 1, 3, 3, 1, 3, 1, 2] => 2, 1, 1, 3, 3, 1, 3, 1, 2
[2, 1, 1, 3, 3, 1, 3, 1, 3] => 2, 1, 1, 3, 3, 1, 3, 1, 3
[2, 1, 1, 3, 3, 1, 3, 2, 1] => 2, 1, 1, 3, 3, 1, 3, 2, 1
[2, 1, 1, 3, 3, 1, 3, 2, 2] => 2, 1, 1, 3, 3, 1, 3, 2, 2
[2, 1, 1, 3, 3, 1, 3, 2, 3] => 2, 1, 1, 3, 3, 1, 3, 2, 3
[2, 1, 1, 3, 3, 1, 3, 3, 1] => 2, 1, 1, 3, 3, 1, 3, 3, 1
[2, 1, 1, 3, 3, 1, 3, 3, 2] => 2, 1, 1, 3, 3, 1, 3, 3, 2
[2, 1, 1, 3, 3, 1, 3, 3, 3] => 2, 1, 1, 3, 3, 1, 3, 3, 3
[2, 1, 1, 3, 3, 2, 1, 1, 1] => 2, 1, 1, 3, 3, 2, 1, 1, 1
[2, 1, 1, 3, 3, 2, 1, 1, 2] => 2, 1, 1, 3, 3, 2, 1, 1, 2
[2, 1, 1, 3, 3, 2, 1, 1, 3] => 2, 1, 1, 3, 3, 2, 1, 1, 3
[2, 1, 1, 3, 3, 2, 1, 2, 1] => 2, 1, 1, 3, 3, 2, 1, 2, 1
[2, 1, 1, 3, 3, 2, 1, 2, 2] => 2, 1, 1, 3, 3, 2, 1, 2, 2
[2, 1, 1, 3, 3, 2, 1, 2, 3] => 2, 1, 1, 3, 3, 2, 1, 2, 3
[2, 1, 1, 3, 3, 2, 1, 3, 1] => 2, 1, 1, 3, 3, 2, 1, 3, 1
[2, 1, 1, 3, 3, 2, 1, 3, 2] => 2, 1, 1, 3, 3, 2, 1, 3, 2
[2, 1, 1, 3, 3, 2, 1, 3, 3] => 2, 1, 1, 3, 3, 2, 1, 3, 3
[2, 1, 1, 3, 3, 2, 2, 1, 1] => 2, 1, 1, 3, 3, 2, 2, 1, 1
[2, 1, 1, 3, 3, 2, 2, 1, 2] => 2, 1, 1, 3, 3, 2, 2, 1, 2
[2, 1, 1, 3, 3, 2, 2, 1, 3] => 2, 1, 1, 3, 3, 2, 2, 1, 3
[2, 1, 1, 3, 3, 2, 2, 2, 1] => 2, 1, 1, 3, 3, 2, 2, 2, 1
[2, 1, 1, 3, 3, 2, 2, 2, 2] => 2, 1, 1, 3, 3, 2, 2, 2, 2
[2, 1, 1, 3, 3, 2, 2, 2, 3] => 2, 1, 1, 3, 3, 2, 2, 2, 3
[2, 1, 1, 3, 3, 2, 2, 3, 1] => 2, 1, 1, 3, 3, 2, 2, 3, 1
[2, 1, 1, 3, 3, 2, 2, 3, 2] => 2, 1, 1, 3, 3, 2, 2, 3, 2
[2, 1, 1, 3, 3, 2, 2, 3, 3] => 2, 1, 1, 3, 3, 2, 2, 3, 3
[2, 1, 1, 3, 3, 2, 3, 1, 1] => 2, 1, 1, 3, 3, 2, 3, 1, 1
[2, 1, 1, 3, 3, 2, 3, 1, 2] => 2, 1, 1, 3, 3, 2, 3, 1, 2
[2, 1, 1, 3, 3, 2, 3, 1, 3] => 2, 1, 1, 3, 3, 2, 3, 1, 3
[2, 1, 1, 3, 3, 2, 3, 2, 1] => 2, 1, 1, 3, 3, 2, 3, 2, 1
[2, 1, 1, 3, 3, 2, 3, 2, 2] => 2, 1, 1, 3, 3, 2, 3, 2, 2
[2, 1, 1, 3, 3, 2, 3, 2, 3] => 2, 1, 1, 3, 3, 2, 3, 2, 3
[2, 1, 1, 3, 3, 2, 3, 3, 1] => 2, 1, 1, 3, 3, 2, 3, 3, 1
[2, 1, 1, 3, 3, 2, 3, 3, 2] => 2, 1, 1, 3, 3, 2, 3, 3, 2
[2, 1, 1, 3, 3, 2, 3, 3, 3] => 2, 1, 1, 3, 3, 2, 3, 3, 3
[2, 1, 1, 3, 3, 3, 1, 1, 1] => 2, 1, 1, 3, 3, 3, 1, 1, 1
[2, 1, 1, 3, 3, 3, 1, 1, 2] => 2, 1, 1, 3, 3, 3, 1, 1, 2
[2, 1, 1, 3, 3, 3, 1, 1, 3] => 2, 1, 1, 3, 3, 3, 1, 1, 3
[2, 1, 1, 3, 3, 3, 1, 2, 1] => 2, 1, 1, 3, 3, 3, 1, 2, 1
[2, 1, 1, 3, 3, 3, 1, 2, 2] => 2, 1, 1, 3, 3, 3, 1, 2, 2
[2, 1, 1, 3, 3, 3, 1, 2, 3] => 2, 1, 1, 3, 3, 3, 1, 2, 3
[2, 1, 1, 3, 3, 3, 1, 3, 1] => 2, 1, 1, 3, 3, 3, 1, 3, 1
[2, 1, 1, 3, 3, 3, 1, 3, 2] => 2, 1, 1, 3, 3, 3, 1, 3, 2
[2, 1, 1, 3, 3, 3, 1, 3, 3] => 2, 1, 1, 3, 3, 3, 1, 3, 3
[2, 1, 1, 3, 3, 3, 2, 1, 1] => 2, 1, 1, 3, 3, 3, 2, 1, 1
[2, 1, 1, 3, 3, 3, 2, 1, 2] => 2, 1, 1, 3, 3, 3, 2, 1, 2
[2, 1, 1, 3, 3, 3, 2, 1, 3] => 2, 1, 1, 3, 3, 3, 2, 1, 3
[2, 1, 1, 3, 3, 3, 2, 2, 1] => 2, 1, 1, 3, 3, 3, 2, 2, 1
[2, 1, 1, 3, 3, 3, 2, 2, 2] => 2, 1, 1, 3, 3, 3, 2, 2, 2
[2, 1, 1, 3, 3, 3, 2, 2, 3] => 2, 1, 1, 3, 3, 3, 2, 2, 3
[2, 1, 1, 3, 3, 3, 2, 3, 1] => 2, 1, 1, 3, 3, 3, 2, 3, 1
[2, 1, 1, 3, 3, 3, 2, 3, 2] => 2, 1, 1, 3, 3, 3, 2, 3, 2
[2, 1, 1, 3, 3, 3, 2, 3, 3] => 2, 1, 1, 3, 3, 3, 2, 3, 3
[2, 1, 1, 3, 3, 3, 3, 1, 1] => 2, 1, 1, 3, 3, 3, 3, 1, 1
[2, 1, 1, 3, 3, 3, 3, 1, 2] => 2, 1, 1, 3, 3, 3, 3, 1, 2
[2, 1, 1, 3, 3, 3, 3, 1, 3] => 2, 1, 1, 3, 3, 3, 3, 1, 3
[2, 1, 1, 3, 3, 3, 3, 2, 1] => 2, 1, 1, 3, 3, 3, 3, 2, 1
[2, 1, 1, 3, 3, 3, 3, 2, 2] => 2, 1, 1, 3, 3, 3, 3, 2, 2
[2, 1, 1, 3, 3, 3, 3, 2, 3] => 2, 1, 1, 3, 3, 3, 3, 2, 3
[2, 1, 1, 3, 3, 3, 3, 3, 1] => 2, 1, 1, 3, 3, 3, 3, 3, 1
[2, 1, 1, 3, 3, 3, 3, 3, 2] => 2, 1, 1, 3, 3, 3, 3, 3, 2
[2, 1, 1, 3, 3, 3, 3, 3, 3] => 2, 1, 1, 3, 3, 3, 3, 3, 3
[2, 1, 2, 1, 1, 1, 1, 1, 1] => 2, 1, 2, 1, 1, 1, 1, 1, 1
[2, 1, 2, 1, 1, 1, 1, 1, 2] => 2, 1, 2, 1, 1, 1, 1, 1, 2
[2, 1, 2, 1, 1, 1, 1, 1, 3] => 2, 1, 2, 1, 1, 1, 1, 1, 3
[2, 1, 2, 1, 1, 1, 1, 2, 1] => 2, 1, 2, 1, 1, 1, 1, 2, 1
[2, 1, 2, 1, 1, 1, 1, 2, 2] => 2, 1, 2, 1, 1, 1, 1, 2, 2
[2, 1, 2, 1, 1, 1, 1, 2, 3] => 2, 1, 2, 1, 1, 1, 1, 2, 3
[2, 1, 2, 1, 1, 1, 1, 3, 1] => 2, 1, 2, 1, 1, 1, 1, 3, 1
[2, 1, 2, 1, 1, 1, 1, 3, 2] => 2, 1, 2, 1, 1, 1, 1, 3, 2
[2, 1, 2, 1, 1, 1, 1, 3, 3] => 2, 1, 2, 1, 1, 1, 1, 3, 3
[2, 1, 2, 1, 1, 1, 2, 1, 1] => 2, 1, 2, 1, 1, 1, 2, 1, 1
[2, 1, 2, 1, 1, 1, 2, 1, 2] => 2, 1, 2, 1, 1, 1, 2, 1, 2
[2, 1, 2, 1, 1, 1, 2, 1, 3] => 2, 1, 2, 1, 1, 1, 2, 1, 3
[2, 1, 2, 1, 1, 1, 2, 2, 1] => 2, 1, 2, 1, 1, 1, 2, 2, 1
[2, 1, 2, 1, 1, 1, 2, 2, 2] => 2, 1, 2, 1, 1, 1, 2, 2, 2
[2, 1, 2, 1, 1, 1, 2, 2, 3] => 2, 1, 2, 1, 1, 1, 2, 2, 3
[2, 1, 2, 1, 1, 1, 2, 3, 1] => 2, 1, 2, 1, 1, 1, 2, 3, 1
[2, 1, 2, 1, 1, 1, 2, 3, 2] => 2, 1, 2, 1, 1, 1, 2, 3, 2
[2, 1, 2, 1, 1, 1, 2, 3, 3] => 2, 1, 2, 1, 1, 1, 2, 3, 3
[2, 1, 2, 1, 1, 1, 3, 1, 1] => 2, 1, 2, 1, 1, 1, 3, 1, 1
[2, 1, 2, 1, 1, 1, 3, 1, 2] => 2, 1, 2, 1, 1, 1, 3, 1, 2
[2, 1, 2, 1, 1, 1, 3, 1, 3] => 2, 1, 2, 1, 1, 1, 3, 1, 3
[2, 1, 2, 1, 1, 1, 3, 2, 1] => 2, 1, 2, 1, 1, 1, 3, 2, 1
[2, 1, 2, 1, 1, 1, 3, 2, 2] => 2, 1, 2, 1, 1, 1, 3, 2, 2
[2, 1, 2, 1, 1, 1, 3, 2, 3] => 2, 1, 2, 1, 1, 1, 3, 2, 3
[2, 1, 2, 1, 1, 1, 3, 3, 1] => 2, 1, 2, 1, 1, 1, 3, 3, 1
[2, 1, 2, 1, 1, 1, 3, 3, 2] => 2, 1, 2, 1, 1, 1, 3, 3, 2
[2, 1, 2, 1, 1, 1, 3, 3, 3] => 2, 1, 2, 1, 1, 1, 3, 3, 3
[2, 1, 2, 1, 1, 2, 1, 1, 1] => 2, 1, 2, 1, 1, 2, 1, 1, 1
[2, 1, 2, 1, 1, 2, 1, 1, 2] => 2, 1, 2, 1, 1, 2, 1, 1, 2
[2, 1, 2, 1, 1, 2, 1, 1, 3] => 2, 1, 2, 1, 1, 2, 1, 1, 3
[2, 1, 2, 1, 1, 2, 1, 2, 1] => 2, 1, 2, 1, 1, 2, 1, 2, 1
[2, 1, 2, 1, 1, 2, 1, 2, 2] => 2, 1, 2, 1, 1, 2, 1, 2, 2
[2, 1, 2, 1, 1, 2, 1, 2, 3] => 2, 1, 2, 1, 1, 2, 1, 2, 3
[2, 1, 2, 1, 1, 2, 1, 3, 1] => 2, 1, 2, 1, 1, 2, 1, 3, 1
[2, 1, 2, 1, 1, 2, 1, 3, 2] => 2, 1, 2, 1, 1, 2, 1, 3, 2
[2, 1, 2, 1, 1, 2, 1, 3, 3] => 2, 1, 2, 1, 1, 2, 1, 3, 3
[2, 1, 2, 1, 1, 2, 2, 1, 1] => 2, 1, 2, 1, 1, 2, 2, 1, 1
[2, 1, 2, 1, 1, 2, 2, 1, 2] => 2, 1, 2, 1, 1, 2, 2, 1, 2
[2, 1, 2, 1, 1, 2, 2, 1, 3] => 2, 1, 2, 1, 1, 2, 2, 1, 3
[2, 1, 2, 1, 1, 2, 2, 2, 1] => 2, 1, 2, 1, 1, 2, 2, 2, 1
[2, 1, 2, 1, 1, 2, 2, 2, 2] => 2, 1, 2, 1, 1, 2, 2, 2, 2
[2, 1, 2, 1, 1, 2, 2, 2, 3] => 2, 1, 2, 1, 1, 2, 2, 2, 3
[2, 1, 2, 1, 1, 2, 2, 3, 1] => 2, 1, 2, 1, 1, 2, 2, 3, 1
[2, 1, 2, 1, 1, 2, 2, 3, 2] => 2, 1, 2, 1, 1, 2, 2, 3, 2
[2, 1, 2, 1, 1, 2, 2, 3, 3] => 2, 1, 2, 1, 1, 2, 2, 3, 3
[2, 1, 2, 1, 1, 2, 3, 1, 1] => 2, 1, 2, 1, 1, 2, 3, 1, 1
[2, 1, 2, 1, 1, 2, 3, 1, 2] => 2, 1, 2, 1, 1, 2, 3, 1, 2
[2, 1, 2, 1, 1, 2, 3, 1, 3] => 2, 1, 2, 1, 1, 2, 3, 1, 3
[2, 1, 2, 1, 1, 2, 3, 2, 1] => 2, 1, 2, 1, 1, 2, 3, 2, 1
[2, 1, 2, 1, 1, 2, 3, 2, 2] => 2, 1, 2, 1, 1, 2, 3, 2, 2
[2, 1, 2, 1, 1, 2, 3, 2, 3] => 2, 1, 2, 1, 1, 2, 3, 2, 3
[2, 1, 2, 1, 1, 2, 3, 3, 1] => 2, 1, 2, 1, 1, 2, 3, 3, 1
[2, 1, 2, 1, 1, 2, 3, 3, 2] => 2, 1, 2, 1, 1, 2, 3, 3, 2
[2, 1, 2, 1, 1, 2, 3, 3, 3] => 2, 1, 2, 1, 1, 2, 3, 3, 3
[2, 1, 2, 1, 1, 3, 1, 1, 1] => 2, 1, 2, 1, 1, 3, 1, 1, 1
[2, 1, 2, 1, 1, 3, 1, 1, 2] => 2, 1, 2, 1, 1, 3, 1, 1, 2
[2, 1, 2, 1, 1, 3, 1, 1, 3] => 2, 1, 2, 1, 1, 3, 1, 1, 3
[2, 1, 2, 1, 1, 3, 1, 2, 1] => 2, 1, 2, 1, 1, 3, 1, 2, 1
[2, 1, 2, 1, 1, 3, 1, 2, 2] => 2, 1, 2, 1, 1, 3, 1, 2, 2
[2, 1, 2, 1, 1, 3, 1, 2, 3] => 2, 1, 2, 1, 1, 3, 1, 2, 3
[2, 1, 2, 1, 1, 3, 1, 3, 1] => 2, 1, 2, 1, 1, 3, 1, 3, 1
[2, 1, 2, 1, 1, 3, 1, 3, 2] => 2, 1, 2, 1, 1, 3, 1, 3, 2
[2, 1, 2, 1, 1, 3, 1, 3, 3] => 2, 1, 2, 1, 1, 3, 1, 3, 3
[2, 1, 2, 1, 1, 3, 2, 1, 1] => 2, 1, 2, 1, 1, 3, 2, 1, 1
[2, 1, 2, 1, 1, 3, 2, 1, 2] => 2, 1, 2, 1, 1, 3, 2, 1, 2
[2, 1, 2, 1, 1, 3, 2, 1, 3] => 2, 1, 2, 1, 1, 3, 2, 1, 3
[2, 1, 2, 1, 1, 3, 2, 2, 1] => 2, 1, 2, 1, 1, 3, 2, 2, 1
[2, 1, 2, 1, 1, 3, 2, 2, 2] => 2, 1, 2, 1, 1, 3, 2, 2, 2
[2, 1, 2, 1, 1, 3, 2, 2, 3] => 2, 1, 2, 1, 1, 3, 2, 2, 3
[2, 1, 2, 1, 1, 3, 2, 3, 1] => 2, 1, 2, 1, 1, 3, 2, 3, 1
[2, 1, 2, 1, 1, 3, 2, 3, 2] => 2, 1, 2, 1, 1, 3, 2, 3, 2
[2, 1, 2, 1, 1, 3, 2, 3, 3] => 2, 1, 2, 1, 1, 3, 2, 3, 3
[2, 1, 2, 1, 1, 3, 3, 1, 1] => 2, 1, 2, 1, 1, 3, 3, 1, 1
[2, 1, 2, 1, 1, 3, 3, 1, 2] => 2, 1, 2, 1, 1, 3, 3, 1, 2
[2, 1, 2, 1, 1, 3, 3, 1, 3] => 2, 1, 2, 1, 1, 3, 3, 1, 3
[2, 1, 2, 1, 1, 3, 3, 2, 1] => 2, 1, 2, 1, 1, 3, 3, 2, 1
[2, 1, 2, 1, 1, 3, 3, 2, 2] => 2, 1, 2, 1, 1, 3, 3, 2, 2
[2, 1, 2, 1, 1, 3, 3, 2, 3] => 2, 1, 2, 1, 1, 3, 3, 2, 3
[2, 1, 2, 1, 1, 3, 3, 3, 1] => 2, 1, 2, 1, 1, 3, 3, 3, 1
[2, 1, 2, 1, 1, 3, 3, 3, 2] => 2, 1, 2, 1, 1, 3, 3, 3, 2
[2, 1, 2, 1, 1, 3, 3, 3, 3] => 2, 1, 2, 1, 1, 3, 3, 3, 3
[2, 1, 2, 1, 2, 1, 1, 1, 1] => 2, 1, 2, 1, 2, 1, 1, 1, 1
[2, 1, 2, 1, 2, 1, 1, 1, 2] => 2, 1, 2, 1, 2, 1, 1, 1, 2
[2, 1, 2, 1, 2, 1, 1, 1, 3] => 2, 1, 2, 1, 2, 1, 1, 1, 3
[2, 1, 2, 1, 2, 1, 1, 2, 1] => 2, 1, 2, 1, 2, 1, 1, 2, 1
[2, 1, 2, 1, 2, 1, 1, 2, 2] => 2, 1, 2, 1, 2, 1, 1, 2, 2
[2, 1, 2, 1, 2, 1, 1, 2, 3] => 2, 1, 2, 1, 2, 1, 1, 2, 3
[2, 1, 2, 1, 2, 1, 1, 3, 1] => 2, 1, 2, 1, 2, 1, 1, 3, 1
[2, 1, 2, 1, 2, 1, 1, 3, 2] => 2, 1, 2, 1, 2, 1, 1, 3, 2
[2, 1, 2, 1, 2, 1, 1, 3, 3] => 2, 1, 2, 1, 2, 1, 1, 3, 3
[2, 1, 2, 1, 2, 1, 2, 1, 1] => 2, 1, 2, 1, 2, 1, 2, 1, 1
[2, 1, 2, 1, 2, 1, 2, 1, 2] => 2, 1, 2, 1, 2, 1, 2, 1, 2
[2, 1, 2, 1, 2, 1, 2, 1, 3] => 2, 1, 2, 1, 2, 1, 2, 1, 3
[2, 1, 2, 1, 2, 1, 2, 2, 1] => 2, 1, 2, 1, 2, 1, 2, 2, 1
[2, 1, 2, 1, 2, 1, 2, 2, 2] => 2, 1, 2, 1, 2, 1, 2, 2, 2
[2, 1, 2, 1, 2, 1, 2, 2, 3] => 2, 1, 2, 1, 2, 1, 2, 2, 3
[2, 1, 2, 1, 2, 1, 2, 3, 1] => 2, 1, 2, 1, 2, 1, 2, 3, 1
[2, 1, 2, 1, 2, 1, 2, 3, 2] => 2, 1, 2, 1, 2, 1, 2, 3, 2
[2, 1, 2, 1, 2, 1, 2, 3, 3] => 2, 1, 2, 1, 2, 1, 2, 3, 3
[2, 1, 2, 1, 2, 1, 3, 1, 1] => 2, 1, 2, 1, 2, 1, 3, 1, 1
[2, 1, 2, 1, 2, 1, 3, 1, 2] => 2, 1, 2, 1, 2, 1, 3, 1, 2
[2, 1, 2, 1, 2, 1, 3, 1, 3] => 2, 1, 2, 1, 2, 1, 3, 1, 3
[2, 1, 2, 1, 2, 1, 3, 2, 1] => 2, 1, 2, 1, 2, 1, 3, 2, 1
[2, 1, 2, 1, 2, 1, 3, 2, 2] => 2, 1, 2, 1, 2, 1, 3, 2, 2
[2, 1, 2, 1, 2, 1, 3, 2, 3] => 2, 1, 2, 1, 2, 1, 3, 2, 3
[2, 1, 2, 1, 2, 1, 3, 3, 1] => 2, 1, 2, 1, 2, 1, 3, 3, 1
[2, 1, 2, 1, 2, 1, 3, 3, 2] => 2, 1, 2, 1, 2, 1, 3, 3, 2
[2, 1, 2, 1, 2, 1, 3, 3, 3] => 2, 1, 2, 1, 2, 1, 3, 3, 3
[2, 1, 2, 1, 2, 2, 1, 1, 1] => 2, 1, 2, 1, 2, 2, 1, 1, 1
[2, 1, 2, 1, 2, 2, 1, 1, 2] => 2, 1, 2, 1, 2, 2, 1, 1, 2
[2, 1, 2, 1, 2, 2, 1, 1, 3] => 2, 1, 2, 1, 2, 2, 1, 1, 3
[2, 1, 2, 1, 2, 2, 1, 2, 1] => 2, 1, 2, 1, 2, 2, 1, 2, 1
[2, 1, 2, 1, 2, 2, 1, 2, 2] => 2, 1, 2, 1, 2, 2, 1, 2, 2
[2, 1, 2, 1, 2, 2, 1, 2, 3] => 2, 1, 2, 1, 2, 2, 1, 2, 3
[2, 1, 2, 1, 2, 2, 1, 3, 1] => 2, 1, 2, 1, 2, 2, 1, 3, 1
[2, 1, 2, 1, 2, 2, 1, 3, 2] => 2, 1, 2, 1, 2, 2, 1, 3, 2
[2, 1, 2, 1, 2, 2, 1, 3, 3] => 2, 1, 2, 1, 2, 2, 1, 3, 3
[2, 1, 2, 1, 2, 2, 2, 1, 1] => 2, 1, 2, 1, 2, 2, 2, 1, 1
[2, 1, 2, 1, 2, 2, 2, 1, 2] => 2, 1, 2, 1, 2, 2, 2, 1, 2
[2, 1, 2, 1, 2, 2, 2, 1, 3] => 2, 1, 2, 1, 2, 2, 2, 1, 3
[2, 1, 2, 1, 2, 2, 2, 2, 1] => 2, 1, 2, 1, 2, 2, 2, 2, 1
[2, 1, 2, 1, 2, 2, 2, 2, 2] => 2, 1, 2, 1, 2, 2, 2, 2, 2
[2, 1, 2, 1, 2, 2, 2, 2, 3] => 2, 1, 2, 1, 2, 2, 2, 2, 3
[2, 1, 2, 1, 2, 2, 2, 3, 1] => 2, 1, 2, 1, 2, 2, 2, 3, 1
[2, 1, 2, 1, 2, 2, 2, 3, 2] => 2, 1, 2, 1, 2, 2, 2, 3, 2
[2, 1, 2, 1, 2, 2, 2, 3, 3] => 2, 1, 2, 1, 2, 2, 2, 3, 3
[2, 1, 2, 1, 2, 2, 3, 1, 1] => 2, 1, 2, 1, 2, 2, 3, 1, 1
[2, 1, 2, 1, 2, 2, 3, 1, 2] => 2, 1, 2, 1, 2, 2, 3, 1, 2
[2, 1, 2, 1, 2, 2, 3, 1, 3] => 2, 1, 2, 1, 2, 2, 3, 1, 3
[2, 1, 2, 1, 2, 2, 3, 2, 1] => 2, 1, 2, 1, 2, 2, 3, 2, 1
[2, 1, 2, 1, 2, 2, 3, 2, 2] => 2, 1, 2, 1, 2, 2, 3, 2, 2
[2, 1, 2, 1, 2, 2, 3, 2, 3] => 2, 1, 2, 1, 2, 2, 3, 2, 3
[2, 1, 2, 1, 2, 2, 3, 3, 1] => 2, 1, 2, 1, 2, 2, 3, 3, 1
[2, 1, 2, 1, 2, 2, 3, 3, 2] => 2, 1, 2, 1, 2, 2, 3, 3, 2
[2, 1, 2, 1, 2, 2, 3, 3, 3] => 2, 1, 2, 1, 2, 2, 3, 3, 3
[2, 1, 2, 1, 2, 3, 1, 1, 1] => 2, 1, 2, 1, 2, 3, 1, 1, 1
[2, 1, 2, 1, 2, 3, 1, 1, 2] => 2, 1, 2, 1, 2, 3, 1, 1, 2
[2, 1, 2, 1, 2, 3, 1, 1, 3] => 2, 1, 2, 1, 2, 3, 1, 1, 3
[2, 1, 2, 1, 2, 3, 1, 2, 1] => 2, 1, 2, 1, 2, 3, 1, 2, 1
[2, 1, 2, 1, 2, 3, 1, 2, 2] => 2, 1, 2, 1, 2, 3, 1, 2, 2
[2, 1, 2, 1, 2, 3, 1, 2, 3] => 2, 1, 2, 1, 2, 3, 1, 2, 3
[2, 1, 2, 1, 2, 3, 1, 3, 1] => 2, 1, 2, 1, 2, 3, 1, 3, 1
[2, 1, 2, 1, 2, 3, 1, 3, 2] => 2, 1, 2, 1, 2, 3, 1, 3, 2
[2, 1, 2, 1, 2, 3, 1, 3, 3] => 2, 1, 2, 1, 2, 3, 1, 3, 3
[2, 1, 2, 1, 2, 3, 2, 1, 1] => 2, 1, 2, 1, 2, 3, 2, 1, 1
[2, 1, 2, 1, 2, 3, 2, 1, 2] => 2, 1, 2, 1, 2, 3, 2, 1, 2
[2, 1, 2, 1, 2, 3, 2, 1, 3] => 2, 1, 2, 1, 2, 3, 2, 1, 3
[2, 1, 2, 1, 2, 3, 2, 2, 1] => 2, 1, 2, 1, 2, 3, 2, 2, 1
[2, 1, 2, 1, 2, 3, 2, 2, 2] => 2, 1, 2, 1, 2, 3, 2, 2, 2
[2, 1, 2, 1, 2, 3, 2, 2, 3] => 2, 1, 2, 1, 2, 3, 2, 2, 3
[2, 1, 2, 1, 2, 3, 2, 3, 1] => 2, 1, 2, 1, 2, 3, 2, 3, 1
[2, 1, 2, 1, 2, 3, 2, 3, 2] => 2, 1, 2, 1, 2, 3, 2, 3, 2
[2, 1, 2, 1, 2, 3, 2, 3, 3] => 2, 1, 2, 1, 2, 3, 2, 3, 3
[2, 1, 2, 1, 2, 3, 3, 1, 1] => 2, 1, 2, 1, 2, 3, 3, 1, 1
[2, 1, 2, 1, 2, 3, 3, 1, 2] => 2, 1, 2, 1, 2, 3, 3, 1, 2
[2, 1, 2, 1, 2, 3, 3, 1, 3] => 2, 1, 2, 1, 2, 3, 3, 1, 3
[2, 1, 2, 1, 2, 3, 3, 2, 1] => 2, 1, 2, 1, 2, 3, 3, 2, 1
[2, 1, 2, 1, 2, 3, 3, 2, 2] => 2, 1, 2, 1, 2, 3, 3, 2, 2
[2, 1, 2, 1, 2, 3, 3, 2, 3] => 2, 1, 2, 1, 2, 3, 3, 2, 3
[2, 1, 2, 1, 2, 3, 3, 3, 1] => 2, 1, 2, 1, 2, 3, 3, 3, 1
[2, 1, 2, 1, 2, 3, 3, 3, 2] => 2, 1, 2, 1, 2, 3, 3, 3, 2
[2, 1, 2, 1, 2, 3, 3, 3, 3] => 2, 1, 2, 1, 2, 3, 3, 3, 3
[2, 1, 2, 1, 3, 1, 1, 1, 1] => 2, 1, 2, 1, 3, 1, 1, 1, 1
[2, 1, 2, 1, 3, 1, 1, 1, 2] => 2, 1, 2, 1, 3, 1, 1, 1, 2
[2, 1, 2, 1, 3, 1, 1, 1, 3] => 2, 1, 2, 1, 3, 1, 1, 1, 3
[2, 1, 2, 1, 3, 1, 1, 2, 1] => 2, 1, 2, 1, 3, 1, 1, 2, 1
[2, 1, 2, 1, 3, 1, 1, 2, 2] => 2, 1, 2, 1, 3, 1, 1, 2, 2
[2, 1, 2, 1, 3, 1, 1, 2, 3] => 2, 1, 2, 1, 3, 1, 1, 2, 3
[2, 1, 2, 1, 3, 1, 1, 3, 1] => 2, 1, 2, 1, 3, 1, 1, 3, 1
[2, 1, 2, 1, 3, 1, 1, 3, 2] => 2, 1, 2, 1, 3, 1, 1, 3, 2
[2, 1, 2, 1, 3, 1, 1, 3, 3] => 2, 1, 2, 1, 3, 1, 1, 3, 3
[2, 1, 2, 1, 3, 1, 2, 1, 1] => 2, 1, 2, 1, 3, 1, 2, 1, 1
[2, 1, 2, 1, 3, 1, 2, 1, 2] => 2, 1, 2, 1, 3, 1, 2, 1, 2
[2, 1, 2, 1, 3, 1, 2, 1, 3] => 2, 1, 2, 1, 3, 1, 2, 1, 3
[2, 1, 2, 1, 3, 1, 2, 2, 1] => 2, 1, 2, 1, 3, 1, 2, 2, 1
[2, 1, 2, 1, 3, 1, 2, 2, 2] => 2, 1, 2, 1, 3, 1, 2, 2, 2
[2, 1, 2, 1, 3, 1, 2, 2, 3] => 2, 1, 2, 1, 3, 1, 2, 2, 3
[2, 1, 2, 1, 3, 1, 2, 3, 1] => 2, 1, 2, 1, 3, 1, 2, 3, 1
[2, 1, 2, 1, 3, 1, 2, 3, 2] => 2, 1, 2, 1, 3, 1, 2, 3, 2
[2, 1, 2, 1, 3, 1, 2, 3, 3] => 2, 1, 2, 1, 3, 1, 2, 3, 3
[2, 1, 2, 1, 3, 1, 3, 1, 1] => 2, 1, 2, 1, 3, 1, 3, 1, 1
[2, 1, 2, 1, 3, 1, 3, 1, 2] => 2, 1, 2, 1, 3, 1, 3, 1, 2
[2, 1, 2, 1, 3, 1, 3, 1, 3] => 2, 1, 2, 1, 3, 1, 3, 1, 3
[2, 1, 2, 1, 3, 1, 3, 2, 1] => 2, 1, 2, 1, 3, 1, 3, 2, 1
[2, 1, 2, 1, 3, 1, 3, 2, 2] => 2, 1, 2, 1, 3, 1, 3, 2, 2
[2, 1, 2, 1, 3, 1, 3, 2, 3] => 2, 1, 2, 1, 3, 1, 3, 2, 3
[2, 1, 2, 1, 3, 1, 3, 3, 1] => 2, 1, 2, 1, 3, 1, 3, 3, 1
[2, 1, 2, 1, 3, 1, 3, 3, 2] => 2, 1, 2, 1, 3, 1, 3, 3, 2
[2, 1, 2, 1, 3, 1, 3, 3, 3] => 2, 1, 2, 1, 3, 1, 3, 3, 3
[2, 1, 2, 1, 3, 2, 1, 1, 1] => 2, 1, 2, 1, 3, 2, 1, 1, 1
[2, 1, 2, 1, 3, 2, 1, 1, 2] => 2, 1, 2, 1, 3, 2, 1, 1, 2
[2, 1, 2, 1, 3, 2, 1, 1, 3] => 2, 1, 2, 1, 3, 2, 1, 1, 3
[2, 1, 2, 1, 3, 2, 1, 2, 1] => 2, 1, 2, 1, 3, 2, 1, 2, 1
[2, 1, 2, 1, 3, 2, 1, 2, 2] => 2, 1, 2, 1, 3, 2, 1, 2, 2
[2, 1, 2, 1, 3, 2, 1, 2, 3] => 2, 1, 2, 1, 3, 2, 1, 2, 3
[2, 1, 2, 1, 3, 2, 1, 3, 1] => 2, 1, 2, 1, 3, 2, 1, 3, 1
[2, 1, 2, 1, 3, 2, 1, 3, 2] => 2, 1, 2, 1, 3, 2, 1, 3, 2
[2, 1, 2, 1, 3, 2, 1, 3, 3] => 2, 1, 2, 1, 3, 2, 1, 3, 3
[2, 1, 2, 1, 3, 2, 2, 1, 1] => 2, 1, 2, 1, 3, 2, 2, 1, 1
[2, 1, 2, 1, 3, 2, 2, 1, 2] => 2, 1, 2, 1, 3, 2, 2, 1, 2
[2, 1, 2, 1, 3, 2, 2, 1, 3] => 2, 1, 2, 1, 3, 2, 2, 1, 3
[2, 1, 2, 1, 3, 2, 2, 2, 1] => 2, 1, 2, 1, 3, 2, 2, 2, 1
[2, 1, 2, 1, 3, 2, 2, 2, 2] => 2, 1, 2, 1, 3, 2, 2, 2, 2
[2, 1, 2, 1, 3, 2, 2, 2, 3] => 2, 1, 2, 1, 3, 2, 2, 2, 3
[2, 1, 2, 1, 3, 2, 2, 3, 1] => 2, 1, 2, 1, 3, 2, 2, 3, 1
[2, 1, 2, 1, 3, 2, 2, 3, 2] => 2, 1, 2, 1, 3, 2, 2, 3, 2
[2, 1, 2, 1, 3, 2, 2, 3, 3] => 2, 1, 2, 1, 3, 2, 2, 3, 3
[2, 1, 2, 1, 3, 2, 3, 1, 1] => 2, 1, 2, 1, 3, 2, 3, 1, 1
[2, 1, 2, 1, 3, 2, 3, 1, 2] => 2, 1, 2, 1, 3, 2, 3, 1, 2
[2, 1, 2, 1, 3, 2, 3, 1, 3] => 2, 1, 2, 1, 3, 2, 3, 1, 3
[2, 1, 2, 1, 3, 2, 3, 2, 1] => 2, 1, 2, 1, 3, 2, 3, 2, 1
[2, 1, 2, 1, 3, 2, 3, 2, 2] => 2, 1, 2, 1, 3, 2, 3, 2, 2
[2, 1, 2, 1, 3, 2, 3, 2, 3] => 2, 1, 2, 1, 3, 2, 3, 2, 3
[2, 1, 2, 1, 3, 2, 3, 3, 1] => 2, 1, 2, 1, 3, 2, 3, 3, 1
[2, 1, 2, 1, 3, 2, 3, 3, 2] => 2, 1, 2, 1, 3, 2, 3, 3, 2
[2, 1, 2, 1, 3, 2, 3, 3, 3] => 2, 1, 2, 1, 3, 2, 3, 3, 3
[2, 1, 2, 1, 3, 3, 1, 1, 1] => 2, 1, 2, 1, 3, 3, 1, 1, 1
[2, 1, 2, 1, 3, 3, 1, 1, 2] => 2, 1, 2, 1, 3, 3, 1, 1, 2
[2, 1, 2, 1, 3, 3, 1, 1, 3] => 2, 1, 2, 1, 3, 3, 1, 1, 3
[2, 1, 2, 1, 3, 3, 1, 2, 1] => 2, 1, 2, 1, 3, 3, 1, 2, 1
[2, 1, 2, 1, 3, 3, 1, 2, 2] => 2, 1, 2, 1, 3, 3, 1, 2, 2
[2, 1, 2, 1, 3, 3, 1, 2, 3] => 2, 1, 2, 1, 3, 3, 1, 2, 3
[2, 1, 2, 1, 3, 3, 1, 3, 1] => 2, 1, 2, 1, 3, 3, 1, 3, 1
[2, 1, 2, 1, 3, 3, 1, 3, 2] => 2, 1, 2, 1, 3, 3, 1, 3, 2
[2, 1, 2, 1, 3, 3, 1, 3, 3] => 2, 1, 2, 1, 3, 3, 1, 3, 3
[2, 1, 2, 1, 3, 3, 2, 1, 1] => 2, 1, 2, 1, 3, 3, 2, 1, 1
[2, 1, 2, 1, 3, 3, 2, 1, 2] => 2, 1, 2, 1, 3, 3, 2, 1, 2
[2, 1, 2, 1, 3, 3, 2, 1, 3] => 2, 1, 2, 1, 3, 3, 2, 1, 3
[2, 1, 2, 1, 3, 3, 2, 2, 1] => 2, 1, 2, 1, 3, 3, 2, 2, 1
[2, 1, 2, 1, 3, 3, 2, 2, 2] => 2, 1, 2, 1, 3, 3, 2, 2, 2
[2, 1, 2, 1, 3, 3, 2, 2, 3] => 2, 1, 2, 1, 3, 3, 2, 2, 3
[2, 1, 2, 1, 3, 3, 2, 3, 1] => 2, 1, 2, 1, 3, 3, 2, 3, 1
[2, 1, 2, 1, 3, 3, 2, 3, 2] => 2, 1, 2, 1, 3, 3, 2, 3, 2
[2, 1, 2, 1, 3, 3, 2, 3, 3] => 2, 1, 2, 1, 3, 3, 2, 3, 3
[2, 1, 2, 1, 3, 3, 3, 1, 1] => 2, 1, 2, 1, 3, 3, 3, 1, 1
[2, 1, 2, 1, 3, 3, 3, 1, 2] => 2, 1, 2, 1, 3, 3, 3, 1, 2
[2, 1, 2, 1, 3, 3, 3, 1, 3] => 2, 1, 2, 1, 3, 3, 3, 1, 3
[2, 1, 2, 1, 3, 3, 3, 2, 1] => 2, 1, 2, 1, 3, 3, 3, 2, 1
[2, 1, 2, 1, 3, 3, 3, 2, 2] => 2, 1, 2, 1, 3, 3, 3, 2, 2
[2, 1, 2, 1, 3, 3, 3, 2, 3] => 2, 1, 2, 1, 3, 3, 3, 2, 3
[2, 1, 2, 1, 3, 3, 3, 3, 1] => 2, 1, 2, 1, 3, 3, 3, 3, 1
[2, 1, 2, 1, 3, 3, 3, 3, 2] => 2, 1, 2, 1, 3, 3, 3, 3, 2
[2, 1, 2, 1, 3, 3, 3, 3, 3] => 2, 1, 2, 1, 3, 3, 3, 3, 3
[2, 1, 2, 2, 1, 1, 1, 1, 1] => 2, 1, 2, 2, 1, 1, 1, 1, 1
[2, 1, 2, 2, 1, 1, 1, 1, 2] => 2, 1, 2, 2, 1, 1, 1, 1, 2
[2, 1, 2, 2, 1, 1, 1, 1, 3] => 2, 1, 2, 2, 1, 1, 1, 1, 3
[2, 1, 2, 2, 1, 1, 1, 2, 1] => 2, 1, 2, 2, 1, 1, 1, 2, 1
[2, 1, 2, 2, 1, 1, 1, 2, 2] => 2, 1, 2, 2, 1, 1, 1, 2, 2
[2, 1, 2, 2, 1, 1, 1, 2, 3] => 2, 1, 2, 2, 1, 1, 1, 2, 3
[2, 1, 2, 2, 1, 1, 1, 3, 1] => 2, 1, 2, 2, 1, 1, 1, 3, 1
[2, 1, 2, 2, 1, 1, 1, 3, 2] => 2, 1, 2, 2, 1, 1, 1, 3, 2
[2, 1, 2, 2, 1, 1, 1, 3, 3] => 2, 1, 2, 2, 1, 1, 1, 3, 3
[2, 1, 2, 2, 1, 1, 2, 1, 1] => 2, 1, 2, 2, 1, 1, 2, 1, 1
[2, 1, 2, 2, 1, 1, 2, 1, 2] => 2, 1, 2, 2, 1, 1, 2, 1, 2
[2, 1, 2, 2, 1, 1, 2, 1, 3] => 2, 1, 2, 2, 1, 1, 2, 1, 3
[2, 1, 2, 2, 1, 1, 2, 2, 1] => 2, 1, 2, 2, 1, 1, 2, 2, 1
[2, 1, 2, 2, 1, 1, 2, 2, 2] => 2, 1, 2, 2, 1, 1, 2, 2, 2
[2, 1, 2, 2, 1, 1, 2, 2, 3] => 2, 1, 2, 2, 1, 1, 2, 2, 3
[2, 1, 2, 2, 1, 1, 2, 3, 1] => 2, 1, 2, 2, 1, 1, 2, 3, 1
[2, 1, 2, 2, 1, 1, 2, 3, 2] => 2, 1, 2, 2, 1, 1, 2, 3, 2
[2, 1, 2, 2, 1, 1, 2, 3, 3] => 2, 1, 2, 2, 1, 1, 2, 3, 3
[2, 1, 2, 2, 1, 1, 3, 1, 1] => 2, 1, 2, 2, 1, 1, 3, 1, 1
[2, 1, 2, 2, 1, 1, 3, 1, 2] => 2, 1, 2, 2, 1, 1, 3, 1, 2
[2, 1, 2, 2, 1, 1, 3, 1, 3] => 2, 1, 2, 2, 1, 1, 3, 1, 3
[2, 1, 2, 2, 1, 1, 3, 2, 1] => 2, 1, 2, 2, 1, 1, 3, 2, 1
[2, 1, 2, 2, 1, 1, 3, 2, 2] => 2, 1, 2, 2, 1, 1, 3, 2, 2
[2, 1, 2, 2, 1, 1, 3, 2, 3] => 2, 1, 2, 2, 1, 1, 3, 2, 3
[2, 1, 2, 2, 1, 1, 3, 3, 1] => 2, 1, 2, 2, 1, 1, 3, 3, 1
[2, 1, 2, 2, 1, 1, 3, 3, 2] => 2, 1, 2, 2, 1, 1, 3, 3, 2
[2, 1, 2, 2, 1, 1, 3, 3, 3] => 2, 1, 2, 2, 1, 1, 3, 3, 3
[2, 1, 2, 2, 1, 2, 1, 1, 1] => 2, 1, 2, 2, 1, 2, 1, 1, 1
[2, 1, 2, 2, 1, 2, 1, 1, 2] => 2, 1, 2, 2, 1, 2, 1, 1, 2
[2, 1, 2, 2, 1, 2, 1, 1, 3] => 2, 1, 2, 2, 1, 2, 1, 1, 3
[2, 1, 2, 2, 1, 2, 1, 2, 1] => 2, 1, 2, 2, 1, 2, 1, 2, 1
[2, 1, 2, 2, 1, 2, 1, 2, 2] => 2, 1, 2, 2, 1, 2, 1, 2, 2
[2, 1, 2, 2, 1, 2, 1, 2, 3] => 2, 1, 2, 2, 1, 2, 1, 2, 3
[2, 1, 2, 2, 1, 2, 1, 3, 1] => 2, 1, 2, 2, 1, 2, 1, 3, 1
[2, 1, 2, 2, 1, 2, 1, 3, 2] => 2, 1, 2, 2, 1, 2, 1, 3, 2
[2, 1, 2, 2, 1, 2, 1, 3, 3] => 2, 1, 2, 2, 1, 2, 1, 3, 3
[2, 1, 2, 2, 1, 2, 2, 1, 1] => 2, 1, 2, 2, 1, 2, 2, 1, 1
[2, 1, 2, 2, 1, 2, 2, 1, 2] => 2, 1, 2, 2, 1, 2, 2, 1, 2
[2, 1, 2, 2, 1, 2, 2, 1, 3] => 2, 1, 2, 2, 1, 2, 2, 1, 3
[2, 1, 2, 2, 1, 2, 2, 2, 1] => 2, 1, 2, 2, 1, 2, 2, 2, 1
[2, 1, 2, 2, 1, 2, 2, 2, 2] => 2, 1, 2, 2, 1, 2, 2, 2, 2
[2, 1, 2, 2, 1, 2, 2, 2, 3] => 2, 1, 2, 2, 1, 2, 2, 2, 3
[2, 1, 2, 2, 1, 2, 2, 3, 1] => 2, 1, 2, 2, 1, 2, 2, 3, 1
[2, 1, 2, 2, 1, 2, 2, 3, 2] => 2, 1, 2, 2, 1, 2, 2, 3, 2
[2, 1, 2, 2, 1, 2, 2, 3, 3] => 2, 1, 2, 2, 1, 2, 2, 3, 3
[2, 1, 2, 2, 1, 2, 3, 1, 1] => 2, 1, 2, 2, 1, 2, 3, 1, 1
[2, 1, 2, 2, 1, 2, 3, 1, 2] => 2, 1, 2, 2, 1, 2, 3, 1, 2
[2, 1, 2, 2, 1, 2, 3, 1, 3] => 2, 1, 2, 2, 1, 2, 3, 1, 3
[2, 1, 2, 2, 1, 2, 3, 2, 1] => 2, 1, 2, 2, 1, 2, 3, 2, 1
[2, 1, 2, 2, 1, 2, 3, 2, 2] => 2, 1, 2, 2, 1, 2, 3, 2, 2
[2, 1, 2, 2, 1, 2, 3, 2, 3] => 2, 1, 2, 2, 1, 2, 3, 2, 3
[2, 1, 2, 2, 1, 2, 3, 3, 1] => 2, 1, 2, 2, 1, 2, 3, 3, 1
[2, 1, 2, 2, 1, 2, 3, 3, 2] => 2, 1, 2, 2, 1, 2, 3, 3, 2
[2, 1, 2, 2, 1, 2, 3, 3, 3] => 2, 1, 2, 2, 1, 2, 3, 3, 3
[2, 1, 2, 2, 1, 3, 1, 1, 1] => 2, 1, 2, 2, 1, 3, 1, 1, 1
[2, 1, 2, 2, 1, 3, 1, 1, 2] => 2, 1, 2, 2, 1, 3, 1, 1, 2
[2, 1, 2, 2, 1, 3, 1, 1, 3] => 2, 1, 2, 2, 1, 3, 1, 1, 3
[2, 1, 2, 2, 1, 3, 1, 2, 1] => 2, 1, 2, 2, 1, 3, 1, 2, 1
[2, 1, 2, 2, 1, 3, 1, 2, 2] => 2, 1, 2, 2, 1, 3, 1, 2, 2
[2, 1, 2, 2, 1, 3, 1, 2, 3] => 2, 1, 2, 2, 1, 3, 1, 2, 3
[2, 1, 2, 2, 1, 3, 1, 3, 1] => 2, 1, 2, 2, 1, 3, 1, 3, 1
[2, 1, 2, 2, 1, 3, 1, 3, 2] => 2, 1, 2, 2, 1, 3, 1, 3, 2
[2, 1, 2, 2, 1, 3, 1, 3, 3] => 2, 1, 2, 2, 1, 3, 1, 3, 3
[2, 1, 2, 2, 1, 3, 2, 1, 1] => 2, 1, 2, 2, 1, 3, 2, 1, 1
[2, 1, 2, 2, 1, 3, 2, 1, 2] => 2, 1, 2, 2, 1, 3, 2, 1, 2
[2, 1, 2, 2, 1, 3, 2, 1, 3] => 2, 1, 2, 2, 1, 3, 2, 1, 3
[2, 1, 2, 2, 1, 3, 2, 2, 1] => 2, 1, 2, 2, 1, 3, 2, 2, 1
[2, 1, 2, 2, 1, 3, 2, 2, 2] => 2, 1, 2, 2, 1, 3, 2, 2, 2
[2, 1, 2, 2, 1, 3, 2, 2, 3] => 2, 1, 2, 2, 1, 3, 2, 2, 3
[2, 1, 2, 2, 1, 3, 2, 3, 1] => 2, 1, 2, 2, 1, 3, 2, 3, 1
[2, 1, 2, 2, 1, 3, 2, 3, 2] => 2, 1, 2, 2, 1, 3, 2, 3, 2
[2, 1, 2, 2, 1, 3, 2, 3, 3] => 2, 1, 2, 2, 1, 3, 2, 3, 3
[2, 1, 2, 2, 1, 3, 3, 1, 1] => 2, 1, 2, 2, 1, 3, 3, 1, 1
[2, 1, 2, 2, 1, 3, 3, 1, 2] => 2, 1, 2, 2, 1, 3, 3, 1, 2
[2, 1, 2, 2, 1, 3, 3, 1, 3] => 2, 1, 2, 2, 1, 3, 3, 1, 3
[2, 1, 2, 2, 1, 3, 3, 2, 1] => 2, 1, 2, 2, 1, 3, 3, 2, 1
[2, 1, 2, 2, 1, 3, 3, 2, 2] => 2, 1, 2, 2, 1, 3, 3, 2, 2
[2, 1, 2, 2, 1, 3, 3, 2, 3] => 2, 1, 2, 2, 1, 3, 3, 2, 3
[2, 1, 2, 2, 1, 3, 3, 3, 1] => 2, 1, 2, 2, 1, 3, 3, 3, 1
[2, 1, 2, 2, 1, 3, 3, 3, 2] => 2, 1, 2, 2, 1, 3, 3, 3, 2
[2, 1, 2, 2, 1, 3, 3, 3, 3] => 2, 1, 2, 2, 1, 3, 3, 3, 3
[2, 1, 2, 2, 2, 1, 1, 1, 1] => 2, 1, 2, 2, 2, 1, 1, 1, 1
[2, 1, 2, 2, 2, 1, 1, 1, 2] => 2, 1, 2, 2, 2, 1, 1, 1, 2
[2, 1, 2, 2, 2, 1, 1, 1, 3] => 2, 1, 2, 2, 2, 1, 1, 1, 3
[2, 1, 2, 2, 2, 1, 1, 2, 1] => 2, 1, 2, 2, 2, 1, 1, 2, 1
[2, 1, 2, 2, 2, 1, 1, 2, 2] => 2, 1, 2, 2, 2, 1, 1, 2, 2
[2, 1, 2, 2, 2, 1, 1, 2, 3] => 2, 1, 2, 2, 2, 1, 1, 2, 3
[2, 1, 2, 2, 2, 1, 1, 3, 1] => 2, 1, 2, 2, 2, 1, 1, 3, 1
[2, 1, 2, 2, 2, 1, 1, 3, 2] => 2, 1, 2, 2, 2, 1, 1, 3, 2
[2, 1, 2, 2, 2, 1, 1, 3, 3] => 2, 1, 2, 2, 2, 1, 1, 3, 3
[2, 1, 2, 2, 2, 1, 2, 1, 1] => 2, 1, 2, 2, 2, 1, 2, 1, 1
[2, 1, 2, 2, 2, 1, 2, 1, 2] => 2, 1, 2, 2, 2, 1, 2, 1, 2
[2, 1, 2, 2, 2, 1, 2, 1, 3] => 2, 1, 2, 2, 2, 1, 2, 1, 3
[2, 1, 2, 2, 2, 1, 2, 2, 1] => 2, 1, 2, 2, 2, 1, 2, 2, 1
[2, 1, 2, 2, 2, 1, 2, 2, 2] => 2, 1, 2, 2, 2, 1, 2, 2, 2
[2, 1, 2, 2, 2, 1, 2, 2, 3] => 2, 1, 2, 2, 2, 1, 2, 2, 3
[2, 1, 2, 2, 2, 1, 2, 3, 1] => 2, 1, 2, 2, 2, 1, 2, 3, 1
[2, 1, 2, 2, 2, 1, 2, 3, 2] => 2, 1, 2, 2, 2, 1, 2, 3, 2
[2, 1, 2, 2, 2, 1, 2, 3, 3] => 2, 1, 2, 2, 2, 1, 2, 3, 3
[2, 1, 2, 2, 2, 1, 3, 1, 1] => 2, 1, 2, 2, 2, 1, 3, 1, 1
[2, 1, 2, 2, 2, 1, 3, 1, 2] => 2, 1, 2, 2, 2, 1, 3, 1, 2
[2, 1, 2, 2, 2, 1, 3, 1, 3] => 2, 1, 2, 2, 2, 1, 3, 1, 3
[2, 1, 2, 2, 2, 1, 3, 2, 1] => 2, 1, 2, 2, 2, 1, 3, 2, 1
[2, 1, 2, 2, 2, 1, 3, 2, 2] => 2, 1, 2, 2, 2, 1, 3, 2, 2
[2, 1, 2, 2, 2, 1, 3, 2, 3] => 2, 1, 2, 2, 2, 1, 3, 2, 3
[2, 1, 2, 2, 2, 1, 3, 3, 1] => 2, 1, 2, 2, 2, 1, 3, 3, 1
[2, 1, 2, 2, 2, 1, 3, 3, 2] => 2, 1, 2, 2, 2, 1, 3, 3, 2
[2, 1, 2, 2, 2, 1, 3, 3, 3] => 2, 1, 2, 2, 2, 1, 3, 3, 3
[2, 1, 2, 2, 2, 2, 1, 1, 1] => 2, 1, 2, 2, 2, 2, 1, 1, 1
[2, 1, 2, 2, 2, 2, 1, 1, 2] => 2, 1, 2, 2, 2, 2, 1, 1, 2
[2, 1, 2, 2, 2, 2, 1, 1, 3] => 2, 1, 2, 2, 2, 2, 1, 1, 3
[2, 1, 2, 2, 2, 2, 1, 2, 1] => 2, 1, 2, 2, 2, 2, 1, 2, 1
[2, 1, 2, 2, 2, 2, 1, 2, 2] => 2, 1, 2, 2, 2, 2, 1, 2, 2
[2, 1, 2, 2, 2, 2, 1, 2, 3] => 2, 1, 2, 2, 2, 2, 1, 2, 3
[2, 1, 2, 2, 2, 2, 1, 3, 1] => 2, 1, 2, 2, 2, 2, 1, 3, 1
[2, 1, 2, 2, 2, 2, 1, 3, 2] => 2, 1, 2, 2, 2, 2, 1, 3, 2
[2, 1, 2, 2, 2, 2, 1, 3, 3] => 2, 1, 2, 2, 2, 2, 1, 3, 3
[2, 1, 2, 2, 2, 2, 2, 1, 1] => 2, 1, 2, 2, 2, 2, 2, 1, 1
[2, 1, 2, 2, 2, 2, 2, 1, 2] => 2, 1, 2, 2, 2, 2, 2, 1, 2
[2, 1, 2, 2, 2, 2, 2, 1, 3] => 2, 1, 2, 2, 2, 2, 2, 1, 3
[2, 1, 2, 2, 2, 2, 2, 2, 1] => 2, 1, 2, 2, 2, 2, 2, 2, 1
[2, 1, 2, 2, 2, 2, 2, 2, 2] => 2, 1, 2, 2, 2, 2, 2, 2, 2
[2, 1, 2, 2, 2, 2, 2, 2, 3] => 2, 1, 2, 2, 2, 2, 2, 2, 3
[2, 1, 2, 2, 2, 2, 2, 3, 1] => 2, 1, 2, 2, 2, 2, 2, 3, 1
[2, 1, 2, 2, 2, 2, 2, 3, 2] => 2, 1, 2, 2, 2, 2, 2, 3, 2
[2, 1, 2, 2, 2, 2, 2, 3, 3] => 2, 1, 2, 2, 2, 2, 2, 3, 3
[2, 1, 2, 2, 2, 2, 3, 1, 1] => 2, 1, 2, 2, 2, 2, 3, 1, 1
[2, 1, 2, 2, 2, 2, 3, 1, 2] => 2, 1, 2, 2, 2, 2, 3, 1, 2
[2, 1, 2, 2, 2, 2, 3, 1, 3] => 2, 1, 2, 2, 2, 2, 3, 1, 3
[2, 1, 2, 2, 2, 2, 3, 2, 1] => 2, 1, 2, 2, 2, 2, 3, 2, 1
[2, 1, 2, 2, 2, 2, 3, 2, 2] => 2, 1, 2, 2, 2, 2, 3, 2, 2
[2, 1, 2, 2, 2, 2, 3, 2, 3] => 2, 1, 2, 2, 2, 2, 3, 2, 3
[2, 1, 2, 2, 2, 2, 3, 3, 1] => 2, 1, 2, 2, 2, 2, 3, 3, 1
[2, 1, 2, 2, 2, 2, 3, 3, 2] => 2, 1, 2, 2, 2, 2, 3, 3, 2
[2, 1, 2, 2, 2, 2, 3, 3, 3] => 2, 1, 2, 2, 2, 2, 3, 3, 3
[2, 1, 2, 2, 2, 3, 1, 1, 1] => 2, 1, 2, 2, 2, 3, 1, 1, 1
[2, 1, 2, 2, 2, 3, 1, 1, 2] => 2, 1, 2, 2, 2, 3, 1, 1, 2
[2, 1, 2, 2, 2, 3, 1, 1, 3] => 2, 1, 2, 2, 2, 3, 1, 1, 3
[2, 1, 2, 2, 2, 3, 1, 2, 1] => 2, 1, 2, 2, 2, 3, 1, 2, 1
[2, 1, 2, 2, 2, 3, 1, 2, 2] => 2, 1, 2, 2, 2, 3, 1, 2, 2
[2, 1, 2, 2, 2, 3, 1, 2, 3] => 2, 1, 2, 2, 2, 3, 1, 2, 3
[2, 1, 2, 2, 2, 3, 1, 3, 1] => 2, 1, 2, 2, 2, 3, 1, 3, 1
[2, 1, 2, 2, 2, 3, 1, 3, 2] => 2, 1, 2, 2, 2, 3, 1, 3, 2
[2, 1, 2, 2, 2, 3, 1, 3, 3] => 2, 1, 2, 2, 2, 3, 1, 3, 3
[2, 1, 2, 2, 2, 3, 2, 1, 1] => 2, 1, 2, 2, 2, 3, 2, 1, 1
[2, 1, 2, 2, 2, 3, 2, 1, 2] => 2, 1, 2, 2, 2, 3, 2, 1, 2
[2, 1, 2, 2, 2, 3, 2, 1, 3] => 2, 1, 2, 2, 2, 3, 2, 1, 3
[2, 1, 2, 2, 2, 3, 2, 2, 1] => 2, 1, 2, 2, 2, 3, 2, 2, 1
[2, 1, 2, 2, 2, 3, 2, 2, 2] => 2, 1, 2, 2, 2, 3, 2, 2, 2
[2, 1, 2, 2, 2, 3, 2, 2, 3] => 2, 1, 2, 2, 2, 3, 2, 2, 3
[2, 1, 2, 2, 2, 3, 2, 3, 1] => 2, 1, 2, 2, 2, 3, 2, 3, 1
[2, 1, 2, 2, 2, 3, 2, 3, 2] => 2, 1, 2, 2, 2, 3, 2, 3, 2
[2, 1, 2, 2, 2, 3, 2, 3, 3] => 2, 1, 2, 2, 2, 3, 2, 3, 3
[2, 1, 2, 2, 2, 3, 3, 1, 1] => 2, 1, 2, 2, 2, 3, 3, 1, 1
[2, 1, 2, 2, 2, 3, 3, 1, 2] => 2, 1, 2, 2, 2, 3, 3, 1, 2
[2, 1, 2, 2, 2, 3, 3, 1, 3] => 2, 1, 2, 2, 2, 3, 3, 1, 3
[2, 1, 2, 2, 2, 3, 3, 2, 1] => 2, 1, 2, 2, 2, 3, 3, 2, 1
[2, 1, 2, 2, 2, 3, 3, 2, 2] => 2, 1, 2, 2, 2, 3, 3, 2, 2
[2, 1, 2, 2, 2, 3, 3, 2, 3] => 2, 1, 2, 2, 2, 3, 3, 2, 3
[2, 1, 2, 2, 2, 3, 3, 3, 1] => 2, 1, 2, 2, 2, 3, 3, 3, 1
[2, 1, 2, 2, 2, 3, 3, 3, 2] => 2, 1, 2, 2, 2, 3, 3, 3, 2
[2, 1, 2, 2, 2, 3, 3, 3, 3] => 2, 1, 2, 2, 2, 3, 3, 3, 3
[2, 1, 2, 2, 3, 1, 1, 1, 1] => 2, 1, 2, 2, 3, 1, 1, 1, 1
[2, 1, 2, 2, 3, 1, 1, 1, 2] => 2, 1, 2, 2, 3, 1, 1, 1, 2
[2, 1, 2, 2, 3, 1, 1, 1, 3] => 2, 1, 2, 2, 3, 1, 1, 1, 3
[2, 1, 2, 2, 3, 1, 1, 2, 1] => 2, 1, 2, 2, 3, 1, 1, 2, 1
[2, 1, 2, 2, 3, 1, 1, 2, 2] => 2, 1, 2, 2, 3, 1, 1, 2, 2
[2, 1, 2, 2, 3, 1, 1, 2, 3] => 2, 1, 2, 2, 3, 1, 1, 2, 3
[2, 1, 2, 2, 3, 1, 1, 3, 1] => 2, 1, 2, 2, 3, 1, 1, 3, 1
[2, 1, 2, 2, 3, 1, 1, 3, 2] => 2, 1, 2, 2, 3, 1, 1, 3, 2
[2, 1, 2, 2, 3, 1, 1, 3, 3] => 2, 1, 2, 2, 3, 1, 1, 3, 3
[2, 1, 2, 2, 3, 1, 2, 1, 1] => 2, 1, 2, 2, 3, 1, 2, 1, 1
[2, 1, 2, 2, 3, 1, 2, 1, 2] => 2, 1, 2, 2, 3, 1, 2, 1, 2
[2, 1, 2, 2, 3, 1, 2, 1, 3] => 2, 1, 2, 2, 3, 1, 2, 1, 3
[2, 1, 2, 2, 3, 1, 2, 2, 1] => 2, 1, 2, 2, 3, 1, 2, 2, 1
[2, 1, 2, 2, 3, 1, 2, 2, 2] => 2, 1, 2, 2, 3, 1, 2, 2, 2
[2, 1, 2, 2, 3, 1, 2, 2, 3] => 2, 1, 2, 2, 3, 1, 2, 2, 3
[2, 1, 2, 2, 3, 1, 2, 3, 1] => 2, 1, 2, 2, 3, 1, 2, 3, 1
[2, 1, 2, 2, 3, 1, 2, 3, 2] => 2, 1, 2, 2, 3, 1, 2, 3, 2
[2, 1, 2, 2, 3, 1, 2, 3, 3] => 2, 1, 2, 2, 3, 1, 2, 3, 3
[2, 1, 2, 2, 3, 1, 3, 1, 1] => 2, 1, 2, 2, 3, 1, 3, 1, 1
[2, 1, 2, 2, 3, 1, 3, 1, 2] => 2, 1, 2, 2, 3, 1, 3, 1, 2
[2, 1, 2, 2, 3, 1, 3, 1, 3] => 2, 1, 2, 2, 3, 1, 3, 1, 3
[2, 1, 2, 2, 3, 1, 3, 2, 1] => 2, 1, 2, 2, 3, 1, 3, 2, 1
[2, 1, 2, 2, 3, 1, 3, 2, 2] => 2, 1, 2, 2, 3, 1, 3, 2, 2
[2, 1, 2, 2, 3, 1, 3, 2, 3] => 2, 1, 2, 2, 3, 1, 3, 2, 3
[2, 1, 2, 2, 3, 1, 3, 3, 1] => 2, 1, 2, 2, 3, 1, 3, 3, 1
[2, 1, 2, 2, 3, 1, 3, 3, 2] => 2, 1, 2, 2, 3, 1, 3, 3, 2
[2, 1, 2, 2, 3, 1, 3, 3, 3] => 2, 1, 2, 2, 3, 1, 3, 3, 3
[2, 1, 2, 2, 3, 2, 1, 1, 1] => 2, 1, 2, 2, 3, 2, 1, 1, 1
[2, 1, 2, 2, 3, 2, 1, 1, 2] => 2, 1, 2, 2, 3, 2, 1, 1, 2
[2, 1, 2, 2, 3, 2, 1, 1, 3] => 2, 1, 2, 2, 3, 2, 1, 1, 3
[2, 1, 2, 2, 3, 2, 1, 2, 1] => 2, 1, 2, 2, 3, 2, 1, 2, 1
[2, 1, 2, 2, 3, 2, 1, 2, 2] => 2, 1, 2, 2, 3, 2, 1, 2, 2
[2, 1, 2, 2, 3, 2, 1, 2, 3] => 2, 1, 2, 2, 3, 2, 1, 2, 3
[2, 1, 2, 2, 3, 2, 1, 3, 1] => 2, 1, 2, 2, 3, 2, 1, 3, 1
[2, 1, 2, 2, 3, 2, 1, 3, 2] => 2, 1, 2, 2, 3, 2, 1, 3, 2
[2, 1, 2, 2, 3, 2, 1, 3, 3] => 2, 1, 2, 2, 3, 2, 1, 3, 3
[2, 1, 2, 2, 3, 2, 2, 1, 1] => 2, 1, 2, 2, 3, 2, 2, 1, 1
[2, 1, 2, 2, 3, 2, 2, 1, 2] => 2, 1, 2, 2, 3, 2, 2, 1, 2
[2, 1, 2, 2, 3, 2, 2, 1, 3] => 2, 1, 2, 2, 3, 2, 2, 1, 3
[2, 1, 2, 2, 3, 2, 2, 2, 1] => 2, 1, 2, 2, 3, 2, 2, 2, 1
[2, 1, 2, 2, 3, 2, 2, 2, 2] => 2, 1, 2, 2, 3, 2, 2, 2, 2
[2, 1, 2, 2, 3, 2, 2, 2, 3] => 2, 1, 2, 2, 3, 2, 2, 2, 3
[2, 1, 2, 2, 3, 2, 2, 3, 1] => 2, 1, 2, 2, 3, 2, 2, 3, 1
[2, 1, 2, 2, 3, 2, 2, 3, 2] => 2, 1, 2, 2, 3, 2, 2, 3, 2
[2, 1, 2, 2, 3, 2, 2, 3, 3] => 2, 1, 2, 2, 3, 2, 2, 3, 3
[2, 1, 2, 2, 3, 2, 3, 1, 1] => 2, 1, 2, 2, 3, 2, 3, 1, 1
[2, 1, 2, 2, 3, 2, 3, 1, 2] => 2, 1, 2, 2, 3, 2, 3, 1, 2
[2, 1, 2, 2, 3, 2, 3, 1, 3] => 2, 1, 2, 2, 3, 2, 3, 1, 3
[2, 1, 2, 2, 3, 2, 3, 2, 1] => 2, 1, 2, 2, 3, 2, 3, 2, 1
[2, 1, 2, 2, 3, 2, 3, 2, 2] => 2, 1, 2, 2, 3, 2, 3, 2, 2
[2, 1, 2, 2, 3, 2, 3, 2, 3] => 2, 1, 2, 2, 3, 2, 3, 2, 3
[2, 1, 2, 2, 3, 2, 3, 3, 1] => 2, 1, 2, 2, 3, 2, 3, 3, 1
[2, 1, 2, 2, 3, 2, 3, 3, 2] => 2, 1, 2, 2, 3, 2, 3, 3, 2
[2, 1, 2, 2, 3, 2, 3, 3, 3] => 2, 1, 2, 2, 3, 2, 3, 3, 3
[2, 1, 2, 2, 3, 3, 1, 1, 1] => 2, 1, 2, 2, 3, 3, 1, 1, 1
[2, 1, 2, 2, 3, 3, 1, 1, 2] => 2, 1, 2, 2, 3, 3, 1, 1, 2
[2, 1, 2, 2, 3, 3, 1, 1, 3] => 2, 1, 2, 2, 3, 3, 1, 1, 3
[2, 1, 2, 2, 3, 3, 1, 2, 1] => 2, 1, 2, 2, 3, 3, 1, 2, 1
[2, 1, 2, 2, 3, 3, 1, 2, 2] => 2, 1, 2, 2, 3, 3, 1, 2, 2
[2, 1, 2, 2, 3, 3, 1, 2, 3] => 2, 1, 2, 2, 3, 3, 1, 2, 3
[2, 1, 2, 2, 3, 3, 1, 3, 1] => 2, 1, 2, 2, 3, 3, 1, 3, 1
[2, 1, 2, 2, 3, 3, 1, 3, 2] => 2, 1, 2, 2, 3, 3, 1, 3, 2
[2, 1, 2, 2, 3, 3, 1, 3, 3] => 2, 1, 2, 2, 3, 3, 1, 3, 3
[2, 1, 2, 2, 3, 3, 2, 1, 1] => 2, 1, 2, 2, 3, 3, 2, 1, 1
[2, 1, 2, 2, 3, 3, 2, 1, 2] => 2, 1, 2, 2, 3, 3, 2, 1, 2
[2, 1, 2, 2, 3, 3, 2, 1, 3] => 2, 1, 2, 2, 3, 3, 2, 1, 3
[2, 1, 2, 2, 3, 3, 2, 2, 1] => 2, 1, 2, 2, 3, 3, 2, 2, 1
[2, 1, 2, 2, 3, 3, 2, 2, 2] => 2, 1, 2, 2, 3, 3, 2, 2, 2
[2, 1, 2, 2, 3, 3, 2, 2, 3] => 2, 1, 2, 2, 3, 3, 2, 2, 3
[2, 1, 2, 2, 3, 3, 2, 3, 1] => 2, 1, 2, 2, 3, 3, 2, 3, 1
[2, 1, 2, 2, 3, 3, 2, 3, 2] => 2, 1, 2, 2, 3, 3, 2, 3, 2
[2, 1, 2, 2, 3, 3, 2, 3, 3] => 2, 1, 2, 2, 3, 3, 2, 3, 3
[2, 1, 2, 2, 3, 3, 3, 1, 1] => 2, 1, 2, 2, 3, 3, 3, 1, 1
[2, 1, 2, 2, 3, 3, 3, 1, 2] => 2, 1, 2, 2, 3, 3, 3, 1, 2
[2, 1, 2, 2, 3, 3, 3, 1, 3] => 2, 1, 2, 2, 3, 3, 3, 1, 3
[2, 1, 2, 2, 3, 3, 3, 2, 1] => 2, 1, 2, 2, 3, 3, 3, 2, 1
[2, 1, 2, 2, 3, 3, 3, 2, 2] => 2, 1, 2, 2, 3, 3, 3, 2, 2
[2, 1, 2, 2, 3, 3, 3, 2, 3] => 2, 1, 2, 2, 3, 3, 3, 2, 3
[2, 1, 2, 2, 3, 3, 3, 3, 1] => 2, 1, 2, 2, 3, 3, 3, 3, 1
[2, 1, 2, 2, 3, 3, 3, 3, 2] => 2, 1, 2, 2, 3, 3, 3, 3, 2
[2, 1, 2, 2, 3, 3, 3, 3, 3] => 2, 1, 2, 2, 3, 3, 3, 3, 3
[2, 1, 2, 3, 1, 1, 1, 1, 1] => 2, 1, 2, 3, 1, 1, 1, 1, 1
[2, 1, 2, 3, 1, 1, 1, 1, 2] => 2, 1, 2, 3, 1, 1, 1, 1, 2
[2, 1, 2, 3, 1, 1, 1, 1, 3] => 2, 1, 2, 3, 1, 1, 1, 1, 3
[2, 1, 2, 3, 1, 1, 1, 2, 1] => 2, 1, 2, 3, 1, 1, 1, 2, 1
[2, 1, 2, 3, 1, 1, 1, 2, 2] => 2, 1, 2, 3, 1, 1, 1, 2, 2
[2, 1, 2, 3, 1, 1, 1, 2, 3] => 2, 1, 2, 3, 1, 1, 1, 2, 3
[2, 1, 2, 3, 1, 1, 1, 3, 1] => 2, 1, 2, 3, 1, 1, 1, 3, 1
[2, 1, 2, 3, 1, 1, 1, 3, 2] => 2, 1, 2, 3, 1, 1, 1, 3, 2
[2, 1, 2, 3, 1, 1, 1, 3, 3] => 2, 1, 2, 3, 1, 1, 1, 3, 3
[2, 1, 2, 3, 1, 1, 2, 1, 1] => 2, 1, 2, 3, 1, 1, 2, 1, 1
[2, 1, 2, 3, 1, 1, 2, 1, 2] => 2, 1, 2, 3, 1, 1, 2, 1, 2
[2, 1, 2, 3, 1, 1, 2, 1, 3] => 2, 1, 2, 3, 1, 1, 2, 1, 3
[2, 1, 2, 3, 1, 1, 2, 2, 1] => 2, 1, 2, 3, 1, 1, 2, 2, 1
[2, 1, 2, 3, 1, 1, 2, 2, 2] => 2, 1, 2, 3, 1, 1, 2, 2, 2
[2, 1, 2, 3, 1, 1, 2, 2, 3] => 2, 1, 2, 3, 1, 1, 2, 2, 3
[2, 1, 2, 3, 1, 1, 2, 3, 1] => 2, 1, 2, 3, 1, 1, 2, 3, 1
[2, 1, 2, 3, 1, 1, 2, 3, 2] => 2, 1, 2, 3, 1, 1, 2, 3, 2
[2, 1, 2, 3, 1, 1, 2, 3, 3] => 2, 1, 2, 3, 1, 1, 2, 3, 3
[2, 1, 2, 3, 1, 1, 3, 1, 1] => 2, 1, 2, 3, 1, 1, 3, 1, 1
[2, 1, 2, 3, 1, 1, 3, 1, 2] => 2, 1, 2, 3, 1, 1, 3, 1, 2
[2, 1, 2, 3, 1, 1, 3, 1, 3] => 2, 1, 2, 3, 1, 1, 3, 1, 3
[2, 1, 2, 3, 1, 1, 3, 2, 1] => 2, 1, 2, 3, 1, 1, 3, 2, 1
[2, 1, 2, 3, 1, 1, 3, 2, 2] => 2, 1, 2, 3, 1, 1, 3, 2, 2
[2, 1, 2, 3, 1, 1, 3, 2, 3] => 2, 1, 2, 3, 1, 1, 3, 2, 3
[2, 1, 2, 3, 1, 1, 3, 3, 1] => 2, 1, 2, 3, 1, 1, 3, 3, 1
[2, 1, 2, 3, 1, 1, 3, 3, 2] => 2, 1, 2, 3, 1, 1, 3, 3, 2
[2, 1, 2, 3, 1, 1, 3, 3, 3] => 2, 1, 2, 3, 1, 1, 3, 3, 3
[2, 1, 2, 3, 1, 2, 1, 1, 1] => 2, 1, 2, 3, 1, 2, 1, 1, 1
[2, 1, 2, 3, 1, 2, 1, 1, 2] => 2, 1, 2, 3, 1, 2, 1, 1, 2
[2, 1, 2, 3, 1, 2, 1, 1, 3] => 2, 1, 2, 3, 1, 2, 1, 1, 3
[2, 1, 2, 3, 1, 2, 1, 2, 1] => 2, 1, 2, 3, 1, 2, 1, 2, 1
[2, 1, 2, 3, 1, 2, 1, 2, 2] => 2, 1, 2, 3, 1, 2, 1, 2, 2
[2, 1, 2, 3, 1, 2, 1, 2, 3] => 2, 1, 2, 3, 1, 2, 1, 2, 3
[2, 1, 2, 3, 1, 2, 1, 3, 1] => 2, 1, 2, 3, 1, 2, 1, 3, 1
[2, 1, 2, 3, 1, 2, 1, 3, 2] => 2, 1, 2, 3, 1, 2, 1, 3, 2
[2, 1, 2, 3, 1, 2, 1, 3, 3] => 2, 1, 2, 3, 1, 2, 1, 3, 3
[2, 1, 2, 3, 1, 2, 2, 1, 1] => 2, 1, 2, 3, 1, 2, 2, 1, 1
[2, 1, 2, 3, 1, 2, 2, 1, 2] => 2, 1, 2, 3, 1, 2, 2, 1, 2
[2, 1, 2, 3, 1, 2, 2, 1, 3] => 2, 1, 2, 3, 1, 2, 2, 1, 3
[2, 1, 2, 3, 1, 2, 2, 2, 1] => 2, 1, 2, 3, 1, 2, 2, 2, 1
[2, 1, 2, 3, 1, 2, 2, 2, 2] => 2, 1, 2, 3, 1, 2, 2, 2, 2
[2, 1, 2, 3, 1, 2, 2, 2, 3] => 2, 1, 2, 3, 1, 2, 2, 2, 3
[2, 1, 2, 3, 1, 2, 2, 3, 1] => 2, 1, 2, 3, 1, 2, 2, 3, 1
[2, 1, 2, 3, 1, 2, 2, 3, 2] => 2, 1, 2, 3, 1, 2, 2, 3, 2
[2, 1, 2, 3, 1, 2, 2, 3, 3] => 2, 1, 2, 3, 1, 2, 2, 3, 3
[2, 1, 2, 3, 1, 2, 3, 1, 1] => 2, 1, 2, 3, 1, 2, 3, 1, 1
[2, 1, 2, 3, 1, 2, 3, 1, 2] => 2, 1, 2, 3, 1, 2, 3, 1, 2
[2, 1, 2, 3, 1, 2, 3, 1, 3] => 2, 1, 2, 3, 1, 2, 3, 1, 3
[2, 1, 2, 3, 1, 2, 3, 2, 1] => 2, 1, 2, 3, 1, 2, 3, 2, 1
[2, 1, 2, 3, 1, 2, 3, 2, 2] => 2, 1, 2, 3, 1, 2, 3, 2, 2
[2, 1, 2, 3, 1, 2, 3, 2, 3] => 2, 1, 2, 3, 1, 2, 3, 2, 3
[2, 1, 2, 3, 1, 2, 3, 3, 1] => 2, 1, 2, 3, 1, 2, 3, 3, 1
[2, 1, 2, 3, 1, 2, 3, 3, 2] => 2, 1, 2, 3, 1, 2, 3, 3, 2
[2, 1, 2, 3, 1, 2, 3, 3, 3] => 2, 1, 2, 3, 1, 2, 3, 3, 3
[2, 1, 2, 3, 1, 3, 1, 1, 1] => 2, 1, 2, 3, 1, 3, 1, 1, 1
[2, 1, 2, 3, 1, 3, 1, 1, 2] => 2, 1, 2, 3, 1, 3, 1, 1, 2
[2, 1, 2, 3, 1, 3, 1, 1, 3] => 2, 1, 2, 3, 1, 3, 1, 1, 3
[2, 1, 2, 3, 1, 3, 1, 2, 1] => 2, 1, 2, 3, 1, 3, 1, 2, 1
[2, 1, 2, 3, 1, 3, 1, 2, 2] => 2, 1, 2, 3, 1, 3, 1, 2, 2
[2, 1, 2, 3, 1, 3, 1, 2, 3] => 2, 1, 2, 3, 1, 3, 1, 2, 3
[2, 1, 2, 3, 1, 3, 1, 3, 1] => 2, 1, 2, 3, 1, 3, 1, 3, 1
[2, 1, 2, 3, 1, 3, 1, 3, 2] => 2, 1, 2, 3, 1, 3, 1, 3, 2
[2, 1, 2, 3, 1, 3, 1, 3, 3] => 2, 1, 2, 3, 1, 3, 1, 3, 3
[2, 1, 2, 3, 1, 3, 2, 1, 1] => 2, 1, 2, 3, 1, 3, 2, 1, 1
[2, 1, 2, 3, 1, 3, 2, 1, 2] => 2, 1, 2, 3, 1, 3, 2, 1, 2
[2, 1, 2, 3, 1, 3, 2, 1, 3] => 2, 1, 2, 3, 1, 3, 2, 1, 3
[2, 1, 2, 3, 1, 3, 2, 2, 1] => 2, 1, 2, 3, 1, 3, 2, 2, 1
[2, 1, 2, 3, 1, 3, 2, 2, 2] => 2, 1, 2, 3, 1, 3, 2, 2, 2
[2, 1, 2, 3, 1, 3, 2, 2, 3] => 2, 1, 2, 3, 1, 3, 2, 2, 3
[2, 1, 2, 3, 1, 3, 2, 3, 1] => 2, 1, 2, 3, 1, 3, 2, 3, 1
[2, 1, 2, 3, 1, 3, 2, 3, 2] => 2, 1, 2, 3, 1, 3, 2, 3, 2
[2, 1, 2, 3, 1, 3, 2, 3, 3] => 2, 1, 2, 3, 1, 3, 2, 3, 3
[2, 1, 2, 3, 1, 3, 3, 1, 1] => 2, 1, 2, 3, 1, 3, 3, 1, 1
[2, 1, 2, 3, 1, 3, 3, 1, 2] => 2, 1, 2, 3, 1, 3, 3, 1, 2
[2, 1, 2, 3, 1, 3, 3, 1, 3] => 2, 1, 2, 3, 1, 3, 3, 1, 3
[2, 1, 2, 3, 1, 3, 3, 2, 1] => 2, 1, 2, 3, 1, 3, 3, 2, 1
[2, 1, 2, 3, 1, 3, 3, 2, 2] => 2, 1, 2, 3, 1, 3, 3, 2, 2
[2, 1, 2, 3, 1, 3, 3, 2, 3] => 2, 1, 2, 3, 1, 3, 3, 2, 3
[2, 1, 2, 3, 1, 3, 3, 3, 1] => 2, 1, 2, 3, 1, 3, 3, 3, 1
[2, 1, 2, 3, 1, 3, 3, 3, 2] => 2, 1, 2, 3, 1, 3, 3, 3, 2
[2, 1, 2, 3, 1, 3, 3, 3, 3] => 2, 1, 2, 3, 1, 3, 3, 3, 3
[2, 1, 2, 3, 2, 1, 1, 1, 1] => 2, 1, 2, 3, 2, 1, 1, 1, 1
[2, 1, 2, 3, 2, 1, 1, 1, 2] => 2, 1, 2, 3, 2, 1, 1, 1, 2
[2, 1, 2, 3, 2, 1, 1, 1, 3] => 2, 1, 2, 3, 2, 1, 1, 1, 3
[2, 1, 2, 3, 2, 1, 1, 2, 1] => 2, 1, 2, 3, 2, 1, 1, 2, 1
[2, 1, 2, 3, 2, 1, 1, 2, 2] => 2, 1, 2, 3, 2, 1, 1, 2, 2
[2, 1, 2, 3, 2, 1, 1, 2, 3] => 2, 1, 2, 3, 2, 1, 1, 2, 3
[2, 1, 2, 3, 2, 1, 1, 3, 1] => 2, 1, 2, 3, 2, 1, 1, 3, 1
[2, 1, 2, 3, 2, 1, 1, 3, 2] => 2, 1, 2, 3, 2, 1, 1, 3, 2
[2, 1, 2, 3, 2, 1, 1, 3, 3] => 2, 1, 2, 3, 2, 1, 1, 3, 3
[2, 1, 2, 3, 2, 1, 2, 1, 1] => 2, 1, 2, 3, 2, 1, 2, 1, 1
[2, 1, 2, 3, 2, 1, 2, 1, 2] => 2, 1, 2, 3, 2, 1, 2, 1, 2
[2, 1, 2, 3, 2, 1, 2, 1, 3] => 2, 1, 2, 3, 2, 1, 2, 1, 3
[2, 1, 2, 3, 2, 1, 2, 2, 1] => 2, 1, 2, 3, 2, 1, 2, 2, 1
[2, 1, 2, 3, 2, 1, 2, 2, 2] => 2, 1, 2, 3, 2, 1, 2, 2, 2
[2, 1, 2, 3, 2, 1, 2, 2, 3] => 2, 1, 2, 3, 2, 1, 2, 2, 3
[2, 1, 2, 3, 2, 1, 2, 3, 1] => 2, 1, 2, 3, 2, 1, 2, 3, 1
[2, 1, 2, 3, 2, 1, 2, 3, 2] => 2, 1, 2, 3, 2, 1, 2, 3, 2
[2, 1, 2, 3, 2, 1, 2, 3, 3] => 2, 1, 2, 3, 2, 1, 2, 3, 3
[2, 1, 2, 3, 2, 1, 3, 1, 1] => 2, 1, 2, 3, 2, 1, 3, 1, 1
[2, 1, 2, 3, 2, 1, 3, 1, 2] => 2, 1, 2, 3, 2, 1, 3, 1, 2
[2, 1, 2, 3, 2, 1, 3, 1, 3] => 2, 1, 2, 3, 2, 1, 3, 1, 3
[2, 1, 2, 3, 2, 1, 3, 2, 1] => 2, 1, 2, 3, 2, 1, 3, 2, 1
[2, 1, 2, 3, 2, 1, 3, 2, 2] => 2, 1, 2, 3, 2, 1, 3, 2, 2
[2, 1, 2, 3, 2, 1, 3, 2, 3] => 2, 1, 2, 3, 2, 1, 3, 2, 3
[2, 1, 2, 3, 2, 1, 3, 3, 1] => 2, 1, 2, 3, 2, 1, 3, 3, 1
[2, 1, 2, 3, 2, 1, 3, 3, 2] => 2, 1, 2, 3, 2, 1, 3, 3, 2
[2, 1, 2, 3, 2, 1, 3, 3, 3] => 2, 1, 2, 3, 2, 1, 3, 3, 3
[2, 1, 2, 3, 2, 2, 1, 1, 1] => 2, 1, 2, 3, 2, 2, 1, 1, 1
[2, 1, 2, 3, 2, 2, 1, 1, 2] => 2, 1, 2, 3, 2, 2, 1, 1, 2
[2, 1, 2, 3, 2, 2, 1, 1, 3] => 2, 1, 2, 3, 2, 2, 1, 1, 3
[2, 1, 2, 3, 2, 2, 1, 2, 1] => 2, 1, 2, 3, 2, 2, 1, 2, 1
[2, 1, 2, 3, 2, 2, 1, 2, 2] => 2, 1, 2, 3, 2, 2, 1, 2, 2
[2, 1, 2, 3, 2, 2, 1, 2, 3] => 2, 1, 2, 3, 2, 2, 1, 2, 3
[2, 1, 2, 3, 2, 2, 1, 3, 1] => 2, 1, 2, 3, 2, 2, 1, 3, 1
[2, 1, 2, 3, 2, 2, 1, 3, 2] => 2, 1, 2, 3, 2, 2, 1, 3, 2
[2, 1, 2, 3, 2, 2, 1, 3, 3] => 2, 1, 2, 3, 2, 2, 1, 3, 3
[2, 1, 2, 3, 2, 2, 2, 1, 1] => 2, 1, 2, 3, 2, 2, 2, 1, 1
[2, 1, 2, 3, 2, 2, 2, 1, 2] => 2, 1, 2, 3, 2, 2, 2, 1, 2
[2, 1, 2, 3, 2, 2, 2, 1, 3] => 2, 1, 2, 3, 2, 2, 2, 1, 3
[2, 1, 2, 3, 2, 2, 2, 2, 1] => 2, 1, 2, 3, 2, 2, 2, 2, 1
[2, 1, 2, 3, 2, 2, 2, 2, 2] => 2, 1, 2, 3, 2, 2, 2, 2, 2
[2, 1, 2, 3, 2, 2, 2, 2, 3] => 2, 1, 2, 3, 2, 2, 2, 2, 3
[2, 1, 2, 3, 2, 2, 2, 3, 1] => 2, 1, 2, 3, 2, 2, 2, 3, 1
[2, 1, 2, 3, 2, 2, 2, 3, 2] => 2, 1, 2, 3, 2, 2, 2, 3, 2
[2, 1, 2, 3, 2, 2, 2, 3, 3] => 2, 1, 2, 3, 2, 2, 2, 3, 3
[2, 1, 2, 3, 2, 2, 3, 1, 1] => 2, 1, 2, 3, 2, 2, 3, 1, 1
[2, 1, 2, 3, 2, 2, 3, 1, 2] => 2, 1, 2, 3, 2, 2, 3, 1, 2
[2, 1, 2, 3, 2, 2, 3, 1, 3] => 2, 1, 2, 3, 2, 2, 3, 1, 3
[2, 1, 2, 3, 2, 2, 3, 2, 1] => 2, 1, 2, 3, 2, 2, 3, 2, 1
[2, 1, 2, 3, 2, 2, 3, 2, 2] => 2, 1, 2, 3, 2, 2, 3, 2, 2
[2, 1, 2, 3, 2, 2, 3, 2, 3] => 2, 1, 2, 3, 2, 2, 3, 2, 3
[2, 1, 2, 3, 2, 2, 3, 3, 1] => 2, 1, 2, 3, 2, 2, 3, 3, 1
[2, 1, 2, 3, 2, 2, 3, 3, 2] => 2, 1, 2, 3, 2, 2, 3, 3, 2
[2, 1, 2, 3, 2, 2, 3, 3, 3] => 2, 1, 2, 3, 2, 2, 3, 3, 3
[2, 1, 2, 3, 2, 3, 1, 1, 1] => 2, 1, 2, 3, 2, 3, 1, 1, 1
[2, 1, 2, 3, 2, 3, 1, 1, 2] => 2, 1, 2, 3, 2, 3, 1, 1, 2
[2, 1, 2, 3, 2, 3, 1, 1, 3] => 2, 1, 2, 3, 2, 3, 1, 1, 3
[2, 1, 2, 3, 2, 3, 1, 2, 1] => 2, 1, 2, 3, 2, 3, 1, 2, 1
[2, 1, 2, 3, 2, 3, 1, 2, 2] => 2, 1, 2, 3, 2, 3, 1, 2, 2
[2, 1, 2, 3, 2, 3, 1, 2, 3] => 2, 1, 2, 3, 2, 3, 1, 2, 3
[2, 1, 2, 3, 2, 3, 1, 3, 1] => 2, 1, 2, 3, 2, 3, 1, 3, 1
[2, 1, 2, 3, 2, 3, 1, 3, 2] => 2, 1, 2, 3, 2, 3, 1, 3, 2
[2, 1, 2, 3, 2, 3, 1, 3, 3] => 2, 1, 2, 3, 2, 3, 1, 3, 3
[2, 1, 2, 3, 2, 3, 2, 1, 1] => 2, 1, 2, 3, 2, 3, 2, 1, 1
[2, 1, 2, 3, 2, 3, 2, 1, 2] => 2, 1, 2, 3, 2, 3, 2, 1, 2
[2, 1, 2, 3, 2, 3, 2, 1, 3] => 2, 1, 2, 3, 2, 3, 2, 1, 3
[2, 1, 2, 3, 2, 3, 2, 2, 1] => 2, 1, 2, 3, 2, 3, 2, 2, 1
[2, 1, 2, 3, 2, 3, 2, 2, 2] => 2, 1, 2, 3, 2, 3, 2, 2, 2
[2, 1, 2, 3, 2, 3, 2, 2, 3] => 2, 1, 2, 3, 2, 3, 2, 2, 3
[2, 1, 2, 3, 2, 3, 2, 3, 1] => 2, 1, 2, 3, 2, 3, 2, 3, 1
[2, 1, 2, 3, 2, 3, 2, 3, 2] => 2, 1, 2, 3, 2, 3, 2, 3, 2
[2, 1, 2, 3, 2, 3, 2, 3, 3] => 2, 1, 2, 3, 2, 3, 2, 3, 3
[2, 1, 2, 3, 2, 3, 3, 1, 1] => 2, 1, 2, 3, 2, 3, 3, 1, 1
[2, 1, 2, 3, 2, 3, 3, 1, 2] => 2, 1, 2, 3, 2, 3, 3, 1, 2
[2, 1, 2, 3, 2, 3, 3, 1, 3] => 2, 1, 2, 3, 2, 3, 3, 1, 3
[2, 1, 2, 3, 2, 3, 3, 2, 1] => 2, 1, 2, 3, 2, 3, 3, 2, 1
[2, 1, 2, 3, 2, 3, 3, 2, 2] => 2, 1, 2, 3, 2, 3, 3, 2, 2
[2, 1, 2, 3, 2, 3, 3, 2, 3] => 2, 1, 2, 3, 2, 3, 3, 2, 3
[2, 1, 2, 3, 2, 3, 3, 3, 1] => 2, 1, 2, 3, 2, 3, 3, 3, 1
[2, 1, 2, 3, 2, 3, 3, 3, 2] => 2, 1, 2, 3, 2, 3, 3, 3, 2
[2, 1, 2, 3, 2, 3, 3, 3, 3] => 2, 1, 2, 3, 2, 3, 3, 3, 3
[2, 1, 2, 3, 3, 1, 1, 1, 1] => 2, 1, 2, 3, 3, 1, 1, 1, 1
[2, 1, 2, 3, 3, 1, 1, 1, 2] => 2, 1, 2, 3, 3, 1, 1, 1, 2
[2, 1, 2, 3, 3, 1, 1, 1, 3] => 2, 1, 2, 3, 3, 1, 1, 1, 3
[2, 1, 2, 3, 3, 1, 1, 2, 1] => 2, 1, 2, 3, 3, 1, 1, 2, 1
[2, 1, 2, 3, 3, 1, 1, 2, 2] => 2, 1, 2, 3, 3, 1, 1, 2, 2
[2, 1, 2, 3, 3, 1, 1, 2, 3] => 2, 1, 2, 3, 3, 1, 1, 2, 3
[2, 1, 2, 3, 3, 1, 1, 3, 1] => 2, 1, 2, 3, 3, 1, 1, 3, 1
[2, 1, 2, 3, 3, 1, 1, 3, 2] => 2, 1, 2, 3, 3, 1, 1, 3, 2
[2, 1, 2, 3, 3, 1, 1, 3, 3] => 2, 1, 2, 3, 3, 1, 1, 3, 3
[2, 1, 2, 3, 3, 1, 2, 1, 1] => 2, 1, 2, 3, 3, 1, 2, 1, 1
[2, 1, 2, 3, 3, 1, 2, 1, 2] => 2, 1, 2, 3, 3, 1, 2, 1, 2
[2, 1, 2, 3, 3, 1, 2, 1, 3] => 2, 1, 2, 3, 3, 1, 2, 1, 3
[2, 1, 2, 3, 3, 1, 2, 2, 1] => 2, 1, 2, 3, 3, 1, 2, 2, 1
[2, 1, 2, 3, 3, 1, 2, 2, 2] => 2, 1, 2, 3, 3, 1, 2, 2, 2
[2, 1, 2, 3, 3, 1, 2, 2, 3] => 2, 1, 2, 3, 3, 1, 2, 2, 3
[2, 1, 2, 3, 3, 1, 2, 3, 1] => 2, 1, 2, 3, 3, 1, 2, 3, 1
[2, 1, 2, 3, 3, 1, 2, 3, 2] => 2, 1, 2, 3, 3, 1, 2, 3, 2
[2, 1, 2, 3, 3, 1, 2, 3, 3] => 2, 1, 2, 3, 3, 1, 2, 3, 3
[2, 1, 2, 3, 3, 1, 3, 1, 1] => 2, 1, 2, 3, 3, 1, 3, 1, 1
[2, 1, 2, 3, 3, 1, 3, 1, 2] => 2, 1, 2, 3, 3, 1, 3, 1, 2
[2, 1, 2, 3, 3, 1, 3, 1, 3] => 2, 1, 2, 3, 3, 1, 3, 1, 3
[2, 1, 2, 3, 3, 1, 3, 2, 1] => 2, 1, 2, 3, 3, 1, 3, 2, 1
[2, 1, 2, 3, 3, 1, 3, 2, 2] => 2, 1, 2, 3, 3, 1, 3, 2, 2
[2, 1, 2, 3, 3, 1, 3, 2, 3] => 2, 1, 2, 3, 3, 1, 3, 2, 3
[2, 1, 2, 3, 3, 1, 3, 3, 1] => 2, 1, 2, 3, 3, 1, 3, 3, 1
[2, 1, 2, 3, 3, 1, 3, 3, 2] => 2, 1, 2, 3, 3, 1, 3, 3, 2
[2, 1, 2, 3, 3, 1, 3, 3, 3] => 2, 1, 2, 3, 3, 1, 3, 3, 3
[2, 1, 2, 3, 3, 2, 1, 1, 1] => 2, 1, 2, 3, 3, 2, 1, 1, 1
[2, 1, 2, 3, 3, 2, 1, 1, 2] => 2, 1, 2, 3, 3, 2, 1, 1, 2
[2, 1, 2, 3, 3, 2, 1, 1, 3] => 2, 1, 2, 3, 3, 2, 1, 1, 3
[2, 1, 2, 3, 3, 2, 1, 2, 1] => 2, 1, 2, 3, 3, 2, 1, 2, 1
[2, 1, 2, 3, 3, 2, 1, 2, 2] => 2, 1, 2, 3, 3, 2, 1, 2, 2
[2, 1, 2, 3, 3, 2, 1, 2, 3] => 2, 1, 2, 3, 3, 2, 1, 2, 3
[2, 1, 2, 3, 3, 2, 1, 3, 1] => 2, 1, 2, 3, 3, 2, 1, 3, 1
[2, 1, 2, 3, 3, 2, 1, 3, 2] => 2, 1, 2, 3, 3, 2, 1, 3, 2
[2, 1, 2, 3, 3, 2, 1, 3, 3] => 2, 1, 2, 3, 3, 2, 1, 3, 3
[2, 1, 2, 3, 3, 2, 2, 1, 1] => 2, 1, 2, 3, 3, 2, 2, 1, 1
[2, 1, 2, 3, 3, 2, 2, 1, 2] => 2, 1, 2, 3, 3, 2, 2, 1, 2
[2, 1, 2, 3, 3, 2, 2, 1, 3] => 2, 1, 2, 3, 3, 2, 2, 1, 3
[2, 1, 2, 3, 3, 2, 2, 2, 1] => 2, 1, 2, 3, 3, 2, 2, 2, 1
[2, 1, 2, 3, 3, 2, 2, 2, 2] => 2, 1, 2, 3, 3, 2, 2, 2, 2
[2, 1, 2, 3, 3, 2, 2, 2, 3] => 2, 1, 2, 3, 3, 2, 2, 2, 3
[2, 1, 2, 3, 3, 2, 2, 3, 1] => 2, 1, 2, 3, 3, 2, 2, 3, 1
[2, 1, 2, 3, 3, 2, 2, 3, 2] => 2, 1, 2, 3, 3, 2, 2, 3, 2
[2, 1, 2, 3, 3, 2, 2, 3, 3] => 2, 1, 2, 3, 3, 2, 2, 3, 3
[2, 1, 2, 3, 3, 2, 3, 1, 1] => 2, 1, 2, 3, 3, 2, 3, 1, 1
[2, 1, 2, 3, 3, 2, 3, 1, 2] => 2, 1, 2, 3, 3, 2, 3, 1, 2
[2, 1, 2, 3, 3, 2, 3, 1, 3] => 2, 1, 2, 3, 3, 2, 3, 1, 3
[2, 1, 2, 3, 3, 2, 3, 2, 1] => 2, 1, 2, 3, 3, 2, 3, 2, 1
[2, 1, 2, 3, 3, 2, 3, 2, 2] => 2, 1, 2, 3, 3, 2, 3, 2, 2
[2, 1, 2, 3, 3, 2, 3, 2, 3] => 2, 1, 2, 3, 3, 2, 3, 2, 3
[2, 1, 2, 3, 3, 2, 3, 3, 1] => 2, 1, 2, 3, 3, 2, 3, 3, 1
[2, 1, 2, 3, 3, 2, 3, 3, 2] => 2, 1, 2, 3, 3, 2, 3, 3, 2
[2, 1, 2, 3, 3, 2, 3, 3, 3] => 2, 1, 2, 3, 3, 2, 3, 3, 3
[2, 1, 2, 3, 3, 3, 1, 1, 1] => 2, 1, 2, 3, 3, 3, 1, 1, 1
[2, 1, 2, 3, 3, 3, 1, 1, 2] => 2, 1, 2, 3, 3, 3, 1, 1, 2
[2, 1, 2, 3, 3, 3, 1, 1, 3] => 2, 1, 2, 3, 3, 3, 1, 1, 3
[2, 1, 2, 3, 3, 3, 1, 2, 1] => 2, 1, 2, 3, 3, 3, 1, 2, 1
[2, 1, 2, 3, 3, 3, 1, 2, 2] => 2, 1, 2, 3, 3, 3, 1, 2, 2
[2, 1, 2, 3, 3, 3, 1, 2, 3] => 2, 1, 2, 3, 3, 3, 1, 2, 3
[2, 1, 2, 3, 3, 3, 1, 3, 1] => 2, 1, 2, 3, 3, 3, 1, 3, 1
[2, 1, 2, 3, 3, 3, 1, 3, 2] => 2, 1, 2, 3, 3, 3, 1, 3, 2
[2, 1, 2, 3, 3, 3, 1, 3, 3] => 2, 1, 2, 3, 3, 3, 1, 3, 3
[2, 1, 2, 3, 3, 3, 2, 1, 1] => 2, 1, 2, 3, 3, 3, 2, 1, 1
[2, 1, 2, 3, 3, 3, 2, 1, 2] => 2, 1, 2, 3, 3, 3, 2, 1, 2
[2, 1, 2, 3, 3, 3, 2, 1, 3] => 2, 1, 2, 3, 3, 3, 2, 1, 3
[2, 1, 2, 3, 3, 3, 2, 2, 1] => 2, 1, 2, 3, 3, 3, 2, 2, 1
[2, 1, 2, 3, 3, 3, 2, 2, 2] => 2, 1, 2, 3, 3, 3, 2, 2, 2
[2, 1, 2, 3, 3, 3, 2, 2, 3] => 2, 1, 2, 3, 3, 3, 2, 2, 3
[2, 1, 2, 3, 3, 3, 2, 3, 1] => 2, 1, 2, 3, 3, 3, 2, 3, 1
[2, 1, 2, 3, 3, 3, 2, 3, 2] => 2, 1, 2, 3, 3, 3, 2, 3, 2
[2, 1, 2, 3, 3, 3, 2, 3, 3] => 2, 1, 2, 3, 3, 3, 2, 3, 3
[2, 1, 2, 3, 3, 3, 3, 1, 1] => 2, 1, 2, 3, 3, 3, 3, 1, 1
[2, 1, 2, 3, 3, 3, 3, 1, 2] => 2, 1, 2, 3, 3, 3, 3, 1, 2
[2, 1, 2, 3, 3, 3, 3, 1, 3] => 2, 1, 2, 3, 3, 3, 3, 1, 3
[2, 1, 2, 3, 3, 3, 3, 2, 1] => 2, 1, 2, 3, 3, 3, 3, 2, 1
[2, 1, 2, 3, 3, 3, 3, 2, 2] => 2, 1, 2, 3, 3, 3, 3, 2, 2
[2, 1, 2, 3, 3, 3, 3, 2, 3] => 2, 1, 2, 3, 3, 3, 3, 2, 3
[2, 1, 2, 3, 3, 3, 3, 3, 1] => 2, 1, 2, 3, 3, 3, 3, 3, 1
[2, 1, 2, 3, 3, 3, 3, 3, 2] => 2, 1, 2, 3, 3, 3, 3, 3, 2
[2, 1, 2, 3, 3, 3, 3, 3, 3] => 2, 1, 2, 3, 3, 3, 3, 3, 3
[2, 1, 3, 1, 1, 1, 1, 1, 1] => 2, 1, 3, 1, 1, 1, 1, 1, 1
[2, 1, 3, 1, 1, 1, 1, 1, 2] => 2, 1, 3, 1, 1, 1, 1, 1, 2
[2, 1, 3, 1, 1, 1, 1, 1, 3] => 2, 1, 3, 1, 1, 1, 1, 1, 3
[2, 1, 3, 1, 1, 1, 1, 2, 1] => 2, 1, 3, 1, 1, 1, 1, 2, 1
[2, 1, 3, 1, 1, 1, 1, 2, 2] => 2, 1, 3, 1, 1, 1, 1, 2, 2
[2, 1, 3, 1, 1, 1, 1, 2, 3] => 2, 1, 3, 1, 1, 1, 1, 2, 3
[2, 1, 3, 1, 1, 1, 1, 3, 1] => 2, 1, 3, 1, 1, 1, 1, 3, 1
[2, 1, 3, 1, 1, 1, 1, 3, 2] => 2, 1, 3, 1, 1, 1, 1, 3, 2
[2, 1, 3, 1, 1, 1, 1, 3, 3] => 2, 1, 3, 1, 1, 1, 1, 3, 3
[2, 1, 3, 1, 1, 1, 2, 1, 1] => 2, 1, 3, 1, 1, 1, 2, 1, 1
[2, 1, 3, 1, 1, 1, 2, 1, 2] => 2, 1, 3, 1, 1, 1, 2, 1, 2
[2, 1, 3, 1, 1, 1, 2, 1, 3] => 2, 1, 3, 1, 1, 1, 2, 1, 3
[2, 1, 3, 1, 1, 1, 2, 2, 1] => 2, 1, 3, 1, 1, 1, 2, 2, 1
[2, 1, 3, 1, 1, 1, 2, 2, 2] => 2, 1, 3, 1, 1, 1, 2, 2, 2
[2, 1, 3, 1, 1, 1, 2, 2, 3] => 2, 1, 3, 1, 1, 1, 2, 2, 3
[2, 1, 3, 1, 1, 1, 2, 3, 1] => 2, 1, 3, 1, 1, 1, 2, 3, 1
[2, 1, 3, 1, 1, 1, 2, 3, 2] => 2, 1, 3, 1, 1, 1, 2, 3, 2
[2, 1, 3, 1, 1, 1, 2, 3, 3] => 2, 1, 3, 1, 1, 1, 2, 3, 3
[2, 1, 3, 1, 1, 1, 3, 1, 1] => 2, 1, 3, 1, 1, 1, 3, 1, 1
[2, 1, 3, 1, 1, 1, 3, 1, 2] => 2, 1, 3, 1, 1, 1, 3, 1, 2
[2, 1, 3, 1, 1, 1, 3, 1, 3] => 2, 1, 3, 1, 1, 1, 3, 1, 3
[2, 1, 3, 1, 1, 1, 3, 2, 1] => 2, 1, 3, 1, 1, 1, 3, 2, 1
[2, 1, 3, 1, 1, 1, 3, 2, 2] => 2, 1, 3, 1, 1, 1, 3, 2, 2
[2, 1, 3, 1, 1, 1, 3, 2, 3] => 2, 1, 3, 1, 1, 1, 3, 2, 3
[2, 1, 3, 1, 1, 1, 3, 3, 1] => 2, 1, 3, 1, 1, 1, 3, 3, 1
[2, 1, 3, 1, 1, 1, 3, 3, 2] => 2, 1, 3, 1, 1, 1, 3, 3, 2
[2, 1, 3, 1, 1, 1, 3, 3, 3] => 2, 1, 3, 1, 1, 1, 3, 3, 3
[2, 1, 3, 1, 1, 2, 1, 1, 1] => 2, 1, 3, 1, 1, 2, 1, 1, 1
[2, 1, 3, 1, 1, 2, 1, 1, 2] => 2, 1, 3, 1, 1, 2, 1, 1, 2
[2, 1, 3, 1, 1, 2, 1, 1, 3] => 2, 1, 3, 1, 1, 2, 1, 1, 3
[2, 1, 3, 1, 1, 2, 1, 2, 1] => 2, 1, 3, 1, 1, 2, 1, 2, 1
[2, 1, 3, 1, 1, 2, 1, 2, 2] => 2, 1, 3, 1, 1, 2, 1, 2, 2
[2, 1, 3, 1, 1, 2, 1, 2, 3] => 2, 1, 3, 1, 1, 2, 1, 2, 3
[2, 1, 3, 1, 1, 2, 1, 3, 1] => 2, 1, 3, 1, 1, 2, 1, 3, 1
[2, 1, 3, 1, 1, 2, 1, 3, 2] => 2, 1, 3, 1, 1, 2, 1, 3, 2
[2, 1, 3, 1, 1, 2, 1, 3, 3] => 2, 1, 3, 1, 1, 2, 1, 3, 3
[2, 1, 3, 1, 1, 2, 2, 1, 1] => 2, 1, 3, 1, 1, 2, 2, 1, 1
[2, 1, 3, 1, 1, 2, 2, 1, 2] => 2, 1, 3, 1, 1, 2, 2, 1, 2
[2, 1, 3, 1, 1, 2, 2, 1, 3] => 2, 1, 3, 1, 1, 2, 2, 1, 3
[2, 1, 3, 1, 1, 2, 2, 2, 1] => 2, 1, 3, 1, 1, 2, 2, 2, 1
[2, 1, 3, 1, 1, 2, 2, 2, 2] => 2, 1, 3, 1, 1, 2, 2, 2, 2
[2, 1, 3, 1, 1, 2, 2, 2, 3] => 2, 1, 3, 1, 1, 2, 2, 2, 3
[2, 1, 3, 1, 1, 2, 2, 3, 1] => 2, 1, 3, 1, 1, 2, 2, 3, 1
[2, 1, 3, 1, 1, 2, 2, 3, 2] => 2, 1, 3, 1, 1, 2, 2, 3, 2
[2, 1, 3, 1, 1, 2, 2, 3, 3] => 2, 1, 3, 1, 1, 2, 2, 3, 3
[2, 1, 3, 1, 1, 2, 3, 1, 1] => 2, 1, 3, 1, 1, 2, 3, 1, 1
[2, 1, 3, 1, 1, 2, 3, 1, 2] => 2, 1, 3, 1, 1, 2, 3, 1, 2
[2, 1, 3, 1, 1, 2, 3, 1, 3] => 2, 1, 3, 1, 1, 2, 3, 1, 3
[2, 1, 3, 1, 1, 2, 3, 2, 1] => 2, 1, 3, 1, 1, 2, 3, 2, 1
[2, 1, 3, 1, 1, 2, 3, 2, 2] => 2, 1, 3, 1, 1, 2, 3, 2, 2
[2, 1, 3, 1, 1, 2, 3, 2, 3] => 2, 1, 3, 1, 1, 2, 3, 2, 3
[2, 1, 3, 1, 1, 2, 3, 3, 1] => 2, 1, 3, 1, 1, 2, 3, 3, 1
[2, 1, 3, 1, 1, 2, 3, 3, 2] => 2, 1, 3, 1, 1, 2, 3, 3, 2
[2, 1, 3, 1, 1, 2, 3, 3, 3] => 2, 1, 3, 1, 1, 2, 3, 3, 3
[2, 1, 3, 1, 1, 3, 1, 1, 1] => 2, 1, 3, 1, 1, 3, 1, 1, 1
[2, 1, 3, 1, 1, 3, 1, 1, 2] => 2, 1, 3, 1, 1, 3, 1, 1, 2
[2, 1, 3, 1, 1, 3, 1, 1, 3] => 2, 1, 3, 1, 1, 3, 1, 1, 3
[2, 1, 3, 1, 1, 3, 1, 2, 1] => 2, 1, 3, 1, 1, 3, 1, 2, 1
[2, 1, 3, 1, 1, 3, 1, 2, 2] => 2, 1, 3, 1, 1, 3, 1, 2, 2
[2, 1, 3, 1, 1, 3, 1, 2, 3] => 2, 1, 3, 1, 1, 3, 1, 2, 3
[2, 1, 3, 1, 1, 3, 1, 3, 1] => 2, 1, 3, 1, 1, 3, 1, 3, 1
[2, 1, 3, 1, 1, 3, 1, 3, 2] => 2, 1, 3, 1, 1, 3, 1, 3, 2
[2, 1, 3, 1, 1, 3, 1, 3, 3] => 2, 1, 3, 1, 1, 3, 1, 3, 3
[2, 1, 3, 1, 1, 3, 2, 1, 1] => 2, 1, 3, 1, 1, 3, 2, 1, 1
[2, 1, 3, 1, 1, 3, 2, 1, 2] => 2, 1, 3, 1, 1, 3, 2, 1, 2
[2, 1, 3, 1, 1, 3, 2, 1, 3] => 2, 1, 3, 1, 1, 3, 2, 1, 3
[2, 1, 3, 1, 1, 3, 2, 2, 1] => 2, 1, 3, 1, 1, 3, 2, 2, 1
[2, 1, 3, 1, 1, 3, 2, 2, 2] => 2, 1, 3, 1, 1, 3, 2, 2, 2
[2, 1, 3, 1, 1, 3, 2, 2, 3] => 2, 1, 3, 1, 1, 3, 2, 2, 3
[2, 1, 3, 1, 1, 3, 2, 3, 1] => 2, 1, 3, 1, 1, 3, 2, 3, 1
[2, 1, 3, 1, 1, 3, 2, 3, 2] => 2, 1, 3, 1, 1, 3, 2, 3, 2
[2, 1, 3, 1, 1, 3, 2, 3, 3] => 2, 1, 3, 1, 1, 3, 2, 3, 3
[2, 1, 3, 1, 1, 3, 3, 1, 1] => 2, 1, 3, 1, 1, 3, 3, 1, 1
[2, 1, 3, 1, 1, 3, 3, 1, 2] => 2, 1, 3, 1, 1, 3, 3, 1, 2
[2, 1, 3, 1, 1, 3, 3, 1, 3] => 2, 1, 3, 1, 1, 3, 3, 1, 3
[2, 1, 3, 1, 1, 3, 3, 2, 1] => 2, 1, 3, 1, 1, 3, 3, 2, 1
[2, 1, 3, 1, 1, 3, 3, 2, 2] => 2, 1, 3, 1, 1, 3, 3, 2, 2
[2, 1, 3, 1, 1, 3, 3, 2, 3] => 2, 1, 3, 1, 1, 3, 3, 2, 3
[2, 1, 3, 1, 1, 3, 3, 3, 1] => 2, 1, 3, 1, 1, 3, 3, 3, 1
[2, 1, 3, 1, 1, 3, 3, 3, 2] => 2, 1, 3, 1, 1, 3, 3, 3, 2
[2, 1, 3, 1, 1, 3, 3, 3, 3] => 2, 1, 3, 1, 1, 3, 3, 3, 3
[2, 1, 3, 1, 2, 1, 1, 1, 1] => 2, 1, 3, 1, 2, 1, 1, 1, 1
[2, 1, 3, 1, 2, 1, 1, 1, 2] => 2, 1, 3, 1, 2, 1, 1, 1, 2
[2, 1, 3, 1, 2, 1, 1, 1, 3] => 2, 1, 3, 1, 2, 1, 1, 1, 3
[2, 1, 3, 1, 2, 1, 1, 2, 1] => 2, 1, 3, 1, 2, 1, 1, 2, 1
[2, 1, 3, 1, 2, 1, 1, 2, 2] => 2, 1, 3, 1, 2, 1, 1, 2, 2
[2, 1, 3, 1, 2, 1, 1, 2, 3] => 2, 1, 3, 1, 2, 1, 1, 2, 3
[2, 1, 3, 1, 2, 1, 1, 3, 1] => 2, 1, 3, 1, 2, 1, 1, 3, 1
[2, 1, 3, 1, 2, 1, 1, 3, 2] => 2, 1, 3, 1, 2, 1, 1, 3, 2
[2, 1, 3, 1, 2, 1, 1, 3, 3] => 2, 1, 3, 1, 2, 1, 1, 3, 3
[2, 1, 3, 1, 2, 1, 2, 1, 1] => 2, 1, 3, 1, 2, 1, 2, 1, 1
[2, 1, 3, 1, 2, 1, 2, 1, 2] => 2, 1, 3, 1, 2, 1, 2, 1, 2
[2, 1, 3, 1, 2, 1, 2, 1, 3] => 2, 1, 3, 1, 2, 1, 2, 1, 3
[2, 1, 3, 1, 2, 1, 2, 2, 1] => 2, 1, 3, 1, 2, 1, 2, 2, 1
[2, 1, 3, 1, 2, 1, 2, 2, 2] => 2, 1, 3, 1, 2, 1, 2, 2, 2
[2, 1, 3, 1, 2, 1, 2, 2, 3] => 2, 1, 3, 1, 2, 1, 2, 2, 3
[2, 1, 3, 1, 2, 1, 2, 3, 1] => 2, 1, 3, 1, 2, 1, 2, 3, 1
[2, 1, 3, 1, 2, 1, 2, 3, 2] => 2, 1, 3, 1, 2, 1, 2, 3, 2
[2, 1, 3, 1, 2, 1, 2, 3, 3] => 2, 1, 3, 1, 2, 1, 2, 3, 3
[2, 1, 3, 1, 2, 1, 3, 1, 1] => 2, 1, 3, 1, 2, 1, 3, 1, 1
[2, 1, 3, 1, 2, 1, 3, 1, 2] => 2, 1, 3, 1, 2, 1, 3, 1, 2
[2, 1, 3, 1, 2, 1, 3, 1, 3] => 2, 1, 3, 1, 2, 1, 3, 1, 3
[2, 1, 3, 1, 2, 1, 3, 2, 1] => 2, 1, 3, 1, 2, 1, 3, 2, 1
[2, 1, 3, 1, 2, 1, 3, 2, 2] => 2, 1, 3, 1, 2, 1, 3, 2, 2
[2, 1, 3, 1, 2, 1, 3, 2, 3] => 2, 1, 3, 1, 2, 1, 3, 2, 3
[2, 1, 3, 1, 2, 1, 3, 3, 1] => 2, 1, 3, 1, 2, 1, 3, 3, 1
[2, 1, 3, 1, 2, 1, 3, 3, 2] => 2, 1, 3, 1, 2, 1, 3, 3, 2
[2, 1, 3, 1, 2, 1, 3, 3, 3] => 2, 1, 3, 1, 2, 1, 3, 3, 3
[2, 1, 3, 1, 2, 2, 1, 1, 1] => 2, 1, 3, 1, 2, 2, 1, 1, 1
[2, 1, 3, 1, 2, 2, 1, 1, 2] => 2, 1, 3, 1, 2, 2, 1, 1, 2
[2, 1, 3, 1, 2, 2, 1, 1, 3] => 2, 1, 3, 1, 2, 2, 1, 1, 3
[2, 1, 3, 1, 2, 2, 1, 2, 1] => 2, 1, 3, 1, 2, 2, 1, 2, 1
[2, 1, 3, 1, 2, 2, 1, 2, 2] => 2, 1, 3, 1, 2, 2, 1, 2, 2
[2, 1, 3, 1, 2, 2, 1, 2, 3] => 2, 1, 3, 1, 2, 2, 1, 2, 3
[2, 1, 3, 1, 2, 2, 1, 3, 1] => 2, 1, 3, 1, 2, 2, 1, 3, 1
[2, 1, 3, 1, 2, 2, 1, 3, 2] => 2, 1, 3, 1, 2, 2, 1, 3, 2
[2, 1, 3, 1, 2, 2, 1, 3, 3] => 2, 1, 3, 1, 2, 2, 1, 3, 3
[2, 1, 3, 1, 2, 2, 2, 1, 1] => 2, 1, 3, 1, 2, 2, 2, 1, 1
[2, 1, 3, 1, 2, 2, 2, 1, 2] => 2, 1, 3, 1, 2, 2, 2, 1, 2
[2, 1, 3, 1, 2, 2, 2, 1, 3] => 2, 1, 3, 1, 2, 2, 2, 1, 3
[2, 1, 3, 1, 2, 2, 2, 2, 1] => 2, 1, 3, 1, 2, 2, 2, 2, 1
[2, 1, 3, 1, 2, 2, 2, 2, 2] => 2, 1, 3, 1, 2, 2, 2, 2, 2
[2, 1, 3, 1, 2, 2, 2, 2, 3] => 2, 1, 3, 1, 2, 2, 2, 2, 3
[2, 1, 3, 1, 2, 2, 2, 3, 1] => 2, 1, 3, 1, 2, 2, 2, 3, 1
[2, 1, 3, 1, 2, 2, 2, 3, 2] => 2, 1, 3, 1, 2, 2, 2, 3, 2
[2, 1, 3, 1, 2, 2, 2, 3, 3] => 2, 1, 3, 1, 2, 2, 2, 3, 3
[2, 1, 3, 1, 2, 2, 3, 1, 1] => 2, 1, 3, 1, 2, 2, 3, 1, 1
[2, 1, 3, 1, 2, 2, 3, 1, 2] => 2, 1, 3, 1, 2, 2, 3, 1, 2
[2, 1, 3, 1, 2, 2, 3, 1, 3] => 2, 1, 3, 1, 2, 2, 3, 1, 3
[2, 1, 3, 1, 2, 2, 3, 2, 1] => 2, 1, 3, 1, 2, 2, 3, 2, 1
[2, 1, 3, 1, 2, 2, 3, 2, 2] => 2, 1, 3, 1, 2, 2, 3, 2, 2
[2, 1, 3, 1, 2, 2, 3, 2, 3] => 2, 1, 3, 1, 2, 2, 3, 2, 3
[2, 1, 3, 1, 2, 2, 3, 3, 1] => 2, 1, 3, 1, 2, 2, 3, 3, 1
[2, 1, 3, 1, 2, 2, 3, 3, 2] => 2, 1, 3, 1, 2, 2, 3, 3, 2
[2, 1, 3, 1, 2, 2, 3, 3, 3] => 2, 1, 3, 1, 2, 2, 3, 3, 3
[2, 1, 3, 1, 2, 3, 1, 1, 1] => 2, 1, 3, 1, 2, 3, 1, 1, 1
[2, 1, 3, 1, 2, 3, 1, 1, 2] => 2, 1, 3, 1, 2, 3, 1, 1, 2
[2, 1, 3, 1, 2, 3, 1, 1, 3] => 2, 1, 3, 1, 2, 3, 1, 1, 3
[2, 1, 3, 1, 2, 3, 1, 2, 1] => 2, 1, 3, 1, 2, 3, 1, 2, 1
[2, 1, 3, 1, 2, 3, 1, 2, 2] => 2, 1, 3, 1, 2, 3, 1, 2, 2
[2, 1, 3, 1, 2, 3, 1, 2, 3] => 2, 1, 3, 1, 2, 3, 1, 2, 3
[2, 1, 3, 1, 2, 3, 1, 3, 1] => 2, 1, 3, 1, 2, 3, 1, 3, 1
[2, 1, 3, 1, 2, 3, 1, 3, 2] => 2, 1, 3, 1, 2, 3, 1, 3, 2
[2, 1, 3, 1, 2, 3, 1, 3, 3] => 2, 1, 3, 1, 2, 3, 1, 3, 3
[2, 1, 3, 1, 2, 3, 2, 1, 1] => 2, 1, 3, 1, 2, 3, 2, 1, 1
[2, 1, 3, 1, 2, 3, 2, 1, 2] => 2, 1, 3, 1, 2, 3, 2, 1, 2
[2, 1, 3, 1, 2, 3, 2, 1, 3] => 2, 1, 3, 1, 2, 3, 2, 1, 3
[2, 1, 3, 1, 2, 3, 2, 2, 1] => 2, 1, 3, 1, 2, 3, 2, 2, 1
[2, 1, 3, 1, 2, 3, 2, 2, 2] => 2, 1, 3, 1, 2, 3, 2, 2, 2
[2, 1, 3, 1, 2, 3, 2, 2, 3] => 2, 1, 3, 1, 2, 3, 2, 2, 3
[2, 1, 3, 1, 2, 3, 2, 3, 1] => 2, 1, 3, 1, 2, 3, 2, 3, 1
[2, 1, 3, 1, 2, 3, 2, 3, 2] => 2, 1, 3, 1, 2, 3, 2, 3, 2
[2, 1, 3, 1, 2, 3, 2, 3, 3] => 2, 1, 3, 1, 2, 3, 2, 3, 3
[2, 1, 3, 1, 2, 3, 3, 1, 1] => 2, 1, 3, 1, 2, 3, 3, 1, 1
[2, 1, 3, 1, 2, 3, 3, 1, 2] => 2, 1, 3, 1, 2, 3, 3, 1, 2
[2, 1, 3, 1, 2, 3, 3, 1, 3] => 2, 1, 3, 1, 2, 3, 3, 1, 3
[2, 1, 3, 1, 2, 3, 3, 2, 1] => 2, 1, 3, 1, 2, 3, 3, 2, 1
[2, 1, 3, 1, 2, 3, 3, 2, 2] => 2, 1, 3, 1, 2, 3, 3, 2, 2
[2, 1, 3, 1, 2, 3, 3, 2, 3] => 2, 1, 3, 1, 2, 3, 3, 2, 3
[2, 1, 3, 1, 2, 3, 3, 3, 1] => 2, 1, 3, 1, 2, 3, 3, 3, 1
[2, 1, 3, 1, 2, 3, 3, 3, 2] => 2, 1, 3, 1, 2, 3, 3, 3, 2
[2, 1, 3, 1, 2, 3, 3, 3, 3] => 2, 1, 3, 1, 2, 3, 3, 3, 3
[2, 1, 3, 1, 3, 1, 1, 1, 1] => 2, 1, 3, 1, 3, 1, 1, 1, 1
[2, 1, 3, 1, 3, 1, 1, 1, 2] => 2, 1, 3, 1, 3, 1, 1, 1, 2
[2, 1, 3, 1, 3, 1, 1, 1, 3] => 2, 1, 3, 1, 3, 1, 1, 1, 3
[2, 1, 3, 1, 3, 1, 1, 2, 1] => 2, 1, 3, 1, 3, 1, 1, 2, 1
[2, 1, 3, 1, 3, 1, 1, 2, 2] => 2, 1, 3, 1, 3, 1, 1, 2, 2
[2, 1, 3, 1, 3, 1, 1, 2, 3] => 2, 1, 3, 1, 3, 1, 1, 2, 3
[2, 1, 3, 1, 3, 1, 1, 3, 1] => 2, 1, 3, 1, 3, 1, 1, 3, 1
[2, 1, 3, 1, 3, 1, 1, 3, 2] => 2, 1, 3, 1, 3, 1, 1, 3, 2
[2, 1, 3, 1, 3, 1, 1, 3, 3] => 2, 1, 3, 1, 3, 1, 1, 3, 3
[2, 1, 3, 1, 3, 1, 2, 1, 1] => 2, 1, 3, 1, 3, 1, 2, 1, 1
[2, 1, 3, 1, 3, 1, 2, 1, 2] => 2, 1, 3, 1, 3, 1, 2, 1, 2
[2, 1, 3, 1, 3, 1, 2, 1, 3] => 2, 1, 3, 1, 3, 1, 2, 1, 3
[2, 1, 3, 1, 3, 1, 2, 2, 1] => 2, 1, 3, 1, 3, 1, 2, 2, 1
[2, 1, 3, 1, 3, 1, 2, 2, 2] => 2, 1, 3, 1, 3, 1, 2, 2, 2
[2, 1, 3, 1, 3, 1, 2, 2, 3] => 2, 1, 3, 1, 3, 1, 2, 2, 3
[2, 1, 3, 1, 3, 1, 2, 3, 1] => 2, 1, 3, 1, 3, 1, 2, 3, 1
[2, 1, 3, 1, 3, 1, 2, 3, 2] => 2, 1, 3, 1, 3, 1, 2, 3, 2
[2, 1, 3, 1, 3, 1, 2, 3, 3] => 2, 1, 3, 1, 3, 1, 2, 3, 3
[2, 1, 3, 1, 3, 1, 3, 1, 1] => 2, 1, 3, 1, 3, 1, 3, 1, 1
[2, 1, 3, 1, 3, 1, 3, 1, 2] => 2, 1, 3, 1, 3, 1, 3, 1, 2
[2, 1, 3, 1, 3, 1, 3, 1, 3] => 2, 1, 3, 1, 3, 1, 3, 1, 3
[2, 1, 3, 1, 3, 1, 3, 2, 1] => 2, 1, 3, 1, 3, 1, 3, 2, 1
[2, 1, 3, 1, 3, 1, 3, 2, 2] => 2, 1, 3, 1, 3, 1, 3, 2, 2
[2, 1, 3, 1, 3, 1, 3, 2, 3] => 2, 1, 3, 1, 3, 1, 3, 2, 3
[2, 1, 3, 1, 3, 1, 3, 3, 1] => 2, 1, 3, 1, 3, 1, 3, 3, 1
[2, 1, 3, 1, 3, 1, 3, 3, 2] => 2, 1, 3, 1, 3, 1, 3, 3, 2
[2, 1, 3, 1, 3, 1, 3, 3, 3] => 2, 1, 3, 1, 3, 1, 3, 3, 3
[2, 1, 3, 1, 3, 2, 1, 1, 1] => 2, 1, 3, 1, 3, 2, 1, 1, 1
[2, 1, 3, 1, 3, 2, 1, 1, 2] => 2, 1, 3, 1, 3, 2, 1, 1, 2
[2, 1, 3, 1, 3, 2, 1, 1, 3] => 2, 1, 3, 1, 3, 2, 1, 1, 3
[2, 1, 3, 1, 3, 2, 1, 2, 1] => 2, 1, 3, 1, 3, 2, 1, 2, 1
[2, 1, 3, 1, 3, 2, 1, 2, 2] => 2, 1, 3, 1, 3, 2, 1, 2, 2
[2, 1, 3, 1, 3, 2, 1, 2, 3] => 2, 1, 3, 1, 3, 2, 1, 2, 3
[2, 1, 3, 1, 3, 2, 1, 3, 1] => 2, 1, 3, 1, 3, 2, 1, 3, 1
[2, 1, 3, 1, 3, 2, 1, 3, 2] => 2, 1, 3, 1, 3, 2, 1, 3, 2
[2, 1, 3, 1, 3, 2, 1, 3, 3] => 2, 1, 3, 1, 3, 2, 1, 3, 3
[2, 1, 3, 1, 3, 2, 2, 1, 1] => 2, 1, 3, 1, 3, 2, 2, 1, 1
[2, 1, 3, 1, 3, 2, 2, 1, 2] => 2, 1, 3, 1, 3, 2, 2, 1, 2
[2, 1, 3, 1, 3, 2, 2, 1, 3] => 2, 1, 3, 1, 3, 2, 2, 1, 3
[2, 1, 3, 1, 3, 2, 2, 2, 1] => 2, 1, 3, 1, 3, 2, 2, 2, 1
[2, 1, 3, 1, 3, 2, 2, 2, 2] => 2, 1, 3, 1, 3, 2, 2, 2, 2
[2, 1, 3, 1, 3, 2, 2, 2, 3] => 2, 1, 3, 1, 3, 2, 2, 2, 3
[2, 1, 3, 1, 3, 2, 2, 3, 1] => 2, 1, 3, 1, 3, 2, 2, 3, 1
[2, 1, 3, 1, 3, 2, 2, 3, 2] => 2, 1, 3, 1, 3, 2, 2, 3, 2
[2, 1, 3, 1, 3, 2, 2, 3, 3] => 2, 1, 3, 1, 3, 2, 2, 3, 3
[2, 1, 3, 1, 3, 2, 3, 1, 1] => 2, 1, 3, 1, 3, 2, 3, 1, 1
[2, 1, 3, 1, 3, 2, 3, 1, 2] => 2, 1, 3, 1, 3, 2, 3, 1, 2
[2, 1, 3, 1, 3, 2, 3, 1, 3] => 2, 1, 3, 1, 3, 2, 3, 1, 3
[2, 1, 3, 1, 3, 2, 3, 2, 1] => 2, 1, 3, 1, 3, 2, 3, 2, 1
[2, 1, 3, 1, 3, 2, 3, 2, 2] => 2, 1, 3, 1, 3, 2, 3, 2, 2
[2, 1, 3, 1, 3, 2, 3, 2, 3] => 2, 1, 3, 1, 3, 2, 3, 2, 3
[2, 1, 3, 1, 3, 2, 3, 3, 1] => 2, 1, 3, 1, 3, 2, 3, 3, 1
[2, 1, 3, 1, 3, 2, 3, 3, 2] => 2, 1, 3, 1, 3, 2, 3, 3, 2
[2, 1, 3, 1, 3, 2, 3, 3, 3] => 2, 1, 3, 1, 3, 2, 3, 3, 3
[2, 1, 3, 1, 3, 3, 1, 1, 1] => 2, 1, 3, 1, 3, 3, 1, 1, 1
[2, 1, 3, 1, 3, 3, 1, 1, 2] => 2, 1, 3, 1, 3, 3, 1, 1, 2
[2, 1, 3, 1, 3, 3, 1, 1, 3] => 2, 1, 3, 1, 3, 3, 1, 1, 3
[2, 1, 3, 1, 3, 3, 1, 2, 1] => 2, 1, 3, 1, 3, 3, 1, 2, 1
[2, 1, 3, 1, 3, 3, 1, 2, 2] => 2, 1, 3, 1, 3, 3, 1, 2, 2
[2, 1, 3, 1, 3, 3, 1, 2, 3] => 2, 1, 3, 1, 3, 3, 1, 2, 3
[2, 1, 3, 1, 3, 3, 1, 3, 1] => 2, 1, 3, 1, 3, 3, 1, 3, 1
[2, 1, 3, 1, 3, 3, 1, 3, 2] => 2, 1, 3, 1, 3, 3, 1, 3, 2
[2, 1, 3, 1, 3, 3, 1, 3, 3] => 2, 1, 3, 1, 3, 3, 1, 3, 3
[2, 1, 3, 1, 3, 3, 2, 1, 1] => 2, 1, 3, 1, 3, 3, 2, 1, 1
[2, 1, 3, 1, 3, 3, 2, 1, 2] => 2, 1, 3, 1, 3, 3, 2, 1, 2
[2, 1, 3, 1, 3, 3, 2, 1, 3] => 2, 1, 3, 1, 3, 3, 2, 1, 3
[2, 1, 3, 1, 3, 3, 2, 2, 1] => 2, 1, 3, 1, 3, 3, 2, 2, 1
[2, 1, 3, 1, 3, 3, 2, 2, 2] => 2, 1, 3, 1, 3, 3, 2, 2, 2
[2, 1, 3, 1, 3, 3, 2, 2, 3] => 2, 1, 3, 1, 3, 3, 2, 2, 3
[2, 1, 3, 1, 3, 3, 2, 3, 1] => 2, 1, 3, 1, 3, 3, 2, 3, 1
[2, 1, 3, 1, 3, 3, 2, 3, 2] => 2, 1, 3, 1, 3, 3, 2, 3, 2
[2, 1, 3, 1, 3, 3, 2, 3, 3] => 2, 1, 3, 1, 3, 3, 2, 3, 3
[2, 1, 3, 1, 3, 3, 3, 1, 1] => 2, 1, 3, 1, 3, 3, 3, 1, 1
[2, 1, 3, 1, 3, 3, 3, 1, 2] => 2, 1, 3, 1, 3, 3, 3, 1, 2
[2, 1, 3, 1, 3, 3, 3, 1, 3] => 2, 1, 3, 1, 3, 3, 3, 1, 3
[2, 1, 3, 1, 3, 3, 3, 2, 1] => 2, 1, 3, 1, 3, 3, 3, 2, 1
[2, 1, 3, 1, 3, 3, 3, 2, 2] => 2, 1, 3, 1, 3, 3, 3, 2, 2
[2, 1, 3, 1, 3, 3, 3, 2, 3] => 2, 1, 3, 1, 3, 3, 3, 2, 3
[2, 1, 3, 1, 3, 3, 3, 3, 1] => 2, 1, 3, 1, 3, 3, 3, 3, 1
[2, 1, 3, 1, 3, 3, 3, 3, 2] => 2, 1, 3, 1, 3, 3, 3, 3, 2
[2, 1, 3, 1, 3, 3, 3, 3, 3] => 2, 1, 3, 1, 3, 3, 3, 3, 3
[2, 1, 3, 2, 1, 1, 1, 1, 1] => 2, 1, 3, 2, 1, 1, 1, 1, 1
[2, 1, 3, 2, 1, 1, 1, 1, 2] => 2, 1, 3, 2, 1, 1, 1, 1, 2
[2, 1, 3, 2, 1, 1, 1, 1, 3] => 2, 1, 3, 2, 1, 1, 1, 1, 3
[2, 1, 3, 2, 1, 1, 1, 2, 1] => 2, 1, 3, 2, 1, 1, 1, 2, 1
[2, 1, 3, 2, 1, 1, 1, 2, 2] => 2, 1, 3, 2, 1, 1, 1, 2, 2
[2, 1, 3, 2, 1, 1, 1, 2, 3] => 2, 1, 3, 2, 1, 1, 1, 2, 3
[2, 1, 3, 2, 1, 1, 1, 3, 1] => 2, 1, 3, 2, 1, 1, 1, 3, 1
[2, 1, 3, 2, 1, 1, 1, 3, 2] => 2, 1, 3, 2, 1, 1, 1, 3, 2
[2, 1, 3, 2, 1, 1, 1, 3, 3] => 2, 1, 3, 2, 1, 1, 1, 3, 3
[2, 1, 3, 2, 1, 1, 2, 1, 1] => 2, 1, 3, 2, 1, 1, 2, 1, 1
[2, 1, 3, 2, 1, 1, 2, 1, 2] => 2, 1, 3, 2, 1, 1, 2, 1, 2
[2, 1, 3, 2, 1, 1, 2, 1, 3] => 2, 1, 3, 2, 1, 1, 2, 1, 3
[2, 1, 3, 2, 1, 1, 2, 2, 1] => 2, 1, 3, 2, 1, 1, 2, 2, 1
[2, 1, 3, 2, 1, 1, 2, 2, 2] => 2, 1, 3, 2, 1, 1, 2, 2, 2
[2, 1, 3, 2, 1, 1, 2, 2, 3] => 2, 1, 3, 2, 1, 1, 2, 2, 3
[2, 1, 3, 2, 1, 1, 2, 3, 1] => 2, 1, 3, 2, 1, 1, 2, 3, 1
[2, 1, 3, 2, 1, 1, 2, 3, 2] => 2, 1, 3, 2, 1, 1, 2, 3, 2
[2, 1, 3, 2, 1, 1, 2, 3, 3] => 2, 1, 3, 2, 1, 1, 2, 3, 3
[2, 1, 3, 2, 1, 1, 3, 1, 1] => 2, 1, 3, 2, 1, 1, 3, 1, 1
[2, 1, 3, 2, 1, 1, 3, 1, 2] => 2, 1, 3, 2, 1, 1, 3, 1, 2
[2, 1, 3, 2, 1, 1, 3, 1, 3] => 2, 1, 3, 2, 1, 1, 3, 1, 3
[2, 1, 3, 2, 1, 1, 3, 2, 1] => 2, 1, 3, 2, 1, 1, 3, 2, 1
[2, 1, 3, 2, 1, 1, 3, 2, 2] => 2, 1, 3, 2, 1, 1, 3, 2, 2
[2, 1, 3, 2, 1, 1, 3, 2, 3] => 2, 1, 3, 2, 1, 1, 3, 2, 3
[2, 1, 3, 2, 1, 1, 3, 3, 1] => 2, 1, 3, 2, 1, 1, 3, 3, 1
[2, 1, 3, 2, 1, 1, 3, 3, 2] => 2, 1, 3, 2, 1, 1, 3, 3, 2
[2, 1, 3, 2, 1, 1, 3, 3, 3] => 2, 1, 3, 2, 1, 1, 3, 3, 3
[2, 1, 3, 2, 1, 2, 1, 1, 1] => 2, 1, 3, 2, 1, 2, 1, 1, 1
[2, 1, 3, 2, 1, 2, 1, 1, 2] => 2, 1, 3, 2, 1, 2, 1, 1, 2
[2, 1, 3, 2, 1, 2, 1, 1, 3] => 2, 1, 3, 2, 1, 2, 1, 1, 3
[2, 1, 3, 2, 1, 2, 1, 2, 1] => 2, 1, 3, 2, 1, 2, 1, 2, 1
[2, 1, 3, 2, 1, 2, 1, 2, 2] => 2, 1, 3, 2, 1, 2, 1, 2, 2
[2, 1, 3, 2, 1, 2, 1, 2, 3] => 2, 1, 3, 2, 1, 2, 1, 2, 3
[2, 1, 3, 2, 1, 2, 1, 3, 1] => 2, 1, 3, 2, 1, 2, 1, 3, 1
[2, 1, 3, 2, 1, 2, 1, 3, 2] => 2, 1, 3, 2, 1, 2, 1, 3, 2
[2, 1, 3, 2, 1, 2, 1, 3, 3] => 2, 1, 3, 2, 1, 2, 1, 3, 3
[2, 1, 3, 2, 1, 2, 2, 1, 1] => 2, 1, 3, 2, 1, 2, 2, 1, 1
[2, 1, 3, 2, 1, 2, 2, 1, 2] => 2, 1, 3, 2, 1, 2, 2, 1, 2
[2, 1, 3, 2, 1, 2, 2, 1, 3] => 2, 1, 3, 2, 1, 2, 2, 1, 3
[2, 1, 3, 2, 1, 2, 2, 2, 1] => 2, 1, 3, 2, 1, 2, 2, 2, 1
[2, 1, 3, 2, 1, 2, 2, 2, 2] => 2, 1, 3, 2, 1, 2, 2, 2, 2
[2, 1, 3, 2, 1, 2, 2, 2, 3] => 2, 1, 3, 2, 1, 2, 2, 2, 3
[2, 1, 3, 2, 1, 2, 2, 3, 1] => 2, 1, 3, 2, 1, 2, 2, 3, 1
[2, 1, 3, 2, 1, 2, 2, 3, 2] => 2, 1, 3, 2, 1, 2, 2, 3, 2
[2, 1, 3, 2, 1, 2, 2, 3, 3] => 2, 1, 3, 2, 1, 2, 2, 3, 3
[2, 1, 3, 2, 1, 2, 3, 1, 1] => 2, 1, 3, 2, 1, 2, 3, 1, 1
[2, 1, 3, 2, 1, 2, 3, 1, 2] => 2, 1, 3, 2, 1, 2, 3, 1, 2
[2, 1, 3, 2, 1, 2, 3, 1, 3] => 2, 1, 3, 2, 1, 2, 3, 1, 3
[2, 1, 3, 2, 1, 2, 3, 2, 1] => 2, 1, 3, 2, 1, 2, 3, 2, 1
[2, 1, 3, 2, 1, 2, 3, 2, 2] => 2, 1, 3, 2, 1, 2, 3, 2, 2
[2, 1, 3, 2, 1, 2, 3, 2, 3] => 2, 1, 3, 2, 1, 2, 3, 2, 3
[2, 1, 3, 2, 1, 2, 3, 3, 1] => 2, 1, 3, 2, 1, 2, 3, 3, 1
[2, 1, 3, 2, 1, 2, 3, 3, 2] => 2, 1, 3, 2, 1, 2, 3, 3, 2
[2, 1, 3, 2, 1, 2, 3, 3, 3] => 2, 1, 3, 2, 1, 2, 3, 3, 3
[2, 1, 3, 2, 1, 3, 1, 1, 1] => 2, 1, 3, 2, 1, 3, 1, 1, 1
[2, 1, 3, 2, 1, 3, 1, 1, 2] => 2, 1, 3, 2, 1, 3, 1, 1, 2
[2, 1, 3, 2, 1, 3, 1, 1, 3] => 2, 1, 3, 2, 1, 3, 1, 1, 3
[2, 1, 3, 2, 1, 3, 1, 2, 1] => 2, 1, 3, 2, 1, 3, 1, 2, 1
[2, 1, 3, 2, 1, 3, 1, 2, 2] => 2, 1, 3, 2, 1, 3, 1, 2, 2
[2, 1, 3, 2, 1, 3, 1, 2, 3] => 2, 1, 3, 2, 1, 3, 1, 2, 3
[2, 1, 3, 2, 1, 3, 1, 3, 1] => 2, 1, 3, 2, 1, 3, 1, 3, 1
[2, 1, 3, 2, 1, 3, 1, 3, 2] => 2, 1, 3, 2, 1, 3, 1, 3, 2
[2, 1, 3, 2, 1, 3, 1, 3, 3] => 2, 1, 3, 2, 1, 3, 1, 3, 3
[2, 1, 3, 2, 1, 3, 2, 1, 1] => 2, 1, 3, 2, 1, 3, 2, 1, 1
[2, 1, 3, 2, 1, 3, 2, 1, 2] => 2, 1, 3, 2, 1, 3, 2, 1, 2
[2, 1, 3, 2, 1, 3, 2, 1, 3] => 2, 1, 3, 2, 1, 3, 2, 1, 3
[2, 1, 3, 2, 1, 3, 2, 2, 1] => 2, 1, 3, 2, 1, 3, 2, 2, 1
[2, 1, 3, 2, 1, 3, 2, 2, 2] => 2, 1, 3, 2, 1, 3, 2, 2, 2
[2, 1, 3, 2, 1, 3, 2, 2, 3] => 2, 1, 3, 2, 1, 3, 2, 2, 3
[2, 1, 3, 2, 1, 3, 2, 3, 1] => 2, 1, 3, 2, 1, 3, 2, 3, 1
[2, 1, 3, 2, 1, 3, 2, 3, 2] => 2, 1, 3, 2, 1, 3, 2, 3, 2
[2, 1, 3, 2, 1, 3, 2, 3, 3] => 2, 1, 3, 2, 1, 3, 2, 3, 3
[2, 1, 3, 2, 1, 3, 3, 1, 1] => 2, 1, 3, 2, 1, 3, 3, 1, 1
[2, 1, 3, 2, 1, 3, 3, 1, 2] => 2, 1, 3, 2, 1, 3, 3, 1, 2
[2, 1, 3, 2, 1, 3, 3, 1, 3] => 2, 1, 3, 2, 1, 3, 3, 1, 3
[2, 1, 3, 2, 1, 3, 3, 2, 1] => 2, 1, 3, 2, 1, 3, 3, 2, 1
[2, 1, 3, 2, 1, 3, 3, 2, 2] => 2, 1, 3, 2, 1, 3, 3, 2, 2
[2, 1, 3, 2, 1, 3, 3, 2, 3] => 2, 1, 3, 2, 1, 3, 3, 2, 3
[2, 1, 3, 2, 1, 3, 3, 3, 1] => 2, 1, 3, 2, 1, 3, 3, 3, 1
[2, 1, 3, 2, 1, 3, 3, 3, 2] => 2, 1, 3, 2, 1, 3, 3, 3, 2
[2, 1, 3, 2, 1, 3, 3, 3, 3] => 2, 1, 3, 2, 1, 3, 3, 3, 3
[2, 1, 3, 2, 2, 1, 1, 1, 1] => 2, 1, 3, 2, 2, 1, 1, 1, 1
[2, 1, 3, 2, 2, 1, 1, 1, 2] => 2, 1, 3, 2, 2, 1, 1, 1, 2
[2, 1, 3, 2, 2, 1, 1, 1, 3] => 2, 1, 3, 2, 2, 1, 1, 1, 3
[2, 1, 3, 2, 2, 1, 1, 2, 1] => 2, 1, 3, 2, 2, 1, 1, 2, 1
[2, 1, 3, 2, 2, 1, 1, 2, 2] => 2, 1, 3, 2, 2, 1, 1, 2, 2
[2, 1, 3, 2, 2, 1, 1, 2, 3] => 2, 1, 3, 2, 2, 1, 1, 2, 3
[2, 1, 3, 2, 2, 1, 1, 3, 1] => 2, 1, 3, 2, 2, 1, 1, 3, 1
[2, 1, 3, 2, 2, 1, 1, 3, 2] => 2, 1, 3, 2, 2, 1, 1, 3, 2
[2, 1, 3, 2, 2, 1, 1, 3, 3] => 2, 1, 3, 2, 2, 1, 1, 3, 3
[2, 1, 3, 2, 2, 1, 2, 1, 1] => 2, 1, 3, 2, 2, 1, 2, 1, 1
[2, 1, 3, 2, 2, 1, 2, 1, 2] => 2, 1, 3, 2, 2, 1, 2, 1, 2
[2, 1, 3, 2, 2, 1, 2, 1, 3] => 2, 1, 3, 2, 2, 1, 2, 1, 3
[2, 1, 3, 2, 2, 1, 2, 2, 1] => 2, 1, 3, 2, 2, 1, 2, 2, 1
[2, 1, 3, 2, 2, 1, 2, 2, 2] => 2, 1, 3, 2, 2, 1, 2, 2, 2
[2, 1, 3, 2, 2, 1, 2, 2, 3] => 2, 1, 3, 2, 2, 1, 2, 2, 3
[2, 1, 3, 2, 2, 1, 2, 3, 1] => 2, 1, 3, 2, 2, 1, 2, 3, 1
[2, 1, 3, 2, 2, 1, 2, 3, 2] => 2, 1, 3, 2, 2, 1, 2, 3, 2
[2, 1, 3, 2, 2, 1, 2, 3, 3] => 2, 1, 3, 2, 2, 1, 2, 3, 3
[2, 1, 3, 2, 2, 1, 3, 1, 1] => 2, 1, 3, 2, 2, 1, 3, 1, 1
[2, 1, 3, 2, 2, 1, 3, 1, 2] => 2, 1, 3, 2, 2, 1, 3, 1, 2
[2, 1, 3, 2, 2, 1, 3, 1, 3] => 2, 1, 3, 2, 2, 1, 3, 1, 3
[2, 1, 3, 2, 2, 1, 3, 2, 1] => 2, 1, 3, 2, 2, 1, 3, 2, 1
[2, 1, 3, 2, 2, 1, 3, 2, 2] => 2, 1, 3, 2, 2, 1, 3, 2, 2
[2, 1, 3, 2, 2, 1, 3, 2, 3] => 2, 1, 3, 2, 2, 1, 3, 2, 3
[2, 1, 3, 2, 2, 1, 3, 3, 1] => 2, 1, 3, 2, 2, 1, 3, 3, 1
[2, 1, 3, 2, 2, 1, 3, 3, 2] => 2, 1, 3, 2, 2, 1, 3, 3, 2
[2, 1, 3, 2, 2, 1, 3, 3, 3] => 2, 1, 3, 2, 2, 1, 3, 3, 3
[2, 1, 3, 2, 2, 2, 1, 1, 1] => 2, 1, 3, 2, 2, 2, 1, 1, 1
[2, 1, 3, 2, 2, 2, 1, 1, 2] => 2, 1, 3, 2, 2, 2, 1, 1, 2
[2, 1, 3, 2, 2, 2, 1, 1, 3] => 2, 1, 3, 2, 2, 2, 1, 1, 3
[2, 1, 3, 2, 2, 2, 1, 2, 1] => 2, 1, 3, 2, 2, 2, 1, 2, 1
[2, 1, 3, 2, 2, 2, 1, 2, 2] => 2, 1, 3, 2, 2, 2, 1, 2, 2
[2, 1, 3, 2, 2, 2, 1, 2, 3] => 2, 1, 3, 2, 2, 2, 1, 2, 3
[2, 1, 3, 2, 2, 2, 1, 3, 1] => 2, 1, 3, 2, 2, 2, 1, 3, 1
[2, 1, 3, 2, 2, 2, 1, 3, 2] => 2, 1, 3, 2, 2, 2, 1, 3, 2
[2, 1, 3, 2, 2, 2, 1, 3, 3] => 2, 1, 3, 2, 2, 2, 1, 3, 3
[2, 1, 3, 2, 2, 2, 2, 1, 1] => 2, 1, 3, 2, 2, 2, 2, 1, 1
[2, 1, 3, 2, 2, 2, 2, 1, 2] => 2, 1, 3, 2, 2, 2, 2, 1, 2
[2, 1, 3, 2, 2, 2, 2, 1, 3] => 2, 1, 3, 2, 2, 2, 2, 1, 3
[2, 1, 3, 2, 2, 2, 2, 2, 1] => 2, 1, 3, 2, 2, 2, 2, 2, 1
[2, 1, 3, 2, 2, 2, 2, 2, 2] => 2, 1, 3, 2, 2, 2, 2, 2, 2
[2, 1, 3, 2, 2, 2, 2, 2, 3] => 2, 1, 3, 2, 2, 2, 2, 2, 3
[2, 1, 3, 2, 2, 2, 2, 3, 1] => 2, 1, 3, 2, 2, 2, 2, 3, 1
[2, 1, 3, 2, 2, 2, 2, 3, 2] => 2, 1, 3, 2, 2, 2, 2, 3, 2
[2, 1, 3, 2, 2, 2, 2, 3, 3] => 2, 1, 3, 2, 2, 2, 2, 3, 3
[2, 1, 3, 2, 2, 2, 3, 1, 1] => 2, 1, 3, 2, 2, 2, 3, 1, 1
[2, 1, 3, 2, 2, 2, 3, 1, 2] => 2, 1, 3, 2, 2, 2, 3, 1, 2
[2, 1, 3, 2, 2, 2, 3, 1, 3] => 2, 1, 3, 2, 2, 2, 3, 1, 3
[2, 1, 3, 2, 2, 2, 3, 2, 1] => 2, 1, 3, 2, 2, 2, 3, 2, 1
[2, 1, 3, 2, 2, 2, 3, 2, 2] => 2, 1, 3, 2, 2, 2, 3, 2, 2
[2, 1, 3, 2, 2, 2, 3, 2, 3] => 2, 1, 3, 2, 2, 2, 3, 2, 3
[2, 1, 3, 2, 2, 2, 3, 3, 1] => 2, 1, 3, 2, 2, 2, 3, 3, 1
[2, 1, 3, 2, 2, 2, 3, 3, 2] => 2, 1, 3, 2, 2, 2, 3, 3, 2
[2, 1, 3, 2, 2, 2, 3, 3, 3] => 2, 1, 3, 2, 2, 2, 3, 3, 3
[2, 1, 3, 2, 2, 3, 1, 1, 1] => 2, 1, 3, 2, 2, 3, 1, 1, 1
[2, 1, 3, 2, 2, 3, 1, 1, 2] => 2, 1, 3, 2, 2, 3, 1, 1, 2
[2, 1, 3, 2, 2, 3, 1, 1, 3] => 2, 1, 3, 2, 2, 3, 1, 1, 3
[2, 1, 3, 2, 2, 3, 1, 2, 1] => 2, 1, 3, 2, 2, 3, 1, 2, 1
[2, 1, 3, 2, 2, 3, 1, 2, 2] => 2, 1, 3, 2, 2, 3, 1, 2, 2
[2, 1, 3, 2, 2, 3, 1, 2, 3] => 2, 1, 3, 2, 2, 3, 1, 2, 3
[2, 1, 3, 2, 2, 3, 1, 3, 1] => 2, 1, 3, 2, 2, 3, 1, 3, 1
[2, 1, 3, 2, 2, 3, 1, 3, 2] => 2, 1, 3, 2, 2, 3, 1, 3, 2
[2, 1, 3, 2, 2, 3, 1, 3, 3] => 2, 1, 3, 2, 2, 3, 1, 3, 3
[2, 1, 3, 2, 2, 3, 2, 1, 1] => 2, 1, 3, 2, 2, 3, 2, 1, 1
[2, 1, 3, 2, 2, 3, 2, 1, 2] => 2, 1, 3, 2, 2, 3, 2, 1, 2
[2, 1, 3, 2, 2, 3, 2, 1, 3] => 2, 1, 3, 2, 2, 3, 2, 1, 3
[2, 1, 3, 2, 2, 3, 2, 2, 1] => 2, 1, 3, 2, 2, 3, 2, 2, 1
[2, 1, 3, 2, 2, 3, 2, 2, 2] => 2, 1, 3, 2, 2, 3, 2, 2, 2
[2, 1, 3, 2, 2, 3, 2, 2, 3] => 2, 1, 3, 2, 2, 3, 2, 2, 3
[2, 1, 3, 2, 2, 3, 2, 3, 1] => 2, 1, 3, 2, 2, 3, 2, 3, 1
[2, 1, 3, 2, 2, 3, 2, 3, 2] => 2, 1, 3, 2, 2, 3, 2, 3, 2
[2, 1, 3, 2, 2, 3, 2, 3, 3] => 2, 1, 3, 2, 2, 3, 2, 3, 3
[2, 1, 3, 2, 2, 3, 3, 1, 1] => 2, 1, 3, 2, 2, 3, 3, 1, 1
[2, 1, 3, 2, 2, 3, 3, 1, 2] => 2, 1, 3, 2, 2, 3, 3, 1, 2
[2, 1, 3, 2, 2, 3, 3, 1, 3] => 2, 1, 3, 2, 2, 3, 3, 1, 3
[2, 1, 3, 2, 2, 3, 3, 2, 1] => 2, 1, 3, 2, 2, 3, 3, 2, 1
[2, 1, 3, 2, 2, 3, 3, 2, 2] => 2, 1, 3, 2, 2, 3, 3, 2, 2
[2, 1, 3, 2, 2, 3, 3, 2, 3] => 2, 1, 3, 2, 2, 3, 3, 2, 3
[2, 1, 3, 2, 2, 3, 3, 3, 1] => 2, 1, 3, 2, 2, 3, 3, 3, 1
[2, 1, 3, 2, 2, 3, 3, 3, 2] => 2, 1, 3, 2, 2, 3, 3, 3, 2
[2, 1, 3, 2, 2, 3, 3, 3, 3] => 2, 1, 3, 2, 2, 3, 3, 3, 3
[2, 1, 3, 2, 3, 1, 1, 1, 1] => 2, 1, 3, 2, 3, 1, 1, 1, 1
[2, 1, 3, 2, 3, 1, 1, 1, 2] => 2, 1, 3, 2, 3, 1, 1, 1, 2
[2, 1, 3, 2, 3, 1, 1, 1, 3] => 2, 1, 3, 2, 3, 1, 1, 1, 3
[2, 1, 3, 2, 3, 1, 1, 2, 1] => 2, 1, 3, 2, 3, 1, 1, 2, 1
[2, 1, 3, 2, 3, 1, 1, 2, 2] => 2, 1, 3, 2, 3, 1, 1, 2, 2
[2, 1, 3, 2, 3, 1, 1, 2, 3] => 2, 1, 3, 2, 3, 1, 1, 2, 3
[2, 1, 3, 2, 3, 1, 1, 3, 1] => 2, 1, 3, 2, 3, 1, 1, 3, 1
[2, 1, 3, 2, 3, 1, 1, 3, 2] => 2, 1, 3, 2, 3, 1, 1, 3, 2
[2, 1, 3, 2, 3, 1, 1, 3, 3] => 2, 1, 3, 2, 3, 1, 1, 3, 3
[2, 1, 3, 2, 3, 1, 2, 1, 1] => 2, 1, 3, 2, 3, 1, 2, 1, 1
[2, 1, 3, 2, 3, 1, 2, 1, 2] => 2, 1, 3, 2, 3, 1, 2, 1, 2
[2, 1, 3, 2, 3, 1, 2, 1, 3] => 2, 1, 3, 2, 3, 1, 2, 1, 3
[2, 1, 3, 2, 3, 1, 2, 2, 1] => 2, 1, 3, 2, 3, 1, 2, 2, 1
[2, 1, 3, 2, 3, 1, 2, 2, 2] => 2, 1, 3, 2, 3, 1, 2, 2, 2
[2, 1, 3, 2, 3, 1, 2, 2, 3] => 2, 1, 3, 2, 3, 1, 2, 2, 3
[2, 1, 3, 2, 3, 1, 2, 3, 1] => 2, 1, 3, 2, 3, 1, 2, 3, 1
[2, 1, 3, 2, 3, 1, 2, 3, 2] => 2, 1, 3, 2, 3, 1, 2, 3, 2
[2, 1, 3, 2, 3, 1, 2, 3, 3] => 2, 1, 3, 2, 3, 1, 2, 3, 3
[2, 1, 3, 2, 3, 1, 3, 1, 1] => 2, 1, 3, 2, 3, 1, 3, 1, 1
[2, 1, 3, 2, 3, 1, 3, 1, 2] => 2, 1, 3, 2, 3, 1, 3, 1, 2
[2, 1, 3, 2, 3, 1, 3, 1, 3] => 2, 1, 3, 2, 3, 1, 3, 1, 3
[2, 1, 3, 2, 3, 1, 3, 2, 1] => 2, 1, 3, 2, 3, 1, 3, 2, 1
[2, 1, 3, 2, 3, 1, 3, 2, 2] => 2, 1, 3, 2, 3, 1, 3, 2, 2
[2, 1, 3, 2, 3, 1, 3, 2, 3] => 2, 1, 3, 2, 3, 1, 3, 2, 3
[2, 1, 3, 2, 3, 1, 3, 3, 1] => 2, 1, 3, 2, 3, 1, 3, 3, 1
[2, 1, 3, 2, 3, 1, 3, 3, 2] => 2, 1, 3, 2, 3, 1, 3, 3, 2
[2, 1, 3, 2, 3, 1, 3, 3, 3] => 2, 1, 3, 2, 3, 1, 3, 3, 3
[2, 1, 3, 2, 3, 2, 1, 1, 1] => 2, 1, 3, 2, 3, 2, 1, 1, 1
[2, 1, 3, 2, 3, 2, 1, 1, 2] => 2, 1, 3, 2, 3, 2, 1, 1, 2
[2, 1, 3, 2, 3, 2, 1, 1, 3] => 2, 1, 3, 2, 3, 2, 1, 1, 3
[2, 1, 3, 2, 3, 2, 1, 2, 1] => 2, 1, 3, 2, 3, 2, 1, 2, 1
[2, 1, 3, 2, 3, 2, 1, 2, 2] => 2, 1, 3, 2, 3, 2, 1, 2, 2
[2, 1, 3, 2, 3, 2, 1, 2, 3] => 2, 1, 3, 2, 3, 2, 1, 2, 3
[2, 1, 3, 2, 3, 2, 1, 3, 1] => 2, 1, 3, 2, 3, 2, 1, 3, 1
[2, 1, 3, 2, 3, 2, 1, 3, 2] => 2, 1, 3, 2, 3, 2, 1, 3, 2
[2, 1, 3, 2, 3, 2, 1, 3, 3] => 2, 1, 3, 2, 3, 2, 1, 3, 3
[2, 1, 3, 2, 3, 2, 2, 1, 1] => 2, 1, 3, 2, 3, 2, 2, 1, 1
[2, 1, 3, 2, 3, 2, 2, 1, 2] => 2, 1, 3, 2, 3, 2, 2, 1, 2
[2, 1, 3, 2, 3, 2, 2, 1, 3] => 2, 1, 3, 2, 3, 2, 2, 1, 3
[2, 1, 3, 2, 3, 2, 2, 2, 1] => 2, 1, 3, 2, 3, 2, 2, 2, 1
[2, 1, 3, 2, 3, 2, 2, 2, 2] => 2, 1, 3, 2, 3, 2, 2, 2, 2
[2, 1, 3, 2, 3, 2, 2, 2, 3] => 2, 1, 3, 2, 3, 2, 2, 2, 3
[2, 1, 3, 2, 3, 2, 2, 3, 1] => 2, 1, 3, 2, 3, 2, 2, 3, 1
[2, 1, 3, 2, 3, 2, 2, 3, 2] => 2, 1, 3, 2, 3, 2, 2, 3, 2
[2, 1, 3, 2, 3, 2, 2, 3, 3] => 2, 1, 3, 2, 3, 2, 2, 3, 3
[2, 1, 3, 2, 3, 2, 3, 1, 1] => 2, 1, 3, 2, 3, 2, 3, 1, 1
[2, 1, 3, 2, 3, 2, 3, 1, 2] => 2, 1, 3, 2, 3, 2, 3, 1, 2
[2, 1, 3, 2, 3, 2, 3, 1, 3] => 2, 1, 3, 2, 3, 2, 3, 1, 3
[2, 1, 3, 2, 3, 2, 3, 2, 1] => 2, 1, 3, 2, 3, 2, 3, 2, 1
[2, 1, 3, 2, 3, 2, 3, 2, 2] => 2, 1, 3, 2, 3, 2, 3, 2, 2
[2, 1, 3, 2, 3, 2, 3, 2, 3] => 2, 1, 3, 2, 3, 2, 3, 2, 3
[2, 1, 3, 2, 3, 2, 3, 3, 1] => 2, 1, 3, 2, 3, 2, 3, 3, 1
[2, 1, 3, 2, 3, 2, 3, 3, 2] => 2, 1, 3, 2, 3, 2, 3, 3, 2
[2, 1, 3, 2, 3, 2, 3, 3, 3] => 2, 1, 3, 2, 3, 2, 3, 3, 3
[2, 1, 3, 2, 3, 3, 1, 1, 1] => 2, 1, 3, 2, 3, 3, 1, 1, 1
[2, 1, 3, 2, 3, 3, 1, 1, 2] => 2, 1, 3, 2, 3, 3, 1, 1, 2
[2, 1, 3, 2, 3, 3, 1, 1, 3] => 2, 1, 3, 2, 3, 3, 1, 1, 3
[2, 1, 3, 2, 3, 3, 1, 2, 1] => 2, 1, 3, 2, 3, 3, 1, 2, 1
[2, 1, 3, 2, 3, 3, 1, 2, 2] => 2, 1, 3, 2, 3, 3, 1, 2, 2
[2, 1, 3, 2, 3, 3, 1, 2, 3] => 2, 1, 3, 2, 3, 3, 1, 2, 3
[2, 1, 3, 2, 3, 3, 1, 3, 1] => 2, 1, 3, 2, 3, 3, 1, 3, 1
[2, 1, 3, 2, 3, 3, 1, 3, 2] => 2, 1, 3, 2, 3, 3, 1, 3, 2
[2, 1, 3, 2, 3, 3, 1, 3, 3] => 2, 1, 3, 2, 3, 3, 1, 3, 3
[2, 1, 3, 2, 3, 3, 2, 1, 1] => 2, 1, 3, 2, 3, 3, 2, 1, 1
[2, 1, 3, 2, 3, 3, 2, 1, 2] => 2, 1, 3, 2, 3, 3, 2, 1, 2
[2, 1, 3, 2, 3, 3, 2, 1, 3] => 2, 1, 3, 2, 3, 3, 2, 1, 3
[2, 1, 3, 2, 3, 3, 2, 2, 1] => 2, 1, 3, 2, 3, 3, 2, 2, 1
[2, 1, 3, 2, 3, 3, 2, 2, 2] => 2, 1, 3, 2, 3, 3, 2, 2, 2
[2, 1, 3, 2, 3, 3, 2, 2, 3] => 2, 1, 3, 2, 3, 3, 2, 2, 3
[2, 1, 3, 2, 3, 3, 2, 3, 1] => 2, 1, 3, 2, 3, 3, 2, 3, 1
[2, 1, 3, 2, 3, 3, 2, 3, 2] => 2, 1, 3, 2, 3, 3, 2, 3, 2
[2, 1, 3, 2, 3, 3, 2, 3, 3] => 2, 1, 3, 2, 3, 3, 2, 3, 3
[2, 1, 3, 2, 3, 3, 3, 1, 1] => 2, 1, 3, 2, 3, 3, 3, 1, 1
[2, 1, 3, 2, 3, 3, 3, 1, 2] => 2, 1, 3, 2, 3, 3, 3, 1, 2
[2, 1, 3, 2, 3, 3, 3, 1, 3] => 2, 1, 3, 2, 3, 3, 3, 1, 3
[2, 1, 3, 2, 3, 3, 3, 2, 1] => 2, 1, 3, 2, 3, 3, 3, 2, 1
[2, 1, 3, 2, 3, 3, 3, 2, 2] => 2, 1, 3, 2, 3, 3, 3, 2, 2
[2, 1, 3, 2, 3, 3, 3, 2, 3] => 2, 1, 3, 2, 3, 3, 3, 2, 3
[2, 1, 3, 2, 3, 3, 3, 3, 1] => 2, 1, 3, 2, 3, 3, 3, 3, 1
[2, 1, 3, 2, 3, 3, 3, 3, 2] => 2, 1, 3, 2, 3, 3, 3, 3, 2
[2, 1, 3, 2, 3, 3, 3, 3, 3] => 2, 1, 3, 2, 3, 3, 3, 3, 3
[2, 1, 3, 3, 1, 1, 1, 1, 1] => 2, 1, 3, 3, 1, 1, 1, 1, 1
[2, 1, 3, 3, 1, 1, 1, 1, 2] => 2, 1, 3, 3, 1, 1, 1, 1, 2
[2, 1, 3, 3, 1, 1, 1, 1, 3] => 2, 1, 3, 3, 1, 1, 1, 1, 3
[2, 1, 3, 3, 1, 1, 1, 2, 1] => 2, 1, 3, 3, 1, 1, 1, 2, 1
[2, 1, 3, 3, 1, 1, 1, 2, 2] => 2, 1, 3, 3, 1, 1, 1, 2, 2
[2, 1, 3, 3, 1, 1, 1, 2, 3] => 2, 1, 3, 3, 1, 1, 1, 2, 3
[2, 1, 3, 3, 1, 1, 1, 3, 1] => 2, 1, 3, 3, 1, 1, 1, 3, 1
[2, 1, 3, 3, 1, 1, 1, 3, 2] => 2, 1, 3, 3, 1, 1, 1, 3, 2
[2, 1, 3, 3, 1, 1, 1, 3, 3] => 2, 1, 3, 3, 1, 1, 1, 3, 3
[2, 1, 3, 3, 1, 1, 2, 1, 1] => 2, 1, 3, 3, 1, 1, 2, 1, 1
[2, 1, 3, 3, 1, 1, 2, 1, 2] => 2, 1, 3, 3, 1, 1, 2, 1, 2
[2, 1, 3, 3, 1, 1, 2, 1, 3] => 2, 1, 3, 3, 1, 1, 2, 1, 3
[2, 1, 3, 3, 1, 1, 2, 2, 1] => 2, 1, 3, 3, 1, 1, 2, 2, 1
[2, 1, 3, 3, 1, 1, 2, 2, 2] => 2, 1, 3, 3, 1, 1, 2, 2, 2
[2, 1, 3, 3, 1, 1, 2, 2, 3] => 2, 1, 3, 3, 1, 1, 2, 2, 3
[2, 1, 3, 3, 1, 1, 2, 3, 1] => 2, 1, 3, 3, 1, 1, 2, 3, 1
[2, 1, 3, 3, 1, 1, 2, 3, 2] => 2, 1, 3, 3, 1, 1, 2, 3, 2
[2, 1, 3, 3, 1, 1, 2, 3, 3] => 2, 1, 3, 3, 1, 1, 2, 3, 3
[2, 1, 3, 3, 1, 1, 3, 1, 1] => 2, 1, 3, 3, 1, 1, 3, 1, 1
[2, 1, 3, 3, 1, 1, 3, 1, 2] => 2, 1, 3, 3, 1, 1, 3, 1, 2
[2, 1, 3, 3, 1, 1, 3, 1, 3] => 2, 1, 3, 3, 1, 1, 3, 1, 3
[2, 1, 3, 3, 1, 1, 3, 2, 1] => 2, 1, 3, 3, 1, 1, 3, 2, 1
[2, 1, 3, 3, 1, 1, 3, 2, 2] => 2, 1, 3, 3, 1, 1, 3, 2, 2
[2, 1, 3, 3, 1, 1, 3, 2, 3] => 2, 1, 3, 3, 1, 1, 3, 2, 3
[2, 1, 3, 3, 1, 1, 3, 3, 1] => 2, 1, 3, 3, 1, 1, 3, 3, 1
[2, 1, 3, 3, 1, 1, 3, 3, 2] => 2, 1, 3, 3, 1, 1, 3, 3, 2
[2, 1, 3, 3, 1, 1, 3, 3, 3] => 2, 1, 3, 3, 1, 1, 3, 3, 3
[2, 1, 3, 3, 1, 2, 1, 1, 1] => 2, 1, 3, 3, 1, 2, 1, 1, 1
[2, 1, 3, 3, 1, 2, 1, 1, 2] => 2, 1, 3, 3, 1, 2, 1, 1, 2
[2, 1, 3, 3, 1, 2, 1, 1, 3] => 2, 1, 3, 3, 1, 2, 1, 1, 3
[2, 1, 3, 3, 1, 2, 1, 2, 1] => 2, 1, 3, 3, 1, 2, 1, 2, 1
[2, 1, 3, 3, 1, 2, 1, 2, 2] => 2, 1, 3, 3, 1, 2, 1, 2, 2
[2, 1, 3, 3, 1, 2, 1, 2, 3] => 2, 1, 3, 3, 1, 2, 1, 2, 3
[2, 1, 3, 3, 1, 2, 1, 3, 1] => 2, 1, 3, 3, 1, 2, 1, 3, 1
[2, 1, 3, 3, 1, 2, 1, 3, 2] => 2, 1, 3, 3, 1, 2, 1, 3, 2
[2, 1, 3, 3, 1, 2, 1, 3, 3] => 2, 1, 3, 3, 1, 2, 1, 3, 3
[2, 1, 3, 3, 1, 2, 2, 1, 1] => 2, 1, 3, 3, 1, 2, 2, 1, 1
[2, 1, 3, 3, 1, 2, 2, 1, 2] => 2, 1, 3, 3, 1, 2, 2, 1, 2
[2, 1, 3, 3, 1, 2, 2, 1, 3] => 2, 1, 3, 3, 1, 2, 2, 1, 3
[2, 1, 3, 3, 1, 2, 2, 2, 1] => 2, 1, 3, 3, 1, 2, 2, 2, 1
[2, 1, 3, 3, 1, 2, 2, 2, 2] => 2, 1, 3, 3, 1, 2, 2, 2, 2
[2, 1, 3, 3, 1, 2, 2, 2, 3] => 2, 1, 3, 3, 1, 2, 2, 2, 3
[2, 1, 3, 3, 1, 2, 2, 3, 1] => 2, 1, 3, 3, 1, 2, 2, 3, 1
[2, 1, 3, 3, 1, 2, 2, 3, 2] => 2, 1, 3, 3, 1, 2, 2, 3, 2
[2, 1, 3, 3, 1, 2, 2, 3, 3] => 2, 1, 3, 3, 1, 2, 2, 3, 3
[2, 1, 3, 3, 1, 2, 3, 1, 1] => 2, 1, 3, 3, 1, 2, 3, 1, 1
[2, 1, 3, 3, 1, 2, 3, 1, 2] => 2, 1, 3, 3, 1, 2, 3, 1, 2
[2, 1, 3, 3, 1, 2, 3, 1, 3] => 2, 1, 3, 3, 1, 2, 3, 1, 3
[2, 1, 3, 3, 1, 2, 3, 2, 1] => 2, 1, 3, 3, 1, 2, 3, 2, 1
[2, 1, 3, 3, 1, 2, 3, 2, 2] => 2, 1, 3, 3, 1, 2, 3, 2, 2
[2, 1, 3, 3, 1, 2, 3, 2, 3] => 2, 1, 3, 3, 1, 2, 3, 2, 3
[2, 1, 3, 3, 1, 2, 3, 3, 1] => 2, 1, 3, 3, 1, 2, 3, 3, 1
[2, 1, 3, 3, 1, 2, 3, 3, 2] => 2, 1, 3, 3, 1, 2, 3, 3, 2
[2, 1, 3, 3, 1, 2, 3, 3, 3] => 2, 1, 3, 3, 1, 2, 3, 3, 3
[2, 1, 3, 3, 1, 3, 1, 1, 1] => 2, 1, 3, 3, 1, 3, 1, 1, 1
[2, 1, 3, 3, 1, 3, 1, 1, 2] => 2, 1, 3, 3, 1, 3, 1, 1, 2
[2, 1, 3, 3, 1, 3, 1, 1, 3] => 2, 1, 3, 3, 1, 3, 1, 1, 3
[2, 1, 3, 3, 1, 3, 1, 2, 1] => 2, 1, 3, 3, 1, 3, 1, 2, 1
[2, 1, 3, 3, 1, 3, 1, 2, 2] => 2, 1, 3, 3, 1, 3, 1, 2, 2
[2, 1, 3, 3, 1, 3, 1, 2, 3] => 2, 1, 3, 3, 1, 3, 1, 2, 3
[2, 1, 3, 3, 1, 3, 1, 3, 1] => 2, 1, 3, 3, 1, 3, 1, 3, 1
[2, 1, 3, 3, 1, 3, 1, 3, 2] => 2, 1, 3, 3, 1, 3, 1, 3, 2
[2, 1, 3, 3, 1, 3, 1, 3, 3] => 2, 1, 3, 3, 1, 3, 1, 3, 3
[2, 1, 3, 3, 1, 3, 2, 1, 1] => 2, 1, 3, 3, 1, 3, 2, 1, 1
[2, 1, 3, 3, 1, 3, 2, 1, 2] => 2, 1, 3, 3, 1, 3, 2, 1, 2
[2, 1, 3, 3, 1, 3, 2, 1, 3] => 2, 1, 3, 3, 1, 3, 2, 1, 3
[2, 1, 3, 3, 1, 3, 2, 2, 1] => 2, 1, 3, 3, 1, 3, 2, 2, 1
[2, 1, 3, 3, 1, 3, 2, 2, 2] => 2, 1, 3, 3, 1, 3, 2, 2, 2
[2, 1, 3, 3, 1, 3, 2, 2, 3] => 2, 1, 3, 3, 1, 3, 2, 2, 3
[2, 1, 3, 3, 1, 3, 2, 3, 1] => 2, 1, 3, 3, 1, 3, 2, 3, 1
[2, 1, 3, 3, 1, 3, 2, 3, 2] => 2, 1, 3, 3, 1, 3, 2, 3, 2
[2, 1, 3, 3, 1, 3, 2, 3, 3] => 2, 1, 3, 3, 1, 3, 2, 3, 3
[2, 1, 3, 3, 1, 3, 3, 1, 1] => 2, 1, 3, 3, 1, 3, 3, 1, 1
[2, 1, 3, 3, 1, 3, 3, 1, 2] => 2, 1, 3, 3, 1, 3, 3, 1, 2
[2, 1, 3, 3, 1, 3, 3, 1, 3] => 2, 1, 3, 3, 1, 3, 3, 1, 3
[2, 1, 3, 3, 1, 3, 3, 2, 1] => 2, 1, 3, 3, 1, 3, 3, 2, 1
[2, 1, 3, 3, 1, 3, 3, 2, 2] => 2, 1, 3, 3, 1, 3, 3, 2, 2
[2, 1, 3, 3, 1, 3, 3, 2, 3] => 2, 1, 3, 3, 1, 3, 3, 2, 3
[2, 1, 3, 3, 1, 3, 3, 3, 1] => 2, 1, 3, 3, 1, 3, 3, 3, 1
[2, 1, 3, 3, 1, 3, 3, 3, 2] => 2, 1, 3, 3, 1, 3, 3, 3, 2
[2, 1, 3, 3, 1, 3, 3, 3, 3] => 2, 1, 3, 3, 1, 3, 3, 3, 3
[2, 1, 3, 3, 2, 1, 1, 1, 1] => 2, 1, 3, 3, 2, 1, 1, 1, 1
[2, 1, 3, 3, 2, 1, 1, 1, 2] => 2, 1, 3, 3, 2, 1, 1, 1, 2
[2, 1, 3, 3, 2, 1, 1, 1, 3] => 2, 1, 3, 3, 2, 1, 1, 1, 3
[2, 1, 3, 3, 2, 1, 1, 2, 1] => 2, 1, 3, 3, 2, 1, 1, 2, 1
[2, 1, 3, 3, 2, 1, 1, 2, 2] => 2, 1, 3, 3, 2, 1, 1, 2, 2
[2, 1, 3, 3, 2, 1, 1, 2, 3] => 2, 1, 3, 3, 2, 1, 1, 2, 3
[2, 1, 3, 3, 2, 1, 1, 3, 1] => 2, 1, 3, 3, 2, 1, 1, 3, 1
[2, 1, 3, 3, 2, 1, 1, 3, 2] => 2, 1, 3, 3, 2, 1, 1, 3, 2
[2, 1, 3, 3, 2, 1, 1, 3, 3] => 2, 1, 3, 3, 2, 1, 1, 3, 3
[2, 1, 3, 3, 2, 1, 2, 1, 1] => 2, 1, 3, 3, 2, 1, 2, 1, 1
[2, 1, 3, 3, 2, 1, 2, 1, 2] => 2, 1, 3, 3, 2, 1, 2, 1, 2
[2, 1, 3, 3, 2, 1, 2, 1, 3] => 2, 1, 3, 3, 2, 1, 2, 1, 3
[2, 1, 3, 3, 2, 1, 2, 2, 1] => 2, 1, 3, 3, 2, 1, 2, 2, 1
[2, 1, 3, 3, 2, 1, 2, 2, 2] => 2, 1, 3, 3, 2, 1, 2, 2, 2
[2, 1, 3, 3, 2, 1, 2, 2, 3] => 2, 1, 3, 3, 2, 1, 2, 2, 3
[2, 1, 3, 3, 2, 1, 2, 3, 1] => 2, 1, 3, 3, 2, 1, 2, 3, 1
[2, 1, 3, 3, 2, 1, 2, 3, 2] => 2, 1, 3, 3, 2, 1, 2, 3, 2
[2, 1, 3, 3, 2, 1, 2, 3, 3] => 2, 1, 3, 3, 2, 1, 2, 3, 3
[2, 1, 3, 3, 2, 1, 3, 1, 1] => 2, 1, 3, 3, 2, 1, 3, 1, 1
[2, 1, 3, 3, 2, 1, 3, 1, 2] => 2, 1, 3, 3, 2, 1, 3, 1, 2
[2, 1, 3, 3, 2, 1, 3, 1, 3] => 2, 1, 3, 3, 2, 1, 3, 1, 3
[2, 1, 3, 3, 2, 1, 3, 2, 1] => 2, 1, 3, 3, 2, 1, 3, 2, 1
[2, 1, 3, 3, 2, 1, 3, 2, 2] => 2, 1, 3, 3, 2, 1, 3, 2, 2
[2, 1, 3, 3, 2, 1, 3, 2, 3] => 2, 1, 3, 3, 2, 1, 3, 2, 3
[2, 1, 3, 3, 2, 1, 3, 3, 1] => 2, 1, 3, 3, 2, 1, 3, 3, 1
[2, 1, 3, 3, 2, 1, 3, 3, 2] => 2, 1, 3, 3, 2, 1, 3, 3, 2
[2, 1, 3, 3, 2, 1, 3, 3, 3] => 2, 1, 3, 3, 2, 1, 3, 3, 3
[2, 1, 3, 3, 2, 2, 1, 1, 1] => 2, 1, 3, 3, 2, 2, 1, 1, 1
[2, 1, 3, 3, 2, 2, 1, 1, 2] => 2, 1, 3, 3, 2, 2, 1, 1, 2
[2, 1, 3, 3, 2, 2, 1, 1, 3] => 2, 1, 3, 3, 2, 2, 1, 1, 3
[2, 1, 3, 3, 2, 2, 1, 2, 1] => 2, 1, 3, 3, 2, 2, 1, 2, 1
[2, 1, 3, 3, 2, 2, 1, 2, 2] => 2, 1, 3, 3, 2, 2, 1, 2, 2
[2, 1, 3, 3, 2, 2, 1, 2, 3] => 2, 1, 3, 3, 2, 2, 1, 2, 3
[2, 1, 3, 3, 2, 2, 1, 3, 1] => 2, 1, 3, 3, 2, 2, 1, 3, 1
[2, 1, 3, 3, 2, 2, 1, 3, 2] => 2, 1, 3, 3, 2, 2, 1, 3, 2
[2, 1, 3, 3, 2, 2, 1, 3, 3] => 2, 1, 3, 3, 2, 2, 1, 3, 3
[2, 1, 3, 3, 2, 2, 2, 1, 1] => 2, 1, 3, 3, 2, 2, 2, 1, 1
[2, 1, 3, 3, 2, 2, 2, 1, 2] => 2, 1, 3, 3, 2, 2, 2, 1, 2
[2, 1, 3, 3, 2, 2, 2, 1, 3] => 2, 1, 3, 3, 2, 2, 2, 1, 3
[2, 1, 3, 3, 2, 2, 2, 2, 1] => 2, 1, 3, 3, 2, 2, 2, 2, 1
[2, 1, 3, 3, 2, 2, 2, 2, 2] => 2, 1, 3, 3, 2, 2, 2, 2, 2
[2, 1, 3, 3, 2, 2, 2, 2, 3] => 2, 1, 3, 3, 2, 2, 2, 2, 3
[2, 1, 3, 3, 2, 2, 2, 3, 1] => 2, 1, 3, 3, 2, 2, 2, 3, 1
[2, 1, 3, 3, 2, 2, 2, 3, 2] => 2, 1, 3, 3, 2, 2, 2, 3, 2
[2, 1, 3, 3, 2, 2, 2, 3, 3] => 2, 1, 3, 3, 2, 2, 2, 3, 3
[2, 1, 3, 3, 2, 2, 3, 1, 1] => 2, 1, 3, 3, 2, 2, 3, 1, 1
[2, 1, 3, 3, 2, 2, 3, 1, 2] => 2, 1, 3, 3, 2, 2, 3, 1, 2
[2, 1, 3, 3, 2, 2, 3, 1, 3] => 2, 1, 3, 3, 2, 2, 3, 1, 3
[2, 1, 3, 3, 2, 2, 3, 2, 1] => 2, 1, 3, 3, 2, 2, 3, 2, 1
[2, 1, 3, 3, 2, 2, 3, 2, 2] => 2, 1, 3, 3, 2, 2, 3, 2, 2
[2, 1, 3, 3, 2, 2, 3, 2, 3] => 2, 1, 3, 3, 2, 2, 3, 2, 3
[2, 1, 3, 3, 2, 2, 3, 3, 1] => 2, 1, 3, 3, 2, 2, 3, 3, 1
[2, 1, 3, 3, 2, 2, 3, 3, 2] => 2, 1, 3, 3, 2, 2, 3, 3, 2
[2, 1, 3, 3, 2, 2, 3, 3, 3] => 2, 1, 3, 3, 2, 2, 3, 3, 3
[2, 1, 3, 3, 2, 3, 1, 1, 1] => 2, 1, 3, 3, 2, 3, 1, 1, 1
[2, 1, 3, 3, 2, 3, 1, 1, 2] => 2, 1, 3, 3, 2, 3, 1, 1, 2
[2, 1, 3, 3, 2, 3, 1, 1, 3] => 2, 1, 3, 3, 2, 3, 1, 1, 3
[2, 1, 3, 3, 2, 3, 1, 2, 1] => 2, 1, 3, 3, 2, 3, 1, 2, 1
[2, 1, 3, 3, 2, 3, 1, 2, 2] => 2, 1, 3, 3, 2, 3, 1, 2, 2
[2, 1, 3, 3, 2, 3, 1, 2, 3] => 2, 1, 3, 3, 2, 3, 1, 2, 3
[2, 1, 3, 3, 2, 3, 1, 3, 1] => 2, 1, 3, 3, 2, 3, 1, 3, 1
[2, 1, 3, 3, 2, 3, 1, 3, 2] => 2, 1, 3, 3, 2, 3, 1, 3, 2
[2, 1, 3, 3, 2, 3, 1, 3, 3] => 2, 1, 3, 3, 2, 3, 1, 3, 3
[2, 1, 3, 3, 2, 3, 2, 1, 1] => 2, 1, 3, 3, 2, 3, 2, 1, 1
[2, 1, 3, 3, 2, 3, 2, 1, 2] => 2, 1, 3, 3, 2, 3, 2, 1, 2
[2, 1, 3, 3, 2, 3, 2, 1, 3] => 2, 1, 3, 3, 2, 3, 2, 1, 3
[2, 1, 3, 3, 2, 3, 2, 2, 1] => 2, 1, 3, 3, 2, 3, 2, 2, 1
[2, 1, 3, 3, 2, 3, 2, 2, 2] => 2, 1, 3, 3, 2, 3, 2, 2, 2
[2, 1, 3, 3, 2, 3, 2, 2, 3] => 2, 1, 3, 3, 2, 3, 2, 2, 3
[2, 1, 3, 3, 2, 3, 2, 3, 1] => 2, 1, 3, 3, 2, 3, 2, 3, 1
[2, 1, 3, 3, 2, 3, 2, 3, 2] => 2, 1, 3, 3, 2, 3, 2, 3, 2
[2, 1, 3, 3, 2, 3, 2, 3, 3] => 2, 1, 3, 3, 2, 3, 2, 3, 3
[2, 1, 3, 3, 2, 3, 3, 1, 1] => 2, 1, 3, 3, 2, 3, 3, 1, 1
[2, 1, 3, 3, 2, 3, 3, 1, 2] => 2, 1, 3, 3, 2, 3, 3, 1, 2
[2, 1, 3, 3, 2, 3, 3, 1, 3] => 2, 1, 3, 3, 2, 3, 3, 1, 3
[2, 1, 3, 3, 2, 3, 3, 2, 1] => 2, 1, 3, 3, 2, 3, 3, 2, 1
[2, 1, 3, 3, 2, 3, 3, 2, 2] => 2, 1, 3, 3, 2, 3, 3, 2, 2
[2, 1, 3, 3, 2, 3, 3, 2, 3] => 2, 1, 3, 3, 2, 3, 3, 2, 3
[2, 1, 3, 3, 2, 3, 3, 3, 1] => 2, 1, 3, 3, 2, 3, 3, 3, 1
[2, 1, 3, 3, 2, 3, 3, 3, 2] => 2, 1, 3, 3, 2, 3, 3, 3, 2
[2, 1, 3, 3, 2, 3, 3, 3, 3] => 2, 1, 3, 3, 2, 3, 3, 3, 3
[2, 1, 3, 3, 3, 1, 1, 1, 1] => 2, 1, 3, 3, 3, 1, 1, 1, 1
[2, 1, 3, 3, 3, 1, 1, 1, 2] => 2, 1, 3, 3, 3, 1, 1, 1, 2
[2, 1, 3, 3, 3, 1, 1, 1, 3] => 2, 1, 3, 3, 3, 1, 1, 1, 3
[2, 1, 3, 3, 3, 1, 1, 2, 1] => 2, 1, 3, 3, 3, 1, 1, 2, 1
[2, 1, 3, 3, 3, 1, 1, 2, 2] => 2, 1, 3, 3, 3, 1, 1, 2, 2
[2, 1, 3, 3, 3, 1, 1, 2, 3] => 2, 1, 3, 3, 3, 1, 1, 2, 3
[2, 1, 3, 3, 3, 1, 1, 3, 1] => 2, 1, 3, 3, 3, 1, 1, 3, 1
[2, 1, 3, 3, 3, 1, 1, 3, 2] => 2, 1, 3, 3, 3, 1, 1, 3, 2
[2, 1, 3, 3, 3, 1, 1, 3, 3] => 2, 1, 3, 3, 3, 1, 1, 3, 3
[2, 1, 3, 3, 3, 1, 2, 1, 1] => 2, 1, 3, 3, 3, 1, 2, 1, 1
[2, 1, 3, 3, 3, 1, 2, 1, 2] => 2, 1, 3, 3, 3, 1, 2, 1, 2
[2, 1, 3, 3, 3, 1, 2, 1, 3] => 2, 1, 3, 3, 3, 1, 2, 1, 3
[2, 1, 3, 3, 3, 1, 2, 2, 1] => 2, 1, 3, 3, 3, 1, 2, 2, 1
[2, 1, 3, 3, 3, 1, 2, 2, 2] => 2, 1, 3, 3, 3, 1, 2, 2, 2
[2, 1, 3, 3, 3, 1, 2, 2, 3] => 2, 1, 3, 3, 3, 1, 2, 2, 3
[2, 1, 3, 3, 3, 1, 2, 3, 1] => 2, 1, 3, 3, 3, 1, 2, 3, 1
[2, 1, 3, 3, 3, 1, 2, 3, 2] => 2, 1, 3, 3, 3, 1, 2, 3, 2
[2, 1, 3, 3, 3, 1, 2, 3, 3] => 2, 1, 3, 3, 3, 1, 2, 3, 3
[2, 1, 3, 3, 3, 1, 3, 1, 1] => 2, 1, 3, 3, 3, 1, 3, 1, 1
[2, 1, 3, 3, 3, 1, 3, 1, 2] => 2, 1, 3, 3, 3, 1, 3, 1, 2
[2, 1, 3, 3, 3, 1, 3, 1, 3] => 2, 1, 3, 3, 3, 1, 3, 1, 3
[2, 1, 3, 3, 3, 1, 3, 2, 1] => 2, 1, 3, 3, 3, 1, 3, 2, 1
[2, 1, 3, 3, 3, 1, 3, 2, 2] => 2, 1, 3, 3, 3, 1, 3, 2, 2
[2, 1, 3, 3, 3, 1, 3, 2, 3] => 2, 1, 3, 3, 3, 1, 3, 2, 3
[2, 1, 3, 3, 3, 1, 3, 3, 1] => 2, 1, 3, 3, 3, 1, 3, 3, 1
[2, 1, 3, 3, 3, 1, 3, 3, 2] => 2, 1, 3, 3, 3, 1, 3, 3, 2
[2, 1, 3, 3, 3, 1, 3, 3, 3] => 2, 1, 3, 3, 3, 1, 3, 3, 3
[2, 1, 3, 3, 3, 2, 1, 1, 1] => 2, 1, 3, 3, 3, 2, 1, 1, 1
[2, 1, 3, 3, 3, 2, 1, 1, 2] => 2, 1, 3, 3, 3, 2, 1, 1, 2
[2, 1, 3, 3, 3, 2, 1, 1, 3] => 2, 1, 3, 3, 3, 2, 1, 1, 3
[2, 1, 3, 3, 3, 2, 1, 2, 1] => 2, 1, 3, 3, 3, 2, 1, 2, 1
[2, 1, 3, 3, 3, 2, 1, 2, 2] => 2, 1, 3, 3, 3, 2, 1, 2, 2
[2, 1, 3, 3, 3, 2, 1, 2, 3] => 2, 1, 3, 3, 3, 2, 1, 2, 3
[2, 1, 3, 3, 3, 2, 1, 3, 1] => 2, 1, 3, 3, 3, 2, 1, 3, 1
[2, 1, 3, 3, 3, 2, 1, 3, 2] => 2, 1, 3, 3, 3, 2, 1, 3, 2
[2, 1, 3, 3, 3, 2, 1, 3, 3] => 2, 1, 3, 3, 3, 2, 1, 3, 3
[2, 1, 3, 3, 3, 2, 2, 1, 1] => 2, 1, 3, 3, 3, 2, 2, 1, 1
[2, 1, 3, 3, 3, 2, 2, 1, 2] => 2, 1, 3, 3, 3, 2, 2, 1, 2
[2, 1, 3, 3, 3, 2, 2, 1, 3] => 2, 1, 3, 3, 3, 2, 2, 1, 3
[2, 1, 3, 3, 3, 2, 2, 2, 1] => 2, 1, 3, 3, 3, 2, 2, 2, 1
[2, 1, 3, 3, 3, 2, 2, 2, 2] => 2, 1, 3, 3, 3, 2, 2, 2, 2
[2, 1, 3, 3, 3, 2, 2, 2, 3] => 2, 1, 3, 3, 3, 2, 2, 2, 3
[2, 1, 3, 3, 3, 2, 2, 3, 1] => 2, 1, 3, 3, 3, 2, 2, 3, 1
[2, 1, 3, 3, 3, 2, 2, 3, 2] => 2, 1, 3, 3, 3, 2, 2, 3, 2
[2, 1, 3, 3, 3, 2, 2, 3, 3] => 2, 1, 3, 3, 3, 2, 2, 3, 3
[2, 1, 3, 3, 3, 2, 3, 1, 1] => 2, 1, 3, 3, 3, 2, 3, 1, 1
[2, 1, 3, 3, 3, 2, 3, 1, 2] => 2, 1, 3, 3, 3, 2, 3, 1, 2
[2, 1, 3, 3, 3, 2, 3, 1, 3] => 2, 1, 3, 3, 3, 2, 3, 1, 3
[2, 1, 3, 3, 3, 2, 3, 2, 1] => 2, 1, 3, 3, 3, 2, 3, 2, 1
[2, 1, 3, 3, 3, 2, 3, 2, 2] => 2, 1, 3, 3, 3, 2, 3, 2, 2
[2, 1, 3, 3, 3, 2, 3, 2, 3] => 2, 1, 3, 3, 3, 2, 3, 2, 3
[2, 1, 3, 3, 3, 2, 3, 3, 1] => 2, 1, 3, 3, 3, 2, 3, 3, 1
[2, 1, 3, 3, 3, 2, 3, 3, 2] => 2, 1, 3, 3, 3, 2, 3, 3, 2
[2, 1, 3, 3, 3, 2, 3, 3, 3] => 2, 1, 3, 3, 3, 2, 3, 3, 3
[2, 1, 3, 3, 3, 3, 1, 1, 1] => 2, 1, 3, 3, 3, 3, 1, 1, 1
[2, 1, 3, 3, 3, 3, 1, 1, 2] => 2, 1, 3, 3, 3, 3, 1, 1, 2
[2, 1, 3, 3, 3, 3, 1, 1, 3] => 2, 1, 3, 3, 3, 3, 1, 1, 3
[2, 1, 3, 3, 3, 3, 1, 2, 1] => 2, 1, 3, 3, 3, 3, 1, 2, 1
[2, 1, 3, 3, 3, 3, 1, 2, 2] => 2, 1, 3, 3, 3, 3, 1, 2, 2
[2, 1, 3, 3, 3, 3, 1, 2, 3] => 2, 1, 3, 3, 3, 3, 1, 2, 3
[2, 1, 3, 3, 3, 3, 1, 3, 1] => 2, 1, 3, 3, 3, 3, 1, 3, 1
[2, 1, 3, 3, 3, 3, 1, 3, 2] => 2, 1, 3, 3, 3, 3, 1, 3, 2
[2, 1, 3, 3, 3, 3, 1, 3, 3] => 2, 1, 3, 3, 3, 3, 1, 3, 3
[2, 1, 3, 3, 3, 3, 2, 1, 1] => 2, 1, 3, 3, 3, 3, 2, 1, 1
[2, 1, 3, 3, 3, 3, 2, 1, 2] => 2, 1, 3, 3, 3, 3, 2, 1, 2
[2, 1, 3, 3, 3, 3, 2, 1, 3] => 2, 1, 3, 3, 3, 3, 2, 1, 3
[2, 1, 3, 3, 3, 3, 2, 2, 1] => 2, 1, 3, 3, 3, 3, 2, 2, 1
[2, 1, 3, 3, 3, 3, 2, 2, 2] => 2, 1, 3, 3, 3, 3, 2, 2, 2
[2, 1, 3, 3, 3, 3, 2, 2, 3] => 2, 1, 3, 3, 3, 3, 2, 2, 3
[2, 1, 3, 3, 3, 3, 2, 3, 1] => 2, 1, 3, 3, 3, 3, 2, 3, 1
[2, 1, 3, 3, 3, 3, 2, 3, 2] => 2, 1, 3, 3, 3, 3, 2, 3, 2
[2, 1, 3, 3, 3, 3, 2, 3, 3] => 2, 1, 3, 3, 3, 3, 2, 3, 3
[2, 1, 3, 3, 3, 3, 3, 1, 1] => 2, 1, 3, 3, 3, 3, 3, 1, 1
[2, 1, 3, 3, 3, 3, 3, 1, 2] => 2, 1, 3, 3, 3, 3, 3, 1, 2
[2, 1, 3, 3, 3, 3, 3, 1, 3] => 2, 1, 3, 3, 3, 3, 3, 1, 3
[2, 1, 3, 3, 3, 3, 3, 2, 1] => 2, 1, 3, 3, 3, 3, 3, 2, 1
[2, 1, 3, 3, 3, 3, 3, 2, 2] => 2, 1, 3, 3, 3, 3, 3, 2, 2
[2, 1, 3, 3, 3, 3, 3, 2, 3] => 2, 1, 3, 3, 3, 3, 3, 2, 3
[2, 1, 3, 3, 3, 3, 3, 3, 1] => 2, 1, 3, 3, 3, 3, 3, 3, 1
[2, 1, 3, 3, 3, 3, 3, 3, 2] => 2, 1, 3, 3, 3, 3, 3, 3, 2
[2, 1, 3, 3, 3, 3, 3, 3, 3] => 2, 1, 3, 3, 3, 3, 3, 3, 3
[2, 2, 1, 1, 1, 1, 1, 1, 1] => 2, 2, 1, 1, 1, 1, 1, 1, 1
[2, 2, 1, 1, 1, 1, 1, 1, 2] => 2, 2, 1, 1, 1, 1, 1, 1, 2
[2, 2, 1, 1, 1, 1, 1, 1, 3] => 2, 2, 1, 1, 1, 1, 1, 1, 3
[2, 2, 1, 1, 1, 1, 1, 2, 1] => 2, 2, 1, 1, 1, 1, 1, 2, 1
[2, 2, 1, 1, 1, 1, 1, 2, 2] => 2, 2, 1, 1, 1, 1, 1, 2, 2
[2, 2, 1, 1, 1, 1, 1, 2, 3] => 2, 2, 1, 1, 1, 1, 1, 2, 3
[2, 2, 1, 1, 1, 1, 1, 3, 1] => 2, 2, 1, 1, 1, 1, 1, 3, 1
[2, 2, 1, 1, 1, 1, 1, 3, 2] => 2, 2, 1, 1, 1, 1, 1, 3, 2
[2, 2, 1, 1, 1, 1, 1, 3, 3] => 2, 2, 1, 1, 1, 1, 1, 3, 3
[2, 2, 1, 1, 1, 1, 2, 1, 1] => 2, 2, 1, 1, 1, 1, 2, 1, 1
[2, 2, 1, 1, 1, 1, 2, 1, 2] => 2, 2, 1, 1, 1, 1, 2, 1, 2
[2, 2, 1, 1, 1, 1, 2, 1, 3] => 2, 2, 1, 1, 1, 1, 2, 1, 3
[2, 2, 1, 1, 1, 1, 2, 2, 1] => 2, 2, 1, 1, 1, 1, 2, 2, 1
[2, 2, 1, 1, 1, 1, 2, 2, 2] => 2, 2, 1, 1, 1, 1, 2, 2, 2
[2, 2, 1, 1, 1, 1, 2, 2, 3] => 2, 2, 1, 1, 1, 1, 2, 2, 3
[2, 2, 1, 1, 1, 1, 2, 3, 1] => 2, 2, 1, 1, 1, 1, 2, 3, 1
[2, 2, 1, 1, 1, 1, 2, 3, 2] => 2, 2, 1, 1, 1, 1, 2, 3, 2
[2, 2, 1, 1, 1, 1, 2, 3, 3] => 2, 2, 1, 1, 1, 1, 2, 3, 3
[2, 2, 1, 1, 1, 1, 3, 1, 1] => 2, 2, 1, 1, 1, 1, 3, 1, 1
[2, 2, 1, 1, 1, 1, 3, 1, 2] => 2, 2, 1, 1, 1, 1, 3, 1, 2
[2, 2, 1, 1, 1, 1, 3, 1, 3] => 2, 2, 1, 1, 1, 1, 3, 1, 3
[2, 2, 1, 1, 1, 1, 3, 2, 1] => 2, 2, 1, 1, 1, 1, 3, 2, 1
[2, 2, 1, 1, 1, 1, 3, 2, 2] => 2, 2, 1, 1, 1, 1, 3, 2, 2
[2, 2, 1, 1, 1, 1, 3, 2, 3] => 2, 2, 1, 1, 1, 1, 3, 2, 3
[2, 2, 1, 1, 1, 1, 3, 3, 1] => 2, 2, 1, 1, 1, 1, 3, 3, 1
[2, 2, 1, 1, 1, 1, 3, 3, 2] => 2, 2, 1, 1, 1, 1, 3, 3, 2
[2, 2, 1, 1, 1, 1, 3, 3, 3] => 2, 2, 1, 1, 1, 1, 3, 3, 3
[2, 2, 1, 1, 1, 2, 1, 1, 1] => 2, 2, 1, 1, 1, 2, 1, 1, 1
[2, 2, 1, 1, 1, 2, 1, 1, 2] => 2, 2, 1, 1, 1, 2, 1, 1, 2
[2, 2, 1, 1, 1, 2, 1, 1, 3] => 2, 2, 1, 1, 1, 2, 1, 1, 3
[2, 2, 1, 1, 1, 2, 1, 2, 1] => 2, 2, 1, 1, 1, 2, 1, 2, 1
[2, 2, 1, 1, 1, 2, 1, 2, 2] => 2, 2, 1, 1, 1, 2, 1, 2, 2
[2, 2, 1, 1, 1, 2, 1, 2, 3] => 2, 2, 1, 1, 1, 2, 1, 2, 3
[2, 2, 1, 1, 1, 2, 1, 3, 1] => 2, 2, 1, 1, 1, 2, 1, 3, 1
[2, 2, 1, 1, 1, 2, 1, 3, 2] => 2, 2, 1, 1, 1, 2, 1, 3, 2
[2, 2, 1, 1, 1, 2, 1, 3, 3] => 2, 2, 1, 1, 1, 2, 1, 3, 3
[2, 2, 1, 1, 1, 2, 2, 1, 1] => 2, 2, 1, 1, 1, 2, 2, 1, 1
