Identifier
Mp00033: Dyck paths —to two-row standard tableau⟶ Standard tableaux
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
Mp00039: Integer compositions —complement⟶ Integer compositions
Images
[1,0] => [[1],[2]] => [1,1] => [2]
[1,0,1,0] => [[1,3],[2,4]] => [1,2,1] => [2,2]
[1,1,0,0] => [[1,2],[3,4]] => [2,2] => [1,2,1]
[1,0,1,0,1,0] => [[1,3,5],[2,4,6]] => [1,2,2,1] => [2,2,2]
[1,0,1,1,0,0] => [[1,3,4],[2,5,6]] => [1,3,2] => [2,1,2,1]
[1,1,0,0,1,0] => [[1,2,5],[3,4,6]] => [2,3,1] => [1,2,1,2]
[1,1,0,1,0,0] => [[1,2,4],[3,5,6]] => [2,2,2] => [1,2,2,1]
[1,1,1,0,0,0] => [[1,2,3],[4,5,6]] => [3,3] => [1,1,2,1,1]
[1,0,1,0,1,0,1,0] => [[1,3,5,7],[2,4,6,8]] => [1,2,2,2,1] => [2,2,2,2]
[1,0,1,0,1,1,0,0] => [[1,3,5,6],[2,4,7,8]] => [1,2,3,2] => [2,2,1,2,1]
[1,0,1,1,0,0,1,0] => [[1,3,4,7],[2,5,6,8]] => [1,3,3,1] => [2,1,2,1,2]
[1,0,1,1,0,1,0,0] => [[1,3,4,6],[2,5,7,8]] => [1,3,2,2] => [2,1,2,2,1]
[1,0,1,1,1,0,0,0] => [[1,3,4,5],[2,6,7,8]] => [1,4,3] => [2,1,1,2,1,1]
[1,1,0,0,1,0,1,0] => [[1,2,5,7],[3,4,6,8]] => [2,3,2,1] => [1,2,1,2,2]
[1,1,0,0,1,1,0,0] => [[1,2,5,6],[3,4,7,8]] => [2,4,2] => [1,2,1,1,2,1]
[1,1,0,1,0,0,1,0] => [[1,2,4,7],[3,5,6,8]] => [2,2,3,1] => [1,2,2,1,2]
[1,1,0,1,0,1,0,0] => [[1,2,4,6],[3,5,7,8]] => [2,2,2,2] => [1,2,2,2,1]
[1,1,0,1,1,0,0,0] => [[1,2,4,5],[3,6,7,8]] => [2,3,3] => [1,2,1,2,1,1]
[1,1,1,0,0,0,1,0] => [[1,2,3,7],[4,5,6,8]] => [3,4,1] => [1,1,2,1,1,2]
[1,1,1,0,0,1,0,0] => [[1,2,3,6],[4,5,7,8]] => [3,3,2] => [1,1,2,1,2,1]
[1,1,1,0,1,0,0,0] => [[1,2,3,5],[4,6,7,8]] => [3,2,3] => [1,1,2,2,1,1]
[1,1,1,1,0,0,0,0] => [[1,2,3,4],[5,6,7,8]] => [4,4] => [1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9],[2,4,6,8,10]] => [1,2,2,2,2,1] => [2,2,2,2,2]
[1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,8],[2,4,6,9,10]] => [1,2,2,3,2] => [2,2,2,1,2,1]
[1,0,1,0,1,1,0,0,1,0] => [[1,3,5,6,9],[2,4,7,8,10]] => [1,2,3,3,1] => [2,2,1,2,1,2]
[1,0,1,0,1,1,0,1,0,0] => [[1,3,5,6,8],[2,4,7,9,10]] => [1,2,3,2,2] => [2,2,1,2,2,1]
[1,0,1,0,1,1,1,0,0,0] => [[1,3,5,6,7],[2,4,8,9,10]] => [1,2,4,3] => [2,2,1,1,2,1,1]
[1,0,1,1,0,0,1,0,1,0] => [[1,3,4,7,9],[2,5,6,8,10]] => [1,3,3,2,1] => [2,1,2,1,2,2]
[1,0,1,1,0,0,1,1,0,0] => [[1,3,4,7,8],[2,5,6,9,10]] => [1,3,4,2] => [2,1,2,1,1,2,1]
[1,0,1,1,0,1,0,0,1,0] => [[1,3,4,6,9],[2,5,7,8,10]] => [1,3,2,3,1] => [2,1,2,2,1,2]
[1,0,1,1,0,1,0,1,0,0] => [[1,3,4,6,8],[2,5,7,9,10]] => [1,3,2,2,2] => [2,1,2,2,2,1]
[1,0,1,1,0,1,1,0,0,0] => [[1,3,4,6,7],[2,5,8,9,10]] => [1,3,3,3] => [2,1,2,1,2,1,1]
[1,0,1,1,1,0,0,0,1,0] => [[1,3,4,5,9],[2,6,7,8,10]] => [1,4,4,1] => [2,1,1,2,1,1,2]
[1,0,1,1,1,0,0,1,0,0] => [[1,3,4,5,8],[2,6,7,9,10]] => [1,4,3,2] => [2,1,1,2,1,2,1]
[1,0,1,1,1,0,1,0,0,0] => [[1,3,4,5,7],[2,6,8,9,10]] => [1,4,2,3] => [2,1,1,2,2,1,1]
[1,0,1,1,1,1,0,0,0,0] => [[1,3,4,5,6],[2,7,8,9,10]] => [1,5,4] => [2,1,1,1,2,1,1,1]
[1,1,0,0,1,0,1,0,1,0] => [[1,2,5,7,9],[3,4,6,8,10]] => [2,3,2,2,1] => [1,2,1,2,2,2]
[1,1,0,0,1,0,1,1,0,0] => [[1,2,5,7,8],[3,4,6,9,10]] => [2,3,3,2] => [1,2,1,2,1,2,1]
[1,1,0,0,1,1,0,0,1,0] => [[1,2,5,6,9],[3,4,7,8,10]] => [2,4,3,1] => [1,2,1,1,2,1,2]
[1,1,0,0,1,1,0,1,0,0] => [[1,2,5,6,8],[3,4,7,9,10]] => [2,4,2,2] => [1,2,1,1,2,2,1]
[1,1,0,0,1,1,1,0,0,0] => [[1,2,5,6,7],[3,4,8,9,10]] => [2,5,3] => [1,2,1,1,1,2,1,1]
[1,1,0,1,0,0,1,0,1,0] => [[1,2,4,7,9],[3,5,6,8,10]] => [2,2,3,2,1] => [1,2,2,1,2,2]
[1,1,0,1,0,0,1,1,0,0] => [[1,2,4,7,8],[3,5,6,9,10]] => [2,2,4,2] => [1,2,2,1,1,2,1]
[1,1,0,1,0,1,0,0,1,0] => [[1,2,4,6,9],[3,5,7,8,10]] => [2,2,2,3,1] => [1,2,2,2,1,2]
[1,1,0,1,0,1,0,1,0,0] => [[1,2,4,6,8],[3,5,7,9,10]] => [2,2,2,2,2] => [1,2,2,2,2,1]
[1,1,0,1,0,1,1,0,0,0] => [[1,2,4,6,7],[3,5,8,9,10]] => [2,2,3,3] => [1,2,2,1,2,1,1]
[1,1,0,1,1,0,0,0,1,0] => [[1,2,4,5,9],[3,6,7,8,10]] => [2,3,4,1] => [1,2,1,2,1,1,2]
[1,1,0,1,1,0,0,1,0,0] => [[1,2,4,5,8],[3,6,7,9,10]] => [2,3,3,2] => [1,2,1,2,1,2,1]
[1,1,0,1,1,0,1,0,0,0] => [[1,2,4,5,7],[3,6,8,9,10]] => [2,3,2,3] => [1,2,1,2,2,1,1]
[1,1,0,1,1,1,0,0,0,0] => [[1,2,4,5,6],[3,7,8,9,10]] => [2,4,4] => [1,2,1,1,2,1,1,1]
[1,1,1,0,0,0,1,0,1,0] => [[1,2,3,7,9],[4,5,6,8,10]] => [3,4,2,1] => [1,1,2,1,1,2,2]
[1,1,1,0,0,0,1,1,0,0] => [[1,2,3,7,8],[4,5,6,9,10]] => [3,5,2] => [1,1,2,1,1,1,2,1]
[1,1,1,0,0,1,0,0,1,0] => [[1,2,3,6,9],[4,5,7,8,10]] => [3,3,3,1] => [1,1,2,1,2,1,2]
[1,1,1,0,0,1,0,1,0,0] => [[1,2,3,6,8],[4,5,7,9,10]] => [3,3,2,2] => [1,1,2,1,2,2,1]
[1,1,1,0,0,1,1,0,0,0] => [[1,2,3,6,7],[4,5,8,9,10]] => [3,4,3] => [1,1,2,1,1,2,1,1]
[1,1,1,0,1,0,0,0,1,0] => [[1,2,3,5,9],[4,6,7,8,10]] => [3,2,4,1] => [1,1,2,2,1,1,2]
[1,1,1,0,1,0,0,1,0,0] => [[1,2,3,5,8],[4,6,7,9,10]] => [3,2,3,2] => [1,1,2,2,1,2,1]
[1,1,1,0,1,0,1,0,0,0] => [[1,2,3,5,7],[4,6,8,9,10]] => [3,2,2,3] => [1,1,2,2,2,1,1]
[1,1,1,0,1,1,0,0,0,0] => [[1,2,3,5,6],[4,7,8,9,10]] => [3,3,4] => [1,1,2,1,2,1,1,1]
[1,1,1,1,0,0,0,0,1,0] => [[1,2,3,4,9],[5,6,7,8,10]] => [4,5,1] => [1,1,1,2,1,1,1,2]
[1,1,1,1,0,0,0,1,0,0] => [[1,2,3,4,8],[5,6,7,9,10]] => [4,4,2] => [1,1,1,2,1,1,2,1]
[1,1,1,1,0,0,1,0,0,0] => [[1,2,3,4,7],[5,6,8,9,10]] => [4,3,3] => [1,1,1,2,1,2,1,1]
[1,1,1,1,0,1,0,0,0,0] => [[1,2,3,4,6],[5,7,8,9,10]] => [4,2,4] => [1,1,1,2,2,1,1,1]
[1,1,1,1,1,0,0,0,0,0] => [[1,2,3,4,5],[6,7,8,9,10]] => [5,5] => [1,1,1,1,2,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9,11],[2,4,6,8,10,12]] => [1,2,2,2,2,2,1] => [2,2,2,2,2,2]
[1,0,1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,9,10],[2,4,6,8,11,12]] => [1,2,2,2,3,2] => [2,2,2,2,1,2,1]
[1,0,1,0,1,0,1,1,0,0,1,0] => [[1,3,5,7,8,11],[2,4,6,9,10,12]] => [1,2,2,3,3,1] => [2,2,2,1,2,1,2]
[1,0,1,0,1,0,1,1,0,1,0,0] => [[1,3,5,7,8,10],[2,4,6,9,11,12]] => [1,2,2,3,2,2] => [2,2,2,1,2,2,1]
[1,0,1,0,1,0,1,1,1,0,0,0] => [[1,3,5,7,8,9],[2,4,6,10,11,12]] => [1,2,2,4,3] => [2,2,2,1,1,2,1,1]
[1,0,1,0,1,1,0,0,1,0,1,0] => [[1,3,5,6,9,11],[2,4,7,8,10,12]] => [1,2,3,3,2,1] => [2,2,1,2,1,2,2]
[1,0,1,0,1,1,0,0,1,1,0,0] => [[1,3,5,6,9,10],[2,4,7,8,11,12]] => [1,2,3,4,2] => [2,2,1,2,1,1,2,1]
[1,0,1,0,1,1,0,1,0,0,1,0] => [[1,3,5,6,8,11],[2,4,7,9,10,12]] => [1,2,3,2,3,1] => [2,2,1,2,2,1,2]
[1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,6,8,10],[2,4,7,9,11,12]] => [1,2,3,2,2,2] => [2,2,1,2,2,2,1]
[1,0,1,0,1,1,0,1,1,0,0,0] => [[1,3,5,6,8,9],[2,4,7,10,11,12]] => [1,2,3,3,3] => [2,2,1,2,1,2,1,1]
[1,0,1,0,1,1,1,0,0,0,1,0] => [[1,3,5,6,7,11],[2,4,8,9,10,12]] => [1,2,4,4,1] => [2,2,1,1,2,1,1,2]
[1,0,1,0,1,1,1,0,0,1,0,0] => [[1,3,5,6,7,10],[2,4,8,9,11,12]] => [1,2,4,3,2] => [2,2,1,1,2,1,2,1]
[1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,6,7,9],[2,4,8,10,11,12]] => [1,2,4,2,3] => [2,2,1,1,2,2,1,1]
[1,0,1,0,1,1,1,1,0,0,0,0] => [[1,3,5,6,7,8],[2,4,9,10,11,12]] => [1,2,5,4] => [2,2,1,1,1,2,1,1,1]
[1,0,1,1,0,0,1,0,1,0,1,0] => [[1,3,4,7,9,11],[2,5,6,8,10,12]] => [1,3,3,2,2,1] => [2,1,2,1,2,2,2]
[1,0,1,1,0,0,1,0,1,1,0,0] => [[1,3,4,7,9,10],[2,5,6,8,11,12]] => [1,3,3,3,2] => [2,1,2,1,2,1,2,1]
[1,0,1,1,0,0,1,1,0,0,1,0] => [[1,3,4,7,8,11],[2,5,6,9,10,12]] => [1,3,4,3,1] => [2,1,2,1,1,2,1,2]
[1,0,1,1,0,0,1,1,0,1,0,0] => [[1,3,4,7,8,10],[2,5,6,9,11,12]] => [1,3,4,2,2] => [2,1,2,1,1,2,2,1]
[1,0,1,1,0,0,1,1,1,0,0,0] => [[1,3,4,7,8,9],[2,5,6,10,11,12]] => [1,3,5,3] => [2,1,2,1,1,1,2,1,1]
[1,0,1,1,0,1,0,0,1,0,1,0] => [[1,3,4,6,9,11],[2,5,7,8,10,12]] => [1,3,2,3,2,1] => [2,1,2,2,1,2,2]
[1,0,1,1,0,1,0,0,1,1,0,0] => [[1,3,4,6,9,10],[2,5,7,8,11,12]] => [1,3,2,4,2] => [2,1,2,2,1,1,2,1]