[2, 2, 1, 1, 1, 2, 2, 1, 2] => 2, 2, 1, 1, 1, 2, 2, 1, 2
[2, 2, 1, 1, 1, 2, 2, 1, 3] => 2, 2, 1, 1, 1, 2, 2, 1, 3
[2, 2, 1, 1, 1, 2, 2, 2, 1] => 2, 2, 1, 1, 1, 2, 2, 2, 1
[2, 2, 1, 1, 1, 2, 2, 2, 2] => 2, 2, 1, 1, 1, 2, 2, 2, 2
[2, 2, 1, 1, 1, 2, 2, 2, 3] => 2, 2, 1, 1, 1, 2, 2, 2, 3
[2, 2, 1, 1, 1, 2, 2, 3, 1] => 2, 2, 1, 1, 1, 2, 2, 3, 1
[2, 2, 1, 1, 1, 2, 2, 3, 2] => 2, 2, 1, 1, 1, 2, 2, 3, 2
[2, 2, 1, 1, 1, 2, 2, 3, 3] => 2, 2, 1, 1, 1, 2, 2, 3, 3
[2, 2, 1, 1, 1, 2, 3, 1, 1] => 2, 2, 1, 1, 1, 2, 3, 1, 1
[2, 2, 1, 1, 1, 2, 3, 1, 2] => 2, 2, 1, 1, 1, 2, 3, 1, 2
[2, 2, 1, 1, 1, 2, 3, 1, 3] => 2, 2, 1, 1, 1, 2, 3, 1, 3
[2, 2, 1, 1, 1, 2, 3, 2, 1] => 2, 2, 1, 1, 1, 2, 3, 2, 1
[2, 2, 1, 1, 1, 2, 3, 2, 2] => 2, 2, 1, 1, 1, 2, 3, 2, 2
[2, 2, 1, 1, 1, 2, 3, 2, 3] => 2, 2, 1, 1, 1, 2, 3, 2, 3
[2, 2, 1, 1, 1, 2, 3, 3, 1] => 2, 2, 1, 1, 1, 2, 3, 3, 1
[2, 2, 1, 1, 1, 2, 3, 3, 2] => 2, 2, 1, 1, 1, 2, 3, 3, 2
[2, 2, 1, 1, 1, 2, 3, 3, 3] => 2, 2, 1, 1, 1, 2, 3, 3, 3
[2, 2, 1, 1, 1, 3, 1, 1, 1] => 2, 2, 1, 1, 1, 3, 1, 1, 1
[2, 2, 1, 1, 1, 3, 1, 1, 2] => 2, 2, 1, 1, 1, 3, 1, 1, 2
[2, 2, 1, 1, 1, 3, 1, 1, 3] => 2, 2, 1, 1, 1, 3, 1, 1, 3
[2, 2, 1, 1, 1, 3, 1, 2, 1] => 2, 2, 1, 1, 1, 3, 1, 2, 1
[2, 2, 1, 1, 1, 3, 1, 2, 2] => 2, 2, 1, 1, 1, 3, 1, 2, 2
[2, 2, 1, 1, 1, 3, 1, 2, 3] => 2, 2, 1, 1, 1, 3, 1, 2, 3
[2, 2, 1, 1, 1, 3, 1, 3, 1] => 2, 2, 1, 1, 1, 3, 1, 3, 1
[2, 2, 1, 1, 1, 3, 1, 3, 2] => 2, 2, 1, 1, 1, 3, 1, 3, 2
[2, 2, 1, 1, 1, 3, 1, 3, 3] => 2, 2, 1, 1, 1, 3, 1, 3, 3
[2, 2, 1, 1, 1, 3, 2, 1, 1] => 2, 2, 1, 1, 1, 3, 2, 1, 1
[2, 2, 1, 1, 1, 3, 2, 1, 2] => 2, 2, 1, 1, 1, 3, 2, 1, 2
[2, 2, 1, 1, 1, 3, 2, 1, 3] => 2, 2, 1, 1, 1, 3, 2, 1, 3
[2, 2, 1, 1, 1, 3, 2, 2, 1] => 2, 2, 1, 1, 1, 3, 2, 2, 1
[2, 2, 1, 1, 1, 3, 2, 2, 2] => 2, 2, 1, 1, 1, 3, 2, 2, 2
[2, 2, 1, 1, 1, 3, 2, 2, 3] => 2, 2, 1, 1, 1, 3, 2, 2, 3
[2, 2, 1, 1, 1, 3, 2, 3, 1] => 2, 2, 1, 1, 1, 3, 2, 3, 1
[2, 2, 1, 1, 1, 3, 2, 3, 2] => 2, 2, 1, 1, 1, 3, 2, 3, 2
[2, 2, 1, 1, 1, 3, 2, 3, 3] => 2, 2, 1, 1, 1, 3, 2, 3, 3
[2, 2, 1, 1, 1, 3, 3, 1, 1] => 2, 2, 1, 1, 1, 3, 3, 1, 1
[2, 2, 1, 1, 1, 3, 3, 1, 2] => 2, 2, 1, 1, 1, 3, 3, 1, 2
[2, 2, 1, 1, 1, 3, 3, 1, 3] => 2, 2, 1, 1, 1, 3, 3, 1, 3
[2, 2, 1, 1, 1, 3, 3, 2, 1] => 2, 2, 1, 1, 1, 3, 3, 2, 1
[2, 2, 1, 1, 1, 3, 3, 2, 2] => 2, 2, 1, 1, 1, 3, 3, 2, 2
[2, 2, 1, 1, 1, 3, 3, 2, 3] => 2, 2, 1, 1, 1, 3, 3, 2, 3
[2, 2, 1, 1, 1, 3, 3, 3, 1] => 2, 2, 1, 1, 1, 3, 3, 3, 1
[2, 2, 1, 1, 1, 3, 3, 3, 2] => 2, 2, 1, 1, 1, 3, 3, 3, 2
[2, 2, 1, 1, 1, 3, 3, 3, 3] => 2, 2, 1, 1, 1, 3, 3, 3, 3
[2, 2, 1, 1, 2, 1, 1, 1, 1] => 2, 2, 1, 1, 2, 1, 1, 1, 1
[2, 2, 1, 1, 2, 1, 1, 1, 2] => 2, 2, 1, 1, 2, 1, 1, 1, 2
[2, 2, 1, 1, 2, 1, 1, 1, 3] => 2, 2, 1, 1, 2, 1, 1, 1, 3
[2, 2, 1, 1, 2, 1, 1, 2, 1] => 2, 2, 1, 1, 2, 1, 1, 2, 1
[2, 2, 1, 1, 2, 1, 1, 2, 2] => 2, 2, 1, 1, 2, 1, 1, 2, 2
[2, 2, 1, 1, 2, 1, 1, 2, 3] => 2, 2, 1, 1, 2, 1, 1, 2, 3
[2, 2, 1, 1, 2, 1, 1, 3, 1] => 2, 2, 1, 1, 2, 1, 1, 3, 1
[2, 2, 1, 1, 2, 1, 1, 3, 2] => 2, 2, 1, 1, 2, 1, 1, 3, 2
[2, 2, 1, 1, 2, 1, 1, 3, 3] => 2, 2, 1, 1, 2, 1, 1, 3, 3
[2, 2, 1, 1, 2, 1, 2, 1, 1] => 2, 2, 1, 1, 2, 1, 2, 1, 1
[2, 2, 1, 1, 2, 1, 2, 1, 2] => 2, 2, 1, 1, 2, 1, 2, 1, 2
[2, 2, 1, 1, 2, 1, 2, 1, 3] => 2, 2, 1, 1, 2, 1, 2, 1, 3
[2, 2, 1, 1, 2, 1, 2, 2, 1] => 2, 2, 1, 1, 2, 1, 2, 2, 1
[2, 2, 1, 1, 2, 1, 2, 2, 2] => 2, 2, 1, 1, 2, 1, 2, 2, 2
[2, 2, 1, 1, 2, 1, 2, 2, 3] => 2, 2, 1, 1, 2, 1, 2, 2, 3
[2, 2, 1, 1, 2, 1, 2, 3, 1] => 2, 2, 1, 1, 2, 1, 2, 3, 1
[2, 2, 1, 1, 2, 1, 2, 3, 2] => 2, 2, 1, 1, 2, 1, 2, 3, 2
[2, 2, 1, 1, 2, 1, 2, 3, 3] => 2, 2, 1, 1, 2, 1, 2, 3, 3
[2, 2, 1, 1, 2, 1, 3, 1, 1] => 2, 2, 1, 1, 2, 1, 3, 1, 1
[2, 2, 1, 1, 2, 1, 3, 1, 2] => 2, 2, 1, 1, 2, 1, 3, 1, 2
[2, 2, 1, 1, 2, 1, 3, 1, 3] => 2, 2, 1, 1, 2, 1, 3, 1, 3
[2, 2, 1, 1, 2, 1, 3, 2, 1] => 2, 2, 1, 1, 2, 1, 3, 2, 1
[2, 2, 1, 1, 2, 1, 3, 2, 2] => 2, 2, 1, 1, 2, 1, 3, 2, 2
[2, 2, 1, 1, 2, 1, 3, 2, 3] => 2, 2, 1, 1, 2, 1, 3, 2, 3
[2, 2, 1, 1, 2, 1, 3, 3, 1] => 2, 2, 1, 1, 2, 1, 3, 3, 1
[2, 2, 1, 1, 2, 1, 3, 3, 2] => 2, 2, 1, 1, 2, 1, 3, 3, 2
[2, 2, 1, 1, 2, 1, 3, 3, 3] => 2, 2, 1, 1, 2, 1, 3, 3, 3
[2, 2, 1, 1, 2, 2, 1, 1, 1] => 2, 2, 1, 1, 2, 2, 1, 1, 1
[2, 2, 1, 1, 2, 2, 1, 1, 2] => 2, 2, 1, 1, 2, 2, 1, 1, 2
[2, 2, 1, 1, 2, 2, 1, 1, 3] => 2, 2, 1, 1, 2, 2, 1, 1, 3
[2, 2, 1, 1, 2, 2, 1, 2, 1] => 2, 2, 1, 1, 2, 2, 1, 2, 1
[2, 2, 1, 1, 2, 2, 1, 2, 2] => 2, 2, 1, 1, 2, 2, 1, 2, 2
[2, 2, 1, 1, 2, 2, 1, 2, 3] => 2, 2, 1, 1, 2, 2, 1, 2, 3
[2, 2, 1, 1, 2, 2, 1, 3, 1] => 2, 2, 1, 1, 2, 2, 1, 3, 1
[2, 2, 1, 1, 2, 2, 1, 3, 2] => 2, 2, 1, 1, 2, 2, 1, 3, 2
[2, 2, 1, 1, 2, 2, 1, 3, 3] => 2, 2, 1, 1, 2, 2, 1, 3, 3
[2, 2, 1, 1, 2, 2, 2, 1, 1] => 2, 2, 1, 1, 2, 2, 2, 1, 1
[2, 2, 1, 1, 2, 2, 2, 1, 2] => 2, 2, 1, 1, 2, 2, 2, 1, 2
[2, 2, 1, 1, 2, 2, 2, 1, 3] => 2, 2, 1, 1, 2, 2, 2, 1, 3
[2, 2, 1, 1, 2, 2, 2, 2, 1] => 2, 2, 1, 1, 2, 2, 2, 2, 1
[2, 2, 1, 1, 2, 2, 2, 2, 2] => 2, 2, 1, 1, 2, 2, 2, 2, 2
[2, 2, 1, 1, 2, 2, 2, 2, 3] => 2, 2, 1, 1, 2, 2, 2, 2, 3
[2, 2, 1, 1, 2, 2, 2, 3, 1] => 2, 2, 1, 1, 2, 2, 2, 3, 1
[2, 2, 1, 1, 2, 2, 2, 3, 2] => 2, 2, 1, 1, 2, 2, 2, 3, 2
[2, 2, 1, 1, 2, 2, 2, 3, 3] => 2, 2, 1, 1, 2, 2, 2, 3, 3
[2, 2, 1, 1, 2, 2, 3, 1, 1] => 2, 2, 1, 1, 2, 2, 3, 1, 1
[2, 2, 1, 1, 2, 2, 3, 1, 2] => 2, 2, 1, 1, 2, 2, 3, 1, 2
[2, 2, 1, 1, 2, 2, 3, 1, 3] => 2, 2, 1, 1, 2, 2, 3, 1, 3
[2, 2, 1, 1, 2, 2, 3, 2, 1] => 2, 2, 1, 1, 2, 2, 3, 2, 1
[2, 2, 1, 1, 2, 2, 3, 2, 2] => 2, 2, 1, 1, 2, 2, 3, 2, 2
[2, 2, 1, 1, 2, 2, 3, 2, 3] => 2, 2, 1, 1, 2, 2, 3, 2, 3
[2, 2, 1, 1, 2, 2, 3, 3, 1] => 2, 2, 1, 1, 2, 2, 3, 3, 1
[2, 2, 1, 1, 2, 2, 3, 3, 2] => 2, 2, 1, 1, 2, 2, 3, 3, 2
[2, 2, 1, 1, 2, 2, 3, 3, 3] => 2, 2, 1, 1, 2, 2, 3, 3, 3
[2, 2, 1, 1, 2, 3, 1, 1, 1] => 2, 2, 1, 1, 2, 3, 1, 1, 1
[2, 2, 1, 1, 2, 3, 1, 1, 2] => 2, 2, 1, 1, 2, 3, 1, 1, 2
[2, 2, 1, 1, 2, 3, 1, 1, 3] => 2, 2, 1, 1, 2, 3, 1, 1, 3
[2, 2, 1, 1, 2, 3, 1, 2, 1] => 2, 2, 1, 1, 2, 3, 1, 2, 1
[2, 2, 1, 1, 2, 3, 1, 2, 2] => 2, 2, 1, 1, 2, 3, 1, 2, 2
[2, 2, 1, 1, 2, 3, 1, 2, 3] => 2, 2, 1, 1, 2, 3, 1, 2, 3
[2, 2, 1, 1, 2, 3, 1, 3, 1] => 2, 2, 1, 1, 2, 3, 1, 3, 1
[2, 2, 1, 1, 2, 3, 1, 3, 2] => 2, 2, 1, 1, 2, 3, 1, 3, 2
[2, 2, 1, 1, 2, 3, 1, 3, 3] => 2, 2, 1, 1, 2, 3, 1, 3, 3
[2, 2, 1, 1, 2, 3, 2, 1, 1] => 2, 2, 1, 1, 2, 3, 2, 1, 1
[2, 2, 1, 1, 2, 3, 2, 1, 2] => 2, 2, 1, 1, 2, 3, 2, 1, 2
[2, 2, 1, 1, 2, 3, 2, 1, 3] => 2, 2, 1, 1, 2, 3, 2, 1, 3
[2, 2, 1, 1, 2, 3, 2, 2, 1] => 2, 2, 1, 1, 2, 3, 2, 2, 1
[2, 2, 1, 1, 2, 3, 2, 2, 2] => 2, 2, 1, 1, 2, 3, 2, 2, 2
[2, 2, 1, 1, 2, 3, 2, 2, 3] => 2, 2, 1, 1, 2, 3, 2, 2, 3
[2, 2, 1, 1, 2, 3, 2, 3, 1] => 2, 2, 1, 1, 2, 3, 2, 3, 1
[2, 2, 1, 1, 2, 3, 2, 3, 2] => 2, 2, 1, 1, 2, 3, 2, 3, 2
[2, 2, 1, 1, 2, 3, 2, 3, 3] => 2, 2, 1, 1, 2, 3, 2, 3, 3
[2, 2, 1, 1, 2, 3, 3, 1, 1] => 2, 2, 1, 1, 2, 3, 3, 1, 1
[2, 2, 1, 1, 2, 3, 3, 1, 2] => 2, 2, 1, 1, 2, 3, 3, 1, 2
[2, 2, 1, 1, 2, 3, 3, 1, 3] => 2, 2, 1, 1, 2, 3, 3, 1, 3
[2, 2, 1, 1, 2, 3, 3, 2, 1] => 2, 2, 1, 1, 2, 3, 3, 2, 1
[2, 2, 1, 1, 2, 3, 3, 2, 2] => 2, 2, 1, 1, 2, 3, 3, 2, 2
[2, 2, 1, 1, 2, 3, 3, 2, 3] => 2, 2, 1, 1, 2, 3, 3, 2, 3
[2, 2, 1, 1, 2, 3, 3, 3, 1] => 2, 2, 1, 1, 2, 3, 3, 3, 1
[2, 2, 1, 1, 2, 3, 3, 3, 2] => 2, 2, 1, 1, 2, 3, 3, 3, 2
[2, 2, 1, 1, 2, 3, 3, 3, 3] => 2, 2, 1, 1, 2, 3, 3, 3, 3
[2, 2, 1, 1, 3, 1, 1, 1, 1] => 2, 2, 1, 1, 3, 1, 1, 1, 1
[2, 2, 1, 1, 3, 1, 1, 1, 2] => 2, 2, 1, 1, 3, 1, 1, 1, 2
[2, 2, 1, 1, 3, 1, 1, 1, 3] => 2, 2, 1, 1, 3, 1, 1, 1, 3
[2, 2, 1, 1, 3, 1, 1, 2, 1] => 2, 2, 1, 1, 3, 1, 1, 2, 1
[2, 2, 1, 1, 3, 1, 1, 2, 2] => 2, 2, 1, 1, 3, 1, 1, 2, 2
[2, 2, 1, 1, 3, 1, 1, 2, 3] => 2, 2, 1, 1, 3, 1, 1, 2, 3
[2, 2, 1, 1, 3, 1, 1, 3, 1] => 2, 2, 1, 1, 3, 1, 1, 3, 1
[2, 2, 1, 1, 3, 1, 1, 3, 2] => 2, 2, 1, 1, 3, 1, 1, 3, 2
[2, 2, 1, 1, 3, 1, 1, 3, 3] => 2, 2, 1, 1, 3, 1, 1, 3, 3
[2, 2, 1, 1, 3, 1, 2, 1, 1] => 2, 2, 1, 1, 3, 1, 2, 1, 1
[2, 2, 1, 1, 3, 1, 2, 1, 2] => 2, 2, 1, 1, 3, 1, 2, 1, 2
[2, 2, 1, 1, 3, 1, 2, 1, 3] => 2, 2, 1, 1, 3, 1, 2, 1, 3
[2, 2, 1, 1, 3, 1, 2, 2, 1] => 2, 2, 1, 1, 3, 1, 2, 2, 1
[2, 2, 1, 1, 3, 1, 2, 2, 2] => 2, 2, 1, 1, 3, 1, 2, 2, 2
[2, 2, 1, 1, 3, 1, 2, 2, 3] => 2, 2, 1, 1, 3, 1, 2, 2, 3
[2, 2, 1, 1, 3, 1, 2, 3, 1] => 2, 2, 1, 1, 3, 1, 2, 3, 1
[2, 2, 1, 1, 3, 1, 2, 3, 2] => 2, 2, 1, 1, 3, 1, 2, 3, 2
[2, 2, 1, 1, 3, 1, 2, 3, 3] => 2, 2, 1, 1, 3, 1, 2, 3, 3
[2, 2, 1, 1, 3, 1, 3, 1, 1] => 2, 2, 1, 1, 3, 1, 3, 1, 1
[2, 2, 1, 1, 3, 1, 3, 1, 2] => 2, 2, 1, 1, 3, 1, 3, 1, 2
[2, 2, 1, 1, 3, 1, 3, 1, 3] => 2, 2, 1, 1, 3, 1, 3, 1, 3
[2, 2, 1, 1, 3, 1, 3, 2, 1] => 2, 2, 1, 1, 3, 1, 3, 2, 1
[2, 2, 1, 1, 3, 1, 3, 2, 2] => 2, 2, 1, 1, 3, 1, 3, 2, 2
[2, 2, 1, 1, 3, 1, 3, 2, 3] => 2, 2, 1, 1, 3, 1, 3, 2, 3
[2, 2, 1, 1, 3, 1, 3, 3, 1] => 2, 2, 1, 1, 3, 1, 3, 3, 1
[2, 2, 1, 1, 3, 1, 3, 3, 2] => 2, 2, 1, 1, 3, 1, 3, 3, 2
[2, 2, 1, 1, 3, 1, 3, 3, 3] => 2, 2, 1, 1, 3, 1, 3, 3, 3
[2, 2, 1, 1, 3, 2, 1, 1, 1] => 2, 2, 1, 1, 3, 2, 1, 1, 1
[2, 2, 1, 1, 3, 2, 1, 1, 2] => 2, 2, 1, 1, 3, 2, 1, 1, 2
[2, 2, 1, 1, 3, 2, 1, 1, 3] => 2, 2, 1, 1, 3, 2, 1, 1, 3
[2, 2, 1, 1, 3, 2, 1, 2, 1] => 2, 2, 1, 1, 3, 2, 1, 2, 1
[2, 2, 1, 1, 3, 2, 1, 2, 2] => 2, 2, 1, 1, 3, 2, 1, 2, 2
[2, 2, 1, 1, 3, 2, 1, 2, 3] => 2, 2, 1, 1, 3, 2, 1, 2, 3
[2, 2, 1, 1, 3, 2, 1, 3, 1] => 2, 2, 1, 1, 3, 2, 1, 3, 1
[2, 2, 1, 1, 3, 2, 1, 3, 2] => 2, 2, 1, 1, 3, 2, 1, 3, 2
[2, 2, 1, 1, 3, 2, 1, 3, 3] => 2, 2, 1, 1, 3, 2, 1, 3, 3
[2, 2, 1, 1, 3, 2, 2, 1, 1] => 2, 2, 1, 1, 3, 2, 2, 1, 1
[2, 2, 1, 1, 3, 2, 2, 1, 2] => 2, 2, 1, 1, 3, 2, 2, 1, 2
[2, 2, 1, 1, 3, 2, 2, 1, 3] => 2, 2, 1, 1, 3, 2, 2, 1, 3
[2, 2, 1, 1, 3, 2, 2, 2, 1] => 2, 2, 1, 1, 3, 2, 2, 2, 1
[2, 2, 1, 1, 3, 2, 2, 2, 2] => 2, 2, 1, 1, 3, 2, 2, 2, 2
[2, 2, 1, 1, 3, 2, 2, 2, 3] => 2, 2, 1, 1, 3, 2, 2, 2, 3
[2, 2, 1, 1, 3, 2, 2, 3, 1] => 2, 2, 1, 1, 3, 2, 2, 3, 1
[2, 2, 1, 1, 3, 2, 2, 3, 2] => 2, 2, 1, 1, 3, 2, 2, 3, 2
[2, 2, 1, 1, 3, 2, 2, 3, 3] => 2, 2, 1, 1, 3, 2, 2, 3, 3
[2, 2, 1, 1, 3, 2, 3, 1, 1] => 2, 2, 1, 1, 3, 2, 3, 1, 1
[2, 2, 1, 1, 3, 2, 3, 1, 2] => 2, 2, 1, 1, 3, 2, 3, 1, 2
[2, 2, 1, 1, 3, 2, 3, 1, 3] => 2, 2, 1, 1, 3, 2, 3, 1, 3
[2, 2, 1, 1, 3, 2, 3, 2, 1] => 2, 2, 1, 1, 3, 2, 3, 2, 1
[2, 2, 1, 1, 3, 2, 3, 2, 2] => 2, 2, 1, 1, 3, 2, 3, 2, 2
[2, 2, 1, 1, 3, 2, 3, 2, 3] => 2, 2, 1, 1, 3, 2, 3, 2, 3
[2, 2, 1, 1, 3, 2, 3, 3, 1] => 2, 2, 1, 1, 3, 2, 3, 3, 1
[2, 2, 1, 1, 3, 2, 3, 3, 2] => 2, 2, 1, 1, 3, 2, 3, 3, 2
[2, 2, 1, 1, 3, 2, 3, 3, 3] => 2, 2, 1, 1, 3, 2, 3, 3, 3
[2, 2, 1, 1, 3, 3, 1, 1, 1] => 2, 2, 1, 1, 3, 3, 1, 1, 1
[2, 2, 1, 1, 3, 3, 1, 1, 2] => 2, 2, 1, 1, 3, 3, 1, 1, 2
[2, 2, 1, 1, 3, 3, 1, 1, 3] => 2, 2, 1, 1, 3, 3, 1, 1, 3
[2, 2, 1, 1, 3, 3, 1, 2, 1] => 2, 2, 1, 1, 3, 3, 1, 2, 1
[2, 2, 1, 1, 3, 3, 1, 2, 2] => 2, 2, 1, 1, 3, 3, 1, 2, 2
[2, 2, 1, 1, 3, 3, 1, 2, 3] => 2, 2, 1, 1, 3, 3, 1, 2, 3
[2, 2, 1, 1, 3, 3, 1, 3, 1] => 2, 2, 1, 1, 3, 3, 1, 3, 1
[2, 2, 1, 1, 3, 3, 1, 3, 2] => 2, 2, 1, 1, 3, 3, 1, 3, 2
[2, 2, 1, 1, 3, 3, 1, 3, 3] => 2, 2, 1, 1, 3, 3, 1, 3, 3
[2, 2, 1, 1, 3, 3, 2, 1, 1] => 2, 2, 1, 1, 3, 3, 2, 1, 1
[2, 2, 1, 1, 3, 3, 2, 1, 2] => 2, 2, 1, 1, 3, 3, 2, 1, 2
[2, 2, 1, 1, 3, 3, 2, 1, 3] => 2, 2, 1, 1, 3, 3, 2, 1, 3
[2, 2, 1, 1, 3, 3, 2, 2, 1] => 2, 2, 1, 1, 3, 3, 2, 2, 1
[2, 2, 1, 1, 3, 3, 2, 2, 2] => 2, 2, 1, 1, 3, 3, 2, 2, 2
[2, 2, 1, 1, 3, 3, 2, 2, 3] => 2, 2, 1, 1, 3, 3, 2, 2, 3
[2, 2, 1, 1, 3, 3, 2, 3, 1] => 2, 2, 1, 1, 3, 3, 2, 3, 1
[2, 2, 1, 1, 3, 3, 2, 3, 2] => 2, 2, 1, 1, 3, 3, 2, 3, 2
[2, 2, 1, 1, 3, 3, 2, 3, 3] => 2, 2, 1, 1, 3, 3, 2, 3, 3
[2, 2, 1, 1, 3, 3, 3, 1, 1] => 2, 2, 1, 1, 3, 3, 3, 1, 1
[2, 2, 1, 1, 3, 3, 3, 1, 2] => 2, 2, 1, 1, 3, 3, 3, 1, 2
[2, 2, 1, 1, 3, 3, 3, 1, 3] => 2, 2, 1, 1, 3, 3, 3, 1, 3
[2, 2, 1, 1, 3, 3, 3, 2, 1] => 2, 2, 1, 1, 3, 3, 3, 2, 1
[2, 2, 1, 1, 3, 3, 3, 2, 2] => 2, 2, 1, 1, 3, 3, 3, 2, 2
[2, 2, 1, 1, 3, 3, 3, 2, 3] => 2, 2, 1, 1, 3, 3, 3, 2, 3
[2, 2, 1, 1, 3, 3, 3, 3, 1] => 2, 2, 1, 1, 3, 3, 3, 3, 1
[2, 2, 1, 1, 3, 3, 3, 3, 2] => 2, 2, 1, 1, 3, 3, 3, 3, 2
[2, 2, 1, 1, 3, 3, 3, 3, 3] => 2, 2, 1, 1, 3, 3, 3, 3, 3
[2, 2, 1, 2, 1, 1, 1, 1, 1] => 2, 2, 1, 2, 1, 1, 1, 1, 1
[2, 2, 1, 2, 1, 1, 1, 1, 2] => 2, 2, 1, 2, 1, 1, 1, 1, 2
[2, 2, 1, 2, 1, 1, 1, 1, 3] => 2, 2, 1, 2, 1, 1, 1, 1, 3
[2, 2, 1, 2, 1, 1, 1, 2, 1] => 2, 2, 1, 2, 1, 1, 1, 2, 1
[2, 2, 1, 2, 1, 1, 1, 2, 2] => 2, 2, 1, 2, 1, 1, 1, 2, 2
[2, 2, 1, 2, 1, 1, 1, 2, 3] => 2, 2, 1, 2, 1, 1, 1, 2, 3
[2, 2, 1, 2, 1, 1, 1, 3, 1] => 2, 2, 1, 2, 1, 1, 1, 3, 1
[2, 2, 1, 2, 1, 1, 1, 3, 2] => 2, 2, 1, 2, 1, 1, 1, 3, 2
[2, 2, 1, 2, 1, 1, 1, 3, 3] => 2, 2, 1, 2, 1, 1, 1, 3, 3
[2, 2, 1, 2, 1, 1, 2, 1, 1] => 2, 2, 1, 2, 1, 1, 2, 1, 1
[2, 2, 1, 2, 1, 1, 2, 1, 2] => 2, 2, 1, 2, 1, 1, 2, 1, 2
[2, 2, 1, 2, 1, 1, 2, 1, 3] => 2, 2, 1, 2, 1, 1, 2, 1, 3
[2, 2, 1, 2, 1, 1, 2, 2, 1] => 2, 2, 1, 2, 1, 1, 2, 2, 1
[2, 2, 1, 2, 1, 1, 2, 2, 2] => 2, 2, 1, 2, 1, 1, 2, 2, 2
[2, 2, 1, 2, 1, 1, 2, 2, 3] => 2, 2, 1, 2, 1, 1, 2, 2, 3
[2, 2, 1, 2, 1, 1, 2, 3, 1] => 2, 2, 1, 2, 1, 1, 2, 3, 1
[2, 2, 1, 2, 1, 1, 2, 3, 2] => 2, 2, 1, 2, 1, 1, 2, 3, 2
[2, 2, 1, 2, 1, 1, 2, 3, 3] => 2, 2, 1, 2, 1, 1, 2, 3, 3
[2, 2, 1, 2, 1, 1, 3, 1, 1] => 2, 2, 1, 2, 1, 1, 3, 1, 1
[2, 2, 1, 2, 1, 1, 3, 1, 2] => 2, 2, 1, 2, 1, 1, 3, 1, 2
[2, 2, 1, 2, 1, 1, 3, 1, 3] => 2, 2, 1, 2, 1, 1, 3, 1, 3
[2, 2, 1, 2, 1, 1, 3, 2, 1] => 2, 2, 1, 2, 1, 1, 3, 2, 1
[2, 2, 1, 2, 1, 1, 3, 2, 2] => 2, 2, 1, 2, 1, 1, 3, 2, 2
[2, 2, 1, 2, 1, 1, 3, 2, 3] => 2, 2, 1, 2, 1, 1, 3, 2, 3
[2, 2, 1, 2, 1, 1, 3, 3, 1] => 2, 2, 1, 2, 1, 1, 3, 3, 1
[2, 2, 1, 2, 1, 1, 3, 3, 2] => 2, 2, 1, 2, 1, 1, 3, 3, 2
[2, 2, 1, 2, 1, 1, 3, 3, 3] => 2, 2, 1, 2, 1, 1, 3, 3, 3
[2, 2, 1, 2, 1, 2, 1, 1, 1] => 2, 2, 1, 2, 1, 2, 1, 1, 1
[2, 2, 1, 2, 1, 2, 1, 1, 2] => 2, 2, 1, 2, 1, 2, 1, 1, 2
[2, 2, 1, 2, 1, 2, 1, 1, 3] => 2, 2, 1, 2, 1, 2, 1, 1, 3
[2, 2, 1, 2, 1, 2, 1, 2, 1] => 2, 2, 1, 2, 1, 2, 1, 2, 1
[2, 2, 1, 2, 1, 2, 1, 2, 2] => 2, 2, 1, 2, 1, 2, 1, 2, 2
[2, 2, 1, 2, 1, 2, 1, 2, 3] => 2, 2, 1, 2, 1, 2, 1, 2, 3
[2, 2, 1, 2, 1, 2, 1, 3, 1] => 2, 2, 1, 2, 1, 2, 1, 3, 1
[2, 2, 1, 2, 1, 2, 1, 3, 2] => 2, 2, 1, 2, 1, 2, 1, 3, 2
[2, 2, 1, 2, 1, 2, 1, 3, 3] => 2, 2, 1, 2, 1, 2, 1, 3, 3
[2, 2, 1, 2, 1, 2, 2, 1, 1] => 2, 2, 1, 2, 1, 2, 2, 1, 1
[2, 2, 1, 2, 1, 2, 2, 1, 2] => 2, 2, 1, 2, 1, 2, 2, 1, 2
[2, 2, 1, 2, 1, 2, 2, 1, 3] => 2, 2, 1, 2, 1, 2, 2, 1, 3
[2, 2, 1, 2, 1, 2, 2, 2, 1] => 2, 2, 1, 2, 1, 2, 2, 2, 1
[2, 2, 1, 2, 1, 2, 2, 2, 2] => 2, 2, 1, 2, 1, 2, 2, 2, 2
[2, 2, 1, 2, 1, 2, 2, 2, 3] => 2, 2, 1, 2, 1, 2, 2, 2, 3
[2, 2, 1, 2, 1, 2, 2, 3, 1] => 2, 2, 1, 2, 1, 2, 2, 3, 1
[2, 2, 1, 2, 1, 2, 2, 3, 2] => 2, 2, 1, 2, 1, 2, 2, 3, 2
[2, 2, 1, 2, 1, 2, 2, 3, 3] => 2, 2, 1, 2, 1, 2, 2, 3, 3
[2, 2, 1, 2, 1, 2, 3, 1, 1] => 2, 2, 1, 2, 1, 2, 3, 1, 1
[2, 2, 1, 2, 1, 2, 3, 1, 2] => 2, 2, 1, 2, 1, 2, 3, 1, 2
[2, 2, 1, 2, 1, 2, 3, 1, 3] => 2, 2, 1, 2, 1, 2, 3, 1, 3
[2, 2, 1, 2, 1, 2, 3, 2, 1] => 2, 2, 1, 2, 1, 2, 3, 2, 1
[2, 2, 1, 2, 1, 2, 3, 2, 2] => 2, 2, 1, 2, 1, 2, 3, 2, 2
[2, 2, 1, 2, 1, 2, 3, 2, 3] => 2, 2, 1, 2, 1, 2, 3, 2, 3
[2, 2, 1, 2, 1, 2, 3, 3, 1] => 2, 2, 1, 2, 1, 2, 3, 3, 1
[2, 2, 1, 2, 1, 2, 3, 3, 2] => 2, 2, 1, 2, 1, 2, 3, 3, 2
[2, 2, 1, 2, 1, 2, 3, 3, 3] => 2, 2, 1, 2, 1, 2, 3, 3, 3
[2, 2, 1, 2, 1, 3, 1, 1, 1] => 2, 2, 1, 2, 1, 3, 1, 1, 1
[2, 2, 1, 2, 1, 3, 1, 1, 2] => 2, 2, 1, 2, 1, 3, 1, 1, 2
[2, 2, 1, 2, 1, 3, 1, 1, 3] => 2, 2, 1, 2, 1, 3, 1, 1, 3
[2, 2, 1, 2, 1, 3, 1, 2, 1] => 2, 2, 1, 2, 1, 3, 1, 2, 1
[2, 2, 1, 2, 1, 3, 1, 2, 2] => 2, 2, 1, 2, 1, 3, 1, 2, 2
[2, 2, 1, 2, 1, 3, 1, 2, 3] => 2, 2, 1, 2, 1, 3, 1, 2, 3
[2, 2, 1, 2, 1, 3, 1, 3, 1] => 2, 2, 1, 2, 1, 3, 1, 3, 1
[2, 2, 1, 2, 1, 3, 1, 3, 2] => 2, 2, 1, 2, 1, 3, 1, 3, 2
[2, 2, 1, 2, 1, 3, 1, 3, 3] => 2, 2, 1, 2, 1, 3, 1, 3, 3
[2, 2, 1, 2, 1, 3, 2, 1, 1] => 2, 2, 1, 2, 1, 3, 2, 1, 1
[2, 2, 1, 2, 1, 3, 2, 1, 2] => 2, 2, 1, 2, 1, 3, 2, 1, 2
[2, 2, 1, 2, 1, 3, 2, 1, 3] => 2, 2, 1, 2, 1, 3, 2, 1, 3
[2, 2, 1, 2, 1, 3, 2, 2, 1] => 2, 2, 1, 2, 1, 3, 2, 2, 1
[2, 2, 1, 2, 1, 3, 2, 2, 2] => 2, 2, 1, 2, 1, 3, 2, 2, 2
[2, 2, 1, 2, 1, 3, 2, 2, 3] => 2, 2, 1, 2, 1, 3, 2, 2, 3
[2, 2, 1, 2, 1, 3, 2, 3, 1] => 2, 2, 1, 2, 1, 3, 2, 3, 1
[2, 2, 1, 2, 1, 3, 2, 3, 2] => 2, 2, 1, 2, 1, 3, 2, 3, 2
[2, 2, 1, 2, 1, 3, 2, 3, 3] => 2, 2, 1, 2, 1, 3, 2, 3, 3
[2, 2, 1, 2, 1, 3, 3, 1, 1] => 2, 2, 1, 2, 1, 3, 3, 1, 1
[2, 2, 1, 2, 1, 3, 3, 1, 2] => 2, 2, 1, 2, 1, 3, 3, 1, 2
[2, 2, 1, 2, 1, 3, 3, 1, 3] => 2, 2, 1, 2, 1, 3, 3, 1, 3
[2, 2, 1, 2, 1, 3, 3, 2, 1] => 2, 2, 1, 2, 1, 3, 3, 2, 1
[2, 2, 1, 2, 1, 3, 3, 2, 2] => 2, 2, 1, 2, 1, 3, 3, 2, 2
[2, 2, 1, 2, 1, 3, 3, 2, 3] => 2, 2, 1, 2, 1, 3, 3, 2, 3
[2, 2, 1, 2, 1, 3, 3, 3, 1] => 2, 2, 1, 2, 1, 3, 3, 3, 1
[2, 2, 1, 2, 1, 3, 3, 3, 2] => 2, 2, 1, 2, 1, 3, 3, 3, 2
[2, 2, 1, 2, 1, 3, 3, 3, 3] => 2, 2, 1, 2, 1, 3, 3, 3, 3
[2, 2, 1, 2, 2, 1, 1, 1, 1] => 2, 2, 1, 2, 2, 1, 1, 1, 1
[2, 2, 1, 2, 2, 1, 1, 1, 2] => 2, 2, 1, 2, 2, 1, 1, 1, 2
[2, 2, 1, 2, 2, 1, 1, 1, 3] => 2, 2, 1, 2, 2, 1, 1, 1, 3
[2, 2, 1, 2, 2, 1, 1, 2, 1] => 2, 2, 1, 2, 2, 1, 1, 2, 1
[2, 2, 1, 2, 2, 1, 1, 2, 2] => 2, 2, 1, 2, 2, 1, 1, 2, 2
[2, 2, 1, 2, 2, 1, 1, 2, 3] => 2, 2, 1, 2, 2, 1, 1, 2, 3
[2, 2, 1, 2, 2, 1, 1, 3, 1] => 2, 2, 1, 2, 2, 1, 1, 3, 1
[2, 2, 1, 2, 2, 1, 1, 3, 2] => 2, 2, 1, 2, 2, 1, 1, 3, 2
[2, 2, 1, 2, 2, 1, 1, 3, 3] => 2, 2, 1, 2, 2, 1, 1, 3, 3
[2, 2, 1, 2, 2, 1, 2, 1, 1] => 2, 2, 1, 2, 2, 1, 2, 1, 1
[2, 2, 1, 2, 2, 1, 2, 1, 2] => 2, 2, 1, 2, 2, 1, 2, 1, 2
[2, 2, 1, 2, 2, 1, 2, 1, 3] => 2, 2, 1, 2, 2, 1, 2, 1, 3
[2, 2, 1, 2, 2, 1, 2, 2, 1] => 2, 2, 1, 2, 2, 1, 2, 2, 1
[2, 2, 1, 2, 2, 1, 2, 2, 2] => 2, 2, 1, 2, 2, 1, 2, 2, 2
[2, 2, 1, 2, 2, 1, 2, 2, 3] => 2, 2, 1, 2, 2, 1, 2, 2, 3
[2, 2, 1, 2, 2, 1, 2, 3, 1] => 2, 2, 1, 2, 2, 1, 2, 3, 1
[2, 2, 1, 2, 2, 1, 2, 3, 2] => 2, 2, 1, 2, 2, 1, 2, 3, 2
[2, 2, 1, 2, 2, 1, 2, 3, 3] => 2, 2, 1, 2, 2, 1, 2, 3, 3
[2, 2, 1, 2, 2, 1, 3, 1, 1] => 2, 2, 1, 2, 2, 1, 3, 1, 1
[2, 2, 1, 2, 2, 1, 3, 1, 2] => 2, 2, 1, 2, 2, 1, 3, 1, 2
[2, 2, 1, 2, 2, 1, 3, 1, 3] => 2, 2, 1, 2, 2, 1, 3, 1, 3
[2, 2, 1, 2, 2, 1, 3, 2, 1] => 2, 2, 1, 2, 2, 1, 3, 2, 1
[2, 2, 1, 2, 2, 1, 3, 2, 2] => 2, 2, 1, 2, 2, 1, 3, 2, 2
[2, 2, 1, 2, 2, 1, 3, 2, 3] => 2, 2, 1, 2, 2, 1, 3, 2, 3
[2, 2, 1, 2, 2, 1, 3, 3, 1] => 2, 2, 1, 2, 2, 1, 3, 3, 1
[2, 2, 1, 2, 2, 1, 3, 3, 2] => 2, 2, 1, 2, 2, 1, 3, 3, 2
[2, 2, 1, 2, 2, 1, 3, 3, 3] => 2, 2, 1, 2, 2, 1, 3, 3, 3
[2, 2, 1, 2, 2, 2, 1, 1, 1] => 2, 2, 1, 2, 2, 2, 1, 1, 1
[2, 2, 1, 2, 2, 2, 1, 1, 2] => 2, 2, 1, 2, 2, 2, 1, 1, 2
[2, 2, 1, 2, 2, 2, 1, 1, 3] => 2, 2, 1, 2, 2, 2, 1, 1, 3
[2, 2, 1, 2, 2, 2, 1, 2, 1] => 2, 2, 1, 2, 2, 2, 1, 2, 1
[2, 2, 1, 2, 2, 2, 1, 2, 2] => 2, 2, 1, 2, 2, 2, 1, 2, 2
[2, 2, 1, 2, 2, 2, 1, 2, 3] => 2, 2, 1, 2, 2, 2, 1, 2, 3
[2, 2, 1, 2, 2, 2, 1, 3, 1] => 2, 2, 1, 2, 2, 2, 1, 3, 1
[2, 2, 1, 2, 2, 2, 1, 3, 2] => 2, 2, 1, 2, 2, 2, 1, 3, 2
[2, 2, 1, 2, 2, 2, 1, 3, 3] => 2, 2, 1, 2, 2, 2, 1, 3, 3
[2, 2, 1, 2, 2, 2, 2, 1, 1] => 2, 2, 1, 2, 2, 2, 2, 1, 1
[2, 2, 1, 2, 2, 2, 2, 1, 2] => 2, 2, 1, 2, 2, 2, 2, 1, 2
[2, 2, 1, 2, 2, 2, 2, 1, 3] => 2, 2, 1, 2, 2, 2, 2, 1, 3
[2, 2, 1, 2, 2, 2, 2, 2, 1] => 2, 2, 1, 2, 2, 2, 2, 2, 1
[2, 2, 1, 2, 2, 2, 2, 2, 2] => 2, 2, 1, 2, 2, 2, 2, 2, 2
[2, 2, 1, 2, 2, 2, 2, 2, 3] => 2, 2, 1, 2, 2, 2, 2, 2, 3
[2, 2, 1, 2, 2, 2, 2, 3, 1] => 2, 2, 1, 2, 2, 2, 2, 3, 1
[2, 2, 1, 2, 2, 2, 2, 3, 2] => 2, 2, 1, 2, 2, 2, 2, 3, 2
[2, 2, 1, 2, 2, 2, 2, 3, 3] => 2, 2, 1, 2, 2, 2, 2, 3, 3
[2, 2, 1, 2, 2, 2, 3, 1, 1] => 2, 2, 1, 2, 2, 2, 3, 1, 1
[2, 2, 1, 2, 2, 2, 3, 1, 2] => 2, 2, 1, 2, 2, 2, 3, 1, 2
[2, 2, 1, 2, 2, 2, 3, 1, 3] => 2, 2, 1, 2, 2, 2, 3, 1, 3
[2, 2, 1, 2, 2, 2, 3, 2, 1] => 2, 2, 1, 2, 2, 2, 3, 2, 1
[2, 2, 1, 2, 2, 2, 3, 2, 2] => 2, 2, 1, 2, 2, 2, 3, 2, 2
[2, 2, 1, 2, 2, 2, 3, 2, 3] => 2, 2, 1, 2, 2, 2, 3, 2, 3
[2, 2, 1, 2, 2, 2, 3, 3, 1] => 2, 2, 1, 2, 2, 2, 3, 3, 1
[2, 2, 1, 2, 2, 2, 3, 3, 2] => 2, 2, 1, 2, 2, 2, 3, 3, 2
[2, 2, 1, 2, 2, 2, 3, 3, 3] => 2, 2, 1, 2, 2, 2, 3, 3, 3
[2, 2, 1, 2, 2, 3, 1, 1, 1] => 2, 2, 1, 2, 2, 3, 1, 1, 1
[2, 2, 1, 2, 2, 3, 1, 1, 2] => 2, 2, 1, 2, 2, 3, 1, 1, 2
[2, 2, 1, 2, 2, 3, 1, 1, 3] => 2, 2, 1, 2, 2, 3, 1, 1, 3
[2, 2, 1, 2, 2, 3, 1, 2, 1] => 2, 2, 1, 2, 2, 3, 1, 2, 1
[2, 2, 1, 2, 2, 3, 1, 2, 2] => 2, 2, 1, 2, 2, 3, 1, 2, 2
[2, 2, 1, 2, 2, 3, 1, 2, 3] => 2, 2, 1, 2, 2, 3, 1, 2, 3
[2, 2, 1, 2, 2, 3, 1, 3, 1] => 2, 2, 1, 2, 2, 3, 1, 3, 1
[2, 2, 1, 2, 2, 3, 1, 3, 2] => 2, 2, 1, 2, 2, 3, 1, 3, 2
[2, 2, 1, 2, 2, 3, 1, 3, 3] => 2, 2, 1, 2, 2, 3, 1, 3, 3
[2, 2, 1, 2, 2, 3, 2, 1, 1] => 2, 2, 1, 2, 2, 3, 2, 1, 1
[2, 2, 1, 2, 2, 3, 2, 1, 2] => 2, 2, 1, 2, 2, 3, 2, 1, 2
[2, 2, 1, 2, 2, 3, 2, 1, 3] => 2, 2, 1, 2, 2, 3, 2, 1, 3
[2, 2, 1, 2, 2, 3, 2, 2, 1] => 2, 2, 1, 2, 2, 3, 2, 2, 1
[2, 2, 1, 2, 2, 3, 2, 2, 2] => 2, 2, 1, 2, 2, 3, 2, 2, 2
[2, 2, 1, 2, 2, 3, 2, 2, 3] => 2, 2, 1, 2, 2, 3, 2, 2, 3
[2, 2, 1, 2, 2, 3, 2, 3, 1] => 2, 2, 1, 2, 2, 3, 2, 3, 1
[2, 2, 1, 2, 2, 3, 2, 3, 2] => 2, 2, 1, 2, 2, 3, 2, 3, 2
[2, 2, 1, 2, 2, 3, 2, 3, 3] => 2, 2, 1, 2, 2, 3, 2, 3, 3
[2, 2, 1, 2, 2, 3, 3, 1, 1] => 2, 2, 1, 2, 2, 3, 3, 1, 1
[2, 2, 1, 2, 2, 3, 3, 1, 2] => 2, 2, 1, 2, 2, 3, 3, 1, 2
[2, 2, 1, 2, 2, 3, 3, 1, 3] => 2, 2, 1, 2, 2, 3, 3, 1, 3
[2, 2, 1, 2, 2, 3, 3, 2, 1] => 2, 2, 1, 2, 2, 3, 3, 2, 1
[2, 2, 1, 2, 2, 3, 3, 2, 2] => 2, 2, 1, 2, 2, 3, 3, 2, 2
[2, 2, 1, 2, 2, 3, 3, 2, 3] => 2, 2, 1, 2, 2, 3, 3, 2, 3
[2, 2, 1, 2, 2, 3, 3, 3, 1] => 2, 2, 1, 2, 2, 3, 3, 3, 1
[2, 2, 1, 2, 2, 3, 3, 3, 2] => 2, 2, 1, 2, 2, 3, 3, 3, 2
[2, 2, 1, 2, 2, 3, 3, 3, 3] => 2, 2, 1, 2, 2, 3, 3, 3, 3
[2, 2, 1, 2, 3, 1, 1, 1, 1] => 2, 2, 1, 2, 3, 1, 1, 1, 1
[2, 2, 1, 2, 3, 1, 1, 1, 2] => 2, 2, 1, 2, 3, 1, 1, 1, 2
[2, 2, 1, 2, 3, 1, 1, 1, 3] => 2, 2, 1, 2, 3, 1, 1, 1, 3
[2, 2, 1, 2, 3, 1, 1, 2, 1] => 2, 2, 1, 2, 3, 1, 1, 2, 1
[2, 2, 1, 2, 3, 1, 1, 2, 2] => 2, 2, 1, 2, 3, 1, 1, 2, 2
[2, 2, 1, 2, 3, 1, 1, 2, 3] => 2, 2, 1, 2, 3, 1, 1, 2, 3
[2, 2, 1, 2, 3, 1, 1, 3, 1] => 2, 2, 1, 2, 3, 1, 1, 3, 1
[2, 2, 1, 2, 3, 1, 1, 3, 2] => 2, 2, 1, 2, 3, 1, 1, 3, 2
[2, 2, 1, 2, 3, 1, 1, 3, 3] => 2, 2, 1, 2, 3, 1, 1, 3, 3
[2, 2, 1, 2, 3, 1, 2, 1, 1] => 2, 2, 1, 2, 3, 1, 2, 1, 1
[2, 2, 1, 2, 3, 1, 2, 1, 2] => 2, 2, 1, 2, 3, 1, 2, 1, 2
[2, 2, 1, 2, 3, 1, 2, 1, 3] => 2, 2, 1, 2, 3, 1, 2, 1, 3
[2, 2, 1, 2, 3, 1, 2, 2, 1] => 2, 2, 1, 2, 3, 1, 2, 2, 1
[2, 2, 1, 2, 3, 1, 2, 2, 2] => 2, 2, 1, 2, 3, 1, 2, 2, 2
[2, 2, 1, 2, 3, 1, 2, 2, 3] => 2, 2, 1, 2, 3, 1, 2, 2, 3
[2, 2, 1, 2, 3, 1, 2, 3, 1] => 2, 2, 1, 2, 3, 1, 2, 3, 1
[2, 2, 1, 2, 3, 1, 2, 3, 2] => 2, 2, 1, 2, 3, 1, 2, 3, 2
[2, 2, 1, 2, 3, 1, 2, 3, 3] => 2, 2, 1, 2, 3, 1, 2, 3, 3
[2, 2, 1, 2, 3, 1, 3, 1, 1] => 2, 2, 1, 2, 3, 1, 3, 1, 1
[2, 2, 1, 2, 3, 1, 3, 1, 2] => 2, 2, 1, 2, 3, 1, 3, 1, 2
[2, 2, 1, 2, 3, 1, 3, 1, 3] => 2, 2, 1, 2, 3, 1, 3, 1, 3
[2, 2, 1, 2, 3, 1, 3, 2, 1] => 2, 2, 1, 2, 3, 1, 3, 2, 1
[2, 2, 1, 2, 3, 1, 3, 2, 2] => 2, 2, 1, 2, 3, 1, 3, 2, 2
[2, 2, 1, 2, 3, 1, 3, 2, 3] => 2, 2, 1, 2, 3, 1, 3, 2, 3
[2, 2, 1, 2, 3, 1, 3, 3, 1] => 2, 2, 1, 2, 3, 1, 3, 3, 1
[2, 2, 1, 2, 3, 1, 3, 3, 2] => 2, 2, 1, 2, 3, 1, 3, 3, 2
[2, 2, 1, 2, 3, 1, 3, 3, 3] => 2, 2, 1, 2, 3, 1, 3, 3, 3
[2, 2, 1, 2, 3, 2, 1, 1, 1] => 2, 2, 1, 2, 3, 2, 1, 1, 1
[2, 2, 1, 2, 3, 2, 1, 1, 2] => 2, 2, 1, 2, 3, 2, 1, 1, 2
[2, 2, 1, 2, 3, 2, 1, 1, 3] => 2, 2, 1, 2, 3, 2, 1, 1, 3
[2, 2, 1, 2, 3, 2, 1, 2, 1] => 2, 2, 1, 2, 3, 2, 1, 2, 1
[2, 2, 1, 2, 3, 2, 1, 2, 2] => 2, 2, 1, 2, 3, 2, 1, 2, 2
[2, 2, 1, 2, 3, 2, 1, 2, 3] => 2, 2, 1, 2, 3, 2, 1, 2, 3
[2, 2, 1, 2, 3, 2, 1, 3, 1] => 2, 2, 1, 2, 3, 2, 1, 3, 1
[2, 2, 1, 2, 3, 2, 1, 3, 2] => 2, 2, 1, 2, 3, 2, 1, 3, 2
[2, 2, 1, 2, 3, 2, 1, 3, 3] => 2, 2, 1, 2, 3, 2, 1, 3, 3
[2, 2, 1, 2, 3, 2, 2, 1, 1] => 2, 2, 1, 2, 3, 2, 2, 1, 1
[2, 2, 1, 2, 3, 2, 2, 1, 2] => 2, 2, 1, 2, 3, 2, 2, 1, 2
[2, 2, 1, 2, 3, 2, 2, 1, 3] => 2, 2, 1, 2, 3, 2, 2, 1, 3
[2, 2, 1, 2, 3, 2, 2, 2, 1] => 2, 2, 1, 2, 3, 2, 2, 2, 1
[2, 2, 1, 2, 3, 2, 2, 2, 2] => 2, 2, 1, 2, 3, 2, 2, 2, 2
[2, 2, 1, 2, 3, 2, 2, 2, 3] => 2, 2, 1, 2, 3, 2, 2, 2, 3
[2, 2, 1, 2, 3, 2, 2, 3, 1] => 2, 2, 1, 2, 3, 2, 2, 3, 1
[2, 2, 1, 2, 3, 2, 2, 3, 2] => 2, 2, 1, 2, 3, 2, 2, 3, 2
[2, 2, 1, 2, 3, 2, 2, 3, 3] => 2, 2, 1, 2, 3, 2, 2, 3, 3
[2, 2, 1, 2, 3, 2, 3, 1, 1] => 2, 2, 1, 2, 3, 2, 3, 1, 1
[2, 2, 1, 2, 3, 2, 3, 1, 2] => 2, 2, 1, 2, 3, 2, 3, 1, 2
[2, 2, 1, 2, 3, 2, 3, 1, 3] => 2, 2, 1, 2, 3, 2, 3, 1, 3
[2, 2, 1, 2, 3, 2, 3, 2, 1] => 2, 2, 1, 2, 3, 2, 3, 2, 1
[2, 2, 1, 2, 3, 2, 3, 2, 2] => 2, 2, 1, 2, 3, 2, 3, 2, 2
[2, 2, 1, 2, 3, 2, 3, 2, 3] => 2, 2, 1, 2, 3, 2, 3, 2, 3
[2, 2, 1, 2, 3, 2, 3, 3, 1] => 2, 2, 1, 2, 3, 2, 3, 3, 1
[2, 2, 1, 2, 3, 2, 3, 3, 2] => 2, 2, 1, 2, 3, 2, 3, 3, 2
[2, 2, 1, 2, 3, 2, 3, 3, 3] => 2, 2, 1, 2, 3, 2, 3, 3, 3
[2, 2, 1, 2, 3, 3, 1, 1, 1] => 2, 2, 1, 2, 3, 3, 1, 1, 1
[2, 2, 1, 2, 3, 3, 1, 1, 2] => 2, 2, 1, 2, 3, 3, 1, 1, 2
[2, 2, 1, 2, 3, 3, 1, 1, 3] => 2, 2, 1, 2, 3, 3, 1, 1, 3
[2, 2, 1, 2, 3, 3, 1, 2, 1] => 2, 2, 1, 2, 3, 3, 1, 2, 1
[2, 2, 1, 2, 3, 3, 1, 2, 2] => 2, 2, 1, 2, 3, 3, 1, 2, 2
[2, 2, 1, 2, 3, 3, 1, 2, 3] => 2, 2, 1, 2, 3, 3, 1, 2, 3
[2, 2, 1, 2, 3, 3, 1, 3, 1] => 2, 2, 1, 2, 3, 3, 1, 3, 1
[2, 2, 1, 2, 3, 3, 1, 3, 2] => 2, 2, 1, 2, 3, 3, 1, 3, 2
[2, 2, 1, 2, 3, 3, 1, 3, 3] => 2, 2, 1, 2, 3, 3, 1, 3, 3
[2, 2, 1, 2, 3, 3, 2, 1, 1] => 2, 2, 1, 2, 3, 3, 2, 1, 1
[2, 2, 1, 2, 3, 3, 2, 1, 2] => 2, 2, 1, 2, 3, 3, 2, 1, 2
[2, 2, 1, 2, 3, 3, 2, 1, 3] => 2, 2, 1, 2, 3, 3, 2, 1, 3
[2, 2, 1, 2, 3, 3, 2, 2, 1] => 2, 2, 1, 2, 3, 3, 2, 2, 1
[2, 2, 1, 2, 3, 3, 2, 2, 2] => 2, 2, 1, 2, 3, 3, 2, 2, 2
[2, 2, 1, 2, 3, 3, 2, 2, 3] => 2, 2, 1, 2, 3, 3, 2, 2, 3
[2, 2, 1, 2, 3, 3, 2, 3, 1] => 2, 2, 1, 2, 3, 3, 2, 3, 1
[2, 2, 1, 2, 3, 3, 2, 3, 2] => 2, 2, 1, 2, 3, 3, 2, 3, 2
[2, 2, 1, 2, 3, 3, 2, 3, 3] => 2, 2, 1, 2, 3, 3, 2, 3, 3
[2, 2, 1, 2, 3, 3, 3, 1, 1] => 2, 2, 1, 2, 3, 3, 3, 1, 1
[2, 2, 1, 2, 3, 3, 3, 1, 2] => 2, 2, 1, 2, 3, 3, 3, 1, 2
[2, 2, 1, 2, 3, 3, 3, 1, 3] => 2, 2, 1, 2, 3, 3, 3, 1, 3
[2, 2, 1, 2, 3, 3, 3, 2, 1] => 2, 2, 1, 2, 3, 3, 3, 2, 1
[2, 2, 1, 2, 3, 3, 3, 2, 2] => 2, 2, 1, 2, 3, 3, 3, 2, 2
[2, 2, 1, 2, 3, 3, 3, 2, 3] => 2, 2, 1, 2, 3, 3, 3, 2, 3
[2, 2, 1, 2, 3, 3, 3, 3, 1] => 2, 2, 1, 2, 3, 3, 3, 3, 1
[2, 2, 1, 2, 3, 3, 3, 3, 2] => 2, 2, 1, 2, 3, 3, 3, 3, 2
[2, 2, 1, 2, 3, 3, 3, 3, 3] => 2, 2, 1, 2, 3, 3, 3, 3, 3
[2, 2, 1, 3, 1, 1, 1, 1, 1] => 2, 2, 1, 3, 1, 1, 1, 1, 1
[2, 2, 1, 3, 1, 1, 1, 1, 2] => 2, 2, 1, 3, 1, 1, 1, 1, 2
[2, 2, 1, 3, 1, 1, 1, 1, 3] => 2, 2, 1, 3, 1, 1, 1, 1, 3
[2, 2, 1, 3, 1, 1, 1, 2, 1] => 2, 2, 1, 3, 1, 1, 1, 2, 1
[2, 2, 1, 3, 1, 1, 1, 2, 2] => 2, 2, 1, 3, 1, 1, 1, 2, 2
[2, 2, 1, 3, 1, 1, 1, 2, 3] => 2, 2, 1, 3, 1, 1, 1, 2, 3
[2, 2, 1, 3, 1, 1, 1, 3, 1] => 2, 2, 1, 3, 1, 1, 1, 3, 1
[2, 2, 1, 3, 1, 1, 1, 3, 2] => 2, 2, 1, 3, 1, 1, 1, 3, 2
[2, 2, 1, 3, 1, 1, 1, 3, 3] => 2, 2, 1, 3, 1, 1, 1, 3, 3
[2, 2, 1, 3, 1, 1, 2, 1, 1] => 2, 2, 1, 3, 1, 1, 2, 1, 1
[2, 2, 1, 3, 1, 1, 2, 1, 2] => 2, 2, 1, 3, 1, 1, 2, 1, 2
[2, 2, 1, 3, 1, 1, 2, 1, 3] => 2, 2, 1, 3, 1, 1, 2, 1, 3
[2, 2, 1, 3, 1, 1, 2, 2, 1] => 2, 2, 1, 3, 1, 1, 2, 2, 1
[2, 2, 1, 3, 1, 1, 2, 2, 2] => 2, 2, 1, 3, 1, 1, 2, 2, 2
[2, 2, 1, 3, 1, 1, 2, 2, 3] => 2, 2, 1, 3, 1, 1, 2, 2, 3
[2, 2, 1, 3, 1, 1, 2, 3, 1] => 2, 2, 1, 3, 1, 1, 2, 3, 1
[2, 2, 1, 3, 1, 1, 2, 3, 2] => 2, 2, 1, 3, 1, 1, 2, 3, 2
[2, 2, 1, 3, 1, 1, 2, 3, 3] => 2, 2, 1, 3, 1, 1, 2, 3, 3
[2, 2, 1, 3, 1, 1, 3, 1, 1] => 2, 2, 1, 3, 1, 1, 3, 1, 1
[2, 2, 1, 3, 1, 1, 3, 1, 2] => 2, 2, 1, 3, 1, 1, 3, 1, 2
[2, 2, 1, 3, 1, 1, 3, 1, 3] => 2, 2, 1, 3, 1, 1, 3, 1, 3
[2, 2, 1, 3, 1, 1, 3, 2, 1] => 2, 2, 1, 3, 1, 1, 3, 2, 1
[2, 2, 1, 3, 1, 1, 3, 2, 2] => 2, 2, 1, 3, 1, 1, 3, 2, 2
[2, 2, 1, 3, 1, 1, 3, 2, 3] => 2, 2, 1, 3, 1, 1, 3, 2, 3
[2, 2, 1, 3, 1, 1, 3, 3, 1] => 2, 2, 1, 3, 1, 1, 3, 3, 1
[2, 2, 1, 3, 1, 1, 3, 3, 2] => 2, 2, 1, 3, 1, 1, 3, 3, 2
[2, 2, 1, 3, 1, 1, 3, 3, 3] => 2, 2, 1, 3, 1, 1, 3, 3, 3
[2, 2, 1, 3, 1, 2, 1, 1, 1] => 2, 2, 1, 3, 1, 2, 1, 1, 1
[2, 2, 1, 3, 1, 2, 1, 1, 2] => 2, 2, 1, 3, 1, 2, 1, 1, 2
[2, 2, 1, 3, 1, 2, 1, 1, 3] => 2, 2, 1, 3, 1, 2, 1, 1, 3
[2, 2, 1, 3, 1, 2, 1, 2, 1] => 2, 2, 1, 3, 1, 2, 1, 2, 1
[2, 2, 1, 3, 1, 2, 1, 2, 2] => 2, 2, 1, 3, 1, 2, 1, 2, 2
[2, 2, 1, 3, 1, 2, 1, 2, 3] => 2, 2, 1, 3, 1, 2, 1, 2, 3
[2, 2, 1, 3, 1, 2, 1, 3, 1] => 2, 2, 1, 3, 1, 2, 1, 3, 1
[2, 2, 1, 3, 1, 2, 1, 3, 2] => 2, 2, 1, 3, 1, 2, 1, 3, 2
[2, 2, 1, 3, 1, 2, 1, 3, 3] => 2, 2, 1, 3, 1, 2, 1, 3, 3
[2, 2, 1, 3, 1, 2, 2, 1, 1] => 2, 2, 1, 3, 1, 2, 2, 1, 1
[2, 2, 1, 3, 1, 2, 2, 1, 2] => 2, 2, 1, 3, 1, 2, 2, 1, 2
[2, 2, 1, 3, 1, 2, 2, 1, 3] => 2, 2, 1, 3, 1, 2, 2, 1, 3
[2, 2, 1, 3, 1, 2, 2, 2, 1] => 2, 2, 1, 3, 1, 2, 2, 2, 1
[2, 2, 1, 3, 1, 2, 2, 2, 2] => 2, 2, 1, 3, 1, 2, 2, 2, 2
[2, 2, 1, 3, 1, 2, 2, 2, 3] => 2, 2, 1, 3, 1, 2, 2, 2, 3
[2, 2, 1, 3, 1, 2, 2, 3, 1] => 2, 2, 1, 3, 1, 2, 2, 3, 1
[2, 2, 1, 3, 1, 2, 2, 3, 2] => 2, 2, 1, 3, 1, 2, 2, 3, 2
[2, 2, 1, 3, 1, 2, 2, 3, 3] => 2, 2, 1, 3, 1, 2, 2, 3, 3
[2, 2, 1, 3, 1, 2, 3, 1, 1] => 2, 2, 1, 3, 1, 2, 3, 1, 1
[2, 2, 1, 3, 1, 2, 3, 1, 2] => 2, 2, 1, 3, 1, 2, 3, 1, 2
[2, 2, 1, 3, 1, 2, 3, 1, 3] => 2, 2, 1, 3, 1, 2, 3, 1, 3
[2, 2, 1, 3, 1, 2, 3, 2, 1] => 2, 2, 1, 3, 1, 2, 3, 2, 1
[2, 2, 1, 3, 1, 2, 3, 2, 2] => 2, 2, 1, 3, 1, 2, 3, 2, 2
[2, 2, 1, 3, 1, 2, 3, 2, 3] => 2, 2, 1, 3, 1, 2, 3, 2, 3
[2, 2, 1, 3, 1, 2, 3, 3, 1] => 2, 2, 1, 3, 1, 2, 3, 3, 1
[2, 2, 1, 3, 1, 2, 3, 3, 2] => 2, 2, 1, 3, 1, 2, 3, 3, 2
[2, 2, 1, 3, 1, 2, 3, 3, 3] => 2, 2, 1, 3, 1, 2, 3, 3, 3
[2, 2, 1, 3, 1, 3, 1, 1, 1] => 2, 2, 1, 3, 1, 3, 1, 1, 1
[2, 2, 1, 3, 1, 3, 1, 1, 2] => 2, 2, 1, 3, 1, 3, 1, 1, 2
[2, 2, 1, 3, 1, 3, 1, 1, 3] => 2, 2, 1, 3, 1, 3, 1, 1, 3
[2, 2, 1, 3, 1, 3, 1, 2, 1] => 2, 2, 1, 3, 1, 3, 1, 2, 1
[2, 2, 1, 3, 1, 3, 1, 2, 2] => 2, 2, 1, 3, 1, 3, 1, 2, 2
[2, 2, 1, 3, 1, 3, 1, 2, 3] => 2, 2, 1, 3, 1, 3, 1, 2, 3
[2, 2, 1, 3, 1, 3, 1, 3, 1] => 2, 2, 1, 3, 1, 3, 1, 3, 1
[2, 2, 1, 3, 1, 3, 1, 3, 2] => 2, 2, 1, 3, 1, 3, 1, 3, 2
[2, 2, 1, 3, 1, 3, 1, 3, 3] => 2, 2, 1, 3, 1, 3, 1, 3, 3
[2, 2, 1, 3, 1, 3, 2, 1, 1] => 2, 2, 1, 3, 1, 3, 2, 1, 1
[2, 2, 1, 3, 1, 3, 2, 1, 2] => 2, 2, 1, 3, 1, 3, 2, 1, 2
[2, 2, 1, 3, 1, 3, 2, 1, 3] => 2, 2, 1, 3, 1, 3, 2, 1, 3
[2, 2, 1, 3, 1, 3, 2, 2, 1] => 2, 2, 1, 3, 1, 3, 2, 2, 1
[2, 2, 1, 3, 1, 3, 2, 2, 2] => 2, 2, 1, 3, 1, 3, 2, 2, 2
[2, 2, 1, 3, 1, 3, 2, 2, 3] => 2, 2, 1, 3, 1, 3, 2, 2, 3
[2, 2, 1, 3, 1, 3, 2, 3, 1] => 2, 2, 1, 3, 1, 3, 2, 3, 1
[2, 2, 1, 3, 1, 3, 2, 3, 2] => 2, 2, 1, 3, 1, 3, 2, 3, 2
[2, 2, 1, 3, 1, 3, 2, 3, 3] => 2, 2, 1, 3, 1, 3, 2, 3, 3
[2, 2, 1, 3, 1, 3, 3, 1, 1] => 2, 2, 1, 3, 1, 3, 3, 1, 1
[2, 2, 1, 3, 1, 3, 3, 1, 2] => 2, 2, 1, 3, 1, 3, 3, 1, 2
[2, 2, 1, 3, 1, 3, 3, 1, 3] => 2, 2, 1, 3, 1, 3, 3, 1, 3
[2, 2, 1, 3, 1, 3, 3, 2, 1] => 2, 2, 1, 3, 1, 3, 3, 2, 1
[2, 2, 1, 3, 1, 3, 3, 2, 2] => 2, 2, 1, 3, 1, 3, 3, 2, 2
[2, 2, 1, 3, 1, 3, 3, 2, 3] => 2, 2, 1, 3, 1, 3, 3, 2, 3
[2, 2, 1, 3, 1, 3, 3, 3, 1] => 2, 2, 1, 3, 1, 3, 3, 3, 1
[2, 2, 1, 3, 1, 3, 3, 3, 2] => 2, 2, 1, 3, 1, 3, 3, 3, 2
[2, 2, 1, 3, 1, 3, 3, 3, 3] => 2, 2, 1, 3, 1, 3, 3, 3, 3
[2, 2, 1, 3, 2, 1, 1, 1, 1] => 2, 2, 1, 3, 2, 1, 1, 1, 1
[2, 2, 1, 3, 2, 1, 1, 1, 2] => 2, 2, 1, 3, 2, 1, 1, 1, 2
[2, 2, 1, 3, 2, 1, 1, 1, 3] => 2, 2, 1, 3, 2, 1, 1, 1, 3
[2, 2, 1, 3, 2, 1, 1, 2, 1] => 2, 2, 1, 3, 2, 1, 1, 2, 1
[2, 2, 1, 3, 2, 1, 1, 2, 2] => 2, 2, 1, 3, 2, 1, 1, 2, 2
[2, 2, 1, 3, 2, 1, 1, 2, 3] => 2, 2, 1, 3, 2, 1, 1, 2, 3
[2, 2, 1, 3, 2, 1, 1, 3, 1] => 2, 2, 1, 3, 2, 1, 1, 3, 1
[2, 2, 1, 3, 2, 1, 1, 3, 2] => 2, 2, 1, 3, 2, 1, 1, 3, 2
[2, 2, 1, 3, 2, 1, 1, 3, 3] => 2, 2, 1, 3, 2, 1, 1, 3, 3
[2, 2, 1, 3, 2, 1, 2, 1, 1] => 2, 2, 1, 3, 2, 1, 2, 1, 1
[2, 2, 1, 3, 2, 1, 2, 1, 2] => 2, 2, 1, 3, 2, 1, 2, 1, 2
[2, 2, 1, 3, 2, 1, 2, 1, 3] => 2, 2, 1, 3, 2, 1, 2, 1, 3
[2, 2, 1, 3, 2, 1, 2, 2, 1] => 2, 2, 1, 3, 2, 1, 2, 2, 1
[2, 2, 1, 3, 2, 1, 2, 2, 2] => 2, 2, 1, 3, 2, 1, 2, 2, 2
[2, 2, 1, 3, 2, 1, 2, 2, 3] => 2, 2, 1, 3, 2, 1, 2, 2, 3
[2, 2, 1, 3, 2, 1, 2, 3, 1] => 2, 2, 1, 3, 2, 1, 2, 3, 1
[2, 2, 1, 3, 2, 1, 2, 3, 2] => 2, 2, 1, 3, 2, 1, 2, 3, 2
[2, 2, 1, 3, 2, 1, 2, 3, 3] => 2, 2, 1, 3, 2, 1, 2, 3, 3
[2, 2, 1, 3, 2, 1, 3, 1, 1] => 2, 2, 1, 3, 2, 1, 3, 1, 1
[2, 2, 1, 3, 2, 1, 3, 1, 2] => 2, 2, 1, 3, 2, 1, 3, 1, 2
[2, 2, 1, 3, 2, 1, 3, 1, 3] => 2, 2, 1, 3, 2, 1, 3, 1, 3
[2, 2, 1, 3, 2, 1, 3, 2, 1] => 2, 2, 1, 3, 2, 1, 3, 2, 1
[2, 2, 1, 3, 2, 1, 3, 2, 2] => 2, 2, 1, 3, 2, 1, 3, 2, 2
[2, 2, 1, 3, 2, 1, 3, 2, 3] => 2, 2, 1, 3, 2, 1, 3, 2, 3
[2, 2, 1, 3, 2, 1, 3, 3, 1] => 2, 2, 1, 3, 2, 1, 3, 3, 1
[2, 2, 1, 3, 2, 1, 3, 3, 2] => 2, 2, 1, 3, 2, 1, 3, 3, 2
[2, 2, 1, 3, 2, 1, 3, 3, 3] => 2, 2, 1, 3, 2, 1, 3, 3, 3
[2, 2, 1, 3, 2, 2, 1, 1, 1] => 2, 2, 1, 3, 2, 2, 1, 1, 1
[2, 2, 1, 3, 2, 2, 1, 1, 2] => 2, 2, 1, 3, 2, 2, 1, 1, 2
[2, 2, 1, 3, 2, 2, 1, 1, 3] => 2, 2, 1, 3, 2, 2, 1, 1, 3
[2, 2, 1, 3, 2, 2, 1, 2, 1] => 2, 2, 1, 3, 2, 2, 1, 2, 1
[2, 2, 1, 3, 2, 2, 1, 2, 2] => 2, 2, 1, 3, 2, 2, 1, 2, 2
[2, 2, 1, 3, 2, 2, 1, 2, 3] => 2, 2, 1, 3, 2, 2, 1, 2, 3
[2, 2, 1, 3, 2, 2, 1, 3, 1] => 2, 2, 1, 3, 2, 2, 1, 3, 1
[2, 2, 1, 3, 2, 2, 1, 3, 2] => 2, 2, 1, 3, 2, 2, 1, 3, 2
[2, 2, 1, 3, 2, 2, 1, 3, 3] => 2, 2, 1, 3, 2, 2, 1, 3, 3
[2, 2, 1, 3, 2, 2, 2, 1, 1] => 2, 2, 1, 3, 2, 2, 2, 1, 1
[2, 2, 1, 3, 2, 2, 2, 1, 2] => 2, 2, 1, 3, 2, 2, 2, 1, 2
[2, 2, 1, 3, 2, 2, 2, 1, 3] => 2, 2, 1, 3, 2, 2, 2, 1, 3
[2, 2, 1, 3, 2, 2, 2, 2, 1] => 2, 2, 1, 3, 2, 2, 2, 2, 1
[2, 2, 1, 3, 2, 2, 2, 2, 2] => 2, 2, 1, 3, 2, 2, 2, 2, 2
[2, 2, 1, 3, 2, 2, 2, 2, 3] => 2, 2, 1, 3, 2, 2, 2, 2, 3
[2, 2, 1, 3, 2, 2, 2, 3, 1] => 2, 2, 1, 3, 2, 2, 2, 3, 1
[2, 2, 1, 3, 2, 2, 2, 3, 2] => 2, 2, 1, 3, 2, 2, 2, 3, 2
[2, 2, 1, 3, 2, 2, 2, 3, 3] => 2, 2, 1, 3, 2, 2, 2, 3, 3
[2, 2, 1, 3, 2, 2, 3, 1, 1] => 2, 2, 1, 3, 2, 2, 3, 1, 1
[2, 2, 1, 3, 2, 2, 3, 1, 2] => 2, 2, 1, 3, 2, 2, 3, 1, 2
[2, 2, 1, 3, 2, 2, 3, 1, 3] => 2, 2, 1, 3, 2, 2, 3, 1, 3
[2, 2, 1, 3, 2, 2, 3, 2, 1] => 2, 2, 1, 3, 2, 2, 3, 2, 1
[2, 2, 1, 3, 2, 2, 3, 2, 2] => 2, 2, 1, 3, 2, 2, 3, 2, 2
[2, 2, 1, 3, 2, 2, 3, 2, 3] => 2, 2, 1, 3, 2, 2, 3, 2, 3
[2, 2, 1, 3, 2, 2, 3, 3, 1] => 2, 2, 1, 3, 2, 2, 3, 3, 1
[2, 2, 1, 3, 2, 2, 3, 3, 2] => 2, 2, 1, 3, 2, 2, 3, 3, 2
[2, 2, 1, 3, 2, 2, 3, 3, 3] => 2, 2, 1, 3, 2, 2, 3, 3, 3
[2, 2, 1, 3, 2, 3, 1, 1, 1] => 2, 2, 1, 3, 2, 3, 1, 1, 1
[2, 2, 1, 3, 2, 3, 1, 1, 2] => 2, 2, 1, 3, 2, 3, 1, 1, 2
[2, 2, 1, 3, 2, 3, 1, 1, 3] => 2, 2, 1, 3, 2, 3, 1, 1, 3
[2, 2, 1, 3, 2, 3, 1, 2, 1] => 2, 2, 1, 3, 2, 3, 1, 2, 1
[2, 2, 1, 3, 2, 3, 1, 2, 2] => 2, 2, 1, 3, 2, 3, 1, 2, 2
[2, 2, 1, 3, 2, 3, 1, 2, 3] => 2, 2, 1, 3, 2, 3, 1, 2, 3
[2, 2, 1, 3, 2, 3, 1, 3, 1] => 2, 2, 1, 3, 2, 3, 1, 3, 1
[2, 2, 1, 3, 2, 3, 1, 3, 2] => 2, 2, 1, 3, 2, 3, 1, 3, 2
[2, 2, 1, 3, 2, 3, 1, 3, 3] => 2, 2, 1, 3, 2, 3, 1, 3, 3
[2, 2, 1, 3, 2, 3, 2, 1, 1] => 2, 2, 1, 3, 2, 3, 2, 1, 1
[2, 2, 1, 3, 2, 3, 2, 1, 2] => 2, 2, 1, 3, 2, 3, 2, 1, 2
[2, 2, 1, 3, 2, 3, 2, 1, 3] => 2, 2, 1, 3, 2, 3, 2, 1, 3
[2, 2, 1, 3, 2, 3, 2, 2, 1] => 2, 2, 1, 3, 2, 3, 2, 2, 1
[2, 2, 1, 3, 2, 3, 2, 2, 2] => 2, 2, 1, 3, 2, 3, 2, 2, 2
[2, 2, 1, 3, 2, 3, 2, 2, 3] => 2, 2, 1, 3, 2, 3, 2, 2, 3
[2, 2, 1, 3, 2, 3, 2, 3, 1] => 2, 2, 1, 3, 2, 3, 2, 3, 1
[2, 2, 1, 3, 2, 3, 2, 3, 2] => 2, 2, 1, 3, 2, 3, 2, 3, 2
[2, 2, 1, 3, 2, 3, 2, 3, 3] => 2, 2, 1, 3, 2, 3, 2, 3, 3
[2, 2, 1, 3, 2, 3, 3, 1, 1] => 2, 2, 1, 3, 2, 3, 3, 1, 1
[2, 2, 1, 3, 2, 3, 3, 1, 2] => 2, 2, 1, 3, 2, 3, 3, 1, 2
[2, 2, 1, 3, 2, 3, 3, 1, 3] => 2, 2, 1, 3, 2, 3, 3, 1, 3
[2, 2, 1, 3, 2, 3, 3, 2, 1] => 2, 2, 1, 3, 2, 3, 3, 2, 1
[2, 2, 1, 3, 2, 3, 3, 2, 2] => 2, 2, 1, 3, 2, 3, 3, 2, 2
[2, 2, 1, 3, 2, 3, 3, 2, 3] => 2, 2, 1, 3, 2, 3, 3, 2, 3
[2, 2, 1, 3, 2, 3, 3, 3, 1] => 2, 2, 1, 3, 2, 3, 3, 3, 1
[2, 2, 1, 3, 2, 3, 3, 3, 2] => 2, 2, 1, 3, 2, 3, 3, 3, 2
[2, 2, 1, 3, 2, 3, 3, 3, 3] => 2, 2, 1, 3, 2, 3, 3, 3, 3
[2, 2, 1, 3, 3, 1, 1, 1, 1] => 2, 2, 1, 3, 3, 1, 1, 1, 1
[2, 2, 1, 3, 3, 1, 1, 1, 2] => 2, 2, 1, 3, 3, 1, 1, 1, 2
[2, 2, 1, 3, 3, 1, 1, 1, 3] => 2, 2, 1, 3, 3, 1, 1, 1, 3
[2, 2, 1, 3, 3, 1, 1, 2, 1] => 2, 2, 1, 3, 3, 1, 1, 2, 1
[2, 2, 1, 3, 3, 1, 1, 2, 2] => 2, 2, 1, 3, 3, 1, 1, 2, 2
[2, 2, 1, 3, 3, 1, 1, 2, 3] => 2, 2, 1, 3, 3, 1, 1, 2, 3
[2, 2, 1, 3, 3, 1, 1, 3, 1] => 2, 2, 1, 3, 3, 1, 1, 3, 1
[2, 2, 1, 3, 3, 1, 1, 3, 2] => 2, 2, 1, 3, 3, 1, 1, 3, 2
[2, 2, 1, 3, 3, 1, 1, 3, 3] => 2, 2, 1, 3, 3, 1, 1, 3, 3
[2, 2, 1, 3, 3, 1, 2, 1, 1] => 2, 2, 1, 3, 3, 1, 2, 1, 1
[2, 2, 1, 3, 3, 1, 2, 1, 2] => 2, 2, 1, 3, 3, 1, 2, 1, 2
[2, 2, 1, 3, 3, 1, 2, 1, 3] => 2, 2, 1, 3, 3, 1, 2, 1, 3
[2, 2, 1, 3, 3, 1, 2, 2, 1] => 2, 2, 1, 3, 3, 1, 2, 2, 1
[2, 2, 1, 3, 3, 1, 2, 2, 2] => 2, 2, 1, 3, 3, 1, 2, 2, 2
[2, 2, 1, 3, 3, 1, 2, 2, 3] => 2, 2, 1, 3, 3, 1, 2, 2, 3
[2, 2, 1, 3, 3, 1, 2, 3, 1] => 2, 2, 1, 3, 3, 1, 2, 3, 1
[2, 2, 1, 3, 3, 1, 2, 3, 2] => 2, 2, 1, 3, 3, 1, 2, 3, 2
[2, 2, 1, 3, 3, 1, 2, 3, 3] => 2, 2, 1, 3, 3, 1, 2, 3, 3
[2, 2, 1, 3, 3, 1, 3, 1, 1] => 2, 2, 1, 3, 3, 1, 3, 1, 1
[2, 2, 1, 3, 3, 1, 3, 1, 2] => 2, 2, 1, 3, 3, 1, 3, 1, 2
[2, 2, 1, 3, 3, 1, 3, 1, 3] => 2, 2, 1, 3, 3, 1, 3, 1, 3
[2, 2, 1, 3, 3, 1, 3, 2, 1] => 2, 2, 1, 3, 3, 1, 3, 2, 1
[2, 2, 1, 3, 3, 1, 3, 2, 2] => 2, 2, 1, 3, 3, 1, 3, 2, 2
[2, 2, 1, 3, 3, 1, 3, 2, 3] => 2, 2, 1, 3, 3, 1, 3, 2, 3
[2, 2, 1, 3, 3, 1, 3, 3, 1] => 2, 2, 1, 3, 3, 1, 3, 3, 1
[2, 2, 1, 3, 3, 1, 3, 3, 2] => 2, 2, 1, 3, 3, 1, 3, 3, 2
[2, 2, 1, 3, 3, 1, 3, 3, 3] => 2, 2, 1, 3, 3, 1, 3, 3, 3
[2, 2, 1, 3, 3, 2, 1, 1, 1] => 2, 2, 1, 3, 3, 2, 1, 1, 1
[2, 2, 1, 3, 3, 2, 1, 1, 2] => 2, 2, 1, 3, 3, 2, 1, 1, 2
[2, 2, 1, 3, 3, 2, 1, 1, 3] => 2, 2, 1, 3, 3, 2, 1, 1, 3
[2, 2, 1, 3, 3, 2, 1, 2, 1] => 2, 2, 1, 3, 3, 2, 1, 2, 1
[2, 2, 1, 3, 3, 2, 1, 2, 2] => 2, 2, 1, 3, 3, 2, 1, 2, 2
[2, 2, 1, 3, 3, 2, 1, 2, 3] => 2, 2, 1, 3, 3, 2, 1, 2, 3
[2, 2, 1, 3, 3, 2, 1, 3, 1] => 2, 2, 1, 3, 3, 2, 1, 3, 1
[2, 2, 1, 3, 3, 2, 1, 3, 2] => 2, 2, 1, 3, 3, 2, 1, 3, 2
[2, 2, 1, 3, 3, 2, 1, 3, 3] => 2, 2, 1, 3, 3, 2, 1, 3, 3
[2, 2, 1, 3, 3, 2, 2, 1, 1] => 2, 2, 1, 3, 3, 2, 2, 1, 1
[2, 2, 1, 3, 3, 2, 2, 1, 2] => 2, 2, 1, 3, 3, 2, 2, 1, 2
[2, 2, 1, 3, 3, 2, 2, 1, 3] => 2, 2, 1, 3, 3, 2, 2, 1, 3
[2, 2, 1, 3, 3, 2, 2, 2, 1] => 2, 2, 1, 3, 3, 2, 2, 2, 1
[2, 2, 1, 3, 3, 2, 2, 2, 2] => 2, 2, 1, 3, 3, 2, 2, 2, 2
[2, 2, 1, 3, 3, 2, 2, 2, 3] => 2, 2, 1, 3, 3, 2, 2, 2, 3
[2, 2, 1, 3, 3, 2, 2, 3, 1] => 2, 2, 1, 3, 3, 2, 2, 3, 1
[2, 2, 1, 3, 3, 2, 2, 3, 2] => 2, 2, 1, 3, 3, 2, 2, 3, 2
[2, 2, 1, 3, 3, 2, 2, 3, 3] => 2, 2, 1, 3, 3, 2, 2, 3, 3
[2, 2, 1, 3, 3, 2, 3, 1, 1] => 2, 2, 1, 3, 3, 2, 3, 1, 1
[2, 2, 1, 3, 3, 2, 3, 1, 2] => 2, 2, 1, 3, 3, 2, 3, 1, 2
[2, 2, 1, 3, 3, 2, 3, 1, 3] => 2, 2, 1, 3, 3, 2, 3, 1, 3
[2, 2, 1, 3, 3, 2, 3, 2, 1] => 2, 2, 1, 3, 3, 2, 3, 2, 1
[2, 2, 1, 3, 3, 2, 3, 2, 2] => 2, 2, 1, 3, 3, 2, 3, 2, 2
[2, 2, 1, 3, 3, 2, 3, 2, 3] => 2, 2, 1, 3, 3, 2, 3, 2, 3
[2, 2, 1, 3, 3, 2, 3, 3, 1] => 2, 2, 1, 3, 3, 2, 3, 3, 1
[2, 2, 1, 3, 3, 2, 3, 3, 2] => 2, 2, 1, 3, 3, 2, 3, 3, 2
[2, 2, 1, 3, 3, 2, 3, 3, 3] => 2, 2, 1, 3, 3, 2, 3, 3, 3
[2, 2, 1, 3, 3, 3, 1, 1, 1] => 2, 2, 1, 3, 3, 3, 1, 1, 1
[2, 2, 1, 3, 3, 3, 1, 1, 2] => 2, 2, 1, 3, 3, 3, 1, 1, 2
[2, 2, 1, 3, 3, 3, 1, 1, 3] => 2, 2, 1, 3, 3, 3, 1, 1, 3
[2, 2, 1, 3, 3, 3, 1, 2, 1] => 2, 2, 1, 3, 3, 3, 1, 2, 1
[2, 2, 1, 3, 3, 3, 1, 2, 2] => 2, 2, 1, 3, 3, 3, 1, 2, 2
[2, 2, 1, 3, 3, 3, 1, 2, 3] => 2, 2, 1, 3, 3, 3, 1, 2, 3
[2, 2, 1, 3, 3, 3, 1, 3, 1] => 2, 2, 1, 3, 3, 3, 1, 3, 1
[2, 2, 1, 3, 3, 3, 1, 3, 2] => 2, 2, 1, 3, 3, 3, 1, 3, 2
[2, 2, 1, 3, 3, 3, 1, 3, 3] => 2, 2, 1, 3, 3, 3, 1, 3, 3
[2, 2, 1, 3, 3, 3, 2, 1, 1] => 2, 2, 1, 3, 3, 3, 2, 1, 1
[2, 2, 1, 3, 3, 3, 2, 1, 2] => 2, 2, 1, 3, 3, 3, 2, 1, 2
[2, 2, 1, 3, 3, 3, 2, 1, 3] => 2, 2, 1, 3, 3, 3, 2, 1, 3
[2, 2, 1, 3, 3, 3, 2, 2, 1] => 2, 2, 1, 3, 3, 3, 2, 2, 1
[2, 2, 1, 3, 3, 3, 2, 2, 2] => 2, 2, 1, 3, 3, 3, 2, 2, 2
[2, 2, 1, 3, 3, 3, 2, 2, 3] => 2, 2, 1, 3, 3, 3, 2, 2, 3
[2, 2, 1, 3, 3, 3, 2, 3, 1] => 2, 2, 1, 3, 3, 3, 2, 3, 1
[2, 2, 1, 3, 3, 3, 2, 3, 2] => 2, 2, 1, 3, 3, 3, 2, 3, 2
[2, 2, 1, 3, 3, 3, 2, 3, 3] => 2, 2, 1, 3, 3, 3, 2, 3, 3
[2, 2, 1, 3, 3, 3, 3, 1, 1] => 2, 2, 1, 3, 3, 3, 3, 1, 1
[2, 2, 1, 3, 3, 3, 3, 1, 2] => 2, 2, 1, 3, 3, 3, 3, 1, 2
[2, 2, 1, 3, 3, 3, 3, 1, 3] => 2, 2, 1, 3, 3, 3, 3, 1, 3
[2, 2, 1, 3, 3, 3, 3, 2, 1] => 2, 2, 1, 3, 3, 3, 3, 2, 1
[2, 2, 1, 3, 3, 3, 3, 2, 2] => 2, 2, 1, 3, 3, 3, 3, 2, 2
[2, 2, 1, 3, 3, 3, 3, 2, 3] => 2, 2, 1, 3, 3, 3, 3, 2, 3
[2, 2, 1, 3, 3, 3, 3, 3, 1] => 2, 2, 1, 3, 3, 3, 3, 3, 1
[2, 2, 1, 3, 3, 3, 3, 3, 2] => 2, 2, 1, 3, 3, 3, 3, 3, 2
[2, 2, 1, 3, 3, 3, 3, 3, 3] => 2, 2, 1, 3, 3, 3, 3, 3, 3
[2, 2, 2, 1, 1, 1, 1, 1, 1] => 2, 2, 2, 1, 1, 1, 1, 1, 1
[2, 2, 2, 1, 1, 1, 1, 1, 2] => 2, 2, 2, 1, 1, 1, 1, 1, 2
[2, 2, 2, 1, 1, 1, 1, 1, 3] => 2, 2, 2, 1, 1, 1, 1, 1, 3
[2, 2, 2, 1, 1, 1, 1, 2, 1] => 2, 2, 2, 1, 1, 1, 1, 2, 1
[2, 2, 2, 1, 1, 1, 1, 2, 2] => 2, 2, 2, 1, 1, 1, 1, 2, 2
[2, 2, 2, 1, 1, 1, 1, 2, 3] => 2, 2, 2, 1, 1, 1, 1, 2, 3
[2, 2, 2, 1, 1, 1, 1, 3, 1] => 2, 2, 2, 1, 1, 1, 1, 3, 1
[2, 2, 2, 1, 1, 1, 1, 3, 2] => 2, 2, 2, 1, 1, 1, 1, 3, 2
[2, 2, 2, 1, 1, 1, 1, 3, 3] => 2, 2, 2, 1, 1, 1, 1, 3, 3
[2, 2, 2, 1, 1, 1, 2, 1, 1] => 2, 2, 2, 1, 1, 1, 2, 1, 1
[2, 2, 2, 1, 1, 1, 2, 1, 2] => 2, 2, 2, 1, 1, 1, 2, 1, 2
[2, 2, 2, 1, 1, 1, 2, 1, 3] => 2, 2, 2, 1, 1, 1, 2, 1, 3
[2, 2, 2, 1, 1, 1, 2, 2, 1] => 2, 2, 2, 1, 1, 1, 2, 2, 1
[2, 2, 2, 1, 1, 1, 2, 2, 2] => 2, 2, 2, 1, 1, 1, 2, 2, 2
[2, 2, 2, 1, 1, 1, 2, 2, 3] => 2, 2, 2, 1, 1, 1, 2, 2, 3
[2, 2, 2, 1, 1, 1, 2, 3, 1] => 2, 2, 2, 1, 1, 1, 2, 3, 1
[2, 2, 2, 1, 1, 1, 2, 3, 2] => 2, 2, 2, 1, 1, 1, 2, 3, 2
[2, 2, 2, 1, 1, 1, 2, 3, 3] => 2, 2, 2, 1, 1, 1, 2, 3, 3
[2, 2, 2, 1, 1, 1, 3, 1, 1] => 2, 2, 2, 1, 1, 1, 3, 1, 1
[2, 2, 2, 1, 1, 1, 3, 1, 2] => 2, 2, 2, 1, 1, 1, 3, 1, 2
[2, 2, 2, 1, 1, 1, 3, 1, 3] => 2, 2, 2, 1, 1, 1, 3, 1, 3
[2, 2, 2, 1, 1, 1, 3, 2, 1] => 2, 2, 2, 1, 1, 1, 3, 2, 1
[2, 2, 2, 1, 1, 1, 3, 2, 2] => 2, 2, 2, 1, 1, 1, 3, 2, 2
[2, 2, 2, 1, 1, 1, 3, 2, 3] => 2, 2, 2, 1, 1, 1, 3, 2, 3
[2, 2, 2, 1, 1, 1, 3, 3, 1] => 2, 2, 2, 1, 1, 1, 3, 3, 1
[2, 2, 2, 1, 1, 1, 3, 3, 2] => 2, 2, 2, 1, 1, 1, 3, 3, 2
[2, 2, 2, 1, 1, 1, 3, 3, 3] => 2, 2, 2, 1, 1, 1, 3, 3, 3
[2, 2, 2, 1, 1, 2, 1, 1, 1] => 2, 2, 2, 1, 1, 2, 1, 1, 1
[2, 2, 2, 1, 1, 2, 1, 1, 2] => 2, 2, 2, 1, 1, 2, 1, 1, 2
[2, 2, 2, 1, 1, 2, 1, 1, 3] => 2, 2, 2, 1, 1, 2, 1, 1, 3
[2, 2, 2, 1, 1, 2, 1, 2, 1] => 2, 2, 2, 1, 1, 2, 1, 2, 1
[2, 2, 2, 1, 1, 2, 1, 2, 2] => 2, 2, 2, 1, 1, 2, 1, 2, 2
[2, 2, 2, 1, 1, 2, 1, 2, 3] => 2, 2, 2, 1, 1, 2, 1, 2, 3
[2, 2, 2, 1, 1, 2, 1, 3, 1] => 2, 2, 2, 1, 1, 2, 1, 3, 1
[2, 2, 2, 1, 1, 2, 1, 3, 2] => 2, 2, 2, 1, 1, 2, 1, 3, 2
[2, 2, 2, 1, 1, 2, 1, 3, 3] => 2, 2, 2, 1, 1, 2, 1, 3, 3
[2, 2, 2, 1, 1, 2, 2, 1, 1] => 2, 2, 2, 1, 1, 2, 2, 1, 1
[2, 2, 2, 1, 1, 2, 2, 1, 2] => 2, 2, 2, 1, 1, 2, 2, 1, 2
[2, 2, 2, 1, 1, 2, 2, 1, 3] => 2, 2, 2, 1, 1, 2, 2, 1, 3
[2, 2, 2, 1, 1, 2, 2, 2, 1] => 2, 2, 2, 1, 1, 2, 2, 2, 1
[2, 2, 2, 1, 1, 2, 2, 2, 2] => 2, 2, 2, 1, 1, 2, 2, 2, 2
[2, 2, 2, 1, 1, 2, 2, 2, 3] => 2, 2, 2, 1, 1, 2, 2, 2, 3
[2, 2, 2, 1, 1, 2, 2, 3, 1] => 2, 2, 2, 1, 1, 2, 2, 3, 1
[2, 2, 2, 1, 1, 2, 2, 3, 2] => 2, 2, 2, 1, 1, 2, 2, 3, 2
[2, 2, 2, 1, 1, 2, 2, 3, 3] => 2, 2, 2, 1, 1, 2, 2, 3, 3
[2, 2, 2, 1, 1, 2, 3, 1, 1] => 2, 2, 2, 1, 1, 2, 3, 1, 1
[2, 2, 2, 1, 1, 2, 3, 1, 2] => 2, 2, 2, 1, 1, 2, 3, 1, 2
[2, 2, 2, 1, 1, 2, 3, 1, 3] => 2, 2, 2, 1, 1, 2, 3, 1, 3
[2, 2, 2, 1, 1, 2, 3, 2, 1] => 2, 2, 2, 1, 1, 2, 3, 2, 1
[2, 2, 2, 1, 1, 2, 3, 2, 2] => 2, 2, 2, 1, 1, 2, 3, 2, 2
[2, 2, 2, 1, 1, 2, 3, 2, 3] => 2, 2, 2, 1, 1, 2, 3, 2, 3
[2, 2, 2, 1, 1, 2, 3, 3, 1] => 2, 2, 2, 1, 1, 2, 3, 3, 1
[2, 2, 2, 1, 1, 2, 3, 3, 2] => 2, 2, 2, 1, 1, 2, 3, 3, 2
[2, 2, 2, 1, 1, 2, 3, 3, 3] => 2, 2, 2, 1, 1, 2, 3, 3, 3
[2, 2, 2, 1, 1, 3, 1, 1, 1] => 2, 2, 2, 1, 1, 3, 1, 1, 1
[2, 2, 2, 1, 1, 3, 1, 1, 2] => 2, 2, 2, 1, 1, 3, 1, 1, 2
[2, 2, 2, 1, 1, 3, 1, 1, 3] => 2, 2, 2, 1, 1, 3, 1, 1, 3
[2, 2, 2, 1, 1, 3, 1, 2, 1] => 2, 2, 2, 1, 1, 3, 1, 2, 1
[2, 2, 2, 1, 1, 3, 1, 2, 2] => 2, 2, 2, 1, 1, 3, 1, 2, 2
[2, 2, 2, 1, 1, 3, 1, 2, 3] => 2, 2, 2, 1, 1, 3, 1, 2, 3
[2, 2, 2, 1, 1, 3, 1, 3, 1] => 2, 2, 2, 1, 1, 3, 1, 3, 1
[2, 2, 2, 1, 1, 3, 1, 3, 2] => 2, 2, 2, 1, 1, 3, 1, 3, 2
[2, 2, 2, 1, 1, 3, 1, 3, 3] => 2, 2, 2, 1, 1, 3, 1, 3, 3
[2, 2, 2, 1, 1, 3, 2, 1, 1] => 2, 2, 2, 1, 1, 3, 2, 1, 1
[2, 2, 2, 1, 1, 3, 2, 1, 2] => 2, 2, 2, 1, 1, 3, 2, 1, 2
[2, 2, 2, 1, 1, 3, 2, 1, 3] => 2, 2, 2, 1, 1, 3, 2, 1, 3
[2, 2, 2, 1, 1, 3, 2, 2, 1] => 2, 2, 2, 1, 1, 3, 2, 2, 1
[2, 2, 2, 1, 1, 3, 2, 2, 2] => 2, 2, 2, 1, 1, 3, 2, 2, 2
[2, 2, 2, 1, 1, 3, 2, 2, 3] => 2, 2, 2, 1, 1, 3, 2, 2, 3
[2, 2, 2, 1, 1, 3, 2, 3, 1] => 2, 2, 2, 1, 1, 3, 2, 3, 1
[2, 2, 2, 1, 1, 3, 2, 3, 2] => 2, 2, 2, 1, 1, 3, 2, 3, 2
[2, 2, 2, 1, 1, 3, 2, 3, 3] => 2, 2, 2, 1, 1, 3, 2, 3, 3
[2, 2, 2, 1, 1, 3, 3, 1, 1] => 2, 2, 2, 1, 1, 3, 3, 1, 1
[2, 2, 2, 1, 1, 3, 3, 1, 2] => 2, 2, 2, 1, 1, 3, 3, 1, 2
[2, 2, 2, 1, 1, 3, 3, 1, 3] => 2, 2, 2, 1, 1, 3, 3, 1, 3
[2, 2, 2, 1, 1, 3, 3, 2, 1] => 2, 2, 2, 1, 1, 3, 3, 2, 1
[2, 2, 2, 1, 1, 3, 3, 2, 2] => 2, 2, 2, 1, 1, 3, 3, 2, 2
[2, 2, 2, 1, 1, 3, 3, 2, 3] => 2, 2, 2, 1, 1, 3, 3, 2, 3
[2, 2, 2, 1, 1, 3, 3, 3, 1] => 2, 2, 2, 1, 1, 3, 3, 3, 1
[2, 2, 2, 1, 1, 3, 3, 3, 2] => 2, 2, 2, 1, 1, 3, 3, 3, 2
[2, 2, 2, 1, 1, 3, 3, 3, 3] => 2, 2, 2, 1, 1, 3, 3, 3, 3
[2, 2, 2, 1, 2, 1, 1, 1, 1] => 2, 2, 2, 1, 2, 1, 1, 1, 1
[2, 2, 2, 1, 2, 1, 1, 1, 2] => 2, 2, 2, 1, 2, 1, 1, 1, 2
[2, 2, 2, 1, 2, 1, 1, 1, 3] => 2, 2, 2, 1, 2, 1, 1, 1, 3
[2, 2, 2, 1, 2, 1, 1, 2, 1] => 2, 2, 2, 1, 2, 1, 1, 2, 1
[2, 2, 2, 1, 2, 1, 1, 2, 2] => 2, 2, 2, 1, 2, 1, 1, 2, 2
[2, 2, 2, 1, 2, 1, 1, 2, 3] => 2, 2, 2, 1, 2, 1, 1, 2, 3
[2, 2, 2, 1, 2, 1, 1, 3, 1] => 2, 2, 2, 1, 2, 1, 1, 3, 1
[2, 2, 2, 1, 2, 1, 1, 3, 2] => 2, 2, 2, 1, 2, 1, 1, 3, 2
[2, 2, 2, 1, 2, 1, 1, 3, 3] => 2, 2, 2, 1, 2, 1, 1, 3, 3
[2, 2, 2, 1, 2, 1, 2, 1, 1] => 2, 2, 2, 1, 2, 1, 2, 1, 1
[2, 2, 2, 1, 2, 1, 2, 1, 2] => 2, 2, 2, 1, 2, 1, 2, 1, 2
[2, 2, 2, 1, 2, 1, 2, 1, 3] => 2, 2, 2, 1, 2, 1, 2, 1, 3
[2, 2, 2, 1, 2, 1, 2, 2, 1] => 2, 2, 2, 1, 2, 1, 2, 2, 1
[2, 2, 2, 1, 2, 1, 2, 2, 2] => 2, 2, 2, 1, 2, 1, 2, 2, 2
[2, 2, 2, 1, 2, 1, 2, 2, 3] => 2, 2, 2, 1, 2, 1, 2, 2, 3
[2, 2, 2, 1, 2, 1, 2, 3, 1] => 2, 2, 2, 1, 2, 1, 2, 3, 1
[2, 2, 2, 1, 2, 1, 2, 3, 2] => 2, 2, 2, 1, 2, 1, 2, 3, 2
[2, 2, 2, 1, 2, 1, 2, 3, 3] => 2, 2, 2, 1, 2, 1, 2, 3, 3
[2, 2, 2, 1, 2, 1, 3, 1, 1] => 2, 2, 2, 1, 2, 1, 3, 1, 1
[2, 2, 2, 1, 2, 1, 3, 1, 2] => 2, 2, 2, 1, 2, 1, 3, 1, 2
[2, 2, 2, 1, 2, 1, 3, 1, 3] => 2, 2, 2, 1, 2, 1, 3, 1, 3
[2, 2, 2, 1, 2, 1, 3, 2, 1] => 2, 2, 2, 1, 2, 1, 3, 2, 1
[2, 2, 2, 1, 2, 1, 3, 2, 2] => 2, 2, 2, 1, 2, 1, 3, 2, 2
[2, 2, 2, 1, 2, 1, 3, 2, 3] => 2, 2, 2, 1, 2, 1, 3, 2, 3
[2, 2, 2, 1, 2, 1, 3, 3, 1] => 2, 2, 2, 1, 2, 1, 3, 3, 1
[2, 2, 2, 1, 2, 1, 3, 3, 2] => 2, 2, 2, 1, 2, 1, 3, 3, 2
[2, 2, 2, 1, 2, 1, 3, 3, 3] => 2, 2, 2, 1, 2, 1, 3, 3, 3
[2, 2, 2, 1, 2, 2, 1, 1, 1] => 2, 2, 2, 1, 2, 2, 1, 1, 1
[2, 2, 2, 1, 2, 2, 1, 1, 2] => 2, 2, 2, 1, 2, 2, 1, 1, 2
[2, 2, 2, 1, 2, 2, 1, 1, 3] => 2, 2, 2, 1, 2, 2, 1, 1, 3
[2, 2, 2, 1, 2, 2, 1, 2, 1] => 2, 2, 2, 1, 2, 2, 1, 2, 1
[2, 2, 2, 1, 2, 2, 1, 2, 2] => 2, 2, 2, 1, 2, 2, 1, 2, 2
[2, 2, 2, 1, 2, 2, 1, 2, 3] => 2, 2, 2, 1, 2, 2, 1, 2, 3
[2, 2, 2, 1, 2, 2, 1, 3, 1] => 2, 2, 2, 1, 2, 2, 1, 3, 1
[2, 2, 2, 1, 2, 2, 1, 3, 2] => 2, 2, 2, 1, 2, 2, 1, 3, 2
[2, 2, 2, 1, 2, 2, 1, 3, 3] => 2, 2, 2, 1, 2, 2, 1, 3, 3
[2, 2, 2, 1, 2, 2, 2, 1, 1] => 2, 2, 2, 1, 2, 2, 2, 1, 1
[2, 2, 2, 1, 2, 2, 2, 1, 2] => 2, 2, 2, 1, 2, 2, 2, 1, 2
[2, 2, 2, 1, 2, 2, 2, 1, 3] => 2, 2, 2, 1, 2, 2, 2, 1, 3
[2, 2, 2, 1, 2, 2, 2, 2, 1] => 2, 2, 2, 1, 2, 2, 2, 2, 1
[2, 2, 2, 1, 2, 2, 2, 2, 2] => 2, 2, 2, 1, 2, 2, 2, 2, 2
[2, 2, 2, 1, 2, 2, 2, 2, 3] => 2, 2, 2, 1, 2, 2, 2, 2, 3
[2, 2, 2, 1, 2, 2, 2, 3, 1] => 2, 2, 2, 1, 2, 2, 2, 3, 1
[2, 2, 2, 1, 2, 2, 2, 3, 2] => 2, 2, 2, 1, 2, 2, 2, 3, 2
[2, 2, 2, 1, 2, 2, 2, 3, 3] => 2, 2, 2, 1, 2, 2, 2, 3, 3
[2, 2, 2, 1, 2, 2, 3, 1, 1] => 2, 2, 2, 1, 2, 2, 3, 1, 1
[2, 2, 2, 1, 2, 2, 3, 1, 2] => 2, 2, 2, 1, 2, 2, 3, 1, 2
[2, 2, 2, 1, 2, 2, 3, 1, 3] => 2, 2, 2, 1, 2, 2, 3, 1, 3
[2, 2, 2, 1, 2, 2, 3, 2, 1] => 2, 2, 2, 1, 2, 2, 3, 2, 1
[2, 2, 2, 1, 2, 2, 3, 2, 2] => 2, 2, 2, 1, 2, 2, 3, 2, 2
[2, 2, 2, 1, 2, 2, 3, 2, 3] => 2, 2, 2, 1, 2, 2, 3, 2, 3
[2, 2, 2, 1, 2, 2, 3, 3, 1] => 2, 2, 2, 1, 2, 2, 3, 3, 1
[2, 2, 2, 1, 2, 2, 3, 3, 2] => 2, 2, 2, 1, 2, 2, 3, 3, 2
[2, 2, 2, 1, 2, 2, 3, 3, 3] => 2, 2, 2, 1, 2, 2, 3, 3, 3
[2, 2, 2, 1, 2, 3, 1, 1, 1] => 2, 2, 2, 1, 2, 3, 1, 1, 1
[2, 2, 2, 1, 2, 3, 1, 1, 2] => 2, 2, 2, 1, 2, 3, 1, 1, 2
[2, 2, 2, 1, 2, 3, 1, 1, 3] => 2, 2, 2, 1, 2, 3, 1, 1, 3
[2, 2, 2, 1, 2, 3, 1, 2, 1] => 2, 2, 2, 1, 2, 3, 1, 2, 1
[2, 2, 2, 1, 2, 3, 1, 2, 2] => 2, 2, 2, 1, 2, 3, 1, 2, 2
[2, 2, 2, 1, 2, 3, 1, 2, 3] => 2, 2, 2, 1, 2, 3, 1, 2, 3
[2, 2, 2, 1, 2, 3, 1, 3, 1] => 2, 2, 2, 1, 2, 3, 1, 3, 1
[2, 2, 2, 1, 2, 3, 1, 3, 2] => 2, 2, 2, 1, 2, 3, 1, 3, 2
[2, 2, 2, 1, 2, 3, 1, 3, 3] => 2, 2, 2, 1, 2, 3, 1, 3, 3
[2, 2, 2, 1, 2, 3, 2, 1, 1] => 2, 2, 2, 1, 2, 3, 2, 1, 1
[2, 2, 2, 1, 2, 3, 2, 1, 2] => 2, 2, 2, 1, 2, 3, 2, 1, 2
[2, 2, 2, 1, 2, 3, 2, 1, 3] => 2, 2, 2, 1, 2, 3, 2, 1, 3
[2, 2, 2, 1, 2, 3, 2, 2, 1] => 2, 2, 2, 1, 2, 3, 2, 2, 1
[2, 2, 2, 1, 2, 3, 2, 2, 2] => 2, 2, 2, 1, 2, 3, 2, 2, 2
[2, 2, 2, 1, 2, 3, 2, 2, 3] => 2, 2, 2, 1, 2, 3, 2, 2, 3
[2, 2, 2, 1, 2, 3, 2, 3, 1] => 2, 2, 2, 1, 2, 3, 2, 3, 1
[2, 2, 2, 1, 2, 3, 2, 3, 2] => 2, 2, 2, 1, 2, 3, 2, 3, 2
[2, 2, 2, 1, 2, 3, 2, 3, 3] => 2, 2, 2, 1, 2, 3, 2, 3, 3
[2, 2, 2, 1, 2, 3, 3, 1, 1] => 2, 2, 2, 1, 2, 3, 3, 1, 1
[2, 2, 2, 1, 2, 3, 3, 1, 2] => 2, 2, 2, 1, 2, 3, 3, 1, 2
[2, 2, 2, 1, 2, 3, 3, 1, 3] => 2, 2, 2, 1, 2, 3, 3, 1, 3
[2, 2, 2, 1, 2, 3, 3, 2, 1] => 2, 2, 2, 1, 2, 3, 3, 2, 1
[2, 2, 2, 1, 2, 3, 3, 2, 2] => 2, 2, 2, 1, 2, 3, 3, 2, 2
[2, 2, 2, 1, 2, 3, 3, 2, 3] => 2, 2, 2, 1, 2, 3, 3, 2, 3
[2, 2, 2, 1, 2, 3, 3, 3, 1] => 2, 2, 2, 1, 2, 3, 3, 3, 1
[2, 2, 2, 1, 2, 3, 3, 3, 2] => 2, 2, 2, 1, 2, 3, 3, 3, 2
[2, 2, 2, 1, 2, 3, 3, 3, 3] => 2, 2, 2, 1, 2, 3, 3, 3, 3
[2, 2, 2, 1, 3, 1, 1, 1, 1] => 2, 2, 2, 1, 3, 1, 1, 1, 1
[2, 2, 2, 1, 3, 1, 1, 1, 2] => 2, 2, 2, 1, 3, 1, 1, 1, 2
[2, 2, 2, 1, 3, 1, 1, 1, 3] => 2, 2, 2, 1, 3, 1, 1, 1, 3
[2, 2, 2, 1, 3, 1, 1, 2, 1] => 2, 2, 2, 1, 3, 1, 1, 2, 1
[2, 2, 2, 1, 3, 1, 1, 2, 2] => 2, 2, 2, 1, 3, 1, 1, 2, 2
[2, 2, 2, 1, 3, 1, 1, 2, 3] => 2, 2, 2, 1, 3, 1, 1, 2, 3
[2, 2, 2, 1, 3, 1, 1, 3, 1] => 2, 2, 2, 1, 3, 1, 1, 3, 1
[2, 2, 2, 1, 3, 1, 1, 3, 2] => 2, 2, 2, 1, 3, 1, 1, 3, 2
[2, 2, 2, 1, 3, 1, 1, 3, 3] => 2, 2, 2, 1, 3, 1, 1, 3, 3
[2, 2, 2, 1, 3, 1, 2, 1, 1] => 2, 2, 2, 1, 3, 1, 2, 1, 1
[2, 2, 2, 1, 3, 1, 2, 1, 2] => 2, 2, 2, 1, 3, 1, 2, 1, 2
[2, 2, 2, 1, 3, 1, 2, 1, 3] => 2, 2, 2, 1, 3, 1, 2, 1, 3
[2, 2, 2, 1, 3, 1, 2, 2, 1] => 2, 2, 2, 1, 3, 1, 2, 2, 1
[2, 2, 2, 1, 3, 1, 2, 2, 2] => 2, 2, 2, 1, 3, 1, 2, 2, 2
[2, 2, 2, 1, 3, 1, 2, 2, 3] => 2, 2, 2, 1, 3, 1, 2, 2, 3
[2, 2, 2, 1, 3, 1, 2, 3, 1] => 2, 2, 2, 1, 3, 1, 2, 3, 1
[2, 2, 2, 1, 3, 1, 2, 3, 2] => 2, 2, 2, 1, 3, 1, 2, 3, 2
[2, 2, 2, 1, 3, 1, 2, 3, 3] => 2, 2, 2, 1, 3, 1, 2, 3, 3
[2, 2, 2, 1, 3, 1, 3, 1, 1] => 2, 2, 2, 1, 3, 1, 3, 1, 1
[2, 2, 2, 1, 3, 1, 3, 1, 2] => 2, 2, 2, 1, 3, 1, 3, 1, 2
[2, 2, 2, 1, 3, 1, 3, 1, 3] => 2, 2, 2, 1, 3, 1, 3, 1, 3
[2, 2, 2, 1, 3, 1, 3, 2, 1] => 2, 2, 2, 1, 3, 1, 3, 2, 1
[2, 2, 2, 1, 3, 1, 3, 2, 2] => 2, 2, 2, 1, 3, 1, 3, 2, 2
[2, 2, 2, 1, 3, 1, 3, 2, 3] => 2, 2, 2, 1, 3, 1, 3, 2, 3
[2, 2, 2, 1, 3, 1, 3, 3, 1] => 2, 2, 2, 1, 3, 1, 3, 3, 1
[2, 2, 2, 1, 3, 1, 3, 3, 2] => 2, 2, 2, 1, 3, 1, 3, 3, 2
[2, 2, 2, 1, 3, 1, 3, 3, 3] => 2, 2, 2, 1, 3, 1, 3, 3, 3
[2, 2, 2, 1, 3, 2, 1, 1, 1] => 2, 2, 2, 1, 3, 2, 1, 1, 1
[2, 2, 2, 1, 3, 2, 1, 1, 2] => 2, 2, 2, 1, 3, 2, 1, 1, 2
[2, 2, 2, 1, 3, 2, 1, 1, 3] => 2, 2, 2, 1, 3, 2, 1, 1, 3
[2, 2, 2, 1, 3, 2, 1, 2, 1] => 2, 2, 2, 1, 3, 2, 1, 2, 1
[2, 2, 2, 1, 3, 2, 1, 2, 2] => 2, 2, 2, 1, 3, 2, 1, 2, 2
[2, 2, 2, 1, 3, 2, 1, 2, 3] => 2, 2, 2, 1, 3, 2, 1, 2, 3
[2, 2, 2, 1, 3, 2, 1, 3, 1] => 2, 2, 2, 1, 3, 2, 1, 3, 1
[2, 2, 2, 1, 3, 2, 1, 3, 2] => 2, 2, 2, 1, 3, 2, 1, 3, 2
[2, 2, 2, 1, 3, 2, 1, 3, 3] => 2, 2, 2, 1, 3, 2, 1, 3, 3
[2, 2, 2, 1, 3, 2, 2, 1, 1] => 2, 2, 2, 1, 3, 2, 2, 1, 1
[2, 2, 2, 1, 3, 2, 2, 1, 2] => 2, 2, 2, 1, 3, 2, 2, 1, 2
[2, 2, 2, 1, 3, 2, 2, 1, 3] => 2, 2, 2, 1, 3, 2, 2, 1, 3
[2, 2, 2, 1, 3, 2, 2, 2, 1] => 2, 2, 2, 1, 3, 2, 2, 2, 1
[2, 2, 2, 1, 3, 2, 2, 2, 2] => 2, 2, 2, 1, 3, 2, 2, 2, 2
[2, 2, 2, 1, 3, 2, 2, 2, 3] => 2, 2, 2, 1, 3, 2, 2, 2, 3
[2, 2, 2, 1, 3, 2, 2, 3, 1] => 2, 2, 2, 1, 3, 2, 2, 3, 1
[2, 2, 2, 1, 3, 2, 2, 3, 2] => 2, 2, 2, 1, 3, 2, 2, 3, 2
[2, 2, 2, 1, 3, 2, 2, 3, 3] => 2, 2, 2, 1, 3, 2, 2, 3, 3
[2, 2, 2, 1, 3, 2, 3, 1, 1] => 2, 2, 2, 1, 3, 2, 3, 1, 1
[2, 2, 2, 1, 3, 2, 3, 1, 2] => 2, 2, 2, 1, 3, 2, 3, 1, 2
[2, 2, 2, 1, 3, 2, 3, 1, 3] => 2, 2, 2, 1, 3, 2, 3, 1, 3
[2, 2, 2, 1, 3, 2, 3, 2, 1] => 2, 2, 2, 1, 3, 2, 3, 2, 1
[2, 2, 2, 1, 3, 2, 3, 2, 2] => 2, 2, 2, 1, 3, 2, 3, 2, 2
[2, 2, 2, 1, 3, 2, 3, 2, 3] => 2, 2, 2, 1, 3, 2, 3, 2, 3
[2, 2, 2, 1, 3, 2, 3, 3, 1] => 2, 2, 2, 1, 3, 2, 3, 3, 1
[2, 2, 2, 1, 3, 2, 3, 3, 2] => 2, 2, 2, 1, 3, 2, 3, 3, 2
[2, 2, 2, 1, 3, 2, 3, 3, 3] => 2, 2, 2, 1, 3, 2, 3, 3, 3
[2, 2, 2, 1, 3, 3, 1, 1, 1] => 2, 2, 2, 1, 3, 3, 1, 1, 1
[2, 2, 2, 1, 3, 3, 1, 1, 2] => 2, 2, 2, 1, 3, 3, 1, 1, 2
[2, 2, 2, 1, 3, 3, 1, 1, 3] => 2, 2, 2, 1, 3, 3, 1, 1, 3
[2, 2, 2, 1, 3, 3, 1, 2, 1] => 2, 2, 2, 1, 3, 3, 1, 2, 1
[2, 2, 2, 1, 3, 3, 1, 2, 2] => 2, 2, 2, 1, 3, 3, 1, 2, 2
[2, 2, 2, 1, 3, 3, 1, 2, 3] => 2, 2, 2, 1, 3, 3, 1, 2, 3
[2, 2, 2, 1, 3, 3, 1, 3, 1] => 2, 2, 2, 1, 3, 3, 1, 3, 1
[2, 2, 2, 1, 3, 3, 1, 3, 2] => 2, 2, 2, 1, 3, 3, 1, 3, 2
[2, 2, 2, 1, 3, 3, 1, 3, 3] => 2, 2, 2, 1, 3, 3, 1, 3, 3
[2, 2, 2, 1, 3, 3, 2, 1, 1] => 2, 2, 2, 1, 3, 3, 2, 1, 1
[2, 2, 2, 1, 3, 3, 2, 1, 2] => 2, 2, 2, 1, 3, 3, 2, 1, 2
[2, 2, 2, 1, 3, 3, 2, 1, 3] => 2, 2, 2, 1, 3, 3, 2, 1, 3
[2, 2, 2, 1, 3, 3, 2, 2, 1] => 2, 2, 2, 1, 3, 3, 2, 2, 1
[2, 2, 2, 1, 3, 3, 2, 2, 2] => 2, 2, 2, 1, 3, 3, 2, 2, 2
[2, 2, 2, 1, 3, 3, 2, 2, 3] => 2, 2, 2, 1, 3, 3, 2, 2, 3
[2, 2, 2, 1, 3, 3, 2, 3, 1] => 2, 2, 2, 1, 3, 3, 2, 3, 1
[2, 2, 2, 1, 3, 3, 2, 3, 2] => 2, 2, 2, 1, 3, 3, 2, 3, 2
[2, 2, 2, 1, 3, 3, 2, 3, 3] => 2, 2, 2, 1, 3, 3, 2, 3, 3
[2, 2, 2, 1, 3, 3, 3, 1, 1] => 2, 2, 2, 1, 3, 3, 3, 1, 1
[2, 2, 2, 1, 3, 3, 3, 1, 2] => 2, 2, 2, 1, 3, 3, 3, 1, 2
[2, 2, 2, 1, 3, 3, 3, 1, 3] => 2, 2, 2, 1, 3, 3, 3, 1, 3
[2, 2, 2, 1, 3, 3, 3, 2, 1] => 2, 2, 2, 1, 3, 3, 3, 2, 1
[2, 2, 2, 1, 3, 3, 3, 2, 2] => 2, 2, 2, 1, 3, 3, 3, 2, 2
[2, 2, 2, 1, 3, 3, 3, 2, 3] => 2, 2, 2, 1, 3, 3, 3, 2, 3
[2, 2, 2, 1, 3, 3, 3, 3, 1] => 2, 2, 2, 1, 3, 3, 3, 3, 1
[2, 2, 2, 1, 3, 3, 3, 3, 2] => 2, 2, 2, 1, 3, 3, 3, 3, 2
[2, 2, 2, 1, 3, 3, 3, 3, 3] => 2, 2, 2, 1, 3, 3, 3, 3, 3
[2, 2, 2, 2, 1, 1, 1, 1, 1] => 2, 2, 2, 2, 1, 1, 1, 1, 1
[2, 2, 2, 2, 1, 1, 1, 1, 2] => 2, 2, 2, 2, 1, 1, 1, 1, 2
[2, 2, 2, 2, 1, 1, 1, 1, 3] => 2, 2, 2, 2, 1, 1, 1, 1, 3
[2, 2, 2, 2, 1, 1, 1, 2, 1] => 2, 2, 2, 2, 1, 1, 1, 2, 1
[2, 2, 2, 2, 1, 1, 1, 2, 2] => 2, 2, 2, 2, 1, 1, 1, 2, 2
[2, 2, 2, 2, 1, 1, 1, 2, 3] => 2, 2, 2, 2, 1, 1, 1, 2, 3
[2, 2, 2, 2, 1, 1, 1, 3, 1] => 2, 2, 2, 2, 1, 1, 1, 3, 1
[2, 2, 2, 2, 1, 1, 1, 3, 2] => 2, 2, 2, 2, 1, 1, 1, 3, 2
[2, 2, 2, 2, 1, 1, 1, 3, 3] => 2, 2, 2, 2, 1, 1, 1, 3, 3
[2, 2, 2, 2, 1, 1, 2, 1, 1] => 2, 2, 2, 2, 1, 1, 2, 1, 1
[2, 2, 2, 2, 1, 1, 2, 1, 2] => 2, 2, 2, 2, 1, 1, 2, 1, 2
[2, 2, 2, 2, 1, 1, 2, 1, 3] => 2, 2, 2, 2, 1, 1, 2, 1, 3
[2, 2, 2, 2, 1, 1, 2, 2, 1] => 2, 2, 2, 2, 1, 1, 2, 2, 1
[2, 2, 2, 2, 1, 1, 2, 2, 2] => 2, 2, 2, 2, 1, 1, 2, 2, 2
[2, 2, 2, 2, 1, 1, 2, 2, 3] => 2, 2, 2, 2, 1, 1, 2, 2, 3
[2, 2, 2, 2, 1, 1, 2, 3, 1] => 2, 2, 2, 2, 1, 1, 2, 3, 1
[2, 2, 2, 2, 1, 1, 2, 3, 2] => 2, 2, 2, 2, 1, 1, 2, 3, 2
[2, 2, 2, 2, 1, 1, 2, 3, 3] => 2, 2, 2, 2, 1, 1, 2, 3, 3
[2, 2, 2, 2, 1, 1, 3, 1, 1] => 2, 2, 2, 2, 1, 1, 3, 1, 1
[2, 2, 2, 2, 1, 1, 3, 1, 2] => 2, 2, 2, 2, 1, 1, 3, 1, 2
[2, 2, 2, 2, 1, 1, 3, 1, 3] => 2, 2, 2, 2, 1, 1, 3, 1, 3
[2, 2, 2, 2, 1, 1, 3, 2, 1] => 2, 2, 2, 2, 1, 1, 3, 2, 1
[2, 2, 2, 2, 1, 1, 3, 2, 2] => 2, 2, 2, 2, 1, 1, 3, 2, 2
[2, 2, 2, 2, 1, 1, 3, 2, 3] => 2, 2, 2, 2, 1, 1, 3, 2, 3
[2, 2, 2, 2, 1, 1, 3, 3, 1] => 2, 2, 2, 2, 1, 1, 3, 3, 1
[2, 2, 2, 2, 1, 1, 3, 3, 2] => 2, 2, 2, 2, 1, 1, 3, 3, 2
[2, 2, 2, 2, 1, 1, 3, 3, 3] => 2, 2, 2, 2, 1, 1, 3, 3, 3
[2, 2, 2, 2, 1, 2, 1, 1, 1] => 2, 2, 2, 2, 1, 2, 1, 1, 1
[2, 2, 2, 2, 1, 2, 1, 1, 2] => 2, 2, 2, 2, 1, 2, 1, 1, 2
[2, 2, 2, 2, 1, 2, 1, 1, 3] => 2, 2, 2, 2, 1, 2, 1, 1, 3
[2, 2, 2, 2, 1, 2, 1, 2, 1] => 2, 2, 2, 2, 1, 2, 1, 2, 1
[2, 2, 2, 2, 1, 2, 1, 2, 2] => 2, 2, 2, 2, 1, 2, 1, 2, 2
[2, 2, 2, 2, 1, 2, 1, 2, 3] => 2, 2, 2, 2, 1, 2, 1, 2, 3
[2, 2, 2, 2, 1, 2, 1, 3, 1] => 2, 2, 2, 2, 1, 2, 1, 3, 1
[2, 2, 2, 2, 1, 2, 1, 3, 2] => 2, 2, 2, 2, 1, 2, 1, 3, 2
[2, 2, 2, 2, 1, 2, 1, 3, 3] => 2, 2, 2, 2, 1, 2, 1, 3, 3
[2, 2, 2, 2, 1, 2, 2, 1, 1] => 2, 2, 2, 2, 1, 2, 2, 1, 1
[2, 2, 2, 2, 1, 2, 2, 1, 2] => 2, 2, 2, 2, 1, 2, 2, 1, 2
[2, 2, 2, 2, 1, 2, 2, 1, 3] => 2, 2, 2, 2, 1, 2, 2, 1, 3
[2, 2, 2, 2, 1, 2, 2, 2, 1] => 2, 2, 2, 2, 1, 2, 2, 2, 1
[2, 2, 2, 2, 1, 2, 2, 2, 2] => 2, 2, 2, 2, 1, 2, 2, 2, 2
[2, 2, 2, 2, 1, 2, 2, 2, 3] => 2, 2, 2, 2, 1, 2, 2, 2, 3
[2, 2, 2, 2, 1, 2, 2, 3, 1] => 2, 2, 2, 2, 1, 2, 2, 3, 1
[2, 2, 2, 2, 1, 2, 2, 3, 2] => 2, 2, 2, 2, 1, 2, 2, 3, 2
[2, 2, 2, 2, 1, 2, 2, 3, 3] => 2, 2, 2, 2, 1, 2, 2, 3, 3
[2, 2, 2, 2, 1, 2, 3, 1, 1] => 2, 2, 2, 2, 1, 2, 3, 1, 1
[2, 2, 2, 2, 1, 2, 3, 1, 2] => 2, 2, 2, 2, 1, 2, 3, 1, 2
[2, 2, 2, 2, 1, 2, 3, 1, 3] => 2, 2, 2, 2, 1, 2, 3, 1, 3
[2, 2, 2, 2, 1, 2, 3, 2, 1] => 2, 2, 2, 2, 1, 2, 3, 2, 1
[2, 2, 2, 2, 1, 2, 3, 2, 2] => 2, 2, 2, 2, 1, 2, 3, 2, 2
[2, 2, 2, 2, 1, 2, 3, 2, 3] => 2, 2, 2, 2, 1, 2, 3, 2, 3
[2, 2, 2, 2, 1, 2, 3, 3, 1] => 2, 2, 2, 2, 1, 2, 3, 3, 1
[2, 2, 2, 2, 1, 2, 3, 3, 2] => 2, 2, 2, 2, 1, 2, 3, 3, 2
[2, 2, 2, 2, 1, 2, 3, 3, 3] => 2, 2, 2, 2, 1, 2, 3, 3, 3
[2, 2, 2, 2, 1, 3, 1, 1, 1] => 2, 2, 2, 2, 1, 3, 1, 1, 1
[2, 2, 2, 2, 1, 3, 1, 1, 2] => 2, 2, 2, 2, 1, 3, 1, 1, 2
[2, 2, 2, 2, 1, 3, 1, 1, 3] => 2, 2, 2, 2, 1, 3, 1, 1, 3
[2, 2, 2, 2, 1, 3, 1, 2, 1] => 2, 2, 2, 2, 1, 3, 1, 2, 1
[2, 2, 2, 2, 1, 3, 1, 2, 2] => 2, 2, 2, 2, 1, 3, 1, 2, 2
[2, 2, 2, 2, 1, 3, 1, 2, 3] => 2, 2, 2, 2, 1, 3, 1, 2, 3
[2, 2, 2, 2, 1, 3, 1, 3, 1] => 2, 2, 2, 2, 1, 3, 1, 3, 1
[2, 2, 2, 2, 1, 3, 1, 3, 2] => 2, 2, 2, 2, 1, 3, 1, 3, 2
[2, 2, 2, 2, 1, 3, 1, 3, 3] => 2, 2, 2, 2, 1, 3, 1, 3, 3
[2, 2, 2, 2, 1, 3, 2, 1, 1] => 2, 2, 2, 2, 1, 3, 2, 1, 1
[2, 2, 2, 2, 1, 3, 2, 1, 2] => 2, 2, 2, 2, 1, 3, 2, 1, 2
[2, 2, 2, 2, 1, 3, 2, 1, 3] => 2, 2, 2, 2, 1, 3, 2, 1, 3
[2, 2, 2, 2, 1, 3, 2, 2, 1] => 2, 2, 2, 2, 1, 3, 2, 2, 1
[2, 2, 2, 2, 1, 3, 2, 2, 2] => 2, 2, 2, 2, 1, 3, 2, 2, 2
[2, 2, 2, 2, 1, 3, 2, 2, 3] => 2, 2, 2, 2, 1, 3, 2, 2, 3
[2, 2, 2, 2, 1, 3, 2, 3, 1] => 2, 2, 2, 2, 1, 3, 2, 3, 1
[2, 2, 2, 2, 1, 3, 2, 3, 2] => 2, 2, 2, 2, 1, 3, 2, 3, 2
[2, 2, 2, 2, 1, 3, 2, 3, 3] => 2, 2, 2, 2, 1, 3, 2, 3, 3
[2, 2, 2, 2, 1, 3, 3, 1, 1] => 2, 2, 2, 2, 1, 3, 3, 1, 1
[2, 2, 2, 2, 1, 3, 3, 1, 2] => 2, 2, 2, 2, 1, 3, 3, 1, 2
[2, 2, 2, 2, 1, 3, 3, 1, 3] => 2, 2, 2, 2, 1, 3, 3, 1, 3
[2, 2, 2, 2, 1, 3, 3, 2, 1] => 2, 2, 2, 2, 1, 3, 3, 2, 1
[2, 2, 2, 2, 1, 3, 3, 2, 2] => 2, 2, 2, 2, 1, 3, 3, 2, 2
[2, 2, 2, 2, 1, 3, 3, 2, 3] => 2, 2, 2, 2, 1, 3, 3, 2, 3
[2, 2, 2, 2, 1, 3, 3, 3, 1] => 2, 2, 2, 2, 1, 3, 3, 3, 1
[2, 2, 2, 2, 1, 3, 3, 3, 2] => 2, 2, 2, 2, 1, 3, 3, 3, 2
[2, 2, 2, 2, 1, 3, 3, 3, 3] => 2, 2, 2, 2, 1, 3, 3, 3, 3
[2, 2, 2, 2, 2, 1, 1, 1, 1] => 2, 2, 2, 2, 2, 1, 1, 1, 1
[2, 2, 2, 2, 2, 1, 1, 1, 2] => 2, 2, 2, 2, 2, 1, 1, 1, 2
[2, 2, 2, 2, 2, 1, 1, 1, 3] => 2, 2, 2, 2, 2, 1, 1, 1, 3
[2, 2, 2, 2, 2, 1, 1, 2, 1] => 2, 2, 2, 2, 2, 1, 1, 2, 1
[2, 2, 2, 2, 2, 1, 1, 2, 2] => 2, 2, 2, 2, 2, 1, 1, 2, 2
[2, 2, 2, 2, 2, 1, 1, 2, 3] => 2, 2, 2, 2, 2, 1, 1, 2, 3
[2, 2, 2, 2, 2, 1, 1, 3, 1] => 2, 2, 2, 2, 2, 1, 1, 3, 1
[2, 2, 2, 2, 2, 1, 1, 3, 2] => 2, 2, 2, 2, 2, 1, 1, 3, 2
[2, 2, 2, 2, 2, 1, 1, 3, 3] => 2, 2, 2, 2, 2, 1, 1, 3, 3
[2, 2, 2, 2, 2, 1, 2, 1, 1] => 2, 2, 2, 2, 2, 1, 2, 1, 1
[2, 2, 2, 2, 2, 1, 2, 1, 2] => 2, 2, 2, 2, 2, 1, 2, 1, 2
[2, 2, 2, 2, 2, 1, 2, 1, 3] => 2, 2, 2, 2, 2, 1, 2, 1, 3
[2, 2, 2, 2, 2, 1, 2, 2, 1] => 2, 2, 2, 2, 2, 1, 2, 2, 1
[2, 2, 2, 2, 2, 1, 2, 2, 2] => 2, 2, 2, 2, 2, 1, 2, 2, 2
[2, 2, 2, 2, 2, 1, 2, 2, 3] => 2, 2, 2, 2, 2, 1, 2, 2, 3
[2, 2, 2, 2, 2, 1, 2, 3, 1] => 2, 2, 2, 2, 2, 1, 2, 3, 1
[2, 2, 2, 2, 2, 1, 2, 3, 2] => 2, 2, 2, 2, 2, 1, 2, 3, 2
[2, 2, 2, 2, 2, 1, 2, 3, 3] => 2, 2, 2, 2, 2, 1, 2, 3, 3
[2, 2, 2, 2, 2, 1, 3, 1, 1] => 2, 2, 2, 2, 2, 1, 3, 1, 1
[2, 2, 2, 2, 2, 1, 3, 1, 2] => 2, 2, 2, 2, 2, 1, 3, 1, 2
[2, 2, 2, 2, 2, 1, 3, 1, 3] => 2, 2, 2, 2, 2, 1, 3, 1, 3
[2, 2, 2, 2, 2, 1, 3, 2, 1] => 2, 2, 2, 2, 2, 1, 3, 2, 1
[2, 2, 2, 2, 2, 1, 3, 2, 2] => 2, 2, 2, 2, 2, 1, 3, 2, 2
[2, 2, 2, 2, 2, 1, 3, 2, 3] => 2, 2, 2, 2, 2, 1, 3, 2, 3
[2, 2, 2, 2, 2, 1, 3, 3, 1] => 2, 2, 2, 2, 2, 1, 3, 3, 1
[2, 2, 2, 2, 2, 1, 3, 3, 2] => 2, 2, 2, 2, 2, 1, 3, 3, 2
[2, 2, 2, 2, 2, 1, 3, 3, 3] => 2, 2, 2, 2, 2, 1, 3, 3, 3
[2, 2, 2, 2, 2, 2, 1, 1, 1] => 2, 2, 2, 2, 2, 2, 1, 1, 1
[2, 2, 2, 2, 2, 2, 1, 1, 2] => 2, 2, 2, 2, 2, 2, 1, 1, 2
[2, 2, 2, 2, 2, 2, 1, 1, 3] => 2, 2, 2, 2, 2, 2, 1, 1, 3
[2, 2, 2, 2, 2, 2, 1, 2, 1] => 2, 2, 2, 2, 2, 2, 1, 2, 1
[2, 2, 2, 2, 2, 2, 1, 2, 2] => 2, 2, 2, 2, 2, 2, 1, 2, 2
[2, 2, 2, 2, 2, 2, 1, 2, 3] => 2, 2, 2, 2, 2, 2, 1, 2, 3
[2, 2, 2, 2, 2, 2, 1, 3, 1] => 2, 2, 2, 2, 2, 2, 1, 3, 1
[2, 2, 2, 2, 2, 2, 1, 3, 2] => 2, 2, 2, 2, 2, 2, 1, 3, 2
[2, 2, 2, 2, 2, 2, 1, 3, 3] => 2, 2, 2, 2, 2, 2, 1, 3, 3
[2, 2, 2, 2, 2, 2, 2, 1, 1] => 2, 2, 2, 2, 2, 2, 2, 1, 1
[2, 2, 2, 2, 2, 2, 2, 1, 2] => 2, 2, 2, 2, 2, 2, 2, 1, 2
[2, 2, 2, 2, 2, 2, 2, 1, 3] => 2, 2, 2, 2, 2, 2, 2, 1, 3
[2, 2, 2, 2, 2, 2, 2, 2, 1] => 2, 2, 2, 2, 2, 2, 2, 2, 1
[2, 2, 2, 2, 2, 2, 2, 2, 2] => 2, 2, 2, 2, 2, 2, 2, 2, 2
[2, 2, 2, 2, 2, 2, 2, 2, 3] => 2, 2, 2, 2, 2, 2, 2, 2, 3
[2, 2, 2, 2, 2, 2, 2, 3, 1] => 2, 2, 2, 2, 2, 2, 2, 3, 1
[2, 2, 2, 2, 2, 2, 2, 3, 2] => 2, 2, 2, 2, 2, 2, 2, 3, 2
[2, 2, 2, 2, 2, 2, 2, 3, 3] => 2, 2, 2, 2, 2, 2, 2, 3, 3
[2, 2, 2, 2, 2, 2, 3, 1, 1] => 2, 2, 2, 2, 2, 2, 3, 1, 1
[2, 2, 2, 2, 2, 2, 3, 1, 2] => 2, 2, 2, 2, 2, 2, 3, 1, 2
[2, 2, 2, 2, 2, 2, 3, 1, 3] => 2, 2, 2, 2, 2, 2, 3, 1, 3
[2, 2, 2, 2, 2, 2, 3, 2, 1] => 2, 2, 2, 2, 2, 2, 3, 2, 1
[2, 2, 2, 2, 2, 2, 3, 2, 2] => 2, 2, 2, 2, 2, 2, 3, 2, 2
[2, 2, 2, 2, 2, 2, 3, 2, 3] => 2, 2, 2, 2, 2, 2, 3, 2, 3
[2, 2, 2, 2, 2, 2, 3, 3, 1] => 2, 2, 2, 2, 2, 2, 3, 3, 1
[2, 2, 2, 2, 2, 2, 3, 3, 2] => 2, 2, 2, 2, 2, 2, 3, 3, 2
[2, 2, 2, 2, 2, 2, 3, 3, 3] => 2, 2, 2, 2, 2, 2, 3, 3, 3
[2, 2, 2, 2, 2, 3, 1, 1, 1] => 2, 2, 2, 2, 2, 3, 1, 1, 1
[2, 2, 2, 2, 2, 3, 1, 1, 2] => 2, 2, 2, 2, 2, 3, 1, 1, 2
[2, 2, 2, 2, 2, 3, 1, 1, 3] => 2, 2, 2, 2, 2, 3, 1, 1, 3
[2, 2, 2, 2, 2, 3, 1, 2, 1] => 2, 2, 2, 2, 2, 3, 1, 2, 1
[2, 2, 2, 2, 2, 3, 1, 2, 2] => 2, 2, 2, 2, 2, 3, 1, 2, 2
[2, 2, 2, 2, 2, 3, 1, 2, 3] => 2, 2, 2, 2, 2, 3, 1, 2, 3
[2, 2, 2, 2, 2, 3, 1, 3, 1] => 2, 2, 2, 2, 2, 3, 1, 3, 1
[2, 2, 2, 2, 2, 3, 1, 3, 2] => 2, 2, 2, 2, 2, 3, 1, 3, 2
[2, 2, 2, 2, 2, 3, 1, 3, 3] => 2, 2, 2, 2, 2, 3, 1, 3, 3
[2, 2, 2, 2, 2, 3, 2, 1, 1] => 2, 2, 2, 2, 2, 3, 2, 1, 1
[2, 2, 2, 2, 2, 3, 2, 1, 2] => 2, 2, 2, 2, 2, 3, 2, 1, 2
[2, 2, 2, 2, 2, 3, 2, 1, 3] => 2, 2, 2, 2, 2, 3, 2, 1, 3
[2, 2, 2, 2, 2, 3, 2, 2, 1] => 2, 2, 2, 2, 2, 3, 2, 2, 1
[2, 2, 2, 2, 2, 3, 2, 2, 2] => 2, 2, 2, 2, 2, 3, 2, 2, 2
[2, 2, 2, 2, 2, 3, 2, 2, 3] => 2, 2, 2, 2, 2, 3, 2, 2, 3
[2, 2, 2, 2, 2, 3, 2, 3, 1] => 2, 2, 2, 2, 2, 3, 2, 3, 1
[2, 2, 2, 2, 2, 3, 2, 3, 2] => 2, 2, 2, 2, 2, 3, 2, 3, 2
[2, 2, 2, 2, 2, 3, 2, 3, 3] => 2, 2, 2, 2, 2, 3, 2, 3, 3
[2, 2, 2, 2, 2, 3, 3, 1, 1] => 2, 2, 2, 2, 2, 3, 3, 1, 1
[2, 2, 2, 2, 2, 3, 3, 1, 2] => 2, 2, 2, 2, 2, 3, 3, 1, 2
[2, 2, 2, 2, 2, 3, 3, 1, 3] => 2, 2, 2, 2, 2, 3, 3, 1, 3
[2, 2, 2, 2, 2, 3, 3, 2, 1] => 2, 2, 2, 2, 2, 3, 3, 2, 1
[2, 2, 2, 2, 2, 3, 3, 2, 2] => 2, 2, 2, 2, 2, 3, 3, 2, 2
[2, 2, 2, 2, 2, 3, 3, 2, 3] => 2, 2, 2, 2, 2, 3, 3, 2, 3
[2, 2, 2, 2, 2, 3, 3, 3, 1] => 2, 2, 2, 2, 2, 3, 3, 3, 1
[2, 2, 2, 2, 2, 3, 3, 3, 2] => 2, 2, 2, 2, 2, 3, 3, 3, 2
[2, 2, 2, 2, 2, 3, 3, 3, 3] => 2, 2, 2, 2, 2, 3, 3, 3, 3
[2, 2, 2, 2, 3, 1, 1, 1, 1] => 2, 2, 2, 2, 3, 1, 1, 1, 1
[2, 2, 2, 2, 3, 1, 1, 1, 2] => 2, 2, 2, 2, 3, 1, 1, 1, 2
[2, 2, 2, 2, 3, 1, 1, 1, 3] => 2, 2, 2, 2, 3, 1, 1, 1, 3
[2, 2, 2, 2, 3, 1, 1, 2, 1] => 2, 2, 2, 2, 3, 1, 1, 2, 1
[2, 2, 2, 2, 3, 1, 1, 2, 2] => 2, 2, 2, 2, 3, 1, 1, 2, 2
[2, 2, 2, 2, 3, 1, 1, 2, 3] => 2, 2, 2, 2, 3, 1, 1, 2, 3
[2, 2, 2, 2, 3, 1, 1, 3, 1] => 2, 2, 2, 2, 3, 1, 1, 3, 1
[2, 2, 2, 2, 3, 1, 1, 3, 2] => 2, 2, 2, 2, 3, 1, 1, 3, 2
[2, 2, 2, 2, 3, 1, 1, 3, 3] => 2, 2, 2, 2, 3, 1, 1, 3, 3
[2, 2, 2, 2, 3, 1, 2, 1, 1] => 2, 2, 2, 2, 3, 1, 2, 1, 1
[2, 2, 2, 2, 3, 1, 2, 1, 2] => 2, 2, 2, 2, 3, 1, 2, 1, 2
[2, 2, 2, 2, 3, 1, 2, 1, 3] => 2, 2, 2, 2, 3, 1, 2, 1, 3
[2, 2, 2, 2, 3, 1, 2, 2, 1] => 2, 2, 2, 2, 3, 1, 2, 2, 1
[2, 2, 2, 2, 3, 1, 2, 2, 2] => 2, 2, 2, 2, 3, 1, 2, 2, 2
[2, 2, 2, 2, 3, 1, 2, 2, 3] => 2, 2, 2, 2, 3, 1, 2, 2, 3
[2, 2, 2, 2, 3, 1, 2, 3, 1] => 2, 2, 2, 2, 3, 1, 2, 3, 1
[2, 2, 2, 2, 3, 1, 2, 3, 2] => 2, 2, 2, 2, 3, 1, 2, 3, 2
[2, 2, 2, 2, 3, 1, 2, 3, 3] => 2, 2, 2, 2, 3, 1, 2, 3, 3
[2, 2, 2, 2, 3, 1, 3, 1, 1] => 2, 2, 2, 2, 3, 1, 3, 1, 1
[2, 2, 2, 2, 3, 1, 3, 1, 2] => 2, 2, 2, 2, 3, 1, 3, 1, 2
[2, 2, 2, 2, 3, 1, 3, 1, 3] => 2, 2, 2, 2, 3, 1, 3, 1, 3
[2, 2, 2, 2, 3, 1, 3, 2, 1] => 2, 2, 2, 2, 3, 1, 3, 2, 1
[2, 2, 2, 2, 3, 1, 3, 2, 2] => 2, 2, 2, 2, 3, 1, 3, 2, 2
[2, 2, 2, 2, 3, 1, 3, 2, 3] => 2, 2, 2, 2, 3, 1, 3, 2, 3
[2, 2, 2, 2, 3, 1, 3, 3, 1] => 2, 2, 2, 2, 3, 1, 3, 3, 1
[2, 2, 2, 2, 3, 1, 3, 3, 2] => 2, 2, 2, 2, 3, 1, 3, 3, 2
[2, 2, 2, 2, 3, 1, 3, 3, 3] => 2, 2, 2, 2, 3, 1, 3, 3, 3
[2, 2, 2, 2, 3, 2, 1, 1, 1] => 2, 2, 2, 2, 3, 2, 1, 1, 1
[2, 2, 2, 2, 3, 2, 1, 1, 2] => 2, 2, 2, 2, 3, 2, 1, 1, 2
[2, 2, 2, 2, 3, 2, 1, 1, 3] => 2, 2, 2, 2, 3, 2, 1, 1, 3
[2, 2, 2, 2, 3, 2, 1, 2, 1] => 2, 2, 2, 2, 3, 2, 1, 2, 1
[2, 2, 2, 2, 3, 2, 1, 2, 2] => 2, 2, 2, 2, 3, 2, 1, 2, 2
[2, 2, 2, 2, 3, 2, 1, 2, 3] => 2, 2, 2, 2, 3, 2, 1, 2, 3
[2, 2, 2, 2, 3, 2, 1, 3, 1] => 2, 2, 2, 2, 3, 2, 1, 3, 1
[2, 2, 2, 2, 3, 2, 1, 3, 2] => 2, 2, 2, 2, 3, 2, 1, 3, 2
[2, 2, 2, 2, 3, 2, 1, 3, 3] => 2, 2, 2, 2, 3, 2, 1, 3, 3
[2, 2, 2, 2, 3, 2, 2, 1, 1] => 2, 2, 2, 2, 3, 2, 2, 1, 1
[2, 2, 2, 2, 3, 2, 2, 1, 2] => 2, 2, 2, 2, 3, 2, 2, 1, 2
[2, 2, 2, 2, 3, 2, 2, 1, 3] => 2, 2, 2, 2, 3, 2, 2, 1, 3
[2, 2, 2, 2, 3, 2, 2, 2, 1] => 2, 2, 2, 2, 3, 2, 2, 2, 1
[2, 2, 2, 2, 3, 2, 2, 2, 2] => 2, 2, 2, 2, 3, 2, 2, 2, 2
[2, 2, 2, 2, 3, 2, 2, 2, 3] => 2, 2, 2, 2, 3, 2, 2, 2, 3
[2, 2, 2, 2, 3, 2, 2, 3, 1] => 2, 2, 2, 2, 3, 2, 2, 3, 1
[2, 2, 2, 2, 3, 2, 2, 3, 2] => 2, 2, 2, 2, 3, 2, 2, 3, 2
[2, 2, 2, 2, 3, 2, 2, 3, 3] => 2, 2, 2, 2, 3, 2, 2, 3, 3
[2, 2, 2, 2, 3, 2, 3, 1, 1] => 2, 2, 2, 2, 3, 2, 3, 1, 1
[2, 2, 2, 2, 3, 2, 3, 1, 2] => 2, 2, 2, 2, 3, 2, 3, 1, 2
[2, 2, 2, 2, 3, 2, 3, 1, 3] => 2, 2, 2, 2, 3, 2, 3, 1, 3
[2, 2, 2, 2, 3, 2, 3, 2, 1] => 2, 2, 2, 2, 3, 2, 3, 2, 1
[2, 2, 2, 2, 3, 2, 3, 2, 2] => 2, 2, 2, 2, 3, 2, 3, 2, 2
[2, 2, 2, 2, 3, 2, 3, 2, 3] => 2, 2, 2, 2, 3, 2, 3, 2, 3
[2, 2, 2, 2, 3, 2, 3, 3, 1] => 2, 2, 2, 2, 3, 2, 3, 3, 1
[2, 2, 2, 2, 3, 2, 3, 3, 2] => 2, 2, 2, 2, 3, 2, 3, 3, 2
[2, 2, 2, 2, 3, 2, 3, 3, 3] => 2, 2, 2, 2, 3, 2, 3, 3, 3
[2, 2, 2, 2, 3, 3, 1, 1, 1] => 2, 2, 2, 2, 3, 3, 1, 1, 1
[2, 2, 2, 2, 3, 3, 1, 1, 2] => 2, 2, 2, 2, 3, 3, 1, 1, 2
[2, 2, 2, 2, 3, 3, 1, 1, 3] => 2, 2, 2, 2, 3, 3, 1, 1, 3
[2, 2, 2, 2, 3, 3, 1, 2, 1] => 2, 2, 2, 2, 3, 3, 1, 2, 1
[2, 2, 2, 2, 3, 3, 1, 2, 2] => 2, 2, 2, 2, 3, 3, 1, 2, 2
[2, 2, 2, 2, 3, 3, 1, 2, 3] => 2, 2, 2, 2, 3, 3, 1, 2, 3
[2, 2, 2, 2, 3, 3, 1, 3, 1] => 2, 2, 2, 2, 3, 3, 1, 3, 1
[2, 2, 2, 2, 3, 3, 1, 3, 2] => 2, 2, 2, 2, 3, 3, 1, 3, 2
[2, 2, 2, 2, 3, 3, 1, 3, 3] => 2, 2, 2, 2, 3, 3, 1, 3, 3
[2, 2, 2, 2, 3, 3, 2, 1, 1] => 2, 2, 2, 2, 3, 3, 2, 1, 1
[2, 2, 2, 2, 3, 3, 2, 1, 2] => 2, 2, 2, 2, 3, 3, 2, 1, 2
[2, 2, 2, 2, 3, 3, 2, 1, 3] => 2, 2, 2, 2, 3, 3, 2, 1, 3
[2, 2, 2, 2, 3, 3, 2, 2, 1] => 2, 2, 2, 2, 3, 3, 2, 2, 1
[2, 2, 2, 2, 3, 3, 2, 2, 2] => 2, 2, 2, 2, 3, 3, 2, 2, 2
[2, 2, 2, 2, 3, 3, 2, 2, 3] => 2, 2, 2, 2, 3, 3, 2, 2, 3
[2, 2, 2, 2, 3, 3, 2, 3, 1] => 2, 2, 2, 2, 3, 3, 2, 3, 1
[2, 2, 2, 2, 3, 3, 2, 3, 2] => 2, 2, 2, 2, 3, 3, 2, 3, 2
[2, 2, 2, 2, 3, 3, 2, 3, 3] => 2, 2, 2, 2, 3, 3, 2, 3, 3
[2, 2, 2, 2, 3, 3, 3, 1, 1] => 2, 2, 2, 2, 3, 3, 3, 1, 1
[2, 2, 2, 2, 3, 3, 3, 1, 2] => 2, 2, 2, 2, 3, 3, 3, 1, 2
[2, 2, 2, 2, 3, 3, 3, 1, 3] => 2, 2, 2, 2, 3, 3, 3, 1, 3
[2, 2, 2, 2, 3, 3, 3, 2, 1] => 2, 2, 2, 2, 3, 3, 3, 2, 1
[2, 2, 2, 2, 3, 3, 3, 2, 2] => 2, 2, 2, 2, 3, 3, 3, 2, 2
[2, 2, 2, 2, 3, 3, 3, 2, 3] => 2, 2, 2, 2, 3, 3, 3, 2, 3
[2, 2, 2, 2, 3, 3, 3, 3, 1] => 2, 2, 2, 2, 3, 3, 3, 3, 1
[2, 2, 2, 2, 3, 3, 3, 3, 2] => 2, 2, 2, 2, 3, 3, 3, 3, 2
[2, 2, 2, 2, 3, 3, 3, 3, 3] => 2, 2, 2, 2, 3, 3, 3, 3, 3
[2, 2, 2, 3, 1, 1, 1, 1, 1] => 2, 2, 2, 3, 1, 1, 1, 1, 1
[2, 2, 2, 3, 1, 1, 1, 1, 2] => 2, 2, 2, 3, 1, 1, 1, 1, 2
[2, 2, 2, 3, 1, 1, 1, 1, 3] => 2, 2, 2, 3, 1, 1, 1, 1, 3
[2, 2, 2, 3, 1, 1, 1, 2, 1] => 2, 2, 2, 3, 1, 1, 1, 2, 1
[2, 2, 2, 3, 1, 1, 1, 2, 2] => 2, 2, 2, 3, 1, 1, 1, 2, 2
[2, 2, 2, 3, 1, 1, 1, 2, 3] => 2, 2, 2, 3, 1, 1, 1, 2, 3
[2, 2, 2, 3, 1, 1, 1, 3, 1] => 2, 2, 2, 3, 1, 1, 1, 3, 1
[2, 2, 2, 3, 1, 1, 1, 3, 2] => 2, 2, 2, 3, 1, 1, 1, 3, 2
[2, 2, 2, 3, 1, 1, 1, 3, 3] => 2, 2, 2, 3, 1, 1, 1, 3, 3
[2, 2, 2, 3, 1, 1, 2, 1, 1] => 2, 2, 2, 3, 1, 1, 2, 1, 1
[2, 2, 2, 3, 1, 1, 2, 1, 2] => 2, 2, 2, 3, 1, 1, 2, 1, 2
[2, 2, 2, 3, 1, 1, 2, 1, 3] => 2, 2, 2, 3, 1, 1, 2, 1, 3
[2, 2, 2, 3, 1, 1, 2, 2, 1] => 2, 2, 2, 3, 1, 1, 2, 2, 1
[2, 2, 2, 3, 1, 1, 2, 2, 2] => 2, 2, 2, 3, 1, 1, 2, 2, 2
[2, 2, 2, 3, 1, 1, 2, 2, 3] => 2, 2, 2, 3, 1, 1, 2, 2, 3
[2, 2, 2, 3, 1, 1, 2, 3, 1] => 2, 2, 2, 3, 1, 1, 2, 3, 1
[2, 2, 2, 3, 1, 1, 2, 3, 2] => 2, 2, 2, 3, 1, 1, 2, 3, 2
[2, 2, 2, 3, 1, 1, 2, 3, 3] => 2, 2, 2, 3, 1, 1, 2, 3, 3
[2, 2, 2, 3, 1, 1, 3, 1, 1] => 2, 2, 2, 3, 1, 1, 3, 1, 1
[2, 2, 2, 3, 1, 1, 3, 1, 2] => 2, 2, 2, 3, 1, 1, 3, 1, 2
[2, 2, 2, 3, 1, 1, 3, 1, 3] => 2, 2, 2, 3, 1, 1, 3, 1, 3
[2, 2, 2, 3, 1, 1, 3, 2, 1] => 2, 2, 2, 3, 1, 1, 3, 2, 1
[2, 2, 2, 3, 1, 1, 3, 2, 2] => 2, 2, 2, 3, 1, 1, 3, 2, 2
[2, 2, 2, 3, 1, 1, 3, 2, 3] => 2, 2, 2, 3, 1, 1, 3, 2, 3
[2, 2, 2, 3, 1, 1, 3, 3, 1] => 2, 2, 2, 3, 1, 1, 3, 3, 1
[2, 2, 2, 3, 1, 1, 3, 3, 2] => 2, 2, 2, 3, 1, 1, 3, 3, 2
[2, 2, 2, 3, 1, 1, 3, 3, 3] => 2, 2, 2, 3, 1, 1, 3, 3, 3
[2, 2, 2, 3, 1, 2, 1, 1, 1] => 2, 2, 2, 3, 1, 2, 1, 1, 1
[2, 2, 2, 3, 1, 2, 1, 1, 2] => 2, 2, 2, 3, 1, 2, 1, 1, 2
[2, 2, 2, 3, 1, 2, 1, 1, 3] => 2, 2, 2, 3, 1, 2, 1, 1, 3
[2, 2, 2, 3, 1, 2, 1, 2, 1] => 2, 2, 2, 3, 1, 2, 1, 2, 1
[2, 2, 2, 3, 1, 2, 1, 2, 2] => 2, 2, 2, 3, 1, 2, 1, 2, 2
[2, 2, 2, 3, 1, 2, 1, 2, 3] => 2, 2, 2, 3, 1, 2, 1, 2, 3
[2, 2, 2, 3, 1, 2, 1, 3, 1] => 2, 2, 2, 3, 1, 2, 1, 3, 1
[2, 2, 2, 3, 1, 2, 1, 3, 2] => 2, 2, 2, 3, 1, 2, 1, 3, 2
[2, 2, 2, 3, 1, 2, 1, 3, 3] => 2, 2, 2, 3, 1, 2, 1, 3, 3
[2, 2, 2, 3, 1, 2, 2, 1, 1] => 2, 2, 2, 3, 1, 2, 2, 1, 1
[2, 2, 2, 3, 1, 2, 2, 1, 2] => 2, 2, 2, 3, 1, 2, 2, 1, 2
[2, 2, 2, 3, 1, 2, 2, 1, 3] => 2, 2, 2, 3, 1, 2, 2, 1, 3
[2, 2, 2, 3, 1, 2, 2, 2, 1] => 2, 2, 2, 3, 1, 2, 2, 2, 1
[2, 2, 2, 3, 1, 2, 2, 2, 2] => 2, 2, 2, 3, 1, 2, 2, 2, 2
[2, 2, 2, 3, 1, 2, 2, 2, 3] => 2, 2, 2, 3, 1, 2, 2, 2, 3
[2, 2, 2, 3, 1, 2, 2, 3, 1] => 2, 2, 2, 3, 1, 2, 2, 3, 1
[2, 2, 2, 3, 1, 2, 2, 3, 2] => 2, 2, 2, 3, 1, 2, 2, 3, 2
[2, 2, 2, 3, 1, 2, 2, 3, 3] => 2, 2, 2, 3, 1, 2, 2, 3, 3
[2, 2, 2, 3, 1, 2, 3, 1, 1] => 2, 2, 2, 3, 1, 2, 3, 1, 1
[2, 2, 2, 3, 1, 2, 3, 1, 2] => 2, 2, 2, 3, 1, 2, 3, 1, 2
[2, 2, 2, 3, 1, 2, 3, 1, 3] => 2, 2, 2, 3, 1, 2, 3, 1, 3
[2, 2, 2, 3, 1, 2, 3, 2, 1] => 2, 2, 2, 3, 1, 2, 3, 2, 1
[2, 2, 2, 3, 1, 2, 3, 2, 2] => 2, 2, 2, 3, 1, 2, 3, 2, 2
[2, 2, 2, 3, 1, 2, 3, 2, 3] => 2, 2, 2, 3, 1, 2, 3, 2, 3
[2, 2, 2, 3, 1, 2, 3, 3, 1] => 2, 2, 2, 3, 1, 2, 3, 3, 1
[2, 2, 2, 3, 1, 2, 3, 3, 2] => 2, 2, 2, 3, 1, 2, 3, 3, 2
[2, 2, 2, 3, 1, 2, 3, 3, 3] => 2, 2, 2, 3, 1, 2, 3, 3, 3
[2, 2, 2, 3, 1, 3, 1, 1, 1] => 2, 2, 2, 3, 1, 3, 1, 1, 1
[2, 2, 2, 3, 1, 3, 1, 1, 2] => 2, 2, 2, 3, 1, 3, 1, 1, 2
[2, 2, 2, 3, 1, 3, 1, 1, 3] => 2, 2, 2, 3, 1, 3, 1, 1, 3
[2, 2, 2, 3, 1, 3, 1, 2, 1] => 2, 2, 2, 3, 1, 3, 1, 2, 1
[2, 2, 2, 3, 1, 3, 1, 2, 2] => 2, 2, 2, 3, 1, 3, 1, 2, 2
[2, 2, 2, 3, 1, 3, 1, 2, 3] => 2, 2, 2, 3, 1, 3, 1, 2, 3
[2, 2, 2, 3, 1, 3, 1, 3, 1] => 2, 2, 2, 3, 1, 3, 1, 3, 1
[2, 2, 2, 3, 1, 3, 1, 3, 2] => 2, 2, 2, 3, 1, 3, 1, 3, 2
[2, 2, 2, 3, 1, 3, 1, 3, 3] => 2, 2, 2, 3, 1, 3, 1, 3, 3
[2, 2, 2, 3, 1, 3, 2, 1, 1] => 2, 2, 2, 3, 1, 3, 2, 1, 1
[2, 2, 2, 3, 1, 3, 2, 1, 2] => 2, 2, 2, 3, 1, 3, 2, 1, 2
[2, 2, 2, 3, 1, 3, 2, 1, 3] => 2, 2, 2, 3, 1, 3, 2, 1, 3
[2, 2, 2, 3, 1, 3, 2, 2, 1] => 2, 2, 2, 3, 1, 3, 2, 2, 1
[2, 2, 2, 3, 1, 3, 2, 2, 2] => 2, 2, 2, 3, 1, 3, 2, 2, 2
[2, 2, 2, 3, 1, 3, 2, 2, 3] => 2, 2, 2, 3, 1, 3, 2, 2, 3
[2, 2, 2, 3, 1, 3, 2, 3, 1] => 2, 2, 2, 3, 1, 3, 2, 3, 1
[2, 2, 2, 3, 1, 3, 2, 3, 2] => 2, 2, 2, 3, 1, 3, 2, 3, 2
[2, 2, 2, 3, 1, 3, 2, 3, 3] => 2, 2, 2, 3, 1, 3, 2, 3, 3
[2, 2, 2, 3, 1, 3, 3, 1, 1] => 2, 2, 2, 3, 1, 3, 3, 1, 1
[2, 2, 2, 3, 1, 3, 3, 1, 2] => 2, 2, 2, 3, 1, 3, 3, 1, 2
[2, 2, 2, 3, 1, 3, 3, 1, 3] => 2, 2, 2, 3, 1, 3, 3, 1, 3
[2, 2, 2, 3, 1, 3, 3, 2, 1] => 2, 2, 2, 3, 1, 3, 3, 2, 1
[2, 2, 2, 3, 1, 3, 3, 2, 2] => 2, 2, 2, 3, 1, 3, 3, 2, 2
[2, 2, 2, 3, 1, 3, 3, 2, 3] => 2, 2, 2, 3, 1, 3, 3, 2, 3
[2, 2, 2, 3, 1, 3, 3, 3, 1] => 2, 2, 2, 3, 1, 3, 3, 3, 1
[2, 2, 2, 3, 1, 3, 3, 3, 2] => 2, 2, 2, 3, 1, 3, 3, 3, 2
[2, 2, 2, 3, 1, 3, 3, 3, 3] => 2, 2, 2, 3, 1, 3, 3, 3, 3
[2, 2, 2, 3, 2, 1, 1, 1, 1] => 2, 2, 2, 3, 2, 1, 1, 1, 1
[2, 2, 2, 3, 2, 1, 1, 1, 2] => 2, 2, 2, 3, 2, 1, 1, 1, 2
[2, 2, 2, 3, 2, 1, 1, 1, 3] => 2, 2, 2, 3, 2, 1, 1, 1, 3
[2, 2, 2, 3, 2, 1, 1, 2, 1] => 2, 2, 2, 3, 2, 1, 1, 2, 1
[2, 2, 2, 3, 2, 1, 1, 2, 2] => 2, 2, 2, 3, 2, 1, 1, 2, 2
[2, 2, 2, 3, 2, 1, 1, 2, 3] => 2, 2, 2, 3, 2, 1, 1, 2, 3
[2, 2, 2, 3, 2, 1, 1, 3, 1] => 2, 2, 2, 3, 2, 1, 1, 3, 1
[2, 2, 2, 3, 2, 1, 1, 3, 2] => 2, 2, 2, 3, 2, 1, 1, 3, 2
[2, 2, 2, 3, 2, 1, 1, 3, 3] => 2, 2, 2, 3, 2, 1, 1, 3, 3
[2, 2, 2, 3, 2, 1, 2, 1, 1] => 2, 2, 2, 3, 2, 1, 2, 1, 1
[2, 2, 2, 3, 2, 1, 2, 1, 2] => 2, 2, 2, 3, 2, 1, 2, 1, 2
[2, 2, 2, 3, 2, 1, 2, 1, 3] => 2, 2, 2, 3, 2, 1, 2, 1, 3
[2, 2, 2, 3, 2, 1, 2, 2, 1] => 2, 2, 2, 3, 2, 1, 2, 2, 1
[2, 2, 2, 3, 2, 1, 2, 2, 2] => 2, 2, 2, 3, 2, 1, 2, 2, 2
[2, 2, 2, 3, 2, 1, 2, 2, 3] => 2, 2, 2, 3, 2, 1, 2, 2, 3
[2, 2, 2, 3, 2, 1, 2, 3, 1] => 2, 2, 2, 3, 2, 1, 2, 3, 1
[2, 2, 2, 3, 2, 1, 2, 3, 2] => 2, 2, 2, 3, 2, 1, 2, 3, 2
[2, 2, 2, 3, 2, 1, 2, 3, 3] => 2, 2, 2, 3, 2, 1, 2, 3, 3
[2, 2, 2, 3, 2, 1, 3, 1, 1] => 2, 2, 2, 3, 2, 1, 3, 1, 1
[2, 2, 2, 3, 2, 1, 3, 1, 2] => 2, 2, 2, 3, 2, 1, 3, 1, 2
[2, 2, 2, 3, 2, 1, 3, 1, 3] => 2, 2, 2, 3, 2, 1, 3, 1, 3
[2, 2, 2, 3, 2, 1, 3, 2, 1] => 2, 2, 2, 3, 2, 1, 3, 2, 1
[2, 2, 2, 3, 2, 1, 3, 2, 2] => 2, 2, 2, 3, 2, 1, 3, 2, 2
[2, 2, 2, 3, 2, 1, 3, 2, 3] => 2, 2, 2, 3, 2, 1, 3, 2, 3
[2, 2, 2, 3, 2, 1, 3, 3, 1] => 2, 2, 2, 3, 2, 1, 3, 3, 1
[2, 2, 2, 3, 2, 1, 3, 3, 2] => 2, 2, 2, 3, 2, 1, 3, 3, 2
[2, 2, 2, 3, 2, 1, 3, 3, 3] => 2, 2, 2, 3, 2, 1, 3, 3, 3
[2, 2, 2, 3, 2, 2, 1, 1, 1] => 2, 2, 2, 3, 2, 2, 1, 1, 1
[2, 2, 2, 3, 2, 2, 1, 1, 2] => 2, 2, 2, 3, 2, 2, 1, 1, 2
[2, 2, 2, 3, 2, 2, 1, 1, 3] => 2, 2, 2, 3, 2, 2, 1, 1, 3
[2, 2, 2, 3, 2, 2, 1, 2, 1] => 2, 2, 2, 3, 2, 2, 1, 2, 1
[2, 2, 2, 3, 2, 2, 1, 2, 2] => 2, 2, 2, 3, 2, 2, 1, 2, 2
[2, 2, 2, 3, 2, 2, 1, 2, 3] => 2, 2, 2, 3, 2, 2, 1, 2, 3
[2, 2, 2, 3, 2, 2, 1, 3, 1] => 2, 2, 2, 3, 2, 2, 1, 3, 1
[2, 2, 2, 3, 2, 2, 1, 3, 2] => 2, 2, 2, 3, 2, 2, 1, 3, 2
[2, 2, 2, 3, 2, 2, 1, 3, 3] => 2, 2, 2, 3, 2, 2, 1, 3, 3
[2, 2, 2, 3, 2, 2, 2, 1, 1] => 2, 2, 2, 3, 2, 2, 2, 1, 1
[2, 2, 2, 3, 2, 2, 2, 1, 2] => 2, 2, 2, 3, 2, 2, 2, 1, 2
[2, 2, 2, 3, 2, 2, 2, 1, 3] => 2, 2, 2, 3, 2, 2, 2, 1, 3
[2, 2, 2, 3, 2, 2, 2, 2, 1] => 2, 2, 2, 3, 2, 2, 2, 2, 1
[2, 2, 2, 3, 2, 2, 2, 2, 2] => 2, 2, 2, 3, 2, 2, 2, 2, 2
[2, 2, 2, 3, 2, 2, 2, 2, 3] => 2, 2, 2, 3, 2, 2, 2, 2, 3
[2, 2, 2, 3, 2, 2, 2, 3, 1] => 2, 2, 2, 3, 2, 2, 2, 3, 1
[2, 2, 2, 3, 2, 2, 2, 3, 2] => 2, 2, 2, 3, 2, 2, 2, 3, 2
[2, 2, 2, 3, 2, 2, 2, 3, 3] => 2, 2, 2, 3, 2, 2, 2, 3, 3
[2, 2, 2, 3, 2, 2, 3, 1, 1] => 2, 2, 2, 3, 2, 2, 3, 1, 1
[2, 2, 2, 3, 2, 2, 3, 1, 2] => 2, 2, 2, 3, 2, 2, 3, 1, 2
[2, 2, 2, 3, 2, 2, 3, 1, 3] => 2, 2, 2, 3, 2, 2, 3, 1, 3
[2, 2, 2, 3, 2, 2, 3, 2, 1] => 2, 2, 2, 3, 2, 2, 3, 2, 1
[2, 2, 2, 3, 2, 2, 3, 2, 2] => 2, 2, 2, 3, 2, 2, 3, 2, 2
[2, 2, 2, 3, 2, 2, 3, 2, 3] => 2, 2, 2, 3, 2, 2, 3, 2, 3
[2, 2, 2, 3, 2, 2, 3, 3, 1] => 2, 2, 2, 3, 2, 2, 3, 3, 1
[2, 2, 2, 3, 2, 2, 3, 3, 2] => 2, 2, 2, 3, 2, 2, 3, 3, 2
[2, 2, 2, 3, 2, 2, 3, 3, 3] => 2, 2, 2, 3, 2, 2, 3, 3, 3
[2, 2, 2, 3, 2, 3, 1, 1, 1] => 2, 2, 2, 3, 2, 3, 1, 1, 1
[2, 2, 2, 3, 2, 3, 1, 1, 2] => 2, 2, 2, 3, 2, 3, 1, 1, 2
[2, 2, 2, 3, 2, 3, 1, 1, 3] => 2, 2, 2, 3, 2, 3, 1, 1, 3
[2, 2, 2, 3, 2, 3, 1, 2, 1] => 2, 2, 2, 3, 2, 3, 1, 2, 1
[2, 2, 2, 3, 2, 3, 1, 2, 2] => 2, 2, 2, 3, 2, 3, 1, 2, 2
[2, 2, 2, 3, 2, 3, 1, 2, 3] => 2, 2, 2, 3, 2, 3, 1, 2, 3
[2, 2, 2, 3, 2, 3, 1, 3, 1] => 2, 2, 2, 3, 2, 3, 1, 3, 1
[2, 2, 2, 3, 2, 3, 1, 3, 2] => 2, 2, 2, 3, 2, 3, 1, 3, 2
[2, 2, 2, 3, 2, 3, 1, 3, 3] => 2, 2, 2, 3, 2, 3, 1, 3, 3
[2, 2, 2, 3, 2, 3, 2, 1, 1] => 2, 2, 2, 3, 2, 3, 2, 1, 1
[2, 2, 2, 3, 2, 3, 2, 1, 2] => 2, 2, 2, 3, 2, 3, 2, 1, 2
[2, 2, 2, 3, 2, 3, 2, 1, 3] => 2, 2, 2, 3, 2, 3, 2, 1, 3
[2, 2, 2, 3, 2, 3, 2, 2, 1] => 2, 2, 2, 3, 2, 3, 2, 2, 1
[2, 2, 2, 3, 2, 3, 2, 2, 2] => 2, 2, 2, 3, 2, 3, 2, 2, 2
[2, 2, 2, 3, 2, 3, 2, 2, 3] => 2, 2, 2, 3, 2, 3, 2, 2, 3
[2, 2, 2, 3, 2, 3, 2, 3, 1] => 2, 2, 2, 3, 2, 3, 2, 3, 1
[2, 2, 2, 3, 2, 3, 2, 3, 2] => 2, 2, 2, 3, 2, 3, 2, 3, 2
[2, 2, 2, 3, 2, 3, 2, 3, 3] => 2, 2, 2, 3, 2, 3, 2, 3, 3
[2, 2, 2, 3, 2, 3, 3, 1, 1] => 2, 2, 2, 3, 2, 3, 3, 1, 1
[2, 2, 2, 3, 2, 3, 3, 1, 2] => 2, 2, 2, 3, 2, 3, 3, 1, 2
[2, 2, 2, 3, 2, 3, 3, 1, 3] => 2, 2, 2, 3, 2, 3, 3, 1, 3
[2, 2, 2, 3, 2, 3, 3, 2, 1] => 2, 2, 2, 3, 2, 3, 3, 2, 1
[2, 2, 2, 3, 2, 3, 3, 2, 2] => 2, 2, 2, 3, 2, 3, 3, 2, 2
[2, 2, 2, 3, 2, 3, 3, 2, 3] => 2, 2, 2, 3, 2, 3, 3, 2, 3
[2, 2, 2, 3, 2, 3, 3, 3, 1] => 2, 2, 2, 3, 2, 3, 3, 3, 1
[2, 2, 2, 3, 2, 3, 3, 3, 2] => 2, 2, 2, 3, 2, 3, 3, 3, 2
[2, 2, 2, 3, 2, 3, 3, 3, 3] => 2, 2, 2, 3, 2, 3, 3, 3, 3
[2, 2, 2, 3, 3, 1, 1, 1, 1] => 2, 2, 2, 3, 3, 1, 1, 1, 1
[2, 2, 2, 3, 3, 1, 1, 1, 2] => 2, 2, 2, 3, 3, 1, 1, 1, 2
[2, 2, 2, 3, 3, 1, 1, 1, 3] => 2, 2, 2, 3, 3, 1, 1, 1, 3
[2, 2, 2, 3, 3, 1, 1, 2, 1] => 2, 2, 2, 3, 3, 1, 1, 2, 1
[2, 2, 2, 3, 3, 1, 1, 2, 2] => 2, 2, 2, 3, 3, 1, 1, 2, 2
[2, 2, 2, 3, 3, 1, 1, 2, 3] => 2, 2, 2, 3, 3, 1, 1, 2, 3
[2, 2, 2, 3, 3, 1, 1, 3, 1] => 2, 2, 2, 3, 3, 1, 1, 3, 1
[2, 2, 2, 3, 3, 1, 1, 3, 2] => 2, 2, 2, 3, 3, 1, 1, 3, 2
[2, 2, 2, 3, 3, 1, 1, 3, 3] => 2, 2, 2, 3, 3, 1, 1, 3, 3
[2, 2, 2, 3, 3, 1, 2, 1, 1] => 2, 2, 2, 3, 3, 1, 2, 1, 1
[2, 2, 2, 3, 3, 1, 2, 1, 2] => 2, 2, 2, 3, 3, 1, 2, 1, 2
[2, 2, 2, 3, 3, 1, 2, 1, 3] => 2, 2, 2, 3, 3, 1, 2, 1, 3
[2, 2, 2, 3, 3, 1, 2, 2, 1] => 2, 2, 2, 3, 3, 1, 2, 2, 1
[2, 2, 2, 3, 3, 1, 2, 2, 2] => 2, 2, 2, 3, 3, 1, 2, 2, 2
[2, 2, 2, 3, 3, 1, 2, 2, 3] => 2, 2, 2, 3, 3, 1, 2, 2, 3
[2, 2, 2, 3, 3, 1, 2, 3, 1] => 2, 2, 2, 3, 3, 1, 2, 3, 1
[2, 2, 2, 3, 3, 1, 2, 3, 2] => 2, 2, 2, 3, 3, 1, 2, 3, 2
[2, 2, 2, 3, 3, 1, 2, 3, 3] => 2, 2, 2, 3, 3, 1, 2, 3, 3
[2, 2, 2, 3, 3, 1, 3, 1, 1] => 2, 2, 2, 3, 3, 1, 3, 1, 1
[2, 2, 2, 3, 3, 1, 3, 1, 2] => 2, 2, 2, 3, 3, 1, 3, 1, 2
[2, 2, 2, 3, 3, 1, 3, 1, 3] => 2, 2, 2, 3, 3, 1, 3, 1, 3
[2, 2, 2, 3, 3, 1, 3, 2, 1] => 2, 2, 2, 3, 3, 1, 3, 2, 1
[2, 2, 2, 3, 3, 1, 3, 2, 2] => 2, 2, 2, 3, 3, 1, 3, 2, 2
[2, 2, 2, 3, 3, 1, 3, 2, 3] => 2, 2, 2, 3, 3, 1, 3, 2, 3
[2, 2, 2, 3, 3, 1, 3, 3, 1] => 2, 2, 2, 3, 3, 1, 3, 3, 1
[2, 2, 2, 3, 3, 1, 3, 3, 2] => 2, 2, 2, 3, 3, 1, 3, 3, 2
[2, 2, 2, 3, 3, 1, 3, 3, 3] => 2, 2, 2, 3, 3, 1, 3, 3, 3
[2, 2, 2, 3, 3, 2, 1, 1, 1] => 2, 2, 2, 3, 3, 2, 1, 1, 1
[2, 2, 2, 3, 3, 2, 1, 1, 2] => 2, 2, 2, 3, 3, 2, 1, 1, 2
[2, 2, 2, 3, 3, 2, 1, 1, 3] => 2, 2, 2, 3, 3, 2, 1, 1, 3
[2, 2, 2, 3, 3, 2, 1, 2, 1] => 2, 2, 2, 3, 3, 2, 1, 2, 1
[2, 2, 2, 3, 3, 2, 1, 2, 2] => 2, 2, 2, 3, 3, 2, 1, 2, 2
[2, 2, 2, 3, 3, 2, 1, 2, 3] => 2, 2, 2, 3, 3, 2, 1, 2, 3
[2, 2, 2, 3, 3, 2, 1, 3, 1] => 2, 2, 2, 3, 3, 2, 1, 3, 1
[2, 2, 2, 3, 3, 2, 1, 3, 2] => 2, 2, 2, 3, 3, 2, 1, 3, 2
[2, 2, 2, 3, 3, 2, 1, 3, 3] => 2, 2, 2, 3, 3, 2, 1, 3, 3
[2, 2, 2, 3, 3, 2, 2, 1, 1] => 2, 2, 2, 3, 3, 2, 2, 1, 1
[2, 2, 2, 3, 3, 2, 2, 1, 2] => 2, 2, 2, 3, 3, 2, 2, 1, 2
[2, 2, 2, 3, 3, 2, 2, 1, 3] => 2, 2, 2, 3, 3, 2, 2, 1, 3
[2, 2, 2, 3, 3, 2, 2, 2, 1] => 2, 2, 2, 3, 3, 2, 2, 2, 1
[2, 2, 2, 3, 3, 2, 2, 2, 2] => 2, 2, 2, 3, 3, 2, 2, 2, 2
[2, 2, 2, 3, 3, 2, 2, 2, 3] => 2, 2, 2, 3, 3, 2, 2, 2, 3
[2, 2, 2, 3, 3, 2, 2, 3, 1] => 2, 2, 2, 3, 3, 2, 2, 3, 1
[2, 2, 2, 3, 3, 2, 2, 3, 2] => 2, 2, 2, 3, 3, 2, 2, 3, 2
[2, 2, 2, 3, 3, 2, 2, 3, 3] => 2, 2, 2, 3, 3, 2, 2, 3, 3
[2, 2, 2, 3, 3, 2, 3, 1, 1] => 2, 2, 2, 3, 3, 2, 3, 1, 1
[2, 2, 2, 3, 3, 2, 3, 1, 2] => 2, 2, 2, 3, 3, 2, 3, 1, 2
[2, 2, 2, 3, 3, 2, 3, 1, 3] => 2, 2, 2, 3, 3, 2, 3, 1, 3
[2, 2, 2, 3, 3, 2, 3, 2, 1] => 2, 2, 2, 3, 3, 2, 3, 2, 1
[2, 2, 2, 3, 3, 2, 3, 2, 2] => 2, 2, 2, 3, 3, 2, 3, 2, 2
[2, 2, 2, 3, 3, 2, 3, 2, 3] => 2, 2, 2, 3, 3, 2, 3, 2, 3
[2, 2, 2, 3, 3, 2, 3, 3, 1] => 2, 2, 2, 3, 3, 2, 3, 3, 1
[2, 2, 2, 3, 3, 2, 3, 3, 2] => 2, 2, 2, 3, 3, 2, 3, 3, 2
[2, 2, 2, 3, 3, 2, 3, 3, 3] => 2, 2, 2, 3, 3, 2, 3, 3, 3
[2, 2, 2, 3, 3, 3, 1, 1, 1] => 2, 2, 2, 3, 3, 3, 1, 1, 1
[2, 2, 2, 3, 3, 3, 1, 1, 2] => 2, 2, 2, 3, 3, 3, 1, 1, 2
[2, 2, 2, 3, 3, 3, 1, 1, 3] => 2, 2, 2, 3, 3, 3, 1, 1, 3
[2, 2, 2, 3, 3, 3, 1, 2, 1] => 2, 2, 2, 3, 3, 3, 1, 2, 1
[2, 2, 2, 3, 3, 3, 1, 2, 2] => 2, 2, 2, 3, 3, 3, 1, 2, 2
[2, 2, 2, 3, 3, 3, 1, 2, 3] => 2, 2, 2, 3, 3, 3, 1, 2, 3
[2, 2, 2, 3, 3, 3, 1, 3, 1] => 2, 2, 2, 3, 3, 3, 1, 3, 1
[2, 2, 2, 3, 3, 3, 1, 3, 2] => 2, 2, 2, 3, 3, 3, 1, 3, 2
[2, 2, 2, 3, 3, 3, 1, 3, 3] => 2, 2, 2, 3, 3, 3, 1, 3, 3
[2, 2, 2, 3, 3, 3, 2, 1, 1] => 2, 2, 2, 3, 3, 3, 2, 1, 1
[2, 2, 2, 3, 3, 3, 2, 1, 2] => 2, 2, 2, 3, 3, 3, 2, 1, 2
[2, 2, 2, 3, 3, 3, 2, 1, 3] => 2, 2, 2, 3, 3, 3, 2, 1, 3
[2, 2, 2, 3, 3, 3, 2, 2, 1] => 2, 2, 2, 3, 3, 3, 2, 2, 1
[2, 2, 2, 3, 3, 3, 2, 2, 2] => 2, 2, 2, 3, 3, 3, 2, 2, 2
[2, 2, 2, 3, 3, 3, 2, 2, 3] => 2, 2, 2, 3, 3, 3, 2, 2, 3
[2, 2, 2, 3, 3, 3, 2, 3, 1] => 2, 2, 2, 3, 3, 3, 2, 3, 1
[2, 2, 2, 3, 3, 3, 2, 3, 2] => 2, 2, 2, 3, 3, 3, 2, 3, 2
[2, 2, 2, 3, 3, 3, 2, 3, 3] => 2, 2, 2, 3, 3, 3, 2, 3, 3
[2, 2, 2, 3, 3, 3, 3, 1, 1] => 2, 2, 2, 3, 3, 3, 3, 1, 1
[2, 2, 2, 3, 3, 3, 3, 1, 2] => 2, 2, 2, 3, 3, 3, 3, 1, 2
[2, 2, 2, 3, 3, 3, 3, 1, 3] => 2, 2, 2, 3, 3, 3, 3, 1, 3
[2, 2, 2, 3, 3, 3, 3, 2, 1] => 2, 2, 2, 3, 3, 3, 3, 2, 1
[2, 2, 2, 3, 3, 3, 3, 2, 2] => 2, 2, 2, 3, 3, 3, 3, 2, 2
[2, 2, 2, 3, 3, 3, 3, 2, 3] => 2, 2, 2, 3, 3, 3, 3, 2, 3
[2, 2, 2, 3, 3, 3, 3, 3, 1] => 2, 2, 2, 3, 3, 3, 3, 3, 1
[2, 2, 2, 3, 3, 3, 3, 3, 2] => 2, 2, 2, 3, 3, 3, 3, 3, 2
[2, 2, 2, 3, 3, 3, 3, 3, 3] => 2, 2, 2, 3, 3, 3, 3, 3, 3
[2, 2, 3, 1, 1, 1, 1, 1, 1] => 2, 2, 3, 1, 1, 1, 1, 1, 1
[2, 2, 3, 1, 1, 1, 1, 1, 2] => 2, 2, 3, 1, 1, 1, 1, 1, 2
[2, 2, 3, 1, 1, 1, 1, 1, 3] => 2, 2, 3, 1, 1, 1, 1, 1, 3
[2, 2, 3, 1, 1, 1, 1, 2, 1] => 2, 2, 3, 1, 1, 1, 1, 2, 1
[2, 2, 3, 1, 1, 1, 1, 2, 2] => 2, 2, 3, 1, 1, 1, 1, 2, 2
[2, 2, 3, 1, 1, 1, 1, 2, 3] => 2, 2, 3, 1, 1, 1, 1, 2, 3
[2, 2, 3, 1, 1, 1, 1, 3, 1] => 2, 2, 3, 1, 1, 1, 1, 3, 1
[2, 2, 3, 1, 1, 1, 1, 3, 2] => 2, 2, 3, 1, 1, 1, 1, 3, 2
[2, 2, 3, 1, 1, 1, 1, 3, 3] => 2, 2, 3, 1, 1, 1, 1, 3, 3
[2, 2, 3, 1, 1, 1, 2, 1, 1] => 2, 2, 3, 1, 1, 1, 2, 1, 1
[2, 2, 3, 1, 1, 1, 2, 1, 2] => 2, 2, 3, 1, 1, 1, 2, 1, 2
[2, 2, 3, 1, 1, 1, 2, 1, 3] => 2, 2, 3, 1, 1, 1, 2, 1, 3
[2, 2, 3, 1, 1, 1, 2, 2, 1] => 2, 2, 3, 1, 1, 1, 2, 2, 1
[2, 2, 3, 1, 1, 1, 2, 2, 2] => 2, 2, 3, 1, 1, 1, 2, 2, 2
[2, 2, 3, 1, 1, 1, 2, 2, 3] => 2, 2, 3, 1, 1, 1, 2, 2, 3
[2, 2, 3, 1, 1, 1, 2, 3, 1] => 2, 2, 3, 1, 1, 1, 2, 3, 1
[2, 2, 3, 1, 1, 1, 2, 3, 2] => 2, 2, 3, 1, 1, 1, 2, 3, 2
[2, 2, 3, 1, 1, 1, 2, 3, 3] => 2, 2, 3, 1, 1, 1, 2, 3, 3
[2, 2, 3, 1, 1, 1, 3, 1, 1] => 2, 2, 3, 1, 1, 1, 3, 1, 1
[2, 2, 3, 1, 1, 1, 3, 1, 2] => 2, 2, 3, 1, 1, 1, 3, 1, 2
[2, 2, 3, 1, 1, 1, 3, 1, 3] => 2, 2, 3, 1, 1, 1, 3, 1, 3
[2, 2, 3, 1, 1, 1, 3, 2, 1] => 2, 2, 3, 1, 1, 1, 3, 2, 1
[2, 2, 3, 1, 1, 1, 3, 2, 2] => 2, 2, 3, 1, 1, 1, 3, 2, 2
[2, 2, 3, 1, 1, 1, 3, 2, 3] => 2, 2, 3, 1, 1, 1, 3, 2, 3
[2, 2, 3, 1, 1, 1, 3, 3, 1] => 2, 2, 3, 1, 1, 1, 3, 3, 1
[2, 2, 3, 1, 1, 1, 3, 3, 2] => 2, 2, 3, 1, 1, 1, 3, 3, 2
[2, 2, 3, 1, 1, 1, 3, 3, 3] => 2, 2, 3, 1, 1, 1, 3, 3, 3
[2, 2, 3, 1, 1, 2, 1, 1, 1] => 2, 2, 3, 1, 1, 2, 1, 1, 1
[2, 2, 3, 1, 1, 2, 1, 1, 2] => 2, 2, 3, 1, 1, 2, 1, 1, 2
[2, 2, 3, 1, 1, 2, 1, 1, 3] => 2, 2, 3, 1, 1, 2, 1, 1, 3
[2, 2, 3, 1, 1, 2, 1, 2, 1] => 2, 2, 3, 1, 1, 2, 1, 2, 1
[2, 2, 3, 1, 1, 2, 1, 2, 2] => 2, 2, 3, 1, 1, 2, 1, 2, 2
[2, 2, 3, 1, 1, 2, 1, 2, 3] => 2, 2, 3, 1, 1, 2, 1, 2, 3
[2, 2, 3, 1, 1, 2, 1, 3, 1] => 2, 2, 3, 1, 1, 2, 1, 3, 1
[2, 2, 3, 1, 1, 2, 1, 3, 2] => 2, 2, 3, 1, 1, 2, 1, 3, 2
[2, 2, 3, 1, 1, 2, 1, 3, 3] => 2, 2, 3, 1, 1, 2, 1, 3, 3
[2, 2, 3, 1, 1, 2, 2, 1, 1] => 2, 2, 3, 1, 1, 2, 2, 1, 1
[2, 2, 3, 1, 1, 2, 2, 1, 2] => 2, 2, 3, 1, 1, 2, 2, 1, 2
[2, 2, 3, 1, 1, 2, 2, 1, 3] => 2, 2, 3, 1, 1, 2, 2, 1, 3
[2, 2, 3, 1, 1, 2, 2, 2, 1] => 2, 2, 3, 1, 1, 2, 2, 2, 1
[2, 2, 3, 1, 1, 2, 2, 2, 2] => 2, 2, 3, 1, 1, 2, 2, 2, 2
[2, 2, 3, 1, 1, 2, 2, 2, 3] => 2, 2, 3, 1, 1, 2, 2, 2, 3
[2, 2, 3, 1, 1, 2, 2, 3, 1] => 2, 2, 3, 1, 1, 2, 2, 3, 1
[2, 2, 3, 1, 1, 2, 2, 3, 2] => 2, 2, 3, 1, 1, 2, 2, 3, 2
[2, 2, 3, 1, 1, 2, 2, 3, 3] => 2, 2, 3, 1, 1, 2, 2, 3, 3
[2, 2, 3, 1, 1, 2, 3, 1, 1] => 2, 2, 3, 1, 1, 2, 3, 1, 1
[2, 2, 3, 1, 1, 2, 3, 1, 2] => 2, 2, 3, 1, 1, 2, 3, 1, 2
[2, 2, 3, 1, 1, 2, 3, 1, 3] => 2, 2, 3, 1, 1, 2, 3, 1, 3
[2, 2, 3, 1, 1, 2, 3, 2, 1] => 2, 2, 3, 1, 1, 2, 3, 2, 1
[2, 2, 3, 1, 1, 2, 3, 2, 2] => 2, 2, 3, 1, 1, 2, 3, 2, 2
[2, 2, 3, 1, 1, 2, 3, 2, 3] => 2, 2, 3, 1, 1, 2, 3, 2, 3
[2, 2, 3, 1, 1, 2, 3, 3, 1] => 2, 2, 3, 1, 1, 2, 3, 3, 1
[2, 2, 3, 1, 1, 2, 3, 3, 2] => 2, 2, 3, 1, 1, 2, 3, 3, 2
[2, 2, 3, 1, 1, 2, 3, 3, 3] => 2, 2, 3, 1, 1, 2, 3, 3, 3
[2, 2, 3, 1, 1, 3, 1, 1, 1] => 2, 2, 3, 1, 1, 3, 1, 1, 1
[2, 2, 3, 1, 1, 3, 1, 1, 2] => 2, 2, 3, 1, 1, 3, 1, 1, 2
[2, 2, 3, 1, 1, 3, 1, 1, 3] => 2, 2, 3, 1, 1, 3, 1, 1, 3
[2, 2, 3, 1, 1, 3, 1, 2, 1] => 2, 2, 3, 1, 1, 3, 1, 2, 1
[2, 2, 3, 1, 1, 3, 1, 2, 2] => 2, 2, 3, 1, 1, 3, 1, 2, 2
[2, 2, 3, 1, 1, 3, 1, 2, 3] => 2, 2, 3, 1, 1, 3, 1, 2, 3
[2, 2, 3, 1, 1, 3, 1, 3, 1] => 2, 2, 3, 1, 1, 3, 1, 3, 1
[2, 2, 3, 1, 1, 3, 1, 3, 2] => 2, 2, 3, 1, 1, 3, 1, 3, 2
[2, 2, 3, 1, 1, 3, 1, 3, 3] => 2, 2, 3, 1, 1, 3, 1, 3, 3
[2, 2, 3, 1, 1, 3, 2, 1, 1] => 2, 2, 3, 1, 1, 3, 2, 1, 1
[2, 2, 3, 1, 1, 3, 2, 1, 2] => 2, 2, 3, 1, 1, 3, 2, 1, 2
[2, 2, 3, 1, 1, 3, 2, 1, 3] => 2, 2, 3, 1, 1, 3, 2, 1, 3
[2, 2, 3, 1, 1, 3, 2, 2, 1] => 2, 2, 3, 1, 1, 3, 2, 2, 1
[2, 2, 3, 1, 1, 3, 2, 2, 2] => 2, 2, 3, 1, 1, 3, 2, 2, 2
[2, 2, 3, 1, 1, 3, 2, 2, 3] => 2, 2, 3, 1, 1, 3, 2, 2, 3
[2, 2, 3, 1, 1, 3, 2, 3, 1] => 2, 2, 3, 1, 1, 3, 2, 3, 1
[2, 2, 3, 1, 1, 3, 2, 3, 2] => 2, 2, 3, 1, 1, 3, 2, 3, 2
[2, 2, 3, 1, 1, 3, 2, 3, 3] => 2, 2, 3, 1, 1, 3, 2, 3, 3
[2, 2, 3, 1, 1, 3, 3, 1, 1] => 2, 2, 3, 1, 1, 3, 3, 1, 1
[2, 2, 3, 1, 1, 3, 3, 1, 2] => 2, 2, 3, 1, 1, 3, 3, 1, 2
[2, 2, 3, 1, 1, 3, 3, 1, 3] => 2, 2, 3, 1, 1, 3, 3, 1, 3
[2, 2, 3, 1, 1, 3, 3, 2, 1] => 2, 2, 3, 1, 1, 3, 3, 2, 1
[2, 2, 3, 1, 1, 3, 3, 2, 2] => 2, 2, 3, 1, 1, 3, 3, 2, 2
[2, 2, 3, 1, 1, 3, 3, 2, 3] => 2, 2, 3, 1, 1, 3, 3, 2, 3
[2, 2, 3, 1, 1, 3, 3, 3, 1] => 2, 2, 3, 1, 1, 3, 3, 3, 1
[2, 2, 3, 1, 1, 3, 3, 3, 2] => 2, 2, 3, 1, 1, 3, 3, 3, 2
[2, 2, 3, 1, 1, 3, 3, 3, 3] => 2, 2, 3, 1, 1, 3, 3, 3, 3
[2, 2, 3, 1, 2, 1, 1, 1, 1] => 2, 2, 3, 1, 2, 1, 1, 1, 1
[2, 2, 3, 1, 2, 1, 1, 1, 2] => 2, 2, 3, 1, 2, 1, 1, 1, 2
[2, 2, 3, 1, 2, 1, 1, 1, 3] => 2, 2, 3, 1, 2, 1, 1, 1, 3
[2, 2, 3, 1, 2, 1, 1, 2, 1] => 2, 2, 3, 1, 2, 1, 1, 2, 1
[2, 2, 3, 1, 2, 1, 1, 2, 2] => 2, 2, 3, 1, 2, 1, 1, 2, 2
[2, 2, 3, 1, 2, 1, 1, 2, 3] => 2, 2, 3, 1, 2, 1, 1, 2, 3
[2, 2, 3, 1, 2, 1, 1, 3, 1] => 2, 2, 3, 1, 2, 1, 1, 3, 1
[2, 2, 3, 1, 2, 1, 1, 3, 2] => 2, 2, 3, 1, 2, 1, 1, 3, 2
[2, 2, 3, 1, 2, 1, 1, 3, 3] => 2, 2, 3, 1, 2, 1, 1, 3, 3
[2, 2, 3, 1, 2, 1, 2, 1, 1] => 2, 2, 3, 1, 2, 1, 2, 1, 1
[2, 2, 3, 1, 2, 1, 2, 1, 2] => 2, 2, 3, 1, 2, 1, 2, 1, 2
[2, 2, 3, 1, 2, 1, 2, 1, 3] => 2, 2, 3, 1, 2, 1, 2, 1, 3
[2, 2, 3, 1, 2, 1, 2, 2, 1] => 2, 2, 3, 1, 2, 1, 2, 2, 1
[2, 2, 3, 1, 2, 1, 2, 2, 2] => 2, 2, 3, 1, 2, 1, 2, 2, 2
[2, 2, 3, 1, 2, 1, 2, 2, 3] => 2, 2, 3, 1, 2, 1, 2, 2, 3
[2, 2, 3, 1, 2, 1, 2, 3, 1] => 2, 2, 3, 1, 2, 1, 2, 3, 1
[2, 2, 3, 1, 2, 1, 2, 3, 2] => 2, 2, 3, 1, 2, 1, 2, 3, 2
[2, 2, 3, 1, 2, 1, 2, 3, 3] => 2, 2, 3, 1, 2, 1, 2, 3, 3
[2, 2, 3, 1, 2, 1, 3, 1, 1] => 2, 2, 3, 1, 2, 1, 3, 1, 1
[2, 2, 3, 1, 2, 1, 3, 1, 2] => 2, 2, 3, 1, 2, 1, 3, 1, 2
[2, 2, 3, 1, 2, 1, 3, 1, 3] => 2, 2, 3, 1, 2, 1, 3, 1, 3
[2, 2, 3, 1, 2, 1, 3, 2, 1] => 2, 2, 3, 1, 2, 1, 3, 2, 1
[2, 2, 3, 1, 2, 1, 3, 2, 2] => 2, 2, 3, 1, 2, 1, 3, 2, 2
[2, 2, 3, 1, 2, 1, 3, 2, 3] => 2, 2, 3, 1, 2, 1, 3, 2, 3
[2, 2, 3, 1, 2, 1, 3, 3, 1] => 2, 2, 3, 1, 2, 1, 3, 3, 1
[2, 2, 3, 1, 2, 1, 3, 3, 2] => 2, 2, 3, 1, 2, 1, 3, 3, 2
[2, 2, 3, 1, 2, 1, 3, 3, 3] => 2, 2, 3, 1, 2, 1, 3, 3, 3
[2, 2, 3, 1, 2, 2, 1, 1, 1] => 2, 2, 3, 1, 2, 2, 1, 1, 1
[2, 2, 3, 1, 2, 2, 1, 1, 2] => 2, 2, 3, 1, 2, 2, 1, 1, 2
[2, 2, 3, 1, 2, 2, 1, 1, 3] => 2, 2, 3, 1, 2, 2, 1, 1, 3
[2, 2, 3, 1, 2, 2, 1, 2, 1] => 2, 2, 3, 1, 2, 2, 1, 2, 1
[2, 2, 3, 1, 2, 2, 1, 2, 2] => 2, 2, 3, 1, 2, 2, 1, 2, 2
[2, 2, 3, 1, 2, 2, 1, 2, 3] => 2, 2, 3, 1, 2, 2, 1, 2, 3
[2, 2, 3, 1, 2, 2, 1, 3, 1] => 2, 2, 3, 1, 2, 2, 1, 3, 1
[2, 2, 3, 1, 2, 2, 1, 3, 2] => 2, 2, 3, 1, 2, 2, 1, 3, 2
[2, 2, 3, 1, 2, 2, 1, 3, 3] => 2, 2, 3, 1, 2, 2, 1, 3, 3
[2, 2, 3, 1, 2, 2, 2, 1, 1] => 2, 2, 3, 1, 2, 2, 2, 1, 1
[2, 2, 3, 1, 2, 2, 2, 1, 2] => 2, 2, 3, 1, 2, 2, 2, 1, 2
[2, 2, 3, 1, 2, 2, 2, 1, 3] => 2, 2, 3, 1, 2, 2, 2, 1, 3
[2, 2, 3, 1, 2, 2, 2, 2, 1] => 2, 2, 3, 1, 2, 2, 2, 2, 1
[2, 2, 3, 1, 2, 2, 2, 2, 2] => 2, 2, 3, 1, 2, 2, 2, 2, 2
[2, 2, 3, 1, 2, 2, 2, 2, 3] => 2, 2, 3, 1, 2, 2, 2, 2, 3
[2, 2, 3, 1, 2, 2, 2, 3, 1] => 2, 2, 3, 1, 2, 2, 2, 3, 1
[2, 2, 3, 1, 2, 2, 2, 3, 2] => 2, 2, 3, 1, 2, 2, 2, 3, 2
[2, 2, 3, 1, 2, 2, 2, 3, 3] => 2, 2, 3, 1, 2, 2, 2, 3, 3
[2, 2, 3, 1, 2, 2, 3, 1, 1] => 2, 2, 3, 1, 2, 2, 3, 1, 1
[2, 2, 3, 1, 2, 2, 3, 1, 2] => 2, 2, 3, 1, 2, 2, 3, 1, 2
[2, 2, 3, 1, 2, 2, 3, 1, 3] => 2, 2, 3, 1, 2, 2, 3, 1, 3
[2, 2, 3, 1, 2, 2, 3, 2, 1] => 2, 2, 3, 1, 2, 2, 3, 2, 1
[2, 2, 3, 1, 2, 2, 3, 2, 2] => 2, 2, 3, 1, 2, 2, 3, 2, 2
[2, 2, 3, 1, 2, 2, 3, 2, 3] => 2, 2, 3, 1, 2, 2, 3, 2, 3
[2, 2, 3, 1, 2, 2, 3, 3, 1] => 2, 2, 3, 1, 2, 2, 3, 3, 1
[2, 2, 3, 1, 2, 2, 3, 3, 2] => 2, 2, 3, 1, 2, 2, 3, 3, 2
[2, 2, 3, 1, 2, 2, 3, 3, 3] => 2, 2, 3, 1, 2, 2, 3, 3, 3
[2, 2, 3, 1, 2, 3, 1, 1, 1] => 2, 2, 3, 1, 2, 3, 1, 1, 1