[1,0,1,1,0,1,0,1,0,0,1,0] => [[1,3,4,6,8,11],[2,5,7,9,10,12]] => [1,3,2,2,3,1] => [2,1,2,2,2,1,2]
[1,0,1,1,0,1,0,1,0,1,0,0] => [[1,3,4,6,8,10],[2,5,7,9,11,12]] => [1,3,2,2,2,2] => [2,1,2,2,2,2,1]
[1,0,1,1,0,1,0,1,1,0,0,0] => [[1,3,4,6,8,9],[2,5,7,10,11,12]] => [1,3,2,3,3] => [2,1,2,2,1,2,1,1]
[1,0,1,1,0,1,1,0,0,0,1,0] => [[1,3,4,6,7,11],[2,5,8,9,10,12]] => [1,3,3,4,1] => [2,1,2,1,2,1,1,2]
[1,0,1,1,0,1,1,0,0,1,0,0] => [[1,3,4,6,7,10],[2,5,8,9,11,12]] => [1,3,3,3,2] => [2,1,2,1,2,1,2,1]
[1,0,1,1,0,1,1,0,1,0,0,0] => [[1,3,4,6,7,9],[2,5,8,10,11,12]] => [1,3,3,2,3] => [2,1,2,1,2,2,1,1]
[1,0,1,1,0,1,1,1,0,0,0,0] => [[1,3,4,6,7,8],[2,5,9,10,11,12]] => [1,3,4,4] => [2,1,2,1,1,2,1,1,1]
[1,0,1,1,1,0,0,0,1,0,1,0] => [[1,3,4,5,9,11],[2,6,7,8,10,12]] => [1,4,4,2,1] => [2,1,1,2,1,1,2,2]
[1,0,1,1,1,0,0,0,1,1,0,0] => [[1,3,4,5,9,10],[2,6,7,8,11,12]] => [1,4,5,2] => [2,1,1,2,1,1,1,2,1]
[1,0,1,1,1,0,0,1,0,0,1,0] => [[1,3,4,5,8,11],[2,6,7,9,10,12]] => [1,4,3,3,1] => [2,1,1,2,1,2,1,2]
[1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,4,5,8,10],[2,6,7,9,11,12]] => [1,4,3,2,2] => [2,1,1,2,1,2,2,1]
[1,0,1,1,1,0,0,1,1,0,0,0] => [[1,3,4,5,8,9],[2,6,7,10,11,12]] => [1,4,4,3] => [2,1,1,2,1,1,2,1,1]
[1,0,1,1,1,0,1,0,0,0,1,0] => [[1,3,4,5,7,11],[2,6,8,9,10,12]] => [1,4,2,4,1] => [2,1,1,2,2,1,1,2]
[1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,10],[2,6,8,9,11,12]] => [1,4,2,3,2] => [2,1,1,2,2,1,2,1]
[1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,4,5,7,9],[2,6,8,10,11,12]] => [1,4,2,2,3] => [2,1,1,2,2,2,1,1]
[1,0,1,1,1,0,1,1,0,0,0,0] => [[1,3,4,5,7,8],[2,6,9,10,11,12]] => [1,4,3,4] => [2,1,1,2,1,2,1,1,1]
>>> Load all 498 entries. <<<
[1,0,1,1,1,1,0,0,0,0,1,0] => [[1,3,4,5,6,11],[2,7,8,9,10,12]] => [1,5,5,1] => [2,1,1,1,2,1,1,1,2]
[1,0,1,1,1,1,0,0,0,1,0,0] => [[1,3,4,5,6,10],[2,7,8,9,11,12]] => [1,5,4,2] => [2,1,1,1,2,1,1,2,1]
[1,0,1,1,1,1,0,0,1,0,0,0] => [[1,3,4,5,6,9],[2,7,8,10,11,12]] => [1,5,3,3] => [2,1,1,1,2,1,2,1,1]
[1,0,1,1,1,1,0,1,0,0,0,0] => [[1,3,4,5,6,8],[2,7,9,10,11,12]] => [1,5,2,4] => [2,1,1,1,2,2,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,0] => [[1,3,4,5,6,7],[2,8,9,10,11,12]] => [1,6,5] => [2,1,1,1,1,2,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,0] => [[1,2,5,7,9,11],[3,4,6,8,10,12]] => [2,3,2,2,2,1] => [1,2,1,2,2,2,2]
[1,1,0,0,1,0,1,0,1,1,0,0] => [[1,2,5,7,9,10],[3,4,6,8,11,12]] => [2,3,2,3,2] => [1,2,1,2,2,1,2,1]
[1,1,0,0,1,0,1,1,0,0,1,0] => [[1,2,5,7,8,11],[3,4,6,9,10,12]] => [2,3,3,3,1] => [1,2,1,2,1,2,1,2]
[1,1,0,0,1,0,1,1,0,1,0,0] => [[1,2,5,7,8,10],[3,4,6,9,11,12]] => [2,3,3,2,2] => [1,2,1,2,1,2,2,1]
[1,1,0,0,1,0,1,1,1,0,0,0] => [[1,2,5,7,8,9],[3,4,6,10,11,12]] => [2,3,4,3] => [1,2,1,2,1,1,2,1,1]
[1,1,0,0,1,1,0,0,1,0,1,0] => [[1,2,5,6,9,11],[3,4,7,8,10,12]] => [2,4,3,2,1] => [1,2,1,1,2,1,2,2]
[1,1,0,0,1,1,0,0,1,1,0,0] => [[1,2,5,6,9,10],[3,4,7,8,11,12]] => [2,4,4,2] => [1,2,1,1,2,1,1,2,1]
[1,1,0,0,1,1,0,1,0,0,1,0] => [[1,2,5,6,8,11],[3,4,7,9,10,12]] => [2,4,2,3,1] => [1,2,1,1,2,2,1,2]
[1,1,0,0,1,1,0,1,0,1,0,0] => [[1,2,5,6,8,10],[3,4,7,9,11,12]] => [2,4,2,2,2] => [1,2,1,1,2,2,2,1]
[1,1,0,0,1,1,0,1,1,0,0,0] => [[1,2,5,6,8,9],[3,4,7,10,11,12]] => [2,4,3,3] => [1,2,1,1,2,1,2,1,1]
[1,1,0,0,1,1,1,0,0,0,1,0] => [[1,2,5,6,7,11],[3,4,8,9,10,12]] => [2,5,4,1] => [1,2,1,1,1,2,1,1,2]
[1,1,0,0,1,1,1,0,0,1,0,0] => [[1,2,5,6,7,10],[3,4,8,9,11,12]] => [2,5,3,2] => [1,2,1,1,1,2,1,2,1]
[1,1,0,0,1,1,1,0,1,0,0,0] => [[1,2,5,6,7,9],[3,4,8,10,11,12]] => [2,5,2,3] => [1,2,1,1,1,2,2,1,1]
[1,1,0,0,1,1,1,1,0,0,0,0] => [[1,2,5,6,7,8],[3,4,9,10,11,12]] => [2,6,4] => [1,2,1,1,1,1,2,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,0] => [[1,2,4,7,9,11],[3,5,6,8,10,12]] => [2,2,3,2,2,1] => [1,2,2,1,2,2,2]
[1,1,0,1,0,0,1,0,1,1,0,0] => [[1,2,4,7,9,10],[3,5,6,8,11,12]] => [2,2,3,3,2] => [1,2,2,1,2,1,2,1]
[1,1,0,1,0,0,1,1,0,0,1,0] => [[1,2,4,7,8,11],[3,5,6,9,10,12]] => [2,2,4,3,1] => [1,2,2,1,1,2,1,2]
[1,1,0,1,0,0,1,1,0,1,0,0] => [[1,2,4,7,8,10],[3,5,6,9,11,12]] => [2,2,4,2,2] => [1,2,2,1,1,2,2,1]
[1,1,0,1,0,0,1,1,1,0,0,0] => [[1,2,4,7,8,9],[3,5,6,10,11,12]] => [2,2,5,3] => [1,2,2,1,1,1,2,1,1]
[1,1,0,1,0,1,0,0,1,0,1,0] => [[1,2,4,6,9,11],[3,5,7,8,10,12]] => [2,2,2,3,2,1] => [1,2,2,2,1,2,2]
[1,1,0,1,0,1,0,0,1,1,0,0] => [[1,2,4,6,9,10],[3,5,7,8,11,12]] => [2,2,2,4,2] => [1,2,2,2,1,1,2,1]
[1,1,0,1,0,1,0,1,0,0,1,0] => [[1,2,4,6,8,11],[3,5,7,9,10,12]] => [2,2,2,2,3,1] => [1,2,2,2,2,1,2]
[1,1,0,1,0,1,0,1,0,1,0,0] => [[1,2,4,6,8,10],[3,5,7,9,11,12]] => [2,2,2,2,2,2] => [1,2,2,2,2,2,1]
[1,1,0,1,0,1,0,1,1,0,0,0] => [[1,2,4,6,8,9],[3,5,7,10,11,12]] => [2,2,2,3,3] => [1,2,2,2,1,2,1,1]
[1,1,0,1,0,1,1,0,0,0,1,0] => [[1,2,4,6,7,11],[3,5,8,9,10,12]] => [2,2,3,4,1] => [1,2,2,1,2,1,1,2]
[1,1,0,1,0,1,1,0,0,1,0,0] => [[1,2,4,6,7,10],[3,5,8,9,11,12]] => [2,2,3,3,2] => [1,2,2,1,2,1,2,1]
[1,1,0,1,0,1,1,0,1,0,0,0] => [[1,2,4,6,7,9],[3,5,8,10,11,12]] => [2,2,3,2,3] => [1,2,2,1,2,2,1,1]
[1,1,0,1,0,1,1,1,0,0,0,0] => [[1,2,4,6,7,8],[3,5,9,10,11,12]] => [2,2,4,4] => [1,2,2,1,1,2,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,0] => [[1,2,4,5,9,11],[3,6,7,8,10,12]] => [2,3,4,2,1] => [1,2,1,2,1,1,2,2]
[1,1,0,1,1,0,0,0,1,1,0,0] => [[1,2,4,5,9,10],[3,6,7,8,11,12]] => [2,3,5,2] => [1,2,1,2,1,1,1,2,1]
[1,1,0,1,1,0,0,1,0,0,1,0] => [[1,2,4,5,8,11],[3,6,7,9,10,12]] => [2,3,3,3,1] => [1,2,1,2,1,2,1,2]
[1,1,0,1,1,0,0,1,0,1,0,0] => [[1,2,4,5,8,10],[3,6,7,9,11,12]] => [2,3,3,2,2] => [1,2,1,2,1,2,2,1]
[1,1,0,1,1,0,0,1,1,0,0,0] => [[1,2,4,5,8,9],[3,6,7,10,11,12]] => [2,3,4,3] => [1,2,1,2,1,1,2,1,1]
[1,1,0,1,1,0,1,0,0,0,1,0] => [[1,2,4,5,7,11],[3,6,8,9,10,12]] => [2,3,2,4,1] => [1,2,1,2,2,1,1,2]
[1,1,0,1,1,0,1,0,0,1,0,0] => [[1,2,4,5,7,10],[3,6,8,9,11,12]] => [2,3,2,3,2] => [1,2,1,2,2,1,2,1]
[1,1,0,1,1,0,1,0,1,0,0,0] => [[1,2,4,5,7,9],[3,6,8,10,11,12]] => [2,3,2,2,3] => [1,2,1,2,2,2,1,1]
[1,1,0,1,1,0,1,1,0,0,0,0] => [[1,2,4,5,7,8],[3,6,9,10,11,12]] => [2,3,3,4] => [1,2,1,2,1,2,1,1,1]
[1,1,0,1,1,1,0,0,0,0,1,0] => [[1,2,4,5,6,11],[3,7,8,9,10,12]] => [2,4,5,1] => [1,2,1,1,2,1,1,1,2]
[1,1,0,1,1,1,0,0,0,1,0,0] => [[1,2,4,5,6,10],[3,7,8,9,11,12]] => [2,4,4,2] => [1,2,1,1,2,1,1,2,1]
[1,1,0,1,1,1,0,0,1,0,0,0] => [[1,2,4,5,6,9],[3,7,8,10,11,12]] => [2,4,3,3] => [1,2,1,1,2,1,2,1,1]
[1,1,0,1,1,1,0,1,0,0,0,0] => [[1,2,4,5,6,8],[3,7,9,10,11,12]] => [2,4,2,4] => [1,2,1,1,2,2,1,1,1]
[1,1,0,1,1,1,1,0,0,0,0,0] => [[1,2,4,5,6,7],[3,8,9,10,11,12]] => [2,5,5] => [1,2,1,1,1,2,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,0] => [[1,2,3,7,9,11],[4,5,6,8,10,12]] => [3,4,2,2,1] => [1,1,2,1,1,2,2,2]
[1,1,1,0,0,0,1,0,1,1,0,0] => [[1,2,3,7,9,10],[4,5,6,8,11,12]] => [3,4,3,2] => [1,1,2,1,1,2,1,2,1]
[1,1,1,0,0,0,1,1,0,0,1,0] => [[1,2,3,7,8,11],[4,5,6,9,10,12]] => [3,5,3,1] => [1,1,2,1,1,1,2,1,2]
[1,1,1,0,0,0,1,1,0,1,0,0] => [[1,2,3,7,8,10],[4,5,6,9,11,12]] => [3,5,2,2] => [1,1,2,1,1,1,2,2,1]
[1,1,1,0,0,0,1,1,1,0,0,0] => [[1,2,3,7,8,9],[4,5,6,10,11,12]] => [3,6,3] => [1,1,2,1,1,1,1,2,1,1]
[1,1,1,0,0,1,0,0,1,0,1,0] => [[1,2,3,6,9,11],[4,5,7,8,10,12]] => [3,3,3,2,1] => [1,1,2,1,2,1,2,2]
[1,1,1,0,0,1,0,0,1,1,0,0] => [[1,2,3,6,9,10],[4,5,7,8,11,12]] => [3,3,4,2] => [1,1,2,1,2,1,1,2,1]
[1,1,1,0,0,1,0,1,0,0,1,0] => [[1,2,3,6,8,11],[4,5,7,9,10,12]] => [3,3,2,3,1] => [1,1,2,1,2,2,1,2]
[1,1,1,0,0,1,0,1,0,1,0,0] => [[1,2,3,6,8,10],[4,5,7,9,11,12]] => [3,3,2,2,2] => [1,1,2,1,2,2,2,1]
[1,1,1,0,0,1,0,1,1,0,0,0] => [[1,2,3,6,8,9],[4,5,7,10,11,12]] => [3,3,3,3] => [1,1,2,1,2,1,2,1,1]