[2, 2, 3, 1, 2, 3, 1, 1, 2] => 2, 2, 3, 1, 2, 3, 1, 1, 2
[2, 2, 3, 1, 2, 3, 1, 1, 3] => 2, 2, 3, 1, 2, 3, 1, 1, 3
[2, 2, 3, 1, 2, 3, 1, 2, 1] => 2, 2, 3, 1, 2, 3, 1, 2, 1
[2, 2, 3, 1, 2, 3, 1, 2, 2] => 2, 2, 3, 1, 2, 3, 1, 2, 2
[2, 2, 3, 1, 2, 3, 1, 2, 3] => 2, 2, 3, 1, 2, 3, 1, 2, 3
[2, 2, 3, 1, 2, 3, 1, 3, 1] => 2, 2, 3, 1, 2, 3, 1, 3, 1
[2, 2, 3, 1, 2, 3, 1, 3, 2] => 2, 2, 3, 1, 2, 3, 1, 3, 2
[2, 2, 3, 1, 2, 3, 1, 3, 3] => 2, 2, 3, 1, 2, 3, 1, 3, 3
[2, 2, 3, 1, 2, 3, 2, 1, 1] => 2, 2, 3, 1, 2, 3, 2, 1, 1
[2, 2, 3, 1, 2, 3, 2, 1, 2] => 2, 2, 3, 1, 2, 3, 2, 1, 2
[2, 2, 3, 1, 2, 3, 2, 1, 3] => 2, 2, 3, 1, 2, 3, 2, 1, 3
[2, 2, 3, 1, 2, 3, 2, 2, 1] => 2, 2, 3, 1, 2, 3, 2, 2, 1
[2, 2, 3, 1, 2, 3, 2, 2, 2] => 2, 2, 3, 1, 2, 3, 2, 2, 2
[2, 2, 3, 1, 2, 3, 2, 2, 3] => 2, 2, 3, 1, 2, 3, 2, 2, 3
[2, 2, 3, 1, 2, 3, 2, 3, 1] => 2, 2, 3, 1, 2, 3, 2, 3, 1
[2, 2, 3, 1, 2, 3, 2, 3, 2] => 2, 2, 3, 1, 2, 3, 2, 3, 2
[2, 2, 3, 1, 2, 3, 2, 3, 3] => 2, 2, 3, 1, 2, 3, 2, 3, 3
[2, 2, 3, 1, 2, 3, 3, 1, 1] => 2, 2, 3, 1, 2, 3, 3, 1, 1
[2, 2, 3, 1, 2, 3, 3, 1, 2] => 2, 2, 3, 1, 2, 3, 3, 1, 2
[2, 2, 3, 1, 2, 3, 3, 1, 3] => 2, 2, 3, 1, 2, 3, 3, 1, 3
[2, 2, 3, 1, 2, 3, 3, 2, 1] => 2, 2, 3, 1, 2, 3, 3, 2, 1
[2, 2, 3, 1, 2, 3, 3, 2, 2] => 2, 2, 3, 1, 2, 3, 3, 2, 2
[2, 2, 3, 1, 2, 3, 3, 2, 3] => 2, 2, 3, 1, 2, 3, 3, 2, 3
[2, 2, 3, 1, 2, 3, 3, 3, 1] => 2, 2, 3, 1, 2, 3, 3, 3, 1
[2, 2, 3, 1, 2, 3, 3, 3, 2] => 2, 2, 3, 1, 2, 3, 3, 3, 2
[2, 2, 3, 1, 2, 3, 3, 3, 3] => 2, 2, 3, 1, 2, 3, 3, 3, 3
[2, 2, 3, 1, 3, 1, 1, 1, 1] => 2, 2, 3, 1, 3, 1, 1, 1, 1
[2, 2, 3, 1, 3, 1, 1, 1, 2] => 2, 2, 3, 1, 3, 1, 1, 1, 2
[2, 2, 3, 1, 3, 1, 1, 1, 3] => 2, 2, 3, 1, 3, 1, 1, 1, 3
[2, 2, 3, 1, 3, 1, 1, 2, 1] => 2, 2, 3, 1, 3, 1, 1, 2, 1
[2, 2, 3, 1, 3, 1, 1, 2, 2] => 2, 2, 3, 1, 3, 1, 1, 2, 2
[2, 2, 3, 1, 3, 1, 1, 2, 3] => 2, 2, 3, 1, 3, 1, 1, 2, 3
[2, 2, 3, 1, 3, 1, 1, 3, 1] => 2, 2, 3, 1, 3, 1, 1, 3, 1
[2, 2, 3, 1, 3, 1, 1, 3, 2] => 2, 2, 3, 1, 3, 1, 1, 3, 2
[2, 2, 3, 1, 3, 1, 1, 3, 3] => 2, 2, 3, 1, 3, 1, 1, 3, 3
[2, 2, 3, 1, 3, 1, 2, 1, 1] => 2, 2, 3, 1, 3, 1, 2, 1, 1
[2, 2, 3, 1, 3, 1, 2, 1, 2] => 2, 2, 3, 1, 3, 1, 2, 1, 2
[2, 2, 3, 1, 3, 1, 2, 1, 3] => 2, 2, 3, 1, 3, 1, 2, 1, 3
[2, 2, 3, 1, 3, 1, 2, 2, 1] => 2, 2, 3, 1, 3, 1, 2, 2, 1
[2, 2, 3, 1, 3, 1, 2, 2, 2] => 2, 2, 3, 1, 3, 1, 2, 2, 2
[2, 2, 3, 1, 3, 1, 2, 2, 3] => 2, 2, 3, 1, 3, 1, 2, 2, 3
[2, 2, 3, 1, 3, 1, 2, 3, 1] => 2, 2, 3, 1, 3, 1, 2, 3, 1
[2, 2, 3, 1, 3, 1, 2, 3, 2] => 2, 2, 3, 1, 3, 1, 2, 3, 2
[2, 2, 3, 1, 3, 1, 2, 3, 3] => 2, 2, 3, 1, 3, 1, 2, 3, 3
[2, 2, 3, 1, 3, 1, 3, 1, 1] => 2, 2, 3, 1, 3, 1, 3, 1, 1
[2, 2, 3, 1, 3, 1, 3, 1, 2] => 2, 2, 3, 1, 3, 1, 3, 1, 2
[2, 2, 3, 1, 3, 1, 3, 1, 3] => 2, 2, 3, 1, 3, 1, 3, 1, 3
[2, 2, 3, 1, 3, 1, 3, 2, 1] => 2, 2, 3, 1, 3, 1, 3, 2, 1
[2, 2, 3, 1, 3, 1, 3, 2, 2] => 2, 2, 3, 1, 3, 1, 3, 2, 2
[2, 2, 3, 1, 3, 1, 3, 2, 3] => 2, 2, 3, 1, 3, 1, 3, 2, 3
[2, 2, 3, 1, 3, 1, 3, 3, 1] => 2, 2, 3, 1, 3, 1, 3, 3, 1
[2, 2, 3, 1, 3, 1, 3, 3, 2] => 2, 2, 3, 1, 3, 1, 3, 3, 2
[2, 2, 3, 1, 3, 1, 3, 3, 3] => 2, 2, 3, 1, 3, 1, 3, 3, 3
[2, 2, 3, 1, 3, 2, 1, 1, 1] => 2, 2, 3, 1, 3, 2, 1, 1, 1
[2, 2, 3, 1, 3, 2, 1, 1, 2] => 2, 2, 3, 1, 3, 2, 1, 1, 2
[2, 2, 3, 1, 3, 2, 1, 1, 3] => 2, 2, 3, 1, 3, 2, 1, 1, 3
[2, 2, 3, 1, 3, 2, 1, 2, 1] => 2, 2, 3, 1, 3, 2, 1, 2, 1
[2, 2, 3, 1, 3, 2, 1, 2, 2] => 2, 2, 3, 1, 3, 2, 1, 2, 2
[2, 2, 3, 1, 3, 2, 1, 2, 3] => 2, 2, 3, 1, 3, 2, 1, 2, 3
[2, 2, 3, 1, 3, 2, 1, 3, 1] => 2, 2, 3, 1, 3, 2, 1, 3, 1
[2, 2, 3, 1, 3, 2, 1, 3, 2] => 2, 2, 3, 1, 3, 2, 1, 3, 2
[2, 2, 3, 1, 3, 2, 1, 3, 3] => 2, 2, 3, 1, 3, 2, 1, 3, 3
[2, 2, 3, 1, 3, 2, 2, 1, 1] => 2, 2, 3, 1, 3, 2, 2, 1, 1
[2, 2, 3, 1, 3, 2, 2, 1, 2] => 2, 2, 3, 1, 3, 2, 2, 1, 2
[2, 2, 3, 1, 3, 2, 2, 1, 3] => 2, 2, 3, 1, 3, 2, 2, 1, 3
[2, 2, 3, 1, 3, 2, 2, 2, 1] => 2, 2, 3, 1, 3, 2, 2, 2, 1
[2, 2, 3, 1, 3, 2, 2, 2, 2] => 2, 2, 3, 1, 3, 2, 2, 2, 2
[2, 2, 3, 1, 3, 2, 2, 2, 3] => 2, 2, 3, 1, 3, 2, 2, 2, 3
[2, 2, 3, 1, 3, 2, 2, 3, 1] => 2, 2, 3, 1, 3, 2, 2, 3, 1
[2, 2, 3, 1, 3, 2, 2, 3, 2] => 2, 2, 3, 1, 3, 2, 2, 3, 2
[2, 2, 3, 1, 3, 2, 2, 3, 3] => 2, 2, 3, 1, 3, 2, 2, 3, 3
[2, 2, 3, 1, 3, 2, 3, 1, 1] => 2, 2, 3, 1, 3, 2, 3, 1, 1
[2, 2, 3, 1, 3, 2, 3, 1, 2] => 2, 2, 3, 1, 3, 2, 3, 1, 2
[2, 2, 3, 1, 3, 2, 3, 1, 3] => 2, 2, 3, 1, 3, 2, 3, 1, 3
[2, 2, 3, 1, 3, 2, 3, 2, 1] => 2, 2, 3, 1, 3, 2, 3, 2, 1
[2, 2, 3, 1, 3, 2, 3, 2, 2] => 2, 2, 3, 1, 3, 2, 3, 2, 2
[2, 2, 3, 1, 3, 2, 3, 2, 3] => 2, 2, 3, 1, 3, 2, 3, 2, 3
[2, 2, 3, 1, 3, 2, 3, 3, 1] => 2, 2, 3, 1, 3, 2, 3, 3, 1
[2, 2, 3, 1, 3, 2, 3, 3, 2] => 2, 2, 3, 1, 3, 2, 3, 3, 2
[2, 2, 3, 1, 3, 2, 3, 3, 3] => 2, 2, 3, 1, 3, 2, 3, 3, 3
[2, 2, 3, 1, 3, 3, 1, 1, 1] => 2, 2, 3, 1, 3, 3, 1, 1, 1
[2, 2, 3, 1, 3, 3, 1, 1, 2] => 2, 2, 3, 1, 3, 3, 1, 1, 2
[2, 2, 3, 1, 3, 3, 1, 1, 3] => 2, 2, 3, 1, 3, 3, 1, 1, 3
[2, 2, 3, 1, 3, 3, 1, 2, 1] => 2, 2, 3, 1, 3, 3, 1, 2, 1
[2, 2, 3, 1, 3, 3, 1, 2, 2] => 2, 2, 3, 1, 3, 3, 1, 2, 2
[2, 2, 3, 1, 3, 3, 1, 2, 3] => 2, 2, 3, 1, 3, 3, 1, 2, 3
[2, 2, 3, 1, 3, 3, 1, 3, 1] => 2, 2, 3, 1, 3, 3, 1, 3, 1
[2, 2, 3, 1, 3, 3, 1, 3, 2] => 2, 2, 3, 1, 3, 3, 1, 3, 2
[2, 2, 3, 1, 3, 3, 1, 3, 3] => 2, 2, 3, 1, 3, 3, 1, 3, 3
[2, 2, 3, 1, 3, 3, 2, 1, 1] => 2, 2, 3, 1, 3, 3, 2, 1, 1
[2, 2, 3, 1, 3, 3, 2, 1, 2] => 2, 2, 3, 1, 3, 3, 2, 1, 2
[2, 2, 3, 1, 3, 3, 2, 1, 3] => 2, 2, 3, 1, 3, 3, 2, 1, 3
[2, 2, 3, 1, 3, 3, 2, 2, 1] => 2, 2, 3, 1, 3, 3, 2, 2, 1
[2, 2, 3, 1, 3, 3, 2, 2, 2] => 2, 2, 3, 1, 3, 3, 2, 2, 2
[2, 2, 3, 1, 3, 3, 2, 2, 3] => 2, 2, 3, 1, 3, 3, 2, 2, 3
[2, 2, 3, 1, 3, 3, 2, 3, 1] => 2, 2, 3, 1, 3, 3, 2, 3, 1
[2, 2, 3, 1, 3, 3, 2, 3, 2] => 2, 2, 3, 1, 3, 3, 2, 3, 2
[2, 2, 3, 1, 3, 3, 2, 3, 3] => 2, 2, 3, 1, 3, 3, 2, 3, 3
[2, 2, 3, 1, 3, 3, 3, 1, 1] => 2, 2, 3, 1, 3, 3, 3, 1, 1
[2, 2, 3, 1, 3, 3, 3, 1, 2] => 2, 2, 3, 1, 3, 3, 3, 1, 2
[2, 2, 3, 1, 3, 3, 3, 1, 3] => 2, 2, 3, 1, 3, 3, 3, 1, 3
[2, 2, 3, 1, 3, 3, 3, 2, 1] => 2, 2, 3, 1, 3, 3, 3, 2, 1
[2, 2, 3, 1, 3, 3, 3, 2, 2] => 2, 2, 3, 1, 3, 3, 3, 2, 2
[2, 2, 3, 1, 3, 3, 3, 2, 3] => 2, 2, 3, 1, 3, 3, 3, 2, 3
[2, 2, 3, 1, 3, 3, 3, 3, 1] => 2, 2, 3, 1, 3, 3, 3, 3, 1
[2, 2, 3, 1, 3, 3, 3, 3, 2] => 2, 2, 3, 1, 3, 3, 3, 3, 2
[2, 2, 3, 1, 3, 3, 3, 3, 3] => 2, 2, 3, 1, 3, 3, 3, 3, 3
[2, 2, 3, 2, 1, 1, 1, 1, 1] => 2, 2, 3, 2, 1, 1, 1, 1, 1
[2, 2, 3, 2, 1, 1, 1, 1, 2] => 2, 2, 3, 2, 1, 1, 1, 1, 2
[2, 2, 3, 2, 1, 1, 1, 1, 3] => 2, 2, 3, 2, 1, 1, 1, 1, 3
[2, 2, 3, 2, 1, 1, 1, 2, 1] => 2, 2, 3, 2, 1, 1, 1, 2, 1
[2, 2, 3, 2, 1, 1, 1, 2, 2] => 2, 2, 3, 2, 1, 1, 1, 2, 2
[2, 2, 3, 2, 1, 1, 1, 2, 3] => 2, 2, 3, 2, 1, 1, 1, 2, 3
[2, 2, 3, 2, 1, 1, 1, 3, 1] => 2, 2, 3, 2, 1, 1, 1, 3, 1
[2, 2, 3, 2, 1, 1, 1, 3, 2] => 2, 2, 3, 2, 1, 1, 1, 3, 2
[2, 2, 3, 2, 1, 1, 1, 3, 3] => 2, 2, 3, 2, 1, 1, 1, 3, 3
[2, 2, 3, 2, 1, 1, 2, 1, 1] => 2, 2, 3, 2, 1, 1, 2, 1, 1
[2, 2, 3, 2, 1, 1, 2, 1, 2] => 2, 2, 3, 2, 1, 1, 2, 1, 2
[2, 2, 3, 2, 1, 1, 2, 1, 3] => 2, 2, 3, 2, 1, 1, 2, 1, 3
[2, 2, 3, 2, 1, 1, 2, 2, 1] => 2, 2, 3, 2, 1, 1, 2, 2, 1
[2, 2, 3, 2, 1, 1, 2, 2, 2] => 2, 2, 3, 2, 1, 1, 2, 2, 2
[2, 2, 3, 2, 1, 1, 2, 2, 3] => 2, 2, 3, 2, 1, 1, 2, 2, 3
[2, 2, 3, 2, 1, 1, 2, 3, 1] => 2, 2, 3, 2, 1, 1, 2, 3, 1
[2, 2, 3, 2, 1, 1, 2, 3, 2] => 2, 2, 3, 2, 1, 1, 2, 3, 2
[2, 2, 3, 2, 1, 1, 2, 3, 3] => 2, 2, 3, 2, 1, 1, 2, 3, 3
[2, 2, 3, 2, 1, 1, 3, 1, 1] => 2, 2, 3, 2, 1, 1, 3, 1, 1
[2, 2, 3, 2, 1, 1, 3, 1, 2] => 2, 2, 3, 2, 1, 1, 3, 1, 2
[2, 2, 3, 2, 1, 1, 3, 1, 3] => 2, 2, 3, 2, 1, 1, 3, 1, 3
[2, 2, 3, 2, 1, 1, 3, 2, 1] => 2, 2, 3, 2, 1, 1, 3, 2, 1
[2, 2, 3, 2, 1, 1, 3, 2, 2] => 2, 2, 3, 2, 1, 1, 3, 2, 2
[2, 2, 3, 2, 1, 1, 3, 2, 3] => 2, 2, 3, 2, 1, 1, 3, 2, 3
[2, 2, 3, 2, 1, 1, 3, 3, 1] => 2, 2, 3, 2, 1, 1, 3, 3, 1
[2, 2, 3, 2, 1, 1, 3, 3, 2] => 2, 2, 3, 2, 1, 1, 3, 3, 2
[2, 2, 3, 2, 1, 1, 3, 3, 3] => 2, 2, 3, 2, 1, 1, 3, 3, 3
[2, 2, 3, 2, 1, 2, 1, 1, 1] => 2, 2, 3, 2, 1, 2, 1, 1, 1
[2, 2, 3, 2, 1, 2, 1, 1, 2] => 2, 2, 3, 2, 1, 2, 1, 1, 2
[2, 2, 3, 2, 1, 2, 1, 1, 3] => 2, 2, 3, 2, 1, 2, 1, 1, 3
[2, 2, 3, 2, 1, 2, 1, 2, 1] => 2, 2, 3, 2, 1, 2, 1, 2, 1
[2, 2, 3, 2, 1, 2, 1, 2, 2] => 2, 2, 3, 2, 1, 2, 1, 2, 2
[2, 2, 3, 2, 1, 2, 1, 2, 3] => 2, 2, 3, 2, 1, 2, 1, 2, 3
[2, 2, 3, 2, 1, 2, 1, 3, 1] => 2, 2, 3, 2, 1, 2, 1, 3, 1
[2, 2, 3, 2, 1, 2, 1, 3, 2] => 2, 2, 3, 2, 1, 2, 1, 3, 2
[2, 2, 3, 2, 1, 2, 1, 3, 3] => 2, 2, 3, 2, 1, 2, 1, 3, 3
[2, 2, 3, 2, 1, 2, 2, 1, 1] => 2, 2, 3, 2, 1, 2, 2, 1, 1
[2, 2, 3, 2, 1, 2, 2, 1, 2] => 2, 2, 3, 2, 1, 2, 2, 1, 2
[2, 2, 3, 2, 1, 2, 2, 1, 3] => 2, 2, 3, 2, 1, 2, 2, 1, 3
[2, 2, 3, 2, 1, 2, 2, 2, 1] => 2, 2, 3, 2, 1, 2, 2, 2, 1
[2, 2, 3, 2, 1, 2, 2, 2, 2] => 2, 2, 3, 2, 1, 2, 2, 2, 2
[2, 2, 3, 2, 1, 2, 2, 2, 3] => 2, 2, 3, 2, 1, 2, 2, 2, 3
[2, 2, 3, 2, 1, 2, 2, 3, 1] => 2, 2, 3, 2, 1, 2, 2, 3, 1
[2, 2, 3, 2, 1, 2, 2, 3, 2] => 2, 2, 3, 2, 1, 2, 2, 3, 2
[2, 2, 3, 2, 1, 2, 2, 3, 3] => 2, 2, 3, 2, 1, 2, 2, 3, 3
[2, 2, 3, 2, 1, 2, 3, 1, 1] => 2, 2, 3, 2, 1, 2, 3, 1, 1
[2, 2, 3, 2, 1, 2, 3, 1, 2] => 2, 2, 3, 2, 1, 2, 3, 1, 2
[2, 2, 3, 2, 1, 2, 3, 1, 3] => 2, 2, 3, 2, 1, 2, 3, 1, 3
[2, 2, 3, 2, 1, 2, 3, 2, 1] => 2, 2, 3, 2, 1, 2, 3, 2, 1
[2, 2, 3, 2, 1, 2, 3, 2, 2] => 2, 2, 3, 2, 1, 2, 3, 2, 2
[2, 2, 3, 2, 1, 2, 3, 2, 3] => 2, 2, 3, 2, 1, 2, 3, 2, 3
[2, 2, 3, 2, 1, 2, 3, 3, 1] => 2, 2, 3, 2, 1, 2, 3, 3, 1
[2, 2, 3, 2, 1, 2, 3, 3, 2] => 2, 2, 3, 2, 1, 2, 3, 3, 2
[2, 2, 3, 2, 1, 2, 3, 3, 3] => 2, 2, 3, 2, 1, 2, 3, 3, 3
[2, 2, 3, 2, 1, 3, 1, 1, 1] => 2, 2, 3, 2, 1, 3, 1, 1, 1
[2, 2, 3, 2, 1, 3, 1, 1, 2] => 2, 2, 3, 2, 1, 3, 1, 1, 2
[2, 2, 3, 2, 1, 3, 1, 1, 3] => 2, 2, 3, 2, 1, 3, 1, 1, 3
[2, 2, 3, 2, 1, 3, 1, 2, 1] => 2, 2, 3, 2, 1, 3, 1, 2, 1
[2, 2, 3, 2, 1, 3, 1, 2, 2] => 2, 2, 3, 2, 1, 3, 1, 2, 2
[2, 2, 3, 2, 1, 3, 1, 2, 3] => 2, 2, 3, 2, 1, 3, 1, 2, 3
[2, 2, 3, 2, 1, 3, 1, 3, 1] => 2, 2, 3, 2, 1, 3, 1, 3, 1
[2, 2, 3, 2, 1, 3, 1, 3, 2] => 2, 2, 3, 2, 1, 3, 1, 3, 2
[2, 2, 3, 2, 1, 3, 1, 3, 3] => 2, 2, 3, 2, 1, 3, 1, 3, 3
[2, 2, 3, 2, 1, 3, 2, 1, 1] => 2, 2, 3, 2, 1, 3, 2, 1, 1
[2, 2, 3, 2, 1, 3, 2, 1, 2] => 2, 2, 3, 2, 1, 3, 2, 1, 2
[2, 2, 3, 2, 1, 3, 2, 1, 3] => 2, 2, 3, 2, 1, 3, 2, 1, 3
[2, 2, 3, 2, 1, 3, 2, 2, 1] => 2, 2, 3, 2, 1, 3, 2, 2, 1
[2, 2, 3, 2, 1, 3, 2, 2, 2] => 2, 2, 3, 2, 1, 3, 2, 2, 2
[2, 2, 3, 2, 1, 3, 2, 2, 3] => 2, 2, 3, 2, 1, 3, 2, 2, 3
[2, 2, 3, 2, 1, 3, 2, 3, 1] => 2, 2, 3, 2, 1, 3, 2, 3, 1
[2, 2, 3, 2, 1, 3, 2, 3, 2] => 2, 2, 3, 2, 1, 3, 2, 3, 2
[2, 2, 3, 2, 1, 3, 2, 3, 3] => 2, 2, 3, 2, 1, 3, 2, 3, 3
[2, 2, 3, 2, 1, 3, 3, 1, 1] => 2, 2, 3, 2, 1, 3, 3, 1, 1
[2, 2, 3, 2, 1, 3, 3, 1, 2] => 2, 2, 3, 2, 1, 3, 3, 1, 2
[2, 2, 3, 2, 1, 3, 3, 1, 3] => 2, 2, 3, 2, 1, 3, 3, 1, 3
[2, 2, 3, 2, 1, 3, 3, 2, 1] => 2, 2, 3, 2, 1, 3, 3, 2, 1
[2, 2, 3, 2, 1, 3, 3, 2, 2] => 2, 2, 3, 2, 1, 3, 3, 2, 2
[2, 2, 3, 2, 1, 3, 3, 2, 3] => 2, 2, 3, 2, 1, 3, 3, 2, 3
[2, 2, 3, 2, 1, 3, 3, 3, 1] => 2, 2, 3, 2, 1, 3, 3, 3, 1
[2, 2, 3, 2, 1, 3, 3, 3, 2] => 2, 2, 3, 2, 1, 3, 3, 3, 2
[2, 2, 3, 2, 1, 3, 3, 3, 3] => 2, 2, 3, 2, 1, 3, 3, 3, 3
[2, 2, 3, 2, 2, 1, 1, 1, 1] => 2, 2, 3, 2, 2, 1, 1, 1, 1
[2, 2, 3, 2, 2, 1, 1, 1, 2] => 2, 2, 3, 2, 2, 1, 1, 1, 2
[2, 2, 3, 2, 2, 1, 1, 1, 3] => 2, 2, 3, 2, 2, 1, 1, 1, 3
[2, 2, 3, 2, 2, 1, 1, 2, 1] => 2, 2, 3, 2, 2, 1, 1, 2, 1
[2, 2, 3, 2, 2, 1, 1, 2, 2] => 2, 2, 3, 2, 2, 1, 1, 2, 2
[2, 2, 3, 2, 2, 1, 1, 2, 3] => 2, 2, 3, 2, 2, 1, 1, 2, 3
[2, 2, 3, 2, 2, 1, 1, 3, 1] => 2, 2, 3, 2, 2, 1, 1, 3, 1
[2, 2, 3, 2, 2, 1, 1, 3, 2] => 2, 2, 3, 2, 2, 1, 1, 3, 2
[2, 2, 3, 2, 2, 1, 1, 3, 3] => 2, 2, 3, 2, 2, 1, 1, 3, 3
[2, 2, 3, 2, 2, 1, 2, 1, 1] => 2, 2, 3, 2, 2, 1, 2, 1, 1
[2, 2, 3, 2, 2, 1, 2, 1, 2] => 2, 2, 3, 2, 2, 1, 2, 1, 2
[2, 2, 3, 2, 2, 1, 2, 1, 3] => 2, 2, 3, 2, 2, 1, 2, 1, 3
[2, 2, 3, 2, 2, 1, 2, 2, 1] => 2, 2, 3, 2, 2, 1, 2, 2, 1
[2, 2, 3, 2, 2, 1, 2, 2, 2] => 2, 2, 3, 2, 2, 1, 2, 2, 2
[2, 2, 3, 2, 2, 1, 2, 2, 3] => 2, 2, 3, 2, 2, 1, 2, 2, 3
[2, 2, 3, 2, 2, 1, 2, 3, 1] => 2, 2, 3, 2, 2, 1, 2, 3, 1
[2, 2, 3, 2, 2, 1, 2, 3, 2] => 2, 2, 3, 2, 2, 1, 2, 3, 2
[2, 2, 3, 2, 2, 1, 2, 3, 3] => 2, 2, 3, 2, 2, 1, 2, 3, 3
[2, 2, 3, 2, 2, 1, 3, 1, 1] => 2, 2, 3, 2, 2, 1, 3, 1, 1
[2, 2, 3, 2, 2, 1, 3, 1, 2] => 2, 2, 3, 2, 2, 1, 3, 1, 2
[2, 2, 3, 2, 2, 1, 3, 1, 3] => 2, 2, 3, 2, 2, 1, 3, 1, 3
[2, 2, 3, 2, 2, 1, 3, 2, 1] => 2, 2, 3, 2, 2, 1, 3, 2, 1
[2, 2, 3, 2, 2, 1, 3, 2, 2] => 2, 2, 3, 2, 2, 1, 3, 2, 2
[2, 2, 3, 2, 2, 1, 3, 2, 3] => 2, 2, 3, 2, 2, 1, 3, 2, 3
[2, 2, 3, 2, 2, 1, 3, 3, 1] => 2, 2, 3, 2, 2, 1, 3, 3, 1
[2, 2, 3, 2, 2, 1, 3, 3, 2] => 2, 2, 3, 2, 2, 1, 3, 3, 2
[2, 2, 3, 2, 2, 1, 3, 3, 3] => 2, 2, 3, 2, 2, 1, 3, 3, 3
[2, 2, 3, 2, 2, 2, 1, 1, 1] => 2, 2, 3, 2, 2, 2, 1, 1, 1
[2, 2, 3, 2, 2, 2, 1, 1, 2] => 2, 2, 3, 2, 2, 2, 1, 1, 2
[2, 2, 3, 2, 2, 2, 1, 1, 3] => 2, 2, 3, 2, 2, 2, 1, 1, 3
[2, 2, 3, 2, 2, 2, 1, 2, 1] => 2, 2, 3, 2, 2, 2, 1, 2, 1
[2, 2, 3, 2, 2, 2, 1, 2, 2] => 2, 2, 3, 2, 2, 2, 1, 2, 2
[2, 2, 3, 2, 2, 2, 1, 2, 3] => 2, 2, 3, 2, 2, 2, 1, 2, 3
[2, 2, 3, 2, 2, 2, 1, 3, 1] => 2, 2, 3, 2, 2, 2, 1, 3, 1
[2, 2, 3, 2, 2, 2, 1, 3, 2] => 2, 2, 3, 2, 2, 2, 1, 3, 2
[2, 2, 3, 2, 2, 2, 1, 3, 3] => 2, 2, 3, 2, 2, 2, 1, 3, 3
[2, 2, 3, 2, 2, 2, 2, 1, 1] => 2, 2, 3, 2, 2, 2, 2, 1, 1
[2, 2, 3, 2, 2, 2, 2, 1, 2] => 2, 2, 3, 2, 2, 2, 2, 1, 2
[2, 2, 3, 2, 2, 2, 2, 1, 3] => 2, 2, 3, 2, 2, 2, 2, 1, 3
[2, 2, 3, 2, 2, 2, 2, 2, 1] => 2, 2, 3, 2, 2, 2, 2, 2, 1
[2, 2, 3, 2, 2, 2, 2, 2, 2] => 2, 2, 3, 2, 2, 2, 2, 2, 2
[2, 2, 3, 2, 2, 2, 2, 2, 3] => 2, 2, 3, 2, 2, 2, 2, 2, 3
[2, 2, 3, 2, 2, 2, 2, 3, 1] => 2, 2, 3, 2, 2, 2, 2, 3, 1
[2, 2, 3, 2, 2, 2, 2, 3, 2] => 2, 2, 3, 2, 2, 2, 2, 3, 2
[2, 2, 3, 2, 2, 2, 2, 3, 3] => 2, 2, 3, 2, 2, 2, 2, 3, 3
[2, 2, 3, 2, 2, 2, 3, 1, 1] => 2, 2, 3, 2, 2, 2, 3, 1, 1
[2, 2, 3, 2, 2, 2, 3, 1, 2] => 2, 2, 3, 2, 2, 2, 3, 1, 2
[2, 2, 3, 2, 2, 2, 3, 1, 3] => 2, 2, 3, 2, 2, 2, 3, 1, 3
[2, 2, 3, 2, 2, 2, 3, 2, 1] => 2, 2, 3, 2, 2, 2, 3, 2, 1
[2, 2, 3, 2, 2, 2, 3, 2, 2] => 2, 2, 3, 2, 2, 2, 3, 2, 2
[2, 2, 3, 2, 2, 2, 3, 2, 3] => 2, 2, 3, 2, 2, 2, 3, 2, 3
[2, 2, 3, 2, 2, 2, 3, 3, 1] => 2, 2, 3, 2, 2, 2, 3, 3, 1
[2, 2, 3, 2, 2, 2, 3, 3, 2] => 2, 2, 3, 2, 2, 2, 3, 3, 2
[2, 2, 3, 2, 2, 2, 3, 3, 3] => 2, 2, 3, 2, 2, 2, 3, 3, 3
[2, 2, 3, 2, 2, 3, 1, 1, 1] => 2, 2, 3, 2, 2, 3, 1, 1, 1
[2, 2, 3, 2, 2, 3, 1, 1, 2] => 2, 2, 3, 2, 2, 3, 1, 1, 2
[2, 2, 3, 2, 2, 3, 1, 1, 3] => 2, 2, 3, 2, 2, 3, 1, 1, 3
[2, 2, 3, 2, 2, 3, 1, 2, 1] => 2, 2, 3, 2, 2, 3, 1, 2, 1
[2, 2, 3, 2, 2, 3, 1, 2, 2] => 2, 2, 3, 2, 2, 3, 1, 2, 2
[2, 2, 3, 2, 2, 3, 1, 2, 3] => 2, 2, 3, 2, 2, 3, 1, 2, 3
[2, 2, 3, 2, 2, 3, 1, 3, 1] => 2, 2, 3, 2, 2, 3, 1, 3, 1
[2, 2, 3, 2, 2, 3, 1, 3, 2] => 2, 2, 3, 2, 2, 3, 1, 3, 2
[2, 2, 3, 2, 2, 3, 1, 3, 3] => 2, 2, 3, 2, 2, 3, 1, 3, 3
[2, 2, 3, 2, 2, 3, 2, 1, 1] => 2, 2, 3, 2, 2, 3, 2, 1, 1
[2, 2, 3, 2, 2, 3, 2, 1, 2] => 2, 2, 3, 2, 2, 3, 2, 1, 2
[2, 2, 3, 2, 2, 3, 2, 1, 3] => 2, 2, 3, 2, 2, 3, 2, 1, 3
[2, 2, 3, 2, 2, 3, 2, 2, 1] => 2, 2, 3, 2, 2, 3, 2, 2, 1
[2, 2, 3, 2, 2, 3, 2, 2, 2] => 2, 2, 3, 2, 2, 3, 2, 2, 2
[2, 2, 3, 2, 2, 3, 2, 2, 3] => 2, 2, 3, 2, 2, 3, 2, 2, 3
[2, 2, 3, 2, 2, 3, 2, 3, 1] => 2, 2, 3, 2, 2, 3, 2, 3, 1
[2, 2, 3, 2, 2, 3, 2, 3, 2] => 2, 2, 3, 2, 2, 3, 2, 3, 2
[2, 2, 3, 2, 2, 3, 2, 3, 3] => 2, 2, 3, 2, 2, 3, 2, 3, 3
[2, 2, 3, 2, 2, 3, 3, 1, 1] => 2, 2, 3, 2, 2, 3, 3, 1, 1
[2, 2, 3, 2, 2, 3, 3, 1, 2] => 2, 2, 3, 2, 2, 3, 3, 1, 2
[2, 2, 3, 2, 2, 3, 3, 1, 3] => 2, 2, 3, 2, 2, 3, 3, 1, 3
[2, 2, 3, 2, 2, 3, 3, 2, 1] => 2, 2, 3, 2, 2, 3, 3, 2, 1
[2, 2, 3, 2, 2, 3, 3, 2, 2] => 2, 2, 3, 2, 2, 3, 3, 2, 2
[2, 2, 3, 2, 2, 3, 3, 2, 3] => 2, 2, 3, 2, 2, 3, 3, 2, 3
[2, 2, 3, 2, 2, 3, 3, 3, 1] => 2, 2, 3, 2, 2, 3, 3, 3, 1
[2, 2, 3, 2, 2, 3, 3, 3, 2] => 2, 2, 3, 2, 2, 3, 3, 3, 2
[2, 2, 3, 2, 2, 3, 3, 3, 3] => 2, 2, 3, 2, 2, 3, 3, 3, 3
[2, 2, 3, 2, 3, 1, 1, 1, 1] => 2, 2, 3, 2, 3, 1, 1, 1, 1
[2, 2, 3, 2, 3, 1, 1, 1, 2] => 2, 2, 3, 2, 3, 1, 1, 1, 2
[2, 2, 3, 2, 3, 1, 1, 1, 3] => 2, 2, 3, 2, 3, 1, 1, 1, 3
[2, 2, 3, 2, 3, 1, 1, 2, 1] => 2, 2, 3, 2, 3, 1, 1, 2, 1
[2, 2, 3, 2, 3, 1, 1, 2, 2] => 2, 2, 3, 2, 3, 1, 1, 2, 2
[2, 2, 3, 2, 3, 1, 1, 2, 3] => 2, 2, 3, 2, 3, 1, 1, 2, 3
[2, 2, 3, 2, 3, 1, 1, 3, 1] => 2, 2, 3, 2, 3, 1, 1, 3, 1
[2, 2, 3, 2, 3, 1, 1, 3, 2] => 2, 2, 3, 2, 3, 1, 1, 3, 2
[2, 2, 3, 2, 3, 1, 1, 3, 3] => 2, 2, 3, 2, 3, 1, 1, 3, 3
[2, 2, 3, 2, 3, 1, 2, 1, 1] => 2, 2, 3, 2, 3, 1, 2, 1, 1
[2, 2, 3, 2, 3, 1, 2, 1, 2] => 2, 2, 3, 2, 3, 1, 2, 1, 2
[2, 2, 3, 2, 3, 1, 2, 1, 3] => 2, 2, 3, 2, 3, 1, 2, 1, 3
[2, 2, 3, 2, 3, 1, 2, 2, 1] => 2, 2, 3, 2, 3, 1, 2, 2, 1
[2, 2, 3, 2, 3, 1, 2, 2, 2] => 2, 2, 3, 2, 3, 1, 2, 2, 2
[2, 2, 3, 2, 3, 1, 2, 2, 3] => 2, 2, 3, 2, 3, 1, 2, 2, 3
[2, 2, 3, 2, 3, 1, 2, 3, 1] => 2, 2, 3, 2, 3, 1, 2, 3, 1
[2, 2, 3, 2, 3, 1, 2, 3, 2] => 2, 2, 3, 2, 3, 1, 2, 3, 2
[2, 2, 3, 2, 3, 1, 2, 3, 3] => 2, 2, 3, 2, 3, 1, 2, 3, 3
[2, 2, 3, 2, 3, 1, 3, 1, 1] => 2, 2, 3, 2, 3, 1, 3, 1, 1
[2, 2, 3, 2, 3, 1, 3, 1, 2] => 2, 2, 3, 2, 3, 1, 3, 1, 2
[2, 2, 3, 2, 3, 1, 3, 1, 3] => 2, 2, 3, 2, 3, 1, 3, 1, 3
[2, 2, 3, 2, 3, 1, 3, 2, 1] => 2, 2, 3, 2, 3, 1, 3, 2, 1
[2, 2, 3, 2, 3, 1, 3, 2, 2] => 2, 2, 3, 2, 3, 1, 3, 2, 2
[2, 2, 3, 2, 3, 1, 3, 2, 3] => 2, 2, 3, 2, 3, 1, 3, 2, 3
[2, 2, 3, 2, 3, 1, 3, 3, 1] => 2, 2, 3, 2, 3, 1, 3, 3, 1
[2, 2, 3, 2, 3, 1, 3, 3, 2] => 2, 2, 3, 2, 3, 1, 3, 3, 2
[2, 2, 3, 2, 3, 1, 3, 3, 3] => 2, 2, 3, 2, 3, 1, 3, 3, 3
[2, 2, 3, 2, 3, 2, 1, 1, 1] => 2, 2, 3, 2, 3, 2, 1, 1, 1
[2, 2, 3, 2, 3, 2, 1, 1, 2] => 2, 2, 3, 2, 3, 2, 1, 1, 2
[2, 2, 3, 2, 3, 2, 1, 1, 3] => 2, 2, 3, 2, 3, 2, 1, 1, 3
[2, 2, 3, 2, 3, 2, 1, 2, 1] => 2, 2, 3, 2, 3, 2, 1, 2, 1
[2, 2, 3, 2, 3, 2, 1, 2, 2] => 2, 2, 3, 2, 3, 2, 1, 2, 2
[2, 2, 3, 2, 3, 2, 1, 2, 3] => 2, 2, 3, 2, 3, 2, 1, 2, 3
[2, 2, 3, 2, 3, 2, 1, 3, 1] => 2, 2, 3, 2, 3, 2, 1, 3, 1
[2, 2, 3, 2, 3, 2, 1, 3, 2] => 2, 2, 3, 2, 3, 2, 1, 3, 2
[2, 2, 3, 2, 3, 2, 1, 3, 3] => 2, 2, 3, 2, 3, 2, 1, 3, 3
[2, 2, 3, 2, 3, 2, 2, 1, 1] => 2, 2, 3, 2, 3, 2, 2, 1, 1
[2, 2, 3, 2, 3, 2, 2, 1, 2] => 2, 2, 3, 2, 3, 2, 2, 1, 2
[2, 2, 3, 2, 3, 2, 2, 1, 3] => 2, 2, 3, 2, 3, 2, 2, 1, 3
[2, 2, 3, 2, 3, 2, 2, 2, 1] => 2, 2, 3, 2, 3, 2, 2, 2, 1
[2, 2, 3, 2, 3, 2, 2, 2, 2] => 2, 2, 3, 2, 3, 2, 2, 2, 2
[2, 2, 3, 2, 3, 2, 2, 2, 3] => 2, 2, 3, 2, 3, 2, 2, 2, 3
[2, 2, 3, 2, 3, 2, 2, 3, 1] => 2, 2, 3, 2, 3, 2, 2, 3, 1
[2, 2, 3, 2, 3, 2, 2, 3, 2] => 2, 2, 3, 2, 3, 2, 2, 3, 2
[2, 2, 3, 2, 3, 2, 2, 3, 3] => 2, 2, 3, 2, 3, 2, 2, 3, 3
[2, 2, 3, 2, 3, 2, 3, 1, 1] => 2, 2, 3, 2, 3, 2, 3, 1, 1
[2, 2, 3, 2, 3, 2, 3, 1, 2] => 2, 2, 3, 2, 3, 2, 3, 1, 2
[2, 2, 3, 2, 3, 2, 3, 1, 3] => 2, 2, 3, 2, 3, 2, 3, 1, 3
[2, 2, 3, 2, 3, 2, 3, 2, 1] => 2, 2, 3, 2, 3, 2, 3, 2, 1
[2, 2, 3, 2, 3, 2, 3, 2, 2] => 2, 2, 3, 2, 3, 2, 3, 2, 2
[2, 2, 3, 2, 3, 2, 3, 2, 3] => 2, 2, 3, 2, 3, 2, 3, 2, 3
[2, 2, 3, 2, 3, 2, 3, 3, 1] => 2, 2, 3, 2, 3, 2, 3, 3, 1
[2, 2, 3, 2, 3, 2, 3, 3, 2] => 2, 2, 3, 2, 3, 2, 3, 3, 2
[2, 2, 3, 2, 3, 2, 3, 3, 3] => 2, 2, 3, 2, 3, 2, 3, 3, 3
[2, 2, 3, 2, 3, 3, 1, 1, 1] => 2, 2, 3, 2, 3, 3, 1, 1, 1
[2, 2, 3, 2, 3, 3, 1, 1, 2] => 2, 2, 3, 2, 3, 3, 1, 1, 2
[2, 2, 3, 2, 3, 3, 1, 1, 3] => 2, 2, 3, 2, 3, 3, 1, 1, 3
[2, 2, 3, 2, 3, 3, 1, 2, 1] => 2, 2, 3, 2, 3, 3, 1, 2, 1
[2, 2, 3, 2, 3, 3, 1, 2, 2] => 2, 2, 3, 2, 3, 3, 1, 2, 2
[2, 2, 3, 2, 3, 3, 1, 2, 3] => 2, 2, 3, 2, 3, 3, 1, 2, 3
[2, 2, 3, 2, 3, 3, 1, 3, 1] => 2, 2, 3, 2, 3, 3, 1, 3, 1
[2, 2, 3, 2, 3, 3, 1, 3, 2] => 2, 2, 3, 2, 3, 3, 1, 3, 2
[2, 2, 3, 2, 3, 3, 1, 3, 3] => 2, 2, 3, 2, 3, 3, 1, 3, 3
[2, 2, 3, 2, 3, 3, 2, 1, 1] => 2, 2, 3, 2, 3, 3, 2, 1, 1
[2, 2, 3, 2, 3, 3, 2, 1, 2] => 2, 2, 3, 2, 3, 3, 2, 1, 2
[2, 2, 3, 2, 3, 3, 2, 1, 3] => 2, 2, 3, 2, 3, 3, 2, 1, 3
[2, 2, 3, 2, 3, 3, 2, 2, 1] => 2, 2, 3, 2, 3, 3, 2, 2, 1
[2, 2, 3, 2, 3, 3, 2, 2, 2] => 2, 2, 3, 2, 3, 3, 2, 2, 2
[2, 2, 3, 2, 3, 3, 2, 2, 3] => 2, 2, 3, 2, 3, 3, 2, 2, 3
[2, 2, 3, 2, 3, 3, 2, 3, 1] => 2, 2, 3, 2, 3, 3, 2, 3, 1
[2, 2, 3, 2, 3, 3, 2, 3, 2] => 2, 2, 3, 2, 3, 3, 2, 3, 2
[2, 2, 3, 2, 3, 3, 2, 3, 3] => 2, 2, 3, 2, 3, 3, 2, 3, 3
[2, 2, 3, 2, 3, 3, 3, 1, 1] => 2, 2, 3, 2, 3, 3, 3, 1, 1
[2, 2, 3, 2, 3, 3, 3, 1, 2] => 2, 2, 3, 2, 3, 3, 3, 1, 2
[2, 2, 3, 2, 3, 3, 3, 1, 3] => 2, 2, 3, 2, 3, 3, 3, 1, 3
[2, 2, 3, 2, 3, 3, 3, 2, 1] => 2, 2, 3, 2, 3, 3, 3, 2, 1
[2, 2, 3, 2, 3, 3, 3, 2, 2] => 2, 2, 3, 2, 3, 3, 3, 2, 2
[2, 2, 3, 2, 3, 3, 3, 2, 3] => 2, 2, 3, 2, 3, 3, 3, 2, 3
[2, 2, 3, 2, 3, 3, 3, 3, 1] => 2, 2, 3, 2, 3, 3, 3, 3, 1
[2, 2, 3, 2, 3, 3, 3, 3, 2] => 2, 2, 3, 2, 3, 3, 3, 3, 2
[2, 2, 3, 2, 3, 3, 3, 3, 3] => 2, 2, 3, 2, 3, 3, 3, 3, 3
[2, 2, 3, 3, 1, 1, 1, 1, 1] => 2, 2, 3, 3, 1, 1, 1, 1, 1
[2, 2, 3, 3, 1, 1, 1, 1, 2] => 2, 2, 3, 3, 1, 1, 1, 1, 2
[2, 2, 3, 3, 1, 1, 1, 1, 3] => 2, 2, 3, 3, 1, 1, 1, 1, 3
[2, 2, 3, 3, 1, 1, 1, 2, 1] => 2, 2, 3, 3, 1, 1, 1, 2, 1
[2, 2, 3, 3, 1, 1, 1, 2, 2] => 2, 2, 3, 3, 1, 1, 1, 2, 2
[2, 2, 3, 3, 1, 1, 1, 2, 3] => 2, 2, 3, 3, 1, 1, 1, 2, 3
[2, 2, 3, 3, 1, 1, 1, 3, 1] => 2, 2, 3, 3, 1, 1, 1, 3, 1
[2, 2, 3, 3, 1, 1, 1, 3, 2] => 2, 2, 3, 3, 1, 1, 1, 3, 2
[2, 2, 3, 3, 1, 1, 1, 3, 3] => 2, 2, 3, 3, 1, 1, 1, 3, 3
[2, 2, 3, 3, 1, 1, 2, 1, 1] => 2, 2, 3, 3, 1, 1, 2, 1, 1
[2, 2, 3, 3, 1, 1, 2, 1, 2] => 2, 2, 3, 3, 1, 1, 2, 1, 2
[2, 2, 3, 3, 1, 1, 2, 1, 3] => 2, 2, 3, 3, 1, 1, 2, 1, 3
[2, 2, 3, 3, 1, 1, 2, 2, 1] => 2, 2, 3, 3, 1, 1, 2, 2, 1
[2, 2, 3, 3, 1, 1, 2, 2, 2] => 2, 2, 3, 3, 1, 1, 2, 2, 2
[2, 2, 3, 3, 1, 1, 2, 2, 3] => 2, 2, 3, 3, 1, 1, 2, 2, 3
[2, 2, 3, 3, 1, 1, 2, 3, 1] => 2, 2, 3, 3, 1, 1, 2, 3, 1
[2, 2, 3, 3, 1, 1, 2, 3, 2] => 2, 2, 3, 3, 1, 1, 2, 3, 2
[2, 2, 3, 3, 1, 1, 2, 3, 3] => 2, 2, 3, 3, 1, 1, 2, 3, 3
[2, 2, 3, 3, 1, 1, 3, 1, 1] => 2, 2, 3, 3, 1, 1, 3, 1, 1
[2, 2, 3, 3, 1, 1, 3, 1, 2] => 2, 2, 3, 3, 1, 1, 3, 1, 2
[2, 2, 3, 3, 1, 1, 3, 1, 3] => 2, 2, 3, 3, 1, 1, 3, 1, 3
[2, 2, 3, 3, 1, 1, 3, 2, 1] => 2, 2, 3, 3, 1, 1, 3, 2, 1
[2, 2, 3, 3, 1, 1, 3, 2, 2] => 2, 2, 3, 3, 1, 1, 3, 2, 2
[2, 2, 3, 3, 1, 1, 3, 2, 3] => 2, 2, 3, 3, 1, 1, 3, 2, 3
[2, 2, 3, 3, 1, 1, 3, 3, 1] => 2, 2, 3, 3, 1, 1, 3, 3, 1
[2, 2, 3, 3, 1, 1, 3, 3, 2] => 2, 2, 3, 3, 1, 1, 3, 3, 2
[2, 2, 3, 3, 1, 1, 3, 3, 3] => 2, 2, 3, 3, 1, 1, 3, 3, 3
[2, 2, 3, 3, 1, 2, 1, 1, 1] => 2, 2, 3, 3, 1, 2, 1, 1, 1
[2, 2, 3, 3, 1, 2, 1, 1, 2] => 2, 2, 3, 3, 1, 2, 1, 1, 2
[2, 2, 3, 3, 1, 2, 1, 1, 3] => 2, 2, 3, 3, 1, 2, 1, 1, 3
[2, 2, 3, 3, 1, 2, 1, 2, 1] => 2, 2, 3, 3, 1, 2, 1, 2, 1
[2, 2, 3, 3, 1, 2, 1, 2, 2] => 2, 2, 3, 3, 1, 2, 1, 2, 2
[2, 2, 3, 3, 1, 2, 1, 2, 3] => 2, 2, 3, 3, 1, 2, 1, 2, 3
[2, 2, 3, 3, 1, 2, 1, 3, 1] => 2, 2, 3, 3, 1, 2, 1, 3, 1
[2, 2, 3, 3, 1, 2, 1, 3, 2] => 2, 2, 3, 3, 1, 2, 1, 3, 2
[2, 2, 3, 3, 1, 2, 1, 3, 3] => 2, 2, 3, 3, 1, 2, 1, 3, 3
[2, 2, 3, 3, 1, 2, 2, 1, 1] => 2, 2, 3, 3, 1, 2, 2, 1, 1
[2, 2, 3, 3, 1, 2, 2, 1, 2] => 2, 2, 3, 3, 1, 2, 2, 1, 2
[2, 2, 3, 3, 1, 2, 2, 1, 3] => 2, 2, 3, 3, 1, 2, 2, 1, 3
[2, 2, 3, 3, 1, 2, 2, 2, 1] => 2, 2, 3, 3, 1, 2, 2, 2, 1
[2, 2, 3, 3, 1, 2, 2, 2, 2] => 2, 2, 3, 3, 1, 2, 2, 2, 2
[2, 2, 3, 3, 1, 2, 2, 2, 3] => 2, 2, 3, 3, 1, 2, 2, 2, 3
[2, 2, 3, 3, 1, 2, 2, 3, 1] => 2, 2, 3, 3, 1, 2, 2, 3, 1
[2, 2, 3, 3, 1, 2, 2, 3, 2] => 2, 2, 3, 3, 1, 2, 2, 3, 2
[2, 2, 3, 3, 1, 2, 2, 3, 3] => 2, 2, 3, 3, 1, 2, 2, 3, 3
[2, 2, 3, 3, 1, 2, 3, 1, 1] => 2, 2, 3, 3, 1, 2, 3, 1, 1
[2, 2, 3, 3, 1, 2, 3, 1, 2] => 2, 2, 3, 3, 1, 2, 3, 1, 2
[2, 2, 3, 3, 1, 2, 3, 1, 3] => 2, 2, 3, 3, 1, 2, 3, 1, 3
[2, 2, 3, 3, 1, 2, 3, 2, 1] => 2, 2, 3, 3, 1, 2, 3, 2, 1
[2, 2, 3, 3, 1, 2, 3, 2, 2] => 2, 2, 3, 3, 1, 2, 3, 2, 2
[2, 2, 3, 3, 1, 2, 3, 2, 3] => 2, 2, 3, 3, 1, 2, 3, 2, 3
[2, 2, 3, 3, 1, 2, 3, 3, 1] => 2, 2, 3, 3, 1, 2, 3, 3, 1
[2, 2, 3, 3, 1, 2, 3, 3, 2] => 2, 2, 3, 3, 1, 2, 3, 3, 2
[2, 2, 3, 3, 1, 2, 3, 3, 3] => 2, 2, 3, 3, 1, 2, 3, 3, 3
[2, 2, 3, 3, 1, 3, 1, 1, 1] => 2, 2, 3, 3, 1, 3, 1, 1, 1
[2, 2, 3, 3, 1, 3, 1, 1, 2] => 2, 2, 3, 3, 1, 3, 1, 1, 2
[2, 2, 3, 3, 1, 3, 1, 1, 3] => 2, 2, 3, 3, 1, 3, 1, 1, 3
[2, 2, 3, 3, 1, 3, 1, 2, 1] => 2, 2, 3, 3, 1, 3, 1, 2, 1
[2, 2, 3, 3, 1, 3, 1, 2, 2] => 2, 2, 3, 3, 1, 3, 1, 2, 2
[2, 2, 3, 3, 1, 3, 1, 2, 3] => 2, 2, 3, 3, 1, 3, 1, 2, 3
[2, 2, 3, 3, 1, 3, 1, 3, 1] => 2, 2, 3, 3, 1, 3, 1, 3, 1
[2, 2, 3, 3, 1, 3, 1, 3, 2] => 2, 2, 3, 3, 1, 3, 1, 3, 2
[2, 2, 3, 3, 1, 3, 1, 3, 3] => 2, 2, 3, 3, 1, 3, 1, 3, 3
[2, 2, 3, 3, 1, 3, 2, 1, 1] => 2, 2, 3, 3, 1, 3, 2, 1, 1
[2, 2, 3, 3, 1, 3, 2, 1, 2] => 2, 2, 3, 3, 1, 3, 2, 1, 2
[2, 2, 3, 3, 1, 3, 2, 1, 3] => 2, 2, 3, 3, 1, 3, 2, 1, 3
[2, 2, 3, 3, 1, 3, 2, 2, 1] => 2, 2, 3, 3, 1, 3, 2, 2, 1
[2, 2, 3, 3, 1, 3, 2, 2, 2] => 2, 2, 3, 3, 1, 3, 2, 2, 2
[2, 2, 3, 3, 1, 3, 2, 2, 3] => 2, 2, 3, 3, 1, 3, 2, 2, 3
[2, 2, 3, 3, 1, 3, 2, 3, 1] => 2, 2, 3, 3, 1, 3, 2, 3, 1
[2, 2, 3, 3, 1, 3, 2, 3, 2] => 2, 2, 3, 3, 1, 3, 2, 3, 2
[2, 2, 3, 3, 1, 3, 2, 3, 3] => 2, 2, 3, 3, 1, 3, 2, 3, 3
[2, 2, 3, 3, 1, 3, 3, 1, 1] => 2, 2, 3, 3, 1, 3, 3, 1, 1
[2, 2, 3, 3, 1, 3, 3, 1, 2] => 2, 2, 3, 3, 1, 3, 3, 1, 2
[2, 2, 3, 3, 1, 3, 3, 1, 3] => 2, 2, 3, 3, 1, 3, 3, 1, 3
[2, 2, 3, 3, 1, 3, 3, 2, 1] => 2, 2, 3, 3, 1, 3, 3, 2, 1
[2, 2, 3, 3, 1, 3, 3, 2, 2] => 2, 2, 3, 3, 1, 3, 3, 2, 2
[2, 2, 3, 3, 1, 3, 3, 2, 3] => 2, 2, 3, 3, 1, 3, 3, 2, 3
[2, 2, 3, 3, 1, 3, 3, 3, 1] => 2, 2, 3, 3, 1, 3, 3, 3, 1
[2, 2, 3, 3, 1, 3, 3, 3, 2] => 2, 2, 3, 3, 1, 3, 3, 3, 2
[2, 2, 3, 3, 1, 3, 3, 3, 3] => 2, 2, 3, 3, 1, 3, 3, 3, 3
[2, 2, 3, 3, 2, 1, 1, 1, 1] => 2, 2, 3, 3, 2, 1, 1, 1, 1
[2, 2, 3, 3, 2, 1, 1, 1, 2] => 2, 2, 3, 3, 2, 1, 1, 1, 2
[2, 2, 3, 3, 2, 1, 1, 1, 3] => 2, 2, 3, 3, 2, 1, 1, 1, 3
[2, 2, 3, 3, 2, 1, 1, 2, 1] => 2, 2, 3, 3, 2, 1, 1, 2, 1
[2, 2, 3, 3, 2, 1, 1, 2, 2] => 2, 2, 3, 3, 2, 1, 1, 2, 2
[2, 2, 3, 3, 2, 1, 1, 2, 3] => 2, 2, 3, 3, 2, 1, 1, 2, 3
[2, 2, 3, 3, 2, 1, 1, 3, 1] => 2, 2, 3, 3, 2, 1, 1, 3, 1
[2, 2, 3, 3, 2, 1, 1, 3, 2] => 2, 2, 3, 3, 2, 1, 1, 3, 2
[2, 2, 3, 3, 2, 1, 1, 3, 3] => 2, 2, 3, 3, 2, 1, 1, 3, 3
[2, 2, 3, 3, 2, 1, 2, 1, 1] => 2, 2, 3, 3, 2, 1, 2, 1, 1
[2, 2, 3, 3, 2, 1, 2, 1, 2] => 2, 2, 3, 3, 2, 1, 2, 1, 2
[2, 2, 3, 3, 2, 1, 2, 1, 3] => 2, 2, 3, 3, 2, 1, 2, 1, 3
[2, 2, 3, 3, 2, 1, 2, 2, 1] => 2, 2, 3, 3, 2, 1, 2, 2, 1
[2, 2, 3, 3, 2, 1, 2, 2, 2] => 2, 2, 3, 3, 2, 1, 2, 2, 2
[2, 2, 3, 3, 2, 1, 2, 2, 3] => 2, 2, 3, 3, 2, 1, 2, 2, 3
[2, 2, 3, 3, 2, 1, 2, 3, 1] => 2, 2, 3, 3, 2, 1, 2, 3, 1
[2, 2, 3, 3, 2, 1, 2, 3, 2] => 2, 2, 3, 3, 2, 1, 2, 3, 2
[2, 2, 3, 3, 2, 1, 2, 3, 3] => 2, 2, 3, 3, 2, 1, 2, 3, 3
[2, 2, 3, 3, 2, 1, 3, 1, 1] => 2, 2, 3, 3, 2, 1, 3, 1, 1
[2, 2, 3, 3, 2, 1, 3, 1, 2] => 2, 2, 3, 3, 2, 1, 3, 1, 2
[2, 2, 3, 3, 2, 1, 3, 1, 3] => 2, 2, 3, 3, 2, 1, 3, 1, 3
[2, 2, 3, 3, 2, 1, 3, 2, 1] => 2, 2, 3, 3, 2, 1, 3, 2, 1
[2, 2, 3, 3, 2, 1, 3, 2, 2] => 2, 2, 3, 3, 2, 1, 3, 2, 2
[2, 2, 3, 3, 2, 1, 3, 2, 3] => 2, 2, 3, 3, 2, 1, 3, 2, 3
[2, 2, 3, 3, 2, 1, 3, 3, 1] => 2, 2, 3, 3, 2, 1, 3, 3, 1
[2, 2, 3, 3, 2, 1, 3, 3, 2] => 2, 2, 3, 3, 2, 1, 3, 3, 2
[2, 2, 3, 3, 2, 1, 3, 3, 3] => 2, 2, 3, 3, 2, 1, 3, 3, 3
[2, 2, 3, 3, 2, 2, 1, 1, 1] => 2, 2, 3, 3, 2, 2, 1, 1, 1
[2, 2, 3, 3, 2, 2, 1, 1, 2] => 2, 2, 3, 3, 2, 2, 1, 1, 2
[2, 2, 3, 3, 2, 2, 1, 1, 3] => 2, 2, 3, 3, 2, 2, 1, 1, 3
[2, 2, 3, 3, 2, 2, 1, 2, 1] => 2, 2, 3, 3, 2, 2, 1, 2, 1
[2, 2, 3, 3, 2, 2, 1, 2, 2] => 2, 2, 3, 3, 2, 2, 1, 2, 2
[2, 2, 3, 3, 2, 2, 1, 2, 3] => 2, 2, 3, 3, 2, 2, 1, 2, 3
[2, 2, 3, 3, 2, 2, 1, 3, 1] => 2, 2, 3, 3, 2, 2, 1, 3, 1
[2, 2, 3, 3, 2, 2, 1, 3, 2] => 2, 2, 3, 3, 2, 2, 1, 3, 2
[2, 2, 3, 3, 2, 2, 1, 3, 3] => 2, 2, 3, 3, 2, 2, 1, 3, 3
[2, 2, 3, 3, 2, 2, 2, 1, 1] => 2, 2, 3, 3, 2, 2, 2, 1, 1
[2, 2, 3, 3, 2, 2, 2, 1, 2] => 2, 2, 3, 3, 2, 2, 2, 1, 2
[2, 2, 3, 3, 2, 2, 2, 1, 3] => 2, 2, 3, 3, 2, 2, 2, 1, 3
[2, 2, 3, 3, 2, 2, 2, 2, 1] => 2, 2, 3, 3, 2, 2, 2, 2, 1
[2, 2, 3, 3, 2, 2, 2, 2, 2] => 2, 2, 3, 3, 2, 2, 2, 2, 2
[2, 2, 3, 3, 2, 2, 2, 2, 3] => 2, 2, 3, 3, 2, 2, 2, 2, 3
[2, 2, 3, 3, 2, 2, 2, 3, 1] => 2, 2, 3, 3, 2, 2, 2, 3, 1
[2, 2, 3, 3, 2, 2, 2, 3, 2] => 2, 2, 3, 3, 2, 2, 2, 3, 2
[2, 2, 3, 3, 2, 2, 2, 3, 3] => 2, 2, 3, 3, 2, 2, 2, 3, 3
[2, 2, 3, 3, 2, 2, 3, 1, 1] => 2, 2, 3, 3, 2, 2, 3, 1, 1
[2, 2, 3, 3, 2, 2, 3, 1, 2] => 2, 2, 3, 3, 2, 2, 3, 1, 2
[2, 2, 3, 3, 2, 2, 3, 1, 3] => 2, 2, 3, 3, 2, 2, 3, 1, 3
[2, 2, 3, 3, 2, 2, 3, 2, 1] => 2, 2, 3, 3, 2, 2, 3, 2, 1
[2, 2, 3, 3, 2, 2, 3, 2, 2] => 2, 2, 3, 3, 2, 2, 3, 2, 2
[2, 2, 3, 3, 2, 2, 3, 2, 3] => 2, 2, 3, 3, 2, 2, 3, 2, 3
[2, 2, 3, 3, 2, 2, 3, 3, 1] => 2, 2, 3, 3, 2, 2, 3, 3, 1
[2, 2, 3, 3, 2, 2, 3, 3, 2] => 2, 2, 3, 3, 2, 2, 3, 3, 2
[2, 2, 3, 3, 2, 2, 3, 3, 3] => 2, 2, 3, 3, 2, 2, 3, 3, 3
[2, 2, 3, 3, 2, 3, 1, 1, 1] => 2, 2, 3, 3, 2, 3, 1, 1, 1
[2, 2, 3, 3, 2, 3, 1, 1, 2] => 2, 2, 3, 3, 2, 3, 1, 1, 2
[2, 2, 3, 3, 2, 3, 1, 1, 3] => 2, 2, 3, 3, 2, 3, 1, 1, 3
[2, 2, 3, 3, 2, 3, 1, 2, 1] => 2, 2, 3, 3, 2, 3, 1, 2, 1
[2, 2, 3, 3, 2, 3, 1, 2, 2] => 2, 2, 3, 3, 2, 3, 1, 2, 2
[2, 2, 3, 3, 2, 3, 1, 2, 3] => 2, 2, 3, 3, 2, 3, 1, 2, 3
[2, 2, 3, 3, 2, 3, 1, 3, 1] => 2, 2, 3, 3, 2, 3, 1, 3, 1
[2, 2, 3, 3, 2, 3, 1, 3, 2] => 2, 2, 3, 3, 2, 3, 1, 3, 2
[2, 2, 3, 3, 2, 3, 1, 3, 3] => 2, 2, 3, 3, 2, 3, 1, 3, 3
[2, 2, 3, 3, 2, 3, 2, 1, 1] => 2, 2, 3, 3, 2, 3, 2, 1, 1
[2, 2, 3, 3, 2, 3, 2, 1, 2] => 2, 2, 3, 3, 2, 3, 2, 1, 2
[2, 2, 3, 3, 2, 3, 2, 1, 3] => 2, 2, 3, 3, 2, 3, 2, 1, 3
[2, 2, 3, 3, 2, 3, 2, 2, 1] => 2, 2, 3, 3, 2, 3, 2, 2, 1
[2, 2, 3, 3, 2, 3, 2, 2, 2] => 2, 2, 3, 3, 2, 3, 2, 2, 2
[2, 2, 3, 3, 2, 3, 2, 2, 3] => 2, 2, 3, 3, 2, 3, 2, 2, 3
[2, 2, 3, 3, 2, 3, 2, 3, 1] => 2, 2, 3, 3, 2, 3, 2, 3, 1
[2, 2, 3, 3, 2, 3, 2, 3, 2] => 2, 2, 3, 3, 2, 3, 2, 3, 2
[2, 2, 3, 3, 2, 3, 2, 3, 3] => 2, 2, 3, 3, 2, 3, 2, 3, 3
[2, 2, 3, 3, 2, 3, 3, 1, 1] => 2, 2, 3, 3, 2, 3, 3, 1, 1
[2, 2, 3, 3, 2, 3, 3, 1, 2] => 2, 2, 3, 3, 2, 3, 3, 1, 2
[2, 2, 3, 3, 2, 3, 3, 1, 3] => 2, 2, 3, 3, 2, 3, 3, 1, 3
[2, 2, 3, 3, 2, 3, 3, 2, 1] => 2, 2, 3, 3, 2, 3, 3, 2, 1
[2, 2, 3, 3, 2, 3, 3, 2, 2] => 2, 2, 3, 3, 2, 3, 3, 2, 2
[2, 2, 3, 3, 2, 3, 3, 2, 3] => 2, 2, 3, 3, 2, 3, 3, 2, 3
[2, 2, 3, 3, 2, 3, 3, 3, 1] => 2, 2, 3, 3, 2, 3, 3, 3, 1
[2, 2, 3, 3, 2, 3, 3, 3, 2] => 2, 2, 3, 3, 2, 3, 3, 3, 2
[2, 2, 3, 3, 2, 3, 3, 3, 3] => 2, 2, 3, 3, 2, 3, 3, 3, 3
[2, 2, 3, 3, 3, 1, 1, 1, 1] => 2, 2, 3, 3, 3, 1, 1, 1, 1
[2, 2, 3, 3, 3, 1, 1, 1, 2] => 2, 2, 3, 3, 3, 1, 1, 1, 2
[2, 2, 3, 3, 3, 1, 1, 1, 3] => 2, 2, 3, 3, 3, 1, 1, 1, 3
[2, 2, 3, 3, 3, 1, 1, 2, 1] => 2, 2, 3, 3, 3, 1, 1, 2, 1
[2, 2, 3, 3, 3, 1, 1, 2, 2] => 2, 2, 3, 3, 3, 1, 1, 2, 2
[2, 2, 3, 3, 3, 1, 1, 2, 3] => 2, 2, 3, 3, 3, 1, 1, 2, 3
[2, 2, 3, 3, 3, 1, 1, 3, 1] => 2, 2, 3, 3, 3, 1, 1, 3, 1
[2, 2, 3, 3, 3, 1, 1, 3, 2] => 2, 2, 3, 3, 3, 1, 1, 3, 2
[2, 2, 3, 3, 3, 1, 1, 3, 3] => 2, 2, 3, 3, 3, 1, 1, 3, 3
[2, 2, 3, 3, 3, 1, 2, 1, 1] => 2, 2, 3, 3, 3, 1, 2, 1, 1
[2, 2, 3, 3, 3, 1, 2, 1, 2] => 2, 2, 3, 3, 3, 1, 2, 1, 2
[2, 2, 3, 3, 3, 1, 2, 1, 3] => 2, 2, 3, 3, 3, 1, 2, 1, 3
[2, 2, 3, 3, 3, 1, 2, 2, 1] => 2, 2, 3, 3, 3, 1, 2, 2, 1
[2, 2, 3, 3, 3, 1, 2, 2, 2] => 2, 2, 3, 3, 3, 1, 2, 2, 2
[2, 2, 3, 3, 3, 1, 2, 2, 3] => 2, 2, 3, 3, 3, 1, 2, 2, 3
[2, 2, 3, 3, 3, 1, 2, 3, 1] => 2, 2, 3, 3, 3, 1, 2, 3, 1
[2, 2, 3, 3, 3, 1, 2, 3, 2] => 2, 2, 3, 3, 3, 1, 2, 3, 2
[2, 2, 3, 3, 3, 1, 2, 3, 3] => 2, 2, 3, 3, 3, 1, 2, 3, 3
[2, 2, 3, 3, 3, 1, 3, 1, 1] => 2, 2, 3, 3, 3, 1, 3, 1, 1
[2, 2, 3, 3, 3, 1, 3, 1, 2] => 2, 2, 3, 3, 3, 1, 3, 1, 2
[2, 2, 3, 3, 3, 1, 3, 1, 3] => 2, 2, 3, 3, 3, 1, 3, 1, 3
[2, 2, 3, 3, 3, 1, 3, 2, 1] => 2, 2, 3, 3, 3, 1, 3, 2, 1
[2, 2, 3, 3, 3, 1, 3, 2, 2] => 2, 2, 3, 3, 3, 1, 3, 2, 2
[2, 2, 3, 3, 3, 1, 3, 2, 3] => 2, 2, 3, 3, 3, 1, 3, 2, 3
[2, 2, 3, 3, 3, 1, 3, 3, 1] => 2, 2, 3, 3, 3, 1, 3, 3, 1
[2, 2, 3, 3, 3, 1, 3, 3, 2] => 2, 2, 3, 3, 3, 1, 3, 3, 2
[2, 2, 3, 3, 3, 1, 3, 3, 3] => 2, 2, 3, 3, 3, 1, 3, 3, 3
[2, 2, 3, 3, 3, 2, 1, 1, 1] => 2, 2, 3, 3, 3, 2, 1, 1, 1
[2, 2, 3, 3, 3, 2, 1, 1, 2] => 2, 2, 3, 3, 3, 2, 1, 1, 2
[2, 2, 3, 3, 3, 2, 1, 1, 3] => 2, 2, 3, 3, 3, 2, 1, 1, 3
[2, 2, 3, 3, 3, 2, 1, 2, 1] => 2, 2, 3, 3, 3, 2, 1, 2, 1
[2, 2, 3, 3, 3, 2, 1, 2, 2] => 2, 2, 3, 3, 3, 2, 1, 2, 2
[2, 2, 3, 3, 3, 2, 1, 2, 3] => 2, 2, 3, 3, 3, 2, 1, 2, 3
[2, 2, 3, 3, 3, 2, 1, 3, 1] => 2, 2, 3, 3, 3, 2, 1, 3, 1
[2, 2, 3, 3, 3, 2, 1, 3, 2] => 2, 2, 3, 3, 3, 2, 1, 3, 2
[2, 2, 3, 3, 3, 2, 1, 3, 3] => 2, 2, 3, 3, 3, 2, 1, 3, 3
[2, 2, 3, 3, 3, 2, 2, 1, 1] => 2, 2, 3, 3, 3, 2, 2, 1, 1
[2, 2, 3, 3, 3, 2, 2, 1, 2] => 2, 2, 3, 3, 3, 2, 2, 1, 2
[2, 2, 3, 3, 3, 2, 2, 1, 3] => 2, 2, 3, 3, 3, 2, 2, 1, 3
[2, 2, 3, 3, 3, 2, 2, 2, 1] => 2, 2, 3, 3, 3, 2, 2, 2, 1
[2, 2, 3, 3, 3, 2, 2, 2, 2] => 2, 2, 3, 3, 3, 2, 2, 2, 2
[2, 2, 3, 3, 3, 2, 2, 2, 3] => 2, 2, 3, 3, 3, 2, 2, 2, 3
[2, 2, 3, 3, 3, 2, 2, 3, 1] => 2, 2, 3, 3, 3, 2, 2, 3, 1
[2, 2, 3, 3, 3, 2, 2, 3, 2] => 2, 2, 3, 3, 3, 2, 2, 3, 2
[2, 2, 3, 3, 3, 2, 2, 3, 3] => 2, 2, 3, 3, 3, 2, 2, 3, 3
[2, 2, 3, 3, 3, 2, 3, 1, 1] => 2, 2, 3, 3, 3, 2, 3, 1, 1
[2, 2, 3, 3, 3, 2, 3, 1, 2] => 2, 2, 3, 3, 3, 2, 3, 1, 2
[2, 2, 3, 3, 3, 2, 3, 1, 3] => 2, 2, 3, 3, 3, 2, 3, 1, 3
[2, 2, 3, 3, 3, 2, 3, 2, 1] => 2, 2, 3, 3, 3, 2, 3, 2, 1
[2, 2, 3, 3, 3, 2, 3, 2, 2] => 2, 2, 3, 3, 3, 2, 3, 2, 2
[2, 2, 3, 3, 3, 2, 3, 2, 3] => 2, 2, 3, 3, 3, 2, 3, 2, 3
[2, 2, 3, 3, 3, 2, 3, 3, 1] => 2, 2, 3, 3, 3, 2, 3, 3, 1
[2, 2, 3, 3, 3, 2, 3, 3, 2] => 2, 2, 3, 3, 3, 2, 3, 3, 2
[2, 2, 3, 3, 3, 2, 3, 3, 3] => 2, 2, 3, 3, 3, 2, 3, 3, 3
[2, 2, 3, 3, 3, 3, 1, 1, 1] => 2, 2, 3, 3, 3, 3, 1, 1, 1
[2, 2, 3, 3, 3, 3, 1, 1, 2] => 2, 2, 3, 3, 3, 3, 1, 1, 2
[2, 2, 3, 3, 3, 3, 1, 1, 3] => 2, 2, 3, 3, 3, 3, 1, 1, 3
[2, 2, 3, 3, 3, 3, 1, 2, 1] => 2, 2, 3, 3, 3, 3, 1, 2, 1
[2, 2, 3, 3, 3, 3, 1, 2, 2] => 2, 2, 3, 3, 3, 3, 1, 2, 2
[2, 2, 3, 3, 3, 3, 1, 2, 3] => 2, 2, 3, 3, 3, 3, 1, 2, 3
[2, 2, 3, 3, 3, 3, 1, 3, 1] => 2, 2, 3, 3, 3, 3, 1, 3, 1
[2, 2, 3, 3, 3, 3, 1, 3, 2] => 2, 2, 3, 3, 3, 3, 1, 3, 2
[2, 2, 3, 3, 3, 3, 1, 3, 3] => 2, 2, 3, 3, 3, 3, 1, 3, 3
[2, 2, 3, 3, 3, 3, 2, 1, 1] => 2, 2, 3, 3, 3, 3, 2, 1, 1
[2, 2, 3, 3, 3, 3, 2, 1, 2] => 2, 2, 3, 3, 3, 3, 2, 1, 2
[2, 2, 3, 3, 3, 3, 2, 1, 3] => 2, 2, 3, 3, 3, 3, 2, 1, 3
[2, 2, 3, 3, 3, 3, 2, 2, 1] => 2, 2, 3, 3, 3, 3, 2, 2, 1
[2, 2, 3, 3, 3, 3, 2, 2, 2] => 2, 2, 3, 3, 3, 3, 2, 2, 2
[2, 2, 3, 3, 3, 3, 2, 2, 3] => 2, 2, 3, 3, 3, 3, 2, 2, 3
[2, 2, 3, 3, 3, 3, 2, 3, 1] => 2, 2, 3, 3, 3, 3, 2, 3, 1
[2, 2, 3, 3, 3, 3, 2, 3, 2] => 2, 2, 3, 3, 3, 3, 2, 3, 2
[2, 2, 3, 3, 3, 3, 2, 3, 3] => 2, 2, 3, 3, 3, 3, 2, 3, 3
[2, 2, 3, 3, 3, 3, 3, 1, 1] => 2, 2, 3, 3, 3, 3, 3, 1, 1
[2, 2, 3, 3, 3, 3, 3, 1, 2] => 2, 2, 3, 3, 3, 3, 3, 1, 2
[2, 2, 3, 3, 3, 3, 3, 1, 3] => 2, 2, 3, 3, 3, 3, 3, 1, 3
[2, 2, 3, 3, 3, 3, 3, 2, 1] => 2, 2, 3, 3, 3, 3, 3, 2, 1
[2, 2, 3, 3, 3, 3, 3, 2, 2] => 2, 2, 3, 3, 3, 3, 3, 2, 2
[2, 2, 3, 3, 3, 3, 3, 2, 3] => 2, 2, 3, 3, 3, 3, 3, 2, 3
[2, 2, 3, 3, 3, 3, 3, 3, 1] => 2, 2, 3, 3, 3, 3, 3, 3, 1
[2, 2, 3, 3, 3, 3, 3, 3, 2] => 2, 2, 3, 3, 3, 3, 3, 3, 2
[2, 2, 3, 3, 3, 3, 3, 3, 3] => 2, 2, 3, 3, 3, 3, 3, 3, 3
[2, 3, 1, 1, 1, 1, 1, 1, 1] => 2, 3, 1, 1, 1, 1, 1, 1, 1
[2, 3, 1, 1, 1, 1, 1, 1, 2] => 2, 3, 1, 1, 1, 1, 1, 1, 2
[2, 3, 1, 1, 1, 1, 1, 1, 3] => 2, 3, 1, 1, 1, 1, 1, 1, 3
[2, 3, 1, 1, 1, 1, 1, 2, 1] => 2, 3, 1, 1, 1, 1, 1, 2, 1
[2, 3, 1, 1, 1, 1, 1, 2, 2] => 2, 3, 1, 1, 1, 1, 1, 2, 2
[2, 3, 1, 1, 1, 1, 1, 2, 3] => 2, 3, 1, 1, 1, 1, 1, 2, 3
[2, 3, 1, 1, 1, 1, 1, 3, 1] => 2, 3, 1, 1, 1, 1, 1, 3, 1
[2, 3, 1, 1, 1, 1, 1, 3, 2] => 2, 3, 1, 1, 1, 1, 1, 3, 2
[2, 3, 1, 1, 1, 1, 1, 3, 3] => 2, 3, 1, 1, 1, 1, 1, 3, 3
[2, 3, 1, 1, 1, 1, 2, 1, 1] => 2, 3, 1, 1, 1, 1, 2, 1, 1
[2, 3, 1, 1, 1, 1, 2, 1, 2] => 2, 3, 1, 1, 1, 1, 2, 1, 2
[2, 3, 1, 1, 1, 1, 2, 1, 3] => 2, 3, 1, 1, 1, 1, 2, 1, 3
[2, 3, 1, 1, 1, 1, 2, 2, 1] => 2, 3, 1, 1, 1, 1, 2, 2, 1
[2, 3, 1, 1, 1, 1, 2, 2, 2] => 2, 3, 1, 1, 1, 1, 2, 2, 2
[2, 3, 1, 1, 1, 1, 2, 2, 3] => 2, 3, 1, 1, 1, 1, 2, 2, 3
[2, 3, 1, 1, 1, 1, 2, 3, 1] => 2, 3, 1, 1, 1, 1, 2, 3, 1
[2, 3, 1, 1, 1, 1, 2, 3, 2] => 2, 3, 1, 1, 1, 1, 2, 3, 2
[2, 3, 1, 1, 1, 1, 2, 3, 3] => 2, 3, 1, 1, 1, 1, 2, 3, 3
[2, 3, 1, 1, 1, 1, 3, 1, 1] => 2, 3, 1, 1, 1, 1, 3, 1, 1
[2, 3, 1, 1, 1, 1, 3, 1, 2] => 2, 3, 1, 1, 1, 1, 3, 1, 2
[2, 3, 1, 1, 1, 1, 3, 1, 3] => 2, 3, 1, 1, 1, 1, 3, 1, 3
[2, 3, 1, 1, 1, 1, 3, 2, 1] => 2, 3, 1, 1, 1, 1, 3, 2, 1
[2, 3, 1, 1, 1, 1, 3, 2, 2] => 2, 3, 1, 1, 1, 1, 3, 2, 2
[2, 3, 1, 1, 1, 1, 3, 2, 3] => 2, 3, 1, 1, 1, 1, 3, 2, 3
[2, 3, 1, 1, 1, 1, 3, 3, 1] => 2, 3, 1, 1, 1, 1, 3, 3, 1
[2, 3, 1, 1, 1, 1, 3, 3, 2] => 2, 3, 1, 1, 1, 1, 3, 3, 2
[2, 3, 1, 1, 1, 1, 3, 3, 3] => 2, 3, 1, 1, 1, 1, 3, 3, 3
[2, 3, 1, 1, 1, 2, 1, 1, 1] => 2, 3, 1, 1, 1, 2, 1, 1, 1
[2, 3, 1, 1, 1, 2, 1, 1, 2] => 2, 3, 1, 1, 1, 2, 1, 1, 2
[2, 3, 1, 1, 1, 2, 1, 1, 3] => 2, 3, 1, 1, 1, 2, 1, 1, 3
[2, 3, 1, 1, 1, 2, 1, 2, 1] => 2, 3, 1, 1, 1, 2, 1, 2, 1
[2, 3, 1, 1, 1, 2, 1, 2, 2] => 2, 3, 1, 1, 1, 2, 1, 2, 2
[2, 3, 1, 1, 1, 2, 1, 2, 3] => 2, 3, 1, 1, 1, 2, 1, 2, 3
[2, 3, 1, 1, 1, 2, 1, 3, 1] => 2, 3, 1, 1, 1, 2, 1, 3, 1
[2, 3, 1, 1, 1, 2, 1, 3, 2] => 2, 3, 1, 1, 1, 2, 1, 3, 2
[2, 3, 1, 1, 1, 2, 1, 3, 3] => 2, 3, 1, 1, 1, 2, 1, 3, 3
[2, 3, 1, 1, 1, 2, 2, 1, 1] => 2, 3, 1, 1, 1, 2, 2, 1, 1
[2, 3, 1, 1, 1, 2, 2, 1, 2] => 2, 3, 1, 1, 1, 2, 2, 1, 2
[2, 3, 1, 1, 1, 2, 2, 1, 3] => 2, 3, 1, 1, 1, 2, 2, 1, 3
[2, 3, 1, 1, 1, 2, 2, 2, 1] => 2, 3, 1, 1, 1, 2, 2, 2, 1
[2, 3, 1, 1, 1, 2, 2, 2, 2] => 2, 3, 1, 1, 1, 2, 2, 2, 2
[2, 3, 1, 1, 1, 2, 2, 2, 3] => 2, 3, 1, 1, 1, 2, 2, 2, 3
[2, 3, 1, 1, 1, 2, 2, 3, 1] => 2, 3, 1, 1, 1, 2, 2, 3, 1
[2, 3, 1, 1, 1, 2, 2, 3, 2] => 2, 3, 1, 1, 1, 2, 2, 3, 2
[2, 3, 1, 1, 1, 2, 2, 3, 3] => 2, 3, 1, 1, 1, 2, 2, 3, 3
[2, 3, 1, 1, 1, 2, 3, 1, 1] => 2, 3, 1, 1, 1, 2, 3, 1, 1
[2, 3, 1, 1, 1, 2, 3, 1, 2] => 2, 3, 1, 1, 1, 2, 3, 1, 2
[2, 3, 1, 1, 1, 2, 3, 1, 3] => 2, 3, 1, 1, 1, 2, 3, 1, 3
[2, 3, 1, 1, 1, 2, 3, 2, 1] => 2, 3, 1, 1, 1, 2, 3, 2, 1
[2, 3, 1, 1, 1, 2, 3, 2, 2] => 2, 3, 1, 1, 1, 2, 3, 2, 2
[2, 3, 1, 1, 1, 2, 3, 2, 3] => 2, 3, 1, 1, 1, 2, 3, 2, 3
[2, 3, 1, 1, 1, 2, 3, 3, 1] => 2, 3, 1, 1, 1, 2, 3, 3, 1
[2, 3, 1, 1, 1, 2, 3, 3, 2] => 2, 3, 1, 1, 1, 2, 3, 3, 2
[2, 3, 1, 1, 1, 2, 3, 3, 3] => 2, 3, 1, 1, 1, 2, 3, 3, 3
[2, 3, 1, 1, 1, 3, 1, 1, 1] => 2, 3, 1, 1, 1, 3, 1, 1, 1
[2, 3, 1, 1, 1, 3, 1, 1, 2] => 2, 3, 1, 1, 1, 3, 1, 1, 2
[2, 3, 1, 1, 1, 3, 1, 1, 3] => 2, 3, 1, 1, 1, 3, 1, 1, 3
[2, 3, 1, 1, 1, 3, 1, 2, 1] => 2, 3, 1, 1, 1, 3, 1, 2, 1
[2, 3, 1, 1, 1, 3, 1, 2, 2] => 2, 3, 1, 1, 1, 3, 1, 2, 2
[2, 3, 1, 1, 1, 3, 1, 2, 3] => 2, 3, 1, 1, 1, 3, 1, 2, 3
[2, 3, 1, 1, 1, 3, 1, 3, 1] => 2, 3, 1, 1, 1, 3, 1, 3, 1
[2, 3, 1, 1, 1, 3, 1, 3, 2] => 2, 3, 1, 1, 1, 3, 1, 3, 2
[2, 3, 1, 1, 1, 3, 1, 3, 3] => 2, 3, 1, 1, 1, 3, 1, 3, 3
[2, 3, 1, 1, 1, 3, 2, 1, 1] => 2, 3, 1, 1, 1, 3, 2, 1, 1
[2, 3, 1, 1, 1, 3, 2, 1, 2] => 2, 3, 1, 1, 1, 3, 2, 1, 2
[2, 3, 1, 1, 1, 3, 2, 1, 3] => 2, 3, 1, 1, 1, 3, 2, 1, 3
[2, 3, 1, 1, 1, 3, 2, 2, 1] => 2, 3, 1, 1, 1, 3, 2, 2, 1
[2, 3, 1, 1, 1, 3, 2, 2, 2] => 2, 3, 1, 1, 1, 3, 2, 2, 2
[2, 3, 1, 1, 1, 3, 2, 2, 3] => 2, 3, 1, 1, 1, 3, 2, 2, 3
[2, 3, 1, 1, 1, 3, 2, 3, 1] => 2, 3, 1, 1, 1, 3, 2, 3, 1
[2, 3, 1, 1, 1, 3, 2, 3, 2] => 2, 3, 1, 1, 1, 3, 2, 3, 2
[2, 3, 1, 1, 1, 3, 2, 3, 3] => 2, 3, 1, 1, 1, 3, 2, 3, 3
[2, 3, 1, 1, 1, 3, 3, 1, 1] => 2, 3, 1, 1, 1, 3, 3, 1, 1
[2, 3, 1, 1, 1, 3, 3, 1, 2] => 2, 3, 1, 1, 1, 3, 3, 1, 2
[2, 3, 1, 1, 1, 3, 3, 1, 3] => 2, 3, 1, 1, 1, 3, 3, 1, 3
[2, 3, 1, 1, 1, 3, 3, 2, 1] => 2, 3, 1, 1, 1, 3, 3, 2, 1
[2, 3, 1, 1, 1, 3, 3, 2, 2] => 2, 3, 1, 1, 1, 3, 3, 2, 2
[2, 3, 1, 1, 1, 3, 3, 2, 3] => 2, 3, 1, 1, 1, 3, 3, 2, 3
[2, 3, 1, 1, 1, 3, 3, 3, 1] => 2, 3, 1, 1, 1, 3, 3, 3, 1
[2, 3, 1, 1, 1, 3, 3, 3, 2] => 2, 3, 1, 1, 1, 3, 3, 3, 2
[2, 3, 1, 1, 1, 3, 3, 3, 3] => 2, 3, 1, 1, 1, 3, 3, 3, 3
[2, 3, 1, 1, 2, 1, 1, 1, 1] => 2, 3, 1, 1, 2, 1, 1, 1, 1
[2, 3, 1, 1, 2, 1, 1, 1, 2] => 2, 3, 1, 1, 2, 1, 1, 1, 2
[2, 3, 1, 1, 2, 1, 1, 1, 3] => 2, 3, 1, 1, 2, 1, 1, 1, 3
[2, 3, 1, 1, 2, 1, 1, 2, 1] => 2, 3, 1, 1, 2, 1, 1, 2, 1
[2, 3, 1, 1, 2, 1, 1, 2, 2] => 2, 3, 1, 1, 2, 1, 1, 2, 2
[2, 3, 1, 1, 2, 1, 1, 2, 3] => 2, 3, 1, 1, 2, 1, 1, 2, 3
[2, 3, 1, 1, 2, 1, 1, 3, 1] => 2, 3, 1, 1, 2, 1, 1, 3, 1
[2, 3, 1, 1, 2, 1, 1, 3, 2] => 2, 3, 1, 1, 2, 1, 1, 3, 2
[2, 3, 1, 1, 2, 1, 1, 3, 3] => 2, 3, 1, 1, 2, 1, 1, 3, 3
[2, 3, 1, 1, 2, 1, 2, 1, 1] => 2, 3, 1, 1, 2, 1, 2, 1, 1
[2, 3, 1, 1, 2, 1, 2, 1, 2] => 2, 3, 1, 1, 2, 1, 2, 1, 2
[2, 3, 1, 1, 2, 1, 2, 1, 3] => 2, 3, 1, 1, 2, 1, 2, 1, 3
[2, 3, 1, 1, 2, 1, 2, 2, 1] => 2, 3, 1, 1, 2, 1, 2, 2, 1
[2, 3, 1, 1, 2, 1, 2, 2, 2] => 2, 3, 1, 1, 2, 1, 2, 2, 2
[2, 3, 1, 1, 2, 1, 2, 2, 3] => 2, 3, 1, 1, 2, 1, 2, 2, 3
[2, 3, 1, 1, 2, 1, 2, 3, 1] => 2, 3, 1, 1, 2, 1, 2, 3, 1
[2, 3, 1, 1, 2, 1, 2, 3, 2] => 2, 3, 1, 1, 2, 1, 2, 3, 2
[2, 3, 1, 1, 2, 1, 2, 3, 3] => 2, 3, 1, 1, 2, 1, 2, 3, 3
[2, 3, 1, 1, 2, 1, 3, 1, 1] => 2, 3, 1, 1, 2, 1, 3, 1, 1
[2, 3, 1, 1, 2, 1, 3, 1, 2] => 2, 3, 1, 1, 2, 1, 3, 1, 2
[2, 3, 1, 1, 2, 1, 3, 1, 3] => 2, 3, 1, 1, 2, 1, 3, 1, 3
[2, 3, 1, 1, 2, 1, 3, 2, 1] => 2, 3, 1, 1, 2, 1, 3, 2, 1
[2, 3, 1, 1, 2, 1, 3, 2, 2] => 2, 3, 1, 1, 2, 1, 3, 2, 2
[2, 3, 1, 1, 2, 1, 3, 2, 3] => 2, 3, 1, 1, 2, 1, 3, 2, 3
[2, 3, 1, 1, 2, 1, 3, 3, 1] => 2, 3, 1, 1, 2, 1, 3, 3, 1
[2, 3, 1, 1, 2, 1, 3, 3, 2] => 2, 3, 1, 1, 2, 1, 3, 3, 2
[2, 3, 1, 1, 2, 1, 3, 3, 3] => 2, 3, 1, 1, 2, 1, 3, 3, 3
[2, 3, 1, 1, 2, 2, 1, 1, 1] => 2, 3, 1, 1, 2, 2, 1, 1, 1
[2, 3, 1, 1, 2, 2, 1, 1, 2] => 2, 3, 1, 1, 2, 2, 1, 1, 2
[2, 3, 1, 1, 2, 2, 1, 1, 3] => 2, 3, 1, 1, 2, 2, 1, 1, 3
[2, 3, 1, 1, 2, 2, 1, 2, 1] => 2, 3, 1, 1, 2, 2, 1, 2, 1
[2, 3, 1, 1, 2, 2, 1, 2, 2] => 2, 3, 1, 1, 2, 2, 1, 2, 2
[2, 3, 1, 1, 2, 2, 1, 2, 3] => 2, 3, 1, 1, 2, 2, 1, 2, 3
[2, 3, 1, 1, 2, 2, 1, 3, 1] => 2, 3, 1, 1, 2, 2, 1, 3, 1
[2, 3, 1, 1, 2, 2, 1, 3, 2] => 2, 3, 1, 1, 2, 2, 1, 3, 2
[2, 3, 1, 1, 2, 2, 1, 3, 3] => 2, 3, 1, 1, 2, 2, 1, 3, 3
[2, 3, 1, 1, 2, 2, 2, 1, 1] => 2, 3, 1, 1, 2, 2, 2, 1, 1
[2, 3, 1, 1, 2, 2, 2, 1, 2] => 2, 3, 1, 1, 2, 2, 2, 1, 2
[2, 3, 1, 1, 2, 2, 2, 1, 3] => 2, 3, 1, 1, 2, 2, 2, 1, 3
[2, 3, 1, 1, 2, 2, 2, 2, 1] => 2, 3, 1, 1, 2, 2, 2, 2, 1
[2, 3, 1, 1, 2, 2, 2, 2, 2] => 2, 3, 1, 1, 2, 2, 2, 2, 2
[2, 3, 1, 1, 2, 2, 2, 2, 3] => 2, 3, 1, 1, 2, 2, 2, 2, 3
[2, 3, 1, 1, 2, 2, 2, 3, 1] => 2, 3, 1, 1, 2, 2, 2, 3, 1
[2, 3, 1, 1, 2, 2, 2, 3, 2] => 2, 3, 1, 1, 2, 2, 2, 3, 2
[2, 3, 1, 1, 2, 2, 2, 3, 3] => 2, 3, 1, 1, 2, 2, 2, 3, 3
[2, 3, 1, 1, 2, 2, 3, 1, 1] => 2, 3, 1, 1, 2, 2, 3, 1, 1
[2, 3, 1, 1, 2, 2, 3, 1, 2] => 2, 3, 1, 1, 2, 2, 3, 1, 2
[2, 3, 1, 1, 2, 2, 3, 1, 3] => 2, 3, 1, 1, 2, 2, 3, 1, 3
[2, 3, 1, 1, 2, 2, 3, 2, 1] => 2, 3, 1, 1, 2, 2, 3, 2, 1
[2, 3, 1, 1, 2, 2, 3, 2, 2] => 2, 3, 1, 1, 2, 2, 3, 2, 2
[2, 3, 1, 1, 2, 2, 3, 2, 3] => 2, 3, 1, 1, 2, 2, 3, 2, 3
[2, 3, 1, 1, 2, 2, 3, 3, 1] => 2, 3, 1, 1, 2, 2, 3, 3, 1
[2, 3, 1, 1, 2, 2, 3, 3, 2] => 2, 3, 1, 1, 2, 2, 3, 3, 2
[2, 3, 1, 1, 2, 2, 3, 3, 3] => 2, 3, 1, 1, 2, 2, 3, 3, 3
[2, 3, 1, 1, 2, 3, 1, 1, 1] => 2, 3, 1, 1, 2, 3, 1, 1, 1
[2, 3, 1, 1, 2, 3, 1, 1, 2] => 2, 3, 1, 1, 2, 3, 1, 1, 2
[2, 3, 1, 1, 2, 3, 1, 1, 3] => 2, 3, 1, 1, 2, 3, 1, 1, 3
[2, 3, 1, 1, 2, 3, 1, 2, 1] => 2, 3, 1, 1, 2, 3, 1, 2, 1
[2, 3, 1, 1, 2, 3, 1, 2, 2] => 2, 3, 1, 1, 2, 3, 1, 2, 2
[2, 3, 1, 1, 2, 3, 1, 2, 3] => 2, 3, 1, 1, 2, 3, 1, 2, 3
[2, 3, 1, 1, 2, 3, 1, 3, 1] => 2, 3, 1, 1, 2, 3, 1, 3, 1
[2, 3, 1, 1, 2, 3, 1, 3, 2] => 2, 3, 1, 1, 2, 3, 1, 3, 2
[2, 3, 1, 1, 2, 3, 1, 3, 3] => 2, 3, 1, 1, 2, 3, 1, 3, 3
[2, 3, 1, 1, 2, 3, 2, 1, 1] => 2, 3, 1, 1, 2, 3, 2, 1, 1
[2, 3, 1, 1, 2, 3, 2, 1, 2] => 2, 3, 1, 1, 2, 3, 2, 1, 2
[2, 3, 1, 1, 2, 3, 2, 1, 3] => 2, 3, 1, 1, 2, 3, 2, 1, 3
[2, 3, 1, 1, 2, 3, 2, 2, 1] => 2, 3, 1, 1, 2, 3, 2, 2, 1
[2, 3, 1, 1, 2, 3, 2, 2, 2] => 2, 3, 1, 1, 2, 3, 2, 2, 2
[2, 3, 1, 1, 2, 3, 2, 2, 3] => 2, 3, 1, 1, 2, 3, 2, 2, 3
[2, 3, 1, 1, 2, 3, 2, 3, 1] => 2, 3, 1, 1, 2, 3, 2, 3, 1
[2, 3, 1, 1, 2, 3, 2, 3, 2] => 2, 3, 1, 1, 2, 3, 2, 3, 2
[2, 3, 1, 1, 2, 3, 2, 3, 3] => 2, 3, 1, 1, 2, 3, 2, 3, 3
[2, 3, 1, 1, 2, 3, 3, 1, 1] => 2, 3, 1, 1, 2, 3, 3, 1, 1
[2, 3, 1, 1, 2, 3, 3, 1, 2] => 2, 3, 1, 1, 2, 3, 3, 1, 2
[2, 3, 1, 1, 2, 3, 3, 1, 3] => 2, 3, 1, 1, 2, 3, 3, 1, 3
[2, 3, 1, 1, 2, 3, 3, 2, 1] => 2, 3, 1, 1, 2, 3, 3, 2, 1
[2, 3, 1, 1, 2, 3, 3, 2, 2] => 2, 3, 1, 1, 2, 3, 3, 2, 2
[2, 3, 1, 1, 2, 3, 3, 2, 3] => 2, 3, 1, 1, 2, 3, 3, 2, 3
[2, 3, 1, 1, 2, 3, 3, 3, 1] => 2, 3, 1, 1, 2, 3, 3, 3, 1
[2, 3, 1, 1, 2, 3, 3, 3, 2] => 2, 3, 1, 1, 2, 3, 3, 3, 2
[2, 3, 1, 1, 2, 3, 3, 3, 3] => 2, 3, 1, 1, 2, 3, 3, 3, 3
[2, 3, 1, 1, 3, 1, 1, 1, 1] => 2, 3, 1, 1, 3, 1, 1, 1, 1
[2, 3, 1, 1, 3, 1, 1, 1, 2] => 2, 3, 1, 1, 3, 1, 1, 1, 2
[2, 3, 1, 1, 3, 1, 1, 1, 3] => 2, 3, 1, 1, 3, 1, 1, 1, 3
[2, 3, 1, 1, 3, 1, 1, 2, 1] => 2, 3, 1, 1, 3, 1, 1, 2, 1
[2, 3, 1, 1, 3, 1, 1, 2, 2] => 2, 3, 1, 1, 3, 1, 1, 2, 2
[2, 3, 1, 1, 3, 1, 1, 2, 3] => 2, 3, 1, 1, 3, 1, 1, 2, 3
[2, 3, 1, 1, 3, 1, 1, 3, 1] => 2, 3, 1, 1, 3, 1, 1, 3, 1
[2, 3, 1, 1, 3, 1, 1, 3, 2] => 2, 3, 1, 1, 3, 1, 1, 3, 2
[2, 3, 1, 1, 3, 1, 1, 3, 3] => 2, 3, 1, 1, 3, 1, 1, 3, 3
[2, 3, 1, 1, 3, 1, 2, 1, 1] => 2, 3, 1, 1, 3, 1, 2, 1, 1
[2, 3, 1, 1, 3, 1, 2, 1, 2] => 2, 3, 1, 1, 3, 1, 2, 1, 2
[2, 3, 1, 1, 3, 1, 2, 1, 3] => 2, 3, 1, 1, 3, 1, 2, 1, 3
[2, 3, 1, 1, 3, 1, 2, 2, 1] => 2, 3, 1, 1, 3, 1, 2, 2, 1
[2, 3, 1, 1, 3, 1, 2, 2, 2] => 2, 3, 1, 1, 3, 1, 2, 2, 2
[2, 3, 1, 1, 3, 1, 2, 2, 3] => 2, 3, 1, 1, 3, 1, 2, 2, 3
[2, 3, 1, 1, 3, 1, 2, 3, 1] => 2, 3, 1, 1, 3, 1, 2, 3, 1
[2, 3, 1, 1, 3, 1, 2, 3, 2] => 2, 3, 1, 1, 3, 1, 2, 3, 2
[2, 3, 1, 1, 3, 1, 2, 3, 3] => 2, 3, 1, 1, 3, 1, 2, 3, 3
[2, 3, 1, 1, 3, 1, 3, 1, 1] => 2, 3, 1, 1, 3, 1, 3, 1, 1
[2, 3, 1, 1, 3, 1, 3, 1, 2] => 2, 3, 1, 1, 3, 1, 3, 1, 2
[2, 3, 1, 1, 3, 1, 3, 1, 3] => 2, 3, 1, 1, 3, 1, 3, 1, 3
[2, 3, 1, 1, 3, 1, 3, 2, 1] => 2, 3, 1, 1, 3, 1, 3, 2, 1
[2, 3, 1, 1, 3, 1, 3, 2, 2] => 2, 3, 1, 1, 3, 1, 3, 2, 2
[2, 3, 1, 1, 3, 1, 3, 2, 3] => 2, 3, 1, 1, 3, 1, 3, 2, 3
[2, 3, 1, 1, 3, 1, 3, 3, 1] => 2, 3, 1, 1, 3, 1, 3, 3, 1
[2, 3, 1, 1, 3, 1, 3, 3, 2] => 2, 3, 1, 1, 3, 1, 3, 3, 2
[2, 3, 1, 1, 3, 1, 3, 3, 3] => 2, 3, 1, 1, 3, 1, 3, 3, 3
[2, 3, 1, 1, 3, 2, 1, 1, 1] => 2, 3, 1, 1, 3, 2, 1, 1, 1
[2, 3, 1, 1, 3, 2, 1, 1, 2] => 2, 3, 1, 1, 3, 2, 1, 1, 2
[2, 3, 1, 1, 3, 2, 1, 1, 3] => 2, 3, 1, 1, 3, 2, 1, 1, 3
[2, 3, 1, 1, 3, 2, 1, 2, 1] => 2, 3, 1, 1, 3, 2, 1, 2, 1
[2, 3, 1, 1, 3, 2, 1, 2, 2] => 2, 3, 1, 1, 3, 2, 1, 2, 2
[2, 3, 1, 1, 3, 2, 1, 2, 3] => 2, 3, 1, 1, 3, 2, 1, 2, 3
[2, 3, 1, 1, 3, 2, 1, 3, 1] => 2, 3, 1, 1, 3, 2, 1, 3, 1
[2, 3, 1, 1, 3, 2, 1, 3, 2] => 2, 3, 1, 1, 3, 2, 1, 3, 2
[2, 3, 1, 1, 3, 2, 1, 3, 3] => 2, 3, 1, 1, 3, 2, 1, 3, 3
[2, 3, 1, 1, 3, 2, 2, 1, 1] => 2, 3, 1, 1, 3, 2, 2, 1, 1
[2, 3, 1, 1, 3, 2, 2, 1, 2] => 2, 3, 1, 1, 3, 2, 2, 1, 2
[2, 3, 1, 1, 3, 2, 2, 1, 3] => 2, 3, 1, 1, 3, 2, 2, 1, 3
[2, 3, 1, 1, 3, 2, 2, 2, 1] => 2, 3, 1, 1, 3, 2, 2, 2, 1
[2, 3, 1, 1, 3, 2, 2, 2, 2] => 2, 3, 1, 1, 3, 2, 2, 2, 2
[2, 3, 1, 1, 3, 2, 2, 2, 3] => 2, 3, 1, 1, 3, 2, 2, 2, 3
[2, 3, 1, 1, 3, 2, 2, 3, 1] => 2, 3, 1, 1, 3, 2, 2, 3, 1
[2, 3, 1, 1, 3, 2, 2, 3, 2] => 2, 3, 1, 1, 3, 2, 2, 3, 2
[2, 3, 1, 1, 3, 2, 2, 3, 3] => 2, 3, 1, 1, 3, 2, 2, 3, 3
[2, 3, 1, 1, 3, 2, 3, 1, 1] => 2, 3, 1, 1, 3, 2, 3, 1, 1
[2, 3, 1, 1, 3, 2, 3, 1, 2] => 2, 3, 1, 1, 3, 2, 3, 1, 2
[2, 3, 1, 1, 3, 2, 3, 1, 3] => 2, 3, 1, 1, 3, 2, 3, 1, 3
[2, 3, 1, 1, 3, 2, 3, 2, 1] => 2, 3, 1, 1, 3, 2, 3, 2, 1
[2, 3, 1, 1, 3, 2, 3, 2, 2] => 2, 3, 1, 1, 3, 2, 3, 2, 2
[2, 3, 1, 1, 3, 2, 3, 2, 3] => 2, 3, 1, 1, 3, 2, 3, 2, 3
[2, 3, 1, 1, 3, 2, 3, 3, 1] => 2, 3, 1, 1, 3, 2, 3, 3, 1
[2, 3, 1, 1, 3, 2, 3, 3, 2] => 2, 3, 1, 1, 3, 2, 3, 3, 2
[2, 3, 1, 1, 3, 2, 3, 3, 3] => 2, 3, 1, 1, 3, 2, 3, 3, 3
[2, 3, 1, 1, 3, 3, 1, 1, 1] => 2, 3, 1, 1, 3, 3, 1, 1, 1
[2, 3, 1, 1, 3, 3, 1, 1, 2] => 2, 3, 1, 1, 3, 3, 1, 1, 2
[2, 3, 1, 1, 3, 3, 1, 1, 3] => 2, 3, 1, 1, 3, 3, 1, 1, 3
[2, 3, 1, 1, 3, 3, 1, 2, 1] => 2, 3, 1, 1, 3, 3, 1, 2, 1
[2, 3, 1, 1, 3, 3, 1, 2, 2] => 2, 3, 1, 1, 3, 3, 1, 2, 2
[2, 3, 1, 1, 3, 3, 1, 2, 3] => 2, 3, 1, 1, 3, 3, 1, 2, 3
[2, 3, 1, 1, 3, 3, 1, 3, 1] => 2, 3, 1, 1, 3, 3, 1, 3, 1
[2, 3, 1, 1, 3, 3, 1, 3, 2] => 2, 3, 1, 1, 3, 3, 1, 3, 2
[2, 3, 1, 1, 3, 3, 1, 3, 3] => 2, 3, 1, 1, 3, 3, 1, 3, 3
[2, 3, 1, 1, 3, 3, 2, 1, 1] => 2, 3, 1, 1, 3, 3, 2, 1, 1
[2, 3, 1, 1, 3, 3, 2, 1, 2] => 2, 3, 1, 1, 3, 3, 2, 1, 2
[2, 3, 1, 1, 3, 3, 2, 1, 3] => 2, 3, 1, 1, 3, 3, 2, 1, 3
[2, 3, 1, 1, 3, 3, 2, 2, 1] => 2, 3, 1, 1, 3, 3, 2, 2, 1
[2, 3, 1, 1, 3, 3, 2, 2, 2] => 2, 3, 1, 1, 3, 3, 2, 2, 2
[2, 3, 1, 1, 3, 3, 2, 2, 3] => 2, 3, 1, 1, 3, 3, 2, 2, 3
[2, 3, 1, 1, 3, 3, 2, 3, 1] => 2, 3, 1, 1, 3, 3, 2, 3, 1
[2, 3, 1, 1, 3, 3, 2, 3, 2] => 2, 3, 1, 1, 3, 3, 2, 3, 2
[2, 3, 1, 1, 3, 3, 2, 3, 3] => 2, 3, 1, 1, 3, 3, 2, 3, 3
[2, 3, 1, 1, 3, 3, 3, 1, 1] => 2, 3, 1, 1, 3, 3, 3, 1, 1
[2, 3, 1, 1, 3, 3, 3, 1, 2] => 2, 3, 1, 1, 3, 3, 3, 1, 2
[2, 3, 1, 1, 3, 3, 3, 1, 3] => 2, 3, 1, 1, 3, 3, 3, 1, 3
[2, 3, 1, 1, 3, 3, 3, 2, 1] => 2, 3, 1, 1, 3, 3, 3, 2, 1
[2, 3, 1, 1, 3, 3, 3, 2, 2] => 2, 3, 1, 1, 3, 3, 3, 2, 2
[2, 3, 1, 1, 3, 3, 3, 2, 3] => 2, 3, 1, 1, 3, 3, 3, 2, 3
[2, 3, 1, 1, 3, 3, 3, 3, 1] => 2, 3, 1, 1, 3, 3, 3, 3, 1
[2, 3, 1, 1, 3, 3, 3, 3, 2] => 2, 3, 1, 1, 3, 3, 3, 3, 2
[2, 3, 1, 1, 3, 3, 3, 3, 3] => 2, 3, 1, 1, 3, 3, 3, 3, 3
[2, 3, 1, 2, 1, 1, 1, 1, 1] => 2, 3, 1, 2, 1, 1, 1, 1, 1
[2, 3, 1, 2, 1, 1, 1, 1, 2] => 2, 3, 1, 2, 1, 1, 1, 1, 2
[2, 3, 1, 2, 1, 1, 1, 1, 3] => 2, 3, 1, 2, 1, 1, 1, 1, 3
[2, 3, 1, 2, 1, 1, 1, 2, 1] => 2, 3, 1, 2, 1, 1, 1, 2, 1
[2, 3, 1, 2, 1, 1, 1, 2, 2] => 2, 3, 1, 2, 1, 1, 1, 2, 2
[2, 3, 1, 2, 1, 1, 1, 2, 3] => 2, 3, 1, 2, 1, 1, 1, 2, 3
[2, 3, 1, 2, 1, 1, 1, 3, 1] => 2, 3, 1, 2, 1, 1, 1, 3, 1
[2, 3, 1, 2, 1, 1, 1, 3, 2] => 2, 3, 1, 2, 1, 1, 1, 3, 2
[2, 3, 1, 2, 1, 1, 1, 3, 3] => 2, 3, 1, 2, 1, 1, 1, 3, 3
[2, 3, 1, 2, 1, 1, 2, 1, 1] => 2, 3, 1, 2, 1, 1, 2, 1, 1
[2, 3, 1, 2, 1, 1, 2, 1, 2] => 2, 3, 1, 2, 1, 1, 2, 1, 2
[2, 3, 1, 2, 1, 1, 2, 1, 3] => 2, 3, 1, 2, 1, 1, 2, 1, 3
[2, 3, 1, 2, 1, 1, 2, 2, 1] => 2, 3, 1, 2, 1, 1, 2, 2, 1
[2, 3, 1, 2, 1, 1, 2, 2, 2] => 2, 3, 1, 2, 1, 1, 2, 2, 2
[2, 3, 1, 2, 1, 1, 2, 2, 3] => 2, 3, 1, 2, 1, 1, 2, 2, 3
[2, 3, 1, 2, 1, 1, 2, 3, 1] => 2, 3, 1, 2, 1, 1, 2, 3, 1
[2, 3, 1, 2, 1, 1, 2, 3, 2] => 2, 3, 1, 2, 1, 1, 2, 3, 2
[2, 3, 1, 2, 1, 1, 2, 3, 3] => 2, 3, 1, 2, 1, 1, 2, 3, 3
[2, 3, 1, 2, 1, 1, 3, 1, 1] => 2, 3, 1, 2, 1, 1, 3, 1, 1
[2, 3, 1, 2, 1, 1, 3, 1, 2] => 2, 3, 1, 2, 1, 1, 3, 1, 2
[2, 3, 1, 2, 1, 1, 3, 1, 3] => 2, 3, 1, 2, 1, 1, 3, 1, 3
[2, 3, 1, 2, 1, 1, 3, 2, 1] => 2, 3, 1, 2, 1, 1, 3, 2, 1
[2, 3, 1, 2, 1, 1, 3, 2, 2] => 2, 3, 1, 2, 1, 1, 3, 2, 2
[2, 3, 1, 2, 1, 1, 3, 2, 3] => 2, 3, 1, 2, 1, 1, 3, 2, 3
[2, 3, 1, 2, 1, 1, 3, 3, 1] => 2, 3, 1, 2, 1, 1, 3, 3, 1
[2, 3, 1, 2, 1, 1, 3, 3, 2] => 2, 3, 1, 2, 1, 1, 3, 3, 2
[2, 3, 1, 2, 1, 1, 3, 3, 3] => 2, 3, 1, 2, 1, 1, 3, 3, 3
[2, 3, 1, 2, 1, 2, 1, 1, 1] => 2, 3, 1, 2, 1, 2, 1, 1, 1
[2, 3, 1, 2, 1, 2, 1, 1, 2] => 2, 3, 1, 2, 1, 2, 1, 1, 2
[2, 3, 1, 2, 1, 2, 1, 1, 3] => 2, 3, 1, 2, 1, 2, 1, 1, 3
[2, 3, 1, 2, 1, 2, 1, 2, 1] => 2, 3, 1, 2, 1, 2, 1, 2, 1
[2, 3, 1, 2, 1, 2, 1, 2, 2] => 2, 3, 1, 2, 1, 2, 1, 2, 2
[2, 3, 1, 2, 1, 2, 1, 2, 3] => 2, 3, 1, 2, 1, 2, 1, 2, 3
[2, 3, 1, 2, 1, 2, 1, 3, 1] => 2, 3, 1, 2, 1, 2, 1, 3, 1
[2, 3, 1, 2, 1, 2, 1, 3, 2] => 2, 3, 1, 2, 1, 2, 1, 3, 2
[2, 3, 1, 2, 1, 2, 1, 3, 3] => 2, 3, 1, 2, 1, 2, 1, 3, 3
[2, 3, 1, 2, 1, 2, 2, 1, 1] => 2, 3, 1, 2, 1, 2, 2, 1, 1
[2, 3, 1, 2, 1, 2, 2, 1, 2] => 2, 3, 1, 2, 1, 2, 2, 1, 2
[2, 3, 1, 2, 1, 2, 2, 1, 3] => 2, 3, 1, 2, 1, 2, 2, 1, 3
[2, 3, 1, 2, 1, 2, 2, 2, 1] => 2, 3, 1, 2, 1, 2, 2, 2, 1
[2, 3, 1, 2, 1, 2, 2, 2, 2] => 2, 3, 1, 2, 1, 2, 2, 2, 2
[2, 3, 1, 2, 1, 2, 2, 2, 3] => 2, 3, 1, 2, 1, 2, 2, 2, 3
[2, 3, 1, 2, 1, 2, 2, 3, 1] => 2, 3, 1, 2, 1, 2, 2, 3, 1
[2, 3, 1, 2, 1, 2, 2, 3, 2] => 2, 3, 1, 2, 1, 2, 2, 3, 2
[2, 3, 1, 2, 1, 2, 2, 3, 3] => 2, 3, 1, 2, 1, 2, 2, 3, 3
[2, 3, 1, 2, 1, 2, 3, 1, 1] => 2, 3, 1, 2, 1, 2, 3, 1, 1
[2, 3, 1, 2, 1, 2, 3, 1, 2] => 2, 3, 1, 2, 1, 2, 3, 1, 2
[2, 3, 1, 2, 1, 2, 3, 1, 3] => 2, 3, 1, 2, 1, 2, 3, 1, 3
[2, 3, 1, 2, 1, 2, 3, 2, 1] => 2, 3, 1, 2, 1, 2, 3, 2, 1
[2, 3, 1, 2, 1, 2, 3, 2, 2] => 2, 3, 1, 2, 1, 2, 3, 2, 2
[2, 3, 1, 2, 1, 2, 3, 2, 3] => 2, 3, 1, 2, 1, 2, 3, 2, 3
[2, 3, 1, 2, 1, 2, 3, 3, 1] => 2, 3, 1, 2, 1, 2, 3, 3, 1
[2, 3, 1, 2, 1, 2, 3, 3, 2] => 2, 3, 1, 2, 1, 2, 3, 3, 2
[2, 3, 1, 2, 1, 2, 3, 3, 3] => 2, 3, 1, 2, 1, 2, 3, 3, 3
[2, 3, 1, 2, 1, 3, 1, 1, 1] => 2, 3, 1, 2, 1, 3, 1, 1, 1
[2, 3, 1, 2, 1, 3, 1, 1, 2] => 2, 3, 1, 2, 1, 3, 1, 1, 2
[2, 3, 1, 2, 1, 3, 1, 1, 3] => 2, 3, 1, 2, 1, 3, 1, 1, 3
[2, 3, 1, 2, 1, 3, 1, 2, 1] => 2, 3, 1, 2, 1, 3, 1, 2, 1
[2, 3, 1, 2, 1, 3, 1, 2, 2] => 2, 3, 1, 2, 1, 3, 1, 2, 2
[2, 3, 1, 2, 1, 3, 1, 2, 3] => 2, 3, 1, 2, 1, 3, 1, 2, 3
[2, 3, 1, 2, 1, 3, 1, 3, 1] => 2, 3, 1, 2, 1, 3, 1, 3, 1
[2, 3, 1, 2, 1, 3, 1, 3, 2] => 2, 3, 1, 2, 1, 3, 1, 3, 2
[2, 3, 1, 2, 1, 3, 1, 3, 3] => 2, 3, 1, 2, 1, 3, 1, 3, 3
[2, 3, 1, 2, 1, 3, 2, 1, 1] => 2, 3, 1, 2, 1, 3, 2, 1, 1
[2, 3, 1, 2, 1, 3, 2, 1, 2] => 2, 3, 1, 2, 1, 3, 2, 1, 2
[2, 3, 1, 2, 1, 3, 2, 1, 3] => 2, 3, 1, 2, 1, 3, 2, 1, 3
[2, 3, 1, 2, 1, 3, 2, 2, 1] => 2, 3, 1, 2, 1, 3, 2, 2, 1
[2, 3, 1, 2, 1, 3, 2, 2, 2] => 2, 3, 1, 2, 1, 3, 2, 2, 2
[2, 3, 1, 2, 1, 3, 2, 2, 3] => 2, 3, 1, 2, 1, 3, 2, 2, 3
[2, 3, 1, 2, 1, 3, 2, 3, 1] => 2, 3, 1, 2, 1, 3, 2, 3, 1
[2, 3, 1, 2, 1, 3, 2, 3, 2] => 2, 3, 1, 2, 1, 3, 2, 3, 2
[2, 3, 1, 2, 1, 3, 2, 3, 3] => 2, 3, 1, 2, 1, 3, 2, 3, 3
[2, 3, 1, 2, 1, 3, 3, 1, 1] => 2, 3, 1, 2, 1, 3, 3, 1, 1
[2, 3, 1, 2, 1, 3, 3, 1, 2] => 2, 3, 1, 2, 1, 3, 3, 1, 2
[2, 3, 1, 2, 1, 3, 3, 1, 3] => 2, 3, 1, 2, 1, 3, 3, 1, 3
[2, 3, 1, 2, 1, 3, 3, 2, 1] => 2, 3, 1, 2, 1, 3, 3, 2, 1
[2, 3, 1, 2, 1, 3, 3, 2, 2] => 2, 3, 1, 2, 1, 3, 3, 2, 2
[2, 3, 1, 2, 1, 3, 3, 2, 3] => 2, 3, 1, 2, 1, 3, 3, 2, 3
[2, 3, 1, 2, 1, 3, 3, 3, 1] => 2, 3, 1, 2, 1, 3, 3, 3, 1
[2, 3, 1, 2, 1, 3, 3, 3, 2] => 2, 3, 1, 2, 1, 3, 3, 3, 2
[2, 3, 1, 2, 1, 3, 3, 3, 3] => 2, 3, 1, 2, 1, 3, 3, 3, 3
[2, 3, 1, 2, 2, 1, 1, 1, 1] => 2, 3, 1, 2, 2, 1, 1, 1, 1
[2, 3, 1, 2, 2, 1, 1, 1, 2] => 2, 3, 1, 2, 2, 1, 1, 1, 2
[2, 3, 1, 2, 2, 1, 1, 1, 3] => 2, 3, 1, 2, 2, 1, 1, 1, 3
[2, 3, 1, 2, 2, 1, 1, 2, 1] => 2, 3, 1, 2, 2, 1, 1, 2, 1
[2, 3, 1, 2, 2, 1, 1, 2, 2] => 2, 3, 1, 2, 2, 1, 1, 2, 2
[2, 3, 1, 2, 2, 1, 1, 2, 3] => 2, 3, 1, 2, 2, 1, 1, 2, 3
[2, 3, 1, 2, 2, 1, 1, 3, 1] => 2, 3, 1, 2, 2, 1, 1, 3, 1
[2, 3, 1, 2, 2, 1, 1, 3, 2] => 2, 3, 1, 2, 2, 1, 1, 3, 2
[2, 3, 1, 2, 2, 1, 1, 3, 3] => 2, 3, 1, 2, 2, 1, 1, 3, 3
[2, 3, 1, 2, 2, 1, 2, 1, 1] => 2, 3, 1, 2, 2, 1, 2, 1, 1
[2, 3, 1, 2, 2, 1, 2, 1, 2] => 2, 3, 1, 2, 2, 1, 2, 1, 2
[2, 3, 1, 2, 2, 1, 2, 1, 3] => 2, 3, 1, 2, 2, 1, 2, 1, 3
[2, 3, 1, 2, 2, 1, 2, 2, 1] => 2, 3, 1, 2, 2, 1, 2, 2, 1
[2, 3, 1, 2, 2, 1, 2, 2, 2] => 2, 3, 1, 2, 2, 1, 2, 2, 2
[2, 3, 1, 2, 2, 1, 2, 2, 3] => 2, 3, 1, 2, 2, 1, 2, 2, 3
[2, 3, 1, 2, 2, 1, 2, 3, 1] => 2, 3, 1, 2, 2, 1, 2, 3, 1
[2, 3, 1, 2, 2, 1, 2, 3, 2] => 2, 3, 1, 2, 2, 1, 2, 3, 2
[2, 3, 1, 2, 2, 1, 2, 3, 3] => 2, 3, 1, 2, 2, 1, 2, 3, 3
[2, 3, 1, 2, 2, 1, 3, 1, 1] => 2, 3, 1, 2, 2, 1, 3, 1, 1
[2, 3, 1, 2, 2, 1, 3, 1, 2] => 2, 3, 1, 2, 2, 1, 3, 1, 2
[2, 3, 1, 2, 2, 1, 3, 1, 3] => 2, 3, 1, 2, 2, 1, 3, 1, 3
[2, 3, 1, 2, 2, 1, 3, 2, 1] => 2, 3, 1, 2, 2, 1, 3, 2, 1
[2, 3, 1, 2, 2, 1, 3, 2, 2] => 2, 3, 1, 2, 2, 1, 3, 2, 2
[2, 3, 1, 2, 2, 1, 3, 2, 3] => 2, 3, 1, 2, 2, 1, 3, 2, 3
[2, 3, 1, 2, 2, 1, 3, 3, 1] => 2, 3, 1, 2, 2, 1, 3, 3, 1
[2, 3, 1, 2, 2, 1, 3, 3, 2] => 2, 3, 1, 2, 2, 1, 3, 3, 2
[2, 3, 1, 2, 2, 1, 3, 3, 3] => 2, 3, 1, 2, 2, 1, 3, 3, 3
[2, 3, 1, 2, 2, 2, 1, 1, 1] => 2, 3, 1, 2, 2, 2, 1, 1, 1
[2, 3, 1, 2, 2, 2, 1, 1, 2] => 2, 3, 1, 2, 2, 2, 1, 1, 2
[2, 3, 1, 2, 2, 2, 1, 1, 3] => 2, 3, 1, 2, 2, 2, 1, 1, 3
[2, 3, 1, 2, 2, 2, 1, 2, 1] => 2, 3, 1, 2, 2, 2, 1, 2, 1
[2, 3, 1, 2, 2, 2, 1, 2, 2] => 2, 3, 1, 2, 2, 2, 1, 2, 2
[2, 3, 1, 2, 2, 2, 1, 2, 3] => 2, 3, 1, 2, 2, 2, 1, 2, 3
[2, 3, 1, 2, 2, 2, 1, 3, 1] => 2, 3, 1, 2, 2, 2, 1, 3, 1
[2, 3, 1, 2, 2, 2, 1, 3, 2] => 2, 3, 1, 2, 2, 2, 1, 3, 2
[2, 3, 1, 2, 2, 2, 1, 3, 3] => 2, 3, 1, 2, 2, 2, 1, 3, 3
[2, 3, 1, 2, 2, 2, 2, 1, 1] => 2, 3, 1, 2, 2, 2, 2, 1, 1
[2, 3, 1, 2, 2, 2, 2, 1, 2] => 2, 3, 1, 2, 2, 2, 2, 1, 2
[2, 3, 1, 2, 2, 2, 2, 1, 3] => 2, 3, 1, 2, 2, 2, 2, 1, 3
[2, 3, 1, 2, 2, 2, 2, 2, 1] => 2, 3, 1, 2, 2, 2, 2, 2, 1
[2, 3, 1, 2, 2, 2, 2, 2, 2] => 2, 3, 1, 2, 2, 2, 2, 2, 2
[2, 3, 1, 2, 2, 2, 2, 2, 3] => 2, 3, 1, 2, 2, 2, 2, 2, 3
[2, 3, 1, 2, 2, 2, 2, 3, 1] => 2, 3, 1, 2, 2, 2, 2, 3, 1
[2, 3, 1, 2, 2, 2, 2, 3, 2] => 2, 3, 1, 2, 2, 2, 2, 3, 2
[2, 3, 1, 2, 2, 2, 2, 3, 3] => 2, 3, 1, 2, 2, 2, 2, 3, 3
[2, 3, 1, 2, 2, 2, 3, 1, 1] => 2, 3, 1, 2, 2, 2, 3, 1, 1
[2, 3, 1, 2, 2, 2, 3, 1, 2] => 2, 3, 1, 2, 2, 2, 3, 1, 2
[2, 3, 1, 2, 2, 2, 3, 1, 3] => 2, 3, 1, 2, 2, 2, 3, 1, 3
[2, 3, 1, 2, 2, 2, 3, 2, 1] => 2, 3, 1, 2, 2, 2, 3, 2, 1
[2, 3, 1, 2, 2, 2, 3, 2, 2] => 2, 3, 1, 2, 2, 2, 3, 2, 2
[2, 3, 1, 2, 2, 2, 3, 2, 3] => 2, 3, 1, 2, 2, 2, 3, 2, 3
[2, 3, 1, 2, 2, 2, 3, 3, 1] => 2, 3, 1, 2, 2, 2, 3, 3, 1
[2, 3, 1, 2, 2, 2, 3, 3, 2] => 2, 3, 1, 2, 2, 2, 3, 3, 2
[2, 3, 1, 2, 2, 2, 3, 3, 3] => 2, 3, 1, 2, 2, 2, 3, 3, 3
[2, 3, 1, 2, 2, 3, 1, 1, 1] => 2, 3, 1, 2, 2, 3, 1, 1, 1
[2, 3, 1, 2, 2, 3, 1, 1, 2] => 2, 3, 1, 2, 2, 3, 1, 1, 2
[2, 3, 1, 2, 2, 3, 1, 1, 3] => 2, 3, 1, 2, 2, 3, 1, 1, 3
[2, 3, 1, 2, 2, 3, 1, 2, 1] => 2, 3, 1, 2, 2, 3, 1, 2, 1
[2, 3, 1, 2, 2, 3, 1, 2, 2] => 2, 3, 1, 2, 2, 3, 1, 2, 2
[2, 3, 1, 2, 2, 3, 1, 2, 3] => 2, 3, 1, 2, 2, 3, 1, 2, 3
[2, 3, 1, 2, 2, 3, 1, 3, 1] => 2, 3, 1, 2, 2, 3, 1, 3, 1
[2, 3, 1, 2, 2, 3, 1, 3, 2] => 2, 3, 1, 2, 2, 3, 1, 3, 2
[2, 3, 1, 2, 2, 3, 1, 3, 3] => 2, 3, 1, 2, 2, 3, 1, 3, 3
[2, 3, 1, 2, 2, 3, 2, 1, 1] => 2, 3, 1, 2, 2, 3, 2, 1, 1
[2, 3, 1, 2, 2, 3, 2, 1, 2] => 2, 3, 1, 2, 2, 3, 2, 1, 2
[2, 3, 1, 2, 2, 3, 2, 1, 3] => 2, 3, 1, 2, 2, 3, 2, 1, 3
[2, 3, 1, 2, 2, 3, 2, 2, 1] => 2, 3, 1, 2, 2, 3, 2, 2, 1
[2, 3, 1, 2, 2, 3, 2, 2, 2] => 2, 3, 1, 2, 2, 3, 2, 2, 2
[2, 3, 1, 2, 2, 3, 2, 2, 3] => 2, 3, 1, 2, 2, 3, 2, 2, 3
[2, 3, 1, 2, 2, 3, 2, 3, 1] => 2, 3, 1, 2, 2, 3, 2, 3, 1
[2, 3, 1, 2, 2, 3, 2, 3, 2] => 2, 3, 1, 2, 2, 3, 2, 3, 2
[2, 3, 1, 2, 2, 3, 2, 3, 3] => 2, 3, 1, 2, 2, 3, 2, 3, 3
[2, 3, 1, 2, 2, 3, 3, 1, 1] => 2, 3, 1, 2, 2, 3, 3, 1, 1
[2, 3, 1, 2, 2, 3, 3, 1, 2] => 2, 3, 1, 2, 2, 3, 3, 1, 2
[2, 3, 1, 2, 2, 3, 3, 1, 3] => 2, 3, 1, 2, 2, 3, 3, 1, 3
[2, 3, 1, 2, 2, 3, 3, 2, 1] => 2, 3, 1, 2, 2, 3, 3, 2, 1
[2, 3, 1, 2, 2, 3, 3, 2, 2] => 2, 3, 1, 2, 2, 3, 3, 2, 2
[2, 3, 1, 2, 2, 3, 3, 2, 3] => 2, 3, 1, 2, 2, 3, 3, 2, 3
[2, 3, 1, 2, 2, 3, 3, 3, 1] => 2, 3, 1, 2, 2, 3, 3, 3, 1
[2, 3, 1, 2, 2, 3, 3, 3, 2] => 2, 3, 1, 2, 2, 3, 3, 3, 2
[2, 3, 1, 2, 2, 3, 3, 3, 3] => 2, 3, 1, 2, 2, 3, 3, 3, 3
[2, 3, 1, 2, 3, 1, 1, 1, 1] => 2, 3, 1, 2, 3, 1, 1, 1, 1
[2, 3, 1, 2, 3, 1, 1, 1, 2] => 2, 3, 1, 2, 3, 1, 1, 1, 2
[2, 3, 1, 2, 3, 1, 1, 1, 3] => 2, 3, 1, 2, 3, 1, 1, 1, 3
[2, 3, 1, 2, 3, 1, 1, 2, 1] => 2, 3, 1, 2, 3, 1, 1, 2, 1
[2, 3, 1, 2, 3, 1, 1, 2, 2] => 2, 3, 1, 2, 3, 1, 1, 2, 2
[2, 3, 1, 2, 3, 1, 1, 2, 3] => 2, 3, 1, 2, 3, 1, 1, 2, 3
[2, 3, 1, 2, 3, 1, 1, 3, 1] => 2, 3, 1, 2, 3, 1, 1, 3, 1
[2, 3, 1, 2, 3, 1, 1, 3, 2] => 2, 3, 1, 2, 3, 1, 1, 3, 2
[2, 3, 1, 2, 3, 1, 1, 3, 3] => 2, 3, 1, 2, 3, 1, 1, 3, 3
[2, 3, 1, 2, 3, 1, 2, 1, 1] => 2, 3, 1, 2, 3, 1, 2, 1, 1
[2, 3, 1, 2, 3, 1, 2, 1, 2] => 2, 3, 1, 2, 3, 1, 2, 1, 2
[2, 3, 1, 2, 3, 1, 2, 1, 3] => 2, 3, 1, 2, 3, 1, 2, 1, 3
[2, 3, 1, 2, 3, 1, 2, 2, 1] => 2, 3, 1, 2, 3, 1, 2, 2, 1
[2, 3, 1, 2, 3, 1, 2, 2, 2] => 2, 3, 1, 2, 3, 1, 2, 2, 2
[2, 3, 1, 2, 3, 1, 2, 2, 3] => 2, 3, 1, 2, 3, 1, 2, 2, 3
[2, 3, 1, 2, 3, 1, 2, 3, 1] => 2, 3, 1, 2, 3, 1, 2, 3, 1
[2, 3, 1, 2, 3, 1, 2, 3, 2] => 2, 3, 1, 2, 3, 1, 2, 3, 2
[2, 3, 1, 2, 3, 1, 2, 3, 3] => 2, 3, 1, 2, 3, 1, 2, 3, 3
[2, 3, 1, 2, 3, 1, 3, 1, 1] => 2, 3, 1, 2, 3, 1, 3, 1, 1
[2, 3, 1, 2, 3, 1, 3, 1, 2] => 2, 3, 1, 2, 3, 1, 3, 1, 2
[2, 3, 1, 2, 3, 1, 3, 1, 3] => 2, 3, 1, 2, 3, 1, 3, 1, 3
[2, 3, 1, 2, 3, 1, 3, 2, 1] => 2, 3, 1, 2, 3, 1, 3, 2, 1
[2, 3, 1, 2, 3, 1, 3, 2, 2] => 2, 3, 1, 2, 3, 1, 3, 2, 2
[2, 3, 1, 2, 3, 1, 3, 2, 3] => 2, 3, 1, 2, 3, 1, 3, 2, 3
[2, 3, 1, 2, 3, 1, 3, 3, 1] => 2, 3, 1, 2, 3, 1, 3, 3, 1
[2, 3, 1, 2, 3, 1, 3, 3, 2] => 2, 3, 1, 2, 3, 1, 3, 3, 2
[2, 3, 1, 2, 3, 1, 3, 3, 3] => 2, 3, 1, 2, 3, 1, 3, 3, 3
[2, 3, 1, 2, 3, 2, 1, 1, 1] => 2, 3, 1, 2, 3, 2, 1, 1, 1
[2, 3, 1, 2, 3, 2, 1, 1, 2] => 2, 3, 1, 2, 3, 2, 1, 1, 2
[2, 3, 1, 2, 3, 2, 1, 1, 3] => 2, 3, 1, 2, 3, 2, 1, 1, 3
[2, 3, 1, 2, 3, 2, 1, 2, 1] => 2, 3, 1, 2, 3, 2, 1, 2, 1
[2, 3, 1, 2, 3, 2, 1, 2, 2] => 2, 3, 1, 2, 3, 2, 1, 2, 2
[2, 3, 1, 2, 3, 2, 1, 2, 3] => 2, 3, 1, 2, 3, 2, 1, 2, 3
[2, 3, 1, 2, 3, 2, 1, 3, 1] => 2, 3, 1, 2, 3, 2, 1, 3, 1
[2, 3, 1, 2, 3, 2, 1, 3, 2] => 2, 3, 1, 2, 3, 2, 1, 3, 2
[2, 3, 1, 2, 3, 2, 1, 3, 3] => 2, 3, 1, 2, 3, 2, 1, 3, 3
[2, 3, 1, 2, 3, 2, 2, 1, 1] => 2, 3, 1, 2, 3, 2, 2, 1, 1
[2, 3, 1, 2, 3, 2, 2, 1, 2] => 2, 3, 1, 2, 3, 2, 2, 1, 2
[2, 3, 1, 2, 3, 2, 2, 1, 3] => 2, 3, 1, 2, 3, 2, 2, 1, 3
[2, 3, 1, 2, 3, 2, 2, 2, 1] => 2, 3, 1, 2, 3, 2, 2, 2, 1
[2, 3, 1, 2, 3, 2, 2, 2, 2] => 2, 3, 1, 2, 3, 2, 2, 2, 2
[2, 3, 1, 2, 3, 2, 2, 2, 3] => 2, 3, 1, 2, 3, 2, 2, 2, 3
[2, 3, 1, 2, 3, 2, 2, 3, 1] => 2, 3, 1, 2, 3, 2, 2, 3, 1
[2, 3, 1, 2, 3, 2, 2, 3, 2] => 2, 3, 1, 2, 3, 2, 2, 3, 2
[2, 3, 1, 2, 3, 2, 2, 3, 3] => 2, 3, 1, 2, 3, 2, 2, 3, 3
[2, 3, 1, 2, 3, 2, 3, 1, 1] => 2, 3, 1, 2, 3, 2, 3, 1, 1
[2, 3, 1, 2, 3, 2, 3, 1, 2] => 2, 3, 1, 2, 3, 2, 3, 1, 2
[2, 3, 1, 2, 3, 2, 3, 1, 3] => 2, 3, 1, 2, 3, 2, 3, 1, 3
[2, 3, 1, 2, 3, 2, 3, 2, 1] => 2, 3, 1, 2, 3, 2, 3, 2, 1
[2, 3, 1, 2, 3, 2, 3, 2, 2] => 2, 3, 1, 2, 3, 2, 3, 2, 2
[2, 3, 1, 2, 3, 2, 3, 2, 3] => 2, 3, 1, 2, 3, 2, 3, 2, 3
[2, 3, 1, 2, 3, 2, 3, 3, 1] => 2, 3, 1, 2, 3, 2, 3, 3, 1
[2, 3, 1, 2, 3, 2, 3, 3, 2] => 2, 3, 1, 2, 3, 2, 3, 3, 2
[2, 3, 1, 2, 3, 2, 3, 3, 3] => 2, 3, 1, 2, 3, 2, 3, 3, 3
[2, 3, 1, 2, 3, 3, 1, 1, 1] => 2, 3, 1, 2, 3, 3, 1, 1, 1
[2, 3, 1, 2, 3, 3, 1, 1, 2] => 2, 3, 1, 2, 3, 3, 1, 1, 2
[2, 3, 1, 2, 3, 3, 1, 1, 3] => 2, 3, 1, 2, 3, 3, 1, 1, 3
[2, 3, 1, 2, 3, 3, 1, 2, 1] => 2, 3, 1, 2, 3, 3, 1, 2, 1
[2, 3, 1, 2, 3, 3, 1, 2, 2] => 2, 3, 1, 2, 3, 3, 1, 2, 2
[2, 3, 1, 2, 3, 3, 1, 2, 3] => 2, 3, 1, 2, 3, 3, 1, 2, 3
[2, 3, 1, 2, 3, 3, 1, 3, 1] => 2, 3, 1, 2, 3, 3, 1, 3, 1
[2, 3, 1, 2, 3, 3, 1, 3, 2] => 2, 3, 1, 2, 3, 3, 1, 3, 2
[2, 3, 1, 2, 3, 3, 1, 3, 3] => 2, 3, 1, 2, 3, 3, 1, 3, 3
[2, 3, 1, 2, 3, 3, 2, 1, 1] => 2, 3, 1, 2, 3, 3, 2, 1, 1
[2, 3, 1, 2, 3, 3, 2, 1, 2] => 2, 3, 1, 2, 3, 3, 2, 1, 2
[2, 3, 1, 2, 3, 3, 2, 1, 3] => 2, 3, 1, 2, 3, 3, 2, 1, 3
[2, 3, 1, 2, 3, 3, 2, 2, 1] => 2, 3, 1, 2, 3, 3, 2, 2, 1
[2, 3, 1, 2, 3, 3, 2, 2, 2] => 2, 3, 1, 2, 3, 3, 2, 2, 2
[2, 3, 1, 2, 3, 3, 2, 2, 3] => 2, 3, 1, 2, 3, 3, 2, 2, 3
[2, 3, 1, 2, 3, 3, 2, 3, 1] => 2, 3, 1, 2, 3, 3, 2, 3, 1
[2, 3, 1, 2, 3, 3, 2, 3, 2] => 2, 3, 1, 2, 3, 3, 2, 3, 2
[2, 3, 1, 2, 3, 3, 2, 3, 3] => 2, 3, 1, 2, 3, 3, 2, 3, 3
[2, 3, 1, 2, 3, 3, 3, 1, 1] => 2, 3, 1, 2, 3, 3, 3, 1, 1
[2, 3, 1, 2, 3, 3, 3, 1, 2] => 2, 3, 1, 2, 3, 3, 3, 1, 2
[2, 3, 1, 2, 3, 3, 3, 1, 3] => 2, 3, 1, 2, 3, 3, 3, 1, 3
[2, 3, 1, 2, 3, 3, 3, 2, 1] => 2, 3, 1, 2, 3, 3, 3, 2, 1
[2, 3, 1, 2, 3, 3, 3, 2, 2] => 2, 3, 1, 2, 3, 3, 3, 2, 2
[2, 3, 1, 2, 3, 3, 3, 2, 3] => 2, 3, 1, 2, 3, 3, 3, 2, 3
[2, 3, 1, 2, 3, 3, 3, 3, 1] => 2, 3, 1, 2, 3, 3, 3, 3, 1
[2, 3, 1, 2, 3, 3, 3, 3, 2] => 2, 3, 1, 2, 3, 3, 3, 3, 2
[2, 3, 1, 2, 3, 3, 3, 3, 3] => 2, 3, 1, 2, 3, 3, 3, 3, 3
[2, 3, 1, 3, 1, 1, 1, 1, 1] => 2, 3, 1, 3, 1, 1, 1, 1, 1
[2, 3, 1, 3, 1, 1, 1, 1, 2] => 2, 3, 1, 3, 1, 1, 1, 1, 2
[2, 3, 1, 3, 1, 1, 1, 1, 3] => 2, 3, 1, 3, 1, 1, 1, 1, 3
[2, 3, 1, 3, 1, 1, 1, 2, 1] => 2, 3, 1, 3, 1, 1, 1, 2, 1
[2, 3, 1, 3, 1, 1, 1, 2, 2] => 2, 3, 1, 3, 1, 1, 1, 2, 2
[2, 3, 1, 3, 1, 1, 1, 2, 3] => 2, 3, 1, 3, 1, 1, 1, 2, 3
[2, 3, 1, 3, 1, 1, 1, 3, 1] => 2, 3, 1, 3, 1, 1, 1, 3, 1
[2, 3, 1, 3, 1, 1, 1, 3, 2] => 2, 3, 1, 3, 1, 1, 1, 3, 2
[2, 3, 1, 3, 1, 1, 1, 3, 3] => 2, 3, 1, 3, 1, 1, 1, 3, 3
[2, 3, 1, 3, 1, 1, 2, 1, 1] => 2, 3, 1, 3, 1, 1, 2, 1, 1
[2, 3, 1, 3, 1, 1, 2, 1, 2] => 2, 3, 1, 3, 1, 1, 2, 1, 2
[2, 3, 1, 3, 1, 1, 2, 1, 3] => 2, 3, 1, 3, 1, 1, 2, 1, 3
[2, 3, 1, 3, 1, 1, 2, 2, 1] => 2, 3, 1, 3, 1, 1, 2, 2, 1
[2, 3, 1, 3, 1, 1, 2, 2, 2] => 2, 3, 1, 3, 1, 1, 2, 2, 2
[2, 3, 1, 3, 1, 1, 2, 2, 3] => 2, 3, 1, 3, 1, 1, 2, 2, 3
[2, 3, 1, 3, 1, 1, 2, 3, 1] => 2, 3, 1, 3, 1, 1, 2, 3, 1
[2, 3, 1, 3, 1, 1, 2, 3, 2] => 2, 3, 1, 3, 1, 1, 2, 3, 2
[2, 3, 1, 3, 1, 1, 2, 3, 3] => 2, 3, 1, 3, 1, 1, 2, 3, 3
[2, 3, 1, 3, 1, 1, 3, 1, 1] => 2, 3, 1, 3, 1, 1, 3, 1, 1
[2, 3, 1, 3, 1, 1, 3, 1, 2] => 2, 3, 1, 3, 1, 1, 3, 1, 2
[2, 3, 1, 3, 1, 1, 3, 1, 3] => 2, 3, 1, 3, 1, 1, 3, 1, 3
[2, 3, 1, 3, 1, 1, 3, 2, 1] => 2, 3, 1, 3, 1, 1, 3, 2, 1
[2, 3, 1, 3, 1, 1, 3, 2, 2] => 2, 3, 1, 3, 1, 1, 3, 2, 2
[2, 3, 1, 3, 1, 1, 3, 2, 3] => 2, 3, 1, 3, 1, 1, 3, 2, 3
[2, 3, 1, 3, 1, 1, 3, 3, 1] => 2, 3, 1, 3, 1, 1, 3, 3, 1
[2, 3, 1, 3, 1, 1, 3, 3, 2] => 2, 3, 1, 3, 1, 1, 3, 3, 2
[2, 3, 1, 3, 1, 1, 3, 3, 3] => 2, 3, 1, 3, 1, 1, 3, 3, 3
[2, 3, 1, 3, 1, 2, 1, 1, 1] => 2, 3, 1, 3, 1, 2, 1, 1, 1
[2, 3, 1, 3, 1, 2, 1, 1, 2] => 2, 3, 1, 3, 1, 2, 1, 1, 2
[2, 3, 1, 3, 1, 2, 1, 1, 3] => 2, 3, 1, 3, 1, 2, 1, 1, 3
[2, 3, 1, 3, 1, 2, 1, 2, 1] => 2, 3, 1, 3, 1, 2, 1, 2, 1
[2, 3, 1, 3, 1, 2, 1, 2, 2] => 2, 3, 1, 3, 1, 2, 1, 2, 2
[2, 3, 1, 3, 1, 2, 1, 2, 3] => 2, 3, 1, 3, 1, 2, 1, 2, 3
[2, 3, 1, 3, 1, 2, 1, 3, 1] => 2, 3, 1, 3, 1, 2, 1, 3, 1
[2, 3, 1, 3, 1, 2, 1, 3, 2] => 2, 3, 1, 3, 1, 2, 1, 3, 2
[2, 3, 1, 3, 1, 2, 1, 3, 3] => 2, 3, 1, 3, 1, 2, 1, 3, 3
[2, 3, 1, 3, 1, 2, 2, 1, 1] => 2, 3, 1, 3, 1, 2, 2, 1, 1
[2, 3, 1, 3, 1, 2, 2, 1, 2] => 2, 3, 1, 3, 1, 2, 2, 1, 2
[2, 3, 1, 3, 1, 2, 2, 1, 3] => 2, 3, 1, 3, 1, 2, 2, 1, 3
[2, 3, 1, 3, 1, 2, 2, 2, 1] => 2, 3, 1, 3, 1, 2, 2, 2, 1
[2, 3, 1, 3, 1, 2, 2, 2, 2] => 2, 3, 1, 3, 1, 2, 2, 2, 2
[2, 3, 1, 3, 1, 2, 2, 2, 3] => 2, 3, 1, 3, 1, 2, 2, 2, 3
[2, 3, 1, 3, 1, 2, 2, 3, 1] => 2, 3, 1, 3, 1, 2, 2, 3, 1
[2, 3, 1, 3, 1, 2, 2, 3, 2] => 2, 3, 1, 3, 1, 2, 2, 3, 2
[2, 3, 1, 3, 1, 2, 2, 3, 3] => 2, 3, 1, 3, 1, 2, 2, 3, 3
[2, 3, 1, 3, 1, 2, 3, 1, 1] => 2, 3, 1, 3, 1, 2, 3, 1, 1
[2, 3, 1, 3, 1, 2, 3, 1, 2] => 2, 3, 1, 3, 1, 2, 3, 1, 2
[2, 3, 1, 3, 1, 2, 3, 1, 3] => 2, 3, 1, 3, 1, 2, 3, 1, 3
[2, 3, 1, 3, 1, 2, 3, 2, 1] => 2, 3, 1, 3, 1, 2, 3, 2, 1
[2, 3, 1, 3, 1, 2, 3, 2, 2] => 2, 3, 1, 3, 1, 2, 3, 2, 2
[2, 3, 1, 3, 1, 2, 3, 2, 3] => 2, 3, 1, 3, 1, 2, 3, 2, 3
[2, 3, 1, 3, 1, 2, 3, 3, 1] => 2, 3, 1, 3, 1, 2, 3, 3, 1
[2, 3, 1, 3, 1, 2, 3, 3, 2] => 2, 3, 1, 3, 1, 2, 3, 3, 2
[2, 3, 1, 3, 1, 2, 3, 3, 3] => 2, 3, 1, 3, 1, 2, 3, 3, 3
[2, 3, 1, 3, 1, 3, 1, 1, 1] => 2, 3, 1, 3, 1, 3, 1, 1, 1
[2, 3, 1, 3, 1, 3, 1, 1, 2] => 2, 3, 1, 3, 1, 3, 1, 1, 2
[2, 3, 1, 3, 1, 3, 1, 1, 3] => 2, 3, 1, 3, 1, 3, 1, 1, 3
[2, 3, 1, 3, 1, 3, 1, 2, 1] => 2, 3, 1, 3, 1, 3, 1, 2, 1
[2, 3, 1, 3, 1, 3, 1, 2, 2] => 2, 3, 1, 3, 1, 3, 1, 2, 2
[2, 3, 1, 3, 1, 3, 1, 2, 3] => 2, 3, 1, 3, 1, 3, 1, 2, 3
[2, 3, 1, 3, 1, 3, 1, 3, 1] => 2, 3, 1, 3, 1, 3, 1, 3, 1
[2, 3, 1, 3, 1, 3, 1, 3, 2] => 2, 3, 1, 3, 1, 3, 1, 3, 2
[2, 3, 1, 3, 1, 3, 1, 3, 3] => 2, 3, 1, 3, 1, 3, 1, 3, 3
[2, 3, 1, 3, 1, 3, 2, 1, 1] => 2, 3, 1, 3, 1, 3, 2, 1, 1
[2, 3, 1, 3, 1, 3, 2, 1, 2] => 2, 3, 1, 3, 1, 3, 2, 1, 2
[2, 3, 1, 3, 1, 3, 2, 1, 3] => 2, 3, 1, 3, 1, 3, 2, 1, 3
[2, 3, 1, 3, 1, 3, 2, 2, 1] => 2, 3, 1, 3, 1, 3, 2, 2, 1
[2, 3, 1, 3, 1, 3, 2, 2, 2] => 2, 3, 1, 3, 1, 3, 2, 2, 2
[2, 3, 1, 3, 1, 3, 2, 2, 3] => 2, 3, 1, 3, 1, 3, 2, 2, 3
[2, 3, 1, 3, 1, 3, 2, 3, 1] => 2, 3, 1, 3, 1, 3, 2, 3, 1
[2, 3, 1, 3, 1, 3, 2, 3, 2] => 2, 3, 1, 3, 1, 3, 2, 3, 2
[2, 3, 1, 3, 1, 3, 2, 3, 3] => 2, 3, 1, 3, 1, 3, 2, 3, 3
[2, 3, 1, 3, 1, 3, 3, 1, 1] => 2, 3, 1, 3, 1, 3, 3, 1, 1
[2, 3, 1, 3, 1, 3, 3, 1, 2] => 2, 3, 1, 3, 1, 3, 3, 1, 2
[2, 3, 1, 3, 1, 3, 3, 1, 3] => 2, 3, 1, 3, 1, 3, 3, 1, 3
[2, 3, 1, 3, 1, 3, 3, 2, 1] => 2, 3, 1, 3, 1, 3, 3, 2, 1
[2, 3, 1, 3, 1, 3, 3, 2, 2] => 2, 3, 1, 3, 1, 3, 3, 2, 2
[2, 3, 1, 3, 1, 3, 3, 2, 3] => 2, 3, 1, 3, 1, 3, 3, 2, 3
[2, 3, 1, 3, 1, 3, 3, 3, 1] => 2, 3, 1, 3, 1, 3, 3, 3, 1
[2, 3, 1, 3, 1, 3, 3, 3, 2] => 2, 3, 1, 3, 1, 3, 3, 3, 2
[2, 3, 1, 3, 1, 3, 3, 3, 3] => 2, 3, 1, 3, 1, 3, 3, 3, 3
[2, 3, 1, 3, 2, 1, 1, 1, 1] => 2, 3, 1, 3, 2, 1, 1, 1, 1
[2, 3, 1, 3, 2, 1, 1, 1, 2] => 2, 3, 1, 3, 2, 1, 1, 1, 2
[2, 3, 1, 3, 2, 1, 1, 1, 3] => 2, 3, 1, 3, 2, 1, 1, 1, 3
[2, 3, 1, 3, 2, 1, 1, 2, 1] => 2, 3, 1, 3, 2, 1, 1, 2, 1
[2, 3, 1, 3, 2, 1, 1, 2, 2] => 2, 3, 1, 3, 2, 1, 1, 2, 2
[2, 3, 1, 3, 2, 1, 1, 2, 3] => 2, 3, 1, 3, 2, 1, 1, 2, 3
[2, 3, 1, 3, 2, 1, 1, 3, 1] => 2, 3, 1, 3, 2, 1, 1, 3, 1
[2, 3, 1, 3, 2, 1, 1, 3, 2] => 2, 3, 1, 3, 2, 1, 1, 3, 2
[2, 3, 1, 3, 2, 1, 1, 3, 3] => 2, 3, 1, 3, 2, 1, 1, 3, 3
[2, 3, 1, 3, 2, 1, 2, 1, 1] => 2, 3, 1, 3, 2, 1, 2, 1, 1
[2, 3, 1, 3, 2, 1, 2, 1, 2] => 2, 3, 1, 3, 2, 1, 2, 1, 2
[2, 3, 1, 3, 2, 1, 2, 1, 3] => 2, 3, 1, 3, 2, 1, 2, 1, 3
[2, 3, 1, 3, 2, 1, 2, 2, 1] => 2, 3, 1, 3, 2, 1, 2, 2, 1
[2, 3, 1, 3, 2, 1, 2, 2, 2] => 2, 3, 1, 3, 2, 1, 2, 2, 2
[2, 3, 1, 3, 2, 1, 2, 2, 3] => 2, 3, 1, 3, 2, 1, 2, 2, 3
[2, 3, 1, 3, 2, 1, 2, 3, 1] => 2, 3, 1, 3, 2, 1, 2, 3, 1
[2, 3, 1, 3, 2, 1, 2, 3, 2] => 2, 3, 1, 3, 2, 1, 2, 3, 2
[2, 3, 1, 3, 2, 1, 2, 3, 3] => 2, 3, 1, 3, 2, 1, 2, 3, 3
[2, 3, 1, 3, 2, 1, 3, 1, 1] => 2, 3, 1, 3, 2, 1, 3, 1, 1
[2, 3, 1, 3, 2, 1, 3, 1, 2] => 2, 3, 1, 3, 2, 1, 3, 1, 2
[2, 3, 1, 3, 2, 1, 3, 1, 3] => 2, 3, 1, 3, 2, 1, 3, 1, 3
[2, 3, 1, 3, 2, 1, 3, 2, 1] => 2, 3, 1, 3, 2, 1, 3, 2, 1
[2, 3, 1, 3, 2, 1, 3, 2, 2] => 2, 3, 1, 3, 2, 1, 3, 2, 2
[2, 3, 1, 3, 2, 1, 3, 2, 3] => 2, 3, 1, 3, 2, 1, 3, 2, 3
[2, 3, 1, 3, 2, 1, 3, 3, 1] => 2, 3, 1, 3, 2, 1, 3, 3, 1
[2, 3, 1, 3, 2, 1, 3, 3, 2] => 2, 3, 1, 3, 2, 1, 3, 3, 2
[2, 3, 1, 3, 2, 1, 3, 3, 3] => 2, 3, 1, 3, 2, 1, 3, 3, 3
[2, 3, 1, 3, 2, 2, 1, 1, 1] => 2, 3, 1, 3, 2, 2, 1, 1, 1
[2, 3, 1, 3, 2, 2, 1, 1, 2] => 2, 3, 1, 3, 2, 2, 1, 1, 2
[2, 3, 1, 3, 2, 2, 1, 1, 3] => 2, 3, 1, 3, 2, 2, 1, 1, 3
[2, 3, 1, 3, 2, 2, 1, 2, 1] => 2, 3, 1, 3, 2, 2, 1, 2, 1
[2, 3, 1, 3, 2, 2, 1, 2, 2] => 2, 3, 1, 3, 2, 2, 1, 2, 2
[2, 3, 1, 3, 2, 2, 1, 2, 3] => 2, 3, 1, 3, 2, 2, 1, 2, 3
[2, 3, 1, 3, 2, 2, 1, 3, 1] => 2, 3, 1, 3, 2, 2, 1, 3, 1
[2, 3, 1, 3, 2, 2, 1, 3, 2] => 2, 3, 1, 3, 2, 2, 1, 3, 2
[2, 3, 1, 3, 2, 2, 1, 3, 3] => 2, 3, 1, 3, 2, 2, 1, 3, 3
[2, 3, 1, 3, 2, 2, 2, 1, 1] => 2, 3, 1, 3, 2, 2, 2, 1, 1
[2, 3, 1, 3, 2, 2, 2, 1, 2] => 2, 3, 1, 3, 2, 2, 2, 1, 2
[2, 3, 1, 3, 2, 2, 2, 1, 3] => 2, 3, 1, 3, 2, 2, 2, 1, 3
[2, 3, 1, 3, 2, 2, 2, 2, 1] => 2, 3, 1, 3, 2, 2, 2, 2, 1
[2, 3, 1, 3, 2, 2, 2, 2, 2] => 2, 3, 1, 3, 2, 2, 2, 2, 2
[2, 3, 1, 3, 2, 2, 2, 2, 3] => 2, 3, 1, 3, 2, 2, 2, 2, 3
[2, 3, 1, 3, 2, 2, 2, 3, 1] => 2, 3, 1, 3, 2, 2, 2, 3, 1
[2, 3, 1, 3, 2, 2, 2, 3, 2] => 2, 3, 1, 3, 2, 2, 2, 3, 2
[2, 3, 1, 3, 2, 2, 2, 3, 3] => 2, 3, 1, 3, 2, 2, 2, 3, 3
[2, 3, 1, 3, 2, 2, 3, 1, 1] => 2, 3, 1, 3, 2, 2, 3, 1, 1
[2, 3, 1, 3, 2, 2, 3, 1, 2] => 2, 3, 1, 3, 2, 2, 3, 1, 2
[2, 3, 1, 3, 2, 2, 3, 1, 3] => 2, 3, 1, 3, 2, 2, 3, 1, 3
[2, 3, 1, 3, 2, 2, 3, 2, 1] => 2, 3, 1, 3, 2, 2, 3, 2, 1
[2, 3, 1, 3, 2, 2, 3, 2, 2] => 2, 3, 1, 3, 2, 2, 3, 2, 2
[2, 3, 1, 3, 2, 2, 3, 2, 3] => 2, 3, 1, 3, 2, 2, 3, 2, 3
[2, 3, 1, 3, 2, 2, 3, 3, 1] => 2, 3, 1, 3, 2, 2, 3, 3, 1
[2, 3, 1, 3, 2, 2, 3, 3, 2] => 2, 3, 1, 3, 2, 2, 3, 3, 2
[2, 3, 1, 3, 2, 2, 3, 3, 3] => 2, 3, 1, 3, 2, 2, 3, 3, 3
[2, 3, 1, 3, 2, 3, 1, 1, 1] => 2, 3, 1, 3, 2, 3, 1, 1, 1
[2, 3, 1, 3, 2, 3, 1, 1, 2] => 2, 3, 1, 3, 2, 3, 1, 1, 2
[2, 3, 1, 3, 2, 3, 1, 1, 3] => 2, 3, 1, 3, 2, 3, 1, 1, 3
[2, 3, 1, 3, 2, 3, 1, 2, 1] => 2, 3, 1, 3, 2, 3, 1, 2, 1
[2, 3, 1, 3, 2, 3, 1, 2, 2] => 2, 3, 1, 3, 2, 3, 1, 2, 2
[2, 3, 1, 3, 2, 3, 1, 2, 3] => 2, 3, 1, 3, 2, 3, 1, 2, 3
[2, 3, 1, 3, 2, 3, 1, 3, 1] => 2, 3, 1, 3, 2, 3, 1, 3, 1
[2, 3, 1, 3, 2, 3, 1, 3, 2] => 2, 3, 1, 3, 2, 3, 1, 3, 2
[2, 3, 1, 3, 2, 3, 1, 3, 3] => 2, 3, 1, 3, 2, 3, 1, 3, 3
[2, 3, 1, 3, 2, 3, 2, 1, 1] => 2, 3, 1, 3, 2, 3, 2, 1, 1
[2, 3, 1, 3, 2, 3, 2, 1, 2] => 2, 3, 1, 3, 2, 3, 2, 1, 2
[2, 3, 1, 3, 2, 3, 2, 1, 3] => 2, 3, 1, 3, 2, 3, 2, 1, 3
[2, 3, 1, 3, 2, 3, 2, 2, 1] => 2, 3, 1, 3, 2, 3, 2, 2, 1
[2, 3, 1, 3, 2, 3, 2, 2, 2] => 2, 3, 1, 3, 2, 3, 2, 2, 2
[2, 3, 1, 3, 2, 3, 2, 2, 3] => 2, 3, 1, 3, 2, 3, 2, 2, 3
[2, 3, 1, 3, 2, 3, 2, 3, 1] => 2, 3, 1, 3, 2, 3, 2, 3, 1
[2, 3, 1, 3, 2, 3, 2, 3, 2] => 2, 3, 1, 3, 2, 3, 2, 3, 2
[2, 3, 1, 3, 2, 3, 2, 3, 3] => 2, 3, 1, 3, 2, 3, 2, 3, 3
[2, 3, 1, 3, 2, 3, 3, 1, 1] => 2, 3, 1, 3, 2, 3, 3, 1, 1
[2, 3, 1, 3, 2, 3, 3, 1, 2] => 2, 3, 1, 3, 2, 3, 3, 1, 2
[2, 3, 1, 3, 2, 3, 3, 1, 3] => 2, 3, 1, 3, 2, 3, 3, 1, 3
[2, 3, 1, 3, 2, 3, 3, 2, 1] => 2, 3, 1, 3, 2, 3, 3, 2, 1
[2, 3, 1, 3, 2, 3, 3, 2, 2] => 2, 3, 1, 3, 2, 3, 3, 2, 2
[2, 3, 1, 3, 2, 3, 3, 2, 3] => 2, 3, 1, 3, 2, 3, 3, 2, 3
[2, 3, 1, 3, 2, 3, 3, 3, 1] => 2, 3, 1, 3, 2, 3, 3, 3, 1
[2, 3, 1, 3, 2, 3, 3, 3, 2] => 2, 3, 1, 3, 2, 3, 3, 3, 2
[2, 3, 1, 3, 2, 3, 3, 3, 3] => 2, 3, 1, 3, 2, 3, 3, 3, 3
[2, 3, 1, 3, 3, 1, 1, 1, 1] => 2, 3, 1, 3, 3, 1, 1, 1, 1
[2, 3, 1, 3, 3, 1, 1, 1, 2] => 2, 3, 1, 3, 3, 1, 1, 1, 2
[2, 3, 1, 3, 3, 1, 1, 1, 3] => 2, 3, 1, 3, 3, 1, 1, 1, 3
[2, 3, 1, 3, 3, 1, 1, 2, 1] => 2, 3, 1, 3, 3, 1, 1, 2, 1
[2, 3, 1, 3, 3, 1, 1, 2, 2] => 2, 3, 1, 3, 3, 1, 1, 2, 2
[2, 3, 1, 3, 3, 1, 1, 2, 3] => 2, 3, 1, 3, 3, 1, 1, 2, 3
[2, 3, 1, 3, 3, 1, 1, 3, 1] => 2, 3, 1, 3, 3, 1, 1, 3, 1
[2, 3, 1, 3, 3, 1, 1, 3, 2] => 2, 3, 1, 3, 3, 1, 1, 3, 2
[2, 3, 1, 3, 3, 1, 1, 3, 3] => 2, 3, 1, 3, 3, 1, 1, 3, 3
[2, 3, 1, 3, 3, 1, 2, 1, 1] => 2, 3, 1, 3, 3, 1, 2, 1, 1
[2, 3, 1, 3, 3, 1, 2, 1, 2] => 2, 3, 1, 3, 3, 1, 2, 1, 2
[2, 3, 1, 3, 3, 1, 2, 1, 3] => 2, 3, 1, 3, 3, 1, 2, 1, 3
[2, 3, 1, 3, 3, 1, 2, 2, 1] => 2, 3, 1, 3, 3, 1, 2, 2, 1
[2, 3, 1, 3, 3, 1, 2, 2, 2] => 2, 3, 1, 3, 3, 1, 2, 2, 2
[2, 3, 1, 3, 3, 1, 2, 2, 3] => 2, 3, 1, 3, 3, 1, 2, 2, 3
[2, 3, 1, 3, 3, 1, 2, 3, 1] => 2, 3, 1, 3, 3, 1, 2, 3, 1
[2, 3, 1, 3, 3, 1, 2, 3, 2] => 2, 3, 1, 3, 3, 1, 2, 3, 2
[2, 3, 1, 3, 3, 1, 2, 3, 3] => 2, 3, 1, 3, 3, 1, 2, 3, 3
[2, 3, 1, 3, 3, 1, 3, 1, 1] => 2, 3, 1, 3, 3, 1, 3, 1, 1
[2, 3, 1, 3, 3, 1, 3, 1, 2] => 2, 3, 1, 3, 3, 1, 3, 1, 2
[2, 3, 1, 3, 3, 1, 3, 1, 3] => 2, 3, 1, 3, 3, 1, 3, 1, 3
[2, 3, 1, 3, 3, 1, 3, 2, 1] => 2, 3, 1, 3, 3, 1, 3, 2, 1
[2, 3, 1, 3, 3, 1, 3, 2, 2] => 2, 3, 1, 3, 3, 1, 3, 2, 2
[2, 3, 1, 3, 3, 1, 3, 2, 3] => 2, 3, 1, 3, 3, 1, 3, 2, 3
[2, 3, 1, 3, 3, 1, 3, 3, 1] => 2, 3, 1, 3, 3, 1, 3, 3, 1
[2, 3, 1, 3, 3, 1, 3, 3, 2] => 2, 3, 1, 3, 3, 1, 3, 3, 2
[2, 3, 1, 3, 3, 1, 3, 3, 3] => 2, 3, 1, 3, 3, 1, 3, 3, 3
[2, 3, 1, 3, 3, 2, 1, 1, 1] => 2, 3, 1, 3, 3, 2, 1, 1, 1
[2, 3, 1, 3, 3, 2, 1, 1, 2] => 2, 3, 1, 3, 3, 2, 1, 1, 2
[2, 3, 1, 3, 3, 2, 1, 1, 3] => 2, 3, 1, 3, 3, 2, 1, 1, 3
[2, 3, 1, 3, 3, 2, 1, 2, 1] => 2, 3, 1, 3, 3, 2, 1, 2, 1
[2, 3, 1, 3, 3, 2, 1, 2, 2] => 2, 3, 1, 3, 3, 2, 1, 2, 2
[2, 3, 1, 3, 3, 2, 1, 2, 3] => 2, 3, 1, 3, 3, 2, 1, 2, 3
[2, 3, 1, 3, 3, 2, 1, 3, 1] => 2, 3, 1, 3, 3, 2, 1, 3, 1
[2, 3, 1, 3, 3, 2, 1, 3, 2] => 2, 3, 1, 3, 3, 2, 1, 3, 2
[2, 3, 1, 3, 3, 2, 1, 3, 3] => 2, 3, 1, 3, 3, 2, 1, 3, 3
[2, 3, 1, 3, 3, 2, 2, 1, 1] => 2, 3, 1, 3, 3, 2, 2, 1, 1
[2, 3, 1, 3, 3, 2, 2, 1, 2] => 2, 3, 1, 3, 3, 2, 2, 1, 2
[2, 3, 1, 3, 3, 2, 2, 1, 3] => 2, 3, 1, 3, 3, 2, 2, 1, 3
[2, 3, 1, 3, 3, 2, 2, 2, 1] => 2, 3, 1, 3, 3, 2, 2, 2, 1
[2, 3, 1, 3, 3, 2, 2, 2, 2] => 2, 3, 1, 3, 3, 2, 2, 2, 2
[2, 3, 1, 3, 3, 2, 2, 2, 3] => 2, 3, 1, 3, 3, 2, 2, 2, 3
[2, 3, 1, 3, 3, 2, 2, 3, 1] => 2, 3, 1, 3, 3, 2, 2, 3, 1
[2, 3, 1, 3, 3, 2, 2, 3, 2] => 2, 3, 1, 3, 3, 2, 2, 3, 2
[2, 3, 1, 3, 3, 2, 2, 3, 3] => 2, 3, 1, 3, 3, 2, 2, 3, 3
[2, 3, 1, 3, 3, 2, 3, 1, 1] => 2, 3, 1, 3, 3, 2, 3, 1, 1
[2, 3, 1, 3, 3, 2, 3, 1, 2] => 2, 3, 1, 3, 3, 2, 3, 1, 2
[2, 3, 1, 3, 3, 2, 3, 1, 3] => 2, 3, 1, 3, 3, 2, 3, 1, 3
[2, 3, 1, 3, 3, 2, 3, 2, 1] => 2, 3, 1, 3, 3, 2, 3, 2, 1
[2, 3, 1, 3, 3, 2, 3, 2, 2] => 2, 3, 1, 3, 3, 2, 3, 2, 2
[2, 3, 1, 3, 3, 2, 3, 2, 3] => 2, 3, 1, 3, 3, 2, 3, 2, 3
[2, 3, 1, 3, 3, 2, 3, 3, 1] => 2, 3, 1, 3, 3, 2, 3, 3, 1
[2, 3, 1, 3, 3, 2, 3, 3, 2] => 2, 3, 1, 3, 3, 2, 3, 3, 2
[2, 3, 1, 3, 3, 2, 3, 3, 3] => 2, 3, 1, 3, 3, 2, 3, 3, 3
[2, 3, 1, 3, 3, 3, 1, 1, 1] => 2, 3, 1, 3, 3, 3, 1, 1, 1
[2, 3, 1, 3, 3, 3, 1, 1, 2] => 2, 3, 1, 3, 3, 3, 1, 1, 2
[2, 3, 1, 3, 3, 3, 1, 1, 3] => 2, 3, 1, 3, 3, 3, 1, 1, 3
[2, 3, 1, 3, 3, 3, 1, 2, 1] => 2, 3, 1, 3, 3, 3, 1, 2, 1
[2, 3, 1, 3, 3, 3, 1, 2, 2] => 2, 3, 1, 3, 3, 3, 1, 2, 2
[2, 3, 1, 3, 3, 3, 1, 2, 3] => 2, 3, 1, 3, 3, 3, 1, 2, 3
[2, 3, 1, 3, 3, 3, 1, 3, 1] => 2, 3, 1, 3, 3, 3, 1, 3, 1
[2, 3, 1, 3, 3, 3, 1, 3, 2] => 2, 3, 1, 3, 3, 3, 1, 3, 2
[2, 3, 1, 3, 3, 3, 1, 3, 3] => 2, 3, 1, 3, 3, 3, 1, 3, 3
[2, 3, 1, 3, 3, 3, 2, 1, 1] => 2, 3, 1, 3, 3, 3, 2, 1, 1
[2, 3, 1, 3, 3, 3, 2, 1, 2] => 2, 3, 1, 3, 3, 3, 2, 1, 2
[2, 3, 1, 3, 3, 3, 2, 1, 3] => 2, 3, 1, 3, 3, 3, 2, 1, 3
[2, 3, 1, 3, 3, 3, 2, 2, 1] => 2, 3, 1, 3, 3, 3, 2, 2, 1
[2, 3, 1, 3, 3, 3, 2, 2, 2] => 2, 3, 1, 3, 3, 3, 2, 2, 2
[2, 3, 1, 3, 3, 3, 2, 2, 3] => 2, 3, 1, 3, 3, 3, 2, 2, 3
[2, 3, 1, 3, 3, 3, 2, 3, 1] => 2, 3, 1, 3, 3, 3, 2, 3, 1
[2, 3, 1, 3, 3, 3, 2, 3, 2] => 2, 3, 1, 3, 3, 3, 2, 3, 2
[2, 3, 1, 3, 3, 3, 2, 3, 3] => 2, 3, 1, 3, 3, 3, 2, 3, 3
[2, 3, 1, 3, 3, 3, 3, 1, 1] => 2, 3, 1, 3, 3, 3, 3, 1, 1
[2, 3, 1, 3, 3, 3, 3, 1, 2] => 2, 3, 1, 3, 3, 3, 3, 1, 2
[2, 3, 1, 3, 3, 3, 3, 1, 3] => 2, 3, 1, 3, 3, 3, 3, 1, 3
[2, 3, 1, 3, 3, 3, 3, 2, 1] => 2, 3, 1, 3, 3, 3, 3, 2, 1
[2, 3, 1, 3, 3, 3, 3, 2, 2] => 2, 3, 1, 3, 3, 3, 3, 2, 2
[2, 3, 1, 3, 3, 3, 3, 2, 3] => 2, 3, 1, 3, 3, 3, 3, 2, 3
[2, 3, 1, 3, 3, 3, 3, 3, 1] => 2, 3, 1, 3, 3, 3, 3, 3, 1
[2, 3, 1, 3, 3, 3, 3, 3, 2] => 2, 3, 1, 3, 3, 3, 3, 3, 2
[2, 3, 1, 3, 3, 3, 3, 3, 3] => 2, 3, 1, 3, 3, 3, 3, 3, 3
[2, 3, 2, 1, 1, 1, 1, 1, 1] => 2, 3, 2, 1, 1, 1, 1, 1, 1
[2, 3, 2, 1, 1, 1, 1, 1, 2] => 2, 3, 2, 1, 1, 1, 1, 1, 2
[2, 3, 2, 1, 1, 1, 1, 1, 3] => 2, 3, 2, 1, 1, 1, 1, 1, 3
[2, 3, 2, 1, 1, 1, 1, 2, 1] => 2, 3, 2, 1, 1, 1, 1, 2, 1
[2, 3, 2, 1, 1, 1, 1, 2, 2] => 2, 3, 2, 1, 1, 1, 1, 2, 2
[2, 3, 2, 1, 1, 1, 1, 2, 3] => 2, 3, 2, 1, 1, 1, 1, 2, 3
[2, 3, 2, 1, 1, 1, 1, 3, 1] => 2, 3, 2, 1, 1, 1, 1, 3, 1
[2, 3, 2, 1, 1, 1, 1, 3, 2] => 2, 3, 2, 1, 1, 1, 1, 3, 2
[2, 3, 2, 1, 1, 1, 1, 3, 3] => 2, 3, 2, 1, 1, 1, 1, 3, 3
[2, 3, 2, 1, 1, 1, 2, 1, 1] => 2, 3, 2, 1, 1, 1, 2, 1, 1
[2, 3, 2, 1, 1, 1, 2, 1, 2] => 2, 3, 2, 1, 1, 1, 2, 1, 2
[2, 3, 2, 1, 1, 1, 2, 1, 3] => 2, 3, 2, 1, 1, 1, 2, 1, 3
[2, 3, 2, 1, 1, 1, 2, 2, 1] => 2, 3, 2, 1, 1, 1, 2, 2, 1
[2, 3, 2, 1, 1, 1, 2, 2, 2] => 2, 3, 2, 1, 1, 1, 2, 2, 2
[2, 3, 2, 1, 1, 1, 2, 2, 3] => 2, 3, 2, 1, 1, 1, 2, 2, 3
[2, 3, 2, 1, 1, 1, 2, 3, 1] => 2, 3, 2, 1, 1, 1, 2, 3, 1
[2, 3, 2, 1, 1, 1, 2, 3, 2] => 2, 3, 2, 1, 1, 1, 2, 3, 2
[2, 3, 2, 1, 1, 1, 2, 3, 3] => 2, 3, 2, 1, 1, 1, 2, 3, 3
[2, 3, 2, 1, 1, 1, 3, 1, 1] => 2, 3, 2, 1, 1, 1, 3, 1, 1
[2, 3, 2, 1, 1, 1, 3, 1, 2] => 2, 3, 2, 1, 1, 1, 3, 1, 2
[2, 3, 2, 1, 1, 1, 3, 1, 3] => 2, 3, 2, 1, 1, 1, 3, 1, 3
[2, 3, 2, 1, 1, 1, 3, 2, 1] => 2, 3, 2, 1, 1, 1, 3, 2, 1
[2, 3, 2, 1, 1, 1, 3, 2, 2] => 2, 3, 2, 1, 1, 1, 3, 2, 2
[2, 3, 2, 1, 1, 1, 3, 2, 3] => 2, 3, 2, 1, 1, 1, 3, 2, 3
[2, 3, 2, 1, 1, 1, 3, 3, 1] => 2, 3, 2, 1, 1, 1, 3, 3, 1
[2, 3, 2, 1, 1, 1, 3, 3, 2] => 2, 3, 2, 1, 1, 1, 3, 3, 2
[2, 3, 2, 1, 1, 1, 3, 3, 3] => 2, 3, 2, 1, 1, 1, 3, 3, 3
[2, 3, 2, 1, 1, 2, 1, 1, 1] => 2, 3, 2, 1, 1, 2, 1, 1, 1
[2, 3, 2, 1, 1, 2, 1, 1, 2] => 2, 3, 2, 1, 1, 2, 1, 1, 2
[2, 3, 2, 1, 1, 2, 1, 1, 3] => 2, 3, 2, 1, 1, 2, 1, 1, 3
[2, 3, 2, 1, 1, 2, 1, 2, 1] => 2, 3, 2, 1, 1, 2, 1, 2, 1
[2, 3, 2, 1, 1, 2, 1, 2, 2] => 2, 3, 2, 1, 1, 2, 1, 2, 2
[2, 3, 2, 1, 1, 2, 1, 2, 3] => 2, 3, 2, 1, 1, 2, 1, 2, 3
[2, 3, 2, 1, 1, 2, 1, 3, 1] => 2, 3, 2, 1, 1, 2, 1, 3, 1
[2, 3, 2, 1, 1, 2, 1, 3, 2] => 2, 3, 2, 1, 1, 2, 1, 3, 2
[2, 3, 2, 1, 1, 2, 1, 3, 3] => 2, 3, 2, 1, 1, 2, 1, 3, 3
[2, 3, 2, 1, 1, 2, 2, 1, 1] => 2, 3, 2, 1, 1, 2, 2, 1, 1
[2, 3, 2, 1, 1, 2, 2, 1, 2] => 2, 3, 2, 1, 1, 2, 2, 1, 2
[2, 3, 2, 1, 1, 2, 2, 1, 3] => 2, 3, 2, 1, 1, 2, 2, 1, 3
[2, 3, 2, 1, 1, 2, 2, 2, 1] => 2, 3, 2, 1, 1, 2, 2, 2, 1
[2, 3, 2, 1, 1, 2, 2, 2, 2] => 2, 3, 2, 1, 1, 2, 2, 2, 2
[2, 3, 2, 1, 1, 2, 2, 2, 3] => 2, 3, 2, 1, 1, 2, 2, 2, 3
[2, 3, 2, 1, 1, 2, 2, 3, 1] => 2, 3, 2, 1, 1, 2, 2, 3, 1
[2, 3, 2, 1, 1, 2, 2, 3, 2] => 2, 3, 2, 1, 1, 2, 2, 3, 2
[2, 3, 2, 1, 1, 2, 2, 3, 3] => 2, 3, 2, 1, 1, 2, 2, 3, 3
[2, 3, 2, 1, 1, 2, 3, 1, 1] => 2, 3, 2, 1, 1, 2, 3, 1, 1
[2, 3, 2, 1, 1, 2, 3, 1, 2] => 2, 3, 2, 1, 1, 2, 3, 1, 2
[2, 3, 2, 1, 1, 2, 3, 1, 3] => 2, 3, 2, 1, 1, 2, 3, 1, 3
[2, 3, 2, 1, 1, 2, 3, 2, 1] => 2, 3, 2, 1, 1, 2, 3, 2, 1
[2, 3, 2, 1, 1, 2, 3, 2, 2] => 2, 3, 2, 1, 1, 2, 3, 2, 2
[2, 3, 2, 1, 1, 2, 3, 2, 3] => 2, 3, 2, 1, 1, 2, 3, 2, 3
[2, 3, 2, 1, 1, 2, 3, 3, 1] => 2, 3, 2, 1, 1, 2, 3, 3, 1
[2, 3, 2, 1, 1, 2, 3, 3, 2] => 2, 3, 2, 1, 1, 2, 3, 3, 2
[2, 3, 2, 1, 1, 2, 3, 3, 3] => 2, 3, 2, 1, 1, 2, 3, 3, 3
[2, 3, 2, 1, 1, 3, 1, 1, 1] => 2, 3, 2, 1, 1, 3, 1, 1, 1
[2, 3, 2, 1, 1, 3, 1, 1, 2] => 2, 3, 2, 1, 1, 3, 1, 1, 2
[2, 3, 2, 1, 1, 3, 1, 1, 3] => 2, 3, 2, 1, 1, 3, 1, 1, 3
[2, 3, 2, 1, 1, 3, 1, 2, 1] => 2, 3, 2, 1, 1, 3, 1, 2, 1
[2, 3, 2, 1, 1, 3, 1, 2, 2] => 2, 3, 2, 1, 1, 3, 1, 2, 2
[2, 3, 2, 1, 1, 3, 1, 2, 3] => 2, 3, 2, 1, 1, 3, 1, 2, 3
[2, 3, 2, 1, 1, 3, 1, 3, 1] => 2, 3, 2, 1, 1, 3, 1, 3, 1
[2, 3, 2, 1, 1, 3, 1, 3, 2] => 2, 3, 2, 1, 1, 3, 1, 3, 2
[2, 3, 2, 1, 1, 3, 1, 3, 3] => 2, 3, 2, 1, 1, 3, 1, 3, 3
[2, 3, 2, 1, 1, 3, 2, 1, 1] => 2, 3, 2, 1, 1, 3, 2, 1, 1
[2, 3, 2, 1, 1, 3, 2, 1, 2] => 2, 3, 2, 1, 1, 3, 2, 1, 2
[2, 3, 2, 1, 1, 3, 2, 1, 3] => 2, 3, 2, 1, 1, 3, 2, 1, 3
[2, 3, 2, 1, 1, 3, 2, 2, 1] => 2, 3, 2, 1, 1, 3, 2, 2, 1
[2, 3, 2, 1, 1, 3, 2, 2, 2] => 2, 3, 2, 1, 1, 3, 2, 2, 2
[2, 3, 2, 1, 1, 3, 2, 2, 3] => 2, 3, 2, 1, 1, 3, 2, 2, 3
[2, 3, 2, 1, 1, 3, 2, 3, 1] => 2, 3, 2, 1, 1, 3, 2, 3, 1
[2, 3, 2, 1, 1, 3, 2, 3, 2] => 2, 3, 2, 1, 1, 3, 2, 3, 2
[2, 3, 2, 1, 1, 3, 2, 3, 3] => 2, 3, 2, 1, 1, 3, 2, 3, 3
[2, 3, 2, 1, 1, 3, 3, 1, 1] => 2, 3, 2, 1, 1, 3, 3, 1, 1
[2, 3, 2, 1, 1, 3, 3, 1, 2] => 2, 3, 2, 1, 1, 3, 3, 1, 2
[2, 3, 2, 1, 1, 3, 3, 1, 3] => 2, 3, 2, 1, 1, 3, 3, 1, 3
[2, 3, 2, 1, 1, 3, 3, 2, 1] => 2, 3, 2, 1, 1, 3, 3, 2, 1
[2, 3, 2, 1, 1, 3, 3, 2, 2] => 2, 3, 2, 1, 1, 3, 3, 2, 2
[2, 3, 2, 1, 1, 3, 3, 2, 3] => 2, 3, 2, 1, 1, 3, 3, 2, 3
[2, 3, 2, 1, 1, 3, 3, 3, 1] => 2, 3, 2, 1, 1, 3, 3, 3, 1
[2, 3, 2, 1, 1, 3, 3, 3, 2] => 2, 3, 2, 1, 1, 3, 3, 3, 2
[2, 3, 2, 1, 1, 3, 3, 3, 3] => 2, 3, 2, 1, 1, 3, 3, 3, 3
[2, 3, 2, 1, 2, 1, 1, 1, 1] => 2, 3, 2, 1, 2, 1, 1, 1, 1
[2, 3, 2, 1, 2, 1, 1, 1, 2] => 2, 3, 2, 1, 2, 1, 1, 1, 2
[2, 3, 2, 1, 2, 1, 1, 1, 3] => 2, 3, 2, 1, 2, 1, 1, 1, 3
[2, 3, 2, 1, 2, 1, 1, 2, 1] => 2, 3, 2, 1, 2, 1, 1, 2, 1
[2, 3, 2, 1, 2, 1, 1, 2, 2] => 2, 3, 2, 1, 2, 1, 1, 2, 2
[2, 3, 2, 1, 2, 1, 1, 2, 3] => 2, 3, 2, 1, 2, 1, 1, 2, 3
[2, 3, 2, 1, 2, 1, 1, 3, 1] => 2, 3, 2, 1, 2, 1, 1, 3, 1
[2, 3, 2, 1, 2, 1, 1, 3, 2] => 2, 3, 2, 1, 2, 1, 1, 3, 2
[2, 3, 2, 1, 2, 1, 1, 3, 3] => 2, 3, 2, 1, 2, 1, 1, 3, 3
[2, 3, 2, 1, 2, 1, 2, 1, 1] => 2, 3, 2, 1, 2, 1, 2, 1, 1
[2, 3, 2, 1, 2, 1, 2, 1, 2] => 2, 3, 2, 1, 2, 1, 2, 1, 2
[2, 3, 2, 1, 2, 1, 2, 1, 3] => 2, 3, 2, 1, 2, 1, 2, 1, 3
[2, 3, 2, 1, 2, 1, 2, 2, 1] => 2, 3, 2, 1, 2, 1, 2, 2, 1
[2, 3, 2, 1, 2, 1, 2, 2, 2] => 2, 3, 2, 1, 2, 1, 2, 2, 2
[2, 3, 2, 1, 2, 1, 2, 2, 3] => 2, 3, 2, 1, 2, 1, 2, 2, 3
[2, 3, 2, 1, 2, 1, 2, 3, 1] => 2, 3, 2, 1, 2, 1, 2, 3, 1
[2, 3, 2, 1, 2, 1, 2, 3, 2] => 2, 3, 2, 1, 2, 1, 2, 3, 2
[2, 3, 2, 1, 2, 1, 2, 3, 3] => 2, 3, 2, 1, 2, 1, 2, 3, 3
[2, 3, 2, 1, 2, 1, 3, 1, 1] => 2, 3, 2, 1, 2, 1, 3, 1, 1
[2, 3, 2, 1, 2, 1, 3, 1, 2] => 2, 3, 2, 1, 2, 1, 3, 1, 2
[2, 3, 2, 1, 2, 1, 3, 1, 3] => 2, 3, 2, 1, 2, 1, 3, 1, 3
[2, 3, 2, 1, 2, 1, 3, 2, 1] => 2, 3, 2, 1, 2, 1, 3, 2, 1
[2, 3, 2, 1, 2, 1, 3, 2, 2] => 2, 3, 2, 1, 2, 1, 3, 2, 2
[2, 3, 2, 1, 2, 1, 3, 2, 3] => 2, 3, 2, 1, 2, 1, 3, 2, 3
[2, 3, 2, 1, 2, 1, 3, 3, 1] => 2, 3, 2, 1, 2, 1, 3, 3, 1
[2, 3, 2, 1, 2, 1, 3, 3, 2] => 2, 3, 2, 1, 2, 1, 3, 3, 2
[2, 3, 2, 1, 2, 1, 3, 3, 3] => 2, 3, 2, 1, 2, 1, 3, 3, 3
[2, 3, 2, 1, 2, 2, 1, 1, 1] => 2, 3, 2, 1, 2, 2, 1, 1, 1
[2, 3, 2, 1, 2, 2, 1, 1, 2] => 2, 3, 2, 1, 2, 2, 1, 1, 2
[2, 3, 2, 1, 2, 2, 1, 1, 3] => 2, 3, 2, 1, 2, 2, 1, 1, 3
[2, 3, 2, 1, 2, 2, 1, 2, 1] => 2, 3, 2, 1, 2, 2, 1, 2, 1
[2, 3, 2, 1, 2, 2, 1, 2, 2] => 2, 3, 2, 1, 2, 2, 1, 2, 2
[2, 3, 2, 1, 2, 2, 1, 2, 3] => 2, 3, 2, 1, 2, 2, 1, 2, 3
[2, 3, 2, 1, 2, 2, 1, 3, 1] => 2, 3, 2, 1, 2, 2, 1, 3, 1
[2, 3, 2, 1, 2, 2, 1, 3, 2] => 2, 3, 2, 1, 2, 2, 1, 3, 2
[2, 3, 2, 1, 2, 2, 1, 3, 3] => 2, 3, 2, 1, 2, 2, 1, 3, 3
[2, 3, 2, 1, 2, 2, 2, 1, 1] => 2, 3, 2, 1, 2, 2, 2, 1, 1
[2, 3, 2, 1, 2, 2, 2, 1, 2] => 2, 3, 2, 1, 2, 2, 2, 1, 2
[2, 3, 2, 1, 2, 2, 2, 1, 3] => 2, 3, 2, 1, 2, 2, 2, 1, 3
[2, 3, 2, 1, 2, 2, 2, 2, 1] => 2, 3, 2, 1, 2, 2, 2, 2, 1
[2, 3, 2, 1, 2, 2, 2, 2, 2] => 2, 3, 2, 1, 2, 2, 2, 2, 2
[2, 3, 2, 1, 2, 2, 2, 2, 3] => 2, 3, 2, 1, 2, 2, 2, 2, 3
[2, 3, 2, 1, 2, 2, 2, 3, 1] => 2, 3, 2, 1, 2, 2, 2, 3, 1
[2, 3, 2, 1, 2, 2, 2, 3, 2] => 2, 3, 2, 1, 2, 2, 2, 3, 2
[2, 3, 2, 1, 2, 2, 2, 3, 3] => 2, 3, 2, 1, 2, 2, 2, 3, 3
[2, 3, 2, 1, 2, 2, 3, 1, 1] => 2, 3, 2, 1, 2, 2, 3, 1, 1
[2, 3, 2, 1, 2, 2, 3, 1, 2] => 2, 3, 2, 1, 2, 2, 3, 1, 2
[2, 3, 2, 1, 2, 2, 3, 1, 3] => 2, 3, 2, 1, 2, 2, 3, 1, 3
[2, 3, 2, 1, 2, 2, 3, 2, 1] => 2, 3, 2, 1, 2, 2, 3, 2, 1
[2, 3, 2, 1, 2, 2, 3, 2, 2] => 2, 3, 2, 1, 2, 2, 3, 2, 2
[2, 3, 2, 1, 2, 2, 3, 2, 3] => 2, 3, 2, 1, 2, 2, 3, 2, 3
[2, 3, 2, 1, 2, 2, 3, 3, 1] => 2, 3, 2, 1, 2, 2, 3, 3, 1
[2, 3, 2, 1, 2, 2, 3, 3, 2] => 2, 3, 2, 1, 2, 2, 3, 3, 2
[2, 3, 2, 1, 2, 2, 3, 3, 3] => 2, 3, 2, 1, 2, 2, 3, 3, 3
[2, 3, 2, 1, 2, 3, 1, 1, 1] => 2, 3, 2, 1, 2, 3, 1, 1, 1
[2, 3, 2, 1, 2, 3, 1, 1, 2] => 2, 3, 2, 1, 2, 3, 1, 1, 2
[2, 3, 2, 1, 2, 3, 1, 1, 3] => 2, 3, 2, 1, 2, 3, 1, 1, 3
[2, 3, 2, 1, 2, 3, 1, 2, 1] => 2, 3, 2, 1, 2, 3, 1, 2, 1
[2, 3, 2, 1, 2, 3, 1, 2, 2] => 2, 3, 2, 1, 2, 3, 1, 2, 2
[2, 3, 2, 1, 2, 3, 1, 2, 3] => 2, 3, 2, 1, 2, 3, 1, 2, 3
[2, 3, 2, 1, 2, 3, 1, 3, 1] => 2, 3, 2, 1, 2, 3, 1, 3, 1
[2, 3, 2, 1, 2, 3, 1, 3, 2] => 2, 3, 2, 1, 2, 3, 1, 3, 2
[2, 3, 2, 1, 2, 3, 1, 3, 3] => 2, 3, 2, 1, 2, 3, 1, 3, 3
[2, 3, 2, 1, 2, 3, 2, 1, 1] => 2, 3, 2, 1, 2, 3, 2, 1, 1
[2, 3, 2, 1, 2, 3, 2, 1, 2] => 2, 3, 2, 1, 2, 3, 2, 1, 2
[2, 3, 2, 1, 2, 3, 2, 1, 3] => 2, 3, 2, 1, 2, 3, 2, 1, 3
[2, 3, 2, 1, 2, 3, 2, 2, 1] => 2, 3, 2, 1, 2, 3, 2, 2, 1
[2, 3, 2, 1, 2, 3, 2, 2, 2] => 2, 3, 2, 1, 2, 3, 2, 2, 2
[2, 3, 2, 1, 2, 3, 2, 2, 3] => 2, 3, 2, 1, 2, 3, 2, 2, 3
[2, 3, 2, 1, 2, 3, 2, 3, 1] => 2, 3, 2, 1, 2, 3, 2, 3, 1
[2, 3, 2, 1, 2, 3, 2, 3, 2] => 2, 3, 2, 1, 2, 3, 2, 3, 2
[2, 3, 2, 1, 2, 3, 2, 3, 3] => 2, 3, 2, 1, 2, 3, 2, 3, 3
[2, 3, 2, 1, 2, 3, 3, 1, 1] => 2, 3, 2, 1, 2, 3, 3, 1, 1
[2, 3, 2, 1, 2, 3, 3, 1, 2] => 2, 3, 2, 1, 2, 3, 3, 1, 2
[2, 3, 2, 1, 2, 3, 3, 1, 3] => 2, 3, 2, 1, 2, 3, 3, 1, 3
[2, 3, 2, 1, 2, 3, 3, 2, 1] => 2, 3, 2, 1, 2, 3, 3, 2, 1
[2, 3, 2, 1, 2, 3, 3, 2, 2] => 2, 3, 2, 1, 2, 3, 3, 2, 2
[2, 3, 2, 1, 2, 3, 3, 2, 3] => 2, 3, 2, 1, 2, 3, 3, 2, 3
[2, 3, 2, 1, 2, 3, 3, 3, 1] => 2, 3, 2, 1, 2, 3, 3, 3, 1
[2, 3, 2, 1, 2, 3, 3, 3, 2] => 2, 3, 2, 1, 2, 3, 3, 3, 2
[2, 3, 2, 1, 2, 3, 3, 3, 3] => 2, 3, 2, 1, 2, 3, 3, 3, 3
[2, 3, 2, 1, 3, 1, 1, 1, 1] => 2, 3, 2, 1, 3, 1, 1, 1, 1
[2, 3, 2, 1, 3, 1, 1, 1, 2] => 2, 3, 2, 1, 3, 1, 1, 1, 2
[2, 3, 2, 1, 3, 1, 1, 1, 3] => 2, 3, 2, 1, 3, 1, 1, 1, 3
[2, 3, 2, 1, 3, 1, 1, 2, 1] => 2, 3, 2, 1, 3, 1, 1, 2, 1
[2, 3, 2, 1, 3, 1, 1, 2, 2] => 2, 3, 2, 1, 3, 1, 1, 2, 2
[2, 3, 2, 1, 3, 1, 1, 2, 3] => 2, 3, 2, 1, 3, 1, 1, 2, 3
[2, 3, 2, 1, 3, 1, 1, 3, 1] => 2, 3, 2, 1, 3, 1, 1, 3, 1
[2, 3, 2, 1, 3, 1, 1, 3, 2] => 2, 3, 2, 1, 3, 1, 1, 3, 2
[2, 3, 2, 1, 3, 1, 1, 3, 3] => 2, 3, 2, 1, 3, 1, 1, 3, 3
[2, 3, 2, 1, 3, 1, 2, 1, 1] => 2, 3, 2, 1, 3, 1, 2, 1, 1
[2, 3, 2, 1, 3, 1, 2, 1, 2] => 2, 3, 2, 1, 3, 1, 2, 1, 2
[2, 3, 2, 1, 3, 1, 2, 1, 3] => 2, 3, 2, 1, 3, 1, 2, 1, 3
[2, 3, 2, 1, 3, 1, 2, 2, 1] => 2, 3, 2, 1, 3, 1, 2, 2, 1
[2, 3, 2, 1, 3, 1, 2, 2, 2] => 2, 3, 2, 1, 3, 1, 2, 2, 2
[2, 3, 2, 1, 3, 1, 2, 2, 3] => 2, 3, 2, 1, 3, 1, 2, 2, 3
[2, 3, 2, 1, 3, 1, 2, 3, 1] => 2, 3, 2, 1, 3, 1, 2, 3, 1
[2, 3, 2, 1, 3, 1, 2, 3, 2] => 2, 3, 2, 1, 3, 1, 2, 3, 2
[2, 3, 2, 1, 3, 1, 2, 3, 3] => 2, 3, 2, 1, 3, 1, 2, 3, 3
[2, 3, 2, 1, 3, 1, 3, 1, 1] => 2, 3, 2, 1, 3, 1, 3, 1, 1
[2, 3, 2, 1, 3, 1, 3, 1, 2] => 2, 3, 2, 1, 3, 1, 3, 1, 2
[2, 3, 2, 1, 3, 1, 3, 1, 3] => 2, 3, 2, 1, 3, 1, 3, 1, 3
[2, 3, 2, 1, 3, 1, 3, 2, 1] => 2, 3, 2, 1, 3, 1, 3, 2, 1
[2, 3, 2, 1, 3, 1, 3, 2, 2] => 2, 3, 2, 1, 3, 1, 3, 2, 2
[2, 3, 2, 1, 3, 1, 3, 2, 3] => 2, 3, 2, 1, 3, 1, 3, 2, 3
[2, 3, 2, 1, 3, 1, 3, 3, 1] => 2, 3, 2, 1, 3, 1, 3, 3, 1
[2, 3, 2, 1, 3, 1, 3, 3, 2] => 2, 3, 2, 1, 3, 1, 3, 3, 2
[2, 3, 2, 1, 3, 1, 3, 3, 3] => 2, 3, 2, 1, 3, 1, 3, 3, 3
[2, 3, 2, 1, 3, 2, 1, 1, 1] => 2, 3, 2, 1, 3, 2, 1, 1, 1
[2, 3, 2, 1, 3, 2, 1, 1, 2] => 2, 3, 2, 1, 3, 2, 1, 1, 2
[2, 3, 2, 1, 3, 2, 1, 1, 3] => 2, 3, 2, 1, 3, 2, 1, 1, 3
[2, 3, 2, 1, 3, 2, 1, 2, 1] => 2, 3, 2, 1, 3, 2, 1, 2, 1
[2, 3, 2, 1, 3, 2, 1, 2, 2] => 2, 3, 2, 1, 3, 2, 1, 2, 2
[2, 3, 2, 1, 3, 2, 1, 2, 3] => 2, 3, 2, 1, 3, 2, 1, 2, 3
[2, 3, 2, 1, 3, 2, 1, 3, 1] => 2, 3, 2, 1, 3, 2, 1, 3, 1
[2, 3, 2, 1, 3, 2, 1, 3, 2] => 2, 3, 2, 1, 3, 2, 1, 3, 2
[2, 3, 2, 1, 3, 2, 1, 3, 3] => 2, 3, 2, 1, 3, 2, 1, 3, 3
[2, 3, 2, 1, 3, 2, 2, 1, 1] => 2, 3, 2, 1, 3, 2, 2, 1, 1
[2, 3, 2, 1, 3, 2, 2, 1, 2] => 2, 3, 2, 1, 3, 2, 2, 1, 2
[2, 3, 2, 1, 3, 2, 2, 1, 3] => 2, 3, 2, 1, 3, 2, 2, 1, 3
[2, 3, 2, 1, 3, 2, 2, 2, 1] => 2, 3, 2, 1, 3, 2, 2, 2, 1
[2, 3, 2, 1, 3, 2, 2, 2, 2] => 2, 3, 2, 1, 3, 2, 2, 2, 2
[2, 3, 2, 1, 3, 2, 2, 2, 3] => 2, 3, 2, 1, 3, 2, 2, 2, 3
[2, 3, 2, 1, 3, 2, 2, 3, 1] => 2, 3, 2, 1, 3, 2, 2, 3, 1
[2, 3, 2, 1, 3, 2, 2, 3, 2] => 2, 3, 2, 1, 3, 2, 2, 3, 2
[2, 3, 2, 1, 3, 2, 2, 3, 3] => 2, 3, 2, 1, 3, 2, 2, 3, 3
[2, 3, 2, 1, 3, 2, 3, 1, 1] => 2, 3, 2, 1, 3, 2, 3, 1, 1
[2, 3, 2, 1, 3, 2, 3, 1, 2] => 2, 3, 2, 1, 3, 2, 3, 1, 2
[2, 3, 2, 1, 3, 2, 3, 1, 3] => 2, 3, 2, 1, 3, 2, 3, 1, 3
[2, 3, 2, 1, 3, 2, 3, 2, 1] => 2, 3, 2, 1, 3, 2, 3, 2, 1
[2, 3, 2, 1, 3, 2, 3, 2, 2] => 2, 3, 2, 1, 3, 2, 3, 2, 2
[2, 3, 2, 1, 3, 2, 3, 2, 3] => 2, 3, 2, 1, 3, 2, 3, 2, 3
[2, 3, 2, 1, 3, 2, 3, 3, 1] => 2, 3, 2, 1, 3, 2, 3, 3, 1
[2, 3, 2, 1, 3, 2, 3, 3, 2] => 2, 3, 2, 1, 3, 2, 3, 3, 2
[2, 3, 2, 1, 3, 2, 3, 3, 3] => 2, 3, 2, 1, 3, 2, 3, 3, 3
[2, 3, 2, 1, 3, 3, 1, 1, 1] => 2, 3, 2, 1, 3, 3, 1, 1, 1
[2, 3, 2, 1, 3, 3, 1, 1, 2] => 2, 3, 2, 1, 3, 3, 1, 1, 2
[2, 3, 2, 1, 3, 3, 1, 1, 3] => 2, 3, 2, 1, 3, 3, 1, 1, 3
[2, 3, 2, 1, 3, 3, 1, 2, 1] => 2, 3, 2, 1, 3, 3, 1, 2, 1
[2, 3, 2, 1, 3, 3, 1, 2, 2] => 2, 3, 2, 1, 3, 3, 1, 2, 2
[2, 3, 2, 1, 3, 3, 1, 2, 3] => 2, 3, 2, 1, 3, 3, 1, 2, 3
[2, 3, 2, 1, 3, 3, 1, 3, 1] => 2, 3, 2, 1, 3, 3, 1, 3, 1
[2, 3, 2, 1, 3, 3, 1, 3, 2] => 2, 3, 2, 1, 3, 3, 1, 3, 2
[2, 3, 2, 1, 3, 3, 1, 3, 3] => 2, 3, 2, 1, 3, 3, 1, 3, 3
[2, 3, 2, 1, 3, 3, 2, 1, 1] => 2, 3, 2, 1, 3, 3, 2, 1, 1
[2, 3, 2, 1, 3, 3, 2, 1, 2] => 2, 3, 2, 1, 3, 3, 2, 1, 2
[2, 3, 2, 1, 3, 3, 2, 1, 3] => 2, 3, 2, 1, 3, 3, 2, 1, 3
[2, 3, 2, 1, 3, 3, 2, 2, 1] => 2, 3, 2, 1, 3, 3, 2, 2, 1
[2, 3, 2, 1, 3, 3, 2, 2, 2] => 2, 3, 2, 1, 3, 3, 2, 2, 2
[2, 3, 2, 1, 3, 3, 2, 2, 3] => 2, 3, 2, 1, 3, 3, 2, 2, 3
[2, 3, 2, 1, 3, 3, 2, 3, 1] => 2, 3, 2, 1, 3, 3, 2, 3, 1
[2, 3, 2, 1, 3, 3, 2, 3, 2] => 2, 3, 2, 1, 3, 3, 2, 3, 2
[2, 3, 2, 1, 3, 3, 2, 3, 3] => 2, 3, 2, 1, 3, 3, 2, 3, 3
[2, 3, 2, 1, 3, 3, 3, 1, 1] => 2, 3, 2, 1, 3, 3, 3, 1, 1