[1,1,1,0,0,1,1,0,0,0,1,0] => [[1,2,3,6,7,11],[4,5,8,9,10,12]] => [3,4,4,1] => [1,1,2,1,1,2,1,1,2]
[1,1,1,0,0,1,1,0,0,1,0,0] => [[1,2,3,6,7,10],[4,5,8,9,11,12]] => [3,4,3,2] => [1,1,2,1,1,2,1,2,1]
[1,1,1,0,0,1,1,0,1,0,0,0] => [[1,2,3,6,7,9],[4,5,8,10,11,12]] => [3,4,2,3] => [1,1,2,1,1,2,2,1,1]
[1,1,1,0,0,1,1,1,0,0,0,0] => [[1,2,3,6,7,8],[4,5,9,10,11,12]] => [3,5,4] => [1,1,2,1,1,1,2,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,0] => [[1,2,3,5,9,11],[4,6,7,8,10,12]] => [3,2,4,2,1] => [1,1,2,2,1,1,2,2]
[1,1,1,0,1,0,0,0,1,1,0,0] => [[1,2,3,5,9,10],[4,6,7,8,11,12]] => [3,2,5,2] => [1,1,2,2,1,1,1,2,1]
[1,1,1,0,1,0,0,1,0,0,1,0] => [[1,2,3,5,8,11],[4,6,7,9,10,12]] => [3,2,3,3,1] => [1,1,2,2,1,2,1,2]
[1,1,1,0,1,0,0,1,0,1,0,0] => [[1,2,3,5,8,10],[4,6,7,9,11,12]] => [3,2,3,2,2] => [1,1,2,2,1,2,2,1]
[1,1,1,0,1,0,0,1,1,0,0,0] => [[1,2,3,5,8,9],[4,6,7,10,11,12]] => [3,2,4,3] => [1,1,2,2,1,1,2,1,1]
[1,1,1,0,1,0,1,0,0,0,1,0] => [[1,2,3,5,7,11],[4,6,8,9,10,12]] => [3,2,2,4,1] => [1,1,2,2,2,1,1,2]
[1,1,1,0,1,0,1,0,0,1,0,0] => [[1,2,3,5,7,10],[4,6,8,9,11,12]] => [3,2,2,3,2] => [1,1,2,2,2,1,2,1]
[1,1,1,0,1,0,1,0,1,0,0,0] => [[1,2,3,5,7,9],[4,6,8,10,11,12]] => [3,2,2,2,3] => [1,1,2,2,2,2,1,1]
[1,1,1,0,1,0,1,1,0,0,0,0] => [[1,2,3,5,7,8],[4,6,9,10,11,12]] => [3,2,3,4] => [1,1,2,2,1,2,1,1,1]
[1,1,1,0,1,1,0,0,0,0,1,0] => [[1,2,3,5,6,11],[4,7,8,9,10,12]] => [3,3,5,1] => [1,1,2,1,2,1,1,1,2]
[1,1,1,0,1,1,0,0,0,1,0,0] => [[1,2,3,5,6,10],[4,7,8,9,11,12]] => [3,3,4,2] => [1,1,2,1,2,1,1,2,1]
[1,1,1,0,1,1,0,0,1,0,0,0] => [[1,2,3,5,6,9],[4,7,8,10,11,12]] => [3,3,3,3] => [1,1,2,1,2,1,2,1,1]
[1,1,1,0,1,1,0,1,0,0,0,0] => [[1,2,3,5,6,8],[4,7,9,10,11,12]] => [3,3,2,4] => [1,1,2,1,2,2,1,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0] => [[1,2,3,5,6,7],[4,8,9,10,11,12]] => [3,4,5] => [1,1,2,1,1,2,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,0] => [[1,2,3,4,9,11],[5,6,7,8,10,12]] => [4,5,2,1] => [1,1,1,2,1,1,1,2,2]
[1,1,1,1,0,0,0,0,1,1,0,0] => [[1,2,3,4,9,10],[5,6,7,8,11,12]] => [4,6,2] => [1,1,1,2,1,1,1,1,2,1]
[1,1,1,1,0,0,0,1,0,0,1,0] => [[1,2,3,4,8,11],[5,6,7,9,10,12]] => [4,4,3,1] => [1,1,1,2,1,1,2,1,2]
[1,1,1,1,0,0,0,1,0,1,0,0] => [[1,2,3,4,8,10],[5,6,7,9,11,12]] => [4,4,2,2] => [1,1,1,2,1,1,2,2,1]
[1,1,1,1,0,0,0,1,1,0,0,0] => [[1,2,3,4,8,9],[5,6,7,10,11,12]] => [4,5,3] => [1,1,1,2,1,1,1,2,1,1]
[1,1,1,1,0,0,1,0,0,0,1,0] => [[1,2,3,4,7,11],[5,6,8,9,10,12]] => [4,3,4,1] => [1,1,1,2,1,2,1,1,2]
[1,1,1,1,0,0,1,0,0,1,0,0] => [[1,2,3,4,7,10],[5,6,8,9,11,12]] => [4,3,3,2] => [1,1,1,2,1,2,1,2,1]
[1,1,1,1,0,0,1,0,1,0,0,0] => [[1,2,3,4,7,9],[5,6,8,10,11,12]] => [4,3,2,3] => [1,1,1,2,1,2,2,1,1]
[1,1,1,1,0,0,1,1,0,0,0,0] => [[1,2,3,4,7,8],[5,6,9,10,11,12]] => [4,4,4] => [1,1,1,2,1,1,2,1,1,1]
[1,1,1,1,0,1,0,0,0,0,1,0] => [[1,2,3,4,6,11],[5,7,8,9,10,12]] => [4,2,5,1] => [1,1,1,2,2,1,1,1,2]
[1,1,1,1,0,1,0,0,0,1,0,0] => [[1,2,3,4,6,10],[5,7,8,9,11,12]] => [4,2,4,2] => [1,1,1,2,2,1,1,2,1]
[1,1,1,1,0,1,0,0,1,0,0,0] => [[1,2,3,4,6,9],[5,7,8,10,11,12]] => [4,2,3,3] => [1,1,1,2,2,1,2,1,1]
[1,1,1,1,0,1,0,1,0,0,0,0] => [[1,2,3,4,6,8],[5,7,9,10,11,12]] => [4,2,2,4] => [1,1,1,2,2,2,1,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0] => [[1,2,3,4,6,7],[5,8,9,10,11,12]] => [4,3,5] => [1,1,1,2,1,2,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,0] => [[1,2,3,4,5,11],[6,7,8,9,10,12]] => [5,6,1] => [1,1,1,1,2,1,1,1,1,2]
[1,1,1,1,1,0,0,0,0,1,0,0] => [[1,2,3,4,5,10],[6,7,8,9,11,12]] => [5,5,2] => [1,1,1,1,2,1,1,1,2,1]
[1,1,1,1,1,0,0,0,1,0,0,0] => [[1,2,3,4,5,9],[6,7,8,10,11,12]] => [5,4,3] => [1,1,1,1,2,1,1,2,1,1]
[1,1,1,1,1,0,0,1,0,0,0,0] => [[1,2,3,4,5,8],[6,7,9,10,11,12]] => [5,3,4] => [1,1,1,1,2,1,2,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0] => [[1,2,3,4,5,7],[6,8,9,10,11,12]] => [5,2,5] => [1,1,1,1,2,2,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => [6,6] => [1,1,1,1,1,2,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9,11,13],[2,4,6,8,10,12,14]] => [1,2,2,2,2,2,2,1] => [2,2,2,2,2,2,2]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,9,11,12],[2,4,6,8,10,13,14]] => [1,2,2,2,2,3,2] => [2,2,2,2,2,1,2,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[1,3,5,7,9,10,12],[2,4,6,8,11,13,14]] => [1,2,2,2,3,2,2] => [2,2,2,2,1,2,2,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[1,3,5,7,9,10,11],[2,4,6,8,12,13,14]] => [1,2,2,2,4,3] => [2,2,2,2,1,1,2,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,7,8,10,12],[2,4,6,9,11,13,14]] => [1,2,2,3,2,2,2] => [2,2,2,1,2,2,2,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[1,3,5,7,8,9,12],[2,4,6,10,11,13,14]] => [1,2,2,4,3,2] => [2,2,2,1,1,2,1,2,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,7,8,9,11],[2,4,6,10,12,13,14]] => [1,2,2,4,2,3] => [2,2,2,1,1,2,2,1,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[1,3,5,7,8,9,10],[2,4,6,11,12,13,14]] => [1,2,2,5,4] => [2,2,2,1,1,1,2,1,1,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[1,3,5,6,8,10,12],[2,4,7,9,11,13,14]] => [1,2,3,2,2,2,2] => [2,2,1,2,2,2,2,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,5,6,7,10,12],[2,4,8,9,11,13,14]] => [1,2,4,3,2,2] => [2,2,1,1,2,1,2,2,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,5,6,7,9,12],[2,4,8,10,11,13,14]] => [1,2,4,2,3,2] => [2,2,1,1,2,2,1,2,1]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [[1,3,5,6,7,9,11],[2,4,8,10,12,13,14]] => [1,2,4,2,2,3] => [2,2,1,1,2,2,2,1,1]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [[1,3,5,6,7,9,10],[2,4,8,11,12,13,14]] => [1,2,4,3,4] => [2,2,1,1,2,1,2,1,1,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[1,3,5,6,7,8,12],[2,4,9,10,11,13,14]] => [1,2,5,4,2] => [2,2,1,1,1,2,1,1,2,1]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [[1,3,5,6,7,8,10],[2,4,9,11,12,13,14]] => [1,2,5,2,4] => [2,2,1,1,1,2,2,1,1,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[1,3,4,6,8,10,12],[2,5,7,9,11,13,14]] => [1,3,2,2,2,2,2] => [2,1,2,2,2,2,2,1]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [[1,3,4,6,7,8,9],[2,5,10,11,12,13,14]] => [1,3,5,5] => [2,1,2,1,1,1,2,1,1,1,1]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [[1,3,4,5,8,11,12],[2,6,7,9,10,13,14]] => [1,4,3,4,2] => [2,1,1,2,1,2,1,1,2,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[1,3,4,5,8,10,12],[2,6,7,9,11,13,14]] => [1,4,3,2,2,2] => [2,1,1,2,1,2,2,2,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[1,3,4,5,7,10,12],[2,6,8,9,11,13,14]] => [1,4,2,3,2,2] => [2,1,1,2,2,1,2,2,1]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [[1,3,4,5,7,9,12],[2,6,8,10,11,13,14]] => [1,4,2,2,3,2] => [2,1,1,2,2,2,1,2,1]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [[1,3,4,5,7,8,12],[2,6,9,10,11,13,14]] => [1,4,3,4,2] => [2,1,1,2,1,2,1,1,2,1]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [[1,3,4,5,7,8,10],[2,6,9,11,12,13,14]] => [1,4,3,2,4] => [2,1,1,2,1,2,2,1,1,1]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [[1,3,4,5,7,8,9],[2,6,10,11,12,13,14]] => [1,4,4,5] => [2,1,1,2,1,1,2,1,1,1,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[1,3,4,5,6,10,12],[2,7,8,9,11,13,14]] => [1,5,4,2,2] => [2,1,1,1,2,1,1,2,2,1]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [[1,3,4,5,6,9,10],[2,7,8,11,12,13,14]] => [1,5,4,4] => [2,1,1,1,2,1,1,2,1,1,1]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [[1,3,4,5,6,8,12],[2,7,9,10,11,13,14]] => [1,5,2,4,2] => [2,1,1,1,2,2,1,1,2,1]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [[1,3,4,5,6,8,11],[2,7,9,10,12,13,14]] => [1,5,2,3,3] => [2,1,1,1,2,2,1,2,1,1]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [[1,3,4,5,6,8,10],[2,7,9,11,12,13,14]] => [1,5,2,2,4] => [2,1,1,1,2,2,2,1,1,1]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [[1,3,4,5,6,8,9],[2,7,10,11,12,13,14]] => [1,5,3,5] => [2,1,1,1,2,1,2,1,1,1,1]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [[1,3,4,5,6,7,12],[2,8,9,10,11,13,14]] => [1,6,5,2] => [2,1,1,1,1,2,1,1,1,2,1]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [[1,3,4,5,6,7,11],[2,8,9,10,12,13,14]] => [1,6,4,3] => [2,1,1,1,1,2,1,1,2,1,1]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [[1,3,4,5,6,7,10],[2,8,9,11,12,13,14]] => [1,6,3,4] => [2,1,1,1,1,2,1,2,1,1,1]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9],[2,8,10,11,12,13,14]] => [1,6,2,5] => [2,1,1,1,1,2,2,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,8],[2,9,10,11,12,13,14]] => [1,7,6] => [2,1,1,1,1,1,2,1,1,1,1,1]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [[1,2,5,7,9,11,12],[3,4,6,8,10,13,14]] => [2,3,2,2,3,2] => [1,2,1,2,2,2,1,2,1]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [[1,2,5,7,9,10,12],[3,4,6,8,11,13,14]] => [2,3,2,3,2,2] => [1,2,1,2,2,1,2,2,1]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [[1,2,5,7,9,10,11],[3,4,6,8,12,13,14]] => [2,3,2,4,3] => [1,2,1,2,2,1,1,2,1,1]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [[1,2,5,7,8,11,12],[3,4,6,9,10,13,14]] => [2,3,3,4,2] => [1,2,1,2,1,2,1,1,2,1]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [[1,2,5,7,8,10,12],[3,4,6,9,11,13,14]] => [2,3,3,2,2,2] => [1,2,1,2,1,2,2,2,1]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [[1,2,5,7,8,10,11],[3,4,6,9,12,13,14]] => [2,3,3,3,3] => [1,2,1,2,1,2,1,2,1,1]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [[1,2,5,7,8,9,12],[3,4,6,10,11,13,14]] => [2,3,4,3,2] => [1,2,1,2,1,1,2,1,2,1]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [[1,2,5,7,8,9,11],[3,4,6,10,12,13,14]] => [2,3,4,2,3] => [1,2,1,2,1,1,2,2,1,1]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [[1,2,5,7,8,9,10],[3,4,6,11,12,13,14]] => [2,3,5,4] => [1,2,1,2,1,1,1,2,1,1,1]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [[1,2,5,6,9,11,12],[3,4,7,8,10,13,14]] => [2,4,3,3,2] => [1,2,1,1,2,1,2,1,2,1]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [[1,2,5,6,9,10,12],[3,4,7,8,11,13,14]] => [2,4,4,2,2] => [1,2,1,1,2,1,1,2,2,1]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [[1,2,5,6,9,10,11],[3,4,7,8,12,13,14]] => [2,4,5,3] => [1,2,1,1,2,1,1,1,2,1,1]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [[1,2,5,6,8,11,12],[3,4,7,9,10,13,14]] => [2,4,2,4,2] => [1,2,1,1,2,2,1,1,2,1]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [[1,2,5,6,8,10,11],[3,4,7,9,12,13,14]] => [2,4,2,3,3] => [1,2,1,1,2,2,1,2,1,1]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [[1,2,5,6,8,9,12],[3,4,7,10,11,13,14]] => [2,4,3,3,2] => [1,2,1,1,2,1,2,1,2,1]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [[1,2,5,6,8,9,10],[3,4,7,11,12,13,14]] => [2,4,4,4] => [1,2,1,1,2,1,1,2,1,1,1]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [[1,2,5,6,7,11,12],[3,4,8,9,10,13,14]] => [2,5,5,2] => [1,2,1,1,1,2,1,1,1,2,1]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [[1,2,5,6,7,10,11],[3,4,8,9,12,13,14]] => [2,5,4,3] => [1,2,1,1,1,2,1,1,2,1,1]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [[1,2,5,6,7,9,10],[3,4,8,11,12,13,14]] => [2,5,3,4] => [1,2,1,1,1,2,1,2,1,1,1]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [[1,2,5,6,7,8,9],[3,4,10,11,12,13,14]] => [2,7,5] => [1,2,1,1,1,1,1,2,1,1,1,1]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [[1,2,4,7,9,11,12],[3,5,6,8,10,13,14]] => [2,2,3,2,3,2] => [1,2,2,1,2,2,1,2,1]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [[1,2,4,7,9,10,12],[3,5,6,8,11,13,14]] => [2,2,3,3,2,2] => [1,2,2,1,2,1,2,2,1]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [[1,2,4,7,9,10,11],[3,5,6,8,12,13,14]] => [2,2,3,4,3] => [1,2,2,1,2,1,1,2,1,1]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [[1,2,4,7,8,11,12],[3,5,6,9,10,13,14]] => [2,2,4,4,2] => [1,2,2,1,1,2,1,1,2,1]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [[1,2,4,7,8,10,11],[3,5,6,9,12,13,14]] => [2,2,4,3,3] => [1,2,2,1,1,2,1,2,1,1]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [[1,2,4,6,9,11,12],[3,5,7,8,10,13,14]] => [2,2,2,3,3,2] => [1,2,2,2,1,2,1,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,2,4,6,8,10,12],[3,5,7,9,11,13,14]] => [2,2,2,2,2,2,2] => [1,2,2,2,2,2,2,1]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [[1,2,4,6,8,10,11],[3,5,7,9,12,13,14]] => [2,2,2,2,3,3] => [1,2,2,2,2,1,2,1,1]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [[1,2,4,6,8,9,12],[3,5,7,10,11,13,14]] => [2,2,2,3,3,2] => [1,2,2,2,1,2,1,2,1]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [[1,2,4,6,8,9,11],[3,5,7,10,12,13,14]] => [2,2,2,3,2,3] => [1,2,2,2,1,2,2,1,1]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [[1,2,4,6,8,9,10],[3,5,7,11,12,13,14]] => [2,2,2,4,4] => [1,2,2,2,1,1,2,1,1,1]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [[1,2,4,6,7,10,12],[3,5,8,9,11,13,14]] => [2,2,3,3,2,2] => [1,2,2,1,2,1,2,2,1]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [[1,2,4,6,7,10,11],[3,5,8,9,12,13,14]] => [2,2,3,4,3] => [1,2,2,1,2,1,1,2,1,1]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [[1,2,4,6,7,9,12],[3,5,8,10,11,13,14]] => [2,2,3,2,3,2] => [1,2,2,1,2,2,1,2,1]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [[1,2,4,6,7,9,11],[3,5,8,10,12,13,14]] => [2,2,3,2,2,3] => [1,2,2,1,2,2,2,1,1]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [[1,2,4,6,7,9,10],[3,5,8,11,12,13,14]] => [2,2,3,3,4] => [1,2,2,1,2,1,2,1,1,1]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [[1,2,4,6,7,8,12],[3,5,9,10,11,13,14]] => [2,2,4,4,2] => [1,2,2,1,1,2,1,1,2,1]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [[1,2,4,6,7,8,11],[3,5,9,10,12,13,14]] => [2,2,4,3,3] => [1,2,2,1,1,2,1,2,1,1]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [[1,2,4,6,7,8,10],[3,5,9,11,12,13,14]] => [2,2,4,2,4] => [1,2,2,1,1,2,2,1,1,1]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [[1,2,4,6,7,8,9],[3,5,10,11,12,13,14]] => [2,2,5,5] => [1,2,2,1,1,1,2,1,1,1,1]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [[1,2,4,5,9,11,12],[3,6,7,8,10,13,14]] => [2,3,4,3,2] => [1,2,1,2,1,1,2,1,2,1]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [[1,2,4,5,8,11,12],[3,6,7,9,10,13,14]] => [2,3,3,4,2] => [1,2,1,2,1,2,1,1,2,1]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [[1,2,4,5,8,10,12],[3,6,7,9,11,13,14]] => [2,3,3,2,2,2] => [1,2,1,2,1,2,2,2,1]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [[1,2,4,5,8,10,11],[3,6,7,9,12,13,14]] => [2,3,3,3,3] => [1,2,1,2,1,2,1,2,1,1]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [[1,2,4,5,8,9,12],[3,6,7,10,11,13,14]] => [2,3,4,3,2] => [1,2,1,2,1,1,2,1,2,1]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [[1,2,4,5,8,9,11],[3,6,7,10,12,13,14]] => [2,3,4,2,3] => [1,2,1,2,1,1,2,2,1,1]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [[1,2,4,5,8,9,10],[3,6,7,11,12,13,14]] => [2,3,5,4] => [1,2,1,2,1,1,1,2,1,1,1]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [[1,2,4,5,7,10,12],[3,6,8,9,11,13,14]] => [2,3,2,3,2,2] => [1,2,1,2,2,1,2,2,1]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [[1,2,4,5,7