[2, 3, 2, 1, 3, 3, 3, 1, 2] => 2, 3, 2, 1, 3, 3, 3, 1, 2
[2, 3, 2, 1, 3, 3, 3, 1, 3] => 2, 3, 2, 1, 3, 3, 3, 1, 3
[2, 3, 2, 1, 3, 3, 3, 2, 1] => 2, 3, 2, 1, 3, 3, 3, 2, 1
[2, 3, 2, 1, 3, 3, 3, 2, 2] => 2, 3, 2, 1, 3, 3, 3, 2, 2
[2, 3, 2, 1, 3, 3, 3, 2, 3] => 2, 3, 2, 1, 3, 3, 3, 2, 3
[2, 3, 2, 1, 3, 3, 3, 3, 1] => 2, 3, 2, 1, 3, 3, 3, 3, 1
[2, 3, 2, 1, 3, 3, 3, 3, 2] => 2, 3, 2, 1, 3, 3, 3, 3, 2
[2, 3, 2, 1, 3, 3, 3, 3, 3] => 2, 3, 2, 1, 3, 3, 3, 3, 3
[2, 3, 2, 2, 1, 1, 1, 1, 1] => 2, 3, 2, 2, 1, 1, 1, 1, 1
[2, 3, 2, 2, 1, 1, 1, 1, 2] => 2, 3, 2, 2, 1, 1, 1, 1, 2
[2, 3, 2, 2, 1, 1, 1, 1, 3] => 2, 3, 2, 2, 1, 1, 1, 1, 3
[2, 3, 2, 2, 1, 1, 1, 2, 1] => 2, 3, 2, 2, 1, 1, 1, 2, 1
[2, 3, 2, 2, 1, 1, 1, 2, 2] => 2, 3, 2, 2, 1, 1, 1, 2, 2
[2, 3, 2, 2, 1, 1, 1, 2, 3] => 2, 3, 2, 2, 1, 1, 1, 2, 3
[2, 3, 2, 2, 1, 1, 1, 3, 1] => 2, 3, 2, 2, 1, 1, 1, 3, 1
[2, 3, 2, 2, 1, 1, 1, 3, 2] => 2, 3, 2, 2, 1, 1, 1, 3, 2
[2, 3, 2, 2, 1, 1, 1, 3, 3] => 2, 3, 2, 2, 1, 1, 1, 3, 3
[2, 3, 2, 2, 1, 1, 2, 1, 1] => 2, 3, 2, 2, 1, 1, 2, 1, 1
[2, 3, 2, 2, 1, 1, 2, 1, 2] => 2, 3, 2, 2, 1, 1, 2, 1, 2
[2, 3, 2, 2, 1, 1, 2, 1, 3] => 2, 3, 2, 2, 1, 1, 2, 1, 3
[2, 3, 2, 2, 1, 1, 2, 2, 1] => 2, 3, 2, 2, 1, 1, 2, 2, 1
[2, 3, 2, 2, 1, 1, 2, 2, 2] => 2, 3, 2, 2, 1, 1, 2, 2, 2
[2, 3, 2, 2, 1, 1, 2, 2, 3] => 2, 3, 2, 2, 1, 1, 2, 2, 3
[2, 3, 2, 2, 1, 1, 2, 3, 1] => 2, 3, 2, 2, 1, 1, 2, 3, 1
[2, 3, 2, 2, 1, 1, 2, 3, 2] => 2, 3, 2, 2, 1, 1, 2, 3, 2
[2, 3, 2, 2, 1, 1, 2, 3, 3] => 2, 3, 2, 2, 1, 1, 2, 3, 3
[2, 3, 2, 2, 1, 1, 3, 1, 1] => 2, 3, 2, 2, 1, 1, 3, 1, 1
[2, 3, 2, 2, 1, 1, 3, 1, 2] => 2, 3, 2, 2, 1, 1, 3, 1, 2
[2, 3, 2, 2, 1, 1, 3, 1, 3] => 2, 3, 2, 2, 1, 1, 3, 1, 3
[2, 3, 2, 2, 1, 1, 3, 2, 1] => 2, 3, 2, 2, 1, 1, 3, 2, 1
[2, 3, 2, 2, 1, 1, 3, 2, 2] => 2, 3, 2, 2, 1, 1, 3, 2, 2
[2, 3, 2, 2, 1, 1, 3, 2, 3] => 2, 3, 2, 2, 1, 1, 3, 2, 3
[2, 3, 2, 2, 1, 1, 3, 3, 1] => 2, 3, 2, 2, 1, 1, 3, 3, 1
[2, 3, 2, 2, 1, 1, 3, 3, 2] => 2, 3, 2, 2, 1, 1, 3, 3, 2
[2, 3, 2, 2, 1, 1, 3, 3, 3] => 2, 3, 2, 2, 1, 1, 3, 3, 3
[2, 3, 2, 2, 1, 2, 1, 1, 1] => 2, 3, 2, 2, 1, 2, 1, 1, 1
[2, 3, 2, 2, 1, 2, 1, 1, 2] => 2, 3, 2, 2, 1, 2, 1, 1, 2
[2, 3, 2, 2, 1, 2, 1, 1, 3] => 2, 3, 2, 2, 1, 2, 1, 1, 3
[2, 3, 2, 2, 1, 2, 1, 2, 1] => 2, 3, 2, 2, 1, 2, 1, 2, 1
[2, 3, 2, 2, 1, 2, 1, 2, 2] => 2, 3, 2, 2, 1, 2, 1, 2, 2
[2, 3, 2, 2, 1, 2, 1, 2, 3] => 2, 3, 2, 2, 1, 2, 1, 2, 3
[2, 3, 2, 2, 1, 2, 1, 3, 1] => 2, 3, 2, 2, 1, 2, 1, 3, 1
[2, 3, 2, 2, 1, 2, 1, 3, 2] => 2, 3, 2, 2, 1, 2, 1, 3, 2
[2, 3, 2, 2, 1, 2, 1, 3, 3] => 2, 3, 2, 2, 1, 2, 1, 3, 3
[2, 3, 2, 2, 1, 2, 2, 1, 1] => 2, 3, 2, 2, 1, 2, 2, 1, 1
[2, 3, 2, 2, 1, 2, 2, 1, 2] => 2, 3, 2, 2, 1, 2, 2, 1, 2
[2, 3, 2, 2, 1, 2, 2, 1, 3] => 2, 3, 2, 2, 1, 2, 2, 1, 3
[2, 3, 2, 2, 1, 2, 2, 2, 1] => 2, 3, 2, 2, 1, 2, 2, 2, 1
[2, 3, 2, 2, 1, 2, 2, 2, 2] => 2, 3, 2, 2, 1, 2, 2, 2, 2
[2, 3, 2, 2, 1, 2, 2, 2, 3] => 2, 3, 2, 2, 1, 2, 2, 2, 3
[2, 3, 2, 2, 1, 2, 2, 3, 1] => 2, 3, 2, 2, 1, 2, 2, 3, 1
[2, 3, 2, 2, 1, 2, 2, 3, 2] => 2, 3, 2, 2, 1, 2, 2, 3, 2
[2, 3, 2, 2, 1, 2, 2, 3, 3] => 2, 3, 2, 2, 1, 2, 2, 3, 3
[2, 3, 2, 2, 1, 2, 3, 1, 1] => 2, 3, 2, 2, 1, 2, 3, 1, 1
[2, 3, 2, 2, 1, 2, 3, 1, 2] => 2, 3, 2, 2, 1, 2, 3, 1, 2
[2, 3, 2, 2, 1, 2, 3, 1, 3] => 2, 3, 2, 2, 1, 2, 3, 1, 3
[2, 3, 2, 2, 1, 2, 3, 2, 1] => 2, 3, 2, 2, 1, 2, 3, 2, 1
[2, 3, 2, 2, 1, 2, 3, 2, 2] => 2, 3, 2, 2, 1, 2, 3, 2, 2
[2, 3, 2, 2, 1, 2, 3, 2, 3] => 2, 3, 2, 2, 1, 2, 3, 2, 3
[2, 3, 2, 2, 1, 2, 3, 3, 1] => 2, 3, 2, 2, 1, 2, 3, 3, 1
[2, 3, 2, 2, 1, 2, 3, 3, 2] => 2, 3, 2, 2, 1, 2, 3, 3, 2
[2, 3, 2, 2, 1, 2, 3, 3, 3] => 2, 3, 2, 2, 1, 2, 3, 3, 3
[2, 3, 2, 2, 1, 3, 1, 1, 1] => 2, 3, 2, 2, 1, 3, 1, 1, 1
[2, 3, 2, 2, 1, 3, 1, 1, 2] => 2, 3, 2, 2, 1, 3, 1, 1, 2
[2, 3, 2, 2, 1, 3, 1, 1, 3] => 2, 3, 2, 2, 1, 3, 1, 1, 3
[2, 3, 2, 2, 1, 3, 1, 2, 1] => 2, 3, 2, 2, 1, 3, 1, 2, 1
[2, 3, 2, 2, 1, 3, 1, 2, 2] => 2, 3, 2, 2, 1, 3, 1, 2, 2
[2, 3, 2, 2, 1, 3, 1, 2, 3] => 2, 3, 2, 2, 1, 3, 1, 2, 3
[2, 3, 2, 2, 1, 3, 1, 3, 1] => 2, 3, 2, 2, 1, 3, 1, 3, 1
[2, 3, 2, 2, 1, 3, 1, 3, 2] => 2, 3, 2, 2, 1, 3, 1, 3, 2
[2, 3, 2, 2, 1, 3, 1, 3, 3] => 2, 3, 2, 2, 1, 3, 1, 3, 3
[2, 3, 2, 2, 1, 3, 2, 1, 1] => 2, 3, 2, 2, 1, 3, 2, 1, 1
[2, 3, 2, 2, 1, 3, 2, 1, 2] => 2, 3, 2, 2, 1, 3, 2, 1, 2
[2, 3, 2, 2, 1, 3, 2, 1, 3] => 2, 3, 2, 2, 1, 3, 2, 1, 3
[2, 3, 2, 2, 1, 3, 2, 2, 1] => 2, 3, 2, 2, 1, 3, 2, 2, 1
[2, 3, 2, 2, 1, 3, 2, 2, 2] => 2, 3, 2, 2, 1, 3, 2, 2, 2
[2, 3, 2, 2, 1, 3, 2, 2, 3] => 2, 3, 2, 2, 1, 3, 2, 2, 3
[2, 3, 2, 2, 1, 3, 2, 3, 1] => 2, 3, 2, 2, 1, 3, 2, 3, 1
[2, 3, 2, 2, 1, 3, 2, 3, 2] => 2, 3, 2, 2, 1, 3, 2, 3, 2
[2, 3, 2, 2, 1, 3, 2, 3, 3] => 2, 3, 2, 2, 1, 3, 2, 3, 3
[2, 3, 2, 2, 1, 3, 3, 1, 1] => 2, 3, 2, 2, 1, 3, 3, 1, 1
[2, 3, 2, 2, 1, 3, 3, 1, 2] => 2, 3, 2, 2, 1, 3, 3, 1, 2
[2, 3, 2, 2, 1, 3, 3, 1, 3] => 2, 3, 2, 2, 1, 3, 3, 1, 3
[2, 3, 2, 2, 1, 3, 3, 2, 1] => 2, 3, 2, 2, 1, 3, 3, 2, 1
[2, 3, 2, 2, 1, 3, 3, 2, 2] => 2, 3, 2, 2, 1, 3, 3, 2, 2
[2, 3, 2, 2, 1, 3, 3, 2, 3] => 2, 3, 2, 2, 1, 3, 3, 2, 3
[2, 3, 2, 2, 1, 3, 3, 3, 1] => 2, 3, 2, 2, 1, 3, 3, 3, 1
[2, 3, 2, 2, 1, 3, 3, 3, 2] => 2, 3, 2, 2, 1, 3, 3, 3, 2
[2, 3, 2, 2, 1, 3, 3, 3, 3] => 2, 3, 2, 2, 1, 3, 3, 3, 3
[2, 3, 2, 2, 2, 1, 1, 1, 1] => 2, 3, 2, 2, 2, 1, 1, 1, 1
[2, 3, 2, 2, 2, 1, 1, 1, 2] => 2, 3, 2, 2, 2, 1, 1, 1, 2
[2, 3, 2, 2, 2, 1, 1, 1, 3] => 2, 3, 2, 2, 2, 1, 1, 1, 3
[2, 3, 2, 2, 2, 1, 1, 2, 1] => 2, 3, 2, 2, 2, 1, 1, 2, 1
[2, 3, 2, 2, 2, 1, 1, 2, 2] => 2, 3, 2, 2, 2, 1, 1, 2, 2
[2, 3, 2, 2, 2, 1, 1, 2, 3] => 2, 3, 2, 2, 2, 1, 1, 2, 3
[2, 3, 2, 2, 2, 1, 1, 3, 1] => 2, 3, 2, 2, 2, 1, 1, 3, 1
[2, 3, 2, 2, 2, 1, 1, 3, 2] => 2, 3, 2, 2, 2, 1, 1, 3, 2
[2, 3, 2, 2, 2, 1, 1, 3, 3] => 2, 3, 2, 2, 2, 1, 1, 3, 3
[2, 3, 2, 2, 2, 1, 2, 1, 1] => 2, 3, 2, 2, 2, 1, 2, 1, 1
[2, 3, 2, 2, 2, 1, 2, 1, 2] => 2, 3, 2, 2, 2, 1, 2, 1, 2
[2, 3, 2, 2, 2, 1, 2, 1, 3] => 2, 3, 2, 2, 2, 1, 2, 1, 3
[2, 3, 2, 2, 2, 1, 2, 2, 1] => 2, 3, 2, 2, 2, 1, 2, 2, 1
[2, 3, 2, 2, 2, 1, 2, 2, 2] => 2, 3, 2, 2, 2, 1, 2, 2, 2
[2, 3, 2, 2, 2, 1, 2, 2, 3] => 2, 3, 2, 2, 2, 1, 2, 2, 3
[2, 3, 2, 2, 2, 1, 2, 3, 1] => 2, 3, 2, 2, 2, 1, 2, 3, 1
[2, 3, 2, 2, 2, 1, 2, 3, 2] => 2, 3, 2, 2, 2, 1, 2, 3, 2
[2, 3, 2, 2, 2, 1, 2, 3, 3] => 2, 3, 2, 2, 2, 1, 2, 3, 3
[2, 3, 2, 2, 2, 1, 3, 1, 1] => 2, 3, 2, 2, 2, 1, 3, 1, 1
[2, 3, 2, 2, 2, 1, 3, 1, 2] => 2, 3, 2, 2, 2, 1, 3, 1, 2
[2, 3, 2, 2, 2, 1, 3, 1, 3] => 2, 3, 2, 2, 2, 1, 3, 1, 3
[2, 3, 2, 2, 2, 1, 3, 2, 1] => 2, 3, 2, 2, 2, 1, 3, 2, 1
[2, 3, 2, 2, 2, 1, 3, 2, 2] => 2, 3, 2, 2, 2, 1, 3, 2, 2
[2, 3, 2, 2, 2, 1, 3, 2, 3] => 2, 3, 2, 2, 2, 1, 3, 2, 3
[2, 3, 2, 2, 2, 1, 3, 3, 1] => 2, 3, 2, 2, 2, 1, 3, 3, 1
[2, 3, 2, 2, 2, 1, 3, 3, 2] => 2, 3, 2, 2, 2, 1, 3, 3, 2
[2, 3, 2, 2, 2, 1, 3, 3, 3] => 2, 3, 2, 2, 2, 1, 3, 3, 3
[2, 3, 2, 2, 2, 2, 1, 1, 1] => 2, 3, 2, 2, 2, 2, 1, 1, 1
[2, 3, 2, 2, 2, 2, 1, 1, 2] => 2, 3, 2, 2, 2, 2, 1, 1, 2
[2, 3, 2, 2, 2, 2, 1, 1, 3] => 2, 3, 2, 2, 2, 2, 1, 1, 3
[2, 3, 2, 2, 2, 2, 1, 2, 1] => 2, 3, 2, 2, 2, 2, 1, 2, 1
[2, 3, 2, 2, 2, 2, 1, 2, 2] => 2, 3, 2, 2, 2, 2, 1, 2, 2
[2, 3, 2, 2, 2, 2, 1, 2, 3] => 2, 3, 2, 2, 2, 2, 1, 2, 3
[2, 3, 2, 2, 2, 2, 1, 3, 1] => 2, 3, 2, 2, 2, 2, 1, 3, 1
[2, 3, 2, 2, 2, 2, 1, 3, 2] => 2, 3, 2, 2, 2, 2, 1, 3, 2
[2, 3, 2, 2, 2, 2, 1, 3, 3] => 2, 3, 2, 2, 2, 2, 1, 3, 3
[2, 3, 2, 2, 2, 2, 2, 1, 1] => 2, 3, 2, 2, 2, 2, 2, 1, 1
[2, 3, 2, 2, 2, 2, 2, 1, 2] => 2, 3, 2, 2, 2, 2, 2, 1, 2
[2, 3, 2, 2, 2, 2, 2, 1, 3] => 2, 3, 2, 2, 2, 2, 2, 1, 3
[2, 3, 2, 2, 2, 2, 2, 2, 1] => 2, 3, 2, 2, 2, 2, 2, 2, 1
[2, 3, 2, 2, 2, 2, 2, 2, 2] => 2, 3, 2, 2, 2, 2, 2, 2, 2
[2, 3, 2, 2, 2, 2, 2, 2, 3] => 2, 3, 2, 2, 2, 2, 2, 2, 3
[2, 3, 2, 2, 2, 2, 2, 3, 1] => 2, 3, 2, 2, 2, 2, 2, 3, 1
[2, 3, 2, 2, 2, 2, 2, 3, 2] => 2, 3, 2, 2, 2, 2, 2, 3, 2
[2, 3, 2, 2, 2, 2, 2, 3, 3] => 2, 3, 2, 2, 2, 2, 2, 3, 3
[2, 3, 2, 2, 2, 2, 3, 1, 1] => 2, 3, 2, 2, 2, 2, 3, 1, 1
[2, 3, 2, 2, 2, 2, 3, 1, 2] => 2, 3, 2, 2, 2, 2, 3, 1, 2
[2, 3, 2, 2, 2, 2, 3, 1, 3] => 2, 3, 2, 2, 2, 2, 3, 1, 3
[2, 3, 2, 2, 2, 2, 3, 2, 1] => 2, 3, 2, 2, 2, 2, 3, 2, 1
[2, 3, 2, 2, 2, 2, 3, 2, 2] => 2, 3, 2, 2, 2, 2, 3, 2, 2
[2, 3, 2, 2, 2, 2, 3, 2, 3] => 2, 3, 2, 2, 2, 2, 3, 2, 3
[2, 3, 2, 2, 2, 2, 3, 3, 1] => 2, 3, 2, 2, 2, 2, 3, 3, 1
[2, 3, 2, 2, 2, 2, 3, 3, 2] => 2, 3, 2, 2, 2, 2, 3, 3, 2
[2, 3, 2, 2, 2, 2, 3, 3, 3] => 2, 3, 2, 2, 2, 2, 3, 3, 3
[2, 3, 2, 2, 2, 3, 1, 1, 1] => 2, 3, 2, 2, 2, 3, 1, 1, 1
[2, 3, 2, 2, 2, 3, 1, 1, 2] => 2, 3, 2, 2, 2, 3, 1, 1, 2
[2, 3, 2, 2, 2, 3, 1, 1, 3] => 2, 3, 2, 2, 2, 3, 1, 1, 3
[2, 3, 2, 2, 2, 3, 1, 2, 1] => 2, 3, 2, 2, 2, 3, 1, 2, 1
[2, 3, 2, 2, 2, 3, 1, 2, 2] => 2, 3, 2, 2, 2, 3, 1, 2, 2
[2, 3, 2, 2, 2, 3, 1, 2, 3] => 2, 3, 2, 2, 2, 3, 1, 2, 3
[2, 3, 2, 2, 2, 3, 1, 3, 1] => 2, 3, 2, 2, 2, 3, 1, 3, 1
[2, 3, 2, 2, 2, 3, 1, 3, 2] => 2, 3, 2, 2, 2, 3, 1, 3, 2
[2, 3, 2, 2, 2, 3, 1, 3, 3] => 2, 3, 2, 2, 2, 3, 1, 3, 3
[2, 3, 2, 2, 2, 3, 2, 1, 1] => 2, 3, 2, 2, 2, 3, 2, 1, 1
[2, 3, 2, 2, 2, 3, 2, 1, 2] => 2, 3, 2, 2, 2, 3, 2, 1, 2
[2, 3, 2, 2, 2, 3, 2, 1, 3] => 2, 3, 2, 2, 2, 3, 2, 1, 3
[2, 3, 2, 2, 2, 3, 2, 2, 1] => 2, 3, 2, 2, 2, 3, 2, 2, 1
[2, 3, 2, 2, 2, 3, 2, 2, 2] => 2, 3, 2, 2, 2, 3, 2, 2, 2
[2, 3, 2, 2, 2, 3, 2, 2, 3] => 2, 3, 2, 2, 2, 3, 2, 2, 3
[2, 3, 2, 2, 2, 3, 2, 3, 1] => 2, 3, 2, 2, 2, 3, 2, 3, 1
[2, 3, 2, 2, 2, 3, 2, 3, 2] => 2, 3, 2, 2, 2, 3, 2, 3, 2
[2, 3, 2, 2, 2, 3, 2, 3, 3] => 2, 3, 2, 2, 2, 3, 2, 3, 3
[2, 3, 2, 2, 2, 3, 3, 1, 1] => 2, 3, 2, 2, 2, 3, 3, 1, 1
[2, 3, 2, 2, 2, 3, 3, 1, 2] => 2, 3, 2, 2, 2, 3, 3, 1, 2
[2, 3, 2, 2, 2, 3, 3, 1, 3] => 2, 3, 2, 2, 2, 3, 3, 1, 3
[2, 3, 2, 2, 2, 3, 3, 2, 1] => 2, 3, 2, 2, 2, 3, 3, 2, 1
[2, 3, 2, 2, 2, 3, 3, 2, 2] => 2, 3, 2, 2, 2, 3, 3, 2, 2
[2, 3, 2, 2, 2, 3, 3, 2, 3] => 2, 3, 2, 2, 2, 3, 3, 2, 3
[2, 3, 2, 2, 2, 3, 3, 3, 1] => 2, 3, 2, 2, 2, 3, 3, 3, 1
[2, 3, 2, 2, 2, 3, 3, 3, 2] => 2, 3, 2, 2, 2, 3, 3, 3, 2
[2, 3, 2, 2, 2, 3, 3, 3, 3] => 2, 3, 2, 2, 2, 3, 3, 3, 3
[2, 3, 2, 2, 3, 1, 1, 1, 1] => 2, 3, 2, 2, 3, 1, 1, 1, 1
[2, 3, 2, 2, 3, 1, 1, 1, 2] => 2, 3, 2, 2, 3, 1, 1, 1, 2
[2, 3, 2, 2, 3, 1, 1, 1, 3] => 2, 3, 2, 2, 3, 1, 1, 1, 3
[2, 3, 2, 2, 3, 1, 1, 2, 1] => 2, 3, 2, 2, 3, 1, 1, 2, 1
[2, 3, 2, 2, 3, 1, 1, 2, 2] => 2, 3, 2, 2, 3, 1, 1, 2, 2
[2, 3, 2, 2, 3, 1, 1, 2, 3] => 2, 3, 2, 2, 3, 1, 1, 2, 3
[2, 3, 2, 2, 3, 1, 1, 3, 1] => 2, 3, 2, 2, 3, 1, 1, 3, 1
[2, 3, 2, 2, 3, 1, 1, 3, 2] => 2, 3, 2, 2, 3, 1, 1, 3, 2
[2, 3, 2, 2, 3, 1, 1, 3, 3] => 2, 3, 2, 2, 3, 1, 1, 3, 3
[2, 3, 2, 2, 3, 1, 2, 1, 1] => 2, 3, 2, 2, 3, 1, 2, 1, 1
[2, 3, 2, 2, 3, 1, 2, 1, 2] => 2, 3, 2, 2, 3, 1, 2, 1, 2
[2, 3, 2, 2, 3, 1, 2, 1, 3] => 2, 3, 2, 2, 3, 1, 2, 1, 3
[2, 3, 2, 2, 3, 1, 2, 2, 1] => 2, 3, 2, 2, 3, 1, 2, 2, 1
[2, 3, 2, 2, 3, 1, 2, 2, 2] => 2, 3, 2, 2, 3, 1, 2, 2, 2
[2, 3, 2, 2, 3, 1, 2, 2, 3] => 2, 3, 2, 2, 3, 1, 2, 2, 3
[2, 3, 2, 2, 3, 1, 2, 3, 1] => 2, 3, 2, 2, 3, 1, 2, 3, 1
[2, 3, 2, 2, 3, 1, 2, 3, 2] => 2, 3, 2, 2, 3, 1, 2, 3, 2
[2, 3, 2, 2, 3, 1, 2, 3, 3] => 2, 3, 2, 2, 3, 1, 2, 3, 3
[2, 3, 2, 2, 3, 1, 3, 1, 1] => 2, 3, 2, 2, 3, 1, 3, 1, 1
[2, 3, 2, 2, 3, 1, 3, 1, 2] => 2, 3, 2, 2, 3, 1, 3, 1, 2
[2, 3, 2, 2, 3, 1, 3, 1, 3] => 2, 3, 2, 2, 3, 1, 3, 1, 3
[2, 3, 2, 2, 3, 1, 3, 2, 1] => 2, 3, 2, 2, 3, 1, 3, 2, 1
[2, 3, 2, 2, 3, 1, 3, 2, 2] => 2, 3, 2, 2, 3, 1, 3, 2, 2
[2, 3, 2, 2, 3, 1, 3, 2, 3] => 2, 3, 2, 2, 3, 1, 3, 2, 3
[2, 3, 2, 2, 3, 1, 3, 3, 1] => 2, 3, 2, 2, 3, 1, 3, 3, 1
[2, 3, 2, 2, 3, 1, 3, 3, 2] => 2, 3, 2, 2, 3, 1, 3, 3, 2
[2, 3, 2, 2, 3, 1, 3, 3, 3] => 2, 3, 2, 2, 3, 1, 3, 3, 3
[2, 3, 2, 2, 3, 2, 1, 1, 1] => 2, 3, 2, 2, 3, 2, 1, 1, 1
[2, 3, 2, 2, 3, 2, 1, 1, 2] => 2, 3, 2, 2, 3, 2, 1, 1, 2
[2, 3, 2, 2, 3, 2, 1, 1, 3] => 2, 3, 2, 2, 3, 2, 1, 1, 3
[2, 3, 2, 2, 3, 2, 1, 2, 1] => 2, 3, 2, 2, 3, 2, 1, 2, 1
[2, 3, 2, 2, 3, 2, 1, 2, 2] => 2, 3, 2, 2, 3, 2, 1, 2, 2
[2, 3, 2, 2, 3, 2, 1, 2, 3] => 2, 3, 2, 2, 3, 2, 1, 2, 3
[2, 3, 2, 2, 3, 2, 1, 3, 1] => 2, 3, 2, 2, 3, 2, 1, 3, 1
[2, 3, 2, 2, 3, 2, 1, 3, 2] => 2, 3, 2, 2, 3, 2, 1, 3, 2
[2, 3, 2, 2, 3, 2, 1, 3, 3] => 2, 3, 2, 2, 3, 2, 1, 3, 3
[2, 3, 2, 2, 3, 2, 2, 1, 1] => 2, 3, 2, 2, 3, 2, 2, 1, 1
[2, 3, 2, 2, 3, 2, 2, 1, 2] => 2, 3, 2, 2, 3, 2, 2, 1, 2
[2, 3, 2, 2, 3, 2, 2, 1, 3] => 2, 3, 2, 2, 3, 2, 2, 1, 3
[2, 3, 2, 2, 3, 2, 2, 2, 1] => 2, 3, 2, 2, 3, 2, 2, 2, 1
[2, 3, 2, 2, 3, 2, 2, 2, 2] => 2, 3, 2, 2, 3, 2, 2, 2, 2
[2, 3, 2, 2, 3, 2, 2, 2, 3] => 2, 3, 2, 2, 3, 2, 2, 2, 3
[2, 3, 2, 2, 3, 2, 2, 3, 1] => 2, 3, 2, 2, 3, 2, 2, 3, 1
[2, 3, 2, 2, 3, 2, 2, 3, 2] => 2, 3, 2, 2, 3, 2, 2, 3, 2
[2, 3, 2, 2, 3, 2, 2, 3, 3] => 2, 3, 2, 2, 3, 2, 2, 3, 3
[2, 3, 2, 2, 3, 2, 3, 1, 1] => 2, 3, 2, 2, 3, 2, 3, 1, 1
[2, 3, 2, 2, 3, 2, 3, 1, 2] => 2, 3, 2, 2, 3, 2, 3, 1, 2
[2, 3, 2, 2, 3, 2, 3, 1, 3] => 2, 3, 2, 2, 3, 2, 3, 1, 3
[2, 3, 2, 2, 3, 2, 3, 2, 1] => 2, 3, 2, 2, 3, 2, 3, 2, 1
[2, 3, 2, 2, 3, 2, 3, 2, 2] => 2, 3, 2, 2, 3, 2, 3, 2, 2
[2, 3, 2, 2, 3, 2, 3, 2, 3] => 2, 3, 2, 2, 3, 2, 3, 2, 3
[2, 3, 2, 2, 3, 2, 3, 3, 1] => 2, 3, 2, 2, 3, 2, 3, 3, 1
[2, 3, 2, 2, 3, 2, 3, 3, 2] => 2, 3, 2, 2, 3, 2, 3, 3, 2
[2, 3, 2, 2, 3, 2, 3, 3, 3] => 2, 3, 2, 2, 3, 2, 3, 3, 3
[2, 3, 2, 2, 3, 3, 1, 1, 1] => 2, 3, 2, 2, 3, 3, 1, 1, 1
[2, 3, 2, 2, 3, 3, 1, 1, 2] => 2, 3, 2, 2, 3, 3, 1, 1, 2
[2, 3, 2, 2, 3, 3, 1, 1, 3] => 2, 3, 2, 2, 3, 3, 1, 1, 3
[2, 3, 2, 2, 3, 3, 1, 2, 1] => 2, 3, 2, 2, 3, 3, 1, 2, 1
[2, 3, 2, 2, 3, 3, 1, 2, 2] => 2, 3, 2, 2, 3, 3, 1, 2, 2
[2, 3, 2, 2, 3, 3, 1, 2, 3] => 2, 3, 2, 2, 3, 3, 1, 2, 3
[2, 3, 2, 2, 3, 3, 1, 3, 1] => 2, 3, 2, 2, 3, 3, 1, 3, 1
[2, 3, 2, 2, 3, 3, 1, 3, 2] => 2, 3, 2, 2, 3, 3, 1, 3, 2
[2, 3, 2, 2, 3, 3, 1, 3, 3] => 2, 3, 2, 2, 3, 3, 1, 3, 3
[2, 3, 2, 2, 3, 3, 2, 1, 1] => 2, 3, 2, 2, 3, 3, 2, 1, 1
[2, 3, 2, 2, 3, 3, 2, 1, 2] => 2, 3, 2, 2, 3, 3, 2, 1, 2
[2, 3, 2, 2, 3, 3, 2, 1, 3] => 2, 3, 2, 2, 3, 3, 2, 1, 3
[2, 3, 2, 2, 3, 3, 2, 2, 1] => 2, 3, 2, 2, 3, 3, 2, 2, 1
[2, 3, 2, 2, 3, 3, 2, 2, 2] => 2, 3, 2, 2, 3, 3, 2, 2, 2
[2, 3, 2, 2, 3, 3, 2, 2, 3] => 2, 3, 2, 2, 3, 3, 2, 2, 3
[2, 3, 2, 2, 3, 3, 2, 3, 1] => 2, 3, 2, 2, 3, 3, 2, 3, 1
[2, 3, 2, 2, 3, 3, 2, 3, 2] => 2, 3, 2, 2, 3, 3, 2, 3, 2
[2, 3, 2, 2, 3, 3, 2, 3, 3] => 2, 3, 2, 2, 3, 3, 2, 3, 3
[2, 3, 2, 2, 3, 3, 3, 1, 1] => 2, 3, 2, 2, 3, 3, 3, 1, 1
[2, 3, 2, 2, 3, 3, 3, 1, 2] => 2, 3, 2, 2, 3, 3, 3, 1, 2
[2, 3, 2, 2, 3, 3, 3, 1, 3] => 2, 3, 2, 2, 3, 3, 3, 1, 3
[2, 3, 2, 2, 3, 3, 3, 2, 1] => 2, 3, 2, 2, 3, 3, 3, 2, 1
[2, 3, 2, 2, 3, 3, 3, 2, 2] => 2, 3, 2, 2, 3, 3, 3, 2, 2
[2, 3, 2, 2, 3, 3, 3, 2, 3] => 2, 3, 2, 2, 3, 3, 3, 2, 3
[2, 3, 2, 2, 3, 3, 3, 3, 1] => 2, 3, 2, 2, 3, 3, 3, 3, 1
[2, 3, 2, 2, 3, 3, 3, 3, 2] => 2, 3, 2, 2, 3, 3, 3, 3, 2
[2, 3, 2, 2, 3, 3, 3, 3, 3] => 2, 3, 2, 2, 3, 3, 3, 3, 3
[2, 3, 2, 3, 1, 1, 1, 1, 1] => 2, 3, 2, 3, 1, 1, 1, 1, 1
[2, 3, 2, 3, 1, 1, 1, 1, 2] => 2, 3, 2, 3, 1, 1, 1, 1, 2
[2, 3, 2, 3, 1, 1, 1, 1, 3] => 2, 3, 2, 3, 1, 1, 1, 1, 3
[2, 3, 2, 3, 1, 1, 1, 2, 1] => 2, 3, 2, 3, 1, 1, 1, 2, 1
[2, 3, 2, 3, 1, 1, 1, 2, 2] => 2, 3, 2, 3, 1, 1, 1, 2, 2
[2, 3, 2, 3, 1, 1, 1, 2, 3] => 2, 3, 2, 3, 1, 1, 1, 2, 3
[2, 3, 2, 3, 1, 1, 1, 3, 1] => 2, 3, 2, 3, 1, 1, 1, 3, 1
[2, 3, 2, 3, 1, 1, 1, 3, 2] => 2, 3, 2, 3, 1, 1, 1, 3, 2
[2, 3, 2, 3, 1, 1, 1, 3, 3] => 2, 3, 2, 3, 1, 1, 1, 3, 3
[2, 3, 2, 3, 1, 1, 2, 1, 1] => 2, 3, 2, 3, 1, 1, 2, 1, 1
[2, 3, 2, 3, 1, 1, 2, 1, 2] => 2, 3, 2, 3, 1, 1, 2, 1, 2
[2, 3, 2, 3, 1, 1, 2, 1, 3] => 2, 3, 2, 3, 1, 1, 2, 1, 3
[2, 3, 2, 3, 1, 1, 2, 2, 1] => 2, 3, 2, 3, 1, 1, 2, 2, 1
[2, 3, 2, 3, 1, 1, 2, 2, 2] => 2, 3, 2, 3, 1, 1, 2, 2, 2
[2, 3, 2, 3, 1, 1, 2, 2, 3] => 2, 3, 2, 3, 1, 1, 2, 2, 3
[2, 3, 2, 3, 1, 1, 2, 3, 1] => 2, 3, 2, 3, 1, 1, 2, 3, 1
[2, 3, 2, 3, 1, 1, 2, 3, 2] => 2, 3, 2, 3, 1, 1, 2, 3, 2
[2, 3, 2, 3, 1, 1, 2, 3, 3] => 2, 3, 2, 3, 1, 1, 2, 3, 3
[2, 3, 2, 3, 1, 1, 3, 1, 1] => 2, 3, 2, 3, 1, 1, 3, 1, 1
[2, 3, 2, 3, 1, 1, 3, 1, 2] => 2, 3, 2, 3, 1, 1, 3, 1, 2
[2, 3, 2, 3, 1, 1, 3, 1, 3] => 2, 3, 2, 3, 1, 1, 3, 1, 3
[2, 3, 2, 3, 1, 1, 3, 2, 1] => 2, 3, 2, 3, 1, 1, 3, 2, 1
[2, 3, 2, 3, 1, 1, 3, 2, 2] => 2, 3, 2, 3, 1, 1, 3, 2, 2
[2, 3, 2, 3, 1, 1, 3, 2, 3] => 2, 3, 2, 3, 1, 1, 3, 2, 3
[2, 3, 2, 3, 1, 1, 3, 3, 1] => 2, 3, 2, 3, 1, 1, 3, 3, 1
[2, 3, 2, 3, 1, 1, 3, 3, 2] => 2, 3, 2, 3, 1, 1, 3, 3, 2
[2, 3, 2, 3, 1, 1, 3, 3, 3] => 2, 3, 2, 3, 1, 1, 3, 3, 3
[2, 3, 2, 3, 1, 2, 1, 1, 1] => 2, 3, 2, 3, 1, 2, 1, 1, 1
[2, 3, 2, 3, 1, 2, 1, 1, 2] => 2, 3, 2, 3, 1, 2, 1, 1, 2
[2, 3, 2, 3, 1, 2, 1, 1, 3] => 2, 3, 2, 3, 1, 2, 1, 1, 3
[2, 3, 2, 3, 1, 2, 1, 2, 1] => 2, 3, 2, 3, 1, 2, 1, 2, 1
[2, 3, 2, 3, 1, 2, 1, 2, 2] => 2, 3, 2, 3, 1, 2, 1, 2, 2
[2, 3, 2, 3, 1, 2, 1, 2, 3] => 2, 3, 2, 3, 1, 2, 1, 2, 3
[2, 3, 2, 3, 1, 2, 1, 3, 1] => 2, 3, 2, 3, 1, 2, 1, 3, 1
[2, 3, 2, 3, 1, 2, 1, 3, 2] => 2, 3, 2, 3, 1, 2, 1, 3, 2
[2, 3, 2, 3, 1, 2, 1, 3, 3] => 2, 3, 2, 3, 1, 2, 1, 3, 3
[2, 3, 2, 3, 1, 2, 2, 1, 1] => 2, 3, 2, 3, 1, 2, 2, 1, 1
[2, 3, 2, 3, 1, 2, 2, 1, 2] => 2, 3, 2, 3, 1, 2, 2, 1, 2
[2, 3, 2, 3, 1, 2, 2, 1, 3] => 2, 3, 2, 3, 1, 2, 2, 1, 3
[2, 3, 2, 3, 1, 2, 2, 2, 1] => 2, 3, 2, 3, 1, 2, 2, 2, 1
[2, 3, 2, 3, 1, 2, 2, 2, 2] => 2, 3, 2, 3, 1, 2, 2, 2, 2
[2, 3, 2, 3, 1, 2, 2, 2, 3] => 2, 3, 2, 3, 1, 2, 2, 2, 3
[2, 3, 2, 3, 1, 2, 2, 3, 1] => 2, 3, 2, 3, 1, 2, 2, 3, 1
[2, 3, 2, 3, 1, 2, 2, 3, 2] => 2, 3, 2, 3, 1, 2, 2, 3, 2
[2, 3, 2, 3, 1, 2, 2, 3, 3] => 2, 3, 2, 3, 1, 2, 2, 3, 3
[2, 3, 2, 3, 1, 2, 3, 1, 1] => 2, 3, 2, 3, 1, 2, 3, 1, 1
[2, 3, 2, 3, 1, 2, 3, 1, 2] => 2, 3, 2, 3, 1, 2, 3, 1, 2
[2, 3, 2, 3, 1, 2, 3, 1, 3] => 2, 3, 2, 3, 1, 2, 3, 1, 3
[2, 3, 2, 3, 1, 2, 3, 2, 1] => 2, 3, 2, 3, 1, 2, 3, 2, 1
[2, 3, 2, 3, 1, 2, 3, 2, 2] => 2, 3, 2, 3, 1, 2, 3, 2, 2
[2, 3, 2, 3, 1, 2, 3, 2, 3] => 2, 3, 2, 3, 1, 2, 3, 2, 3
[2, 3, 2, 3, 1, 2, 3, 3, 1] => 2, 3, 2, 3, 1, 2, 3, 3, 1
[2, 3, 2, 3, 1, 2, 3, 3, 2] => 2, 3, 2, 3, 1, 2, 3, 3, 2
[2, 3, 2, 3, 1, 2, 3, 3, 3] => 2, 3, 2, 3, 1, 2, 3, 3, 3
[2, 3, 2, 3, 1, 3, 1, 1, 1] => 2, 3, 2, 3, 1, 3, 1, 1, 1
[2, 3, 2, 3, 1, 3, 1, 1, 2] => 2, 3, 2, 3, 1, 3, 1, 1, 2
[2, 3, 2, 3, 1, 3, 1, 1, 3] => 2, 3, 2, 3, 1, 3, 1, 1, 3
[2, 3, 2, 3, 1, 3, 1, 2, 1] => 2, 3, 2, 3, 1, 3, 1, 2, 1
[2, 3, 2, 3, 1, 3, 1, 2, 2] => 2, 3, 2, 3, 1, 3, 1, 2, 2
[2, 3, 2, 3, 1, 3, 1, 2, 3] => 2, 3, 2, 3, 1, 3, 1, 2, 3
[2, 3, 2, 3, 1, 3, 1, 3, 1] => 2, 3, 2, 3, 1, 3, 1, 3, 1
[2, 3, 2, 3, 1, 3, 1, 3, 2] => 2, 3, 2, 3, 1, 3, 1, 3, 2
[2, 3, 2, 3, 1, 3, 1, 3, 3] => 2, 3, 2, 3, 1, 3, 1, 3, 3
[2, 3, 2, 3, 1, 3, 2, 1, 1] => 2, 3, 2, 3, 1, 3, 2, 1, 1
[2, 3, 2, 3, 1, 3, 2, 1, 2] => 2, 3, 2, 3, 1, 3, 2, 1, 2
[2, 3, 2, 3, 1, 3, 2, 1, 3] => 2, 3, 2, 3, 1, 3, 2, 1, 3
[2, 3, 2, 3, 1, 3, 2, 2, 1] => 2, 3, 2, 3, 1, 3, 2, 2, 1
[2, 3, 2, 3, 1, 3, 2, 2, 2] => 2, 3, 2, 3, 1, 3, 2, 2, 2
[2, 3, 2, 3, 1, 3, 2, 2, 3] => 2, 3, 2, 3, 1, 3, 2, 2, 3
[2, 3, 2, 3, 1, 3, 2, 3, 1] => 2, 3, 2, 3, 1, 3, 2, 3, 1
[2, 3, 2, 3, 1, 3, 2, 3, 2] => 2, 3, 2, 3, 1, 3, 2, 3, 2
[2, 3, 2, 3, 1, 3, 2, 3, 3] => 2, 3, 2, 3, 1, 3, 2, 3, 3
[2, 3, 2, 3, 1, 3, 3, 1, 1] => 2, 3, 2, 3, 1, 3, 3, 1, 1
[2, 3, 2, 3, 1, 3, 3, 1, 2] => 2, 3, 2, 3, 1, 3, 3, 1, 2
[2, 3, 2, 3, 1, 3, 3, 1, 3] => 2, 3, 2, 3, 1, 3, 3, 1, 3
[2, 3, 2, 3, 1, 3, 3, 2, 1] => 2, 3, 2, 3, 1, 3, 3, 2, 1
[2, 3, 2, 3, 1, 3, 3, 2, 2] => 2, 3, 2, 3, 1, 3, 3, 2, 2
[2, 3, 2, 3, 1, 3, 3, 2, 3] => 2, 3, 2, 3, 1, 3, 3, 2, 3
[2, 3, 2, 3, 1, 3, 3, 3, 1] => 2, 3, 2, 3, 1, 3, 3, 3, 1
[2, 3, 2, 3, 1, 3, 3, 3, 2] => 2, 3, 2, 3, 1, 3, 3, 3, 2
[2, 3, 2, 3, 1, 3, 3, 3, 3] => 2, 3, 2, 3, 1, 3, 3, 3, 3
[2, 3, 2, 3, 2, 1, 1, 1, 1] => 2, 3, 2, 3, 2, 1, 1, 1, 1
[2, 3, 2, 3, 2, 1, 1, 1, 2] => 2, 3, 2, 3, 2, 1, 1, 1, 2
[2, 3, 2, 3, 2, 1, 1, 1, 3] => 2, 3, 2, 3, 2, 1, 1, 1, 3
[2, 3, 2, 3, 2, 1, 1, 2, 1] => 2, 3, 2, 3, 2, 1, 1, 2, 1
[2, 3, 2, 3, 2, 1, 1, 2, 2] => 2, 3, 2, 3, 2, 1, 1, 2, 2
[2, 3, 2, 3, 2, 1, 1, 2, 3] => 2, 3, 2, 3, 2, 1, 1, 2, 3
[2, 3, 2, 3, 2, 1, 1, 3, 1] => 2, 3, 2, 3, 2, 1, 1, 3, 1
[2, 3, 2, 3, 2, 1, 1, 3, 2] => 2, 3, 2, 3, 2, 1, 1, 3, 2
[2, 3, 2, 3, 2, 1, 1, 3, 3] => 2, 3, 2, 3, 2, 1, 1, 3, 3
[2, 3, 2, 3, 2, 1, 2, 1, 1] => 2, 3, 2, 3, 2, 1, 2, 1, 1
[2, 3, 2, 3, 2, 1, 2, 1, 2] => 2, 3, 2, 3, 2, 1, 2, 1, 2
[2, 3, 2, 3, 2, 1, 2, 1, 3] => 2, 3, 2, 3, 2, 1, 2, 1, 3
[2, 3, 2, 3, 2, 1, 2, 2, 1] => 2, 3, 2, 3, 2, 1, 2, 2, 1
[2, 3, 2, 3, 2, 1, 2, 2, 2] => 2, 3, 2, 3, 2, 1, 2, 2, 2
[2, 3, 2, 3, 2, 1, 2, 2, 3] => 2, 3, 2, 3, 2, 1, 2, 2, 3
[2, 3, 2, 3, 2, 1, 2, 3, 1] => 2, 3, 2, 3, 2, 1, 2, 3, 1
[2, 3, 2, 3, 2, 1, 2, 3, 2] => 2, 3, 2, 3, 2, 1, 2, 3, 2
[2, 3, 2, 3, 2, 1, 2, 3, 3] => 2, 3, 2, 3, 2, 1, 2, 3, 3
[2, 3, 2, 3, 2, 1, 3, 1, 1] => 2, 3, 2, 3, 2, 1, 3, 1, 1
[2, 3, 2, 3, 2, 1, 3, 1, 2] => 2, 3, 2, 3, 2, 1, 3, 1, 2
[2, 3, 2, 3, 2, 1, 3, 1, 3] => 2, 3, 2, 3, 2, 1, 3, 1, 3
[2, 3, 2, 3, 2, 1, 3, 2, 1] => 2, 3, 2, 3, 2, 1, 3, 2, 1
[2, 3, 2, 3, 2, 1, 3, 2, 2] => 2, 3, 2, 3, 2, 1, 3, 2, 2
[2, 3, 2, 3, 2, 1, 3, 2, 3] => 2, 3, 2, 3, 2, 1, 3, 2, 3
[2, 3, 2, 3, 2, 1, 3, 3, 1] => 2, 3, 2, 3, 2, 1, 3, 3, 1
[2, 3, 2, 3, 2, 1, 3, 3, 2] => 2, 3, 2, 3, 2, 1, 3, 3, 2
[2, 3, 2, 3, 2, 1, 3, 3, 3] => 2, 3, 2, 3, 2, 1, 3, 3, 3
[2, 3, 2, 3, 2, 2, 1, 1, 1] => 2, 3, 2, 3, 2, 2, 1, 1, 1
[2, 3, 2, 3, 2, 2, 1, 1, 2] => 2, 3, 2, 3, 2, 2, 1, 1, 2
[2, 3, 2, 3, 2, 2, 1, 1, 3] => 2, 3, 2, 3, 2, 2, 1, 1, 3
[2, 3, 2, 3, 2, 2, 1, 2, 1] => 2, 3, 2, 3, 2, 2, 1, 2, 1
[2, 3, 2, 3, 2, 2, 1, 2, 2] => 2, 3, 2, 3, 2, 2, 1, 2, 2
[2, 3, 2, 3, 2, 2, 1, 2, 3] => 2, 3, 2, 3, 2, 2, 1, 2, 3
[2, 3, 2, 3, 2, 2, 1, 3, 1] => 2, 3, 2, 3, 2, 2, 1, 3, 1
[2, 3, 2, 3, 2, 2, 1, 3, 2] => 2, 3, 2, 3, 2, 2, 1, 3, 2
[2, 3, 2, 3, 2, 2, 1, 3, 3] => 2, 3, 2, 3, 2, 2, 1, 3, 3
[2, 3, 2, 3, 2, 2, 2, 1, 1] => 2, 3, 2, 3, 2, 2, 2, 1, 1
[2, 3, 2, 3, 2, 2, 2, 1, 2] => 2, 3, 2, 3, 2, 2, 2, 1, 2
[2, 3, 2, 3, 2, 2, 2, 1, 3] => 2, 3, 2, 3, 2, 2, 2, 1, 3
[2, 3, 2, 3, 2, 2, 2, 2, 1] => 2, 3, 2, 3, 2, 2, 2, 2, 1
[2, 3, 2, 3, 2, 2, 2, 2, 2] => 2, 3, 2, 3, 2, 2, 2, 2, 2
[2, 3, 2, 3, 2, 2, 2, 2, 3] => 2, 3, 2, 3, 2, 2, 2, 2, 3
[2, 3, 2, 3, 2, 2, 2, 3, 1] => 2, 3, 2, 3, 2, 2, 2, 3, 1
[2, 3, 2, 3, 2, 2, 2, 3, 2] => 2, 3, 2, 3, 2, 2, 2, 3, 2
[2, 3, 2, 3, 2, 2, 2, 3, 3] => 2, 3, 2, 3, 2, 2, 2, 3, 3
[2, 3, 2, 3, 2, 2, 3, 1, 1] => 2, 3, 2, 3, 2, 2, 3, 1, 1
[2, 3, 2, 3, 2, 2, 3, 1, 2] => 2, 3, 2, 3, 2, 2, 3, 1, 2
[2, 3, 2, 3, 2, 2, 3, 1, 3] => 2, 3, 2, 3, 2, 2, 3, 1, 3
[2, 3, 2, 3, 2, 2, 3, 2, 1] => 2, 3, 2, 3, 2, 2, 3, 2, 1
[2, 3, 2, 3, 2, 2, 3, 2, 2] => 2, 3, 2, 3, 2, 2, 3, 2, 2
[2, 3, 2, 3, 2, 2, 3, 2, 3] => 2, 3, 2, 3, 2, 2, 3, 2, 3
[2, 3, 2, 3, 2, 2, 3, 3, 1] => 2, 3, 2, 3, 2, 2, 3, 3, 1
[2, 3, 2, 3, 2, 2, 3, 3, 2] => 2, 3, 2, 3, 2, 2, 3, 3, 2
[2, 3, 2, 3, 2, 2, 3, 3, 3] => 2, 3, 2, 3, 2, 2, 3, 3, 3
[2, 3, 2, 3, 2, 3, 1, 1, 1] => 2, 3, 2, 3, 2, 3, 1, 1, 1
[2, 3, 2, 3, 2, 3, 1, 1, 2] => 2, 3, 2, 3, 2, 3, 1, 1, 2
[2, 3, 2, 3, 2, 3, 1, 1, 3] => 2, 3, 2, 3, 2, 3, 1, 1, 3
[2, 3, 2, 3, 2, 3, 1, 2, 1] => 2, 3, 2, 3, 2, 3, 1, 2, 1
[2, 3, 2, 3, 2, 3, 1, 2, 2] => 2, 3, 2, 3, 2, 3, 1, 2, 2
[2, 3, 2, 3, 2, 3, 1, 2, 3] => 2, 3, 2, 3, 2, 3, 1, 2, 3
[2, 3, 2, 3, 2, 3, 1, 3, 1] => 2, 3, 2, 3, 2, 3, 1, 3, 1
[2, 3, 2, 3, 2, 3, 1, 3, 2] => 2, 3, 2, 3, 2, 3, 1, 3, 2
[2, 3, 2, 3, 2, 3, 1, 3, 3] => 2, 3, 2, 3, 2, 3, 1, 3, 3
[2, 3, 2, 3, 2, 3, 2, 1, 1] => 2, 3, 2, 3, 2, 3, 2, 1, 1
[2, 3, 2, 3, 2, 3, 2, 1, 2] => 2, 3, 2, 3, 2, 3, 2, 1, 2
[2, 3, 2, 3, 2, 3, 2, 1, 3] => 2, 3, 2, 3, 2, 3, 2, 1, 3
[2, 3, 2, 3, 2, 3, 2, 2, 1] => 2, 3, 2, 3, 2, 3, 2, 2, 1
[2, 3, 2, 3, 2, 3, 2, 2, 2] => 2, 3, 2, 3, 2, 3, 2, 2, 2
[2, 3, 2, 3, 2, 3, 2, 2, 3] => 2, 3, 2, 3, 2, 3, 2, 2, 3
[2, 3, 2, 3, 2, 3, 2, 3, 1] => 2, 3, 2, 3, 2, 3, 2, 3, 1
[2, 3, 2, 3, 2, 3, 2, 3, 2] => 2, 3, 2, 3, 2, 3, 2, 3, 2
[2, 3, 2, 3, 2, 3, 2, 3, 3] => 2, 3, 2, 3, 2, 3, 2, 3, 3
[2, 3, 2, 3, 2, 3, 3, 1, 1] => 2, 3, 2, 3, 2, 3, 3, 1, 1
[2, 3, 2, 3, 2, 3, 3, 1, 2] => 2, 3, 2, 3, 2, 3, 3, 1, 2
[2, 3, 2, 3, 2, 3, 3, 1, 3] => 2, 3, 2, 3, 2, 3, 3, 1, 3
[2, 3, 2, 3, 2, 3, 3, 2, 1] => 2, 3, 2, 3, 2, 3, 3, 2, 1
[2, 3, 2, 3, 2, 3, 3, 2, 2] => 2, 3, 2, 3, 2, 3, 3, 2, 2
[2, 3, 2, 3, 2, 3, 3, 2, 3] => 2, 3, 2, 3, 2, 3, 3, 2, 3
[2, 3, 2, 3, 2, 3, 3, 3, 1] => 2, 3, 2, 3, 2, 3, 3, 3, 1
[2, 3, 2, 3, 2, 3, 3, 3, 2] => 2, 3, 2, 3, 2, 3, 3, 3, 2
[2, 3, 2, 3, 2, 3, 3, 3, 3] => 2, 3, 2, 3, 2, 3, 3, 3, 3
[2, 3, 2, 3, 3, 1, 1, 1, 1] => 2, 3, 2, 3, 3, 1, 1, 1, 1
[2, 3, 2, 3, 3, 1, 1, 1, 2] => 2, 3, 2, 3, 3, 1, 1, 1, 2
[2, 3, 2, 3, 3, 1, 1, 1, 3] => 2, 3, 2, 3, 3, 1, 1, 1, 3
[2, 3, 2, 3, 3, 1, 1, 2, 1] => 2, 3, 2, 3, 3, 1, 1, 2, 1
[2, 3, 2, 3, 3, 1, 1, 2, 2] => 2, 3, 2, 3, 3, 1, 1, 2, 2
[2, 3, 2, 3, 3, 1, 1, 2, 3] => 2, 3, 2, 3, 3, 1, 1, 2, 3
[2, 3, 2, 3, 3, 1, 1, 3, 1] => 2, 3, 2, 3, 3, 1, 1, 3, 1
[2, 3, 2, 3, 3, 1, 1, 3, 2] => 2, 3, 2, 3, 3, 1, 1, 3, 2
[2, 3, 2, 3, 3, 1, 1, 3, 3] => 2, 3, 2, 3, 3, 1, 1, 3, 3
[2, 3, 2, 3, 3, 1, 2, 1, 1] => 2, 3, 2, 3, 3, 1, 2, 1, 1
[2, 3, 2, 3, 3, 1, 2, 1, 2] => 2, 3, 2, 3, 3, 1, 2, 1, 2
[2, 3, 2, 3, 3, 1, 2, 1, 3] => 2, 3, 2, 3, 3, 1, 2, 1, 3
[2, 3, 2, 3, 3, 1, 2, 2, 1] => 2, 3, 2, 3, 3, 1, 2, 2, 1
[2, 3, 2, 3, 3, 1, 2, 2, 2] => 2, 3, 2, 3, 3, 1, 2, 2, 2
[2, 3, 2, 3, 3, 1, 2, 2, 3] => 2, 3, 2, 3, 3, 1, 2, 2, 3
[2, 3, 2, 3, 3, 1, 2, 3, 1] => 2, 3, 2, 3, 3, 1, 2, 3, 1
[2, 3, 2, 3, 3, 1, 2, 3, 2] => 2, 3, 2, 3, 3, 1, 2, 3, 2
[2, 3, 2, 3, 3, 1, 2, 3, 3] => 2, 3, 2, 3, 3, 1, 2, 3, 3
[2, 3, 2, 3, 3, 1, 3, 1, 1] => 2, 3, 2, 3, 3, 1, 3, 1, 1
[2, 3, 2, 3, 3, 1, 3, 1, 2] => 2, 3, 2, 3, 3, 1, 3, 1, 2
[2, 3, 2, 3, 3, 1, 3, 1, 3] => 2, 3, 2, 3, 3, 1, 3, 1, 3
[2, 3, 2, 3, 3, 1, 3, 2, 1] => 2, 3, 2, 3, 3, 1, 3, 2, 1
[2, 3, 2, 3, 3, 1, 3, 2, 2] => 2, 3, 2, 3, 3, 1, 3, 2, 2
[2, 3, 2, 3, 3, 1, 3, 2, 3] => 2, 3, 2, 3, 3, 1, 3, 2, 3
[2, 3, 2, 3, 3, 1, 3, 3, 1] => 2, 3, 2, 3, 3, 1, 3, 3, 1
[2, 3, 2, 3, 3, 1, 3, 3, 2] => 2, 3, 2, 3, 3, 1, 3, 3, 2
[2, 3, 2, 3, 3, 1, 3, 3, 3] => 2, 3, 2, 3, 3, 1, 3, 3, 3
[2, 3, 2, 3, 3, 2, 1, 1, 1] => 2, 3, 2, 3, 3, 2, 1, 1, 1
[2, 3, 2, 3, 3, 2, 1, 1, 2] => 2, 3, 2, 3, 3, 2, 1, 1, 2
[2, 3, 2, 3, 3, 2, 1, 1, 3] => 2, 3, 2, 3, 3, 2, 1, 1, 3
[2, 3, 2, 3, 3, 2, 1, 2, 1] => 2, 3, 2, 3, 3, 2, 1, 2, 1
[2, 3, 2, 3, 3, 2, 1, 2, 2] => 2, 3, 2, 3, 3, 2, 1, 2, 2
[2, 3, 2, 3, 3, 2, 1, 2, 3] => 2, 3, 2, 3, 3, 2, 1, 2, 3
[2, 3, 2, 3, 3, 2, 1, 3, 1] => 2, 3, 2, 3, 3, 2, 1, 3, 1
[2, 3, 2, 3, 3, 2, 1, 3, 2] => 2, 3, 2, 3, 3, 2, 1, 3, 2
[2, 3, 2, 3, 3, 2, 1, 3, 3] => 2, 3, 2, 3, 3, 2, 1, 3, 3
[2, 3, 2, 3, 3, 2, 2, 1, 1] => 2, 3, 2, 3, 3, 2, 2, 1, 1
[2, 3, 2, 3, 3, 2, 2, 1, 2] => 2, 3, 2, 3, 3, 2, 2, 1, 2
[2, 3, 2, 3, 3, 2, 2, 1, 3] => 2, 3, 2, 3, 3, 2, 2, 1, 3
[2, 3, 2, 3, 3, 2, 2, 2, 1] => 2, 3, 2, 3, 3, 2, 2, 2, 1
[2, 3, 2, 3, 3, 2, 2, 2, 2] => 2, 3, 2, 3, 3, 2, 2, 2, 2
[2, 3, 2, 3, 3, 2, 2, 2, 3] => 2, 3, 2, 3, 3, 2, 2, 2, 3
[2, 3, 2, 3, 3, 2, 2, 3, 1] => 2, 3, 2, 3, 3, 2, 2, 3, 1
[2, 3, 2, 3, 3, 2, 2, 3, 2] => 2, 3, 2, 3, 3, 2, 2, 3, 2
[2, 3, 2, 3, 3, 2, 2, 3, 3] => 2, 3, 2, 3, 3, 2, 2, 3, 3
[2, 3, 2, 3, 3, 2, 3, 1, 1] => 2, 3, 2, 3, 3, 2, 3, 1, 1
[2, 3, 2, 3, 3, 2, 3, 1, 2] => 2, 3, 2, 3, 3, 2, 3, 1, 2
[2, 3, 2, 3, 3, 2, 3, 1, 3] => 2, 3, 2, 3, 3, 2, 3, 1, 3
[2, 3, 2, 3, 3, 2, 3, 2, 1] => 2, 3, 2, 3, 3, 2, 3, 2, 1
[2, 3, 2, 3, 3, 2, 3, 2, 2] => 2, 3, 2, 3, 3, 2, 3, 2, 2
[2, 3, 2, 3, 3, 2, 3, 2, 3] => 2, 3, 2, 3, 3, 2, 3, 2, 3
[2, 3, 2, 3, 3, 2, 3, 3, 1] => 2, 3, 2, 3, 3, 2, 3, 3, 1
[2, 3, 2, 3, 3, 2, 3, 3, 2] => 2, 3, 2, 3, 3, 2, 3, 3, 2
[2, 3, 2, 3, 3, 2, 3, 3, 3] => 2, 3, 2, 3, 3, 2, 3, 3, 3
[2, 3, 2, 3, 3, 3, 1, 1, 1] => 2, 3, 2, 3, 3, 3, 1, 1, 1
[2, 3, 2, 3, 3, 3, 1, 1, 2] => 2, 3, 2, 3, 3, 3, 1, 1, 2
[2, 3, 2, 3, 3, 3, 1, 1, 3] => 2, 3, 2, 3, 3, 3, 1, 1, 3
[2, 3, 2, 3, 3, 3, 1, 2, 1] => 2, 3, 2, 3, 3, 3, 1, 2, 1
[2, 3, 2, 3, 3, 3, 1, 2, 2] => 2, 3, 2, 3, 3, 3, 1, 2, 2
[2, 3, 2, 3, 3, 3, 1, 2, 3] => 2, 3, 2, 3, 3, 3, 1, 2, 3
[2, 3, 2, 3, 3, 3, 1, 3, 1] => 2, 3, 2, 3, 3, 3, 1, 3, 1
[2, 3, 2, 3, 3, 3, 1, 3, 2] => 2, 3, 2, 3, 3, 3, 1, 3, 2
[2, 3, 2, 3, 3, 3, 1, 3, 3] => 2, 3, 2, 3, 3, 3, 1, 3, 3
[2, 3, 2, 3, 3, 3, 2, 1, 1] => 2, 3, 2, 3, 3, 3, 2, 1, 1
[2, 3, 2, 3, 3, 3, 2, 1, 2] => 2, 3, 2, 3, 3, 3, 2, 1, 2
[2, 3, 2, 3, 3, 3, 2, 1, 3] => 2, 3, 2, 3, 3, 3, 2, 1, 3
[2, 3, 2, 3, 3, 3, 2, 2, 1] => 2, 3, 2, 3, 3, 3, 2, 2, 1
[2, 3, 2, 3, 3, 3, 2, 2, 2] => 2, 3, 2, 3, 3, 3, 2, 2, 2
[2, 3, 2, 3, 3, 3, 2, 2, 3] => 2, 3, 2, 3, 3, 3, 2, 2, 3
[2, 3, 2, 3, 3, 3, 2, 3, 1] => 2, 3, 2, 3, 3, 3, 2, 3, 1
[2, 3, 2, 3, 3, 3, 2, 3, 2] => 2, 3, 2, 3, 3, 3, 2, 3, 2
[2, 3, 2, 3, 3, 3, 2, 3, 3] => 2, 3, 2, 3, 3, 3, 2, 3, 3
[2, 3, 2, 3, 3, 3, 3, 1, 1] => 2, 3, 2, 3, 3, 3, 3, 1, 1
[2, 3, 2, 3, 3, 3, 3, 1, 2] => 2, 3, 2, 3, 3, 3, 3, 1, 2
[2, 3, 2, 3, 3, 3, 3, 1, 3] => 2, 3, 2, 3, 3, 3, 3, 1, 3
[2, 3, 2, 3, 3, 3, 3, 2, 1] => 2, 3, 2, 3, 3, 3, 3, 2, 1
[2, 3, 2, 3, 3, 3, 3, 2, 2] => 2, 3, 2, 3, 3, 3, 3, 2, 2
[2, 3, 2, 3, 3, 3, 3, 2, 3] => 2, 3, 2, 3, 3, 3, 3, 2, 3
[2, 3, 2, 3, 3, 3, 3, 3, 1] => 2, 3, 2, 3, 3, 3, 3, 3, 1
[2, 3, 2, 3, 3, 3, 3, 3, 2] => 2, 3, 2, 3, 3, 3, 3, 3, 2
[2, 3, 2, 3, 3, 3, 3, 3, 3] => 2, 3, 2, 3, 3, 3, 3, 3, 3
[2, 3, 3, 1, 1, 1, 1, 1, 1] => 2, 3, 3, 1, 1, 1, 1, 1, 1
[2, 3, 3, 1, 1, 1, 1, 1, 2] => 2, 3, 3, 1, 1, 1, 1, 1, 2
[2, 3, 3, 1, 1, 1, 1, 1, 3] => 2, 3, 3, 1, 1, 1, 1, 1, 3
[2, 3, 3, 1, 1, 1, 1, 2, 1] => 2, 3, 3, 1, 1, 1, 1, 2, 1
[2, 3, 3, 1, 1, 1, 1, 2, 2] => 2, 3, 3, 1, 1, 1, 1, 2, 2
[2, 3, 3, 1, 1, 1, 1, 2, 3] => 2, 3, 3, 1, 1, 1, 1, 2, 3
[2, 3, 3, 1, 1, 1, 1, 3, 1] => 2, 3, 3, 1, 1, 1, 1, 3, 1
[2, 3, 3, 1, 1, 1, 1, 3, 2] => 2, 3, 3, 1, 1, 1, 1, 3, 2
[2, 3, 3, 1, 1, 1, 1, 3, 3] => 2, 3, 3, 1, 1, 1, 1, 3, 3
[2, 3, 3, 1, 1, 1, 2, 1, 1] => 2, 3, 3, 1, 1, 1, 2, 1, 1
[2, 3, 3, 1, 1, 1, 2, 1, 2] => 2, 3, 3, 1, 1, 1, 2, 1, 2
[2, 3, 3, 1, 1, 1, 2, 1, 3] => 2, 3, 3, 1, 1, 1, 2, 1, 3
[2, 3, 3, 1, 1, 1, 2, 2, 1] => 2, 3, 3, 1, 1, 1, 2, 2, 1
[2, 3, 3, 1, 1, 1, 2, 2, 2] => 2, 3, 3, 1, 1, 1, 2, 2, 2
[2, 3, 3, 1, 1, 1, 2, 2, 3] => 2, 3, 3, 1, 1, 1, 2, 2, 3
[2, 3, 3, 1, 1, 1, 2, 3, 1] => 2, 3, 3, 1, 1, 1, 2, 3, 1
[2, 3, 3, 1, 1, 1, 2, 3, 2] => 2, 3, 3, 1, 1, 1, 2, 3, 2
[2, 3, 3, 1, 1, 1, 2, 3, 3] => 2, 3, 3, 1, 1, 1, 2, 3, 3
[2, 3, 3, 1, 1, 1, 3, 1, 1] => 2, 3, 3, 1, 1, 1, 3, 1, 1
[2, 3, 3, 1, 1, 1, 3, 1, 2] => 2, 3, 3, 1, 1, 1, 3, 1, 2
[2, 3, 3, 1, 1, 1, 3, 1, 3] => 2, 3, 3, 1, 1, 1, 3, 1, 3
[2, 3, 3, 1, 1, 1, 3, 2, 1] => 2, 3, 3, 1, 1, 1, 3, 2, 1
[2, 3, 3, 1, 1, 1, 3, 2, 2] => 2, 3, 3, 1, 1, 1, 3, 2, 2
[2, 3, 3, 1, 1, 1, 3, 2, 3] => 2, 3, 3, 1, 1, 1, 3, 2, 3
[2, 3, 3, 1, 1, 1, 3, 3, 1] => 2, 3, 3, 1, 1, 1, 3, 3, 1
[2, 3, 3, 1, 1, 1, 3, 3, 2] => 2, 3, 3, 1, 1, 1, 3, 3, 2
[2, 3, 3, 1, 1, 1, 3, 3, 3] => 2, 3, 3, 1, 1, 1, 3, 3, 3
[2, 3, 3, 1, 1, 2, 1, 1, 1] => 2, 3, 3, 1, 1, 2, 1, 1, 1
[2, 3, 3, 1, 1, 2, 1, 1, 2] => 2, 3, 3, 1, 1, 2, 1, 1, 2
[2, 3, 3, 1, 1, 2, 1, 1, 3] => 2, 3, 3, 1, 1, 2, 1, 1, 3
[2, 3, 3, 1, 1, 2, 1, 2, 1] => 2, 3, 3, 1, 1, 2, 1, 2, 1
[2, 3, 3, 1, 1, 2, 1, 2, 2] => 2, 3, 3, 1, 1, 2, 1, 2, 2
[2, 3, 3, 1, 1, 2, 1, 2, 3] => 2, 3, 3, 1, 1, 2, 1, 2, 3
[2, 3, 3, 1, 1, 2, 1, 3, 1] => 2, 3, 3, 1, 1, 2, 1, 3, 1
[2, 3, 3, 1, 1, 2, 1, 3, 2] => 2, 3, 3, 1, 1, 2, 1, 3, 2
[2, 3, 3, 1, 1, 2, 1, 3, 3] => 2, 3, 3, 1, 1, 2, 1, 3, 3
[2, 3, 3, 1, 1, 2, 2, 1, 1] => 2, 3, 3, 1, 1, 2, 2, 1, 1
[2, 3, 3, 1, 1, 2, 2, 1, 2] => 2, 3, 3, 1, 1, 2, 2, 1, 2
[2, 3, 3, 1, 1, 2, 2, 1, 3] => 2, 3, 3, 1, 1, 2, 2, 1, 3
[2, 3, 3, 1, 1, 2, 2, 2, 1] => 2, 3, 3, 1, 1, 2, 2, 2, 1
[2, 3, 3, 1, 1, 2, 2, 2, 2] => 2, 3, 3, 1, 1, 2, 2, 2, 2
[2, 3, 3, 1, 1, 2, 2, 2, 3] => 2, 3, 3, 1, 1, 2, 2, 2, 3
[2, 3, 3, 1, 1, 2, 2, 3, 1] => 2, 3, 3, 1, 1, 2, 2, 3, 1
[2, 3, 3, 1, 1, 2, 2, 3, 2] => 2, 3, 3, 1, 1, 2, 2, 3, 2
[2, 3, 3, 1, 1, 2, 2, 3, 3] => 2, 3, 3, 1, 1, 2, 2, 3, 3
[2, 3, 3, 1, 1, 2, 3, 1, 1] => 2, 3, 3, 1, 1, 2, 3, 1, 1
[2, 3, 3, 1, 1, 2, 3, 1, 2] => 2, 3, 3, 1, 1, 2, 3, 1, 2
[2, 3, 3, 1, 1, 2, 3, 1, 3] => 2, 3, 3, 1, 1, 2, 3, 1, 3
[2, 3, 3, 1, 1, 2, 3, 2, 1] => 2, 3, 3, 1, 1, 2, 3, 2, 1
[2, 3, 3, 1, 1, 2, 3, 2, 2] => 2, 3, 3, 1, 1, 2, 3, 2, 2
[2, 3, 3, 1, 1, 2, 3, 2, 3] => 2, 3, 3, 1, 1, 2, 3, 2, 3
[2, 3, 3, 1, 1, 2, 3, 3, 1] => 2, 3, 3, 1, 1, 2, 3, 3, 1
[2, 3, 3, 1, 1, 2, 3, 3, 2] => 2, 3, 3, 1, 1, 2, 3, 3, 2
[2, 3, 3, 1, 1, 2, 3, 3, 3] => 2, 3, 3, 1, 1, 2, 3, 3, 3
[2, 3, 3, 1, 1, 3, 1, 1, 1] => 2, 3, 3, 1, 1, 3, 1, 1, 1
[2, 3, 3, 1, 1, 3, 1, 1, 2] => 2, 3, 3, 1, 1, 3, 1, 1, 2
[2, 3, 3, 1, 1, 3, 1, 1, 3] => 2, 3, 3, 1, 1, 3, 1, 1, 3
[2, 3, 3, 1, 1, 3, 1, 2, 1] => 2, 3, 3, 1, 1, 3, 1, 2, 1
[2, 3, 3, 1, 1, 3, 1, 2, 2] => 2, 3, 3, 1, 1, 3, 1, 2, 2
[2, 3, 3, 1, 1, 3, 1, 2, 3] => 2, 3, 3, 1, 1, 3, 1, 2, 3
[2, 3, 3, 1, 1, 3, 1, 3, 1] => 2, 3, 3, 1, 1, 3, 1, 3, 1
[2, 3, 3, 1, 1, 3, 1, 3, 2] => 2, 3, 3, 1, 1, 3, 1, 3, 2
[2, 3, 3, 1, 1, 3, 1, 3, 3] => 2, 3, 3, 1, 1, 3, 1, 3, 3
[2, 3, 3, 1, 1, 3, 2, 1, 1] => 2, 3, 3, 1, 1, 3, 2, 1, 1
[2, 3, 3, 1, 1, 3, 2, 1, 2] => 2, 3, 3, 1, 1, 3, 2, 1, 2
[2, 3, 3, 1, 1, 3, 2, 1, 3] => 2, 3, 3, 1, 1, 3, 2, 1, 3
[2, 3, 3, 1, 1, 3, 2, 2, 1] => 2, 3, 3, 1, 1, 3, 2, 2, 1
[2, 3, 3, 1, 1, 3, 2, 2, 2] => 2, 3, 3, 1, 1, 3, 2, 2, 2
[2, 3, 3, 1, 1, 3, 2, 2, 3] => 2, 3, 3, 1, 1, 3, 2, 2, 3
[2, 3, 3, 1, 1, 3, 2, 3, 1] => 2, 3, 3, 1, 1, 3, 2, 3, 1
[2, 3, 3, 1, 1, 3, 2, 3, 2] => 2, 3, 3, 1, 1, 3, 2, 3, 2
[2, 3, 3, 1, 1, 3, 2, 3, 3] => 2, 3, 3, 1, 1, 3, 2, 3, 3
[2, 3, 3, 1, 1, 3, 3, 1, 1] => 2, 3, 3, 1, 1, 3, 3, 1, 1
[2, 3, 3, 1, 1, 3, 3, 1, 2] => 2, 3, 3, 1, 1, 3, 3, 1, 2
[2, 3, 3, 1, 1, 3, 3, 1, 3] => 2, 3, 3, 1, 1, 3, 3, 1, 3
[2, 3, 3, 1, 1, 3, 3, 2, 1] => 2, 3, 3, 1, 1, 3, 3, 2, 1
[2, 3, 3, 1, 1, 3, 3, 2, 2] => 2, 3, 3, 1, 1, 3, 3, 2, 2
[2, 3, 3, 1, 1, 3, 3, 2, 3] => 2, 3, 3, 1, 1, 3, 3, 2, 3
[2, 3, 3, 1, 1, 3, 3, 3, 1] => 2, 3, 3, 1, 1, 3, 3, 3, 1
[2, 3, 3, 1, 1, 3, 3, 3, 2] => 2, 3, 3, 1, 1, 3, 3, 3, 2
[2, 3, 3, 1, 1, 3, 3, 3, 3] => 2, 3, 3, 1, 1, 3, 3, 3, 3
[2, 3, 3, 1, 2, 1, 1, 1, 1] => 2, 3, 3, 1, 2, 1, 1, 1, 1
[2, 3, 3, 1, 2, 1, 1, 1, 2] => 2, 3, 3, 1, 2, 1, 1, 1, 2
[2, 3, 3, 1, 2, 1, 1, 1, 3] => 2, 3, 3, 1, 2, 1, 1, 1, 3
[2, 3, 3, 1, 2, 1, 1, 2, 1] => 2, 3, 3, 1, 2, 1, 1, 2, 1
[2, 3, 3, 1, 2, 1, 1, 2, 2] => 2, 3, 3, 1, 2, 1, 1, 2, 2
[2, 3, 3, 1, 2, 1, 1, 2, 3] => 2, 3, 3, 1, 2, 1, 1, 2, 3
[2, 3, 3, 1, 2, 1, 1, 3, 1] => 2, 3, 3, 1, 2, 1, 1, 3, 1
[2, 3, 3, 1, 2, 1, 1, 3, 2] => 2, 3, 3, 1, 2, 1, 1, 3, 2
[2, 3, 3, 1, 2, 1, 1, 3, 3] => 2, 3, 3, 1, 2, 1, 1, 3, 3
[2, 3, 3, 1, 2, 1, 2, 1, 1] => 2, 3, 3, 1, 2, 1, 2, 1, 1
[2, 3, 3, 1, 2, 1, 2, 1, 2] => 2, 3, 3, 1, 2, 1, 2, 1, 2
[2, 3, 3, 1, 2, 1, 2, 1, 3] => 2, 3, 3, 1, 2, 1, 2, 1, 3
[2, 3, 3, 1, 2, 1, 2, 2, 1] => 2, 3, 3, 1, 2, 1, 2, 2, 1
[2, 3, 3, 1, 2, 1, 2, 2, 2] => 2, 3, 3, 1, 2, 1, 2, 2, 2
[2, 3, 3, 1, 2, 1, 2, 2, 3] => 2, 3, 3, 1, 2, 1, 2, 2, 3
[2, 3, 3, 1, 2, 1, 2, 3, 1] => 2, 3, 3, 1, 2, 1, 2, 3, 1
[2, 3, 3, 1, 2, 1, 2, 3, 2] => 2, 3, 3, 1, 2, 1, 2, 3, 2
[2, 3, 3, 1, 2, 1, 2, 3, 3] => 2, 3, 3, 1, 2, 1, 2, 3, 3
[2, 3, 3, 1, 2, 1, 3, 1, 1] => 2, 3, 3, 1, 2, 1, 3, 1, 1
[2, 3, 3, 1, 2, 1, 3, 1, 2] => 2, 3, 3, 1, 2, 1, 3, 1, 2
[2, 3, 3, 1, 2, 1, 3, 1, 3] => 2, 3, 3, 1, 2, 1, 3, 1, 3
[2, 3, 3, 1, 2, 1, 3, 2, 1] => 2, 3, 3, 1, 2, 1, 3, 2, 1
[2, 3, 3, 1, 2, 1, 3, 2, 2] => 2, 3, 3, 1, 2, 1, 3, 2, 2
[2, 3, 3, 1, 2, 1, 3, 2, 3] => 2, 3, 3, 1, 2, 1, 3, 2, 3
[2, 3, 3, 1, 2, 1, 3, 3, 1] => 2, 3, 3, 1, 2, 1, 3, 3, 1
[2, 3, 3, 1, 2, 1, 3, 3, 2] => 2, 3, 3, 1, 2, 1, 3, 3, 2
[2, 3, 3, 1, 2, 1, 3, 3, 3] => 2, 3, 3, 1, 2, 1, 3, 3, 3
[2, 3, 3, 1, 2, 2, 1, 1, 1] => 2, 3, 3, 1, 2, 2, 1, 1, 1
[2, 3, 3, 1, 2, 2, 1, 1, 2] => 2, 3, 3, 1, 2, 2, 1, 1, 2
[2, 3, 3, 1, 2, 2, 1, 1, 3] => 2, 3, 3, 1, 2, 2, 1, 1, 3
[2, 3, 3, 1, 2, 2, 1, 2, 1] => 2, 3, 3, 1, 2, 2, 1, 2, 1
[2, 3, 3, 1, 2, 2, 1, 2, 2] => 2, 3, 3, 1, 2, 2, 1, 2, 2
[2, 3, 3, 1, 2, 2, 1, 2, 3] => 2, 3, 3, 1, 2, 2, 1, 2, 3
[2, 3, 3, 1, 2, 2, 1, 3, 1] => 2, 3, 3, 1, 2, 2, 1, 3, 1
[2, 3, 3, 1, 2, 2, 1, 3, 2] => 2, 3, 3, 1, 2, 2, 1, 3, 2
[2, 3, 3, 1, 2, 2, 1, 3, 3] => 2, 3, 3, 1, 2, 2, 1, 3, 3
[2, 3, 3, 1, 2, 2, 2, 1, 1] => 2, 3, 3, 1, 2, 2, 2, 1, 1
[2, 3, 3, 1, 2, 2, 2, 1, 2] => 2, 3, 3, 1, 2, 2, 2, 1, 2
[2, 3, 3, 1, 2, 2, 2, 1, 3] => 2, 3, 3, 1, 2, 2, 2, 1, 3
[2, 3, 3, 1, 2, 2, 2, 2, 1] => 2, 3, 3, 1, 2, 2, 2, 2, 1
[2, 3, 3, 1, 2, 2, 2, 2, 2] => 2, 3, 3, 1, 2, 2, 2, 2, 2
[2, 3, 3, 1, 2, 2, 2, 2, 3] => 2, 3, 3, 1, 2, 2, 2, 2, 3
[2, 3, 3, 1, 2, 2, 2, 3, 1] => 2, 3, 3, 1, 2, 2, 2, 3, 1
[2, 3, 3, 1, 2, 2, 2, 3, 2] => 2, 3, 3, 1, 2, 2, 2, 3, 2
[2, 3, 3, 1, 2, 2, 2, 3, 3] => 2, 3, 3, 1, 2, 2, 2, 3, 3
[2, 3, 3, 1, 2, 2, 3, 1, 1] => 2, 3, 3, 1, 2, 2, 3, 1, 1
[2, 3, 3, 1, 2, 2, 3, 1, 2] => 2, 3, 3, 1, 2, 2, 3, 1, 2
[2, 3, 3, 1, 2, 2, 3, 1, 3] => 2, 3, 3, 1, 2, 2, 3, 1, 3
[2, 3, 3, 1, 2, 2, 3, 2, 1] => 2, 3, 3, 1, 2, 2, 3, 2, 1
[2, 3, 3, 1, 2, 2, 3, 2, 2] => 2, 3, 3, 1, 2, 2, 3, 2, 2
[2, 3, 3, 1, 2, 2, 3, 2, 3] => 2, 3, 3, 1, 2, 2, 3, 2, 3
[2, 3, 3, 1, 2, 2, 3, 3, 1] => 2, 3, 3, 1, 2, 2, 3, 3, 1
[2, 3, 3, 1, 2, 2, 3, 3, 2] => 2, 3, 3, 1, 2, 2, 3, 3, 2
[2, 3, 3, 1, 2, 2, 3, 3, 3] => 2, 3, 3, 1, 2, 2, 3, 3, 3
[2, 3, 3, 1, 2, 3, 1, 1, 1] => 2, 3, 3, 1, 2, 3, 1, 1, 1
[2, 3, 3, 1, 2, 3, 1, 1, 2] => 2, 3, 3, 1, 2, 3, 1, 1, 2
[2, 3, 3, 1, 2, 3, 1, 1, 3] => 2, 3, 3, 1, 2, 3, 1, 1, 3
[2, 3, 3, 1, 2, 3, 1, 2, 1] => 2, 3, 3, 1, 2, 3, 1, 2, 1
[2, 3, 3, 1, 2, 3, 1, 2, 2] => 2, 3, 3, 1, 2, 3, 1, 2, 2
[2, 3, 3, 1, 2, 3, 1, 2, 3] => 2, 3, 3, 1, 2, 3, 1, 2, 3
[2, 3, 3, 1, 2, 3, 1, 3, 1] => 2, 3, 3, 1, 2, 3, 1, 3, 1
[2, 3, 3, 1, 2, 3, 1, 3, 2] => 2, 3, 3, 1, 2, 3, 1, 3, 2
[2, 3, 3, 1, 2, 3, 1, 3, 3] => 2, 3, 3, 1, 2, 3, 1, 3, 3
[2, 3, 3, 1, 2, 3, 2, 1, 1] => 2, 3, 3, 1, 2, 3, 2, 1, 1
[2, 3, 3, 1, 2, 3, 2, 1, 2] => 2, 3, 3, 1, 2, 3, 2, 1, 2
[2, 3, 3, 1, 2, 3, 2, 1, 3] => 2, 3, 3, 1, 2, 3, 2, 1, 3
[2, 3, 3, 1, 2, 3, 2, 2, 1] => 2, 3, 3, 1, 2, 3, 2, 2, 1
[2, 3, 3, 1, 2, 3, 2, 2, 2] => 2, 3, 3, 1, 2, 3, 2, 2, 2
[2, 3, 3, 1, 2, 3, 2, 2, 3] => 2, 3, 3, 1, 2, 3, 2, 2, 3
[2, 3, 3, 1, 2, 3, 2, 3, 1] => 2, 3, 3, 1, 2, 3, 2, 3, 1
[2, 3, 3, 1, 2, 3, 2, 3, 2] => 2, 3, 3, 1, 2, 3, 2, 3, 2
[2, 3, 3, 1, 2, 3, 2, 3, 3] => 2, 3, 3, 1, 2, 3, 2, 3, 3
[2, 3, 3, 1, 2, 3, 3, 1, 1] => 2, 3, 3, 1, 2, 3, 3, 1, 1
[2, 3, 3, 1, 2, 3, 3, 1, 2] => 2, 3, 3, 1, 2, 3, 3, 1, 2
[2, 3, 3, 1, 2, 3, 3, 1, 3] => 2, 3, 3, 1, 2, 3, 3, 1, 3
[2, 3, 3, 1, 2, 3, 3, 2, 1] => 2, 3, 3, 1, 2, 3, 3, 2, 1
[2, 3, 3, 1, 2, 3, 3, 2, 2] => 2, 3, 3, 1, 2, 3, 3, 2, 2
[2, 3, 3, 1, 2, 3, 3, 2, 3] => 2, 3, 3, 1, 2, 3, 3, 2, 3
[2, 3, 3, 1, 2, 3, 3, 3, 1] => 2, 3, 3, 1, 2, 3, 3, 3, 1
[2, 3, 3, 1, 2, 3, 3, 3, 2] => 2, 3, 3, 1, 2, 3, 3, 3, 2
[2, 3, 3, 1, 2, 3, 3, 3, 3] => 2, 3, 3, 1, 2, 3, 3, 3, 3
[2, 3, 3, 1, 3, 1, 1, 1, 1] => 2, 3, 3, 1, 3, 1, 1, 1, 1
[2, 3, 3, 1, 3, 1, 1, 1, 2] => 2, 3, 3, 1, 3, 1, 1, 1, 2
[2, 3, 3, 1, 3, 1, 1, 1, 3] => 2, 3, 3, 1, 3, 1, 1, 1, 3
[2, 3, 3, 1, 3, 1, 1, 2, 1] => 2, 3, 3, 1, 3, 1, 1, 2, 1
[2, 3, 3, 1, 3, 1, 1, 2, 2] => 2, 3, 3, 1, 3, 1, 1, 2, 2
[2, 3, 3, 1, 3, 1, 1, 2, 3] => 2, 3, 3, 1, 3, 1, 1, 2, 3
[2, 3, 3, 1, 3, 1, 1, 3, 1] => 2, 3, 3, 1, 3, 1, 1, 3, 1
[2, 3, 3, 1, 3, 1, 1, 3, 2] => 2, 3, 3, 1, 3, 1, 1, 3, 2
[2, 3, 3, 1, 3, 1, 1, 3, 3] => 2, 3, 3, 1, 3, 1, 1, 3, 3
[2, 3, 3, 1, 3, 1, 2, 1, 1] => 2, 3, 3, 1, 3, 1, 2, 1, 1
[2, 3, 3, 1, 3, 1, 2, 1, 2] => 2, 3, 3, 1, 3, 1, 2, 1, 2
[2, 3, 3, 1, 3, 1, 2, 1, 3] => 2, 3, 3, 1, 3, 1, 2, 1, 3
[2, 3, 3, 1, 3, 1, 2, 2, 1] => 2, 3, 3, 1, 3, 1, 2, 2, 1
[2, 3, 3, 1, 3, 1, 2, 2, 2] => 2, 3, 3, 1, 3, 1, 2, 2, 2
[2, 3, 3, 1, 3, 1, 2, 2, 3] => 2, 3, 3, 1, 3, 1, 2, 2, 3
[2, 3, 3, 1, 3, 1, 2, 3, 1] => 2, 3, 3, 1, 3, 1, 2, 3, 1
[2, 3, 3, 1, 3, 1, 2, 3, 2] => 2, 3, 3, 1, 3, 1, 2, 3, 2
[2, 3, 3, 1, 3, 1, 2, 3, 3] => 2, 3, 3, 1, 3, 1, 2, 3, 3
[2, 3, 3, 1, 3, 1, 3, 1, 1] => 2, 3, 3, 1, 3, 1, 3, 1, 1
[2, 3, 3, 1, 3, 1, 3, 1, 2] => 2, 3, 3, 1, 3, 1, 3, 1, 2
[2, 3, 3, 1, 3, 1, 3, 1, 3] => 2, 3, 3, 1, 3, 1, 3, 1, 3
[2, 3, 3, 1, 3, 1, 3, 2, 1] => 2, 3, 3, 1, 3, 1, 3, 2, 1
[2, 3, 3, 1, 3, 1, 3, 2, 2] => 2, 3, 3, 1, 3, 1, 3, 2, 2
[2, 3, 3, 1, 3, 1, 3, 2, 3] => 2, 3, 3, 1, 3, 1, 3, 2, 3
[2, 3, 3, 1, 3, 1, 3, 3, 1] => 2, 3, 3, 1, 3, 1, 3, 3, 1
[2, 3, 3, 1, 3, 1, 3, 3, 2] => 2, 3, 3, 1, 3, 1, 3, 3, 2
[2, 3, 3, 1, 3, 1, 3, 3, 3] => 2, 3, 3, 1, 3, 1, 3, 3, 3
[2, 3, 3, 1, 3, 2, 1, 1, 1] => 2, 3, 3, 1, 3, 2, 1, 1, 1
[2, 3, 3, 1, 3, 2, 1, 1, 2] => 2, 3, 3, 1, 3, 2, 1, 1, 2
[2, 3, 3, 1, 3, 2, 1, 1, 3] => 2, 3, 3, 1, 3, 2, 1, 1, 3
[2, 3, 3, 1, 3, 2, 1, 2, 1] => 2, 3, 3, 1, 3, 2, 1, 2, 1
[2, 3, 3, 1, 3, 2, 1, 2, 2] => 2, 3, 3, 1, 3, 2, 1, 2, 2
[2, 3, 3, 1, 3, 2, 1, 2, 3] => 2, 3, 3, 1, 3, 2, 1, 2, 3
[2, 3, 3, 1, 3, 2, 1, 3, 1] => 2, 3, 3, 1, 3, 2, 1, 3, 1
[2, 3, 3, 1, 3, 2, 1, 3, 2] => 2, 3, 3, 1, 3, 2, 1, 3, 2
[2, 3, 3, 1, 3, 2, 1, 3, 3] => 2, 3, 3, 1, 3, 2, 1, 3, 3
[2, 3, 3, 1, 3, 2, 2, 1, 1] => 2, 3, 3, 1, 3, 2, 2, 1, 1
[2, 3, 3, 1, 3, 2, 2, 1, 2] => 2, 3, 3, 1, 3, 2, 2, 1, 2
[2, 3, 3, 1, 3, 2, 2, 1, 3] => 2, 3, 3, 1, 3, 2, 2, 1, 3
[2, 3, 3, 1, 3, 2, 2, 2, 1] => 2, 3, 3, 1, 3, 2, 2, 2, 1
[2, 3, 3, 1, 3, 2, 2, 2, 2] => 2, 3, 3, 1, 3, 2, 2, 2, 2
[2, 3, 3, 1, 3, 2, 2, 2, 3] => 2, 3, 3, 1, 3, 2, 2, 2, 3
[2, 3, 3, 1, 3, 2, 2, 3, 1] => 2, 3, 3, 1, 3, 2, 2, 3, 1
[2, 3, 3, 1, 3, 2, 2, 3, 2] => 2, 3, 3, 1, 3, 2, 2, 3, 2
[2, 3, 3, 1, 3, 2, 2, 3, 3] => 2, 3, 3, 1, 3, 2, 2, 3, 3
[2, 3, 3, 1, 3, 2, 3, 1, 1] => 2, 3, 3, 1, 3, 2, 3, 1, 1
[2, 3, 3, 1, 3, 2, 3, 1, 2] => 2, 3, 3, 1, 3, 2, 3, 1, 2
[2, 3, 3, 1, 3, 2, 3, 1, 3] => 2, 3, 3, 1, 3, 2, 3, 1, 3
[2, 3, 3, 1, 3, 2, 3, 2, 1] => 2, 3, 3, 1, 3, 2, 3, 2, 1
[2, 3, 3, 1, 3, 2, 3, 2, 2] => 2, 3, 3, 1, 3, 2, 3, 2, 2
[2, 3, 3, 1, 3, 2, 3, 2, 3] => 2, 3, 3, 1, 3, 2, 3, 2, 3
[2, 3, 3, 1, 3, 2, 3, 3, 1] => 2, 3, 3, 1, 3, 2, 3, 3, 1
[2, 3, 3, 1, 3, 2, 3, 3, 2] => 2, 3, 3, 1, 3, 2, 3, 3, 2
[2, 3, 3, 1, 3, 2, 3, 3, 3] => 2, 3, 3, 1, 3, 2, 3, 3, 3
[2, 3, 3, 1, 3, 3, 1, 1, 1] => 2, 3, 3, 1, 3, 3, 1, 1, 1
[2, 3, 3, 1, 3, 3, 1, 1, 2] => 2, 3, 3, 1, 3, 3, 1, 1, 2
[2, 3, 3, 1, 3, 3, 1, 1, 3] => 2, 3, 3, 1, 3, 3, 1, 1, 3
[2, 3, 3, 1, 3, 3, 1, 2, 1] => 2, 3, 3, 1, 3, 3, 1, 2, 1
[2, 3, 3, 1, 3, 3, 1, 2, 2] => 2, 3, 3, 1, 3, 3, 1, 2, 2
[2, 3, 3, 1, 3, 3, 1, 2, 3] => 2, 3, 3, 1, 3, 3, 1, 2, 3
[2, 3, 3, 1, 3, 3, 1, 3, 1] => 2, 3, 3, 1, 3, 3, 1, 3, 1
[2, 3, 3, 1, 3, 3, 1, 3, 2] => 2, 3, 3, 1, 3, 3, 1, 3, 2
[2, 3, 3, 1, 3, 3, 1, 3, 3] => 2, 3, 3, 1, 3, 3, 1, 3, 3
[2, 3, 3, 1, 3, 3, 2, 1, 1] => 2, 3, 3, 1, 3, 3, 2, 1, 1
[2, 3, 3, 1, 3, 3, 2, 1, 2] => 2, 3, 3, 1, 3, 3, 2, 1, 2
[2, 3, 3, 1, 3, 3, 2, 1, 3] => 2, 3, 3, 1, 3, 3, 2, 1, 3
[2, 3, 3, 1, 3, 3, 2, 2, 1] => 2, 3, 3, 1, 3, 3, 2, 2, 1
[2, 3, 3, 1, 3, 3, 2, 2, 2] => 2, 3, 3, 1, 3, 3, 2, 2, 2
[2, 3, 3, 1, 3, 3, 2, 2, 3] => 2, 3, 3, 1, 3, 3, 2, 2, 3
[2, 3, 3, 1, 3, 3, 2, 3, 1] => 2, 3, 3, 1, 3, 3, 2, 3, 1
[2, 3, 3, 1, 3, 3, 2, 3, 2] => 2, 3, 3, 1, 3, 3, 2, 3, 2
[2, 3, 3, 1, 3, 3, 2, 3, 3] => 2, 3, 3, 1, 3, 3, 2, 3, 3
[2, 3, 3, 1, 3, 3, 3, 1, 1] => 2, 3, 3, 1, 3, 3, 3, 1, 1
[2, 3, 3, 1, 3, 3, 3, 1, 2] => 2, 3, 3, 1, 3, 3, 3, 1, 2
[2, 3, 3, 1, 3, 3, 3, 1, 3] => 2, 3, 3, 1, 3, 3, 3, 1, 3
[2, 3, 3, 1, 3, 3, 3, 2, 1] => 2, 3, 3, 1, 3, 3, 3, 2, 1
[2, 3, 3, 1, 3, 3, 3, 2, 2] => 2, 3, 3, 1, 3, 3, 3, 2, 2
[2, 3, 3, 1, 3, 3, 3, 2, 3] => 2, 3, 3, 1, 3, 3, 3, 2, 3
[2, 3, 3, 1, 3, 3, 3, 3, 1] => 2, 3, 3, 1, 3, 3, 3, 3, 1
[2, 3, 3, 1, 3, 3, 3, 3, 2] => 2, 3, 3, 1, 3, 3, 3, 3, 2
[2, 3, 3, 1, 3, 3, 3, 3, 3] => 2, 3, 3, 1, 3, 3, 3, 3, 3
[2, 3, 3, 2, 1, 1, 1, 1, 1] => 2, 3, 3, 2, 1, 1, 1, 1, 1
[2, 3, 3, 2, 1, 1, 1, 1, 2] => 2, 3, 3, 2, 1, 1, 1, 1, 2
[2, 3, 3, 2, 1, 1, 1, 1, 3] => 2, 3, 3, 2, 1, 1, 1, 1, 3
[2, 3, 3, 2, 1, 1, 1, 2, 1] => 2, 3, 3, 2, 1, 1, 1, 2, 1
[2, 3, 3, 2, 1, 1, 1, 2, 2] => 2, 3, 3, 2, 1, 1, 1, 2, 2
[2, 3, 3, 2, 1, 1, 1, 2, 3] => 2, 3, 3, 2, 1, 1, 1, 2, 3
[2, 3, 3, 2, 1, 1, 1, 3, 1] => 2, 3, 3, 2, 1, 1, 1, 3, 1
[2, 3, 3, 2, 1, 1, 1, 3, 2] => 2, 3, 3, 2, 1, 1, 1, 3, 2
[2, 3, 3, 2, 1, 1, 1, 3, 3] => 2, 3, 3, 2, 1, 1, 1, 3, 3
[2, 3, 3, 2, 1, 1, 2, 1, 1] => 2, 3, 3, 2, 1, 1, 2, 1, 1
[2, 3, 3, 2, 1, 1, 2, 1, 2] => 2, 3, 3, 2, 1, 1, 2, 1, 2
[2, 3, 3, 2, 1, 1, 2, 1, 3] => 2, 3, 3, 2, 1, 1, 2, 1, 3
[2, 3, 3, 2, 1, 1, 2, 2, 1] => 2, 3, 3, 2, 1, 1, 2, 2, 1
[2, 3, 3, 2, 1, 1, 2, 2, 2] => 2, 3, 3, 2, 1, 1, 2, 2, 2
[2, 3, 3, 2, 1, 1, 2, 2, 3] => 2, 3, 3, 2, 1, 1, 2, 2, 3
[2, 3, 3, 2, 1, 1, 2, 3, 1] => 2, 3, 3, 2, 1, 1, 2, 3, 1
[2, 3, 3, 2, 1, 1, 2, 3, 2] => 2, 3, 3, 2, 1, 1, 2, 3, 2
[2, 3, 3, 2, 1, 1, 2, 3, 3] => 2, 3, 3, 2, 1, 1, 2, 3, 3
[2, 3, 3, 2, 1, 1, 3, 1, 1] => 2, 3, 3, 2, 1, 1, 3, 1, 1
[2, 3, 3, 2, 1, 1, 3, 1, 2] => 2, 3, 3, 2, 1, 1, 3, 1, 2
[2, 3, 3, 2, 1, 1, 3, 1, 3] => 2, 3, 3, 2, 1, 1, 3, 1, 3
[2, 3, 3, 2, 1, 1, 3, 2, 1] => 2, 3, 3, 2, 1, 1, 3, 2, 1
[2, 3, 3, 2, 1, 1, 3, 2, 2] => 2, 3, 3, 2, 1, 1, 3, 2, 2
[2, 3, 3, 2, 1, 1, 3, 2, 3] => 2, 3, 3, 2, 1, 1, 3, 2, 3
[2, 3, 3, 2, 1, 1, 3, 3, 1] => 2, 3, 3, 2, 1, 1, 3, 3, 1
[2, 3, 3, 2, 1, 1, 3, 3, 2] => 2, 3, 3, 2, 1, 1, 3, 3, 2
[2, 3, 3, 2, 1, 1, 3, 3, 3] => 2, 3, 3, 2, 1, 1, 3, 3, 3
[2, 3, 3, 2, 1, 2, 1, 1, 1] => 2, 3, 3, 2, 1, 2, 1, 1, 1
[2, 3, 3, 2, 1, 2, 1, 1, 2] => 2, 3, 3, 2, 1, 2, 1, 1, 2
[2, 3, 3, 2, 1, 2, 1, 1, 3] => 2, 3, 3, 2, 1, 2, 1, 1, 3
[2, 3, 3, 2, 1, 2, 1, 2, 1] => 2, 3, 3, 2, 1, 2, 1, 2, 1
[2, 3, 3, 2, 1, 2, 1, 2, 2] => 2, 3, 3, 2, 1, 2, 1, 2, 2
[2, 3, 3, 2, 1, 2, 1, 2, 3] => 2, 3, 3, 2, 1, 2, 1, 2, 3
[2, 3, 3, 2, 1, 2, 1, 3, 1] => 2, 3, 3, 2, 1, 2, 1, 3, 1
[2, 3, 3, 2, 1, 2, 1, 3, 2] => 2, 3, 3, 2, 1, 2, 1, 3, 2
[2, 3, 3, 2, 1, 2, 1, 3, 3] => 2, 3, 3, 2, 1, 2, 1, 3, 3
[2, 3, 3, 2, 1, 2, 2, 1, 1] => 2, 3, 3, 2, 1, 2, 2, 1, 1
[2, 3, 3, 2, 1, 2, 2, 1, 2] => 2, 3, 3, 2, 1, 2, 2, 1, 2
[2, 3, 3, 2, 1, 2, 2, 1, 3] => 2, 3, 3, 2, 1, 2, 2, 1, 3
[2, 3, 3, 2, 1, 2, 2, 2, 1] => 2, 3, 3, 2, 1, 2, 2, 2, 1
[2, 3, 3, 2, 1, 2, 2, 2, 2] => 2, 3, 3, 2, 1, 2, 2, 2, 2
[2, 3, 3, 2, 1, 2, 2, 2, 3] => 2, 3, 3, 2, 1, 2, 2, 2, 3
[2, 3, 3, 2, 1, 2, 2, 3, 1] => 2, 3, 3, 2, 1, 2, 2, 3, 1
[2, 3, 3, 2, 1, 2, 2, 3, 2] => 2, 3, 3, 2, 1, 2, 2, 3, 2
[2, 3, 3, 2, 1, 2, 2, 3, 3] => 2, 3, 3, 2, 1, 2, 2, 3, 3
[2, 3, 3, 2, 1, 2, 3, 1, 1] => 2, 3, 3, 2, 1, 2, 3, 1, 1
[2, 3, 3, 2, 1, 2, 3, 1, 2] => 2, 3, 3, 2, 1, 2, 3, 1, 2
[2, 3, 3, 2, 1, 2, 3, 1, 3] => 2, 3, 3, 2, 1, 2, 3, 1, 3
[2, 3, 3, 2, 1, 2, 3, 2, 1] => 2, 3, 3, 2, 1, 2, 3, 2, 1
[2, 3, 3, 2, 1, 2, 3, 2, 2] => 2, 3, 3, 2, 1, 2, 3, 2, 2
[2, 3, 3, 2, 1, 2, 3, 2, 3] => 2, 3, 3, 2, 1, 2, 3, 2, 3
[2, 3, 3, 2, 1, 2, 3, 3, 1] => 2, 3, 3, 2, 1, 2, 3, 3, 1
[2, 3, 3, 2, 1, 2, 3, 3, 2] => 2, 3, 3, 2, 1, 2, 3, 3, 2
[2, 3, 3, 2, 1, 2, 3, 3, 3] => 2, 3, 3, 2, 1, 2, 3, 3, 3
[2, 3, 3, 2, 1, 3, 1, 1, 1] => 2, 3, 3, 2, 1, 3, 1, 1, 1
[2, 3, 3, 2, 1, 3, 1, 1, 2] => 2, 3, 3, 2, 1, 3, 1, 1, 2
[2, 3, 3, 2, 1, 3, 1, 1, 3] => 2, 3, 3, 2, 1, 3, 1, 1, 3
[2, 3, 3, 2, 1, 3, 1, 2, 1] => 2, 3, 3, 2, 1, 3, 1, 2, 1
[2, 3, 3, 2, 1, 3, 1, 2, 2] => 2, 3, 3, 2, 1, 3, 1, 2, 2
[2, 3, 3, 2, 1, 3, 1, 2, 3] => 2, 3, 3, 2, 1, 3, 1, 2, 3
[2, 3, 3, 2, 1, 3, 1, 3, 1] => 2, 3, 3, 2, 1, 3, 1, 3, 1
[2, 3, 3, 2, 1, 3, 1, 3, 2] => 2, 3, 3, 2, 1, 3, 1, 3, 2
[2, 3, 3, 2, 1, 3, 1, 3, 3] => 2, 3, 3, 2, 1, 3, 1, 3, 3
[2, 3, 3, 2, 1, 3, 2, 1, 1] => 2, 3, 3, 2, 1, 3, 2, 1, 1
[2, 3, 3, 2, 1, 3, 2, 1, 2] => 2, 3, 3, 2, 1, 3, 2, 1, 2
[2, 3, 3, 2, 1, 3, 2, 1, 3] => 2, 3, 3, 2, 1, 3, 2, 1, 3
[2, 3, 3, 2, 1, 3, 2, 2, 1] => 2, 3, 3, 2, 1, 3, 2, 2, 1
[2, 3, 3, 2, 1, 3, 2, 2, 2] => 2, 3, 3, 2, 1, 3, 2, 2, 2
[2, 3, 3, 2, 1, 3, 2, 2, 3] => 2, 3, 3, 2, 1, 3, 2, 2, 3
[2, 3, 3, 2, 1, 3, 2, 3, 1] => 2, 3, 3, 2, 1, 3, 2, 3, 1
[2, 3, 3, 2, 1, 3, 2, 3, 2] => 2, 3, 3, 2, 1, 3, 2, 3, 2
[2, 3, 3, 2, 1, 3, 2, 3, 3] => 2, 3, 3, 2, 1, 3, 2, 3, 3
[2, 3, 3, 2, 1, 3, 3, 1, 1] => 2, 3, 3, 2, 1, 3, 3, 1, 1
[2, 3, 3, 2, 1, 3, 3, 1, 2] => 2, 3, 3, 2, 1, 3, 3, 1, 2
[2, 3, 3, 2, 1, 3, 3, 1, 3] => 2, 3, 3, 2, 1, 3, 3, 1, 3
[2, 3, 3, 2, 1, 3, 3, 2, 1] => 2, 3, 3, 2, 1, 3, 3, 2, 1
[2, 3, 3, 2, 1, 3, 3, 2, 2] => 2, 3, 3, 2, 1, 3, 3, 2, 2
[2, 3, 3, 2, 1, 3, 3, 2, 3] => 2, 3, 3, 2, 1, 3, 3, 2, 3
[2, 3, 3, 2, 1, 3, 3, 3, 1] => 2, 3, 3, 2, 1, 3, 3, 3, 1
[2, 3, 3, 2, 1, 3, 3, 3, 2] => 2, 3, 3, 2, 1, 3, 3, 3, 2
[2, 3, 3, 2, 1, 3, 3, 3, 3] => 2, 3, 3, 2, 1, 3, 3, 3, 3
[2, 3, 3, 2, 2, 1, 1, 1, 1] => 2, 3, 3, 2, 2, 1, 1, 1, 1
[2, 3, 3, 2, 2, 1, 1, 1, 2] => 2, 3, 3, 2, 2, 1, 1, 1, 2
[2, 3, 3, 2, 2, 1, 1, 1, 3] => 2, 3, 3, 2, 2, 1, 1, 1, 3
[2, 3, 3, 2, 2, 1, 1, 2, 1] => 2, 3, 3, 2, 2, 1, 1, 2, 1
[2, 3, 3, 2, 2, 1, 1, 2, 2] => 2, 3, 3, 2, 2, 1, 1, 2, 2
[2, 3, 3, 2, 2, 1, 1, 2, 3] => 2, 3, 3, 2, 2, 1, 1, 2, 3
[2, 3, 3, 2, 2, 1, 1, 3, 1] => 2, 3, 3, 2, 2, 1, 1, 3, 1
[2, 3, 3, 2, 2, 1, 1, 3, 2] => 2, 3, 3, 2, 2, 1, 1, 3, 2
[2, 3, 3, 2, 2, 1, 1, 3, 3] => 2, 3, 3, 2, 2, 1, 1, 3, 3
[2, 3, 3, 2, 2, 1, 2, 1, 1] => 2, 3, 3, 2, 2, 1, 2, 1, 1
[2, 3, 3, 2, 2, 1, 2, 1, 2] => 2, 3, 3, 2, 2, 1, 2, 1, 2
[2, 3, 3, 2, 2, 1, 2, 1, 3] => 2, 3, 3, 2, 2, 1, 2, 1, 3
[2, 3, 3, 2, 2, 1, 2, 2, 1] => 2, 3, 3, 2, 2, 1, 2, 2, 1
[2, 3, 3, 2, 2, 1, 2, 2, 2] => 2, 3, 3, 2, 2, 1, 2, 2, 2
[2, 3, 3, 2, 2, 1, 2, 2, 3] => 2, 3, 3, 2, 2, 1, 2, 2, 3
[2, 3, 3, 2, 2, 1, 2, 3, 1] => 2, 3, 3, 2, 2, 1, 2, 3, 1
[2, 3, 3, 2, 2, 1, 2, 3, 2] => 2, 3, 3, 2, 2, 1, 2, 3, 2
[2, 3, 3, 2, 2, 1, 2, 3, 3] => 2, 3, 3, 2, 2, 1, 2, 3, 3
[2, 3, 3, 2, 2, 1, 3, 1, 1] => 2, 3, 3, 2, 2, 1, 3, 1, 1
[2, 3, 3, 2, 2, 1, 3, 1, 2] => 2, 3, 3, 2, 2, 1, 3, 1, 2
[2, 3, 3, 2, 2, 1, 3, 1, 3] => 2, 3, 3, 2, 2, 1, 3, 1, 3
[2, 3, 3, 2, 2, 1, 3, 2, 1] => 2, 3, 3, 2, 2, 1, 3, 2, 1
[2, 3, 3, 2, 2, 1, 3, 2, 2] => 2, 3, 3, 2, 2, 1, 3, 2, 2
[2, 3, 3, 2, 2, 1, 3, 2, 3] => 2, 3, 3, 2, 2, 1, 3, 2, 3
[2, 3, 3, 2, 2, 1, 3, 3, 1] => 2, 3, 3, 2, 2, 1, 3, 3, 1
[2, 3, 3, 2, 2, 1, 3, 3, 2] => 2, 3, 3, 2, 2, 1, 3, 3, 2
[2, 3, 3, 2, 2, 1, 3, 3, 3] => 2, 3, 3, 2, 2, 1, 3, 3, 3
[2, 3, 3, 2, 2, 2, 1, 1, 1] => 2, 3, 3, 2, 2, 2, 1, 1, 1
[2, 3, 3, 2, 2, 2, 1, 1, 2] => 2, 3, 3, 2, 2, 2, 1, 1, 2
[2, 3, 3, 2, 2, 2, 1, 1, 3] => 2, 3, 3, 2, 2, 2, 1, 1, 3
[2, 3, 3, 2, 2, 2, 1, 2, 1] => 2, 3, 3, 2, 2, 2, 1, 2, 1
[2, 3, 3, 2, 2, 2, 1, 2, 2] => 2, 3, 3, 2, 2, 2, 1, 2, 2
[2, 3, 3, 2, 2, 2, 1, 2, 3] => 2, 3, 3, 2, 2, 2, 1, 2, 3
[2, 3, 3, 2, 2, 2, 1, 3, 1] => 2, 3, 3, 2, 2, 2, 1, 3, 1
[2, 3, 3, 2, 2, 2, 1, 3, 2] => 2, 3, 3, 2, 2, 2, 1, 3, 2
[2, 3, 3, 2, 2, 2, 1, 3, 3] => 2, 3, 3, 2, 2, 2, 1, 3, 3
[2, 3, 3, 2, 2, 2, 2, 1, 1] => 2, 3, 3, 2, 2, 2, 2, 1, 1
[2, 3, 3, 2, 2, 2, 2, 1, 2] => 2, 3, 3, 2, 2, 2, 2, 1, 2
[2, 3, 3, 2, 2, 2, 2, 1, 3] => 2, 3, 3, 2, 2, 2, 2, 1, 3
[2, 3, 3, 2, 2, 2, 2, 2, 1] => 2, 3, 3, 2, 2, 2, 2, 2, 1
[2, 3, 3, 2, 2, 2, 2, 2, 2] => 2, 3, 3, 2, 2, 2, 2, 2, 2
[2, 3, 3, 2, 2, 2, 2, 2, 3] => 2, 3, 3, 2, 2, 2, 2, 2, 3
[2, 3, 3, 2, 2, 2, 2, 3, 1] => 2, 3, 3, 2, 2, 2, 2, 3, 1
[2, 3, 3, 2, 2, 2, 2, 3, 2] => 2, 3, 3, 2, 2, 2, 2, 3, 2
[2, 3, 3, 2, 2, 2, 2, 3, 3] => 2, 3, 3, 2, 2, 2, 2, 3, 3
[2, 3, 3, 2, 2, 2, 3, 1, 1] => 2, 3, 3, 2, 2, 2, 3, 1, 1
[2, 3, 3, 2, 2, 2, 3, 1, 2] => 2, 3, 3, 2, 2, 2, 3, 1, 2
[2, 3, 3, 2, 2, 2, 3, 1, 3] => 2, 3, 3, 2, 2, 2, 3, 1, 3
[2, 3, 3, 2, 2, 2, 3, 2, 1] => 2, 3, 3, 2, 2, 2, 3, 2, 1
[2, 3, 3, 2, 2, 2, 3, 2, 2] => 2, 3, 3, 2, 2, 2, 3, 2, 2
[2, 3, 3, 2, 2, 2, 3, 2, 3] => 2, 3, 3, 2, 2, 2, 3, 2, 3
[2, 3, 3, 2, 2, 2, 3, 3, 1] => 2, 3, 3, 2, 2, 2, 3, 3, 1
[2, 3, 3, 2, 2, 2, 3, 3, 2] => 2, 3, 3, 2, 2, 2, 3, 3, 2
[2, 3, 3, 2, 2, 2, 3, 3, 3] => 2, 3, 3, 2, 2, 2, 3, 3, 3
[2, 3, 3, 2, 2, 3, 1, 1, 1] => 2, 3, 3, 2, 2, 3, 1, 1, 1
[2, 3, 3, 2, 2, 3, 1, 1, 2] => 2, 3, 3, 2, 2, 3, 1, 1, 2
[2, 3, 3, 2, 2, 3, 1, 1, 3] => 2, 3, 3, 2, 2, 3, 1, 1, 3
[2, 3, 3, 2, 2, 3, 1, 2, 1] => 2, 3, 3, 2, 2, 3, 1, 2, 1
[2, 3, 3, 2, 2, 3, 1, 2, 2] => 2, 3, 3, 2, 2, 3, 1, 2, 2
[2, 3, 3, 2, 2, 3, 1, 2, 3] => 2, 3, 3, 2, 2, 3, 1, 2, 3
[2, 3, 3, 2, 2, 3, 1, 3, 1] => 2, 3, 3, 2, 2, 3, 1, 3, 1
[2, 3, 3, 2, 2, 3, 1, 3, 2] => 2, 3, 3, 2, 2, 3, 1, 3, 2
[2, 3, 3, 2, 2, 3, 1, 3, 3] => 2, 3, 3, 2, 2, 3, 1, 3, 3
[2, 3, 3, 2, 2, 3, 2, 1, 1] => 2, 3, 3, 2, 2, 3, 2, 1, 1
[2, 3, 3, 2, 2, 3, 2, 1, 2] => 2, 3, 3, 2, 2, 3, 2, 1, 2
[2, 3, 3, 2, 2, 3, 2, 1, 3] => 2, 3, 3, 2, 2, 3, 2, 1, 3
[2, 3, 3, 2, 2, 3, 2, 2, 1] => 2, 3, 3, 2, 2, 3, 2, 2, 1
[2, 3, 3, 2, 2, 3, 2, 2, 2] => 2, 3, 3, 2, 2, 3, 2, 2, 2
[2, 3, 3, 2, 2, 3, 2, 2, 3] => 2, 3, 3, 2, 2, 3, 2, 2, 3
[2, 3, 3, 2, 2, 3, 2, 3, 1] => 2, 3, 3, 2, 2, 3, 2, 3, 1
[2, 3, 3, 2, 2, 3, 2, 3, 2] => 2, 3, 3, 2, 2, 3, 2, 3, 2
[2, 3, 3, 2, 2, 3, 2, 3, 3] => 2, 3, 3, 2, 2, 3, 2, 3, 3
[2, 3, 3, 2, 2, 3, 3, 1, 1] => 2, 3, 3, 2, 2, 3, 3, 1, 1
[2, 3, 3, 2, 2, 3, 3, 1, 2] => 2, 3, 3, 2, 2, 3, 3, 1, 2
[2, 3, 3, 2, 2, 3, 3, 1, 3] => 2, 3, 3, 2, 2, 3, 3, 1, 3
[2, 3, 3, 2, 2, 3, 3, 2, 1] => 2, 3, 3, 2, 2, 3, 3, 2, 1
[2, 3, 3, 2, 2, 3, 3, 2, 2] => 2, 3, 3, 2, 2, 3, 3, 2, 2
[2, 3, 3, 2, 2, 3, 3, 2, 3] => 2, 3, 3, 2, 2, 3, 3, 2, 3
[2, 3, 3, 2, 2, 3, 3, 3, 1] => 2, 3, 3, 2, 2, 3, 3, 3, 1
[2, 3, 3, 2, 2, 3, 3, 3, 2] => 2, 3, 3, 2, 2, 3, 3, 3, 2
[2, 3, 3, 2, 2, 3, 3, 3, 3] => 2, 3, 3, 2, 2, 3, 3, 3, 3
[2, 3, 3, 2, 3, 1, 1, 1, 1] => 2, 3, 3, 2, 3, 1, 1, 1, 1
[2, 3, 3, 2, 3, 1, 1, 1, 2] => 2, 3, 3, 2, 3, 1, 1, 1, 2
[2, 3, 3, 2, 3, 1, 1, 1, 3] => 2, 3, 3, 2, 3, 1, 1, 1, 3
[2, 3, 3, 2, 3, 1, 1, 2, 1] => 2, 3, 3, 2, 3, 1, 1, 2, 1
[2, 3, 3, 2, 3, 1, 1, 2, 2] => 2, 3, 3, 2, 3, 1, 1, 2, 2
[2, 3, 3, 2, 3, 1, 1, 2, 3] => 2, 3, 3, 2, 3, 1, 1, 2, 3
[2, 3, 3, 2, 3, 1, 1, 3, 1] => 2, 3, 3, 2, 3, 1, 1, 3, 1
[2, 3, 3, 2, 3, 1, 1, 3, 2] => 2, 3, 3, 2, 3, 1, 1, 3, 2
[2, 3, 3, 2, 3, 1, 1, 3, 3] => 2, 3, 3, 2, 3, 1, 1, 3, 3
[2, 3, 3, 2, 3, 1, 2, 1, 1] => 2, 3, 3, 2, 3, 1, 2, 1, 1
[2, 3, 3, 2, 3, 1, 2, 1, 2] => 2, 3, 3, 2, 3, 1, 2, 1, 2
[2, 3, 3, 2, 3, 1, 2, 1, 3] => 2, 3, 3, 2, 3, 1, 2, 1, 3
[2, 3, 3, 2, 3, 1, 2, 2, 1] => 2, 3, 3, 2, 3, 1, 2, 2, 1
[2, 3, 3, 2, 3, 1, 2, 2, 2] => 2, 3, 3, 2, 3, 1, 2, 2, 2
[2, 3, 3, 2, 3, 1, 2, 2, 3] => 2, 3, 3, 2, 3, 1, 2, 2, 3
[2, 3, 3, 2, 3, 1, 2, 3, 1] => 2, 3, 3, 2, 3, 1, 2, 3, 1
[2, 3, 3, 2, 3, 1, 2, 3, 2] => 2, 3, 3, 2, 3, 1, 2, 3, 2
[2, 3, 3, 2, 3, 1, 2, 3, 3] => 2, 3, 3, 2, 3, 1, 2, 3, 3
[2, 3, 3, 2, 3, 1, 3, 1, 1] => 2, 3, 3, 2, 3, 1, 3, 1, 1
[2, 3, 3, 2, 3, 1, 3, 1, 2] => 2, 3, 3, 2, 3, 1, 3, 1, 2
[2, 3, 3, 2, 3, 1, 3, 1, 3] => 2, 3, 3, 2, 3, 1, 3, 1, 3
[2, 3, 3, 2, 3, 1, 3, 2, 1] => 2, 3, 3, 2, 3, 1, 3, 2, 1
[2, 3, 3, 2, 3, 1, 3, 2, 2] => 2, 3, 3, 2, 3, 1, 3, 2, 2
[2, 3, 3, 2, 3, 1, 3, 2, 3] => 2, 3, 3, 2, 3, 1, 3, 2, 3
[2, 3, 3, 2, 3, 1, 3, 3, 1] => 2, 3, 3, 2, 3, 1, 3, 3, 1
[2, 3, 3, 2, 3, 1, 3, 3, 2] => 2, 3, 3, 2, 3, 1, 3, 3, 2
[2, 3, 3, 2, 3, 1, 3, 3, 3] => 2, 3, 3, 2, 3, 1, 3, 3, 3
[2, 3, 3, 2, 3, 2, 1, 1, 1] => 2, 3, 3, 2, 3, 2, 1, 1, 1
[2, 3, 3, 2, 3, 2, 1, 1, 2] => 2, 3, 3, 2, 3, 2, 1, 1, 2
[2, 3, 3, 2, 3, 2, 1, 1, 3] => 2, 3, 3, 2, 3, 2, 1, 1, 3
[2, 3, 3, 2, 3, 2, 1, 2, 1] => 2, 3, 3, 2, 3, 2, 1, 2, 1
[2, 3, 3, 2, 3, 2, 1, 2, 2] => 2, 3, 3, 2, 3, 2, 1, 2, 2
[2, 3, 3, 2, 3, 2, 1, 2, 3] => 2, 3, 3, 2, 3, 2, 1, 2, 3
[2, 3, 3, 2, 3, 2, 1, 3, 1] => 2, 3, 3, 2, 3, 2, 1, 3, 1
[2, 3, 3, 2, 3, 2, 1, 3, 2] => 2, 3, 3, 2, 3, 2, 1, 3, 2
[2, 3, 3, 2, 3, 2, 1, 3, 3] => 2, 3, 3, 2, 3, 2, 1, 3, 3
[2, 3, 3, 2, 3, 2, 2, 1, 1] => 2, 3, 3, 2, 3, 2, 2, 1, 1
[2, 3, 3, 2, 3, 2, 2, 1, 2] => 2, 3, 3, 2, 3, 2, 2, 1, 2
[2, 3, 3, 2, 3, 2, 2, 1, 3] => 2, 3, 3, 2, 3, 2, 2, 1, 3
[2, 3, 3, 2, 3, 2, 2, 2, 1] => 2, 3, 3, 2, 3, 2, 2, 2, 1
[2, 3, 3, 2, 3, 2, 2, 2, 2] => 2, 3, 3, 2, 3, 2, 2, 2, 2
[2, 3, 3, 2, 3, 2, 2, 2, 3] => 2, 3, 3, 2, 3, 2, 2, 2, 3
[2, 3, 3, 2, 3, 2, 2, 3, 1] => 2, 3, 3, 2, 3, 2, 2, 3, 1
[2, 3, 3, 2, 3, 2, 2, 3, 2] => 2, 3, 3, 2, 3, 2, 2, 3, 2
[2, 3, 3, 2, 3, 2, 2, 3, 3] => 2, 3, 3, 2, 3, 2, 2, 3, 3
[2, 3, 3, 2, 3, 2, 3, 1, 1] => 2, 3, 3, 2, 3, 2, 3, 1, 1
[2, 3, 3, 2, 3, 2, 3, 1, 2] => 2, 3, 3, 2, 3, 2, 3, 1, 2
[2, 3, 3, 2, 3, 2, 3, 1, 3] => 2, 3, 3, 2, 3, 2, 3, 1, 3
[2, 3, 3, 2, 3, 2, 3, 2, 1] => 2, 3, 3, 2, 3, 2, 3, 2, 1
[2, 3, 3, 2, 3, 2, 3, 2, 2] => 2, 3, 3, 2, 3, 2, 3, 2, 2
[2, 3, 3, 2, 3, 2, 3, 2, 3] => 2, 3, 3, 2, 3, 2, 3, 2, 3
[2, 3, 3, 2, 3, 2, 3, 3, 1] => 2, 3, 3, 2, 3, 2, 3, 3, 1
[2, 3, 3, 2, 3, 2, 3, 3, 2] => 2, 3, 3, 2, 3, 2, 3, 3, 2
[2, 3, 3, 2, 3, 2, 3, 3, 3] => 2, 3, 3, 2, 3, 2, 3, 3, 3
[2, 3, 3, 2, 3, 3, 1, 1, 1] => 2, 3, 3, 2, 3, 3, 1, 1, 1
[2, 3, 3, 2, 3, 3, 1, 1, 2] => 2, 3, 3, 2, 3, 3, 1, 1, 2
[2, 3, 3, 2, 3, 3, 1, 1, 3] => 2, 3, 3, 2, 3, 3, 1, 1, 3
[2, 3, 3, 2, 3, 3, 1, 2, 1] => 2, 3, 3, 2, 3, 3, 1, 2, 1
[2, 3, 3, 2, 3, 3, 1, 2, 2] => 2, 3, 3, 2, 3, 3, 1, 2, 2
[2, 3, 3, 2, 3, 3, 1, 2, 3] => 2, 3, 3, 2, 3, 3, 1, 2, 3
[2, 3, 3, 2, 3, 3, 1, 3, 1] => 2, 3, 3, 2, 3, 3, 1, 3, 1
[2, 3, 3, 2, 3, 3, 1, 3, 2] => 2, 3, 3, 2, 3, 3, 1, 3, 2
[2, 3, 3, 2, 3, 3, 1, 3, 3] => 2, 3, 3, 2, 3, 3, 1, 3, 3
[2, 3, 3, 2, 3, 3, 2, 1, 1] => 2, 3, 3, 2, 3, 3, 2, 1, 1
[2, 3, 3, 2, 3, 3, 2, 1, 2] => 2, 3, 3, 2, 3, 3, 2, 1, 2
[2, 3, 3, 2, 3, 3, 2, 1, 3] => 2, 3, 3, 2, 3, 3, 2, 1, 3
[2, 3, 3, 2, 3, 3, 2, 2, 1] => 2, 3, 3, 2, 3, 3, 2, 2, 1
[2, 3, 3, 2, 3, 3, 2, 2, 2] => 2, 3, 3, 2, 3, 3, 2, 2, 2
[2, 3, 3, 2, 3, 3, 2, 2, 3] => 2, 3, 3, 2, 3, 3, 2, 2, 3
[2, 3, 3, 2, 3, 3, 2, 3, 1] => 2, 3, 3, 2, 3, 3, 2, 3, 1
[2, 3, 3, 2, 3, 3, 2, 3, 2] => 2, 3, 3, 2, 3, 3, 2, 3, 2
[2, 3, 3, 2, 3, 3, 2, 3, 3] => 2, 3, 3, 2, 3, 3, 2, 3, 3
[2, 3, 3, 2, 3, 3, 3, 1, 1] => 2, 3, 3, 2, 3, 3, 3, 1, 1
[2, 3, 3, 2, 3, 3, 3, 1, 2] => 2, 3, 3, 2, 3, 3, 3, 1, 2
[2, 3, 3, 2, 3, 3, 3, 1, 3] => 2, 3, 3, 2, 3, 3, 3, 1, 3
[2, 3, 3, 2, 3, 3, 3, 2, 1] => 2, 3, 3, 2, 3, 3, 3, 2, 1
[2, 3, 3, 2, 3, 3, 3, 2, 2] => 2, 3, 3, 2, 3, 3, 3, 2, 2
[2, 3, 3, 2, 3, 3, 3, 2, 3] => 2, 3, 3, 2, 3, 3, 3, 2, 3
[2, 3, 3, 2, 3, 3, 3, 3, 1] => 2, 3, 3, 2, 3, 3, 3, 3, 1
[2, 3, 3, 2, 3, 3, 3, 3, 2] => 2, 3, 3, 2, 3, 3, 3, 3, 2
[2, 3, 3, 2, 3, 3, 3, 3, 3] => 2, 3, 3, 2, 3, 3, 3, 3, 3
[2, 3, 3, 3, 1, 1, 1, 1, 1] => 2, 3, 3, 3, 1, 1, 1, 1, 1
[2, 3, 3, 3, 1, 1, 1, 1, 2] => 2, 3, 3, 3, 1, 1, 1, 1, 2
[2, 3, 3, 3, 1, 1, 1, 1, 3] => 2, 3, 3, 3, 1, 1, 1, 1, 3
[2, 3, 3, 3, 1, 1, 1, 2, 1] => 2, 3, 3, 3, 1, 1, 1, 2, 1
[2, 3, 3, 3, 1, 1, 1, 2, 2] => 2, 3, 3, 3, 1, 1, 1, 2, 2
[2, 3, 3, 3, 1, 1, 1, 2, 3] => 2, 3, 3, 3, 1, 1, 1, 2, 3
[2, 3, 3, 3, 1, 1, 1, 3, 1] => 2, 3, 3, 3, 1, 1, 1, 3, 1
[2, 3, 3, 3, 1, 1, 1, 3, 2] => 2, 3, 3, 3, 1, 1, 1, 3, 2
[2, 3, 3, 3, 1, 1, 1, 3, 3] => 2, 3, 3, 3, 1, 1, 1, 3, 3
[2, 3, 3, 3, 1, 1, 2, 1, 1] => 2, 3, 3, 3, 1, 1, 2, 1, 1
[2, 3, 3, 3, 1, 1, 2, 1, 2] => 2, 3, 3, 3, 1, 1, 2, 1, 2
[2, 3, 3, 3, 1, 1, 2, 1, 3] => 2, 3, 3, 3, 1, 1, 2, 1, 3
[2, 3, 3, 3, 1, 1, 2, 2, 1] => 2, 3, 3, 3, 1, 1, 2, 2, 1
[2, 3, 3, 3, 1, 1, 2, 2, 2] => 2, 3, 3, 3, 1, 1, 2, 2, 2
[2, 3, 3, 3, 1, 1, 2, 2, 3] => 2, 3, 3, 3, 1, 1, 2, 2, 3
[2, 3, 3, 3, 1, 1, 2, 3, 1] => 2, 3, 3, 3, 1, 1, 2, 3, 1
[2, 3, 3, 3, 1, 1, 2, 3, 2] => 2, 3, 3, 3, 1, 1, 2, 3, 2
[2, 3, 3, 3, 1, 1, 2, 3, 3] => 2, 3, 3, 3, 1, 1, 2, 3, 3
[2, 3, 3, 3, 1, 1, 3, 1, 1] => 2, 3, 3, 3, 1, 1, 3, 1, 1
[2, 3, 3, 3, 1, 1, 3, 1, 2] => 2, 3, 3, 3, 1, 1, 3, 1, 2
[2, 3, 3, 3, 1, 1, 3, 1, 3] => 2, 3, 3, 3, 1, 1, 3, 1, 3
[2, 3, 3, 3, 1, 1, 3, 2, 1] => 2, 3, 3, 3, 1, 1, 3, 2, 1
[2, 3, 3, 3, 1, 1, 3, 2, 2] => 2, 3, 3, 3, 1, 1, 3, 2, 2
[2, 3, 3, 3, 1, 1, 3, 2, 3] => 2, 3, 3, 3, 1, 1, 3, 2, 3
[2, 3, 3, 3, 1, 1, 3, 3, 1] => 2, 3, 3, 3, 1, 1, 3, 3, 1
[2, 3, 3, 3, 1, 1, 3, 3, 2] => 2, 3, 3, 3, 1, 1, 3, 3, 2
[2, 3, 3, 3, 1, 1, 3, 3, 3] => 2, 3, 3, 3, 1, 1, 3, 3, 3
[2, 3, 3, 3, 1, 2, 1, 1, 1] => 2, 3, 3, 3, 1, 2, 1, 1, 1
[2, 3, 3, 3, 1, 2, 1, 1, 2] => 2, 3, 3, 3, 1, 2, 1, 1, 2
[2, 3, 3, 3, 1, 2, 1, 1, 3] => 2, 3, 3, 3, 1, 2, 1, 1, 3
[2, 3, 3, 3, 1, 2, 1, 2, 1] => 2, 3, 3, 3, 1, 2, 1, 2, 1
[2, 3, 3, 3, 1, 2, 1, 2, 2] => 2, 3, 3, 3, 1, 2, 1, 2, 2
[2, 3, 3, 3, 1, 2, 1, 2, 3] => 2, 3, 3, 3, 1, 2, 1, 2, 3
[2, 3, 3, 3, 1, 2, 1, 3, 1] => 2, 3, 3, 3, 1, 2, 1, 3, 1
[2, 3, 3, 3, 1, 2, 1, 3, 2] => 2, 3, 3, 3, 1, 2, 1, 3, 2
[2, 3, 3, 3, 1, 2, 1, 3, 3] => 2, 3, 3, 3, 1, 2, 1, 3, 3
[2, 3, 3, 3, 1, 2, 2, 1, 1] => 2, 3, 3, 3, 1, 2, 2, 1, 1
[2, 3, 3, 3, 1, 2, 2, 1, 2] => 2, 3, 3, 3, 1, 2, 2, 1, 2
[2, 3, 3, 3, 1, 2, 2, 1, 3] => 2, 3, 3, 3, 1, 2, 2, 1, 3
[2, 3, 3, 3, 1, 2, 2, 2, 1] => 2, 3, 3, 3, 1, 2, 2, 2, 1
[2, 3, 3, 3, 1, 2, 2, 2, 2] => 2, 3, 3, 3, 1, 2, 2, 2, 2
[2, 3, 3, 3, 1, 2, 2, 2, 3] => 2, 3, 3, 3, 1, 2, 2, 2, 3
[2, 3, 3, 3, 1, 2, 2, 3, 1] => 2, 3, 3, 3, 1, 2, 2, 3, 1
[2, 3, 3, 3, 1, 2, 2, 3, 2] => 2, 3, 3, 3, 1, 2, 2, 3, 2
[2, 3, 3, 3, 1, 2, 2, 3, 3] => 2, 3, 3, 3, 1, 2, 2, 3, 3
[2, 3, 3, 3, 1, 2, 3, 1, 1] => 2, 3, 3, 3, 1, 2, 3, 1, 1
[2, 3, 3, 3, 1, 2, 3, 1, 2] => 2, 3, 3, 3, 1, 2, 3, 1, 2
[2, 3, 3, 3, 1, 2, 3, 1, 3] => 2, 3, 3, 3, 1, 2, 3, 1, 3
[2, 3, 3, 3, 1, 2, 3, 2, 1] => 2, 3, 3, 3, 1, 2, 3, 2, 1
[2, 3, 3, 3, 1, 2, 3, 2, 2] => 2, 3, 3, 3, 1, 2, 3, 2, 2
[2, 3, 3, 3, 1, 2, 3, 2, 3] => 2, 3, 3, 3, 1, 2, 3, 2, 3
[2, 3, 3, 3, 1, 2, 3, 3, 1] => 2, 3, 3, 3, 1, 2, 3, 3, 1
[2, 3, 3, 3, 1, 2, 3, 3, 2] => 2, 3, 3, 3, 1, 2, 3, 3, 2
[2, 3, 3, 3, 1, 2, 3, 3, 3] => 2, 3, 3, 3, 1, 2, 3, 3, 3
[2, 3, 3, 3, 1, 3, 1, 1, 1] => 2, 3, 3, 3, 1, 3, 1, 1, 1
[2, 3, 3, 3, 1, 3, 1, 1, 2] => 2, 3, 3, 3, 1, 3, 1, 1, 2
[2, 3, 3, 3, 1, 3, 1, 1, 3] => 2, 3, 3, 3, 1, 3, 1, 1, 3
[2, 3, 3, 3, 1, 3, 1, 2, 1] => 2, 3, 3, 3, 1, 3, 1, 2, 1
[2, 3, 3, 3, 1, 3, 1, 2, 2] => 2, 3, 3, 3, 1, 3, 1, 2, 2
[2, 3, 3, 3, 1, 3, 1, 2, 3] => 2, 3, 3, 3, 1, 3, 1, 2, 3
[2, 3, 3, 3, 1, 3, 1, 3, 1] => 2, 3, 3, 3, 1, 3, 1, 3, 1
[2, 3, 3, 3, 1, 3, 1, 3, 2] => 2, 3, 3, 3, 1, 3, 1, 3, 2
[2, 3, 3, 3, 1, 3, 1, 3, 3] => 2, 3, 3, 3, 1, 3, 1, 3, 3
[2, 3, 3, 3, 1, 3, 2, 1, 1] => 2, 3, 3, 3, 1, 3, 2, 1, 1
[2, 3, 3, 3, 1, 3, 2, 1, 2] => 2, 3, 3, 3, 1, 3, 2, 1, 2
[2, 3, 3, 3, 1, 3, 2, 1, 3] => 2, 3, 3, 3, 1, 3, 2, 1, 3
[2, 3, 3, 3, 1, 3, 2, 2, 1] => 2, 3, 3, 3, 1, 3, 2, 2, 1
[2, 3, 3, 3, 1, 3, 2, 2, 2] => 2, 3, 3, 3, 1, 3, 2, 2, 2
[2, 3, 3, 3, 1, 3, 2, 2, 3] => 2, 3, 3, 3, 1, 3, 2, 2, 3
[2, 3, 3, 3, 1, 3, 2, 3, 1] => 2, 3, 3, 3, 1, 3, 2, 3, 1
[2, 3, 3, 3, 1, 3, 2, 3, 2] => 2, 3, 3, 3, 1, 3, 2, 3, 2
[2, 3, 3, 3, 1, 3, 2, 3, 3] => 2, 3, 3, 3, 1, 3, 2, 3, 3
[2, 3, 3, 3, 1, 3, 3, 1, 1] => 2, 3, 3, 3, 1, 3, 3, 1, 1
[2, 3, 3, 3, 1, 3, 3, 1, 2] => 2, 3, 3, 3, 1, 3, 3, 1, 2
[2, 3, 3, 3, 1, 3, 3, 1, 3] => 2, 3, 3, 3, 1, 3, 3, 1, 3
[2, 3, 3, 3, 1, 3, 3, 2, 1] => 2, 3, 3, 3, 1, 3, 3, 2, 1
[2, 3, 3, 3, 1, 3, 3, 2, 2] => 2, 3, 3, 3, 1, 3, 3, 2, 2
[2, 3, 3, 3, 1, 3, 3, 2, 3] => 2, 3, 3, 3, 1, 3, 3, 2, 3
[2, 3, 3, 3, 1, 3, 3, 3, 1] => 2, 3, 3, 3, 1, 3, 3, 3, 1
[2, 3, 3, 3, 1, 3, 3, 3, 2] => 2, 3, 3, 3, 1, 3, 3, 3, 2
[2, 3, 3, 3, 1, 3, 3, 3, 3] => 2, 3, 3, 3, 1, 3, 3, 3, 3
[2, 3, 3, 3, 2, 1, 1, 1, 1] => 2, 3, 3, 3, 2, 1, 1, 1, 1
[2, 3, 3, 3, 2, 1, 1, 1, 2] => 2, 3, 3, 3, 2, 1, 1, 1, 2
[2, 3, 3, 3, 2, 1, 1, 1, 3] => 2, 3, 3, 3, 2, 1, 1, 1, 3
[2, 3, 3, 3, 2, 1, 1, 2, 1] => 2, 3, 3, 3, 2, 1, 1, 2, 1
[2, 3, 3, 3, 2, 1, 1, 2, 2] => 2, 3, 3, 3, 2, 1, 1, 2, 2
[2, 3, 3, 3, 2, 1, 1, 2, 3] => 2, 3, 3, 3, 2, 1, 1, 2, 3
[2, 3, 3, 3, 2, 1, 1, 3, 1] => 2, 3, 3, 3, 2, 1, 1, 3, 1
[2, 3, 3, 3, 2, 1, 1, 3, 2] => 2, 3, 3, 3, 2, 1, 1, 3, 2
[2, 3, 3, 3, 2, 1, 1, 3, 3] => 2, 3, 3, 3, 2, 1, 1, 3, 3
[2, 3, 3, 3, 2, 1, 2, 1, 1] => 2, 3, 3, 3, 2, 1, 2, 1, 1
[2, 3, 3, 3, 2, 1, 2, 1, 2] => 2, 3, 3, 3, 2, 1, 2, 1, 2
[2, 3, 3, 3, 2, 1, 2, 1, 3] => 2, 3, 3, 3, 2, 1, 2, 1, 3
[2, 3, 3, 3, 2, 1, 2, 2, 1] => 2, 3, 3, 3, 2, 1, 2, 2, 1
[2, 3, 3, 3, 2, 1, 2, 2, 2] => 2, 3, 3, 3, 2, 1, 2, 2, 2
[2, 3, 3, 3, 2, 1, 2, 2, 3] => 2, 3, 3, 3, 2, 1, 2, 2, 3
[2, 3, 3, 3, 2, 1, 2, 3, 1] => 2, 3, 3, 3, 2, 1, 2, 3, 1
[2, 3, 3, 3, 2, 1, 2, 3, 2] => 2, 3, 3, 3, 2, 1, 2, 3, 2
[2, 3, 3, 3, 2, 1, 2, 3, 3] => 2, 3, 3, 3, 2, 1, 2, 3, 3
[2, 3, 3, 3, 2, 1, 3, 1, 1] => 2, 3, 3, 3, 2, 1, 3, 1, 1
[2, 3, 3, 3, 2, 1, 3, 1, 2] => 2, 3, 3, 3, 2, 1, 3, 1, 2
[2, 3, 3, 3, 2, 1, 3, 1, 3] => 2, 3, 3, 3, 2, 1, 3, 1, 3
[2, 3, 3, 3, 2, 1, 3, 2, 1] => 2, 3, 3, 3, 2, 1, 3, 2, 1
[2, 3, 3, 3, 2, 1, 3, 2, 2] => 2, 3, 3, 3, 2, 1, 3, 2, 2
[2, 3, 3, 3, 2, 1, 3, 2, 3] => 2, 3, 3, 3, 2, 1, 3, 2, 3
[2, 3, 3, 3, 2, 1, 3, 3, 1] => 2, 3, 3, 3, 2, 1, 3, 3, 1
[2, 3, 3, 3, 2, 1, 3, 3, 2] => 2, 3, 3, 3, 2, 1, 3, 3, 2
[2, 3, 3, 3, 2, 1, 3, 3, 3] => 2, 3, 3, 3, 2, 1, 3, 3, 3
[2, 3, 3, 3, 2, 2, 1, 1, 1] => 2, 3, 3, 3, 2, 2, 1, 1, 1
[2, 3, 3, 3, 2, 2, 1, 1, 2] => 2, 3, 3, 3, 2, 2, 1, 1, 2
[2, 3, 3, 3, 2, 2, 1, 1, 3] => 2, 3, 3, 3, 2, 2, 1, 1, 3
[2, 3, 3, 3, 2, 2, 1, 2, 1] => 2, 3, 3, 3, 2, 2, 1, 2, 1
[2, 3, 3, 3, 2, 2, 1, 2, 2] => 2, 3, 3, 3, 2, 2, 1, 2, 2
[2, 3, 3, 3, 2, 2, 1, 2, 3] => 2, 3, 3, 3, 2, 2, 1, 2, 3
[2, 3, 3, 3, 2, 2, 1, 3, 1] => 2, 3, 3, 3, 2, 2, 1, 3, 1
[2, 3, 3, 3, 2, 2, 1, 3, 2] => 2, 3, 3, 3, 2, 2, 1, 3, 2
[2, 3, 3, 3, 2, 2, 1, 3, 3] => 2, 3, 3, 3, 2, 2, 1, 3, 3
[2, 3, 3, 3, 2, 2, 2, 1, 1] => 2, 3, 3, 3, 2, 2, 2, 1, 1
[2, 3, 3, 3, 2, 2, 2, 1, 2] => 2, 3, 3, 3, 2, 2, 2, 1, 2
[2, 3, 3, 3, 2, 2, 2, 1, 3] => 2, 3, 3, 3, 2, 2, 2, 1, 3
[2, 3, 3, 3, 2, 2, 2, 2, 1] => 2, 3, 3, 3, 2, 2, 2, 2, 1
[2, 3, 3, 3, 2, 2, 2, 2, 2] => 2, 3, 3, 3, 2, 2, 2, 2, 2
[2, 3, 3, 3, 2, 2, 2, 2, 3] => 2, 3, 3, 3, 2, 2, 2, 2, 3
[2, 3, 3, 3, 2, 2, 2, 3, 1] => 2, 3, 3, 3, 2, 2, 2, 3, 1
[2, 3, 3, 3, 2, 2, 2, 3, 2] => 2, 3, 3, 3, 2, 2, 2, 3, 2
[2, 3, 3, 3, 2, 2, 2, 3, 3] => 2, 3, 3, 3, 2, 2, 2, 3, 3
[2, 3, 3, 3, 2, 2, 3, 1, 1] => 2, 3, 3, 3, 2, 2, 3, 1, 1
[2, 3, 3, 3, 2, 2, 3, 1, 2] => 2, 3, 3, 3, 2, 2, 3, 1, 2
[2, 3, 3, 3, 2, 2, 3, 1, 3] => 2, 3, 3, 3, 2, 2, 3, 1, 3
[2, 3, 3, 3, 2, 2, 3, 2, 1] => 2, 3, 3, 3, 2, 2, 3, 2, 1
[2, 3, 3, 3, 2, 2, 3, 2, 2] => 2, 3, 3, 3, 2, 2, 3, 2, 2
[2, 3, 3, 3, 2, 2, 3, 2, 3] => 2, 3, 3, 3, 2, 2, 3, 2, 3
[2, 3, 3, 3, 2, 2, 3, 3, 1] => 2, 3, 3, 3, 2, 2, 3, 3, 1
[2, 3, 3, 3, 2, 2, 3, 3, 2] => 2, 3, 3, 3, 2, 2, 3, 3, 2
[2, 3, 3, 3, 2, 2, 3, 3, 3] => 2, 3, 3, 3, 2, 2, 3, 3, 3
[2, 3, 3, 3, 2, 3, 1, 1, 1] => 2, 3, 3, 3, 2, 3, 1, 1, 1
[2, 3, 3, 3, 2, 3, 1, 1, 2] => 2, 3, 3, 3, 2, 3, 1, 1, 2
[2, 3, 3, 3, 2, 3, 1, 1, 3] => 2, 3, 3, 3, 2, 3, 1, 1, 3
[2, 3, 3, 3, 2, 3, 1, 2, 1] => 2, 3, 3, 3, 2, 3, 1, 2, 1
[2, 3, 3, 3, 2, 3, 1, 2, 2] => 2, 3, 3, 3, 2, 3, 1, 2, 2
[2, 3, 3, 3, 2, 3, 1, 2, 3] => 2, 3, 3, 3, 2, 3, 1, 2, 3
[2, 3, 3, 3, 2, 3, 1, 3, 1] => 2, 3, 3, 3, 2, 3, 1, 3, 1
[2, 3, 3, 3, 2, 3, 1, 3, 2] => 2, 3, 3, 3, 2, 3, 1, 3, 2
[2, 3, 3, 3, 2, 3, 1, 3, 3] => 2, 3, 3, 3, 2, 3, 1, 3, 3
[2, 3, 3, 3, 2, 3, 2, 1, 1] => 2, 3, 3, 3, 2, 3, 2, 1, 1
[2, 3, 3, 3, 2, 3, 2, 1, 2] => 2, 3, 3, 3, 2, 3, 2, 1, 2
[2, 3, 3, 3, 2, 3, 2, 1, 3] => 2, 3, 3, 3, 2, 3, 2, 1, 3
[2, 3, 3, 3, 2, 3, 2, 2, 1] => 2, 3, 3, 3, 2, 3, 2, 2, 1
[2, 3, 3, 3, 2, 3, 2, 2, 2] => 2, 3, 3, 3, 2, 3, 2, 2, 2
[2, 3, 3, 3, 2, 3, 2, 2, 3] => 2, 3, 3, 3, 2, 3, 2, 2, 3
[2, 3, 3, 3, 2, 3, 2, 3, 1] => 2, 3, 3, 3, 2, 3, 2, 3, 1
[2, 3, 3, 3, 2, 3, 2, 3, 2] => 2, 3, 3, 3, 2, 3, 2, 3, 2
[2, 3, 3, 3, 2, 3, 2, 3, 3] => 2, 3, 3, 3, 2, 3, 2, 3, 3
[2, 3, 3, 3, 2, 3, 3, 1, 1] => 2, 3, 3, 3, 2, 3, 3, 1, 1
[2, 3, 3, 3, 2, 3, 3, 1, 2] => 2, 3, 3, 3, 2, 3, 3, 1, 2
[2, 3, 3, 3, 2, 3, 3, 1, 3] => 2, 3, 3, 3, 2, 3, 3, 1, 3
[2, 3, 3, 3, 2, 3, 3, 2, 1] => 2, 3, 3, 3, 2, 3, 3, 2, 1
[2, 3, 3, 3, 2, 3, 3, 2, 2] => 2, 3, 3, 3, 2, 3, 3, 2, 2
[2, 3, 3, 3, 2, 3, 3, 2, 3] => 2, 3, 3, 3, 2, 3, 3, 2, 3
[2, 3, 3, 3, 2, 3, 3, 3, 1] => 2, 3, 3, 3, 2, 3, 3, 3, 1
[2, 3, 3, 3, 2, 3, 3, 3, 2] => 2, 3, 3, 3, 2, 3, 3, 3, 2
[2, 3, 3, 3, 2, 3, 3, 3, 3] => 2, 3, 3, 3, 2, 3, 3, 3, 3
[2, 3, 3, 3, 3, 1, 1, 1, 1] => 2, 3, 3, 3, 3, 1, 1, 1, 1
[2, 3, 3, 3, 3, 1, 1, 1, 2] => 2, 3, 3, 3, 3, 1, 1, 1, 2
[2, 3, 3, 3, 3, 1, 1, 1, 3] => 2, 3, 3, 3, 3, 1, 1, 1, 3
[2, 3, 3, 3, 3, 1, 1, 2, 1] => 2, 3, 3, 3, 3, 1, 1, 2, 1
[2, 3, 3, 3, 3, 1, 1, 2, 2] => 2, 3, 3, 3, 3, 1, 1, 2, 2
[2, 3, 3, 3, 3, 1, 1, 2, 3] => 2, 3, 3, 3, 3, 1, 1, 2, 3
[2, 3, 3, 3, 3, 1, 1, 3, 1] => 2, 3, 3, 3, 3, 1, 1, 3, 1
[2, 3, 3, 3, 3, 1, 1, 3, 2] => 2, 3, 3, 3, 3, 1, 1, 3, 2
[2, 3, 3, 3, 3, 1, 1, 3, 3] => 2, 3, 3, 3, 3, 1, 1, 3, 3
[2, 3, 3, 3, 3, 1, 2, 1, 1] => 2, 3, 3, 3, 3, 1, 2, 1, 1
[2, 3, 3, 3, 3, 1, 2, 1, 2] => 2, 3, 3, 3, 3, 1, 2, 1, 2
[2, 3, 3, 3, 3, 1, 2, 1, 3] => 2, 3, 3, 3, 3, 1, 2, 1, 3
[2, 3, 3, 3, 3, 1, 2, 2, 1] => 2, 3, 3, 3, 3, 1, 2, 2, 1
[2, 3, 3, 3, 3, 1, 2, 2, 2] => 2, 3, 3, 3, 3, 1, 2, 2, 2
[2, 3, 3, 3, 3, 1, 2, 2, 3] => 2, 3, 3, 3, 3, 1, 2, 2, 3
[2, 3, 3, 3, 3, 1, 2, 3, 1] => 2, 3, 3, 3, 3, 1, 2, 3, 1
[2, 3, 3, 3, 3, 1, 2, 3, 2] => 2, 3, 3, 3, 3, 1, 2, 3, 2
[2, 3, 3, 3, 3, 1, 2, 3, 3] => 2, 3, 3, 3, 3, 1, 2, 3, 3
[2, 3, 3, 3, 3, 1, 3, 1, 1] => 2, 3, 3, 3, 3, 1, 3, 1, 1
[2, 3, 3, 3, 3, 1, 3, 1, 2] => 2, 3, 3, 3, 3, 1, 3, 1, 2
[2, 3, 3, 3, 3, 1, 3, 1, 3] => 2, 3, 3, 3, 3, 1, 3, 1, 3
[2, 3, 3, 3, 3, 1, 3, 2, 1] => 2, 3, 3, 3, 3, 1, 3, 2, 1
[2, 3, 3, 3, 3, 1, 3, 2, 2] => 2, 3, 3, 3, 3, 1, 3, 2, 2
[2, 3, 3, 3, 3, 1, 3, 2, 3] => 2, 3, 3, 3, 3, 1, 3, 2, 3
[2, 3, 3, 3, 3, 1, 3, 3, 1] => 2, 3, 3, 3, 3, 1, 3, 3, 1
[2, 3, 3, 3, 3, 1, 3, 3, 2] => 2, 3, 3, 3, 3, 1, 3, 3, 2
[2, 3, 3, 3, 3, 1, 3, 3, 3] => 2, 3, 3, 3, 3, 1, 3, 3, 3
[2, 3, 3, 3, 3, 2, 1, 1, 1] => 2, 3, 3, 3, 3, 2, 1, 1, 1
[2, 3, 3, 3, 3, 2, 1, 1, 2] => 2, 3, 3, 3, 3, 2, 1, 1, 2
[2, 3, 3, 3, 3, 2, 1, 1, 3] => 2, 3, 3, 3, 3, 2, 1, 1, 3
[2, 3, 3, 3, 3, 2, 1, 2, 1] => 2, 3, 3, 3, 3, 2, 1, 2, 1
[2, 3, 3, 3, 3, 2, 1, 2, 2] => 2, 3, 3, 3, 3, 2, 1, 2, 2
[2, 3, 3, 3, 3, 2, 1, 2, 3] => 2, 3, 3, 3, 3, 2, 1, 2, 3
[2, 3, 3, 3, 3, 2, 1, 3, 1] => 2, 3, 3, 3, 3, 2, 1, 3, 1
[2, 3, 3, 3, 3, 2, 1, 3, 2] => 2, 3, 3, 3, 3, 2, 1, 3, 2
[2, 3, 3, 3, 3, 2, 1, 3, 3] => 2, 3, 3, 3, 3, 2, 1, 3, 3
[2, 3, 3, 3, 3, 2, 2, 1, 1] => 2, 3, 3, 3, 3, 2, 2, 1, 1
[2, 3, 3, 3, 3, 2, 2, 1, 2] => 2, 3, 3, 3, 3, 2, 2, 1, 2
[2, 3, 3, 3, 3, 2, 2, 1, 3] => 2, 3, 3, 3, 3, 2, 2, 1, 3
[2, 3, 3, 3, 3, 2, 2, 2, 1] => 2, 3, 3, 3, 3, 2, 2, 2, 1
[2, 3, 3, 3, 3, 2, 2, 2, 2] => 2, 3, 3, 3, 3, 2, 2, 2, 2
[2, 3, 3, 3, 3, 2, 2, 2, 3] => 2, 3, 3, 3, 3, 2, 2, 2, 3
[2, 3, 3, 3, 3, 2, 2, 3, 1] => 2, 3, 3, 3, 3, 2, 2, 3, 1
[2, 3, 3, 3, 3, 2, 2, 3, 2] => 2, 3, 3, 3, 3, 2, 2, 3, 2
[2, 3, 3, 3, 3, 2, 2, 3, 3] => 2, 3, 3, 3, 3, 2, 2, 3, 3
[2, 3, 3, 3, 3, 2, 3, 1, 1] => 2, 3, 3, 3, 3, 2, 3, 1, 1
[2, 3, 3, 3, 3, 2, 3, 1, 2] => 2, 3, 3, 3, 3, 2, 3, 1, 2
[2, 3, 3, 3, 3, 2, 3, 1, 3] => 2, 3, 3, 3, 3, 2, 3, 1, 3
[2, 3, 3, 3, 3, 2, 3, 2, 1] => 2, 3, 3, 3, 3, 2, 3, 2, 1
[2, 3, 3, 3, 3, 2, 3, 2, 2] => 2, 3, 3, 3, 3, 2, 3, 2, 2
[2, 3, 3, 3, 3, 2, 3, 2, 3] => 2, 3, 3, 3, 3, 2, 3, 2, 3
[2, 3, 3, 3, 3, 2, 3, 3, 1] => 2, 3, 3, 3, 3, 2, 3, 3, 1
[2, 3, 3, 3, 3, 2, 3, 3, 2] => 2, 3, 3, 3, 3, 2, 3, 3, 2
[2, 3, 3, 3, 3, 2, 3, 3, 3] => 2, 3, 3, 3, 3, 2, 3, 3, 3
[2, 3, 3, 3, 3, 3, 1, 1, 1] => 2, 3, 3, 3, 3, 3, 1, 1, 1
[2, 3, 3, 3, 3, 3, 1, 1, 2] => 2, 3, 3, 3, 3, 3, 1, 1, 2
[2, 3, 3, 3, 3, 3, 1, 1, 3] => 2, 3, 3, 3, 3, 3, 1, 1, 3
[2, 3, 3, 3, 3, 3, 1, 2, 1] => 2, 3, 3, 3, 3, 3, 1, 2, 1
[2, 3, 3, 3, 3, 3, 1, 2, 2] => 2, 3, 3, 3, 3, 3, 1, 2, 2
[2, 3, 3, 3, 3, 3, 1, 2, 3] => 2, 3, 3, 3, 3, 3, 1, 2, 3
[2, 3, 3, 3, 3, 3, 1, 3, 1] => 2, 3, 3, 3, 3, 3, 1, 3, 1
[2, 3, 3, 3, 3, 3, 1, 3, 2] => 2, 3, 3, 3, 3, 3, 1, 3, 2
[2, 3, 3, 3, 3, 3, 1, 3, 3] => 2, 3, 3, 3, 3, 3, 1, 3, 3
[2, 3, 3, 3, 3, 3, 2, 1, 1] => 2, 3, 3, 3, 3, 3, 2, 1, 1
[2, 3, 3, 3, 3, 3, 2, 1, 2] => 2, 3, 3, 3, 3, 3, 2, 1, 2
[2, 3, 3, 3, 3, 3, 2, 1, 3] => 2, 3, 3, 3, 3, 3, 2, 1, 3
[2, 3, 3, 3, 3, 3, 2, 2, 1] => 2, 3, 3, 3, 3, 3, 2, 2, 1
[2, 3, 3, 3, 3, 3, 2, 2, 2] => 2, 3, 3, 3, 3, 3, 2, 2, 2
[2, 3, 3, 3, 3, 3, 2, 2, 3] => 2, 3, 3, 3, 3, 3, 2, 2, 3
[2, 3, 3, 3, 3, 3, 2, 3, 1] => 2, 3, 3, 3, 3, 3, 2, 3, 1
[2, 3, 3, 3, 3, 3, 2, 3, 2] => 2, 3, 3, 3, 3, 3, 2, 3, 2
[2, 3, 3, 3, 3, 3, 2, 3, 3] => 2, 3, 3, 3, 3, 3, 2, 3, 3
[2, 3, 3, 3, 3, 3, 3, 1, 1] => 2, 3, 3, 3, 3, 3, 3, 1, 1
[2, 3, 3, 3, 3, 3, 3, 1, 2] => 2, 3, 3, 3, 3, 3, 3, 1, 2
[2, 3, 3, 3, 3, 3, 3, 1, 3] => 2, 3, 3, 3, 3, 3, 3, 1, 3
[2, 3, 3, 3, 3, 3, 3, 2, 1] => 2, 3, 3, 3, 3, 3, 3, 2, 1
[2, 3, 3, 3, 3, 3, 3, 2, 2] => 2, 3, 3, 3, 3, 3, 3, 2, 2
[2, 3, 3, 3, 3, 3, 3, 2, 3] => 2, 3, 3, 3, 3, 3, 3, 2, 3
[2, 3, 3, 3, 3, 3, 3, 3, 1] => 2, 3, 3, 3, 3, 3, 3, 3, 1
[2, 3, 3, 3, 3, 3, 3, 3, 2] => 2, 3, 3, 3, 3, 3, 3, 3, 2
[2, 3, 3, 3, 3, 3, 3, 3, 3] => 2, 3, 3, 3, 3, 3, 3, 3, 3
[3, 1, 1, 1, 1, 1, 1, 1, 1] => 3, 1, 1, 1, 1, 1, 1, 1, 1
[3, 1, 1, 1, 1, 1, 1, 1, 2] => 3, 1, 1, 1, 1, 1, 1, 1, 2
[3, 1, 1, 1, 1, 1, 1, 1, 3] => 3, 1, 1, 1, 1, 1, 1, 1, 3
[3, 1, 1, 1, 1, 1, 1, 2, 1] => 3, 1, 1, 1, 1, 1, 1, 2, 1
[3, 1, 1, 1, 1, 1, 1, 2, 2] => 3, 1, 1, 1, 1, 1, 1, 2, 2
[3, 1, 1, 1, 1, 1, 1, 2, 3] => 3, 1, 1, 1, 1, 1, 1, 2, 3
[3, 1, 1, 1, 1, 1, 1, 3, 1] => 3, 1, 1, 1, 1, 1, 1, 3, 1
[3, 1, 1, 1, 1, 1, 1, 3, 2] => 3, 1, 1, 1, 1, 1, 1, 3, 2
[3, 1, 1, 1, 1, 1, 1, 3, 3] => 3, 1, 1, 1, 1, 1, 1, 3, 3
[3, 1, 1, 1, 1, 1, 2, 1, 1] => 3, 1, 1, 1, 1, 1, 2, 1, 1
[3, 1, 1, 1, 1, 1, 2, 1, 2] => 3, 1, 1, 1, 1, 1, 2, 1, 2
[3, 1, 1, 1, 1, 1, 2, 1, 3] => 3, 1, 1, 1, 1, 1, 2, 1, 3
[3, 1, 1, 1, 1, 1, 2, 2, 1] => 3, 1, 1, 1, 1, 1, 2, 2, 1
[3, 1, 1, 1, 1, 1, 2, 2, 2] => 3, 1, 1, 1, 1, 1, 2, 2, 2
[3, 1, 1, 1, 1, 1, 2, 2, 3] => 3, 1, 1, 1, 1, 1, 2, 2, 3
[3, 1, 1, 1, 1, 1, 2, 3, 1] => 3, 1, 1, 1, 1, 1, 2, 3, 1
[3, 1, 1, 1, 1, 1, 2, 3, 2] => 3, 1, 1, 1, 1, 1, 2, 3, 2
[3, 1, 1, 1, 1, 1, 2, 3, 3] => 3, 1, 1, 1, 1, 1, 2, 3, 3
[3, 1, 1, 1, 1, 1, 3, 1, 1] => 3, 1, 1, 1, 1, 1, 3, 1, 1
[3, 1, 1, 1, 1, 1, 3, 1, 2] => 3, 1, 1, 1, 1, 1, 3, 1, 2
[3, 1, 1, 1, 1, 1, 3, 1, 3] => 3, 1, 1, 1, 1, 1, 3, 1, 3
[3, 1, 1, 1, 1, 1, 3, 2, 1] => 3, 1, 1, 1, 1, 1, 3, 2, 1
[3, 1, 1, 1, 1, 1, 3, 2, 2] => 3, 1, 1, 1, 1, 1, 3, 2, 2
[3, 1, 1, 1, 1, 1, 3, 2, 3] => 3, 1, 1, 1, 1, 1, 3, 2, 3
[3, 1, 1, 1, 1, 1, 3, 3, 1] => 3, 1, 1, 1, 1, 1, 3, 3, 1
[3, 1, 1, 1, 1, 1, 3, 3, 2] => 3, 1, 1, 1, 1, 1, 3, 3, 2
[3, 1, 1, 1, 1, 1, 3, 3, 3] => 3, 1, 1, 1, 1, 1, 3, 3, 3
[3, 1, 1, 1, 1, 2, 1, 1, 1] => 3, 1, 1, 1, 1, 2, 1, 1, 1
[3, 1, 1, 1, 1, 2, 1, 1, 2] => 3, 1, 1, 1, 1, 2, 1, 1, 2
[3, 1, 1, 1, 1, 2, 1, 1, 3] => 3, 1, 1, 1, 1, 2, 1, 1, 3
[3, 1, 1, 1, 1, 2, 1, 2, 1] => 3, 1, 1, 1, 1, 2, 1, 2, 1
[3, 1, 1, 1, 1, 2, 1, 2, 2] => 3, 1, 1, 1, 1, 2, 1, 2, 2
[3, 1, 1, 1, 1, 2, 1, 2, 3] => 3, 1, 1, 1, 1, 2, 1, 2, 3
[3, 1, 1, 1, 1, 2, 1, 3, 1] => 3, 1, 1, 1, 1, 2, 1, 3, 1
[3, 1, 1, 1, 1, 2, 1, 3, 2] => 3, 1, 1, 1, 1, 2, 1, 3, 2
[3, 1, 1, 1, 1, 2, 1, 3, 3] => 3, 1, 1, 1, 1, 2, 1, 3, 3
[3, 1, 1, 1, 1, 2, 2, 1, 1] => 3, 1, 1, 1, 1, 2, 2, 1, 1
[3, 1, 1, 1, 1, 2, 2, 1, 2] => 3, 1, 1, 1, 1, 2, 2, 1, 2
[3, 1, 1, 1, 1, 2, 2, 1, 3] => 3, 1, 1, 1, 1, 2, 2, 1, 3
[3, 1, 1, 1, 1, 2, 2, 2, 1] => 3, 1, 1, 1, 1, 2, 2, 2, 1
[3, 1, 1, 1, 1, 2, 2, 2, 2] => 3, 1, 1, 1, 1, 2, 2, 2, 2
[3, 1, 1, 1, 1, 2, 2, 2, 3] => 3, 1, 1, 1, 1, 2, 2, 2, 3
[3, 1, 1, 1, 1, 2, 2, 3, 1] => 3, 1, 1, 1, 1, 2, 2, 3, 1
[3, 1, 1, 1, 1, 2, 2, 3, 2] => 3, 1, 1, 1, 1, 2, 2, 3, 2
[3, 1, 1, 1, 1, 2, 2, 3, 3] => 3, 1, 1, 1, 1, 2, 2, 3, 3
[3, 1, 1, 1, 1, 2, 3, 1, 1] => 3, 1, 1, 1, 1, 2, 3, 1, 1
[3, 1, 1, 1, 1, 2, 3, 1, 2] => 3, 1, 1, 1, 1, 2, 3, 1, 2
[3, 1, 1, 1, 1, 2, 3, 1, 3] => 3, 1, 1, 1, 1, 2, 3, 1, 3
[3, 1, 1, 1, 1, 2, 3, 2, 1] => 3, 1, 1, 1, 1, 2, 3, 2, 1
[3, 1, 1, 1, 1, 2, 3, 2, 2] => 3, 1, 1, 1, 1, 2, 3, 2, 2
[3, 1, 1, 1, 1, 2, 3, 2, 3] => 3, 1, 1, 1, 1, 2, 3, 2, 3
[3, 1, 1, 1, 1, 2, 3, 3, 1] => 3, 1, 1, 1, 1, 2, 3, 3, 1
[3, 1, 1, 1, 1, 2, 3, 3, 2] => 3, 1, 1, 1, 1, 2, 3, 3, 2
[3, 1, 1, 1, 1, 2, 3, 3, 3] => 3, 1, 1, 1, 1, 2, 3, 3, 3
[3, 1, 1, 1, 1, 3, 1, 1, 1] => 3, 1, 1, 1, 1, 3, 1, 1, 1
[3, 1, 1, 1, 1, 3, 1, 1, 2] => 3, 1, 1, 1, 1, 3, 1, 1, 2
[3, 1, 1, 1, 1, 3, 1, 1, 3] => 3, 1, 1, 1, 1, 3, 1, 1, 3
[3, 1, 1, 1, 1, 3, 1, 2, 1] => 3, 1, 1, 1, 1, 3, 1, 2, 1
[3, 1, 1, 1, 1, 3, 1, 2, 2] => 3, 1, 1, 1, 1, 3, 1, 2, 2
[3, 1, 1, 1, 1, 3, 1, 2, 3] => 3, 1, 1, 1, 1, 3, 1, 2, 3
[3, 1, 1, 1, 1, 3, 1, 3, 1] => 3, 1, 1, 1, 1, 3, 1, 3, 1
[3, 1, 1, 1, 1, 3, 1, 3, 2] => 3, 1, 1, 1, 1, 3, 1, 3, 2
[3, 1, 1, 1, 1, 3, 1, 3, 3] => 3, 1, 1, 1, 1, 3, 1, 3, 3
[3, 1, 1, 1, 1, 3, 2, 1, 1] => 3, 1, 1, 1, 1, 3, 2, 1, 1
[3, 1, 1, 1, 1, 3, 2, 1, 2] => 3, 1, 1, 1, 1, 3, 2, 1, 2
[3, 1, 1, 1, 1, 3, 2, 1, 3] => 3, 1, 1, 1, 1, 3, 2, 1, 3
[3, 1, 1, 1, 1, 3, 2, 2, 1] => 3, 1, 1, 1, 1, 3, 2, 2, 1
[3, 1, 1, 1, 1, 3, 2, 2, 2] => 3, 1, 1, 1, 1, 3, 2, 2, 2
[3, 1, 1, 1, 1, 3, 2, 2, 3] => 3, 1, 1, 1, 1, 3, 2, 2, 3
[3, 1, 1, 1, 1, 3, 2, 3, 1] => 3, 1, 1, 1, 1, 3, 2, 3, 1
[3, 1, 1, 1, 1, 3, 2, 3, 2] => 3, 1, 1, 1, 1, 3, 2, 3, 2
[3, 1, 1, 1, 1, 3, 2, 3, 3] => 3, 1, 1, 1, 1, 3, 2, 3, 3
[3, 1, 1, 1, 1, 3, 3, 1, 1] => 3, 1, 1, 1, 1, 3, 3, 1, 1
[3, 1, 1, 1, 1, 3, 3, 1, 2] => 3, 1, 1, 1, 1, 3, 3, 1, 2
[3, 1, 1, 1, 1, 3, 3, 1, 3] => 3, 1, 1, 1, 1, 3, 3, 1, 3
[3, 1, 1, 1, 1, 3, 3, 2, 1] => 3, 1, 1, 1, 1, 3, 3, 2, 1
[3, 1, 1, 1, 1, 3, 3, 2, 2] => 3, 1, 1, 1, 1, 3, 3, 2, 2
[3, 1, 1, 1, 1, 3, 3, 2, 3] => 3, 1, 1, 1, 1, 3, 3, 2, 3
[3, 1, 1, 1, 1, 3, 3, 3, 1] => 3, 1, 1, 1, 1, 3, 3, 3, 1
[3, 1, 1, 1, 1, 3, 3, 3, 2] => 3, 1, 1, 1, 1, 3, 3, 3, 2
[3, 1, 1, 1, 1, 3, 3, 3, 3] => 3, 1, 1, 1, 1, 3, 3, 3, 3
[3, 1, 1, 1, 2, 1, 1, 1, 1] => 3, 1, 1, 1, 2, 1, 1, 1, 1
[3, 1, 1, 1, 2, 1, 1, 1, 2] => 3, 1, 1, 1, 2, 1, 1, 1, 2
[3, 1, 1, 1, 2, 1, 1, 1, 3] => 3, 1, 1, 1, 2, 1, 1, 1, 3
[3, 1, 1, 1, 2, 1, 1, 2, 1] => 3, 1, 1, 1, 2, 1, 1, 2, 1
[3, 1, 1, 1, 2, 1, 1, 2, 2] => 3, 1, 1, 1, 2, 1, 1, 2, 2
[3, 1, 1, 1, 2, 1, 1, 2, 3] => 3, 1, 1, 1, 2, 1, 1, 2, 3
[3, 1, 1, 1, 2, 1, 1, 3, 1] => 3, 1, 1, 1, 2, 1, 1, 3, 1
[3, 1, 1, 1, 2, 1, 1, 3, 2] => 3, 1, 1, 1, 2, 1, 1, 3, 2
[3, 1, 1, 1, 2, 1, 1, 3, 3] => 3, 1, 1, 1, 2, 1, 1, 3, 3
[3, 1, 1, 1, 2, 1, 2, 1, 1] => 3, 1, 1, 1, 2, 1, 2, 1, 1
[3, 1, 1, 1, 2, 1, 2, 1, 2] => 3, 1, 1, 1, 2, 1, 2, 1, 2
[3, 1, 1, 1, 2, 1, 2, 1, 3] => 3, 1, 1, 1, 2, 1, 2, 1, 3
[3, 1, 1, 1, 2, 1, 2, 2, 1] => 3, 1, 1, 1, 2, 1, 2, 2, 1
[3, 1, 1, 1, 2, 1, 2, 2, 2] => 3, 1, 1, 1, 2, 1, 2, 2, 2
[3, 1, 1, 1, 2, 1, 2, 2, 3] => 3, 1, 1, 1, 2, 1, 2, 2, 3
[3, 1, 1, 1, 2, 1, 2, 3, 1] => 3, 1, 1, 1, 2, 1, 2, 3, 1
[3, 1, 1, 1, 2, 1, 2, 3, 2] => 3, 1, 1, 1, 2, 1, 2, 3, 2
[3, 1, 1, 1, 2, 1, 2, 3, 3] => 3, 1, 1, 1, 2, 1, 2, 3, 3
[3, 1, 1, 1, 2, 1, 3, 1, 1] => 3, 1, 1, 1, 2, 1, 3, 1, 1
[3, 1, 1, 1, 2, 1, 3, 1, 2] => 3, 1, 1, 1, 2, 1, 3, 1, 2
[3, 1, 1, 1, 2, 1, 3, 1, 3] => 3, 1, 1, 1, 2, 1, 3, 1, 3
[3, 1, 1, 1, 2, 1, 3, 2, 1] => 3, 1, 1, 1, 2, 1, 3, 2, 1
[3, 1, 1, 1, 2, 1, 3, 2, 2] => 3, 1, 1, 1, 2, 1, 3, 2, 2
[3, 1, 1, 1, 2, 1, 3, 2, 3] => 3, 1, 1, 1, 2, 1, 3, 2, 3
[3, 1, 1, 1, 2, 1, 3, 3, 1] => 3, 1, 1, 1, 2, 1, 3, 3, 1
[3, 1, 1, 1, 2, 1, 3, 3, 2] => 3, 1, 1, 1, 2, 1, 3, 3, 2
[3, 1, 1, 1, 2, 1, 3, 3, 3] => 3, 1, 1, 1, 2, 1, 3, 3, 3
[3, 1, 1, 1, 2, 2, 1, 1, 1] => 3, 1, 1, 1, 2, 2, 1, 1, 1
[3, 1, 1, 1, 2, 2, 1, 1, 2] => 3, 1, 1, 1, 2, 2, 1, 1, 2
[3, 1, 1, 1, 2, 2, 1, 1, 3] => 3, 1, 1, 1, 2, 2, 1, 1, 3
[3, 1, 1, 1, 2, 2, 1, 2, 1] => 3, 1, 1, 1, 2, 2, 1, 2, 1
[3, 1, 1, 1, 2, 2, 1, 2, 2] => 3, 1, 1, 1, 2, 2, 1, 2, 2
[3, 1, 1, 1, 2, 2, 1, 2, 3] => 3, 1, 1, 1, 2, 2, 1, 2, 3
[3, 1, 1, 1, 2, 2, 1, 3, 1] => 3, 1, 1, 1, 2, 2, 1, 3, 1
[3, 1, 1, 1, 2, 2, 1, 3, 2] => 3, 1, 1, 1, 2, 2, 1, 3, 2
[3, 1, 1, 1, 2, 2, 1, 3, 3] => 3, 1, 1, 1, 2, 2, 1, 3, 3
[3, 1, 1, 1, 2, 2, 2, 1, 1] => 3, 1, 1, 1, 2, 2, 2, 1, 1
[3, 1, 1, 1, 2, 2, 2, 1, 2] => 3, 1, 1, 1, 2, 2, 2, 1, 2
[3, 1, 1, 1, 2, 2, 2, 1, 3] => 3, 1, 1, 1, 2, 2, 2, 1, 3
[3, 1, 1, 1, 2, 2, 2, 2, 1] => 3, 1, 1, 1, 2, 2, 2, 2, 1
[3, 1, 1, 1, 2, 2, 2, 2, 2] => 3, 1, 1, 1, 2, 2, 2, 2, 2
[3, 1, 1, 1, 2, 2, 2, 2, 3] => 3, 1, 1, 1, 2, 2, 2, 2, 3
[3, 1, 1, 1, 2, 2, 2, 3, 1] => 3, 1, 1, 1, 2, 2, 2, 3, 1
[3, 1, 1, 1, 2, 2, 2, 3, 2] => 3, 1, 1, 1, 2, 2, 2, 3, 2
[3, 1, 1, 1, 2, 2, 2, 3, 3] => 3, 1, 1, 1, 2, 2, 2, 3, 3
[3, 1, 1, 1, 2, 2, 3, 1, 1] => 3, 1, 1, 1, 2, 2, 3, 1, 1
[3, 1, 1, 1, 2, 2, 3, 1, 2] => 3, 1, 1, 1, 2, 2, 3, 1, 2
[3, 1, 1, 1, 2, 2, 3, 1, 3] => 3, 1, 1, 1, 2, 2, 3, 1, 3
[3, 1, 1, 1, 2, 2, 3, 2, 1] => 3, 1, 1, 1, 2, 2, 3, 2, 1
[3, 1, 1, 1, 2, 2, 3, 2, 2] => 3, 1, 1, 1, 2, 2, 3, 2, 2
[3, 1, 1, 1, 2, 2, 3, 2, 3] => 3, 1, 1, 1, 2, 2, 3, 2, 3
[3, 1, 1, 1, 2, 2, 3, 3, 1] => 3, 1, 1, 1, 2, 2, 3, 3, 1
[3, 1, 1, 1, 2, 2, 3, 3, 2] => 3, 1, 1, 1, 2, 2, 3, 3, 2
[3, 1, 1, 1, 2, 2, 3, 3, 3] => 3, 1, 1, 1, 2, 2, 3, 3, 3
[3, 1, 1, 1, 2, 3, 1, 1, 1] => 3, 1, 1, 1, 2, 3, 1, 1, 1
[3, 1, 1, 1, 2, 3, 1, 1, 2] => 3, 1, 1, 1, 2, 3, 1, 1, 2
[3, 1, 1, 1, 2, 3, 1, 1, 3] => 3, 1, 1, 1, 2, 3, 1, 1, 3
[3, 1, 1, 1, 2, 3, 1, 2, 1] => 3, 1, 1, 1, 2, 3, 1, 2, 1
[3, 1, 1, 1, 2, 3, 1, 2, 2] => 3, 1, 1, 1, 2, 3, 1, 2, 2
[3, 1, 1, 1, 2, 3, 1, 2, 3] => 3, 1, 1, 1, 2, 3, 1, 2, 3
[3, 1, 1, 1, 2, 3, 1, 3, 1] => 3, 1, 1, 1, 2, 3, 1, 3, 1
[3, 1, 1, 1, 2, 3, 1, 3, 2] => 3, 1, 1, 1, 2, 3, 1, 3, 2
[3, 1, 1, 1, 2, 3, 1, 3, 3] => 3, 1, 1, 1, 2, 3, 1, 3, 3
[3, 1, 1, 1, 2, 3, 2, 1, 1] => 3, 1, 1, 1, 2, 3, 2, 1, 1
[3, 1, 1, 1, 2, 3, 2, 1, 2] => 3, 1, 1, 1, 2, 3, 2, 1, 2
[3, 1, 1, 1, 2, 3, 2, 1, 3] => 3, 1, 1, 1, 2, 3, 2, 1, 3
[3, 1, 1, 1, 2, 3, 2, 2, 1] => 3, 1, 1, 1, 2, 3, 2, 2, 1
[3, 1, 1, 1, 2, 3, 2, 2, 2] => 3, 1, 1, 1, 2, 3, 2, 2, 2
[3, 1, 1, 1, 2, 3, 2, 2, 3] => 3, 1, 1, 1, 2, 3, 2, 2, 3
[3, 1, 1, 1, 2, 3, 2, 3, 1] => 3, 1, 1, 1, 2, 3, 2, 3, 1
[3, 1, 1, 1, 2, 3, 2, 3, 2] => 3, 1, 1, 1, 2, 3, 2, 3, 2
[3, 1, 1, 1, 2, 3, 2, 3, 3] => 3, 1, 1, 1, 2, 3, 2, 3, 3
[3, 1, 1, 1, 2, 3, 3, 1, 1] => 3, 1, 1, 1, 2, 3, 3, 1, 1
[3, 1, 1, 1, 2, 3, 3, 1, 2] => 3, 1, 1, 1, 2, 3, 3, 1, 2
[3, 1, 1, 1, 2, 3, 3, 1, 3] => 3, 1, 1, 1, 2, 3, 3, 1, 3
[3, 1, 1, 1, 2, 3, 3, 2, 1] => 3, 1, 1, 1, 2, 3, 3, 2, 1
[3, 1, 1, 1, 2, 3, 3, 2, 2] => 3, 1, 1, 1, 2, 3, 3, 2, 2
[3, 1, 1, 1, 2, 3, 3, 2, 3] => 3, 1, 1, 1, 2, 3, 3, 2, 3
[3, 1, 1, 1, 2, 3, 3, 3, 1] => 3, 1, 1, 1, 2, 3, 3, 3, 1
[3, 1, 1, 1, 2, 3, 3, 3, 2] => 3, 1, 1, 1, 2, 3, 3, 3, 2
[3, 1, 1, 1, 2, 3, 3, 3, 3] => 3, 1, 1, 1, 2, 3, 3, 3, 3
[3, 1, 1, 1, 3, 1, 1, 1, 1] => 3, 1, 1, 1, 3, 1, 1, 1, 1
[3, 1, 1, 1, 3, 1, 1, 1, 2] => 3, 1, 1, 1, 3, 1, 1, 1, 2
[3, 1, 1, 1, 3, 1, 1, 1, 3] => 3, 1, 1, 1, 3, 1, 1, 1, 3
[3, 1, 1, 1, 3, 1, 1, 2, 1] => 3, 1, 1, 1, 3, 1, 1, 2, 1
[3, 1, 1, 1, 3, 1, 1, 2, 2] => 3, 1, 1, 1, 3, 1, 1, 2, 2
[3, 1, 1, 1, 3, 1, 1, 2, 3] => 3, 1, 1, 1, 3, 1, 1, 2, 3
[3, 1, 1, 1, 3, 1, 1, 3, 1] => 3, 1, 1, 1, 3, 1, 1, 3, 1
[3, 1, 1, 1, 3, 1, 1, 3, 2] => 3, 1, 1, 1, 3, 1, 1, 3, 2
[3, 1, 1, 1, 3, 1, 1, 3, 3] => 3, 1, 1, 1, 3, 1, 1, 3, 3
[3, 1, 1, 1, 3, 1, 2, 1, 1] => 3, 1, 1, 1, 3, 1, 2, 1, 1
[3, 1, 1, 1, 3, 1, 2, 1, 2] => 3, 1, 1, 1, 3, 1, 2, 1, 2
[3, 1, 1, 1, 3, 1, 2, 1, 3] => 3, 1, 1, 1, 3, 1, 2, 1, 3
[3, 1, 1, 1, 3, 1, 2, 2, 1] => 3, 1, 1, 1, 3, 1, 2, 2, 1
[3, 1, 1, 1, 3, 1, 2, 2, 2] => 3, 1, 1, 1, 3, 1, 2, 2, 2
[3, 1, 1, 1, 3, 1, 2, 2, 3] => 3, 1, 1, 1, 3, 1, 2, 2, 3
[3, 1, 1, 1, 3, 1, 2, 3, 1] => 3, 1, 1, 1, 3, 1, 2, 3, 1
[3, 1, 1, 1, 3, 1, 2, 3, 2] => 3, 1, 1, 1, 3, 1, 2, 3, 2
[3, 1, 1, 1, 3, 1, 2, 3, 3] => 3, 1, 1, 1, 3, 1, 2, 3, 3
[3, 1, 1, 1, 3, 1, 3, 1, 1] => 3, 1, 1, 1, 3, 1, 3, 1, 1
[3, 1, 1, 1, 3, 1, 3, 1, 2] => 3, 1, 1, 1, 3, 1, 3, 1, 2
[3, 1, 1, 1, 3, 1, 3, 1, 3] => 3, 1, 1, 1, 3, 1, 3, 1, 3
[3, 1, 1, 1, 3, 1, 3, 2, 1] => 3, 1, 1, 1, 3, 1, 3, 2, 1
[3, 1, 1, 1, 3, 1, 3, 2, 2] => 3, 1, 1, 1, 3, 1, 3, 2, 2
[3, 1, 1, 1, 3, 1, 3, 2, 3] => 3, 1, 1, 1, 3, 1, 3, 2, 3
[3, 1, 1, 1, 3, 1, 3, 3, 1] => 3, 1, 1, 1, 3, 1, 3, 3, 1
[3, 1, 1, 1, 3, 1, 3, 3, 2] => 3, 1, 1, 1, 3, 1, 3, 3, 2
[3, 1, 1, 1, 3, 1, 3, 3, 3] => 3, 1, 1, 1, 3, 1, 3, 3, 3
[3, 1, 1, 1, 3, 2, 1, 1, 1] => 3, 1, 1, 1, 3, 2, 1, 1, 1
[3, 1, 1, 1, 3, 2, 1, 1, 2] => 3, 1, 1, 1, 3, 2, 1, 1, 2
[3, 1, 1, 1, 3, 2, 1, 1, 3] => 3, 1, 1, 1, 3, 2, 1, 1, 3
[3, 1, 1, 1, 3, 2, 1, 2, 1] => 3, 1, 1, 1, 3, 2, 1, 2, 1
[3, 1, 1, 1, 3, 2, 1, 2, 2] => 3, 1, 1, 1, 3, 2, 1, 2, 2
[3, 1, 1, 1, 3, 2, 1, 2, 3] => 3, 1, 1, 1, 3, 2, 1, 2, 3
[3, 1, 1, 1, 3, 2, 1, 3, 1] => 3, 1, 1, 1, 3, 2, 1, 3, 1
[3, 1, 1, 1, 3, 2, 1, 3, 2] => 3, 1, 1, 1, 3, 2, 1, 3, 2
[3, 1, 1, 1, 3, 2, 1, 3, 3] => 3, 1, 1, 1, 3, 2, 1, 3, 3
[3, 1, 1, 1, 3, 2, 2, 1, 1] => 3, 1, 1, 1, 3, 2, 2, 1, 1
[3, 1, 1, 1, 3, 2, 2, 1, 2] => 3, 1, 1, 1, 3, 2, 2, 1, 2
[3, 1, 1, 1, 3, 2, 2, 1, 3] => 3, 1, 1, 1, 3, 2, 2, 1, 3
[3, 1, 1, 1, 3, 2, 2, 2, 1] => 3, 1, 1, 1, 3, 2, 2, 2, 1
[3, 1, 1, 1, 3, 2, 2, 2, 2] => 3, 1, 1, 1, 3, 2, 2, 2, 2
[3, 1, 1, 1, 3, 2, 2, 2, 3] => 3, 1, 1, 1, 3, 2, 2, 2, 3
[3, 1, 1, 1, 3, 2, 2, 3, 1] => 3, 1, 1, 1, 3, 2, 2, 3, 1
[3, 1, 1, 1, 3, 2, 2, 3, 2] => 3, 1, 1, 1, 3, 2, 2, 3, 2
[3, 1, 1, 1, 3, 2, 2, 3, 3] => 3, 1, 1, 1, 3, 2, 2, 3, 3
[3, 1, 1, 1, 3, 2, 3, 1, 1] => 3, 1, 1, 1, 3, 2, 3, 1, 1
[3, 1, 1, 1, 3, 2, 3, 1, 2] => 3, 1, 1, 1, 3, 2, 3, 1, 2
[3, 1, 1, 1, 3, 2, 3, 1, 3] => 3, 1, 1, 1, 3, 2, 3, 1, 3
[3, 1, 1, 1, 3, 2, 3, 2, 1] => 3, 1, 1, 1, 3, 2, 3, 2, 1
[3, 1, 1, 1, 3, 2, 3, 2, 2] => 3, 1, 1, 1, 3, 2, 3, 2, 2
[3, 1, 1, 1, 3, 2, 3, 2, 3] => 3, 1, 1, 1, 3, 2, 3, 2, 3
[3, 1, 1, 1, 3, 2, 3, 3, 1] => 3, 1, 1, 1, 3, 2, 3, 3, 1
[3, 1, 1, 1, 3, 2, 3, 3, 2] => 3, 1, 1, 1, 3, 2, 3, 3, 2
[3, 1, 1, 1, 3, 2, 3, 3, 3] => 3, 1, 1, 1, 3, 2, 3, 3, 3
[3, 1, 1, 1, 3, 3, 1, 1, 1] => 3, 1, 1, 1, 3, 3, 1, 1, 1
[3, 1, 1, 1, 3, 3, 1, 1, 2] => 3, 1, 1, 1, 3, 3, 1, 1, 2
[3, 1, 1, 1, 3, 3, 1, 1, 3] => 3, 1, 1, 1, 3, 3, 1, 1, 3
[3, 1, 1, 1, 3, 3, 1, 2, 1] => 3, 1, 1, 1, 3, 3, 1, 2, 1
[3, 1, 1, 1, 3, 3, 1, 2, 2] => 3, 1, 1, 1, 3, 3, 1, 2, 2
[3, 1, 1, 1, 3, 3, 1, 2, 3] => 3, 1, 1, 1, 3, 3, 1, 2, 3
[3, 1, 1, 1, 3, 3, 1, 3, 1] => 3, 1, 1, 1, 3, 3, 1, 3, 1
[3, 1, 1, 1, 3, 3, 1, 3, 2] => 3, 1, 1, 1, 3, 3, 1, 3, 2
[3, 1, 1, 1, 3, 3, 1, 3, 3] => 3, 1, 1, 1, 3, 3, 1, 3, 3
[3, 1, 1, 1, 3, 3, 2, 1, 1] => 3, 1, 1, 1, 3, 3, 2, 1, 1
[3, 1, 1, 1, 3, 3, 2, 1, 2] => 3, 1, 1, 1, 3, 3, 2, 1, 2
[3, 1, 1, 1, 3, 3, 2, 1, 3] => 3, 1, 1, 1, 3, 3, 2, 1, 3
[3, 1, 1, 1, 3, 3, 2, 2, 1] => 3, 1, 1, 1, 3, 3, 2, 2, 1
[3, 1, 1, 1, 3, 3, 2, 2, 2] => 3, 1, 1, 1, 3, 3, 2, 2, 2
[3, 1, 1, 1, 3, 3, 2, 2, 3] => 3, 1, 1, 1, 3, 3, 2, 2, 3
[3, 1, 1, 1, 3, 3, 2, 3, 1] => 3, 1, 1, 1, 3, 3, 2, 3, 1
[3, 1, 1, 1, 3, 3, 2, 3, 2] => 3, 1, 1, 1, 3, 3, 2, 3, 2
[3, 1, 1, 1, 3, 3, 2, 3, 3] => 3, 1, 1, 1, 3, 3, 2, 3, 3
[3, 1, 1, 1, 3, 3, 3, 1, 1] => 3, 1, 1, 1, 3, 3, 3, 1, 1
[3, 1, 1, 1, 3, 3, 3, 1, 2] => 3, 1, 1, 1, 3, 3, 3, 1, 2
[3, 1, 1, 1, 3, 3, 3, 1, 3] => 3, 1, 1, 1, 3, 3, 3, 1, 3
[3, 1, 1, 1, 3, 3, 3, 2, 1] => 3, 1, 1, 1, 3, 3, 3, 2, 1
[3, 1, 1, 1, 3, 3, 3, 2, 2] => 3, 1, 1, 1, 3, 3, 3, 2, 2
[3, 1, 1, 1, 3, 3, 3, 2, 3] => 3, 1, 1, 1, 3, 3, 3, 2, 3
[3, 1, 1, 1, 3, 3, 3, 3, 1] => 3, 1, 1, 1, 3, 3, 3, 3, 1
[3, 1, 1, 1, 3, 3, 3, 3, 2] => 3, 1, 1, 1, 3, 3, 3, 3, 2
[3, 1, 1, 1, 3, 3, 3, 3, 3] => 3, 1, 1, 1, 3, 3, 3, 3, 3
[3, 1, 1, 2, 1, 1, 1, 1, 1] => 3, 1, 1, 2, 1, 1, 1, 1, 1
[3, 1, 1, 2, 1, 1, 1, 1, 2] => 3, 1, 1, 2, 1, 1, 1, 1, 2
[3, 1, 1, 2, 1, 1, 1, 1, 3] => 3, 1, 1, 2, 1, 1, 1, 1, 3
[3, 1, 1, 2, 1, 1, 1, 2, 1] => 3, 1, 1, 2, 1, 1, 1, 2, 1
[3, 1, 1, 2, 1, 1, 1, 2, 2] => 3, 1, 1, 2, 1, 1, 1, 2, 2
[3, 1, 1, 2, 1, 1, 1, 2, 3] => 3, 1, 1, 2, 1, 1, 1, 2, 3
[3, 1, 1, 2, 1, 1, 1, 3, 1] => 3, 1, 1, 2, 1, 1, 1, 3, 1
[3, 1, 1, 2, 1, 1, 1, 3, 2] => 3, 1, 1, 2, 1, 1, 1, 3, 2
[3, 1, 1, 2, 1, 1, 1, 3, 3] => 3, 1, 1, 2, 1, 1, 1, 3, 3
[3, 1, 1, 2, 1, 1, 2, 1, 1] => 3, 1, 1, 2, 1, 1, 2, 1, 1
[3, 1, 1, 2, 1, 1, 2, 1, 2] => 3, 1, 1, 2, 1, 1, 2, 1, 2
[3, 1, 1, 2, 1, 1, 2, 1, 3] => 3, 1, 1, 2, 1, 1, 2, 1, 3
[3, 1, 1, 2, 1, 1, 2, 2, 1] => 3, 1, 1, 2, 1, 1, 2, 2, 1
[3, 1, 1, 2, 1, 1, 2, 2, 2] => 3, 1, 1, 2, 1, 1, 2, 2, 2
[3, 1, 1, 2, 1, 1, 2, 2, 3] => 3, 1, 1, 2, 1, 1, 2, 2, 3
[3, 1, 1, 2, 1, 1, 2, 3, 1] => 3, 1, 1, 2, 1, 1, 2, 3, 1
[3, 1, 1, 2, 1, 1, 2, 3, 2] => 3, 1, 1, 2, 1, 1, 2, 3, 2
[3, 1, 1, 2, 1, 1, 2, 3, 3] => 3, 1, 1, 2, 1, 1, 2, 3, 3
[3, 1, 1, 2, 1, 1, 3, 1, 1] => 3, 1, 1, 2, 1, 1, 3, 1, 1
[3, 1, 1, 2, 1, 1, 3, 1, 2] => 3, 1, 1, 2, 1, 1, 3, 1, 2
[3, 1, 1, 2, 1, 1, 3, 1, 3] => 3, 1, 1, 2, 1, 1, 3, 1, 3
[3, 1, 1, 2, 1, 1, 3, 2, 1] => 3, 1, 1, 2, 1, 1, 3, 2, 1
[3, 1, 1, 2, 1, 1, 3, 2, 2] => 3, 1, 1, 2, 1, 1, 3, 2, 2
[3, 1, 1, 2, 1, 1, 3, 2, 3] => 3, 1, 1, 2, 1, 1, 3, 2, 3
[3, 1, 1, 2, 1, 1, 3, 3, 1] => 3, 1, 1, 2, 1, 1, 3, 3, 1
[3, 1, 1, 2, 1, 1, 3, 3, 2] => 3, 1, 1, 2, 1, 1, 3, 3, 2
[3, 1, 1, 2, 1, 1, 3, 3, 3] => 3, 1, 1, 2, 1, 1, 3, 3, 3
[3, 1, 1, 2, 1, 2, 1, 1, 1] => 3, 1, 1, 2, 1, 2, 1, 1, 1
[3, 1, 1, 2, 1, 2, 1, 1, 2] => 3, 1, 1, 2, 1, 2, 1, 1, 2
[3, 1, 1, 2, 1, 2, 1, 1, 3] => 3, 1, 1, 2, 1, 2, 1, 1, 3
[3, 1, 1, 2, 1, 2, 1, 2, 1] => 3, 1, 1, 2, 1, 2, 1, 2, 1
[3, 1, 1, 2, 1, 2, 1, 2, 2] => 3, 1, 1, 2, 1, 2, 1, 2, 2
[3, 1, 1, 2, 1, 2, 1, 2, 3] => 3, 1, 1, 2, 1, 2, 1, 2, 3
[3, 1, 1, 2, 1, 2, 1, 3, 1] => 3, 1, 1, 2, 1, 2, 1, 3, 1
[3, 1, 1, 2, 1, 2, 1, 3, 2] => 3, 1, 1, 2, 1, 2, 1, 3, 2
[3, 1, 1, 2, 1, 2, 1, 3, 3] => 3, 1, 1, 2, 1, 2, 1, 3, 3
[3, 1, 1, 2, 1, 2, 2, 1, 1] => 3, 1, 1, 2, 1, 2, 2, 1, 1
[3, 1, 1, 2, 1, 2, 2, 1, 2] => 3, 1, 1, 2, 1, 2, 2, 1, 2
[3, 1, 1, 2, 1, 2, 2, 1, 3] => 3, 1, 1, 2, 1, 2, 2, 1, 3
[3, 1, 1, 2, 1, 2, 2, 2, 1] => 3, 1, 1, 2, 1, 2, 2, 2, 1
[3, 1, 1, 2, 1, 2, 2, 2, 2] => 3, 1, 1, 2, 1, 2, 2, 2, 2
[3, 1, 1, 2, 1, 2, 2, 2, 3] => 3, 1, 1, 2, 1, 2, 2, 2, 3
[3, 1, 1, 2, 1, 2, 2, 3, 1] => 3, 1, 1, 2, 1, 2, 2, 3, 1
[3, 1, 1, 2, 1, 2, 2, 3, 2] => 3, 1, 1, 2, 1, 2, 2, 3, 2
[3, 1, 1, 2, 1, 2, 2, 3, 3] => 3, 1, 1, 2, 1, 2, 2, 3, 3
[3, 1, 1, 2, 1, 2, 3, 1, 1] => 3, 1, 1, 2, 1, 2, 3, 1, 1
[3, 1, 1, 2, 1, 2, 3, 1, 2] => 3, 1, 1, 2, 1, 2, 3, 1, 2
[3, 1, 1, 2, 1, 2, 3, 1, 3] => 3, 1, 1, 2, 1, 2, 3, 1, 3
[3, 1, 1, 2, 1, 2, 3, 2, 1] => 3, 1, 1, 2, 1, 2, 3, 2, 1
[3, 1, 1, 2, 1, 2, 3, 2, 2] => 3, 1, 1, 2, 1, 2, 3, 2, 2
[3, 1, 1, 2, 1, 2, 3, 2, 3] => 3, 1, 1, 2, 1, 2, 3, 2, 3
[3, 1, 1, 2, 1, 2, 3, 3, 1] => 3, 1, 1, 2, 1, 2, 3, 3, 1
[3, 1, 1, 2, 1, 2, 3, 3, 2] => 3, 1, 1, 2, 1, 2, 3, 3, 2
[3, 1, 1, 2, 1, 2, 3, 3, 3] => 3, 1, 1, 2, 1, 2, 3, 3, 3
[3, 1, 1, 2, 1, 3, 1, 1, 1] => 3, 1, 1, 2, 1, 3, 1, 1, 1
[3, 1, 1, 2, 1, 3, 1, 1, 2] => 3, 1, 1, 2, 1, 3, 1, 1, 2
[3, 1, 1, 2, 1, 3, 1, 1, 3] => 3, 1, 1, 2, 1, 3, 1, 1, 3
[3, 1, 1, 2, 1, 3, 1, 2, 1] => 3, 1, 1, 2, 1, 3, 1, 2, 1
[3, 1, 1, 2, 1, 3, 1, 2, 2] => 3, 1, 1, 2, 1, 3, 1, 2, 2
[3, 1, 1, 2, 1, 3, 1, 2, 3] => 3, 1, 1, 2, 1, 3, 1, 2, 3
[3, 1, 1, 2, 1, 3, 1, 3, 1] => 3, 1, 1, 2, 1, 3, 1, 3, 1
[3, 1, 1, 2, 1, 3, 1, 3, 2] => 3, 1, 1, 2, 1, 3, 1, 3, 2
[3, 1, 1, 2, 1, 3, 1, 3, 3] => 3, 1, 1, 2, 1, 3, 1, 3, 3
[3, 1, 1, 2, 1, 3, 2, 1, 1] => 3, 1, 1, 2, 1, 3, 2, 1, 1
[3, 1, 1, 2, 1, 3, 2, 1, 2] => 3, 1, 1, 2, 1, 3, 2, 1, 2
[3, 1, 1, 2, 1, 3, 2, 1, 3] => 3, 1, 1, 2, 1, 3, 2, 1, 3
[3, 1, 1, 2, 1, 3, 2, 2, 1] => 3, 1, 1, 2, 1, 3, 2, 2, 1
[3, 1, 1, 2, 1, 3, 2, 2, 2] => 3, 1, 1, 2, 1, 3, 2, 2, 2
[3, 1, 1, 2, 1, 3, 2, 2, 3] => 3, 1, 1, 2, 1, 3, 2, 2, 3
[3, 1, 1, 2, 1, 3, 2, 3, 1] => 3, 1, 1, 2, 1, 3, 2, 3, 1
[3, 1, 1, 2, 1, 3, 2, 3, 2] => 3, 1, 1, 2, 1, 3, 2, 3, 2
[3, 1, 1, 2, 1, 3, 2, 3, 3] => 3, 1, 1, 2, 1, 3, 2, 3, 3
[3, 1, 1, 2, 1, 3, 3, 1, 1] => 3, 1, 1, 2, 1, 3, 3, 1, 1
[3, 1, 1, 2, 1, 3, 3, 1, 2] => 3, 1, 1, 2, 1, 3, 3, 1, 2
[3, 1, 1, 2, 1, 3, 3, 1, 3] => 3, 1, 1, 2, 1, 3, 3, 1, 3
[3, 1, 1, 2, 1, 3, 3, 2, 1] => 3, 1, 1, 2, 1, 3, 3, 2, 1
[3, 1, 1, 2, 1, 3, 3, 2, 2] => 3, 1, 1, 2, 1, 3, 3, 2, 2
[3, 1, 1, 2, 1, 3, 3, 2, 3] => 3, 1, 1, 2, 1, 3, 3, 2, 3
[3, 1, 1, 2, 1, 3, 3, 3, 1] => 3, 1, 1, 2, 1, 3, 3, 3, 1
[3, 1, 1, 2, 1, 3, 3, 3, 2] => 3, 1, 1, 2, 1, 3, 3, 3, 2
[3, 1, 1, 2, 1, 3, 3, 3, 3] => 3, 1, 1, 2, 1, 3, 3, 3, 3
[3, 1, 1, 2, 2, 1, 1, 1, 1] => 3, 1, 1, 2, 2, 1, 1, 1, 1
[3, 1, 1, 2, 2, 1, 1, 1, 2] => 3, 1, 1, 2, 2, 1, 1, 1, 2
[3, 1, 1, 2, 2, 1, 1, 1, 3] => 3, 1, 1, 2, 2, 1, 1, 1, 3
[3, 1, 1, 2, 2, 1, 1, 2, 1] => 3, 1, 1, 2, 2, 1, 1, 2, 1
[3, 1, 1, 2, 2, 1, 1, 2, 2] => 3, 1, 1, 2, 2, 1, 1, 2, 2
[3, 1, 1, 2, 2, 1, 1, 2, 3] => 3, 1, 1, 2, 2, 1, 1, 2, 3
[3, 1, 1, 2, 2, 1, 1, 3, 1] => 3, 1, 1, 2, 2, 1, 1, 3, 1
[3, 1, 1, 2, 2, 1, 1, 3, 2] => 3, 1, 1, 2, 2, 1, 1, 3, 2
[3, 1, 1, 2, 2, 1, 1, 3, 3] => 3, 1, 1, 2, 2, 1, 1, 3, 3
[3, 1, 1, 2, 2, 1, 2, 1, 1] => 3, 1, 1, 2, 2, 1, 2, 1, 1
[3, 1, 1, 2, 2, 1, 2, 1, 2] => 3, 1, 1, 2, 2, 1, 2, 1, 2
[3, 1, 1, 2, 2, 1, 2, 1, 3] => 3, 1, 1, 2, 2, 1, 2, 1, 3
[3, 1, 1, 2, 2, 1, 2, 2, 1] => 3, 1, 1, 2, 2, 1, 2, 2, 1
[3, 1, 1, 2, 2, 1, 2, 2, 2] => 3, 1, 1, 2, 2, 1, 2, 2, 2
[3, 1, 1, 2, 2, 1, 2, 2, 3] => 3, 1, 1, 2, 2, 1, 2, 2, 3
[3, 1, 1, 2, 2, 1, 2, 3, 1] => 3, 1, 1, 2, 2, 1, 2, 3, 1
[3, 1, 1, 2, 2, 1, 2, 3, 2] => 3, 1, 1, 2, 2, 1, 2, 3, 2
[3, 1, 1, 2, 2, 1, 2, 3, 3] => 3, 1, 1, 2, 2, 1, 2, 3, 3
[3, 1, 1, 2, 2, 1, 3, 1, 1] => 3, 1, 1, 2, 2, 1, 3, 1, 1
[3, 1, 1, 2, 2, 1, 3, 1, 2] => 3, 1, 1, 2, 2, 1, 3, 1, 2
[3, 1, 1, 2, 2, 1, 3, 1, 3] => 3, 1, 1, 2, 2, 1, 3, 1, 3
[3, 1, 1, 2, 2, 1, 3, 2, 1] => 3, 1, 1, 2, 2, 1, 3, 2, 1
[3, 1, 1, 2, 2, 1, 3, 2, 2] => 3, 1, 1, 2, 2, 1, 3, 2, 2
[3, 1, 1, 2, 2, 1, 3, 2, 3] => 3, 1, 1, 2, 2, 1, 3, 2, 3
[3, 1, 1, 2, 2, 1, 3, 3, 1] => 3, 1, 1, 2, 2, 1, 3, 3, 1
[3, 1, 1, 2, 2, 1, 3, 3, 2] => 3, 1, 1, 2, 2, 1, 3, 3, 2
[3, 1, 1, 2, 2, 1, 3, 3, 3] => 3, 1, 1, 2, 2, 1, 3, 3, 3
[3, 1, 1, 2, 2, 2, 1, 1, 1] => 3, 1, 1, 2, 2, 2, 1, 1, 1
[3, 1, 1, 2, 2, 2, 1, 1, 2] => 3, 1, 1, 2, 2, 2, 1, 1, 2
[3, 1, 1, 2, 2, 2, 1, 1, 3] => 3, 1, 1, 2, 2, 2, 1, 1, 3
[3, 1, 1, 2, 2, 2, 1, 2, 1] => 3, 1, 1, 2, 2, 2, 1, 2, 1
[3, 1, 1, 2, 2, 2, 1, 2, 2] => 3, 1, 1, 2, 2, 2, 1, 2, 2
[3, 1, 1, 2, 2, 2, 1, 2, 3] => 3, 1, 1, 2, 2, 2, 1, 2, 3
[3, 1, 1, 2, 2, 2, 1, 3, 1] => 3, 1, 1, 2, 2, 2, 1, 3, 1
[3, 1, 1, 2, 2, 2, 1, 3, 2] => 3, 1, 1, 2, 2, 2, 1, 3, 2
[3, 1, 1, 2, 2, 2, 1, 3, 3] => 3, 1, 1, 2, 2, 2, 1, 3, 3
[3, 1, 1, 2, 2, 2, 2, 1, 1] => 3, 1, 1, 2, 2, 2, 2, 1, 1
[3, 1, 1, 2, 2, 2, 2, 1, 2] => 3, 1, 1, 2, 2, 2, 2, 1, 2
[3, 1, 1, 2, 2, 2, 2, 1, 3] => 3, 1, 1, 2, 2, 2, 2, 1, 3
[3, 1, 1, 2, 2, 2, 2, 2, 1] => 3, 1, 1, 2, 2, 2, 2, 2, 1
[3, 1, 1, 2, 2, 2, 2, 2, 2] => 3, 1, 1, 2, 2, 2, 2, 2, 2
[3, 1, 1, 2, 2, 2, 2, 2, 3] => 3, 1, 1, 2, 2, 2, 2, 2, 3
[3, 1, 1, 2, 2, 2, 2, 3, 1] => 3, 1, 1, 2, 2, 2, 2, 3, 1
[3, 1, 1, 2, 2, 2, 2, 3, 2] => 3, 1, 1, 2, 2, 2, 2, 3, 2
[3, 1, 1, 2, 2, 2, 2, 3, 3] => 3, 1, 1, 2, 2, 2, 2, 3, 3
[3, 1, 1, 2, 2, 2, 3, 1, 1] => 3, 1, 1, 2, 2, 2, 3, 1, 1
[3, 1, 1, 2, 2, 2, 3, 1, 2] => 3, 1, 1, 2, 2, 2, 3, 1, 2
[3, 1, 1, 2, 2, 2, 3, 1, 3] => 3, 1, 1, 2, 2, 2, 3, 1, 3
[3, 1, 1, 2, 2, 2, 3, 2, 1] => 3, 1, 1, 2, 2, 2, 3, 2, 1
[3, 1, 1, 2, 2, 2, 3, 2, 2] => 3, 1, 1, 2, 2, 2, 3, 2, 2
[3, 1, 1, 2, 2, 2, 3, 2, 3] => 3, 1, 1, 2, 2, 2, 3, 2, 3
[3, 1, 1, 2, 2, 2, 3, 3, 1] => 3, 1, 1, 2, 2, 2, 3, 3, 1
[3, 1, 1, 2, 2, 2, 3, 3, 2] => 3, 1, 1, 2, 2, 2, 3, 3, 2
[3, 1, 1, 2, 2, 2, 3, 3, 3] => 3, 1, 1, 2, 2, 2, 3, 3, 3
[3, 1, 1, 2, 2, 3, 1, 1, 1] => 3, 1, 1, 2, 2, 3, 1, 1, 1
[3, 1, 1, 2, 2, 3, 1, 1, 2] => 3, 1, 1, 2, 2, 3, 1, 1, 2
[3, 1, 1, 2, 2, 3, 1, 1, 3] => 3, 1, 1, 2, 2, 3, 1, 1, 3
[3, 1, 1, 2, 2, 3, 1, 2, 1] => 3, 1, 1, 2, 2, 3, 1, 2, 1
[3, 1, 1, 2, 2, 3, 1, 2, 2] => 3, 1, 1, 2, 2, 3, 1, 2, 2
[3, 1, 1, 2, 2, 3, 1, 2, 3] => 3, 1, 1, 2, 2, 3, 1, 2, 3
[3, 1, 1, 2, 2, 3, 1, 3, 1] => 3, 1, 1, 2, 2, 3, 1, 3, 1
[3, 1, 1, 2, 2, 3, 1, 3, 2] => 3, 1, 1, 2, 2, 3, 1, 3, 2
[3, 1, 1, 2, 2, 3, 1, 3, 3] => 3, 1, 1, 2, 2, 3, 1, 3, 3
[3, 1, 1, 2, 2, 3, 2, 1, 1] => 3, 1, 1, 2, 2, 3, 2, 1, 1
[3, 1, 1, 2, 2, 3, 2, 1, 2] => 3, 1, 1, 2, 2, 3, 2, 1, 2
[3, 1, 1, 2, 2, 3, 2, 1, 3] => 3, 1, 1, 2, 2, 3, 2, 1, 3
[3, 1, 1, 2, 2, 3, 2, 2, 1] => 3, 1, 1, 2, 2, 3, 2, 2, 1
[3, 1, 1, 2, 2, 3, 2, 2, 2] => 3, 1, 1, 2, 2, 3, 2, 2, 2
[3, 1, 1, 2, 2, 3, 2, 2, 3] => 3, 1, 1, 2, 2, 3, 2, 2, 3
[3, 1, 1, 2, 2, 3, 2, 3, 1] => 3, 1, 1, 2, 2, 3, 2, 3, 1
[3, 1, 1, 2, 2, 3, 2, 3, 2] => 3, 1, 1, 2, 2, 3, 2, 3, 2
[3, 1, 1, 2, 2, 3, 2, 3, 3] => 3, 1, 1, 2, 2, 3, 2, 3, 3
[3, 1, 1, 2, 2, 3, 3, 1, 1] => 3, 1, 1, 2, 2, 3, 3, 1, 1
[3, 1, 1, 2, 2, 3, 3, 1, 2] => 3, 1, 1, 2, 2, 3, 3, 1, 2
[3, 1, 1, 2, 2, 3, 3, 1, 3] => 3, 1, 1, 2, 2, 3, 3, 1, 3
[3, 1, 1, 2, 2, 3, 3, 2, 1] => 3, 1, 1, 2, 2, 3, 3, 2, 1
[3, 1, 1, 2, 2, 3, 3, 2, 2] => 3, 1, 1, 2, 2, 3, 3, 2, 2
[3, 1, 1, 2, 2, 3, 3, 2, 3] => 3, 1, 1, 2, 2, 3, 3, 2, 3
[3, 1, 1, 2, 2, 3, 3, 3, 1] => 3, 1, 1, 2, 2, 3, 3, 3, 1
[3, 1, 1, 2, 2, 3, 3, 3, 2] => 3, 1, 1, 2, 2, 3, 3, 3, 2
[3, 1, 1, 2, 2, 3, 3, 3, 3] => 3, 1, 1, 2, 2, 3, 3, 3, 3
[3, 1, 1, 2, 3, 1, 1, 1, 1] => 3, 1, 1, 2, 3, 1, 1, 1, 1
[3, 1, 1, 2, 3, 1, 1, 1, 2] => 3, 1, 1, 2, 3, 1, 1, 1, 2
[3, 1, 1, 2, 3, 1, 1, 1, 3] => 3, 1, 1, 2, 3, 1, 1, 1, 3
[3, 1, 1, 2, 3, 1, 1, 2, 1] => 3, 1, 1, 2, 3, 1, 1, 2, 1
[3, 1, 1, 2, 3, 1, 1, 2, 2] => 3, 1, 1, 2, 3, 1, 1, 2, 2
[3, 1, 1, 2, 3, 1, 1, 2, 3] => 3, 1, 1, 2, 3, 1, 1, 2, 3
[3, 1, 1, 2, 3, 1, 1, 3, 1] => 3, 1, 1, 2, 3, 1, 1, 3, 1
[3, 1, 1, 2, 3, 1, 1, 3, 2] => 3, 1, 1, 2, 3, 1, 1, 3, 2
[3, 1, 1, 2, 3, 1, 1, 3, 3] => 3, 1, 1, 2, 3, 1, 1, 3, 3
[3, 1, 1, 2, 3, 1, 2, 1, 1] => 3, 1, 1, 2, 3, 1, 2, 1, 1
[3, 1, 1, 2, 3, 1, 2, 1, 2] => 3, 1, 1, 2, 3, 1, 2, 1, 2
[3, 1, 1, 2, 3, 1, 2, 1, 3] => 3, 1, 1, 2, 3, 1, 2, 1, 3
[3, 1, 1, 2, 3, 1, 2, 2, 1] => 3, 1, 1, 2, 3, 1, 2, 2, 1
[3, 1, 1, 2, 3, 1, 2, 2, 2] => 3, 1, 1, 2, 3, 1, 2, 2, 2
[3, 1, 1, 2, 3, 1, 2, 2, 3] => 3, 1, 1, 2, 3, 1, 2, 2, 3
[3, 1, 1, 2, 3, 1, 2, 3, 1] => 3, 1, 1, 2, 3, 1, 2, 3, 1
[3, 1, 1, 2, 3, 1, 2, 3, 2] => 3, 1, 1, 2, 3, 1, 2, 3, 2
[3, 1, 1, 2, 3, 1, 2, 3, 3] => 3, 1, 1, 2, 3, 1, 2, 3, 3
[3, 1, 1, 2, 3, 1, 3, 1, 1] => 3, 1, 1, 2, 3, 1, 3, 1, 1
[3, 1, 1, 2, 3, 1, 3, 1, 2] => 3, 1, 1, 2, 3, 1, 3, 1, 2
[3, 1, 1, 2, 3, 1, 3, 1, 3] => 3, 1, 1, 2, 3, 1, 3, 1, 3
[3, 1, 1, 2, 3, 1, 3, 2, 1] => 3, 1, 1, 2, 3, 1, 3, 2, 1
[3, 1, 1, 2, 3, 1, 3, 2, 2] => 3, 1, 1, 2, 3, 1, 3, 2, 2
[3, 1, 1, 2, 3, 1, 3, 2, 3] => 3, 1, 1, 2, 3, 1, 3, 2, 3
[3, 1, 1, 2, 3, 1, 3, 3, 1] => 3, 1, 1, 2, 3, 1, 3, 3, 1
[3, 1, 1, 2, 3, 1, 3, 3, 2] => 3, 1, 1, 2, 3, 1, 3, 3, 2
[3, 1, 1, 2, 3, 1, 3, 3, 3] => 3, 1, 1, 2, 3, 1, 3, 3, 3
[3, 1, 1, 2, 3, 2, 1, 1, 1] => 3, 1, 1, 2, 3, 2, 1, 1, 1
[3, 1, 1, 2, 3, 2, 1, 1, 2] => 3, 1, 1, 2, 3, 2, 1, 1, 2
[3, 1, 1, 2, 3, 2, 1, 1, 3] => 3, 1, 1, 2, 3, 2, 1, 1, 3
[3, 1, 1, 2, 3, 2, 1, 2, 1] => 3, 1, 1, 2, 3, 2, 1, 2, 1
[3, 1, 1, 2, 3, 2, 1, 2, 2] => 3, 1, 1, 2, 3, 2, 1, 2, 2
[3, 1, 1, 2, 3, 2, 1, 2, 3] => 3, 1, 1, 2, 3, 2, 1, 2, 3
[3, 1, 1, 2, 3, 2, 1, 3, 1] => 3, 1, 1, 2, 3, 2, 1, 3, 1
[3, 1, 1, 2, 3, 2, 1, 3, 2] => 3, 1, 1, 2, 3, 2, 1, 3, 2
[3, 1, 1, 2, 3, 2, 1, 3, 3] => 3, 1, 1, 2, 3, 2, 1, 3, 3
[3, 1, 1, 2, 3, 2, 2, 1, 1] => 3, 1, 1, 2, 3, 2, 2, 1, 1
[3, 1, 1, 2, 3, 2, 2, 1, 2] => 3, 1, 1, 2, 3, 2, 2, 1, 2
[3, 1, 1, 2, 3, 2, 2, 1, 3] => 3, 1, 1, 2, 3, 2, 2, 1, 3
[3, 1, 1, 2, 3, 2, 2, 2, 1] => 3, 1, 1, 2, 3, 2, 2, 2, 1
[3, 1, 1, 2, 3, 2, 2, 2, 2] => 3, 1, 1, 2, 3, 2, 2, 2, 2
[3, 1, 1, 2, 3, 2, 2, 2, 3] => 3, 1, 1, 2, 3, 2, 2, 2, 3
[3, 1, 1, 2, 3, 2, 2, 3, 1] => 3, 1, 1, 2, 3, 2, 2, 3, 1
[3, 1, 1, 2, 3, 2, 2, 3, 2] => 3, 1, 1, 2, 3, 2, 2, 3, 2
[3, 1, 1, 2, 3, 2, 2, 3, 3] => 3, 1, 1, 2, 3, 2, 2, 3, 3
[3, 1, 1, 2, 3, 2, 3, 1, 1] => 3, 1, 1, 2, 3, 2, 3, 1, 1
[3, 1, 1, 2, 3, 2, 3, 1, 2] => 3, 1, 1, 2, 3, 2, 3, 1, 2
[3, 1, 1, 2, 3, 2, 3, 1, 3] => 3, 1, 1, 2, 3, 2, 3, 1, 3
[3, 1, 1, 2, 3, 2, 3, 2, 1] => 3, 1, 1, 2, 3, 2, 3, 2, 1
[3, 1, 1, 2, 3, 2, 3, 2, 2] => 3, 1, 1, 2, 3, 2, 3, 2, 2
[3, 1, 1, 2, 3, 2, 3, 2, 3] => 3, 1, 1, 2, 3, 2, 3, 2, 3
[3, 1, 1, 2, 3, 2, 3, 3, 1] => 3, 1, 1, 2, 3, 2, 3, 3, 1
[3, 1, 1, 2, 3, 2, 3, 3, 2] => 3, 1, 1, 2, 3, 2, 3, 3, 2
[3, 1, 1, 2, 3, 2, 3, 3, 3] => 3, 1, 1, 2, 3, 2, 3, 3, 3
[3, 1, 1, 2, 3, 3, 1, 1, 1] => 3, 1, 1, 2, 3, 3, 1, 1, 1
[3, 1, 1, 2, 3, 3, 1, 1, 2] => 3, 1, 1, 2, 3, 3, 1, 1, 2
[3, 1, 1, 2, 3, 3, 1, 1, 3] => 3, 1, 1, 2, 3, 3, 1, 1, 3
[3, 1, 1, 2, 3, 3, 1, 2, 1] => 3, 1, 1, 2, 3, 3, 1, 2, 1
[3, 1, 1, 2, 3, 3, 1, 2, 2] => 3, 1, 1, 2, 3, 3, 1, 2, 2
[3, 1, 1, 2, 3, 3, 1, 2, 3] => 3, 1, 1, 2, 3, 3, 1, 2, 3
[3, 1, 1, 2, 3, 3, 1, 3, 1] => 3, 1, 1, 2, 3, 3, 1, 3, 1
[3, 1, 1, 2, 3, 3, 1, 3, 2] => 3, 1, 1, 2, 3, 3, 1, 3, 2
[3, 1, 1, 2, 3, 3, 1, 3, 3] => 3, 1, 1, 2, 3, 3, 1, 3, 3
[3, 1, 1, 2, 3, 3, 2, 1, 1] => 3, 1, 1, 2, 3, 3, 2, 1, 1
[3, 1, 1, 2, 3, 3, 2, 1, 2] => 3, 1, 1, 2, 3, 3, 2, 1, 2
[3, 1, 1, 2, 3, 3, 2, 1, 3] => 3, 1, 1, 2, 3, 3, 2, 1, 3
[3, 1, 1, 2, 3, 3, 2, 2, 1] => 3, 1, 1, 2, 3, 3, 2, 2, 1
[3, 1, 1, 2, 3, 3, 2, 2, 2] => 3, 1, 1, 2, 3, 3, 2, 2, 2
[3, 1, 1, 2, 3, 3, 2, 2, 3] => 3, 1, 1, 2, 3, 3, 2, 2, 3
[3, 1, 1, 2, 3, 3, 2, 3, 1] => 3, 1, 1, 2, 3, 3, 2, 3, 1
[3, 1, 1, 2, 3, 3, 2, 3, 2] => 3, 1, 1, 2, 3, 3, 2, 3, 2
[3, 1, 1, 2, 3, 3, 2, 3, 3] => 3, 1, 1, 2, 3, 3, 2, 3, 3
[3, 1, 1, 2, 3, 3, 3, 1, 1] => 3, 1, 1, 2, 3, 3, 3, 1, 1
[3, 1, 1, 2, 3, 3, 3, 1, 2] => 3, 1, 1, 2, 3, 3, 3, 1, 2
[3, 1, 1, 2, 3, 3, 3, 1, 3] => 3, 1, 1, 2, 3, 3, 3, 1, 3
[3, 1, 1, 2, 3, 3, 3, 2, 1] => 3, 1, 1, 2, 3, 3, 3, 2, 1
[3, 1, 1, 2, 3, 3, 3, 2, 2] => 3, 1, 1, 2, 3, 3, 3, 2, 2
[3, 1, 1, 2, 3, 3, 3, 2, 3] => 3, 1, 1, 2, 3, 3, 3, 2, 3
[3, 1, 1, 2, 3, 3, 3, 3, 1] => 3, 1, 1, 2, 3, 3, 3, 3, 1
[3, 1, 1, 2, 3, 3, 3, 3, 2] => 3, 1, 1, 2, 3, 3, 3, 3, 2
[3, 1, 1, 2, 3, 3, 3, 3, 3] => 3, 1, 1, 2, 3, 3, 3, 3, 3
[3, 1, 1, 3, 1, 1, 1, 1, 1] => 3, 1, 1, 3, 1, 1, 1, 1, 1
[3, 1, 1, 3, 1, 1, 1, 1, 2] => 3, 1, 1, 3, 1, 1, 1, 1, 2
[3, 1, 1, 3, 1, 1, 1, 1, 3] => 3, 1, 1, 3, 1, 1, 1, 1, 3
[3, 1, 1, 3, 1, 1, 1, 2, 1] => 3, 1, 1, 3, 1, 1, 1, 2, 1
[3, 1, 1, 3, 1, 1, 1, 2, 2] => 3, 1, 1, 3, 1, 1, 1, 2, 2
[3, 1, 1, 3, 1, 1, 1, 2, 3] => 3, 1, 1, 3, 1, 1, 1, 2, 3
[3, 1, 1, 3, 1, 1, 1, 3, 1] => 3, 1, 1, 3, 1, 1, 1, 3, 1
[3, 1, 1, 3, 1, 1, 1, 3, 2] => 3, 1, 1, 3, 1, 1, 1, 3, 2
[3, 1, 1, 3, 1, 1, 1, 3, 3] => 3, 1, 1, 3, 1, 1, 1, 3, 3
[3, 1, 1, 3, 1, 1, 2, 1, 1] => 3, 1, 1, 3, 1, 1, 2, 1, 1
[3, 1, 1, 3, 1, 1, 2, 1, 2] => 3, 1, 1, 3, 1, 1, 2, 1, 2
[3, 1, 1, 3, 1, 1, 2, 1, 3] => 3, 1, 1, 3, 1, 1, 2, 1, 3
[3, 1, 1, 3, 1, 1, 2, 2, 1] => 3, 1, 1, 3, 1, 1, 2, 2, 1
[3, 1, 1, 3, 1, 1, 2, 2, 2] => 3, 1, 1, 3, 1, 1, 2, 2, 2
[3, 1, 1, 3, 1, 1, 2, 2, 3] => 3, 1, 1, 3, 1, 1, 2, 2, 3
[3, 1, 1, 3, 1, 1, 2, 3, 1] => 3, 1, 1, 3, 1, 1, 2, 3, 1
[3, 1, 1, 3, 1, 1, 2, 3, 2] => 3, 1, 1, 3, 1, 1, 2, 3, 2
[3, 1, 1, 3, 1, 1, 2, 3, 3] => 3, 1, 1, 3, 1, 1, 2, 3, 3
[3, 1, 1, 3, 1, 1, 3, 1, 1] => 3, 1, 1, 3, 1, 1, 3, 1, 1
[3, 1, 1, 3, 1, 1, 3, 1, 2] => 3, 1, 1, 3, 1, 1, 3, 1, 2
[3, 1, 1, 3, 1, 1, 3, 1, 3] => 3, 1, 1, 3, 1, 1, 3, 1, 3
[3, 1, 1, 3, 1, 1, 3, 2, 1] => 3, 1, 1, 3, 1, 1, 3, 2, 1
[3, 1, 1, 3, 1, 1, 3, 2, 2] => 3, 1, 1, 3, 1, 1, 3, 2, 2
[3, 1, 1, 3, 1, 1, 3, 2, 3] => 3, 1, 1, 3, 1, 1, 3, 2, 3
[3, 1, 1, 3, 1, 1, 3, 3, 1] => 3, 1, 1, 3, 1, 1, 3, 3, 1
[3, 1, 1, 3, 1, 1, 3, 3, 2] => 3, 1, 1, 3, 1, 1, 3, 3, 2
[3, 1, 1, 3, 1, 1, 3, 3, 3] => 3, 1, 1, 3, 1, 1, 3, 3, 3
[3, 1, 1, 3, 1, 2, 1, 1, 1] => 3, 1, 1, 3, 1, 2, 1, 1, 1
[3, 1, 1, 3, 1, 2, 1, 1, 2] => 3, 1, 1, 3, 1, 2, 1, 1, 2
[3, 1, 1, 3, 1, 2, 1, 1, 3] => 3, 1, 1, 3, 1, 2, 1, 1, 3
[3, 1, 1, 3, 1, 2, 1, 2, 1] => 3, 1, 1, 3, 1, 2, 1, 2, 1
[3, 1, 1, 3, 1, 2, 1, 2, 2] => 3, 1, 1, 3, 1, 2, 1, 2, 2
[3, 1, 1, 3, 1, 2, 1, 2, 3] => 3, 1, 1, 3, 1, 2, 1, 2, 3
[3, 1, 1, 3, 1, 2, 1, 3, 1] => 3, 1, 1, 3, 1, 2, 1, 3, 1
[3, 1, 1, 3, 1, 2, 1, 3, 2] => 3, 1, 1, 3, 1, 2, 1, 3, 2
[3, 1, 1, 3, 1, 2, 1, 3, 3] => 3, 1, 1, 3, 1, 2, 1, 3, 3
[3, 1, 1, 3, 1, 2, 2, 1, 1] => 3, 1, 1, 3, 1, 2, 2, 1, 1
[3, 1, 1, 3, 1, 2, 2, 1, 2] => 3, 1, 1, 3, 1, 2, 2, 1, 2
[3, 1, 1, 3, 1, 2, 2, 1, 3] => 3, 1, 1, 3, 1, 2, 2, 1, 3
[3, 1, 1, 3, 1, 2, 2, 2, 1] => 3, 1, 1, 3, 1, 2, 2, 2, 1
[3, 1, 1, 3, 1, 2, 2, 2, 2] => 3, 1, 1, 3, 1, 2, 2, 2, 2
[3, 1, 1, 3, 1, 2, 2, 2, 3] => 3, 1, 1, 3, 1, 2, 2, 2, 3
[3, 1, 1, 3, 1, 2, 2, 3, 1] => 3, 1, 1, 3, 1, 2, 2, 3, 1
[3, 1, 1, 3, 1, 2, 2, 3, 2] => 3, 1, 1, 3, 1, 2, 2, 3, 2
[3, 1, 1, 3, 1, 2, 2, 3, 3] => 3, 1, 1, 3, 1, 2, 2, 3, 3
[3, 1, 1, 3, 1, 2, 3, 1, 1] => 3, 1, 1, 3, 1, 2, 3, 1, 1
[3, 1, 1, 3, 1, 2, 3, 1, 2] => 3, 1, 1, 3, 1, 2, 3, 1, 2
[3, 1, 1, 3, 1, 2, 3, 1, 3] => 3, 1, 1, 3, 1, 2, 3, 1, 3
[3, 1, 1, 3, 1, 2, 3, 2, 1] => 3, 1, 1, 3, 1, 2, 3, 2, 1
[3, 1, 1, 3, 1, 2, 3, 2, 2] => 3, 1, 1, 3, 1, 2, 3, 2, 2
[3, 1, 1, 3, 1, 2, 3, 2, 3] => 3, 1, 1, 3, 1, 2, 3, 2, 3
[3, 1, 1, 3, 1, 2, 3, 3, 1] => 3, 1, 1, 3, 1, 2, 3, 3, 1
[3, 1, 1, 3, 1, 2, 3, 3, 2] => 3, 1, 1, 3, 1, 2, 3, 3, 2
[3, 1, 1, 3, 1, 2, 3, 3, 3] => 3, 1, 1, 3, 1, 2, 3, 3, 3
[3, 1, 1, 3, 1, 3, 1, 1, 1] => 3, 1, 1, 3, 1, 3, 1, 1, 1
[3, 1, 1, 3, 1, 3, 1, 1, 2] => 3, 1, 1, 3, 1, 3, 1, 1, 2
[3, 1, 1, 3, 1, 3, 1, 1, 3] => 3, 1, 1, 3, 1, 3, 1, 1, 3
[3, 1, 1, 3, 1, 3, 1, 2, 1] => 3, 1, 1, 3, 1, 3, 1, 2, 1
[3, 1, 1, 3, 1, 3, 1, 2, 2] => 3, 1, 1, 3, 1, 3, 1, 2, 2
[3, 1, 1, 3, 1, 3, 1, 2, 3] => 3, 1, 1, 3, 1, 3, 1, 2, 3
[3, 1, 1, 3, 1, 3, 1, 3, 1] => 3, 1, 1, 3, 1, 3, 1, 3, 1
[3, 1, 1, 3, 1, 3, 1, 3, 2] => 3, 1, 1, 3, 1, 3, 1, 3, 2
[3, 1, 1, 3, 1, 3, 1, 3, 3] => 3, 1, 1, 3, 1, 3, 1, 3, 3
[3, 1, 1, 3, 1, 3, 2, 1, 1] => 3, 1, 1, 3, 1, 3, 2, 1, 1
[3, 1, 1, 3, 1, 3, 2, 1, 2] => 3, 1, 1, 3, 1, 3, 2, 1, 2
[3, 1, 1, 3, 1, 3, 2, 1, 3] => 3, 1, 1, 3, 1, 3, 2, 1, 3
[3, 1, 1, 3, 1, 3, 2, 2, 1] => 3, 1, 1, 3, 1, 3, 2, 2, 1
[3, 1, 1, 3, 1, 3, 2, 2, 2] => 3, 1, 1, 3, 1, 3, 2, 2, 2
[3, 1, 1, 3, 1, 3, 2, 2, 3] => 3, 1, 1, 3, 1, 3, 2, 2, 3
[3, 1, 1, 3, 1, 3, 2, 3, 1] => 3, 1, 1, 3, 1, 3, 2, 3, 1
[3, 1, 1, 3, 1, 3, 2, 3, 2] => 3, 1, 1, 3, 1, 3, 2, 3, 2
[3, 1, 1, 3, 1, 3, 2, 3, 3] => 3, 1, 1, 3, 1, 3, 2, 3, 3
[3, 1, 1, 3, 1, 3, 3, 1, 1] => 3, 1, 1, 3, 1, 3, 3, 1, 1
[3, 1, 1, 3, 1, 3, 3, 1, 2] => 3, 1, 1, 3, 1, 3, 3, 1, 2
[3, 1, 1, 3, 1, 3, 3, 1, 3] => 3, 1, 1, 3, 1, 3, 3, 1, 3
[3, 1, 1, 3, 1, 3, 3, 2, 1] => 3, 1, 1, 3, 1, 3, 3, 2, 1
[3, 1, 1, 3, 1, 3, 3, 2, 2] => 3, 1, 1, 3, 1, 3, 3, 2, 2
[3, 1, 1, 3, 1, 3, 3, 2, 3] => 3, 1, 1, 3, 1, 3, 3, 2, 3
[3, 1, 1, 3, 1, 3, 3, 3, 1] => 3, 1, 1, 3, 1, 3, 3, 3, 1
[3, 1, 1, 3, 1, 3, 3, 3, 2] => 3, 1, 1, 3, 1, 3, 3, 3, 2
[3, 1, 1, 3, 1, 3, 3, 3, 3] => 3, 1, 1, 3, 1, 3, 3, 3, 3
[3, 1, 1, 3, 2, 1, 1, 1, 1] => 3, 1, 1, 3, 2, 1, 1, 1, 1
[3, 1, 1, 3, 2, 1, 1, 1, 2] => 3, 1, 1, 3, 2, 1, 1, 1, 2
[3, 1, 1, 3, 2, 1, 1, 1, 3] => 3, 1, 1, 3, 2, 1, 1, 1, 3
[3, 1, 1, 3, 2, 1, 1, 2, 1] => 3, 1, 1, 3, 2, 1, 1, 2, 1
[3, 1, 1, 3, 2, 1, 1, 2, 2] => 3, 1, 1, 3, 2, 1, 1, 2, 2
[3, 1, 1, 3, 2, 1, 1, 2, 3] => 3, 1, 1, 3, 2, 1, 1, 2, 3
[3, 1, 1, 3, 2, 1, 1, 3, 1] => 3, 1, 1, 3, 2, 1, 1, 3, 1
[3, 1, 1, 3, 2, 1, 1, 3, 2] => 3, 1, 1, 3, 2, 1, 1, 3, 2
[3, 1, 1, 3, 2, 1, 1, 3, 3] => 3, 1, 1, 3, 2, 1, 1, 3, 3
[3, 1, 1, 3, 2, 1, 2, 1, 1] => 3, 1, 1, 3, 2, 1, 2, 1, 1
[3, 1, 1, 3, 2, 1, 2, 1, 2] => 3, 1, 1, 3, 2, 1, 2, 1, 2
[3, 1, 1, 3, 2, 1, 2, 1, 3] => 3, 1, 1, 3, 2, 1, 2, 1, 3
[3, 1, 1, 3, 2, 1, 2, 2, 1] => 3, 1, 1, 3, 2, 1, 2, 2, 1
[3, 1, 1, 3, 2, 1, 2, 2, 2] => 3, 1, 1, 3, 2, 1, 2, 2, 2
[3, 1, 1, 3, 2, 1, 2, 2, 3] => 3, 1, 1, 3, 2, 1, 2, 2, 3
[3, 1, 1, 3, 2, 1, 2, 3, 1] => 3, 1, 1, 3, 2, 1, 2, 3, 1
[3, 1, 1, 3, 2, 1, 2, 3, 2] => 3, 1, 1, 3, 2, 1, 2, 3, 2
[3, 1, 1, 3, 2, 1, 2, 3, 3] => 3, 1, 1, 3, 2, 1, 2, 3, 3
[3, 1, 1, 3, 2, 1, 3, 1, 1] => 3, 1, 1, 3, 2, 1, 3, 1, 1
[3, 1, 1, 3, 2, 1, 3, 1, 2] => 3, 1, 1, 3, 2, 1, 3, 1, 2
[3, 1, 1, 3, 2, 1, 3, 1, 3] => 3, 1, 1, 3, 2, 1, 3, 1, 3
[3, 1, 1, 3, 2, 1, 3, 2, 1] => 3, 1, 1, 3, 2, 1, 3, 2, 1
[3, 1, 1, 3, 2, 1, 3, 2, 2] => 3, 1, 1, 3, 2, 1, 3, 2, 2
[3, 1, 1, 3, 2, 1, 3, 2, 3] => 3, 1, 1, 3, 2, 1, 3, 2, 3
[3, 1, 1, 3, 2, 1, 3, 3, 1] => 3, 1, 1, 3, 2, 1, 3, 3, 1
[3, 1, 1, 3, 2, 1, 3, 3, 2] => 3, 1, 1, 3, 2, 1, 3, 3, 2
[3, 1, 1, 3, 2, 1, 3, 3, 3] => 3, 1, 1, 3, 2, 1, 3, 3, 3
[3, 1, 1, 3, 2, 2, 1, 1, 1] => 3, 1, 1, 3, 2, 2, 1, 1, 1
[3, 1, 1, 3, 2, 2, 1, 1, 2] => 3, 1, 1, 3, 2, 2, 1, 1, 2
[3, 1, 1, 3, 2, 2, 1, 1, 3] => 3, 1, 1, 3, 2, 2, 1, 1, 3
[3, 1, 1, 3, 2, 2, 1, 2, 1] => 3, 1, 1, 3, 2, 2, 1, 2, 1
[3, 1, 1, 3, 2, 2, 1, 2, 2] => 3, 1, 1, 3, 2, 2, 1, 2, 2
[3, 1, 1, 3, 2, 2, 1, 2, 3] => 3, 1, 1, 3, 2, 2, 1, 2, 3
[3, 1, 1, 3, 2, 2, 1, 3, 1] => 3, 1, 1, 3, 2, 2, 1, 3, 1
[3, 1, 1, 3, 2, 2, 1, 3, 2] => 3, 1, 1, 3, 2, 2, 1, 3, 2
[3, 1, 1, 3, 2, 2, 1, 3, 3] => 3, 1, 1, 3, 2, 2, 1, 3, 3
[3, 1, 1, 3, 2, 2, 2, 1, 1] => 3, 1, 1, 3, 2, 2, 2, 1, 1
[3, 1, 1, 3, 2, 2, 2, 1, 2] => 3, 1, 1, 3, 2, 2, 2, 1, 2
[3, 1, 1, 3, 2, 2, 2, 1, 3] => 3, 1, 1, 3, 2, 2, 2, 1, 3
[3, 1, 1, 3, 2, 2, 2, 2, 1] => 3, 1, 1, 3, 2, 2, 2, 2, 1
[3, 1, 1, 3, 2, 2, 2, 2, 2] => 3, 1, 1, 3, 2, 2, 2, 2, 2
[3, 1, 1, 3, 2, 2, 2, 2, 3] => 3, 1, 1, 3, 2, 2, 2, 2, 3
[3, 1, 1, 3, 2, 2, 2, 3, 1] => 3, 1, 1, 3, 2, 2, 2, 3, 1
[3, 1, 1, 3, 2, 2, 2, 3, 2] => 3, 1, 1, 3, 2, 2, 2, 3, 2
[3, 1, 1, 3, 2, 2, 2, 3, 3] => 3, 1, 1, 3, 2, 2, 2, 3, 3
[3, 1, 1, 3, 2, 2, 3, 1, 1] => 3, 1, 1, 3, 2, 2, 3, 1, 1
[3, 1, 1, 3, 2, 2, 3, 1, 2] => 3, 1, 1, 3, 2, 2, 3, 1, 2
[3, 1, 1, 3, 2, 2, 3, 1, 3] => 3, 1, 1, 3, 2, 2, 3, 1, 3
[3, 1, 1, 3, 2, 2, 3, 2, 1] => 3, 1, 1, 3, 2, 2, 3, 2, 1
[3, 1, 1, 3, 2, 2, 3, 2, 2] => 3, 1, 1, 3, 2, 2, 3, 2, 2
[3, 1, 1, 3, 2, 2, 3, 2, 3] => 3, 1, 1, 3, 2, 2, 3, 2, 3
[3, 1, 1, 3, 2, 2, 3, 3, 1] => 3, 1, 1, 3, 2, 2, 3, 3, 1
[3, 1, 1, 3, 2, 2, 3, 3, 2] => 3, 1, 1, 3, 2, 2, 3, 3, 2
[3, 1, 1, 3, 2, 2, 3, 3, 3] => 3, 1, 1, 3, 2, 2, 3, 3, 3
[3, 1, 1, 3, 2, 3, 1, 1, 1] => 3, 1, 1, 3, 2, 3, 1, 1, 1
[3, 1, 1, 3, 2, 3, 1, 1, 2] => 3, 1, 1, 3, 2, 3, 1, 1, 2
[3, 1, 1, 3, 2, 3, 1, 1, 3] => 3, 1, 1, 3, 2, 3, 1, 1, 3
[3, 1, 1, 3, 2, 3, 1, 2, 1] => 3, 1, 1, 3, 2, 3, 1, 2, 1
[3, 1, 1, 3, 2, 3, 1, 2, 2] => 3, 1, 1, 3, 2, 3, 1, 2, 2
[3, 1, 1, 3, 2, 3, 1, 2, 3] => 3, 1, 1, 3, 2, 3, 1, 2, 3
[3, 1, 1, 3, 2, 3, 1, 3, 1] => 3, 1, 1, 3, 2, 3, 1, 3, 1
[3, 1, 1, 3, 2, 3, 1, 3, 2] => 3, 1, 1, 3, 2, 3, 1, 3, 2
[3, 1, 1, 3, 2, 3, 1, 3, 3] => 3, 1, 1, 3, 2, 3, 1, 3, 3
[3, 1, 1, 3, 2, 3, 2, 1, 1] => 3, 1, 1, 3, 2, 3, 2, 1, 1
[3, 1, 1, 3, 2, 3, 2, 1, 2] => 3, 1, 1, 3, 2, 3, 2, 1, 2
[3, 1, 1, 3, 2, 3, 2, 1, 3] => 3, 1, 1, 3, 2, 3, 2, 1, 3
[3, 1, 1, 3, 2, 3, 2, 2, 1] => 3, 1, 1, 3, 2, 3, 2, 2, 1
[3, 1, 1, 3, 2, 3, 2, 2, 2] => 3, 1, 1, 3, 2, 3, 2, 2, 2
[3, 1, 1, 3, 2, 3, 2, 2, 3] => 3, 1, 1, 3, 2, 3, 2, 2, 3
[3, 1, 1, 3, 2, 3, 2, 3, 1] => 3, 1, 1, 3, 2, 3, 2, 3, 1
[3, 1, 1, 3, 2, 3, 2, 3, 2] => 3, 1, 1, 3, 2, 3, 2, 3, 2
[3, 1, 1, 3, 2, 3, 2, 3, 3] => 3, 1, 1, 3, 2, 3, 2, 3, 3
[3, 1, 1, 3, 2, 3, 3, 1, 1] => 3, 1, 1, 3, 2, 3, 3, 1, 1
[3, 1, 1, 3, 2, 3, 3, 1, 2] => 3, 1, 1, 3, 2, 3, 3, 1, 2
[3, 1, 1, 3, 2, 3, 3, 1, 3] => 3, 1, 1, 3, 2, 3, 3, 1, 3
[3, 1, 1, 3, 2, 3, 3, 2, 1] => 3, 1, 1, 3, 2, 3, 3, 2, 1
[3, 1, 1, 3, 2, 3, 3, 2, 2] => 3, 1, 1, 3, 2, 3, 3, 2, 2
[3, 1, 1, 3, 2, 3, 3, 2, 3] => 3, 1, 1, 3, 2, 3, 3, 2, 3
[3, 1, 1, 3, 2, 3, 3, 3, 1] => 3, 1, 1, 3, 2, 3, 3, 3, 1
[3, 1, 1, 3, 2, 3, 3, 3, 2] => 3, 1, 1, 3, 2, 3, 3, 3, 2
[3, 1, 1, 3, 2, 3, 3, 3, 3] => 3, 1, 1, 3, 2, 3, 3, 3, 3
[3, 1, 1, 3, 3, 1, 1, 1, 1] => 3, 1, 1, 3, 3, 1, 1, 1, 1
[3, 1, 1, 3, 3, 1, 1, 1, 2] => 3, 1, 1, 3, 3, 1, 1, 1, 2
[3, 1, 1, 3, 3, 1, 1, 1, 3] => 3, 1, 1, 3, 3, 1, 1, 1, 3
[3, 1, 1, 3, 3, 1, 1, 2, 1] => 3, 1, 1, 3, 3, 1, 1, 2, 1
[3, 1, 1, 3, 3, 1, 1, 2, 2] => 3, 1, 1, 3, 3, 1, 1, 2, 2
[3, 1, 1, 3, 3, 1, 1, 2, 3] => 3, 1, 1, 3, 3, 1, 1, 2, 3
[3, 1, 1, 3, 3, 1, 1, 3, 1] => 3, 1, 1, 3, 3, 1, 1, 3, 1
[3, 1, 1, 3, 3, 1, 1, 3, 2] => 3, 1, 1, 3, 3, 1, 1, 3, 2
[3, 1, 1, 3, 3, 1, 1, 3, 3] => 3, 1, 1, 3, 3, 1, 1, 3, 3
[3, 1, 1, 3, 3, 1, 2, 1, 1] => 3, 1, 1, 3, 3, 1, 2, 1, 1
[3, 1, 1, 3, 3, 1, 2, 1, 2] => 3, 1, 1, 3, 3, 1, 2, 1, 2
[3, 1, 1, 3, 3, 1, 2, 1, 3] => 3, 1, 1, 3, 3, 1, 2, 1, 3
[3, 1, 1, 3, 3, 1, 2, 2, 1] => 3, 1, 1, 3, 3, 1, 2, 2, 1
[3, 1, 1, 3, 3, 1, 2, 2, 2] => 3, 1, 1, 3, 3, 1, 2, 2, 2
[3, 1, 1, 3, 3, 1, 2, 2, 3] => 3, 1, 1, 3, 3, 1, 2, 2, 3
[3, 1, 1, 3, 3, 1, 2, 3, 1] => 3, 1, 1, 3, 3, 1, 2, 3, 1
[3, 1, 1, 3, 3, 1, 2, 3, 2] => 3, 1, 1, 3, 3, 1, 2, 3, 2
[3, 1, 1, 3, 3, 1, 2, 3, 3] => 3, 1, 1, 3, 3, 1, 2, 3, 3
[3, 1, 1, 3, 3, 1, 3, 1, 1] => 3, 1, 1, 3, 3, 1, 3, 1, 1
[3, 1, 1, 3, 3, 1, 3, 1, 2] => 3, 1, 1, 3, 3, 1, 3, 1, 2
[3, 1, 1, 3, 3, 1, 3, 1, 3] => 3, 1, 1, 3, 3, 1, 3, 1, 3
[3, 1, 1, 3, 3, 1, 3, 2, 1] => 3, 1, 1, 3, 3, 1, 3, 2, 1
[3, 1, 1, 3, 3, 1, 3, 2, 2] => 3, 1, 1, 3, 3, 1, 3, 2, 2
[3, 1, 1, 3, 3, 1, 3, 2, 3] => 3, 1, 1, 3, 3, 1, 3, 2, 3
[3, 1, 1, 3, 3, 1, 3, 3, 1] => 3, 1, 1, 3, 3, 1, 3, 3, 1
[3, 1, 1, 3, 3, 1, 3, 3, 2] => 3, 1, 1, 3, 3, 1, 3, 3, 2
[3, 1, 1, 3, 3, 1, 3, 3, 3] => 3, 1, 1, 3, 3, 1, 3, 3, 3
[3, 1, 1, 3, 3, 2, 1, 1, 1] => 3, 1, 1, 3, 3, 2, 1, 1, 1
[3, 1, 1, 3, 3, 2, 1, 1, 2] => 3, 1, 1, 3, 3, 2, 1, 1, 2
[3, 1, 1, 3, 3, 2, 1, 1, 3] => 3, 1, 1, 3, 3, 2, 1, 1, 3
[3, 1, 1, 3, 3, 2, 1, 2, 1] => 3, 1, 1, 3, 3, 2, 1, 2, 1
[3, 1, 1, 3, 3, 2, 1, 2, 2] => 3, 1, 1, 3, 3, 2, 1, 2, 2
[3, 1, 1, 3, 3, 2, 1, 2, 3] => 3, 1, 1, 3, 3, 2, 1, 2, 3
[3, 1, 1, 3, 3, 2, 1, 3, 1] => 3, 1, 1, 3, 3, 2, 1, 3, 1
[3, 1, 1, 3, 3, 2, 1, 3, 2] => 3, 1, 1, 3, 3, 2, 1, 3, 2
[3, 1, 1, 3, 3, 2, 1, 3, 3] => 3, 1, 1, 3, 3, 2, 1, 3, 3
[3, 1, 1, 3, 3, 2, 2, 1, 1] => 3, 1, 1, 3, 3, 2, 2, 1, 1
[3, 1, 1, 3, 3, 2, 2, 1, 2] => 3, 1, 1, 3, 3, 2, 2, 1, 2
[3, 1, 1, 3, 3, 2, 2, 1, 3] => 3, 1, 1, 3, 3, 2, 2, 1, 3
[3, 1, 1, 3, 3, 2, 2, 2, 1] => 3, 1, 1, 3, 3, 2, 2, 2, 1
[3, 1, 1, 3, 3, 2, 2, 2, 2] => 3, 1, 1, 3, 3, 2, 2, 2, 2
[3, 1, 1, 3, 3, 2, 2, 2, 3] => 3, 1, 1, 3, 3, 2, 2, 2, 3
[3, 1, 1, 3, 3, 2, 2, 3, 1] => 3, 1, 1, 3, 3, 2, 2, 3, 1
[3, 1, 1, 3, 3, 2, 2, 3, 2] => 3, 1, 1, 3, 3, 2, 2, 3, 2
[3, 1, 1, 3, 3, 2, 2, 3, 3] => 3, 1, 1, 3, 3, 2, 2, 3, 3
[3, 1, 1, 3, 3, 2, 3, 1, 1] => 3, 1, 1, 3, 3, 2, 3, 1, 1
[3, 1, 1, 3, 3, 2, 3, 1, 2] => 3, 1, 1, 3, 3, 2, 3, 1, 2
[3, 1, 1, 3, 3, 2, 3, 1, 3] => 3, 1, 1, 3, 3, 2, 3, 1, 3
[3, 1, 1, 3, 3, 2, 3, 2, 1] => 3, 1, 1, 3, 3, 2, 3, 2, 1
[3, 1, 1, 3, 3, 2, 3, 2, 2] => 3, 1, 1, 3, 3, 2, 3, 2, 2
[3, 1, 1, 3, 3, 2, 3, 2, 3] => 3, 1, 1, 3, 3, 2, 3, 2, 3
[3, 1, 1, 3, 3, 2, 3, 3, 1] => 3, 1, 1, 3, 3, 2, 3, 3, 1
[3, 1, 1, 3, 3, 2, 3, 3, 2] => 3, 1, 1, 3, 3, 2, 3, 3, 2
[3, 1, 1, 3, 3, 2, 3, 3, 3] => 3, 1, 1, 3, 3, 2, 3, 3, 3
[3, 1, 1, 3, 3, 3, 1, 1, 1] => 3, 1, 1, 3, 3, 3, 1, 1, 1
[3, 1, 1, 3, 3, 3, 1, 1, 2] => 3, 1, 1, 3, 3, 3, 1, 1, 2
[3, 1, 1, 3, 3, 3, 1, 1, 3] => 3, 1, 1, 3, 3, 3, 1, 1, 3
[3, 1, 1, 3, 3, 3, 1, 2, 1] => 3, 1, 1, 3, 3, 3, 1, 2, 1
[3, 1, 1, 3, 3, 3, 1, 2, 2] => 3, 1, 1, 3, 3, 3, 1, 2, 2
[3, 1, 1, 3, 3, 3, 1, 2, 3] => 3, 1, 1, 3, 3, 3, 1, 2, 3
[3, 1, 1, 3, 3, 3, 1, 3, 1] => 3, 1, 1, 3, 3, 3, 1, 3, 1
[3, 1, 1, 3, 3, 3, 1, 3, 2] => 3, 1, 1, 3, 3, 3, 1, 3, 2
[3, 1, 1, 3, 3, 3, 1, 3, 3] => 3, 1, 1, 3, 3, 3, 1, 3, 3
[3, 1, 1, 3, 3, 3, 2, 1, 1] => 3, 1, 1, 3, 3, 3, 2, 1, 1
[3, 1, 1, 3, 3, 3, 2, 1, 2] => 3, 1, 1, 3, 3, 3, 2, 1, 2
[3, 1, 1, 3, 3, 3, 2, 1, 3] => 3, 1, 1, 3, 3, 3, 2, 1, 3
[3, 1, 1, 3, 3, 3, 2, 2, 1] => 3, 1, 1, 3, 3, 3, 2, 2, 1
[3, 1, 1, 3, 3, 3, 2, 2, 2] => 3, 1, 1, 3, 3, 3, 2, 2, 2
[3, 1, 1, 3, 3, 3, 2, 2, 3] => 3, 1, 1, 3, 3, 3, 2, 2, 3
[3, 1, 1, 3, 3, 3, 2, 3, 1] => 3, 1, 1, 3, 3, 3, 2, 3, 1
[3, 1, 1, 3, 3, 3, 2, 3, 2] => 3, 1, 1, 3, 3, 3, 2, 3, 2
[3, 1, 1, 3, 3, 3, 2, 3, 3] => 3, 1, 1, 3, 3, 3, 2, 3, 3
[3, 1, 1, 3, 3, 3, 3, 1, 1] => 3, 1, 1, 3, 3, 3, 3, 1, 1
[3, 1, 1, 3, 3, 3, 3, 1, 2] => 3, 1, 1, 3, 3, 3, 3, 1, 2
[3, 1, 1, 3, 3, 3, 3, 1, 3] => 3, 1, 1, 3, 3, 3, 3, 1, 3
[3, 1, 1, 3, 3, 3, 3, 2, 1] => 3, 1, 1, 3, 3, 3, 3, 2, 1
[3, 1, 1, 3, 3, 3, 3, 2, 2] => 3, 1, 1, 3, 3, 3, 3, 2, 2
[3, 1, 1, 3, 3, 3, 3, 2, 3] => 3, 1, 1, 3, 3, 3, 3, 2, 3
[3, 1, 1, 3, 3, 3, 3, 3, 1] => 3, 1, 1, 3, 3, 3, 3, 3, 1
[3, 1, 1, 3, 3, 3, 3, 3, 2] => 3, 1, 1, 3, 3, 3, 3, 3, 2
[3, 1, 1, 3, 3, 3, 3, 3, 3] => 3, 1, 1, 3, 3, 3, 3, 3, 3
[3, 1, 2, 1, 1, 1, 1, 1, 1] => 3, 1, 2, 1, 1, 1, 1, 1, 1
[3, 1, 2, 1, 1, 1, 1, 1, 2] => 3, 1, 2, 1, 1, 1, 1, 1, 2
[3, 1, 2, 1, 1, 1, 1, 1, 3] => 3, 1, 2, 1, 1, 1, 1, 1, 3
[3, 1, 2, 1, 1, 1, 1, 2, 1] => 3, 1, 2, 1, 1, 1, 1, 2, 1
[3, 1, 2, 1, 1, 1, 1, 2, 2] => 3, 1, 2, 1, 1, 1, 1, 2, 2
[3, 1, 2, 1, 1, 1, 1, 2, 3] => 3, 1, 2, 1, 1, 1, 1, 2, 3
[3, 1, 2, 1, 1, 1, 1, 3, 1] => 3, 1, 2, 1, 1, 1, 1, 3, 1
[3, 1, 2, 1, 1, 1, 1, 3, 2] => 3, 1, 2, 1, 1, 1, 1, 3, 2
[3, 1, 2, 1, 1, 1, 1, 3, 3] => 3, 1, 2, 1, 1, 1, 1, 3, 3
[3, 1, 2, 1, 1, 1, 2, 1, 1] => 3, 1, 2, 1, 1, 1, 2, 1, 1
[3, 1, 2, 1, 1, 1, 2, 1, 2] => 3, 1, 2, 1, 1, 1, 2, 1, 2
[3, 1, 2, 1, 1, 1, 2, 1, 3] => 3, 1, 2, 1, 1, 1, 2, 1, 3
[3, 1, 2, 1, 1, 1, 2, 2, 1] => 3, 1, 2, 1, 1, 1, 2, 2, 1
[3, 1, 2, 1, 1, 1, 2, 2, 2] => 3, 1, 2, 1, 1, 1, 2, 2, 2
[3, 1, 2, 1, 1, 1, 2, 2, 3] => 3, 1, 2, 1, 1, 1, 2, 2, 3
[3, 1, 2, 1, 1, 1, 2, 3, 1] => 3, 1, 2, 1, 1, 1, 2, 3, 1
[3, 1, 2, 1, 1, 1, 2, 3, 2] => 3, 1, 2, 1, 1, 1, 2, 3, 2
[3, 1, 2, 1, 1, 1, 2, 3, 3] => 3, 1, 2, 1, 1, 1, 2, 3, 3
[3, 1, 2, 1, 1, 1, 3, 1, 1] => 3, 1, 2, 1, 1, 1, 3, 1, 1
[3, 1, 2, 1, 1, 1, 3, 1, 2] => 3, 1, 2, 1, 1, 1, 3, 1, 2
[3, 1, 2, 1, 1, 1, 3, 1, 3] => 3, 1, 2, 1, 1, 1, 3, 1, 3
[3, 1, 2, 1, 1, 1, 3, 2, 1] => 3, 1, 2, 1, 1, 1, 3, 2, 1
[3, 1, 2, 1, 1, 1, 3, 2, 2] => 3, 1, 2, 1, 1, 1, 3, 2, 2
[3, 1, 2, 1, 1, 1, 3, 2, 3] => 3, 1, 2, 1, 1, 1, 3, 2, 3
[3, 1, 2, 1, 1, 1, 3, 3, 1] => 3, 1, 2, 1, 1, 1, 3, 3, 1
[3, 1, 2, 1, 1, 1, 3, 3, 2] => 3, 1, 2, 1, 1, 1, 3, 3, 2
[3, 1, 2, 1, 1, 1, 3, 3, 3] => 3, 1, 2, 1, 1, 1, 3, 3, 3
[3, 1, 2, 1, 1, 2, 1, 1, 1] => 3, 1, 2, 1, 1, 2, 1, 1, 1
[3, 1, 2, 1, 1, 2, 1, 1, 2] => 3, 1, 2, 1, 1, 2, 1, 1, 2
[3, 1, 2, 1, 1, 2, 1, 1, 3] => 3, 1, 2, 1, 1, 2, 1, 1, 3
[3, 1, 2, 1, 1, 2, 1, 2, 1] => 3, 1, 2, 1, 1, 2, 1, 2, 1
[3, 1, 2, 1, 1, 2, 1, 2, 2] => 3, 1, 2, 1, 1, 2, 1, 2, 2
[3, 1, 2, 1, 1, 2, 1, 2, 3] => 3, 1, 2, 1, 1, 2, 1, 2, 3
[3, 1, 2, 1, 1, 2, 1, 3, 1] => 3, 1, 2, 1, 1, 2, 1, 3, 1
[3, 1, 2, 1, 1, 2, 1, 3, 2] => 3, 1, 2, 1, 1, 2, 1, 3, 2
[3, 1, 2, 1, 1, 2, 1, 3, 3] => 3, 1, 2, 1, 1, 2, 1, 3, 3
[3, 1, 2, 1, 1, 2, 2, 1, 1] => 3, 1, 2, 1, 1, 2, 2, 1, 1
[3, 1, 2, 1, 1, 2, 2, 1, 2] => 3, 1, 2, 1, 1, 2, 2, 1, 2
[3, 1, 2, 1, 1, 2, 2, 1, 3] => 3, 1, 2, 1, 1, 2, 2, 1, 3
[3, 1, 2, 1, 1, 2, 2, 2, 1] => 3, 1, 2, 1, 1, 2, 2, 2, 1
[3, 1, 2, 1, 1, 2, 2, 2, 2] => 3, 1, 2, 1, 1, 2, 2, 2, 2
[3, 1, 2, 1, 1, 2, 2, 2, 3] => 3, 1, 2, 1, 1, 2, 2, 2, 3
[3, 1, 2, 1, 1, 2, 2, 3, 1] => 3, 1, 2, 1, 1, 2, 2, 3, 1
[3, 1, 2, 1, 1, 2, 2, 3, 2] => 3, 1, 2, 1, 1, 2, 2, 3, 2
[3, 1, 2, 1, 1, 2, 2, 3, 3] => 3, 1, 2, 1, 1, 2, 2, 3, 3
[3, 1, 2, 1, 1, 2, 3, 1, 1] => 3, 1, 2, 1, 1, 2, 3, 1, 1
[3, 1, 2, 1, 1, 2, 3, 1, 2] => 3, 1, 2, 1, 1, 2, 3, 1, 2
[3, 1, 2, 1, 1, 2, 3, 1, 3] => 3, 1, 2, 1, 1, 2, 3, 1, 3
[3, 1, 2, 1, 1, 2, 3, 2, 1] => 3, 1, 2, 1, 1, 2, 3, 2, 1
[3, 1, 2, 1, 1, 2, 3, 2, 2] => 3, 1, 2, 1, 1, 2, 3, 2, 2
[3, 1, 2, 1, 1, 2, 3, 2, 3] => 3, 1, 2, 1, 1, 2, 3, 2, 3
[3, 1, 2, 1, 1, 2, 3, 3, 1] => 3, 1, 2, 1, 1, 2, 3, 3, 1
[3, 1, 2, 1, 1, 2, 3, 3, 2] => 3, 1, 2, 1, 1, 2, 3, 3, 2
[3, 1, 2, 1, 1, 2, 3, 3, 3] => 3, 1, 2, 1, 1, 2, 3, 3, 3
[3, 1, 2, 1, 1, 3, 1, 1, 1] => 3, 1, 2, 1, 1, 3, 1, 1, 1
[3, 1, 2, 1, 1, 3, 1, 1, 2] => 3, 1, 2, 1, 1, 3, 1, 1, 2
[3, 1, 2, 1, 1, 3, 1, 1, 3] => 3, 1, 2, 1, 1, 3, 1, 1, 3
[3, 1, 2, 1, 1, 3, 1, 2, 1] => 3, 1, 2, 1, 1, 3, 1, 2, 1
[3, 1, 2, 1, 1, 3, 1, 2, 2] => 3, 1, 2, 1, 1, 3, 1, 2, 2
[3, 1, 2, 1, 1, 3, 1, 2, 3] => 3, 1, 2, 1, 1, 3, 1, 2, 3
[3, 1, 2, 1, 1, 3, 1, 3, 1] => 3, 1, 2, 1, 1, 3, 1, 3, 1
[3, 1, 2, 1, 1, 3, 1, 3, 2] => 3, 1, 2, 1, 1, 3, 1, 3, 2
[3, 1, 2, 1, 1, 3, 1, 3, 3] => 3, 1, 2, 1, 1, 3, 1, 3, 3
[3, 1, 2, 1, 1, 3, 2, 1, 1] => 3, 1, 2, 1, 1, 3, 2, 1, 1
[3, 1, 2, 1, 1, 3, 2, 1, 2] => 3, 1, 2, 1, 1, 3, 2, 1, 2
[3, 1, 2, 1, 1, 3, 2, 1, 3] => 3, 1, 2, 1, 1, 3, 2, 1, 3
[3, 1, 2, 1, 1, 3, 2, 2, 1] => 3, 1, 2, 1, 1, 3, 2, 2, 1
[3, 1, 2, 1, 1, 3, 2, 2, 2] => 3, 1, 2, 1, 1, 3, 2, 2, 2
[3, 1, 2, 1, 1, 3, 2, 2, 3] => 3, 1, 2, 1, 1, 3, 2, 2, 3
[3, 1, 2, 1, 1, 3, 2, 3, 1] => 3, 1, 2, 1, 1, 3, 2, 3, 1
[3, 1, 2, 1, 1, 3, 2, 3, 2] => 3, 1, 2, 1, 1, 3, 2, 3, 2
[3, 1, 2, 1, 1, 3, 2, 3, 3] => 3, 1, 2, 1, 1, 3, 2, 3, 3
[3, 1, 2, 1, 1, 3, 3, 1, 1] => 3, 1, 2, 1, 1, 3, 3, 1, 1
[3, 1, 2, 1, 1, 3, 3, 1, 2] => 3, 1, 2, 1, 1, 3, 3, 1, 2
[3, 1, 2, 1, 1, 3, 3, 1, 3] => 3, 1, 2, 1, 1, 3, 3, 1, 3
[3, 1, 2, 1, 1, 3, 3, 2, 1] => 3, 1, 2, 1, 1, 3, 3, 2, 1
[3, 1, 2, 1, 1, 3, 3, 2, 2] => 3, 1, 2, 1, 1, 3, 3, 2, 2
[3, 1, 2, 1, 1, 3, 3, 2, 3] => 3, 1, 2, 1, 1, 3, 3, 2, 3
[3, 1, 2, 1, 1, 3, 3, 3, 1] => 3, 1, 2, 1, 1, 3, 3, 3, 1
[3, 1, 2, 1, 1, 3, 3, 3, 2] => 3, 1, 2, 1, 1, 3, 3, 3, 2
[3, 1, 2, 1, 1, 3, 3, 3, 3] => 3, 1, 2, 1, 1, 3, 3, 3, 3
[3, 1, 2, 1, 2, 1, 1, 1, 1] => 3, 1, 2, 1, 2, 1, 1, 1, 1
[3, 1, 2, 1, 2, 1, 1, 1, 2] => 3, 1, 2, 1, 2, 1, 1, 1, 2
[3, 1, 2, 1, 2, 1, 1, 1, 3] => 3, 1, 2, 1, 2, 1, 1, 1, 3
[3, 1, 2, 1, 2, 1, 1, 2, 1] => 3, 1, 2, 1, 2, 1, 1, 2, 1
[3, 1, 2, 1, 2, 1, 1, 2, 2] => 3, 1, 2, 1, 2, 1, 1, 2, 2
[3, 1, 2, 1, 2, 1, 1, 2, 3] => 3, 1, 2, 1, 2, 1, 1, 2, 3
[3, 1, 2, 1, 2, 1, 1, 3, 1] => 3, 1, 2, 1, 2, 1, 1, 3, 1
[3, 1, 2, 1, 2, 1, 1, 3, 2] => 3, 1, 2, 1, 2, 1, 1, 3, 2
[3, 1, 2, 1, 2, 1, 1, 3, 3] => 3, 1, 2, 1, 2, 1, 1, 3, 3
[3, 1, 2, 1, 2, 1, 2, 1, 1] => 3, 1, 2, 1, 2, 1, 2, 1, 1
[3, 1, 2, 1, 2, 1, 2, 1, 2] => 3, 1, 2, 1, 2, 1, 2, 1, 2
[3, 1, 2, 1, 2, 1, 2, 1, 3] => 3, 1, 2, 1, 2, 1, 2, 1, 3
[3, 1, 2, 1, 2, 1, 2, 2, 1] => 3, 1, 2, 1, 2, 1, 2, 2, 1
[3, 1, 2, 1, 2, 1, 2, 2, 2] => 3, 1, 2, 1, 2, 1, 2, 2, 2
[3, 1, 2, 1, 2, 1, 2, 2, 3] => 3, 1, 2, 1, 2, 1, 2, 2, 3
[3, 1, 2, 1, 2, 1, 2, 3, 1] => 3, 1, 2, 1, 2, 1, 2, 3, 1
[3, 1, 2, 1, 2, 1, 2, 3, 2] => 3, 1, 2, 1, 2, 1, 2, 3, 2
[3, 1, 2, 1, 2, 1, 2, 3, 3] => 3, 1, 2, 1, 2, 1, 2, 3, 3
[3, 1, 2, 1, 2, 1, 3, 1, 1] => 3, 1, 2, 1, 2, 1, 3, 1, 1
[3, 1, 2, 1, 2, 1, 3, 1, 2] => 3, 1, 2, 1, 2, 1, 3, 1, 2
[3, 1, 2, 1, 2, 1, 3, 1, 3] => 3, 1, 2, 1, 2, 1, 3, 1, 3
[3, 1, 2, 1, 2, 1, 3, 2, 1] => 3, 1, 2, 1, 2, 1, 3, 2, 1
[3, 1, 2, 1, 2, 1, 3, 2, 2] => 3, 1, 2, 1, 2, 1, 3, 2, 2
[3, 1, 2, 1, 2, 1, 3, 2, 3] => 3, 1, 2, 1, 2, 1, 3, 2, 3
[3, 1, 2, 1, 2, 1, 3, 3, 1] => 3, 1, 2, 1, 2, 1, 3, 3, 1
[3, 1, 2, 1, 2, 1, 3, 3, 2] => 3, 1, 2, 1, 2, 1, 3, 3, 2
[3, 1, 2, 1, 2, 1, 3, 3, 3] => 3, 1, 2, 1, 2, 1, 3, 3, 3
[3, 1, 2, 1, 2, 2, 1, 1, 1] => 3, 1, 2, 1, 2, 2, 1, 1, 1
[3, 1, 2, 1, 2, 2, 1, 1, 2] => 3, 1, 2, 1, 2, 2, 1, 1, 2
[3, 1, 2, 1, 2, 2, 1, 1, 3] => 3, 1, 2, 1, 2, 2, 1, 1, 3
[3, 1, 2, 1, 2, 2, 1, 2, 1] => 3, 1, 2, 1, 2, 2, 1, 2, 1
[3, 1, 2, 1, 2, 2, 1, 2, 2] => 3, 1, 2, 1, 2, 2, 1, 2, 2
[3, 1, 2, 1, 2, 2, 1, 2, 3] => 3, 1, 2, 1, 2, 2, 1, 2, 3
[3, 1, 2, 1, 2, 2, 1, 3, 1] => 3, 1, 2, 1, 2, 2, 1, 3, 1
[3, 1, 2, 1, 2, 2, 1, 3, 2] => 3, 1, 2, 1, 2, 2, 1, 3, 2
[3, 1, 2, 1, 2, 2, 1, 3, 3] => 3, 1, 2, 1, 2, 2, 1, 3, 3
[3, 1, 2, 1, 2, 2, 2, 1, 1] => 3, 1, 2, 1, 2, 2, 2, 1, 1
[3, 1, 2, 1, 2, 2, 2, 1, 2] => 3, 1, 2, 1, 2, 2, 2, 1, 2
[3, 1, 2, 1, 2, 2, 2, 1, 3] => 3, 1, 2, 1, 2, 2, 2, 1, 3
[3, 1, 2, 1, 2, 2, 2, 2, 1] => 3, 1, 2, 1, 2, 2, 2, 2, 1
[3, 1, 2, 1, 2, 2, 2, 2, 2] => 3, 1, 2, 1, 2, 2, 2, 2, 2
[3, 1, 2, 1, 2, 2, 2, 2, 3] => 3, 1, 2, 1, 2, 2, 2, 2, 3
[3, 1, 2, 1, 2, 2, 2, 3, 1] => 3, 1, 2, 1, 2, 2, 2, 3, 1
[3, 1, 2, 1, 2, 2, 2, 3, 2] => 3, 1, 2, 1, 2, 2, 2, 3, 2
[3, 1, 2, 1, 2, 2, 2, 3, 3] => 3, 1, 2, 1, 2, 2, 2, 3, 3
[3, 1, 2, 1, 2, 2, 3, 1, 1] => 3, 1, 2, 1, 2, 2, 3, 1, 1
[3, 1, 2, 1, 2, 2, 3, 1, 2] => 3, 1, 2, 1, 2, 2, 3, 1, 2
[3, 1, 2, 1, 2, 2, 3, 1, 3] => 3, 1, 2, 1, 2, 2, 3, 1, 3
[3, 1, 2, 1, 2, 2, 3, 2, 1] => 3, 1, 2, 1, 2, 2, 3, 2, 1
[3, 1, 2, 1, 2, 2, 3, 2, 2] => 3, 1, 2, 1, 2, 2, 3, 2, 2
[3, 1, 2, 1, 2, 2, 3, 2, 3] => 3, 1, 2, 1, 2, 2, 3, 2, 3
[3, 1, 2, 1, 2, 2, 3, 3, 1] => 3, 1, 2, 1, 2, 2, 3, 3, 1
[3, 1, 2, 1, 2, 2, 3, 3, 2] => 3, 1, 2, 1, 2, 2, 3, 3, 2
[3, 1, 2, 1, 2, 2, 3, 3, 3] => 3, 1, 2, 1, 2, 2, 3, 3, 3
[3, 1, 2, 1, 2, 3, 1, 1, 1] => 3, 1, 2, 1, 2, 3, 1, 1, 1
[3, 1, 2, 1, 2, 3, 1, 1, 2] => 3, 1, 2, 1, 2, 3, 1, 1, 2
[3, 1, 2, 1, 2, 3, 1, 1, 3] => 3, 1, 2, 1, 2, 3, 1, 1, 3
[3, 1, 2, 1, 2, 3, 1, 2, 1] => 3, 1, 2, 1, 2, 3, 1, 2, 1
[3, 1, 2, 1, 2, 3, 1, 2, 2] => 3, 1, 2, 1, 2, 3, 1, 2, 2
[3, 1, 2, 1, 2, 3, 1, 2, 3] => 3, 1, 2, 1, 2, 3, 1, 2, 3
[3, 1, 2, 1, 2, 3, 1, 3, 1] => 3, 1, 2, 1, 2, 3, 1, 3, 1
[3, 1, 2, 1, 2, 3, 1, 3, 2] => 3, 1, 2, 1, 2, 3, 1, 3, 2
[3, 1, 2, 1, 2, 3, 1, 3, 3] => 3, 1, 2, 1, 2, 3, 1, 3, 3
[3, 1, 2, 1, 2, 3, 2, 1, 1] => 3, 1, 2, 1, 2, 3, 2, 1, 1
[3, 1, 2, 1, 2, 3, 2, 1, 2] => 3, 1, 2, 1, 2, 3, 2, 1, 2
[3, 1, 2, 1, 2, 3, 2, 1, 3] => 3, 1, 2, 1, 2, 3, 2, 1, 3
[3, 1, 2, 1, 2, 3, 2, 2, 1] => 3, 1, 2, 1, 2, 3, 2, 2, 1
[3, 1, 2, 1, 2, 3, 2, 2, 2] => 3, 1, 2, 1, 2, 3, 2, 2, 2
[3, 1, 2, 1, 2, 3, 2, 2, 3] => 3, 1, 2, 1, 2, 3, 2, 2, 3
[3, 1, 2, 1, 2, 3, 2, 3, 1] => 3, 1, 2, 1, 2, 3, 2, 3, 1
[3, 1, 2, 1, 2, 3, 2, 3, 2] => 3, 1, 2, 1, 2, 3, 2, 3, 2
[3, 1, 2, 1, 2, 3, 2, 3, 3] => 3, 1, 2, 1, 2, 3, 2, 3, 3
[3, 1, 2, 1, 2, 3, 3, 1, 1] => 3, 1, 2, 1, 2, 3, 3, 1, 1
[3, 1, 2, 1, 2, 3, 3, 1, 2] => 3, 1, 2, 1, 2, 3, 3, 1, 2
[3, 1, 2, 1, 2, 3, 3, 1, 3] => 3, 1, 2, 1, 2, 3, 3, 1, 3
[3, 1, 2, 1, 2, 3, 3, 2, 1] => 3, 1, 2, 1, 2, 3, 3, 2, 1
[3, 1, 2, 1, 2, 3, 3, 2, 2] => 3, 1, 2, 1, 2, 3, 3, 2, 2
[3, 1, 2, 1, 2, 3, 3, 2, 3] => 3, 1, 2, 1, 2, 3, 3, 2, 3
[3, 1, 2, 1, 2, 3, 3, 3, 1] => 3, 1, 2, 1, 2, 3, 3, 3, 1
[3, 1, 2, 1, 2, 3, 3, 3, 2] => 3, 1, 2, 1, 2, 3, 3, 3, 2
[3, 1, 2, 1, 2, 3, 3, 3, 3] => 3, 1, 2, 1, 2, 3, 3, 3, 3
[3, 1, 2, 1, 3, 1, 1, 1, 1] => 3, 1, 2, 1, 3, 1, 1, 1, 1
[3, 1, 2, 1, 3, 1, 1, 1, 2] => 3, 1, 2, 1, 3, 1, 1, 1, 2
[3, 1, 2, 1, 3, 1, 1, 1, 3] => 3, 1, 2, 1, 3, 1, 1, 1, 3
[3, 1, 2, 1, 3, 1, 1, 2, 1] => 3, 1, 2, 1, 3, 1, 1, 2, 1
[3, 1, 2, 1, 3, 1, 1, 2, 2] => 3, 1, 2, 1, 3, 1, 1, 2, 2
[3, 1, 2, 1, 3, 1, 1, 2, 3] => 3, 1, 2, 1, 3, 1, 1, 2, 3
[3, 1, 2, 1, 3, 1, 1, 3, 1] => 3, 1, 2, 1, 3, 1, 1, 3, 1
[3, 1, 2, 1, 3, 1, 1, 3, 2] => 3, 1, 2, 1, 3, 1, 1, 3, 2
[3, 1, 2, 1, 3, 1, 1, 3, 3] => 3, 1, 2, 1, 3, 1, 1, 3, 3
[3, 1, 2, 1, 3, 1, 2, 1, 1] => 3, 1, 2, 1, 3, 1, 2, 1, 1
[3, 1, 2, 1, 3, 1, 2, 1, 2] => 3, 1, 2, 1, 3, 1, 2, 1, 2
[3, 1, 2, 1, 3, 1, 2, 1, 3] => 3, 1, 2, 1, 3, 1, 2, 1, 3
[3, 1, 2, 1, 3, 1, 2, 2, 1] => 3, 1, 2, 1, 3, 1, 2, 2, 1
[3, 1, 2, 1, 3, 1, 2, 2, 2] => 3, 1, 2, 1, 3, 1, 2, 2, 2
[3, 1, 2, 1, 3, 1, 2, 2, 3] => 3, 1, 2, 1, 3, 1, 2, 2, 3
[3, 1, 2, 1, 3, 1, 2, 3, 1] => 3, 1, 2, 1, 3, 1, 2, 3, 1
[3, 1, 2, 1, 3, 1, 2, 3, 2] => 3, 1, 2, 1, 3, 1, 2, 3, 2
[3, 1, 2, 1, 3, 1, 2, 3, 3] => 3, 1, 2, 1, 3, 1, 2, 3, 3
[3, 1, 2, 1, 3, 1, 3, 1, 1] => 3, 1, 2, 1, 3, 1, 3, 1, 1
[3, 1, 2, 1, 3, 1, 3, 1, 2] => 3, 1, 2, 1, 3, 1, 3, 1, 2
[3, 1, 2, 1, 3, 1, 3, 1, 3] => 3, 1, 2, 1, 3, 1, 3, 1, 3
[3, 1, 2, 1, 3, 1, 3, 2, 1] => 3, 1, 2, 1, 3, 1, 3, 2, 1
[3, 1, 2, 1, 3, 1, 3, 2, 2] => 3, 1, 2, 1, 3, 1, 3, 2, 2
[3, 1, 2, 1, 3, 1, 3, 2, 3] => 3, 1, 2, 1, 3, 1, 3, 2, 3
[3, 1, 2, 1, 3, 1, 3, 3, 1] => 3, 1, 2, 1, 3, 1, 3, 3, 1
[3, 1, 2, 1, 3, 1, 3, 3, 2] => 3, 1, 2, 1, 3, 1, 3, 3, 2
[3, 1, 2, 1, 3, 1, 3, 3, 3] => 3, 1, 2, 1, 3, 1, 3, 3, 3
[3, 1, 2, 1, 3, 2, 1, 1, 1] => 3, 1, 2, 1, 3, 2, 1, 1, 1
[3, 1, 2, 1, 3, 2, 1, 1, 2] => 3, 1, 2, 1, 3, 2, 1, 1, 2
[3, 1, 2, 1, 3, 2, 1, 1, 3] => 3, 1, 2, 1, 3, 2, 1, 1, 3
[3, 1, 2, 1, 3, 2, 1, 2, 1] => 3, 1, 2, 1, 3, 2, 1, 2, 1
[3, 1, 2, 1, 3, 2, 1, 2, 2] => 3, 1, 2, 1, 3, 2, 1, 2, 2
[3, 1, 2, 1, 3, 2, 1, 2, 3] => 3, 1, 2, 1, 3, 2, 1, 2, 3
[3, 1, 2, 1, 3, 2, 1, 3, 1] => 3, 1, 2, 1, 3, 2, 1, 3, 1
[3, 1, 2, 1, 3, 2, 1, 3, 2] => 3, 1, 2, 1, 3, 2, 1, 3, 2
[3, 1, 2, 1, 3, 2, 1, 3, 3] => 3, 1, 2, 1, 3, 2, 1, 3, 3
[3, 1, 2, 1, 3, 2, 2, 1, 1] => 3, 1, 2, 1, 3, 2, 2, 1, 1
[3, 1, 2, 1, 3, 2, 2, 1, 2] => 3, 1, 2, 1, 3, 2, 2, 1, 2
[3, 1, 2, 1, 3, 2, 2, 1, 3] => 3, 1, 2, 1, 3, 2, 2, 1, 3
[3, 1, 2, 1, 3, 2, 2, 2, 1] => 3, 1, 2, 1, 3, 2, 2, 2, 1
[3, 1, 2, 1, 3, 2, 2, 2, 2] => 3, 1, 2, 1, 3, 2, 2, 2, 2
[3, 1, 2, 1, 3, 2, 2, 2, 3] => 3, 1, 2, 1, 3, 2, 2, 2, 3
[3, 1, 2, 1, 3, 2, 2, 3, 1] => 3, 1, 2, 1, 3, 2, 2, 3, 1
[3, 1, 2, 1, 3, 2, 2, 3, 2] => 3, 1, 2, 1, 3, 2, 2, 3, 2
[3, 1, 2, 1, 3, 2, 2, 3, 3] => 3, 1, 2, 1, 3, 2, 2, 3, 3
[3, 1, 2, 1, 3, 2, 3, 1, 1] => 3, 1, 2, 1, 3, 2, 3, 1, 1
[3, 1, 2, 1, 3, 2, 3, 1, 2] => 3, 1, 2, 1, 3, 2, 3, 1, 2
[3, 1, 2, 1, 3, 2, 3, 1, 3] => 3, 1, 2, 1, 3, 2, 3, 1, 3
[3, 1, 2, 1, 3, 2, 3, 2, 1] => 3, 1, 2, 1, 3, 2, 3, 2, 1
[3, 1, 2, 1, 3, 2, 3, 2, 2] => 3, 1, 2, 1, 3, 2, 3, 2, 2
[3, 1, 2, 1, 3, 2, 3, 2, 3] => 3, 1, 2, 1, 3, 2, 3, 2, 3
[3, 1, 2, 1, 3, 2, 3, 3, 1] => 3, 1, 2, 1, 3, 2, 3, 3, 1
[3, 1, 2, 1, 3, 2, 3, 3, 2] => 3, 1, 2, 1, 3, 2, 3, 3, 2
[3, 1, 2, 1, 3, 2, 3, 3, 3] => 3, 1, 2, 1, 3, 2, 3, 3, 3
[3, 1, 2, 1, 3, 3, 1, 1, 1] => 3, 1, 2, 1, 3, 3, 1, 1, 1
[3, 1, 2, 1, 3, 3, 1, 1, 2] => 3, 1, 2, 1, 3, 3, 1, 1, 2
[3, 1, 2, 1, 3, 3, 1, 1, 3] => 3, 1, 2, 1, 3, 3, 1, 1, 3
[3, 1, 2, 1, 3, 3, 1, 2, 1] => 3, 1, 2, 1, 3, 3, 1, 2, 1
[3, 1, 2, 1, 3, 3, 1, 2, 2] => 3, 1, 2, 1, 3, 3, 1, 2, 2
[3, 1, 2, 1, 3, 3, 1, 2, 3] => 3, 1, 2, 1, 3, 3, 1, 2, 3
[3, 1, 2, 1, 3, 3, 1, 3, 1] => 3, 1, 2, 1, 3, 3, 1, 3, 1
[3, 1, 2, 1, 3, 3, 1, 3, 2] => 3, 1, 2, 1, 3, 3, 1, 3, 2
[3, 1, 2, 1, 3, 3, 1, 3, 3] => 3, 1, 2, 1, 3, 3, 1, 3, 3
[3, 1, 2, 1, 3, 3, 2, 1, 1] => 3, 1, 2, 1, 3, 3, 2, 1, 1
[3, 1, 2, 1, 3, 3, 2, 1, 2] => 3, 1, 2, 1, 3, 3, 2, 1, 2
[3, 1, 2, 1, 3, 3, 2, 1, 3] => 3, 1, 2, 1, 3, 3, 2, 1, 3
[3, 1, 2, 1, 3, 3, 2, 2, 1] => 3, 1, 2, 1, 3, 3, 2, 2, 1
[3, 1, 2, 1, 3, 3, 2, 2, 2] => 3, 1, 2, 1, 3, 3, 2, 2, 2
[3, 1, 2, 1, 3, 3, 2, 2, 3] => 3, 1, 2, 1, 3, 3, 2, 2, 3
[3, 1, 2, 1, 3, 3, 2, 3, 1] => 3, 1, 2, 1, 3, 3, 2, 3, 1
[3, 1, 2, 1, 3, 3, 2, 3, 2] => 3, 1, 2, 1, 3, 3, 2, 3, 2
[3, 1, 2, 1, 3, 3, 2, 3, 3] => 3, 1, 2, 1, 3, 3, 2, 3, 3
[3, 1, 2, 1, 3, 3, 3, 1, 1] => 3, 1, 2, 1, 3, 3, 3, 1, 1
[3, 1, 2, 1, 3, 3, 3, 1, 2] => 3, 1, 2, 1, 3, 3, 3, 1, 2
[3, 1, 2, 1, 3, 3, 3, 1, 3] => 3, 1, 2, 1, 3, 3, 3, 1, 3
[3, 1, 2, 1, 3, 3, 3, 2, 1] => 3, 1, 2, 1, 3, 3, 3, 2, 1
[3, 1, 2, 1, 3, 3, 3, 2, 2] => 3, 1, 2, 1, 3, 3, 3, 2, 2
[3, 1, 2, 1, 3, 3, 3, 2, 3] => 3, 1, 2, 1, 3, 3, 3, 2, 3
[3, 1, 2, 1, 3, 3, 3, 3, 1] => 3, 1, 2, 1, 3, 3, 3, 3, 1
[3, 1, 2, 1, 3, 3, 3, 3, 2] => 3, 1, 2, 1, 3, 3, 3, 3, 2
[3, 1, 2, 1, 3, 3, 3, 3, 3] => 3, 1, 2, 1, 3, 3, 3, 3, 3
[3, 1, 2, 2, 1, 1, 1, 1, 1] => 3, 1, 2, 2, 1, 1, 1, 1, 1
[3, 1, 2, 2, 1, 1, 1, 1, 2] => 3, 1, 2, 2, 1, 1, 1, 1, 2
[3, 1, 2, 2, 1, 1, 1, 1, 3] => 3, 1, 2, 2, 1, 1, 1, 1, 3
[3, 1, 2, 2, 1, 1, 1, 2, 1] => 3, 1, 2, 2, 1, 1, 1, 2, 1
[3, 1, 2, 2, 1, 1, 1, 2, 2] => 3, 1, 2, 2, 1, 1, 1, 2, 2
[3, 1, 2, 2, 1, 1, 1, 2, 3] => 3, 1, 2, 2, 1, 1, 1, 2, 3
[3, 1, 2, 2, 1, 1, 1, 3, 1] => 3, 1, 2, 2, 1, 1, 1, 3, 1
[3, 1, 2, 2, 1, 1, 1, 3, 2] => 3, 1, 2, 2, 1, 1, 1, 3, 2
[3, 1, 2, 2, 1, 1, 1, 3, 3] => 3, 1, 2, 2, 1, 1, 1, 3, 3
[3, 1, 2, 2, 1, 1, 2, 1, 1] => 3, 1, 2, 2, 1, 1, 2, 1, 1
[3, 1, 2, 2, 1, 1, 2, 1, 2] => 3, 1, 2, 2, 1, 1, 2, 1, 2
[3, 1, 2, 2, 1, 1, 2, 1, 3] => 3, 1, 2, 2, 1, 1, 2, 1, 3
[3, 1, 2, 2, 1, 1, 2, 2, 1] => 3, 1, 2, 2, 1, 1, 2, 2, 1
[3, 1, 2, 2, 1, 1, 2, 2, 2] => 3, 1, 2, 2, 1, 1, 2, 2, 2
[3, 1, 2, 2, 1, 1, 2, 2, 3] => 3, 1, 2, 2, 1, 1, 2, 2, 3
[3, 1, 2, 2, 1, 1, 2, 3, 1] => 3, 1, 2, 2, 1, 1, 2, 3, 1
[3, 1, 2, 2, 1, 1, 2, 3, 2] => 3, 1, 2, 2, 1, 1, 2, 3, 2
[3, 1, 2, 2, 1, 1, 2, 3, 3] => 3, 1, 2, 2, 1, 1, 2, 3, 3
[3, 1, 2, 2, 1, 1, 3, 1, 1] => 3, 1, 2, 2, 1, 1, 3, 1, 1
[3, 1, 2, 2, 1, 1, 3, 1, 2] => 3, 1, 2, 2, 1, 1, 3, 1, 2
[3, 1, 2, 2, 1, 1, 3, 1, 3] => 3, 1, 2, 2, 1, 1, 3, 1, 3
[3, 1, 2, 2, 1, 1, 3, 2, 1] => 3, 1, 2, 2, 1, 1, 3, 2, 1
[3, 1, 2, 2, 1, 1, 3, 2, 2] => 3, 1, 2, 2, 1, 1, 3, 2, 2
[3, 1, 2, 2, 1, 1, 3, 2, 3] => 3, 1, 2, 2, 1, 1, 3, 2, 3
[3, 1, 2, 2, 1, 1, 3, 3, 1] => 3, 1, 2, 2, 1, 1, 3, 3, 1
[3, 1, 2, 2, 1, 1, 3, 3, 2] => 3, 1, 2, 2, 1, 1, 3, 3, 2
[3, 1, 2, 2, 1, 1, 3, 3, 3] => 3, 1, 2, 2, 1, 1, 3, 3, 3
[3, 1, 2, 2, 1, 2, 1, 1, 1] => 3, 1, 2, 2, 1, 2, 1, 1, 1
[3, 1, 2, 2, 1, 2, 1, 1, 2] => 3, 1, 2, 2, 1, 2, 1, 1, 2
[3, 1, 2, 2, 1, 2, 1, 1, 3] => 3, 1, 2, 2, 1, 2, 1, 1, 3
[3, 1, 2, 2, 1, 2, 1, 2, 1] => 3, 1, 2, 2, 1, 2, 1, 2, 1
[3, 1, 2, 2, 1, 2, 1, 2, 2] => 3, 1, 2, 2, 1, 2, 1, 2, 2
[3, 1, 2, 2, 1, 2, 1, 2, 3] => 3, 1, 2, 2, 1, 2, 1, 2, 3
[3, 1, 2, 2, 1, 2, 1, 3, 1] => 3, 1, 2, 2, 1, 2, 1, 3, 1
[3, 1, 2, 2, 1, 2, 1, 3, 2] => 3, 1, 2, 2, 1, 2, 1, 3, 2
[3, 1, 2, 2, 1, 2, 1, 3, 3] => 3, 1, 2, 2, 1, 2, 1, 3, 3
[3, 1, 2, 2, 1, 2, 2, 1, 1] => 3, 1, 2, 2, 1, 2, 2, 1, 1
[3, 1, 2, 2, 1, 2, 2, 1, 2] => 3, 1, 2, 2, 1, 2, 2, 1, 2
[3, 1, 2, 2, 1, 2, 2, 1, 3] => 3, 1, 2, 2, 1, 2, 2, 1, 3
[3, 1, 2, 2, 1, 2, 2, 2, 1] => 3, 1, 2, 2, 1, 2, 2, 2, 1
[3, 1, 2, 2, 1, 2, 2, 2, 2] => 3, 1, 2, 2, 1, 2, 2, 2, 2
[3, 1, 2, 2, 1, 2, 2, 2, 3] => 3, 1, 2, 2, 1, 2, 2, 2, 3
[3, 1, 2, 2, 1, 2, 2, 3, 1] => 3, 1, 2, 2, 1, 2, 2, 3, 1
[3, 1, 2, 2, 1, 2, 2, 3, 2] => 3, 1, 2, 2, 1, 2, 2, 3, 2
[3, 1, 2, 2, 1, 2, 2, 3, 3] => 3, 1, 2, 2, 1, 2, 2, 3, 3
[3, 1, 2, 2, 1, 2, 3, 1, 1] => 3, 1, 2, 2, 1, 2, 3, 1, 1
[3, 1, 2, 2, 1, 2, 3, 1, 2] => 3, 1, 2, 2, 1, 2, 3, 1, 2
[3, 1, 2, 2, 1, 2, 3, 1, 3] => 3, 1, 2, 2, 1, 2, 3, 1, 3
[3, 1, 2, 2, 1, 2, 3, 2, 1] => 3, 1, 2, 2, 1, 2, 3, 2, 1
[3, 1, 2, 2, 1, 2, 3, 2, 2] => 3, 1, 2, 2, 1, 2, 3, 2, 2
[3, 1, 2, 2, 1, 2, 3, 2, 3] => 3, 1, 2, 2, 1, 2, 3, 2, 3
[3, 1, 2, 2, 1, 2, 3, 3, 1] => 3, 1, 2, 2, 1, 2, 3, 3, 1
[3, 1, 2, 2, 1, 2, 3, 3, 2] => 3, 1, 2, 2, 1, 2, 3, 3, 2
[3, 1, 2, 2, 1, 2, 3, 3, 3] => 3, 1, 2, 2, 1, 2, 3, 3, 3
[3, 1, 2, 2, 1, 3, 1, 1, 1] => 3, 1, 2, 2, 1, 3, 1, 1, 1
[3, 1, 2, 2, 1, 3, 1, 1, 2] => 3, 1, 2, 2, 1, 3, 1, 1, 2
[3, 1, 2, 2, 1, 3, 1, 1, 3] => 3, 1, 2, 2, 1, 3, 1, 1, 3
[3, 1, 2, 2, 1, 3, 1, 2, 1] => 3, 1, 2, 2, 1, 3, 1, 2, 1
[3, 1, 2, 2, 1, 3, 1, 2, 2] => 3, 1, 2, 2, 1, 3, 1, 2, 2
[3, 1, 2, 2, 1, 3, 1, 2, 3] => 3, 1, 2, 2, 1, 3, 1, 2, 3
[3, 1, 2, 2, 1, 3, 1, 3, 1] => 3, 1, 2, 2, 1, 3, 1, 3, 1
[3, 1, 2, 2, 1, 3, 1, 3, 2] => 3, 1, 2, 2, 1, 3, 1, 3, 2
[3, 1, 2, 2, 1, 3, 1, 3, 3] => 3, 1, 2, 2, 1, 3, 1, 3, 3
[3, 1, 2, 2, 1, 3, 2, 1, 1] => 3, 1, 2, 2, 1, 3, 2, 1, 1
[3, 1, 2, 2, 1, 3, 2, 1, 2] => 3, 1, 2, 2, 1, 3, 2, 1, 2
[3, 1, 2, 2, 1, 3, 2, 1, 3] => 3, 1, 2, 2, 1, 3, 2, 1, 3
[3, 1, 2, 2, 1, 3, 2, 2, 1] => 3, 1, 2, 2, 1, 3, 2, 2, 1
[3, 1, 2, 2, 1, 3, 2, 2, 2] => 3, 1, 2, 2, 1, 3, 2, 2, 2
[3, 1, 2, 2, 1, 3, 2, 2, 3] => 3, 1, 2, 2, 1, 3, 2, 2, 3
[3, 1, 2, 2, 1, 3, 2, 3, 1] => 3, 1, 2, 2, 1, 3, 2, 3, 1
[3, 1, 2, 2, 1, 3, 2, 3, 2] => 3, 1, 2, 2, 1, 3, 2, 3, 2
[3, 1, 2, 2, 1, 3, 2, 3, 3] => 3, 1, 2, 2, 1, 3, 2, 3, 3
[3, 1, 2, 2, 1, 3, 3, 1, 1] => 3, 1, 2, 2, 1, 3, 3, 1, 1
[3, 1, 2, 2, 1, 3, 3, 1, 2] => 3, 1, 2, 2, 1, 3, 3, 1, 2
[3, 1, 2, 2, 1, 3, 3, 1, 3] => 3, 1, 2, 2, 1, 3, 3, 1, 3
[3, 1, 2, 2, 1, 3, 3, 2, 1] => 3, 1, 2, 2, 1, 3, 3, 2, 1
[3, 1, 2, 2, 1, 3, 3, 2, 2] => 3, 1, 2, 2, 1, 3, 3, 2, 2
[3, 1, 2, 2, 1, 3, 3, 2, 3] => 3, 1, 2, 2, 1, 3, 3, 2, 3
[3, 1, 2, 2, 1, 3, 3, 3, 1] => 3, 1, 2, 2, 1, 3, 3, 3, 1
[3, 1, 2, 2, 1, 3, 3, 3, 2] => 3, 1, 2, 2, 1, 3, 3, 3, 2
[3, 1, 2, 2, 1, 3, 3, 3, 3] => 3, 1, 2, 2, 1, 3, 3, 3, 3
[3, 1, 2, 2, 2, 1, 1, 1, 1] => 3, 1, 2, 2, 2, 1, 1, 1, 1
[3, 1, 2, 2, 2, 1, 1, 1, 2] => 3, 1, 2, 2, 2, 1, 1, 1, 2
[3, 1, 2, 2, 2, 1, 1, 1, 3] => 3, 1, 2, 2, 2, 1, 1, 1, 3
[3, 1, 2, 2, 2, 1, 1, 2, 1] => 3, 1, 2, 2, 2, 1, 1, 2, 1
[3, 1, 2, 2, 2, 1, 1, 2, 2] => 3, 1, 2, 2, 2, 1, 1, 2, 2
[3, 1, 2, 2, 2, 1, 1, 2, 3] => 3, 1, 2, 2, 2, 1, 1, 2, 3
[3, 1, 2, 2, 2, 1, 1, 3, 1] => 3, 1, 2, 2, 2, 1, 1, 3, 1
[3, 1, 2, 2, 2, 1, 1, 3, 2] => 3, 1, 2, 2, 2, 1, 1, 3, 2
[3, 1, 2, 2, 2, 1, 1, 3, 3] => 3, 1, 2, 2, 2, 1, 1, 3, 3
[3, 1, 2, 2, 2, 1, 2, 1, 1] => 3, 1, 2, 2, 2, 1, 2, 1, 1
[3, 1, 2, 2, 2, 1, 2, 1, 2] => 3, 1, 2, 2, 2, 1, 2, 1, 2
[3, 1, 2, 2, 2, 1, 2, 1, 3] => 3, 1, 2, 2, 2, 1, 2, 1, 3
[3, 1, 2, 2, 2, 1, 2, 2, 1] => 3, 1, 2, 2, 2, 1, 2, 2, 1
[3, 1, 2, 2, 2, 1, 2, 2, 2] => 3, 1, 2, 2, 2, 1, 2, 2, 2
[3, 1, 2, 2, 2, 1, 2, 2, 3] => 3, 1, 2, 2, 2, 1, 2, 2, 3
[3, 1, 2, 2, 2, 1, 2, 3, 1] => 3, 1, 2, 2, 2, 1, 2, 3, 1
[3, 1, 2, 2, 2, 1, 2, 3, 2] => 3, 1, 2, 2, 2, 1, 2, 3, 2
[3, 1, 2, 2, 2, 1, 2, 3, 3] => 3, 1, 2, 2, 2, 1, 2, 3, 3
[3, 1, 2, 2, 2, 1, 3, 1, 1] => 3, 1, 2, 2, 2, 1, 3, 1, 1
[3, 1, 2, 2, 2, 1, 3, 1, 2] => 3, 1, 2, 2, 2, 1, 3, 1, 2
[3, 1, 2, 2, 2, 1, 3, 1, 3] => 3, 1, 2, 2, 2, 1, 3, 1, 3
[3, 1, 2, 2, 2, 1, 3, 2, 1] => 3, 1, 2, 2, 2, 1, 3, 2, 1
[3, 1, 2, 2, 2, 1, 3, 2, 2] => 3, 1, 2, 2, 2, 1, 3, 2, 2
[3, 1, 2, 2, 2, 1, 3, 2, 3] => 3, 1, 2, 2, 2, 1, 3, 2, 3
[3, 1, 2, 2, 2, 1, 3, 3, 1] => 3, 1, 2, 2, 2, 1, 3, 3, 1
[3, 1, 2, 2, 2, 1, 3, 3, 2] => 3, 1, 2, 2, 2, 1, 3, 3, 2
[3, 1, 2, 2, 2, 1, 3, 3, 3] => 3, 1, 2, 2, 2, 1, 3, 3, 3
[3, 1, 2, 2, 2, 2, 1, 1, 1] => 3, 1, 2, 2, 2, 2, 1, 1, 1
[3, 1, 2, 2, 2, 2, 1, 1, 2] => 3, 1, 2, 2, 2, 2, 1, 1, 2
[3, 1, 2, 2, 2, 2, 1, 1, 3] => 3, 1, 2, 2, 2, 2, 1, 1, 3
[3, 1, 2, 2, 2, 2, 1, 2, 1] => 3, 1, 2, 2, 2, 2, 1, 2, 1
[3, 1, 2, 2, 2, 2, 1, 2, 2] => 3, 1, 2, 2, 2, 2, 1, 2, 2
[3, 1, 2, 2, 2, 2, 1, 2, 3] => 3, 1, 2, 2, 2, 2, 1, 2, 3
[3, 1, 2, 2, 2, 2, 1, 3, 1] => 3, 1, 2, 2, 2, 2, 1, 3, 1
[3, 1, 2, 2, 2, 2, 1, 3, 2] => 3, 1, 2, 2, 2, 2, 1, 3, 2
[3, 1, 2, 2, 2, 2, 1, 3, 3] => 3, 1, 2, 2, 2, 2, 1, 3, 3
[3, 1, 2, 2, 2, 2, 2, 1, 1] => 3, 1, 2, 2, 2, 2, 2, 1, 1
[3, 1, 2, 2, 2, 2, 2, 1, 2] => 3, 1, 2, 2, 2, 2, 2, 1, 2
[3, 1, 2, 2, 2, 2, 2, 1, 3] => 3, 1, 2, 2, 2, 2, 2, 1, 3
[3, 1, 2, 2, 2, 2, 2, 2, 1] => 3, 1, 2, 2, 2, 2, 2, 2, 1
[3, 1, 2, 2, 2, 2, 2, 2, 2] => 3, 1, 2, 2, 2, 2, 2, 2, 2
[3, 1, 2, 2, 2, 2, 2, 2, 3] => 3, 1, 2, 2, 2, 2, 2, 2, 3
[3, 1, 2, 2, 2, 2, 2, 3, 1] => 3, 1, 2, 2, 2, 2, 2, 3, 1
[3, 1, 2, 2, 2, 2, 2, 3, 2] => 3, 1, 2, 2, 2, 2, 2, 3, 2
[3, 1, 2, 2, 2, 2, 2, 3, 3] => 3, 1, 2, 2, 2, 2, 2, 3, 3
[3, 1, 2, 2, 2, 2, 3, 1, 1] => 3, 1, 2, 2, 2, 2, 3, 1, 1
[3, 1, 2, 2, 2, 2, 3, 1, 2] => 3, 1, 2, 2, 2, 2, 3, 1, 2
[3, 1, 2, 2, 2, 2, 3, 1, 3] => 3, 1, 2, 2, 2, 2, 3, 1, 3
[3, 1, 2, 2, 2, 2, 3, 2, 1] => 3, 1, 2, 2, 2, 2, 3, 2, 1
[3, 1, 2, 2, 2, 2, 3, 2, 2] => 3, 1, 2, 2, 2, 2, 3, 2, 2
[3, 1, 2, 2, 2, 2, 3, 2, 3] => 3, 1, 2, 2, 2, 2, 3, 2, 3
[3, 1, 2, 2, 2, 2, 3, 3, 1] => 3, 1, 2, 2, 2, 2, 3, 3, 1
[3, 1, 2, 2, 2, 2, 3, 3, 2] => 3, 1, 2, 2, 2, 2, 3, 3, 2
[3, 1, 2, 2, 2, 2, 3, 3, 3] => 3, 1, 2, 2, 2, 2, 3, 3, 3
[3, 1, 2, 2, 2, 3, 1, 1, 1] => 3, 1, 2, 2, 2, 3, 1, 1, 1
[3, 1, 2, 2, 2, 3, 1, 1, 2] => 3, 1, 2, 2, 2, 3, 1, 1, 2
[3, 1, 2, 2, 2, 3, 1, 1, 3] => 3, 1, 2, 2, 2, 3, 1, 1, 3
[3, 1, 2, 2, 2, 3, 1, 2, 1] => 3, 1, 2, 2, 2, 3, 1, 2, 1
[3, 1, 2, 2, 2, 3, 1, 2, 2] => 3, 1, 2, 2, 2, 3, 1, 2, 2
[3, 1, 2, 2, 2, 3, 1, 2, 3] => 3, 1, 2, 2, 2, 3, 1, 2, 3
[3, 1, 2, 2, 2, 3, 1, 3, 1] => 3, 1, 2, 2, 2, 3, 1, 3, 1
[3, 1, 2, 2, 2, 3, 1, 3, 2] => 3, 1, 2, 2, 2, 3, 1, 3, 2
[3, 1, 2, 2, 2, 3, 1, 3, 3] => 3, 1, 2, 2, 2, 3, 1, 3, 3
[3, 1, 2, 2, 2, 3, 2, 1, 1] => 3, 1, 2, 2, 2, 3, 2, 1, 1
[3, 1, 2, 2, 2, 3, 2, 1, 2] => 3, 1, 2, 2, 2, 3, 2, 1, 2
[3, 1, 2, 2, 2, 3, 2, 1, 3] => 3, 1, 2, 2, 2, 3, 2, 1, 3
[3, 1, 2, 2, 2, 3, 2, 2, 1] => 3, 1, 2, 2, 2, 3, 2, 2, 1
[3, 1, 2, 2, 2, 3, 2, 2, 2] => 3, 1, 2, 2, 2, 3, 2, 2, 2
[3, 1, 2, 2, 2, 3, 2, 2, 3] => 3, 1, 2, 2, 2, 3, 2, 2, 3
[3, 1, 2, 2, 2, 3, 2, 3, 1] => 3, 1, 2, 2, 2, 3, 2, 3, 1
[3, 1, 2, 2, 2, 3, 2, 3, 2] => 3, 1, 2, 2, 2, 3, 2, 3, 2
[3, 1, 2, 2, 2, 3, 2, 3, 3] => 3, 1, 2, 2, 2, 3, 2, 3, 3
[3, 1, 2, 2, 2, 3, 3, 1, 1] => 3, 1, 2, 2, 2, 3, 3, 1, 1
[3, 1, 2, 2, 2, 3, 3, 1, 2] => 3, 1, 2, 2, 2, 3, 3, 1, 2
[3, 1, 2, 2, 2, 3, 3, 1, 3] => 3, 1, 2, 2, 2, 3, 3, 1, 3
[3, 1, 2, 2, 2, 3, 3, 2, 1] => 3, 1, 2, 2, 2, 3, 3, 2, 1
[3, 1, 2, 2, 2, 3, 3, 2, 2] => 3, 1, 2, 2, 2, 3, 3, 2, 2
[3, 1, 2, 2, 2, 3, 3, 2, 3] => 3, 1, 2, 2, 2, 3, 3, 2, 3
[3, 1, 2, 2, 2, 3, 3, 3, 1] => 3, 1, 2, 2, 2, 3, 3, 3, 1
[3, 1, 2, 2, 2, 3, 3, 3, 2] => 3, 1, 2, 2, 2, 3, 3, 3, 2
[3, 1, 2, 2, 2, 3, 3, 3, 3] => 3, 1, 2, 2, 2, 3, 3, 3, 3
[3, 1, 2, 2, 3, 1, 1, 1, 1] => 3, 1, 2, 2, 3, 1, 1, 1, 1
[3, 1, 2, 2, 3, 1, 1, 1, 2] => 3, 1, 2, 2, 3, 1, 1, 1, 2
[3, 1, 2, 2, 3, 1, 1, 1, 3] => 3, 1, 2, 2, 3, 1, 1, 1, 3
[3, 1, 2, 2, 3, 1, 1, 2, 1] => 3, 1, 2, 2, 3, 1, 1, 2, 1
[3, 1, 2, 2, 3, 1, 1, 2, 2] => 3, 1, 2, 2, 3, 1, 1, 2, 2
[3, 1, 2, 2, 3, 1, 1, 2, 3] => 3, 1, 2, 2, 3, 1, 1, 2, 3
[3, 1, 2, 2, 3, 1, 1, 3, 1] => 3, 1, 2, 2, 3, 1, 1, 3, 1
[3, 1, 2, 2, 3, 1, 1, 3, 2] => 3, 1, 2, 2, 3, 1, 1, 3, 2
[3, 1, 2, 2, 3, 1, 1, 3, 3] => 3, 1, 2, 2, 3, 1, 1, 3, 3
[3, 1, 2, 2, 3, 1, 2, 1, 1] => 3, 1, 2, 2, 3, 1, 2, 1, 1
[3, 1, 2, 2, 3, 1, 2, 1, 2] => 3, 1, 2, 2, 3, 1, 2, 1, 2
[3, 1, 2, 2, 3, 1, 2, 1, 3] => 3, 1, 2, 2, 3, 1, 2, 1, 3
[3, 1, 2, 2, 3, 1, 2, 2, 1] => 3, 1, 2, 2, 3, 1, 2, 2, 1
[3, 1, 2, 2, 3, 1, 2, 2, 2] => 3, 1, 2, 2, 3, 1, 2, 2, 2
[3, 1, 2, 2, 3, 1, 2, 2, 3] => 3, 1, 2, 2, 3, 1, 2, 2, 3
[3, 1, 2, 2, 3, 1, 2, 3, 1] => 3, 1, 2, 2, 3, 1, 2, 3, 1
[3, 1, 2, 2, 3, 1, 2, 3, 2] => 3, 1, 2, 2, 3, 1, 2, 3, 2
[3, 1, 2, 2, 3, 1, 2, 3, 3] => 3, 1, 2, 2, 3, 1, 2, 3, 3
[3, 1, 2, 2, 3, 1, 3, 1, 1] => 3, 1, 2, 2, 3, 1, 3, 1, 1
[3, 1, 2, 2, 3, 1, 3, 1, 2] => 3, 1, 2, 2, 3, 1, 3, 1, 2
[3, 1, 2, 2, 3, 1, 3, 1, 3] => 3, 1, 2, 2, 3, 1, 3, 1, 3
[3, 1, 2, 2, 3, 1, 3, 2, 1] => 3, 1, 2, 2, 3, 1, 3, 2, 1
[3, 1, 2, 2, 3, 1, 3, 2, 2] => 3, 1, 2, 2, 3, 1, 3, 2, 2
[3, 1, 2, 2, 3, 1, 3, 2, 3] => 3, 1, 2, 2, 3, 1, 3, 2, 3
[3, 1, 2, 2, 3, 1, 3, 3, 1] => 3, 1, 2, 2, 3, 1, 3, 3, 1
[3, 1, 2, 2, 3, 1, 3, 3, 2] => 3, 1, 2, 2, 3, 1, 3, 3, 2
[3, 1, 2, 2, 3, 1, 3, 3, 3] => 3, 1, 2, 2, 3, 1, 3, 3, 3
[3, 1, 2, 2, 3, 2, 1, 1, 1] => 3, 1, 2, 2, 3, 2, 1, 1, 1
[3, 1, 2, 2, 3, 2, 1, 1, 2] => 3, 1, 2, 2, 3, 2, 1, 1, 2
[3, 1, 2, 2, 3, 2, 1, 1, 3] => 3, 1, 2, 2, 3, 2, 1, 1, 3
[3, 1, 2, 2, 3, 2, 1, 2, 1] => 3, 1, 2, 2, 3, 2, 1, 2, 1
[3, 1, 2, 2, 3, 2, 1, 2, 2] => 3, 1, 2, 2, 3, 2, 1, 2, 2
[3, 1, 2, 2, 3, 2, 1, 2, 3] => 3, 1, 2, 2, 3, 2, 1, 2, 3
[3, 1, 2, 2, 3, 2, 1, 3, 1] => 3, 1, 2, 2, 3, 2, 1, 3, 1
[3, 1, 2, 2, 3, 2, 1, 3, 2] => 3, 1, 2, 2, 3, 2, 1, 3, 2
[3, 1, 2, 2, 3, 2, 1, 3, 3] => 3, 1, 2, 2, 3, 2, 1, 3, 3
[3, 1, 2, 2, 3, 2, 2, 1, 1] => 3, 1, 2, 2, 3, 2, 2, 1, 1
[3, 1, 2, 2, 3, 2, 2, 1, 2] => 3, 1, 2, 2, 3, 2, 2, 1, 2
[3, 1, 2, 2, 3, 2, 2, 1, 3] => 3, 1, 2, 2, 3, 2, 2, 1, 3
[3, 1, 2, 2, 3, 2, 2, 2, 1] => 3, 1, 2, 2, 3, 2, 2, 2, 1
[3, 1, 2, 2, 3, 2, 2, 2, 2] => 3, 1, 2, 2, 3, 2, 2, 2, 2
[3, 1, 2, 2, 3, 2, 2, 2, 3] => 3, 1, 2, 2, 3, 2, 2, 2, 3
[3, 1, 2, 2, 3, 2, 2, 3, 1] => 3, 1, 2, 2, 3, 2, 2, 3, 1
[3, 1, 2, 2, 3, 2, 2, 3, 2] => 3, 1, 2, 2, 3, 2, 2, 3, 2
[3, 1, 2, 2, 3, 2, 2, 3, 3] => 3, 1, 2, 2, 3, 2, 2, 3, 3
[3, 1, 2, 2, 3, 2, 3, 1, 1] => 3, 1, 2, 2, 3, 2, 3, 1, 1
[3, 1, 2, 2, 3, 2, 3, 1, 2] => 3, 1, 2, 2, 3, 2, 3, 1, 2
[3, 1, 2, 2, 3, 2, 3, 1, 3] => 3, 1, 2, 2, 3, 2, 3, 1, 3
[3, 1, 2, 2, 3, 2, 3, 2, 1] => 3, 1, 2, 2, 3, 2, 3, 2, 1
[3, 1, 2, 2, 3, 2, 3, 2, 2] => 3, 1, 2, 2, 3, 2, 3, 2, 2
[3, 1, 2, 2, 3, 2, 3, 2, 3] => 3, 1, 2, 2, 3, 2, 3, 2, 3
[3, 1, 2, 2, 3, 2, 3, 3, 1] => 3, 1, 2, 2, 3, 2, 3, 3, 1
[3, 1, 2, 2, 3, 2, 3, 3, 2] => 3, 1, 2, 2, 3, 2, 3, 3, 2
[3, 1, 2, 2, 3, 2, 3, 3, 3] => 3, 1, 2, 2, 3, 2, 3, 3, 3
[3, 1, 2, 2, 3, 3, 1, 1, 1] => 3, 1, 2, 2, 3, 3, 1, 1, 1
[3, 1, 2, 2, 3, 3, 1, 1, 2] => 3, 1, 2, 2, 3, 3, 1, 1, 2
[3, 1, 2, 2, 3, 3, 1, 1, 3] => 3, 1, 2, 2, 3, 3, 1, 1, 3
[3, 1, 2, 2, 3, 3, 1, 2, 1] => 3, 1, 2, 2, 3, 3, 1, 2, 1
[3, 1, 2, 2, 3, 3, 1, 2, 2] => 3, 1, 2, 2, 3, 3, 1, 2, 2
[3, 1, 2, 2, 3, 3, 1, 2, 3] => 3, 1, 2, 2, 3, 3, 1, 2, 3
[3, 1, 2, 2, 3, 3, 1, 3, 1] => 3, 1, 2, 2, 3, 3, 1, 3, 1
[3, 1, 2, 2, 3, 3, 1, 3, 2] => 3, 1, 2, 2, 3, 3, 1, 3, 2
[3, 1, 2, 2, 3, 3, 1, 3, 3] => 3, 1, 2, 2, 3, 3, 1, 3, 3
[3, 1, 2, 2, 3, 3, 2, 1, 1] => 3, 1, 2, 2, 3, 3, 2, 1, 1
[3, 1, 2, 2, 3, 3, 2, 1, 2] => 3, 1, 2, 2, 3, 3, 2, 1, 2
[3, 1, 2, 2, 3, 3, 2, 1, 3] => 3, 1, 2, 2, 3, 3, 2, 1, 3
[3, 1, 2, 2, 3, 3, 2, 2, 1] => 3, 1, 2, 2, 3, 3, 2, 2, 1
[3, 1, 2, 2, 3, 3, 2, 2, 2] => 3, 1, 2, 2, 3, 3, 2, 2, 2
[3, 1, 2, 2, 3, 3, 2, 2, 3] => 3, 1, 2, 2, 3, 3, 2, 2, 3
[3, 1, 2, 2, 3, 3, 2, 3, 1] => 3, 1, 2, 2, 3, 3, 2, 3, 1
[3, 1, 2, 2, 3, 3, 2, 3, 2] => 3, 1, 2, 2, 3, 3, 2, 3, 2
[3, 1, 2, 2, 3, 3, 2, 3, 3] => 3, 1, 2, 2, 3, 3, 2, 3, 3
[3, 1, 2, 2, 3, 3, 3, 1, 1] => 3, 1, 2, 2, 3, 3, 3, 1, 1
[3, 1, 2, 2, 3, 3, 3, 1, 2] => 3, 1, 2, 2, 3, 3, 3, 1, 2
[3, 1, 2, 2, 3, 3, 3, 1, 3] => 3, 1, 2, 2, 3, 3, 3, 1, 3
[3, 1, 2, 2, 3, 3, 3, 2, 1] => 3, 1, 2, 2, 3, 3, 3, 2, 1
[3, 1, 2, 2, 3, 3, 3, 2, 2] => 3, 1, 2, 2, 3, 3, 3, 2, 2
[3, 1, 2, 2, 3, 3, 3, 2, 3] => 3, 1, 2, 2, 3, 3, 3, 2, 3
[3, 1, 2, 2, 3, 3, 3, 3, 1] => 3, 1, 2, 2, 3, 3, 3, 3, 1
[3, 1, 2, 2, 3, 3, 3, 3, 2] => 3, 1, 2, 2, 3, 3, 3, 3, 2
[3, 1, 2, 2, 3, 3, 3, 3, 3] => 3, 1, 2, 2, 3, 3, 3, 3, 3
[3, 1, 2, 3, 1, 1, 1, 1, 1] => 3, 1, 2, 3, 1, 1, 1, 1, 1
[3, 1, 2, 3, 1, 1, 1, 1, 2] => 3, 1, 2, 3, 1, 1, 1, 1, 2
[3, 1, 2, 3, 1, 1, 1, 1, 3] => 3, 1, 2, 3, 1, 1, 1, 1, 3
[3, 1, 2, 3, 1, 1, 1, 2, 1] => 3, 1, 2, 3, 1, 1, 1, 2, 1
[3, 1, 2, 3, 1, 1, 1, 2, 2] => 3, 1, 2, 3, 1, 1, 1, 2, 2
[3, 1, 2, 3, 1, 1, 1, 2, 3] => 3, 1, 2, 3, 1, 1, 1, 2, 3
[3, 1, 2, 3, 1, 1, 1, 3, 1] => 3, 1, 2, 3, 1, 1, 1, 3, 1
[3, 1, 2, 3, 1, 1, 1, 3, 2] => 3, 1, 2, 3, 1, 1, 1, 3, 2
[3, 1, 2, 3, 1, 1, 1, 3, 3] => 3, 1, 2, 3, 1, 1, 1, 3, 3
[3, 1, 2, 3, 1, 1, 2, 1, 1] => 3, 1, 2, 3, 1, 1, 2, 1, 1
[3, 1, 2, 3, 1, 1, 2, 1, 2] => 3, 1, 2, 3, 1, 1, 2, 1, 2
[3, 1, 2, 3, 1, 1, 2, 1, 3] => 3, 1, 2, 3, 1, 1, 2, 1, 3
[3, 1, 2, 3, 1, 1, 2, 2, 1] => 3, 1, 2, 3, 1, 1, 2, 2, 1
[3, 1, 2, 3, 1, 1, 2, 2, 2] => 3, 1, 2, 3, 1, 1, 2, 2, 2
[3, 1, 2, 3, 1, 1, 2, 2, 3] => 3, 1, 2, 3, 1, 1, 2, 2, 3
[3, 1, 2, 3, 1, 1, 2, 3, 1] => 3, 1, 2, 3, 1, 1, 2, 3, 1
[3, 1, 2, 3, 1, 1, 2, 3, 2] => 3, 1, 2, 3, 1, 1, 2, 3, 2
[3, 1, 2, 3, 1, 1, 2, 3, 3] => 3, 1, 2, 3, 1, 1, 2, 3, 3
[3, 1, 2, 3, 1, 1, 3, 1, 1] => 3, 1, 2, 3, 1, 1, 3, 1, 1
[3, 1, 2, 3, 1, 1, 3, 1, 2] => 3, 1, 2, 3, 1, 1, 3, 1, 2
[3, 1, 2, 3, 1, 1, 3, 1, 3] => 3, 1, 2, 3, 1, 1, 3, 1, 3
[3, 1, 2, 3, 1, 1, 3, 2, 1] => 3, 1, 2, 3, 1, 1, 3, 2, 1
[3, 1, 2, 3, 1, 1, 3, 2, 2] => 3, 1, 2, 3, 1, 1, 3, 2, 2
[3, 1, 2, 3, 1, 1, 3, 2, 3] => 3, 1, 2, 3, 1, 1, 3, 2, 3
[3, 1, 2, 3, 1, 1, 3, 3, 1] => 3, 1, 2, 3, 1, 1, 3, 3, 1
[3, 1, 2, 3, 1, 1, 3, 3, 2] => 3, 1, 2, 3, 1, 1, 3, 3, 2
[3, 1, 2, 3, 1, 1, 3, 3, 3] => 3, 1, 2, 3, 1, 1, 3, 3, 3
[3, 1, 2, 3, 1, 2, 1, 1, 1] => 3, 1, 2, 3, 1, 2, 1, 1, 1
[3, 1, 2, 3, 1, 2, 1, 1, 2] => 3, 1, 2, 3, 1, 2, 1, 1, 2
[3, 1, 2, 3, 1, 2, 1, 1, 3] => 3, 1, 2, 3, 1, 2, 1, 1, 3
[3, 1, 2, 3, 1, 2, 1, 2, 1] => 3, 1, 2, 3, 1, 2, 1, 2, 1
[3, 1, 2, 3, 1, 2, 1, 2, 2] => 3, 1, 2, 3, 1, 2, 1, 2, 2
[3, 1, 2, 3, 1, 2, 1, 2, 3] => 3, 1, 2, 3, 1, 2, 1, 2, 3
[3, 1, 2, 3, 1, 2, 1, 3, 1] => 3, 1, 2, 3, 1, 2, 1, 3, 1
[3, 1, 2, 3, 1, 2, 1, 3, 2] => 3, 1, 2, 3, 1, 2, 1, 3, 2
[3, 1, 2, 3, 1, 2, 1, 3, 3] => 3, 1, 2, 3, 1, 2, 1, 3, 3
[3, 1, 2, 3, 1, 2, 2, 1, 1] => 3, 1, 2, 3, 1, 2, 2, 1, 1
[3, 1, 2, 3, 1, 2, 2, 1, 2] => 3, 1, 2, 3, 1, 2, 2, 1, 2
[3, 1, 2, 3, 1, 2, 2, 1, 3] => 3, 1, 2, 3, 1, 2, 2, 1, 3
[3, 1, 2, 3, 1, 2, 2, 2, 1] => 3, 1, 2, 3, 1, 2, 2, 2, 1
[3, 1, 2, 3, 1, 2, 2, 2, 2] => 3, 1, 2, 3, 1, 2, 2, 2, 2
[3, 1, 2, 3, 1, 2, 2, 2, 3] => 3, 1, 2, 3, 1, 2, 2, 2, 3
[3, 1, 2, 3, 1, 2, 2, 3, 1] => 3, 1, 2, 3, 1, 2, 2, 3, 1
[3, 1, 2, 3, 1, 2, 2, 3, 2] => 3, 1, 2, 3, 1, 2, 2, 3, 2
[3, 1, 2, 3, 1, 2, 2, 3, 3] => 3, 1, 2, 3, 1, 2, 2, 3, 3
[3, 1, 2, 3, 1, 2, 3, 1, 1] => 3, 1, 2, 3, 1, 2, 3, 1, 1
[3, 1, 2, 3, 1, 2, 3, 1, 2] => 3, 1, 2, 3, 1, 2, 3, 1, 2
[3, 1, 2, 3, 1, 2, 3, 1, 3] => 3, 1, 2, 3, 1, 2, 3, 1, 3
[3, 1, 2, 3, 1, 2, 3, 2, 1] => 3, 1, 2, 3, 1, 2, 3, 2, 1
[3, 1, 2, 3, 1, 2, 3, 2, 2] => 3, 1, 2, 3, 1, 2, 3, 2, 2
[3, 1, 2, 3, 1, 2, 3, 2, 3] => 3, 1, 2, 3, 1, 2, 3, 2, 3
[3, 1, 2, 3, 1, 2, 3, 3, 1] => 3, 1, 2, 3, 1, 2, 3, 3, 1
[3, 1, 2, 3, 1, 2, 3, 3, 2] => 3, 1, 2, 3, 1, 2, 3, 3, 2
[3, 1, 2, 3, 1, 2, 3, 3, 3] => 3, 1, 2, 3, 1, 2, 3, 3, 3
[3, 1, 2, 3, 1, 3, 1, 1, 1] => 3, 1, 2, 3, 1, 3, 1, 1, 1
[3, 1, 2, 3, 1, 3, 1, 1, 2] => 3, 1, 2, 3, 1, 3, 1, 1, 2
[3, 1, 2, 3, 1, 3, 1, 1, 3] => 3, 1, 2, 3, 1, 3, 1, 1, 3
[3, 1, 2, 3, 1, 3, 1, 2, 1] => 3, 1, 2, 3, 1, 3, 1, 2, 1
[3, 1, 2, 3, 1, 3, 1, 2, 2] => 3, 1, 2, 3, 1, 3, 1, 2, 2
[3, 1, 2, 3, 1, 3, 1, 2, 3] => 3, 1, 2, 3, 1, 3, 1, 2, 3
[3, 1, 2, 3, 1, 3, 1, 3, 1] => 3, 1, 2, 3, 1, 3, 1, 3, 1
[3, 1, 2, 3, 1, 3, 1, 3, 2] => 3, 1, 2, 3, 1, 3, 1, 3, 2
[3, 1, 2, 3, 1, 3, 1, 3, 3] => 3, 1, 2, 3, 1, 3, 1, 3, 3
[3, 1, 2, 3, 1, 3, 2, 1, 1] => 3, 1, 2, 3, 1, 3, 2, 1, 1
[3, 1, 2, 3, 1, 3, 2, 1, 2] => 3, 1, 2, 3, 1, 3, 2, 1, 2
[3, 1, 2, 3, 1, 3, 2, 1, 3] => 3, 1, 2, 3, 1, 3, 2, 1, 3
[3, 1, 2, 3, 1, 3, 2, 2, 1] => 3, 1, 2, 3, 1, 3, 2, 2, 1
[3, 1, 2, 3, 1, 3, 2, 2, 2] => 3, 1, 2, 3, 1, 3, 2, 2, 2
[3, 1, 2, 3, 1, 3, 2, 2, 3] => 3, 1, 2, 3, 1, 3, 2, 2, 3
[3, 1, 2, 3, 1, 3, 2, 3, 1] => 3, 1, 2, 3, 1, 3, 2, 3, 1
[3, 1, 2, 3, 1, 3, 2, 3, 2] => 3, 1, 2, 3, 1, 3, 2, 3, 2
[3, 1, 2, 3, 1, 3, 2, 3, 3] => 3, 1, 2, 3, 1, 3, 2, 3, 3
[3, 1, 2, 3, 1, 3, 3, 1, 1] => 3, 1, 2, 3, 1, 3, 3, 1, 1
[3, 1, 2, 3, 1, 3, 3, 1, 2] => 3, 1, 2, 3, 1, 3, 3, 1, 2
[3, 1, 2, 3, 1, 3, 3, 1, 3] => 3, 1, 2, 3, 1, 3, 3, 1, 3
[3, 1, 2, 3, 1, 3, 3, 2, 1] => 3, 1, 2, 3, 1, 3, 3, 2, 1
[3, 1, 2, 3, 1, 3, 3, 2, 2] => 3, 1, 2, 3, 1, 3, 3, 2, 2
[3, 1, 2, 3, 1, 3, 3, 2, 3] => 3, 1, 2, 3, 1, 3, 3, 2, 3
[3, 1, 2, 3, 1, 3, 3, 3, 1] => 3, 1, 2, 3, 1, 3, 3, 3, 1
[3, 1, 2, 3, 1, 3, 3, 3, 2] => 3, 1, 2, 3, 1, 3, 3, 3, 2
[3, 1, 2, 3, 1, 3, 3, 3, 3] => 3, 1, 2, 3, 1, 3, 3, 3, 3
[3, 1, 2, 3, 2, 1, 1, 1, 1] => 3, 1, 2, 3, 2, 1, 1, 1, 1
[3, 1, 2, 3, 2, 1, 1, 1, 2] => 3, 1, 2, 3, 2, 1, 1, 1, 2
[3, 1, 2, 3, 2, 1, 1, 1, 3] => 3, 1, 2, 3, 2, 1, 1, 1, 3
[3, 1, 2, 3, 2, 1, 1, 2, 1] => 3, 1, 2, 3, 2, 1, 1, 2, 1
[3, 1, 2, 3, 2, 1, 1, 2, 2] => 3, 1, 2, 3, 2, 1, 1, 2, 2
[3, 1, 2, 3, 2, 1, 1, 2, 3] => 3, 1, 2, 3, 2, 1, 1, 2, 3
[3, 1, 2, 3, 2, 1, 1, 3, 1] => 3, 1, 2, 3, 2, 1, 1, 3, 1
[3, 1, 2, 3, 2, 1, 1, 3, 2] => 3, 1, 2, 3, 2, 1, 1, 3, 2
[3, 1, 2, 3, 2, 1, 1, 3, 3] => 3, 1, 2, 3, 2, 1, 1, 3, 3
[3, 1, 2, 3, 2, 1, 2, 1, 1] => 3, 1, 2, 3, 2, 1, 2, 1, 1
[3, 1, 2, 3, 2, 1, 2, 1, 2] => 3, 1, 2, 3, 2, 1, 2, 1, 2
[3, 1, 2, 3, 2, 1, 2, 1, 3] => 3, 1, 2, 3, 2, 1, 2, 1, 3
[3, 1, 2, 3, 2, 1, 2, 2, 1] => 3, 1, 2, 3, 2, 1, 2, 2, 1
[3, 1, 2, 3, 2, 1, 2, 2, 2] => 3, 1, 2, 3, 2, 1, 2, 2, 2
[3, 1, 2, 3, 2, 1, 2, 2, 3] => 3, 1, 2, 3, 2, 1, 2, 2, 3
[3, 1, 2, 3, 2, 1, 2, 3, 1] => 3, 1, 2, 3, 2, 1, 2, 3, 1
[3, 1, 2, 3, 2, 1, 2, 3, 2] => 3, 1, 2, 3, 2, 1, 2, 3, 2
[3, 1, 2, 3, 2, 1, 2, 3, 3] => 3, 1, 2, 3, 2, 1, 2, 3, 3
[3, 1, 2, 3, 2, 1, 3, 1, 1] => 3, 1, 2, 3, 2, 1, 3, 1, 1
[3, 1, 2, 3, 2, 1, 3, 1, 2] => 3, 1, 2, 3, 2, 1, 3, 1, 2
[3, 1, 2, 3, 2, 1, 3, 1, 3] => 3, 1, 2, 3, 2, 1, 3, 1, 3
[3, 1, 2, 3, 2, 1, 3, 2, 1] => 3, 1, 2, 3, 2, 1, 3, 2, 1
[3, 1, 2, 3, 2, 1, 3, 2, 2] => 3, 1, 2, 3, 2, 1, 3, 2, 2
[3, 1, 2, 3, 2, 1, 3, 2, 3] => 3, 1, 2, 3, 2, 1, 3, 2, 3
[3, 1, 2, 3, 2, 1, 3, 3, 1] => 3, 1, 2, 3, 2, 1, 3, 3, 1
[3, 1, 2, 3, 2, 1, 3, 3, 2] => 3, 1, 2, 3, 2, 1, 3, 3, 2
[3, 1, 2, 3, 2, 1, 3, 3, 3] => 3, 1, 2, 3, 2, 1, 3, 3, 3
[3, 1, 2, 3, 2, 2, 1, 1, 1] => 3, 1, 2, 3, 2, 2, 1, 1, 1
[3, 1, 2, 3, 2, 2, 1, 1, 2] => 3, 1, 2, 3, 2, 2, 1, 1, 2
[3, 1, 2, 3, 2, 2, 1, 1, 3] => 3, 1, 2, 3, 2, 2, 1, 1, 3
[3, 1, 2, 3, 2, 2, 1, 2, 1] => 3, 1, 2, 3, 2, 2, 1, 2, 1
[3, 1, 2, 3, 2, 2, 1, 2, 2] => 3, 1, 2, 3, 2, 2, 1, 2, 2
[3, 1, 2, 3, 2, 2, 1, 2, 3] => 3, 1, 2, 3, 2, 2, 1, 2, 3
[3, 1, 2, 3, 2, 2, 1, 3, 1] => 3, 1, 2, 3, 2, 2, 1, 3, 1
[3, 1, 2, 3, 2, 2, 1, 3, 2] => 3, 1, 2, 3, 2, 2, 1, 3, 2
[3, 1, 2, 3, 2, 2, 1, 3, 3] => 3, 1, 2, 3, 2, 2, 1, 3, 3
[3, 1, 2, 3, 2, 2, 2, 1, 1] => 3, 1, 2, 3, 2, 2, 2, 1, 1
[3, 1, 2, 3, 2, 2, 2, 1, 2] => 3, 1, 2, 3, 2, 2, 2, 1, 2
[3, 1, 2, 3, 2, 2, 2, 1, 3] => 3, 1, 2, 3, 2, 2, 2, 1, 3
[3, 1, 2, 3, 2, 2, 2, 2, 1] => 3, 1, 2, 3, 2, 2, 2, 2, 1
[3, 1, 2, 3, 2, 2, 2, 2, 2] => 3, 1, 2, 3, 2, 2, 2, 2, 2
[3, 1, 2, 3, 2, 2, 2, 2, 3] => 3, 1, 2, 3, 2, 2, 2, 2, 3
[3, 1, 2, 3, 2, 2, 2, 3, 1] => 3, 1, 2, 3, 2, 2, 2, 3, 1
[3, 1, 2, 3, 2, 2, 2, 3, 2] => 3, 1, 2, 3, 2, 2, 2, 3, 2
[3, 1, 2, 3, 2, 2, 2, 3, 3] => 3, 1, 2, 3, 2, 2, 2, 3, 3
[3, 1, 2, 3, 2, 2, 3, 1, 1] => 3, 1, 2, 3, 2, 2, 3, 1, 1
[3, 1, 2, 3, 2, 2, 3, 1, 2] => 3, 1, 2, 3, 2, 2, 3, 1, 2
[3, 1, 2, 3, 2, 2, 3, 1, 3] => 3, 1, 2, 3, 2, 2, 3, 1, 3
[3, 1, 2, 3, 2, 2, 3, 2, 1] => 3, 1, 2, 3, 2, 2, 3, 2, 1
[3, 1, 2, 3, 2, 2, 3, 2, 2] => 3, 1, 2, 3, 2, 2, 3, 2, 2
[3, 1, 2, 3, 2, 2, 3, 2, 3] => 3, 1, 2, 3, 2, 2, 3, 2, 3
[3, 1, 2, 3, 2, 2, 3, 3, 1] => 3, 1, 2, 3, 2, 2, 3, 3, 1
[3, 1, 2, 3, 2, 2, 3, 3, 2] => 3, 1, 2, 3, 2, 2, 3, 3, 2
[3, 1, 2, 3, 2, 2, 3, 3, 3] => 3, 1, 2, 3, 2, 2, 3, 3, 3
[3, 1, 2, 3, 2, 3, 1, 1, 1] => 3, 1, 2, 3, 2, 3, 1, 1, 1
[3, 1, 2, 3, 2, 3, 1, 1, 2] => 3, 1, 2, 3, 2, 3, 1, 1, 2
[3, 1, 2, 3, 2, 3, 1, 1, 3] => 3, 1, 2, 3, 2, 3, 1, 1, 3
[3, 1, 2, 3, 2, 3, 1, 2, 1] => 3, 1, 2, 3, 2, 3, 1, 2, 1
[3, 1, 2, 3, 2, 3, 1, 2, 2] => 3, 1, 2, 3, 2, 3, 1, 2, 2
[3, 1, 2, 3, 2, 3, 1, 2, 3] => 3, 1, 2, 3, 2, 3, 1, 2, 3
[3, 1, 2, 3, 2, 3, 1, 3, 1] => 3, 1, 2, 3, 2, 3, 1, 3, 1
[3, 1, 2, 3, 2, 3, 1, 3, 2] => 3, 1, 2, 3, 2, 3, 1, 3, 2
[3, 1, 2, 3, 2, 3, 1, 3, 3] => 3, 1, 2, 3, 2, 3, 1, 3, 3
[3, 1, 2, 3, 2, 3, 2, 1, 1] => 3, 1, 2, 3, 2, 3, 2, 1, 1
[3, 1, 2, 3, 2, 3, 2, 1, 2] => 3, 1, 2, 3, 2, 3, 2, 1, 2
[3, 1, 2, 3, 2, 3, 2, 1, 3] => 3, 1, 2, 3, 2, 3, 2, 1, 3
[3, 1, 2, 3, 2, 3, 2, 2, 1] => 3, 1, 2, 3, 2, 3, 2, 2, 1
[3, 1, 2, 3, 2, 3, 2, 2, 2] => 3, 1, 2, 3, 2, 3, 2, 2, 2
[3, 1, 2, 3, 2, 3, 2, 2, 3] => 3, 1, 2, 3, 2, 3, 2, 2, 3
[3, 1, 2, 3, 2, 3, 2, 3, 1] => 3, 1, 2, 3, 2, 3, 2, 3, 1
[3, 1, 2, 3, 2, 3, 2, 3, 2] => 3, 1, 2, 3, 2, 3, 2, 3, 2
[3, 1, 2, 3, 2, 3, 2, 3, 3] => 3, 1, 2, 3, 2, 3, 2, 3, 3
[3, 1, 2, 3, 2, 3, 3, 1, 1] => 3, 1, 2, 3, 2, 3, 3, 1, 1
[3, 1, 2, 3, 2, 3, 3, 1, 2] => 3, 1, 2, 3, 2, 3, 3, 1, 2
[3, 1, 2, 3, 2, 3, 3, 1, 3] => 3, 1, 2, 3, 2, 3, 3, 1, 3
[3, 1, 2, 3, 2, 3, 3, 2, 1] => 3, 1, 2, 3, 2, 3, 3, 2, 1
[3, 1, 2, 3, 2, 3, 3, 2, 2] => 3, 1, 2, 3, 2, 3, 3, 2, 2
[3, 1, 2, 3, 2, 3, 3, 2, 3] => 3, 1, 2, 3, 2, 3, 3, 2, 3
[3, 1, 2, 3, 2, 3, 3, 3, 1] => 3, 1, 2, 3, 2, 3, 3, 3, 1
[3, 1, 2, 3, 2, 3, 3, 3, 2] => 3, 1, 2, 3, 2, 3, 3, 3, 2
[3, 1, 2, 3, 2, 3, 3, 3, 3] => 3, 1, 2, 3, 2, 3, 3, 3, 3
[3, 1, 2, 3, 3, 1, 1, 1, 1] => 3, 1, 2, 3, 3, 1, 1, 1, 1
[3, 1, 2, 3, 3, 1, 1, 1, 2] => 3, 1, 2, 3, 3, 1, 1, 1, 2
[3, 1, 2, 3, 3, 1, 1, 1, 3] => 3, 1, 2, 3, 3, 1, 1, 1, 3
[3, 1, 2, 3, 3, 1, 1, 2, 1] => 3, 1, 2, 3, 3, 1, 1, 2, 1
[3, 1, 2, 3, 3, 1, 1, 2, 2] => 3, 1, 2, 3, 3, 1, 1, 2, 2
[3, 1, 2, 3, 3, 1, 1, 2, 3] => 3, 1, 2, 3, 3, 1, 1, 2, 3
[3, 1, 2, 3, 3, 1, 1, 3, 1] => 3, 1, 2, 3, 3, 1, 1, 3, 1
[3, 1, 2, 3, 3, 1, 1, 3, 2] => 3, 1, 2, 3, 3, 1, 1, 3, 2
[3, 1, 2, 3, 3, 1, 1, 3, 3] => 3, 1, 2, 3, 3, 1, 1, 3, 3
[3, 1, 2, 3, 3, 1, 2, 1, 1] => 3, 1, 2, 3, 3, 1, 2, 1, 1
[3, 1, 2, 3, 3, 1, 2, 1, 2] => 3, 1, 2, 3, 3, 1, 2, 1, 2
[3, 1, 2, 3, 3, 1, 2, 1, 3] => 3, 1, 2, 3, 3, 1, 2, 1, 3
[3, 1, 2, 3, 3, 1, 2, 2, 1] => 3, 1, 2, 3, 3, 1, 2, 2, 1
[3, 1, 2, 3, 3, 1, 2, 2, 2] => 3, 1, 2, 3, 3, 1, 2, 2, 2
[3, 1, 2, 3, 3, 1, 2, 2, 3] => 3, 1, 2, 3, 3, 1, 2, 2, 3
[3, 1, 2, 3, 3, 1, 2, 3, 1] => 3, 1, 2, 3, 3, 1, 2, 3, 1
[3, 1, 2, 3, 3, 1, 2, 3, 2] => 3, 1, 2, 3, 3, 1, 2, 3, 2
[3, 1, 2, 3, 3, 1, 2, 3, 3] => 3, 1, 2, 3, 3, 1, 2, 3, 3
[3, 1, 2, 3, 3, 1, 3, 1, 1] => 3, 1, 2, 3, 3, 1, 3, 1, 1
[3, 1, 2, 3, 3, 1, 3, 1, 2] => 3, 1, 2, 3, 3, 1, 3, 1, 2
[3, 1, 2, 3, 3, 1, 3, 1, 3] => 3, 1, 2, 3, 3, 1, 3, 1, 3
[3, 1, 2, 3, 3, 1, 3, 2, 1] => 3, 1, 2, 3, 3, 1, 3, 2, 1
[3, 1, 2, 3, 3, 1, 3, 2, 2] => 3, 1, 2, 3, 3, 1, 3, 2, 2
[3, 1, 2, 3, 3, 1, 3, 2, 3] => 3, 1, 2, 3, 3, 1, 3, 2, 3
[3, 1, 2, 3, 3, 1, 3, 3, 1] => 3, 1, 2, 3, 3, 1, 3, 3, 1
[3, 1, 2, 3, 3, 1, 3, 3, 2] => 3, 1, 2, 3, 3, 1, 3, 3, 2
[3, 1, 2, 3, 3, 1, 3, 3, 3] => 3, 1, 2, 3, 3, 1, 3, 3, 3
[3, 1, 2, 3, 3, 2, 1, 1, 1] => 3, 1, 2, 3, 3, 2, 1, 1, 1
[3, 1, 2, 3, 3, 2, 1, 1, 2] => 3, 1, 2, 3, 3, 2, 1, 1, 2
[3, 1, 2, 3, 3, 2, 1, 1, 3] => 3, 1, 2, 3, 3, 2, 1, 1, 3
[3, 1, 2, 3, 3, 2, 1, 2, 1] => 3, 1, 2, 3, 3, 2, 1, 2, 1
[3, 1, 2, 3, 3, 2, 1, 2, 2] => 3, 1, 2, 3, 3, 2, 1, 2, 2
[3, 1, 2, 3, 3, 2, 1, 2, 3] => 3, 1, 2, 3, 3, 2, 1, 2, 3
[3, 1, 2, 3, 3, 2, 1, 3, 1] => 3, 1, 2, 3, 3, 2, 1, 3, 1
[3, 1, 2, 3, 3, 2, 1, 3, 2] => 3, 1, 2, 3, 3, 2, 1, 3, 2
[3, 1, 2, 3, 3, 2, 1, 3, 3] => 3, 1, 2, 3, 3, 2, 1, 3, 3
[3, 1, 2, 3, 3, 2, 2, 1, 1] => 3, 1, 2, 3, 3, 2, 2, 1, 1
[3, 1, 2, 3, 3, 2, 2, 1, 2] => 3, 1, 2, 3, 3, 2, 2, 1, 2
[3, 1, 2, 3, 3, 2, 2, 1, 3] => 3, 1, 2, 3, 3, 2, 2, 1, 3
[3, 1, 2, 3, 3, 2, 2, 2, 1] => 3, 1, 2, 3, 3, 2, 2, 2, 1
[3, 1, 2, 3, 3, 2, 2, 2, 2] => 3, 1, 2, 3, 3, 2, 2, 2, 2
[3, 1, 2, 3, 3, 2, 2, 2, 3] => 3, 1, 2, 3, 3, 2, 2, 2, 3
[3, 1, 2, 3, 3, 2, 2, 3, 1] => 3, 1, 2, 3, 3, 2, 2, 3, 1
[3, 1, 2, 3, 3, 2, 2, 3, 2] => 3, 1, 2, 3, 3, 2, 2, 3, 2
[3, 1, 2, 3, 3, 2, 2, 3, 3] => 3, 1, 2, 3, 3, 2, 2, 3, 3
[3, 1, 2, 3, 3, 2, 3, 1, 1] => 3, 1, 2, 3, 3, 2, 3, 1, 1
[3, 1, 2, 3, 3, 2, 3, 1, 2] => 3, 1, 2, 3, 3, 2, 3, 1, 2
[3, 1, 2, 3, 3, 2, 3, 1, 3] => 3, 1, 2, 3, 3, 2, 3, 1, 3
[3, 1, 2, 3, 3, 2, 3, 2, 1] => 3, 1, 2, 3, 3, 2, 3, 2, 1
[3, 1, 2, 3, 3, 2, 3, 2, 2] => 3, 1, 2, 3, 3, 2, 3, 2, 2
[3, 1, 2, 3, 3, 2, 3, 2, 3] => 3, 1, 2, 3, 3, 2, 3, 2, 3
[3, 1, 2, 3, 3, 2, 3, 3, 1] => 3, 1, 2, 3, 3, 2, 3, 3, 1
[3, 1, 2, 3, 3, 2, 3, 3, 2] => 3, 1, 2, 3, 3, 2, 3, 3, 2
[3, 1, 2, 3, 3, 2, 3, 3, 3] => 3, 1, 2, 3, 3, 2, 3, 3, 3
[3, 1, 2, 3, 3, 3, 1, 1, 1] => 3, 1, 2, 3, 3, 3, 1, 1, 1
[3, 1, 2, 3, 3, 3, 1, 1, 2] => 3, 1, 2, 3, 3, 3, 1, 1, 2
[3, 1, 2, 3, 3, 3, 1, 1, 3] => 3, 1, 2, 3, 3, 3, 1, 1, 3
[3, 1, 2, 3, 3, 3, 1, 2, 1] => 3, 1, 2, 3, 3, 3, 1, 2, 1
[3, 1, 2, 3, 3, 3, 1, 2, 2] => 3, 1, 2, 3, 3, 3, 1, 2, 2
[3, 1, 2, 3, 3, 3, 1, 2, 3] => 3, 1, 2, 3, 3, 3, 1, 2, 3
[3, 1, 2, 3, 3, 3, 1, 3, 1] => 3, 1, 2, 3, 3, 3, 1, 3, 1
[3, 1, 2, 3, 3, 3, 1, 3, 2] => 3, 1, 2, 3, 3, 3, 1, 3, 2
[3, 1, 2, 3, 3, 3, 1, 3, 3] => 3, 1, 2, 3, 3, 3, 1, 3, 3
[3, 1, 2, 3, 3, 3, 2, 1, 1] => 3, 1, 2, 3, 3, 3, 2, 1, 1
[3, 1, 2, 3, 3, 3, 2, 1, 2] => 3, 1, 2, 3, 3, 3, 2, 1, 2
[3, 1, 2, 3, 3, 3, 2, 1, 3] => 3, 1, 2, 3, 3, 3, 2, 1, 3
[3, 1, 2, 3, 3, 3, 2, 2, 1] => 3, 1, 2, 3, 3, 3, 2, 2, 1
[3, 1, 2, 3, 3, 3, 2, 2, 2] => 3, 1, 2, 3, 3, 3, 2, 2, 2
[3, 1, 2, 3, 3, 3, 2, 2, 3] => 3, 1, 2, 3, 3, 3, 2, 2, 3
[3, 1, 2, 3, 3, 3, 2, 3, 1] => 3, 1, 2, 3, 3, 3, 2, 3, 1
[3, 1, 2, 3, 3, 3, 2, 3, 2] => 3, 1, 2, 3, 3, 3, 2, 3, 2
[3, 1, 2, 3, 3, 3, 2, 3, 3] => 3, 1, 2, 3, 3, 3, 2, 3, 3
[3, 1, 2, 3, 3, 3, 3, 1, 1] => 3, 1, 2, 3, 3, 3, 3, 1, 1
[3, 1, 2, 3, 3, 3, 3, 1, 2] => 3, 1, 2, 3, 3, 3, 3, 1, 2
[3, 1, 2, 3, 3, 3, 3, 1, 3] => 3, 1, 2, 3, 3, 3, 3, 1, 3
[3, 1, 2, 3, 3, 3, 3, 2, 1] => 3, 1, 2, 3, 3, 3, 3, 2, 1
[3, 1, 2, 3, 3, 3, 3, 2, 2] => 3, 1, 2, 3, 3, 3, 3, 2, 2
[3, 1, 2, 3, 3, 3, 3, 2, 3] => 3, 1, 2, 3, 3, 3, 3, 2, 3
[3, 1, 2, 3, 3, 3, 3, 3, 1] => 3, 1, 2, 3, 3, 3, 3, 3, 1
[3, 1, 2, 3, 3, 3, 3, 3, 2] => 3, 1, 2, 3, 3, 3, 3, 3, 2
[3, 1, 2, 3, 3, 3, 3, 3, 3] => 3, 1, 2, 3, 3, 3, 3, 3, 3
[3, 1, 3, 1, 1, 1, 1, 1, 1] => 3, 1, 3, 1, 1, 1, 1, 1, 1
[3, 1, 3, 1, 1, 1, 1, 1, 2] => 3, 1, 3, 1, 1, 1, 1, 1, 2
[3, 1, 3, 1, 1, 1, 1, 1, 3] => 3, 1, 3, 1, 1, 1, 1, 1, 3
[3, 1, 3, 1, 1, 1, 1, 2, 1] => 3, 1, 3, 1, 1, 1, 1, 2, 1
[3, 1, 3, 1, 1, 1, 1, 2, 2] => 3, 1, 3, 1, 1, 1, 1, 2, 2
[3, 1, 3, 1, 1, 1, 1, 2, 3] => 3, 1, 3, 1, 1, 1, 1, 2, 3
[3, 1, 3, 1, 1, 1, 1, 3, 1] => 3, 1, 3, 1, 1, 1, 1, 3, 1
[3, 1, 3, 1, 1, 1, 1, 3, 2] => 3, 1, 3, 1, 1, 1, 1, 3, 2
[3, 1, 3, 1, 1, 1, 1, 3, 3] => 3, 1, 3, 1, 1, 1, 1, 3, 3
[3, 1, 3, 1, 1, 1, 2, 1, 1] => 3, 1, 3, 1, 1, 1, 2, 1, 1
[3, 1, 3, 1, 1, 1, 2, 1, 2] => 3, 1, 3, 1, 1, 1, 2, 1, 2
[3, 1, 3, 1, 1, 1, 2, 1, 3] => 3, 1, 3, 1, 1, 1, 2, 1, 3
[3, 1, 3, 1, 1, 1, 2, 2, 1] => 3, 1, 3, 1, 1, 1, 2, 2, 1
[3, 1, 3, 1, 1, 1, 2, 2, 2] => 3, 1, 3, 1, 1, 1, 2, 2, 2
[3, 1, 3, 1, 1, 1, 2, 2, 3] => 3, 1, 3, 1, 1, 1, 2, 2, 3
[3, 1, 3, 1, 1, 1, 2, 3, 1] => 3, 1, 3, 1, 1, 1, 2, 3, 1
[3, 1, 3, 1, 1, 1, 2, 3, 2] => 3, 1, 3, 1, 1, 1, 2, 3, 2
[3, 1, 3, 1, 1, 1, 2, 3, 3] => 3, 1, 3, 1, 1, 1, 2, 3, 3
[3, 1, 3, 1, 1, 1, 3, 1, 1] => 3, 1, 3, 1, 1, 1, 3, 1, 1
[3, 1, 3, 1, 1, 1, 3, 1, 2] => 3, 1, 3, 1, 1, 1, 3, 1, 2
[3, 1, 3, 1, 1, 1, 3, 1, 3] => 3, 1, 3, 1, 1, 1, 3, 1, 3
[3, 1, 3, 1, 1, 1, 3, 2, 1] => 3, 1, 3, 1, 1, 1, 3, 2, 1
[3, 1, 3, 1, 1, 1, 3, 2, 2] => 3, 1, 3, 1, 1, 1, 3, 2, 2
[3, 1, 3, 1, 1, 1, 3, 2, 3] => 3, 1, 3, 1, 1, 1, 3, 2, 3
[3, 1, 3, 1, 1, 1, 3, 3, 1] => 3, 1, 3, 1, 1, 1, 3, 3, 1
[3, 1, 3, 1, 1, 1, 3, 3, 2] => 3, 1, 3, 1, 1, 1, 3, 3, 2
[3, 1, 3, 1, 1, 1, 3, 3, 3] => 3, 1, 3, 1, 1, 1, 3, 3, 3
[3, 1, 3, 1, 1, 2, 1, 1, 1] => 3, 1, 3, 1, 1, 2, 1, 1, 1
[3, 1, 3, 1, 1, 2, 1, 1, 2] => 3, 1, 3, 1, 1, 2, 1, 1, 2
[3, 1, 3, 1, 1, 2, 1, 1, 3] => 3, 1, 3, 1, 1, 2, 1, 1, 3
[3, 1, 3, 1, 1, 2, 1, 2, 1] => 3, 1, 3, 1, 1, 2, 1, 2, 1
[3, 1, 3, 1, 1, 2, 1, 2, 2] => 3, 1, 3, 1, 1, 2, 1, 2, 2
[3, 1, 3, 1, 1, 2, 1, 2, 3] => 3, 1, 3, 1, 1, 2, 1, 2, 3
[3, 1, 3, 1, 1, 2, 1, 3, 1] => 3, 1, 3, 1, 1, 2, 1, 3, 1
[3, 1, 3, 1, 1, 2, 1, 3, 2] => 3, 1, 3, 1, 1, 2, 1, 3, 2
[3, 1, 3, 1, 1, 2, 1, 3, 3] => 3, 1, 3, 1, 1, 2, 1, 3, 3
[3, 1, 3, 1, 1, 2, 2, 1, 1] => 3, 1, 3, 1, 1, 2, 2, 1, 1
[3, 1, 3, 1, 1, 2, 2, 1, 2] => 3, 1, 3, 1, 1, 2, 2, 1, 2
[3, 1, 3, 1, 1, 2, 2, 1, 3] => 3, 1, 3, 1, 1, 2, 2, 1, 3
[3, 1, 3, 1, 1, 2, 2, 2, 1] => 3, 1, 3, 1, 1, 2, 2, 2, 1
[3, 1, 3, 1, 1, 2, 2, 2, 2] => 3, 1, 3, 1, 1, 2, 2, 2, 2
[3, 1, 3, 1, 1, 2, 2, 2, 3] => 3, 1, 3, 1, 1, 2, 2, 2, 3
[3, 1, 3, 1, 1, 2, 2, 3, 1] => 3, 1, 3, 1, 1, 2, 2, 3, 1
[3, 1, 3, 1, 1, 2, 2, 3, 2] => 3, 1, 3, 1, 1, 2, 2, 3, 2
[3, 1, 3, 1, 1, 2, 2, 3, 3] => 3, 1, 3, 1, 1, 2, 2, 3, 3
[3, 1, 3, 1, 1, 2, 3, 1, 1] => 3, 1, 3, 1, 1, 2, 3, 1, 1
[3, 1, 3, 1, 1, 2, 3, 1, 2] => 3, 1, 3, 1, 1, 2, 3, 1, 2
[3, 1, 3, 1, 1, 2, 3, 1, 3] => 3, 1, 3, 1, 1, 2, 3, 1, 3
[3, 1, 3, 1, 1, 2, 3, 2, 1] => 3, 1, 3, 1, 1, 2, 3, 2, 1
[3, 1, 3, 1, 1, 2, 3, 2, 2] => 3, 1, 3, 1, 1, 2, 3, 2, 2
[3, 1, 3, 1, 1, 2, 3, 2, 3] => 3, 1, 3, 1, 1, 2, 3, 2, 3
[3, 1, 3, 1, 1, 2, 3, 3, 1] => 3, 1, 3, 1, 1, 2, 3, 3, 1
[3, 1, 3, 1, 1, 2, 3, 3, 2] => 3, 1, 3, 1, 1, 2, 3, 3, 2
[3, 1, 3, 1, 1, 2, 3, 3, 3] => 3, 1, 3, 1, 1, 2, 3, 3, 3
[3, 1, 3, 1, 1, 3, 1, 1, 1] => 3, 1, 3, 1, 1, 3, 1, 1, 1
[3, 1, 3, 1, 1, 3, 1, 1, 2] => 3, 1, 3, 1, 1, 3, 1, 1, 2
[3, 1, 3, 1, 1, 3, 1, 1, 3] => 3, 1, 3, 1, 1, 3, 1, 1, 3
[3, 1, 3, 1, 1, 3, 1, 2, 1] => 3, 1, 3, 1, 1, 3, 1, 2, 1
[3, 1, 3, 1, 1, 3, 1, 2, 2] => 3, 1, 3, 1, 1, 3, 1, 2, 2
[3, 1, 3, 1, 1, 3, 1, 2, 3] => 3, 1, 3, 1, 1, 3, 1, 2, 3
[3, 1, 3, 1, 1, 3, 1, 3, 1] => 3, 1, 3, 1, 1, 3, 1, 3, 1
[3, 1, 3, 1, 1, 3, 1, 3, 2] => 3, 1, 3, 1, 1, 3, 1, 3, 2
[3, 1, 3, 1, 1, 3, 1, 3, 3] => 3, 1, 3, 1, 1, 3, 1, 3, 3
[3, 1, 3, 1, 1, 3, 2, 1, 1] => 3, 1, 3, 1, 1, 3, 2, 1, 1
[3, 1, 3, 1, 1, 3, 2, 1, 2] => 3, 1, 3, 1, 1, 3, 2, 1, 2
[3, 1, 3, 1, 1, 3, 2, 1, 3] => 3, 1, 3, 1, 1, 3, 2, 1, 3
[3, 1, 3, 1, 1, 3, 2, 2, 1] => 3, 1, 3, 1, 1, 3, 2, 2, 1
[3, 1, 3, 1, 1, 3, 2, 2, 2] => 3, 1, 3, 1, 1, 3, 2, 2, 2
[3, 1, 3, 1, 1, 3, 2, 2, 3] => 3, 1, 3, 1, 1, 3, 2, 2, 3
[3, 1, 3, 1, 1, 3, 2, 3, 1] => 3, 1, 3, 1, 1, 3, 2, 3, 1
[3, 1, 3, 1, 1, 3, 2, 3, 2] => 3, 1, 3, 1, 1, 3, 2, 3, 2
[3, 1, 3, 1, 1, 3, 2, 3, 3] => 3, 1, 3, 1, 1, 3, 2, 3, 3
[3, 1, 3, 1, 1, 3, 3, 1, 1] => 3, 1, 3, 1, 1, 3, 3, 1, 1
[3, 1, 3, 1, 1, 3, 3, 1, 2] => 3, 1, 3, 1, 1, 3, 3, 1, 2
[3, 1, 3, 1, 1, 3, 3, 1, 3] => 3, 1, 3, 1, 1, 3, 3, 1, 3
[3, 1, 3, 1, 1, 3, 3, 2, 1] => 3, 1, 3, 1, 1, 3, 3, 2, 1
[3, 1, 3, 1, 1, 3, 3, 2, 2] => 3, 1, 3, 1, 1, 3, 3, 2, 2
[3, 1, 3, 1, 1, 3, 3, 2, 3] => 3, 1, 3, 1, 1, 3, 3, 2, 3
[3, 1, 3, 1, 1, 3, 3, 3, 1] => 3, 1, 3, 1, 1, 3, 3, 3, 1
[3, 1, 3, 1, 1, 3, 3, 3, 2] => 3, 1, 3, 1, 1, 3, 3, 3, 2
[3, 1, 3, 1, 1, 3, 3, 3, 3] => 3, 1, 3, 1, 1, 3, 3, 3, 3
[3, 1, 3, 1, 2, 1, 1, 1, 1] => 3, 1, 3, 1, 2, 1, 1, 1, 1
[3, 1, 3, 1, 2, 1, 1, 1, 2] => 3, 1, 3, 1, 2, 1, 1, 1, 2
[3, 1, 3, 1, 2, 1, 1, 1, 3] => 3, 1, 3, 1, 2, 1, 1, 1, 3
[3, 1, 3, 1, 2, 1, 1, 2, 1] => 3, 1, 3, 1, 2, 1, 1, 2, 1
[3, 1, 3, 1, 2, 1, 1, 2, 2] => 3, 1, 3, 1, 2, 1, 1, 2, 2
[3, 1, 3, 1, 2, 1, 1, 2, 3] => 3, 1, 3, 1, 2, 1, 1, 2, 3
[3, 1, 3, 1, 2, 1, 1, 3, 1] => 3, 1, 3, 1, 2, 1, 1, 3, 1
[3, 1, 3, 1, 2, 1, 1, 3, 2] => 3, 1, 3, 1, 2, 1, 1, 3, 2
[3, 1, 3, 1, 2, 1, 1, 3, 3] => 3, 1, 3, 1, 2, 1, 1, 3, 3
[3, 1, 3, 1, 2, 1, 2, 1, 1] => 3, 1, 3, 1, 2, 1, 2, 1, 1
[3, 1, 3, 1, 2, 1, 2, 1, 2] => 3, 1, 3, 1, 2, 1, 2, 1, 2
[3, 1, 3, 1, 2, 1, 2, 1, 3] => 3, 1, 3, 1, 2, 1, 2, 1, 3
[3, 1, 3, 1, 2, 1, 2, 2, 1] => 3, 1, 3, 1, 2, 1, 2, 2, 1
[3, 1, 3, 1, 2, 1, 2, 2, 2] => 3, 1, 3, 1, 2, 1, 2, 2, 2
[3, 1, 3, 1, 2, 1, 2, 2, 3] => 3, 1, 3, 1, 2, 1, 2, 2, 3
[3, 1, 3, 1, 2, 1, 2, 3, 1] => 3, 1, 3, 1, 2, 1, 2, 3, 1
[3, 1, 3, 1, 2, 1, 2, 3, 2] => 3, 1, 3, 1, 2, 1, 2, 3, 2
[3, 1, 3, 1, 2, 1, 2, 3, 3] => 3, 1, 3, 1, 2, 1, 2, 3, 3
[3, 1, 3, 1, 2, 1, 3, 1, 1] => 3, 1, 3, 1, 2, 1, 3, 1, 1
[3, 1, 3, 1, 2, 1, 3, 1, 2] => 3, 1, 3, 1, 2, 1, 3, 1, 2
[3, 1, 3, 1, 2, 1, 3, 1, 3] => 3, 1, 3, 1, 2, 1, 3, 1, 3
[3, 1, 3, 1, 2, 1, 3, 2, 1] => 3, 1, 3, 1, 2, 1, 3, 2, 1
[3, 1, 3, 1, 2, 1, 3, 2, 2] => 3, 1, 3, 1, 2, 1, 3, 2, 2
[3, 1, 3, 1, 2, 1, 3, 2, 3] => 3, 1, 3, 1, 2, 1, 3, 2, 3
[3, 1, 3, 1, 2, 1, 3, 3, 1] => 3, 1, 3, 1, 2, 1, 3, 3, 1
[3, 1, 3, 1, 2, 1, 3, 3, 2] => 3, 1, 3, 1, 2, 1, 3, 3, 2
[3, 1, 3, 1, 2, 1, 3, 3, 3] => 3, 1, 3, 1, 2, 1, 3, 3, 3
[3, 1, 3, 1, 2, 2, 1, 1, 1] => 3, 1, 3, 1, 2, 2, 1, 1, 1
[3, 1, 3, 1, 2, 2, 1, 1, 2] => 3, 1, 3, 1, 2, 2, 1, 1, 2
[3, 1, 3, 1, 2, 2, 1, 1, 3] => 3, 1, 3, 1, 2, 2, 1, 1, 3
[3, 1, 3, 1, 2, 2, 1, 2, 1] => 3, 1, 3, 1, 2, 2, 1, 2, 1
[3, 1, 3, 1, 2, 2, 1, 2, 2] => 3, 1, 3, 1, 2, 2, 1, 2, 2
[3, 1, 3, 1, 2, 2, 1, 2, 3] => 3, 1, 3, 1, 2, 2, 1, 2, 3
[3, 1, 3, 1, 2, 2, 1, 3, 1] => 3, 1, 3, 1, 2, 2, 1, 3, 1
[3, 1, 3, 1, 2, 2, 1, 3, 2] => 3, 1, 3, 1, 2, 2, 1, 3, 2
[3, 1, 3, 1, 2, 2, 1, 3, 3] => 3, 1, 3, 1, 2, 2, 1, 3, 3
[3, 1, 3, 1, 2, 2, 2, 1, 1] => 3, 1, 3, 1, 2, 2, 2, 1, 1
[3, 1, 3, 1, 2, 2, 2, 1, 2] => 3, 1, 3, 1, 2, 2, 2, 1, 2
[3, 1, 3, 1, 2, 2, 2, 1, 3] => 3, 1, 3, 1, 2, 2, 2, 1, 3
[3, 1, 3, 1, 2, 2, 2, 2, 1] => 3, 1, 3, 1, 2, 2, 2, 2, 1
[3, 1, 3, 1, 2, 2, 2, 2, 2] => 3, 1, 3, 1, 2, 2, 2, 2, 2
[3, 1, 3, 1, 2, 2, 2, 2, 3] => 3, 1, 3, 1, 2, 2, 2, 2, 3
[3, 1, 3, 1, 2, 2, 2, 3, 1] => 3, 1, 3, 1, 2, 2, 2, 3, 1
[3, 1, 3, 1, 2, 2, 2, 3, 2] => 3, 1, 3, 1, 2, 2, 2, 3, 2
[3, 1, 3, 1, 2, 2, 2, 3, 3] => 3, 1, 3, 1, 2, 2, 2, 3, 3
[3, 1, 3, 1, 2, 2, 3, 1, 1] => 3, 1, 3, 1, 2, 2, 3, 1, 1
[3, 1, 3, 1, 2, 2, 3, 1, 2] => 3, 1, 3, 1, 2, 2, 3, 1, 2
[3, 1, 3, 1, 2, 2, 3, 1, 3] => 3, 1, 3, 1, 2, 2, 3, 1, 3
[3, 1, 3, 1, 2, 2, 3, 2, 1] => 3, 1, 3, 1, 2, 2, 3, 2, 1
[3, 1, 3, 1, 2, 2, 3, 2, 2] => 3, 1, 3, 1, 2, 2, 3, 2, 2
[3, 1, 3, 1, 2, 2, 3, 2, 3] => 3, 1, 3, 1, 2, 2, 3, 2, 3
[3, 1, 3, 1, 2, 2, 3, 3, 1] => 3, 1, 3, 1, 2, 2, 3, 3, 1
[3, 1, 3, 1, 2, 2, 3, 3, 2] => 3, 1, 3, 1, 2, 2, 3, 3, 2
[3, 1, 3, 1, 2, 2, 3, 3, 3] => 3, 1, 3, 1, 2, 2, 3, 3, 3
[3, 1, 3, 1, 2, 3, 1, 1, 1] => 3, 1, 3, 1, 2, 3, 1, 1, 1
[3, 1, 3, 1, 2, 3, 1, 1, 2] => 3, 1, 3, 1, 2, 3, 1, 1, 2
[3, 1, 3, 1, 2, 3, 1, 1, 3] => 3, 1, 3, 1, 2, 3, 1, 1, 3
[3, 1, 3, 1, 2, 3, 1, 2, 1] => 3, 1, 3, 1, 2, 3, 1, 2, 1
[3, 1, 3, 1, 2, 3, 1, 2, 2] => 3, 1, 3, 1, 2, 3, 1, 2, 2
[3, 1, 3, 1, 2, 3, 1, 2, 3] => 3, 1, 3, 1, 2, 3, 1, 2, 3
[3, 1, 3, 1, 2, 3, 1, 3, 1] => 3, 1, 3, 1, 2, 3, 1, 3, 1
[3, 1, 3, 1, 2, 3, 1, 3, 2] => 3, 1, 3, 1, 2, 3, 1, 3, 2
[3, 1, 3, 1, 2, 3, 1, 3, 3] => 3, 1, 3, 1, 2, 3, 1, 3, 3
[3, 1, 3, 1, 2, 3, 2, 1, 1] => 3, 1, 3, 1, 2, 3, 2, 1, 1
[3, 1, 3, 1, 2, 3, 2, 1, 2] => 3, 1, 3, 1, 2, 3, 2, 1, 2
[3, 1, 3, 1, 2, 3, 2, 1, 3] => 3, 1, 3, 1, 2, 3, 2, 1, 3
[3, 1, 3, 1, 2, 3, 2, 2, 1] => 3, 1, 3, 1, 2, 3, 2, 2, 1
[3, 1, 3, 1, 2, 3, 2, 2, 2] => 3, 1, 3, 1, 2, 3, 2, 2, 2
[3, 1, 3, 1, 2, 3, 2, 2, 3] => 3, 1, 3, 1, 2, 3, 2, 2, 3
[3, 1, 3, 1, 2, 3, 2, 3, 1] => 3, 1, 3, 1, 2, 3, 2, 3, 1
[3, 1, 3, 1, 2, 3, 2, 3, 2] => 3, 1, 3, 1, 2, 3, 2, 3, 2
[3, 1, 3, 1, 2, 3, 2, 3, 3] => 3, 1, 3, 1, 2, 3, 2, 3, 3
[3, 1, 3, 1, 2, 3, 3, 1, 1] => 3, 1, 3, 1, 2, 3, 3, 1, 1
[3, 1, 3, 1, 2, 3, 3, 1, 2] => 3, 1, 3, 1, 2, 3, 3, 1, 2
[3, 1, 3, 1, 2, 3, 3, 1, 3] => 3, 1, 3, 1, 2, 3, 3, 1, 3
[3, 1, 3, 1, 2, 3, 3, 2, 1] => 3, 1, 3, 1, 2, 3, 3, 2, 1
[3, 1, 3, 1, 2, 3, 3, 2, 2] => 3, 1, 3, 1, 2, 3, 3, 2, 2
[3, 1, 3, 1, 2, 3, 3, 2, 3] => 3, 1, 3, 1, 2, 3, 3, 2, 3
[3, 1, 3, 1, 2, 3, 3, 3, 1] => 3, 1, 3, 1, 2, 3, 3, 3, 1
[3, 1, 3, 1, 2, 3, 3, 3, 2] => 3, 1, 3, 1, 2, 3, 3, 3, 2
[3, 1, 3, 1, 2, 3, 3, 3, 3] => 3, 1, 3, 1, 2, 3, 3, 3, 3
[3, 1, 3, 1, 3, 1, 1, 1, 1] => 3, 1, 3, 1, 3, 1, 1, 1, 1
[3, 1, 3, 1, 3, 1, 1, 1, 2] => 3, 1, 3, 1, 3, 1, 1, 1, 2
[3, 1, 3, 1, 3, 1, 1, 1, 3] => 3, 1, 3, 1, 3, 1, 1, 1, 3
[3, 1, 3, 1, 3, 1, 1, 2, 1] => 3, 1, 3, 1, 3, 1, 1, 2, 1
[3, 1, 3, 1, 3, 1, 1, 2, 2] => 3, 1, 3, 1, 3, 1, 1, 2, 2
[3, 1, 3, 1, 3, 1, 1, 2, 3] => 3, 1, 3, 1, 3, 1, 1, 2, 3
[3, 1, 3, 1, 3, 1, 1, 3, 1] => 3, 1, 3, 1, 3, 1, 1, 3, 1
[3, 1, 3, 1, 3, 1, 1, 3, 2] => 3, 1, 3, 1, 3, 1, 1, 3, 2
[3, 1, 3, 1, 3, 1, 1, 3, 3] => 3, 1, 3, 1, 3, 1, 1, 3, 3
[3, 1, 3, 1, 3, 1, 2, 1, 1] => 3, 1, 3, 1, 3, 1, 2, 1, 1
[3, 1, 3, 1, 3, 1, 2, 1, 2] => 3, 1, 3, 1, 3, 1, 2, 1, 2
[3, 1, 3, 1, 3, 1, 2, 1, 3] => 3, 1, 3, 1, 3, 1, 2, 1, 3
[3, 1, 3, 1, 3, 1, 2, 2, 1] => 3, 1, 3, 1, 3, 1, 2, 2, 1
[3, 1, 3, 1, 3, 1, 2, 2, 2] => 3, 1, 3, 1, 3, 1, 2, 2, 2
[3, 1, 3, 1, 3, 1, 2, 2, 3] => 3, 1, 3, 1, 3, 1, 2, 2, 3
[3, 1, 3, 1, 3, 1, 2, 3, 1] => 3, 1, 3, 1, 3, 1, 2, 3, 1
[3, 1, 3, 1, 3, 1, 2, 3, 2] => 3, 1, 3, 1, 3, 1, 2, 3, 2
[3, 1, 3, 1, 3, 1, 2, 3, 3] => 3, 1, 3, 1, 3, 1, 2, 3, 3
[3, 1, 3, 1, 3, 1, 3, 1, 1] => 3, 1, 3, 1, 3, 1, 3, 1, 1
[3, 1, 3, 1, 3, 1, 3, 1, 2] => 3, 1, 3, 1, 3, 1, 3, 1, 2
[3, 1, 3, 1, 3, 1, 3, 1, 3] => 3, 1, 3, 1, 3, 1, 3, 1, 3
[3, 1, 3, 1, 3, 1, 3, 2, 1] => 3, 1, 3, 1, 3, 1, 3, 2, 1
[3, 1, 3, 1, 3, 1, 3, 2, 2] => 3, 1, 3, 1, 3, 1, 3, 2, 2
[3, 1, 3, 1, 3, 1, 3, 2, 3] => 3, 1, 3, 1, 3, 1, 3, 2, 3
[3, 1, 3, 1, 3, 1, 3, 3, 1] => 3, 1, 3, 1, 3, 1, 3, 3, 1
[3, 1, 3, 1, 3, 1, 3, 3, 2] => 3, 1, 3, 1, 3, 1, 3, 3, 2
[3, 1, 3, 1, 3, 1, 3, 3, 3] => 3, 1, 3, 1, 3, 1, 3, 3, 3
[3, 1, 3, 1, 3, 2, 1, 1, 1] => 3, 1, 3, 1, 3, 2, 1, 1, 1
[3, 1, 3, 1, 3, 2, 1, 1, 2] => 3, 1, 3, 1, 3, 2, 1, 1, 2
[3, 1, 3, 1, 3, 2, 1, 1, 3] => 3, 1, 3, 1, 3, 2, 1, 1, 3
[3, 1, 3, 1, 3, 2, 1, 2, 1] => 3, 1, 3, 1, 3, 2, 1, 2, 1
[3, 1, 3, 1, 3, 2, 1, 2, 2] => 3, 1, 3, 1, 3, 2, 1, 2, 2
[3, 1, 3, 1, 3, 2, 1, 2, 3] => 3, 1, 3, 1, 3, 2, 1, 2, 3
[3, 1, 3, 1, 3, 2, 1, 3, 1] => 3, 1, 3, 1, 3, 2, 1, 3, 1
[3, 1, 3, 1, 3, 2, 1, 3, 2] => 3, 1, 3, 1, 3, 2, 1, 3, 2
[3, 1, 3, 1, 3, 2, 1, 3, 3] => 3, 1, 3, 1, 3, 2, 1, 3, 3
[3, 1, 3, 1, 3, 2, 2, 1, 1] => 3, 1, 3, 1, 3, 2, 2, 1, 1
[3, 1, 3, 1, 3, 2, 2, 1, 2] => 3, 1, 3, 1, 3, 2, 2, 1, 2
[3, 1, 3, 1, 3, 2, 2, 1, 3] => 3, 1, 3, 1, 3, 2, 2, 1, 3
[3, 1, 3, 1, 3, 2, 2, 2, 1] => 3, 1, 3, 1, 3, 2, 2, 2, 1
[3, 1, 3, 1, 3, 2, 2, 2, 2] => 3, 1, 3, 1, 3, 2, 2, 2, 2
[3, 1, 3, 1, 3, 2, 2, 2, 3] => 3, 1, 3, 1, 3, 2, 2, 2, 3
[3, 1, 3, 1, 3, 2, 2, 3, 1] => 3, 1, 3, 1, 3, 2, 2, 3, 1
[3, 1, 3, 1, 3, 2, 2, 3, 2] => 3, 1, 3, 1, 3, 2, 2, 3, 2
[3, 1, 3, 1, 3, 2, 2, 3, 3] => 3, 1, 3, 1, 3, 2, 2, 3, 3
[3, 1, 3, 1, 3, 2, 3, 1, 1] => 3, 1, 3, 1, 3, 2, 3, 1, 1
[3, 1, 3, 1, 3, 2, 3, 1, 2] => 3, 1, 3, 1, 3, 2, 3, 1, 2
[3, 1, 3, 1, 3, 2, 3, 1, 3] => 3, 1, 3, 1, 3, 2, 3, 1, 3
[3, 1, 3, 1, 3, 2, 3, 2, 1] => 3, 1, 3, 1, 3, 2, 3, 2, 1
[3, 1, 3, 1, 3, 2, 3, 2, 2] => 3, 1, 3, 1, 3, 2, 3, 2, 2
[3, 1, 3, 1, 3, 2, 3, 2, 3] => 3, 1, 3, 1, 3, 2, 3, 2, 3
[3, 1, 3, 1, 3, 2, 3, 3, 1] => 3, 1, 3, 1, 3, 2, 3, 3, 1
[3, 1, 3, 1, 3, 2, 3, 3, 2] => 3, 1, 3, 1, 3, 2, 3, 3, 2
[3, 1, 3, 1, 3, 2, 3, 3, 3] => 3, 1, 3, 1, 3, 2, 3, 3, 3
[3, 1, 3, 1, 3, 3, 1, 1, 1] => 3, 1, 3, 1, 3, 3, 1, 1, 1
[3, 1, 3, 1, 3, 3, 1, 1, 2] => 3, 1, 3, 1, 3, 3, 1, 1, 2
[3, 1, 3, 1, 3, 3, 1, 1, 3] => 3, 1, 3, 1, 3, 3, 1, 1, 3
[3, 1, 3, 1, 3, 3, 1, 2, 1] => 3, 1, 3, 1, 3, 3, 1, 2, 1
[3, 1, 3, 1, 3, 3, 1, 2, 2] => 3, 1, 3, 1, 3, 3, 1, 2, 2
[3, 1, 3, 1, 3, 3, 1, 2, 3] => 3, 1, 3, 1, 3, 3, 1, 2, 3
[3, 1, 3, 1, 3, 3, 1, 3, 1] => 3, 1, 3, 1, 3, 3, 1, 3, 1
[3, 1, 3, 1, 3, 3, 1, 3, 2] => 3, 1, 3, 1, 3, 3, 1, 3, 2
[3, 1, 3, 1, 3, 3, 1, 3, 3] => 3, 1, 3, 1, 3, 3, 1, 3, 3
[3, 1, 3, 1, 3, 3, 2, 1, 1] => 3, 1, 3, 1, 3, 3, 2, 1, 1
[3, 1, 3, 1, 3, 3, 2, 1, 2] => 3, 1, 3, 1, 3, 3, 2, 1, 2
[3, 1, 3, 1, 3, 3, 2, 1, 3] => 3, 1, 3, 1, 3, 3, 2, 1, 3
[3, 1, 3, 1, 3, 3, 2, 2, 1] => 3, 1, 3, 1, 3, 3, 2, 2, 1
[3, 1, 3, 1, 3, 3, 2, 2, 2] => 3, 1, 3, 1, 3, 3, 2, 2, 2
[3, 1, 3, 1, 3, 3, 2, 2, 3] => 3, 1, 3, 1, 3, 3, 2, 2, 3
[3, 1, 3, 1, 3, 3, 2, 3, 1] => 3, 1, 3, 1, 3, 3, 2, 3, 1
[3, 1, 3, 1, 3, 3, 2, 3, 2] => 3, 1, 3, 1, 3, 3, 2, 3, 2
[3, 1, 3, 1, 3, 3, 2, 3, 3] => 3, 1, 3, 1, 3, 3, 2, 3, 3
[3, 1, 3, 1, 3, 3, 3, 1, 1] => 3, 1, 3, 1, 3, 3, 3, 1, 1
[3, 1, 3, 1, 3, 3, 3, 1, 2] => 3, 1, 3, 1, 3, 3, 3, 1, 2
[3, 1, 3, 1, 3, 3, 3, 1, 3] => 3, 1, 3, 1, 3, 3, 3, 1, 3
[3, 1, 3, 1, 3, 3, 3, 2, 1] => 3, 1, 3, 1, 3, 3, 3, 2, 1
[3, 1, 3, 1, 3, 3, 3, 2, 2] => 3, 1, 3, 1, 3, 3, 3, 2, 2
[3, 1, 3, 1, 3, 3, 3, 2, 3] => 3, 1, 3, 1, 3, 3, 3, 2, 3
[3, 1, 3, 1, 3, 3, 3, 3, 1] => 3, 1, 3, 1, 3, 3, 3, 3, 1
[3, 1, 3, 1, 3, 3, 3, 3, 2] => 3, 1, 3, 1, 3, 3, 3, 3, 2
[3, 1, 3, 1, 3, 3, 3, 3, 3] => 3, 1, 3, 1, 3, 3, 3, 3, 3
[3, 1, 3, 2, 1, 1, 1, 1, 1] => 3, 1, 3, 2, 1, 1, 1, 1, 1
[3, 1, 3, 2, 1, 1, 1, 1, 2] => 3, 1, 3, 2, 1, 1, 1, 1, 2
[3, 1, 3, 2, 1, 1, 1, 1, 3] => 3, 1, 3, 2, 1, 1, 1, 1, 3
[3, 1, 3, 2, 1, 1, 1, 2, 1] => 3, 1, 3, 2, 1, 1, 1, 2, 1
[3, 1, 3, 2, 1, 1, 1, 2, 2] => 3, 1, 3, 2, 1, 1, 1, 2, 2
[3, 1, 3, 2, 1, 1, 1, 2, 3] => 3, 1, 3, 2, 1, 1, 1, 2, 3
[3, 1, 3, 2, 1, 1, 1, 3, 1] => 3, 1, 3, 2, 1, 1, 1, 3, 1
[3, 1, 3, 2, 1, 1, 1, 3, 2] => 3, 1, 3, 2, 1, 1, 1, 3, 2
[3, 1, 3, 2, 1, 1, 1, 3, 3] => 3, 1, 3, 2, 1, 1, 1, 3, 3
[3, 1, 3, 2, 1, 1, 2, 1, 1] => 3, 1, 3, 2, 1, 1, 2, 1, 1
[3, 1, 3, 2, 1, 1, 2, 1, 2] => 3, 1, 3, 2, 1, 1, 2, 1, 2
[3, 1, 3, 2, 1, 1, 2, 1, 3] => 3, 1, 3, 2, 1, 1, 2, 1, 3
[3, 1, 3, 2, 1, 1, 2, 2, 1] => 3, 1, 3, 2, 1, 1, 2, 2, 1
[3, 1, 3, 2, 1, 1, 2, 2, 2] => 3, 1, 3, 2, 1, 1, 2, 2, 2
[3, 1, 3, 2, 1, 1, 2, 2, 3] => 3, 1, 3, 2, 1, 1, 2, 2, 3
[3, 1, 3, 2, 1, 1, 2, 3, 1] => 3, 1, 3, 2, 1, 1, 2, 3, 1
[3, 1, 3, 2, 1, 1, 2, 3, 2] => 3, 1, 3, 2, 1, 1, 2, 3, 2
[3, 1, 3, 2, 1, 1, 2, 3, 3] => 3, 1, 3, 2, 1, 1, 2, 3, 3
[3, 1, 3, 2, 1, 1, 3, 1, 1] => 3, 1, 3, 2, 1, 1, 3, 1, 1
[3, 1, 3, 2, 1, 1, 3, 1, 2] => 3, 1, 3, 2, 1, 1, 3, 1, 2
[3, 1, 3, 2, 1, 1, 3, 1, 3] => 3, 1, 3, 2, 1, 1, 3, 1, 3
[3, 1, 3, 2, 1, 1, 3, 2, 1] => 3, 1, 3, 2, 1, 1, 3, 2, 1
[3, 1, 3, 2, 1, 1, 3, 2, 2] => 3, 1, 3, 2, 1, 1, 3, 2, 2
[3, 1, 3, 2, 1, 1, 3, 2, 3] => 3, 1, 3, 2, 1, 1, 3, 2, 3
[3, 1, 3, 2, 1, 1, 3, 3, 1] => 3, 1, 3, 2, 1, 1, 3, 3, 1
[3, 1, 3, 2, 1, 1, 3, 3, 2] => 3, 1, 3, 2, 1, 1, 3, 3, 2
[3, 1, 3, 2, 1, 1, 3, 3, 3] => 3, 1, 3, 2, 1, 1, 3, 3, 3
[3, 1, 3, 2, 1, 2, 1, 1, 1] => 3, 1, 3, 2, 1, 2, 1, 1, 1
[3, 1, 3, 2, 1, 2, 1, 1, 2] => 3, 1, 3, 2, 1, 2, 1, 1, 2
[3, 1, 3, 2, 1, 2, 1, 1, 3] => 3, 1, 3, 2, 1, 2, 1, 1, 3
[3, 1, 3, 2, 1, 2, 1, 2, 1] => 3, 1, 3, 2, 1, 2, 1, 2, 1
[3, 1, 3, 2, 1, 2, 1, 2, 2] => 3, 1, 3, 2, 1, 2, 1, 2, 2
[3, 1, 3, 2, 1, 2, 1, 2, 3] => 3, 1, 3, 2, 1, 2, 1, 2, 3
[3, 1, 3, 2, 1, 2, 1, 3, 1] => 3, 1, 3, 2, 1, 2, 1, 3, 1
[3, 1, 3, 2, 1, 2, 1, 3, 2] => 3, 1, 3, 2, 1, 2, 1, 3, 2
[3, 1, 3, 2, 1, 2, 1, 3, 3] => 3, 1, 3, 2, 1, 2, 1, 3, 3
[3, 1, 3, 2, 1, 2, 2, 1, 1] => 3, 1, 3, 2, 1, 2, 2, 1, 1
[3, 1, 3, 2, 1, 2, 2, 1, 2] => 3, 1, 3, 2, 1, 2, 2, 1, 2
[3, 1, 3, 2, 1, 2, 2, 1, 3] => 3, 1, 3, 2, 1, 2, 2, 1, 3
[3, 1, 3, 2, 1, 2, 2, 2, 1] => 3, 1, 3, 2, 1, 2, 2, 2, 1
[3, 1, 3, 2, 1, 2, 2, 2, 2] => 3, 1, 3, 2, 1, 2, 2, 2, 2
[3, 1, 3, 2, 1, 2, 2, 2, 3] => 3, 1, 3, 2, 1, 2, 2, 2, 3
[3, 1, 3, 2, 1, 2, 2, 3, 1] => 3, 1, 3, 2, 1, 2, 2, 3, 1
[3, 1, 3, 2, 1, 2, 2, 3, 2] => 3, 1, 3, 2, 1, 2, 2, 3, 2
[3, 1, 3, 2, 1, 2, 2, 3, 3] => 3, 1, 3, 2, 1, 2, 2, 3, 3
[3, 1, 3, 2, 1, 2, 3, 1, 1] => 3, 1, 3, 2, 1, 2, 3, 1, 1
[3, 1, 3, 2, 1, 2, 3, 1, 2] => 3, 1, 3, 2, 1, 2, 3, 1, 2
[3, 1, 3, 2, 1, 2, 3, 1, 3] => 3, 1, 3, 2, 1, 2, 3, 1, 3
[3, 1, 3, 2, 1, 2, 3, 2, 1] => 3, 1, 3, 2, 1, 2, 3, 2, 1
[3, 1, 3, 2, 1, 2, 3, 2, 2] => 3, 1, 3, 2, 1, 2, 3, 2, 2
[3, 1, 3, 2, 1, 2, 3, 2, 3] => 3, 1, 3, 2, 1, 2, 3, 2, 3
[3, 1, 3, 2, 1, 2, 3, 3, 1] => 3, 1, 3, 2, 1, 2, 3, 3, 1
[3, 1, 3, 2, 1, 2, 3, 3, 2] => 3, 1, 3, 2, 1, 2, 3, 3, 2
[3, 1, 3, 2, 1, 2, 3, 3, 3] => 3, 1, 3, 2, 1, 2, 3, 3, 3
[3, 1, 3, 2, 1, 3, 1, 1, 1] => 3, 1, 3, 2, 1, 3, 1, 1, 1
[3, 1, 3, 2, 1, 3, 1, 1, 2] => 3, 1, 3, 2, 1, 3, 1, 1, 2
[3, 1, 3, 2, 1, 3, 1, 1, 3] => 3, 1, 3, 2, 1, 3, 1, 1, 3
[3, 1, 3, 2, 1, 3, 1, 2, 1] => 3, 1, 3, 2, 1, 3, 1, 2, 1
[3, 1, 3, 2, 1, 3, 1, 2, 2] => 3, 1, 3, 2, 1, 3, 1, 2, 2
[3, 1, 3, 2, 1, 3, 1, 2, 3] => 3, 1, 3, 2, 1, 3, 1, 2, 3
[3, 1, 3, 2, 1, 3, 1, 3, 1] => 3, 1, 3, 2, 1, 3, 1, 3, 1
[3, 1, 3, 2, 1, 3, 1, 3, 2] => 3, 1, 3, 2, 1, 3, 1, 3, 2
[3, 1, 3, 2, 1, 3, 1, 3, 3] => 3, 1, 3, 2, 1, 3, 1, 3, 3
[3, 1, 3, 2, 1, 3, 2, 1, 1] => 3, 1, 3, 2, 1, 3, 2, 1, 1
[3, 1, 3, 2, 1, 3, 2, 1, 2] => 3, 1, 3, 2, 1, 3, 2, 1, 2
[3, 1, 3, 2, 1, 3, 2, 1, 3] => 3, 1, 3, 2, 1, 3, 2, 1, 3
[3, 1, 3, 2, 1, 3, 2, 2, 1] => 3, 1, 3, 2, 1, 3, 2, 2, 1
[3, 1, 3, 2, 1, 3, 2, 2, 2] => 3, 1, 3, 2, 1, 3, 2, 2, 2
[3, 1, 3, 2, 1, 3, 2, 2, 3] => 3, 1, 3, 2, 1, 3, 2, 2, 3
[3, 1, 3, 2, 1, 3, 2, 3, 1] => 3, 1, 3, 2, 1, 3, 2, 3, 1
[3, 1, 3, 2, 1, 3, 2, 3, 2] => 3, 1, 3, 2, 1, 3, 2, 3, 2
[3, 1, 3, 2, 1, 3, 2, 3, 3] => 3, 1, 3, 2, 1, 3, 2, 3, 3
[3, 1, 3, 2, 1, 3, 3, 1, 1] => 3, 1, 3, 2, 1, 3, 3, 1, 1
[3, 1, 3, 2, 1, 3, 3, 1, 2] => 3, 1, 3, 2, 1, 3, 3, 1, 2
[3, 1, 3, 2, 1, 3, 3, 1, 3] => 3, 1, 3, 2, 1, 3, 3, 1, 3
[3, 1, 3, 2, 1, 3, 3, 2, 1] => 3, 1, 3, 2, 1, 3, 3, 2, 1
[3, 1, 3, 2, 1, 3, 3, 2, 2] => 3, 1, 3, 2, 1, 3, 3, 2, 2
[3, 1, 3, 2, 1, 3, 3, 2, 3] => 3, 1, 3, 2, 1, 3, 3, 2, 3
[3, 1, 3, 2, 1, 3, 3, 3, 1] => 3, 1, 3, 2, 1, 3, 3, 3, 1
[3, 1, 3, 2, 1, 3, 3, 3, 2] => 3, 1, 3, 2, 1, 3, 3, 3, 2
[3, 1, 3, 2, 1, 3, 3, 3, 3] => 3, 1, 3, 2, 1, 3, 3, 3, 3
[3, 1, 3, 2, 2, 1, 1, 1, 1] => 3, 1, 3, 2, 2, 1, 1, 1, 1
[3, 1, 3, 2, 2, 1, 1, 1, 2] => 3, 1, 3, 2, 2, 1, 1, 1, 2
[3, 1, 3, 2, 2, 1, 1, 1, 3] => 3, 1, 3, 2, 2, 1, 1, 1, 3
[3, 1, 3, 2, 2, 1, 1, 2, 1] => 3, 1, 3, 2, 2, 1, 1, 2, 1
[3, 1, 3, 2, 2, 1, 1, 2, 2] => 3, 1, 3, 2, 2, 1, 1, 2, 2
[3, 1, 3, 2, 2, 1, 1, 2, 3] => 3, 1, 3, 2, 2, 1, 1, 2, 3
[3, 1, 3, 2, 2, 1, 1, 3, 1] => 3, 1, 3, 2, 2, 1, 1, 3, 1
[3, 1, 3, 2, 2, 1, 1, 3, 2] => 3, 1, 3, 2, 2, 1, 1, 3, 2
[3, 1, 3, 2, 2, 1, 1, 3, 3] => 3, 1, 3, 2, 2, 1, 1, 3, 3
[3, 1, 3, 2, 2, 1, 2, 1, 1] => 3, 1, 3, 2, 2, 1, 2, 1, 1
[3, 1, 3, 2, 2, 1, 2, 1, 2] => 3, 1, 3, 2, 2, 1, 2, 1, 2
[3, 1, 3, 2, 2, 1, 2, 1, 3] => 3, 1, 3, 2, 2, 1, 2, 1, 3
[3, 1, 3, 2, 2, 1, 2, 2, 1] => 3, 1, 3, 2, 2, 1, 2, 2, 1
[3, 1, 3, 2, 2, 1, 2, 2, 2] => 3, 1, 3, 2, 2, 1, 2, 2, 2
[3, 1, 3, 2, 2, 1, 2, 2, 3] => 3, 1, 3, 2, 2, 1, 2, 2, 3
[3, 1, 3, 2, 2, 1, 2, 3, 1] => 3, 1, 3, 2, 2, 1, 2, 3, 1
[3, 1, 3, 2, 2, 1, 2, 3, 2] => 3, 1, 3, 2, 2, 1, 2, 3, 2
[3, 1, 3, 2, 2, 1, 2, 3, 3] => 3, 1, 3, 2, 2, 1, 2, 3, 3
[3, 1, 3, 2, 2, 1, 3, 1, 1] => 3, 1, 3, 2, 2, 1, 3, 1, 1
[3, 1, 3, 2, 2, 1, 3, 1, 2] => 3, 1, 3, 2, 2, 1, 3, 1, 2
[3, 1, 3, 2, 2, 1, 3, 1, 3] => 3, 1, 3, 2, 2, 1, 3, 1, 3
[3, 1, 3, 2, 2, 1, 3, 2, 1] => 3, 1, 3, 2, 2, 1, 3, 2, 1
[3, 1, 3, 2, 2, 1, 3, 2, 2] => 3, 1, 3, 2, 2, 1, 3, 2, 2
[3, 1, 3, 2, 2, 1, 3, 2, 3] => 3, 1, 3, 2, 2, 1, 3, 2, 3
[3, 1, 3, 2, 2, 1, 3, 3, 1] => 3, 1, 3, 2, 2, 1, 3, 3, 1
[3, 1, 3, 2, 2, 1, 3, 3, 2] => 3, 1, 3, 2, 2, 1, 3, 3, 2
[3, 1, 3, 2, 2, 1, 3, 3, 3] => 3, 1, 3, 2, 2, 1, 3, 3, 3
[3, 1, 3, 2, 2, 2, 1, 1, 1] => 3, 1, 3, 2, 2, 2, 1, 1, 1
[3, 1, 3, 2, 2, 2, 1, 1, 2] => 3, 1, 3, 2, 2, 2, 1, 1, 2
[3, 1, 3, 2, 2, 2, 1, 1, 3] => 3, 1, 3, 2, 2, 2, 1, 1, 3
[3, 1, 3, 2, 2, 2, 1, 2, 1] => 3, 1, 3, 2, 2, 2, 1, 2, 1
[3, 1, 3, 2, 2, 2, 1, 2, 2] => 3, 1, 3, 2, 2, 2, 1, 2, 2
[3, 1, 3, 2, 2, 2, 1, 2, 3] => 3, 1, 3, 2, 2, 2, 1, 2, 3
[3, 1, 3, 2, 2, 2, 1, 3, 1] => 3, 1, 3, 2, 2, 2, 1, 3, 1
[3, 1, 3, 2, 2, 2, 1, 3, 2] => 3, 1, 3, 2, 2, 2, 1, 3, 2
[3, 1, 3, 2, 2, 2, 1, 3, 3] => 3, 1, 3, 2, 2, 2, 1, 3, 3
[3, 1, 3, 2, 2, 2, 2, 1, 1] => 3, 1, 3, 2, 2, 2, 2, 1, 1
[3, 1, 3, 2, 2, 2, 2, 1, 2] => 3, 1, 3, 2, 2, 2, 2, 1, 2
[3, 1, 3, 2, 2, 2, 2, 1, 3] => 3, 1, 3, 2, 2, 2, 2, 1, 3
[3, 1, 3, 2, 2, 2, 2, 2, 1] => 3, 1, 3, 2, 2, 2, 2, 2, 1
[3, 1, 3, 2, 2, 2, 2, 2, 2] => 3, 1, 3, 2, 2, 2, 2, 2, 2
[3, 1, 3, 2, 2, 2, 2, 2, 3] => 3, 1, 3, 2, 2, 2, 2, 2, 3
[3, 1, 3, 2, 2, 2, 2, 3, 1] => 3, 1, 3, 2, 2, 2, 2, 3, 1
[3, 1, 3, 2, 2, 2, 2, 3, 2] => 3, 1, 3, 2, 2, 2, 2, 3, 2
[3, 1, 3, 2, 2, 2, 2, 3, 3] => 3, 1, 3, 2, 2, 2, 2, 3, 3
[3, 1, 3, 2, 2, 2, 3, 1, 1] => 3, 1, 3, 2, 2, 2, 3, 1, 1
[3, 1, 3, 2, 2, 2, 3, 1, 2] => 3, 1, 3, 2, 2, 2, 3, 1, 2
[3, 1, 3, 2, 2, 2, 3, 1, 3] => 3, 1, 3, 2, 2, 2, 3, 1, 3
[3, 1, 3, 2, 2, 2, 3, 2, 1] => 3, 1, 3, 2, 2, 2, 3, 2, 1
[3, 1, 3, 2, 2, 2, 3, 2, 2] => 3, 1, 3, 2, 2, 2, 3, 2, 2
[3, 1, 3, 2, 2, 2, 3, 2, 3] => 3, 1, 3, 2, 2, 2, 3, 2, 3
[3, 1, 3, 2, 2, 2, 3, 3, 1] => 3, 1, 3, 2, 2, 2, 3, 3, 1
[3, 1, 3, 2, 2, 2, 3, 3, 2] => 3, 1, 3, 2, 2, 2, 3, 3, 2
[3, 1, 3, 2, 2, 2, 3, 3, 3] => 3, 1, 3, 2, 2, 2, 3, 3, 3
[3, 1, 3, 2, 2, 3, 1, 1, 1] => 3, 1, 3, 2, 2, 3, 1, 1, 1
[3, 1, 3, 2, 2, 3, 1, 1, 2] => 3, 1, 3, 2, 2, 3, 1, 1, 2
[3, 1, 3, 2, 2, 3, 1, 1, 3] => 3, 1, 3, 2, 2, 3, 1, 1, 3
[3, 1, 3, 2, 2, 3, 1, 2, 1] => 3, 1, 3, 2, 2, 3, 1, 2, 1
[3, 1, 3, 2, 2, 3, 1, 2, 2] => 3, 1, 3, 2, 2, 3, 1, 2, 2
[3, 1, 3, 2, 2, 3, 1, 2, 3] => 3, 1, 3, 2, 2, 3, 1, 2, 3
[3, 1, 3, 2, 2, 3, 1, 3, 1] => 3, 1, 3, 2, 2, 3, 1, 3, 1
[3, 1, 3, 2, 2, 3, 1, 3, 2] => 3, 1, 3, 2, 2, 3, 1, 3, 2
[3, 1, 3, 2, 2, 3, 1, 3, 3] => 3, 1, 3, 2, 2, 3, 1, 3, 3
[3, 1, 3, 2, 2, 3, 2, 1, 1] => 3, 1, 3, 2, 2, 3, 2, 1, 1
[3, 1, 3, 2, 2, 3, 2, 1, 2] => 3, 1, 3, 2, 2, 3, 2, 1, 2
[3, 1, 3, 2, 2, 3, 2, 1, 3] => 3, 1, 3, 2, 2, 3, 2, 1, 3
[3, 1, 3, 2, 2, 3, 2, 2, 1] => 3, 1, 3, 2, 2, 3, 2, 2, 1
[3, 1, 3, 2, 2, 3, 2, 2, 2] => 3, 1, 3, 2, 2, 3, 2, 2, 2
[3, 1, 3, 2, 2, 3, 2, 2, 3] => 3, 1, 3, 2, 2, 3, 2, 2, 3
[3, 1, 3, 2, 2, 3, 2, 3, 1] => 3, 1, 3, 2, 2, 3, 2, 3, 1
[3, 1, 3, 2, 2, 3, 2, 3, 2] => 3, 1, 3, 2, 2, 3, 2, 3, 2
[3, 1, 3, 2, 2, 3, 2, 3, 3] => 3, 1, 3, 2, 2, 3, 2, 3, 3
[3, 1, 3, 2, 2, 3, 3, 1, 1] => 3, 1, 3, 2, 2, 3, 3, 1, 1
[3, 1, 3, 2, 2, 3, 3, 1, 2] => 3, 1, 3, 2, 2, 3, 3, 1, 2
[3, 1, 3, 2, 2, 3, 3, 1, 3] => 3, 1, 3, 2, 2, 3, 3, 1, 3
[3, 1, 3, 2, 2, 3, 3, 2, 1] => 3, 1, 3, 2, 2, 3, 3, 2, 1
[3, 1, 3, 2, 2, 3, 3, 2, 2] => 3, 1, 3, 2, 2, 3, 3, 2, 2
[3, 1, 3, 2, 2, 3, 3, 2, 3] => 3, 1, 3, 2, 2, 3, 3, 2, 3
[3, 1, 3, 2, 2, 3, 3, 3, 1] => 3, 1, 3, 2, 2, 3, 3, 3, 1
[3, 1, 3, 2, 2, 3, 3, 3, 2] => 3, 1, 3, 2, 2, 3, 3, 3, 2
[3, 1, 3, 2, 2, 3, 3, 3, 3] => 3, 1, 3, 2, 2, 3, 3, 3, 3
[3, 1, 3, 2, 3, 1, 1, 1, 1] => 3, 1, 3, 2, 3, 1, 1, 1, 1
[3, 1, 3, 2, 3, 1, 1, 1, 2] => 3, 1, 3, 2, 3, 1, 1, 1, 2
[3, 1, 3, 2, 3, 1, 1, 1, 3] => 3, 1, 3, 2, 3, 1, 1, 1, 3
[3, 1, 3, 2, 3, 1, 1, 2, 1] => 3, 1, 3, 2, 3, 1, 1, 2, 1
[3, 1, 3, 2, 3, 1, 1, 2, 2] => 3, 1, 3, 2, 3, 1, 1, 2, 2
[3, 1, 3, 2, 3, 1, 1, 2, 3] => 3, 1, 3, 2, 3, 1, 1, 2, 3
[3, 1, 3, 2, 3, 1, 1, 3, 1] => 3, 1, 3, 2, 3, 1, 1, 3, 1
[3, 1, 3, 2, 3, 1, 1, 3, 2] => 3, 1, 3, 2, 3, 1, 1, 3, 2
[3, 1, 3, 2, 3, 1, 1, 3, 3] => 3, 1, 3, 2, 3, 1, 1, 3, 3
[3, 1, 3, 2, 3, 1, 2, 1, 1] => 3, 1, 3, 2, 3, 1, 2, 1, 1
[3, 1, 3, 2, 3, 1, 2, 1, 2] => 3, 1, 3, 2, 3, 1, 2, 1, 2
[3, 1, 3, 2, 3, 1, 2, 1, 3] => 3, 1, 3, 2, 3, 1, 2, 1, 3
[3, 1, 3, 2, 3, 1, 2, 2, 1] => 3, 1, 3, 2, 3, 1, 2, 2, 1
[3, 1, 3, 2, 3, 1, 2, 2, 2] => 3, 1, 3, 2, 3, 1, 2, 2, 2
[3, 1, 3, 2, 3, 1, 2, 2, 3] => 3, 1, 3, 2, 3, 1, 2, 2, 3
[3, 1, 3, 2, 3, 1, 2, 3, 1] => 3, 1, 3, 2, 3, 1, 2, 3, 1
[3, 1, 3, 2, 3, 1, 2, 3, 2] => 3, 1, 3, 2, 3, 1, 2, 3, 2
[3, 1, 3, 2, 3, 1, 2, 3, 3] => 3, 1, 3, 2, 3, 1, 2, 3, 3
[3, 1, 3, 2, 3, 1, 3, 1, 1] => 3, 1, 3, 2, 3, 1, 3, 1, 1
[3, 1, 3, 2, 3, 1, 3, 1, 2] => 3, 1, 3, 2, 3, 1, 3, 1, 2
[3, 1, 3, 2, 3, 1, 3, 1, 3] => 3, 1, 3, 2, 3, 1, 3, 1, 3
[3, 1, 3, 2, 3, 1, 3, 2, 1] => 3, 1, 3, 2, 3, 1, 3, 2, 1
[3, 1, 3, 2, 3, 1, 3, 2, 2] => 3, 1, 3, 2, 3, 1, 3, 2, 2
[3, 1, 3, 2, 3, 1, 3, 2, 3] => 3, 1, 3, 2, 3, 1, 3, 2, 3
[3, 1, 3, 2, 3, 1, 3, 3, 1] => 3, 1, 3, 2, 3, 1, 3, 3, 1
[3, 1, 3, 2, 3, 1, 3, 3, 2] => 3, 1, 3, 2, 3, 1, 3, 3, 2
[3, 1, 3, 2, 3, 1, 3, 3, 3] => 3, 1, 3, 2, 3, 1, 3, 3, 3