,10,11],[3,6,8,9,12,13,14]] => [2,3,2,4,3] => [1,2,1,2,2,1,1,2,1,1]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [[1,2,4,5,7,9,12],[3,6,8,10,11,13,14]] => [2,3,2,2,3,2] => [1,2,1,2,2,2,1,2,1]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [[1,2,4,5,7,9,11],[3,6,8,10,12,13,14]] => [2,3,2,2,2,3] => [1,2,1,2,2,2,2,1,1]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [[1,2,4,5,7,9,10],[3,6,8,11,12,13,14]] => [2,3,2,3,4] => [1,2,1,2,2,1,2,1,1,1]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [[1,2,4,5,7,8,12],[3,6,9,10,11,13,14]] => [2,3,3,4,2] => [1,2,1,2,1,2,1,1,2,1]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [[1,2,4,5,7,8,11],[3,6,9,10,12,13,14]] => [2,3,3,3,3] => [1,2,1,2,1,2,1,2,1,1]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [[1,2,4,5,7,8,10],[3,6,9,11,12,13,14]] => [2,3,3,2,4] => [1,2,1,2,1,2,2,1,1,1]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [[1,2,4,5,7,8,9],[3,6,10,11,12,13,14]] => [2,3,4,5] => [1,2,1,2,1,1,2,1,1,1,1]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [[1,2,4,5,6,10,12],[3,7,8,9,11,13,14]] => [2,4,4,2,2] => [1,2,1,1,2,1,1,2,2,1]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [[1,2,4,5,6,10,11],[3,7,8,9,12,13,14]] => [2,4,5,3] => [1,2,1,1,2,1,1,1,2,1,1]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [[1,2,4,5,6,9,12],[3,7,8,10,11,13,14]] => [2,4,3,3,2] => [1,2,1,1,2,1,2,1,2,1]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [[1,2,4,5,6,9,11],[3,7,8,10,12,13,14]] => [2,4,3,2,3] => [1,2,1,1,2,1,2,2,1,1]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [[1,2,4,5,6,9,10],[3,7,8,11,12,13,14]] => [2,4,4,4] => [1,2,1,1,2,1,1,2,1,1,1]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [[1,2,4,5,6,8,12],[3,7,9,10,11,13,14]] => [2,4,2,4,2] => [1,2,1,1,2,2,1,1,2,1]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [[1,2,4,5,6,8,11],[3,7,9,10,12,13,14]] => [2,4,2,3,3] => [1,2,1,1,2,2,1,2,1,1]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [[1,2,4,5,6,8,10],[3,7,9,11,12,13,14]] => [2,4,2,2,4] => [1,2,1,1,2,2,2,1,1,1]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [[1,2,4,5,6,8,9],[3,7,10,11,12,13,14]] => [2,4,3,5] => [1,2,1,1,2,1,2,1,1,1,1]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [[1,2,4,5,6,7,13],[3,8,9,10,11,12,14]] => [2,5,6,1] => [1,2,1,1,1,2,1,1,1,1,2]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [[1,2,4,5,6,7,12],[3,8,9,10,11,13,14]] => [2,5,5,2] => [1,2,1,1,1,2,1,1,1,2,1]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [[1,2,4,5,6,7,11],[3,8,9,10,12,13,14]] => [2,5,4,3] => [1,2,1,1,1,2,1,1,2,1,1]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [[1,2,4,5,6,7,10],[3,8,9,11,12,13,14]] => [2,5,3,4] => [1,2,1,1,1,2,1,2,1,1,1]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [[1,2,4,5,6,7,9],[3,8,10,11,12,13,14]] => [2,5,2,5] => [1,2,1,1,1,2,2,1,1,1,1]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [[1,2,4,5,6,7,8],[3,9,10,11,12,13,14]] => [2,6,6] => [1,2,1,1,1,1,2,1,1,1,1,1]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [[1,2,3,7,9,11,12],[4,5,6,8,10,13,14]] => [3,4,2,3,2] => [1,1,2,1,1,2,2,1,2,1]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [[1,2,3,7,9,10,12],[4,5,6,8,11,13,14]] => [3,4,3,2,2] => [1,1,2,1,1,2,1,2,2,1]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [[1,2,3,7,9,10,11],[4,5,6,8,12,13,14]] => [3,4,4,3] => [1,1,2,1,1,2,1,1,2,1,1]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [[1,2,3,7,8,11,12],[4,5,6,9,10,13,14]] => [3,5,4,2] => [1,1,2,1,1,1,2,1,1,2,1]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [[1,2,3,7,8,10,11],[4,5,6,9,12,13,14]] => [3,5,3,3] => [1,1,2,1,1,1,2,1,2,1,1]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [[1,2,3,6,9,11,12],[4,5,7,8,10,13,14]] => [3,3,3,3,2] => [1,1,2,1,2,1,2,1,2,1]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [[1,2,3,6,9,10,12],[4,5,7,8,11,13,14]] => [3,3,4,2,2] => [1,1,2,1,2,1,1,2,2,1]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [[1,2,3,6,9,10,11],[4,5,7,8,12,13,14]] => [3,3,5,3] => [1,1,2,1,2,1,1,1,2,1,1]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [[1,2,3,6,8,11,12],[4,5,7,9,10,13,14]] => [3,3,2,4,2] => [1,1,2,1,2,2,1,1,2,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[1,2,3,6,8,10,12],[4,5,7,9,11,13,14]] => [3,3,2,2,2,2] => [1,1,2,1,2,2,2,2,1]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [[1,2,3,6,8,10,11],[4,5,7,9,12,13,14]] => [3,3,2,3,3] => [1,1,2,1,2,2,1,2,1,1]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [[1,2,3,6,8,9,12],[4,5,7,10,11,13,14]] => [3,3,3,3,2] => [1,1,2,1,2,1,2,1,2,1]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [[1,2,3,6,8,9,11],[4,5,7,10,12,13,14]] => [3,3,3,2,3] => [1,1,2,1,2,1,2,2,1,1]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [[1,2,3,6,8,9,10],[4,5,7,11,12,13,14]] => [3,3,4,4] => [1,1,2,1,2,1,1,2,1,1,1]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [[1,2,3,6,7,11,12],[4,5,8,9,10,13,14]] => [3,4,5,2] => [1,1,2,1,1,2,1,1,1,2,1]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [[1,2,3,6,7,10,12],[4,5,8,9,11,13,14]] => [3,4,3,2,2] => [1,1,2,1,1,2,1,2,2,1]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [[1,2,3,6,7,10,11],[4,5,8,9,12,13,14]] => [3,4,4,3] => [1,1,2,1,1,2,1,1,2,1,1]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [[1,2,3,6,7,9,12],[4,5,8,10,11,13,14]] => [3,4,2,3,2] => [1,1,2,1,1,2,2,1,2,1]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [[1,2,3,6,7,9,11],[4,5,8,10,12,13,14]] => [3,4,2,2,3] => [1,1,2,1,1,2,2,2,1,1]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [[1,2,3,6,7,9,10],[4,5,8,11,12,13,14]] => [3,4,3,4] => [1,1,2,1,1,2,1,2,1,1,1]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [[1,2,3,6,7,8,12],[4,5,9,10,11,13,14]] => [3,5,4,2] => [1,1,2,1,1,1,2,1,1,2,1]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [[1,2,3,6,7,8,11],[4,5,9,10,12,13,14]] => [3,5,3,3] => [1,1,2,1,1,1,2,1,2,1,1]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [[1,2,3,6,7,8,10],[4,5,9,11,12,13,14]] => [3,5,2,4] => [1,1,2,1,1,1,2,2,1,1,1]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [[1,2,3,6,7,8,9],[4,5,10,11,12,13,14]] => [3,6,5] => [1,1,2,1,1,1,1,2,1,1,1,1]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [[1,2,3,5,9,11,12],[4,6,7,8,10,13,14]] => [3,2,4,3,2] => [1,1,2,2,1,1,2,1,2,1]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [[1,2,3,5,8,11,12],[4,6,7,9,10,13,14]] => [3,2,3,4,2] => [1,1,2,2,1,2,1,1,2,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[1,2,3,5,8,10,12],[4,6,7,9,11,13,14]] => [3,2,3,2,2,2] => [1,1,2,2,1,2,2,2,1]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [[1,2,3,5,8,10,11],[4,6,7,9,12,13,14]] => [3,2,3,3,3] => [1,1,2,2,1,2,1,2,1,1]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [[1,2,3,5,8,9,12],[4,6,7,10,11,13,14]] => [3,2,4,3,2] => [1,1,2,2,1,1,2,1,2,1]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [[1,2,3,5,8,9,11],[4,6,7,10,12,13,14]] => [3,2,4,2,3] => [1,1,2,2,1,1,2,2,1,1]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [[1,2,3,5,8,9,10],[4,6,7,11,12,13,14]] => [3,2,5,4] => [1,1,2,2,1,1,1,2,1,1,1]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [[1,2,3,5,7,10,12],[4,6,8,9,11,13,14]] => [3,2,2,3,2,2] => [1,1,2,2,2,1,2,2,1]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [[1,2,3,5,7,10,11],[4,6,8,9,12,13,14]] => [3,2,2,4,3] => [1,1,2,2,2,1,1,2,1,1]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [[1,2,