[3, 1, 3, 2, 3, 2, 1, 1, 1] => 3, 1, 3, 2, 3, 2, 1, 1, 1
[3, 1, 3, 2, 3, 2, 1, 1, 2] => 3, 1, 3, 2, 3, 2, 1, 1, 2
[3, 1, 3, 2, 3, 2, 1, 1, 3] => 3, 1, 3, 2, 3, 2, 1, 1, 3
[3, 1, 3, 2, 3, 2, 1, 2, 1] => 3, 1, 3, 2, 3, 2, 1, 2, 1
[3, 1, 3, 2, 3, 2, 1, 2, 2] => 3, 1, 3, 2, 3, 2, 1, 2, 2
[3, 1, 3, 2, 3, 2, 1, 2, 3] => 3, 1, 3, 2, 3, 2, 1, 2, 3
[3, 1, 3, 2, 3, 2, 1, 3, 1] => 3, 1, 3, 2, 3, 2, 1, 3, 1
[3, 1, 3, 2, 3, 2, 1, 3, 2] => 3, 1, 3, 2, 3, 2, 1, 3, 2
[3, 1, 3, 2, 3, 2, 1, 3, 3] => 3, 1, 3, 2, 3, 2, 1, 3, 3
[3, 1, 3, 2, 3, 2, 2, 1, 1] => 3, 1, 3, 2, 3, 2, 2, 1, 1
[3, 1, 3, 2, 3, 2, 2, 1, 2] => 3, 1, 3, 2, 3, 2, 2, 1, 2
[3, 1, 3, 2, 3, 2, 2, 1, 3] => 3, 1, 3, 2, 3, 2, 2, 1, 3
[3, 1, 3, 2, 3, 2, 2, 2, 1] => 3, 1, 3, 2, 3, 2, 2, 2, 1
[3, 1, 3, 2, 3, 2, 2, 2, 2] => 3, 1, 3, 2, 3, 2, 2, 2, 2
[3, 1, 3, 2, 3, 2, 2, 2, 3] => 3, 1, 3, 2, 3, 2, 2, 2, 3
[3, 1, 3, 2, 3, 2, 2, 3, 1] => 3, 1, 3, 2, 3, 2, 2, 3, 1
[3, 1, 3, 2, 3, 2, 2, 3, 2] => 3, 1, 3, 2, 3, 2, 2, 3, 2
[3, 1, 3, 2, 3, 2, 2, 3, 3] => 3, 1, 3, 2, 3, 2, 2, 3, 3
[3, 1, 3, 2, 3, 2, 3, 1, 1] => 3, 1, 3, 2, 3, 2, 3, 1, 1
[3, 1, 3, 2, 3, 2, 3, 1, 2] => 3, 1, 3, 2, 3, 2, 3, 1, 2
[3, 1, 3, 2, 3, 2, 3, 1, 3] => 3, 1, 3, 2, 3, 2, 3, 1, 3
[3, 1, 3, 2, 3, 2, 3, 2, 1] => 3, 1, 3, 2, 3, 2, 3, 2, 1
[3, 1, 3, 2, 3, 2, 3, 2, 2] => 3, 1, 3, 2, 3, 2, 3, 2, 2
[3, 1, 3, 2, 3, 2, 3, 2, 3] => 3, 1, 3, 2, 3, 2, 3, 2, 3
[3, 1, 3, 2, 3, 2, 3, 3, 1] => 3, 1, 3, 2, 3, 2, 3, 3, 1
[3, 1, 3, 2, 3, 2, 3, 3, 2] => 3, 1, 3, 2, 3, 2, 3, 3, 2
[3, 1, 3, 2, 3, 2, 3, 3, 3] => 3, 1, 3, 2, 3, 2, 3, 3, 3
[3, 1, 3, 2, 3, 3, 1, 1, 1] => 3, 1, 3, 2, 3, 3, 1, 1, 1
[3, 1, 3, 2, 3, 3, 1, 1, 2] => 3, 1, 3, 2, 3, 3, 1, 1, 2
[3, 1, 3, 2, 3, 3, 1, 1, 3] => 3, 1, 3, 2, 3, 3, 1, 1, 3
[3, 1, 3, 2, 3, 3, 1, 2, 1] => 3, 1, 3, 2, 3, 3, 1, 2, 1
[3, 1, 3, 2, 3, 3, 1, 2, 2] => 3, 1, 3, 2, 3, 3, 1, 2, 2
[3, 1, 3, 2, 3, 3, 1, 2, 3] => 3, 1, 3, 2, 3, 3, 1, 2, 3
[3, 1, 3, 2, 3, 3, 1, 3, 1] => 3, 1, 3, 2, 3, 3, 1, 3, 1
[3, 1, 3, 2, 3, 3, 1, 3, 2] => 3, 1, 3, 2, 3, 3, 1, 3, 2
[3, 1, 3, 2, 3, 3, 1, 3, 3] => 3, 1, 3, 2, 3, 3, 1, 3, 3
[3, 1, 3, 2, 3, 3, 2, 1, 1] => 3, 1, 3, 2, 3, 3, 2, 1, 1
[3, 1, 3, 2, 3, 3, 2, 1, 2] => 3, 1, 3, 2, 3, 3, 2, 1, 2
[3, 1, 3, 2, 3, 3, 2, 1, 3] => 3, 1, 3, 2, 3, 3, 2, 1, 3
[3, 1, 3, 2, 3, 3, 2, 2, 1] => 3, 1, 3, 2, 3, 3, 2, 2, 1
[3, 1, 3, 2, 3, 3, 2, 2, 2] => 3, 1, 3, 2, 3, 3, 2, 2, 2
[3, 1, 3, 2, 3, 3, 2, 2, 3] => 3, 1, 3, 2, 3, 3, 2, 2, 3
[3, 1, 3, 2, 3, 3, 2, 3, 1] => 3, 1, 3, 2, 3, 3, 2, 3, 1
[3, 1, 3, 2, 3, 3, 2, 3, 2] => 3, 1, 3, 2, 3, 3, 2, 3, 2
[3, 1, 3, 2, 3, 3, 2, 3, 3] => 3, 1, 3, 2, 3, 3, 2, 3, 3
[3, 1, 3, 2, 3, 3, 3, 1, 1] => 3, 1, 3, 2, 3, 3, 3, 1, 1
[3, 1, 3, 2, 3, 3, 3, 1, 2] => 3, 1, 3, 2, 3, 3, 3, 1, 2
[3, 1, 3, 2, 3, 3, 3, 1, 3] => 3, 1, 3, 2, 3, 3, 3, 1, 3
[3, 1, 3, 2, 3, 3, 3, 2, 1] => 3, 1, 3, 2, 3, 3, 3, 2, 1
[3, 1, 3, 2, 3, 3, 3, 2, 2] => 3, 1, 3, 2, 3, 3, 3, 2, 2
[3, 1, 3, 2, 3, 3, 3, 2, 3] => 3, 1, 3, 2, 3, 3, 3, 2, 3
[3, 1, 3, 2, 3, 3, 3, 3, 1] => 3, 1, 3, 2, 3, 3, 3, 3, 1
[3, 1, 3, 2, 3, 3, 3, 3, 2] => 3, 1, 3, 2, 3, 3, 3, 3, 2
[3, 1, 3, 2, 3, 3, 3, 3, 3] => 3, 1, 3, 2, 3, 3, 3, 3, 3
[3, 1, 3, 3, 1, 1, 1, 1, 1] => 3, 1, 3, 3, 1, 1, 1, 1, 1
[3, 1, 3, 3, 1, 1, 1, 1, 2] => 3, 1, 3, 3, 1, 1, 1, 1, 2
[3, 1, 3, 3, 1, 1, 1, 1, 3] => 3, 1, 3, 3, 1, 1, 1, 1, 3
[3, 1, 3, 3, 1, 1, 1, 2, 1] => 3, 1, 3, 3, 1, 1, 1, 2, 1
[3, 1, 3, 3, 1, 1, 1, 2, 2] => 3, 1, 3, 3, 1, 1, 1, 2, 2
[3, 1, 3, 3, 1, 1, 1, 2, 3] => 3, 1, 3, 3, 1, 1, 1, 2, 3
[3, 1, 3, 3, 1, 1, 1, 3, 1] => 3, 1, 3, 3, 1, 1, 1, 3, 1
[3, 1, 3, 3, 1, 1, 1, 3, 2] => 3, 1, 3, 3, 1, 1, 1, 3, 2
[3, 1, 3, 3, 1, 1, 1, 3, 3] => 3, 1, 3, 3, 1, 1, 1, 3, 3
[3, 1, 3, 3, 1, 1, 2, 1, 1] => 3, 1, 3, 3, 1, 1, 2, 1, 1
[3, 1, 3, 3, 1, 1, 2, 1, 2] => 3, 1, 3, 3, 1, 1, 2, 1, 2
[3, 1, 3, 3, 1, 1, 2, 1, 3] => 3, 1, 3, 3, 1, 1, 2, 1, 3
[3, 1, 3, 3, 1, 1, 2, 2, 1] => 3, 1, 3, 3, 1, 1, 2, 2, 1
[3, 1, 3, 3, 1, 1, 2, 2, 2] => 3, 1, 3, 3, 1, 1, 2, 2, 2
[3, 1, 3, 3, 1, 1, 2, 2, 3] => 3, 1, 3, 3, 1, 1, 2, 2, 3
[3, 1, 3, 3, 1, 1, 2, 3, 1] => 3, 1, 3, 3, 1, 1, 2, 3, 1
[3, 1, 3, 3, 1, 1, 2, 3, 2] => 3, 1, 3, 3, 1, 1, 2, 3, 2
[3, 1, 3, 3, 1, 1, 2, 3, 3] => 3, 1, 3, 3, 1, 1, 2, 3, 3
[3, 1, 3, 3, 1, 1, 3, 1, 1] => 3, 1, 3, 3, 1, 1, 3, 1, 1
[3, 1, 3, 3, 1, 1, 3, 1, 2] => 3, 1, 3, 3, 1, 1, 3, 1, 2
[3, 1, 3, 3, 1, 1, 3, 1, 3] => 3, 1, 3, 3, 1, 1, 3, 1, 3
[3, 1, 3, 3, 1, 1, 3, 2, 1] => 3, 1, 3, 3, 1, 1, 3, 2, 1
[3, 1, 3, 3, 1, 1, 3, 2, 2] => 3, 1, 3, 3, 1, 1, 3, 2, 2
[3, 1, 3, 3, 1, 1, 3, 2, 3] => 3, 1, 3, 3, 1, 1, 3, 2, 3
[3, 1, 3, 3, 1, 1, 3, 3, 1] => 3, 1, 3, 3, 1, 1, 3, 3, 1
[3, 1, 3, 3, 1, 1, 3, 3, 2] => 3, 1, 3, 3, 1, 1, 3, 3, 2
[3, 1, 3, 3, 1, 1, 3, 3, 3] => 3, 1, 3, 3, 1, 1, 3, 3, 3
[3, 1, 3, 3, 1, 2, 1, 1, 1] => 3, 1, 3, 3, 1, 2, 1, 1, 1
[3, 1, 3, 3, 1, 2, 1, 1, 2] => 3, 1, 3, 3, 1, 2, 1, 1, 2
[3, 1, 3, 3, 1, 2, 1, 1, 3] => 3, 1, 3, 3, 1, 2, 1, 1, 3
[3, 1, 3, 3, 1, 2, 1, 2, 1] => 3, 1, 3, 3, 1, 2, 1, 2, 1
[3, 1, 3, 3, 1, 2, 1, 2, 2] => 3, 1, 3, 3, 1, 2, 1, 2, 2
[3, 1, 3, 3, 1, 2, 1, 2, 3] => 3, 1, 3, 3, 1, 2, 1, 2, 3
[3, 1, 3, 3, 1, 2, 1, 3, 1] => 3, 1, 3, 3, 1, 2, 1, 3, 1
[3, 1, 3, 3, 1, 2, 1, 3, 2] => 3, 1, 3, 3, 1, 2, 1, 3, 2
[3, 1, 3, 3, 1, 2, 1, 3, 3] => 3, 1, 3, 3, 1, 2, 1, 3, 3
[3, 1, 3, 3, 1, 2, 2, 1, 1] => 3, 1, 3, 3, 1, 2, 2, 1, 1
[3, 1, 3, 3, 1, 2, 2, 1, 2] => 3, 1, 3, 3, 1, 2, 2, 1, 2
[3, 1, 3, 3, 1, 2, 2, 1, 3] => 3, 1, 3, 3, 1, 2, 2, 1, 3
[3, 1, 3, 3, 1, 2, 2, 2, 1] => 3, 1, 3, 3, 1, 2, 2, 2, 1
[3, 1, 3, 3, 1, 2, 2, 2, 2] => 3, 1, 3, 3, 1, 2, 2, 2, 2
[3, 1, 3, 3, 1, 2, 2, 2, 3] => 3, 1, 3, 3, 1, 2, 2, 2, 3
[3, 1, 3, 3, 1, 2, 2, 3, 1] => 3, 1, 3, 3, 1, 2, 2, 3, 1
[3, 1, 3, 3, 1, 2, 2, 3, 2] => 3, 1, 3, 3, 1, 2, 2, 3, 2
[3, 1, 3, 3, 1, 2, 2, 3, 3] => 3, 1, 3, 3, 1, 2, 2, 3, 3
[3, 1, 3, 3, 1, 2, 3, 1, 1] => 3, 1, 3, 3, 1, 2, 3, 1, 1
[3, 1, 3, 3, 1, 2, 3, 1, 2] => 3, 1, 3, 3, 1, 2, 3, 1, 2
[3, 1, 3, 3, 1, 2, 3, 1, 3] => 3, 1, 3, 3, 1, 2, 3, 1, 3
[3, 1, 3, 3, 1, 2, 3, 2, 1] => 3, 1, 3, 3, 1, 2, 3, 2, 1
[3, 1, 3, 3, 1, 2, 3, 2, 2] => 3, 1, 3, 3, 1, 2, 3, 2, 2
[3, 1, 3, 3, 1, 2, 3, 2, 3] => 3, 1, 3, 3, 1, 2, 3, 2, 3
[3, 1, 3, 3, 1, 2, 3, 3, 1] => 3, 1, 3, 3, 1, 2, 3, 3, 1
[3, 1, 3, 3, 1, 2, 3, 3, 2] => 3, 1, 3, 3, 1, 2, 3, 3, 2
[3, 1, 3, 3, 1, 2, 3, 3, 3] => 3, 1, 3, 3, 1, 2, 3, 3, 3
[3, 1, 3, 3, 1, 3, 1, 1, 1] => 3, 1, 3, 3, 1, 3, 1, 1, 1
[3, 1, 3, 3, 1, 3, 1, 1, 2] => 3, 1, 3, 3, 1, 3, 1, 1, 2
[3, 1, 3, 3, 1, 3, 1, 1, 3] => 3, 1, 3, 3, 1, 3, 1, 1, 3
[3, 1, 3, 3, 1, 3, 1, 2, 1] => 3, 1, 3, 3, 1, 3, 1, 2, 1
[3, 1, 3, 3, 1, 3, 1, 2, 2] => 3, 1, 3, 3, 1, 3, 1, 2, 2
[3, 1, 3, 3, 1, 3, 1, 2, 3] => 3, 1, 3, 3, 1, 3, 1, 2, 3
[3, 1, 3, 3, 1, 3, 1, 3, 1] => 3, 1, 3, 3, 1, 3, 1, 3, 1
[3, 1, 3, 3, 1, 3, 1, 3, 2] => 3, 1, 3, 3, 1, 3, 1, 3, 2
[3, 1, 3, 3, 1, 3, 1, 3, 3] => 3, 1, 3, 3, 1, 3, 1, 3, 3
[3, 1, 3, 3, 1, 3, 2, 1, 1] => 3, 1, 3, 3, 1, 3, 2, 1, 1
[3, 1, 3, 3, 1, 3, 2, 1, 2] => 3, 1, 3, 3, 1, 3, 2, 1, 2
[3, 1, 3, 3, 1, 3, 2, 1, 3] => 3, 1, 3, 3, 1, 3, 2, 1, 3
[3, 1, 3, 3, 1, 3, 2, 2, 1] => 3, 1, 3, 3, 1, 3, 2, 2, 1
[3, 1, 3, 3, 1, 3, 2, 2, 2] => 3, 1, 3, 3, 1, 3, 2, 2, 2
[3, 1, 3, 3, 1, 3, 2, 2, 3] => 3, 1, 3, 3, 1, 3, 2, 2, 3
[3, 1, 3, 3, 1, 3, 2, 3, 1] => 3, 1, 3, 3, 1, 3, 2, 3, 1
[3, 1, 3, 3, 1, 3, 2, 3, 2] => 3, 1, 3, 3, 1, 3, 2, 3, 2
[3, 1, 3, 3, 1, 3, 2, 3, 3] => 3, 1, 3, 3, 1, 3, 2, 3, 3
[3, 1, 3, 3, 1, 3, 3, 1, 1] => 3, 1, 3, 3, 1, 3, 3, 1, 1
[3, 1, 3, 3, 1, 3, 3, 1, 2] => 3, 1, 3, 3, 1, 3, 3, 1, 2
[3, 1, 3, 3, 1, 3, 3, 1, 3] => 3, 1, 3, 3, 1, 3, 3, 1, 3
[3, 1, 3, 3, 1, 3, 3, 2, 1] => 3, 1, 3, 3, 1, 3, 3, 2, 1
[3, 1, 3, 3, 1, 3, 3, 2, 2] => 3, 1, 3, 3, 1, 3, 3, 2, 2
[3, 1, 3, 3, 1, 3, 3, 2, 3] => 3, 1, 3, 3, 1, 3, 3, 2, 3
[3, 1, 3, 3, 1, 3, 3, 3, 1] => 3, 1, 3, 3, 1, 3, 3, 3, 1
[3, 1, 3, 3, 1, 3, 3, 3, 2] => 3, 1, 3, 3, 1, 3, 3, 3, 2
[3, 1, 3, 3, 1, 3, 3, 3, 3] => 3, 1, 3, 3, 1, 3, 3, 3, 3
[3, 1, 3, 3, 2, 1, 1, 1, 1] => 3, 1, 3, 3, 2, 1, 1, 1, 1
[3, 1, 3, 3, 2, 1, 1, 1, 2] => 3, 1, 3, 3, 2, 1, 1, 1, 2
[3, 1, 3, 3, 2, 1, 1, 1, 3] => 3, 1, 3, 3, 2, 1, 1, 1, 3
[3, 1, 3, 3, 2, 1, 1, 2, 1] => 3, 1, 3, 3, 2, 1, 1, 2, 1
[3, 1, 3, 3, 2, 1, 1, 2, 2] => 3, 1, 3, 3, 2, 1, 1, 2, 2
[3, 1, 3, 3, 2, 1, 1, 2, 3] => 3, 1, 3, 3, 2, 1, 1, 2, 3
[3, 1, 3, 3, 2, 1, 1, 3, 1] => 3, 1, 3, 3, 2, 1, 1, 3, 1
[3, 1, 3, 3, 2, 1, 1, 3, 2] => 3, 1, 3, 3, 2, 1, 1, 3, 2
[3, 1, 3, 3, 2, 1, 1, 3, 3] => 3, 1, 3, 3, 2, 1, 1, 3, 3
[3, 1, 3, 3, 2, 1, 2, 1, 1] => 3, 1, 3, 3, 2, 1, 2, 1, 1
[3, 1, 3, 3, 2, 1, 2, 1, 2] => 3, 1, 3, 3, 2, 1, 2, 1, 2
[3, 1, 3, 3, 2, 1, 2, 1, 3] => 3, 1, 3, 3, 2, 1, 2, 1, 3
[3, 1, 3, 3, 2, 1, 2, 2, 1] => 3, 1, 3, 3, 2, 1, 2, 2, 1
[3, 1, 3, 3, 2, 1, 2, 2, 2] => 3, 1, 3, 3, 2, 1, 2, 2, 2
[3, 1, 3, 3, 2, 1, 2, 2, 3] => 3, 1, 3, 3, 2, 1, 2, 2, 3
[3, 1, 3, 3, 2, 1, 2, 3, 1] => 3, 1, 3, 3, 2, 1, 2, 3, 1
[3, 1, 3, 3, 2, 1, 2, 3, 2] => 3, 1, 3, 3, 2, 1, 2, 3, 2
[3, 1, 3, 3, 2, 1, 2, 3, 3] => 3, 1, 3, 3, 2, 1, 2, 3, 3
[3, 1, 3, 3, 2, 1, 3, 1, 1] => 3, 1, 3, 3, 2, 1, 3, 1, 1
[3, 1, 3, 3, 2, 1, 3, 1, 2] => 3, 1, 3, 3, 2, 1, 3, 1, 2
[3, 1, 3, 3, 2, 1, 3, 1, 3] => 3, 1, 3, 3, 2, 1, 3, 1, 3
[3, 1, 3, 3, 2, 1, 3, 2, 1] => 3, 1, 3, 3, 2, 1, 3, 2, 1
[3, 1, 3, 3, 2, 1, 3, 2, 2] => 3, 1, 3, 3, 2, 1, 3, 2, 2
[3, 1, 3, 3, 2, 1, 3, 2, 3] => 3, 1, 3, 3, 2, 1, 3, 2, 3
[3, 1, 3, 3, 2, 1, 3, 3, 1] => 3, 1, 3, 3, 2, 1, 3, 3, 1
[3, 1, 3, 3, 2, 1, 3, 3, 2] => 3, 1, 3, 3, 2, 1, 3, 3, 2
[3, 1, 3, 3, 2, 1, 3, 3, 3] => 3, 1, 3, 3, 2, 1, 3, 3, 3
[3, 1, 3, 3, 2, 2, 1, 1, 1] => 3, 1, 3, 3, 2, 2, 1, 1, 1
[3, 1, 3, 3, 2, 2, 1, 1, 2] => 3, 1, 3, 3, 2, 2, 1, 1, 2
[3, 1, 3, 3, 2, 2, 1, 1, 3] => 3, 1, 3, 3, 2, 2, 1, 1, 3
[3, 1, 3, 3, 2, 2, 1, 2, 1] => 3, 1, 3, 3, 2, 2, 1, 2, 1
[3, 1, 3, 3, 2, 2, 1, 2, 2] => 3, 1, 3, 3, 2, 2, 1, 2, 2
[3, 1, 3, 3, 2, 2, 1, 2, 3] => 3, 1, 3, 3, 2, 2, 1, 2, 3
[3, 1, 3, 3, 2, 2, 1, 3, 1] => 3, 1, 3, 3, 2, 2, 1, 3, 1
[3, 1, 3, 3, 2, 2, 1, 3, 2] => 3, 1, 3, 3, 2, 2, 1, 3, 2
[3, 1, 3, 3, 2, 2, 1, 3, 3] => 3, 1, 3, 3, 2, 2, 1, 3, 3
[3, 1, 3, 3, 2, 2, 2, 1, 1] => 3, 1, 3, 3, 2, 2, 2, 1, 1
[3, 1, 3, 3, 2, 2, 2, 1, 2] => 3, 1, 3, 3, 2, 2, 2, 1, 2
[3, 1, 3, 3, 2, 2, 2, 1, 3] => 3, 1, 3, 3, 2, 2, 2, 1, 3
[3, 1, 3, 3, 2, 2, 2, 2, 1] => 3, 1, 3, 3, 2, 2, 2, 2, 1
[3, 1, 3, 3, 2, 2, 2, 2, 2] => 3, 1, 3, 3, 2, 2, 2, 2, 2
[3, 1, 3, 3, 2, 2, 2, 2, 3] => 3, 1, 3, 3, 2, 2, 2, 2, 3
[3, 1, 3, 3, 2, 2, 2, 3, 1] => 3, 1, 3, 3, 2, 2, 2, 3, 1
[3, 1, 3, 3, 2, 2, 2, 3, 2] => 3, 1, 3, 3, 2, 2, 2, 3, 2
[3, 1, 3, 3, 2, 2, 2, 3, 3] => 3, 1, 3, 3, 2, 2, 2, 3, 3
[3, 1, 3, 3, 2, 2, 3, 1, 1] => 3, 1, 3, 3, 2, 2, 3, 1, 1
[3, 1, 3, 3, 2, 2, 3, 1, 2] => 3, 1, 3, 3, 2, 2, 3, 1, 2
[3, 1, 3, 3, 2, 2, 3, 1, 3] => 3, 1, 3, 3, 2, 2, 3, 1, 3
[3, 1, 3, 3, 2, 2, 3, 2, 1] => 3, 1, 3, 3, 2, 2, 3, 2, 1
[3, 1, 3, 3, 2, 2, 3, 2, 2] => 3, 1, 3, 3, 2, 2, 3, 2, 2
[3, 1, 3, 3, 2, 2, 3, 2, 3] => 3, 1, 3, 3, 2, 2, 3, 2, 3
[3, 1, 3, 3, 2, 2, 3, 3, 1] => 3, 1, 3, 3, 2, 2, 3, 3, 1
[3, 1, 3, 3, 2, 2, 3, 3, 2] => 3, 1, 3, 3, 2, 2, 3, 3, 2
[3, 1, 3, 3, 2, 2, 3, 3, 3] => 3, 1, 3, 3, 2, 2, 3, 3, 3
[3, 1, 3, 3, 2, 3, 1, 1, 1] => 3, 1, 3, 3, 2, 3, 1, 1, 1
[3, 1, 3, 3, 2, 3, 1, 1, 2] => 3, 1, 3, 3, 2, 3, 1, 1, 2
[3, 1, 3, 3, 2, 3, 1, 1, 3] => 3, 1, 3, 3, 2, 3, 1, 1, 3
[3, 1, 3, 3, 2, 3, 1, 2, 1] => 3, 1, 3, 3, 2, 3, 1, 2, 1
[3, 1, 3, 3, 2, 3, 1, 2, 2] => 3, 1, 3, 3, 2, 3, 1, 2, 2
[3, 1, 3, 3, 2, 3, 1, 2, 3] => 3, 1, 3, 3, 2, 3, 1, 2, 3
[3, 1, 3, 3, 2, 3, 1, 3, 1] => 3, 1, 3, 3, 2, 3, 1, 3, 1
[3, 1, 3, 3, 2, 3, 1, 3, 2] => 3, 1, 3, 3, 2, 3, 1, 3, 2
[3, 1, 3, 3, 2, 3, 1, 3, 3] => 3, 1, 3, 3, 2, 3, 1, 3, 3
[3, 1, 3, 3, 2, 3, 2, 1, 1] => 3, 1, 3, 3, 2, 3, 2, 1, 1
[3, 1, 3, 3, 2, 3, 2, 1, 2] => 3, 1, 3, 3, 2, 3, 2, 1, 2
[3, 1, 3, 3, 2, 3, 2, 1, 3] => 3, 1, 3, 3, 2, 3, 2, 1, 3
[3, 1, 3, 3, 2, 3, 2, 2, 1] => 3, 1, 3, 3, 2, 3, 2, 2, 1
[3, 1, 3, 3, 2, 3, 2, 2, 2] => 3, 1, 3, 3, 2, 3, 2, 2, 2
[3, 1, 3, 3, 2, 3, 2, 2, 3] => 3, 1, 3, 3, 2, 3, 2, 2, 3
[3, 1, 3, 3, 2, 3, 2, 3, 1] => 3, 1, 3, 3, 2, 3, 2, 3, 1
[3, 1, 3, 3, 2, 3, 2, 3, 2] => 3, 1, 3, 3, 2, 3, 2, 3, 2
[3, 1, 3, 3, 2, 3, 2, 3, 3] => 3, 1, 3, 3, 2, 3, 2, 3, 3
[3, 1, 3, 3, 2, 3, 3, 1, 1] => 3, 1, 3, 3, 2, 3, 3, 1, 1
[3, 1, 3, 3, 2, 3, 3, 1, 2] => 3, 1, 3, 3, 2, 3, 3, 1, 2
[3, 1, 3, 3, 2, 3, 3, 1, 3] => 3, 1, 3, 3, 2, 3, 3, 1, 3
[3, 1, 3, 3, 2, 3, 3, 2, 1] => 3, 1, 3, 3, 2, 3, 3, 2, 1
[3, 1, 3, 3, 2, 3, 3, 2, 2] => 3, 1, 3, 3, 2, 3, 3, 2, 2
[3, 1, 3, 3, 2, 3, 3, 2, 3] => 3, 1, 3, 3, 2, 3, 3, 2, 3
[3, 1, 3, 3, 2, 3, 3, 3, 1] => 3, 1, 3, 3, 2, 3, 3, 3, 1
[3, 1, 3, 3, 2, 3, 3, 3, 2] => 3, 1, 3, 3, 2, 3, 3, 3, 2
[3, 1, 3, 3, 2, 3, 3, 3, 3] => 3, 1, 3, 3, 2, 3, 3, 3, 3
[3, 1, 3, 3, 3, 1, 1, 1, 1] => 3, 1, 3, 3, 3, 1, 1, 1, 1
[3, 1, 3, 3, 3, 1, 1, 1, 2] => 3, 1, 3, 3, 3, 1, 1, 1, 2
[3, 1, 3, 3, 3, 1, 1, 1, 3] => 3, 1, 3, 3, 3, 1, 1, 1, 3
[3, 1, 3, 3, 3, 1, 1, 2, 1] => 3, 1, 3, 3, 3, 1, 1, 2, 1
[3, 1, 3, 3, 3, 1, 1, 2, 2] => 3, 1, 3, 3, 3, 1, 1, 2, 2
[3, 1, 3, 3, 3, 1, 1, 2, 3] => 3, 1, 3, 3, 3, 1, 1, 2, 3
[3, 1, 3, 3, 3, 1, 1, 3, 1] => 3, 1, 3, 3, 3, 1, 1, 3, 1
[3, 1, 3, 3, 3, 1, 1, 3, 2] => 3, 1, 3, 3, 3, 1, 1, 3, 2
[3, 1, 3, 3, 3, 1, 1, 3, 3] => 3, 1, 3, 3, 3, 1, 1, 3, 3
[3, 1, 3, 3, 3, 1, 2, 1, 1] => 3, 1, 3, 3, 3, 1, 2, 1, 1
[3, 1, 3, 3, 3, 1, 2, 1, 2] => 3, 1, 3, 3, 3, 1, 2, 1, 2
[3, 1, 3, 3, 3, 1, 2, 1, 3] => 3, 1, 3, 3, 3, 1, 2, 1, 3
[3, 1, 3, 3, 3, 1, 2, 2, 1] => 3, 1, 3, 3, 3, 1, 2, 2, 1
[3, 1, 3, 3, 3, 1, 2, 2, 2] => 3, 1, 3, 3, 3, 1, 2, 2, 2
[3, 1, 3, 3, 3, 1, 2, 2, 3] => 3, 1, 3, 3, 3, 1, 2, 2, 3
[3, 1, 3, 3, 3, 1, 2, 3, 1] => 3, 1, 3, 3, 3, 1, 2, 3, 1
[3, 1, 3, 3, 3, 1, 2, 3, 2] => 3, 1, 3, 3, 3, 1, 2, 3, 2
[3, 1, 3, 3, 3, 1, 2, 3, 3] => 3, 1, 3, 3, 3, 1, 2, 3, 3
[3, 1, 3, 3, 3, 1, 3, 1, 1] => 3, 1, 3, 3, 3, 1, 3, 1, 1
[3, 1, 3, 3, 3, 1, 3, 1, 2] => 3, 1, 3, 3, 3, 1, 3, 1, 2
[3, 1, 3, 3, 3, 1, 3, 1, 3] => 3, 1, 3, 3, 3, 1, 3, 1, 3
[3, 1, 3, 3, 3, 1, 3, 2, 1] => 3, 1, 3, 3, 3, 1, 3, 2, 1
[3, 1, 3, 3, 3, 1, 3, 2, 2] => 3, 1, 3, 3, 3, 1, 3, 2, 2
[3, 1, 3, 3, 3, 1, 3, 2, 3] => 3, 1, 3, 3, 3, 1, 3, 2, 3
[3, 1, 3, 3, 3, 1, 3, 3, 1] => 3, 1, 3, 3, 3, 1, 3, 3, 1
[3, 1, 3, 3, 3, 1, 3, 3, 2] => 3, 1, 3, 3, 3, 1, 3, 3, 2
[3, 1, 3, 3, 3, 1, 3, 3, 3] => 3, 1, 3, 3, 3, 1, 3, 3, 3
[3, 1, 3, 3, 3, 2, 1, 1, 1] => 3, 1, 3, 3, 3, 2, 1, 1, 1
[3, 1, 3, 3, 3, 2, 1, 1, 2] => 3, 1, 3, 3, 3, 2, 1, 1, 2
[3, 1, 3, 3, 3, 2, 1, 1, 3] => 3, 1, 3, 3, 3, 2, 1, 1, 3
[3, 1, 3, 3, 3, 2, 1, 2, 1] => 3, 1, 3, 3, 3, 2, 1, 2, 1
[3, 1, 3, 3, 3, 2, 1, 2, 2] => 3, 1, 3, 3, 3, 2, 1, 2, 2
[3, 1, 3, 3, 3, 2, 1, 2, 3] => 3, 1, 3, 3, 3, 2, 1, 2, 3
[3, 1, 3, 3, 3, 2, 1, 3, 1] => 3, 1, 3, 3, 3, 2, 1, 3, 1
[3, 1, 3, 3, 3, 2, 1, 3, 2] => 3, 1, 3, 3, 3, 2, 1, 3, 2
[3, 1, 3, 3, 3, 2, 1, 3, 3] => 3, 1, 3, 3, 3, 2, 1, 3, 3
[3, 1, 3, 3, 3, 2, 2, 1, 1] => 3, 1, 3, 3, 3, 2, 2, 1, 1
[3, 1, 3, 3, 3, 2, 2, 1, 2] => 3, 1, 3, 3, 3, 2, 2, 1, 2
[3, 1, 3, 3, 3, 2, 2, 1, 3] => 3, 1, 3, 3, 3, 2, 2, 1, 3
[3, 1, 3, 3, 3, 2, 2, 2, 1] => 3, 1, 3, 3, 3, 2, 2, 2, 1
[3, 1, 3, 3, 3, 2, 2, 2, 2] => 3, 1, 3, 3, 3, 2, 2, 2, 2
[3, 1, 3, 3, 3, 2, 2, 2, 3] => 3, 1, 3, 3, 3, 2, 2, 2, 3
[3, 1, 3, 3, 3, 2, 2, 3, 1] => 3, 1, 3, 3, 3, 2, 2, 3, 1
[3, 1, 3, 3, 3, 2, 2, 3, 2] => 3, 1, 3, 3, 3, 2, 2, 3, 2
[3, 1, 3, 3, 3, 2, 2, 3, 3] => 3, 1, 3, 3, 3, 2, 2, 3, 3
[3, 1, 3, 3, 3, 2, 3, 1, 1] => 3, 1, 3, 3, 3, 2, 3, 1, 1
[3, 1, 3, 3, 3, 2, 3, 1, 2] => 3, 1, 3, 3, 3, 2, 3, 1, 2
[3, 1, 3, 3, 3, 2, 3, 1, 3] => 3, 1, 3, 3, 3, 2, 3, 1, 3
[3, 1, 3, 3, 3, 2, 3, 2, 1] => 3, 1, 3, 3, 3, 2, 3, 2, 1
[3, 1, 3, 3, 3, 2, 3, 2, 2] => 3, 1, 3, 3, 3, 2, 3, 2, 2
[3, 1, 3, 3, 3, 2, 3, 2, 3] => 3, 1, 3, 3, 3, 2, 3, 2, 3
[3, 1, 3, 3, 3, 2, 3, 3, 1] => 3, 1, 3, 3, 3, 2, 3, 3, 1
[3, 1, 3, 3, 3, 2, 3, 3, 2] => 3, 1, 3, 3, 3, 2, 3, 3, 2
[3, 1, 3, 3, 3, 2, 3, 3, 3] => 3, 1, 3, 3, 3, 2, 3, 3, 3
[3, 1, 3, 3, 3, 3, 1, 1, 1] => 3, 1, 3, 3, 3, 3, 1, 1, 1
[3, 1, 3, 3, 3, 3, 1, 1, 2] => 3, 1, 3, 3, 3, 3, 1, 1, 2
[3, 1, 3, 3, 3, 3, 1, 1, 3] => 3, 1, 3, 3, 3, 3, 1, 1, 3
[3, 1, 3, 3, 3, 3, 1, 2, 1] => 3, 1, 3, 3, 3, 3, 1, 2, 1
[3, 1, 3, 3, 3, 3, 1, 2, 2] => 3, 1, 3, 3, 3, 3, 1, 2, 2
[3, 1, 3, 3, 3, 3, 1, 2, 3] => 3, 1, 3, 3, 3, 3, 1, 2, 3
[3, 1, 3, 3, 3, 3, 1, 3, 1] => 3, 1, 3, 3, 3, 3, 1, 3, 1
[3, 1, 3, 3, 3, 3, 1, 3, 2] => 3, 1, 3, 3, 3, 3, 1, 3, 2
[3, 1, 3, 3, 3, 3, 1, 3, 3] => 3, 1, 3, 3, 3, 3, 1, 3, 3
[3, 1, 3, 3, 3, 3, 2, 1, 1] => 3, 1, 3, 3, 3, 3, 2, 1, 1
[3, 1, 3, 3, 3, 3, 2, 1, 2] => 3, 1, 3, 3, 3, 3, 2, 1, 2
[3, 1, 3, 3, 3, 3, 2, 1, 3] => 3, 1, 3, 3, 3, 3, 2, 1, 3
[3, 1, 3, 3, 3, 3, 2, 2, 1] => 3, 1, 3, 3, 3, 3, 2, 2, 1
[3, 1, 3, 3, 3, 3, 2, 2, 2] => 3, 1, 3, 3, 3, 3, 2, 2, 2
[3, 1, 3, 3, 3, 3, 2, 2, 3] => 3, 1, 3, 3, 3, 3, 2, 2, 3
[3, 1, 3, 3, 3, 3, 2, 3, 1] => 3, 1, 3, 3, 3, 3, 2, 3, 1
[3, 1, 3, 3, 3, 3, 2, 3, 2] => 3, 1, 3, 3, 3, 3, 2, 3, 2
[3, 1, 3, 3, 3, 3, 2, 3, 3] => 3, 1, 3, 3, 3, 3, 2, 3, 3
[3, 1, 3, 3, 3, 3, 3, 1, 1] => 3, 1, 3, 3, 3, 3, 3, 1, 1
[3, 1, 3, 3, 3, 3, 3, 1, 2] => 3, 1, 3, 3, 3, 3, 3, 1, 2
[3, 1, 3, 3, 3, 3, 3, 1, 3] => 3, 1, 3, 3, 3, 3, 3, 1, 3
[3, 1, 3, 3, 3, 3, 3, 2, 1] => 3, 1, 3, 3, 3, 3, 3, 2, 1
[3, 1, 3, 3, 3, 3, 3, 2, 2] => 3, 1, 3, 3, 3, 3, 3, 2, 2
[3, 1, 3, 3, 3, 3, 3, 2, 3] => 3, 1, 3, 3, 3, 3, 3, 2, 3
[3, 1, 3, 3, 3, 3, 3, 3, 1] => 3, 1, 3, 3, 3, 3, 3, 3, 1
[3, 1, 3, 3, 3, 3, 3, 3, 2] => 3, 1, 3, 3, 3, 3, 3, 3, 2
[3, 1, 3, 3, 3, 3, 3, 3, 3] => 3, 1, 3, 3, 3, 3, 3, 3, 3
[3, 2, 1, 1, 1, 1, 1, 1, 1] => 3, 2, 1, 1, 1, 1, 1, 1, 1
[3, 2, 1, 1, 1, 1, 1, 1, 2] => 3, 2, 1, 1, 1, 1, 1, 1, 2
[3, 2, 1, 1, 1, 1, 1, 1, 3] => 3, 2, 1, 1, 1, 1, 1, 1, 3
[3, 2, 1, 1, 1, 1, 1, 2, 1] => 3, 2, 1, 1, 1, 1, 1, 2, 1
[3, 2, 1, 1, 1, 1, 1, 2, 2] => 3, 2, 1, 1, 1, 1, 1, 2, 2
[3, 2, 1, 1, 1, 1, 1, 2, 3] => 3, 2, 1, 1, 1, 1, 1, 2, 3
[3, 2, 1, 1, 1, 1, 1, 3, 1] => 3, 2, 1, 1, 1, 1, 1, 3, 1
[3, 2, 1, 1, 1, 1, 1, 3, 2] => 3, 2, 1, 1, 1, 1, 1, 3, 2
[3, 2, 1, 1, 1, 1, 1, 3, 3] => 3, 2, 1, 1, 1, 1, 1, 3, 3
[3, 2, 1, 1, 1, 1, 2, 1, 1] => 3, 2, 1, 1, 1, 1, 2, 1, 1
[3, 2, 1, 1, 1, 1, 2, 1, 2] => 3, 2, 1, 1, 1, 1, 2, 1, 2
[3, 2, 1, 1, 1, 1, 2, 1, 3] => 3, 2, 1, 1, 1, 1, 2, 1, 3
[3, 2, 1, 1, 1, 1, 2, 2, 1] => 3, 2, 1, 1, 1, 1, 2, 2, 1
[3, 2, 1, 1, 1, 1, 2, 2, 2] => 3, 2, 1, 1, 1, 1, 2, 2, 2
[3, 2, 1, 1, 1, 1, 2, 2, 3] => 3, 2, 1, 1, 1, 1, 2, 2, 3
[3, 2, 1, 1, 1, 1, 2, 3, 1] => 3, 2, 1, 1, 1, 1, 2, 3, 1
[3, 2, 1, 1, 1, 1, 2, 3, 2] => 3, 2, 1, 1, 1, 1, 2, 3, 2
[3, 2, 1, 1, 1, 1, 2, 3, 3] => 3, 2, 1, 1, 1, 1, 2, 3, 3
[3, 2, 1, 1, 1, 1, 3, 1, 1] => 3, 2, 1, 1, 1, 1, 3, 1, 1
[3, 2, 1, 1, 1, 1, 3, 1, 2] => 3, 2, 1, 1, 1, 1, 3, 1, 2
[3, 2, 1, 1, 1, 1, 3, 1, 3] => 3, 2, 1, 1, 1, 1, 3, 1, 3
[3, 2, 1, 1, 1, 1, 3, 2, 1] => 3, 2, 1, 1, 1, 1, 3, 2, 1
[3, 2, 1, 1, 1, 1, 3, 2, 2] => 3, 2, 1, 1, 1, 1, 3, 2, 2
[3, 2, 1, 1, 1, 1, 3, 2, 3] => 3, 2, 1, 1, 1, 1, 3, 2, 3
[3, 2, 1, 1, 1, 1, 3, 3, 1] => 3, 2, 1, 1, 1, 1, 3, 3, 1
[3, 2, 1, 1, 1, 1, 3, 3, 2] => 3, 2, 1, 1, 1, 1, 3, 3, 2
[3, 2, 1, 1, 1, 1, 3, 3, 3] => 3, 2, 1, 1, 1, 1, 3, 3, 3
[3, 2, 1, 1, 1, 2, 1, 1, 1] => 3, 2, 1, 1, 1, 2, 1, 1, 1
[3, 2, 1, 1, 1, 2, 1, 1, 2] => 3, 2, 1, 1, 1, 2, 1, 1, 2
[3, 2, 1, 1, 1, 2, 1, 1, 3] => 3, 2, 1, 1, 1, 2, 1, 1, 3
[3, 2, 1, 1, 1, 2, 1, 2, 1] => 3, 2, 1, 1, 1, 2, 1, 2, 1
[3, 2, 1, 1, 1, 2, 1, 2, 2] => 3, 2, 1, 1, 1, 2, 1, 2, 2
[3, 2, 1, 1, 1, 2, 1, 2, 3] => 3, 2, 1, 1, 1, 2, 1, 2, 3
[3, 2, 1, 1, 1, 2, 1, 3, 1] => 3, 2, 1, 1, 1, 2, 1, 3, 1
[3, 2, 1, 1, 1, 2, 1, 3, 2] => 3, 2, 1, 1, 1, 2, 1, 3, 2
[3, 2, 1, 1, 1, 2, 1, 3, 3] => 3, 2, 1, 1, 1, 2, 1, 3, 3
[3, 2, 1, 1, 1, 2, 2, 1, 1] => 3, 2, 1, 1, 1, 2, 2, 1, 1
[3, 2, 1, 1, 1, 2, 2, 1, 2] => 3, 2, 1, 1, 1, 2, 2, 1, 2
[3, 2, 1, 1, 1, 2, 2, 1, 3] => 3, 2, 1, 1, 1, 2, 2, 1, 3
[3, 2, 1, 1, 1, 2, 2, 2, 1] => 3, 2, 1, 1, 1, 2, 2, 2, 1
[3, 2, 1, 1, 1, 2, 2, 2, 2] => 3, 2, 1, 1, 1, 2, 2, 2, 2
[3, 2, 1, 1, 1, 2, 2, 2, 3] => 3, 2, 1, 1, 1, 2, 2, 2, 3
[3, 2, 1, 1, 1, 2, 2, 3, 1] => 3, 2, 1, 1, 1, 2, 2, 3, 1
[3, 2, 1, 1, 1, 2, 2, 3, 2] => 3, 2, 1, 1, 1, 2, 2, 3, 2
[3, 2, 1, 1, 1, 2, 2, 3, 3] => 3, 2, 1, 1, 1, 2, 2, 3, 3
[3, 2, 1, 1, 1, 2, 3, 1, 1] => 3, 2, 1, 1, 1, 2, 3, 1, 1
[3, 2, 1, 1, 1, 2, 3, 1, 2] => 3, 2, 1, 1, 1, 2, 3, 1, 2
[3, 2, 1, 1, 1, 2, 3, 1, 3] => 3, 2, 1, 1, 1, 2, 3, 1, 3
[3, 2, 1, 1, 1, 2, 3, 2, 1] => 3, 2, 1, 1, 1, 2, 3, 2, 1
[3, 2, 1, 1, 1, 2, 3, 2, 2] => 3, 2, 1, 1, 1, 2, 3, 2, 2
[3, 2, 1, 1, 1, 2, 3, 2, 3] => 3, 2, 1, 1, 1, 2, 3, 2, 3
[3, 2, 1, 1, 1, 2, 3, 3, 1] => 3, 2, 1, 1, 1, 2, 3, 3, 1
[3, 2, 1, 1, 1, 2, 3, 3, 2] => 3, 2, 1, 1, 1, 2, 3, 3, 2
[3, 2, 1, 1, 1, 2, 3, 3, 3] => 3, 2, 1, 1, 1, 2, 3, 3, 3
[3, 2, 1, 1, 1, 3, 1, 1, 1] => 3, 2, 1, 1, 1, 3, 1, 1, 1
[3, 2, 1, 1, 1, 3, 1, 1, 2] => 3, 2, 1, 1, 1, 3, 1, 1, 2
[3, 2, 1, 1, 1, 3, 1, 1, 3] => 3, 2, 1, 1, 1, 3, 1, 1, 3
[3, 2, 1, 1, 1, 3, 1, 2, 1] => 3, 2, 1, 1, 1, 3, 1, 2, 1
[3, 2, 1, 1, 1, 3, 1, 2, 2] => 3, 2, 1, 1, 1, 3, 1, 2, 2
[3, 2, 1, 1, 1, 3, 1, 2, 3] => 3, 2, 1, 1, 1, 3, 1, 2, 3
[3, 2, 1, 1, 1, 3, 1, 3, 1] => 3, 2, 1, 1, 1, 3, 1, 3, 1
[3, 2, 1, 1, 1, 3, 1, 3, 2] => 3, 2, 1, 1, 1, 3, 1, 3, 2
[3, 2, 1, 1, 1, 3, 1, 3, 3] => 3, 2, 1, 1, 1, 3, 1, 3, 3
[3, 2, 1, 1, 1, 3, 2, 1, 1] => 3, 2, 1, 1, 1, 3, 2, 1, 1
[3, 2, 1, 1, 1, 3, 2, 1, 2] => 3, 2, 1, 1, 1, 3, 2, 1, 2
[3, 2, 1, 1, 1, 3, 2, 1, 3] => 3, 2, 1, 1, 1, 3, 2, 1, 3
[3, 2, 1, 1, 1, 3, 2, 2, 1] => 3, 2, 1, 1, 1, 3, 2, 2, 1
[3, 2, 1, 1, 1, 3, 2, 2, 2] => 3, 2, 1, 1, 1, 3, 2, 2, 2
[3, 2, 1, 1, 1, 3, 2, 2, 3] => 3, 2, 1, 1, 1, 3, 2, 2, 3
[3, 2, 1, 1, 1, 3, 2, 3, 1] => 3, 2, 1, 1, 1, 3, 2, 3, 1
[3, 2, 1, 1, 1, 3, 2, 3, 2] => 3, 2, 1, 1, 1, 3, 2, 3, 2
[3, 2, 1, 1, 1, 3, 2, 3, 3] => 3, 2, 1, 1, 1, 3, 2, 3, 3
[3, 2, 1, 1, 1, 3, 3, 1, 1] => 3, 2, 1, 1, 1, 3, 3, 1, 1
[3, 2, 1, 1, 1, 3, 3, 1, 2] => 3, 2, 1, 1, 1, 3, 3, 1, 2
[3, 2, 1, 1, 1, 3, 3, 1, 3] => 3, 2, 1, 1, 1, 3, 3, 1, 3
[3, 2, 1, 1, 1, 3, 3, 2, 1] => 3, 2, 1, 1, 1, 3, 3, 2, 1
[3, 2, 1, 1, 1, 3, 3, 2, 2] => 3, 2, 1, 1, 1, 3, 3, 2, 2
[3, 2, 1, 1, 1, 3, 3, 2, 3] => 3, 2, 1, 1, 1, 3, 3, 2, 3
[3, 2, 1, 1, 1, 3, 3, 3, 1] => 3, 2, 1, 1, 1, 3, 3, 3, 1
[3, 2, 1, 1, 1, 3, 3, 3, 2] => 3, 2, 1, 1, 1, 3, 3, 3, 2
[3, 2, 1, 1, 1, 3, 3, 3, 3] => 3, 2, 1, 1, 1, 3, 3, 3, 3
[3, 2, 1, 1, 2, 1, 1, 1, 1] => 3, 2, 1, 1, 2, 1, 1, 1, 1
[3, 2, 1, 1, 2, 1, 1, 1, 2] => 3, 2, 1, 1, 2, 1, 1, 1, 2
[3, 2, 1, 1, 2, 1, 1, 1, 3] => 3, 2, 1, 1, 2, 1, 1, 1, 3
[3, 2, 1, 1, 2, 1, 1, 2, 1] => 3, 2, 1, 1, 2, 1, 1, 2, 1
[3, 2, 1, 1, 2, 1, 1, 2, 2] => 3, 2, 1, 1, 2, 1, 1, 2, 2
[3, 2, 1, 1, 2, 1, 1, 2, 3] => 3, 2, 1, 1, 2, 1, 1, 2, 3
[3, 2, 1, 1, 2, 1, 1, 3, 1] => 3, 2, 1, 1, 2, 1, 1, 3, 1
[3, 2, 1, 1, 2, 1, 1, 3, 2] => 3, 2, 1, 1, 2, 1, 1, 3, 2
[3, 2, 1, 1, 2, 1, 1, 3, 3] => 3, 2, 1, 1, 2, 1, 1, 3, 3
[3, 2, 1, 1, 2, 1, 2, 1, 1] => 3, 2, 1, 1, 2, 1, 2, 1, 1
[3, 2, 1, 1, 2, 1, 2, 1, 2] => 3, 2, 1, 1, 2, 1, 2, 1, 2
[3, 2, 1, 1, 2, 1, 2, 1, 3] => 3, 2, 1, 1, 2, 1, 2, 1, 3
[3, 2, 1, 1, 2, 1, 2, 2, 1] => 3, 2, 1, 1, 2, 1, 2, 2, 1
[3, 2, 1, 1, 2, 1, 2, 2, 2] => 3, 2, 1, 1, 2, 1, 2, 2, 2
[3, 2, 1, 1, 2, 1, 2, 2, 3] => 3, 2, 1, 1, 2, 1, 2, 2, 3
[3, 2, 1, 1, 2, 1, 2, 3, 1] => 3, 2, 1, 1, 2, 1, 2, 3, 1
[3, 2, 1, 1, 2, 1, 2, 3, 2] => 3, 2, 1, 1, 2, 1, 2, 3, 2
[3, 2, 1, 1, 2, 1, 2, 3, 3] => 3, 2, 1, 1, 2, 1, 2, 3, 3
[3, 2, 1, 1, 2, 1, 3, 1, 1] => 3, 2, 1, 1, 2, 1, 3, 1, 1
[3, 2, 1, 1, 2, 1, 3, 1, 2] => 3, 2, 1, 1, 2, 1, 3, 1, 2
[3, 2, 1, 1, 2, 1, 3, 1, 3] => 3, 2, 1, 1, 2, 1, 3, 1, 3
[3, 2, 1, 1, 2, 1, 3, 2, 1] => 3, 2, 1, 1, 2, 1, 3, 2, 1
[3, 2, 1, 1, 2, 1, 3, 2, 2] => 3, 2, 1, 1, 2, 1, 3, 2, 2
[3, 2, 1, 1, 2, 1, 3, 2, 3] => 3, 2, 1, 1, 2, 1, 3, 2, 3
[3, 2, 1, 1, 2, 1, 3, 3, 1] => 3, 2, 1, 1, 2, 1, 3, 3, 1
[3, 2, 1, 1, 2, 1, 3, 3, 2] => 3, 2, 1, 1, 2, 1, 3, 3, 2
[3, 2, 1, 1, 2, 1, 3, 3, 3] => 3, 2, 1, 1, 2, 1, 3, 3, 3
[3, 2, 1, 1, 2, 2, 1, 1, 1] => 3, 2, 1, 1, 2, 2, 1, 1, 1
[3, 2, 1, 1, 2, 2, 1, 1, 2] => 3, 2, 1, 1, 2, 2, 1, 1, 2
[3, 2, 1, 1, 2, 2, 1, 1, 3] => 3, 2, 1, 1, 2, 2, 1, 1, 3
[3, 2, 1, 1, 2, 2, 1, 2, 1] => 3, 2, 1, 1, 2, 2, 1, 2, 1
[3, 2, 1, 1, 2, 2, 1, 2, 2] => 3, 2, 1, 1, 2, 2, 1, 2, 2
[3, 2, 1, 1, 2, 2, 1, 2, 3] => 3, 2, 1, 1, 2, 2, 1, 2, 3
[3, 2, 1, 1, 2, 2, 1, 3, 1] => 3, 2, 1, 1, 2, 2, 1, 3, 1
[3, 2, 1, 1, 2, 2, 1, 3, 2] => 3, 2, 1, 1, 2, 2, 1, 3, 2
[3, 2, 1, 1, 2, 2, 1, 3, 3] => 3, 2, 1, 1, 2, 2, 1, 3, 3
[3, 2, 1, 1, 2, 2, 2, 1, 1] => 3, 2, 1, 1, 2, 2, 2, 1, 1
[3, 2, 1, 1, 2, 2, 2, 1, 2] => 3, 2, 1, 1, 2, 2, 2, 1, 2
[3, 2, 1, 1, 2, 2, 2, 1, 3] => 3, 2, 1, 1, 2, 2, 2, 1, 3
[3, 2, 1, 1, 2, 2, 2, 2, 1] => 3, 2, 1, 1, 2, 2, 2, 2, 1
[3, 2, 1, 1, 2, 2, 2, 2, 2] => 3, 2, 1, 1, 2, 2, 2, 2, 2
[3, 2, 1, 1, 2, 2, 2, 2, 3] => 3, 2, 1, 1, 2, 2, 2, 2, 3
[3, 2, 1, 1, 2, 2, 2, 3, 1] => 3, 2, 1, 1, 2, 2, 2, 3, 1
[3, 2, 1, 1, 2, 2, 2, 3, 2] => 3, 2, 1, 1, 2, 2, 2, 3, 2
[3, 2, 1, 1, 2, 2, 2, 3, 3] => 3, 2, 1, 1, 2, 2, 2, 3, 3
[3, 2, 1, 1, 2, 2, 3, 1, 1] => 3, 2, 1, 1, 2, 2, 3, 1, 1
[3, 2, 1, 1, 2, 2, 3, 1, 2] => 3, 2, 1, 1, 2, 2, 3, 1, 2
[3, 2, 1, 1, 2, 2, 3, 1, 3] => 3, 2, 1, 1, 2, 2, 3, 1, 3
[3, 2, 1, 1, 2, 2, 3, 2, 1] => 3, 2, 1, 1, 2, 2, 3, 2, 1
[3, 2, 1, 1, 2, 2, 3, 2, 2] => 3, 2, 1, 1, 2, 2, 3, 2, 2
[3, 2, 1, 1, 2, 2, 3, 2, 3] => 3, 2, 1, 1, 2, 2, 3, 2, 3
[3, 2, 1, 1, 2, 2, 3, 3, 1] => 3, 2, 1, 1, 2, 2, 3, 3, 1
[3, 2, 1, 1, 2, 2, 3, 3, 2] => 3, 2, 1, 1, 2, 2, 3, 3, 2
[3, 2, 1, 1, 2, 2, 3, 3, 3] => 3, 2, 1, 1, 2, 2, 3, 3, 3
[3, 2, 1, 1, 2, 3, 1, 1, 1] => 3, 2, 1, 1, 2, 3, 1, 1, 1
[3, 2, 1, 1, 2, 3, 1, 1, 2] => 3, 2, 1, 1, 2, 3, 1, 1, 2
[3, 2, 1, 1, 2, 3, 1, 1, 3] => 3, 2, 1, 1, 2, 3, 1, 1, 3
[3, 2, 1, 1, 2, 3, 1, 2, 1] => 3, 2, 1, 1, 2, 3, 1, 2, 1
[3, 2, 1, 1, 2, 3, 1, 2, 2] => 3, 2, 1, 1, 2, 3, 1, 2, 2
[3, 2, 1, 1, 2, 3, 1, 2, 3] => 3, 2, 1, 1, 2, 3, 1, 2, 3
[3, 2, 1, 1, 2, 3, 1, 3, 1] => 3, 2, 1, 1, 2, 3, 1, 3, 1
[3, 2, 1, 1, 2, 3, 1, 3, 2] => 3, 2, 1, 1, 2, 3, 1, 3, 2
[3, 2, 1, 1, 2, 3, 1, 3, 3] => 3, 2, 1, 1, 2, 3, 1, 3, 3
[3, 2, 1, 1, 2, 3, 2, 1, 1] => 3, 2, 1, 1, 2, 3, 2, 1, 1
[3, 2, 1, 1, 2, 3, 2, 1, 2] => 3, 2, 1, 1, 2, 3, 2, 1, 2
[3, 2, 1, 1, 2, 3, 2, 1, 3] => 3, 2, 1, 1, 2, 3, 2, 1, 3
[3, 2, 1, 1, 2, 3, 2, 2, 1] => 3, 2, 1, 1, 2, 3, 2, 2, 1
[3, 2, 1, 1, 2, 3, 2, 2, 2] => 3, 2, 1, 1, 2, 3, 2, 2, 2
[3, 2, 1, 1, 2, 3, 2, 2, 3] => 3, 2, 1, 1, 2, 3, 2, 2, 3
[3, 2, 1, 1, 2, 3, 2, 3, 1] => 3, 2, 1, 1, 2, 3, 2, 3, 1
[3, 2, 1, 1, 2, 3, 2, 3, 2] => 3, 2, 1, 1, 2, 3, 2, 3, 2
[3, 2, 1, 1, 2, 3, 2, 3, 3] => 3, 2, 1, 1, 2, 3, 2, 3, 3
[3, 2, 1, 1, 2, 3, 3, 1, 1] => 3, 2, 1, 1, 2, 3, 3, 1, 1
[3, 2, 1, 1, 2, 3, 3, 1, 2] => 3, 2, 1, 1, 2, 3, 3, 1, 2
[3, 2, 1, 1, 2, 3, 3, 1, 3] => 3, 2, 1, 1, 2, 3, 3, 1, 3
[3, 2, 1, 1, 2, 3, 3, 2, 1] => 3, 2, 1, 1, 2, 3, 3, 2, 1
[3, 2, 1, 1, 2, 3, 3, 2, 2] => 3, 2, 1, 1, 2, 3, 3, 2, 2
[3, 2, 1, 1, 2, 3, 3, 2, 3] => 3, 2, 1, 1, 2, 3, 3, 2, 3
[3, 2, 1, 1, 2, 3, 3, 3, 1] => 3, 2, 1, 1, 2, 3, 3, 3, 1
[3, 2, 1, 1, 2, 3, 3, 3, 2] => 3, 2, 1, 1, 2, 3, 3, 3, 2
[3, 2, 1, 1, 2, 3, 3, 3, 3] => 3, 2, 1, 1, 2, 3, 3, 3, 3
[3, 2, 1, 1, 3, 1, 1, 1, 1] => 3, 2, 1, 1, 3, 1, 1, 1, 1
[3, 2, 1, 1, 3, 1, 1, 1, 2] => 3, 2, 1, 1, 3, 1, 1, 1, 2
[3, 2, 1, 1, 3, 1, 1, 1, 3] => 3, 2, 1, 1, 3, 1, 1, 1, 3
[3, 2, 1, 1, 3, 1, 1, 2, 1] => 3, 2, 1, 1, 3, 1, 1, 2, 1
[3, 2, 1, 1, 3, 1, 1, 2, 2] => 3, 2, 1, 1, 3, 1, 1, 2, 2
[3, 2, 1, 1, 3, 1, 1, 2, 3] => 3, 2, 1, 1, 3, 1, 1, 2, 3
[3, 2, 1, 1, 3, 1, 1, 3, 1] => 3, 2, 1, 1, 3, 1, 1, 3, 1
[3, 2, 1, 1, 3, 1, 1, 3, 2] => 3, 2, 1, 1, 3, 1, 1, 3, 2
[3, 2, 1, 1, 3, 1, 1, 3, 3] => 3, 2, 1, 1, 3, 1, 1, 3, 3
[3, 2, 1, 1, 3, 1, 2, 1, 1] => 3, 2, 1, 1, 3, 1, 2, 1, 1
[3, 2, 1, 1, 3, 1, 2, 1, 2] => 3, 2, 1, 1, 3, 1, 2, 1, 2
[3, 2, 1, 1, 3, 1, 2, 1, 3] => 3, 2, 1, 1, 3, 1, 2, 1, 3
[3, 2, 1, 1, 3, 1, 2, 2, 1] => 3, 2, 1, 1, 3, 1, 2, 2, 1
[3, 2, 1, 1, 3, 1, 2, 2, 2] => 3, 2, 1, 1, 3, 1, 2, 2, 2
[3, 2, 1, 1, 3, 1, 2, 2, 3] => 3, 2, 1, 1, 3, 1, 2, 2, 3
[3, 2, 1, 1, 3, 1, 2, 3, 1] => 3, 2, 1, 1, 3, 1, 2, 3, 1
[3, 2, 1, 1, 3, 1, 2, 3, 2] => 3, 2, 1, 1, 3, 1, 2, 3, 2
[3, 2, 1, 1, 3, 1, 2, 3, 3] => 3, 2, 1, 1, 3, 1, 2, 3, 3
[3, 2, 1, 1, 3, 1, 3, 1, 1] => 3, 2, 1, 1, 3, 1, 3, 1, 1
[3, 2, 1, 1, 3, 1, 3, 1, 2] => 3, 2, 1, 1, 3, 1, 3, 1, 2
[3, 2, 1, 1, 3, 1, 3, 1, 3] => 3, 2, 1, 1, 3, 1, 3, 1, 3
[3, 2, 1, 1, 3, 1, 3, 2, 1] => 3, 2, 1, 1, 3, 1, 3, 2, 1
[3, 2, 1, 1, 3, 1, 3, 2, 2] => 3, 2, 1, 1, 3, 1, 3, 2, 2
[3, 2, 1, 1, 3, 1, 3, 2, 3] => 3, 2, 1, 1, 3, 1, 3, 2, 3
[3, 2, 1, 1, 3, 1, 3, 3, 1] => 3, 2, 1, 1, 3, 1, 3, 3, 1
[3, 2, 1, 1, 3, 1, 3, 3, 2] => 3, 2, 1, 1, 3, 1, 3, 3, 2
[3, 2, 1, 1, 3, 1, 3, 3, 3] => 3, 2, 1, 1, 3, 1, 3, 3, 3
[3, 2, 1, 1, 3, 2, 1, 1, 1] => 3, 2, 1, 1, 3, 2, 1, 1, 1
[3, 2, 1, 1, 3, 2, 1, 1, 2] => 3, 2, 1, 1, 3, 2, 1, 1, 2
[3, 2, 1, 1, 3, 2, 1, 1, 3] => 3, 2, 1, 1, 3, 2, 1, 1, 3
[3, 2, 1, 1, 3, 2, 1, 2, 1] => 3, 2, 1, 1, 3, 2, 1, 2, 1
[3, 2, 1, 1, 3, 2, 1, 2, 2] => 3, 2, 1, 1, 3, 2, 1, 2, 2
[3, 2, 1, 1, 3, 2, 1, 2, 3] => 3, 2, 1, 1, 3, 2, 1, 2, 3
[3, 2, 1, 1, 3, 2, 1, 3, 1] => 3, 2, 1, 1, 3, 2, 1, 3, 1
[3, 2, 1, 1, 3, 2, 1, 3, 2] => 3, 2, 1, 1, 3, 2, 1, 3, 2
[3, 2, 1, 1, 3, 2, 1, 3, 3] => 3, 2, 1, 1, 3, 2, 1, 3, 3
[3, 2, 1, 1, 3, 2, 2, 1, 1] => 3, 2, 1, 1, 3, 2, 2, 1, 1
[3, 2, 1, 1, 3, 2, 2, 1, 2] => 3, 2, 1, 1, 3, 2, 2, 1, 2
[3, 2, 1, 1, 3, 2, 2, 1, 3] => 3, 2, 1, 1, 3, 2, 2, 1, 3
[3, 2, 1, 1, 3, 2, 2, 2, 1] => 3, 2, 1, 1, 3, 2, 2, 2, 1
[3, 2, 1, 1, 3, 2, 2, 2, 2] => 3, 2, 1, 1, 3, 2, 2, 2, 2
[3, 2, 1, 1, 3, 2, 2, 2, 3] => 3, 2, 1, 1, 3, 2, 2, 2, 3
[3, 2, 1, 1, 3, 2, 2, 3, 1] => 3, 2, 1, 1, 3, 2, 2, 3, 1
[3, 2, 1, 1, 3, 2, 2, 3, 2] => 3, 2, 1, 1, 3, 2, 2, 3, 2
[3, 2, 1, 1, 3, 2, 2, 3, 3] => 3, 2, 1, 1, 3, 2, 2, 3, 3
[3, 2, 1, 1, 3, 2, 3, 1, 1] => 3, 2, 1, 1, 3, 2, 3, 1, 1
[3, 2, 1, 1, 3, 2, 3, 1, 2] => 3, 2, 1, 1, 3, 2, 3, 1, 2
[3, 2, 1, 1, 3, 2, 3, 1, 3] => 3, 2, 1, 1, 3, 2, 3, 1, 3
[3, 2, 1, 1, 3, 2, 3, 2, 1] => 3, 2, 1, 1, 3, 2, 3, 2, 1
[3, 2, 1, 1, 3, 2, 3, 2, 2] => 3, 2, 1, 1, 3, 2, 3, 2, 2
[3, 2, 1, 1, 3, 2, 3, 2, 3] => 3, 2, 1, 1, 3, 2, 3, 2, 3
[3, 2, 1, 1, 3, 2, 3, 3, 1] => 3, 2, 1, 1, 3, 2, 3, 3, 1
[3, 2, 1, 1, 3, 2, 3, 3, 2] => 3, 2, 1, 1, 3, 2, 3, 3, 2
[3, 2, 1, 1, 3, 2, 3, 3, 3] => 3, 2, 1, 1, 3, 2, 3, 3, 3
[3, 2, 1, 1, 3, 3, 1, 1, 1] => 3, 2, 1, 1, 3, 3, 1, 1, 1
[3, 2, 1, 1, 3, 3, 1, 1, 2] => 3, 2, 1, 1, 3, 3, 1, 1, 2
[3, 2, 1, 1, 3, 3, 1, 1, 3] => 3, 2, 1, 1, 3, 3, 1, 1, 3
[3, 2, 1, 1, 3, 3, 1, 2, 1] => 3, 2, 1, 1, 3, 3, 1, 2, 1
[3, 2, 1, 1, 3, 3, 1, 2, 2] => 3, 2, 1, 1, 3, 3, 1, 2, 2
[3, 2, 1, 1, 3, 3, 1, 2, 3] => 3, 2, 1, 1, 3, 3, 1, 2, 3
[3, 2, 1, 1, 3, 3, 1, 3, 1] => 3, 2, 1, 1, 3, 3, 1, 3, 1
[3, 2, 1, 1, 3, 3, 1, 3, 2] => 3, 2, 1, 1, 3, 3, 1, 3, 2
[3, 2, 1, 1, 3, 3, 1, 3, 3] => 3, 2, 1, 1, 3, 3, 1, 3, 3
[3, 2, 1, 1, 3, 3, 2, 1, 1] => 3, 2, 1, 1, 3, 3, 2, 1, 1
[3, 2, 1, 1, 3, 3, 2, 1, 2] => 3, 2, 1, 1, 3, 3, 2, 1, 2
[3, 2, 1, 1, 3, 3, 2, 1, 3] => 3, 2, 1, 1, 3, 3, 2, 1, 3
[3, 2, 1, 1, 3, 3, 2, 2, 1] => 3, 2, 1, 1, 3, 3, 2, 2, 1
[3, 2, 1, 1, 3, 3, 2, 2, 2] => 3, 2, 1, 1, 3, 3, 2, 2, 2
[3, 2, 1, 1, 3, 3, 2, 2, 3] => 3, 2, 1, 1, 3, 3, 2, 2, 3
[3, 2, 1, 1, 3, 3, 2, 3, 1] => 3, 2, 1, 1, 3, 3, 2, 3, 1
[3, 2, 1, 1, 3, 3, 2, 3, 2] => 3, 2, 1, 1, 3, 3, 2, 3, 2
[3, 2, 1, 1, 3, 3, 2, 3, 3] => 3, 2, 1, 1, 3, 3, 2, 3, 3
[3, 2, 1, 1, 3, 3, 3, 1, 1] => 3, 2, 1, 1, 3, 3, 3, 1, 1
[3, 2, 1, 1, 3, 3, 3, 1, 2] => 3, 2, 1, 1, 3, 3, 3, 1, 2
[3, 2, 1, 1, 3, 3, 3, 1, 3] => 3, 2, 1, 1, 3, 3, 3, 1, 3
[3, 2, 1, 1, 3, 3, 3, 2, 1] => 3, 2, 1, 1, 3, 3, 3, 2, 1
[3, 2, 1, 1, 3, 3, 3, 2, 2] => 3, 2, 1, 1, 3, 3, 3, 2, 2
[3, 2, 1, 1, 3, 3, 3, 2, 3] => 3, 2, 1, 1, 3, 3, 3, 2, 3
[3, 2, 1, 1, 3, 3, 3, 3, 1] => 3, 2, 1, 1, 3, 3, 3, 3, 1
[3, 2, 1, 1, 3, 3, 3, 3, 2] => 3, 2, 1, 1, 3, 3, 3, 3, 2
[3, 2, 1, 1, 3, 3, 3, 3, 3] => 3, 2, 1, 1, 3, 3, 3, 3, 3
[3, 2, 1, 2, 1, 1, 1, 1, 1] => 3, 2, 1, 2, 1, 1, 1, 1, 1
[3, 2, 1, 2, 1, 1, 1, 1, 2] => 3, 2, 1, 2, 1, 1, 1, 1, 2
[3, 2, 1, 2, 1, 1, 1, 1, 3] => 3, 2, 1, 2, 1, 1, 1, 1, 3
[3, 2, 1, 2, 1, 1, 1, 2, 1] => 3, 2, 1, 2, 1, 1, 1, 2, 1
[3, 2, 1, 2, 1, 1, 1, 2, 2] => 3, 2, 1, 2, 1, 1, 1, 2, 2
[3, 2, 1, 2, 1, 1, 1, 2, 3] => 3, 2, 1, 2, 1, 1, 1, 2, 3
[3, 2, 1, 2, 1, 1, 1, 3, 1] => 3, 2, 1, 2, 1, 1, 1, 3, 1
[3, 2, 1, 2, 1, 1, 1, 3, 2] => 3, 2, 1, 2, 1, 1, 1, 3, 2
[3, 2, 1, 2, 1, 1, 1, 3, 3] => 3, 2, 1, 2, 1, 1, 1, 3, 3
[3, 2, 1, 2, 1, 1, 2, 1, 1] => 3, 2, 1, 2, 1, 1, 2, 1, 1
[3, 2, 1, 2, 1, 1, 2, 1, 2] => 3, 2, 1, 2, 1, 1, 2, 1, 2
[3, 2, 1, 2, 1, 1, 2, 1, 3] => 3, 2, 1, 2, 1, 1, 2, 1, 3
[3, 2, 1, 2, 1, 1, 2, 2, 1] => 3, 2, 1, 2, 1, 1, 2, 2, 1
[3, 2, 1, 2, 1, 1, 2, 2, 2] => 3, 2, 1, 2, 1, 1, 2, 2, 2
[3, 2, 1, 2, 1, 1, 2, 2, 3] => 3, 2, 1, 2, 1, 1, 2, 2, 3
[3, 2, 1, 2, 1, 1, 2, 3, 1] => 3, 2, 1, 2, 1, 1, 2, 3, 1
[3, 2, 1, 2, 1, 1, 2, 3, 2] => 3, 2, 1, 2, 1, 1, 2, 3, 2
[3, 2, 1, 2, 1, 1, 2, 3, 3] => 3, 2, 1, 2, 1, 1, 2, 3, 3
[3, 2, 1, 2, 1, 1, 3, 1, 1] => 3, 2, 1, 2, 1, 1, 3, 1, 1
[3, 2, 1, 2, 1, 1, 3, 1, 2] => 3, 2, 1, 2, 1, 1, 3, 1, 2
[3, 2, 1, 2, 1, 1, 3, 1, 3] => 3, 2, 1, 2, 1, 1, 3, 1, 3
[3, 2, 1, 2, 1, 1, 3, 2, 1] => 3, 2, 1, 2, 1, 1, 3, 2, 1
[3, 2, 1, 2, 1, 1, 3, 2, 2] => 3, 2, 1, 2, 1, 1, 3, 2, 2
[3, 2, 1, 2, 1, 1, 3, 2, 3] => 3, 2, 1, 2, 1, 1, 3, 2, 3
[3, 2, 1, 2, 1, 1, 3, 3, 1] => 3, 2, 1, 2, 1, 1, 3, 3, 1
[3, 2, 1, 2, 1, 1, 3, 3, 2] => 3, 2, 1, 2, 1, 1, 3, 3, 2
[3, 2, 1, 2, 1, 1, 3, 3, 3] => 3, 2, 1, 2, 1, 1, 3, 3, 3
[3, 2, 1, 2, 1, 2, 1, 1, 1] => 3, 2, 1, 2, 1, 2, 1, 1, 1
[3, 2, 1, 2, 1, 2, 1, 1, 2] => 3, 2, 1, 2, 1, 2, 1, 1, 2
[3, 2, 1, 2, 1, 2, 1, 1, 3] => 3, 2, 1, 2, 1, 2, 1, 1, 3
[3, 2, 1, 2, 1, 2, 1, 2, 1] => 3, 2, 1, 2, 1, 2, 1, 2, 1
[3, 2, 1, 2, 1, 2, 1, 2, 2] => 3, 2, 1, 2, 1, 2, 1, 2, 2
[3, 2, 1, 2, 1, 2, 1, 2, 3] => 3, 2, 1, 2, 1, 2, 1, 2, 3
[3, 2, 1, 2, 1, 2, 1, 3, 1] => 3, 2, 1, 2, 1, 2, 1, 3, 1
[3, 2, 1, 2, 1, 2, 1, 3, 2] => 3, 2, 1, 2, 1, 2, 1, 3, 2
[3, 2, 1, 2, 1, 2, 1, 3, 3] => 3, 2, 1, 2, 1, 2, 1, 3, 3
[3, 2, 1, 2, 1, 2, 2, 1, 1] => 3, 2, 1, 2, 1, 2, 2, 1, 1
[3, 2, 1, 2, 1, 2, 2, 1, 2] => 3, 2, 1, 2, 1, 2, 2, 1, 2
[3, 2, 1, 2, 1, 2, 2, 1, 3] => 3, 2, 1, 2, 1, 2, 2, 1, 3
[3, 2, 1, 2, 1, 2, 2, 2, 1] => 3, 2, 1, 2, 1, 2, 2, 2, 1
[3, 2, 1, 2, 1, 2, 2, 2, 2] => 3, 2, 1, 2, 1, 2, 2, 2, 2
[3, 2, 1, 2, 1, 2, 2, 2, 3] => 3, 2, 1, 2, 1, 2, 2, 2, 3
[3, 2, 1, 2, 1, 2, 2, 3, 1] => 3, 2, 1, 2, 1, 2, 2, 3, 1
[3, 2, 1, 2, 1, 2, 2, 3, 2] => 3, 2, 1, 2, 1, 2, 2, 3, 2
[3, 2, 1, 2, 1, 2, 2, 3, 3] => 3, 2, 1, 2, 1, 2, 2, 3, 3
[3, 2, 1, 2, 1, 2, 3, 1, 1] => 3, 2, 1, 2, 1, 2, 3, 1, 1
[3, 2, 1, 2, 1, 2, 3, 1, 2] => 3, 2, 1, 2, 1, 2, 3, 1, 2
[3, 2, 1, 2, 1, 2, 3, 1, 3] => 3, 2, 1, 2, 1, 2, 3, 1, 3
[3, 2, 1, 2, 1, 2, 3, 2, 1] => 3, 2, 1, 2, 1, 2, 3, 2, 1
[3, 2, 1, 2, 1, 2, 3, 2, 2] => 3, 2, 1, 2, 1, 2, 3, 2, 2
[3, 2, 1, 2, 1, 2, 3, 2, 3] => 3, 2, 1, 2, 1, 2, 3, 2, 3
[3, 2, 1, 2, 1, 2, 3, 3, 1] => 3, 2, 1, 2, 1, 2, 3, 3, 1
[3, 2, 1, 2, 1, 2, 3, 3, 2] => 3, 2, 1, 2, 1, 2, 3, 3, 2
[3, 2, 1, 2, 1, 2, 3, 3, 3] => 3, 2, 1, 2, 1, 2, 3, 3, 3
[3, 2, 1, 2, 1, 3, 1, 1, 1] => 3, 2, 1, 2, 1, 3, 1, 1, 1
[3, 2, 1, 2, 1, 3, 1, 1, 2] => 3, 2, 1, 2, 1, 3, 1, 1, 2
[3, 2, 1, 2, 1, 3, 1, 1, 3] => 3, 2, 1, 2, 1, 3, 1, 1, 3
[3, 2, 1, 2, 1, 3, 1, 2, 1] => 3, 2, 1, 2, 1, 3, 1, 2, 1
[3, 2, 1, 2, 1, 3, 1, 2, 2] => 3, 2, 1, 2, 1, 3, 1, 2, 2
[3, 2, 1, 2, 1, 3, 1, 2, 3] => 3, 2, 1, 2, 1, 3, 1, 2, 3
[3, 2, 1, 2, 1, 3, 1, 3, 1] => 3, 2, 1, 2, 1, 3, 1, 3, 1
[3, 2, 1, 2, 1, 3, 1, 3, 2] => 3, 2, 1, 2, 1, 3, 1, 3, 2
[3, 2, 1, 2, 1, 3, 1, 3, 3] => 3, 2, 1, 2, 1, 3, 1, 3, 3
[3, 2, 1, 2, 1, 3, 2, 1, 1] => 3, 2, 1, 2, 1, 3, 2, 1, 1
[3, 2, 1, 2, 1, 3, 2, 1, 2] => 3, 2, 1, 2, 1, 3, 2, 1, 2
[3, 2, 1, 2, 1, 3, 2, 1, 3] => 3, 2, 1, 2, 1, 3, 2, 1, 3
[3, 2, 1, 2, 1, 3, 2, 2, 1] => 3, 2, 1, 2, 1, 3, 2, 2, 1
[3, 2, 1, 2, 1, 3, 2, 2, 2] => 3, 2, 1, 2, 1, 3, 2, 2, 2
[3, 2, 1, 2, 1, 3, 2, 2, 3] => 3, 2, 1, 2, 1, 3, 2, 2, 3
[3, 2, 1, 2, 1, 3, 2, 3, 1] => 3, 2, 1, 2, 1, 3, 2, 3, 1
[3, 2, 1, 2, 1, 3, 2, 3, 2] => 3, 2, 1, 2, 1, 3, 2, 3, 2
[3, 2, 1, 2, 1, 3, 2, 3, 3] => 3, 2, 1, 2, 1, 3, 2, 3, 3
[3, 2, 1, 2, 1, 3, 3, 1, 1] => 3, 2, 1, 2, 1, 3, 3, 1, 1
[3, 2, 1, 2, 1, 3, 3, 1, 2] => 3, 2, 1, 2, 1, 3, 3, 1, 2
[3, 2, 1, 2, 1, 3, 3, 1, 3] => 3, 2, 1, 2, 1, 3, 3, 1, 3
[3, 2, 1, 2, 1, 3, 3, 2, 1] => 3, 2, 1, 2, 1, 3, 3, 2, 1
[3, 2, 1, 2, 1, 3, 3, 2, 2] => 3, 2, 1, 2, 1, 3, 3, 2, 2
[3, 2, 1, 2, 1, 3, 3, 2, 3] => 3, 2, 1, 2, 1, 3, 3, 2, 3
[3, 2, 1, 2, 1, 3, 3, 3, 1] => 3, 2, 1, 2, 1, 3, 3, 3, 1
[3, 2, 1, 2, 1, 3, 3, 3, 2] => 3, 2, 1, 2, 1, 3, 3, 3, 2
[3, 2, 1, 2, 1, 3, 3, 3, 3] => 3, 2, 1, 2, 1, 3, 3, 3, 3
[3, 2, 1, 2, 2, 1, 1, 1, 1] => 3, 2, 1, 2, 2, 1, 1, 1, 1
[3, 2, 1, 2, 2, 1, 1, 1, 2] => 3, 2, 1, 2, 2, 1, 1, 1, 2
[3, 2, 1, 2, 2, 1, 1, 1, 3] => 3, 2, 1, 2, 2, 1, 1, 1, 3
[3, 2, 1, 2, 2, 1, 1, 2, 1] => 3, 2, 1, 2, 2, 1, 1, 2, 1
[3, 2, 1, 2, 2, 1, 1, 2, 2] => 3, 2, 1, 2, 2, 1, 1, 2, 2
[3, 2, 1, 2, 2, 1, 1, 2, 3] => 3, 2, 1, 2, 2, 1, 1, 2, 3
[3, 2, 1, 2, 2, 1, 1, 3, 1] => 3, 2, 1, 2, 2, 1, 1, 3, 1
[3, 2, 1, 2, 2, 1, 1, 3, 2] => 3, 2, 1, 2, 2, 1, 1, 3, 2
[3, 2, 1, 2, 2, 1, 1, 3, 3] => 3, 2, 1, 2, 2, 1, 1, 3, 3
[3, 2, 1, 2, 2, 1, 2, 1, 1] => 3, 2, 1, 2, 2, 1, 2, 1, 1
[3, 2, 1, 2, 2, 1, 2, 1, 2] => 3, 2, 1, 2, 2, 1, 2, 1, 2
[3, 2, 1, 2, 2, 1, 2, 1, 3] => 3, 2, 1, 2, 2, 1, 2, 1, 3
[3, 2, 1, 2, 2, 1, 2, 2, 1] => 3, 2, 1, 2, 2, 1, 2, 2, 1
[3, 2, 1, 2, 2, 1, 2, 2, 2] => 3, 2, 1, 2, 2, 1, 2, 2, 2
[3, 2, 1, 2, 2, 1, 2, 2, 3] => 3, 2, 1, 2, 2, 1, 2, 2, 3
[3, 2, 1, 2, 2, 1, 2, 3, 1] => 3, 2, 1, 2, 2, 1, 2, 3, 1
[3, 2, 1, 2, 2, 1, 2, 3, 2] => 3, 2, 1, 2, 2, 1, 2, 3, 2
[3, 2, 1, 2, 2, 1, 2, 3, 3] => 3, 2, 1, 2, 2, 1, 2, 3, 3
[3, 2, 1, 2, 2, 1, 3, 1, 1] => 3, 2, 1, 2, 2, 1, 3, 1, 1
[3, 2, 1, 2, 2, 1, 3, 1, 2] => 3, 2, 1, 2, 2, 1, 3, 1, 2
[3, 2, 1, 2, 2, 1, 3, 1, 3] => 3, 2, 1, 2, 2, 1, 3, 1, 3
[3, 2, 1, 2, 2, 1, 3, 2, 1] => 3, 2, 1, 2, 2, 1, 3, 2, 1
[3, 2, 1, 2, 2, 1, 3, 2, 2] => 3, 2, 1, 2, 2, 1, 3, 2, 2
[3, 2, 1, 2, 2, 1, 3, 2, 3] => 3, 2, 1, 2, 2, 1, 3, 2, 3
[3, 2, 1, 2, 2, 1, 3, 3, 1] => 3, 2, 1, 2, 2, 1, 3, 3, 1
[3, 2, 1, 2, 2, 1, 3, 3, 2] => 3, 2, 1, 2, 2, 1, 3, 3, 2
[3, 2, 1, 2, 2, 1, 3, 3, 3] => 3, 2, 1, 2, 2, 1, 3, 3, 3
[3, 2, 1, 2, 2, 2, 1, 1, 1] => 3, 2, 1, 2, 2, 2, 1, 1, 1
[3, 2, 1, 2, 2, 2, 1, 1, 2] => 3, 2, 1, 2, 2, 2, 1, 1, 2
[3, 2, 1, 2, 2, 2, 1, 1, 3] => 3, 2, 1, 2, 2, 2, 1, 1, 3
[3, 2, 1, 2, 2, 2, 1, 2, 1] => 3, 2, 1, 2, 2, 2, 1, 2, 1
[3, 2, 1, 2, 2, 2, 1, 2, 2] => 3, 2, 1, 2, 2, 2, 1, 2, 2
[3, 2, 1, 2, 2, 2, 1, 2, 3] => 3, 2, 1, 2, 2, 2, 1, 2, 3
[3, 2, 1, 2, 2, 2, 1, 3, 1] => 3, 2, 1, 2, 2, 2, 1, 3, 1
[3, 2, 1, 2, 2, 2, 1, 3, 2] => 3, 2, 1, 2, 2, 2, 1, 3, 2
[3, 2, 1, 2, 2, 2, 1, 3, 3] => 3, 2, 1, 2, 2, 2, 1, 3, 3
[3, 2, 1, 2, 2, 2, 2, 1, 1] => 3, 2, 1, 2, 2, 2, 2, 1, 1
[3, 2, 1, 2, 2, 2, 2, 1, 2] => 3, 2, 1, 2, 2, 2, 2, 1, 2
[3, 2, 1, 2, 2, 2, 2, 1, 3] => 3, 2, 1, 2, 2, 2, 2, 1, 3
[3, 2, 1, 2, 2, 2, 2, 2, 1] => 3, 2, 1, 2, 2, 2, 2, 2, 1
[3, 2, 1, 2, 2, 2, 2, 2, 2] => 3, 2, 1, 2, 2, 2, 2, 2, 2
[3, 2, 1, 2, 2, 2, 2, 2, 3] => 3, 2, 1, 2, 2, 2, 2, 2, 3
[3, 2, 1, 2, 2, 2, 2, 3, 1] => 3, 2, 1, 2, 2, 2, 2, 3, 1
[3, 2, 1, 2, 2, 2, 2, 3, 2] => 3, 2, 1, 2, 2, 2, 2, 3, 2
[3, 2, 1, 2, 2, 2, 2, 3, 3] => 3, 2, 1, 2, 2, 2, 2, 3, 3
[3, 2, 1, 2, 2, 2, 3, 1, 1] => 3, 2, 1, 2, 2, 2, 3, 1, 1
[3, 2, 1, 2, 2, 2, 3, 1, 2] => 3, 2, 1, 2, 2, 2, 3, 1, 2
[3, 2, 1, 2, 2, 2, 3, 1, 3] => 3, 2, 1, 2, 2, 2, 3, 1, 3
[3, 2, 1, 2, 2, 2, 3, 2, 1] => 3, 2, 1, 2, 2, 2, 3, 2, 1
[3, 2, 1, 2, 2, 2, 3, 2, 2] => 3, 2, 1, 2, 2, 2, 3, 2, 2
[3, 2, 1, 2, 2, 2, 3, 2, 3] => 3, 2, 1, 2, 2, 2, 3, 2, 3
[3, 2, 1, 2, 2, 2, 3, 3, 1] => 3, 2, 1, 2, 2, 2, 3, 3, 1
[3, 2, 1, 2, 2, 2, 3, 3, 2] => 3, 2, 1, 2, 2, 2, 3, 3, 2
[3, 2, 1, 2, 2, 2, 3, 3, 3] => 3, 2, 1, 2, 2, 2, 3, 3, 3
[3, 2, 1, 2, 2, 3, 1, 1, 1] => 3, 2, 1, 2, 2, 3, 1, 1, 1
[3, 2, 1, 2, 2, 3, 1, 1, 2] => 3, 2, 1, 2, 2, 3, 1, 1, 2
[3, 2, 1, 2, 2, 3, 1, 1, 3] => 3, 2, 1, 2, 2, 3, 1, 1, 3
[3, 2, 1, 2, 2, 3, 1, 2, 1] => 3, 2, 1, 2, 2, 3, 1, 2, 1
[3, 2, 1, 2, 2, 3, 1, 2, 2] => 3, 2, 1, 2, 2, 3, 1, 2, 2
[3, 2, 1, 2, 2, 3, 1, 2, 3] => 3, 2, 1, 2, 2, 3, 1, 2, 3
[3, 2, 1, 2, 2, 3, 1, 3, 1] => 3, 2, 1, 2, 2, 3, 1, 3, 1
[3, 2, 1, 2, 2, 3, 1, 3, 2] => 3, 2, 1, 2, 2, 3, 1, 3, 2
[3, 2, 1, 2, 2, 3, 1, 3, 3] => 3, 2, 1, 2, 2, 3, 1, 3, 3
[3, 2, 1, 2, 2, 3, 2, 1, 1] => 3, 2, 1, 2, 2, 3, 2, 1, 1
[3, 2, 1, 2, 2, 3, 2, 1, 2] => 3, 2, 1, 2, 2, 3, 2, 1, 2
[3, 2, 1, 2, 2, 3, 2, 1, 3] => 3, 2, 1, 2, 2, 3, 2, 1, 3
[3, 2, 1, 2, 2, 3, 2, 2, 1] => 3, 2, 1, 2, 2, 3, 2, 2, 1
[3, 2, 1, 2, 2, 3, 2, 2, 2] => 3, 2, 1, 2, 2, 3, 2, 2, 2
[3, 2, 1, 2, 2, 3, 2, 2, 3] => 3, 2, 1, 2, 2, 3, 2, 2, 3
[3, 2, 1, 2, 2, 3, 2, 3, 1] => 3, 2, 1, 2, 2, 3, 2, 3, 1
[3, 2, 1, 2, 2, 3, 2, 3, 2] => 3, 2, 1, 2, 2, 3, 2, 3, 2
[3, 2, 1, 2, 2, 3, 2, 3, 3] => 3, 2, 1, 2, 2, 3, 2, 3, 3
[3, 2, 1, 2, 2, 3, 3, 1, 1] => 3, 2, 1, 2, 2, 3, 3, 1, 1
[3, 2, 1, 2, 2, 3, 3, 1, 2] => 3, 2, 1, 2, 2, 3, 3, 1, 2
[3, 2, 1, 2, 2, 3, 3, 1, 3] => 3, 2, 1, 2, 2, 3, 3, 1, 3
[3, 2, 1, 2, 2, 3, 3, 2, 1] => 3, 2, 1, 2, 2, 3, 3, 2, 1
[3, 2, 1, 2, 2, 3, 3, 2, 2] => 3, 2, 1, 2, 2, 3, 3, 2, 2
[3, 2, 1, 2, 2, 3, 3, 2, 3] => 3, 2, 1, 2, 2, 3, 3, 2, 3
[3, 2, 1, 2, 2, 3, 3, 3, 1] => 3, 2, 1, 2, 2, 3, 3, 3, 1
[3, 2, 1, 2, 2, 3, 3, 3, 2] => 3, 2, 1, 2, 2, 3, 3, 3, 2
[3, 2, 1, 2, 2, 3, 3, 3, 3] => 3, 2, 1, 2, 2, 3, 3, 3, 3
[3, 2, 1, 2, 3, 1, 1, 1, 1] => 3, 2, 1, 2, 3, 1, 1, 1, 1
[3, 2, 1, 2, 3, 1, 1, 1, 2] => 3, 2, 1, 2, 3, 1, 1, 1, 2
[3, 2, 1, 2, 3, 1, 1, 1, 3] => 3, 2, 1, 2, 3, 1, 1, 1, 3
[3, 2, 1, 2, 3, 1, 1, 2, 1] => 3, 2, 1, 2, 3, 1, 1, 2, 1
[3, 2, 1, 2, 3, 1, 1, 2, 2] => 3, 2, 1, 2, 3, 1, 1, 2, 2
[3, 2, 1, 2, 3, 1, 1, 2, 3] => 3, 2, 1, 2, 3, 1, 1, 2, 3
[3, 2, 1, 2, 3, 1, 1, 3, 1] => 3, 2, 1, 2, 3, 1, 1, 3, 1
[3, 2, 1, 2, 3, 1, 1, 3, 2] => 3, 2, 1, 2, 3, 1, 1, 3, 2
[3, 2, 1, 2, 3, 1, 1, 3, 3] => 3, 2, 1, 2, 3, 1, 1, 3, 3
[3, 2, 1, 2, 3, 1, 2, 1, 1] => 3, 2, 1, 2, 3, 1, 2, 1, 1
[3, 2, 1, 2, 3, 1, 2, 1, 2] => 3, 2, 1, 2, 3, 1, 2, 1, 2
[3, 2, 1, 2, 3, 1, 2, 1, 3] => 3, 2, 1, 2, 3, 1, 2, 1, 3
[3, 2, 1, 2, 3, 1, 2, 2, 1] => 3, 2, 1, 2, 3, 1, 2, 2, 1
[3, 2, 1, 2, 3, 1, 2, 2, 2] => 3, 2, 1, 2, 3, 1, 2, 2, 2
[3, 2, 1, 2, 3, 1, 2, 2, 3] => 3, 2, 1, 2, 3, 1, 2, 2, 3
[3, 2, 1, 2, 3, 1, 2, 3, 1] => 3, 2, 1, 2, 3, 1, 2, 3, 1
[3, 2, 1, 2, 3, 1, 2, 3, 2] => 3, 2, 1, 2, 3, 1, 2, 3, 2
[3, 2, 1, 2, 3, 1, 2, 3, 3] => 3, 2, 1, 2, 3, 1, 2, 3, 3
[3, 2, 1, 2, 3, 1, 3, 1, 1] => 3, 2, 1, 2, 3, 1, 3, 1, 1
[3, 2, 1, 2, 3, 1, 3, 1, 2] => 3, 2, 1, 2, 3, 1, 3, 1, 2
[3, 2, 1, 2, 3, 1, 3, 1, 3] => 3, 2, 1, 2, 3, 1, 3, 1, 3
[3, 2, 1, 2, 3, 1, 3, 2, 1] => 3, 2, 1, 2, 3, 1, 3, 2, 1
[3, 2, 1, 2, 3, 1, 3, 2, 2] => 3, 2, 1, 2, 3, 1, 3, 2, 2
[3, 2, 1, 2, 3, 1, 3, 2, 3] => 3, 2, 1, 2, 3, 1, 3, 2, 3
[3, 2, 1, 2, 3, 1, 3, 3, 1] => 3, 2, 1, 2, 3, 1, 3, 3, 1
[3, 2, 1, 2, 3, 1, 3, 3, 2] => 3, 2, 1, 2, 3, 1, 3, 3, 2
[3, 2, 1, 2, 3, 1, 3, 3, 3] => 3, 2, 1, 2, 3, 1, 3, 3, 3
[3, 2, 1, 2, 3, 2, 1, 1, 1] => 3, 2, 1, 2, 3, 2, 1, 1, 1
[3, 2, 1, 2, 3, 2, 1, 1, 2] => 3, 2, 1, 2, 3, 2, 1, 1, 2
[3, 2, 1, 2, 3, 2, 1, 1, 3] => 3, 2, 1, 2, 3, 2, 1, 1, 3
[3, 2, 1, 2, 3, 2, 1, 2, 1] => 3, 2, 1, 2, 3, 2, 1, 2, 1
[3, 2, 1, 2, 3, 2, 1, 2, 2] => 3, 2, 1, 2, 3, 2, 1, 2, 2
[3, 2, 1, 2, 3, 2, 1, 2, 3] => 3, 2, 1, 2, 3, 2, 1, 2, 3
[3, 2, 1, 2, 3, 2, 1, 3, 1] => 3, 2, 1, 2, 3, 2, 1, 3, 1
[3, 2, 1, 2, 3, 2, 1, 3, 2] => 3, 2, 1, 2, 3, 2, 1, 3, 2
[3, 2, 1, 2, 3, 2, 1, 3, 3] => 3, 2, 1, 2, 3, 2, 1, 3, 3
[3, 2, 1, 2, 3, 2, 2, 1, 1] => 3, 2, 1, 2, 3, 2, 2, 1, 1
[3, 2, 1, 2, 3, 2, 2, 1, 2] => 3, 2, 1, 2, 3, 2, 2, 1, 2
[3, 2, 1, 2, 3, 2, 2, 1, 3] => 3, 2, 1, 2, 3, 2, 2, 1, 3
[3, 2, 1, 2, 3, 2, 2, 2, 1] => 3, 2, 1, 2, 3, 2, 2, 2, 1
[3, 2, 1, 2, 3, 2, 2, 2, 2] => 3, 2, 1, 2, 3, 2, 2, 2, 2
[3, 2, 1, 2, 3, 2, 2, 2, 3] => 3, 2, 1, 2, 3, 2, 2, 2, 3
[3, 2, 1, 2, 3, 2, 2, 3, 1] => 3, 2, 1, 2, 3, 2, 2, 3, 1
[3, 2, 1, 2, 3, 2, 2, 3, 2] => 3, 2, 1, 2, 3, 2, 2, 3, 2
[3, 2, 1, 2, 3, 2, 2, 3, 3] => 3, 2, 1, 2, 3, 2, 2, 3, 3
[3, 2, 1, 2, 3, 2, 3, 1, 1] => 3, 2, 1, 2, 3, 2, 3, 1, 1
[3, 2, 1, 2, 3, 2, 3, 1, 2] => 3, 2, 1, 2, 3, 2, 3, 1, 2
[3, 2, 1, 2, 3, 2, 3, 1, 3] => 3, 2, 1, 2, 3, 2, 3, 1, 3
[3, 2, 1, 2, 3, 2, 3, 2, 1] => 3, 2, 1, 2, 3, 2, 3, 2, 1
[3, 2, 1, 2, 3, 2, 3, 2, 2] => 3, 2, 1, 2, 3, 2, 3, 2, 2
[3, 2, 1, 2, 3, 2, 3, 2, 3] => 3, 2, 1, 2, 3, 2, 3, 2, 3
[3, 2, 1, 2, 3, 2, 3, 3, 1] => 3, 2, 1, 2, 3, 2, 3, 3, 1
[3, 2, 1, 2, 3, 2, 3, 3, 2] => 3, 2, 1, 2, 3, 2, 3, 3, 2
[3, 2, 1, 2, 3, 2, 3, 3, 3] => 3, 2, 1, 2, 3, 2, 3, 3, 3
[3, 2, 1, 2, 3, 3, 1, 1, 1] => 3, 2, 1, 2, 3, 3, 1, 1, 1
[3, 2, 1, 2, 3, 3, 1, 1, 2] => 3, 2, 1, 2, 3, 3, 1, 1, 2
[3, 2, 1, 2, 3, 3, 1, 1, 3] => 3, 2, 1, 2, 3, 3, 1, 1, 3
[3, 2, 1, 2, 3, 3, 1, 2, 1] => 3, 2, 1, 2, 3, 3, 1, 2, 1
[3, 2, 1, 2, 3, 3, 1, 2, 2] => 3, 2, 1, 2, 3, 3, 1, 2, 2
[3, 2, 1, 2, 3, 3, 1, 2, 3] => 3, 2, 1, 2, 3, 3, 1, 2, 3
[3, 2, 1, 2, 3, 3, 1, 3, 1] => 3, 2, 1, 2, 3, 3, 1, 3, 1
[3, 2, 1, 2, 3, 3, 1, 3, 2] => 3, 2, 1, 2, 3, 3, 1, 3, 2
[3, 2, 1, 2, 3, 3, 1, 3, 3] => 3, 2, 1, 2, 3, 3, 1, 3, 3
[3, 2, 1, 2, 3, 3, 2, 1, 1] => 3, 2, 1, 2, 3, 3, 2, 1, 1
[3, 2, 1, 2, 3, 3, 2, 1, 2] => 3, 2, 1, 2, 3, 3, 2, 1, 2
[3, 2, 1, 2, 3, 3, 2, 1, 3] => 3, 2, 1, 2, 3, 3, 2, 1, 3
[3, 2, 1, 2, 3, 3, 2, 2, 1] => 3, 2, 1, 2, 3, 3, 2, 2, 1
[3, 2, 1, 2, 3, 3, 2, 2, 2] => 3, 2, 1, 2, 3, 3, 2, 2, 2
[3, 2, 1, 2, 3, 3, 2, 2, 3] => 3, 2, 1, 2, 3, 3, 2, 2, 3
[3, 2, 1, 2, 3, 3, 2, 3, 1] => 3, 2, 1, 2, 3, 3, 2, 3, 1
[3, 2, 1, 2, 3, 3, 2, 3, 2] => 3, 2, 1, 2, 3, 3, 2, 3, 2
[3, 2, 1, 2, 3, 3, 2, 3, 3] => 3, 2, 1, 2, 3, 3, 2, 3, 3
[3, 2, 1, 2, 3, 3, 3, 1, 1] => 3, 2, 1, 2, 3, 3, 3, 1, 1
[3, 2, 1, 2, 3, 3, 3, 1, 2] => 3, 2, 1, 2, 3, 3, 3, 1, 2
[3, 2, 1, 2, 3, 3, 3, 1, 3] => 3, 2, 1, 2, 3, 3, 3, 1, 3
[3, 2, 1, 2, 3, 3, 3, 2, 1] => 3, 2, 1, 2, 3, 3, 3, 2, 1
[3, 2, 1, 2, 3, 3, 3, 2, 2] => 3, 2, 1, 2, 3, 3, 3, 2, 2
[3, 2, 1, 2, 3, 3, 3, 2, 3] => 3, 2, 1, 2, 3, 3, 3, 2, 3
[3, 2, 1, 2, 3, 3, 3, 3, 1] => 3, 2, 1, 2, 3, 3, 3, 3, 1
[3, 2, 1, 2, 3, 3, 3, 3, 2] => 3, 2, 1, 2, 3, 3, 3, 3, 2
[3, 2, 1, 2, 3, 3, 3, 3, 3] => 3, 2, 1, 2, 3, 3, 3, 3, 3
[3, 2, 1, 3, 1, 1, 1, 1, 1] => 3, 2, 1, 3, 1, 1, 1, 1, 1
[3, 2, 1, 3, 1, 1, 1, 1, 2] => 3, 2, 1, 3, 1, 1, 1, 1, 2
[3, 2, 1, 3, 1, 1, 1, 1, 3] => 3, 2, 1, 3, 1, 1, 1, 1, 3
[3, 2, 1, 3, 1, 1, 1, 2, 1] => 3, 2, 1, 3, 1, 1, 1, 2, 1
[3, 2, 1, 3, 1, 1, 1, 2, 2] => 3, 2, 1, 3, 1, 1, 1, 2, 2
[3, 2, 1, 3, 1, 1, 1, 2, 3] => 3, 2, 1, 3, 1, 1, 1, 2, 3
[3, 2, 1, 3, 1, 1, 1, 3, 1] => 3, 2, 1, 3, 1, 1, 1, 3, 1
[3, 2, 1, 3, 1, 1, 1, 3, 2] => 3, 2, 1, 3, 1, 1, 1, 3, 2
[3, 2, 1, 3, 1, 1, 1, 3, 3] => 3, 2, 1, 3, 1, 1, 1, 3, 3
[3, 2, 1, 3, 1, 1, 2, 1, 1] => 3, 2, 1, 3, 1, 1, 2, 1, 1
[3, 2, 1, 3, 1, 1, 2, 1, 2] => 3, 2, 1, 3, 1, 1, 2, 1, 2
[3, 2, 1, 3, 1, 1, 2, 1, 3] => 3, 2, 1, 3, 1, 1, 2, 1, 3
[3, 2, 1, 3, 1, 1, 2, 2, 1] => 3, 2, 1, 3, 1, 1, 2, 2, 1
[3, 2, 1, 3, 1, 1, 2, 2, 2] => 3, 2, 1, 3, 1, 1, 2, 2, 2
[3, 2, 1, 3, 1, 1, 2, 2, 3] => 3, 2, 1, 3, 1, 1, 2, 2, 3
[3, 2, 1, 3, 1, 1, 2, 3, 1] => 3, 2, 1, 3, 1, 1, 2, 3, 1
[3, 2, 1, 3, 1, 1, 2, 3, 2] => 3, 2, 1, 3, 1, 1, 2, 3, 2
[3, 2, 1, 3, 1, 1, 2, 3, 3] => 3, 2, 1, 3, 1, 1, 2, 3, 3
[3, 2, 1, 3, 1, 1, 3, 1, 1] => 3, 2, 1, 3, 1, 1, 3, 1, 1
[3, 2, 1, 3, 1, 1, 3, 1, 2] => 3, 2, 1, 3, 1, 1, 3, 1, 2
[3, 2, 1, 3, 1, 1, 3, 1, 3] => 3, 2, 1, 3, 1, 1, 3, 1, 3
[3, 2, 1, 3, 1, 1, 3, 2, 1] => 3, 2, 1, 3, 1, 1, 3, 2, 1
[3, 2, 1, 3, 1, 1, 3, 2, 2] => 3, 2, 1, 3, 1, 1, 3, 2, 2
[3, 2, 1, 3, 1, 1, 3, 2, 3] => 3, 2, 1, 3, 1, 1, 3, 2, 3
[3, 2, 1, 3, 1, 1, 3, 3, 1] => 3, 2, 1, 3, 1, 1, 3, 3, 1
[3, 2, 1, 3, 1, 1, 3, 3, 2] => 3, 2, 1, 3, 1, 1, 3, 3, 2
[3, 2, 1, 3, 1, 1, 3, 3, 3] => 3, 2, 1, 3, 1, 1, 3, 3, 3
[3, 2, 1, 3, 1, 2, 1, 1, 1] => 3, 2, 1, 3, 1, 2, 1, 1, 1
[3, 2, 1, 3, 1, 2, 1, 1, 2] => 3, 2, 1, 3, 1, 2, 1, 1, 2
[3, 2, 1, 3, 1, 2, 1, 1, 3] => 3, 2, 1, 3, 1, 2, 1, 1, 3
[3, 2, 1, 3, 1, 2, 1, 2, 1] => 3, 2, 1, 3, 1, 2, 1, 2, 1
[3, 2, 1, 3, 1, 2, 1, 2, 2] => 3, 2, 1, 3, 1, 2, 1, 2, 2
[3, 2, 1, 3, 1, 2, 1, 2, 3] => 3, 2, 1, 3, 1, 2, 1, 2, 3
[3, 2, 1, 3, 1, 2, 1, 3, 1] => 3, 2, 1, 3, 1, 2, 1, 3, 1
[3, 2, 1, 3, 1, 2, 1, 3, 2] => 3, 2, 1, 3, 1, 2, 1, 3, 2
[3, 2, 1, 3, 1, 2, 1, 3, 3] => 3, 2, 1, 3, 1, 2, 1, 3, 3
[3, 2, 1, 3, 1, 2, 2, 1, 1] => 3, 2, 1, 3, 1, 2, 2, 1, 1
[3, 2, 1, 3, 1, 2, 2, 1, 2] => 3, 2, 1, 3, 1, 2, 2, 1, 2
[3, 2, 1, 3, 1, 2, 2, 1, 3] => 3, 2, 1, 3, 1, 2, 2, 1, 3
[3, 2, 1, 3, 1, 2, 2, 2, 1] => 3, 2, 1, 3, 1, 2, 2, 2, 1
[3, 2, 1, 3, 1, 2, 2, 2, 2] => 3, 2, 1, 3, 1, 2, 2, 2, 2
[3, 2, 1, 3, 1, 2, 2, 2, 3] => 3, 2, 1, 3, 1, 2, 2, 2, 3
[3, 2, 1, 3, 1, 2, 2, 3, 1] => 3, 2, 1, 3, 1, 2, 2, 3, 1
[3, 2, 1, 3, 1, 2, 2, 3, 2] => 3, 2, 1, 3, 1, 2, 2, 3, 2
[3, 2, 1, 3, 1, 2, 2, 3, 3] => 3, 2, 1, 3, 1, 2, 2, 3, 3
[3, 2, 1, 3, 1, 2, 3, 1, 1] => 3, 2, 1, 3, 1, 2, 3, 1, 1
[3, 2, 1, 3, 1, 2, 3, 1, 2] => 3, 2, 1, 3, 1, 2, 3, 1, 2
[3, 2, 1, 3, 1, 2, 3, 1, 3] => 3, 2, 1, 3, 1, 2, 3, 1, 3
[3, 2, 1, 3, 1, 2, 3, 2, 1] => 3, 2, 1, 3, 1, 2, 3, 2, 1
[3, 2, 1, 3, 1, 2, 3, 2, 2] => 3, 2, 1, 3, 1, 2, 3, 2, 2
[3, 2, 1, 3, 1, 2, 3, 2, 3] => 3, 2, 1, 3, 1, 2, 3, 2, 3
[3, 2, 1, 3, 1, 2, 3, 3, 1] => 3, 2, 1, 3, 1, 2, 3, 3, 1
[3, 2, 1, 3, 1, 2, 3, 3, 2] => 3, 2, 1, 3, 1, 2, 3, 3, 2
[3, 2, 1, 3, 1, 2, 3, 3, 3] => 3, 2, 1, 3, 1, 2, 3, 3, 3
[3, 2, 1, 3, 1, 3, 1, 1, 1] => 3, 2, 1, 3, 1, 3, 1, 1, 1
[3, 2, 1, 3, 1, 3, 1, 1, 2] => 3, 2, 1, 3, 1, 3, 1, 1, 2
[3, 2, 1, 3, 1, 3, 1, 1, 3] => 3, 2, 1, 3, 1, 3, 1, 1, 3
[3, 2, 1, 3, 1, 3, 1, 2, 1] => 3, 2, 1, 3, 1, 3, 1, 2, 1
[3, 2, 1, 3, 1, 3, 1, 2, 2] => 3, 2, 1, 3, 1, 3, 1, 2, 2
[3, 2, 1, 3, 1, 3, 1, 2, 3] => 3, 2, 1, 3, 1, 3, 1, 2, 3
[3, 2, 1, 3, 1, 3, 1, 3, 1] => 3, 2, 1, 3, 1, 3, 1, 3, 1
[3, 2, 1, 3, 1, 3, 1, 3, 2] => 3, 2, 1, 3, 1, 3, 1, 3, 2
[3, 2, 1, 3, 1, 3, 1, 3, 3] => 3, 2, 1, 3, 1, 3, 1, 3, 3
[3, 2, 1, 3, 1, 3, 2, 1, 1] => 3, 2, 1, 3, 1, 3, 2, 1, 1
[3, 2, 1, 3, 1, 3, 2, 1, 2] => 3, 2, 1, 3, 1, 3, 2, 1, 2
[3, 2, 1, 3, 1, 3, 2, 1, 3] => 3, 2, 1, 3, 1, 3, 2, 1, 3
[3, 2, 1, 3, 1, 3, 2, 2, 1] => 3, 2, 1, 3, 1, 3, 2, 2, 1
[3, 2, 1, 3, 1, 3, 2, 2, 2] => 3, 2, 1, 3, 1, 3, 2, 2, 2
[3, 2, 1, 3, 1, 3, 2, 2, 3] => 3, 2, 1, 3, 1, 3, 2, 2, 3
[3, 2, 1, 3, 1, 3, 2, 3, 1] => 3, 2, 1, 3, 1, 3, 2, 3, 1
[3, 2, 1, 3, 1, 3, 2, 3, 2] => 3, 2, 1, 3, 1, 3, 2, 3, 2
[3, 2, 1, 3, 1, 3, 2, 3, 3] => 3, 2, 1, 3, 1, 3, 2, 3, 3
[3, 2, 1, 3, 1, 3, 3, 1, 1] => 3, 2, 1, 3, 1, 3, 3, 1, 1
[3, 2, 1, 3, 1, 3, 3, 1, 2] => 3, 2, 1, 3, 1, 3, 3, 1, 2
[3, 2, 1, 3, 1, 3, 3, 1, 3] => 3, 2, 1, 3, 1, 3, 3, 1, 3
[3, 2, 1, 3, 1, 3, 3, 2, 1] => 3, 2, 1, 3, 1, 3, 3, 2, 1
[3, 2, 1, 3, 1, 3, 3, 2, 2] => 3, 2, 1, 3, 1, 3, 3, 2, 2
[3, 2, 1, 3, 1, 3, 3, 2, 3] => 3, 2, 1, 3, 1, 3, 3, 2, 3
[3, 2, 1, 3, 1, 3, 3, 3, 1] => 3, 2, 1, 3, 1, 3, 3, 3, 1
[3, 2, 1, 3, 1, 3, 3, 3, 2] => 3, 2, 1, 3, 1, 3, 3, 3, 2
[3, 2, 1, 3, 1, 3, 3, 3, 3] => 3, 2, 1, 3, 1, 3, 3, 3, 3
[3, 2, 1, 3, 2, 1, 1, 1, 1] => 3, 2, 1, 3, 2, 1, 1, 1, 1
[3, 2, 1, 3, 2, 1, 1, 1, 2] => 3, 2, 1, 3, 2, 1, 1, 1, 2
[3, 2, 1, 3, 2, 1, 1, 1, 3] => 3, 2, 1, 3, 2, 1, 1, 1, 3
[3, 2, 1, 3, 2, 1, 1, 2, 1] => 3, 2, 1, 3, 2, 1, 1, 2, 1
[3, 2, 1, 3, 2, 1, 1, 2, 2] => 3, 2, 1, 3, 2, 1, 1, 2, 2
[3, 2, 1, 3, 2, 1, 1, 2, 3] => 3, 2, 1, 3, 2, 1, 1, 2, 3
[3, 2, 1, 3, 2, 1, 1, 3, 1] => 3, 2, 1, 3, 2, 1, 1, 3, 1
[3, 2, 1, 3, 2, 1, 1, 3, 2] => 3, 2, 1, 3, 2, 1, 1, 3, 2
[3, 2, 1, 3, 2, 1, 1, 3, 3] => 3, 2, 1, 3, 2, 1, 1, 3, 3
[3, 2, 1, 3, 2, 1, 2, 1, 1] => 3, 2, 1, 3, 2, 1, 2, 1, 1
[3, 2, 1, 3, 2, 1, 2, 1, 2] => 3, 2, 1, 3, 2, 1, 2, 1, 2
[3, 2, 1, 3, 2, 1, 2, 1, 3] => 3, 2, 1, 3, 2, 1, 2, 1, 3
[3, 2, 1, 3, 2, 1, 2, 2, 1] => 3, 2, 1, 3, 2, 1, 2, 2, 1
[3, 2, 1, 3, 2, 1, 2, 2, 2] => 3, 2, 1, 3, 2, 1, 2, 2, 2
[3, 2, 1, 3, 2, 1, 2, 2, 3] => 3, 2, 1, 3, 2, 1, 2, 2, 3
[3, 2, 1, 3, 2, 1, 2, 3, 1] => 3, 2, 1, 3, 2, 1, 2, 3, 1
[3, 2, 1, 3, 2, 1, 2, 3, 2] => 3, 2, 1, 3, 2, 1, 2, 3, 2
[3, 2, 1, 3, 2, 1, 2, 3, 3] => 3, 2, 1, 3, 2, 1, 2, 3, 3
[3, 2, 1, 3, 2, 1, 3, 1, 1] => 3, 2, 1, 3, 2, 1, 3, 1, 1
[3, 2, 1, 3, 2, 1, 3, 1, 2] => 3, 2, 1, 3, 2, 1, 3, 1, 2
[3, 2, 1, 3, 2, 1, 3, 1, 3] => 3, 2, 1, 3, 2, 1, 3, 1, 3
[3, 2, 1, 3, 2, 1, 3, 2, 1] => 3, 2, 1, 3, 2, 1, 3, 2, 1
[3, 2, 1, 3, 2, 1, 3, 2, 2] => 3, 2, 1, 3, 2, 1, 3, 2, 2
[3, 2, 1, 3, 2, 1, 3, 2, 3] => 3, 2, 1, 3, 2, 1, 3, 2, 3
[3, 2, 1, 3, 2, 1, 3, 3, 1] => 3, 2, 1, 3, 2, 1, 3, 3, 1
[3, 2, 1, 3, 2, 1, 3, 3, 2] => 3, 2, 1, 3, 2, 1, 3, 3, 2
[3, 2, 1, 3, 2, 1, 3, 3, 3] => 3, 2, 1, 3, 2, 1, 3, 3, 3
[3, 2, 1, 3, 2, 2, 1, 1, 1] => 3, 2, 1, 3, 2, 2, 1, 1, 1
[3, 2, 1, 3, 2, 2, 1, 1, 2] => 3, 2, 1, 3, 2, 2, 1, 1, 2
[3, 2, 1, 3, 2, 2, 1, 1, 3] => 3, 2, 1, 3, 2, 2, 1, 1, 3
[3, 2, 1, 3, 2, 2, 1, 2, 1] => 3, 2, 1, 3, 2, 2, 1, 2, 1
[3, 2, 1, 3, 2, 2, 1, 2, 2] => 3, 2, 1, 3, 2, 2, 1, 2, 2
[3, 2, 1, 3, 2, 2, 1, 2, 3] => 3, 2, 1, 3, 2, 2, 1, 2, 3
[3, 2, 1, 3, 2, 2, 1, 3, 1] => 3, 2, 1, 3, 2, 2, 1, 3, 1
[3, 2, 1, 3, 2, 2, 1, 3, 2] => 3, 2, 1, 3, 2, 2, 1, 3, 2
[3, 2, 1, 3, 2, 2, 1, 3, 3] => 3, 2, 1, 3, 2, 2, 1, 3, 3
[3, 2, 1, 3, 2, 2, 2, 1, 1] => 3, 2, 1, 3, 2, 2, 2, 1, 1
[3, 2, 1, 3, 2, 2, 2, 1, 2] => 3, 2, 1, 3, 2, 2, 2, 1, 2
[3, 2, 1, 3, 2, 2, 2, 1, 3] => 3, 2, 1, 3, 2, 2, 2, 1, 3
[3, 2, 1, 3, 2, 2, 2, 2, 1] => 3, 2, 1, 3, 2, 2, 2, 2, 1
[3, 2, 1, 3, 2, 2, 2, 2, 2] => 3, 2, 1, 3, 2, 2, 2, 2, 2
[3, 2, 1, 3, 2, 2, 2, 2, 3] => 3, 2, 1, 3, 2, 2, 2, 2, 3
[3, 2, 1, 3, 2, 2, 2, 3, 1] => 3, 2, 1, 3, 2, 2, 2, 3, 1
[3, 2, 1, 3, 2, 2, 2, 3, 2] => 3, 2, 1, 3, 2, 2, 2, 3, 2
[3, 2, 1, 3, 2, 2, 2, 3, 3] => 3, 2, 1, 3, 2, 2, 2, 3, 3
[3, 2, 1, 3, 2, 2, 3, 1, 1] => 3, 2, 1, 3, 2, 2, 3, 1, 1
[3, 2, 1, 3, 2, 2, 3, 1, 2] => 3, 2, 1, 3, 2, 2, 3, 1, 2
[3, 2, 1, 3, 2, 2, 3, 1, 3] => 3, 2, 1, 3, 2, 2, 3, 1, 3
[3, 2, 1, 3, 2, 2, 3, 2, 1] => 3, 2, 1, 3, 2, 2, 3, 2, 1
[3, 2, 1, 3, 2, 2, 3, 2, 2] => 3, 2, 1, 3, 2, 2, 3, 2, 2
[3, 2, 1, 3, 2, 2, 3, 2, 3] => 3, 2, 1, 3, 2, 2, 3, 2, 3
[3, 2, 1, 3, 2, 2, 3, 3, 1] => 3, 2, 1, 3, 2, 2, 3, 3, 1
[3, 2, 1, 3, 2, 2, 3, 3, 2] => 3, 2, 1, 3, 2, 2, 3, 3, 2
[3, 2, 1, 3, 2, 2, 3, 3, 3] => 3, 2, 1, 3, 2, 2, 3, 3, 3
[3, 2, 1, 3, 2, 3, 1, 1, 1] => 3, 2, 1, 3, 2, 3, 1, 1, 1
[3, 2, 1, 3, 2, 3, 1, 1, 2] => 3, 2, 1, 3, 2, 3, 1, 1, 2
[3, 2, 1, 3, 2, 3, 1, 1, 3] => 3, 2, 1, 3, 2, 3, 1, 1, 3
[3, 2, 1, 3, 2, 3, 1, 2, 1] => 3, 2, 1, 3, 2, 3, 1, 2, 1
[3, 2, 1, 3, 2, 3, 1, 2, 2] => 3, 2, 1, 3, 2, 3, 1, 2, 2
[3, 2, 1, 3, 2, 3, 1, 2, 3] => 3, 2, 1, 3, 2, 3, 1, 2, 3
[3, 2, 1, 3, 2, 3, 1, 3, 1] => 3, 2, 1, 3, 2, 3, 1, 3, 1
[3, 2, 1, 3, 2, 3, 1, 3, 2] => 3, 2, 1, 3, 2, 3, 1, 3, 2
[3, 2, 1, 3, 2, 3, 1, 3, 3] => 3, 2, 1, 3, 2, 3, 1, 3, 3
[3, 2, 1, 3, 2, 3, 2, 1, 1] => 3, 2, 1, 3, 2, 3, 2, 1, 1
[3, 2, 1, 3, 2, 3, 2, 1, 2] => 3, 2, 1, 3, 2, 3, 2, 1, 2
[3, 2, 1, 3, 2, 3, 2, 1, 3] => 3, 2, 1, 3, 2, 3, 2, 1, 3
[3, 2, 1, 3, 2, 3, 2, 2, 1] => 3, 2, 1, 3, 2, 3, 2, 2, 1
[3, 2, 1, 3, 2, 3, 2, 2, 2] => 3, 2, 1, 3, 2, 3, 2, 2, 2
[3, 2, 1, 3, 2, 3, 2, 2, 3] => 3, 2, 1, 3, 2, 3, 2, 2, 3
[3, 2, 1, 3, 2, 3, 2, 3, 1] => 3, 2, 1, 3, 2, 3, 2, 3, 1
[3, 2, 1, 3, 2, 3, 2, 3, 2] => 3, 2, 1, 3, 2, 3, 2, 3, 2
[3, 2, 1, 3, 2, 3, 2, 3, 3] => 3, 2, 1, 3, 2, 3, 2, 3, 3
[3, 2, 1, 3, 2, 3, 3, 1, 1] => 3, 2, 1, 3, 2, 3, 3, 1, 1
[3, 2, 1, 3, 2, 3, 3, 1, 2] => 3, 2, 1, 3, 2, 3, 3, 1, 2
[3, 2, 1, 3, 2, 3, 3, 1, 3] => 3, 2, 1, 3, 2, 3, 3, 1, 3
[3, 2, 1, 3, 2, 3, 3, 2, 1] => 3, 2, 1, 3, 2, 3, 3, 2, 1
[3, 2, 1, 3, 2, 3, 3, 2, 2] => 3, 2, 1, 3, 2, 3, 3, 2, 2
[3, 2, 1, 3, 2, 3, 3, 2, 3] => 3, 2, 1, 3, 2, 3, 3, 2, 3
[3, 2, 1, 3, 2, 3, 3, 3, 1] => 3, 2, 1, 3, 2, 3, 3, 3, 1
[3, 2, 1, 3, 2, 3, 3, 3, 2] => 3, 2, 1, 3, 2, 3, 3, 3, 2
[3, 2, 1, 3, 2, 3, 3, 3, 3] => 3, 2, 1, 3, 2, 3, 3, 3, 3
[3, 2, 1, 3, 3, 1, 1, 1, 1] => 3, 2, 1, 3, 3, 1, 1, 1, 1
[3, 2, 1, 3, 3, 1, 1, 1, 2] => 3, 2, 1, 3, 3, 1, 1, 1, 2
[3, 2, 1, 3, 3, 1, 1, 1, 3] => 3, 2, 1, 3, 3, 1, 1, 1, 3
[3, 2, 1, 3, 3, 1, 1, 2, 1] => 3, 2, 1, 3, 3, 1, 1, 2, 1
[3, 2, 1, 3, 3, 1, 1, 2, 2] => 3, 2, 1, 3, 3, 1, 1, 2, 2
[3, 2, 1, 3, 3, 1, 1, 2, 3] => 3, 2, 1, 3, 3, 1, 1, 2, 3
[3, 2, 1, 3, 3, 1, 1, 3, 1] => 3, 2, 1, 3, 3, 1, 1, 3, 1
[3, 2, 1, 3, 3, 1, 1, 3, 2] => 3, 2, 1, 3, 3, 1, 1, 3, 2
[3, 2, 1, 3, 3, 1, 1, 3, 3] => 3, 2, 1, 3, 3, 1, 1, 3, 3
[3, 2, 1, 3, 3, 1, 2, 1, 1] => 3, 2, 1, 3, 3, 1, 2, 1, 1
[3, 2, 1, 3, 3, 1, 2, 1, 2] => 3, 2, 1, 3, 3, 1, 2, 1, 2
[3, 2, 1, 3, 3, 1, 2, 1, 3] => 3, 2, 1, 3, 3, 1, 2, 1, 3
[3, 2, 1, 3, 3, 1, 2, 2, 1] => 3, 2, 1, 3, 3, 1, 2, 2, 1
[3, 2, 1, 3, 3, 1, 2, 2, 2] => 3, 2, 1, 3, 3, 1, 2, 2, 2
[3, 2, 1, 3, 3, 1, 2, 2, 3] => 3, 2, 1, 3, 3, 1, 2, 2, 3
[3, 2, 1, 3, 3, 1, 2, 3, 1] => 3, 2, 1, 3, 3, 1, 2, 3, 1
[3, 2, 1, 3, 3, 1, 2, 3, 2] => 3, 2, 1, 3, 3, 1, 2, 3, 2
[3, 2, 1, 3, 3, 1, 2, 3, 3] => 3, 2, 1, 3, 3, 1, 2, 3, 3
[3, 2, 1, 3, 3, 1, 3, 1, 1] => 3, 2, 1, 3, 3, 1, 3, 1, 1
[3, 2, 1, 3, 3, 1, 3, 1, 2] => 3, 2, 1, 3, 3, 1, 3, 1, 2
[3, 2, 1, 3, 3, 1, 3, 1, 3] => 3, 2, 1, 3, 3, 1, 3, 1, 3
[3, 2, 1, 3, 3, 1, 3, 2, 1] => 3, 2, 1, 3, 3, 1, 3, 2, 1
[3, 2, 1, 3, 3, 1, 3, 2, 2] => 3, 2, 1, 3, 3, 1, 3, 2, 2
[3, 2, 1, 3, 3, 1, 3, 2, 3] => 3, 2, 1, 3, 3, 1, 3, 2, 3
[3, 2, 1, 3, 3, 1, 3, 3, 1] => 3, 2, 1, 3, 3, 1, 3, 3, 1
[3, 2, 1, 3, 3, 1, 3, 3, 2] => 3, 2, 1, 3, 3, 1, 3, 3, 2
[3, 2, 1, 3, 3, 1, 3, 3, 3] => 3, 2, 1, 3, 3, 1, 3, 3, 3
[3, 2, 1, 3, 3, 2, 1, 1, 1] => 3, 2, 1, 3, 3, 2, 1, 1, 1
[3, 2, 1, 3, 3, 2, 1, 1, 2] => 3, 2, 1, 3, 3, 2, 1, 1, 2
[3, 2, 1, 3, 3, 2, 1, 1, 3] => 3, 2, 1, 3, 3, 2, 1, 1, 3
[3, 2, 1, 3, 3, 2, 1, 2, 1] => 3, 2, 1, 3, 3, 2, 1, 2, 1
[3, 2, 1, 3, 3, 2, 1, 2, 2] => 3, 2, 1, 3, 3, 2, 1, 2, 2
[3, 2, 1, 3, 3, 2, 1, 2, 3] => 3, 2, 1, 3, 3, 2, 1, 2, 3
[3, 2, 1, 3, 3, 2, 1, 3, 1] => 3, 2, 1, 3, 3, 2, 1, 3, 1
[3, 2, 1, 3, 3, 2, 1, 3, 2] => 3, 2, 1, 3, 3, 2, 1, 3, 2
[3, 2, 1, 3, 3, 2, 1, 3, 3] => 3, 2, 1, 3, 3, 2, 1, 3, 3
[3, 2, 1, 3, 3, 2, 2, 1, 1] => 3, 2, 1, 3, 3, 2, 2, 1, 1
[3, 2, 1, 3, 3, 2, 2, 1, 2] => 3, 2, 1, 3, 3, 2, 2, 1, 2
[3, 2, 1, 3, 3, 2, 2, 1, 3] => 3, 2, 1, 3, 3, 2, 2, 1, 3
[3, 2, 1, 3, 3, 2, 2, 2, 1] => 3, 2, 1, 3, 3, 2, 2, 2, 1
[3, 2, 1, 3, 3, 2, 2, 2, 2] => 3, 2, 1, 3, 3, 2, 2, 2, 2
[3, 2, 1, 3, 3, 2, 2, 2, 3] => 3, 2, 1, 3, 3, 2, 2, 2, 3
[3, 2, 1, 3, 3, 2, 2, 3, 1] => 3, 2, 1, 3, 3, 2, 2, 3, 1
[3, 2, 1, 3, 3, 2, 2, 3, 2] => 3, 2, 1, 3, 3, 2, 2, 3, 2
[3, 2, 1, 3, 3, 2, 2, 3, 3] => 3, 2, 1, 3, 3, 2, 2, 3, 3
[3, 2, 1, 3, 3, 2, 3, 1, 1] => 3, 2, 1, 3, 3, 2, 3, 1, 1
[3, 2, 1, 3, 3, 2, 3, 1, 2] => 3, 2, 1, 3, 3, 2, 3, 1, 2
[3, 2, 1, 3, 3, 2, 3, 1, 3] => 3, 2, 1, 3, 3, 2, 3, 1, 3
[3, 2, 1, 3, 3, 2, 3, 2, 1] => 3, 2, 1, 3, 3, 2, 3, 2, 1
[3, 2, 1, 3, 3, 2, 3, 2, 2] => 3, 2, 1, 3, 3, 2, 3, 2, 2
[3, 2, 1, 3, 3, 2, 3, 2, 3] => 3, 2, 1, 3, 3, 2, 3, 2, 3
[3, 2, 1, 3, 3, 2, 3, 3, 1] => 3, 2, 1, 3, 3, 2, 3, 3, 1
[3, 2, 1, 3, 3, 2, 3, 3, 2] => 3, 2, 1, 3, 3, 2, 3, 3, 2
[3, 2, 1, 3, 3, 2, 3, 3, 3] => 3, 2, 1, 3, 3, 2, 3, 3, 3
[3, 2, 1, 3, 3, 3, 1, 1, 1] => 3, 2, 1, 3, 3, 3, 1, 1, 1
[3, 2, 1, 3, 3, 3, 1, 1, 2] => 3, 2, 1, 3, 3, 3, 1, 1, 2
[3, 2, 1, 3, 3, 3, 1, 1, 3] => 3, 2, 1, 3, 3, 3, 1, 1, 3
[3, 2, 1, 3, 3, 3, 1, 2, 1] => 3, 2, 1, 3, 3, 3, 1, 2, 1
[3, 2, 1, 3, 3, 3, 1, 2, 2] => 3, 2, 1, 3, 3, 3, 1, 2, 2
[3, 2, 1, 3, 3, 3, 1, 2, 3] => 3, 2, 1, 3, 3, 3, 1, 2, 3
[3, 2, 1, 3, 3, 3, 1, 3, 1] => 3, 2, 1, 3, 3, 3, 1, 3, 1
[3, 2, 1, 3, 3, 3, 1, 3, 2] => 3, 2, 1, 3, 3, 3, 1, 3, 2
[3, 2, 1, 3, 3, 3, 1, 3, 3] => 3, 2, 1, 3, 3, 3, 1, 3, 3
[3, 2, 1, 3, 3, 3, 2, 1, 1] => 3, 2, 1, 3, 3, 3, 2, 1, 1
[3, 2, 1, 3, 3, 3, 2, 1, 2] => 3, 2, 1, 3, 3, 3, 2, 1, 2
[3, 2, 1, 3, 3, 3, 2, 1, 3] => 3, 2, 1, 3, 3, 3, 2, 1, 3
[3, 2, 1, 3, 3, 3, 2, 2, 1] => 3, 2, 1, 3, 3, 3, 2, 2, 1
[3, 2, 1, 3, 3, 3, 2, 2, 2] => 3, 2, 1, 3, 3, 3, 2, 2, 2
[3, 2, 1, 3, 3, 3, 2, 2, 3] => 3, 2, 1, 3, 3, 3, 2, 2, 3
[3, 2, 1, 3, 3, 3, 2, 3, 1] => 3, 2, 1, 3, 3, 3, 2, 3, 1
[3, 2, 1, 3, 3, 3, 2, 3, 2] => 3, 2, 1, 3, 3, 3, 2, 3, 2
[3, 2, 1, 3, 3, 3, 2, 3, 3] => 3, 2, 1, 3, 3, 3, 2, 3, 3
[3, 2, 1, 3, 3, 3, 3, 1, 1] => 3, 2, 1, 3, 3, 3, 3, 1, 1
[3, 2, 1, 3, 3, 3, 3, 1, 2] => 3, 2, 1, 3, 3, 3, 3, 1, 2
[3, 2, 1, 3, 3, 3, 3, 1, 3] => 3, 2, 1, 3, 3, 3, 3, 1, 3
[3, 2, 1, 3, 3, 3, 3, 2, 1] => 3, 2, 1, 3, 3, 3, 3, 2, 1
[3, 2, 1, 3, 3, 3, 3, 2, 2] => 3, 2, 1, 3, 3, 3, 3, 2, 2
[3, 2, 1, 3, 3, 3, 3, 2, 3] => 3, 2, 1, 3, 3, 3, 3, 2, 3
[3, 2, 1, 3, 3, 3, 3, 3, 1] => 3, 2, 1, 3, 3, 3, 3, 3, 1
[3, 2, 1, 3, 3, 3, 3, 3, 2] => 3, 2, 1, 3, 3, 3, 3, 3, 2
[3, 2, 1, 3, 3, 3, 3, 3, 3] => 3, 2, 1, 3, 3, 3, 3, 3, 3
[3, 2, 2, 1, 1, 1, 1, 1, 1] => 3, 2, 2, 1, 1, 1, 1, 1, 1
[3, 2, 2, 1, 1, 1, 1, 1, 2] => 3, 2, 2, 1, 1, 1, 1, 1, 2
[3, 2, 2, 1, 1, 1, 1, 1, 3] => 3, 2, 2, 1, 1, 1, 1, 1, 3
[3, 2, 2, 1, 1, 1, 1, 2, 1] => 3, 2, 2, 1, 1, 1, 1, 2, 1
[3, 2, 2, 1, 1, 1, 1, 2, 2] => 3, 2, 2, 1, 1, 1, 1, 2, 2
[3, 2, 2, 1, 1, 1, 1, 2, 3] => 3, 2, 2, 1, 1, 1, 1, 2, 3
[3, 2, 2, 1, 1, 1, 1, 3, 1] => 3, 2, 2, 1, 1, 1, 1, 3, 1
[3, 2, 2, 1, 1, 1, 1, 3, 2] => 3, 2, 2, 1, 1, 1, 1, 3, 2
[3, 2, 2, 1, 1, 1, 1, 3, 3] => 3, 2, 2, 1, 1, 1, 1, 3, 3
[3, 2, 2, 1, 1, 1, 2, 1, 1] => 3, 2, 2, 1, 1, 1, 2, 1, 1
[3, 2, 2, 1, 1, 1, 2, 1, 2] => 3, 2, 2, 1, 1, 1, 2, 1, 2
[3, 2, 2, 1, 1, 1, 2, 1, 3] => 3, 2, 2, 1, 1, 1, 2, 1, 3
[3, 2, 2, 1, 1, 1, 2, 2, 1] => 3, 2, 2, 1, 1, 1, 2, 2, 1
[3, 2, 2, 1, 1, 1, 2, 2, 2] => 3, 2, 2, 1, 1, 1, 2, 2, 2
[3, 2, 2, 1, 1, 1, 2, 2, 3] => 3, 2, 2, 1, 1, 1, 2, 2, 3
[3, 2, 2, 1, 1, 1, 2, 3, 1] => 3, 2, 2, 1, 1, 1, 2, 3, 1
[3, 2, 2, 1, 1, 1, 2, 3, 2] => 3, 2, 2, 1, 1, 1, 2, 3, 2
[3, 2, 2, 1, 1, 1, 2, 3, 3] => 3, 2, 2, 1, 1, 1, 2, 3, 3
[3, 2, 2, 1, 1, 1, 3, 1, 1] => 3, 2, 2, 1, 1, 1, 3, 1, 1
[3, 2, 2, 1, 1, 1, 3, 1, 2] => 3, 2, 2, 1, 1, 1, 3, 1, 2
[3, 2, 2, 1, 1, 1, 3, 1, 3] => 3, 2, 2, 1, 1, 1, 3, 1, 3
[3, 2, 2, 1, 1, 1, 3, 2, 1] => 3, 2, 2, 1, 1, 1, 3, 2, 1
[3, 2, 2, 1, 1, 1, 3, 2, 2] => 3, 2, 2, 1, 1, 1, 3, 2, 2
[3, 2, 2, 1, 1, 1, 3, 2, 3] => 3, 2, 2, 1, 1, 1, 3, 2, 3
[3, 2, 2, 1, 1, 1, 3, 3, 1] => 3, 2, 2, 1, 1, 1, 3, 3, 1
[3, 2, 2, 1, 1, 1, 3, 3, 2] => 3, 2, 2, 1, 1, 1, 3, 3, 2
[3, 2, 2, 1, 1, 1, 3, 3, 3] => 3, 2, 2, 1, 1, 1, 3, 3, 3
[3, 2, 2, 1, 1, 2, 1, 1, 1] => 3, 2, 2, 1, 1, 2, 1, 1, 1
[3, 2, 2, 1, 1, 2, 1, 1, 2] => 3, 2, 2, 1, 1, 2, 1, 1, 2
[3, 2, 2, 1, 1, 2, 1, 1, 3] => 3, 2, 2, 1, 1, 2, 1, 1, 3
[3, 2, 2, 1, 1, 2, 1, 2, 1] => 3, 2, 2, 1, 1, 2, 1, 2, 1
[3, 2, 2, 1, 1, 2, 1, 2, 2] => 3, 2, 2, 1, 1, 2, 1, 2, 2
[3, 2, 2, 1, 1, 2, 1, 2, 3] => 3, 2, 2, 1, 1, 2, 1, 2, 3
[3, 2, 2, 1, 1, 2, 1, 3, 1] => 3, 2, 2, 1, 1, 2, 1, 3, 1
[3, 2, 2, 1, 1, 2, 1, 3, 2] => 3, 2, 2, 1, 1, 2, 1, 3, 2
[3, 2, 2, 1, 1, 2, 1, 3, 3] => 3, 2, 2, 1, 1, 2, 1, 3, 3
[3, 2, 2, 1, 1, 2, 2, 1, 1] => 3, 2, 2, 1, 1, 2, 2, 1, 1
[3, 2, 2, 1, 1, 2, 2, 1, 2] => 3, 2, 2, 1, 1, 2, 2, 1, 2
[3, 2, 2, 1, 1, 2, 2, 1, 3] => 3, 2, 2, 1, 1, 2, 2, 1, 3
[3, 2, 2, 1, 1, 2, 2, 2, 1] => 3, 2, 2, 1, 1, 2, 2, 2, 1
[3, 2, 2, 1, 1, 2, 2, 2, 2] => 3, 2, 2, 1, 1, 2, 2, 2, 2
[3, 2, 2, 1, 1, 2, 2, 2, 3] => 3, 2, 2, 1, 1, 2, 2, 2, 3
[3, 2, 2, 1, 1, 2, 2, 3, 1] => 3, 2, 2, 1, 1, 2, 2, 3, 1
[3, 2, 2, 1, 1, 2, 2, 3, 2] => 3, 2, 2, 1, 1, 2, 2, 3, 2
[3, 2, 2, 1, 1, 2, 2, 3, 3] => 3, 2, 2, 1, 1, 2, 2, 3, 3
[3, 2, 2, 1, 1, 2, 3, 1, 1] => 3, 2, 2, 1, 1, 2, 3, 1, 1
[3, 2, 2, 1, 1, 2, 3, 1, 2] => 3, 2, 2, 1, 1, 2, 3, 1, 2
[3, 2, 2, 1, 1, 2, 3, 1, 3] => 3, 2, 2, 1, 1, 2, 3, 1, 3
[3, 2, 2, 1, 1, 2, 3, 2, 1] => 3, 2, 2, 1, 1, 2, 3, 2, 1
[3, 2, 2, 1, 1, 2, 3, 2, 2] => 3, 2, 2, 1, 1, 2, 3, 2, 2
[3, 2, 2, 1, 1, 2, 3, 2, 3] => 3, 2, 2, 1, 1, 2, 3, 2, 3
[3, 2, 2, 1, 1, 2, 3, 3, 1] => 3, 2, 2, 1, 1, 2, 3, 3, 1
[3, 2, 2, 1, 1, 2, 3, 3, 2] => 3, 2, 2, 1, 1, 2, 3, 3, 2
[3, 2, 2, 1, 1, 2, 3, 3, 3] => 3, 2, 2, 1, 1, 2, 3, 3, 3
[3, 2, 2, 1, 1, 3, 1, 1, 1] => 3, 2, 2, 1, 1, 3, 1, 1, 1
[3, 2, 2, 1, 1, 3, 1, 1, 2] => 3, 2, 2, 1, 1, 3, 1, 1, 2
[3, 2, 2, 1, 1, 3, 1, 1, 3] => 3, 2, 2, 1, 1, 3, 1, 1, 3
[3, 2, 2, 1, 1, 3, 1, 2, 1] => 3, 2, 2, 1, 1, 3, 1, 2, 1
[3, 2, 2, 1, 1, 3, 1, 2, 2] => 3, 2, 2, 1, 1, 3, 1, 2, 2
[3, 2, 2, 1, 1, 3, 1, 2, 3] => 3, 2, 2, 1, 1, 3, 1, 2, 3
[3, 2, 2, 1, 1, 3, 1, 3, 1] => 3, 2, 2, 1, 1, 3, 1, 3, 1
[3, 2, 2, 1, 1, 3, 1, 3, 2] => 3, 2, 2, 1, 1, 3, 1, 3, 2
[3, 2, 2, 1, 1, 3, 1, 3, 3] => 3, 2, 2, 1, 1, 3, 1, 3, 3
[3, 2, 2, 1, 1, 3, 2, 1, 1] => 3, 2, 2, 1, 1, 3, 2, 1, 1
[3, 2, 2, 1, 1, 3, 2, 1, 2] => 3, 2, 2, 1, 1, 3, 2, 1, 2
[3, 2, 2, 1, 1, 3, 2, 1, 3] => 3, 2, 2, 1, 1, 3, 2, 1, 3
[3, 2, 2, 1, 1, 3, 2, 2, 1] => 3, 2, 2, 1, 1, 3, 2, 2, 1
[3, 2, 2, 1, 1, 3, 2, 2, 2] => 3, 2, 2, 1, 1, 3, 2, 2, 2
[3, 2, 2, 1, 1, 3, 2, 2, 3] => 3, 2, 2, 1, 1, 3, 2, 2, 3
[3, 2, 2, 1, 1, 3, 2, 3, 1] => 3, 2, 2, 1, 1, 3, 2, 3, 1
[3, 2, 2, 1, 1, 3, 2, 3, 2] => 3, 2, 2, 1, 1, 3, 2, 3, 2
[3, 2, 2, 1, 1, 3, 2, 3, 3] => 3, 2, 2, 1, 1, 3, 2, 3, 3
[3, 2, 2, 1, 1, 3, 3, 1, 1] => 3, 2, 2, 1, 1, 3, 3, 1, 1
[3, 2, 2, 1, 1, 3, 3, 1, 2] => 3, 2, 2, 1, 1, 3, 3, 1, 2
[3, 2, 2, 1, 1, 3, 3, 1, 3] => 3, 2, 2, 1, 1, 3, 3, 1, 3
[3, 2, 2, 1, 1, 3, 3, 2, 1] => 3, 2, 2, 1, 1, 3, 3, 2, 1
[3, 2, 2, 1, 1, 3, 3, 2, 2] => 3, 2, 2, 1, 1, 3, 3, 2, 2
[3, 2, 2, 1, 1, 3, 3, 2, 3] => 3, 2, 2, 1, 1, 3, 3, 2, 3
[3, 2, 2, 1, 1, 3, 3, 3, 1] => 3, 2, 2, 1, 1, 3, 3, 3, 1
[3, 2, 2, 1, 1, 3, 3, 3, 2] => 3, 2, 2, 1, 1, 3, 3, 3, 2
[3, 2, 2, 1, 1, 3, 3, 3, 3] => 3, 2, 2, 1, 1, 3, 3, 3, 3
[3, 2, 2, 1, 2, 1, 1, 1, 1] => 3, 2, 2, 1, 2, 1, 1, 1, 1
[3, 2, 2, 1, 2, 1, 1, 1, 2] => 3, 2, 2, 1, 2, 1, 1, 1, 2
[3, 2, 2, 1, 2, 1, 1, 1, 3] => 3, 2, 2, 1, 2, 1, 1, 1, 3
[3, 2, 2, 1, 2, 1, 1, 2, 1] => 3, 2, 2, 1, 2, 1, 1, 2, 1
[3, 2, 2, 1, 2, 1, 1, 2, 2] => 3, 2, 2, 1, 2, 1, 1, 2, 2
[3, 2, 2, 1, 2, 1, 1, 2, 3] => 3, 2, 2, 1, 2, 1, 1, 2, 3
[3, 2, 2, 1, 2, 1, 1, 3, 1] => 3, 2, 2, 1, 2, 1, 1, 3, 1
[3, 2, 2, 1, 2, 1, 1, 3, 2] => 3, 2, 2, 1, 2, 1, 1, 3, 2
[3, 2, 2, 1, 2, 1, 1, 3, 3] => 3, 2, 2, 1, 2, 1, 1, 3, 3
[3, 2, 2, 1, 2, 1, 2, 1, 1] => 3, 2, 2, 1, 2, 1, 2, 1, 1
[3, 2, 2, 1, 2, 1, 2, 1, 2] => 3, 2, 2, 1, 2, 1, 2, 1, 2
[3, 2, 2, 1, 2, 1, 2, 1, 3] => 3, 2, 2, 1, 2, 1, 2, 1, 3
[3, 2, 2, 1, 2, 1, 2, 2, 1] => 3, 2, 2, 1, 2, 1, 2, 2, 1
[3, 2, 2, 1, 2, 1, 2, 2, 2] => 3, 2, 2, 1, 2, 1, 2, 2, 2
[3, 2, 2, 1, 2, 1, 2, 2, 3] => 3, 2, 2, 1, 2, 1, 2, 2, 3
[3, 2, 2, 1, 2, 1, 2, 3, 1] => 3, 2, 2, 1, 2, 1, 2, 3, 1
[3, 2, 2, 1, 2, 1, 2, 3, 2] => 3, 2, 2, 1, 2, 1, 2, 3, 2
[3, 2, 2, 1, 2, 1, 2, 3, 3] => 3, 2, 2, 1, 2, 1, 2, 3, 3
[3, 2, 2, 1, 2, 1, 3, 1, 1] => 3, 2, 2, 1, 2, 1, 3, 1, 1
[3, 2, 2, 1, 2, 1, 3, 1, 2] => 3, 2, 2, 1, 2, 1, 3, 1, 2
[3, 2, 2, 1, 2, 1, 3, 1, 3] => 3, 2, 2, 1, 2, 1, 3, 1, 3
[3, 2, 2, 1, 2, 1, 3, 2, 1] => 3, 2, 2, 1, 2, 1, 3, 2, 1
[3, 2, 2, 1, 2, 1, 3, 2, 2] => 3, 2, 2, 1, 2, 1, 3, 2, 2
[3, 2, 2, 1, 2, 1, 3, 2, 3] => 3, 2, 2, 1, 2, 1, 3, 2, 3
[3, 2, 2, 1, 2, 1, 3, 3, 1] => 3, 2, 2, 1, 2, 1, 3, 3, 1
[3, 2, 2, 1, 2, 1, 3, 3, 2] => 3, 2, 2, 1, 2, 1, 3, 3, 2
[3, 2, 2, 1, 2, 1, 3, 3, 3] => 3, 2, 2, 1, 2, 1, 3, 3, 3
[3, 2, 2, 1, 2, 2, 1, 1, 1] => 3, 2, 2, 1, 2, 2, 1, 1, 1
[3, 2, 2, 1, 2, 2, 1, 1, 2] => 3, 2, 2, 1, 2, 2, 1, 1, 2
[3, 2, 2, 1, 2, 2, 1, 1, 3] => 3, 2, 2, 1, 2, 2, 1, 1, 3
[3, 2, 2, 1, 2, 2, 1, 2, 1] => 3, 2, 2, 1, 2, 2, 1, 2, 1
[3, 2, 2, 1, 2, 2, 1, 2, 2] => 3, 2, 2, 1, 2, 2, 1, 2, 2
[3, 2, 2, 1, 2, 2, 1, 2, 3] => 3, 2, 2, 1, 2, 2, 1, 2, 3
[3, 2, 2, 1, 2, 2, 1, 3, 1] => 3, 2, 2, 1, 2, 2, 1, 3, 1
[3, 2, 2, 1, 2, 2, 1, 3, 2] => 3, 2, 2, 1, 2, 2, 1, 3, 2
[3, 2, 2, 1, 2, 2, 1, 3, 3] => 3, 2, 2, 1, 2, 2, 1, 3, 3
[3, 2, 2, 1, 2, 2, 2, 1, 1] => 3, 2, 2, 1, 2, 2, 2, 1, 1
[3, 2, 2, 1, 2, 2, 2, 1, 2] => 3, 2, 2, 1, 2, 2, 2, 1, 2
[3, 2, 2, 1, 2, 2, 2, 1, 3] => 3, 2, 2, 1, 2, 2, 2, 1, 3
[3, 2, 2, 1, 2, 2, 2, 2, 1] => 3, 2, 2, 1, 2, 2, 2, 2, 1
[3, 2, 2, 1, 2, 2, 2, 2, 2] => 3, 2, 2, 1, 2, 2, 2, 2, 2
[3, 2, 2, 1, 2, 2, 2, 2, 3] => 3, 2, 2, 1, 2, 2, 2, 2, 3
[3, 2, 2, 1, 2, 2, 2, 3, 1] => 3, 2, 2, 1, 2, 2, 2, 3, 1
[3, 2, 2, 1, 2, 2, 2, 3, 2] => 3, 2, 2, 1, 2, 2, 2, 3, 2
[3, 2, 2, 1, 2, 2, 2, 3, 3] => 3, 2, 2, 1, 2, 2, 2, 3, 3
[3, 2, 2, 1, 2, 2, 3, 1, 1] => 3, 2, 2, 1, 2, 2, 3, 1, 1
[3, 2, 2, 1, 2, 2, 3, 1, 2] => 3, 2, 2, 1, 2, 2, 3, 1, 2
[3, 2, 2, 1, 2, 2, 3, 1, 3] => 3, 2, 2, 1, 2, 2, 3, 1, 3
[3, 2, 2, 1, 2, 2, 3, 2, 1] => 3, 2, 2, 1, 2, 2, 3, 2, 1
[3, 2, 2, 1, 2, 2, 3, 2, 2] => 3, 2, 2, 1, 2, 2, 3, 2, 2
[3, 2, 2, 1, 2, 2, 3, 2, 3] => 3, 2, 2, 1, 2, 2, 3, 2, 3
[3, 2, 2, 1, 2, 2, 3, 3, 1] => 3, 2, 2, 1, 2, 2, 3, 3, 1
[3, 2, 2, 1, 2, 2, 3, 3, 2] => 3, 2, 2, 1, 2, 2, 3, 3, 2
[3, 2, 2, 1, 2, 2, 3, 3, 3] => 3, 2, 2, 1, 2, 2, 3, 3, 3
[3, 2, 2, 1, 2, 3, 1, 1, 1] => 3, 2, 2, 1, 2, 3, 1, 1, 1
[3, 2, 2, 1, 2, 3, 1, 1, 2] => 3, 2, 2, 1, 2, 3, 1, 1, 2
[3, 2, 2, 1, 2, 3, 1, 1, 3] => 3, 2, 2, 1, 2, 3, 1, 1, 3
[3, 2, 2, 1, 2, 3, 1, 2, 1] => 3, 2, 2, 1, 2, 3, 1, 2, 1
[3, 2, 2, 1, 2, 3, 1, 2, 2] => 3, 2, 2, 1, 2, 3, 1, 2, 2
[3, 2, 2, 1, 2, 3, 1, 2, 3] => 3, 2, 2, 1, 2, 3, 1, 2, 3
[3, 2, 2, 1, 2, 3, 1, 3, 1] => 3, 2, 2, 1, 2, 3, 1, 3, 1
[3, 2, 2, 1, 2, 3, 1, 3, 2] => 3, 2, 2, 1, 2, 3, 1, 3, 2
[3, 2, 2, 1, 2, 3, 1, 3, 3] => 3, 2, 2, 1, 2, 3, 1, 3, 3
[3, 2, 2, 1, 2, 3, 2, 1, 1] => 3, 2, 2, 1, 2, 3, 2, 1, 1
[3, 2, 2, 1, 2, 3, 2, 1, 2] => 3, 2, 2, 1, 2, 3, 2, 1, 2
[3, 2, 2, 1, 2, 3, 2, 1, 3] => 3, 2, 2, 1, 2, 3, 2, 1, 3
[3, 2, 2, 1, 2, 3, 2, 2, 1] => 3, 2, 2, 1, 2, 3, 2, 2, 1
[3, 2, 2, 1, 2, 3, 2, 2, 2] => 3, 2, 2, 1, 2, 3, 2, 2, 2
[3, 2, 2, 1, 2, 3, 2, 2, 3] => 3, 2, 2, 1, 2, 3, 2, 2, 3
[3, 2, 2, 1, 2, 3, 2, 3, 1] => 3, 2, 2, 1, 2, 3, 2, 3, 1
[3, 2, 2, 1, 2, 3, 2, 3, 2] => 3, 2, 2, 1, 2, 3, 2, 3, 2
[3, 2, 2, 1, 2, 3, 2, 3, 3] => 3, 2, 2, 1, 2, 3, 2, 3, 3
[3, 2, 2, 1, 2, 3, 3, 1, 1] => 3, 2, 2, 1, 2, 3, 3, 1, 1
[3, 2, 2, 1, 2, 3, 3, 1, 2] => 3, 2, 2, 1, 2, 3, 3, 1, 2
[3, 2, 2, 1, 2, 3, 3, 1, 3] => 3, 2, 2, 1, 2, 3, 3, 1, 3
[3, 2, 2, 1, 2, 3, 3, 2, 1] => 3, 2, 2, 1, 2, 3, 3, 2, 1
[3, 2, 2, 1, 2, 3, 3, 2, 2] => 3, 2, 2, 1, 2, 3, 3, 2, 2
[3, 2, 2, 1, 2, 3, 3, 2, 3] => 3, 2, 2, 1, 2, 3, 3, 2, 3
[3, 2, 2, 1, 2, 3, 3, 3, 1] => 3, 2, 2, 1, 2, 3, 3, 3, 1
[3, 2, 2, 1, 2, 3, 3, 3, 2] => 3, 2, 2, 1, 2, 3, 3, 3, 2
[3, 2, 2, 1, 2, 3, 3, 3, 3] => 3, 2, 2, 1, 2, 3, 3, 3, 3
[3, 2, 2, 1, 3, 1, 1, 1, 1] => 3, 2, 2, 1, 3, 1, 1, 1, 1
[3, 2, 2, 1, 3, 1, 1, 1, 2] => 3, 2, 2, 1, 3, 1, 1, 1, 2
[3, 2, 2, 1, 3, 1, 1, 1, 3] => 3, 2, 2, 1, 3, 1, 1, 1, 3
[3, 2, 2, 1, 3, 1, 1, 2, 1] => 3, 2, 2, 1, 3, 1, 1, 2, 1
[3, 2, 2, 1, 3, 1, 1, 2, 2] => 3, 2, 2, 1, 3, 1, 1, 2, 2
[3, 2, 2, 1, 3, 1, 1, 2, 3] => 3, 2, 2, 1, 3, 1, 1, 2, 3
[3, 2, 2, 1, 3, 1, 1, 3, 1] => 3, 2, 2, 1, 3, 1, 1, 3, 1
[3, 2, 2, 1, 3, 1, 1, 3, 2] => 3, 2, 2, 1, 3, 1, 1, 3, 2
[3, 2, 2, 1, 3, 1, 1, 3, 3] => 3, 2, 2, 1, 3, 1, 1, 3, 3
[3, 2, 2, 1, 3, 1, 2, 1, 1] => 3, 2, 2, 1, 3, 1, 2, 1, 1
[3, 2, 2, 1, 3, 1, 2, 1, 2] => 3, 2, 2, 1, 3, 1, 2, 1, 2
[3, 2, 2, 1, 3, 1, 2, 1, 3] => 3, 2, 2, 1, 3, 1, 2, 1, 3
[3, 2, 2, 1, 3, 1, 2, 2, 1] => 3, 2, 2, 1, 3, 1, 2, 2, 1
[3, 2, 2, 1, 3, 1, 2, 2, 2] => 3, 2, 2, 1, 3, 1, 2, 2, 2
[3, 2, 2, 1, 3, 1, 2, 2, 3] => 3, 2, 2, 1, 3, 1, 2, 2, 3
[3, 2, 2, 1, 3, 1, 2, 3, 1] => 3, 2, 2, 1, 3, 1, 2, 3, 1
[3, 2, 2, 1, 3, 1, 2, 3, 2] => 3, 2, 2, 1, 3, 1, 2, 3, 2
[3, 2, 2, 1, 3, 1, 2, 3, 3] => 3, 2, 2, 1, 3, 1, 2, 3, 3
[3, 2, 2, 1, 3, 1, 3, 1, 1] => 3, 2, 2, 1, 3, 1, 3, 1, 1
[3, 2, 2, 1, 3, 1, 3, 1, 2] => 3, 2, 2, 1, 3, 1, 3, 1, 2
[3, 2, 2, 1, 3, 1, 3, 1, 3] => 3, 2, 2, 1, 3, 1, 3, 1, 3
[3, 2, 2, 1, 3, 1, 3, 2, 1] => 3, 2, 2, 1, 3, 1, 3, 2, 1
[3, 2, 2, 1, 3, 1, 3, 2, 2] => 3, 2, 2, 1, 3, 1, 3, 2, 2
[3, 2, 2, 1, 3, 1, 3, 2, 3] => 3, 2, 2, 1, 3, 1, 3, 2, 3
[3, 2, 2, 1, 3, 1, 3, 3, 1] => 3, 2, 2, 1, 3, 1, 3, 3, 1
[3, 2, 2, 1, 3, 1, 3, 3, 2] => 3, 2, 2, 1, 3, 1, 3, 3, 2
[3, 2, 2, 1, 3, 1, 3, 3, 3] => 3, 2, 2, 1, 3, 1, 3, 3, 3
[3, 2, 2, 1, 3, 2, 1, 1, 1] => 3, 2, 2, 1, 3, 2, 1, 1, 1
[3, 2, 2, 1, 3, 2, 1, 1, 2] => 3, 2, 2, 1, 3, 2, 1, 1, 2
[3, 2, 2, 1, 3, 2, 1, 1, 3] => 3, 2, 2, 1, 3, 2, 1, 1, 3
[3, 2, 2, 1, 3, 2, 1, 2, 1] => 3, 2, 2, 1, 3, 2, 1, 2, 1
[3, 2, 2, 1, 3, 2, 1, 2, 2] => 3, 2, 2, 1, 3, 2, 1, 2, 2
[3, 2, 2, 1, 3, 2, 1, 2, 3] => 3, 2, 2, 1, 3, 2, 1, 2, 3
[3, 2, 2, 1, 3, 2, 1, 3, 1] => 3, 2, 2, 1, 3, 2, 1, 3, 1
[3, 2, 2, 1, 3, 2, 1, 3, 2] => 3, 2, 2, 1, 3, 2, 1, 3, 2
[3, 2, 2, 1, 3, 2, 1, 3, 3] => 3, 2, 2, 1, 3, 2, 1, 3, 3
[3, 2, 2, 1, 3, 2, 2, 1, 1] => 3, 2, 2, 1, 3, 2, 2, 1, 1
[3, 2, 2, 1, 3, 2, 2, 1, 2] => 3, 2, 2, 1, 3, 2, 2, 1, 2
[3, 2, 2, 1, 3, 2, 2, 1, 3] => 3, 2, 2, 1, 3, 2, 2, 1, 3
[3, 2, 2, 1, 3, 2, 2, 2, 1] => 3, 2, 2, 1, 3, 2, 2, 2, 1
[3, 2, 2, 1, 3, 2, 2, 2, 2] => 3, 2, 2, 1, 3, 2, 2, 2, 2
[3, 2, 2, 1, 3, 2, 2, 2, 3] => 3, 2, 2, 1, 3, 2, 2, 2, 3
[3, 2, 2, 1, 3, 2, 2, 3, 1] => 3, 2, 2, 1, 3, 2, 2, 3, 1
[3, 2, 2, 1, 3, 2, 2, 3, 2] => 3, 2, 2, 1, 3, 2, 2, 3, 2
[3, 2, 2, 1, 3, 2, 2, 3, 3] => 3, 2, 2, 1, 3, 2, 2, 3, 3
[3, 2, 2, 1, 3, 2, 3, 1, 1] => 3, 2, 2, 1, 3, 2, 3, 1, 1
[3, 2, 2, 1, 3, 2, 3, 1, 2] => 3, 2, 2, 1, 3, 2, 3, 1, 2
[3, 2, 2, 1, 3, 2, 3, 1, 3] => 3, 2, 2, 1, 3, 2, 3, 1, 3
[3, 2, 2, 1, 3, 2, 3, 2, 1] => 3, 2, 2, 1, 3, 2, 3, 2, 1
[3, 2, 2, 1, 3, 2, 3, 2, 2] => 3, 2, 2, 1, 3, 2, 3, 2, 2
[3, 2, 2, 1, 3, 2, 3, 2, 3] => 3, 2, 2, 1, 3, 2, 3, 2, 3
[3, 2, 2, 1, 3, 2, 3, 3, 1] => 3, 2, 2, 1, 3, 2, 3, 3, 1
[3, 2, 2, 1, 3, 2, 3, 3, 2] => 3, 2, 2, 1, 3, 2, 3, 3, 2
[3, 2, 2, 1, 3, 2, 3, 3, 3] => 3, 2, 2, 1, 3, 2, 3, 3, 3
[3, 2, 2, 1, 3, 3, 1, 1, 1] => 3, 2, 2, 1, 3, 3, 1, 1, 1
[3, 2, 2, 1, 3, 3, 1, 1, 2] => 3, 2, 2, 1, 3, 3, 1, 1, 2
[3, 2, 2, 1, 3, 3, 1, 1, 3] => 3, 2, 2, 1, 3, 3, 1, 1, 3
[3, 2, 2, 1, 3, 3, 1, 2, 1] => 3, 2, 2, 1, 3, 3, 1, 2, 1
[3, 2, 2, 1, 3, 3, 1, 2, 2] => 3, 2, 2, 1, 3, 3, 1, 2, 2
[3, 2, 2, 1, 3, 3, 1, 2, 3] => 3, 2, 2, 1, 3, 3, 1, 2, 3
[3, 2, 2, 1, 3, 3, 1, 3, 1] => 3, 2, 2, 1, 3, 3, 1, 3, 1
[3, 2, 2, 1, 3, 3, 1, 3, 2] => 3, 2, 2, 1, 3, 3, 1, 3, 2
[3, 2, 2, 1, 3, 3, 1, 3, 3] => 3, 2, 2, 1, 3, 3, 1, 3, 3
[3, 2, 2, 1, 3, 3, 2, 1, 1] => 3, 2, 2, 1, 3, 3, 2, 1, 1
[3, 2, 2, 1, 3, 3, 2, 1, 2] => 3, 2, 2, 1, 3, 3, 2, 1, 2
[3, 2, 2, 1, 3, 3, 2, 1, 3] => 3, 2, 2, 1, 3, 3, 2, 1, 3
[3, 2, 2, 1, 3, 3, 2, 2, 1] => 3, 2, 2, 1, 3, 3, 2, 2, 1
[3, 2, 2, 1, 3, 3, 2, 2, 2] => 3, 2, 2, 1, 3, 3, 2, 2, 2
[3, 2, 2, 1, 3, 3, 2, 2, 3] => 3, 2, 2, 1, 3, 3, 2, 2, 3
[3, 2, 2, 1, 3, 3, 2, 3, 1] => 3, 2, 2, 1, 3, 3, 2, 3, 1
[3, 2, 2, 1, 3, 3, 2, 3, 2] => 3, 2, 2, 1, 3, 3, 2, 3, 2
[3, 2, 2, 1, 3, 3, 2, 3, 3] => 3, 2, 2, 1, 3, 3, 2, 3, 3
[3, 2, 2, 1, 3, 3, 3, 1, 1] => 3, 2, 2, 1, 3, 3, 3, 1, 1
[3, 2, 2, 1, 3, 3, 3, 1, 2] => 3, 2, 2, 1, 3, 3, 3, 1, 2
[3, 2, 2, 1, 3, 3, 3, 1, 3] => 3, 2, 2, 1, 3, 3, 3, 1, 3
[3, 2, 2, 1, 3, 3, 3, 2, 1] => 3, 2, 2, 1, 3, 3, 3, 2, 1
[3, 2, 2, 1, 3, 3, 3, 2, 2] => 3, 2, 2, 1, 3, 3, 3, 2, 2
[3, 2, 2, 1, 3, 3, 3, 2, 3] => 3, 2, 2, 1, 3, 3, 3, 2, 3
[3, 2, 2, 1, 3, 3, 3, 3, 1] => 3, 2, 2, 1, 3, 3, 3, 3, 1
[3, 2, 2, 1, 3, 3, 3, 3, 2] => 3, 2, 2, 1, 3, 3, 3, 3, 2
[3, 2, 2, 1, 3, 3, 3, 3, 3] => 3, 2, 2, 1, 3, 3, 3, 3, 3
[3, 2, 2, 2, 1, 1, 1, 1, 1] => 3, 2, 2, 2, 1, 1, 1, 1, 1
[3, 2, 2, 2, 1, 1, 1, 1, 2] => 3, 2, 2, 2, 1, 1, 1, 1, 2
[3, 2, 2, 2, 1, 1, 1, 1, 3] => 3, 2, 2, 2, 1, 1, 1, 1, 3
[3, 2, 2, 2, 1, 1, 1, 2, 1] => 3, 2, 2, 2, 1, 1, 1, 2, 1
[3, 2, 2, 2, 1, 1, 1, 2, 2] => 3, 2, 2, 2, 1, 1, 1, 2, 2
[3, 2, 2, 2, 1, 1, 1, 2, 3] => 3, 2, 2, 2, 1, 1, 1, 2, 3
[3, 2, 2, 2, 1, 1, 1, 3, 1] => 3, 2, 2, 2, 1, 1, 1, 3, 1
[3, 2, 2, 2, 1, 1, 1, 3, 2] => 3, 2, 2, 2, 1, 1, 1, 3, 2
[3, 2, 2, 2, 1, 1, 1, 3, 3] => 3, 2, 2, 2, 1, 1, 1, 3, 3
[3, 2, 2, 2, 1, 1, 2, 1, 1] => 3, 2, 2, 2, 1, 1, 2, 1, 1
[3, 2, 2, 2, 1, 1, 2, 1, 2] => 3, 2, 2, 2, 1, 1, 2, 1, 2
[3, 2, 2, 2, 1, 1, 2, 1, 3] => 3, 2, 2, 2, 1, 1, 2, 1, 3
[3, 2, 2, 2, 1, 1, 2, 2, 1] => 3, 2, 2, 2, 1, 1, 2, 2, 1
[3, 2, 2, 2, 1, 1, 2, 2, 2] => 3, 2, 2, 2, 1, 1, 2, 2, 2
[3, 2, 2, 2, 1, 1, 2, 2, 3] => 3, 2, 2, 2, 1, 1, 2, 2, 3
[3, 2, 2, 2, 1, 1, 2, 3, 1] => 3, 2, 2, 2, 1, 1, 2, 3, 1
[3, 2, 2, 2, 1, 1, 2, 3, 2] => 3, 2, 2, 2, 1, 1, 2, 3, 2
[3, 2, 2, 2, 1, 1, 2, 3, 3] => 3, 2, 2, 2, 1, 1, 2, 3, 3
[3, 2, 2, 2, 1, 1, 3, 1, 1] => 3, 2, 2, 2, 1, 1, 3, 1, 1
[3, 2, 2, 2, 1, 1, 3, 1, 2] => 3, 2, 2, 2, 1, 1, 3, 1, 2
[3, 2, 2, 2, 1, 1, 3, 1, 3] => 3, 2, 2, 2, 1, 1, 3, 1, 3
[3, 2, 2, 2, 1, 1, 3, 2, 1] => 3, 2, 2, 2, 1, 1, 3, 2, 1
[3, 2, 2, 2, 1, 1, 3, 2, 2] => 3, 2, 2, 2, 1, 1, 3, 2, 2
[3, 2, 2, 2, 1, 1, 3, 2, 3] => 3, 2, 2, 2, 1, 1, 3, 2, 3
[3, 2, 2, 2, 1, 1, 3, 3, 1] => 3, 2, 2, 2, 1, 1, 3, 3, 1
[3, 2, 2, 2, 1, 1, 3, 3, 2] => 3, 2, 2, 2, 1, 1, 3, 3, 2
[3, 2, 2, 2, 1, 1, 3, 3, 3] => 3, 2, 2, 2, 1, 1, 3, 3, 3
[3, 2, 2, 2, 1, 2, 1, 1, 1] => 3, 2, 2, 2, 1, 2, 1, 1, 1
[3, 2, 2, 2, 1, 2, 1, 1, 2] => 3, 2, 2, 2, 1, 2, 1, 1, 2
[3, 2, 2, 2, 1, 2, 1, 1, 3] => 3, 2, 2, 2, 1, 2, 1, 1, 3
[3, 2, 2, 2, 1, 2, 1, 2, 1] => 3, 2, 2, 2, 1, 2, 1, 2, 1
[3, 2, 2, 2, 1, 2, 1, 2, 2] => 3, 2, 2, 2, 1, 2, 1, 2, 2
[3, 2, 2, 2, 1, 2, 1, 2, 3] => 3, 2, 2, 2, 1, 2, 1, 2, 3
[3, 2, 2, 2, 1, 2, 1, 3, 1] => 3, 2, 2, 2, 1, 2, 1, 3, 1
[3, 2, 2, 2, 1, 2, 1, 3, 2] => 3, 2, 2, 2, 1, 2, 1, 3, 2
[3, 2, 2, 2, 1, 2, 1, 3, 3] => 3, 2, 2, 2, 1, 2, 1, 3, 3
[3, 2, 2, 2, 1, 2, 2, 1, 1] => 3, 2, 2, 2, 1, 2, 2, 1, 1
[3, 2, 2, 2, 1, 2, 2, 1, 2] => 3, 2, 2, 2, 1, 2, 2, 1, 2
[3, 2, 2, 2, 1, 2, 2, 1, 3] => 3, 2, 2, 2, 1, 2, 2, 1, 3
[3, 2, 2, 2, 1, 2, 2, 2, 1] => 3, 2, 2, 2, 1, 2, 2, 2, 1
[3, 2, 2, 2, 1, 2, 2, 2, 2] => 3, 2, 2, 2, 1, 2, 2, 2, 2
[3, 2, 2, 2, 1, 2, 2, 2, 3] => 3, 2, 2, 2, 1, 2, 2, 2, 3
[3, 2, 2, 2, 1, 2, 2, 3, 1] => 3, 2, 2, 2, 1, 2, 2, 3, 1
[3, 2, 2, 2, 1, 2, 2, 3, 2] => 3, 2, 2, 2, 1, 2, 2, 3, 2
[3, 2, 2, 2, 1, 2, 2, 3, 3] => 3, 2, 2, 2, 1, 2, 2, 3, 3
[3, 2, 2, 2, 1, 2, 3, 1, 1] => 3, 2, 2, 2, 1, 2, 3, 1, 1
[3, 2, 2, 2, 1, 2, 3, 1, 2] => 3, 2, 2, 2, 1, 2, 3, 1, 2
[3, 2, 2, 2, 1, 2, 3, 1, 3] => 3, 2, 2, 2, 1, 2, 3, 1, 3
[3, 2, 2, 2, 1, 2, 3, 2, 1] => 3, 2, 2, 2, 1, 2, 3, 2, 1
[3, 2, 2, 2, 1, 2, 3, 2, 2] => 3, 2, 2, 2, 1, 2, 3, 2, 2
[3, 2, 2, 2, 1, 2, 3, 2, 3] => 3, 2, 2, 2, 1, 2, 3, 2, 3
[3, 2, 2, 2, 1, 2, 3, 3, 1] => 3, 2, 2, 2, 1, 2, 3, 3, 1
[3, 2, 2, 2, 1, 2, 3, 3, 2] => 3, 2, 2, 2, 1, 2, 3, 3, 2
[3, 2, 2, 2, 1, 2, 3, 3, 3] => 3, 2, 2, 2, 1, 2, 3, 3, 3
[3, 2, 2, 2, 1, 3, 1, 1, 1] => 3, 2, 2, 2, 1, 3, 1, 1, 1
[3, 2, 2, 2, 1, 3, 1, 1, 2] => 3, 2, 2, 2, 1, 3, 1, 1, 2
[3, 2, 2, 2, 1, 3, 1, 1, 3] => 3, 2, 2, 2, 1, 3, 1, 1, 3
[3, 2, 2, 2, 1, 3, 1, 2, 1] => 3, 2, 2, 2, 1, 3, 1, 2, 1
[3, 2, 2, 2, 1, 3, 1, 2, 2] => 3, 2, 2, 2, 1, 3, 1, 2, 2
[3, 2, 2, 2, 1, 3, 1, 2, 3] => 3, 2, 2, 2, 1, 3, 1, 2, 3
[3, 2, 2, 2, 1, 3, 1, 3, 1] => 3, 2, 2, 2, 1, 3, 1, 3, 1
[3, 2, 2, 2, 1, 3, 1, 3, 2] => 3, 2, 2, 2, 1, 3, 1, 3, 2
[3, 2, 2, 2, 1, 3, 1, 3, 3] => 3, 2, 2, 2, 1, 3, 1, 3, 3
[3, 2, 2, 2, 1, 3, 2, 1, 1] => 3, 2, 2, 2, 1, 3, 2, 1, 1
[3, 2, 2, 2, 1, 3, 2, 1, 2] => 3, 2, 2, 2, 1, 3, 2, 1, 2
[3, 2, 2, 2, 1, 3, 2, 1, 3] => 3, 2, 2, 2, 1, 3, 2, 1, 3
[3, 2, 2, 2, 1, 3, 2, 2, 1] => 3, 2, 2, 2, 1, 3, 2, 2, 1
[3, 2, 2, 2, 1, 3, 2, 2, 2] => 3, 2, 2, 2, 1, 3, 2, 2, 2
[3, 2, 2, 2, 1, 3, 2, 2, 3] => 3, 2, 2, 2, 1, 3, 2, 2, 3
[3, 2, 2, 2, 1, 3, 2, 3, 1] => 3, 2, 2, 2, 1, 3, 2, 3, 1
[3, 2, 2, 2, 1, 3, 2, 3, 2] => 3, 2, 2, 2, 1, 3, 2, 3, 2
[3, 2, 2, 2, 1, 3, 2, 3, 3] => 3, 2, 2, 2, 1, 3, 2, 3, 3
[3, 2, 2, 2, 1, 3, 3, 1, 1] => 3, 2, 2, 2, 1, 3, 3, 1, 1
[3, 2, 2, 2, 1, 3, 3, 1, 2] => 3, 2, 2, 2, 1, 3, 3, 1, 2
[3, 2, 2, 2, 1, 3, 3, 1, 3] => 3, 2, 2, 2, 1, 3, 3, 1, 3
[3, 2, 2, 2, 1, 3, 3, 2, 1] => 3, 2, 2, 2, 1, 3, 3, 2, 1
[3, 2, 2, 2, 1, 3, 3, 2, 2] => 3, 2, 2, 2, 1, 3, 3, 2, 2
[3, 2, 2, 2, 1, 3, 3, 2, 3] => 3, 2, 2, 2, 1, 3, 3, 2, 3
[3, 2, 2, 2, 1, 3, 3, 3, 1] => 3, 2, 2, 2, 1, 3, 3, 3, 1
[3, 2, 2, 2, 1, 3, 3, 3, 2] => 3, 2, 2, 2, 1, 3, 3, 3, 2
[3, 2, 2, 2, 1, 3, 3, 3, 3] => 3, 2, 2, 2, 1, 3, 3, 3, 3
[3, 2, 2, 2, 2, 1, 1, 1, 1] => 3, 2, 2, 2, 2, 1, 1, 1, 1
[3, 2, 2, 2, 2, 1, 1, 1, 2] => 3, 2, 2, 2, 2, 1, 1, 1, 2
[3, 2, 2, 2, 2, 1, 1, 1, 3] => 3, 2, 2, 2, 2, 1, 1, 1, 3
[3, 2, 2, 2, 2, 1, 1, 2, 1] => 3, 2, 2, 2, 2, 1, 1, 2, 1
[3, 2, 2, 2, 2, 1, 1, 2, 2] => 3, 2, 2, 2, 2, 1, 1, 2, 2
[3, 2, 2, 2, 2, 1, 1, 2, 3] => 3, 2, 2, 2, 2, 1, 1, 2, 3
[3, 2, 2, 2, 2, 1, 1, 3, 1] => 3, 2, 2, 2, 2, 1, 1, 3, 1
[3, 2, 2, 2, 2, 1, 1, 3, 2] => 3, 2, 2, 2, 2, 1, 1, 3, 2
[3, 2, 2, 2, 2, 1, 1, 3, 3] => 3, 2, 2, 2, 2, 1, 1, 3, 3
[3, 2, 2, 2, 2, 1, 2, 1, 1] => 3, 2, 2, 2, 2, 1, 2, 1, 1
[3, 2, 2, 2, 2, 1, 2, 1, 2] => 3, 2, 2, 2, 2, 1, 2, 1, 2
[3, 2, 2, 2, 2, 1, 2, 1, 3] => 3, 2, 2, 2, 2, 1, 2, 1, 3
[3, 2, 2, 2, 2, 1, 2, 2, 1] => 3, 2, 2, 2, 2, 1, 2, 2, 1
[3, 2, 2, 2, 2, 1, 2, 2, 2] => 3, 2, 2, 2, 2, 1, 2, 2, 2
[3, 2, 2, 2, 2, 1, 2, 2, 3] => 3, 2, 2, 2, 2, 1, 2, 2, 3
[3, 2, 2, 2, 2, 1, 2, 3, 1] => 3, 2, 2, 2, 2, 1, 2, 3, 1
[3, 2, 2, 2, 2, 1, 2, 3, 2] => 3, 2, 2, 2, 2, 1, 2, 3, 2
[3, 2, 2, 2, 2, 1, 2, 3, 3] => 3, 2, 2, 2, 2, 1, 2, 3, 3
[3, 2, 2, 2, 2, 1, 3, 1, 1] => 3, 2, 2, 2, 2, 1, 3, 1, 1
[3, 2, 2, 2, 2, 1, 3, 1, 2] => 3, 2, 2, 2, 2, 1, 3, 1, 2
[3, 2, 2, 2, 2, 1, 3, 1, 3] => 3, 2, 2, 2, 2, 1, 3, 1, 3
[3, 2, 2, 2, 2, 1, 3, 2, 1] => 3, 2, 2, 2, 2, 1, 3, 2, 1
[3, 2, 2, 2, 2, 1, 3, 2, 2] => 3, 2, 2, 2, 2, 1, 3, 2, 2
[3, 2, 2, 2, 2, 1, 3, 2, 3] => 3, 2, 2, 2, 2, 1, 3, 2, 3
[3, 2, 2, 2, 2, 1, 3, 3, 1] => 3, 2, 2, 2, 2, 1, 3, 3, 1
[3, 2, 2, 2, 2, 1, 3, 3, 2] => 3, 2, 2, 2, 2, 1, 3, 3, 2
[3, 2, 2, 2, 2, 1, 3, 3, 3] => 3, 2, 2, 2, 2, 1, 3, 3, 3
[3, 2, 2, 2, 2, 2, 1, 1, 1] => 3, 2, 2, 2, 2, 2, 1, 1, 1
[3, 2, 2, 2, 2, 2, 1, 1, 2] => 3, 2, 2, 2, 2, 2, 1, 1, 2
[3, 2, 2, 2, 2, 2, 1, 1, 3] => 3, 2, 2, 2, 2, 2, 1, 1, 3
[3, 2, 2, 2, 2, 2, 1, 2, 1] => 3, 2, 2, 2, 2, 2, 1, 2, 1
[3, 2, 2, 2, 2, 2, 1, 2, 2] => 3, 2, 2, 2, 2, 2, 1, 2, 2
[3, 2, 2, 2, 2, 2, 1, 2, 3] => 3, 2, 2, 2, 2, 2, 1, 2, 3
[3, 2, 2, 2, 2, 2, 1, 3, 1] => 3, 2, 2, 2, 2, 2, 1, 3, 1
[3, 2, 2, 2, 2, 2, 1, 3, 2] => 3, 2, 2, 2, 2, 2, 1, 3, 2
[3, 2, 2, 2, 2, 2, 1, 3, 3] => 3, 2, 2, 2, 2, 2, 1, 3, 3
[3, 2, 2, 2, 2, 2, 2, 1, 1] => 3, 2, 2, 2, 2, 2, 2, 1, 1
[3, 2, 2, 2, 2, 2, 2, 1, 2] => 3, 2, 2, 2, 2, 2, 2, 1, 2
[3, 2, 2, 2, 2, 2, 2, 1, 3] => 3, 2, 2, 2, 2, 2, 2, 1, 3
[3, 2, 2, 2, 2, 2, 2, 2, 1] => 3, 2, 2, 2, 2, 2, 2, 2, 1
[3, 2, 2, 2, 2, 2, 2, 2, 2] => 3, 2, 2, 2, 2, 2, 2, 2, 2
[3, 2, 2, 2, 2, 2, 2, 2, 3] => 3, 2, 2, 2, 2, 2, 2, 2, 3
[3, 2, 2, 2, 2, 2, 2, 3, 1] => 3, 2, 2, 2, 2, 2, 2, 3, 1
[3, 2, 2, 2, 2, 2, 2, 3, 2] => 3, 2, 2, 2, 2, 2, 2, 3, 2
[3, 2, 2, 2, 2, 2, 2, 3, 3] => 3, 2, 2, 2, 2, 2, 2, 3, 3
[3, 2, 2, 2, 2, 2, 3, 1, 1] => 3, 2, 2, 2, 2, 2, 3, 1, 1
[3, 2, 2, 2, 2, 2, 3, 1, 2] => 3, 2, 2, 2, 2, 2, 3, 1, 2
[3, 2, 2, 2, 2, 2, 3, 1, 3] => 3, 2, 2, 2, 2, 2, 3, 1, 3
[3, 2, 2, 2, 2, 2, 3, 2, 1] => 3, 2, 2, 2, 2, 2, 3, 2, 1
[3, 2, 2, 2, 2, 2, 3, 2, 2] => 3, 2, 2, 2, 2, 2, 3, 2, 2
[3, 2, 2, 2, 2, 2, 3, 2, 3] => 3, 2, 2, 2, 2, 2, 3, 2, 3
[3, 2, 2, 2, 2, 2, 3, 3, 1] => 3, 2, 2, 2, 2, 2, 3, 3, 1
[3, 2, 2, 2, 2, 2, 3, 3, 2] => 3, 2, 2, 2, 2, 2, 3, 3, 2
[3, 2, 2, 2, 2, 2, 3, 3, 3] => 3, 2, 2, 2, 2, 2, 3, 3, 3
[3, 2, 2, 2, 2, 3, 1, 1, 1] => 3, 2, 2, 2, 2, 3, 1, 1, 1
[3, 2, 2, 2, 2, 3, 1, 1, 2] => 3, 2, 2, 2, 2, 3, 1, 1, 2
[3, 2, 2, 2, 2, 3, 1, 1, 3] => 3, 2, 2, 2, 2, 3, 1, 1, 3
[3, 2, 2, 2, 2, 3, 1, 2, 1] => 3, 2, 2, 2, 2, 3, 1, 2, 1
[3, 2, 2, 2, 2, 3, 1, 2, 2] => 3, 2, 2, 2, 2, 3, 1, 2, 2
[3, 2, 2, 2, 2, 3, 1, 2, 3] => 3, 2, 2, 2, 2, 3, 1, 2, 3
[3, 2, 2, 2, 2, 3, 1, 3, 1] => 3, 2, 2, 2, 2, 3, 1, 3, 1
[3, 2, 2, 2, 2, 3, 1, 3, 2] => 3, 2, 2, 2, 2, 3, 1, 3, 2
[3, 2, 2, 2, 2, 3, 1, 3, 3] => 3, 2, 2, 2, 2, 3, 1, 3, 3
[3, 2, 2, 2, 2, 3, 2, 1, 1] => 3, 2, 2, 2, 2, 3, 2, 1, 1
[3, 2, 2, 2, 2, 3, 2, 1, 2] => 3, 2, 2, 2, 2, 3, 2, 1, 2
[3, 2, 2, 2, 2, 3, 2, 1, 3] => 3, 2, 2, 2, 2, 3, 2, 1, 3
[3, 2, 2, 2, 2, 3, 2, 2, 1] => 3, 2, 2, 2, 2, 3, 2, 2, 1
[3, 2, 2, 2, 2, 3, 2, 2, 2] => 3, 2, 2, 2, 2, 3, 2, 2, 2
[3, 2, 2, 2, 2, 3, 2, 2, 3] => 3, 2, 2, 2, 2, 3, 2, 2, 3
[3, 2, 2, 2, 2, 3, 2, 3, 1] => 3, 2, 2, 2, 2, 3, 2, 3, 1
[3, 2, 2, 2, 2, 3, 2, 3, 2] => 3, 2, 2, 2, 2, 3, 2, 3, 2
[3, 2, 2, 2, 2, 3, 2, 3, 3] => 3, 2, 2, 2, 2, 3, 2, 3, 3
[3, 2, 2, 2, 2, 3, 3, 1, 1] => 3, 2, 2, 2, 2, 3, 3, 1, 1
[3, 2, 2, 2, 2, 3, 3, 1, 2] => 3, 2, 2, 2, 2, 3, 3, 1, 2
[3, 2, 2, 2, 2, 3, 3, 1, 3] => 3, 2, 2, 2, 2, 3, 3, 1, 3
[3, 2, 2, 2, 2, 3, 3, 2, 1] => 3, 2, 2, 2, 2, 3, 3, 2, 1
[3, 2, 2, 2, 2, 3, 3, 2, 2] => 3, 2, 2, 2, 2, 3, 3, 2, 2
[3, 2, 2, 2, 2, 3, 3, 2, 3] => 3, 2, 2, 2, 2, 3, 3, 2, 3
[3, 2, 2, 2, 2, 3, 3, 3, 1] => 3, 2, 2, 2, 2, 3, 3, 3, 1
[3, 2, 2, 2, 2, 3, 3, 3, 2] => 3, 2, 2, 2, 2, 3, 3, 3, 2
[3, 2, 2, 2, 2, 3, 3, 3, 3] => 3, 2, 2, 2, 2, 3, 3, 3, 3
[3, 2, 2, 2, 3, 1, 1, 1, 1] => 3, 2, 2, 2, 3, 1, 1, 1, 1
[3, 2, 2, 2, 3, 1, 1, 1, 2] => 3, 2, 2, 2, 3, 1, 1, 1, 2
[3, 2, 2, 2, 3, 1, 1, 1, 3] => 3, 2, 2, 2, 3, 1, 1, 1, 3
[3, 2, 2, 2, 3, 1, 1, 2, 1] => 3, 2, 2, 2, 3, 1, 1, 2, 1
[3, 2, 2, 2, 3, 1, 1, 2, 2] => 3, 2, 2, 2, 3, 1, 1, 2, 2
[3, 2, 2, 2, 3, 1, 1, 2, 3] => 3, 2, 2, 2, 3, 1, 1, 2, 3
[3, 2, 2, 2, 3, 1, 1, 3, 1] => 3, 2, 2, 2, 3, 1, 1, 3, 1
[3, 2, 2, 2, 3, 1, 1, 3, 2] => 3, 2, 2, 2, 3, 1, 1, 3, 2
[3, 2, 2, 2, 3, 1, 1, 3, 3] => 3, 2, 2, 2, 3, 1, 1, 3, 3
[3, 2, 2, 2, 3, 1, 2, 1, 1] => 3, 2, 2, 2, 3, 1, 2, 1, 1
[3, 2, 2, 2, 3, 1, 2, 1, 2] => 3, 2, 2, 2, 3, 1, 2, 1, 2
[3, 2, 2, 2, 3, 1, 2, 1, 3] => 3, 2, 2, 2, 3, 1, 2, 1, 3
[3, 2, 2, 2, 3, 1, 2, 2, 1] => 3, 2, 2, 2, 3, 1, 2, 2, 1
[3, 2, 2, 2, 3, 1, 2, 2, 2] => 3, 2, 2, 2, 3, 1, 2, 2, 2
[3, 2, 2, 2, 3, 1, 2, 2, 3] => 3, 2, 2, 2, 3, 1, 2, 2, 3
[3, 2, 2, 2, 3, 1, 2, 3, 1] => 3, 2, 2, 2, 3, 1, 2, 3, 1
[3, 2, 2, 2, 3, 1, 2, 3, 2] => 3, 2, 2, 2, 3, 1, 2, 3, 2
[3, 2, 2, 2, 3, 1, 2, 3, 3] => 3, 2, 2, 2, 3, 1, 2, 3, 3
[3, 2, 2, 2, 3, 1, 3, 1, 1] => 3, 2, 2, 2, 3, 1, 3, 1, 1
[3, 2, 2, 2, 3, 1, 3, 1, 2] => 3, 2, 2, 2, 3, 1, 3, 1, 2
[3, 2, 2, 2, 3, 1, 3, 1, 3] => 3, 2, 2, 2, 3, 1, 3, 1, 3
[3, 2, 2, 2, 3, 1, 3, 2, 1] => 3, 2, 2, 2, 3, 1, 3, 2, 1
[3, 2, 2, 2, 3, 1, 3, 2, 2] => 3, 2, 2, 2, 3, 1, 3, 2, 2
[3, 2, 2, 2, 3, 1, 3, 2, 3] => 3, 2, 2, 2, 3, 1, 3, 2, 3
[3, 2, 2, 2, 3, 1, 3, 3, 1] => 3, 2, 2, 2, 3, 1, 3, 3, 1
[3, 2, 2, 2, 3, 1, 3, 3, 2] => 3, 2, 2, 2, 3, 1, 3, 3, 2
[3, 2, 2, 2, 3, 1, 3, 3, 3] => 3, 2, 2, 2, 3, 1, 3, 3, 3
[3, 2, 2, 2, 3, 2, 1, 1, 1] => 3, 2, 2, 2, 3, 2, 1, 1, 1
[3, 2, 2, 2, 3, 2, 1, 1, 2] => 3, 2, 2, 2, 3, 2, 1, 1, 2
[3, 2, 2, 2, 3, 2, 1, 1, 3] => 3, 2, 2, 2, 3, 2, 1, 1, 3
[3, 2, 2, 2, 3, 2, 1, 2, 1] => 3, 2, 2, 2, 3, 2, 1, 2, 1
[3, 2, 2, 2, 3, 2, 1, 2, 2] => 3, 2, 2, 2, 3, 2, 1, 2, 2
[3, 2, 2, 2, 3, 2, 1, 2, 3] => 3, 2, 2, 2, 3, 2, 1, 2, 3
[3, 2, 2, 2, 3, 2, 1, 3, 1] => 3, 2, 2, 2, 3, 2, 1, 3, 1
[3, 2, 2, 2, 3, 2, 1, 3, 2] => 3, 2, 2, 2, 3, 2, 1, 3, 2
[3, 2, 2, 2, 3, 2, 1, 3, 3] => 3, 2, 2, 2, 3, 2, 1, 3, 3
[3, 2, 2, 2, 3, 2, 2, 1, 1] => 3, 2, 2, 2, 3, 2, 2, 1, 1
[3, 2, 2, 2, 3, 2, 2, 1, 2] => 3, 2, 2, 2, 3, 2, 2, 1, 2
[3, 2, 2, 2, 3, 2, 2, 1, 3] => 3, 2, 2, 2, 3, 2, 2, 1, 3
[3, 2, 2, 2, 3, 2, 2, 2, 1] => 3, 2, 2, 2, 3, 2, 2, 2, 1
[3, 2, 2, 2, 3, 2, 2, 2, 2] => 3, 2, 2, 2, 3, 2, 2, 2, 2
[3, 2, 2, 2, 3, 2, 2, 2, 3] => 3, 2, 2, 2, 3, 2, 2, 2, 3
[3, 2, 2, 2, 3, 2, 2, 3, 1] => 3, 2, 2, 2, 3, 2, 2, 3, 1
[3, 2, 2, 2, 3, 2, 2, 3, 2] => 3, 2, 2, 2, 3, 2, 2, 3, 2
[3, 2, 2, 2, 3, 2, 2, 3, 3] => 3, 2, 2, 2, 3, 2, 2, 3, 3
[3, 2, 2, 2, 3, 2, 3, 1, 1] => 3, 2, 2, 2, 3, 2, 3, 1, 1
[3, 2, 2, 2, 3, 2, 3, 1, 2] => 3, 2, 2, 2, 3, 2, 3, 1, 2
[3, 2, 2, 2, 3, 2, 3, 1, 3] => 3, 2, 2, 2, 3, 2, 3, 1, 3
[3, 2, 2, 2, 3, 2, 3, 2, 1] => 3, 2, 2, 2, 3, 2, 3, 2, 1
[3, 2, 2, 2, 3, 2, 3, 2, 2] => 3, 2, 2, 2, 3, 2, 3, 2, 2
[3, 2, 2, 2, 3, 2, 3, 2, 3] => 3, 2, 2, 2, 3, 2, 3, 2, 3
[3, 2, 2, 2, 3, 2, 3, 3, 1] => 3, 2, 2, 2, 3, 2, 3, 3, 1
[3, 2, 2, 2, 3, 2, 3, 3, 2] => 3, 2, 2, 2, 3, 2, 3, 3, 2
[3, 2, 2, 2, 3, 2, 3, 3, 3] => 3, 2, 2, 2, 3, 2, 3, 3, 3
[3, 2, 2, 2, 3, 3, 1, 1, 1] => 3, 2, 2, 2, 3, 3, 1, 1, 1
[3, 2, 2, 2, 3, 3, 1, 1, 2] => 3, 2, 2, 2, 3, 3, 1, 1, 2
[3, 2, 2, 2, 3, 3, 1, 1, 3] => 3, 2, 2, 2, 3, 3, 1, 1, 3
[3, 2, 2, 2, 3, 3, 1, 2, 1] => 3, 2, 2, 2, 3, 3, 1, 2, 1
[3, 2, 2, 2, 3, 3, 1, 2, 2] => 3, 2, 2, 2, 3, 3, 1, 2, 2
[3, 2, 2, 2, 3, 3, 1, 2, 3] => 3, 2, 2, 2, 3, 3, 1, 2, 3
[3, 2, 2, 2, 3, 3, 1, 3, 1] => 3, 2, 2, 2, 3, 3, 1, 3, 1
[3, 2, 2, 2, 3, 3, 1, 3, 2] => 3, 2, 2, 2, 3, 3, 1, 3, 2
[3, 2, 2, 2, 3, 3, 1, 3, 3] => 3, 2, 2, 2, 3, 3, 1, 3, 3
[3, 2, 2, 2, 3, 3, 2, 1, 1] => 3, 2, 2, 2, 3, 3, 2, 1, 1
[3, 2, 2, 2, 3, 3, 2, 1, 2] => 3, 2, 2, 2, 3, 3, 2, 1, 2
[3, 2, 2, 2, 3, 3, 2, 1, 3] => 3, 2, 2, 2, 3, 3, 2, 1, 3
[3, 2, 2, 2, 3, 3, 2, 2, 1] => 3, 2, 2, 2, 3, 3, 2, 2, 1
[3, 2, 2, 2, 3, 3, 2, 2, 2] => 3, 2, 2, 2, 3, 3, 2, 2, 2
[3, 2, 2, 2, 3, 3, 2, 2, 3] => 3, 2, 2, 2, 3, 3, 2, 2, 3
[3, 2, 2, 2, 3, 3, 2, 3, 1] => 3, 2, 2, 2, 3, 3, 2, 3, 1
[3, 2, 2, 2, 3, 3, 2, 3, 2] => 3, 2, 2, 2, 3, 3, 2, 3, 2
[3, 2, 2, 2, 3, 3, 2, 3, 3] => 3, 2, 2, 2, 3, 3, 2, 3, 3
[3, 2, 2, 2, 3, 3, 3, 1, 1] => 3, 2, 2, 2, 3, 3, 3, 1, 1
[3, 2, 2, 2, 3, 3, 3, 1, 2] => 3, 2, 2, 2, 3, 3, 3, 1, 2
[3, 2, 2, 2, 3, 3, 3, 1, 3] => 3, 2, 2, 2, 3, 3, 3, 1, 3
[3, 2, 2, 2, 3, 3, 3, 2, 1] => 3, 2, 2, 2, 3, 3, 3, 2, 1
[3, 2, 2, 2, 3, 3, 3, 2, 2] => 3, 2, 2, 2, 3, 3, 3, 2, 2
[3, 2, 2, 2, 3, 3, 3, 2, 3] => 3, 2, 2, 2, 3, 3, 3, 2, 3
[3, 2, 2, 2, 3, 3, 3, 3, 1] => 3, 2, 2, 2, 3, 3, 3, 3, 1
[3, 2, 2, 2, 3, 3, 3, 3, 2] => 3, 2, 2, 2, 3, 3, 3, 3, 2
[3, 2, 2, 2, 3, 3, 3, 3, 3] => 3, 2, 2, 2, 3, 3, 3, 3, 3
[3, 2, 2, 3, 1, 1, 1, 1, 1] => 3, 2, 2, 3, 1, 1, 1, 1, 1
[3, 2, 2, 3, 1, 1, 1, 1, 2] => 3, 2, 2, 3, 1, 1, 1, 1, 2
[3, 2, 2, 3, 1, 1, 1, 1, 3] => 3, 2, 2, 3, 1, 1, 1, 1, 3
[3, 2, 2, 3, 1, 1, 1, 2, 1] => 3, 2, 2, 3, 1, 1, 1, 2, 1
[3, 2, 2, 3, 1, 1, 1, 2, 2] => 3, 2, 2, 3, 1, 1, 1, 2, 2
[3, 2, 2, 3, 1, 1, 1, 2, 3] => 3, 2, 2, 3, 1, 1, 1, 2, 3
[3, 2, 2, 3, 1, 1, 1, 3, 1] => 3, 2, 2, 3, 1, 1, 1, 3, 1
[3, 2, 2, 3, 1, 1, 1, 3, 2] => 3, 2, 2, 3, 1, 1, 1, 3, 2
[3, 2, 2, 3, 1, 1, 1, 3, 3] => 3, 2, 2, 3, 1, 1, 1, 3, 3
[3, 2, 2, 3, 1, 1, 2, 1, 1] => 3, 2, 2, 3, 1, 1, 2, 1, 1
[3, 2, 2, 3, 1, 1, 2, 1, 2] => 3, 2, 2, 3, 1, 1, 2, 1, 2
[3, 2, 2, 3, 1, 1, 2, 1, 3] => 3, 2, 2, 3, 1, 1, 2, 1, 3
[3, 2, 2, 3, 1, 1, 2, 2, 1] => 3, 2, 2, 3, 1, 1, 2, 2, 1
[3, 2, 2, 3, 1, 1, 2, 2, 2] => 3, 2, 2, 3, 1, 1, 2, 2, 2
[3, 2, 2, 3, 1, 1, 2, 2, 3] => 3, 2, 2, 3, 1, 1, 2, 2, 3
[3, 2, 2, 3, 1, 1, 2, 3, 1] => 3, 2, 2, 3, 1, 1, 2, 3, 1
[3, 2, 2, 3, 1, 1, 2, 3, 2] => 3, 2, 2, 3, 1, 1, 2, 3, 2
[3, 2, 2, 3, 1, 1, 2, 3, 3] => 3, 2, 2, 3, 1, 1, 2, 3, 3
[3, 2, 2, 3, 1, 1, 3, 1, 1] => 3, 2, 2, 3, 1, 1, 3, 1, 1
[3, 2, 2, 3, 1, 1, 3, 1, 2] => 3, 2, 2, 3, 1, 1, 3, 1, 2
[3, 2, 2, 3, 1, 1, 3, 1, 3] => 3, 2, 2, 3, 1, 1, 3, 1, 3
[3, 2, 2, 3, 1, 1, 3, 2, 1] => 3, 2, 2, 3, 1, 1, 3, 2, 1
[3, 2, 2, 3, 1, 1, 3, 2, 2] => 3, 2, 2, 3, 1, 1, 3, 2, 2
[3, 2, 2, 3, 1, 1, 3, 2, 3] => 3, 2, 2, 3, 1, 1, 3, 2, 3
[3, 2, 2, 3, 1, 1, 3, 3, 1] => 3, 2, 2, 3, 1, 1, 3, 3, 1
[3, 2, 2, 3, 1, 1, 3, 3, 2] => 3, 2, 2, 3, 1, 1, 3, 3, 2
[3, 2, 2, 3, 1, 1, 3, 3, 3] => 3, 2, 2, 3, 1, 1, 3, 3, 3
[3, 2, 2, 3, 1, 2, 1, 1, 1] => 3, 2, 2, 3, 1, 2, 1, 1, 1
[3, 2, 2, 3, 1, 2, 1, 1, 2] => 3, 2, 2, 3, 1, 2, 1, 1, 2
[3, 2, 2, 3, 1, 2, 1, 1, 3] => 3, 2, 2, 3, 1, 2, 1, 1, 3
[3, 2, 2, 3, 1, 2, 1, 2, 1] => 3, 2, 2, 3, 1, 2, 1, 2, 1
[3, 2, 2, 3, 1, 2, 1, 2, 2] => 3, 2, 2, 3, 1, 2, 1, 2, 2
[3, 2, 2, 3, 1, 2, 1, 2, 3] => 3, 2, 2, 3, 1, 2, 1, 2, 3
[3, 2, 2, 3, 1, 2, 1, 3, 1] => 3, 2, 2, 3, 1, 2, 1, 3, 1
[3, 2, 2, 3, 1, 2, 1, 3, 2] => 3, 2, 2, 3, 1, 2, 1, 3, 2
[3, 2, 2, 3, 1, 2, 1, 3, 3] => 3, 2, 2, 3, 1, 2, 1, 3, 3
[3, 2, 2, 3, 1, 2, 2, 1, 1] => 3, 2, 2, 3, 1, 2, 2, 1, 1
[3, 2, 2, 3, 1, 2, 2, 1, 2] => 3, 2, 2, 3, 1, 2, 2, 1, 2
[3, 2, 2, 3, 1, 2, 2, 1, 3] => 3, 2, 2, 3, 1, 2, 2, 1, 3
[3, 2, 2, 3, 1, 2, 2, 2, 1] => 3, 2, 2, 3, 1, 2, 2, 2, 1
[3, 2, 2, 3, 1, 2, 2, 2, 2] => 3, 2, 2, 3, 1, 2, 2, 2, 2
[3, 2, 2, 3, 1, 2, 2, 2, 3] => 3, 2, 2, 3, 1, 2, 2, 2, 3
[3, 2, 2, 3, 1, 2, 2, 3, 1] => 3, 2, 2, 3, 1, 2, 2, 3, 1
[3, 2, 2, 3, 1, 2, 2, 3, 2] => 3, 2, 2, 3, 1, 2, 2, 3, 2
[3, 2, 2, 3, 1, 2, 2, 3, 3] => 3, 2, 2, 3, 1, 2, 2, 3, 3
[3, 2, 2, 3, 1, 2, 3, 1, 1] => 3, 2, 2, 3, 1, 2, 3, 1, 1
[3, 2, 2, 3, 1, 2, 3, 1, 2] => 3, 2, 2, 3, 1, 2, 3, 1, 2
[3, 2, 2, 3, 1, 2, 3, 1, 3] => 3, 2, 2, 3, 1, 2, 3, 1, 3
[3, 2, 2, 3, 1, 2, 3, 2, 1] => 3, 2, 2, 3, 1, 2, 3, 2, 1
[3, 2, 2, 3, 1, 2, 3, 2, 2] => 3, 2, 2, 3, 1, 2, 3, 2, 2
[3, 2, 2, 3, 1, 2, 3, 2, 3] => 3, 2, 2, 3, 1, 2, 3, 2, 3
[3, 2, 2, 3, 1, 2, 3, 3, 1] => 3, 2, 2, 3, 1, 2, 3, 3, 1
[3, 2, 2, 3, 1, 2, 3, 3, 2] => 3, 2, 2, 3, 1, 2, 3, 3, 2
[3, 2, 2, 3, 1, 2, 3, 3, 3] => 3, 2, 2, 3, 1, 2, 3, 3, 3
[3, 2, 2, 3, 1, 3, 1, 1, 1] => 3, 2, 2, 3, 1, 3, 1, 1, 1
[3, 2, 2, 3, 1, 3, 1, 1, 2] => 3, 2, 2, 3, 1, 3, 1, 1, 2
[3, 2, 2, 3, 1, 3, 1, 1, 3] => 3, 2, 2, 3, 1, 3, 1, 1, 3
[3, 2, 2, 3, 1, 3, 1, 2, 1] => 3, 2, 2, 3, 1, 3, 1, 2, 1
[3, 2, 2, 3, 1, 3, 1, 2, 2] => 3, 2, 2, 3, 1, 3, 1, 2, 2
[3, 2, 2, 3, 1, 3, 1, 2, 3] => 3, 2, 2, 3, 1, 3, 1, 2, 3
[3, 2, 2, 3, 1, 3, 1, 3, 1] => 3, 2, 2, 3, 1, 3, 1, 3, 1
[3, 2, 2, 3, 1, 3, 1, 3, 2] => 3, 2, 2, 3, 1, 3, 1, 3, 2
[3, 2, 2, 3, 1, 3, 1, 3, 3] => 3, 2, 2, 3, 1, 3, 1, 3, 3
[3, 2, 2, 3, 1, 3, 2, 1, 1] => 3, 2, 2, 3, 1, 3, 2, 1, 1
[3, 2, 2, 3, 1, 3, 2, 1, 2] => 3, 2, 2, 3, 1, 3, 2, 1, 2
[3, 2, 2, 3, 1, 3, 2, 1, 3] => 3, 2, 2, 3, 1, 3, 2, 1, 3
[3, 2, 2, 3, 1, 3, 2, 2, 1] => 3, 2, 2, 3, 1, 3, 2, 2, 1
[3, 2, 2, 3, 1, 3, 2, 2, 2] => 3, 2, 2, 3, 1, 3, 2, 2, 2
[3, 2, 2, 3, 1, 3, 2, 2, 3] => 3, 2, 2, 3, 1, 3, 2, 2, 3
[3, 2, 2, 3, 1, 3, 2, 3, 1] => 3, 2, 2, 3, 1, 3, 2, 3, 1
[3, 2, 2, 3, 1, 3, 2, 3, 2] => 3, 2, 2, 3, 1, 3, 2, 3, 2
[3, 2, 2, 3, 1, 3, 2, 3, 3] => 3, 2, 2, 3, 1, 3, 2, 3, 3
[3, 2, 2, 3, 1, 3, 3, 1, 1] => 3, 2, 2, 3, 1, 3, 3, 1, 1
[3, 2, 2, 3, 1, 3, 3, 1, 2] => 3, 2, 2, 3, 1, 3, 3, 1, 2
[3, 2, 2, 3, 1, 3, 3, 1, 3] => 3, 2, 2, 3, 1, 3, 3, 1, 3
[3, 2, 2, 3, 1, 3, 3, 2, 1] => 3, 2, 2, 3, 1, 3, 3, 2, 1
[3, 2, 2, 3, 1, 3, 3, 2, 2] => 3, 2, 2, 3, 1, 3, 3, 2, 2
[3, 2, 2, 3, 1, 3, 3, 2, 3] => 3, 2, 2, 3, 1, 3, 3, 2, 3
[3, 2, 2, 3, 1, 3, 3, 3, 1] => 3, 2, 2, 3, 1, 3, 3, 3, 1
[3, 2, 2, 3, 1, 3, 3, 3, 2] => 3, 2, 2, 3, 1, 3, 3, 3, 2
[3, 2, 2, 3, 1, 3, 3, 3, 3] => 3, 2, 2, 3, 1, 3, 3, 3, 3
[3, 2, 2, 3, 2, 1, 1, 1, 1] => 3, 2, 2, 3, 2, 1, 1, 1, 1
[3, 2, 2, 3, 2, 1, 1, 1, 2] => 3, 2, 2, 3, 2, 1, 1, 1, 2
[3, 2, 2, 3, 2, 1, 1, 1, 3] => 3, 2, 2, 3, 2, 1, 1, 1, 3
[3, 2, 2, 3, 2, 1, 1, 2, 1] => 3, 2, 2, 3, 2, 1, 1, 2, 1
[3, 2, 2, 3, 2, 1, 1, 2, 2] => 3, 2, 2, 3, 2, 1, 1, 2, 2
[3, 2, 2, 3, 2, 1, 1, 2, 3] => 3, 2, 2, 3, 2, 1, 1, 2, 3
[3, 2, 2, 3, 2, 1, 1, 3, 1] => 3, 2, 2, 3, 2, 1, 1, 3, 1
[3, 2, 2, 3, 2, 1, 1, 3, 2] => 3, 2, 2, 3, 2, 1, 1, 3, 2
[3, 2, 2, 3, 2, 1, 1, 3, 3] => 3, 2, 2, 3, 2, 1, 1, 3, 3
[3, 2, 2, 3, 2, 1, 2, 1, 1] => 3, 2, 2, 3, 2, 1, 2, 1, 1
[3, 2, 2, 3, 2, 1, 2, 1, 2] => 3, 2, 2, 3, 2, 1, 2, 1, 2
[3, 2, 2, 3, 2, 1, 2, 1, 3] => 3, 2, 2, 3, 2, 1, 2, 1, 3
[3, 2, 2, 3, 2, 1, 2, 2, 1] => 3, 2, 2, 3, 2, 1, 2, 2, 1
[3, 2, 2, 3, 2, 1, 2, 2, 2] => 3, 2, 2, 3, 2, 1, 2, 2, 2
[3, 2, 2, 3, 2, 1, 2, 2, 3] => 3, 2, 2, 3, 2, 1, 2, 2, 3
[3, 2, 2, 3, 2, 1, 2, 3, 1] => 3, 2, 2, 3, 2, 1, 2, 3, 1
[3, 2, 2, 3, 2, 1, 2, 3, 2] => 3, 2, 2, 3, 2, 1, 2, 3, 2
[3, 2, 2, 3, 2, 1, 2, 3, 3] => 3, 2, 2, 3, 2, 1, 2, 3, 3
[3, 2, 2, 3, 2, 1, 3, 1, 1] => 3, 2, 2, 3, 2, 1, 3, 1, 1
[3, 2, 2, 3, 2, 1, 3, 1, 2] => 3, 2, 2, 3, 2, 1, 3, 1, 2
[3, 2, 2, 3, 2, 1, 3, 1, 3] => 3, 2, 2, 3, 2, 1, 3, 1, 3
[3, 2, 2, 3, 2, 1, 3, 2, 1] => 3, 2, 2, 3, 2, 1, 3, 2, 1
[3, 2, 2, 3, 2, 1, 3, 2, 2] => 3, 2, 2, 3, 2, 1, 3, 2, 2
[3, 2, 2, 3, 2, 1, 3, 2, 3] => 3, 2, 2, 3, 2, 1, 3, 2, 3
[3, 2, 2, 3, 2, 1, 3, 3, 1] => 3, 2, 2, 3, 2, 1, 3, 3, 1
[3, 2, 2, 3, 2, 1, 3, 3, 2] => 3, 2, 2, 3, 2, 1, 3, 3, 2
[3, 2, 2, 3, 2, 1, 3, 3, 3] => 3, 2, 2, 3, 2, 1, 3, 3, 3
[3, 2, 2, 3, 2, 2, 1, 1, 1] => 3, 2, 2, 3, 2, 2, 1, 1, 1
[3, 2, 2, 3, 2, 2, 1, 1, 2] => 3, 2, 2, 3, 2, 2, 1, 1, 2
[3, 2, 2, 3, 2, 2, 1, 1, 3] => 3, 2, 2, 3, 2, 2, 1, 1, 3
[3, 2, 2, 3, 2, 2, 1, 2, 1] => 3, 2, 2, 3, 2, 2, 1, 2, 1
[3, 2, 2, 3, 2, 2, 1, 2, 2] => 3, 2, 2, 3, 2, 2, 1, 2, 2
[3, 2, 2, 3, 2, 2, 1, 2, 3] => 3, 2, 2, 3, 2, 2, 1, 2, 3
[3, 2, 2, 3, 2, 2, 1, 3, 1] => 3, 2, 2, 3, 2, 2, 1, 3, 1
[3, 2, 2, 3, 2, 2, 1, 3, 2] => 3, 2, 2, 3, 2, 2, 1, 3, 2
[3, 2, 2, 3, 2, 2, 1, 3, 3] => 3, 2, 2, 3, 2, 2, 1, 3, 3
[3, 2, 2, 3, 2, 2, 2, 1, 1] => 3, 2, 2, 3, 2, 2, 2, 1, 1
[3, 2, 2, 3, 2, 2, 2, 1, 2] => 3, 2, 2, 3, 2, 2, 2, 1, 2
[3, 2, 2, 3, 2, 2, 2, 1, 3] => 3, 2, 2, 3, 2, 2, 2, 1, 3
[3, 2, 2, 3, 2, 2, 2, 2, 1] => 3, 2, 2, 3, 2, 2, 2, 2, 1
[3, 2, 2, 3, 2, 2, 2, 2, 2] => 3, 2, 2, 3, 2, 2, 2, 2, 2
[3, 2, 2, 3, 2, 2, 2, 2, 3] => 3, 2, 2, 3, 2, 2, 2, 2, 3
[3, 2, 2, 3, 2, 2, 2, 3, 1] => 3, 2, 2, 3, 2, 2, 2, 3, 1
[3, 2, 2, 3, 2, 2, 2, 3, 2] => 3, 2, 2, 3, 2, 2, 2, 3, 2
[3, 2, 2, 3, 2, 2, 2, 3, 3] => 3, 2, 2, 3, 2, 2, 2, 3, 3
[3, 2, 2, 3, 2, 2, 3, 1, 1] => 3, 2, 2, 3, 2, 2, 3, 1, 1
[3, 2, 2, 3, 2, 2, 3, 1, 2] => 3, 2, 2, 3, 2, 2, 3, 1, 2
[3, 2, 2, 3, 2, 2, 3, 1, 3] => 3, 2, 2, 3, 2, 2, 3, 1, 3
[3, 2, 2, 3, 2, 2, 3, 2, 1] => 3, 2, 2, 3, 2, 2, 3, 2, 1
[3, 2, 2, 3, 2, 2, 3, 2, 2] => 3, 2, 2, 3, 2, 2, 3, 2, 2
[3, 2, 2, 3, 2, 2, 3, 2, 3] => 3, 2, 2, 3, 2, 2, 3, 2, 3
[3, 2, 2, 3, 2, 2, 3, 3, 1] => 3, 2, 2, 3, 2, 2, 3, 3, 1
[3, 2, 2, 3, 2, 2, 3, 3, 2] => 3, 2, 2, 3, 2, 2, 3, 3, 2
[3, 2, 2, 3, 2, 2, 3, 3, 3] => 3, 2, 2, 3, 2, 2, 3, 3, 3
[3, 2, 2, 3, 2, 3, 1, 1, 1] => 3, 2, 2, 3, 2, 3, 1, 1, 1
[3, 2, 2, 3, 2, 3, 1, 1, 2] => 3, 2, 2, 3, 2, 3, 1, 1, 2
[3, 2, 2, 3, 2, 3, 1, 1, 3] => 3, 2, 2, 3, 2, 3, 1, 1, 3
[3, 2, 2, 3, 2, 3, 1, 2, 1] => 3, 2, 2, 3, 2, 3, 1, 2, 1
[3, 2, 2, 3, 2, 3, 1, 2, 2] => 3, 2, 2, 3, 2, 3, 1, 2, 2
[3, 2, 2, 3, 2, 3, 1, 2, 3] => 3, 2, 2, 3, 2, 3, 1, 2, 3
[3, 2, 2, 3, 2, 3, 1, 3, 1] => 3, 2, 2, 3, 2, 3, 1, 3, 1
[3, 2, 2, 3, 2, 3, 1, 3, 2] => 3, 2, 2, 3, 2, 3, 1, 3, 2
[3, 2, 2, 3, 2, 3, 1, 3, 3] => 3, 2, 2, 3, 2, 3, 1, 3, 3
[3, 2, 2, 3, 2, 3, 2, 1, 1] => 3, 2, 2, 3, 2, 3, 2, 1, 1
[3, 2, 2, 3, 2, 3, 2, 1, 2] => 3, 2, 2, 3, 2, 3, 2, 1, 2
[3, 2, 2, 3, 2, 3, 2, 1, 3] => 3, 2, 2, 3, 2, 3, 2, 1, 3
[3, 2, 2, 3, 2, 3, 2, 2, 1] => 3, 2, 2, 3, 2, 3, 2, 2, 1
[3, 2, 2, 3, 2, 3, 2, 2, 2] => 3, 2, 2, 3, 2, 3, 2, 2, 2
[3, 2, 2, 3, 2, 3, 2, 2, 3] => 3, 2, 2, 3, 2, 3, 2, 2, 3
[3, 2, 2, 3, 2, 3, 2, 3, 1] => 3, 2, 2, 3, 2, 3, 2, 3, 1
[3, 2, 2, 3, 2, 3, 2, 3, 2] => 3, 2, 2, 3, 2, 3, 2, 3, 2
[3, 2, 2, 3, 2, 3, 2, 3, 3] => 3, 2, 2, 3, 2, 3, 2, 3, 3
[3, 2, 2, 3, 2, 3, 3, 1, 1] => 3, 2, 2, 3, 2, 3, 3, 1, 1
[3, 2, 2, 3, 2, 3, 3, 1, 2] => 3, 2, 2, 3, 2, 3, 3, 1, 2
[3, 2, 2, 3, 2, 3, 3, 1, 3] => 3, 2, 2, 3, 2, 3, 3, 1, 3
[3, 2, 2, 3, 2, 3, 3, 2, 1] => 3, 2, 2, 3, 2, 3, 3, 2, 1
[3, 2, 2, 3, 2, 3, 3, 2, 2] => 3, 2, 2, 3, 2, 3, 3, 2, 2
[3, 2, 2, 3, 2, 3, 3, 2, 3] => 3, 2, 2, 3, 2, 3, 3, 2, 3
[3, 2, 2, 3, 2, 3, 3, 3, 1] => 3, 2, 2, 3, 2, 3, 3, 3, 1
[3, 2, 2, 3, 2, 3, 3, 3, 2] => 3, 2, 2, 3, 2, 3, 3, 3, 2
[3, 2, 2, 3, 2, 3, 3, 3, 3] => 3, 2, 2, 3, 2, 3, 3, 3, 3
[3, 2, 2, 3, 3, 1, 1, 1, 1] => 3, 2, 2, 3, 3, 1, 1, 1, 1
[3, 2, 2, 3, 3, 1, 1, 1, 2] => 3, 2, 2, 3, 3, 1, 1, 1, 2
[3, 2, 2, 3, 3, 1, 1, 1, 3] => 3, 2, 2, 3, 3, 1, 1, 1, 3
[3, 2, 2, 3, 3, 1, 1, 2, 1] => 3, 2, 2, 3, 3, 1, 1, 2, 1
[3, 2, 2, 3, 3, 1, 1, 2, 2] => 3, 2, 2, 3, 3, 1, 1, 2, 2
[3, 2, 2, 3, 3, 1, 1, 2, 3] => 3, 2, 2, 3, 3, 1, 1, 2, 3
[3, 2, 2, 3, 3, 1, 1, 3, 1] => 3, 2, 2, 3, 3, 1, 1, 3, 1
[3, 2, 2, 3, 3, 1, 1, 3, 2] => 3, 2, 2, 3, 3, 1, 1, 3, 2
[3, 2, 2, 3, 3, 1, 1, 3, 3] => 3, 2, 2, 3, 3, 1, 1, 3, 3
[3, 2, 2, 3, 3, 1, 2, 1, 1] => 3, 2, 2, 3, 3, 1, 2, 1, 1
[3, 2, 2, 3, 3, 1, 2, 1, 2] => 3, 2, 2, 3, 3, 1, 2, 1, 2
[3, 2, 2, 3, 3, 1, 2, 1, 3] => 3, 2, 2, 3, 3, 1, 2, 1, 3
[3, 2, 2, 3, 3, 1, 2, 2, 1] => 3, 2, 2, 3, 3, 1, 2, 2, 1
[3, 2, 2, 3, 3, 1, 2, 2, 2] => 3, 2, 2, 3, 3, 1, 2, 2, 2
[3, 2, 2, 3, 3, 1, 2, 2, 3] => 3, 2, 2, 3, 3, 1, 2, 2, 3
[3, 2, 2, 3, 3, 1, 2, 3, 1] => 3, 2, 2, 3, 3, 1, 2, 3, 1
[3, 2, 2, 3, 3, 1, 2, 3, 2] => 3, 2, 2, 3, 3, 1, 2, 3, 2
[3, 2, 2, 3, 3, 1, 2, 3, 3] => 3, 2, 2, 3, 3, 1, 2, 3, 3
[3, 2, 2, 3, 3, 1, 3, 1, 1] => 3, 2, 2, 3, 3, 1, 3, 1, 1
[3, 2, 2, 3, 3, 1, 3, 1, 2] => 3, 2, 2, 3, 3, 1, 3, 1, 2
[3, 2, 2, 3, 3, 1, 3, 1, 3] => 3, 2, 2, 3, 3, 1, 3, 1, 3
[3, 2, 2, 3, 3, 1, 3, 2, 1] => 3, 2, 2, 3, 3, 1, 3, 2, 1
[3, 2, 2, 3, 3, 1, 3, 2, 2] => 3, 2, 2, 3, 3, 1, 3, 2, 2
[3, 2, 2, 3, 3, 1, 3, 2, 3] => 3, 2, 2, 3, 3, 1, 3, 2, 3
[3, 2, 2, 3, 3, 1, 3, 3, 1] => 3, 2, 2, 3, 3, 1, 3, 3, 1
[3, 2, 2, 3, 3, 1, 3, 3, 2] => 3, 2, 2, 3, 3, 1, 3, 3, 2
[3, 2, 2, 3, 3, 1, 3, 3, 3] => 3, 2, 2, 3, 3, 1, 3, 3, 3
[3, 2, 2, 3, 3, 2, 1, 1, 1] => 3, 2, 2, 3, 3, 2, 1, 1, 1
[3, 2, 2, 3, 3, 2, 1, 1, 2] => 3, 2, 2, 3, 3, 2, 1, 1, 2
[3, 2, 2, 3, 3, 2, 1, 1, 3] => 3, 2, 2, 3, 3, 2, 1, 1, 3
[3, 2, 2, 3, 3, 2, 1, 2, 1] => 3, 2, 2, 3, 3, 2, 1, 2, 1
[3, 2, 2, 3, 3, 2, 1, 2, 2] => 3, 2, 2, 3, 3, 2, 1, 2, 2
[3, 2, 2, 3, 3, 2, 1, 2, 3] => 3, 2, 2, 3, 3, 2, 1, 2, 3
[3, 2, 2, 3, 3, 2, 1, 3, 1] => 3, 2, 2, 3, 3, 2, 1, 3, 1
[3, 2, 2, 3, 3, 2, 1, 3, 2] => 3, 2, 2, 3, 3, 2, 1, 3, 2
[3, 2, 2, 3, 3, 2, 1, 3, 3] => 3, 2, 2, 3, 3, 2, 1, 3, 3
[3, 2, 2, 3, 3, 2, 2, 1, 1] => 3, 2, 2, 3, 3, 2, 2, 1, 1
[3, 2, 2, 3, 3, 2, 2, 1, 2] => 3, 2, 2, 3, 3, 2, 2, 1, 2
[3, 2, 2, 3, 3, 2, 2, 1, 3] => 3, 2, 2, 3, 3, 2, 2, 1, 3
[3, 2, 2, 3, 3, 2, 2, 2, 1] => 3, 2, 2, 3, 3, 2, 2, 2, 1
[3, 2, 2, 3, 3, 2, 2, 2, 2] => 3, 2, 2, 3, 3, 2, 2, 2, 2
[3, 2, 2, 3, 3, 2, 2, 2, 3] => 3, 2, 2, 3, 3, 2, 2, 2, 3
[3, 2, 2, 3, 3, 2, 2, 3, 1] => 3, 2, 2, 3, 3, 2, 2, 3, 1
[3, 2, 2, 3, 3, 2, 2, 3, 2] => 3, 2, 2, 3, 3, 2, 2, 3, 2
[3, 2, 2, 3, 3, 2, 2, 3, 3] => 3, 2, 2, 3, 3, 2, 2, 3, 3
[3, 2, 2, 3, 3, 2, 3, 1, 1] => 3, 2, 2, 3, 3, 2, 3, 1, 1
[3, 2, 2, 3, 3, 2, 3, 1, 2] => 3, 2, 2, 3, 3, 2, 3, 1, 2
[3, 2, 2, 3, 3, 2, 3, 1, 3] => 3, 2, 2, 3, 3, 2, 3, 1, 3
[3, 2, 2, 3, 3, 2, 3, 2, 1] => 3, 2, 2, 3, 3, 2, 3, 2, 1
[3, 2, 2, 3, 3, 2, 3, 2, 2] => 3, 2, 2, 3, 3, 2, 3, 2, 2
[3, 2, 2, 3, 3, 2, 3, 2, 3] => 3, 2, 2, 3, 3, 2, 3, 2, 3
[3, 2, 2, 3, 3, 2, 3, 3, 1] => 3, 2, 2, 3, 3, 2, 3, 3, 1
[3, 2, 2, 3, 3, 2, 3, 3, 2] => 3, 2, 2, 3, 3, 2, 3, 3, 2
[3, 2, 2, 3, 3, 2, 3, 3, 3] => 3, 2, 2, 3, 3, 2, 3, 3, 3
[3, 2, 2, 3, 3, 3, 1, 1, 1] => 3, 2, 2, 3, 3, 3, 1, 1, 1
[3, 2, 2, 3, 3, 3, 1, 1, 2] => 3, 2, 2, 3, 3, 3, 1, 1, 2
[3, 2, 2, 3, 3, 3, 1, 1, 3] => 3, 2, 2, 3, 3, 3, 1, 1, 3
[3, 2, 2, 3, 3, 3, 1, 2, 1] => 3, 2, 2, 3, 3, 3, 1, 2, 1
[3, 2, 2, 3, 3, 3, 1, 2, 2] => 3, 2, 2, 3, 3, 3, 1, 2, 2
[3, 2, 2, 3, 3, 3, 1, 2, 3] => 3, 2, 2, 3, 3, 3, 1, 2, 3
[3, 2, 2, 3, 3, 3, 1, 3, 1] => 3, 2, 2, 3, 3, 3, 1, 3, 1
[3, 2, 2, 3, 3, 3, 1, 3, 2] => 3, 2, 2, 3, 3, 3, 1, 3, 2
[3, 2, 2, 3, 3, 3, 1, 3, 3] => 3, 2, 2, 3, 3, 3, 1, 3, 3
[3, 2, 2, 3, 3, 3, 2, 1, 1] => 3, 2, 2, 3, 3, 3, 2, 1, 1
[3, 2, 2, 3, 3, 3, 2, 1, 2] => 3, 2, 2, 3, 3, 3, 2, 1, 2
[3, 2, 2, 3, 3, 3, 2, 1, 3] => 3, 2, 2, 3, 3, 3, 2, 1, 3
[3, 2, 2, 3, 3, 3, 2, 2, 1] => 3, 2, 2, 3, 3, 3, 2, 2, 1
[3, 2, 2, 3, 3, 3, 2, 2, 2] => 3, 2, 2, 3, 3, 3, 2, 2, 2
[3, 2, 2, 3, 3, 3, 2, 2, 3] => 3, 2, 2, 3, 3, 3, 2, 2, 3
[3, 2, 2, 3, 3, 3, 2, 3, 1] => 3, 2, 2, 3, 3, 3, 2, 3, 1
[3, 2, 2, 3, 3, 3, 2, 3, 2] => 3, 2, 2, 3, 3, 3, 2, 3, 2
[3, 2, 2, 3, 3, 3, 2, 3, 3] => 3, 2, 2, 3, 3, 3, 2, 3, 3
[3, 2, 2, 3, 3, 3, 3, 1, 1] => 3, 2, 2, 3, 3, 3, 3, 1, 1
[3, 2, 2, 3, 3, 3, 3, 1, 2] => 3, 2, 2, 3, 3, 3, 3, 1, 2
[3, 2, 2, 3, 3, 3, 3, 1, 3] => 3, 2, 2, 3, 3, 3, 3, 1, 3
[3, 2, 2, 3, 3, 3, 3, 2, 1] => 3, 2, 2, 3, 3, 3, 3, 2, 1
[3, 2, 2, 3, 3, 3, 3, 2, 2] => 3, 2, 2, 3, 3, 3, 3, 2, 2
[3, 2, 2, 3, 3, 3, 3, 2, 3] => 3, 2, 2, 3, 3, 3, 3, 2, 3
[3, 2, 2, 3, 3, 3, 3, 3, 1] => 3, 2, 2, 3, 3, 3, 3, 3, 1
[3, 2, 2, 3, 3, 3, 3, 3, 2] => 3, 2, 2, 3, 3, 3, 3, 3, 2
[3, 2, 2, 3, 3, 3, 3, 3, 3] => 3, 2, 2, 3, 3, 3, 3, 3, 3
[3, 2, 3, 1, 1, 1, 1, 1, 1] => 3, 2, 3, 1, 1, 1, 1, 1, 1
[3, 2, 3, 1, 1, 1, 1, 1, 2] => 3, 2, 3, 1, 1, 1, 1, 1, 2
[3, 2, 3, 1, 1, 1, 1, 1, 3] => 3, 2, 3, 1, 1, 1, 1, 1, 3
[3, 2, 3, 1, 1, 1, 1, 2, 1] => 3, 2, 3, 1, 1, 1, 1, 2, 1
[3, 2, 3, 1, 1, 1, 1, 2, 2] => 3, 2, 3, 1, 1, 1, 1, 2, 2
[3, 2, 3, 1, 1, 1, 1, 2, 3] => 3, 2, 3, 1, 1, 1, 1, 2, 3
[3, 2, 3, 1, 1, 1, 1, 3, 1] => 3, 2, 3, 1, 1, 1, 1, 3, 1
[3, 2, 3, 1, 1, 1, 1, 3, 2] => 3, 2, 3, 1, 1, 1, 1, 3, 2
[3, 2, 3, 1, 1, 1, 1, 3, 3] => 3, 2, 3, 1, 1, 1, 1, 3, 3
[3, 2, 3, 1, 1, 1, 2, 1, 1] => 3, 2, 3, 1, 1, 1, 2, 1, 1
[3, 2, 3, 1, 1, 1, 2, 1, 2] => 3, 2, 3, 1, 1, 1, 2, 1, 2
[3, 2, 3, 1, 1, 1, 2, 1, 3] => 3, 2, 3, 1, 1, 1, 2, 1, 3
[3, 2, 3, 1, 1, 1, 2, 2, 1] => 3, 2, 3, 1, 1, 1, 2, 2, 1
[3, 2, 3, 1, 1, 1, 2, 2, 2] => 3, 2, 3, 1, 1, 1, 2, 2, 2
[3, 2, 3, 1, 1, 1, 2, 2, 3] => 3, 2, 3, 1, 1, 1, 2, 2, 3
[3, 2, 3, 1, 1, 1, 2, 3, 1] => 3, 2, 3, 1, 1, 1, 2, 3, 1
[3, 2, 3, 1, 1, 1, 2, 3, 2] => 3, 2, 3, 1, 1, 1, 2, 3, 2
[3, 2, 3, 1, 1, 1, 2, 3, 3] => 3, 2, 3, 1, 1, 1, 2, 3, 3
[3, 2, 3, 1, 1, 1, 3, 1, 1] => 3, 2, 3, 1, 1, 1, 3, 1, 1
[3, 2, 3, 1, 1, 1, 3, 1, 2] => 3, 2, 3, 1, 1, 1, 3, 1, 2
[3, 2, 3, 1, 1, 1, 3, 1, 3] => 3, 2, 3, 1, 1, 1, 3, 1, 3
[3, 2, 3, 1, 1, 1, 3, 2, 1] => 3, 2, 3, 1, 1, 1, 3, 2, 1
[3, 2, 3, 1, 1, 1, 3, 2, 2] => 3, 2, 3, 1, 1, 1, 3, 2, 2
[3, 2, 3, 1, 1, 1, 3, 2, 3] => 3, 2, 3, 1, 1, 1, 3, 2, 3
[3, 2, 3, 1, 1, 1, 3, 3, 1] => 3, 2, 3, 1, 1, 1, 3, 3, 1
[3, 2, 3, 1, 1, 1, 3, 3, 2] => 3, 2, 3, 1, 1, 1, 3, 3, 2
[3, 2, 3, 1, 1, 1, 3, 3, 3] => 3, 2, 3, 1, 1, 1, 3, 3, 3
[3, 2, 3, 1, 1, 2, 1, 1, 1] => 3, 2, 3, 1, 1, 2, 1, 1, 1
[3, 2, 3, 1, 1, 2, 1, 1, 2] => 3, 2, 3, 1, 1, 2, 1, 1, 2
[3, 2, 3, 1, 1, 2, 1, 1, 3] => 3, 2, 3, 1, 1, 2, 1, 1, 3
[3, 2, 3, 1, 1, 2, 1, 2, 1] => 3, 2, 3, 1, 1, 2, 1, 2, 1
[3, 2, 3, 1, 1, 2, 1, 2, 2] => 3, 2, 3, 1, 1, 2, 1, 2, 2
[3, 2, 3, 1, 1, 2, 1, 2, 3] => 3, 2, 3, 1, 1, 2, 1, 2, 3
[3, 2, 3, 1, 1, 2, 1, 3, 1] => 3, 2, 3, 1, 1, 2, 1, 3, 1
[3, 2, 3, 1, 1, 2, 1, 3, 2] => 3, 2, 3, 1, 1, 2, 1, 3, 2
[3, 2, 3, 1, 1, 2, 1, 3, 3] => 3, 2, 3, 1, 1, 2, 1, 3, 3
[3, 2, 3, 1, 1, 2, 2, 1, 1] => 3, 2, 3, 1, 1, 2, 2, 1, 1
[3, 2, 3, 1, 1, 2, 2, 1, 2] => 3, 2, 3, 1, 1, 2, 2, 1, 2
[3, 2, 3, 1, 1, 2, 2, 1, 3] => 3, 2, 3, 1, 1, 2, 2, 1, 3
[3, 2, 3, 1, 1, 2, 2, 2, 1] => 3, 2, 3, 1, 1, 2, 2, 2, 1
[3, 2, 3, 1, 1, 2, 2, 2, 2] => 3, 2, 3, 1, 1, 2, 2, 2, 2
[3, 2, 3, 1, 1, 2, 2, 2, 3] => 3, 2, 3, 1, 1, 2, 2, 2, 3
[3, 2, 3, 1, 1, 2, 2, 3, 1] => 3, 2, 3, 1, 1, 2, 2, 3, 1
[3, 2, 3, 1, 1, 2, 2, 3, 2] => 3, 2, 3, 1, 1, 2, 2, 3, 2
[3, 2, 3, 1, 1, 2, 2, 3, 3] => 3, 2, 3, 1, 1, 2, 2, 3, 3
[3, 2, 3, 1, 1, 2, 3, 1, 1] => 3, 2, 3, 1, 1, 2, 3, 1, 1
[3, 2, 3, 1, 1, 2, 3, 1, 2] => 3, 2, 3, 1, 1, 2, 3, 1, 2
[3, 2, 3, 1, 1, 2, 3, 1, 3] => 3, 2, 3, 1, 1, 2, 3, 1, 3
[3, 2, 3, 1, 1, 2, 3, 2, 1] => 3, 2, 3, 1, 1, 2, 3, 2, 1
[3, 2, 3, 1, 1, 2, 3, 2, 2] => 3, 2, 3, 1, 1, 2, 3, 2, 2
[3, 2, 3, 1, 1, 2, 3, 2, 3] => 3, 2, 3, 1, 1, 2, 3, 2, 3
[3, 2, 3, 1, 1, 2, 3, 3, 1] => 3, 2, 3, 1, 1, 2, 3, 3, 1
[3, 2, 3, 1, 1, 2, 3, 3, 2] => 3, 2, 3, 1, 1, 2, 3, 3, 2
[3, 2, 3, 1, 1, 2, 3, 3, 3] => 3, 2, 3, 1, 1, 2, 3, 3, 3
[3, 2, 3, 1, 1, 3, 1, 1, 1] => 3, 2, 3, 1, 1, 3, 1, 1, 1
[3, 2, 3, 1, 1, 3, 1, 1, 2] => 3, 2, 3, 1, 1, 3, 1, 1, 2
[3, 2, 3, 1, 1, 3, 1, 1, 3] => 3, 2, 3, 1, 1, 3, 1, 1, 3
[3, 2, 3, 1, 1, 3, 1, 2, 1] => 3, 2, 3, 1, 1, 3, 1, 2, 1
[3, 2, 3, 1, 1, 3, 1, 2, 2] => 3, 2, 3, 1, 1, 3, 1, 2, 2
[3, 2, 3, 1, 1, 3, 1, 2, 3] => 3, 2, 3, 1, 1, 3, 1, 2, 3
[3, 2, 3, 1, 1, 3, 1, 3, 1] => 3, 2, 3, 1, 1, 3, 1, 3, 1
[3, 2, 3, 1, 1, 3, 1, 3, 2] => 3, 2, 3, 1, 1, 3, 1, 3, 2
[3, 2, 3, 1, 1, 3, 1, 3, 3] => 3, 2, 3, 1, 1, 3, 1, 3, 3
[3, 2, 3, 1, 1, 3, 2, 1, 1] => 3, 2, 3, 1, 1, 3, 2, 1, 1
[3, 2, 3, 1, 1, 3, 2, 1, 2] => 3, 2, 3, 1, 1, 3, 2, 1, 2
[3, 2, 3, 1, 1, 3, 2, 1, 3] => 3, 2, 3, 1, 1, 3, 2, 1, 3
[3, 2, 3, 1, 1, 3, 2, 2, 1] => 3, 2, 3, 1, 1, 3, 2, 2, 1
[3, 2, 3, 1, 1, 3, 2, 2, 2] => 3, 2, 3, 1, 1, 3, 2, 2, 2
[3, 2, 3, 1, 1, 3, 2, 2, 3] => 3, 2, 3, 1, 1, 3, 2, 2, 3
[3, 2, 3, 1, 1, 3, 2, 3, 1] => 3, 2, 3, 1, 1, 3, 2, 3, 1
[3, 2, 3, 1, 1, 3, 2, 3, 2] => 3, 2, 3, 1, 1, 3, 2, 3, 2
[3, 2, 3, 1, 1, 3, 2, 3, 3] => 3, 2, 3, 1, 1, 3, 2, 3, 3
[3, 2, 3, 1, 1, 3, 3, 1, 1] => 3, 2, 3, 1, 1, 3, 3, 1, 1
[3, 2, 3, 1, 1, 3, 3, 1, 2] => 3, 2, 3, 1, 1, 3, 3, 1, 2
[3, 2, 3, 1, 1, 3, 3, 1, 3] => 3, 2, 3, 1, 1, 3, 3, 1, 3
[3, 2, 3, 1, 1, 3, 3, 2, 1] => 3, 2, 3, 1, 1, 3, 3, 2, 1
[3, 2, 3, 1, 1, 3, 3, 2, 2] => 3, 2, 3, 1, 1, 3, 3, 2, 2
[3, 2, 3, 1, 1, 3, 3, 2, 3] => 3, 2, 3, 1, 1, 3, 3, 2, 3
[3, 2, 3, 1, 1, 3, 3, 3, 1] => 3, 2, 3, 1, 1, 3, 3, 3, 1
[3, 2, 3, 1, 1, 3, 3, 3, 2] => 3, 2, 3, 1, 1, 3, 3, 3, 2
[3, 2, 3, 1, 1, 3, 3, 3, 3] => 3, 2, 3, 1, 1, 3, 3, 3, 3
[3, 2, 3, 1, 2, 1, 1, 1, 1] => 3, 2, 3, 1, 2, 1, 1, 1, 1
[3, 2, 3, 1, 2, 1, 1, 1, 2] => 3, 2, 3, 1, 2, 1, 1, 1, 2
[3, 2, 3, 1, 2, 1, 1, 1, 3] => 3, 2, 3, 1, 2, 1, 1, 1, 3
[3, 2, 3, 1, 2, 1, 1, 2, 1] => 3, 2, 3, 1, 2, 1, 1, 2, 1
[3, 2, 3, 1, 2, 1, 1, 2, 2] => 3, 2, 3, 1, 2, 1, 1, 2, 2
[3, 2, 3, 1, 2, 1, 1, 2, 3] => 3, 2, 3, 1, 2, 1, 1, 2, 3
[3, 2, 3, 1, 2, 1, 1, 3, 1] => 3, 2, 3, 1, 2, 1, 1, 3, 1
[3, 2, 3, 1, 2, 1, 1, 3, 2] => 3, 2, 3, 1, 2, 1, 1, 3, 2
[3, 2, 3, 1, 2, 1, 1, 3, 3] => 3, 2, 3, 1, 2, 1, 1, 3, 3
[3, 2, 3, 1, 2, 1, 2, 1, 1] => 3, 2, 3, 1, 2, 1, 2, 1, 1
[3, 2, 3, 1, 2, 1, 2, 1, 2] => 3, 2, 3, 1, 2, 1, 2, 1, 2
[3, 2, 3, 1, 2, 1, 2, 1, 3] => 3, 2, 3, 1, 2, 1, 2, 1, 3
[3, 2, 3, 1, 2, 1, 2, 2, 1] => 3, 2, 3, 1, 2, 1, 2, 2, 1
[3, 2, 3, 1, 2, 1, 2, 2, 2] => 3, 2, 3, 1, 2, 1, 2, 2, 2
[3, 2, 3, 1, 2, 1, 2, 2, 3] => 3, 2, 3, 1, 2, 1, 2, 2, 3
[3, 2, 3, 1, 2, 1, 2, 3, 1] => 3, 2, 3, 1, 2, 1, 2, 3, 1
[3, 2, 3, 1, 2, 1, 2, 3, 2] => 3, 2, 3, 1, 2, 1, 2, 3, 2
[3, 2, 3, 1, 2, 1, 2, 3, 3] => 3, 2, 3, 1, 2, 1, 2, 3, 3
[3, 2, 3, 1, 2, 1, 3, 1, 1] => 3, 2, 3, 1, 2, 1, 3, 1, 1
[3, 2, 3, 1, 2, 1, 3, 1, 2] => 3, 2, 3, 1, 2, 1, 3, 1, 2
[3, 2, 3, 1, 2, 1, 3, 1, 3] => 3, 2, 3, 1, 2, 1, 3, 1, 3
[3, 2, 3, 1, 2, 1, 3, 2, 1] => 3, 2, 3, 1, 2, 1, 3, 2, 1
[3, 2, 3, 1, 2, 1, 3, 2, 2] => 3, 2, 3, 1, 2, 1, 3, 2, 2
[3, 2, 3, 1, 2, 1, 3, 2, 3] => 3, 2, 3, 1, 2, 1, 3, 2, 3
[3, 2, 3, 1, 2, 1, 3, 3, 1] => 3, 2, 3, 1, 2, 1, 3, 3, 1
[3, 2, 3, 1, 2, 1, 3, 3, 2] => 3, 2, 3, 1, 2, 1, 3, 3, 2
[3, 2, 3, 1, 2, 1, 3, 3, 3] => 3, 2, 3, 1, 2, 1, 3, 3, 3
[3, 2, 3, 1, 2, 2, 1, 1, 1] => 3, 2, 3, 1, 2, 2, 1, 1, 1
[3, 2, 3, 1, 2, 2, 1, 1, 2] => 3, 2, 3, 1, 2, 2, 1, 1, 2
[3, 2, 3, 1, 2, 2, 1, 1, 3] => 3, 2, 3, 1, 2, 2, 1, 1, 3
[3, 2, 3, 1, 2, 2, 1, 2, 1] => 3, 2, 3, 1, 2, 2, 1, 2, 1
[3, 2, 3, 1, 2, 2, 1, 2, 2] => 3, 2, 3, 1, 2, 2, 1, 2, 2
[3, 2, 3, 1, 2, 2, 1, 2, 3] => 3, 2, 3, 1, 2, 2, 1, 2, 3
[3, 2, 3, 1, 2, 2, 1, 3, 1] => 3, 2, 3, 1, 2, 2, 1, 3, 1
[3, 2, 3, 1, 2, 2, 1, 3, 2] => 3, 2, 3, 1, 2, 2, 1, 3, 2
[3, 2, 3, 1, 2, 2, 1, 3, 3] => 3, 2, 3, 1, 2, 2, 1, 3, 3
[3, 2, 3, 1, 2, 2, 2, 1, 1] => 3, 2, 3, 1, 2, 2, 2, 1, 1
[3, 2, 3, 1, 2, 2, 2, 1, 2] => 3, 2, 3, 1, 2, 2, 2, 1, 2
[3, 2, 3, 1, 2, 2, 2, 1, 3] => 3, 2, 3, 1, 2, 2, 2, 1, 3
[3, 2, 3, 1, 2, 2, 2, 2, 1] => 3, 2, 3, 1, 2, 2, 2, 2, 1
[3, 2, 3, 1, 2, 2, 2, 2, 2] => 3, 2, 3, 1, 2, 2, 2, 2, 2
[3, 2, 3, 1, 2, 2, 2, 2, 3] => 3, 2, 3, 1, 2, 2, 2, 2, 3
[3, 2, 3, 1, 2, 2, 2, 3, 1] => 3, 2, 3, 1, 2, 2, 2, 3, 1
[3, 2, 3, 1, 2, 2, 2, 3, 2] => 3, 2, 3, 1, 2, 2, 2, 3, 2
[3, 2, 3, 1, 2, 2, 2, 3, 3] => 3, 2, 3, 1, 2, 2, 2, 3, 3
[3, 2, 3, 1, 2, 2, 3, 1, 1] => 3, 2, 3, 1, 2, 2, 3, 1, 1
[3, 2, 3, 1, 2, 2, 3, 1, 2] => 3, 2, 3, 1, 2, 2, 3, 1, 2
[3, 2, 3, 1, 2, 2, 3, 1, 3] => 3, 2, 3, 1, 2, 2, 3, 1, 3
[3, 2, 3, 1, 2, 2, 3, 2, 1] => 3, 2, 3, 1, 2, 2, 3, 2, 1
[3, 2, 3, 1, 2, 2, 3, 2, 2] => 3, 2, 3, 1, 2, 2, 3, 2, 2
[3, 2, 3, 1, 2, 2, 3, 2, 3] => 3, 2, 3, 1, 2, 2, 3, 2, 3
[3, 2, 3, 1, 2, 2, 3, 3, 1] => 3, 2, 3, 1, 2, 2, 3, 3, 1
[3, 2, 3, 1, 2, 2, 3, 3, 2] => 3, 2, 3, 1, 2, 2, 3, 3, 2
[3, 2, 3, 1, 2, 2, 3, 3, 3] => 3, 2, 3, 1, 2, 2, 3, 3, 3
[3, 2, 3, 1, 2, 3, 1, 1, 1] => 3, 2, 3, 1, 2, 3, 1, 1, 1
[3, 2, 3, 1, 2, 3, 1, 1, 2] => 3, 2, 3, 1, 2, 3, 1, 1, 2
[3, 2, 3, 1, 2, 3, 1, 1, 3] => 3, 2, 3, 1, 2, 3, 1, 1, 3
[3, 2, 3, 1, 2, 3, 1, 2, 1] => 3, 2, 3, 1, 2, 3, 1, 2, 1
[3, 2, 3, 1, 2, 3, 1, 2, 2] => 3, 2, 3, 1, 2, 3, 1, 2, 2
[3, 2, 3, 1, 2, 3, 1, 2, 3] => 3, 2, 3, 1, 2, 3, 1, 2, 3
[3, 2, 3, 1, 2, 3, 1, 3, 1] => 3, 2, 3, 1, 2, 3, 1, 3, 1
[3, 2, 3, 1, 2, 3, 1, 3, 2] => 3, 2, 3, 1, 2, 3, 1, 3, 2
[3, 2, 3, 1, 2, 3, 1, 3, 3] => 3, 2, 3, 1, 2, 3, 1, 3, 3
[3, 2, 3, 1, 2, 3, 2, 1, 1] => 3, 2, 3, 1, 2, 3, 2, 1, 1
[3, 2, 3, 1, 2, 3, 2, 1, 2] => 3, 2, 3, 1, 2, 3, 2, 1, 2
[3, 2, 3, 1, 2, 3, 2, 1, 3] => 3, 2, 3, 1, 2, 3, 2, 1, 3
[3, 2, 3, 1, 2, 3, 2, 2, 1] => 3, 2, 3, 1, 2, 3, 2, 2, 1
[3, 2, 3, 1, 2, 3, 2, 2, 2] => 3, 2, 3, 1, 2, 3, 2, 2, 2
[3, 2, 3, 1, 2, 3, 2, 2, 3] => 3, 2, 3, 1, 2, 3, 2, 2, 3
[3, 2, 3, 1, 2, 3, 2, 3, 1] => 3, 2, 3, 1, 2, 3, 2, 3, 1
[3, 2, 3, 1, 2, 3, 2, 3, 2] => 3, 2, 3, 1, 2, 3, 2, 3, 2
[3, 2, 3, 1, 2, 3, 2, 3, 3] => 3, 2, 3, 1, 2, 3, 2, 3, 3
[3, 2, 3, 1, 2, 3, 3, 1, 1] => 3, 2, 3, 1, 2, 3, 3, 1, 1
[3, 2, 3, 1, 2, 3, 3, 1, 2] => 3, 2, 3, 1, 2, 3, 3, 1, 2
[3, 2, 3, 1, 2, 3, 3, 1, 3] => 3, 2, 3, 1, 2, 3, 3, 1, 3
[3, 2, 3, 1, 2, 3, 3, 2, 1] => 3, 2, 3, 1, 2, 3, 3, 2, 1
[3, 2, 3, 1, 2, 3, 3, 2, 2] => 3, 2, 3, 1, 2, 3, 3, 2, 2
[3, 2, 3, 1, 2, 3, 3, 2, 3] => 3, 2, 3, 1, 2, 3, 3, 2, 3
[3, 2, 3, 1, 2, 3, 3, 3, 1] => 3, 2, 3, 1, 2, 3, 3, 3, 1
[3, 2, 3, 1, 2, 3, 3, 3, 2] => 3, 2, 3, 1, 2, 3, 3, 3, 2
[3, 2, 3, 1, 2, 3, 3, 3, 3] => 3, 2, 3, 1, 2, 3, 3, 3, 3
[3, 2, 3, 1, 3, 1, 1, 1, 1] => 3, 2, 3, 1, 3, 1, 1, 1, 1
[3, 2, 3, 1, 3, 1, 1, 1, 2] => 3, 2, 3, 1, 3, 1, 1, 1, 2
[3, 2, 3, 1, 3, 1, 1, 1, 3] => 3, 2, 3, 1, 3, 1, 1, 1, 3
[3, 2, 3, 1, 3, 1, 1, 2, 1] => 3, 2, 3, 1, 3, 1, 1, 2, 1
[3, 2, 3, 1, 3, 1, 1, 2, 2] => 3, 2, 3, 1, 3, 1, 1, 2, 2
[3, 2, 3, 1, 3, 1, 1, 2, 3] => 3, 2, 3, 1, 3, 1, 1, 2, 3
[3, 2, 3, 1, 3, 1, 1, 3, 1] => 3, 2, 3, 1, 3, 1, 1, 3, 1
[3, 2, 3, 1, 3, 1, 1, 3, 2] => 3, 2, 3, 1, 3, 1, 1, 3, 2
[3, 2, 3, 1, 3, 1, 1, 3, 3] => 3, 2, 3, 1, 3, 1, 1, 3, 3
[3, 2, 3, 1, 3, 1, 2, 1, 1] => 3, 2, 3, 1, 3, 1, 2, 1, 1
[3, 2, 3, 1, 3, 1, 2, 1, 2] => 3, 2, 3, 1, 3, 1, 2, 1, 2
[3, 2, 3, 1, 3, 1, 2, 1, 3] => 3, 2, 3, 1, 3, 1, 2, 1, 3
[3, 2, 3, 1, 3, 1, 2, 2, 1] => 3, 2, 3, 1, 3, 1, 2, 2, 1
[3, 2, 3, 1, 3, 1, 2, 2, 2] => 3, 2, 3, 1, 3, 1, 2, 2, 2
[3, 2, 3, 1, 3, 1, 2, 2, 3] => 3, 2, 3, 1, 3, 1, 2, 2, 3
[3, 2, 3, 1, 3, 1, 2, 3, 1] => 3, 2, 3, 1, 3, 1, 2, 3, 1
[3, 2, 3, 1, 3, 1, 2, 3, 2] => 3, 2, 3, 1, 3, 1, 2, 3, 2
[3, 2, 3, 1, 3, 1, 2, 3, 3] => 3, 2, 3, 1, 3, 1, 2, 3, 3
[3, 2, 3, 1, 3, 1, 3, 1, 1] => 3, 2, 3, 1, 3, 1, 3, 1, 1
[3, 2, 3, 1, 3, 1, 3, 1, 2] => 3, 2, 3, 1, 3, 1, 3, 1, 2
[3, 2, 3, 1, 3, 1, 3, 1, 3] => 3, 2, 3, 1, 3, 1, 3, 1, 3
[3, 2, 3, 1, 3, 1, 3, 2, 1] => 3, 2, 3, 1, 3, 1, 3, 2, 1
[3, 2, 3, 1, 3, 1, 3, 2, 2] => 3, 2, 3, 1, 3, 1, 3, 2, 2
[3, 2, 3, 1, 3, 1, 3, 2, 3] => 3, 2, 3, 1, 3, 1, 3, 2, 3
[3, 2, 3, 1, 3, 1, 3, 3, 1] => 3, 2, 3, 1, 3, 1, 3, 3, 1
[3, 2, 3, 1, 3, 1, 3, 3, 2] => 3, 2, 3, 1, 3, 1, 3, 3, 2
[3, 2, 3, 1, 3, 1, 3, 3, 3] => 3, 2, 3, 1, 3, 1, 3, 3, 3
[3, 2, 3, 1, 3, 2, 1, 1, 1] => 3, 2, 3, 1, 3, 2, 1, 1, 1
[3, 2, 3, 1, 3, 2, 1, 1, 2] => 3, 2, 3, 1, 3, 2, 1, 1, 2
[3, 2, 3, 1, 3, 2, 1, 1, 3] => 3, 2, 3, 1, 3, 2, 1, 1, 3
[3, 2, 3, 1, 3, 2, 1, 2, 1] => 3, 2, 3, 1, 3, 2, 1, 2, 1
[3, 2, 3, 1, 3, 2, 1, 2, 2] => 3, 2, 3, 1, 3, 2, 1, 2, 2
[3, 2, 3, 1, 3, 2, 1, 2, 3] => 3, 2, 3, 1, 3, 2, 1, 2, 3
[3, 2, 3, 1, 3, 2, 1, 3, 1] => 3, 2, 3, 1, 3, 2, 1, 3, 1
[3, 2, 3, 1, 3, 2, 1, 3, 2] => 3, 2, 3, 1, 3, 2, 1, 3, 2
[3, 2, 3, 1, 3, 2, 1, 3, 3] => 3, 2, 3, 1, 3, 2, 1, 3, 3
[3, 2, 3, 1, 3, 2, 2, 1, 1] => 3, 2, 3, 1, 3, 2, 2, 1, 1
[3, 2, 3, 1, 3, 2, 2, 1, 2] => 3, 2, 3, 1, 3, 2, 2, 1, 2
[3, 2, 3, 1, 3, 2, 2, 1, 3] => 3, 2, 3, 1, 3, 2, 2, 1, 3
[3, 2, 3, 1, 3, 2, 2, 2, 1] => 3, 2, 3, 1, 3, 2, 2, 2, 1
[3, 2, 3, 1, 3, 2, 2, 2, 2] => 3, 2, 3, 1, 3, 2, 2, 2, 2
[3, 2, 3, 1, 3, 2, 2, 2, 3] => 3, 2, 3, 1, 3, 2, 2, 2, 3
[3, 2, 3, 1, 3, 2, 2, 3, 1] => 3, 2, 3, 1, 3, 2, 2, 3, 1
[3, 2, 3, 1, 3, 2, 2, 3, 2] => 3, 2, 3, 1, 3, 2, 2, 3, 2
[3, 2, 3, 1, 3, 2, 2, 3, 3] => 3, 2, 3, 1, 3, 2, 2, 3, 3
[3, 2, 3, 1, 3, 2, 3, 1, 1] => 3, 2, 3, 1, 3, 2, 3, 1, 1
[3, 2, 3, 1, 3, 2, 3, 1, 2] => 3, 2, 3, 1, 3, 2, 3, 1, 2
[3, 2, 3, 1, 3, 2, 3, 1, 3] => 3, 2, 3, 1, 3, 2, 3, 1, 3
[3, 2, 3, 1, 3, 2, 3, 2, 1] => 3, 2, 3, 1, 3, 2, 3, 2, 1
[3, 2, 3, 1, 3, 2, 3, 2, 2] => 3, 2, 3, 1, 3, 2, 3, 2, 2
[3, 2, 3, 1, 3, 2, 3, 2, 3] => 3, 2, 3, 1, 3, 2, 3, 2, 3
[3, 2, 3, 1, 3, 2, 3, 3, 1] => 3, 2, 3, 1, 3, 2, 3, 3, 1
[3, 2, 3, 1, 3, 2, 3, 3, 2] => 3, 2, 3, 1, 3, 2, 3, 3, 2
[3, 2, 3, 1, 3, 2, 3, 3, 3] => 3, 2, 3, 1, 3, 2, 3, 3, 3
[3, 2, 3, 1, 3, 3, 1, 1, 1] => 3, 2, 3, 1, 3, 3, 1, 1, 1
[3, 2, 3, 1, 3, 3, 1, 1, 2] => 3, 2, 3, 1, 3, 3, 1, 1, 2
[3, 2, 3, 1, 3, 3, 1, 1, 3] => 3, 2, 3, 1, 3, 3, 1, 1, 3
[3, 2, 3, 1, 3, 3, 1, 2, 1] => 3, 2, 3, 1, 3, 3, 1, 2, 1
[3, 2, 3, 1, 3, 3, 1, 2, 2] => 3, 2, 3, 1, 3, 3, 1, 2, 2
[3, 2, 3, 1, 3, 3, 1, 2, 3] => 3, 2, 3, 1, 3, 3, 1, 2, 3
[3, 2, 3, 1, 3, 3, 1, 3, 1] => 3, 2, 3, 1, 3, 3, 1, 3, 1
[3, 2, 3, 1, 3, 3, 1, 3, 2] => 3, 2, 3, 1, 3, 3, 1, 3, 2
[3, 2, 3, 1, 3, 3, 1, 3, 3] => 3, 2, 3, 1, 3, 3, 1, 3, 3
[3, 2, 3, 1, 3, 3, 2, 1, 1] => 3, 2, 3, 1, 3, 3, 2, 1, 1
[3, 2, 3, 1, 3, 3, 2, 1, 2] => 3, 2, 3, 1, 3, 3, 2, 1, 2
[3, 2, 3, 1, 3, 3, 2, 1, 3] => 3, 2, 3, 1, 3, 3, 2, 1, 3
[3, 2, 3, 1, 3, 3, 2, 2, 1] => 3, 2, 3, 1, 3, 3, 2, 2, 1
[3, 2, 3, 1, 3, 3, 2, 2, 2] => 3, 2, 3, 1, 3, 3, 2, 2, 2
[3, 2, 3, 1, 3, 3, 2, 2, 3] => 3, 2, 3, 1, 3, 3, 2, 2, 3
[3, 2, 3, 1, 3, 3, 2, 3, 1] => 3, 2, 3, 1, 3, 3, 2, 3, 1
[3, 2, 3, 1, 3, 3, 2, 3, 2] => 3, 2, 3, 1, 3, 3, 2, 3, 2
[3, 2, 3, 1, 3, 3, 2, 3, 3] => 3, 2, 3, 1, 3, 3, 2, 3, 3
[3, 2, 3, 1, 3, 3, 3, 1, 1] => 3, 2, 3, 1, 3, 3, 3, 1, 1
[3, 2, 3, 1, 3, 3, 3, 1, 2] => 3, 2, 3, 1, 3, 3, 3, 1, 2
[3, 2, 3, 1, 3, 3, 3, 1, 3] => 3, 2, 3, 1, 3, 3, 3, 1, 3
[3, 2, 3, 1, 3, 3, 3, 2, 1] => 3, 2, 3, 1, 3, 3, 3, 2, 1
[3, 2, 3, 1, 3, 3, 3, 2, 2] => 3, 2, 3, 1, 3, 3, 3, 2, 2
[3, 2, 3, 1, 3, 3, 3, 2, 3] => 3, 2, 3, 1, 3, 3, 3, 2, 3
[3, 2, 3, 1, 3, 3, 3, 3, 1] => 3, 2, 3, 1, 3, 3, 3, 3, 1
[3, 2, 3, 1, 3, 3, 3, 3, 2] => 3, 2, 3, 1, 3, 3, 3, 3, 2
[3, 2, 3, 1, 3, 3, 3, 3, 3] => 3, 2, 3, 1, 3, 3, 3, 3, 3
[3, 2, 3, 2, 1, 1, 1, 1, 1] => 3, 2, 3, 2, 1, 1, 1, 1, 1
[3, 2, 3, 2, 1, 1, 1, 1, 2] => 3, 2, 3, 2, 1, 1, 1, 1, 2
[3, 2, 3, 2, 1, 1, 1, 1, 3] => 3, 2, 3, 2, 1, 1, 1, 1, 3
[3, 2, 3, 2, 1, 1, 1, 2, 1] => 3, 2, 3, 2, 1, 1, 1, 2, 1
[3, 2, 3, 2, 1, 1, 1, 2, 2] => 3, 2, 3, 2, 1, 1, 1, 2, 2
[3, 2, 3, 2, 1, 1, 1, 2, 3] => 3, 2, 3, 2, 1, 1, 1, 2, 3
[3, 2, 3, 2, 1, 1, 1, 3, 1] => 3, 2, 3, 2, 1, 1, 1, 3, 1
[3, 2, 3, 2, 1, 1, 1, 3, 2] => 3, 2, 3, 2, 1, 1, 1, 3, 2
[3, 2, 3, 2, 1, 1, 1, 3, 3] => 3, 2, 3, 2, 1, 1, 1, 3, 3
[3, 2, 3, 2, 1, 1, 2, 1, 1] => 3, 2, 3, 2, 1, 1, 2, 1, 1
[3, 2, 3, 2, 1, 1, 2, 1, 2] => 3, 2, 3, 2, 1, 1, 2, 1, 2
[3, 2, 3, 2, 1, 1, 2, 1, 3] => 3, 2, 3, 2, 1, 1, 2, 1, 3
[3, 2, 3, 2, 1, 1, 2, 2, 1] => 3, 2, 3, 2, 1, 1, 2, 2, 1
[3, 2, 3, 2, 1, 1, 2, 2, 2] => 3, 2, 3, 2, 1, 1, 2, 2, 2
[3, 2, 3, 2, 1, 1, 2, 2, 3] => 3, 2, 3, 2, 1, 1, 2, 2, 3
[3, 2, 3, 2, 1, 1, 2, 3, 1] => 3, 2, 3, 2, 1, 1, 2, 3, 1
[3, 2, 3, 2, 1, 1, 2, 3, 2] => 3, 2, 3, 2, 1, 1, 2, 3, 2
[3, 2, 3, 2, 1, 1, 2, 3, 3] => 3, 2, 3, 2, 1, 1, 2, 3, 3
[3, 2, 3, 2, 1, 1, 3, 1, 1] => 3, 2, 3, 2, 1, 1, 3, 1, 1
[3, 2, 3, 2, 1, 1, 3, 1, 2] => 3, 2, 3, 2, 1, 1, 3, 1, 2
[3, 2, 3, 2, 1, 1, 3, 1, 3] => 3, 2, 3, 2, 1, 1, 3, 1, 3
[3, 2, 3, 2, 1, 1, 3, 2, 1] => 3, 2, 3, 2, 1, 1, 3, 2, 1
[3, 2, 3, 2, 1, 1, 3, 2, 2] => 3, 2, 3, 2, 1, 1, 3, 2, 2
[3, 2, 3, 2, 1, 1, 3, 2, 3] => 3, 2, 3, 2, 1, 1, 3, 2, 3
[3, 2, 3, 2, 1, 1, 3, 3, 1] => 3, 2, 3, 2, 1, 1, 3, 3, 1
[3, 2, 3, 2, 1, 1, 3, 3, 2] => 3, 2, 3, 2, 1, 1, 3, 3, 2
[3, 2, 3, 2, 1, 1, 3, 3, 3] => 3, 2, 3, 2, 1, 1, 3, 3, 3
[3, 2, 3, 2, 1, 2, 1, 1, 1] => 3, 2, 3, 2, 1, 2, 1, 1, 1
[3, 2, 3, 2, 1, 2, 1, 1, 2] => 3, 2, 3, 2, 1, 2, 1, 1, 2
[3, 2, 3, 2, 1, 2, 1, 1, 3] => 3, 2, 3, 2, 1, 2, 1, 1, 3
[3, 2, 3, 2, 1, 2, 1, 2, 1] => 3, 2, 3, 2, 1, 2, 1, 2, 1
[3, 2, 3, 2, 1, 2, 1, 2, 2] => 3, 2, 3, 2, 1, 2, 1, 2, 2
[3, 2, 3, 2, 1, 2, 1, 2, 3] => 3, 2, 3, 2, 1, 2, 1, 2, 3
[3, 2, 3, 2, 1, 2, 1, 3, 1] => 3, 2, 3, 2, 1, 2, 1, 3, 1
[3, 2, 3, 2, 1, 2, 1, 3, 2] => 3, 2, 3, 2, 1, 2, 1, 3, 2
[3, 2, 3, 2, 1, 2, 1, 3, 3] => 3, 2, 3, 2, 1, 2, 1, 3, 3
[3, 2, 3, 2, 1, 2, 2, 1, 1] => 3, 2, 3, 2, 1, 2, 2, 1, 1
[3, 2, 3, 2, 1, 2, 2, 1, 2] => 3, 2, 3, 2, 1, 2, 2, 1, 2
[3, 2, 3, 2, 1, 2, 2, 1, 3] => 3, 2, 3, 2, 1, 2, 2, 1, 3
[3, 2, 3, 2, 1, 2, 2, 2, 1] => 3, 2, 3, 2, 1, 2, 2, 2, 1
[3, 2, 3, 2, 1, 2, 2, 2, 2] => 3, 2, 3, 2, 1, 2, 2, 2, 2
[3, 2, 3, 2, 1, 2, 2, 2, 3] => 3, 2, 3, 2, 1, 2, 2, 2, 3
[3, 2, 3, 2, 1, 2, 2, 3, 1] => 3, 2, 3, 2, 1, 2, 2, 3, 1
[3, 2, 3, 2, 1, 2, 2, 3, 2] => 3, 2, 3, 2, 1, 2, 2, 3, 2
[3, 2, 3, 2, 1, 2, 2, 3, 3] => 3, 2, 3, 2, 1, 2, 2, 3, 3
[3, 2, 3, 2, 1, 2, 3, 1, 1] => 3, 2, 3, 2, 1, 2, 3, 1, 1
[3, 2, 3, 2, 1, 2, 3, 1, 2] => 3, 2, 3, 2, 1, 2, 3, 1, 2
[3, 2, 3, 2, 1, 2, 3, 1, 3] => 3, 2, 3, 2, 1, 2, 3, 1, 3
[3, 2, 3, 2, 1, 2, 3, 2, 1] => 3, 2, 3, 2, 1, 2, 3, 2, 1
[3, 2, 3, 2, 1, 2, 3, 2, 2] => 3, 2, 3, 2, 1, 2, 3, 2, 2
[3, 2, 3, 2, 1, 2, 3, 2, 3] => 3, 2, 3, 2, 1, 2, 3, 2, 3
[3, 2, 3, 2, 1, 2, 3, 3, 1] => 3, 2, 3, 2, 1, 2, 3, 3, 1
[3, 2, 3, 2, 1, 2, 3, 3, 2] => 3, 2, 3, 2, 1, 2, 3, 3, 2
[3, 2, 3, 2, 1, 2, 3, 3, 3] => 3, 2, 3, 2, 1, 2, 3, 3, 3
[3, 2, 3, 2, 1, 3, 1, 1, 1] => 3, 2, 3, 2, 1, 3, 1, 1, 1
[3, 2, 3, 2, 1, 3, 1, 1, 2] => 3, 2, 3, 2, 1, 3, 1, 1, 2
[3, 2, 3, 2, 1, 3, 1, 1, 3] => 3, 2, 3, 2, 1, 3, 1, 1, 3
[3, 2, 3, 2, 1, 3, 1, 2, 1] => 3, 2, 3, 2, 1, 3, 1, 2, 1
[3, 2, 3, 2, 1, 3, 1, 2, 2] => 3, 2, 3, 2, 1, 3, 1, 2, 2
[3, 2, 3, 2, 1, 3, 1, 2, 3] => 3, 2, 3, 2, 1, 3, 1, 2, 3
[3, 2, 3, 2, 1, 3, 1, 3, 1] => 3, 2, 3, 2, 1, 3, 1, 3, 1
[3, 2, 3, 2, 1, 3, 1, 3, 2] => 3, 2, 3, 2, 1, 3, 1, 3, 2
[3, 2, 3, 2, 1, 3, 1, 3, 3] => 3, 2, 3, 2, 1, 3, 1, 3, 3
[3, 2, 3, 2, 1, 3, 2, 1, 1] => 3, 2, 3, 2, 1, 3, 2, 1, 1
[3, 2, 3, 2, 1, 3, 2, 1, 2] => 3, 2, 3, 2, 1, 3, 2, 1, 2
[3, 2, 3, 2, 1, 3, 2, 1, 3] => 3, 2, 3, 2, 1, 3, 2, 1, 3
[3, 2, 3, 2, 1, 3, 2, 2, 1] => 3, 2, 3, 2, 1, 3, 2, 2, 1
[3, 2, 3, 2, 1, 3, 2, 2, 2] => 3, 2, 3, 2, 1, 3, 2, 2, 2
[3, 2, 3, 2, 1, 3, 2, 2, 3] => 3, 2, 3, 2, 1, 3, 2, 2, 3
[3, 2, 3, 2, 1, 3, 2, 3, 1] => 3, 2, 3, 2, 1, 3, 2, 3, 1
[3, 2, 3, 2, 1, 3, 2, 3, 2] => 3, 2, 3, 2, 1, 3, 2, 3, 2
[3, 2, 3, 2, 1, 3, 2, 3, 3] => 3, 2, 3, 2, 1, 3, 2, 3, 3
[3, 2, 3, 2, 1, 3, 3, 1, 1] => 3, 2, 3, 2, 1, 3, 3, 1, 1
[3, 2, 3, 2, 1, 3, 3, 1, 2] => 3, 2, 3, 2, 1, 3, 3, 1, 2
[3, 2, 3, 2, 1, 3, 3, 1, 3] => 3, 2, 3, 2, 1, 3, 3, 1, 3
[3, 2, 3, 2, 1, 3, 3, 2, 1] => 3, 2, 3, 2, 1, 3, 3, 2, 1
[3, 2, 3, 2, 1, 3, 3, 2, 2] => 3, 2, 3, 2, 1, 3, 3, 2, 2
[3, 2, 3, 2, 1, 3, 3, 2, 3] => 3, 2, 3, 2, 1, 3, 3, 2, 3
[3, 2, 3, 2, 1, 3, 3, 3, 1] => 3, 2, 3, 2, 1, 3, 3, 3, 1
[3, 2, 3, 2, 1, 3, 3, 3, 2] => 3, 2, 3, 2, 1, 3, 3, 3, 2
[3, 2, 3, 2, 1, 3, 3, 3, 3] => 3, 2, 3, 2, 1, 3, 3, 3, 3
[3, 2, 3, 2, 2, 1, 1, 1, 1] => 3, 2, 3, 2, 2, 1, 1, 1, 1
[3, 2, 3, 2, 2, 1, 1, 1, 2] => 3, 2, 3, 2, 2, 1, 1, 1, 2
[3, 2, 3, 2, 2, 1, 1, 1, 3] => 3, 2, 3, 2, 2, 1, 1, 1, 3
[3, 2, 3, 2, 2, 1, 1, 2, 1] => 3, 2, 3, 2, 2, 1, 1, 2, 1
[3, 2, 3, 2, 2, 1, 1, 2, 2] => 3, 2, 3, 2, 2, 1, 1, 2, 2
[3, 2, 3, 2, 2, 1, 1, 2, 3] => 3, 2, 3, 2, 2, 1, 1, 2, 3
[3, 2, 3, 2, 2, 1, 1, 3, 1] => 3, 2, 3, 2, 2, 1, 1, 3, 1
[3, 2, 3, 2, 2, 1, 1, 3, 2] => 3, 2, 3, 2, 2, 1, 1, 3, 2
[3, 2, 3, 2, 2, 1, 1, 3, 3] => 3, 2, 3, 2, 2, 1, 1, 3, 3
[3, 2, 3, 2, 2, 1, 2, 1, 1] => 3, 2, 3, 2, 2, 1, 2, 1, 1
[3, 2, 3, 2, 2, 1, 2, 1, 2] => 3, 2, 3, 2, 2, 1, 2, 1, 2
[3, 2, 3, 2, 2, 1, 2, 1, 3] => 3, 2, 3, 2, 2, 1, 2, 1, 3
[3, 2, 3, 2, 2, 1, 2, 2, 1] => 3, 2, 3, 2, 2, 1, 2, 2, 1
[3, 2, 3, 2, 2, 1, 2, 2, 2] => 3, 2, 3, 2, 2, 1, 2, 2, 2
[3, 2, 3, 2, 2, 1, 2, 2, 3] => 3, 2, 3, 2, 2, 1, 2, 2, 3
[3, 2, 3, 2, 2, 1, 2, 3, 1] => 3, 2, 3, 2, 2, 1, 2, 3, 1
[3, 2, 3, 2, 2, 1, 2, 3, 2] => 3, 2, 3, 2, 2, 1, 2, 3, 2
[3, 2, 3, 2, 2, 1, 2, 3, 3] => 3, 2, 3, 2, 2, 1, 2, 3, 3
[3, 2, 3, 2, 2, 1, 3, 1, 1] => 3, 2, 3, 2, 2, 1, 3, 1, 1
[3, 2, 3, 2, 2, 1, 3, 1, 2] => 3, 2, 3, 2, 2, 1, 3, 1, 2
[3, 2, 3, 2, 2, 1, 3, 1, 3] => 3, 2, 3, 2, 2, 1, 3, 1, 3
[3, 2, 3, 2, 2, 1, 3, 2, 1] => 3, 2, 3, 2, 2, 1, 3, 2, 1
[3, 2, 3, 2, 2, 1, 3, 2, 2] => 3, 2, 3, 2, 2, 1, 3, 2, 2
[3, 2, 3, 2, 2, 1, 3, 2, 3] => 3, 2, 3, 2, 2, 1, 3, 2, 3
[3, 2, 3, 2, 2, 1, 3, 3, 1] => 3, 2, 3, 2, 2, 1, 3, 3, 1
[3, 2, 3, 2, 2, 1, 3, 3, 2] => 3, 2, 3, 2, 2, 1, 3, 3, 2
[3, 2, 3, 2, 2, 1, 3, 3, 3] => 3, 2, 3, 2, 2, 1, 3, 3, 3
[3, 2, 3, 2, 2, 2, 1, 1, 1] => 3, 2, 3, 2, 2, 2, 1, 1, 1
[3, 2, 3, 2, 2, 2, 1, 1, 2] => 3, 2, 3, 2, 2, 2, 1, 1, 2
[3, 2, 3, 2, 2, 2, 1, 1, 3] => 3, 2, 3, 2, 2, 2, 1, 1, 3
[3, 2, 3, 2, 2, 2, 1, 2, 1] => 3, 2, 3, 2, 2, 2, 1, 2, 1
[3, 2, 3, 2, 2, 2, 1, 2, 2] => 3, 2, 3, 2, 2, 2, 1, 2, 2
[3, 2, 3, 2, 2, 2, 1, 2, 3] => 3, 2, 3, 2, 2, 2, 1, 2, 3
[3, 2, 3, 2, 2, 2, 1, 3, 1] => 3, 2, 3, 2, 2, 2, 1, 3, 1
[3, 2, 3, 2, 2, 2, 1, 3, 2] => 3, 2, 3, 2, 2, 2, 1, 3, 2
[3, 2, 3, 2, 2, 2, 1, 3, 3] => 3, 2, 3, 2, 2, 2, 1, 3, 3
[3, 2, 3, 2, 2, 2, 2, 1, 1] => 3, 2, 3, 2, 2, 2, 2, 1, 1
[3, 2, 3, 2, 2, 2, 2, 1, 2] => 3, 2, 3, 2, 2, 2, 2, 1, 2
[3, 2, 3, 2, 2, 2, 2, 1, 3] => 3, 2, 3, 2, 2, 2, 2, 1, 3
[3, 2, 3, 2, 2, 2, 2, 2, 1] => 3, 2, 3, 2, 2, 2, 2, 2, 1
[3, 2, 3, 2, 2, 2, 2, 2, 2] => 3, 2, 3, 2, 2, 2, 2, 2, 2
[3, 2, 3, 2, 2, 2, 2, 2, 3] => 3, 2, 3, 2, 2, 2, 2, 2, 3
[3, 2, 3, 2, 2, 2, 2, 3, 1] => 3, 2, 3, 2, 2, 2, 2, 3, 1
[3, 2, 3, 2, 2, 2, 2, 3, 2] => 3, 2, 3, 2, 2, 2, 2, 3, 2
[3, 2, 3, 2, 2, 2, 2, 3, 3] => 3, 2, 3, 2, 2, 2, 2, 3, 3
[3, 2, 3, 2, 2, 2, 3, 1, 1] => 3, 2, 3, 2, 2, 2, 3, 1, 1
[3, 2, 3, 2, 2, 2, 3, 1, 2] => 3, 2, 3, 2, 2, 2, 3, 1, 2
[3, 2, 3, 2, 2, 2, 3, 1, 3] => 3, 2, 3, 2, 2, 2, 3, 1, 3
[3, 2, 3, 2, 2, 2, 3, 2, 1] => 3, 2, 3, 2, 2, 2, 3, 2, 1
[3, 2, 3, 2, 2, 2, 3, 2, 2] => 3, 2, 3, 2, 2, 2, 3, 2, 2
[3, 2, 3, 2, 2, 2, 3, 2, 3] => 3, 2, 3, 2, 2, 2, 3, 2, 3
[3, 2, 3, 2, 2, 2, 3, 3, 1] => 3, 2, 3, 2, 2, 2, 3, 3, 1
[3, 2, 3, 2, 2, 2, 3, 3, 2] => 3, 2, 3, 2, 2, 2, 3, 3, 2
[3, 2, 3, 2, 2, 2, 3, 3, 3] => 3, 2, 3, 2, 2, 2, 3, 3, 3
[3, 2, 3, 2, 2, 3, 1, 1, 1] => 3, 2, 3, 2, 2, 3, 1, 1, 1
[3, 2, 3, 2, 2, 3, 1, 1, 2] => 3, 2, 3, 2, 2, 3, 1, 1, 2
[3, 2, 3, 2, 2, 3, 1, 1, 3] => 3, 2, 3, 2, 2, 3, 1, 1, 3
[3, 2, 3, 2, 2, 3, 1, 2, 1] => 3, 2, 3, 2, 2, 3, 1, 2, 1
[3, 2, 3, 2, 2, 3, 1, 2, 2] => 3, 2, 3, 2, 2, 3, 1, 2, 2
[3, 2, 3, 2, 2, 3, 1, 2, 3] => 3, 2, 3, 2, 2, 3, 1, 2, 3
[3, 2, 3, 2, 2, 3, 1, 3, 1] => 3, 2, 3, 2, 2, 3, 1, 3, 1
[3, 2, 3, 2, 2, 3, 1, 3, 2] => 3, 2, 3, 2, 2, 3, 1, 3, 2
[3, 2, 3, 2, 2, 3, 1, 3, 3] => 3, 2, 3, 2, 2, 3, 1, 3, 3
[3, 2, 3, 2, 2, 3, 2, 1, 1] => 3, 2, 3, 2, 2, 3, 2, 1, 1
[3, 2, 3, 2, 2, 3, 2, 1, 2] => 3, 2, 3, 2, 2, 3, 2, 1, 2
[3, 2, 3, 2, 2, 3, 2, 1, 3] => 3, 2, 3, 2, 2, 3, 2, 1, 3
[3, 2, 3, 2, 2, 3, 2, 2, 1] => 3, 2, 3, 2, 2, 3, 2, 2, 1
[3, 2, 3, 2, 2, 3, 2, 2, 2] => 3, 2, 3, 2, 2, 3, 2, 2, 2
[3, 2, 3, 2, 2, 3, 2, 2, 3] => 3, 2, 3, 2, 2, 3, 2, 2, 3
[3, 2, 3, 2, 2, 3, 2, 3, 1] => 3, 2, 3, 2, 2, 3, 2, 3, 1
[3, 2, 3, 2, 2, 3, 2, 3, 2] => 3, 2, 3, 2, 2, 3, 2, 3, 2
[3, 2, 3, 2, 2, 3, 2, 3, 3] => 3, 2, 3, 2, 2, 3, 2, 3, 3
[3, 2, 3, 2, 2, 3, 3, 1, 1] => 3, 2, 3, 2, 2, 3, 3, 1, 1
[3, 2, 3, 2, 2, 3, 3, 1, 2] => 3, 2, 3, 2, 2, 3, 3, 1, 2
[3, 2, 3, 2, 2, 3, 3, 1, 3] => 3, 2, 3, 2, 2, 3, 3, 1, 3
[3, 2, 3, 2, 2, 3, 3, 2, 1] => 3, 2, 3, 2, 2, 3, 3, 2, 1
[3, 2, 3, 2, 2, 3, 3, 2, 2] => 3, 2, 3, 2, 2, 3, 3, 2, 2
[3, 2, 3, 2, 2, 3, 3, 2, 3] => 3, 2, 3, 2, 2, 3, 3, 2, 3
[3, 2, 3, 2, 2, 3, 3, 3, 1] => 3, 2, 3, 2, 2, 3, 3, 3, 1
[3, 2, 3, 2, 2, 3, 3, 3, 2] => 3, 2, 3, 2, 2, 3, 3, 3, 2
[3, 2, 3, 2, 2, 3, 3, 3, 3] => 3, 2, 3, 2, 2, 3, 3, 3, 3
[3, 2, 3, 2, 3, 1, 1, 1, 1] => 3, 2, 3, 2, 3, 1, 1, 1, 1
[3, 2, 3, 2, 3, 1, 1, 1, 2] => 3, 2, 3, 2, 3, 1, 1, 1, 2
[3, 2, 3, 2, 3, 1, 1, 1, 3] => 3, 2, 3, 2, 3, 1, 1, 1, 3
[3, 2, 3, 2, 3, 1, 1, 2, 1] => 3, 2, 3, 2, 3, 1, 1, 2, 1
[3, 2, 3, 2, 3, 1, 1, 2, 2] => 3, 2, 3, 2, 3, 1, 1, 2, 2
[3, 2, 3, 2, 3, 1, 1, 2, 3] => 3, 2, 3, 2, 3, 1, 1, 2, 3
[3, 2, 3, 2, 3, 1, 1, 3, 1] => 3, 2, 3, 2, 3, 1, 1, 3, 1
[3, 2, 3, 2, 3, 1, 1, 3, 2] => 3, 2, 3, 2, 3, 1, 1, 3, 2
[3, 2, 3, 2, 3, 1, 1, 3, 3] => 3, 2, 3, 2, 3, 1, 1, 3, 3
[3, 2, 3, 2, 3, 1, 2, 1, 1] => 3, 2, 3, 2, 3, 1, 2, 1, 1
[3, 2, 3, 2, 3, 1, 2, 1, 2] => 3, 2, 3, 2, 3, 1, 2, 1, 2
[3, 2, 3, 2, 3, 1, 2, 1, 3] => 3, 2, 3, 2, 3, 1, 2, 1, 3
[3, 2, 3, 2, 3, 1, 2, 2, 1] => 3, 2, 3, 2, 3, 1, 2, 2, 1
[3, 2, 3, 2, 3, 1, 2, 2, 2] => 3, 2, 3, 2, 3, 1, 2, 2, 2
[3, 2, 3, 2, 3, 1, 2, 2, 3] => 3, 2, 3, 2, 3, 1, 2, 2, 3
[3, 2, 3, 2, 3, 1, 2, 3, 1] => 3, 2, 3, 2, 3, 1, 2, 3, 1
[3, 2, 3, 2, 3, 1, 2, 3, 2] => 3, 2, 3, 2, 3, 1, 2, 3, 2
[3, 2, 3, 2, 3, 1, 2, 3, 3] => 3, 2, 3, 2, 3, 1, 2, 3, 3
[3, 2, 3, 2, 3, 1, 3, 1, 1] => 3, 2, 3, 2, 3, 1, 3, 1, 1
[3, 2, 3, 2, 3, 1, 3, 1, 2] => 3, 2, 3, 2, 3, 1, 3, 1, 2
[3, 2, 3, 2, 3, 1, 3, 1, 3] => 3, 2, 3, 2, 3, 1, 3, 1, 3
[3, 2, 3, 2, 3, 1, 3, 2, 1] => 3, 2, 3, 2, 3, 1, 3, 2, 1
[3, 2, 3, 2, 3, 1, 3, 2, 2] => 3, 2, 3, 2, 3, 1, 3, 2, 2
[3, 2, 3, 2, 3, 1, 3, 2, 3] => 3, 2, 3, 2, 3, 1, 3, 2, 3
[3, 2, 3, 2, 3, 1, 3, 3, 1] => 3, 2, 3, 2, 3, 1, 3, 3, 1
[3, 2, 3, 2, 3, 1, 3, 3, 2] => 3, 2, 3, 2, 3, 1, 3, 3, 2
[3, 2, 3, 2, 3, 1, 3, 3, 3] => 3, 2, 3, 2, 3, 1, 3, 3, 3
[3, 2, 3, 2, 3, 2, 1, 1, 1] => 3, 2, 3, 2, 3, 2, 1, 1, 1
[3, 2, 3, 2, 3, 2, 1, 1, 2] => 3, 2, 3, 2, 3, 2, 1, 1, 2
[3, 2, 3, 2, 3, 2, 1, 1, 3] => 3, 2, 3, 2, 3, 2, 1, 1, 3
[3, 2, 3, 2, 3, 2, 1, 2, 1] => 3, 2, 3, 2, 3, 2, 1, 2, 1
[3, 2, 3, 2, 3, 2, 1, 2, 2] => 3, 2, 3, 2, 3, 2, 1, 2, 2
[3, 2, 3, 2, 3, 2, 1, 2, 3] => 3, 2, 3, 2, 3, 2, 1, 2, 3
[3, 2, 3, 2, 3, 2, 1, 3, 1] => 3, 2, 3, 2, 3, 2, 1, 3, 1
[3, 2, 3, 2, 3, 2, 1, 3, 2] => 3, 2, 3, 2, 3, 2, 1, 3, 2
[3, 2, 3, 2, 3, 2, 1, 3, 3] => 3, 2, 3, 2, 3, 2, 1, 3, 3
[3, 2, 3, 2, 3, 2, 2, 1, 1] => 3, 2, 3, 2, 3, 2, 2, 1, 1
[3, 2, 3, 2, 3, 2, 2, 1, 2] => 3, 2, 3, 2, 3, 2, 2, 1, 2
[3, 2, 3, 2, 3, 2, 2, 1, 3] => 3, 2, 3, 2, 3, 2, 2, 1, 3
[3, 2, 3, 2, 3, 2, 2, 2, 1] => 3, 2, 3, 2, 3, 2, 2, 2, 1
[3, 2, 3, 2, 3, 2, 2, 2, 2] => 3, 2, 3, 2, 3, 2, 2, 2, 2
[3, 2, 3, 2, 3, 2, 2, 2, 3] => 3, 2, 3, 2, 3, 2, 2, 2, 3
[3, 2, 3, 2, 3, 2, 2, 3, 1] => 3, 2, 3, 2, 3, 2, 2, 3, 1
[3, 2, 3, 2, 3, 2, 2, 3, 2] => 3, 2, 3, 2, 3, 2, 2, 3, 2
[3, 2, 3, 2, 3, 2, 2, 3, 3] => 3, 2, 3, 2, 3, 2, 2, 3, 3
[3, 2, 3, 2, 3, 2, 3, 1, 1] => 3, 2, 3, 2, 3, 2, 3, 1, 1
[3, 2, 3, 2, 3, 2, 3, 1, 2] => 3, 2, 3, 2, 3, 2, 3, 1, 2
[3, 2, 3, 2, 3, 2, 3, 1, 3] => 3, 2, 3, 2, 3, 2, 3, 1, 3
[3, 2, 3, 2, 3, 2, 3, 2, 1] => 3, 2, 3, 2, 3, 2, 3, 2, 1
[3, 2, 3, 2, 3, 2, 3, 2, 2] => 3, 2, 3, 2, 3, 2, 3, 2, 2
[3, 2, 3, 2, 3, 2, 3, 2, 3] => 3, 2, 3, 2, 3, 2, 3, 2, 3
[3, 2, 3, 2, 3, 2, 3, 3, 1] => 3, 2, 3, 2, 3, 2, 3, 3, 1
[3, 2, 3, 2, 3, 2, 3, 3, 2] => 3, 2, 3, 2, 3, 2, 3, 3, 2
[3, 2, 3, 2, 3, 2, 3, 3, 3] => 3, 2, 3, 2, 3, 2, 3, 3, 3
[3, 2, 3, 2, 3, 3, 1, 1, 1] => 3, 2, 3, 2, 3, 3, 1, 1, 1
[3, 2, 3, 2, 3, 3, 1, 1, 2] => 3, 2, 3, 2, 3, 3, 1, 1, 2
[3, 2, 3, 2, 3, 3, 1, 1, 3] => 3, 2, 3, 2, 3, 3, 1, 1, 3
[3, 2, 3, 2, 3, 3, 1, 2, 1] => 3, 2, 3, 2, 3, 3, 1, 2, 1
[3, 2, 3, 2, 3, 3, 1, 2, 2] => 3, 2, 3, 2, 3, 3, 1, 2, 2
[3, 2, 3, 2, 3, 3, 1, 2, 3] => 3, 2, 3, 2, 3, 3, 1, 2, 3
[3, 2, 3, 2, 3, 3, 1, 3, 1] => 3, 2, 3, 2, 3, 3, 1, 3, 1
[3, 2, 3, 2, 3, 3, 1, 3, 2] => 3, 2, 3, 2, 3, 3, 1, 3, 2
[3, 2, 3, 2, 3, 3, 1, 3, 3] => 3, 2, 3, 2, 3, 3, 1, 3, 3
[3, 2, 3, 2, 3, 3, 2, 1, 1] => 3, 2, 3, 2, 3, 3, 2, 1, 1
[3, 2, 3, 2, 3, 3, 2, 1, 2] => 3, 2, 3, 2, 3, 3, 2, 1, 2
[3, 2, 3, 2, 3, 3, 2, 1, 3] => 3, 2, 3, 2, 3, 3, 2, 1, 3
[3, 2, 3, 2, 3, 3, 2, 2, 1] => 3, 2, 3, 2, 3, 3, 2, 2, 1
[3, 2, 3, 2, 3, 3, 2, 2, 2] => 3, 2, 3, 2, 3, 3, 2, 2, 2
[3, 2, 3, 2, 3, 3, 2, 2, 3] => 3, 2, 3, 2, 3, 3, 2, 2, 3
[3, 2, 3, 2, 3, 3, 2, 3, 1] => 3, 2, 3, 2, 3, 3, 2, 3, 1
[3, 2, 3, 2, 3, 3, 2, 3, 2] => 3, 2, 3, 2, 3, 3, 2, 3, 2
[3, 2, 3, 2, 3, 3, 2, 3, 3] => 3, 2, 3, 2, 3, 3, 2, 3, 3
[3, 2, 3, 2, 3, 3, 3, 1, 1] => 3, 2, 3, 2, 3, 3, 3, 1, 1
[3, 2, 3, 2, 3, 3, 3, 1, 2] => 3, 2, 3, 2, 3, 3, 3, 1, 2
[3, 2, 3, 2, 3, 3, 3, 1, 3] => 3, 2, 3, 2, 3, 3, 3, 1, 3
[3, 2, 3, 2, 3, 3, 3, 2, 1] => 3, 2, 3, 2, 3, 3, 3, 2, 1
[3, 2, 3, 2, 3, 3, 3, 2, 2] => 3, 2, 3, 2, 3, 3, 3, 2, 2
[3, 2, 3, 2, 3, 3, 3, 2, 3] => 3, 2, 3, 2, 3, 3, 3, 2, 3
[3, 2, 3, 2, 3, 3, 3, 3, 1] => 3, 2, 3, 2, 3, 3, 3, 3, 1
[3, 2, 3, 2, 3, 3, 3, 3, 2] => 3, 2, 3, 2, 3, 3, 3, 3, 2
[3, 2, 3, 2, 3, 3, 3, 3, 3] => 3, 2, 3, 2, 3, 3, 3, 3, 3
[3, 2, 3, 3, 1, 1, 1, 1, 1] => 3, 2, 3, 3, 1, 1, 1, 1, 1
[3, 2, 3, 3, 1, 1, 1, 1, 2] => 3, 2, 3, 3, 1, 1, 1, 1, 2
[3, 2, 3, 3, 1, 1, 1, 1, 3] => 3, 2, 3, 3, 1, 1, 1, 1, 3
[3, 2, 3, 3, 1, 1, 1, 2, 1] => 3, 2, 3, 3, 1, 1, 1, 2, 1
[3, 2, 3, 3, 1, 1, 1, 2, 2] => 3, 2, 3, 3, 1, 1, 1, 2, 2
[3, 2, 3, 3, 1, 1, 1, 2, 3] => 3, 2, 3, 3, 1, 1, 1, 2, 3
[3, 2, 3, 3, 1, 1, 1, 3, 1] => 3, 2, 3, 3, 1, 1, 1, 3, 1
[3, 2, 3, 3, 1, 1, 1, 3, 2] => 3, 2, 3, 3, 1, 1, 1, 3, 2
[3, 2, 3, 3, 1, 1, 1, 3, 3] => 3, 2, 3, 3, 1, 1, 1, 3, 3
[3, 2, 3, 3, 1, 1, 2, 1, 1] => 3, 2, 3, 3, 1, 1, 2, 1, 1
[3, 2, 3, 3, 1, 1, 2, 1, 2] => 3, 2, 3, 3, 1, 1, 2, 1, 2
[3, 2, 3, 3, 1, 1, 2, 1, 3] => 3, 2, 3, 3, 1, 1, 2, 1, 3
[3, 2, 3, 3, 1, 1, 2, 2, 1] => 3, 2, 3, 3, 1, 1, 2, 2, 1
[3, 2, 3, 3, 1, 1, 2, 2, 2] => 3, 2, 3, 3, 1, 1, 2, 2, 2
[3, 2, 3, 3, 1, 1, 2, 2, 3] => 3, 2, 3, 3, 1, 1, 2, 2, 3
[3, 2, 3, 3, 1, 1, 2, 3, 1] => 3, 2, 3, 3, 1, 1, 2, 3, 1
[3, 2, 3, 3, 1, 1, 2, 3, 2] => 3, 2, 3, 3, 1, 1, 2, 3, 2
[3, 2, 3, 3, 1, 1, 2, 3, 3] => 3, 2, 3, 3, 1, 1, 2, 3, 3
[3, 2, 3, 3, 1, 1, 3, 1, 1] => 3, 2, 3, 3, 1, 1, 3, 1, 1
[3, 2, 3, 3, 1, 1, 3, 1, 2] => 3, 2, 3, 3, 1, 1, 3, 1, 2
[3, 2, 3, 3, 1, 1, 3, 1, 3] => 3, 2, 3, 3, 1, 1, 3, 1, 3
[3, 2, 3, 3, 1, 1, 3, 2, 1] => 3, 2, 3, 3, 1, 1, 3, 2, 1
[3, 2, 3, 3, 1, 1, 3, 2, 2] => 3, 2, 3, 3, 1, 1, 3, 2, 2
[3, 2, 3, 3, 1, 1, 3, 2, 3] => 3, 2, 3, 3, 1, 1, 3, 2, 3
[3, 2, 3, 3, 1, 1, 3, 3, 1] => 3, 2, 3, 3, 1, 1, 3, 3, 1
[3, 2, 3, 3, 1, 1, 3, 3, 2] => 3, 2, 3, 3, 1, 1, 3, 3, 2
[3, 2, 3, 3, 1, 1, 3, 3, 3] => 3, 2, 3, 3, 1, 1, 3, 3, 3
[3, 2, 3, 3, 1, 2, 1, 1, 1] => 3, 2, 3, 3, 1, 2, 1, 1, 1
[3, 2, 3, 3, 1, 2, 1, 1, 2] => 3, 2, 3, 3, 1, 2, 1, 1, 2
[3, 2, 3, 3, 1, 2, 1, 1, 3] => 3, 2, 3, 3, 1, 2, 1, 1, 3
[3, 2, 3, 3, 1, 2, 1, 2, 1] => 3, 2, 3, 3, 1, 2, 1, 2, 1
[3, 2, 3, 3, 1, 2, 1, 2, 2] => 3, 2, 3, 3, 1, 2, 1, 2, 2
[3, 2, 3, 3, 1, 2, 1, 2, 3] => 3, 2, 3, 3, 1, 2, 1, 2, 3
[3, 2, 3, 3, 1, 2, 1, 3, 1] => 3, 2, 3, 3, 1, 2, 1, 3, 1
[3, 2, 3, 3, 1, 2, 1, 3, 2] => 3, 2, 3, 3, 1, 2, 1, 3, 2
[3, 2, 3, 3, 1, 2, 1, 3, 3] => 3, 2, 3, 3, 1, 2, 1, 3, 3
[3, 2, 3, 3, 1, 2, 2, 1, 1] => 3, 2, 3, 3, 1, 2, 2, 1, 1
[3, 2, 3, 3, 1, 2, 2, 1, 2] => 3, 2, 3, 3, 1, 2, 2, 1, 2
[3, 2, 3, 3, 1, 2, 2, 1, 3] => 3, 2, 3, 3, 1, 2, 2, 1, 3
[3, 2, 3, 3, 1, 2, 2, 2, 1] => 3, 2, 3, 3, 1, 2, 2, 2, 1
[3, 2, 3, 3, 1, 2, 2, 2, 2] => 3, 2, 3, 3, 1, 2, 2, 2, 2
[3, 2, 3, 3, 1, 2, 2, 2, 3] => 3, 2, 3, 3, 1, 2, 2, 2, 3
[3, 2, 3, 3, 1, 2, 2, 3, 1] => 3, 2, 3, 3, 1, 2, 2, 3, 1
[3, 2, 3, 3, 1, 2, 2, 3, 2] => 3, 2, 3, 3, 1, 2, 2, 3, 2
[3, 2, 3, 3, 1, 2, 2, 3, 3] => 3, 2, 3, 3, 1, 2, 2, 3, 3
[3, 2, 3, 3, 1, 2, 3, 1, 1] => 3, 2, 3, 3, 1, 2, 3, 1, 1
[3, 2, 3, 3, 1, 2, 3, 1, 2] => 3, 2, 3, 3, 1, 2, 3, 1, 2
[3, 2, 3, 3, 1, 2, 3, 1, 3] => 3, 2, 3, 3, 1, 2, 3, 1, 3
[3, 2, 3, 3, 1, 2, 3, 2, 1] => 3, 2, 3, 3, 1, 2, 3, 2, 1
[3, 2, 3, 3, 1, 2, 3, 2, 2] => 3, 2, 3, 3, 1, 2, 3, 2, 2
[3, 2, 3, 3, 1, 2, 3, 2, 3] => 3, 2, 3, 3, 1, 2, 3, 2, 3
[3, 2, 3, 3, 1, 2, 3, 3, 1] => 3, 2, 3, 3, 1, 2, 3, 3, 1
[3, 2, 3, 3, 1, 2, 3, 3, 2] => 3, 2, 3, 3, 1, 2, 3, 3, 2
[3, 2, 3, 3, 1, 2, 3, 3, 3] => 3, 2, 3, 3, 1, 2, 3, 3, 3
[3, 2, 3, 3, 1, 3, 1, 1, 1] => 3, 2, 3, 3, 1, 3, 1, 1, 1
[3, 2, 3, 3, 1, 3, 1, 1, 2] => 3, 2, 3, 3, 1, 3, 1, 1, 2
[3, 2, 3, 3, 1, 3, 1, 1, 3] => 3, 2, 3, 3, 1, 3, 1, 1, 3
[3, 2, 3, 3, 1, 3, 1, 2, 1] => 3, 2, 3, 3, 1, 3, 1, 2, 1
[3, 2, 3, 3, 1, 3, 1, 2, 2] => 3, 2, 3, 3, 1, 3, 1, 2, 2
[3, 2, 3, 3, 1, 3, 1, 2, 3] => 3, 2, 3, 3, 1, 3, 1, 2, 3
[3, 2, 3, 3, 1, 3, 1, 3, 1] => 3, 2, 3, 3, 1, 3, 1, 3, 1
[3, 2, 3, 3, 1, 3, 1, 3, 2] => 3, 2, 3, 3, 1, 3, 1, 3, 2
[3, 2, 3, 3, 1, 3, 1, 3, 3] => 3, 2, 3, 3, 1, 3, 1, 3, 3
[3, 2, 3, 3, 1, 3, 2, 1, 1] => 3, 2, 3, 3, 1, 3, 2, 1, 1
[3, 2, 3, 3, 1, 3, 2, 1, 2] => 3, 2, 3, 3, 1, 3, 2, 1, 2
[3, 2, 3, 3, 1, 3, 2, 1, 3] => 3, 2, 3, 3, 1, 3, 2, 1, 3
[3, 2, 3, 3, 1, 3, 2, 2, 1] => 3, 2, 3, 3, 1, 3, 2, 2, 1
[3, 2, 3, 3, 1, 3, 2, 2, 2] => 3, 2, 3, 3, 1, 3, 2, 2, 2
[3, 2, 3, 3, 1, 3, 2, 2, 3] => 3, 2, 3, 3, 1, 3, 2, 2, 3
[3, 2, 3, 3, 1, 3, 2, 3, 1] => 3, 2, 3, 3, 1, 3, 2, 3, 1
[3, 2, 3, 3, 1, 3, 2, 3, 2] => 3, 2, 3, 3, 1, 3, 2, 3, 2
[3, 2, 3, 3, 1, 3, 2, 3, 3] => 3, 2, 3, 3, 1, 3, 2, 3, 3
[3, 2, 3, 3, 1, 3, 3, 1, 1] => 3, 2, 3, 3, 1, 3, 3, 1, 1
[3, 2, 3, 3, 1, 3, 3, 1, 2] => 3, 2, 3, 3, 1, 3, 3, 1, 2
[3, 2, 3, 3, 1, 3, 3, 1, 3] => 3, 2, 3, 3, 1, 3, 3, 1, 3
[3, 2, 3, 3, 1, 3, 3, 2, 1] => 3, 2, 3, 3, 1, 3, 3, 2, 1
[3, 2, 3, 3, 1, 3, 3, 2, 2] => 3, 2, 3, 3, 1, 3, 3, 2, 2
[3, 2, 3, 3, 1, 3, 3, 2, 3] => 3, 2, 3, 3, 1, 3, 3, 2, 3
[3, 2, 3, 3, 1, 3, 3, 3, 1] => 3, 2, 3, 3, 1, 3, 3, 3, 1
[3, 2, 3, 3, 1, 3, 3, 3, 2] => 3, 2, 3, 3, 1, 3, 3, 3, 2
[3, 2, 3, 3, 1, 3, 3, 3, 3] => 3, 2, 3, 3, 1, 3, 3, 3, 3
[3, 2, 3, 3, 2, 1, 1, 1, 1] => 3, 2, 3, 3, 2, 1, 1, 1, 1
[3, 2, 3, 3, 2, 1, 1, 1, 2] => 3, 2, 3, 3, 2, 1, 1, 1, 2
[3, 2, 3, 3, 2, 1, 1, 1, 3] => 3, 2, 3, 3, 2, 1, 1, 1, 3
[3, 2, 3, 3, 2, 1, 1, 2, 1] => 3, 2, 3, 3, 2, 1, 1, 2, 1
[3, 2, 3, 3, 2, 1, 1, 2, 2] => 3, 2, 3, 3, 2, 1, 1, 2, 2
[3, 2, 3, 3, 2, 1, 1, 2, 3] => 3, 2, 3, 3, 2, 1, 1, 2, 3
[3, 2, 3, 3, 2, 1, 1, 3, 1] => 3, 2, 3, 3, 2, 1, 1, 3, 1
[3, 2, 3, 3, 2, 1, 1, 3, 2] => 3, 2, 3, 3, 2, 1, 1, 3, 2
[3, 2, 3, 3, 2, 1, 1, 3, 3] => 3, 2, 3, 3, 2, 1, 1, 3, 3
[3, 2, 3, 3, 2, 1, 2, 1, 1] => 3, 2, 3, 3, 2, 1, 2, 1, 1
[3, 2, 3, 3, 2, 1, 2, 1, 2] => 3, 2, 3, 3, 2, 1, 2, 1, 2
[3, 2, 3, 3, 2, 1, 2, 1, 3] => 3, 2, 3, 3, 2, 1, 2, 1, 3
[3, 2, 3, 3, 2, 1, 2, 2, 1] => 3, 2, 3, 3, 2, 1, 2, 2, 1
[3, 2, 3, 3, 2, 1, 2, 2, 2] => 3, 2, 3, 3, 2, 1, 2, 2, 2
[3, 2, 3, 3, 2, 1, 2, 2, 3] => 3, 2, 3, 3, 2, 1, 2, 2, 3
[3, 2, 3, 3, 2, 1, 2, 3, 1] => 3, 2, 3, 3, 2, 1, 2, 3, 1
[3, 2, 3, 3, 2, 1, 2, 3, 2] => 3, 2, 3, 3, 2, 1, 2, 3, 2
[3, 2, 3, 3, 2, 1, 2, 3, 3] => 3, 2, 3, 3, 2, 1, 2, 3, 3
[3, 2, 3, 3, 2, 1, 3, 1, 1] => 3, 2, 3, 3, 2, 1, 3, 1, 1
[3, 2, 3, 3, 2, 1, 3, 1, 2] => 3, 2, 3, 3, 2, 1, 3, 1, 2
[3, 2, 3, 3, 2, 1, 3, 1, 3] => 3, 2, 3, 3, 2, 1, 3, 1, 3
[3, 2, 3, 3, 2, 1, 3, 2, 1] => 3, 2, 3, 3, 2, 1, 3, 2, 1
[3, 2, 3, 3, 2, 1, 3, 2, 2] => 3, 2, 3, 3, 2, 1, 3, 2, 2
[3, 2, 3, 3, 2, 1, 3, 2, 3] => 3, 2, 3, 3, 2, 1, 3, 2, 3
[3, 2, 3, 3, 2, 1, 3, 3, 1] => 3, 2, 3, 3, 2, 1, 3, 3, 1
[3, 2, 3, 3, 2, 1, 3, 3, 2] => 3, 2, 3, 3, 2, 1, 3, 3, 2
[3, 2, 3, 3, 2, 1, 3, 3, 3] => 3, 2, 3, 3, 2, 1, 3, 3, 3
[3, 2, 3, 3, 2, 2, 1, 1, 1] => 3, 2, 3, 3, 2, 2, 1, 1, 1
[3, 2, 3, 3, 2, 2, 1, 1, 2] => 3, 2, 3, 3, 2, 2, 1, 1, 2
[3, 2, 3, 3, 2, 2, 1, 1, 3] => 3, 2, 3, 3, 2, 2, 1, 1, 3
[3, 2, 3, 3, 2, 2, 1, 2, 1] => 3, 2, 3, 3, 2, 2, 1, 2, 1
[3, 2, 3, 3, 2, 2, 1, 2, 2] => 3, 2, 3, 3, 2, 2, 1, 2, 2
[3, 2, 3, 3, 2, 2, 1, 2, 3] => 3, 2, 3, 3, 2, 2, 1, 2, 3
[3, 2, 3, 3, 2, 2, 1, 3, 1] => 3, 2, 3, 3, 2, 2, 1, 3, 1
[3, 2, 3, 3, 2, 2, 1, 3, 2] => 3, 2, 3, 3, 2, 2, 1, 3, 2
[3, 2, 3, 3, 2, 2, 1, 3, 3] => 3, 2, 3, 3, 2, 2, 1, 3, 3
[3, 2, 3, 3, 2, 2, 2, 1, 1] => 3, 2, 3, 3, 2, 2, 2, 1, 1
[3, 2, 3, 3, 2, 2, 2, 1, 2] => 3, 2, 3, 3, 2, 2, 2, 1, 2
[3, 2, 3, 3, 2, 2, 2, 1, 3] => 3, 2, 3, 3, 2, 2, 2, 1, 3
[3, 2, 3, 3, 2, 2, 2, 2, 1] => 3, 2, 3, 3, 2, 2, 2, 2, 1
[3, 2, 3, 3, 2, 2, 2, 2, 2] => 3, 2, 3, 3, 2, 2, 2, 2, 2
[3, 2, 3, 3, 2, 2, 2, 2, 3] => 3, 2, 3, 3, 2, 2, 2, 2, 3
[3, 2, 3, 3, 2, 2, 2, 3, 1] => 3, 2, 3, 3, 2, 2, 2, 3, 1
[3, 2, 3, 3, 2, 2, 2, 3, 2] => 3, 2, 3, 3, 2, 2, 2, 3, 2
[3, 2, 3, 3, 2, 2, 2, 3, 3] => 3, 2, 3, 3, 2, 2, 2, 3, 3
[3, 2, 3, 3, 2, 2, 3, 1, 1] => 3, 2, 3, 3, 2, 2, 3, 1, 1
[3, 2, 3, 3, 2, 2, 3, 1, 2] => 3, 2, 3, 3, 2, 2, 3, 1, 2
[3, 2, 3, 3, 2, 2, 3, 1, 3] => 3, 2, 3, 3, 2, 2, 3, 1, 3
[3, 2, 3, 3, 2, 2, 3, 2, 1] => 3, 2, 3, 3, 2, 2, 3, 2, 1
[3, 2, 3, 3, 2, 2, 3, 2, 2] => 3, 2, 3, 3, 2, 2, 3, 2, 2
[3, 2, 3, 3, 2, 2, 3, 2, 3] => 3, 2, 3, 3, 2, 2, 3, 2, 3
[3, 2, 3, 3, 2, 2, 3, 3, 1] => 3, 2, 3, 3, 2, 2, 3, 3, 1
[3, 2, 3, 3, 2, 2, 3, 3, 2] => 3, 2, 3, 3, 2, 2, 3, 3, 2
[3, 2, 3, 3, 2, 2, 3, 3, 3] => 3, 2, 3, 3, 2, 2, 3, 3, 3
[3, 2, 3, 3, 2, 3, 1, 1, 1] => 3, 2, 3, 3, 2, 3, 1, 1, 1
[3, 2, 3, 3, 2, 3, 1, 1, 2] => 3, 2, 3, 3, 2, 3, 1, 1, 2
[3, 2, 3, 3, 2, 3, 1, 1, 3] => 3, 2, 3, 3, 2, 3, 1, 1, 3
[3, 2, 3, 3, 2, 3, 1, 2, 1] => 3, 2, 3, 3, 2, 3, 1, 2, 1
[3, 2, 3, 3, 2, 3, 1, 2, 2] => 3, 2, 3, 3, 2, 3, 1, 2, 2
[3, 2, 3, 3, 2, 3, 1, 2, 3] => 3, 2, 3, 3, 2, 3, 1, 2, 3
[3, 2, 3, 3, 2, 3, 1, 3, 1] => 3, 2, 3, 3, 2, 3, 1, 3, 1
[3, 2, 3, 3, 2, 3, 1, 3, 2] => 3, 2, 3, 3, 2, 3, 1, 3, 2
[3, 2, 3, 3, 2, 3, 1, 3, 3] => 3, 2, 3, 3, 2, 3, 1, 3, 3
[3, 2, 3, 3, 2, 3, 2, 1, 1] => 3, 2, 3, 3, 2, 3, 2, 1, 1
[3, 2, 3, 3, 2, 3, 2, 1, 2] => 3, 2, 3, 3, 2, 3, 2, 1, 2
[3, 2, 3, 3, 2, 3, 2, 1, 3] => 3, 2, 3, 3, 2, 3, 2, 1, 3
[3, 2, 3, 3, 2, 3, 2, 2, 1] => 3, 2, 3, 3, 2, 3, 2, 2, 1
[3, 2, 3, 3, 2, 3, 2, 2, 2] => 3, 2, 3, 3, 2, 3, 2, 2, 2
[3, 2, 3, 3, 2, 3, 2, 2, 3] => 3, 2, 3, 3, 2, 3, 2, 2, 3
[3, 2, 3, 3, 2, 3, 2, 3, 1] => 3, 2, 3, 3, 2, 3, 2, 3, 1
[3, 2, 3, 3, 2, 3, 2, 3, 2] => 3, 2, 3, 3, 2, 3, 2, 3, 2
[3, 2, 3, 3, 2, 3, 2, 3, 3] => 3, 2, 3, 3, 2, 3, 2, 3, 3
[3, 2, 3, 3, 2, 3, 3, 1, 1] => 3, 2, 3, 3, 2, 3, 3, 1, 1
[3, 2, 3, 3, 2, 3, 3, 1, 2] => 3, 2, 3, 3, 2, 3, 3, 1, 2
[3, 2, 3, 3, 2, 3, 3, 1, 3] => 3, 2, 3, 3, 2, 3, 3, 1, 3
[3, 2, 3, 3, 2, 3, 3, 2, 1] => 3, 2, 3, 3, 2, 3, 3, 2, 1
[3, 2, 3, 3, 2, 3, 3, 2, 2] => 3, 2, 3, 3, 2, 3, 3, 2, 2
[3, 2, 3, 3, 2, 3, 3, 2, 3] => 3, 2, 3, 3, 2, 3, 3, 2, 3
[3, 2, 3, 3, 2, 3, 3, 3, 1] => 3, 2, 3, 3, 2, 3, 3, 3, 1
[3, 2, 3, 3, 2, 3, 3, 3, 2] => 3, 2, 3, 3, 2, 3, 3, 3, 2
[3, 2, 3, 3, 2, 3, 3, 3, 3] => 3, 2, 3, 3, 2, 3, 3, 3, 3
[3, 2, 3, 3, 3, 1, 1, 1, 1] => 3, 2, 3, 3, 3, 1, 1, 1, 1
[3, 2, 3, 3, 3, 1, 1, 1, 2] => 3, 2, 3, 3, 3, 1, 1, 1, 2
[3, 2, 3, 3, 3, 1, 1, 1, 3] => 3, 2, 3, 3, 3, 1, 1, 1, 3
[3, 2, 3, 3, 3, 1, 1, 2, 1] => 3, 2, 3, 3, 3, 1, 1, 2, 1
[3, 2, 3, 3, 3, 1, 1, 2, 2] => 3, 2, 3, 3, 3, 1, 1, 2, 2
[3, 2, 3, 3, 3, 1, 1, 2, 3] => 3, 2, 3, 3, 3, 1, 1, 2, 3
[3, 2, 3, 3, 3, 1, 1, 3, 1] => 3, 2, 3, 3, 3, 1, 1, 3, 1
[3, 2, 3, 3, 3, 1, 1, 3, 2] => 3, 2, 3, 3, 3, 1, 1, 3, 2
[3, 2, 3, 3, 3, 1, 1, 3, 3] => 3, 2, 3, 3, 3, 1, 1, 3, 3
[3, 2, 3, 3, 3, 1, 2, 1, 1] => 3, 2, 3, 3, 3, 1, 2, 1, 1
[3, 2, 3, 3, 3, 1, 2, 1, 2] => 3, 2, 3, 3, 3, 1, 2, 1, 2
[3, 2, 3, 3, 3, 1, 2, 1, 3] => 3, 2, 3, 3, 3, 1, 2, 1, 3
[3, 2, 3, 3, 3, 1, 2, 2, 1] => 3, 2, 3, 3, 3, 1, 2, 2, 1
[3, 2, 3, 3, 3, 1, 2, 2, 2] => 3, 2, 3, 3, 3, 1, 2, 2, 2
[3, 2, 3, 3, 3, 1, 2, 2, 3] => 3, 2, 3, 3, 3, 1, 2, 2, 3
[3, 2, 3, 3, 3, 1, 2, 3, 1] => 3, 2, 3, 3, 3, 1, 2, 3, 1
[3, 2, 3, 3, 3, 1, 2, 3, 2] => 3, 2, 3, 3, 3, 1, 2, 3, 2
[3, 2, 3, 3, 3, 1, 2, 3, 3] => 3, 2, 3, 3, 3, 1, 2, 3, 3
[3, 2, 3, 3, 3, 1, 3, 1, 1] => 3, 2, 3, 3, 3, 1, 3, 1, 1
[3, 2, 3, 3, 3, 1, 3, 1, 2] => 3, 2, 3, 3, 3, 1, 3, 1, 2
[3, 2, 3, 3, 3, 1, 3, 1, 3] => 3, 2, 3, 3, 3, 1, 3, 1, 3
[3, 2, 3, 3, 3, 1, 3, 2, 1] => 3, 2, 3, 3, 3, 1, 3, 2, 1
[3, 2, 3, 3, 3, 1, 3, 2, 2] => 3, 2, 3, 3, 3, 1, 3, 2, 2
[3, 2, 3, 3, 3, 1, 3, 2, 3] => 3, 2, 3, 3, 3, 1, 3, 2, 3
[3, 2, 3, 3, 3, 1, 3, 3, 1] => 3, 2, 3, 3, 3, 1, 3, 3, 1
[3, 2, 3, 3, 3, 1, 3, 3, 2] => 3, 2, 3, 3, 3, 1, 3, 3, 2
[3, 2, 3, 3, 3, 1, 3, 3, 3] => 3, 2, 3, 3, 3, 1, 3, 3, 3
[3, 2, 3, 3, 3, 2, 1, 1, 1] => 3, 2, 3, 3, 3, 2, 1, 1, 1
[3, 2, 3, 3, 3, 2, 1, 1, 2] => 3, 2, 3, 3, 3, 2, 1, 1, 2
[3, 2, 3, 3, 3, 2, 1, 1, 3] => 3, 2, 3, 3, 3, 2, 1, 1, 3
[3, 2, 3, 3, 3, 2, 1, 2, 1] => 3, 2, 3, 3, 3, 2, 1, 2, 1
[3, 2, 3, 3, 3, 2, 1, 2, 2] => 3, 2, 3, 3, 3, 2, 1, 2, 2
[3, 2, 3, 3, 3, 2, 1, 2, 3] => 3, 2, 3, 3, 3, 2, 1, 2, 3
[3, 2, 3, 3, 3, 2, 1, 3, 1] => 3, 2, 3, 3, 3, 2, 1, 3, 1
[3, 2, 3, 3, 3, 2, 1, 3, 2] => 3, 2, 3, 3, 3, 2, 1, 3, 2
[3, 2, 3, 3, 3, 2, 1, 3, 3] => 3, 2, 3, 3, 3, 2, 1, 3, 3
[3, 2, 3, 3, 3, 2, 2, 1, 1] => 3, 2, 3, 3, 3, 2, 2, 1, 1
[3, 2, 3, 3, 3, 2, 2, 1, 2] => 3, 2, 3, 3, 3, 2, 2, 1, 2
[3, 2, 3, 3, 3, 2, 2, 1, 3] => 3, 2, 3, 3, 3, 2, 2, 1, 3
[3, 2, 3, 3, 3, 2, 2, 2, 1] => 3, 2, 3, 3, 3, 2, 2, 2, 1
[3, 2, 3, 3, 3, 2, 2, 2, 2] => 3, 2, 3, 3, 3, 2, 2, 2, 2
[3, 2, 3, 3, 3, 2, 2, 2, 3] => 3, 2, 3, 3, 3, 2, 2, 2, 3
[3, 2, 3, 3, 3, 2, 2, 3, 1] => 3, 2, 3, 3, 3, 2, 2, 3, 1
[3, 2, 3, 3, 3, 2, 2, 3, 2] => 3, 2, 3, 3, 3, 2, 2, 3, 2
[3, 2, 3, 3, 3, 2, 2, 3, 3] => 3, 2, 3, 3, 3, 2, 2, 3, 3
[3, 2, 3, 3, 3, 2, 3, 1, 1] => 3, 2, 3, 3, 3, 2, 3, 1, 1
[3, 2, 3, 3, 3, 2, 3, 1, 2] => 3, 2, 3, 3, 3, 2, 3, 1, 2
[3, 2, 3, 3, 3, 2, 3, 1, 3] => 3, 2, 3, 3, 3, 2, 3, 1, 3
[3, 2, 3, 3, 3, 2, 3, 2, 1] => 3, 2, 3, 3, 3, 2, 3, 2, 1
[3, 2, 3, 3, 3, 2, 3, 2, 2] => 3, 2, 3, 3, 3, 2, 3, 2, 2
[3, 2, 3, 3, 3, 2, 3, 2, 3] => 3, 2, 3, 3, 3, 2, 3, 2, 3
[3, 2, 3, 3, 3, 2, 3, 3, 1] => 3, 2, 3, 3, 3, 2, 3, 3, 1
[3, 2, 3, 3, 3, 2, 3, 3, 2] => 3, 2, 3, 3, 3, 2, 3, 3, 2
[3, 2, 3, 3, 3, 2, 3, 3, 3] => 3, 2, 3, 3, 3, 2, 3, 3, 3
[3, 2, 3, 3, 3, 3, 1, 1, 1] => 3, 2, 3, 3, 3, 3, 1, 1, 1
[3, 2, 3, 3, 3, 3, 1, 1, 2] => 3, 2, 3, 3, 3, 3, 1, 1, 2
[3, 2, 3, 3, 3, 3, 1, 1, 3] => 3, 2, 3, 3, 3, 3, 1, 1, 3
[3, 2, 3, 3, 3, 3, 1, 2, 1] => 3, 2, 3, 3, 3, 3, 1, 2, 1
[3, 2, 3, 3, 3, 3, 1, 2, 2] => 3, 2, 3, 3, 3, 3, 1, 2, 2
[3, 2, 3, 3, 3, 3, 1, 2, 3] => 3, 2, 3, 3, 3, 3, 1, 2, 3
[3, 2, 3, 3, 3, 3, 1, 3, 1] => 3, 2, 3, 3, 3, 3, 1, 3, 1
[3, 2, 3, 3, 3, 3, 1, 3, 2] => 3, 2, 3, 3, 3, 3, 1, 3, 2
[3, 2, 3, 3, 3, 3, 1, 3, 3] => 3, 2, 3, 3, 3, 3, 1, 3, 3
[3, 2, 3, 3, 3, 3, 2, 1, 1] => 3, 2, 3, 3, 3, 3, 2, 1, 1
[3, 2, 3, 3, 3, 3, 2, 1, 2] => 3, 2, 3, 3, 3, 3, 2, 1, 2
[3, 2, 3, 3, 3, 3, 2, 1, 3] => 3, 2, 3, 3, 3, 3, 2, 1, 3
[3, 2, 3, 3, 3, 3, 2, 2, 1] => 3, 2, 3, 3, 3, 3, 2, 2, 1
[3, 2, 3, 3, 3, 3, 2, 2, 2] => 3, 2, 3, 3, 3, 3, 2, 2, 2
[3, 2, 3, 3, 3, 3, 2, 2, 3] => 3, 2, 3, 3, 3, 3, 2, 2, 3
[3, 2, 3, 3, 3, 3, 2, 3, 1] => 3, 2, 3, 3, 3, 3, 2, 3, 1
[3, 2, 3, 3, 3, 3, 2, 3, 2] => 3, 2, 3, 3, 3, 3, 2, 3, 2
[3, 2, 3, 3, 3, 3, 2, 3, 3] => 3, 2, 3, 3, 3, 3, 2, 3, 3
[3, 2, 3, 3, 3, 3, 3, 1, 1] => 3, 2, 3, 3, 3, 3, 3, 1, 1
[3, 2, 3, 3, 3, 3, 3, 1, 2] => 3, 2, 3, 3, 3, 3, 3, 1, 2
[3, 2, 3, 3, 3, 3, 3, 1, 3] => 3, 2, 3, 3, 3, 3, 3, 1, 3
[3, 2, 3, 3, 3, 3, 3, 2, 1] => 3, 2, 3, 3, 3, 3, 3, 2, 1
[3, 2, 3, 3, 3, 3, 3, 2, 2] => 3, 2, 3, 3, 3, 3, 3, 2, 2
[3, 2, 3, 3, 3, 3, 3, 2, 3] => 3, 2, 3, 3, 3, 3, 3, 2, 3
[3, 2, 3, 3, 3, 3, 3, 3, 1] => 3, 2, 3, 3, 3, 3, 3, 3, 1
[3, 2, 3, 3, 3, 3, 3, 3, 2] => 3, 2, 3, 3, 3, 3, 3, 3, 2
[3, 2, 3, 3, 3, 3, 3, 3, 3] => 3, 2, 3, 3, 3, 3, 3, 3, 3
[3, 3, 1, 1, 1, 1, 1, 1, 1] => 3, 3, 1, 1, 1, 1, 1, 1, 1
[3, 3, 1, 1, 1, 1, 1, 1, 2] => 3, 3, 1, 1, 1, 1, 1, 1, 2
[3, 3, 1, 1, 1, 1, 1, 1, 3] => 3, 3, 1, 1, 1, 1, 1, 1, 3
[3, 3, 1, 1, 1, 1, 1, 2, 1] => 3, 3, 1, 1, 1, 1, 1, 2, 1
[3, 3, 1, 1, 1, 1, 1, 2, 2] => 3, 3, 1, 1, 1, 1, 1, 2, 2
[3, 3, 1, 1, 1, 1, 1, 2, 3] => 3, 3, 1, 1, 1, 1, 1, 2, 3
[3, 3, 1, 1, 1, 1, 1, 3, 1] => 3, 3, 1, 1, 1, 1, 1, 3, 1
[3, 3, 1, 1, 1, 1, 1, 3, 2] => 3, 3, 1, 1, 1, 1, 1, 3, 2
[3, 3, 1, 1, 1, 1, 1, 3, 3] => 3, 3, 1, 1, 1, 1, 1, 3, 3
[3, 3, 1, 1, 1, 1, 2, 1, 1] => 3, 3, 1, 1, 1, 1, 2, 1, 1
[3, 3, 1, 1, 1, 1, 2, 1, 2] => 3, 3, 1, 1, 1, 1, 2, 1, 2
[3, 3, 1, 1, 1, 1, 2, 1, 3] => 3, 3, 1, 1, 1, 1, 2, 1, 3
[3, 3, 1, 1, 1, 1, 2, 2, 1] => 3, 3, 1, 1, 1, 1, 2, 2, 1
[3, 3, 1, 1, 1, 1, 2, 2, 2] => 3, 3, 1, 1, 1, 1, 2, 2, 2
[3, 3, 1, 1, 1, 1, 2, 2, 3] => 3, 3, 1, 1, 1, 1, 2, 2, 3
[3, 3, 1, 1, 1, 1, 2, 3, 1] => 3, 3, 1, 1, 1, 1, 2, 3, 1
[3, 3, 1, 1, 1, 1, 2, 3, 2] => 3, 3, 1, 1, 1, 1, 2, 3, 2
[3, 3, 1, 1, 1, 1, 2, 3, 3] => 3, 3, 1, 1, 1, 1, 2, 3, 3
[3, 3, 1, 1, 1, 1, 3, 1, 1] => 3, 3, 1, 1, 1, 1, 3, 1, 1
[3, 3, 1, 1, 1, 1, 3, 1, 2] => 3, 3, 1, 1, 1, 1, 3, 1, 2
[3, 3, 1, 1, 1, 1, 3, 1, 3] => 3, 3, 1, 1, 1, 1, 3, 1, 3
[3, 3, 1, 1, 1, 1, 3, 2, 1] => 3, 3, 1, 1, 1, 1, 3, 2, 1
[3, 3, 1, 1, 1, 1, 3, 2, 2] => 3, 3, 1, 1, 1, 1, 3, 2, 2
[3, 3, 1, 1, 1, 1, 3, 2, 3] => 3, 3, 1, 1, 1, 1, 3, 2, 3
[3, 3, 1, 1, 1, 1, 3, 3, 1] => 3, 3, 1, 1, 1, 1, 3, 3, 1
[3, 3, 1, 1, 1, 1, 3, 3, 2] => 3, 3, 1, 1, 1, 1, 3, 3, 2
[3, 3, 1, 1, 1, 1, 3, 3, 3] => 3, 3, 1, 1, 1, 1, 3, 3, 3
[3, 3, 1, 1, 1, 2, 1, 1, 1] => 3, 3, 1, 1, 1, 2, 1, 1, 1
[3, 3, 1, 1, 1, 2, 1, 1, 2] => 3, 3, 1, 1, 1, 2, 1, 1, 2
[3, 3, 1, 1, 1, 2, 1, 1, 3] => 3, 3, 1, 1, 1, 2, 1, 1, 3
[3, 3, 1, 1, 1, 2, 1, 2, 1] => 3, 3, 1, 1, 1, 2, 1, 2, 1
[3, 3, 1, 1, 1, 2, 1, 2, 2] => 3, 3, 1, 1, 1, 2, 1, 2, 2
[3, 3, 1, 1, 1, 2, 1, 2, 3] => 3, 3, 1, 1, 1, 2, 1, 2, 3
[3, 3, 1, 1, 1, 2, 1, 3, 1] => 3, 3, 1, 1, 1, 2, 1, 3, 1
[3, 3, 1, 1, 1, 2, 1, 3, 2] => 3, 3, 1, 1, 1, 2, 1, 3, 2
[3, 3, 1, 1, 1, 2, 1, 3, 3] => 3, 3, 1, 1, 1, 2, 1, 3, 3
[3, 3, 1, 1, 1, 2, 2, 1, 1] => 3, 3, 1, 1, 1, 2, 2, 1, 1
[3, 3, 1, 1, 1, 2, 2, 1, 2] => 3, 3, 1, 1, 1, 2, 2, 1, 2
[3, 3, 1, 1, 1, 2, 2, 1, 3] => 3, 3, 1, 1, 1, 2, 2, 1, 3
[3, 3, 1, 1, 1, 2, 2, 2, 1] => 3, 3, 1, 1, 1, 2, 2, 2, 1
[3, 3, 1, 1, 1, 2, 2, 2, 2] => 3, 3, 1, 1, 1, 2, 2, 2, 2
[3, 3, 1, 1, 1, 2, 2, 2, 3] => 3, 3, 1, 1, 1, 2, 2, 2, 3
[3, 3, 1, 1, 1, 2, 2, 3, 1] => 3, 3, 1, 1, 1, 2, 2, 3, 1
[3, 3, 1, 1, 1, 2, 2, 3, 2] => 3, 3, 1, 1, 1, 2, 2, 3, 2
[3, 3, 1, 1, 1, 2, 2, 3, 3] => 3, 3, 1, 1, 1, 2, 2, 3, 3
[3, 3, 1, 1, 1, 2, 3, 1, 1] => 3, 3, 1, 1, 1, 2, 3, 1, 1
[3, 3, 1, 1, 1, 2, 3, 1, 2] => 3, 3, 1, 1, 1, 2, 3, 1, 2
[3, 3, 1, 1, 1, 2, 3, 1, 3] => 3, 3, 1, 1, 1, 2, 3, 1, 3
[3, 3, 1, 1, 1, 2, 3, 2, 1] => 3, 3, 1, 1, 1, 2, 3, 2, 1
[3, 3, 1, 1, 1, 2, 3, 2, 2] => 3, 3, 1, 1, 1, 2, 3, 2, 2
[3, 3, 1, 1, 1, 2, 3, 2, 3] => 3, 3, 1, 1, 1, 2, 3, 2, 3
[3, 3, 1, 1, 1, 2, 3, 3, 1] => 3, 3, 1, 1, 1, 2, 3, 3, 1
[3, 3, 1, 1, 1, 2, 3, 3, 2] => 3, 3, 1, 1, 1, 2, 3, 3, 2
[3, 3, 1, 1, 1, 2, 3, 3, 3] => 3, 3, 1, 1, 1, 2, 3, 3, 3
[3, 3, 1, 1, 1, 3, 1, 1, 1] => 3, 3, 1, 1, 1, 3, 1, 1, 1
[3, 3, 1, 1, 1, 3, 1, 1, 2] => 3, 3, 1, 1, 1, 3, 1, 1, 2
[3, 3, 1, 1, 1, 3, 1, 1, 3] => 3, 3, 1, 1, 1, 3, 1, 1, 3
[3, 3, 1, 1, 1, 3, 1, 2, 1] => 3, 3, 1, 1, 1, 3, 1, 2, 1
[3, 3, 1, 1, 1, 3, 1, 2, 2] => 3, 3, 1, 1, 1, 3, 1, 2, 2
[3, 3, 1, 1, 1, 3, 1, 2, 3] => 3, 3, 1, 1, 1, 3, 1, 2, 3
[3, 3, 1, 1, 1, 3, 1, 3, 1] => 3, 3, 1, 1, 1, 3, 1, 3, 1
[3, 3, 1, 1, 1, 3, 1, 3, 2] => 3, 3, 1, 1, 1, 3, 1, 3, 2
[3, 3, 1, 1, 1, 3, 1, 3, 3] => 3, 3, 1, 1, 1, 3, 1, 3, 3
[3, 3, 1, 1, 1, 3, 2, 1, 1] => 3, 3, 1, 1, 1, 3, 2, 1, 1
[3, 3, 1, 1, 1, 3, 2, 1, 2] => 3, 3, 1, 1, 1, 3, 2, 1, 2
[3, 3, 1, 1, 1, 3, 2, 1, 3] => 3, 3, 1, 1, 1, 3, 2, 1, 3
[3, 3, 1, 1, 1, 3, 2, 2, 1] => 3, 3, 1, 1, 1, 3, 2, 2, 1
[3, 3, 1, 1, 1, 3, 2, 2, 2] => 3, 3, 1, 1, 1, 3, 2, 2, 2
[3, 3, 1, 1, 1, 3, 2, 2, 3] => 3, 3, 1, 1, 1, 3, 2, 2, 3
[3, 3, 1, 1, 1, 3, 2, 3, 1] => 3, 3, 1, 1, 1, 3, 2, 3, 1
[3, 3, 1, 1, 1, 3, 2, 3, 2] => 3, 3, 1, 1, 1, 3, 2, 3, 2
[3, 3, 1, 1, 1, 3, 2, 3, 3] => 3, 3, 1, 1, 1, 3, 2, 3, 3
[3, 3, 1, 1, 1, 3, 3, 1, 1] => 3, 3, 1, 1, 1, 3, 3, 1, 1
[3, 3, 1, 1, 1, 3, 3, 1, 2] => 3, 3, 1, 1, 1, 3, 3, 1, 2
[3, 3, 1, 1, 1, 3, 3, 1, 3] => 3, 3, 1, 1, 1, 3, 3, 1, 3
[3, 3, 1, 1, 1, 3, 3, 2, 1] => 3, 3, 1, 1, 1, 3, 3, 2, 1
[3, 3, 1, 1, 1, 3, 3, 2, 2] => 3, 3, 1, 1, 1, 3, 3, 2, 2
[3, 3, 1, 1, 1, 3, 3, 2, 3] => 3, 3, 1, 1, 1, 3, 3, 2, 3
[3, 3, 1, 1, 1, 3, 3, 3, 1] => 3, 3, 1, 1, 1, 3, 3, 3, 1
[3, 3, 1, 1, 1, 3, 3, 3, 2] => 3, 3, 1, 1, 1, 3, 3, 3, 2
[3, 3, 1, 1, 1, 3, 3, 3, 3] => 3, 3, 1, 1, 1, 3, 3, 3, 3
[3, 3, 1, 1, 2, 1, 1, 1, 1] => 3, 3, 1, 1, 2, 1, 1, 1, 1
[3, 3, 1, 1, 2, 1, 1, 1, 2] => 3, 3, 1, 1, 2, 1, 1, 1, 2
[3, 3, 1, 1, 2, 1, 1, 1, 3] => 3, 3, 1, 1, 2, 1, 1, 1, 3
[3, 3, 1, 1, 2, 1, 1, 2, 1] => 3, 3, 1, 1, 2, 1, 1, 2, 1
[3, 3, 1, 1, 2, 1, 1, 2, 2] => 3, 3, 1, 1, 2, 1, 1, 2, 2
[3, 3, 1, 1, 2, 1, 1, 2, 3] => 3, 3, 1, 1, 2, 1, 1, 2, 3
[3, 3, 1, 1, 2, 1, 1, 3, 1] => 3, 3, 1, 1, 2, 1, 1, 3, 1
[3, 3, 1, 1, 2, 1, 1, 3, 2] => 3, 3, 1, 1, 2, 1, 1, 3, 2
[3, 3, 1, 1, 2, 1, 1, 3, 3] => 3, 3, 1, 1, 2, 1, 1, 3, 3
[3, 3, 1, 1, 2, 1, 2, 1, 1] => 3, 3, 1, 1, 2, 1, 2, 1, 1
[3, 3, 1, 1, 2, 1, 2, 1, 2] => 3, 3, 1, 1, 2, 1, 2, 1, 2
[3, 3, 1, 1, 2, 1, 2, 1, 3] => 3, 3, 1, 1, 2, 1, 2, 1, 3
[3, 3, 1, 1, 2, 1, 2, 2, 1] => 3, 3, 1, 1, 2, 1, 2, 2, 1
[3, 3, 1, 1, 2, 1, 2, 2, 2] => 3, 3, 1, 1, 2, 1, 2, 2, 2
[3, 3, 1, 1, 2, 1, 2, 2, 3] => 3, 3, 1, 1, 2, 1, 2, 2, 3
[3, 3, 1, 1, 2, 1, 2, 3, 1] => 3, 3, 1, 1, 2, 1, 2, 3, 1
[3, 3, 1, 1, 2, 1, 2, 3, 2] => 3, 3, 1, 1, 2, 1, 2, 3, 2
[3, 3, 1, 1, 2, 1, 2, 3, 3] => 3, 3, 1, 1, 2, 1, 2, 3, 3
[3, 3, 1, 1, 2, 1, 3, 1, 1] => 3, 3, 1, 1, 2, 1, 3, 1, 1
[3, 3, 1, 1, 2, 1, 3, 1, 2] => 3, 3, 1, 1, 2, 1, 3, 1, 2
[3, 3, 1, 1, 2, 1, 3, 1, 3] => 3, 3, 1, 1, 2, 1, 3, 1, 3
[3, 3, 1, 1, 2, 1, 3, 2, 1] => 3, 3, 1, 1, 2, 1, 3, 2, 1
[3, 3, 1, 1, 2, 1, 3, 2, 2] => 3, 3, 1, 1, 2, 1, 3, 2, 2
[3, 3, 1, 1, 2, 1, 3, 2, 3] => 3, 3, 1, 1, 2, 1, 3, 2, 3
[3, 3, 1, 1, 2, 1, 3, 3, 1] => 3, 3, 1, 1, 2, 1, 3, 3, 1
[3, 3, 1, 1, 2, 1, 3, 3, 2] => 3, 3, 1, 1, 2, 1, 3, 3, 2
[3, 3, 1, 1, 2, 1, 3, 3, 3] => 3, 3, 1, 1, 2, 1, 3, 3, 3
[3, 3, 1, 1, 2, 2, 1, 1, 1] => 3, 3, 1, 1, 2, 2, 1, 1, 1
[3, 3, 1, 1, 2, 2, 1, 1, 2] => 3, 3, 1, 1, 2, 2, 1, 1, 2
[3, 3, 1, 1, 2, 2, 1, 1, 3] => 3, 3, 1, 1, 2, 2, 1, 1, 3
[3, 3, 1, 1, 2, 2, 1, 2, 1] => 3, 3, 1, 1, 2, 2, 1, 2, 1
[3, 3, 1, 1, 2, 2, 1, 2, 2] => 3, 3, 1, 1, 2, 2, 1, 2, 2
[3, 3, 1, 1, 2, 2, 1, 2, 3] => 3, 3, 1, 1, 2, 2, 1, 2, 3
[3, 3, 1, 1, 2, 2, 1, 3, 1] => 3, 3, 1, 1, 2, 2, 1, 3, 1
[3, 3, 1, 1, 2, 2, 1, 3, 2] => 3, 3, 1, 1, 2, 2, 1, 3, 2
[3, 3, 1, 1, 2, 2, 1, 3, 3] => 3, 3, 1, 1, 2, 2, 1, 3, 3
[3, 3, 1, 1, 2, 2, 2, 1, 1] => 3, 3, 1, 1, 2, 2, 2, 1, 1
[3, 3, 1, 1, 2, 2, 2, 1, 2] => 3, 3, 1, 1, 2, 2, 2, 1, 2
[3, 3, 1, 1, 2, 2, 2, 1, 3] => 3, 3, 1, 1, 2, 2, 2, 1, 3
[3, 3, 1, 1, 2, 2, 2, 2, 1] => 3, 3, 1, 1, 2, 2, 2, 2, 1
[3, 3, 1, 1, 2, 2, 2, 2, 2] => 3, 3, 1, 1, 2, 2, 2, 2, 2
[3, 3, 1, 1, 2, 2, 2, 2, 3] => 3, 3, 1, 1, 2, 2, 2, 2, 3
[3, 3, 1, 1, 2, 2, 2, 3, 1] => 3, 3, 1, 1, 2, 2, 2, 3, 1
[3, 3, 1, 1, 2, 2, 2, 3, 2] => 3, 3, 1, 1, 2, 2, 2, 3, 2
[3, 3, 1, 1, 2, 2, 2, 3, 3] => 3, 3, 1, 1, 2, 2, 2, 3, 3
[3, 3, 1, 1, 2, 2, 3, 1, 1] => 3, 3, 1, 1, 2, 2, 3, 1, 1
[3, 3, 1, 1, 2, 2, 3, 1, 2] => 3, 3, 1, 1, 2, 2, 3, 1, 2
[3, 3, 1, 1, 2, 2, 3, 1, 3] => 3, 3, 1, 1, 2, 2, 3, 1, 3
[3, 3, 1, 1, 2, 2, 3, 2, 1] => 3, 3, 1, 1, 2, 2, 3, 2, 1
[3, 3, 1, 1, 2, 2, 3, 2, 2] => 3, 3, 1, 1, 2, 2, 3, 2, 2
[3, 3, 1, 1, 2, 2, 3, 2, 3] => 3, 3, 1, 1, 2, 2, 3, 2, 3
[3, 3, 1, 1, 2, 2, 3, 3, 1] => 3, 3, 1, 1, 2, 2, 3, 3, 1
[3, 3, 1, 1, 2, 2, 3, 3, 2] => 3, 3, 1, 1, 2, 2, 3, 3, 2
[3, 3, 1, 1, 2, 2, 3, 3, 3] => 3, 3, 1, 1, 2, 2, 3, 3, 3
[3, 3, 1, 1, 2, 3, 1, 1, 1] => 3, 3, 1, 1, 2, 3, 1, 1, 1
[3, 3, 1, 1, 2, 3, 1, 1, 2] => 3, 3, 1, 1, 2, 3, 1, 1, 2
[3, 3, 1, 1, 2, 3, 1, 1, 3] => 3, 3, 1, 1, 2, 3, 1, 1, 3
[3, 3, 1, 1, 2, 3, 1, 2, 1] => 3, 3, 1, 1, 2, 3, 1, 2, 1
[3, 3, 1, 1, 2, 3, 1, 2, 2] => 3, 3, 1, 1, 2, 3, 1, 2, 2
[3, 3, 1, 1, 2, 3, 1, 2, 3] => 3, 3, 1, 1, 2, 3, 1, 2, 3
[3, 3, 1, 1, 2, 3, 1, 3, 1] => 3, 3, 1, 1, 2, 3, 1, 3, 1
[3, 3, 1, 1, 2, 3, 1, 3, 2] => 3, 3, 1, 1, 2, 3, 1, 3, 2
[3, 3, 1, 1, 2, 3, 1, 3, 3] => 3, 3, 1, 1, 2, 3, 1, 3, 3
[3, 3, 1, 1, 2, 3, 2, 1, 1] => 3, 3, 1, 1, 2, 3, 2, 1, 1
[3, 3, 1, 1, 2, 3, 2, 1, 2] => 3, 3, 1, 1, 2, 3, 2, 1, 2
[3, 3, 1, 1, 2, 3, 2, 1, 3] => 3, 3, 1, 1, 2, 3, 2, 1, 3
[3, 3, 1, 1, 2, 3, 2, 2, 1] => 3, 3, 1, 1, 2, 3, 2, 2, 1
[3, 3, 1, 1, 2, 3, 2, 2, 2] => 3, 3, 1, 1, 2, 3, 2, 2, 2
[3, 3, 1, 1, 2, 3, 2, 2, 3] => 3, 3, 1, 1, 2, 3, 2, 2, 3
[3, 3, 1, 1, 2, 3, 2, 3, 1] => 3, 3, 1, 1, 2, 3, 2, 3, 1
[3, 3, 1, 1, 2, 3, 2, 3, 2] => 3, 3, 1, 1, 2, 3, 2, 3, 2
[3, 3, 1, 1, 2, 3, 2, 3, 3] => 3, 3, 1, 1, 2, 3, 2, 3, 3
[3, 3, 1, 1, 2, 3, 3, 1, 1] => 3, 3, 1, 1, 2, 3, 3, 1, 1
[3, 3, 1, 1, 2, 3, 3, 1, 2] => 3, 3, 1, 1, 2, 3, 3, 1, 2
[3, 3, 1, 1, 2, 3, 3, 1, 3] => 3, 3, 1, 1, 2, 3, 3, 1, 3
[3, 3, 1, 1, 2, 3, 3, 2, 1] => 3, 3, 1, 1, 2, 3, 3, 2, 1
[3, 3, 1, 1, 2, 3, 3, 2, 2] => 3, 3, 1, 1, 2, 3, 3, 2, 2
[3, 3, 1, 1, 2, 3, 3, 2, 3] => 3, 3, 1, 1, 2, 3, 3, 2, 3
[3, 3, 1, 1, 2, 3, 3, 3, 1] => 3, 3, 1, 1, 2, 3, 3, 3, 1
[3, 3, 1, 1, 2, 3, 3, 3, 2] => 3, 3, 1, 1, 2, 3, 3, 3, 2
[3, 3, 1, 1, 2, 3, 3, 3, 3] => 3, 3, 1, 1, 2, 3, 3, 3, 3
[3, 3, 1, 1, 3, 1, 1, 1, 1] => 3, 3, 1, 1, 3, 1, 1, 1, 1
[3, 3, 1, 1, 3, 1, 1, 1, 2] => 3, 3, 1, 1, 3, 1, 1, 1, 2
[3, 3, 1, 1, 3, 1, 1, 1, 3] => 3, 3, 1, 1, 3, 1, 1, 1, 3
[3, 3, 1, 1, 3, 1, 1, 2, 1] => 3, 3, 1, 1, 3, 1, 1, 2, 1
[3, 3, 1, 1, 3, 1, 1, 2, 2] => 3, 3, 1, 1, 3, 1, 1, 2, 2
[3, 3, 1, 1, 3, 1, 1, 2, 3] => 3, 3, 1, 1, 3, 1, 1, 2, 3
[3, 3, 1, 1, 3, 1, 1, 3, 1] => 3, 3, 1, 1, 3, 1, 1, 3, 1
[3, 3, 1, 1, 3, 1, 1, 3, 2] => 3, 3, 1, 1, 3, 1, 1, 3, 2
[3, 3, 1, 1, 3, 1, 1, 3, 3] => 3, 3, 1, 1, 3, 1, 1, 3, 3
[3, 3, 1, 1, 3, 1, 2, 1, 1] => 3, 3, 1, 1, 3, 1, 2, 1, 1
[3, 3, 1, 1, 3, 1, 2, 1, 2] => 3, 3, 1, 1, 3, 1, 2, 1, 2
[3, 3, 1, 1, 3, 1, 2, 1, 3] => 3, 3, 1, 1, 3, 1, 2, 1, 3
[3, 3, 1, 1, 3, 1, 2, 2, 1] => 3, 3, 1, 1, 3, 1, 2, 2, 1
[3, 3, 1, 1, 3, 1, 2, 2, 2] => 3, 3, 1, 1, 3, 1, 2, 2, 2
[3, 3, 1, 1, 3, 1, 2, 2, 3] => 3, 3, 1, 1, 3, 1, 2, 2, 3
[3, 3, 1, 1, 3, 1, 2, 3, 1] => 3, 3, 1, 1, 3, 1, 2, 3, 1
[3, 3, 1, 1, 3, 1, 2, 3, 2] => 3, 3, 1, 1, 3, 1, 2, 3, 2
[3, 3, 1, 1, 3, 1, 2, 3, 3] => 3, 3, 1, 1, 3, 1, 2, 3, 3
[3, 3, 1, 1, 3, 1, 3, 1, 1] => 3, 3, 1, 1, 3, 1, 3, 1, 1
[3, 3, 1, 1, 3, 1, 3, 1, 2] => 3, 3, 1, 1, 3, 1, 3, 1, 2
[3, 3, 1, 1, 3, 1, 3, 1, 3] => 3, 3, 1, 1, 3, 1, 3, 1, 3
[3, 3, 1, 1, 3, 1, 3, 2, 1] => 3, 3, 1, 1, 3, 1, 3, 2, 1
[3, 3, 1, 1, 3, 1, 3, 2, 2] => 3, 3, 1, 1, 3, 1, 3, 2, 2
[3, 3, 1, 1, 3, 1, 3, 2, 3] => 3, 3, 1, 1, 3, 1, 3, 2, 3
[3, 3, 1, 1, 3, 1, 3, 3, 1] => 3, 3, 1, 1, 3, 1, 3, 3, 1
[3, 3, 1, 1, 3, 1, 3, 3, 2] => 3, 3, 1, 1, 3, 1, 3, 3, 2
[3, 3, 1, 1, 3, 1, 3, 3, 3] => 3, 3, 1, 1, 3, 1, 3, 3, 3
[3, 3, 1, 1, 3, 2, 1, 1, 1] => 3, 3, 1, 1, 3, 2, 1, 1, 1
[3, 3, 1, 1, 3, 2, 1, 1, 2] => 3, 3, 1, 1, 3, 2, 1, 1, 2
[3, 3, 1, 1, 3, 2, 1, 1, 3] => 3, 3, 1, 1, 3, 2, 1, 1, 3
[3, 3, 1, 1, 3, 2, 1, 2, 1] => 3, 3, 1, 1, 3, 2, 1, 2, 1
[3, 3, 1, 1, 3, 2, 1, 2, 2] => 3, 3, 1, 1, 3, 2, 1, 2, 2
[3, 3, 1, 1, 3, 2, 1, 2, 3] => 3, 3, 1, 1, 3, 2, 1, 2, 3
[3, 3, 1, 1, 3, 2, 1, 3, 1] => 3, 3, 1, 1, 3, 2, 1, 3, 1
[3, 3, 1, 1, 3, 2, 1, 3, 2] => 3, 3, 1, 1, 3, 2, 1, 3, 2
[3, 3, 1, 1, 3, 2, 1, 3, 3] => 3, 3, 1, 1, 3, 2, 1, 3, 3
[3, 3, 1, 1, 3, 2, 2, 1, 1] => 3, 3, 1, 1, 3, 2, 2, 1, 1
[3, 3, 1, 1, 3, 2, 2, 1, 2] => 3, 3, 1, 1, 3, 2, 2, 1, 2
[3, 3, 1, 1, 3, 2, 2, 1, 3] => 3, 3, 1, 1, 3, 2, 2, 1, 3
[3, 3, 1, 1, 3, 2, 2, 2, 1] => 3, 3, 1, 1, 3, 2, 2, 2, 1
[3, 3, 1, 1, 3, 2, 2, 2, 2] => 3, 3, 1, 1, 3, 2, 2, 2, 2
[3, 3, 1, 1, 3, 2, 2, 2, 3] => 3, 3, 1, 1, 3, 2, 2, 2, 3
[3, 3, 1, 1, 3, 2, 2, 3, 1] => 3, 3, 1, 1, 3, 2, 2, 3, 1
[3, 3, 1, 1, 3, 2, 2, 3, 2] => 3, 3, 1, 1, 3, 2, 2, 3, 2
[3, 3, 1, 1, 3, 2, 2, 3, 3] => 3, 3, 1, 1, 3, 2, 2, 3, 3
[3, 3, 1, 1, 3, 2, 3, 1, 1] => 3, 3, 1, 1, 3, 2, 3, 1, 1
[3, 3, 1, 1, 3, 2, 3, 1, 2] => 3, 3, 1, 1, 3, 2, 3, 1, 2
[3, 3, 1, 1, 3, 2, 3, 1, 3] => 3, 3, 1, 1, 3, 2, 3, 1, 3
[3, 3, 1, 1, 3, 2, 3, 2, 1] => 3, 3, 1, 1, 3, 2, 3, 2, 1
[3, 3, 1, 1, 3, 2, 3, 2, 2] => 3, 3, 1, 1, 3, 2, 3, 2, 2
[3, 3, 1, 1, 3, 2, 3, 2, 3] => 3, 3, 1, 1, 3, 2, 3, 2, 3
[3, 3, 1, 1, 3, 2, 3, 3, 1] => 3, 3, 1, 1, 3, 2, 3, 3, 1
[3, 3, 1, 1, 3, 2, 3, 3, 2] => 3, 3, 1, 1, 3, 2, 3, 3, 2
[3, 3, 1, 1, 3, 2, 3, 3, 3] => 3, 3, 1, 1, 3, 2, 3, 3, 3
[3, 3, 1, 1, 3, 3, 1, 1, 1] => 3, 3, 1, 1, 3, 3, 1, 1, 1
[3, 3, 1, 1, 3, 3, 1, 1, 2] => 3, 3, 1, 1, 3, 3, 1, 1, 2
[3, 3, 1, 1, 3, 3, 1, 1, 3] => 3, 3, 1, 1, 3, 3, 1, 1, 3
[3, 3, 1, 1, 3, 3, 1, 2, 1] => 3, 3, 1, 1, 3, 3, 1, 2, 1
[3, 3, 1, 1, 3, 3, 1, 2, 2] => 3, 3, 1, 1, 3, 3, 1, 2, 2
[3, 3, 1, 1, 3, 3, 1, 2, 3] => 3, 3, 1, 1, 3, 3, 1, 2, 3
[3, 3, 1, 1, 3, 3, 1, 3, 1] => 3, 3, 1, 1, 3, 3, 1, 3, 1
[3, 3, 1, 1, 3, 3, 1, 3, 2] => 3, 3, 1, 1, 3, 3, 1, 3, 2
[3, 3, 1, 1, 3, 3, 1, 3, 3] => 3, 3, 1, 1, 3, 3, 1, 3, 3
[3, 3, 1, 1, 3, 3, 2, 1, 1] => 3, 3, 1, 1, 3, 3, 2, 1, 1
[3, 3, 1, 1, 3, 3, 2, 1, 2] => 3, 3, 1, 1, 3, 3, 2, 1, 2
[3, 3, 1, 1, 3, 3, 2, 1, 3] => 3, 3, 1, 1, 3, 3, 2, 1, 3
[3, 3, 1, 1, 3, 3, 2, 2, 1] => 3, 3, 1, 1, 3, 3, 2, 2, 1
[3, 3, 1, 1, 3, 3, 2, 2, 2] => 3, 3, 1, 1, 3, 3, 2, 2, 2
[3, 3, 1, 1, 3, 3, 2, 2, 3] => 3, 3, 1, 1, 3, 3, 2, 2, 3
[3, 3, 1, 1, 3, 3, 2, 3, 1] => 3, 3, 1, 1, 3, 3, 2, 3, 1
[3, 3, 1, 1, 3, 3, 2, 3, 2] => 3, 3, 1, 1, 3, 3, 2, 3, 2
[3, 3, 1, 1, 3, 3, 2, 3, 3] => 3, 3, 1, 1, 3, 3, 2, 3, 3
[3, 3, 1, 1, 3, 3, 3, 1, 1] => 3, 3, 1, 1, 3, 3, 3, 1, 1
[3, 3, 1, 1, 3, 3, 3, 1, 2] => 3, 3, 1, 1, 3, 3, 3, 1, 2
[3, 3, 1, 1, 3, 3, 3, 1, 3] => 3, 3, 1, 1, 3, 3, 3, 1, 3
[3, 3, 1, 1, 3, 3, 3, 2, 1] => 3, 3, 1, 1, 3, 3, 3, 2, 1
[3, 3, 1, 1, 3, 3, 3, 2, 2] => 3, 3, 1, 1, 3, 3, 3, 2, 2
[3, 3, 1, 1, 3, 3, 3, 2, 3] => 3, 3, 1, 1, 3, 3, 3, 2, 3
[3, 3, 1, 1, 3, 3, 3, 3, 1] => 3, 3, 1, 1, 3, 3, 3, 3, 1
[3, 3, 1, 1, 3, 3, 3, 3, 2] => 3, 3, 1, 1, 3, 3, 3, 3, 2
[3, 3, 1, 1, 3, 3, 3, 3, 3] => 3, 3, 1, 1, 3, 3, 3, 3, 3
[3, 3, 1, 2, 1, 1, 1, 1, 1] => 3, 3, 1, 2, 1, 1, 1, 1, 1
[3, 3, 1, 2, 1, 1, 1, 1, 2] => 3, 3, 1, 2, 1, 1, 1, 1, 2
[3, 3, 1, 2, 1, 1, 1, 1, 3] => 3, 3, 1, 2, 1, 1, 1, 1, 3
[3, 3, 1, 2, 1, 1, 1, 2, 1] => 3, 3, 1, 2, 1, 1, 1, 2, 1
[3, 3, 1, 2, 1, 1, 1, 2, 2] => 3, 3, 1, 2, 1, 1, 1, 2, 2
[3, 3, 1, 2, 1, 1, 1, 2, 3] => 3, 3, 1, 2, 1, 1, 1, 2, 3
[3, 3, 1, 2, 1, 1, 1, 3, 1] => 3, 3, 1, 2, 1, 1, 1, 3, 1
[3, 3, 1, 2, 1, 1, 1, 3, 2] => 3, 3, 1, 2, 1, 1, 1, 3, 2
[3, 3, 1, 2, 1, 1, 1, 3, 3] => 3, 3, 1, 2, 1, 1, 1, 3, 3
[3, 3, 1, 2, 1, 1, 2, 1, 1] => 3, 3, 1, 2, 1, 1, 2, 1, 1
[3, 3, 1, 2, 1, 1, 2, 1, 2] => 3, 3, 1, 2, 1, 1, 2, 1, 2
[3, 3, 1, 2, 1, 1, 2, 1, 3] => 3, 3, 1, 2, 1, 1, 2, 1, 3
[3, 3, 1, 2, 1, 1, 2, 2, 1] => 3, 3, 1, 2, 1, 1, 2, 2, 1
[3, 3, 1, 2, 1, 1, 2, 2, 2] => 3, 3, 1, 2, 1, 1, 2, 2, 2
[3, 3, 1, 2, 1, 1, 2, 2, 3] => 3, 3, 1, 2, 1, 1, 2, 2, 3
[3, 3, 1, 2, 1, 1, 2, 3, 1] => 3, 3, 1, 2, 1, 1, 2, 3, 1
[3, 3, 1, 2, 1, 1, 2, 3, 2] => 3, 3, 1, 2, 1, 1, 2, 3, 2
[3, 3, 1, 2, 1, 1, 2, 3, 3] => 3, 3, 1, 2, 1, 1, 2, 3, 3
[3, 3, 1, 2, 1, 1, 3, 1, 1] => 3, 3, 1, 2, 1, 1, 3, 1, 1
[3, 3, 1, 2, 1, 1, 3, 1, 2] => 3, 3, 1, 2, 1, 1, 3, 1, 2
[3, 3, 1, 2, 1, 1, 3, 1, 3] => 3, 3, 1, 2, 1, 1, 3, 1, 3
[3, 3, 1, 2, 1, 1, 3, 2, 1] => 3, 3, 1, 2, 1, 1, 3, 2, 1
[3, 3, 1, 2, 1, 1, 3, 2, 2] => 3, 3, 1, 2, 1, 1, 3, 2, 2
[3, 3, 1, 2, 1, 1, 3, 2, 3] => 3, 3, 1, 2, 1, 1, 3, 2, 3
[3, 3, 1, 2, 1, 1, 3, 3, 1] => 3, 3, 1, 2, 1, 1, 3, 3, 1
[3, 3, 1, 2, 1, 1, 3, 3, 2] => 3, 3, 1, 2, 1, 1, 3, 3, 2
[3, 3, 1, 2, 1, 1, 3, 3, 3] => 3, 3, 1, 2, 1, 1, 3, 3, 3
[3, 3, 1, 2, 1, 2, 1, 1, 1] => 3, 3, 1, 2, 1, 2, 1, 1, 1
[3, 3, 1, 2, 1, 2, 1, 1, 2] => 3, 3, 1, 2, 1, 2, 1, 1, 2
[3, 3, 1, 2, 1, 2, 1, 1, 3] => 3, 3, 1, 2, 1, 2, 1, 1, 3
[3, 3, 1, 2, 1, 2, 1, 2, 1] => 3, 3, 1, 2, 1, 2, 1, 2, 1
[3, 3, 1, 2, 1, 2, 1, 2, 2] => 3, 3, 1, 2, 1, 2, 1, 2, 2
[3, 3, 1, 2, 1, 2, 1, 2, 3] => 3, 3, 1, 2, 1, 2, 1, 2, 3
[3, 3, 1, 2, 1, 2, 1, 3, 1] => 3, 3, 1, 2, 1, 2, 1, 3, 1
[3, 3, 1, 2, 1, 2, 1, 3, 2] => 3, 3, 1, 2, 1, 2, 1, 3, 2
[3, 3, 1, 2, 1, 2, 1, 3, 3] => 3, 3, 1, 2, 1, 2, 1, 3, 3
[3, 3, 1, 2, 1, 2, 2, 1, 1] => 3, 3, 1, 2, 1, 2, 2, 1, 1
[3, 3, 1, 2, 1, 2, 2, 1, 2] => 3, 3, 1, 2, 1, 2, 2, 1, 2
[3, 3, 1, 2, 1, 2, 2, 1, 3] => 3, 3, 1, 2, 1, 2, 2, 1, 3
[3, 3, 1, 2, 1, 2, 2, 2, 1] => 3, 3, 1, 2, 1, 2, 2, 2, 1
[3, 3, 1, 2, 1, 2, 2, 2, 2] => 3, 3, 1, 2, 1, 2, 2, 2, 2
[3, 3, 1, 2, 1, 2, 2, 2, 3] => 3, 3, 1, 2, 1, 2, 2, 2, 3
[3, 3, 1, 2, 1, 2, 2, 3, 1] => 3, 3, 1, 2, 1, 2, 2, 3, 1
[3, 3, 1, 2, 1, 2, 2, 3, 2] => 3, 3, 1, 2, 1, 2, 2, 3, 2
[3, 3, 1, 2, 1, 2, 2, 3, 3] => 3, 3, 1, 2, 1, 2, 2, 3, 3
[3, 3, 1, 2, 1, 2, 3, 1, 1] => 3, 3, 1, 2, 1, 2, 3, 1, 1
[3, 3, 1, 2, 1, 2, 3, 1, 2] => 3, 3, 1, 2, 1, 2, 3, 1, 2
[3, 3, 1, 2, 1, 2, 3, 1, 3] => 3, 3, 1, 2, 1, 2, 3, 1, 3
[3, 3, 1, 2, 1, 2, 3, 2, 1] => 3, 3, 1, 2, 1, 2, 3, 2, 1
[3, 3, 1, 2, 1, 2, 3, 2, 2] => 3, 3, 1, 2, 1, 2, 3, 2, 2
[3, 3, 1, 2, 1, 2, 3, 2, 3] => 3, 3, 1, 2, 1, 2, 3, 2, 3
[3, 3, 1, 2, 1, 2, 3, 3, 1] => 3, 3, 1, 2, 1, 2, 3, 3, 1
[3, 3, 1, 2, 1, 2, 3, 3, 2] => 3, 3, 1, 2, 1, 2, 3, 3, 2
[3, 3, 1, 2, 1, 2, 3, 3, 3] => 3, 3, 1, 2, 1, 2, 3, 3, 3
[3, 3, 1, 2, 1, 3, 1, 1, 1] => 3, 3, 1, 2, 1, 3, 1, 1, 1
[3, 3, 1, 2, 1, 3, 1, 1, 2] => 3, 3, 1, 2, 1, 3, 1, 1, 2
[3, 3, 1, 2, 1, 3, 1, 1, 3] => 3, 3, 1, 2, 1, 3, 1, 1, 3
[3, 3, 1, 2, 1, 3, 1, 2, 1] => 3, 3, 1, 2, 1, 3, 1, 2, 1
[3, 3, 1, 2, 1, 3, 1, 2, 2] => 3, 3, 1, 2, 1, 3, 1, 2, 2
[3, 3, 1, 2, 1, 3, 1, 2, 3] => 3, 3, 1, 2, 1, 3, 1, 2, 3
[3, 3, 1, 2, 1, 3, 1, 3, 1] => 3, 3, 1, 2, 1, 3, 1, 3, 1
[3, 3, 1, 2, 1, 3, 1, 3, 2] => 3, 3, 1, 2, 1, 3, 1, 3, 2
[3, 3, 1, 2, 1, 3, 1, 3, 3] => 3, 3, 1, 2, 1, 3, 1, 3, 3
[3, 3, 1, 2, 1, 3, 2, 1, 1] => 3, 3, 1, 2, 1, 3, 2, 1, 1
[3, 3, 1, 2, 1, 3, 2, 1, 2] => 3, 3, 1, 2, 1, 3, 2, 1, 2
[3, 3, 1, 2, 1, 3, 2, 1, 3] => 3, 3, 1, 2, 1, 3, 2, 1, 3
[3, 3, 1, 2, 1, 3, 2, 2, 1] => 3, 3, 1, 2, 1, 3, 2, 2, 1
[3, 3, 1, 2, 1, 3, 2, 2, 2] => 3, 3, 1, 2, 1, 3, 2, 2, 2
[3, 3, 1, 2, 1, 3, 2, 2, 3] => 3, 3, 1, 2, 1, 3, 2, 2, 3
[3, 3, 1, 2, 1, 3, 2, 3, 1] => 3, 3, 1, 2, 1, 3, 2, 3, 1
[3, 3, 1, 2, 1, 3, 2, 3, 2] => 3, 3, 1, 2, 1, 3, 2, 3, 2
[3, 3, 1, 2, 1, 3, 2, 3, 3] => 3, 3, 1, 2, 1, 3, 2, 3, 3
[3, 3, 1, 2, 1, 3, 3, 1, 1] => 3, 3, 1, 2, 1, 3, 3, 1, 1
[3, 3, 1, 2, 1, 3, 3, 1, 2] => 3, 3, 1, 2, 1, 3, 3, 1, 2
[3, 3, 1, 2, 1, 3, 3, 1, 3] => 3, 3, 1, 2, 1, 3, 3, 1, 3
[3, 3, 1, 2, 1, 3, 3, 2, 1] => 3, 3, 1, 2, 1, 3, 3, 2, 1
[3, 3, 1, 2, 1, 3, 3, 2, 2] => 3, 3, 1, 2, 1, 3, 3, 2, 2
[3, 3, 1, 2, 1, 3, 3, 2, 3] => 3, 3, 1, 2, 1, 3, 3, 2, 3
[3, 3, 1, 2, 1, 3, 3, 3, 1] => 3, 3, 1, 2, 1, 3, 3, 3, 1
[3, 3, 1, 2, 1, 3, 3, 3, 2] => 3, 3, 1, 2, 1, 3, 3, 3, 2
[3, 3, 1, 2, 1, 3, 3, 3, 3] => 3, 3, 1, 2, 1, 3, 3, 3, 3
[3, 3, 1, 2, 2, 1, 1, 1, 1] => 3, 3, 1, 2, 2, 1, 1, 1, 1
[3, 3, 1, 2, 2, 1, 1, 1, 2] => 3, 3, 1, 2, 2, 1, 1, 1, 2
[3, 3, 1, 2, 2, 1, 1, 1, 3] => 3, 3, 1, 2, 2, 1, 1, 1, 3
[3, 3, 1, 2, 2, 1, 1, 2, 1] => 3, 3, 1, 2, 2, 1, 1, 2, 1
[3, 3, 1, 2, 2, 1, 1, 2, 2] => 3, 3, 1, 2, 2, 1, 1, 2, 2
[3, 3, 1, 2, 2, 1, 1, 2, 3] => 3, 3, 1, 2, 2, 1, 1, 2, 3
[3, 3, 1, 2, 2, 1, 1, 3, 1] => 3, 3, 1, 2, 2, 1, 1, 3, 1
[3, 3, 1, 2, 2, 1, 1, 3, 2] => 3, 3, 1, 2, 2, 1, 1, 3, 2
[3, 3, 1, 2, 2, 1, 1, 3, 3] => 3, 3, 1, 2, 2, 1, 1, 3, 3
[3, 3, 1, 2, 2, 1, 2, 1, 1] => 3, 3, 1, 2, 2, 1, 2, 1, 1
[3, 3, 1, 2, 2, 1, 2, 1, 2] => 3, 3, 1, 2, 2, 1, 2, 1, 2
[3, 3, 1, 2, 2, 1, 2, 1, 3] => 3, 3, 1, 2, 2, 1, 2, 1, 3
[3, 3, 1, 2, 2, 1, 2, 2, 1] => 3, 3, 1, 2, 2, 1, 2, 2, 1
[3, 3, 1, 2, 2, 1, 2, 2, 2] => 3, 3, 1, 2, 2, 1, 2, 2, 2
[3, 3, 1, 2, 2, 1, 2, 2, 3] => 3, 3, 1, 2, 2, 1, 2, 2, 3
[3, 3, 1, 2, 2, 1, 2, 3, 1] => 3, 3, 1, 2, 2, 1, 2, 3, 1
[3, 3, 1, 2, 2, 1, 2, 3, 2] => 3, 3, 1, 2, 2, 1, 2, 3, 2
[3, 3, 1, 2, 2, 1, 2, 3, 3] => 3, 3, 1, 2, 2, 1, 2, 3, 3
[3, 3, 1, 2, 2, 1, 3, 1, 1] => 3, 3, 1, 2, 2, 1, 3, 1, 1
[3, 3, 1, 2, 2, 1, 3, 1, 2] => 3, 3, 1, 2, 2, 1, 3, 1, 2
[3, 3, 1, 2, 2, 1, 3, 1, 3] => 3, 3, 1, 2, 2, 1, 3, 1, 3
[3, 3, 1, 2, 2, 1, 3, 2, 1] => 3, 3, 1, 2, 2, 1, 3, 2, 1
[3, 3, 1, 2, 2, 1, 3, 2, 2] => 3, 3, 1, 2, 2, 1, 3, 2, 2
[3, 3, 1, 2, 2, 1, 3, 2, 3] => 3, 3, 1, 2, 2, 1, 3, 2, 3
[3, 3, 1, 2, 2, 1, 3, 3, 1] => 3, 3, 1, 2, 2, 1, 3, 3, 1
[3, 3, 1, 2, 2, 1, 3, 3, 2] => 3, 3, 1, 2, 2, 1, 3, 3, 2
[3, 3, 1, 2, 2, 1, 3, 3, 3] => 3, 3, 1, 2, 2, 1, 3, 3, 3
[3, 3, 1, 2, 2, 2, 1, 1, 1] => 3, 3, 1, 2, 2, 2, 1, 1, 1
[3, 3, 1, 2, 2, 2, 1, 1, 2] => 3, 3, 1, 2, 2, 2, 1, 1, 2
[3, 3, 1, 2, 2, 2, 1, 1, 3] => 3, 3, 1, 2, 2, 2, 1, 1, 3
[3, 3, 1, 2, 2, 2, 1, 2, 1] => 3, 3, 1, 2, 2, 2, 1, 2, 1
[3, 3, 1, 2, 2, 2, 1, 2, 2] => 3, 3, 1, 2, 2, 2, 1, 2, 2
[3, 3, 1, 2, 2, 2, 1, 2, 3] => 3, 3, 1, 2, 2, 2, 1, 2, 3
[3, 3, 1, 2, 2, 2, 1, 3, 1] => 3, 3, 1, 2, 2, 2, 1, 3, 1
[3, 3, 1, 2, 2, 2, 1, 3, 2] => 3, 3, 1, 2, 2, 2, 1, 3, 2
[3, 3, 1, 2, 2, 2, 1, 3, 3] => 3, 3, 1, 2, 2, 2, 1, 3, 3
[3, 3, 1, 2, 2, 2, 2, 1, 1] => 3, 3, 1, 2, 2, 2, 2, 1, 1
[3, 3, 1, 2, 2, 2, 2, 1, 2] => 3, 3, 1, 2, 2, 2, 2, 1, 2
[3, 3, 1, 2, 2, 2, 2, 1, 3] => 3, 3, 1, 2, 2, 2, 2, 1, 3
[3, 3, 1, 2, 2, 2, 2, 2, 1] => 3, 3, 1, 2, 2, 2, 2, 2, 1
[3, 3, 1, 2, 2, 2, 2, 2, 2] => 3, 3, 1, 2, 2, 2, 2, 2, 2
[3, 3, 1, 2, 2, 2, 2, 2, 3] => 3, 3, 1, 2, 2, 2, 2, 2, 3
[3, 3, 1, 2, 2, 2, 2, 3, 1] => 3, 3, 1, 2, 2, 2, 2, 3, 1
[3, 3, 1, 2, 2, 2, 2, 3, 2] => 3, 3, 1, 2, 2, 2, 2, 3, 2
[3, 3, 1, 2, 2, 2, 2, 3, 3] => 3, 3, 1, 2, 2, 2, 2, 3, 3
[3, 3, 1, 2, 2, 2, 3, 1, 1] => 3, 3, 1, 2, 2, 2, 3, 1, 1
[3, 3, 1, 2, 2, 2, 3, 1, 2] => 3, 3, 1, 2, 2, 2, 3, 1, 2
[3, 3, 1, 2, 2, 2, 3, 1, 3] => 3, 3, 1, 2, 2, 2, 3, 1, 3
[3, 3, 1, 2, 2, 2, 3, 2, 1] => 3, 3, 1, 2, 2, 2, 3, 2, 1
[3, 3, 1, 2, 2, 2, 3, 2, 2] => 3, 3, 1, 2, 2, 2, 3, 2, 2
[3, 3, 1, 2, 2, 2, 3, 2, 3] => 3, 3, 1, 2, 2, 2, 3, 2, 3
[3, 3, 1, 2, 2, 2, 3, 3, 1] => 3, 3, 1, 2, 2, 2, 3, 3, 1
[3, 3, 1, 2, 2, 2, 3, 3, 2] => 3, 3, 1, 2, 2, 2, 3, 3, 2
[3, 3, 1, 2, 2, 2, 3, 3, 3] => 3, 3, 1, 2, 2, 2, 3, 3, 3
[3, 3, 1, 2, 2, 3, 1, 1, 1] => 3, 3, 1, 2, 2, 3, 1, 1, 1
[3, 3, 1, 2, 2, 3, 1, 1, 2] => 3, 3, 1, 2, 2, 3, 1, 1, 2
[3, 3, 1, 2, 2, 3, 1, 1, 3] => 3, 3, 1, 2, 2, 3, 1, 1, 3
[3, 3, 1, 2, 2, 3, 1, 2, 1] => 3, 3, 1, 2, 2, 3, 1, 2, 1
[3, 3, 1, 2, 2, 3, 1, 2, 2] => 3, 3, 1, 2, 2, 3, 1, 2, 2
[3, 3, 1, 2, 2, 3, 1, 2, 3] => 3, 3, 1, 2, 2, 3, 1, 2, 3
[3, 3, 1, 2, 2, 3, 1, 3, 1] => 3, 3, 1, 2, 2, 3, 1, 3, 1
[3, 3, 1, 2, 2, 3, 1, 3, 2] => 3, 3, 1, 2, 2, 3, 1, 3, 2
[3, 3, 1, 2, 2, 3, 1, 3, 3] => 3, 3, 1, 2, 2, 3, 1, 3, 3
[3, 3, 1, 2, 2, 3, 2, 1, 1] => 3, 3, 1, 2, 2, 3, 2, 1, 1
[3, 3, 1, 2, 2, 3, 2, 1, 2] => 3, 3, 1, 2, 2, 3, 2, 1, 2
[3, 3, 1, 2, 2, 3, 2, 1, 3] => 3, 3, 1, 2, 2, 3, 2, 1, 3
[3, 3, 1, 2, 2, 3, 2, 2, 1] => 3, 3, 1, 2, 2, 3, 2, 2, 1
[3, 3, 1, 2, 2, 3, 2, 2, 2] => 3, 3, 1, 2, 2, 3, 2, 2, 2
[3, 3, 1, 2, 2, 3, 2, 2, 3] => 3, 3, 1, 2, 2, 3, 2, 2, 3
[3, 3, 1, 2, 2, 3, 2, 3, 1] => 3, 3, 1, 2, 2, 3, 2, 3, 1
[3, 3, 1, 2, 2, 3, 2, 3, 2] => 3, 3, 1, 2, 2, 3, 2, 3, 2
[3, 3, 1, 2, 2, 3, 2, 3, 3] => 3, 3, 1, 2, 2, 3, 2, 3, 3
[3, 3, 1, 2, 2, 3, 3, 1, 1] => 3, 3, 1, 2, 2, 3, 3, 1, 1
[3, 3, 1, 2, 2, 3, 3, 1, 2] => 3, 3, 1, 2, 2, 3, 3, 1, 2
[3, 3, 1, 2, 2, 3, 3, 1, 3] => 3, 3, 1, 2, 2, 3, 3, 1, 3
[3, 3, 1, 2, 2, 3, 3, 2, 1] => 3, 3, 1, 2, 2, 3, 3, 2, 1
[3, 3, 1, 2, 2, 3, 3, 2, 2] => 3, 3, 1, 2, 2, 3, 3, 2, 2
[3, 3, 1, 2, 2, 3, 3, 2, 3] => 3, 3, 1, 2, 2, 3, 3, 2, 3
[3, 3, 1, 2, 2, 3, 3, 3, 1] => 3, 3, 1, 2, 2, 3, 3, 3, 1
[3, 3, 1, 2, 2, 3, 3, 3, 2] => 3, 3, 1, 2, 2, 3, 3, 3, 2
[3, 3, 1, 2, 2, 3, 3, 3, 3] => 3, 3, 1, 2, 2, 3, 3, 3, 3
[3, 3, 1, 2, 3, 1, 1, 1, 1] => 3, 3, 1, 2, 3, 1, 1, 1, 1
[3, 3, 1, 2, 3, 1, 1, 1, 2] => 3, 3, 1, 2, 3, 1, 1, 1, 2
[3, 3, 1, 2, 3, 1, 1, 1, 3] => 3, 3, 1, 2, 3, 1, 1, 1, 3
[3, 3, 1, 2, 3, 1, 1, 2, 1] => 3, 3, 1, 2, 3, 1, 1, 2, 1
[3, 3, 1, 2, 3, 1, 1, 2, 2] => 3, 3, 1, 2, 3, 1, 1, 2, 2
[3, 3, 1, 2, 3, 1, 1, 2, 3] => 3, 3, 1, 2, 3, 1, 1, 2, 3
[3, 3, 1, 2, 3, 1, 1, 3, 1] => 3, 3, 1, 2, 3, 1, 1, 3, 1
[3, 3, 1, 2, 3, 1, 1, 3, 2] => 3, 3, 1, 2, 3, 1, 1, 3, 2
[3, 3, 1, 2, 3, 1, 1, 3, 3] => 3, 3, 1, 2, 3, 1, 1, 3, 3
[3, 3, 1, 2, 3, 1, 2, 1, 1] => 3, 3, 1, 2, 3, 1, 2, 1, 1
[3, 3, 1, 2, 3, 1, 2, 1, 2] => 3, 3, 1, 2, 3, 1, 2, 1, 2
[3, 3, 1, 2, 3, 1, 2, 1, 3] => 3, 3, 1, 2, 3, 1, 2, 1, 3
[3, 3, 1, 2, 3, 1, 2, 2, 1] => 3, 3, 1, 2, 3, 1, 2, 2, 1
[3, 3, 1, 2, 3, 1, 2, 2, 2] => 3, 3, 1, 2, 3, 1, 2, 2, 2
[3, 3, 1, 2, 3, 1, 2, 2, 3] => 3, 3, 1, 2, 3, 1, 2, 2, 3
[3, 3, 1, 2, 3, 1, 2, 3, 1] => 3, 3, 1, 2, 3, 1, 2, 3, 1
[3, 3, 1, 2, 3, 1, 2, 3, 2] => 3, 3, 1, 2, 3, 1, 2, 3, 2
[3, 3, 1, 2, 3, 1, 2, 3, 3] => 3, 3, 1, 2, 3, 1, 2, 3, 3
[3, 3, 1, 2, 3, 1, 3, 1, 1] => 3, 3, 1, 2, 3, 1, 3, 1, 1
[3, 3, 1, 2, 3, 1, 3, 1, 2] => 3, 3, 1, 2, 3, 1, 3, 1, 2
[3, 3, 1, 2, 3, 1, 3, 1, 3] => 3, 3, 1, 2, 3, 1, 3, 1, 3
[3, 3, 1, 2, 3, 1, 3, 2, 1] => 3, 3, 1, 2, 3, 1, 3, 2, 1
[3, 3, 1, 2, 3, 1, 3, 2, 2] => 3, 3, 1, 2, 3, 1, 3, 2, 2
[3, 3, 1, 2, 3, 1, 3, 2, 3] => 3, 3, 1, 2, 3, 1, 3, 2, 3
[3, 3, 1, 2, 3, 1, 3, 3, 1] => 3, 3, 1, 2, 3, 1, 3, 3, 1
[3, 3, 1, 2, 3, 1, 3, 3, 2] => 3, 3, 1, 2, 3, 1, 3, 3, 2
[3, 3, 1, 2, 3, 1, 3, 3, 3] => 3, 3, 1, 2, 3, 1, 3, 3, 3
[3, 3, 1, 2, 3, 2, 1, 1, 1] => 3, 3, 1, 2, 3, 2, 1, 1, 1
[3, 3, 1, 2, 3, 2, 1, 1, 2] => 3, 3, 1, 2, 3, 2, 1, 1, 2
[3, 3, 1, 2, 3, 2, 1, 1, 3] => 3, 3, 1, 2, 3, 2, 1, 1, 3
[3, 3, 1, 2, 3, 2, 1, 2, 1] => 3, 3, 1, 2, 3, 2, 1, 2, 1
[3, 3, 1, 2, 3, 2, 1, 2, 2] => 3, 3, 1, 2, 3, 2, 1, 2, 2
[3, 3, 1, 2, 3, 2, 1, 2, 3] => 3, 3, 1, 2, 3, 2, 1, 2, 3
[3, 3, 1, 2, 3, 2, 1, 3, 1] => 3, 3, 1, 2, 3, 2, 1, 3, 1
[3, 3, 1, 2, 3, 2, 1, 3, 2] => 3, 3, 1, 2, 3, 2, 1, 3, 2
[3, 3, 1, 2, 3, 2, 1, 3, 3] => 3, 3, 1, 2, 3, 2, 1, 3, 3
[3, 3, 1, 2, 3, 2, 2, 1, 1] => 3, 3, 1, 2, 3, 2, 2, 1, 1
[3, 3, 1, 2, 3, 2, 2, 1, 2] => 3, 3, 1, 2, 3, 2, 2, 1, 2
[3, 3, 1, 2, 3, 2, 2, 1, 3] => 3, 3, 1, 2, 3, 2, 2, 1, 3
[3, 3, 1, 2, 3, 2, 2, 2, 1] => 3, 3, 1, 2, 3, 2, 2, 2, 1
[3, 3, 1, 2, 3, 2, 2, 2, 2] => 3, 3, 1, 2, 3, 2, 2, 2, 2
[3, 3, 1, 2, 3, 2, 2, 2, 3] => 3, 3, 1, 2, 3, 2, 2, 2, 3
[3, 3, 1, 2, 3, 2, 2, 3, 1] => 3, 3, 1, 2, 3, 2, 2, 3, 1
[3, 3, 1, 2, 3, 2, 2, 3, 2] => 3, 3, 1, 2, 3, 2, 2, 3, 2
[3, 3, 1, 2, 3, 2, 2, 3, 3] => 3, 3, 1, 2, 3, 2, 2, 3, 3
[3, 3, 1, 2, 3, 2, 3, 1, 1] => 3, 3, 1, 2, 3, 2, 3, 1, 1
[3, 3, 1, 2, 3, 2, 3, 1, 2] => 3, 3, 1, 2, 3, 2, 3, 1, 2
[3, 3, 1, 2, 3, 2, 3, 1, 3] => 3, 3, 1, 2, 3, 2, 3, 1, 3
[3, 3, 1, 2, 3, 2, 3, 2, 1] => 3, 3, 1, 2, 3, 2, 3, 2, 1
[3, 3, 1, 2, 3, 2, 3, 2, 2] => 3, 3, 1, 2, 3, 2, 3, 2, 2
[3, 3, 1, 2, 3, 2, 3, 2, 3] => 3, 3, 1, 2, 3, 2, 3, 2, 3
[3, 3, 1, 2, 3, 2, 3, 3, 1] => 3, 3, 1, 2, 3, 2, 3, 3, 1
[3, 3, 1, 2, 3, 2, 3, 3, 2] => 3, 3, 1, 2, 3, 2, 3, 3, 2
[3, 3, 1, 2, 3, 2, 3, 3, 3] => 3, 3, 1, 2, 3, 2, 3, 3, 3
[3, 3, 1, 2, 3, 3, 1, 1, 1] => 3, 3, 1, 2, 3, 3, 1, 1, 1
[3, 3, 1, 2, 3, 3, 1, 1, 2] => 3, 3, 1, 2, 3, 3, 1, 1, 2
[3, 3, 1, 2, 3, 3, 1, 1, 3] => 3, 3, 1, 2, 3, 3, 1, 1, 3
[3, 3, 1, 2, 3, 3, 1, 2, 1] => 3, 3, 1, 2, 3, 3, 1, 2, 1
[3, 3, 1, 2, 3, 3, 1, 2, 2] => 3, 3, 1, 2, 3, 3, 1, 2, 2
[3, 3, 1, 2, 3, 3, 1, 2, 3] => 3, 3, 1, 2, 3, 3, 1, 2, 3
[3, 3, 1, 2, 3, 3, 1, 3, 1] => 3, 3, 1, 2, 3, 3, 1, 3, 1
[3, 3, 1, 2, 3, 3, 1, 3, 2] => 3, 3, 1, 2, 3, 3, 1, 3, 2
[3, 3, 1, 2, 3, 3, 1, 3, 3] => 3, 3, 1, 2, 3, 3, 1, 3, 3
[3, 3, 1, 2, 3, 3, 2, 1, 1] => 3, 3, 1, 2, 3, 3, 2, 1, 1
[3, 3, 1, 2, 3, 3, 2, 1, 2] => 3, 3, 1, 2, 3, 3, 2, 1, 2
[3, 3, 1, 2, 3, 3, 2, 1, 3] => 3, 3, 1, 2, 3, 3, 2, 1, 3
[3, 3, 1, 2, 3, 3, 2, 2, 1] => 3, 3, 1, 2, 3, 3, 2, 2, 1
[3, 3, 1, 2, 3, 3, 2, 2, 2] => 3, 3, 1, 2, 3, 3, 2, 2, 2
[3, 3, 1, 2, 3, 3, 2, 2, 3] => 3, 3, 1, 2, 3, 3, 2, 2, 3
[3, 3, 1, 2, 3, 3, 2, 3, 1] => 3, 3, 1, 2, 3, 3, 2, 3, 1
[3, 3, 1, 2, 3, 3, 2, 3, 2] => 3, 3, 1, 2, 3, 3, 2, 3, 2
[3, 3, 1, 2, 3, 3, 2, 3, 3] => 3, 3, 1, 2, 3, 3, 2, 3, 3
[3, 3, 1, 2, 3, 3, 3, 1, 1] => 3, 3, 1, 2, 3, 3, 3, 1, 1
[3, 3, 1, 2, 3, 3, 3, 1, 2] => 3, 3, 1, 2, 3, 3, 3, 1, 2
[3, 3, 1, 2, 3, 3, 3, 1, 3] => 3, 3, 1, 2, 3, 3, 3, 1, 3
[3, 3, 1, 2, 3, 3, 3, 2, 1] => 3, 3, 1, 2, 3, 3, 3, 2, 1
[3, 3, 1, 2, 3, 3, 3, 2, 2] => 3, 3, 1, 2, 3, 3, 3, 2, 2
[3, 3, 1, 2, 3, 3, 3, 2, 3] => 3, 3, 1, 2, 3, 3, 3, 2, 3
[3, 3, 1, 2, 3, 3, 3, 3, 1] => 3, 3, 1, 2, 3, 3, 3, 3, 1
[3, 3, 1, 2, 3, 3, 3, 3, 2] => 3, 3, 1, 2, 3, 3, 3, 3, 2
[3, 3, 1, 2, 3, 3, 3, 3, 3] => 3, 3, 1, 2, 3, 3, 3, 3, 3
[3, 3, 1, 3, 1, 1, 1, 1, 1] => 3, 3, 1, 3, 1, 1, 1, 1, 1
[3, 3, 1, 3, 1, 1, 1, 1, 2] => 3, 3, 1, 3, 1, 1, 1, 1, 2
[3, 3, 1, 3, 1, 1, 1, 1, 3] => 3, 3, 1, 3, 1, 1, 1, 1, 3
[3, 3, 1, 3, 1, 1, 1, 2, 1] => 3, 3, 1, 3, 1, 1, 1, 2, 1
[3, 3, 1, 3, 1, 1, 1, 2, 2] => 3, 3, 1, 3, 1, 1, 1, 2, 2
[3, 3, 1, 3, 1, 1, 1, 2, 3] => 3, 3, 1, 3, 1, 1, 1, 2, 3
[3, 3, 1, 3, 1, 1, 1, 3, 1] => 3, 3, 1, 3, 1, 1, 1, 3, 1
[3, 3, 1, 3, 1, 1, 1, 3, 2] => 3, 3, 1, 3, 1, 1, 1, 3, 2
[3, 3, 1, 3, 1, 1, 1, 3, 3] => 3, 3, 1, 3, 1, 1, 1, 3, 3
[3, 3, 1, 3, 1, 1, 2, 1, 1] => 3, 3, 1, 3, 1, 1, 2, 1, 1
[3, 3, 1, 3, 1, 1, 2, 1, 2] => 3, 3, 1, 3, 1, 1, 2, 1, 2
[3, 3, 1, 3, 1, 1, 2, 1, 3] => 3, 3, 1, 3, 1, 1, 2, 1, 3
[3, 3, 1, 3, 1, 1, 2, 2, 1] => 3, 3, 1, 3, 1, 1, 2, 2, 1
[3, 3, 1, 3, 1, 1, 2, 2, 2] => 3, 3, 1, 3, 1, 1, 2, 2, 2
[3, 3, 1, 3, 1, 1, 2, 2, 3] => 3, 3, 1, 3, 1, 1, 2, 2, 3
[3, 3, 1, 3, 1, 1, 2, 3, 1] => 3, 3, 1, 3, 1, 1, 2, 3, 1
[3, 3, 1, 3, 1, 1, 2, 3, 2] => 3, 3, 1, 3, 1, 1, 2, 3, 2
[3, 3, 1, 3, 1, 1, 2, 3, 3] => 3, 3, 1, 3, 1, 1, 2, 3, 3
[3, 3, 1, 3, 1, 1, 3, 1, 1] => 3, 3, 1, 3, 1, 1, 3, 1, 1
[3, 3, 1, 3, 1, 1, 3, 1, 2] => 3, 3, 1, 3, 1, 1, 3, 1, 2
[3, 3, 1, 3, 1, 1, 3, 1, 3] => 3, 3, 1, 3, 1, 1, 3, 1, 3
[3, 3, 1, 3, 1, 1, 3, 2, 1] => 3, 3, 1, 3, 1, 1, 3, 2, 1
[3, 3, 1, 3, 1, 1, 3, 2, 2] => 3, 3, 1, 3, 1, 1, 3, 2, 2
[3, 3, 1, 3, 1, 1, 3, 2, 3] => 3, 3, 1, 3, 1, 1, 3, 2, 3
[3, 3, 1, 3, 1, 1, 3, 3, 1] => 3, 3, 1, 3, 1, 1, 3, 3, 1
[3, 3, 1, 3, 1, 1, 3, 3, 2] => 3, 3, 1, 3, 1, 1, 3, 3, 2
[3, 3, 1, 3, 1, 1, 3, 3, 3] => 3, 3, 1, 3, 1, 1, 3, 3, 3
[3, 3, 1, 3, 1, 2, 1, 1, 1] => 3, 3, 1, 3, 1, 2, 1, 1, 1
[3, 3, 1, 3, 1, 2, 1, 1, 2] => 3, 3, 1, 3, 1, 2, 1, 1, 2
[3, 3, 1, 3, 1, 2, 1, 1, 3] => 3, 3, 1, 3, 1, 2, 1, 1, 3
[3, 3, 1, 3, 1, 2, 1, 2, 1] => 3, 3, 1, 3, 1, 2, 1, 2, 1
[3, 3, 1, 3, 1, 2, 1, 2, 2] => 3, 3, 1, 3, 1, 2, 1, 2, 2
[3, 3, 1, 3, 1, 2, 1, 2, 3] => 3, 3, 1, 3, 1, 2, 1, 2, 3
[3, 3, 1, 3, 1, 2, 1, 3, 1] => 3, 3, 1, 3, 1, 2, 1, 3, 1
[3, 3, 1, 3, 1, 2, 1, 3, 2] => 3, 3, 1, 3, 1, 2, 1, 3, 2
[3, 3, 1, 3, 1, 2, 1, 3, 3] => 3, 3, 1, 3, 1, 2, 1, 3, 3
[3, 3, 1, 3, 1, 2, 2, 1, 1] => 3, 3, 1, 3, 1, 2, 2, 1, 1
[3, 3, 1, 3, 1, 2, 2, 1, 2] => 3, 3, 1, 3, 1, 2, 2, 1, 2
[3, 3, 1, 3, 1, 2, 2, 1, 3] => 3, 3, 1, 3, 1, 2, 2, 1, 3
[3, 3, 1, 3, 1, 2, 2, 2, 1] => 3, 3, 1, 3, 1, 2, 2, 2, 1
[3, 3, 1, 3, 1, 2, 2, 2, 2] => 3, 3, 1, 3, 1, 2, 2, 2, 2
[3, 3, 1, 3, 1, 2, 2, 2, 3] => 3, 3, 1, 3, 1, 2, 2, 2, 3
[3, 3, 1, 3, 1, 2, 2, 3, 1] => 3, 3, 1, 3, 1, 2, 2, 3, 1
[3, 3, 1, 3, 1, 2, 2, 3, 2] => 3, 3, 1, 3, 1, 2, 2, 3, 2
[3, 3, 1, 3, 1, 2, 2, 3, 3] => 3, 3, 1, 3, 1, 2, 2, 3, 3
[3, 3, 1, 3, 1, 2, 3, 1, 1] => 3, 3, 1, 3, 1, 2, 3, 1, 1
[3, 3, 1, 3, 1, 2, 3, 1, 2] => 3, 3, 1, 3, 1, 2, 3, 1, 2
[3, 3, 1, 3, 1, 2, 3, 1, 3] => 3, 3, 1, 3, 1, 2, 3, 1, 3
[3, 3, 1, 3, 1, 2, 3, 2, 1] => 3, 3, 1, 3, 1, 2, 3, 2, 1
[3, 3, 1, 3, 1, 2, 3, 2, 2] => 3, 3, 1, 3, 1, 2, 3, 2, 2
[3, 3, 1, 3, 1, 2, 3, 2, 3] => 3, 3, 1, 3, 1, 2, 3, 2, 3
[3, 3, 1, 3, 1, 2, 3, 3, 1] => 3, 3, 1, 3, 1, 2, 3, 3, 1
[3, 3, 1, 3, 1, 2, 3, 3, 2] => 3, 3, 1, 3, 1, 2, 3, 3, 2
[3, 3, 1, 3, 1, 2, 3, 3, 3] => 3, 3, 1, 3, 1, 2, 3, 3, 3
[3, 3, 1, 3, 1, 3, 1, 1, 1] => 3, 3, 1, 3, 1, 3, 1, 1, 1
[3, 3, 1, 3, 1, 3, 1, 1, 2] => 3, 3, 1, 3, 1, 3, 1, 1, 2
[3, 3, 1, 3, 1, 3, 1, 1, 3] => 3, 3, 1, 3, 1, 3, 1, 1, 3
[3, 3, 1, 3, 1, 3, 1, 2, 1] => 3, 3, 1, 3, 1, 3, 1, 2, 1
[3, 3, 1, 3, 1, 3, 1, 2, 2] => 3, 3, 1, 3, 1, 3, 1, 2, 2
[3, 3, 1, 3, 1, 3, 1, 2, 3] => 3, 3, 1, 3, 1, 3, 1, 2, 3
[3, 3, 1, 3, 1, 3, 1, 3, 1] => 3, 3, 1, 3, 1, 3, 1, 3, 1
[3, 3, 1, 3, 1, 3, 1, 3, 2] => 3, 3, 1, 3, 1, 3, 1, 3, 2
[3, 3, 1, 3, 1, 3, 1, 3, 3] => 3, 3, 1, 3, 1, 3, 1, 3, 3
[3, 3, 1, 3, 1, 3, 2, 1, 1] => 3, 3, 1, 3, 1, 3, 2, 1, 1
[3, 3, 1, 3, 1, 3, 2, 1, 2] => 3, 3, 1, 3, 1, 3, 2, 1, 2
[3, 3, 1, 3, 1, 3, 2, 1, 3] => 3, 3, 1, 3, 1, 3, 2, 1, 3
[3, 3, 1, 3, 1, 3, 2, 2, 1] => 3, 3, 1, 3, 1, 3, 2, 2, 1
[3, 3, 1, 3, 1, 3, 2, 2, 2] => 3, 3, 1, 3, 1, 3, 2, 2, 2
[3, 3, 1, 3, 1, 3, 2, 2, 3] => 3, 3, 1, 3, 1, 3, 2, 2, 3
[3, 3, 1, 3, 1, 3, 2, 3, 1] => 3, 3, 1, 3, 1, 3, 2, 3, 1
[3, 3, 1, 3, 1, 3, 2, 3, 2] => 3, 3, 1, 3, 1, 3, 2, 3, 2
[3, 3, 1, 3, 1, 3, 2, 3, 3] => 3, 3, 1, 3, 1, 3, 2, 3, 3
[3, 3, 1, 3, 1, 3, 3, 1, 1] => 3, 3, 1, 3, 1, 3, 3, 1, 1
[3, 3, 1, 3, 1, 3, 3, 1, 2] => 3, 3, 1, 3, 1, 3, 3, 1, 2
[3, 3, 1, 3, 1, 3, 3, 1, 3] => 3, 3, 1, 3, 1, 3, 3, 1, 3
[3, 3, 1, 3, 1, 3, 3, 2, 1] => 3, 3, 1, 3, 1, 3, 3, 2, 1
[3, 3, 1, 3, 1, 3, 3, 2, 2] => 3, 3, 1, 3, 1, 3, 3, 2, 2
[3, 3, 1, 3, 1, 3, 3, 2, 3] => 3, 3, 1, 3, 1, 3, 3, 2, 3
[3, 3, 1, 3, 1, 3, 3, 3, 1] => 3, 3, 1, 3, 1, 3, 3, 3, 1
[3, 3, 1, 3, 1, 3, 3, 3, 2] => 3, 3, 1, 3, 1, 3, 3, 3, 2
[3, 3, 1, 3, 1, 3, 3, 3, 3] => 3, 3, 1, 3, 1, 3, 3, 3, 3
[3, 3, 1, 3, 2, 1, 1, 1, 1] => 3, 3, 1, 3, 2, 1, 1, 1, 1
[3, 3, 1, 3, 2, 1, 1, 1, 2] => 3, 3, 1, 3, 2, 1, 1, 1, 2
[3, 3, 1, 3, 2, 1, 1, 1, 3] => 3, 3, 1, 3, 2, 1, 1, 1, 3
[3, 3, 1, 3, 2, 1, 1, 2, 1] => 3, 3, 1, 3, 2, 1, 1, 2, 1
[3, 3, 1, 3, 2, 1, 1, 2, 2] => 3, 3, 1, 3, 2, 1, 1, 2, 2
[3, 3, 1, 3, 2, 1, 1, 2, 3] => 3, 3, 1, 3, 2, 1, 1, 2, 3
[3, 3, 1, 3, 2, 1, 1, 3, 1] => 3, 3, 1, 3, 2, 1, 1, 3, 1
[3, 3, 1, 3, 2, 1, 1, 3, 2] => 3, 3, 1, 3, 2, 1, 1, 3, 2
[3, 3, 1, 3, 2, 1, 1, 3, 3] => 3, 3, 1, 3, 2, 1, 1, 3, 3
[3, 3, 1, 3, 2, 1, 2, 1, 1] => 3, 3, 1, 3, 2, 1, 2, 1, 1
[3, 3, 1, 3, 2, 1, 2, 1, 2] => 3, 3, 1, 3, 2, 1, 2, 1, 2
[3, 3, 1, 3, 2, 1, 2, 1, 3] => 3, 3, 1, 3, 2, 1, 2, 1, 3
[3, 3, 1, 3, 2, 1, 2, 2, 1] => 3, 3, 1, 3, 2, 1, 2, 2, 1
[3, 3, 1, 3, 2, 1, 2, 2, 2] => 3, 3, 1, 3, 2, 1, 2, 2, 2
[3, 3, 1, 3, 2, 1, 2, 2, 3] => 3, 3, 1, 3, 2, 1, 2, 2, 3
[3, 3, 1, 3, 2, 1, 2, 3, 1] => 3, 3, 1, 3, 2, 1, 2, 3, 1
[3, 3, 1, 3, 2, 1, 2, 3, 2] => 3, 3, 1, 3, 2, 1, 2, 3, 2
[3, 3, 1, 3, 2, 1, 2, 3, 3] => 3, 3, 1, 3, 2, 1, 2, 3, 3
[3, 3, 1, 3, 2, 1, 3, 1, 1] => 3, 3, 1, 3, 2, 1, 3, 1, 1
[3, 3, 1, 3, 2, 1, 3, 1, 2] => 3, 3, 1, 3, 2, 1, 3, 1, 2
[3, 3, 1, 3, 2, 1, 3, 1, 3] => 3, 3, 1, 3, 2, 1, 3, 1, 3
[3, 3, 1, 3, 2, 1, 3, 2, 1] => 3, 3, 1, 3, 2, 1, 3, 2, 1
[3, 3, 1, 3, 2, 1, 3, 2, 2] => 3, 3, 1, 3, 2, 1, 3, 2, 2
[3, 3, 1, 3, 2, 1, 3, 2, 3] => 3, 3, 1, 3, 2, 1, 3, 2, 3
[3, 3, 1, 3, 2, 1, 3, 3, 1] => 3, 3, 1, 3, 2, 1, 3, 3, 1
[3, 3, 1, 3, 2, 1, 3, 3, 2] => 3, 3, 1, 3, 2, 1, 3, 3, 2
[3, 3, 1, 3, 2, 1, 3, 3, 3] => 3, 3, 1, 3, 2, 1, 3, 3, 3
[3, 3, 1, 3, 2, 2, 1, 1, 1] => 3, 3, 1, 3, 2, 2, 1, 1, 1
[3, 3, 1, 3, 2, 2, 1, 1, 2] => 3, 3, 1, 3, 2, 2, 1, 1, 2
[3, 3, 1, 3, 2, 2, 1, 1, 3] => 3, 3, 1, 3, 2, 2, 1, 1, 3
[3, 3, 1, 3, 2, 2, 1, 2, 1] => 3, 3, 1, 3, 2, 2, 1, 2, 1
[3, 3, 1, 3, 2, 2, 1, 2, 2] => 3, 3, 1, 3, 2, 2, 1, 2, 2
[3, 3, 1, 3, 2, 2, 1, 2, 3] => 3, 3, 1, 3, 2, 2, 1, 2, 3
[3, 3, 1, 3, 2, 2, 1, 3, 1] => 3, 3, 1, 3, 2, 2, 1, 3, 1
[3, 3, 1, 3, 2, 2, 1, 3, 2] => 3, 3, 1, 3, 2, 2, 1, 3, 2
[3, 3, 1, 3, 2, 2, 1, 3, 3] => 3, 3, 1, 3, 2, 2, 1, 3, 3
[3, 3, 1, 3, 2, 2, 2, 1, 1] => 3, 3, 1, 3, 2, 2, 2, 1, 1
[3, 3, 1, 3, 2, 2, 2, 1, 2] => 3, 3, 1, 3, 2, 2, 2, 1, 2
[3, 3, 1, 3, 2, 2, 2, 1, 3] => 3, 3, 1, 3, 2, 2, 2, 1, 3
[3, 3, 1, 3, 2, 2, 2, 2, 1] => 3, 3, 1, 3, 2, 2, 2, 2, 1
[3, 3, 1, 3, 2, 2, 2, 2, 2] => 3, 3, 1, 3, 2, 2, 2, 2, 2
[3, 3, 1, 3, 2, 2, 2, 2, 3] => 3, 3, 1, 3, 2, 2, 2, 2, 3
[3, 3, 1, 3, 2, 2, 2, 3, 1] => 3, 3, 1, 3, 2, 2, 2, 3, 1
[3, 3, 1, 3, 2, 2, 2, 3, 2] => 3, 3, 1, 3, 2, 2, 2, 3, 2
[3, 3, 1, 3, 2, 2, 2, 3, 3] => 3, 3, 1, 3, 2, 2, 2, 3, 3
[3, 3, 1, 3, 2, 2, 3, 1, 1] => 3, 3, 1, 3, 2, 2, 3, 1, 1
[3, 3, 1, 3, 2, 2, 3, 1, 2] => 3, 3, 1, 3, 2, 2, 3, 1, 2
[3, 3, 1, 3, 2, 2, 3, 1, 3] => 3, 3, 1, 3, 2, 2, 3, 1, 3
[3, 3, 1, 3, 2, 2, 3, 2, 1] => 3, 3, 1, 3, 2, 2, 3, 2, 1
[3, 3, 1, 3, 2, 2, 3, 2, 2] => 3, 3, 1, 3, 2, 2, 3, 2, 2
[3, 3, 1, 3, 2, 2, 3, 2, 3] => 3, 3, 1, 3, 2, 2, 3, 2, 3
[3, 3, 1, 3, 2, 2, 3, 3, 1] => 3, 3, 1, 3, 2, 2, 3, 3, 1
[3, 3, 1, 3, 2, 2, 3, 3, 2] => 3, 3, 1, 3, 2, 2, 3, 3, 2
[3, 3, 1, 3, 2, 2, 3, 3, 3] => 3, 3, 1, 3, 2, 2, 3, 3, 3
[3, 3, 1, 3, 2, 3, 1, 1, 1] => 3, 3, 1, 3, 2, 3, 1, 1, 1
[3, 3, 1, 3, 2, 3, 1, 1, 2] => 3, 3, 1, 3, 2, 3, 1, 1, 2
[3, 3, 1, 3, 2, 3, 1, 1, 3] => 3, 3, 1, 3, 2, 3, 1, 1, 3
[3, 3, 1, 3, 2, 3, 1, 2, 1] => 3, 3, 1, 3, 2, 3, 1, 2, 1
[3, 3, 1, 3, 2, 3, 1, 2, 2] => 3, 3, 1, 3, 2, 3, 1, 2, 2
[3, 3, 1, 3, 2, 3, 1, 2, 3] => 3, 3, 1, 3, 2, 3, 1, 2, 3
[3, 3, 1, 3, 2, 3, 1, 3, 1] => 3, 3, 1, 3, 2, 3, 1, 3, 1
[3, 3, 1, 3, 2, 3, 1, 3, 2] => 3, 3, 1, 3, 2, 3, 1, 3, 2
[3, 3, 1, 3, 2, 3, 1, 3, 3] => 3, 3, 1, 3, 2, 3, 1, 3, 3