3,5,7,9,12],[4,6,8,10,11,13,14]] => [3,2,2,2,3,2] => [1,1,2,2,2,2,1,2,1]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [[1,2,3,5,7,9,11],[4,6,8,10,12,13,14]] => [3,2,2,2,2,3] => [1,1,2,2,2,2,2,1,1]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [[1,2,3,5,7,9,10],[4,6,8,11,12,13,14]] => [3,2,2,3,4] => [1,1,2,2,2,1,2,1,1,1]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [[1,2,3,5,7,8,12],[4,6,9,10,11,13,14]] => [3,2,3,4,2] => [1,1,2,2,1,2,1,1,2,1]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [[1,2,3,5,7,8,11],[4,6,9,10,12,13,14]] => [3,2,3,3,3] => [1,1,2,2,1,2,1,2,1,1]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [[1,2,3,5,7,8,10],[4,6,9,11,12,13,14]] => [3,2,3,2,4] => [1,1,2,2,1,2,2,1,1,1]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [[1,2,3,5,7,8,9],[4,6,10,11,12,13,14]] => [3,2,4,5] => [1,1,2,2,1,1,2,1,1,1,1]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [[1,2,3,5,6,10,12],[4,7,8,9,11,13,14]] => [3,3,4,2,2] => [1,1,2,1,2,1,1,2,2,1]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [[1,2,3,5,6,10,11],[4,7,8,9,12,13,14]] => [3,3,5,3] => [1,1,2,1,2,1,1,1,2,1,1]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [[1,2,3,5,6,9,12],[4,7,8,10,11,13,14]] => [3,3,3,3,2] => [1,1,2,1,2,1,2,1,2,1]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [[1,2,3,5,6,9,11],[4,7,8,10,12,13,14]] => [3,3,3,2,3] => [1,1,2,1,2,1,2,2,1,1]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [[1,2,3,5,6,9,10],[4,7,8,11,12,13,14]] => [3,3,4,4] => [1,1,2,1,2,1,1,2,1,1,1]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [[1,2,3,5,6,8,13],[4,7,9,10,11,12,14]] => [3,3,2,5,1] => [1,1,2,1,2,2,1,1,1,2]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [[1,2,3,5,6,8,12],[4,7,9,10,11,13,14]] => [3,3,2,4,2] => [1,1,2,1,2,2,1,1,2,1]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [[1,2,3,5,6,8,11],[4,7,9,10,12,13,14]] => [3,3,2,3,3] => [1,1,2,1,2,2,1,2,1,1]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [[1,2,3,5,6,8,10],[4,7,9,11,12,13,14]] => [3,3,2,2,4] => [1,1,2,1,2,2,2,1,1,1]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [[1,2,3,5,6,8,9],[4,7,10,11,12,13,14]] => [3,3,3,5] => [1,1,2,1,2,1,2,1,1,1,1]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [[1,2,3,5,6,7,13],[4,8,9,10,11,12,14]] => [3,4,6,1] => [1,1,2,1,1,2,1,1,1,1,2]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [[1,2,3,5,6,7,12],[4,8,9,10,11,13,14]] => [3,4,5,2] => [1,1,2,1,1,2,1,1,1,2,1]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [[1,2,3,5,6,7,11],[4,8,9,10,12,13,14]] => [3,4,4,3] => [1,1,2,1,1,2,1,1,2,1,1]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [[1,2,3,5,6,7,10],[4,8,9,11,12,13,14]] => [3,4,3,4] => [1,1,2,1,1,2,1,2,1,1,1]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [[1,2,3,5,6,7,9],[4,8,10,11,12,13,14]] => [3,4,2,5] => [1,1,2,1,1,2,2,1,1,1,1]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [[1,2,3,5,6,7,8],[4,9,10,11,12,13,14]] => [3,5,6] => [1,1,2,1,1,1,2,1,1,1,1,1]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [[1,2,3,4,9,11,12],[5,6,7,8,10,13,14]] => [4,5,3,2] => [1,1,1,2,1,1,1,2,1,2,1]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [[1,2,3,4,8,11,13],[5,6,7,9,10,12,14]] => [4,4,3,2,1] => [1,1,1,2,1,1,2,1,2,2]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [[1,2,3,4,8,11,12],[5,6,7,9,10,13,14]] => [4,4,4,2] => [1,1,1,2,1,1,2,1,1,2,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[1,2,3,4,8,10,12],[5,6,7,9,11,13,14]] => [4,4,2,2,2] => [1,1,1,2,1,1,2,2,2,1]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [[1,2,3,4,8,10,11],[5,6,7,9,12,13,14]] => [4,4,3,3] => [1,1,1,2,1,1,2,1,2,1,1]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [[1,2,3,4,8,9,12],[5,6,7,10,11,13,14]] => [4,5,3,2] => [1,1,1,2,1,1,1,2,1,2,1]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [[1,2,3,4,8,9,11],[5,6,7,10,12,13,14]] => [4,5,2,3] => [1,1,1,2,1,1,1,2,2,1,1]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [[1,2,3,4,8,9,10],[5,6,7,11,12,13,14]] => [4,6,4] => [1,1,1,2,1,1,1,1,2,1,1,1]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [[1,2,3,4,7,11,12],[5,6,8,9,10,13,14]] => [4,3,5,2] => [1,1,1,2,1,2,1,1,1,2,1]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [[1,2,3,4,7,10,12],[5,6,8,9,11,13,14]] => [4,3,3,2,2] => [1,1,1,2,1,2,1,2,2,1]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [[1,2,3,4,7,10,11],[5,6,8,9,12,13,14]] => [4,3,4,3] => [1,1,1,2,1,2,1,1,2,1,1]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [[1,2,3,4,7,9,12],[5,6,8,10,11,13,14]] => [4,3,2,3,2] => [1,1,1,2,1,2,2,1,2,1]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [[1,2,3,4,7,9,11],[5,6,8,10,12,13,14]] => [4,3,2,2,3] => [1,1,1,2,1,2,2,2,1,1]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [[1,2,3,4,7,9,10],[5,6,8,11,12,13,14]] => [4,3,3,4] => [1,1,1,2,1,2,1,2,1,1,1]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [[1,2,3,4,7,8,13],[5,6,9,10,11,12,14]] => [4,4,5,1] => [1,1,1,2,1,1,2,1,1,1,2]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [[1,2,3,4,7,8,12],[5,6,9,10,11,13,14]] => [4,4,4,2] => [1,1,1,2,1,1,2,1,1,2,1]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [[1,2,3,4,7,8,11],[5,6,9,10,12,13,14]] => [4,4,3,3] => [1,1,1,2,1,1,2,1,2,1,1]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [[1,2,3,4,7,8,10],[5,6,9,11,12,13,14]] => [4,4,2,4] => [1,1,1,2,1,1,2,2,1,1,1]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [[1,2,3,4,7,8,9],[5,6,10,11,12,13,14]] => [4,5,5] => [1,1,1,2,1,1,1,2,1,1,1,1]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [[1,2,3,4,6,10,12],[5,7,8,9,11,13,14]] => [4,2,4,2,2] => [1,1,1,2,2,1,1,2,2,1]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [[1,2,3,4,6,10,11],[5,7,8,9,12,13,14]] => [4,2,5,3] => [1,1,1,2,2,1,1,1,2,1,1]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [[1,2,3,4,6,9,13],[5,7,8,10,11,12,14]] => [4,2,3,4,1] => [1,1,1,2,2,1,2,1,1,2]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [[1,2,3,4,6,9,12],[5,7,8,10,11,13,14]] => [4,2,3,3,2] => [1,1,1,2,2,1,2,1,2,1]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [[1,2,3,4,6,9,11],[5,7,8,10,12,13,14]] => [4,2,3,2,3] => [1,1,1,2,2,1,2,2,1,1]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [[1,2,3,4,6,9,10],[5,7,8,11,12,13,14]] => [4,2,4,4] => [1,1,1,2,2,1,1,2,1,1,1]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [[1,2,3,4,6,8,13],[5,7,9,10,11,12,14]] => [4,2,2,5,1] => [1,1,1,2,2,2,1,1,1,2]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [[1,2,3,4,6,8,12],[5,7,9,10,11,13,14]] => [4,2,2,4,2] => [1,1,1,2,2,2,1,1,2,1]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [[1,2,3,4,6,8,11],[5,7,9,10,12,13,14]] => [4,2,2,3,3] => [1,1,1,2,2,2,1,2,1,1]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [[1,2,3,4,6,8,10],[5,7,9,11,12,13,14]] => [4,2,2,2,4] => [1,1,1,2,2,2,2,1,1,1]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [[1,2,3,4,6,8,9],[5,7,10,11,12,13,14]] => [4,2,3,5] => [1,1,1,2,2,1,2,1,1,1,1]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [[1,2,3,4,6,7,13],[5,8,9,10,11,12,14]] => [4,3,6,1] => [1,1,1,2,1,2,1,1,1,1,2]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [[1,2,3,4,6,7,12],[5,8,9,10,11,13,14]] => [4,3,5,2] => [1,1,1,2,1,2,1,1,1,2,1]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [[1,2,3,4,6,7,11],[5,8,9,10,12,13,14]] => [4,3,4,3] => [1,1,1,2,1,2,1,1,2,1,1]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [[1,2,3,4,6,7,10],[5,8,9,11,12,13,14]] => [4,3,3,4] => [1,1,1,2,1,2,1,2,1,1,1]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [[1,2,3,4,6,7,9],[5,8,10,11,12,13,14]] => [4,3,2,5] => [1,1,1,2,1,2,2,1,1,1,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,2,3,4,6,7,8],[5,9,10,11,12,13,14]] => [4,4,6] => [1,1,1,2,1,1,2,1,1,1,1,1]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [[1,2,3,4,5,11,12],[6,7,8,9,10,13,14]] => [5,7,2] => [1,1,1,1,2,1,1,1,1,1,2,1]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [[1,2,3,4,5,10,13],[6,7,8,9,11,12,14]] => [5,5,3,1] => [1,1,1,1,2,1,1,1,2,1,2]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [[1,2,3,4,5,10,12],[6,7,8,9,11,13,14]] => [5,5,2,2] => [1,1,1,1,2,1,1,1,2,2,1]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [[1,2,3,4,5,10,11],[6,7,8,9,12,13,14]] => [5,6,3] => [1,1,1,1,2,1,1,1,1,2,1,1]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [[1,2,3,4,5,9,13],[6,7,8,10,11,12,14]] => [5,4,4,1] => [1,1,1,1,2,1,1,2,1,1,2]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [[1,2,3,4,5,9,12],[6,7,8,10,11,13,14]] => [5,4,3,2] => [1,1,1,1,2,1,1,2,1,2,1]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [[1,2,3,4,5,9,11],[6,7,8,10,12,13,14]] => [5,4,2,3] => [1,1,1,1,2,1,1,2,2,1,1]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [[1,2,3,4,5,9,10],[6,7,8,11,12,13,14]] => [5,5,4] => [1,1,1,1,2,1,1,1,2,1,1,1]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [[1,2,3,4,5,8,13],[6,7,9,10,11,12,14]] => [5,3,5,1] => [1,1,1,1,2,1,2,1,1,1,2]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [[1,2,3,4,5,8,12],[6,7,9,10,11,13,14]] => [5,3,4,2] => [1,1,1,1,2,1,2,1,1,2,1]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [[1,2,3,4,5,8,11],[6,7,9,10,12,13,14]] => [5,3,3,3] => [1,1,1,1,2,1,2,1,2,1,1]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [[1,2,3,4,5,8,10],[6,7,9,11,12,13,14]] => [5,3,2,4] => [1,1,1,1,2,1,2,2,1,1,1]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [[1,2,3,4,5,8,9],[6,7,10,11,12,13,14]] => [5,4,5] => [1,1,1,1,2,1,1,2,1,1,1,1]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [[1,2,3,4,5,7,13],[6,8,9,10,11,12,14]] => [5,2,6,1] => [1,1,1,1,2,2,1,1,1,1,2]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [[1,2,3,4,5,7,12],[6,8,9,10,11,13,14]] => [5,2,5,2] => [1,1,1,1,2,2,1,1,1,2,1]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [[1,2,3,4,5,7,11],[6,8,9,10,12,13,14]] => [5,2,4,3] => [1,1,1,1,2,2,1,1,2,1,1]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [[1,2,3,4,5,7,10],[6,8,9,11,12,13,14]] => [5,2,3,4] => [1,1,1,1,2,2,1,2,1,1,1]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,2,3,4,5,7,9],[6,8,10,11,12,13,14]] => [5,2,2,5] => [1,1,1,1,2,2,2,1,1,1,1]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[1,2,3,4,5,7,8],[6,9,10,11,12,13,14]] => [5,3,6] => [1,1,1,1,2,1,2,1,1,1,1,1]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,13],[7,8,9,10,11,12,14]] => [6,7,1] => [1,1,1,1,1,2,1,1,1,1,1,2]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [[1,2,3,4,5,6,12],[7,8,9,10,11,13,14]] => [6,6,2] => [1,1,1,1,1,2,1,1,1,1,2,1]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [[1,2,3,4,5,6,11],[7,8,9,10,12,13,14]] => [6,5,3] => [1,1,1,1,1,2,1,1,1,2,1,1]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[1,2,3,4,5,6,10],[7,8,9,11,12,13,14]] => [6,4,4] => [1,1,1,1,1,2,1,1,2,1,1,1]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[1,2,3,4,5,6,9],[7,8,10,11,12,13,14]] => [6,3,5] => [1,1,1,1,1,2,1,2,1,1,1,1]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[1,2,3,4,5,6,8],[7,9,10,11,12,13,14]] => [6,2,6] => [1,1,1,1,1,2,2,1,1,1,1,1]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[1,2,3,4,5,6,7],[8,9,10,11,12,13,14]] => [7,7] => [1,1,1,1,1,1,2,1,1,1,1,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9,11,13,15],[2,4,6,8,10,12,14,16]] => [1,2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,2,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,9,11,13,14],[2,4,6,8,10,12,15,16]] => [1,2,2,2,2,2,3,2] => [2,2,2,2,2,2,1,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[1,3,5,7,9,11,12,14],[2,4,6,8,10,13,15,16]] => [1,2,2,2,2,3,2,2] => [2,2,2,2,2,1,2,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[1,3,5,7,9,11,12,13],[2,4,6,8,10,14,15,16]] => [1,2,2,2,2,4,3] => [2,2,2,2,2,1,1,2,1,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,7,9,10,12,14],[2,4,6,8,11,13,15,16]] => [1,2,2,2,3,2,2,2] => [2,2,2,2,1,2,2,2,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[1,3,5,7,9,10,11,14],[2,4,6,8,12,13,15,16]] => [1,2,2,2,4,3,2] => [2,2,2,2,1,1,2,1,2,1]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [[1,3,5,7,9,10,11,13],[2,4,6,8,12,14,15,16]] => [1,2,2,2,4,2,3] => [2,2,2,2,1,1,2,2,1,1]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [[1,3,5,7,9,10,11,12],[2,4,6,8,13,14,15,16]] => [1,2,2,2,5,4] => [2,2,2,2,1,1,1,2,1,1,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[1,3,5,7,8,10,12,14],[2,4,6,9,11,13,15,16]] => [1,2,2,3,2,2,2,2] => [2,2,2,1,2,2,2,2,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,5,7,8,9,12,14],[2,4,6,10,11,13,15,16]] => [1,2,2,4,3,2,2] => [2,2,2,1,1,2,1,2,2,1]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [[1,3,5,7,8,9,11,14],[2,4,6,10,12,13,15,16]] => [1,2,2,4,2,3,2] => [2,2,2,1,1,2,2,1,2,1]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [[1,3,5,7,8,9,10,14],[2,4,6,11,12,13,15,16]] => [1,2,2,5,4,2] => [2,2,2,1,1,1,2,1,1,2,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[1,3,5,6,8,10,12,14],[2,4,7,9,11,13,15,16]] => [1,2,3,2,2,2,2,2] => [2,2,1,2,2,2,2,2,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[1,3,5,6,7,10,12,14],[2,4,8,9,11,13,15,16]] => [1,2,4,3,2,2,2] => [2,2,1,1,2,1,2,2,2,1]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [[1,3,5,6,7,9,12,14],[2,4,8,10,11,13,15,16]] => [1,2,4,2,3,2,2] => [2,2,1,1,2,2,1,2,2,1]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [[1,3,5,6,7,8,12,14],[2,4,9,10,11,13,15,16]] => [1,2,5,4,2,2] => [2,2,1,1,1,2,1,1,2,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,3,4,6,8,10,12,14],[2,5,7,9,11,13,15,16]] => [1,3,2,2,2,2,2,2] => [2,1,2,2,2,2,2,2,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[1,3,4,5,8,10,12,14],[2,6,7,9,11,13,15,16]] => [1,4,3,2,2,2,2] => [2,1,1,2,1,2,2,2,2,1]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [[1,3,4,5,7,10,12,14],[2,6,8,9,11,13,15,16]] => [1,4,2,3,2,2,2] => [2,1,1,2,2,1,2,2,2,1]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [[1,3,4,5,6,10,12,14],[2,7,8,9,11,13,15,16]] => [1,5,4,2,2,2] => [2,1,1,1,2,1,1,2,2,2,1]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,8,9,10],[2,7,11,12,13,14,15,16]] => [1,5,4,6] => [2,1,1,1,2,1,1,2,1,1,1,1,1]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,9,11],[2,8,10,12,13,14,15,16]] => [1,6,2,2,5] => [2,1,1,1,1,2,2,2,1,1,1,1]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,9,10],[2,8,11,12,13,14,15,16]] => [1,6,3,6] => [2,1,1,1,1,2,1,2,1,1,1,1,1]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [[1,3,4,5,6,7,8,12],[2,9,10,11,13,14,15,16]] => [1,7,4,4] => [2,1,1,1,1,1,2,1,1,2,1,1,1]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [[1,3,4,5,6,7,8,11],[2,9,10,12,13,14,15,16]] => [1,7,3,5] => [2,1,1,1,1,1,2,1,2,1,1,1,1]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10],[2,9,11,12,13,14,15,16]] => [1,7,2,6] => [2,1,1,1,1,1,2,2,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