[3, 3, 1, 3, 2, 3, 2, 1, 1] => 3, 3, 1, 3, 2, 3, 2, 1, 1
[3, 3, 1, 3, 2, 3, 2, 1, 2] => 3, 3, 1, 3, 2, 3, 2, 1, 2
[3, 3, 1, 3, 2, 3, 2, 1, 3] => 3, 3, 1, 3, 2, 3, 2, 1, 3
[3, 3, 1, 3, 2, 3, 2, 2, 1] => 3, 3, 1, 3, 2, 3, 2, 2, 1
[3, 3, 1, 3, 2, 3, 2, 2, 2] => 3, 3, 1, 3, 2, 3, 2, 2, 2
[3, 3, 1, 3, 2, 3, 2, 2, 3] => 3, 3, 1, 3, 2, 3, 2, 2, 3
[3, 3, 1, 3, 2, 3, 2, 3, 1] => 3, 3, 1, 3, 2, 3, 2, 3, 1
[3, 3, 1, 3, 2, 3, 2, 3, 2] => 3, 3, 1, 3, 2, 3, 2, 3, 2
[3, 3, 1, 3, 2, 3, 2, 3, 3] => 3, 3, 1, 3, 2, 3, 2, 3, 3
[3, 3, 1, 3, 2, 3, 3, 1, 1] => 3, 3, 1, 3, 2, 3, 3, 1, 1
[3, 3, 1, 3, 2, 3, 3, 1, 2] => 3, 3, 1, 3, 2, 3, 3, 1, 2
[3, 3, 1, 3, 2, 3, 3, 1, 3] => 3, 3, 1, 3, 2, 3, 3, 1, 3
[3, 3, 1, 3, 2, 3, 3, 2, 1] => 3, 3, 1, 3, 2, 3, 3, 2, 1
[3, 3, 1, 3, 2, 3, 3, 2, 2] => 3, 3, 1, 3, 2, 3, 3, 2, 2
[3, 3, 1, 3, 2, 3, 3, 2, 3] => 3, 3, 1, 3, 2, 3, 3, 2, 3
[3, 3, 1, 3, 2, 3, 3, 3, 1] => 3, 3, 1, 3, 2, 3, 3, 3, 1
[3, 3, 1, 3, 2, 3, 3, 3, 2] => 3, 3, 1, 3, 2, 3, 3, 3, 2
[3, 3, 1, 3, 2, 3, 3, 3, 3] => 3, 3, 1, 3, 2, 3, 3, 3, 3
[3, 3, 1, 3, 3, 1, 1, 1, 1] => 3, 3, 1, 3, 3, 1, 1, 1, 1
[3, 3, 1, 3, 3, 1, 1, 1, 2] => 3, 3, 1, 3, 3, 1, 1, 1, 2
[3, 3, 1, 3, 3, 1, 1, 1, 3] => 3, 3, 1, 3, 3, 1, 1, 1, 3
[3, 3, 1, 3, 3, 1, 1, 2, 1] => 3, 3, 1, 3, 3, 1, 1, 2, 1
[3, 3, 1, 3, 3, 1, 1, 2, 2] => 3, 3, 1, 3, 3, 1, 1, 2, 2
[3, 3, 1, 3, 3, 1, 1, 2, 3] => 3, 3, 1, 3, 3, 1, 1, 2, 3
[3, 3, 1, 3, 3, 1, 1, 3, 1] => 3, 3, 1, 3, 3, 1, 1, 3, 1
[3, 3, 1, 3, 3, 1, 1, 3, 2] => 3, 3, 1, 3, 3, 1, 1, 3, 2
[3, 3, 1, 3, 3, 1, 1, 3, 3] => 3, 3, 1, 3, 3, 1, 1, 3, 3
[3, 3, 1, 3, 3, 1, 2, 1, 1] => 3, 3, 1, 3, 3, 1, 2, 1, 1
[3, 3, 1, 3, 3, 1, 2, 1, 2] => 3, 3, 1, 3, 3, 1, 2, 1, 2
[3, 3, 1, 3, 3, 1, 2, 1, 3] => 3, 3, 1, 3, 3, 1, 2, 1, 3
[3, 3, 1, 3, 3, 1, 2, 2, 1] => 3, 3, 1, 3, 3, 1, 2, 2, 1
[3, 3, 1, 3, 3, 1, 2, 2, 2] => 3, 3, 1, 3, 3, 1, 2, 2, 2
[3, 3, 1, 3, 3, 1, 2, 2, 3] => 3, 3, 1, 3, 3, 1, 2, 2, 3
[3, 3, 1, 3, 3, 1, 2, 3, 1] => 3, 3, 1, 3, 3, 1, 2, 3, 1
[3, 3, 1, 3, 3, 1, 2, 3, 2] => 3, 3, 1, 3, 3, 1, 2, 3, 2
[3, 3, 1, 3, 3, 1, 2, 3, 3] => 3, 3, 1, 3, 3, 1, 2, 3, 3
[3, 3, 1, 3, 3, 1, 3, 1, 1] => 3, 3, 1, 3, 3, 1, 3, 1, 1
[3, 3, 1, 3, 3, 1, 3, 1, 2] => 3, 3, 1, 3, 3, 1, 3, 1, 2
[3, 3, 1, 3, 3, 1, 3, 1, 3] => 3, 3, 1, 3, 3, 1, 3, 1, 3
[3, 3, 1, 3, 3, 1, 3, 2, 1] => 3, 3, 1, 3, 3, 1, 3, 2, 1
[3, 3, 1, 3, 3, 1, 3, 2, 2] => 3, 3, 1, 3, 3, 1, 3, 2, 2
[3, 3, 1, 3, 3, 1, 3, 2, 3] => 3, 3, 1, 3, 3, 1, 3, 2, 3
[3, 3, 1, 3, 3, 1, 3, 3, 1] => 3, 3, 1, 3, 3, 1, 3, 3, 1
[3, 3, 1, 3, 3, 1, 3, 3, 2] => 3, 3, 1, 3, 3, 1, 3, 3, 2
[3, 3, 1, 3, 3, 1, 3, 3, 3] => 3, 3, 1, 3, 3, 1, 3, 3, 3
[3, 3, 1, 3, 3, 2, 1, 1, 1] => 3, 3, 1, 3, 3, 2, 1, 1, 1
[3, 3, 1, 3, 3, 2, 1, 1, 2] => 3, 3, 1, 3, 3, 2, 1, 1, 2
[3, 3, 1, 3, 3, 2, 1, 1, 3] => 3, 3, 1, 3, 3, 2, 1, 1, 3
[3, 3, 1, 3, 3, 2, 1, 2, 1] => 3, 3, 1, 3, 3, 2, 1, 2, 1
[3, 3, 1, 3, 3, 2, 1, 2, 2] => 3, 3, 1, 3, 3, 2, 1, 2, 2
[3, 3, 1, 3, 3, 2, 1, 2, 3] => 3, 3, 1, 3, 3, 2, 1, 2, 3
[3, 3, 1, 3, 3, 2, 1, 3, 1] => 3, 3, 1, 3, 3, 2, 1, 3, 1
[3, 3, 1, 3, 3, 2, 1, 3, 2] => 3, 3, 1, 3, 3, 2, 1, 3, 2
[3, 3, 1, 3, 3, 2, 1, 3, 3] => 3, 3, 1, 3, 3, 2, 1, 3, 3
[3, 3, 1, 3, 3, 2, 2, 1, 1] => 3, 3, 1, 3, 3, 2, 2, 1, 1
[3, 3, 1, 3, 3, 2, 2, 1, 2] => 3, 3, 1, 3, 3, 2, 2, 1, 2
[3, 3, 1, 3, 3, 2, 2, 1, 3] => 3, 3, 1, 3, 3, 2, 2, 1, 3
[3, 3, 1, 3, 3, 2, 2, 2, 1] => 3, 3, 1, 3, 3, 2, 2, 2, 1
[3, 3, 1, 3, 3, 2, 2, 2, 2] => 3, 3, 1, 3, 3, 2, 2, 2, 2
[3, 3, 1, 3, 3, 2, 2, 2, 3] => 3, 3, 1, 3, 3, 2, 2, 2, 3
[3, 3, 1, 3, 3, 2, 2, 3, 1] => 3, 3, 1, 3, 3, 2, 2, 3, 1
[3, 3, 1, 3, 3, 2, 2, 3, 2] => 3, 3, 1, 3, 3, 2, 2, 3, 2
[3, 3, 1, 3, 3, 2, 2, 3, 3] => 3, 3, 1, 3, 3, 2, 2, 3, 3
[3, 3, 1, 3, 3, 2, 3, 1, 1] => 3, 3, 1, 3, 3, 2, 3, 1, 1
[3, 3, 1, 3, 3, 2, 3, 1, 2] => 3, 3, 1, 3, 3, 2, 3, 1, 2
[3, 3, 1, 3, 3, 2, 3, 1, 3] => 3, 3, 1, 3, 3, 2, 3, 1, 3
[3, 3, 1, 3, 3, 2, 3, 2, 1] => 3, 3, 1, 3, 3, 2, 3, 2, 1
[3, 3, 1, 3, 3, 2, 3, 2, 2] => 3, 3, 1, 3, 3, 2, 3, 2, 2
[3, 3, 1, 3, 3, 2, 3, 2, 3] => 3, 3, 1, 3, 3, 2, 3, 2, 3
[3, 3, 1, 3, 3, 2, 3, 3, 1] => 3, 3, 1, 3, 3, 2, 3, 3, 1
[3, 3, 1, 3, 3, 2, 3, 3, 2] => 3, 3, 1, 3, 3, 2, 3, 3, 2
[3, 3, 1, 3, 3, 2, 3, 3, 3] => 3, 3, 1, 3, 3, 2, 3, 3, 3
[3, 3, 1, 3, 3, 3, 1, 1, 1] => 3, 3, 1, 3, 3, 3, 1, 1, 1
[3, 3, 1, 3, 3, 3, 1, 1, 2] => 3, 3, 1, 3, 3, 3, 1, 1, 2
[3, 3, 1, 3, 3, 3, 1, 1, 3] => 3, 3, 1, 3, 3, 3, 1, 1, 3
[3, 3, 1, 3, 3, 3, 1, 2, 1] => 3, 3, 1, 3, 3, 3, 1, 2, 1
[3, 3, 1, 3, 3, 3, 1, 2, 2] => 3, 3, 1, 3, 3, 3, 1, 2, 2
[3, 3, 1, 3, 3, 3, 1, 2, 3] => 3, 3, 1, 3, 3, 3, 1, 2, 3
[3, 3, 1, 3, 3, 3, 1, 3, 1] => 3, 3, 1, 3, 3, 3, 1, 3, 1
[3, 3, 1, 3, 3, 3, 1, 3, 2] => 3, 3, 1, 3, 3, 3, 1, 3, 2
[3, 3, 1, 3, 3, 3, 1, 3, 3] => 3, 3, 1, 3, 3, 3, 1, 3, 3
[3, 3, 1, 3, 3, 3, 2, 1, 1] => 3, 3, 1, 3, 3, 3, 2, 1, 1
[3, 3, 1, 3, 3, 3, 2, 1, 2] => 3, 3, 1, 3, 3, 3, 2, 1, 2
[3, 3, 1, 3, 3, 3, 2, 1, 3] => 3, 3, 1, 3, 3, 3, 2, 1, 3
[3, 3, 1, 3, 3, 3, 2, 2, 1] => 3, 3, 1, 3, 3, 3, 2, 2, 1
[3, 3, 1, 3, 3, 3, 2, 2, 2] => 3, 3, 1, 3, 3, 3, 2, 2, 2
[3, 3, 1, 3, 3, 3, 2, 2, 3] => 3, 3, 1, 3, 3, 3, 2, 2, 3
[3, 3, 1, 3, 3, 3, 2, 3, 1] => 3, 3, 1, 3, 3, 3, 2, 3, 1
[3, 3, 1, 3, 3, 3, 2, 3, 2] => 3, 3, 1, 3, 3, 3, 2, 3, 2
[3, 3, 1, 3, 3, 3, 2, 3, 3] => 3, 3, 1, 3, 3, 3, 2, 3, 3
[3, 3, 1, 3, 3, 3, 3, 1, 1] => 3, 3, 1, 3, 3, 3, 3, 1, 1
[3, 3, 1, 3, 3, 3, 3, 1, 2] => 3, 3, 1, 3, 3, 3, 3, 1, 2
[3, 3, 1, 3, 3, 3, 3, 1, 3] => 3, 3, 1, 3, 3, 3, 3, 1, 3
[3, 3, 1, 3, 3, 3, 3, 2, 1] => 3, 3, 1, 3, 3, 3, 3, 2, 1
[3, 3, 1, 3, 3, 3, 3, 2, 2] => 3, 3, 1, 3, 3, 3, 3, 2, 2
[3, 3, 1, 3, 3, 3, 3, 2, 3] => 3, 3, 1, 3, 3, 3, 3, 2, 3
[3, 3, 1, 3, 3, 3, 3, 3, 1] => 3, 3, 1, 3, 3, 3, 3, 3, 1
[3, 3, 1, 3, 3, 3, 3, 3, 2] => 3, 3, 1, 3, 3, 3, 3, 3, 2
[3, 3, 1, 3, 3, 3, 3, 3, 3] => 3, 3, 1, 3, 3, 3, 3, 3, 3
[3, 3, 2, 1, 1, 1, 1, 1, 1] => 3, 3, 2, 1, 1, 1, 1, 1, 1
[3, 3, 2, 1, 1, 1, 1, 1, 2] => 3, 3, 2, 1, 1, 1, 1, 1, 2
[3, 3, 2, 1, 1, 1, 1, 1, 3] => 3, 3, 2, 1, 1, 1, 1, 1, 3
[3, 3, 2, 1, 1, 1, 1, 2, 1] => 3, 3, 2, 1, 1, 1, 1, 2, 1
[3, 3, 2, 1, 1, 1, 1, 2, 2] => 3, 3, 2, 1, 1, 1, 1, 2, 2
[3, 3, 2, 1, 1, 1, 1, 2, 3] => 3, 3, 2, 1, 1, 1, 1, 2, 3
[3, 3, 2, 1, 1, 1, 1, 3, 1] => 3, 3, 2, 1, 1, 1, 1, 3, 1
[3, 3, 2, 1, 1, 1, 1, 3, 2] => 3, 3, 2, 1, 1, 1, 1, 3, 2
[3, 3, 2, 1, 1, 1, 1, 3, 3] => 3, 3, 2, 1, 1, 1, 1, 3, 3
[3, 3, 2, 1, 1, 1, 2, 1, 1] => 3, 3, 2, 1, 1, 1, 2, 1, 1
[3, 3, 2, 1, 1, 1, 2, 1, 2] => 3, 3, 2, 1, 1, 1, 2, 1, 2
[3, 3, 2, 1, 1, 1, 2, 1, 3] => 3, 3, 2, 1, 1, 1, 2, 1, 3
[3, 3, 2, 1, 1, 1, 2, 2, 1] => 3, 3, 2, 1, 1, 1, 2, 2, 1
[3, 3, 2, 1, 1, 1, 2, 2, 2] => 3, 3, 2, 1, 1, 1, 2, 2, 2
[3, 3, 2, 1, 1, 1, 2, 2, 3] => 3, 3, 2, 1, 1, 1, 2, 2, 3
[3, 3, 2, 1, 1, 1, 2, 3, 1] => 3, 3, 2, 1, 1, 1, 2, 3, 1
[3, 3, 2, 1, 1, 1, 2, 3, 2] => 3, 3, 2, 1, 1, 1, 2, 3, 2
[3, 3, 2, 1, 1, 1, 2, 3, 3] => 3, 3, 2, 1, 1, 1, 2, 3, 3
[3, 3, 2, 1, 1, 1, 3, 1, 1] => 3, 3, 2, 1, 1, 1, 3, 1, 1
[3, 3, 2, 1, 1, 1, 3, 1, 2] => 3, 3, 2, 1, 1, 1, 3, 1, 2
[3, 3, 2, 1, 1, 1, 3, 1, 3] => 3, 3, 2, 1, 1, 1, 3, 1, 3
[3, 3, 2, 1, 1, 1, 3, 2, 1] => 3, 3, 2, 1, 1, 1, 3, 2, 1
[3, 3, 2, 1, 1, 1, 3, 2, 2] => 3, 3, 2, 1, 1, 1, 3, 2, 2
[3, 3, 2, 1, 1, 1, 3, 2, 3] => 3, 3, 2, 1, 1, 1, 3, 2, 3
[3, 3, 2, 1, 1, 1, 3, 3, 1] => 3, 3, 2, 1, 1, 1, 3, 3, 1
[3, 3, 2, 1, 1, 1, 3, 3, 2] => 3, 3, 2, 1, 1, 1, 3, 3, 2
[3, 3, 2, 1, 1, 1, 3, 3, 3] => 3, 3, 2, 1, 1, 1, 3, 3, 3
[3, 3, 2, 1, 1, 2, 1, 1, 1] => 3, 3, 2, 1, 1, 2, 1, 1, 1
[3, 3, 2, 1, 1, 2, 1, 1, 2] => 3, 3, 2, 1, 1, 2, 1, 1, 2
[3, 3, 2, 1, 1, 2, 1, 1, 3] => 3, 3, 2, 1, 1, 2, 1, 1, 3
[3, 3, 2, 1, 1, 2, 1, 2, 1] => 3, 3, 2, 1, 1, 2, 1, 2, 1
[3, 3, 2, 1, 1, 2, 1, 2, 2] => 3, 3, 2, 1, 1, 2, 1, 2, 2
[3, 3, 2, 1, 1, 2, 1, 2, 3] => 3, 3, 2, 1, 1, 2, 1, 2, 3
[3, 3, 2, 1, 1, 2, 1, 3, 1] => 3, 3, 2, 1, 1, 2, 1, 3, 1
[3, 3, 2, 1, 1, 2, 1, 3, 2] => 3, 3, 2, 1, 1, 2, 1, 3, 2
[3, 3, 2, 1, 1, 2, 1, 3, 3] => 3, 3, 2, 1, 1, 2, 1, 3, 3
[3, 3, 2, 1, 1, 2, 2, 1, 1] => 3, 3, 2, 1, 1, 2, 2, 1, 1
[3, 3, 2, 1, 1, 2, 2, 1, 2] => 3, 3, 2, 1, 1, 2, 2, 1, 2
[3, 3, 2, 1, 1, 2, 2, 1, 3] => 3, 3, 2, 1, 1, 2, 2, 1, 3
[3, 3, 2, 1, 1, 2, 2, 2, 1] => 3, 3, 2, 1, 1, 2, 2, 2, 1
[3, 3, 2, 1, 1, 2, 2, 2, 2] => 3, 3, 2, 1, 1, 2, 2, 2, 2
[3, 3, 2, 1, 1, 2, 2, 2, 3] => 3, 3, 2, 1, 1, 2, 2, 2, 3
[3, 3, 2, 1, 1, 2, 2, 3, 1] => 3, 3, 2, 1, 1, 2, 2, 3, 1
[3, 3, 2, 1, 1, 2, 2, 3, 2] => 3, 3, 2, 1, 1, 2, 2, 3, 2
[3, 3, 2, 1, 1, 2, 2, 3, 3] => 3, 3, 2, 1, 1, 2, 2, 3, 3
[3, 3, 2, 1, 1, 2, 3, 1, 1] => 3, 3, 2, 1, 1, 2, 3, 1, 1
[3, 3, 2, 1, 1, 2, 3, 1, 2] => 3, 3, 2, 1, 1, 2, 3, 1, 2
[3, 3, 2, 1, 1, 2, 3, 1, 3] => 3, 3, 2, 1, 1, 2, 3, 1, 3
[3, 3, 2, 1, 1, 2, 3, 2, 1] => 3, 3, 2, 1, 1, 2, 3, 2, 1
[3, 3, 2, 1, 1, 2, 3, 2, 2] => 3, 3, 2, 1, 1, 2, 3, 2, 2
[3, 3, 2, 1, 1, 2, 3, 2, 3] => 3, 3, 2, 1, 1, 2, 3, 2, 3
[3, 3, 2, 1, 1, 2, 3, 3, 1] => 3, 3, 2, 1, 1, 2, 3, 3, 1
[3, 3, 2, 1, 1, 2, 3, 3, 2] => 3, 3, 2, 1, 1, 2, 3, 3, 2
[3, 3, 2, 1, 1, 2, 3, 3, 3] => 3, 3, 2, 1, 1, 2, 3, 3, 3
[3, 3, 2, 1, 1, 3, 1, 1, 1] => 3, 3, 2, 1, 1, 3, 1, 1, 1
[3, 3, 2, 1, 1, 3, 1, 1, 2] => 3, 3, 2, 1, 1, 3, 1, 1, 2
[3, 3, 2, 1, 1, 3, 1, 1, 3] => 3, 3, 2, 1, 1, 3, 1, 1, 3
[3, 3, 2, 1, 1, 3, 1, 2, 1] => 3, 3, 2, 1, 1, 3, 1, 2, 1
[3, 3, 2, 1, 1, 3, 1, 2, 2] => 3, 3, 2, 1, 1, 3, 1, 2, 2
[3, 3, 2, 1, 1, 3, 1, 2, 3] => 3, 3, 2, 1, 1, 3, 1, 2, 3
[3, 3, 2, 1, 1, 3, 1, 3, 1] => 3, 3, 2, 1, 1, 3, 1, 3, 1
[3, 3, 2, 1, 1, 3, 1, 3, 2] => 3, 3, 2, 1, 1, 3, 1, 3, 2
[3, 3, 2, 1, 1, 3, 1, 3, 3] => 3, 3, 2, 1, 1, 3, 1, 3, 3
[3, 3, 2, 1, 1, 3, 2, 1, 1] => 3, 3, 2, 1, 1, 3, 2, 1, 1
[3, 3, 2, 1, 1, 3, 2, 1, 2] => 3, 3, 2, 1, 1, 3, 2, 1, 2
[3, 3, 2, 1, 1, 3, 2, 1, 3] => 3, 3, 2, 1, 1, 3, 2, 1, 3
[3, 3, 2, 1, 1, 3, 2, 2, 1] => 3, 3, 2, 1, 1, 3, 2, 2, 1
[3, 3, 2, 1, 1, 3, 2, 2, 2] => 3, 3, 2, 1, 1, 3, 2, 2, 2
[3, 3, 2, 1, 1, 3, 2, 2, 3] => 3, 3, 2, 1, 1, 3, 2, 2, 3
[3, 3, 2, 1, 1, 3, 2, 3, 1] => 3, 3, 2, 1, 1, 3, 2, 3, 1
[3, 3, 2, 1, 1, 3, 2, 3, 2] => 3, 3, 2, 1, 1, 3, 2, 3, 2
[3, 3, 2, 1, 1, 3, 2, 3, 3] => 3, 3, 2, 1, 1, 3, 2, 3, 3
[3, 3, 2, 1, 1, 3, 3, 1, 1] => 3, 3, 2, 1, 1, 3, 3, 1, 1
[3, 3, 2, 1, 1, 3, 3, 1, 2] => 3, 3, 2, 1, 1, 3, 3, 1, 2
[3, 3, 2, 1, 1, 3, 3, 1, 3] => 3, 3, 2, 1, 1, 3, 3, 1, 3
[3, 3, 2, 1, 1, 3, 3, 2, 1] => 3, 3, 2, 1, 1, 3, 3, 2, 1
[3, 3, 2, 1, 1, 3, 3, 2, 2] => 3, 3, 2, 1, 1, 3, 3, 2, 2
[3, 3, 2, 1, 1, 3, 3, 2, 3] => 3, 3, 2, 1, 1, 3, 3, 2, 3
[3, 3, 2, 1, 1, 3, 3, 3, 1] => 3, 3, 2, 1, 1, 3, 3, 3, 1
[3, 3, 2, 1, 1, 3, 3, 3, 2] => 3, 3, 2, 1, 1, 3, 3, 3, 2
[3, 3, 2, 1, 1, 3, 3, 3, 3] => 3, 3, 2, 1, 1, 3, 3, 3, 3
[3, 3, 2, 1, 2, 1, 1, 1, 1] => 3, 3, 2, 1, 2, 1, 1, 1, 1
[3, 3, 2, 1, 2, 1, 1, 1, 2] => 3, 3, 2, 1, 2, 1, 1, 1, 2
[3, 3, 2, 1, 2, 1, 1, 1, 3] => 3, 3, 2, 1, 2, 1, 1, 1, 3
[3, 3, 2, 1, 2, 1, 1, 2, 1] => 3, 3, 2, 1, 2, 1, 1, 2, 1
[3, 3, 2, 1, 2, 1, 1, 2, 2] => 3, 3, 2, 1, 2, 1, 1, 2, 2
[3, 3, 2, 1, 2, 1, 1, 2, 3] => 3, 3, 2, 1, 2, 1, 1, 2, 3
[3, 3, 2, 1, 2, 1, 1, 3, 1] => 3, 3, 2, 1, 2, 1, 1, 3, 1
[3, 3, 2, 1, 2, 1, 1, 3, 2] => 3, 3, 2, 1, 2, 1, 1, 3, 2
[3, 3, 2, 1, 2, 1, 1, 3, 3] => 3, 3, 2, 1, 2, 1, 1, 3, 3
[3, 3, 2, 1, 2, 1, 2, 1, 1] => 3, 3, 2, 1, 2, 1, 2, 1, 1
[3, 3, 2, 1, 2, 1, 2, 1, 2] => 3, 3, 2, 1, 2, 1, 2, 1, 2
[3, 3, 2, 1, 2, 1, 2, 1, 3] => 3, 3, 2, 1, 2, 1, 2, 1, 3
[3, 3, 2, 1, 2, 1, 2, 2, 1] => 3, 3, 2, 1, 2, 1, 2, 2, 1
[3, 3, 2, 1, 2, 1, 2, 2, 2] => 3, 3, 2, 1, 2, 1, 2, 2, 2
[3, 3, 2, 1, 2, 1, 2, 2, 3] => 3, 3, 2, 1, 2, 1, 2, 2, 3
[3, 3, 2, 1, 2, 1, 2, 3, 1] => 3, 3, 2, 1, 2, 1, 2, 3, 1
[3, 3, 2, 1, 2, 1, 2, 3, 2] => 3, 3, 2, 1, 2, 1, 2, 3, 2
[3, 3, 2, 1, 2, 1, 2, 3, 3] => 3, 3, 2, 1, 2, 1, 2, 3, 3
[3, 3, 2, 1, 2, 1, 3, 1, 1] => 3, 3, 2, 1, 2, 1, 3, 1, 1
[3, 3, 2, 1, 2, 1, 3, 1, 2] => 3, 3, 2, 1, 2, 1, 3, 1, 2
[3, 3, 2, 1, 2, 1, 3, 1, 3] => 3, 3, 2, 1, 2, 1, 3, 1, 3
[3, 3, 2, 1, 2, 1, 3, 2, 1] => 3, 3, 2, 1, 2, 1, 3, 2, 1
[3, 3, 2, 1, 2, 1, 3, 2, 2] => 3, 3, 2, 1, 2, 1, 3, 2, 2
[3, 3, 2, 1, 2, 1, 3, 2, 3] => 3, 3, 2, 1, 2, 1, 3, 2, 3
[3, 3, 2, 1, 2, 1, 3, 3, 1] => 3, 3, 2, 1, 2, 1, 3, 3, 1
[3, 3, 2, 1, 2, 1, 3, 3, 2] => 3, 3, 2, 1, 2, 1, 3, 3, 2
[3, 3, 2, 1, 2, 1, 3, 3, 3] => 3, 3, 2, 1, 2, 1, 3, 3, 3
[3, 3, 2, 1, 2, 2, 1, 1, 1] => 3, 3, 2, 1, 2, 2, 1, 1, 1
[3, 3, 2, 1, 2, 2, 1, 1, 2] => 3, 3, 2, 1, 2, 2, 1, 1, 2
[3, 3, 2, 1, 2, 2, 1, 1, 3] => 3, 3, 2, 1, 2, 2, 1, 1, 3
[3, 3, 2, 1, 2, 2, 1, 2, 1] => 3, 3, 2, 1, 2, 2, 1, 2, 1
[3, 3, 2, 1, 2, 2, 1, 2, 2] => 3, 3, 2, 1, 2, 2, 1, 2, 2
[3, 3, 2, 1, 2, 2, 1, 2, 3] => 3, 3, 2, 1, 2, 2, 1, 2, 3
[3, 3, 2, 1, 2, 2, 1, 3, 1] => 3, 3, 2, 1, 2, 2, 1, 3, 1
[3, 3, 2, 1, 2, 2, 1, 3, 2] => 3, 3, 2, 1, 2, 2, 1, 3, 2
[3, 3, 2, 1, 2, 2, 1, 3, 3] => 3, 3, 2, 1, 2, 2, 1, 3, 3
[3, 3, 2, 1, 2, 2, 2, 1, 1] => 3, 3, 2, 1, 2, 2, 2, 1, 1
[3, 3, 2, 1, 2, 2, 2, 1, 2] => 3, 3, 2, 1, 2, 2, 2, 1, 2
[3, 3, 2, 1, 2, 2, 2, 1, 3] => 3, 3, 2, 1, 2, 2, 2, 1, 3
[3, 3, 2, 1, 2, 2, 2, 2, 1] => 3, 3, 2, 1, 2, 2, 2, 2, 1
[3, 3, 2, 1, 2, 2, 2, 2, 2] => 3, 3, 2, 1, 2, 2, 2, 2, 2
[3, 3, 2, 1, 2, 2, 2, 2, 3] => 3, 3, 2, 1, 2, 2, 2, 2, 3
[3, 3, 2, 1, 2, 2, 2, 3, 1] => 3, 3, 2, 1, 2, 2, 2, 3, 1
[3, 3, 2, 1, 2, 2, 2, 3, 2] => 3, 3, 2, 1, 2, 2, 2, 3, 2
[3, 3, 2, 1, 2, 2, 2, 3, 3] => 3, 3, 2, 1, 2, 2, 2, 3, 3
[3, 3, 2, 1, 2, 2, 3, 1, 1] => 3, 3, 2, 1, 2, 2, 3, 1, 1
[3, 3, 2, 1, 2, 2, 3, 1, 2] => 3, 3, 2, 1, 2, 2, 3, 1, 2
[3, 3, 2, 1, 2, 2, 3, 1, 3] => 3, 3, 2, 1, 2, 2, 3, 1, 3
[3, 3, 2, 1, 2, 2, 3, 2, 1] => 3, 3, 2, 1, 2, 2, 3, 2, 1
[3, 3, 2, 1, 2, 2, 3, 2, 2] => 3, 3, 2, 1, 2, 2, 3, 2, 2
[3, 3, 2, 1, 2, 2, 3, 2, 3] => 3, 3, 2, 1, 2, 2, 3, 2, 3
[3, 3, 2, 1, 2, 2, 3, 3, 1] => 3, 3, 2, 1, 2, 2, 3, 3, 1
[3, 3, 2, 1, 2, 2, 3, 3, 2] => 3, 3, 2, 1, 2, 2, 3, 3, 2
[3, 3, 2, 1, 2, 2, 3, 3, 3] => 3, 3, 2, 1, 2, 2, 3, 3, 3
[3, 3, 2, 1, 2, 3, 1, 1, 1] => 3, 3, 2, 1, 2, 3, 1, 1, 1
[3, 3, 2, 1, 2, 3, 1, 1, 2] => 3, 3, 2, 1, 2, 3, 1, 1, 2
[3, 3, 2, 1, 2, 3, 1, 1, 3] => 3, 3, 2, 1, 2, 3, 1, 1, 3
[3, 3, 2, 1, 2, 3, 1, 2, 1] => 3, 3, 2, 1, 2, 3, 1, 2, 1
[3, 3, 2, 1, 2, 3, 1, 2, 2] => 3, 3, 2, 1, 2, 3, 1, 2, 2
[3, 3, 2, 1, 2, 3, 1, 2, 3] => 3, 3, 2, 1, 2, 3, 1, 2, 3
[3, 3, 2, 1, 2, 3, 1, 3, 1] => 3, 3, 2, 1, 2, 3, 1, 3, 1
[3, 3, 2, 1, 2, 3, 1, 3, 2] => 3, 3, 2, 1, 2, 3, 1, 3, 2
[3, 3, 2, 1, 2, 3, 1, 3, 3] => 3, 3, 2, 1, 2, 3, 1, 3, 3
[3, 3, 2, 1, 2, 3, 2, 1, 1] => 3, 3, 2, 1, 2, 3, 2, 1, 1
[3, 3, 2, 1, 2, 3, 2, 1, 2] => 3, 3, 2, 1, 2, 3, 2, 1, 2
[3, 3, 2, 1, 2, 3, 2, 1, 3] => 3, 3, 2, 1, 2, 3, 2, 1, 3
[3, 3, 2, 1, 2, 3, 2, 2, 1] => 3, 3, 2, 1, 2, 3, 2, 2, 1
[3, 3, 2, 1, 2, 3, 2, 2, 2] => 3, 3, 2, 1, 2, 3, 2, 2, 2
[3, 3, 2, 1, 2, 3, 2, 2, 3] => 3, 3, 2, 1, 2, 3, 2, 2, 3
[3, 3, 2, 1, 2, 3, 2, 3, 1] => 3, 3, 2, 1, 2, 3, 2, 3, 1
[3, 3, 2, 1, 2, 3, 2, 3, 2] => 3, 3, 2, 1, 2, 3, 2, 3, 2
[3, 3, 2, 1, 2, 3, 2, 3, 3] => 3, 3, 2, 1, 2, 3, 2, 3, 3
[3, 3, 2, 1, 2, 3, 3, 1, 1] => 3, 3, 2, 1, 2, 3, 3, 1, 1
[3, 3, 2, 1, 2, 3, 3, 1, 2] => 3, 3, 2, 1, 2, 3, 3, 1, 2
[3, 3, 2, 1, 2, 3, 3, 1, 3] => 3, 3, 2, 1, 2, 3, 3, 1, 3
[3, 3, 2, 1, 2, 3, 3, 2, 1] => 3, 3, 2, 1, 2, 3, 3, 2, 1
[3, 3, 2, 1, 2, 3, 3, 2, 2] => 3, 3, 2, 1, 2, 3, 3, 2, 2
[3, 3, 2, 1, 2, 3, 3, 2, 3] => 3, 3, 2, 1, 2, 3, 3, 2, 3
[3, 3, 2, 1, 2, 3, 3, 3, 1] => 3, 3, 2, 1, 2, 3, 3, 3, 1
[3, 3, 2, 1, 2, 3, 3, 3, 2] => 3, 3, 2, 1, 2, 3, 3, 3, 2
[3, 3, 2, 1, 2, 3, 3, 3, 3] => 3, 3, 2, 1, 2, 3, 3, 3, 3
[3, 3, 2, 1, 3, 1, 1, 1, 1] => 3, 3, 2, 1, 3, 1, 1, 1, 1
[3, 3, 2, 1, 3, 1, 1, 1, 2] => 3, 3, 2, 1, 3, 1, 1, 1, 2
[3, 3, 2, 1, 3, 1, 1, 1, 3] => 3, 3, 2, 1, 3, 1, 1, 1, 3
[3, 3, 2, 1, 3, 1, 1, 2, 1] => 3, 3, 2, 1, 3, 1, 1, 2, 1
[3, 3, 2, 1, 3, 1, 1, 2, 2] => 3, 3, 2, 1, 3, 1, 1, 2, 2
[3, 3, 2, 1, 3, 1, 1, 2, 3] => 3, 3, 2, 1, 3, 1, 1, 2, 3
[3, 3, 2, 1, 3, 1, 1, 3, 1] => 3, 3, 2, 1, 3, 1, 1, 3, 1
[3, 3, 2, 1, 3, 1, 1, 3, 2] => 3, 3, 2, 1, 3, 1, 1, 3, 2
[3, 3, 2, 1, 3, 1, 1, 3, 3] => 3, 3, 2, 1, 3, 1, 1, 3, 3
[3, 3, 2, 1, 3, 1, 2, 1, 1] => 3, 3, 2, 1, 3, 1, 2, 1, 1
[3, 3, 2, 1, 3, 1, 2, 1, 2] => 3, 3, 2, 1, 3, 1, 2, 1, 2
[3, 3, 2, 1, 3, 1, 2, 1, 3] => 3, 3, 2, 1, 3, 1, 2, 1, 3
[3, 3, 2, 1, 3, 1, 2, 2, 1] => 3, 3, 2, 1, 3, 1, 2, 2, 1
[3, 3, 2, 1, 3, 1, 2, 2, 2] => 3, 3, 2, 1, 3, 1, 2, 2, 2
[3, 3, 2, 1, 3, 1, 2, 2, 3] => 3, 3, 2, 1, 3, 1, 2, 2, 3
[3, 3, 2, 1, 3, 1, 2, 3, 1] => 3, 3, 2, 1, 3, 1, 2, 3, 1
[3, 3, 2, 1, 3, 1, 2, 3, 2] => 3, 3, 2, 1, 3, 1, 2, 3, 2
[3, 3, 2, 1, 3, 1, 2, 3, 3] => 3, 3, 2, 1, 3, 1, 2, 3, 3
[3, 3, 2, 1, 3, 1, 3, 1, 1] => 3, 3, 2, 1, 3, 1, 3, 1, 1
[3, 3, 2, 1, 3, 1, 3, 1, 2] => 3, 3, 2, 1, 3, 1, 3, 1, 2
[3, 3, 2, 1, 3, 1, 3, 1, 3] => 3, 3, 2, 1, 3, 1, 3, 1, 3
[3, 3, 2, 1, 3, 1, 3, 2, 1] => 3, 3, 2, 1, 3, 1, 3, 2, 1
[3, 3, 2, 1, 3, 1, 3, 2, 2] => 3, 3, 2, 1, 3, 1, 3, 2, 2
[3, 3, 2, 1, 3, 1, 3, 2, 3] => 3, 3, 2, 1, 3, 1, 3, 2, 3
[3, 3, 2, 1, 3, 1, 3, 3, 1] => 3, 3, 2, 1, 3, 1, 3, 3, 1
[3, 3, 2, 1, 3, 1, 3, 3, 2] => 3, 3, 2, 1, 3, 1, 3, 3, 2
[3, 3, 2, 1, 3, 1, 3, 3, 3] => 3, 3, 2, 1, 3, 1, 3, 3, 3
[3, 3, 2, 1, 3, 2, 1, 1, 1] => 3, 3, 2, 1, 3, 2, 1, 1, 1
[3, 3, 2, 1, 3, 2, 1, 1, 2] => 3, 3, 2, 1, 3, 2, 1, 1, 2
[3, 3, 2, 1, 3, 2, 1, 1, 3] => 3, 3, 2, 1, 3, 2, 1, 1, 3
[3, 3, 2, 1, 3, 2, 1, 2, 1] => 3, 3, 2, 1, 3, 2, 1, 2, 1
[3, 3, 2, 1, 3, 2, 1, 2, 2] => 3, 3, 2, 1, 3, 2, 1, 2, 2
[3, 3, 2, 1, 3, 2, 1, 2, 3] => 3, 3, 2, 1, 3, 2, 1, 2, 3
[3, 3, 2, 1, 3, 2, 1, 3, 1] => 3, 3, 2, 1, 3, 2, 1, 3, 1
[3, 3, 2, 1, 3, 2, 1, 3, 2] => 3, 3, 2, 1, 3, 2, 1, 3, 2
[3, 3, 2, 1, 3, 2, 1, 3, 3] => 3, 3, 2, 1, 3, 2, 1, 3, 3
[3, 3, 2, 1, 3, 2, 2, 1, 1] => 3, 3, 2, 1, 3, 2, 2, 1, 1
[3, 3, 2, 1, 3, 2, 2, 1, 2] => 3, 3, 2, 1, 3, 2, 2, 1, 2
[3, 3, 2, 1, 3, 2, 2, 1, 3] => 3, 3, 2, 1, 3, 2, 2, 1, 3
[3, 3, 2, 1, 3, 2, 2, 2, 1] => 3, 3, 2, 1, 3, 2, 2, 2, 1
[3, 3, 2, 1, 3, 2, 2, 2, 2] => 3, 3, 2, 1, 3, 2, 2, 2, 2
[3, 3, 2, 1, 3, 2, 2, 2, 3] => 3, 3, 2, 1, 3, 2, 2, 2, 3
[3, 3, 2, 1, 3, 2, 2, 3, 1] => 3, 3, 2, 1, 3, 2, 2, 3, 1
[3, 3, 2, 1, 3, 2, 2, 3, 2] => 3, 3, 2, 1, 3, 2, 2, 3, 2
[3, 3, 2, 1, 3, 2, 2, 3, 3] => 3, 3, 2, 1, 3, 2, 2, 3, 3
[3, 3, 2, 1, 3, 2, 3, 1, 1] => 3, 3, 2, 1, 3, 2, 3, 1, 1
[3, 3, 2, 1, 3, 2, 3, 1, 2] => 3, 3, 2, 1, 3, 2, 3, 1, 2
[3, 3, 2, 1, 3, 2, 3, 1, 3] => 3, 3, 2, 1, 3, 2, 3, 1, 3
[3, 3, 2, 1, 3, 2, 3, 2, 1] => 3, 3, 2, 1, 3, 2, 3, 2, 1
[3, 3, 2, 1, 3, 2, 3, 2, 2] => 3, 3, 2, 1, 3, 2, 3, 2, 2
[3, 3, 2, 1, 3, 2, 3, 2, 3] => 3, 3, 2, 1, 3, 2, 3, 2, 3
[3, 3, 2, 1, 3, 2, 3, 3, 1] => 3, 3, 2, 1, 3, 2, 3, 3, 1
[3, 3, 2, 1, 3, 2, 3, 3, 2] => 3, 3, 2, 1, 3, 2, 3, 3, 2
[3, 3, 2, 1, 3, 2, 3, 3, 3] => 3, 3, 2, 1, 3, 2, 3, 3, 3
[3, 3, 2, 1, 3, 3, 1, 1, 1] => 3, 3, 2, 1, 3, 3, 1, 1, 1
[3, 3, 2, 1, 3, 3, 1, 1, 2] => 3, 3, 2, 1, 3, 3, 1, 1, 2
[3, 3, 2, 1, 3, 3, 1, 1, 3] => 3, 3, 2, 1, 3, 3, 1, 1, 3
[3, 3, 2, 1, 3, 3, 1, 2, 1] => 3, 3, 2, 1, 3, 3, 1, 2, 1
[3, 3, 2, 1, 3, 3, 1, 2, 2] => 3, 3, 2, 1, 3, 3, 1, 2, 2
[3, 3, 2, 1, 3, 3, 1, 2, 3] => 3, 3, 2, 1, 3, 3, 1, 2, 3
[3, 3, 2, 1, 3, 3, 1, 3, 1] => 3, 3, 2, 1, 3, 3, 1, 3, 1
[3, 3, 2, 1, 3, 3, 1, 3, 2] => 3, 3, 2, 1, 3, 3, 1, 3, 2
[3, 3, 2, 1, 3, 3, 1, 3, 3] => 3, 3, 2, 1, 3, 3, 1, 3, 3
[3, 3, 2, 1, 3, 3, 2, 1, 1] => 3, 3, 2, 1, 3, 3, 2, 1, 1
[3, 3, 2, 1, 3, 3, 2, 1, 2] => 3, 3, 2, 1, 3, 3, 2, 1, 2
[3, 3, 2, 1, 3, 3, 2, 1, 3] => 3, 3, 2, 1, 3, 3, 2, 1, 3
[3, 3, 2, 1, 3, 3, 2, 2, 1] => 3, 3, 2, 1, 3, 3, 2, 2, 1
[3, 3, 2, 1, 3, 3, 2, 2, 2] => 3, 3, 2, 1, 3, 3, 2, 2, 2
[3, 3, 2, 1, 3, 3, 2, 2, 3] => 3, 3, 2, 1, 3, 3, 2, 2, 3
[3, 3, 2, 1, 3, 3, 2, 3, 1] => 3, 3, 2, 1, 3, 3, 2, 3, 1
[3, 3, 2, 1, 3, 3, 2, 3, 2] => 3, 3, 2, 1, 3, 3, 2, 3, 2
[3, 3, 2, 1, 3, 3, 2, 3, 3] => 3, 3, 2, 1, 3, 3, 2, 3, 3
[3, 3, 2, 1, 3, 3, 3, 1, 1] => 3, 3, 2, 1, 3, 3, 3, 1, 1
[3, 3, 2, 1, 3, 3, 3, 1, 2] => 3, 3, 2, 1, 3, 3, 3, 1, 2
[3, 3, 2, 1, 3, 3, 3, 1, 3] => 3, 3, 2, 1, 3, 3, 3, 1, 3
[3, 3, 2, 1, 3, 3, 3, 2, 1] => 3, 3, 2, 1, 3, 3, 3, 2, 1
[3, 3, 2, 1, 3, 3, 3, 2, 2] => 3, 3, 2, 1, 3, 3, 3, 2, 2
[3, 3, 2, 1, 3, 3, 3, 2, 3] => 3, 3, 2, 1, 3, 3, 3, 2, 3
[3, 3, 2, 1, 3, 3, 3, 3, 1] => 3, 3, 2, 1, 3, 3, 3, 3, 1
[3, 3, 2, 1, 3, 3, 3, 3, 2] => 3, 3, 2, 1, 3, 3, 3, 3, 2
[3, 3, 2, 1, 3, 3, 3, 3, 3] => 3, 3, 2, 1, 3, 3, 3, 3, 3
[3, 3, 2, 2, 1, 1, 1, 1, 1] => 3, 3, 2, 2, 1, 1, 1, 1, 1
[3, 3, 2, 2, 1, 1, 1, 1, 2] => 3, 3, 2, 2, 1, 1, 1, 1, 2
[3, 3, 2, 2, 1, 1, 1, 1, 3] => 3, 3, 2, 2, 1, 1, 1, 1, 3
[3, 3, 2, 2, 1, 1, 1, 2, 1] => 3, 3, 2, 2, 1, 1, 1, 2, 1
[3, 3, 2, 2, 1, 1, 1, 2, 2] => 3, 3, 2, 2, 1, 1, 1, 2, 2
[3, 3, 2, 2, 1, 1, 1, 2, 3] => 3, 3, 2, 2, 1, 1, 1, 2, 3
[3, 3, 2, 2, 1, 1, 1, 3, 1] => 3, 3, 2, 2, 1, 1, 1, 3, 1
[3, 3, 2, 2, 1, 1, 1, 3, 2] => 3, 3, 2, 2, 1, 1, 1, 3, 2
[3, 3, 2, 2, 1, 1, 1, 3, 3] => 3, 3, 2, 2, 1, 1, 1, 3, 3
[3, 3, 2, 2, 1, 1, 2, 1, 1] => 3, 3, 2, 2, 1, 1, 2, 1, 1
[3, 3, 2, 2, 1, 1, 2, 1, 2] => 3, 3, 2, 2, 1, 1, 2, 1, 2
[3, 3, 2, 2, 1, 1, 2, 1, 3] => 3, 3, 2, 2, 1, 1, 2, 1, 3
[3, 3, 2, 2, 1, 1, 2, 2, 1] => 3, 3, 2, 2, 1, 1, 2, 2, 1
[3, 3, 2, 2, 1, 1, 2, 2, 2] => 3, 3, 2, 2, 1, 1, 2, 2, 2
[3, 3, 2, 2, 1, 1, 2, 2, 3] => 3, 3, 2, 2, 1, 1, 2, 2, 3
[3, 3, 2, 2, 1, 1, 2, 3, 1] => 3, 3, 2, 2, 1, 1, 2, 3, 1
[3, 3, 2, 2, 1, 1, 2, 3, 2] => 3, 3, 2, 2, 1, 1, 2, 3, 2
[3, 3, 2, 2, 1, 1, 2, 3, 3] => 3, 3, 2, 2, 1, 1, 2, 3, 3
[3, 3, 2, 2, 1, 1, 3, 1, 1] => 3, 3, 2, 2, 1, 1, 3, 1, 1
[3, 3, 2, 2, 1, 1, 3, 1, 2] => 3, 3, 2, 2, 1, 1, 3, 1, 2
[3, 3, 2, 2, 1, 1, 3, 1, 3] => 3, 3, 2, 2, 1, 1, 3, 1, 3
[3, 3, 2, 2, 1, 1, 3, 2, 1] => 3, 3, 2, 2, 1, 1, 3, 2, 1
[3, 3, 2, 2, 1, 1, 3, 2, 2] => 3, 3, 2, 2, 1, 1, 3, 2, 2
[3, 3, 2, 2, 1, 1, 3, 2, 3] => 3, 3, 2, 2, 1, 1, 3, 2, 3
[3, 3, 2, 2, 1, 1, 3, 3, 1] => 3, 3, 2, 2, 1, 1, 3, 3, 1
[3, 3, 2, 2, 1, 1, 3, 3, 2] => 3, 3, 2, 2, 1, 1, 3, 3, 2
[3, 3, 2, 2, 1, 1, 3, 3, 3] => 3, 3, 2, 2, 1, 1, 3, 3, 3
[3, 3, 2, 2, 1, 2, 1, 1, 1] => 3, 3, 2, 2, 1, 2, 1, 1, 1
[3, 3, 2, 2, 1, 2, 1, 1, 2] => 3, 3, 2, 2, 1, 2, 1, 1, 2
[3, 3, 2, 2, 1, 2, 1, 1, 3] => 3, 3, 2, 2, 1, 2, 1, 1, 3
[3, 3, 2, 2, 1, 2, 1, 2, 1] => 3, 3, 2, 2, 1, 2, 1, 2, 1
[3, 3, 2, 2, 1, 2, 1, 2, 2] => 3, 3, 2, 2, 1, 2, 1, 2, 2
[3, 3, 2, 2, 1, 2, 1, 2, 3] => 3, 3, 2, 2, 1, 2, 1, 2, 3
[3, 3, 2, 2, 1, 2, 1, 3, 1] => 3, 3, 2, 2, 1, 2, 1, 3, 1
[3, 3, 2, 2, 1, 2, 1, 3, 2] => 3, 3, 2, 2, 1, 2, 1, 3, 2
[3, 3, 2, 2, 1, 2, 1, 3, 3] => 3, 3, 2, 2, 1, 2, 1, 3, 3
[3, 3, 2, 2, 1, 2, 2, 1, 1] => 3, 3, 2, 2, 1, 2, 2, 1, 1
[3, 3, 2, 2, 1, 2, 2, 1, 2] => 3, 3, 2, 2, 1, 2, 2, 1, 2
[3, 3, 2, 2, 1, 2, 2, 1, 3] => 3, 3, 2, 2, 1, 2, 2, 1, 3
[3, 3, 2, 2, 1, 2, 2, 2, 1] => 3, 3, 2, 2, 1, 2, 2, 2, 1
[3, 3, 2, 2, 1, 2, 2, 2, 2] => 3, 3, 2, 2, 1, 2, 2, 2, 2
[3, 3, 2, 2, 1, 2, 2, 2, 3] => 3, 3, 2, 2, 1, 2, 2, 2, 3
[3, 3, 2, 2, 1, 2, 2, 3, 1] => 3, 3, 2, 2, 1, 2, 2, 3, 1
[3, 3, 2, 2, 1, 2, 2, 3, 2] => 3, 3, 2, 2, 1, 2, 2, 3, 2
[3, 3, 2, 2, 1, 2, 2, 3, 3] => 3, 3, 2, 2, 1, 2, 2, 3, 3
[3, 3, 2, 2, 1, 2, 3, 1, 1] => 3, 3, 2, 2, 1, 2, 3, 1, 1
[3, 3, 2, 2, 1, 2, 3, 1, 2] => 3, 3, 2, 2, 1, 2, 3, 1, 2
[3, 3, 2, 2, 1, 2, 3, 1, 3] => 3, 3, 2, 2, 1, 2, 3, 1, 3
[3, 3, 2, 2, 1, 2, 3, 2, 1] => 3, 3, 2, 2, 1, 2, 3, 2, 1
[3, 3, 2, 2, 1, 2, 3, 2, 2] => 3, 3, 2, 2, 1, 2, 3, 2, 2
[3, 3, 2, 2, 1, 2, 3, 2, 3] => 3, 3, 2, 2, 1, 2, 3, 2, 3
[3, 3, 2, 2, 1, 2, 3, 3, 1] => 3, 3, 2, 2, 1, 2, 3, 3, 1
[3, 3, 2, 2, 1, 2, 3, 3, 2] => 3, 3, 2, 2, 1, 2, 3, 3, 2
[3, 3, 2, 2, 1, 2, 3, 3, 3] => 3, 3, 2, 2, 1, 2, 3, 3, 3
[3, 3, 2, 2, 1, 3, 1, 1, 1] => 3, 3, 2, 2, 1, 3, 1, 1, 1
[3, 3, 2, 2, 1, 3, 1, 1, 2] => 3, 3, 2, 2, 1, 3, 1, 1, 2
[3, 3, 2, 2, 1, 3, 1, 1, 3] => 3, 3, 2, 2, 1, 3, 1, 1, 3
[3, 3, 2, 2, 1, 3, 1, 2, 1] => 3, 3, 2, 2, 1, 3, 1, 2, 1
[3, 3, 2, 2, 1, 3, 1, 2, 2] => 3, 3, 2, 2, 1, 3, 1, 2, 2
[3, 3, 2, 2, 1, 3, 1, 2, 3] => 3, 3, 2, 2, 1, 3, 1, 2, 3
[3, 3, 2, 2, 1, 3, 1, 3, 1] => 3, 3, 2, 2, 1, 3, 1, 3, 1
[3, 3, 2, 2, 1, 3, 1, 3, 2] => 3, 3, 2, 2, 1, 3, 1, 3, 2
[3, 3, 2, 2, 1, 3, 1, 3, 3] => 3, 3, 2, 2, 1, 3, 1, 3, 3
[3, 3, 2, 2, 1, 3, 2, 1, 1] => 3, 3, 2, 2, 1, 3, 2, 1, 1
[3, 3, 2, 2, 1, 3, 2, 1, 2] => 3, 3, 2, 2, 1, 3, 2, 1, 2
[3, 3, 2, 2, 1, 3, 2, 1, 3] => 3, 3, 2, 2, 1, 3, 2, 1, 3
[3, 3, 2, 2, 1, 3, 2, 2, 1] => 3, 3, 2, 2, 1, 3, 2, 2, 1
[3, 3, 2, 2, 1, 3, 2, 2, 2] => 3, 3, 2, 2, 1, 3, 2, 2, 2
[3, 3, 2, 2, 1, 3, 2, 2, 3] => 3, 3, 2, 2, 1, 3, 2, 2, 3
[3, 3, 2, 2, 1, 3, 2, 3, 1] => 3, 3, 2, 2, 1, 3, 2, 3, 1
[3, 3, 2, 2, 1, 3, 2, 3, 2] => 3, 3, 2, 2, 1, 3, 2, 3, 2
[3, 3, 2, 2, 1, 3, 2, 3, 3] => 3, 3, 2, 2, 1, 3, 2, 3, 3
[3, 3, 2, 2, 1, 3, 3, 1, 1] => 3, 3, 2, 2, 1, 3, 3, 1, 1
[3, 3, 2, 2, 1, 3, 3, 1, 2] => 3, 3, 2, 2, 1, 3, 3, 1, 2
[3, 3, 2, 2, 1, 3, 3, 1, 3] => 3, 3, 2, 2, 1, 3, 3, 1, 3
[3, 3, 2, 2, 1, 3, 3, 2, 1] => 3, 3, 2, 2, 1, 3, 3, 2, 1
[3, 3, 2, 2, 1, 3, 3, 2, 2] => 3, 3, 2, 2, 1, 3, 3, 2, 2
[3, 3, 2, 2, 1, 3, 3, 2, 3] => 3, 3, 2, 2, 1, 3, 3, 2, 3
[3, 3, 2, 2, 1, 3, 3, 3, 1] => 3, 3, 2, 2, 1, 3, 3, 3, 1
[3, 3, 2, 2, 1, 3, 3, 3, 2] => 3, 3, 2, 2, 1, 3, 3, 3, 2
[3, 3, 2, 2, 1, 3, 3, 3, 3] => 3, 3, 2, 2, 1, 3, 3, 3, 3
[3, 3, 2, 2, 2, 1, 1, 1, 1] => 3, 3, 2, 2, 2, 1, 1, 1, 1
[3, 3, 2, 2, 2, 1, 1, 1, 2] => 3, 3, 2, 2, 2, 1, 1, 1, 2
[3, 3, 2, 2, 2, 1, 1, 1, 3] => 3, 3, 2, 2, 2, 1, 1, 1, 3
[3, 3, 2, 2, 2, 1, 1, 2, 1] => 3, 3, 2, 2, 2, 1, 1, 2, 1
[3, 3, 2, 2, 2, 1, 1, 2, 2] => 3, 3, 2, 2, 2, 1, 1, 2, 2
[3, 3, 2, 2, 2, 1, 1, 2, 3] => 3, 3, 2, 2, 2, 1, 1, 2, 3
[3, 3, 2, 2, 2, 1, 1, 3, 1] => 3, 3, 2, 2, 2, 1, 1, 3, 1
[3, 3, 2, 2, 2, 1, 1, 3, 2] => 3, 3, 2, 2, 2, 1, 1, 3, 2
[3, 3, 2, 2, 2, 1, 1, 3, 3] => 3, 3, 2, 2, 2, 1, 1, 3, 3
[3, 3, 2, 2, 2, 1, 2, 1, 1] => 3, 3, 2, 2, 2, 1, 2, 1, 1
[3, 3, 2, 2, 2, 1, 2, 1, 2] => 3, 3, 2, 2, 2, 1, 2, 1, 2
[3, 3, 2, 2, 2, 1, 2, 1, 3] => 3, 3, 2, 2, 2, 1, 2, 1, 3
[3, 3, 2, 2, 2, 1, 2, 2, 1] => 3, 3, 2, 2, 2, 1, 2, 2, 1
[3, 3, 2, 2, 2, 1, 2, 2, 2] => 3, 3, 2, 2, 2, 1, 2, 2, 2
[3, 3, 2, 2, 2, 1, 2, 2, 3] => 3, 3, 2, 2, 2, 1, 2, 2, 3
[3, 3, 2, 2, 2, 1, 2, 3, 1] => 3, 3, 2, 2, 2, 1, 2, 3, 1
[3, 3, 2, 2, 2, 1, 2, 3, 2] => 3, 3, 2, 2, 2, 1, 2, 3, 2
[3, 3, 2, 2, 2, 1, 2, 3, 3] => 3, 3, 2, 2, 2, 1, 2, 3, 3
[3, 3, 2, 2, 2, 1, 3, 1, 1] => 3, 3, 2, 2, 2, 1, 3, 1, 1
[3, 3, 2, 2, 2, 1, 3, 1, 2] => 3, 3, 2, 2, 2, 1, 3, 1, 2
[3, 3, 2, 2, 2, 1, 3, 1, 3] => 3, 3, 2, 2, 2, 1, 3, 1, 3
[3, 3, 2, 2, 2, 1, 3, 2, 1] => 3, 3, 2, 2, 2, 1, 3, 2, 1
[3, 3, 2, 2, 2, 1, 3, 2, 2] => 3, 3, 2, 2, 2, 1, 3, 2, 2
[3, 3, 2, 2, 2, 1, 3, 2, 3] => 3, 3, 2, 2, 2, 1, 3, 2, 3
[3, 3, 2, 2, 2, 1, 3, 3, 1] => 3, 3, 2, 2, 2, 1, 3, 3, 1
[3, 3, 2, 2, 2, 1, 3, 3, 2] => 3, 3, 2, 2, 2, 1, 3, 3, 2
[3, 3, 2, 2, 2, 1, 3, 3, 3] => 3, 3, 2, 2, 2, 1, 3, 3, 3
[3, 3, 2, 2, 2, 2, 1, 1, 1] => 3, 3, 2, 2, 2, 2, 1, 1, 1
[3, 3, 2, 2, 2, 2, 1, 1, 2] => 3, 3, 2, 2, 2, 2, 1, 1, 2
[3, 3, 2, 2, 2, 2, 1, 1, 3] => 3, 3, 2, 2, 2, 2, 1, 1, 3
[3, 3, 2, 2, 2, 2, 1, 2, 1] => 3, 3, 2, 2, 2, 2, 1, 2, 1
[3, 3, 2, 2, 2, 2, 1, 2, 2] => 3, 3, 2, 2, 2, 2, 1, 2, 2
[3, 3, 2, 2, 2, 2, 1, 2, 3] => 3, 3, 2, 2, 2, 2, 1, 2, 3
[3, 3, 2, 2, 2, 2, 1, 3, 1] => 3, 3, 2, 2, 2, 2, 1, 3, 1
[3, 3, 2, 2, 2, 2, 1, 3, 2] => 3, 3, 2, 2, 2, 2, 1, 3, 2
[3, 3, 2, 2, 2, 2, 1, 3, 3] => 3, 3, 2, 2, 2, 2, 1, 3, 3
[3, 3, 2, 2, 2, 2, 2, 1, 1] => 3, 3, 2, 2, 2, 2, 2, 1, 1
[3, 3, 2, 2, 2, 2, 2, 1, 2] => 3, 3, 2, 2, 2, 2, 2, 1, 2
[3, 3, 2, 2, 2, 2, 2, 1, 3] => 3, 3, 2, 2, 2, 2, 2, 1, 3
[3, 3, 2, 2, 2, 2, 2, 2, 1] => 3, 3, 2, 2, 2, 2, 2, 2, 1
[3, 3, 2, 2, 2, 2, 2, 2, 2] => 3, 3, 2, 2, 2, 2, 2, 2, 2
[3, 3, 2, 2, 2, 2, 2, 2, 3] => 3, 3, 2, 2, 2, 2, 2, 2, 3
[3, 3, 2, 2, 2, 2, 2, 3, 1] => 3, 3, 2, 2, 2, 2, 2, 3, 1
[3, 3, 2, 2, 2, 2, 2, 3, 2] => 3, 3, 2, 2, 2, 2, 2, 3, 2
[3, 3, 2, 2, 2, 2, 2, 3, 3] => 3, 3, 2, 2, 2, 2, 2, 3, 3
[3, 3, 2, 2, 2, 2, 3, 1, 1] => 3, 3, 2, 2, 2, 2, 3, 1, 1
[3, 3, 2, 2, 2, 2, 3, 1, 2] => 3, 3, 2, 2, 2, 2, 3, 1, 2
[3, 3, 2, 2, 2, 2, 3, 1, 3] => 3, 3, 2, 2, 2, 2, 3, 1, 3
[3, 3, 2, 2, 2, 2, 3, 2, 1] => 3, 3, 2, 2, 2, 2, 3, 2, 1
[3, 3, 2, 2, 2, 2, 3, 2, 2] => 3, 3, 2, 2, 2, 2, 3, 2, 2
[3, 3, 2, 2, 2, 2, 3, 2, 3] => 3, 3, 2, 2, 2, 2, 3, 2, 3
[3, 3, 2, 2, 2, 2, 3, 3, 1] => 3, 3, 2, 2, 2, 2, 3, 3, 1
[3, 3, 2, 2, 2, 2, 3, 3, 2] => 3, 3, 2, 2, 2, 2, 3, 3, 2
[3, 3, 2, 2, 2, 2, 3, 3, 3] => 3, 3, 2, 2, 2, 2, 3, 3, 3
[3, 3, 2, 2, 2, 3, 1, 1, 1] => 3, 3, 2, 2, 2, 3, 1, 1, 1
[3, 3, 2, 2, 2, 3, 1, 1, 2] => 3, 3, 2, 2, 2, 3, 1, 1, 2
[3, 3, 2, 2, 2, 3, 1, 1, 3] => 3, 3, 2, 2, 2, 3, 1, 1, 3
[3, 3, 2, 2, 2, 3, 1, 2, 1] => 3, 3, 2, 2, 2, 3, 1, 2, 1
[3, 3, 2, 2, 2, 3, 1, 2, 2] => 3, 3, 2, 2, 2, 3, 1, 2, 2
[3, 3, 2, 2, 2, 3, 1, 2, 3] => 3, 3, 2, 2, 2, 3, 1, 2, 3
[3, 3, 2, 2, 2, 3, 1, 3, 1] => 3, 3, 2, 2, 2, 3, 1, 3, 1
[3, 3, 2, 2, 2, 3, 1, 3, 2] => 3, 3, 2, 2, 2, 3, 1, 3, 2
[3, 3, 2, 2, 2, 3, 1, 3, 3] => 3, 3, 2, 2, 2, 3, 1, 3, 3
[3, 3, 2, 2, 2, 3, 2, 1, 1] => 3, 3, 2, 2, 2, 3, 2, 1, 1
[3, 3, 2, 2, 2, 3, 2, 1, 2] => 3, 3, 2, 2, 2, 3, 2, 1, 2
[3, 3, 2, 2, 2, 3, 2, 1, 3] => 3, 3, 2, 2, 2, 3, 2, 1, 3
[3, 3, 2, 2, 2, 3, 2, 2, 1] => 3, 3, 2, 2, 2, 3, 2, 2, 1
[3, 3, 2, 2, 2, 3, 2, 2, 2] => 3, 3, 2, 2, 2, 3, 2, 2, 2
[3, 3, 2, 2, 2, 3, 2, 2, 3] => 3, 3, 2, 2, 2, 3, 2, 2, 3
[3, 3, 2, 2, 2, 3, 2, 3, 1] => 3, 3, 2, 2, 2, 3, 2, 3, 1
[3, 3, 2, 2, 2, 3, 2, 3, 2] => 3, 3, 2, 2, 2, 3, 2, 3, 2
[3, 3, 2, 2, 2, 3, 2, 3, 3] => 3, 3, 2, 2, 2, 3, 2, 3, 3
[3, 3, 2, 2, 2, 3, 3, 1, 1] => 3, 3, 2, 2, 2, 3, 3, 1, 1
[3, 3, 2, 2, 2, 3, 3, 1, 2] => 3, 3, 2, 2, 2, 3, 3, 1, 2
[3, 3, 2, 2, 2, 3, 3, 1, 3] => 3, 3, 2, 2, 2, 3, 3, 1, 3
[3, 3, 2, 2, 2, 3, 3, 2, 1] => 3, 3, 2, 2, 2, 3, 3, 2, 1
[3, 3, 2, 2, 2, 3, 3, 2, 2] => 3, 3, 2, 2, 2, 3, 3, 2, 2
[3, 3, 2, 2, 2, 3, 3, 2, 3] => 3, 3, 2, 2, 2, 3, 3, 2, 3
[3, 3, 2, 2, 2, 3, 3, 3, 1] => 3, 3, 2, 2, 2, 3, 3, 3, 1
[3, 3, 2, 2, 2, 3, 3, 3, 2] => 3, 3, 2, 2, 2, 3, 3, 3, 2
[3, 3, 2, 2, 2, 3, 3, 3, 3] => 3, 3, 2, 2, 2, 3, 3, 3, 3
[3, 3, 2, 2, 3, 1, 1, 1, 1] => 3, 3, 2, 2, 3, 1, 1, 1, 1
[3, 3, 2, 2, 3, 1, 1, 1, 2] => 3, 3, 2, 2, 3, 1, 1, 1, 2
[3, 3, 2, 2, 3, 1, 1, 1, 3] => 3, 3, 2, 2, 3, 1, 1, 1, 3
[3, 3, 2, 2, 3, 1, 1, 2, 1] => 3, 3, 2, 2, 3, 1, 1, 2, 1
[3, 3, 2, 2, 3, 1, 1, 2, 2] => 3, 3, 2, 2, 3, 1, 1, 2, 2
[3, 3, 2, 2, 3, 1, 1, 2, 3] => 3, 3, 2, 2, 3, 1, 1, 2, 3
[3, 3, 2, 2, 3, 1, 1, 3, 1] => 3, 3, 2, 2, 3, 1, 1, 3, 1
[3, 3, 2, 2, 3, 1, 1, 3, 2] => 3, 3, 2, 2, 3, 1, 1, 3, 2
[3, 3, 2, 2, 3, 1, 1, 3, 3] => 3, 3, 2, 2, 3, 1, 1, 3, 3
[3, 3, 2, 2, 3, 1, 2, 1, 1] => 3, 3, 2, 2, 3, 1, 2, 1, 1
[3, 3, 2, 2, 3, 1, 2, 1, 2] => 3, 3, 2, 2, 3, 1, 2, 1, 2
[3, 3, 2, 2, 3, 1, 2, 1, 3] => 3, 3, 2, 2, 3, 1, 2, 1, 3
[3, 3, 2, 2, 3, 1, 2, 2, 1] => 3, 3, 2, 2, 3, 1, 2, 2, 1
[3, 3, 2, 2, 3, 1, 2, 2, 2] => 3, 3, 2, 2, 3, 1, 2, 2, 2
[3, 3, 2, 2, 3, 1, 2, 2, 3] => 3, 3, 2, 2, 3, 1, 2, 2, 3
[3, 3, 2, 2, 3, 1, 2, 3, 1] => 3, 3, 2, 2, 3, 1, 2, 3, 1
[3, 3, 2, 2, 3, 1, 2, 3, 2] => 3, 3, 2, 2, 3, 1, 2, 3, 2
[3, 3, 2, 2, 3, 1, 2, 3, 3] => 3, 3, 2, 2, 3, 1, 2, 3, 3
[3, 3, 2, 2, 3, 1, 3, 1, 1] => 3, 3, 2, 2, 3, 1, 3, 1, 1
[3, 3, 2, 2, 3, 1, 3, 1, 2] => 3, 3, 2, 2, 3, 1, 3, 1, 2
[3, 3, 2, 2, 3, 1, 3, 1, 3] => 3, 3, 2, 2, 3, 1, 3, 1, 3
[3, 3, 2, 2, 3, 1, 3, 2, 1] => 3, 3, 2, 2, 3, 1, 3, 2, 1
[3, 3, 2, 2, 3, 1, 3, 2, 2] => 3, 3, 2, 2, 3, 1, 3, 2, 2
[3, 3, 2, 2, 3, 1, 3, 2, 3] => 3, 3, 2, 2, 3, 1, 3, 2, 3
[3, 3, 2, 2, 3, 1, 3, 3, 1] => 3, 3, 2, 2, 3, 1, 3, 3, 1
[3, 3, 2, 2, 3, 1, 3, 3, 2] => 3, 3, 2, 2, 3, 1, 3, 3, 2
[3, 3, 2, 2, 3, 1, 3, 3, 3] => 3, 3, 2, 2, 3, 1, 3, 3, 3
[3, 3, 2, 2, 3, 2, 1, 1, 1] => 3, 3, 2, 2, 3, 2, 1, 1, 1
[3, 3, 2, 2, 3, 2, 1, 1, 2] => 3, 3, 2, 2, 3, 2, 1, 1, 2
[3, 3, 2, 2, 3, 2, 1, 1, 3] => 3, 3, 2, 2, 3, 2, 1, 1, 3
[3, 3, 2, 2, 3, 2, 1, 2, 1] => 3, 3, 2, 2, 3, 2, 1, 2, 1
[3, 3, 2, 2, 3, 2, 1, 2, 2] => 3, 3, 2, 2, 3, 2, 1, 2, 2
[3, 3, 2, 2, 3, 2, 1, 2, 3] => 3, 3, 2, 2, 3, 2, 1, 2, 3
[3, 3, 2, 2, 3, 2, 1, 3, 1] => 3, 3, 2, 2, 3, 2, 1, 3, 1
[3, 3, 2, 2, 3, 2, 1, 3, 2] => 3, 3, 2, 2, 3, 2, 1, 3, 2
[3, 3, 2, 2, 3, 2, 1, 3, 3] => 3, 3, 2, 2, 3, 2, 1, 3, 3
[3, 3, 2, 2, 3, 2, 2, 1, 1] => 3, 3, 2, 2, 3, 2, 2, 1, 1
[3, 3, 2, 2, 3, 2, 2, 1, 2] => 3, 3, 2, 2, 3, 2, 2, 1, 2
[3, 3, 2, 2, 3, 2, 2, 1, 3] => 3, 3, 2, 2, 3, 2, 2, 1, 3
[3, 3, 2, 2, 3, 2, 2, 2, 1] => 3, 3, 2, 2, 3, 2, 2, 2, 1
[3, 3, 2, 2, 3, 2, 2, 2, 2] => 3, 3, 2, 2, 3, 2, 2, 2, 2
[3, 3, 2, 2, 3, 2, 2, 2, 3] => 3, 3, 2, 2, 3, 2, 2, 2, 3
[3, 3, 2, 2, 3, 2, 2, 3, 1] => 3, 3, 2, 2, 3, 2, 2, 3, 1
[3, 3, 2, 2, 3, 2, 2, 3, 2] => 3, 3, 2, 2, 3, 2, 2, 3, 2
[3, 3, 2, 2, 3, 2, 2, 3, 3] => 3, 3, 2, 2, 3, 2, 2, 3, 3
[3, 3, 2, 2, 3, 2, 3, 1, 1] => 3, 3, 2, 2, 3, 2, 3, 1, 1
[3, 3, 2, 2, 3, 2, 3, 1, 2] => 3, 3, 2, 2, 3, 2, 3, 1, 2
[3, 3, 2, 2, 3, 2, 3, 1, 3] => 3, 3, 2, 2, 3, 2, 3, 1, 3
[3, 3, 2, 2, 3, 2, 3, 2, 1] => 3, 3, 2, 2, 3, 2, 3, 2, 1
[3, 3, 2, 2, 3, 2, 3, 2, 2] => 3, 3, 2, 2, 3, 2, 3, 2, 2
[3, 3, 2, 2, 3, 2, 3, 2, 3] => 3, 3, 2, 2, 3, 2, 3, 2, 3
[3, 3, 2, 2, 3, 2, 3, 3, 1] => 3, 3, 2, 2, 3, 2, 3, 3, 1
[3, 3, 2, 2, 3, 2, 3, 3, 2] => 3, 3, 2, 2, 3, 2, 3, 3, 2
[3, 3, 2, 2, 3, 2, 3, 3, 3] => 3, 3, 2, 2, 3, 2, 3, 3, 3
[3, 3, 2, 2, 3, 3, 1, 1, 1] => 3, 3, 2, 2, 3, 3, 1, 1, 1
[3, 3, 2, 2, 3, 3, 1, 1, 2] => 3, 3, 2, 2, 3, 3, 1, 1, 2
[3, 3, 2, 2, 3, 3, 1, 1, 3] => 3, 3, 2, 2, 3, 3, 1, 1, 3
[3, 3, 2, 2, 3, 3, 1, 2, 1] => 3, 3, 2, 2, 3, 3, 1, 2, 1
[3, 3, 2, 2, 3, 3, 1, 2, 2] => 3, 3, 2, 2, 3, 3, 1, 2, 2
[3, 3, 2, 2, 3, 3, 1, 2, 3] => 3, 3, 2, 2, 3, 3, 1, 2, 3
[3, 3, 2, 2, 3, 3, 1, 3, 1] => 3, 3, 2, 2, 3, 3, 1, 3, 1
[3, 3, 2, 2, 3, 3, 1, 3, 2] => 3, 3, 2, 2, 3, 3, 1, 3, 2
[3, 3, 2, 2, 3, 3, 1, 3, 3] => 3, 3, 2, 2, 3, 3, 1, 3, 3
[3, 3, 2, 2, 3, 3, 2, 1, 1] => 3, 3, 2, 2, 3, 3, 2, 1, 1
[3, 3, 2, 2, 3, 3, 2, 1, 2] => 3, 3, 2, 2, 3, 3, 2, 1, 2
[3, 3, 2, 2, 3, 3, 2, 1, 3] => 3, 3, 2, 2, 3, 3, 2, 1, 3
[3, 3, 2, 2, 3, 3, 2, 2, 1] => 3, 3, 2, 2, 3, 3, 2, 2, 1
[3, 3, 2, 2, 3, 3, 2, 2, 2] => 3, 3, 2, 2, 3, 3, 2, 2, 2
[3, 3, 2, 2, 3, 3, 2, 2, 3] => 3, 3, 2, 2, 3, 3, 2, 2, 3
[3, 3, 2, 2, 3, 3, 2, 3, 1] => 3, 3, 2, 2, 3, 3, 2, 3, 1
[3, 3, 2, 2, 3, 3, 2, 3, 2] => 3, 3, 2, 2, 3, 3, 2, 3, 2
[3, 3, 2, 2, 3, 3, 2, 3, 3] => 3, 3, 2, 2, 3, 3, 2, 3, 3
[3, 3, 2, 2, 3, 3, 3, 1, 1] => 3, 3, 2, 2, 3, 3, 3, 1, 1
[3, 3, 2, 2, 3, 3, 3, 1, 2] => 3, 3, 2, 2, 3, 3, 3, 1, 2
[3, 3, 2, 2, 3, 3, 3, 1, 3] => 3, 3, 2, 2, 3, 3, 3, 1, 3
[3, 3, 2, 2, 3, 3, 3, 2, 1] => 3, 3, 2, 2, 3, 3, 3, 2, 1
[3, 3, 2, 2, 3, 3, 3, 2, 2] => 3, 3, 2, 2, 3, 3, 3, 2, 2
[3, 3, 2, 2, 3, 3, 3, 2, 3] => 3, 3, 2, 2, 3, 3, 3, 2, 3
[3, 3, 2, 2, 3, 3, 3, 3, 1] => 3, 3, 2, 2, 3, 3, 3, 3, 1
[3, 3, 2, 2, 3, 3, 3, 3, 2] => 3, 3, 2, 2, 3, 3, 3, 3, 2
[3, 3, 2, 2, 3, 3, 3, 3, 3] => 3, 3, 2, 2, 3, 3, 3, 3, 3
[3, 3, 2, 3, 1, 1, 1, 1, 1] => 3, 3, 2, 3, 1, 1, 1, 1, 1
[3, 3, 2, 3, 1, 1, 1, 1, 2] => 3, 3, 2, 3, 1, 1, 1, 1, 2
[3, 3, 2, 3, 1, 1, 1, 1, 3] => 3, 3, 2, 3, 1, 1, 1, 1, 3
[3, 3, 2, 3, 1, 1, 1, 2, 1] => 3, 3, 2, 3, 1, 1, 1, 2, 1
[3, 3, 2, 3, 1, 1, 1, 2, 2] => 3, 3, 2, 3, 1, 1, 1, 2, 2
[3, 3, 2, 3, 1, 1, 1, 2, 3] => 3, 3, 2, 3, 1, 1, 1, 2, 3
[3, 3, 2, 3, 1, 1, 1, 3, 1] => 3, 3, 2, 3, 1, 1, 1, 3, 1
[3, 3, 2, 3, 1, 1, 1, 3, 2] => 3, 3, 2, 3, 1, 1, 1, 3, 2
[3, 3, 2, 3, 1, 1, 1, 3, 3] => 3, 3, 2, 3, 1, 1, 1, 3, 3
[3, 3, 2, 3, 1, 1, 2, 1, 1] => 3, 3, 2, 3, 1, 1, 2, 1, 1
[3, 3, 2, 3, 1, 1, 2, 1, 2] => 3, 3, 2, 3, 1, 1, 2, 1, 2
[3, 3, 2, 3, 1, 1, 2, 1, 3] => 3, 3, 2, 3, 1, 1, 2, 1, 3
[3, 3, 2, 3, 1, 1, 2, 2, 1] => 3, 3, 2, 3, 1, 1, 2, 2, 1
[3, 3, 2, 3, 1, 1, 2, 2, 2] => 3, 3, 2, 3, 1, 1, 2, 2, 2
[3, 3, 2, 3, 1, 1, 2, 2, 3] => 3, 3, 2, 3, 1, 1, 2, 2, 3
[3, 3, 2, 3, 1, 1, 2, 3, 1] => 3, 3, 2, 3, 1, 1, 2, 3, 1
[3, 3, 2, 3, 1, 1, 2, 3, 2] => 3, 3, 2, 3, 1, 1, 2, 3, 2
[3, 3, 2, 3, 1, 1, 2, 3, 3] => 3, 3, 2, 3, 1, 1, 2, 3, 3
[3, 3, 2, 3, 1, 1, 3, 1, 1] => 3, 3, 2, 3, 1, 1, 3, 1, 1
[3, 3, 2, 3, 1, 1, 3, 1, 2] => 3, 3, 2, 3, 1, 1, 3, 1, 2
[3, 3, 2, 3, 1, 1, 3, 1, 3] => 3, 3, 2, 3, 1, 1, 3, 1, 3
[3, 3, 2, 3, 1, 1, 3, 2, 1] => 3, 3, 2, 3, 1, 1, 3, 2, 1
[3, 3, 2, 3, 1, 1, 3, 2, 2] => 3, 3, 2, 3, 1, 1, 3, 2, 2
[3, 3, 2, 3, 1, 1, 3, 2, 3] => 3, 3, 2, 3, 1, 1, 3, 2, 3
[3, 3, 2, 3, 1, 1, 3, 3, 1] => 3, 3, 2, 3, 1, 1, 3, 3, 1
[3, 3, 2, 3, 1, 1, 3, 3, 2] => 3, 3, 2, 3, 1, 1, 3, 3, 2
[3, 3, 2, 3, 1, 1, 3, 3, 3] => 3, 3, 2, 3, 1, 1, 3, 3, 3
[3, 3, 2, 3, 1, 2, 1, 1, 1] => 3, 3, 2, 3, 1, 2, 1, 1, 1
[3, 3, 2, 3, 1, 2, 1, 1, 2] => 3, 3, 2, 3, 1, 2, 1, 1, 2
[3, 3, 2, 3, 1, 2, 1, 1, 3] => 3, 3, 2, 3, 1, 2, 1, 1, 3
[3, 3, 2, 3, 1, 2, 1, 2, 1] => 3, 3, 2, 3, 1, 2, 1, 2, 1
[3, 3, 2, 3, 1, 2, 1, 2, 2] => 3, 3, 2, 3, 1, 2, 1, 2, 2
[3, 3, 2, 3, 1, 2, 1, 2, 3] => 3, 3, 2, 3, 1, 2, 1, 2, 3
[3, 3, 2, 3, 1, 2, 1, 3, 1] => 3, 3, 2, 3, 1, 2, 1, 3, 1
[3, 3, 2, 3, 1, 2, 1, 3, 2] => 3, 3, 2, 3, 1, 2, 1, 3, 2
[3, 3, 2, 3, 1, 2, 1, 3, 3] => 3, 3, 2, 3, 1, 2, 1, 3, 3
[3, 3, 2, 3, 1, 2, 2, 1, 1] => 3, 3, 2, 3, 1, 2, 2, 1, 1
[3, 3, 2, 3, 1, 2, 2, 1, 2] => 3, 3, 2, 3, 1, 2, 2, 1, 2
[3, 3, 2, 3, 1, 2, 2, 1, 3] => 3, 3, 2, 3, 1, 2, 2, 1, 3
[3, 3, 2, 3, 1, 2, 2, 2, 1] => 3, 3, 2, 3, 1, 2, 2, 2, 1
[3, 3, 2, 3, 1, 2, 2, 2, 2] => 3, 3, 2, 3, 1, 2, 2, 2, 2
[3, 3, 2, 3, 1, 2, 2, 2, 3] => 3, 3, 2, 3, 1, 2, 2, 2, 3
[3, 3, 2, 3, 1, 2, 2, 3, 1] => 3, 3, 2, 3, 1, 2, 2, 3, 1
[3, 3, 2, 3, 1, 2, 2, 3, 2] => 3, 3, 2, 3, 1, 2, 2, 3, 2
[3, 3, 2, 3, 1, 2, 2, 3, 3] => 3, 3, 2, 3, 1, 2, 2, 3, 3
[3, 3, 2, 3, 1, 2, 3, 1, 1] => 3, 3, 2, 3, 1, 2, 3, 1, 1
[3, 3, 2, 3, 1, 2, 3, 1, 2] => 3, 3, 2, 3, 1, 2, 3, 1, 2
[3, 3, 2, 3, 1, 2, 3, 1, 3] => 3, 3, 2, 3, 1, 2, 3, 1, 3
[3, 3, 2, 3, 1, 2, 3, 2, 1] => 3, 3, 2, 3, 1, 2, 3, 2, 1
[3, 3, 2, 3, 1, 2, 3, 2, 2] => 3, 3, 2, 3, 1, 2, 3, 2, 2
[3, 3, 2, 3, 1, 2, 3, 2, 3] => 3, 3, 2, 3, 1, 2, 3, 2, 3
[3, 3, 2, 3, 1, 2, 3, 3, 1] => 3, 3, 2, 3, 1, 2, 3, 3, 1
[3, 3, 2, 3, 1, 2, 3, 3, 2] => 3, 3, 2, 3, 1, 2, 3, 3, 2
[3, 3, 2, 3, 1, 2, 3, 3, 3] => 3, 3, 2, 3, 1, 2, 3, 3, 3
[3, 3, 2, 3, 1, 3, 1, 1, 1] => 3, 3, 2, 3, 1, 3, 1, 1, 1
[3, 3, 2, 3, 1, 3, 1, 1, 2] => 3, 3, 2, 3, 1, 3, 1, 1, 2
[3, 3, 2, 3, 1, 3, 1, 1, 3] => 3, 3, 2, 3, 1, 3, 1, 1, 3
[3, 3, 2, 3, 1, 3, 1, 2, 1] => 3, 3, 2, 3, 1, 3, 1, 2, 1
[3, 3, 2, 3, 1, 3, 1, 2, 2] => 3, 3, 2, 3, 1, 3, 1, 2, 2
[3, 3, 2, 3, 1, 3, 1, 2, 3] => 3, 3, 2, 3, 1, 3, 1, 2, 3
[3, 3, 2, 3, 1, 3, 1, 3, 1] => 3, 3, 2, 3, 1, 3, 1, 3, 1
[3, 3, 2, 3, 1, 3, 1, 3, 2] => 3, 3, 2, 3, 1, 3, 1, 3, 2
[3, 3, 2, 3, 1, 3, 1, 3, 3] => 3, 3, 2, 3, 1, 3, 1, 3, 3
[3, 3, 2, 3, 1, 3, 2, 1, 1] => 3, 3, 2, 3, 1, 3, 2, 1, 1
[3, 3, 2, 3, 1, 3, 2, 1, 2] => 3, 3, 2, 3, 1, 3, 2, 1, 2
[3, 3, 2, 3, 1, 3, 2, 1, 3] => 3, 3, 2, 3, 1, 3, 2, 1, 3
[3, 3, 2, 3, 1, 3, 2, 2, 1] => 3, 3, 2, 3, 1, 3, 2, 2, 1
[3, 3, 2, 3, 1, 3, 2, 2, 2] => 3, 3, 2, 3, 1, 3, 2, 2, 2
[3, 3, 2, 3, 1, 3, 2, 2, 3] => 3, 3, 2, 3, 1, 3, 2, 2, 3
[3, 3, 2, 3, 1, 3, 2, 3, 1] => 3, 3, 2, 3, 1, 3, 2, 3, 1
[3, 3, 2, 3, 1, 3, 2, 3, 2] => 3, 3, 2, 3, 1, 3, 2, 3, 2
[3, 3, 2, 3, 1, 3, 2, 3, 3] => 3, 3, 2, 3, 1, 3, 2, 3, 3
[3, 3, 2, 3, 1, 3, 3, 1, 1] => 3, 3, 2, 3, 1, 3, 3, 1, 1
[3, 3, 2, 3, 1, 3, 3, 1, 2] => 3, 3, 2, 3, 1, 3, 3, 1, 2
[3, 3, 2, 3, 1, 3, 3, 1, 3] => 3, 3, 2, 3, 1, 3, 3, 1, 3
[3, 3, 2, 3, 1, 3, 3, 2, 1] => 3, 3, 2, 3, 1, 3, 3, 2, 1
[3, 3, 2, 3, 1, 3, 3, 2, 2] => 3, 3, 2, 3, 1, 3, 3, 2, 2
[3, 3, 2, 3, 1, 3, 3, 2, 3] => 3, 3, 2, 3, 1, 3, 3, 2, 3
[3, 3, 2, 3, 1, 3, 3, 3, 1] => 3, 3, 2, 3, 1, 3, 3, 3, 1
[3, 3, 2, 3, 1, 3, 3, 3, 2] => 3, 3, 2, 3, 1, 3, 3, 3, 2
[3, 3, 2, 3, 1, 3, 3, 3, 3] => 3, 3, 2, 3, 1, 3, 3, 3, 3
[3, 3, 2, 3, 2, 1, 1, 1, 1] => 3, 3, 2, 3, 2, 1, 1, 1, 1
[3, 3, 2, 3, 2, 1, 1, 1, 2] => 3, 3, 2, 3, 2, 1, 1, 1, 2
[3, 3, 2, 3, 2, 1, 1, 1, 3] => 3, 3, 2, 3, 2, 1, 1, 1, 3
[3, 3, 2, 3, 2, 1, 1, 2, 1] => 3, 3, 2, 3, 2, 1, 1, 2, 1
[3, 3, 2, 3, 2, 1, 1, 2, 2] => 3, 3, 2, 3, 2, 1, 1, 2, 2
[3, 3, 2, 3, 2, 1, 1, 2, 3] => 3, 3, 2, 3, 2, 1, 1, 2, 3
[3, 3, 2, 3, 2, 1, 1, 3, 1] => 3, 3, 2, 3, 2, 1, 1, 3, 1
[3, 3, 2, 3, 2, 1, 1, 3, 2] => 3, 3, 2, 3, 2, 1, 1, 3, 2
[3, 3, 2, 3, 2, 1, 1, 3, 3] => 3, 3, 2, 3, 2, 1, 1, 3, 3
[3, 3, 2, 3, 2, 1, 2, 1, 1] => 3, 3, 2, 3, 2, 1, 2, 1, 1
[3, 3, 2, 3, 2, 1, 2, 1, 2] => 3, 3, 2, 3, 2, 1, 2, 1, 2
[3, 3, 2, 3, 2, 1, 2, 1, 3] => 3, 3, 2, 3, 2, 1, 2, 1, 3
[3, 3, 2, 3, 2, 1, 2, 2, 1] => 3, 3, 2, 3, 2, 1, 2, 2, 1
[3, 3, 2, 3, 2, 1, 2, 2, 2] => 3, 3, 2, 3, 2, 1, 2, 2, 2
[3, 3, 2, 3, 2, 1, 2, 2, 3] => 3, 3, 2, 3, 2, 1, 2, 2, 3
[3, 3, 2, 3, 2, 1, 2, 3, 1] => 3, 3, 2, 3, 2, 1, 2, 3, 1
[3, 3, 2, 3, 2, 1, 2, 3, 2] => 3, 3, 2, 3, 2, 1, 2, 3, 2
[3, 3, 2, 3, 2, 1, 2, 3, 3] => 3, 3, 2, 3, 2, 1, 2, 3, 3
[3, 3, 2, 3, 2, 1, 3, 1, 1] => 3, 3, 2, 3, 2, 1, 3, 1, 1
[3, 3, 2, 3, 2, 1, 3, 1, 2] => 3, 3, 2, 3, 2, 1, 3, 1, 2
[3, 3, 2, 3, 2, 1, 3, 1, 3] => 3, 3, 2, 3, 2, 1, 3, 1, 3
[3, 3, 2, 3, 2, 1, 3, 2, 1] => 3, 3, 2, 3, 2, 1, 3, 2, 1
[3, 3, 2, 3, 2, 1, 3, 2, 2] => 3, 3, 2, 3, 2, 1, 3, 2, 2
[3, 3, 2, 3, 2, 1, 3, 2, 3] => 3, 3, 2, 3, 2, 1, 3, 2, 3
[3, 3, 2, 3, 2, 1, 3, 3, 1] => 3, 3, 2, 3, 2, 1, 3, 3, 1
[3, 3, 2, 3, 2, 1, 3, 3, 2] => 3, 3, 2, 3, 2, 1, 3, 3, 2
[3, 3, 2, 3, 2, 1, 3, 3, 3] => 3, 3, 2, 3, 2, 1, 3, 3, 3
[3, 3, 2, 3, 2, 2, 1, 1, 1] => 3, 3, 2, 3, 2, 2, 1, 1, 1
[3, 3, 2, 3, 2, 2, 1, 1, 2] => 3, 3, 2, 3, 2, 2, 1, 1, 2
[3, 3, 2, 3, 2, 2, 1, 1, 3] => 3, 3, 2, 3, 2, 2, 1, 1, 3
[3, 3, 2, 3, 2, 2, 1, 2, 1] => 3, 3, 2, 3, 2, 2, 1, 2, 1
[3, 3, 2, 3, 2, 2, 1, 2, 2] => 3, 3, 2, 3, 2, 2, 1, 2, 2
[3, 3, 2, 3, 2, 2, 1, 2, 3] => 3, 3, 2, 3, 2, 2, 1, 2, 3
[3, 3, 2, 3, 2, 2, 1, 3, 1] => 3, 3, 2, 3, 2, 2, 1, 3, 1
[3, 3, 2, 3, 2, 2, 1, 3, 2] => 3, 3, 2, 3, 2, 2, 1, 3, 2
[3, 3, 2, 3, 2, 2, 1, 3, 3] => 3, 3, 2, 3, 2, 2, 1, 3, 3
[3, 3, 2, 3, 2, 2, 2, 1, 1] => 3, 3, 2, 3, 2, 2, 2, 1, 1
[3, 3, 2, 3, 2, 2, 2, 1, 2] => 3, 3, 2, 3, 2, 2, 2, 1, 2
[3, 3, 2, 3, 2, 2, 2, 1, 3] => 3, 3, 2, 3, 2, 2, 2, 1, 3
[3, 3, 2, 3, 2, 2, 2, 2, 1] => 3, 3, 2, 3, 2, 2, 2, 2, 1
[3, 3, 2, 3, 2, 2, 2, 2, 2] => 3, 3, 2, 3, 2, 2, 2, 2, 2
[3, 3, 2, 3, 2, 2, 2, 2, 3] => 3, 3, 2, 3, 2, 2, 2, 2, 3
[3, 3, 2, 3, 2, 2, 2, 3, 1] => 3, 3, 2, 3, 2, 2, 2, 3, 1
[3, 3, 2, 3, 2, 2, 2, 3, 2] => 3, 3, 2, 3, 2, 2, 2, 3, 2
[3, 3, 2, 3, 2, 2, 2, 3, 3] => 3, 3, 2, 3, 2, 2, 2, 3, 3
[3, 3, 2, 3, 2, 2, 3, 1, 1] => 3, 3, 2, 3, 2, 2, 3, 1, 1
[3, 3, 2, 3, 2, 2, 3, 1, 2] => 3, 3, 2, 3, 2, 2, 3, 1, 2
[3, 3, 2, 3, 2, 2, 3, 1, 3] => 3, 3, 2, 3, 2, 2, 3, 1, 3
[3, 3, 2, 3, 2, 2, 3, 2, 1] => 3, 3, 2, 3, 2, 2, 3, 2, 1
[3, 3, 2, 3, 2, 2, 3, 2, 2] => 3, 3, 2, 3, 2, 2, 3, 2, 2
[3, 3, 2, 3, 2, 2, 3, 2, 3] => 3, 3, 2, 3, 2, 2, 3, 2, 3
[3, 3, 2, 3, 2, 2, 3, 3, 1] => 3, 3, 2, 3, 2, 2, 3, 3, 1
[3, 3, 2, 3, 2, 2, 3, 3, 2] => 3, 3, 2, 3, 2, 2, 3, 3, 2
[3, 3, 2, 3, 2, 2, 3, 3, 3] => 3, 3, 2, 3, 2, 2, 3, 3, 3
[3, 3, 2, 3, 2, 3, 1, 1, 1] => 3, 3, 2, 3, 2, 3, 1, 1, 1
[3, 3, 2, 3, 2, 3, 1, 1, 2] => 3, 3, 2, 3, 2, 3, 1, 1, 2
[3, 3, 2, 3, 2, 3, 1, 1, 3] => 3, 3, 2, 3, 2, 3, 1, 1, 3
[3, 3, 2, 3, 2, 3, 1, 2, 1] => 3, 3, 2, 3, 2, 3, 1, 2, 1
[3, 3, 2, 3, 2, 3, 1, 2, 2] => 3, 3, 2, 3, 2, 3, 1, 2, 2
[3, 3, 2, 3, 2, 3, 1, 2, 3] => 3, 3, 2, 3, 2, 3, 1, 2, 3
[3, 3, 2, 3, 2, 3, 1, 3, 1] => 3, 3, 2, 3, 2, 3, 1, 3, 1
[3, 3, 2, 3, 2, 3, 1, 3, 2] => 3, 3, 2, 3, 2, 3, 1, 3, 2
[3, 3, 2, 3, 2, 3, 1, 3, 3] => 3, 3, 2, 3, 2, 3, 1, 3, 3
[3, 3, 2, 3, 2, 3, 2, 1, 1] => 3, 3, 2, 3, 2, 3, 2, 1, 1
[3, 3, 2, 3, 2, 3, 2, 1, 2] => 3, 3, 2, 3, 2, 3, 2, 1, 2
[3, 3, 2, 3, 2, 3, 2, 1, 3] => 3, 3, 2, 3, 2, 3, 2, 1, 3
[3, 3, 2, 3, 2, 3, 2, 2, 1] => 3, 3, 2, 3, 2, 3, 2, 2, 1
[3, 3, 2, 3, 2, 3, 2, 2, 2] => 3, 3, 2, 3, 2, 3, 2, 2, 2
[3, 3, 2, 3, 2, 3, 2, 2, 3] => 3, 3, 2, 3, 2, 3, 2, 2, 3
[3, 3, 2, 3, 2, 3, 2, 3, 1] => 3, 3, 2, 3, 2, 3, 2, 3, 1
[3, 3, 2, 3, 2, 3, 2, 3, 2] => 3, 3, 2, 3, 2, 3, 2, 3, 2
[3, 3, 2, 3, 2, 3, 2, 3, 3] => 3, 3, 2, 3, 2, 3, 2, 3, 3
[3, 3, 2, 3, 2, 3, 3, 1, 1] => 3, 3, 2, 3, 2, 3, 3, 1, 1
[3, 3, 2, 3, 2, 3, 3, 1, 2] => 3, 3, 2, 3, 2, 3, 3, 1, 2
[3, 3, 2, 3, 2, 3, 3, 1, 3] => 3, 3, 2, 3, 2, 3, 3, 1, 3
[3, 3, 2, 3, 2, 3, 3, 2, 1] => 3, 3, 2, 3, 2, 3, 3, 2, 1
[3, 3, 2, 3, 2, 3, 3, 2, 2] => 3, 3, 2, 3, 2, 3, 3, 2, 2
[3, 3, 2, 3, 2, 3, 3, 2, 3] => 3, 3, 2, 3, 2, 3, 3, 2, 3
[3, 3, 2, 3, 2, 3, 3, 3, 1] => 3, 3, 2, 3, 2, 3, 3, 3, 1
[3, 3, 2, 3, 2, 3, 3, 3, 2] => 3, 3, 2, 3, 2, 3, 3, 3, 2
[3, 3, 2, 3, 2, 3, 3, 3, 3] => 3, 3, 2, 3, 2, 3, 3, 3, 3
[3, 3, 2, 3, 3, 1, 1, 1, 1] => 3, 3, 2, 3, 3, 1, 1, 1, 1
[3, 3, 2, 3, 3, 1, 1, 1, 2] => 3, 3, 2, 3, 3, 1, 1, 1, 2
[3, 3, 2, 3, 3, 1, 1, 1, 3] => 3, 3, 2, 3, 3, 1, 1, 1, 3
[3, 3, 2, 3, 3, 1, 1, 2, 1] => 3, 3, 2, 3, 3, 1, 1, 2, 1
[3, 3, 2, 3, 3, 1, 1, 2, 2] => 3, 3, 2, 3, 3, 1, 1, 2, 2
[3, 3, 2, 3, 3, 1, 1, 2, 3] => 3, 3, 2, 3, 3, 1, 1, 2, 3
[3, 3, 2, 3, 3, 1, 1, 3, 1] => 3, 3, 2, 3, 3, 1, 1, 3, 1
[3, 3, 2, 3, 3, 1, 1, 3, 2] => 3, 3, 2, 3, 3, 1, 1, 3, 2
[3, 3, 2, 3, 3, 1, 1, 3, 3] => 3, 3, 2, 3, 3, 1, 1, 3, 3
[3, 3, 2, 3, 3, 1, 2, 1, 1] => 3, 3, 2, 3, 3, 1, 2, 1, 1
[3, 3, 2, 3, 3, 1, 2, 1, 2] => 3, 3, 2, 3, 3, 1, 2, 1, 2
[3, 3, 2, 3, 3, 1, 2, 1, 3] => 3, 3, 2, 3, 3, 1, 2, 1, 3
[3, 3, 2, 3, 3, 1, 2, 2, 1] => 3, 3, 2, 3, 3, 1, 2, 2, 1
[3, 3, 2, 3, 3, 1, 2, 2, 2] => 3, 3, 2, 3, 3, 1, 2, 2, 2
[3, 3, 2, 3, 3, 1, 2, 2, 3] => 3, 3, 2, 3, 3, 1, 2, 2, 3
[3, 3, 2, 3, 3, 1, 2, 3, 1] => 3, 3, 2, 3, 3, 1, 2, 3, 1
[3, 3, 2, 3, 3, 1, 2, 3, 2] => 3, 3, 2, 3, 3, 1, 2, 3, 2
[3, 3, 2, 3, 3, 1, 2, 3, 3] => 3, 3, 2, 3, 3, 1, 2, 3, 3
[3, 3, 2, 3, 3, 1, 3, 1, 1] => 3, 3, 2, 3, 3, 1, 3, 1, 1
[3, 3, 2, 3, 3, 1, 3, 1, 2] => 3, 3, 2, 3, 3, 1, 3, 1, 2
[3, 3, 2, 3, 3, 1, 3, 1, 3] => 3, 3, 2, 3, 3, 1, 3, 1, 3
[3, 3, 2, 3, 3, 1, 3, 2, 1] => 3, 3, 2, 3, 3, 1, 3, 2, 1
[3, 3, 2, 3, 3, 1, 3, 2, 2] => 3, 3, 2, 3, 3, 1, 3, 2, 2
[3, 3, 2, 3, 3, 1, 3, 2, 3] => 3, 3, 2, 3, 3, 1, 3, 2, 3
[3, 3, 2, 3, 3, 1, 3, 3, 1] => 3, 3, 2, 3, 3, 1, 3, 3, 1
[3, 3, 2, 3, 3, 1, 3, 3, 2] => 3, 3, 2, 3, 3, 1, 3, 3, 2
[3, 3, 2, 3, 3, 1, 3, 3, 3] => 3, 3, 2, 3, 3, 1, 3, 3, 3
[3, 3, 2, 3, 3, 2, 1, 1, 1] => 3, 3, 2, 3, 3, 2, 1, 1, 1
[3, 3, 2, 3, 3, 2, 1, 1, 2] => 3, 3, 2, 3, 3, 2, 1, 1, 2
[3, 3, 2, 3, 3, 2, 1, 1, 3] => 3, 3, 2, 3, 3, 2, 1, 1, 3
[3, 3, 2, 3, 3, 2, 1, 2, 1] => 3, 3, 2, 3, 3, 2, 1, 2, 1
[3, 3, 2, 3, 3, 2, 1, 2, 2] => 3, 3, 2, 3, 3, 2, 1, 2, 2
[3, 3, 2, 3, 3, 2, 1, 2, 3] => 3, 3, 2, 3, 3, 2, 1, 2, 3
[3, 3, 2, 3, 3, 2, 1, 3, 1] => 3, 3, 2, 3, 3, 2, 1, 3, 1
[3, 3, 2, 3, 3, 2, 1, 3, 2] => 3, 3, 2, 3, 3, 2, 1, 3, 2
[3, 3, 2, 3, 3, 2, 1, 3, 3] => 3, 3, 2, 3, 3, 2, 1, 3, 3
[3, 3, 2, 3, 3, 2, 2, 1, 1] => 3, 3, 2, 3, 3, 2, 2, 1, 1
[3, 3, 2, 3, 3, 2, 2, 1, 2] => 3, 3, 2, 3, 3, 2, 2, 1, 2
[3, 3, 2, 3, 3, 2, 2, 1, 3] => 3, 3, 2, 3, 3, 2, 2, 1, 3
[3, 3, 2, 3, 3, 2, 2, 2, 1] => 3, 3, 2, 3, 3, 2, 2, 2, 1
[3, 3, 2, 3, 3, 2, 2, 2, 2] => 3, 3, 2, 3, 3, 2, 2, 2, 2
[3, 3, 2, 3, 3, 2, 2, 2, 3] => 3, 3, 2, 3, 3, 2, 2, 2, 3
[3, 3, 2, 3, 3, 2, 2, 3, 1] => 3, 3, 2, 3, 3, 2, 2, 3, 1
[3, 3, 2, 3, 3, 2, 2, 3, 2] => 3, 3, 2, 3, 3, 2, 2, 3, 2
[3, 3, 2, 3, 3, 2, 2, 3, 3] => 3, 3, 2, 3, 3, 2, 2, 3, 3
[3, 3, 2, 3, 3, 2, 3, 1, 1] => 3, 3, 2, 3, 3, 2, 3, 1, 1
[3, 3, 2, 3, 3, 2, 3, 1, 2] => 3, 3, 2, 3, 3, 2, 3, 1, 2
[3, 3, 2, 3, 3, 2, 3, 1, 3] => 3, 3, 2, 3, 3, 2, 3, 1, 3
[3, 3, 2, 3, 3, 2, 3, 2, 1] => 3, 3, 2, 3, 3, 2, 3, 2, 1
[3, 3, 2, 3, 3, 2, 3, 2, 2] => 3, 3, 2, 3, 3, 2, 3, 2, 2
[3, 3, 2, 3, 3, 2, 3, 2, 3] => 3, 3, 2, 3, 3, 2, 3, 2, 3
[3, 3, 2, 3, 3, 2, 3, 3, 1] => 3, 3, 2, 3, 3, 2, 3, 3, 1
[3, 3, 2, 3, 3, 2, 3, 3, 2] => 3, 3, 2, 3, 3, 2, 3, 3, 2
[3, 3, 2, 3, 3, 2, 3, 3, 3] => 3, 3, 2, 3, 3, 2, 3, 3, 3
[3, 3, 2, 3, 3, 3, 1, 1, 1] => 3, 3, 2, 3, 3, 3, 1, 1, 1
[3, 3, 2, 3, 3, 3, 1, 1, 2] => 3, 3, 2, 3, 3, 3, 1, 1, 2
[3, 3, 2, 3, 3, 3, 1, 1, 3] => 3, 3, 2, 3, 3, 3, 1, 1, 3
[3, 3, 2, 3, 3, 3, 1, 2, 1] => 3, 3, 2, 3, 3, 3, 1, 2, 1
[3, 3, 2, 3, 3, 3, 1, 2, 2] => 3, 3, 2, 3, 3, 3, 1, 2, 2
[3, 3, 2, 3, 3, 3, 1, 2, 3] => 3, 3, 2, 3, 3, 3, 1, 2, 3
[3, 3, 2, 3, 3, 3, 1, 3, 1] => 3, 3, 2, 3, 3, 3, 1, 3, 1
[3, 3, 2, 3, 3, 3, 1, 3, 2] => 3, 3, 2, 3, 3, 3, 1, 3, 2
[3, 3, 2, 3, 3, 3, 1, 3, 3] => 3, 3, 2, 3, 3, 3, 1, 3, 3
[3, 3, 2, 3, 3, 3, 2, 1, 1] => 3, 3, 2, 3, 3, 3, 2, 1, 1
[3, 3, 2, 3, 3, 3, 2, 1, 2] => 3, 3, 2, 3, 3, 3, 2, 1, 2
[3, 3, 2, 3, 3, 3, 2, 1, 3] => 3, 3, 2, 3, 3, 3, 2, 1, 3
[3, 3, 2, 3, 3, 3, 2, 2, 1] => 3, 3, 2, 3, 3, 3, 2, 2, 1
[3, 3, 2, 3, 3, 3, 2, 2, 2] => 3, 3, 2, 3, 3, 3, 2, 2, 2
[3, 3, 2, 3, 3, 3, 2, 2, 3] => 3, 3, 2, 3, 3, 3, 2, 2, 3
[3, 3, 2, 3, 3, 3, 2, 3, 1] => 3, 3, 2, 3, 3, 3, 2, 3, 1
[3, 3, 2, 3, 3, 3, 2, 3, 2] => 3, 3, 2, 3, 3, 3, 2, 3, 2
[3, 3, 2, 3, 3, 3, 2, 3, 3] => 3, 3, 2, 3, 3, 3, 2, 3, 3
[3, 3, 2, 3, 3, 3, 3, 1, 1] => 3, 3, 2, 3, 3, 3, 3, 1, 1
[3, 3, 2, 3, 3, 3, 3, 1, 2] => 3, 3, 2, 3, 3, 3, 3, 1, 2
[3, 3, 2, 3, 3, 3, 3, 1, 3] => 3, 3, 2, 3, 3, 3, 3, 1, 3
[3, 3, 2, 3, 3, 3, 3, 2, 1] => 3, 3, 2, 3, 3, 3, 3, 2, 1
[3, 3, 2, 3, 3, 3, 3, 2, 2] => 3, 3, 2, 3, 3, 3, 3, 2, 2
[3, 3, 2, 3, 3, 3, 3, 2, 3] => 3, 3, 2, 3, 3, 3, 3, 2, 3
[3, 3, 2, 3, 3, 3, 3, 3, 1] => 3, 3, 2, 3, 3, 3, 3, 3, 1
[3, 3, 2, 3, 3, 3, 3, 3, 2] => 3, 3, 2, 3, 3, 3, 3, 3, 2
[3, 3, 2, 3, 3, 3, 3, 3, 3] => 3, 3, 2, 3, 3, 3, 3, 3, 3
[3, 3, 3, 1, 1, 1, 1, 1, 1] => 3, 3, 3, 1, 1, 1, 1, 1, 1
[3, 3, 3, 1, 1, 1, 1, 1, 2] => 3, 3, 3, 1, 1, 1, 1, 1, 2
[3, 3, 3, 1, 1, 1, 1, 1, 3] => 3, 3, 3, 1, 1, 1, 1, 1, 3
[3, 3, 3, 1, 1, 1, 1, 2, 1] => 3, 3, 3, 1, 1, 1, 1, 2, 1
[3, 3, 3, 1, 1, 1, 1, 2, 2] => 3, 3, 3, 1, 1, 1, 1, 2, 2
[3, 3, 3, 1, 1, 1, 1, 2, 3] => 3, 3, 3, 1, 1, 1, 1, 2, 3
[3, 3, 3, 1, 1, 1, 1, 3, 1] => 3, 3, 3, 1, 1, 1, 1, 3, 1
[3, 3, 3, 1, 1, 1, 1, 3, 2] => 3, 3, 3, 1, 1, 1, 1, 3, 2
[3, 3, 3, 1, 1, 1, 1, 3, 3] => 3, 3, 3, 1, 1, 1, 1, 3, 3
[3, 3, 3, 1, 1, 1, 2, 1, 1] => 3, 3, 3, 1, 1, 1, 2, 1, 1
[3, 3, 3, 1, 1, 1, 2, 1, 2] => 3, 3, 3, 1, 1, 1, 2, 1, 2
[3, 3, 3, 1, 1, 1, 2, 1, 3] => 3, 3, 3, 1, 1, 1, 2, 1, 3
[3, 3, 3, 1, 1, 1, 2, 2, 1] => 3, 3, 3, 1, 1, 1, 2, 2, 1
[3, 3, 3, 1, 1, 1, 2, 2, 2] => 3, 3, 3, 1, 1, 1, 2, 2, 2
[3, 3, 3, 1, 1, 1, 2, 2, 3] => 3, 3, 3, 1, 1, 1, 2, 2, 3
[3, 3, 3, 1, 1, 1, 2, 3, 1] => 3, 3, 3, 1, 1, 1, 2, 3, 1
[3, 3, 3, 1, 1, 1, 2, 3, 2] => 3, 3, 3, 1, 1, 1, 2, 3, 2
[3, 3, 3, 1, 1, 1, 2, 3, 3] => 3, 3, 3, 1, 1, 1, 2, 3, 3
[3, 3, 3, 1, 1, 1, 3, 1, 1] => 3, 3, 3, 1, 1, 1, 3, 1, 1
[3, 3, 3, 1, 1, 1, 3, 1, 2] => 3, 3, 3, 1, 1, 1, 3, 1, 2
[3, 3, 3, 1, 1, 1, 3, 1, 3] => 3, 3, 3, 1, 1, 1, 3, 1, 3
[3, 3, 3, 1, 1, 1, 3, 2, 1] => 3, 3, 3, 1, 1, 1, 3, 2, 1
[3, 3, 3, 1, 1, 1, 3, 2, 2] => 3, 3, 3, 1, 1, 1, 3, 2, 2
[3, 3, 3, 1, 1, 1, 3, 2, 3] => 3, 3, 3, 1, 1, 1, 3, 2, 3
[3, 3, 3, 1, 1, 1, 3, 3, 1] => 3, 3, 3, 1, 1, 1, 3, 3, 1
[3, 3, 3, 1, 1, 1, 3, 3, 2] => 3, 3, 3, 1, 1, 1, 3, 3, 2
[3, 3, 3, 1, 1, 1, 3, 3, 3] => 3, 3, 3, 1, 1, 1, 3, 3, 3
[3, 3, 3, 1, 1, 2, 1, 1, 1] => 3, 3, 3, 1, 1, 2, 1, 1, 1
[3, 3, 3, 1, 1, 2, 1, 1, 2] => 3, 3, 3, 1, 1, 2, 1, 1, 2
[3, 3, 3, 1, 1, 2, 1, 1, 3] => 3, 3, 3, 1, 1, 2, 1, 1, 3
[3, 3, 3, 1, 1, 2, 1, 2, 1] => 3, 3, 3, 1, 1, 2, 1, 2, 1
[3, 3, 3, 1, 1, 2, 1, 2, 2] => 3, 3, 3, 1, 1, 2, 1, 2, 2
[3, 3, 3, 1, 1, 2, 1, 2, 3] => 3, 3, 3, 1, 1, 2, 1, 2, 3
[3, 3, 3, 1, 1, 2, 1, 3, 1] => 3, 3, 3, 1, 1, 2, 1, 3, 1
[3, 3, 3, 1, 1, 2, 1, 3, 2] => 3, 3, 3, 1, 1, 2, 1, 3, 2
[3, 3, 3, 1, 1, 2, 1, 3, 3] => 3, 3, 3, 1, 1, 2, 1, 3, 3
[3, 3, 3, 1, 1, 2, 2, 1, 1] => 3, 3, 3, 1, 1, 2, 2, 1, 1
[3, 3, 3, 1, 1, 2, 2, 1, 2] => 3, 3, 3, 1, 1, 2, 2, 1, 2
[3, 3, 3, 1, 1, 2, 2, 1, 3] => 3, 3, 3, 1, 1, 2, 2, 1, 3
[3, 3, 3, 1, 1, 2, 2, 2, 1] => 3, 3, 3, 1, 1, 2, 2, 2, 1
[3, 3, 3, 1, 1, 2, 2, 2, 2] => 3, 3, 3, 1, 1, 2, 2, 2, 2
[3, 3, 3, 1, 1, 2, 2, 2, 3] => 3, 3, 3, 1, 1, 2, 2, 2, 3
[3, 3, 3, 1, 1, 2, 2, 3, 1] => 3, 3, 3, 1, 1, 2, 2, 3, 1
[3, 3, 3, 1, 1, 2, 2, 3, 2] => 3, 3, 3, 1, 1, 2, 2, 3, 2
[3, 3, 3, 1, 1, 2, 2, 3, 3] => 3, 3, 3, 1, 1, 2, 2, 3, 3
[3, 3, 3, 1, 1, 2, 3, 1, 1] => 3, 3, 3, 1, 1, 2, 3, 1, 1
[3, 3, 3, 1, 1, 2, 3, 1, 2] => 3, 3, 3, 1, 1, 2, 3, 1, 2
[3, 3, 3, 1, 1, 2, 3, 1, 3] => 3, 3, 3, 1, 1, 2, 3, 1, 3
[3, 3, 3, 1, 1, 2, 3, 2, 1] => 3, 3, 3, 1, 1, 2, 3, 2, 1
[3, 3, 3, 1, 1, 2, 3, 2, 2] => 3, 3, 3, 1, 1, 2, 3, 2, 2
[3, 3, 3, 1, 1, 2, 3, 2, 3] => 3, 3, 3, 1, 1, 2, 3, 2, 3
[3, 3, 3, 1, 1, 2, 3, 3, 1] => 3, 3, 3, 1, 1, 2, 3, 3, 1
[3, 3, 3, 1, 1, 2, 3, 3, 2] => 3, 3, 3, 1, 1, 2, 3, 3, 2
[3, 3, 3, 1, 1, 2, 3, 3, 3] => 3, 3, 3, 1, 1, 2, 3, 3, 3
[3, 3, 3, 1, 1, 3, 1, 1, 1] => 3, 3, 3, 1, 1, 3, 1, 1, 1
[3, 3, 3, 1, 1, 3, 1, 1, 2] => 3, 3, 3, 1, 1, 3, 1, 1, 2
[3, 3, 3, 1, 1, 3, 1, 1, 3] => 3, 3, 3, 1, 1, 3, 1, 1, 3
[3, 3, 3, 1, 1, 3, 1, 2, 1] => 3, 3, 3, 1, 1, 3, 1, 2, 1
[3, 3, 3, 1, 1, 3, 1, 2, 2] => 3, 3, 3, 1, 1, 3, 1, 2, 2
[3, 3, 3, 1, 1, 3, 1, 2, 3] => 3, 3, 3, 1, 1, 3, 1, 2, 3
[3, 3, 3, 1, 1, 3, 1, 3, 1] => 3, 3, 3, 1, 1, 3, 1, 3, 1
[3, 3, 3, 1, 1, 3, 1, 3, 2] => 3, 3, 3, 1, 1, 3, 1, 3, 2
[3, 3, 3, 1, 1, 3, 1, 3, 3] => 3, 3, 3, 1, 1, 3, 1, 3, 3
[3, 3, 3, 1, 1, 3, 2, 1, 1] => 3, 3, 3, 1, 1, 3, 2, 1, 1
[3, 3, 3, 1, 1, 3, 2, 1, 2] => 3, 3, 3, 1, 1, 3, 2, 1, 2
[3, 3, 3, 1, 1, 3, 2, 1, 3] => 3, 3, 3, 1, 1, 3, 2, 1, 3
[3, 3, 3, 1, 1, 3, 2, 2, 1] => 3, 3, 3, 1, 1, 3, 2, 2, 1
[3, 3, 3, 1, 1, 3, 2, 2, 2] => 3, 3, 3, 1, 1, 3, 2, 2, 2
[3, 3, 3, 1, 1, 3, 2, 2, 3] => 3, 3, 3, 1, 1, 3, 2, 2, 3
[3, 3, 3, 1, 1, 3, 2, 3, 1] => 3, 3, 3, 1, 1, 3, 2, 3, 1
[3, 3, 3, 1, 1, 3, 2, 3, 2] => 3, 3, 3, 1, 1, 3, 2, 3, 2
[3, 3, 3, 1, 1, 3, 2, 3, 3] => 3, 3, 3, 1, 1, 3, 2, 3, 3
[3, 3, 3, 1, 1, 3, 3, 1, 1] => 3, 3, 3, 1, 1, 3, 3, 1, 1
[3, 3, 3, 1, 1, 3, 3, 1, 2] => 3, 3, 3, 1, 1, 3, 3, 1, 2
[3, 3, 3, 1, 1, 3, 3, 1, 3] => 3, 3, 3, 1, 1, 3, 3, 1, 3
[3, 3, 3, 1, 1, 3, 3, 2, 1] => 3, 3, 3, 1, 1, 3, 3, 2, 1
[3, 3, 3, 1, 1, 3, 3, 2, 2] => 3, 3, 3, 1, 1, 3, 3, 2, 2
[3, 3, 3, 1, 1, 3, 3, 2, 3] => 3, 3, 3, 1, 1, 3, 3, 2, 3
[3, 3, 3, 1, 1, 3, 3, 3, 1] => 3, 3, 3, 1, 1, 3, 3, 3, 1
[3, 3, 3, 1, 1, 3, 3, 3, 2] => 3, 3, 3, 1, 1, 3, 3, 3, 2
[3, 3, 3, 1, 1, 3, 3, 3, 3] => 3, 3, 3, 1, 1, 3, 3, 3, 3
[3, 3, 3, 1, 2, 1, 1, 1, 1] => 3, 3, 3, 1, 2, 1, 1, 1, 1
[3, 3, 3, 1, 2, 1, 1, 1, 2] => 3, 3, 3, 1, 2, 1, 1, 1, 2
[3, 3, 3, 1, 2, 1, 1, 1, 3] => 3, 3, 3, 1, 2, 1, 1, 1, 3
[3, 3, 3, 1, 2, 1, 1, 2, 1] => 3, 3, 3, 1, 2, 1, 1, 2, 1
[3, 3, 3, 1, 2, 1, 1, 2, 2] => 3, 3, 3, 1, 2, 1, 1, 2, 2
[3, 3, 3, 1, 2, 1, 1, 2, 3] => 3, 3, 3, 1, 2, 1, 1, 2, 3
[3, 3, 3, 1, 2, 1, 1, 3, 1] => 3, 3, 3, 1, 2, 1, 1, 3, 1
[3, 3, 3, 1, 2, 1, 1, 3, 2] => 3, 3, 3, 1, 2, 1, 1, 3, 2
[3, 3, 3, 1, 2, 1, 1, 3, 3] => 3, 3, 3, 1, 2, 1, 1, 3, 3
[3, 3, 3, 1, 2, 1, 2, 1, 1] => 3, 3, 3, 1, 2, 1, 2, 1, 1
[3, 3, 3, 1, 2, 1, 2, 1, 2] => 3, 3, 3, 1, 2, 1, 2, 1, 2
[3, 3, 3, 1, 2, 1, 2, 1, 3] => 3, 3, 3, 1, 2, 1, 2, 1, 3
[3, 3, 3, 1, 2, 1, 2, 2, 1] => 3, 3, 3, 1, 2, 1, 2, 2, 1
[3, 3, 3, 1, 2, 1, 2, 2, 2] => 3, 3, 3, 1, 2, 1, 2, 2, 2
[3, 3, 3, 1, 2, 1, 2, 2, 3] => 3, 3, 3, 1, 2, 1, 2, 2, 3
[3, 3, 3, 1, 2, 1, 2, 3, 1] => 3, 3, 3, 1, 2, 1, 2, 3, 1
[3, 3, 3, 1, 2, 1, 2, 3, 2] => 3, 3, 3, 1, 2, 1, 2, 3, 2
[3, 3, 3, 1, 2, 1, 2, 3, 3] => 3, 3, 3, 1, 2, 1, 2, 3, 3
[3, 3, 3, 1, 2, 1, 3, 1, 1] => 3, 3, 3, 1, 2, 1, 3, 1, 1
[3, 3, 3, 1, 2, 1, 3, 1, 2] => 3, 3, 3, 1, 2, 1, 3, 1, 2
[3, 3, 3, 1, 2, 1, 3, 1, 3] => 3, 3, 3, 1, 2, 1, 3, 1, 3
[3, 3, 3, 1, 2, 1, 3, 2, 1] => 3, 3, 3, 1, 2, 1, 3, 2, 1
[3, 3, 3, 1, 2, 1, 3, 2, 2] => 3, 3, 3, 1, 2, 1, 3, 2, 2
[3, 3, 3, 1, 2, 1, 3, 2, 3] => 3, 3, 3, 1, 2, 1, 3, 2, 3
[3, 3, 3, 1, 2, 1, 3, 3, 1] => 3, 3, 3, 1, 2, 1, 3, 3, 1
[3, 3, 3, 1, 2, 1, 3, 3, 2] => 3, 3, 3, 1, 2, 1, 3, 3, 2
[3, 3, 3, 1, 2, 1, 3, 3, 3] => 3, 3, 3, 1, 2, 1, 3, 3, 3
[3, 3, 3, 1, 2, 2, 1, 1, 1] => 3, 3, 3, 1, 2, 2, 1, 1, 1
[3, 3, 3, 1, 2, 2, 1, 1, 2] => 3, 3, 3, 1, 2, 2, 1, 1, 2
[3, 3, 3, 1, 2, 2, 1, 1, 3] => 3, 3, 3, 1, 2, 2, 1, 1, 3
[3, 3, 3, 1, 2, 2, 1, 2, 1] => 3, 3, 3, 1, 2, 2, 1, 2, 1
[3, 3, 3, 1, 2, 2, 1, 2, 2] => 3, 3, 3, 1, 2, 2, 1, 2, 2
[3, 3, 3, 1, 2, 2, 1, 2, 3] => 3, 3, 3, 1, 2, 2, 1, 2, 3
[3, 3, 3, 1, 2, 2, 1, 3, 1] => 3, 3, 3, 1, 2, 2, 1, 3, 1
[3, 3, 3, 1, 2, 2, 1, 3, 2] => 3, 3, 3, 1, 2, 2, 1, 3, 2
[3, 3, 3, 1, 2, 2, 1, 3, 3] => 3, 3, 3, 1, 2, 2, 1, 3, 3
[3, 3, 3, 1, 2, 2, 2, 1, 1] => 3, 3, 3, 1, 2, 2, 2, 1, 1
[3, 3, 3, 1, 2, 2, 2, 1, 2] => 3, 3, 3, 1, 2, 2, 2, 1, 2
[3, 3, 3, 1, 2, 2, 2, 1, 3] => 3, 3, 3, 1, 2, 2, 2, 1, 3
[3, 3, 3, 1, 2, 2, 2, 2, 1] => 3, 3, 3, 1, 2, 2, 2, 2, 1
[3, 3, 3, 1, 2, 2, 2, 2, 2] => 3, 3, 3, 1, 2, 2, 2, 2, 2
[3, 3, 3, 1, 2, 2, 2, 2, 3] => 3, 3, 3, 1, 2, 2, 2, 2, 3
[3, 3, 3, 1, 2, 2, 2, 3, 1] => 3, 3, 3, 1, 2, 2, 2, 3, 1
[3, 3, 3, 1, 2, 2, 2, 3, 2] => 3, 3, 3, 1, 2, 2, 2, 3, 2
[3, 3, 3, 1, 2, 2, 2, 3, 3] => 3, 3, 3, 1, 2, 2, 2, 3, 3
[3, 3, 3, 1, 2, 2, 3, 1, 1] => 3, 3, 3, 1, 2, 2, 3, 1, 1
[3, 3, 3, 1, 2, 2, 3, 1, 2] => 3, 3, 3, 1, 2, 2, 3, 1, 2
[3, 3, 3, 1, 2, 2, 3, 1, 3] => 3, 3, 3, 1, 2, 2, 3, 1, 3
[3, 3, 3, 1, 2, 2, 3, 2, 1] => 3, 3, 3, 1, 2, 2, 3, 2, 1
[3, 3, 3, 1, 2, 2, 3, 2, 2] => 3, 3, 3, 1, 2, 2, 3, 2, 2
[3, 3, 3, 1, 2, 2, 3, 2, 3] => 3, 3, 3, 1, 2, 2, 3, 2, 3
[3, 3, 3, 1, 2, 2, 3, 3, 1] => 3, 3, 3, 1, 2, 2, 3, 3, 1
[3, 3, 3, 1, 2, 2, 3, 3, 2] => 3, 3, 3, 1, 2, 2, 3, 3, 2
[3, 3, 3, 1, 2, 2, 3, 3, 3] => 3, 3, 3, 1, 2, 2, 3, 3, 3
[3, 3, 3, 1, 2, 3, 1, 1, 1] => 3, 3, 3, 1, 2, 3, 1, 1, 1
[3, 3, 3, 1, 2, 3, 1, 1, 2] => 3, 3, 3, 1, 2, 3, 1, 1, 2
[3, 3, 3, 1, 2, 3, 1, 1, 3] => 3, 3, 3, 1, 2, 3, 1, 1, 3
[3, 3, 3, 1, 2, 3, 1, 2, 1] => 3, 3, 3, 1, 2, 3, 1, 2, 1
[3, 3, 3, 1, 2, 3, 1, 2, 2] => 3, 3, 3, 1, 2, 3, 1, 2, 2
[3, 3, 3, 1, 2, 3, 1, 2, 3] => 3, 3, 3, 1, 2, 3, 1, 2, 3
[3, 3, 3, 1, 2, 3, 1, 3, 1] => 3, 3, 3, 1, 2, 3, 1, 3, 1
[3, 3, 3, 1, 2, 3, 1, 3, 2] => 3, 3, 3, 1, 2, 3, 1, 3, 2
[3, 3, 3, 1, 2, 3, 1, 3, 3] => 3, 3, 3, 1, 2, 3, 1, 3, 3
[3, 3, 3, 1, 2, 3, 2, 1, 1] => 3, 3, 3, 1, 2, 3, 2, 1, 1
[3, 3, 3, 1, 2, 3, 2, 1, 2] => 3, 3, 3, 1, 2, 3, 2, 1, 2
[3, 3, 3, 1, 2, 3, 2, 1, 3] => 3, 3, 3, 1, 2, 3, 2, 1, 3
[3, 3, 3, 1, 2, 3, 2, 2, 1] => 3, 3, 3, 1, 2, 3, 2, 2, 1
[3, 3, 3, 1, 2, 3, 2, 2, 2] => 3, 3, 3, 1, 2, 3, 2, 2, 2
[3, 3, 3, 1, 2, 3, 2, 2, 3] => 3, 3, 3, 1, 2, 3, 2, 2, 3
[3, 3, 3, 1, 2, 3, 2, 3, 1] => 3, 3, 3, 1, 2, 3, 2, 3, 1
[3, 3, 3, 1, 2, 3, 2, 3, 2] => 3, 3, 3, 1, 2, 3, 2, 3, 2
[3, 3, 3, 1, 2, 3, 2, 3, 3] => 3, 3, 3, 1, 2, 3, 2, 3, 3
[3, 3, 3, 1, 2, 3, 3, 1, 1] => 3, 3, 3, 1, 2, 3, 3, 1, 1
[3, 3, 3, 1, 2, 3, 3, 1, 2] => 3, 3, 3, 1, 2, 3, 3, 1, 2
[3, 3, 3, 1, 2, 3, 3, 1, 3] => 3, 3, 3, 1, 2, 3, 3, 1, 3
[3, 3, 3, 1, 2, 3, 3, 2, 1] => 3, 3, 3, 1, 2, 3, 3, 2, 1
[3, 3, 3, 1, 2, 3, 3, 2, 2] => 3, 3, 3, 1, 2, 3, 3, 2, 2
[3, 3, 3, 1, 2, 3, 3, 2, 3] => 3, 3, 3, 1, 2, 3, 3, 2, 3
[3, 3, 3, 1, 2, 3, 3, 3, 1] => 3, 3, 3, 1, 2, 3, 3, 3, 1
[3, 3, 3, 1, 2, 3, 3, 3, 2] => 3, 3, 3, 1, 2, 3, 3, 3, 2
[3, 3, 3, 1, 2, 3, 3, 3, 3] => 3, 3, 3, 1, 2, 3, 3, 3, 3
[3, 3, 3, 1, 3, 1, 1, 1, 1] => 3, 3, 3, 1, 3, 1, 1, 1, 1
[3, 3, 3, 1, 3, 1, 1, 1, 2] => 3, 3, 3, 1, 3, 1, 1, 1, 2
[3, 3, 3, 1, 3, 1, 1, 1, 3] => 3, 3, 3, 1, 3, 1, 1, 1, 3
[3, 3, 3, 1, 3, 1, 1, 2, 1] => 3, 3, 3, 1, 3, 1, 1, 2, 1
[3, 3, 3, 1, 3, 1, 1, 2, 2] => 3, 3, 3, 1, 3, 1, 1, 2, 2
[3, 3, 3, 1, 3, 1, 1, 2, 3] => 3, 3, 3, 1, 3, 1, 1, 2, 3
[3, 3, 3, 1, 3, 1, 1, 3, 1] => 3, 3, 3, 1, 3, 1, 1, 3, 1
[3, 3, 3, 1, 3, 1, 1, 3, 2] => 3, 3, 3, 1, 3, 1, 1, 3, 2
[3, 3, 3, 1, 3, 1, 1, 3, 3] => 3, 3, 3, 1, 3, 1, 1, 3, 3
[3, 3, 3, 1, 3, 1, 2, 1, 1] => 3, 3, 3, 1, 3, 1, 2, 1, 1
[3, 3, 3, 1, 3, 1, 2, 1, 2] => 3, 3, 3, 1, 3, 1, 2, 1, 2
[3, 3, 3, 1, 3, 1, 2, 1, 3] => 3, 3, 3, 1, 3, 1, 2, 1, 3
[3, 3, 3, 1, 3, 1, 2, 2, 1] => 3, 3, 3, 1, 3, 1, 2, 2, 1
[3, 3, 3, 1, 3, 1, 2, 2, 2] => 3, 3, 3, 1, 3, 1, 2, 2, 2
[3, 3, 3, 1, 3, 1, 2, 2, 3] => 3, 3, 3, 1, 3, 1, 2, 2, 3
[3, 3, 3, 1, 3, 1, 2, 3, 1] => 3, 3, 3, 1, 3, 1, 2, 3, 1
[3, 3, 3, 1, 3, 1, 2, 3, 2] => 3, 3, 3, 1, 3, 1, 2, 3, 2
[3, 3, 3, 1, 3, 1, 2, 3, 3] => 3, 3, 3, 1, 3, 1, 2, 3, 3
[3, 3, 3, 1, 3, 1, 3, 1, 1] => 3, 3, 3, 1, 3, 1, 3, 1, 1
[3, 3, 3, 1, 3, 1, 3, 1, 2] => 3, 3, 3, 1, 3, 1, 3, 1, 2
[3, 3, 3, 1, 3, 1, 3, 1, 3] => 3, 3, 3, 1, 3, 1, 3, 1, 3
[3, 3, 3, 1, 3, 1, 3, 2, 1] => 3, 3, 3, 1, 3, 1, 3, 2, 1
[3, 3, 3, 1, 3, 1, 3, 2, 2] => 3, 3, 3, 1, 3, 1, 3, 2, 2
[3, 3, 3, 1, 3, 1, 3, 2, 3] => 3, 3, 3, 1, 3, 1, 3, 2, 3
[3, 3, 3, 1, 3, 1, 3, 3, 1] => 3, 3, 3, 1, 3, 1, 3, 3, 1
[3, 3, 3, 1, 3, 1, 3, 3, 2] => 3, 3, 3, 1, 3, 1, 3, 3, 2
[3, 3, 3, 1, 3, 1, 3, 3, 3] => 3, 3, 3, 1, 3, 1, 3, 3, 3
[3, 3, 3, 1, 3, 2, 1, 1, 1] => 3, 3, 3, 1, 3, 2, 1, 1, 1
[3, 3, 3, 1, 3, 2, 1, 1, 2] => 3, 3, 3, 1, 3, 2, 1, 1, 2
[3, 3, 3, 1, 3, 2, 1, 1, 3] => 3, 3, 3, 1, 3, 2, 1, 1, 3
[3, 3, 3, 1, 3, 2, 1, 2, 1] => 3, 3, 3, 1, 3, 2, 1, 2, 1
[3, 3, 3, 1, 3, 2, 1, 2, 2] => 3, 3, 3, 1, 3, 2, 1, 2, 2
[3, 3, 3, 1, 3, 2, 1, 2, 3] => 3, 3, 3, 1, 3, 2, 1, 2, 3
[3, 3, 3, 1, 3, 2, 1, 3, 1] => 3, 3, 3, 1, 3, 2, 1, 3, 1
[3, 3, 3, 1, 3, 2, 1, 3, 2] => 3, 3, 3, 1, 3, 2, 1, 3, 2
[3, 3, 3, 1, 3, 2, 1, 3, 3] => 3, 3, 3, 1, 3, 2, 1, 3, 3
[3, 3, 3, 1, 3, 2, 2, 1, 1] => 3, 3, 3, 1, 3, 2, 2, 1, 1
[3, 3, 3, 1, 3, 2, 2, 1, 2] => 3, 3, 3, 1, 3, 2, 2, 1, 2
[3, 3, 3, 1, 3, 2, 2, 1, 3] => 3, 3, 3, 1, 3, 2, 2, 1, 3
[3, 3, 3, 1, 3, 2, 2, 2, 1] => 3, 3, 3, 1, 3, 2, 2, 2, 1
[3, 3, 3, 1, 3, 2, 2, 2, 2] => 3, 3, 3, 1, 3, 2, 2, 2, 2
[3, 3, 3, 1, 3, 2, 2, 2, 3] => 3, 3, 3, 1, 3, 2, 2, 2, 3
[3, 3, 3, 1, 3, 2, 2, 3, 1] => 3, 3, 3, 1, 3, 2, 2, 3, 1
[3, 3, 3, 1, 3, 2, 2, 3, 2] => 3, 3, 3, 1, 3, 2, 2, 3, 2
[3, 3, 3, 1, 3, 2, 2, 3, 3] => 3, 3, 3, 1, 3, 2, 2, 3, 3
[3, 3, 3, 1, 3, 2, 3, 1, 1] => 3, 3, 3, 1, 3, 2, 3, 1, 1
[3, 3, 3, 1, 3, 2, 3, 1, 2] => 3, 3, 3, 1, 3, 2, 3, 1, 2
[3, 3, 3, 1, 3, 2, 3, 1, 3] => 3, 3, 3, 1, 3, 2, 3, 1, 3
[3, 3, 3, 1, 3, 2, 3, 2, 1] => 3, 3, 3, 1, 3, 2, 3, 2, 1
[3, 3, 3, 1, 3, 2, 3, 2, 2] => 3, 3, 3, 1, 3, 2, 3, 2, 2
[3, 3, 3, 1, 3, 2, 3, 2, 3] => 3, 3, 3, 1, 3, 2, 3, 2, 3
[3, 3, 3, 1, 3, 2, 3, 3, 1] => 3, 3, 3, 1, 3, 2, 3, 3, 1
[3, 3, 3, 1, 3, 2, 3, 3, 2] => 3, 3, 3, 1, 3, 2, 3, 3, 2
[3, 3, 3, 1, 3, 2, 3, 3, 3] => 3, 3, 3, 1, 3, 2, 3, 3, 3
[3, 3, 3, 1, 3, 3, 1, 1, 1] => 3, 3, 3, 1, 3, 3, 1, 1, 1
[3, 3, 3, 1, 3, 3, 1, 1, 2] => 3, 3, 3, 1, 3, 3, 1, 1, 2
[3, 3, 3, 1, 3, 3, 1, 1, 3] => 3, 3, 3, 1, 3, 3, 1, 1, 3
[3, 3, 3, 1, 3, 3, 1, 2, 1] => 3, 3, 3, 1, 3, 3, 1, 2, 1
[3, 3, 3, 1, 3, 3, 1, 2, 2] => 3, 3, 3, 1, 3, 3, 1, 2, 2
[3, 3, 3, 1, 3, 3, 1, 2, 3] => 3, 3, 3, 1, 3, 3, 1, 2, 3
[3, 3, 3, 1, 3, 3, 1, 3, 1] => 3, 3, 3, 1, 3, 3, 1, 3, 1
[3, 3, 3, 1, 3, 3, 1, 3, 2] => 3, 3, 3, 1, 3, 3, 1, 3, 2
[3, 3, 3, 1, 3, 3, 1, 3, 3] => 3, 3, 3, 1, 3, 3, 1, 3, 3
[3, 3, 3, 1, 3, 3, 2, 1, 1] => 3, 3, 3, 1, 3, 3, 2, 1, 1
[3, 3, 3, 1, 3, 3, 2, 1, 2] => 3, 3, 3, 1, 3, 3, 2, 1, 2
[3, 3, 3, 1, 3, 3, 2, 1, 3] => 3, 3, 3, 1, 3, 3, 2, 1, 3
[3, 3, 3, 1, 3, 3, 2, 2, 1] => 3, 3, 3, 1, 3, 3, 2, 2, 1
[3, 3, 3, 1, 3, 3, 2, 2, 2] => 3, 3, 3, 1, 3, 3, 2, 2, 2
[3, 3, 3, 1, 3, 3, 2, 2, 3] => 3, 3, 3, 1, 3, 3, 2, 2, 3
[3, 3, 3, 1, 3, 3, 2, 3, 1] => 3, 3, 3, 1, 3, 3, 2, 3, 1
[3, 3, 3, 1, 3, 3, 2, 3, 2] => 3, 3, 3, 1, 3, 3, 2, 3, 2
[3, 3, 3, 1, 3, 3, 2, 3, 3] => 3, 3, 3, 1, 3, 3, 2, 3, 3
[3, 3, 3, 1, 3, 3, 3, 1, 1] => 3, 3, 3, 1, 3, 3, 3, 1, 1
[3, 3, 3, 1, 3, 3, 3, 1, 2] => 3, 3, 3, 1, 3, 3, 3, 1, 2
[3, 3, 3, 1, 3, 3, 3, 1, 3] => 3, 3, 3, 1, 3, 3, 3, 1, 3
[3, 3, 3, 1, 3, 3, 3, 2, 1] => 3, 3, 3, 1, 3, 3, 3, 2, 1
[3, 3, 3, 1, 3, 3, 3, 2, 2] => 3, 3, 3, 1, 3, 3, 3, 2, 2
[3, 3, 3, 1, 3, 3, 3, 2, 3] => 3, 3, 3, 1, 3, 3, 3, 2, 3
[3, 3, 3, 1, 3, 3, 3, 3, 1] => 3, 3, 3, 1, 3, 3, 3, 3, 1
[3, 3, 3, 1, 3, 3, 3, 3, 2] => 3, 3, 3, 1, 3, 3, 3, 3, 2
[3, 3, 3, 1, 3, 3, 3, 3, 3] => 3, 3, 3, 1, 3, 3, 3, 3, 3
[3, 3, 3, 2, 1, 1, 1, 1, 1] => 3, 3, 3, 2, 1, 1, 1, 1, 1
[3, 3, 3, 2, 1, 1, 1, 1, 2] => 3, 3, 3, 2, 1, 1, 1, 1, 2
[3, 3, 3, 2, 1, 1, 1, 1, 3] => 3, 3, 3, 2, 1, 1, 1, 1, 3
[3, 3, 3, 2, 1, 1, 1, 2, 1] => 3, 3, 3, 2, 1, 1, 1, 2, 1
[3, 3, 3, 2, 1, 1, 1, 2, 2] => 3, 3, 3, 2, 1, 1, 1, 2, 2
[3, 3, 3, 2, 1, 1, 1, 2, 3] => 3, 3, 3, 2, 1, 1, 1, 2, 3
[3, 3, 3, 2, 1, 1, 1, 3, 1] => 3, 3, 3, 2, 1, 1, 1, 3, 1
[3, 3, 3, 2, 1, 1, 1, 3, 2] => 3, 3, 3, 2, 1, 1, 1, 3, 2
[3, 3, 3, 2, 1, 1, 1, 3, 3] => 3, 3, 3, 2, 1, 1, 1, 3, 3
[3, 3, 3, 2, 1, 1, 2, 1, 1] => 3, 3, 3, 2, 1, 1, 2, 1, 1
[3, 3, 3, 2, 1, 1, 2, 1, 2] => 3, 3, 3, 2, 1, 1, 2, 1, 2
[3, 3, 3, 2, 1, 1, 2, 1, 3] => 3, 3, 3, 2, 1, 1, 2, 1, 3
[3, 3, 3, 2, 1, 1, 2, 2, 1] => 3, 3, 3, 2, 1, 1, 2, 2, 1
[3, 3, 3, 2, 1, 1, 2, 2, 2] => 3, 3, 3, 2, 1, 1, 2, 2, 2
[3, 3, 3, 2, 1, 1, 2, 2, 3] => 3, 3, 3, 2, 1, 1, 2, 2, 3
[3, 3, 3, 2, 1, 1, 2, 3, 1] => 3, 3, 3, 2, 1, 1, 2, 3, 1
[3, 3, 3, 2, 1, 1, 2, 3, 2] => 3, 3, 3, 2, 1, 1, 2, 3, 2
[3, 3, 3, 2, 1, 1, 2, 3, 3] => 3, 3, 3, 2, 1, 1, 2, 3, 3
[3, 3, 3, 2, 1, 1, 3, 1, 1] => 3, 3, 3, 2, 1, 1, 3, 1, 1
[3, 3, 3, 2, 1, 1, 3, 1, 2] => 3, 3, 3, 2, 1, 1, 3, 1, 2
[3, 3, 3, 2, 1, 1, 3, 1, 3] => 3, 3, 3, 2, 1, 1, 3, 1, 3
[3, 3, 3, 2, 1, 1, 3, 2, 1] => 3, 3, 3, 2, 1, 1, 3, 2, 1
[3, 3, 3, 2, 1, 1, 3, 2, 2] => 3, 3, 3, 2, 1, 1, 3, 2, 2
[3, 3, 3, 2, 1, 1, 3, 2, 3] => 3, 3, 3, 2, 1, 1, 3, 2, 3
[3, 3, 3, 2, 1, 1, 3, 3, 1] => 3, 3, 3, 2, 1, 1, 3, 3, 1
[3, 3, 3, 2, 1, 1, 3, 3, 2] => 3, 3, 3, 2, 1, 1, 3, 3, 2
[3, 3, 3, 2, 1, 1, 3, 3, 3] => 3, 3, 3, 2, 1, 1, 3, 3, 3
[3, 3, 3, 2, 1, 2, 1, 1, 1] => 3, 3, 3, 2, 1, 2, 1, 1, 1
[3, 3, 3, 2, 1, 2, 1, 1, 2] => 3, 3, 3, 2, 1, 2, 1, 1, 2
[3, 3, 3, 2, 1, 2, 1, 1, 3] => 3, 3, 3, 2, 1, 2, 1, 1, 3
[3, 3, 3, 2, 1, 2, 1, 2, 1] => 3, 3, 3, 2, 1, 2, 1, 2, 1
[3, 3, 3, 2, 1, 2, 1, 2, 2] => 3, 3, 3, 2, 1, 2, 1, 2, 2
[3, 3, 3, 2, 1, 2, 1, 2, 3] => 3, 3, 3, 2, 1, 2, 1, 2, 3
[3, 3, 3, 2, 1, 2, 1, 3, 1] => 3, 3, 3, 2, 1, 2, 1, 3, 1
[3, 3, 3, 2, 1, 2, 1, 3, 2] => 3, 3, 3, 2, 1, 2, 1, 3, 2
[3, 3, 3, 2, 1, 2, 1, 3, 3] => 3, 3, 3, 2, 1, 2, 1, 3, 3
[3, 3, 3, 2, 1, 2, 2, 1, 1] => 3, 3, 3, 2, 1, 2, 2, 1, 1
[3, 3, 3, 2, 1, 2, 2, 1, 2] => 3, 3, 3, 2, 1, 2, 2, 1, 2
[3, 3, 3, 2, 1, 2, 2, 1, 3] => 3, 3, 3, 2, 1, 2, 2, 1, 3
[3, 3, 3, 2, 1, 2, 2, 2, 1] => 3, 3, 3, 2, 1, 2, 2, 2, 1
[3, 3, 3, 2, 1, 2, 2, 2, 2] => 3, 3, 3, 2, 1, 2, 2, 2, 2
[3, 3, 3, 2, 1, 2, 2, 2, 3] => 3, 3, 3, 2, 1, 2, 2, 2, 3
[3, 3, 3, 2, 1, 2, 2, 3, 1] => 3, 3, 3, 2, 1, 2, 2, 3, 1
[3, 3, 3, 2, 1, 2, 2, 3, 2] => 3, 3, 3, 2, 1, 2, 2, 3, 2
[3, 3, 3, 2, 1, 2, 2, 3, 3] => 3, 3, 3, 2, 1, 2, 2, 3, 3
[3, 3, 3, 2, 1, 2, 3, 1, 1] => 3, 3, 3, 2, 1, 2, 3, 1, 1
[3, 3, 3, 2, 1, 2, 3, 1, 2] => 3, 3, 3, 2, 1, 2, 3, 1, 2
[3, 3, 3, 2, 1, 2, 3, 1, 3] => 3, 3, 3, 2, 1, 2, 3, 1, 3
[3, 3, 3, 2, 1, 2, 3, 2, 1] => 3, 3, 3, 2, 1, 2, 3, 2, 1
[3, 3, 3, 2, 1, 2, 3, 2, 2] => 3, 3, 3, 2, 1, 2, 3, 2, 2
[3, 3, 3, 2, 1, 2, 3, 2, 3] => 3, 3, 3, 2, 1, 2, 3, 2, 3
[3, 3, 3, 2, 1, 2, 3, 3, 1] => 3, 3, 3, 2, 1, 2, 3, 3, 1
[3, 3, 3, 2, 1, 2, 3, 3, 2] => 3, 3, 3, 2, 1, 2, 3, 3, 2
[3, 3, 3, 2, 1, 2, 3, 3, 3] => 3, 3, 3, 2, 1, 2, 3, 3, 3
[3, 3, 3, 2, 1, 3, 1, 1, 1] => 3, 3, 3, 2, 1, 3, 1, 1, 1
[3, 3, 3, 2, 1, 3, 1, 1, 2] => 3, 3, 3, 2, 1, 3, 1, 1, 2
[3, 3, 3, 2, 1, 3, 1, 1, 3] => 3, 3, 3, 2, 1, 3, 1, 1, 3
[3, 3, 3, 2, 1, 3, 1, 2, 1] => 3, 3, 3, 2, 1, 3, 1, 2, 1
[3, 3, 3, 2, 1, 3, 1, 2, 2] => 3, 3, 3, 2, 1, 3, 1, 2, 2
[3, 3, 3, 2, 1, 3, 1, 2, 3] => 3, 3, 3, 2, 1, 3, 1, 2, 3
[3, 3, 3, 2, 1, 3, 1, 3, 1] => 3, 3, 3, 2, 1, 3, 1, 3, 1
[3, 3, 3, 2, 1, 3, 1, 3, 2] => 3, 3, 3, 2, 1, 3, 1, 3, 2
[3, 3, 3, 2, 1, 3, 1, 3, 3] => 3, 3, 3, 2, 1, 3, 1, 3, 3
[3, 3, 3, 2, 1, 3, 2, 1, 1] => 3, 3, 3, 2, 1, 3, 2, 1, 1
[3, 3, 3, 2, 1, 3, 2, 1, 2] => 3, 3, 3, 2, 1, 3, 2, 1, 2
[3, 3, 3, 2, 1, 3, 2, 1, 3] => 3, 3, 3, 2, 1, 3, 2, 1, 3
[3, 3, 3, 2, 1, 3, 2, 2, 1] => 3, 3, 3, 2, 1, 3, 2, 2, 1
[3, 3, 3, 2, 1, 3, 2, 2, 2] => 3, 3, 3, 2, 1, 3, 2, 2, 2
[3, 3, 3, 2, 1, 3, 2, 2, 3] => 3, 3, 3, 2, 1, 3, 2, 2, 3
[3, 3, 3, 2, 1, 3, 2, 3, 1] => 3, 3, 3, 2, 1, 3, 2, 3, 1
[3, 3, 3, 2, 1, 3, 2, 3, 2] => 3, 3, 3, 2, 1, 3, 2, 3, 2
[3, 3, 3, 2, 1, 3, 2, 3, 3] => 3, 3, 3, 2, 1, 3, 2, 3, 3
[3, 3, 3, 2, 1, 3, 3, 1, 1] => 3, 3, 3, 2, 1, 3, 3, 1, 1
[3, 3, 3, 2, 1, 3, 3, 1, 2] => 3, 3, 3, 2, 1, 3, 3, 1, 2
[3, 3, 3, 2, 1, 3, 3, 1, 3] => 3, 3, 3, 2, 1, 3, 3, 1, 3
[3, 3, 3, 2, 1, 3, 3, 2, 1] => 3, 3, 3, 2, 1, 3, 3, 2, 1
[3, 3, 3, 2, 1, 3, 3, 2, 2] => 3, 3, 3, 2, 1, 3, 3, 2, 2
[3, 3, 3, 2, 1, 3, 3, 2, 3] => 3, 3, 3, 2, 1, 3, 3, 2, 3
[3, 3, 3, 2, 1, 3, 3, 3, 1] => 3, 3, 3, 2, 1, 3, 3, 3, 1
[3, 3, 3, 2, 1, 3, 3, 3, 2] => 3, 3, 3, 2, 1, 3, 3, 3, 2
[3, 3, 3, 2, 1, 3, 3, 3, 3] => 3, 3, 3, 2, 1, 3, 3, 3, 3
[3, 3, 3, 2, 2, 1, 1, 1, 1] => 3, 3, 3, 2, 2, 1, 1, 1, 1
[3, 3, 3, 2, 2, 1, 1, 1, 2] => 3, 3, 3, 2, 2, 1, 1, 1, 2
[3, 3, 3, 2, 2, 1, 1, 1, 3] => 3, 3, 3, 2, 2, 1, 1, 1, 3
[3, 3, 3, 2, 2, 1, 1, 2, 1] => 3, 3, 3, 2, 2, 1, 1, 2, 1
[3, 3, 3, 2, 2, 1, 1, 2, 2] => 3, 3, 3, 2, 2, 1, 1, 2, 2
[3, 3, 3, 2, 2, 1, 1, 2, 3] => 3, 3, 3, 2, 2, 1, 1, 2, 3
[3, 3, 3, 2, 2, 1, 1, 3, 1] => 3, 3, 3, 2, 2, 1, 1, 3, 1
[3, 3, 3, 2, 2, 1, 1, 3, 2] => 3, 3, 3, 2, 2, 1, 1, 3, 2
[3, 3, 3, 2, 2, 1, 1, 3, 3] => 3, 3, 3, 2, 2, 1, 1, 3, 3
[3, 3, 3, 2, 2, 1, 2, 1, 1] => 3, 3, 3, 2, 2, 1, 2, 1, 1
[3, 3, 3, 2, 2, 1, 2, 1, 2] => 3, 3, 3, 2, 2, 1, 2, 1, 2
[3, 3, 3, 2, 2, 1, 2, 1, 3] => 3, 3, 3, 2, 2, 1, 2, 1, 3
[3, 3, 3, 2, 2, 1, 2, 2, 1] => 3, 3, 3, 2, 2, 1, 2, 2, 1
[3, 3, 3, 2, 2, 1, 2, 2, 2] => 3, 3, 3, 2, 2, 1, 2, 2, 2
[3, 3, 3, 2, 2, 1, 2, 2, 3] => 3, 3, 3, 2, 2, 1, 2, 2, 3
[3, 3, 3, 2, 2, 1, 2, 3, 1] => 3, 3, 3, 2, 2, 1, 2, 3, 1
[3, 3, 3, 2, 2, 1, 2, 3, 2] => 3, 3, 3, 2, 2, 1, 2, 3, 2
[3, 3, 3, 2, 2, 1, 2, 3, 3] => 3, 3, 3, 2, 2, 1, 2, 3, 3
[3, 3, 3, 2, 2, 1, 3, 1, 1] => 3, 3, 3, 2, 2, 1, 3, 1, 1
[3, 3, 3, 2, 2, 1, 3, 1, 2] => 3, 3, 3, 2, 2, 1, 3, 1, 2
[3, 3, 3, 2, 2, 1, 3, 1, 3] => 3, 3, 3, 2, 2, 1, 3, 1, 3
[3, 3, 3, 2, 2, 1, 3, 2, 1] => 3, 3, 3, 2, 2, 1, 3, 2, 1
[3, 3, 3, 2, 2, 1, 3, 2, 2] => 3, 3, 3, 2, 2, 1, 3, 2, 2
[3, 3, 3, 2, 2, 1, 3, 2, 3] => 3, 3, 3, 2, 2, 1, 3, 2, 3
[3, 3, 3, 2, 2, 1, 3, 3, 1] => 3, 3, 3, 2, 2, 1, 3, 3, 1
[3, 3, 3, 2, 2, 1, 3, 3, 2] => 3, 3, 3, 2, 2, 1, 3, 3, 2
[3, 3, 3, 2, 2, 1, 3, 3, 3] => 3, 3, 3, 2, 2, 1, 3, 3, 3
[3, 3, 3, 2, 2, 2, 1, 1, 1] => 3, 3, 3, 2, 2, 2, 1, 1, 1
[3, 3, 3, 2, 2, 2, 1, 1, 2] => 3, 3, 3, 2, 2, 2, 1, 1, 2
[3, 3, 3, 2, 2, 2, 1, 1, 3] => 3, 3, 3, 2, 2, 2, 1, 1, 3
[3, 3, 3, 2, 2, 2, 1, 2, 1] => 3, 3, 3, 2, 2, 2, 1, 2, 1
[3, 3, 3, 2, 2, 2, 1, 2, 2] => 3, 3, 3, 2, 2, 2, 1, 2, 2
[3, 3, 3, 2, 2, 2, 1, 2, 3] => 3, 3, 3, 2, 2, 2, 1, 2, 3
[3, 3, 3, 2, 2, 2, 1, 3, 1] => 3, 3, 3, 2, 2, 2, 1, 3, 1
[3, 3, 3, 2, 2, 2, 1, 3, 2] => 3, 3, 3, 2, 2, 2, 1, 3, 2
[3, 3, 3, 2, 2, 2, 1, 3, 3] => 3, 3, 3, 2, 2, 2, 1, 3, 3
[3, 3, 3, 2, 2, 2, 2, 1, 1] => 3, 3, 3, 2, 2, 2, 2, 1, 1
[3, 3, 3, 2, 2, 2, 2, 1, 2] => 3, 3, 3, 2, 2, 2, 2, 1, 2
[3, 3, 3, 2, 2, 2, 2, 1, 3] => 3, 3, 3, 2, 2, 2, 2, 1, 3
[3, 3, 3, 2, 2, 2, 2, 2, 1] => 3, 3, 3, 2, 2, 2, 2, 2, 1
[3, 3, 3, 2, 2, 2, 2, 2, 2] => 3, 3, 3, 2, 2, 2, 2, 2, 2
[3, 3, 3, 2, 2, 2, 2, 2, 3] => 3, 3, 3, 2, 2, 2, 2, 2, 3
[3, 3, 3, 2, 2, 2, 2, 3, 1] => 3, 3, 3, 2, 2, 2, 2, 3, 1
[3, 3, 3, 2, 2, 2, 2, 3, 2] => 3, 3, 3, 2, 2, 2, 2, 3, 2
[3, 3, 3, 2, 2, 2, 2, 3, 3] => 3, 3, 3, 2, 2, 2, 2, 3, 3
[3, 3, 3, 2, 2, 2, 3, 1, 1] => 3, 3, 3, 2, 2, 2, 3, 1, 1
[3, 3, 3, 2, 2, 2, 3, 1, 2] => 3, 3, 3, 2, 2, 2, 3, 1, 2
[3, 3, 3, 2, 2, 2, 3, 1, 3] => 3, 3, 3, 2, 2, 2, 3, 1, 3
[3, 3, 3, 2, 2, 2, 3, 2, 1] => 3, 3, 3, 2, 2, 2, 3, 2, 1
[3, 3, 3, 2, 2, 2, 3, 2, 2] => 3, 3, 3, 2, 2, 2, 3, 2, 2
[3, 3, 3, 2, 2, 2, 3, 2, 3] => 3, 3, 3, 2, 2, 2, 3, 2, 3
[3, 3, 3, 2, 2, 2, 3, 3, 1] => 3, 3, 3, 2, 2, 2, 3, 3, 1
[3, 3, 3, 2, 2, 2, 3, 3, 2] => 3, 3, 3, 2, 2, 2, 3, 3, 2
[3, 3, 3, 2, 2, 2, 3, 3, 3] => 3, 3, 3, 2, 2, 2, 3, 3, 3
[3, 3, 3, 2, 2, 3, 1, 1, 1] => 3, 3, 3, 2, 2, 3, 1, 1, 1
[3, 3, 3, 2, 2, 3, 1, 1, 2] => 3, 3, 3, 2, 2, 3, 1, 1, 2
[3, 3, 3, 2, 2, 3, 1, 1, 3] => 3, 3, 3, 2, 2, 3, 1, 1, 3
[3, 3, 3, 2, 2, 3, 1, 2, 1] => 3, 3, 3, 2, 2, 3, 1, 2, 1
[3, 3, 3, 2, 2, 3, 1, 2, 2] => 3, 3, 3, 2, 2, 3, 1, 2, 2
[3, 3, 3, 2, 2, 3, 1, 2, 3] => 3, 3, 3, 2, 2, 3, 1, 2, 3
[3, 3, 3, 2, 2, 3, 1, 3, 1] => 3, 3, 3, 2, 2, 3, 1, 3, 1
[3, 3, 3, 2, 2, 3, 1, 3, 2] => 3, 3, 3, 2, 2, 3, 1, 3, 2
[3, 3, 3, 2, 2, 3, 1, 3, 3] => 3, 3, 3, 2, 2, 3, 1, 3, 3
[3, 3, 3, 2, 2, 3, 2, 1, 1] => 3, 3, 3, 2, 2, 3, 2, 1, 1
[3, 3, 3, 2, 2, 3, 2, 1, 2] => 3, 3, 3, 2, 2, 3, 2, 1, 2
[3, 3, 3, 2, 2, 3, 2, 1, 3] => 3, 3, 3, 2, 2, 3, 2, 1, 3
[3, 3, 3, 2, 2, 3, 2, 2, 1] => 3, 3, 3, 2, 2, 3, 2, 2, 1
[3, 3, 3, 2, 2, 3, 2, 2, 2] => 3, 3, 3, 2, 2, 3, 2, 2, 2
[3, 3, 3, 2, 2, 3, 2, 2, 3] => 3, 3, 3, 2, 2, 3, 2, 2, 3
[3, 3, 3, 2, 2, 3, 2, 3, 1] => 3, 3, 3, 2, 2, 3, 2, 3, 1
[3, 3, 3, 2, 2, 3, 2, 3, 2] => 3, 3, 3, 2, 2, 3, 2, 3, 2
[3, 3, 3, 2, 2, 3, 2, 3, 3] => 3, 3, 3, 2, 2, 3, 2, 3, 3
[3, 3, 3, 2, 2, 3, 3, 1, 1] => 3, 3, 3, 2, 2, 3, 3, 1, 1
[3, 3, 3, 2, 2, 3, 3, 1, 2] => 3, 3, 3, 2, 2, 3, 3, 1, 2
[3, 3, 3, 2, 2, 3, 3, 1, 3] => 3, 3, 3, 2, 2, 3, 3, 1, 3
[3, 3, 3, 2, 2, 3, 3, 2, 1] => 3, 3, 3, 2, 2, 3, 3, 2, 1
[3, 3, 3, 2, 2, 3, 3, 2, 2] => 3, 3, 3, 2, 2, 3, 3, 2, 2
[3, 3, 3, 2, 2, 3, 3, 2, 3] => 3, 3, 3, 2, 2, 3, 3, 2, 3
[3, 3, 3, 2, 2, 3, 3, 3, 1] => 3, 3, 3, 2, 2, 3, 3, 3, 1
[3, 3, 3, 2, 2, 3, 3, 3, 2] => 3, 3, 3, 2, 2, 3, 3, 3, 2
[3, 3, 3, 2, 2, 3, 3, 3, 3] => 3, 3, 3, 2, 2, 3, 3, 3, 3
[3, 3, 3, 2, 3, 1, 1, 1, 1] => 3, 3, 3, 2, 3, 1, 1, 1, 1
[3, 3, 3, 2, 3, 1, 1, 1, 2] => 3, 3, 3, 2, 3, 1, 1, 1, 2
[3, 3, 3, 2, 3, 1, 1, 1, 3] => 3, 3, 3, 2, 3, 1, 1, 1, 3
[3, 3, 3, 2, 3, 1, 1, 2, 1] => 3, 3, 3, 2, 3, 1, 1, 2, 1
[3, 3, 3, 2, 3, 1, 1, 2, 2] => 3, 3, 3, 2, 3, 1, 1, 2, 2
[3, 3, 3, 2, 3, 1, 1, 2, 3] => 3, 3, 3, 2, 3, 1, 1, 2, 3
[3, 3, 3, 2, 3, 1, 1, 3, 1] => 3, 3, 3, 2, 3, 1, 1, 3, 1
[3, 3, 3, 2, 3, 1, 1, 3, 2] => 3, 3, 3, 2, 3, 1, 1, 3, 2
[3, 3, 3, 2, 3, 1, 1, 3, 3] => 3, 3, 3, 2, 3, 1, 1, 3, 3
[3, 3, 3, 2, 3, 1, 2, 1, 1] => 3, 3, 3, 2, 3, 1, 2, 1, 1
[3, 3, 3, 2, 3, 1, 2, 1, 2] => 3, 3, 3, 2, 3, 1, 2, 1, 2
[3, 3, 3, 2, 3, 1, 2, 1, 3] => 3, 3, 3, 2, 3, 1, 2, 1, 3
[3, 3, 3, 2, 3, 1, 2, 2, 1] => 3, 3, 3, 2, 3, 1, 2, 2, 1
[3, 3, 3, 2, 3, 1, 2, 2, 2] => 3, 3, 3, 2, 3, 1, 2, 2, 2
[3, 3, 3, 2, 3, 1, 2, 2, 3] => 3, 3, 3, 2, 3, 1, 2, 2, 3
[3, 3, 3, 2, 3, 1, 2, 3, 1] => 3, 3, 3, 2, 3, 1, 2, 3, 1
[3, 3, 3, 2, 3, 1, 2, 3, 2] => 3, 3, 3, 2, 3, 1, 2, 3, 2
[3, 3, 3, 2, 3, 1, 2, 3, 3] => 3, 3, 3, 2, 3, 1, 2, 3, 3
[3, 3, 3, 2, 3, 1, 3, 1, 1] => 3, 3, 3, 2, 3, 1, 3, 1, 1
[3, 3, 3, 2, 3, 1, 3, 1, 2] => 3, 3, 3, 2, 3, 1, 3, 1, 2
[3, 3, 3, 2, 3, 1, 3, 1, 3] => 3, 3, 3, 2, 3, 1, 3, 1, 3
[3, 3, 3, 2, 3, 1, 3, 2, 1] => 3, 3, 3, 2, 3, 1, 3, 2, 1
[3, 3, 3, 2, 3, 1, 3, 2, 2] => 3, 3, 3, 2, 3, 1, 3, 2, 2
[3, 3, 3, 2, 3, 1, 3, 2, 3] => 3, 3, 3, 2, 3, 1, 3, 2, 3
[3, 3, 3, 2, 3, 1, 3, 3, 1] => 3, 3, 3, 2, 3, 1, 3, 3, 1
[3, 3, 3, 2, 3, 1, 3, 3, 2] => 3, 3, 3, 2, 3, 1, 3, 3, 2
[3, 3, 3, 2, 3, 1, 3, 3, 3] => 3, 3, 3, 2, 3, 1, 3, 3, 3
[3, 3, 3, 2, 3, 2, 1, 1, 1] => 3, 3, 3, 2, 3, 2, 1, 1, 1
[3, 3, 3, 2, 3, 2, 1, 1, 2] => 3, 3, 3, 2, 3, 2, 1, 1, 2
[3, 3, 3, 2, 3, 2, 1, 1, 3] => 3, 3, 3, 2, 3, 2, 1, 1, 3
[3, 3, 3, 2, 3, 2, 1, 2, 1] => 3, 3, 3, 2, 3, 2, 1, 2, 1
[3, 3, 3, 2, 3, 2, 1, 2, 2] => 3, 3, 3, 2, 3, 2, 1, 2, 2
[3, 3, 3, 2, 3, 2, 1, 2, 3] => 3, 3, 3, 2, 3, 2, 1, 2, 3
[3, 3, 3, 2, 3, 2, 1, 3, 1] => 3, 3, 3, 2, 3, 2, 1, 3, 1
[3, 3, 3, 2, 3, 2, 1, 3, 2] => 3, 3, 3, 2, 3, 2, 1, 3, 2
[3, 3, 3, 2, 3, 2, 1, 3, 3] => 3, 3, 3, 2, 3, 2, 1, 3, 3
[3, 3, 3, 2, 3, 2, 2, 1, 1] => 3, 3, 3, 2, 3, 2, 2, 1, 1
[3, 3, 3, 2, 3, 2, 2, 1, 2] => 3, 3, 3, 2, 3, 2, 2, 1, 2
[3, 3, 3, 2, 3, 2, 2, 1, 3] => 3, 3, 3, 2, 3, 2, 2, 1, 3
[3, 3, 3, 2, 3, 2, 2, 2, 1] => 3, 3, 3, 2, 3, 2, 2, 2, 1
[3, 3, 3, 2, 3, 2, 2, 2, 2] => 3, 3, 3, 2, 3, 2, 2, 2, 2
[3, 3, 3, 2, 3, 2, 2, 2, 3] => 3, 3, 3, 2, 3, 2, 2, 2, 3
[3, 3, 3, 2, 3, 2, 2, 3, 1] => 3, 3, 3, 2, 3, 2, 2, 3, 1
[3, 3, 3, 2, 3, 2, 2, 3, 2] => 3, 3, 3, 2, 3, 2, 2, 3, 2
[3, 3, 3, 2, 3, 2, 2, 3, 3] => 3, 3, 3, 2, 3, 2, 2, 3, 3
[3, 3, 3, 2, 3, 2, 3, 1, 1] => 3, 3, 3, 2, 3, 2, 3, 1, 1
[3, 3, 3, 2, 3, 2, 3, 1, 2] => 3, 3, 3, 2, 3, 2, 3, 1, 2
[3, 3, 3, 2, 3, 2, 3, 1, 3] => 3, 3, 3, 2, 3, 2, 3, 1, 3
[3, 3, 3, 2, 3, 2, 3, 2, 1] => 3, 3, 3, 2, 3, 2, 3, 2, 1
[3, 3, 3, 2, 3, 2, 3, 2, 2] => 3, 3, 3, 2, 3, 2, 3, 2, 2
[3, 3, 3, 2, 3, 2, 3, 2, 3] => 3, 3, 3, 2, 3, 2, 3, 2, 3
[3, 3, 3, 2, 3, 2, 3, 3, 1] => 3, 3, 3, 2, 3, 2, 3, 3, 1
[3, 3, 3, 2, 3, 2, 3, 3, 2] => 3, 3, 3, 2, 3, 2, 3, 3, 2
[3, 3, 3, 2, 3, 2, 3, 3, 3] => 3, 3, 3, 2, 3, 2, 3, 3, 3
[3, 3, 3, 2, 3, 3, 1, 1, 1] => 3, 3, 3, 2, 3, 3, 1, 1, 1
[3, 3, 3, 2, 3, 3, 1, 1, 2] => 3, 3, 3, 2, 3, 3, 1, 1, 2
[3, 3, 3, 2, 3, 3, 1, 1, 3] => 3, 3, 3, 2, 3, 3, 1, 1, 3
[3, 3, 3, 2, 3, 3, 1, 2, 1] => 3, 3, 3, 2, 3, 3, 1, 2, 1
[3, 3, 3, 2, 3, 3, 1, 2, 2] => 3, 3, 3, 2, 3, 3, 1, 2, 2
[3, 3, 3, 2, 3, 3, 1, 2, 3] => 3, 3, 3, 2, 3, 3, 1, 2, 3
[3, 3, 3, 2, 3, 3, 1, 3, 1] => 3, 3, 3, 2, 3, 3, 1, 3, 1
[3, 3, 3, 2, 3, 3, 1, 3, 2] => 3, 3, 3, 2, 3, 3, 1, 3, 2
[3, 3, 3, 2, 3, 3, 1, 3, 3] => 3, 3, 3, 2, 3, 3, 1, 3, 3
[3, 3, 3, 2, 3, 3, 2, 1, 1] => 3, 3, 3, 2, 3, 3, 2, 1, 1
[3, 3, 3, 2, 3, 3, 2, 1, 2] => 3, 3, 3, 2, 3, 3, 2, 1, 2
[3, 3, 3, 2, 3, 3, 2, 1, 3] => 3, 3, 3, 2, 3, 3, 2, 1, 3
[3, 3, 3, 2, 3, 3, 2, 2, 1] => 3, 3, 3, 2, 3, 3, 2, 2, 1
[3, 3, 3, 2, 3, 3, 2, 2, 2] => 3, 3, 3, 2, 3, 3, 2, 2, 2
[3, 3, 3, 2, 3, 3, 2, 2, 3] => 3, 3, 3, 2, 3, 3, 2, 2, 3
[3, 3, 3, 2, 3, 3, 2, 3, 1] => 3, 3, 3, 2, 3, 3, 2, 3, 1
[3, 3, 3, 2, 3, 3, 2, 3, 2] => 3, 3, 3, 2, 3, 3, 2, 3, 2
[3, 3, 3, 2, 3, 3, 2, 3, 3] => 3, 3, 3, 2, 3, 3, 2, 3, 3
[3, 3, 3, 2, 3, 3, 3, 1, 1] => 3, 3, 3, 2, 3, 3, 3, 1, 1
[3, 3, 3, 2, 3, 3, 3, 1, 2] => 3, 3, 3, 2, 3, 3, 3, 1, 2
[3, 3, 3, 2, 3, 3, 3, 1, 3] => 3, 3, 3, 2, 3, 3, 3, 1, 3
[3, 3, 3, 2, 3, 3, 3, 2, 1] => 3, 3, 3, 2, 3, 3, 3, 2, 1
[3, 3, 3, 2, 3, 3, 3, 2, 2] => 3, 3, 3, 2, 3, 3, 3, 2, 2
[3, 3, 3, 2, 3, 3, 3, 2, 3] => 3, 3, 3, 2, 3, 3, 3, 2, 3
[3, 3, 3, 2, 3, 3, 3, 3, 1] => 3, 3, 3, 2, 3, 3, 3, 3, 1
[3, 3, 3, 2, 3, 3, 3, 3, 2] => 3, 3, 3, 2, 3, 3, 3, 3, 2
[3, 3, 3, 2, 3, 3, 3, 3, 3] => 3, 3, 3, 2, 3, 3, 3, 3, 3
[3, 3, 3, 3, 1, 1, 1, 1, 1] => 3, 3, 3, 3, 1, 1, 1, 1, 1
[3, 3, 3, 3, 1, 1, 1, 1, 2] => 3, 3, 3, 3, 1, 1, 1, 1, 2
[3, 3, 3, 3, 1, 1, 1, 1, 3] => 3, 3, 3, 3, 1, 1, 1, 1, 3
[3, 3, 3, 3, 1, 1, 1, 2, 1] => 3, 3, 3, 3, 1, 1, 1, 2, 1
[3, 3, 3, 3, 1, 1, 1, 2, 2] => 3, 3, 3, 3, 1, 1, 1, 2, 2
[3, 3, 3, 3, 1, 1, 1, 2, 3] => 3, 3, 3, 3, 1, 1, 1, 2, 3
[3, 3, 3, 3, 1, 1, 1, 3, 1] => 3, 3, 3, 3, 1, 1, 1, 3, 1
[3, 3, 3, 3, 1, 1, 1, 3, 2] => 3, 3, 3, 3, 1, 1, 1, 3, 2
[3, 3, 3, 3, 1, 1, 1, 3, 3] => 3, 3, 3, 3, 1, 1, 1, 3, 3
[3, 3, 3, 3, 1, 1, 2, 1, 1] => 3, 3, 3, 3, 1, 1, 2, 1, 1
[3, 3, 3, 3, 1, 1, 2, 1, 2] => 3, 3, 3, 3, 1, 1, 2, 1, 2
[3, 3, 3, 3, 1, 1, 2, 1, 3] => 3, 3, 3, 3, 1, 1, 2, 1, 3
[3, 3, 3, 3, 1, 1, 2, 2, 1] => 3, 3, 3, 3, 1, 1, 2, 2, 1
[3, 3, 3, 3, 1, 1, 2, 2, 2] => 3, 3, 3, 3, 1, 1, 2, 2, 2
[3, 3, 3, 3, 1, 1, 2, 2, 3] => 3, 3, 3, 3, 1, 1, 2, 2, 3
[3, 3, 3, 3, 1, 1, 2, 3, 1] => 3, 3, 3, 3, 1, 1, 2, 3, 1
[3, 3, 3, 3, 1, 1, 2, 3, 2] => 3, 3, 3, 3, 1, 1, 2, 3, 2
[3, 3, 3, 3, 1, 1, 2, 3, 3] => 3, 3, 3, 3, 1, 1, 2, 3, 3
[3, 3, 3, 3, 1, 1, 3, 1, 1] => 3, 3, 3, 3, 1, 1, 3, 1, 1
[3, 3, 3, 3, 1, 1, 3, 1, 2] => 3, 3, 3, 3, 1, 1, 3, 1, 2
[3, 3, 3, 3, 1, 1, 3, 1, 3] => 3, 3, 3, 3, 1, 1, 3, 1, 3
[3, 3, 3, 3, 1, 1, 3, 2, 1] => 3, 3, 3, 3, 1, 1, 3, 2, 1
[3, 3, 3, 3, 1, 1, 3, 2, 2] => 3, 3, 3, 3, 1, 1, 3, 2, 2
[3, 3, 3, 3, 1, 1, 3, 2, 3] => 3, 3, 3, 3, 1, 1, 3, 2, 3
[3, 3, 3, 3, 1, 1, 3, 3, 1] => 3, 3, 3, 3, 1, 1, 3, 3, 1
[3, 3, 3, 3, 1, 1, 3, 3, 2] => 3, 3, 3, 3, 1, 1, 3, 3, 2
[3, 3, 3, 3, 1, 1, 3, 3, 3] => 3, 3, 3, 3, 1, 1, 3, 3, 3
[3, 3, 3, 3, 1, 2, 1, 1, 1] => 3, 3, 3, 3, 1, 2, 1, 1, 1
[3, 3, 3, 3, 1, 2, 1, 1, 2] => 3, 3, 3, 3, 1, 2, 1, 1, 2
[3, 3, 3, 3, 1, 2, 1, 1, 3] => 3, 3, 3, 3, 1, 2, 1, 1, 3
[3, 3, 3, 3, 1, 2, 1, 2, 1] => 3, 3, 3, 3, 1, 2, 1, 2, 1
[3, 3, 3, 3, 1, 2, 1, 2, 2] => 3, 3, 3, 3, 1, 2, 1, 2, 2
[3, 3, 3, 3, 1, 2, 1, 2, 3] => 3, 3, 3, 3, 1, 2, 1, 2, 3
[3, 3, 3, 3, 1, 2, 1, 3, 1] => 3, 3, 3, 3, 1, 2, 1, 3, 1
[3, 3, 3, 3, 1, 2, 1, 3, 2] => 3, 3, 3, 3, 1, 2, 1, 3, 2
[3, 3, 3, 3, 1, 2, 1, 3, 3] => 3, 3, 3, 3, 1, 2, 1, 3, 3
[3, 3, 3, 3, 1, 2, 2, 1, 1] => 3, 3, 3, 3, 1, 2, 2, 1, 1
[3, 3, 3, 3, 1, 2, 2, 1, 2] => 3, 3, 3, 3, 1, 2, 2, 1, 2
[3, 3, 3, 3, 1, 2, 2, 1, 3] => 3, 3, 3, 3, 1, 2, 2, 1, 3
[3, 3, 3, 3, 1, 2, 2, 2, 1] => 3, 3, 3, 3, 1, 2, 2, 2, 1
[3, 3, 3, 3, 1, 2, 2, 2, 2] => 3, 3, 3, 3, 1, 2, 2, 2, 2
[3, 3, 3, 3, 1, 2, 2, 2, 3] => 3, 3, 3, 3, 1, 2, 2, 2, 3
[3, 3, 3, 3, 1, 2, 2, 3, 1] => 3, 3, 3, 3, 1, 2, 2, 3, 1
[3, 3, 3, 3, 1, 2, 2, 3, 2] => 3, 3, 3, 3, 1, 2, 2, 3, 2
[3, 3, 3, 3, 1, 2, 2, 3, 3] => 3, 3, 3, 3, 1, 2, 2, 3, 3
[3, 3, 3, 3, 1, 2, 3, 1, 1] => 3, 3, 3, 3, 1, 2, 3, 1, 1
[3, 3, 3, 3, 1, 2, 3, 1, 2] => 3, 3, 3, 3, 1, 2, 3, 1, 2
[3, 3, 3, 3, 1, 2, 3, 1, 3] => 3, 3, 3, 3, 1, 2, 3, 1, 3
[3, 3, 3, 3, 1, 2, 3, 2, 1] => 3, 3, 3, 3, 1, 2, 3, 2, 1
[3, 3, 3, 3, 1, 2, 3, 2, 2] => 3, 3, 3, 3, 1, 2, 3, 2, 2
[3, 3, 3, 3, 1, 2, 3, 2, 3] => 3, 3, 3, 3, 1, 2, 3, 2, 3
[3, 3, 3, 3, 1, 2, 3, 3, 1] => 3, 3, 3, 3, 1, 2, 3, 3, 1
[3, 3, 3, 3, 1, 2, 3, 3, 2] => 3, 3, 3, 3, 1, 2, 3, 3, 2
[3, 3, 3, 3, 1, 2, 3, 3, 3] => 3, 3, 3, 3, 1, 2, 3, 3, 3
[3, 3, 3, 3, 1, 3, 1, 1, 1] => 3, 3, 3, 3, 1, 3, 1, 1, 1
[3, 3, 3, 3, 1, 3, 1, 1, 2] => 3, 3, 3, 3, 1, 3, 1, 1, 2
[3, 3, 3, 3, 1, 3, 1, 1, 3] => 3, 3, 3, 3, 1, 3, 1, 1, 3
[3, 3, 3, 3, 1, 3, 1, 2, 1] => 3, 3, 3, 3, 1, 3, 1, 2, 1
[3, 3, 3, 3, 1, 3, 1, 2, 2] => 3, 3, 3, 3, 1, 3, 1, 2, 2
[3, 3, 3, 3, 1, 3, 1, 2, 3] => 3, 3, 3, 3, 1, 3, 1, 2, 3
[3, 3, 3, 3, 1, 3, 1, 3, 1] => 3, 3, 3, 3, 1, 3, 1, 3, 1
[3, 3, 3, 3, 1, 3, 1, 3, 2] => 3, 3, 3, 3, 1, 3, 1, 3, 2
[3, 3, 3, 3, 1, 3, 1, 3, 3] => 3, 3, 3, 3, 1, 3, 1, 3, 3
[3, 3, 3, 3, 1, 3, 2, 1, 1] => 3, 3, 3, 3, 1, 3, 2, 1, 1
[3, 3, 3, 3, 1, 3, 2, 1, 2] => 3, 3, 3, 3, 1, 3, 2, 1, 2
[3, 3, 3, 3, 1, 3, 2, 1, 3] => 3, 3, 3, 3, 1, 3, 2, 1, 3
[3, 3, 3, 3, 1, 3, 2, 2, 1] => 3, 3, 3, 3, 1, 3, 2, 2, 1
[3, 3, 3, 3, 1, 3, 2, 2, 2] => 3, 3, 3, 3, 1, 3, 2, 2, 2
[3, 3, 3, 3, 1, 3, 2, 2, 3] => 3, 3, 3, 3, 1, 3, 2, 2, 3
[3, 3, 3, 3, 1, 3, 2, 3, 1] => 3, 3, 3, 3, 1, 3, 2, 3, 1
[3, 3, 3, 3, 1, 3, 2, 3, 2] => 3, 3, 3, 3, 1, 3, 2, 3, 2
[3, 3, 3, 3, 1, 3, 2, 3, 3] => 3, 3, 3, 3, 1, 3, 2, 3, 3
[3, 3, 3, 3, 1, 3, 3, 1, 1] => 3, 3, 3, 3, 1, 3, 3, 1, 1
[3, 3, 3, 3, 1, 3, 3, 1, 2] => 3, 3, 3, 3, 1, 3, 3, 1, 2
[3, 3, 3, 3, 1, 3, 3, 1, 3] => 3, 3, 3, 3, 1, 3, 3, 1, 3
[3, 3, 3, 3, 1, 3, 3, 2, 1] => 3, 3, 3, 3, 1, 3, 3, 2, 1
[3, 3, 3, 3, 1, 3, 3, 2, 2] => 3, 3, 3, 3, 1, 3, 3, 2, 2
[3, 3, 3, 3, 1, 3, 3, 2, 3] => 3, 3, 3, 3, 1, 3, 3, 2, 3
[3, 3, 3, 3, 1, 3, 3, 3, 1] => 3, 3, 3, 3, 1, 3, 3, 3, 1
[3, 3, 3, 3, 1, 3, 3, 3, 2] => 3, 3, 3, 3, 1, 3, 3, 3, 2
[3, 3, 3, 3, 1, 3, 3, 3, 3] => 3, 3, 3, 3, 1, 3, 3, 3, 3
[3, 3, 3, 3, 2, 1, 1, 1, 1] => 3, 3, 3, 3, 2, 1, 1, 1, 1
[3, 3, 3, 3, 2, 1, 1, 1, 2] => 3, 3, 3, 3, 2, 1, 1, 1, 2
[3, 3, 3, 3, 2, 1, 1, 1, 3] => 3, 3, 3, 3, 2, 1, 1, 1, 3
[3, 3, 3, 3, 2, 1, 1, 2, 1] => 3, 3, 3, 3, 2, 1, 1, 2, 1
[3, 3, 3, 3, 2, 1, 1, 2, 2] => 3, 3, 3, 3, 2, 1, 1, 2, 2
[3, 3, 3, 3, 2, 1, 1, 2, 3] => 3, 3, 3, 3, 2, 1, 1, 2, 3
[3, 3, 3, 3, 2, 1, 1, 3, 1] => 3, 3, 3, 3, 2, 1, 1, 3, 1
[3, 3, 3, 3, 2, 1, 1, 3, 2] => 3, 3, 3, 3, 2, 1, 1, 3, 2
[3, 3, 3, 3, 2, 1, 1, 3, 3] => 3, 3, 3, 3, 2, 1, 1, 3, 3
[3, 3, 3, 3, 2, 1, 2, 1, 1] => 3, 3, 3, 3, 2, 1, 2, 1, 1
[3, 3, 3, 3, 2, 1, 2, 1, 2] => 3, 3, 3, 3, 2, 1, 2, 1, 2
[3, 3, 3, 3, 2, 1, 2, 1, 3] => 3, 3, 3, 3, 2, 1, 2, 1, 3
[3, 3, 3, 3, 2, 1, 2, 2, 1] => 3, 3, 3, 3, 2, 1, 2, 2, 1
[3, 3, 3, 3, 2, 1, 2, 2, 2] => 3, 3, 3, 3, 2, 1, 2, 2, 2
[3, 3, 3, 3, 2, 1, 2, 2, 3] => 3, 3, 3, 3, 2, 1, 2, 2, 3
[3, 3, 3, 3, 2, 1, 2, 3, 1] => 3, 3, 3, 3, 2, 1, 2, 3, 1
[3, 3, 3, 3, 2, 1, 2, 3, 2] => 3, 3, 3, 3, 2, 1, 2, 3, 2
[3, 3, 3, 3, 2, 1, 2, 3, 3] => 3, 3, 3, 3, 2, 1, 2, 3, 3
[3, 3, 3, 3, 2, 1, 3, 1, 1] => 3, 3, 3, 3, 2, 1, 3, 1, 1
[3, 3, 3, 3, 2, 1, 3, 1, 2] => 3, 3, 3, 3, 2, 1, 3, 1, 2
[3, 3, 3, 3, 2, 1, 3, 1, 3] => 3, 3, 3, 3, 2, 1, 3, 1, 3
[3, 3, 3, 3, 2, 1, 3, 2, 1] => 3, 3, 3, 3, 2, 1, 3, 2, 1
[3, 3, 3, 3, 2, 1, 3, 2, 2] => 3, 3, 3, 3, 2, 1, 3, 2, 2
[3, 3, 3, 3, 2, 1, 3, 2, 3] => 3, 3, 3, 3, 2, 1, 3, 2, 3
[3, 3, 3, 3, 2, 1, 3, 3, 1] => 3, 3, 3, 3, 2, 1, 3, 3, 1
[3, 3, 3, 3, 2, 1, 3, 3, 2] => 3, 3, 3, 3, 2, 1, 3, 3, 2
[3, 3, 3, 3, 2, 1, 3, 3, 3] => 3, 3, 3, 3, 2, 1, 3, 3, 3
[3, 3, 3, 3, 2, 2, 1, 1, 1] => 3, 3, 3, 3, 2, 2, 1, 1, 1
[3, 3, 3, 3, 2, 2, 1, 1, 2] => 3, 3, 3, 3, 2, 2, 1, 1, 2
[3, 3, 3, 3, 2, 2, 1, 1, 3] => 3, 3, 3, 3, 2, 2, 1, 1, 3
[3, 3, 3, 3, 2, 2, 1, 2, 1] => 3, 3, 3, 3, 2, 2, 1, 2, 1
[3, 3, 3, 3, 2, 2, 1, 2, 2] => 3, 3, 3, 3, 2, 2, 1, 2, 2
[3, 3, 3, 3, 2, 2, 1, 2, 3] => 3, 3, 3, 3, 2, 2, 1, 2, 3
[3, 3, 3, 3, 2, 2, 1, 3, 1] => 3, 3, 3, 3, 2, 2, 1, 3, 1
[3, 3, 3, 3, 2, 2, 1, 3, 2] => 3, 3, 3, 3, 2, 2, 1, 3, 2
[3, 3, 3, 3, 2, 2, 1, 3, 3] => 3, 3, 3, 3, 2, 2, 1, 3, 3
[3, 3, 3, 3, 2, 2, 2, 1, 1] => 3, 3, 3, 3, 2, 2, 2, 1, 1
[3, 3, 3, 3, 2, 2, 2, 1, 2] => 3, 3, 3, 3, 2, 2, 2, 1, 2
[3, 3, 3, 3, 2, 2, 2, 1, 3] => 3, 3, 3, 3, 2, 2, 2, 1, 3
[3, 3, 3, 3, 2, 2, 2, 2, 1] => 3, 3, 3, 3, 2, 2, 2, 2, 1
[3, 3, 3, 3, 2, 2, 2, 2, 2] => 3, 3, 3, 3, 2, 2, 2, 2, 2
[3, 3, 3, 3, 2, 2, 2, 2, 3] => 3, 3, 3, 3, 2, 2, 2, 2, 3
[3, 3, 3, 3, 2, 2, 2, 3, 1] => 3, 3, 3, 3, 2, 2, 2, 3, 1
[3, 3, 3, 3, 2, 2, 2, 3, 2] => 3, 3, 3, 3, 2, 2, 2, 3, 2
[3, 3, 3, 3, 2, 2, 2, 3, 3] => 3, 3, 3, 3, 2, 2, 2, 3, 3
[3, 3, 3, 3, 2, 2, 3, 1, 1] => 3, 3, 3, 3, 2, 2, 3, 1, 1
[3, 3, 3, 3, 2, 2, 3, 1, 2] => 3, 3, 3, 3, 2, 2, 3, 1, 2
[3, 3, 3, 3, 2, 2, 3, 1, 3] => 3, 3, 3, 3, 2, 2, 3, 1, 3
[3, 3, 3, 3, 2, 2, 3, 2, 1] => 3, 3, 3, 3, 2, 2, 3, 2, 1
[3, 3, 3, 3, 2, 2, 3, 2, 2] => 3, 3, 3, 3, 2, 2, 3, 2, 2
[3, 3, 3, 3, 2, 2, 3, 2, 3] => 3, 3, 3, 3, 2, 2, 3, 2, 3
[3, 3, 3, 3, 2, 2, 3, 3, 1] => 3, 3, 3, 3, 2, 2, 3, 3, 1
[3, 3, 3, 3, 2, 2, 3, 3, 2] => 3, 3, 3, 3, 2, 2, 3, 3, 2
[3, 3, 3, 3, 2, 2, 3, 3, 3] => 3, 3, 3, 3, 2, 2, 3, 3, 3
[3, 3, 3, 3, 2, 3, 1, 1, 1] => 3, 3, 3, 3, 2, 3, 1, 1, 1
[3, 3, 3, 3, 2, 3, 1, 1, 2] => 3, 3, 3, 3, 2, 3, 1, 1, 2
[3, 3, 3, 3, 2, 3, 1, 1, 3] => 3, 3, 3, 3, 2, 3, 1, 1, 3
[3, 3, 3, 3, 2, 3, 1, 2, 1] => 3, 3, 3, 3, 2, 3, 1, 2, 1
[3, 3, 3, 3, 2, 3, 1, 2, 2] => 3, 3, 3, 3, 2, 3, 1, 2, 2
[3, 3, 3, 3, 2, 3, 1, 2, 3] => 3, 3, 3, 3, 2, 3, 1, 2, 3
[3, 3, 3, 3, 2, 3, 1, 3, 1] => 3, 3, 3, 3, 2, 3, 1, 3, 1
[3, 3, 3, 3, 2, 3, 1, 3, 2] => 3, 3, 3, 3, 2, 3, 1, 3, 2
[3, 3, 3, 3, 2, 3, 1, 3, 3] => 3, 3, 3, 3, 2, 3, 1, 3, 3
[3, 3, 3, 3, 2, 3, 2, 1, 1] => 3, 3, 3, 3, 2, 3, 2, 1, 1
[3, 3, 3, 3, 2, 3, 2, 1, 2] => 3, 3, 3, 3, 2, 3, 2, 1, 2
[3, 3, 3, 3, 2, 3, 2, 1, 3] => 3, 3, 3, 3, 2, 3, 2, 1, 3
[3, 3, 3, 3, 2, 3, 2, 2, 1] => 3, 3, 3, 3, 2, 3, 2, 2, 1
[3, 3, 3, 3, 2, 3, 2, 2, 2] => 3, 3, 3, 3, 2, 3, 2, 2, 2
[3, 3, 3, 3, 2, 3, 2, 2, 3] => 3, 3, 3, 3, 2, 3, 2, 2, 3
[3, 3, 3, 3, 2, 3, 2, 3, 1] => 3, 3, 3, 3, 2, 3, 2, 3, 1
[3, 3, 3, 3, 2, 3, 2, 3, 2] => 3, 3, 3, 3, 2, 3, 2, 3, 2
[3, 3, 3, 3, 2, 3, 2, 3, 3] => 3, 3, 3, 3, 2, 3, 2, 3, 3
[3, 3, 3, 3, 2, 3, 3, 1, 1] => 3, 3, 3, 3, 2, 3, 3, 1, 1
[3, 3, 3, 3, 2, 3, 3, 1, 2] => 3, 3, 3, 3, 2, 3, 3, 1, 2
[3, 3, 3, 3, 2, 3, 3, 1, 3] => 3, 3, 3, 3, 2, 3, 3, 1, 3
[3, 3, 3, 3, 2, 3, 3, 2, 1] => 3, 3, 3, 3, 2, 3, 3, 2, 1
[3, 3, 3, 3, 2, 3, 3, 2, 2] => 3, 3, 3, 3, 2, 3, 3, 2, 2
[3, 3, 3, 3, 2, 3, 3, 2, 3] => 3, 3, 3, 3, 2, 3, 3, 2, 3
[3, 3, 3, 3, 2, 3, 3, 3, 1] => 3, 3, 3, 3, 2, 3, 3, 3, 1
[3, 3, 3, 3, 2, 3, 3, 3, 2] => 3, 3, 3, 3, 2, 3, 3, 3, 2
[3, 3, 3, 3, 2, 3, 3, 3, 3] => 3, 3, 3, 3, 2, 3, 3, 3, 3
[3, 3, 3, 3, 3, 1, 1, 1, 1] => 3, 3, 3, 3, 3, 1, 1, 1, 1
[3, 3, 3, 3, 3, 1, 1, 1, 2] => 3, 3, 3, 3, 3, 1, 1, 1, 2
[3, 3, 3, 3, 3, 1, 1, 1, 3] => 3, 3, 3, 3, 3, 1, 1, 1, 3
[3, 3, 3, 3, 3, 1, 1, 2, 1] => 3, 3, 3, 3, 3, 1, 1, 2, 1
[3, 3, 3, 3, 3, 1, 1, 2, 2] => 3, 3, 3, 3, 3, 1, 1, 2, 2
[3, 3, 3, 3, 3, 1, 1, 2, 3] => 3, 3, 3, 3, 3, 1, 1, 2, 3
[3, 3, 3, 3, 3, 1, 1, 3, 1] => 3, 3, 3, 3, 3, 1, 1, 3, 1
[3, 3, 3, 3, 3, 1, 1, 3, 2] => 3, 3, 3, 3, 3, 1, 1, 3, 2
[3, 3, 3, 3, 3, 1, 1, 3, 3] => 3, 3, 3, 3, 3, 1, 1, 3, 3
[3, 3, 3, 3, 3, 1, 2, 1, 1] => 3, 3, 3, 3, 3, 1, 2, 1, 1
[3, 3, 3, 3, 3, 1, 2, 1, 2] => 3, 3, 3, 3, 3, 1, 2, 1, 2
[3, 3, 3, 3, 3, 1, 2, 1, 3] => 3, 3, 3, 3, 3, 1, 2, 1, 3
[3, 3, 3, 3, 3, 1, 2, 2, 1] => 3, 3, 3, 3, 3, 1, 2, 2, 1
[3, 3, 3, 3, 3, 1, 2, 2, 2] => 3, 3, 3, 3, 3, 1, 2, 2, 2
[3, 3, 3, 3, 3, 1, 2, 2, 3] => 3, 3, 3, 3, 3, 1, 2, 2, 3
[3, 3, 3, 3, 3, 1, 2, 3, 1] => 3, 3, 3, 3, 3, 1, 2, 3, 1
[3, 3, 3, 3, 3, 1, 2, 3, 2] => 3, 3, 3, 3, 3, 1, 2, 3, 2
[3, 3, 3, 3, 3, 1, 2, 3, 3] => 3, 3, 3, 3, 3, 1, 2, 3, 3
[3, 3, 3, 3, 3, 1, 3, 1, 1] => 3, 3, 3, 3, 3, 1, 3, 1, 1
[3, 3, 3, 3, 3, 1, 3, 1, 2] => 3, 3, 3, 3, 3, 1, 3, 1, 2
[3, 3, 3, 3, 3, 1, 3, 1, 3] => 3, 3, 3, 3, 3, 1, 3, 1, 3
[3, 3, 3, 3, 3, 1, 3, 2, 1] => 3, 3, 3, 3, 3, 1, 3, 2, 1
[3, 3, 3, 3, 3, 1, 3, 2, 2] => 3, 3, 3, 3, 3, 1, 3, 2, 2
[3, 3, 3, 3, 3, 1, 3, 2, 3] => 3, 3, 3, 3, 3, 1, 3, 2, 3
[3, 3, 3, 3, 3, 1, 3, 3, 1] => 3, 3, 3, 3, 3, 1, 3, 3, 1
[3, 3, 3, 3, 3, 1, 3, 3, 2] => 3, 3, 3, 3, 3, 1, 3, 3, 2
[3, 3, 3, 3, 3, 1, 3, 3, 3] => 3, 3, 3, 3, 3, 1, 3, 3, 3
[3, 3, 3, 3, 3, 2, 1, 1, 1] => 3, 3, 3, 3, 3, 2, 1, 1, 1
[3, 3, 3, 3, 3, 2, 1, 1, 2] => 3, 3, 3, 3, 3, 2, 1, 1, 2
[3, 3, 3, 3, 3, 2, 1, 1, 3] => 3, 3, 3, 3, 3, 2, 1, 1, 3
[3, 3, 3, 3, 3, 2, 1, 2, 1] => 3, 3, 3, 3, 3, 2, 1, 2, 1
[3, 3, 3, 3, 3, 2, 1, 2, 2] => 3, 3, 3, 3, 3, 2, 1, 2, 2
[3, 3, 3, 3, 3, 2, 1, 2, 3] => 3, 3, 3, 3, 3, 2, 1, 2, 3
[3, 3, 3, 3, 3, 2, 1, 3, 1] => 3, 3, 3, 3, 3, 2, 1, 3, 1
[3, 3, 3, 3, 3, 2, 1, 3, 2] => 3, 3, 3, 3, 3, 2, 1, 3, 2
[3, 3, 3, 3, 3, 2, 1, 3, 3] => 3, 3, 3, 3, 3, 2, 1, 3, 3
[3, 3, 3, 3, 3, 2, 2, 1, 1] => 3, 3, 3, 3, 3, 2, 2, 1, 1
[3, 3, 3, 3, 3, 2, 2, 1, 2] => 3, 3, 3, 3, 3, 2, 2, 1, 2
[3, 3, 3, 3, 3, 2, 2, 1, 3] => 3, 3, 3, 3, 3, 2, 2, 1, 3
[3, 3, 3, 3, 3, 2, 2, 2, 1] => 3, 3, 3, 3, 3, 2, 2, 2, 1
[3, 3, 3, 3, 3, 2, 2, 2, 2] => 3, 3, 3, 3, 3, 2, 2, 2, 2
[3, 3, 3, 3, 3, 2, 2, 2, 3] => 3, 3, 3, 3, 3, 2, 2, 2, 3
[3, 3, 3, 3, 3, 2, 2, 3, 1] => 3, 3, 3, 3, 3, 2, 2, 3, 1
[3, 3, 3, 3, 3, 2, 2, 3, 2] => 3, 3, 3, 3, 3, 2, 2, 3, 2
[3, 3, 3, 3, 3, 2, 2, 3, 3] => 3, 3, 3, 3, 3, 2, 2, 3, 3
[3, 3, 3, 3, 3, 2, 3, 1, 1] => 3, 3, 3, 3, 3, 2, 3, 1, 1
[3, 3, 3, 3, 3, 2, 3, 1, 2] => 3, 3, 3, 3, 3, 2, 3, 1, 2
[3, 3, 3, 3, 3, 2, 3, 1, 3] => 3, 3, 3, 3, 3, 2, 3, 1, 3
[3, 3, 3, 3, 3, 2, 3, 2, 1] => 3, 3, 3, 3, 3, 2, 3, 2, 1
[3, 3, 3, 3, 3, 2, 3, 2, 2] => 3, 3, 3, 3, 3, 2, 3, 2, 2
[3, 3, 3, 3, 3, 2, 3, 2, 3] => 3, 3, 3, 3, 3, 2, 3, 2, 3
[3, 3, 3, 3, 3, 2, 3, 3, 1] => 3, 3, 3, 3, 3, 2, 3, 3, 1
[3, 3, 3, 3, 3, 2, 3, 3, 2] => 3, 3, 3, 3, 3, 2, 3, 3, 2
[3, 3, 3, 3, 3, 2, 3, 3, 3] => 3, 3, 3, 3, 3, 2, 3, 3, 3
[3, 3, 3, 3, 3, 3, 1, 1, 1] => 3, 3, 3, 3, 3, 3, 1, 1, 1
[3, 3, 3, 3, 3, 3, 1, 1, 2] => 3, 3, 3, 3, 3, 3, 1, 1, 2
[3, 3, 3, 3, 3, 3, 1, 1, 3] => 3, 3, 3, 3, 3, 3, 1, 1, 3
[3, 3, 3, 3, 3, 3, 1, 2, 1] => 3, 3, 3, 3, 3, 3, 1, 2, 1
[3, 3, 3, 3, 3, 3, 1, 2, 2] => 3, 3, 3, 3, 3, 3, 1, 2, 2
[3, 3, 3, 3, 3, 3, 1, 2, 3] => 3, 3, 3, 3, 3, 3, 1, 2, 3
[3, 3, 3, 3, 3, 3, 1, 3, 1] => 3, 3, 3, 3, 3, 3, 1, 3, 1
[3, 3, 3, 3, 3, 3, 1, 3, 2] => 3, 3, 3, 3, 3, 3, 1, 3, 2
[3, 3, 3, 3, 3, 3, 1, 3, 3] => 3, 3, 3, 3, 3, 3, 1, 3, 3
[3, 3, 3, 3, 3, 3, 2, 1, 1] => 3, 3, 3, 3, 3, 3, 2, 1, 1
[3, 3, 3, 3, 3, 3, 2, 1, 2] => 3, 3, 3, 3, 3, 3, 2, 1, 2
[3, 3, 3, 3, 3, 3, 2, 1, 3] => 3, 3, 3, 3, 3, 3, 2, 1, 3
[3, 3, 3, 3, 3, 3, 2, 2, 1] => 3, 3, 3, 3, 3, 3, 2, 2, 1
[3, 3, 3, 3, 3, 3, 2, 2, 2] => 3, 3, 3, 3, 3, 3, 2, 2, 2
[3, 3, 3, 3, 3, 3, 2, 2, 3] => 3, 3, 3, 3, 3, 3, 2, 2, 3
[3, 3, 3, 3, 3, 3, 2, 3, 1] => 3, 3, 3, 3, 3, 3, 2, 3, 1
[3, 3, 3, 3, 3, 3, 2, 3, 2] => 3, 3, 3, 3, 3, 3, 2, 3, 2
[3, 3, 3, 3, 3, 3, 2, 3, 3] => 3, 3, 3, 3, 3, 3, 2, 3, 3
[3, 3, 3, 3, 3, 3, 3, 1, 1] => 3, 3, 3, 3, 3, 3, 3, 1, 1
[3, 3, 3, 3, 3, 3, 3, 1, 2] => 3, 3, 3, 3, 3, 3, 3, 1, 2
[3, 3, 3, 3, 3, 3, 3, 1, 3] => 3, 3, 3, 3, 3, 3, 3, 1, 3
[3, 3, 3, 3, 3, 3, 3, 2, 1] => 3, 3, 3, 3, 3, 3, 3, 2, 1
[3, 3, 3, 3, 3, 3, 3, 2, 2] => 3, 3, 3, 3, 3, 3, 3, 2, 2
[3, 3, 3, 3, 3, 3, 3, 2, 3] => 3, 3, 3, 3, 3, 3, 3, 2, 3
[3, 3, 3, 3, 3, 3, 3, 3, 1] => 3, 3, 3, 3, 3, 3, 3, 3, 1
[3, 3, 3, 3, 3, 3, 3, 3, 2] => 3, 3, 3, 3, 3, 3, 3, 3, 2
[3, 3, 3, 3, 3, 3, 3, 3, 3] => 3, 3, 3, 3, 3, 3, 3, 3, 3