9],[2,10,11,12,13,14,15,16]] => [1,8,7] => [2,1,1,1,1,1,1,2,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,2,4,6,8,10,12,14],[3,5,7,9,11,13,15,16]] => [2,2,2,2,2,2,2,2] => [1,2,2,2,2,2,2,2,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,2,3,6,8,10,12,14],[4,5,7,9,11,13,15,16]] => [3,3,2,2,2,2,2] => [1,1,2,1,2,2,2,2,2,1]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [[1,2,3,5,8,10,12,14],[4,6,7,9,11,13,15,16]] => [3,2,3,2,2,2,2] => [1,1,2,2,1,2,2,2,2,1]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [[1,2,3,4,8,10,12,14],[5,6,7,9,11,13,15,16]] => [4,4,2,2,2,2] => [1,1,1,2,1,1,2,2,2,2,1]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [[1,2,3,4,6,7,8,15],[5,9,10,11,12,13,14,16]] => [4,4,7,1] => [1,1,1,2,1,1,2,1,1,1,1,1,2]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [[1,2,3,4,5,7,9,15],[6,8,10,11,12,13,14,16]] => [5,2,2,6,1] => [1,1,1,1,2,2,2,1,1,1,1,2]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,7,8,15],[6,9,10,11,12,13,14,16]] => [5,3,7,1] => [1,1,1,1,2,1,2,1,1,1,1,1,2]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [[1,2,3,4,5,6,10,15],[7,8,9,11,12,13,14,16]] => [6,4,5,1] => [1,1,1,1,1,2,1,1,2,1,1,1,2]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,9,15],[7,8,10,11,12,13,14,16]] => [6,3,6,1] => [1,1,1,1,1,2,1,2,1,1,1,1,2]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,8,15],[7,9,10,11,12,13,14,16]] => [6,2,7,1] => [1,1,1,1,1,2,2,1,1,1,1,1,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,7,15],[8,9,10,11,12,13,14,16]] => [7,8,1] => [1,1,1,1,1,1,2,1,1,1,1,1,1,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,7,8,17],[9,10,11,12,13,14,15,16,18]] => [8,9,1] => [1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,2]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,10],[2,11,12,13,14,15,16,17,18]] => [1,9,8] => [2,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,7,8,9,19],[10,11,12,13,14,15,16,17,18,20]] => [9,10,1] => [1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,2]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,7,9,17],[8,10,11,12,13,14,15,16,18]] => [7,2,8,1] => [1,1,1,1,1,1,2,2,1,1,1,1,1,1,2]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,11],[2,10,12,13,14,15,16,17,18]] => [1,8,2,7] => [2,1,1,1,1,1,1,2,2,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,10,11],[2,12,13,14,15,16,17,18,19,20]] => [1,10,9] => [2,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,7,8,9,10,21],[11,12,13,14,15,16,17,18,19,20,22]] => [10,11,1] => [1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1,2]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,7,8,10,19],[9,11,12,13,14,15,16,17,18,20]] => [8,2,9,1] => [1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1,2]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,7,10,17],[8,9,11,12,13,14,15,16,18]] => [7,3,7,1] => [1,1,1,1,1,1,2,1,2,1,1,1,1,1,2]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [[1,2,3,4,5,6,8,9,17],[7,10,11,12,13,14,15,16,18]] => [6,3,8,1] => [1,1,1,1,1,2,1,2,1,1,1,1,1,1,2]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,12],[2,10,11,13,14,15,16,17,18]] => [1,8,3,6] => [2,1,1,1,1,1,1,2,1,2,1,1,1,1,1]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,10,11],[2,9,12,13,14,15,16,17,18]] => [1,7,3,7] => [2,1,1,1,1,1,2,1,2,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,10,12],[2,11,13,14,15,16,17,18,19,20]] => [1,9,2,8] => [2,1,1,1,1,1,1,1,2,2,1,1,1,1,1,1,1]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [[1,3,4,5,6,7,8,9,10,11,12],[2,13,14,15,16,17,18,19,20,21,22]] => [1,11,10] => [2,1,1,1,1,1,1,1,1,1,2,1,1,1,1,1,1,1,1,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,2,4,6,8,10,12,14,16],[3,5,7,9,11,13,15,17,18]] => [2,2,2,2,2,2,2,2,2] => [1,2,2,2,2,2,2,2,2,1]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,2,3,6,8,10,12,14,16],[4,5,7,9,11,13,15,17,18]] => [3,3,2,2,2,2,2,2] => [1,1,2,1,2,2,2,2,2,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9,11,13,15,17],[2,4,6,8,10,12,14,16,18]] => [1,2,2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,2,2,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,9,11,13,15,16],[2,4,6,8,10,12,14,17,18]] => [1,2,2,2,2,2,2,3,2] => [2,2,2,2,2,2,2,1,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[1,3,5,7,9,11,13,14,16],[2,4,6,8,10,12,15,17,18]] => [1,2,2,2,2,2,3,2,2] => [2,2,2,2,2,2,1,2,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,7,9,11,12,14,16],[2,4,6,8,10,13,15,17,18]] => [1,2,2,2,2,3,2,2,2] => [2,2,2,2,2,1,2,2,2,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[1,3,5,7,9,10,12,14,16],[2,4,6,8,11,13,15,17,18]] => [1,2,2,2,3,2,2,2,2] => [2,2,2,2,1,2,2,2,2,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[1,3,5,7,8,10,12,14,16],[2,4,6,9,11,13,15,17,18]] => [1,2,2,3,2,2,2,2,2] => [2,2,2,1,2,2,2,2,2,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,3,5,6,8,10,12,14,16],[2,4,7,9,11,13,15,17,18]] => [1,2,3,2,2,2,2,2,2] => [2,2,1,2,2,2,2,2,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,3,4,6,8,10,12,14,16],[2,5,7,9,11,13,15,17,18]] => [1,3,2,2,2,2,2,2,2] => [2,1,2,2,2,2,2,2,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [[1,3,5,7,9,11,13,15,17,19],[2,4,6,8,10,12,14,16,18,20]] => [1,2,2,2,2,2,2,2,2,2,1] => [2,2,2,2,2,2,2,2,2,2]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [[1,3,5,7,9,11,13,15,17,18],[2,4,6,8,10,12,14,16,19,20]] => [1,2,2,2,2,2,2,2,3,2] => [2,2,2,2,2,2,2,2,1,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [[1,3,5,7,9,11,13,14,15],[2,4,6,8,10,12,16,17,18]] => [1,2,2,2,2,2,4,3] => [2,2,2,2,2,2,1,1,2,1,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [[1,3,5,7,9,11,13,15,16,18],[2,4,6,8,10,12,14,17,19,20]] => [1,2,2,2,2,2,2,3,2,2] => [2,2,2,2,2,2,2,1,2,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [[1,3,5,7,9,11,12,13,16],[2,4,6,8,10,14,15,17,18]] => [1,2,2,2,2,4,3,2] => [2,2,2,2,2,1,1,2,1,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [[1,3,5,7,9,11,13,14,16,18],[2,4,6,8,10,12,15,17,19,20]] => [1,2,2,2,2,2,3,2,2,2] => [2,2,2,2,2,2,1,2,2,2,1]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [[1,3,5,7,9,10,11,14,16],[2,4,6,8,12,13,15,17,18]] => [1,2,2,2,4,3,2,2] => [2,2,2,2,1,1,2,1,2,2,1]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [[1,3,5,7,9,11,12,14,16,18],[2,4,6,8,10,13,15,17,19,20]] => [1,2,2,2,2,3,2,2,2,2] => [2,2,2,2,2,1,2,2,2,2,1]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [[1,3,5,7,8,9,12,14,16],[2,4,6,10,11,13,15,17,18]] => [1,2,2,4,3,2,2,2] => [2,2,2,1,1,2,1,2,2,2,1]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [[1,3,5,7,9,10,12,14,16,18],[2,4,6,8,11,13,15,17,19,20]] => [1,2,2,2,3,2,2,2,2,2] => [2,2,2,2,1,2,2,2,2,2,1]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [[1,3,5,6,7,10,12,14,16],[2,4,8,9,11,13,15,17,18]] => [1,2,4,3,2,2,2,2] => [2,2,1,1,2,1,2,2,2,2,1]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,3,5,7,8,10,12,14,16,18],[2,4,6,9,11,13,15,17,19,20]] => [1,2,2,3,2,2,2,2,2,2] => [2,2,2,1,2,2,2,2,2,2,1]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,3,4,5,8,10,12,14,16],[2,6,7,9,11,13,15,17,18]] => [1,4,3,2,2,2,2,2] => [2,1,1,2,1,2,2,2,2,2,1]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,3,5,6,8,10,12,14,16,18],[2,4,7,9,11,13,15,17,19,20]] => [1,2,3,2,2,2,2,2,2,2] => [2,2,1,2,2,2,2,2,2,2,1]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,3,4,6,8,10,12,14,16,18],[2,5,7,9,11,13,15,17,19,20]] => [1,3,2,2,2,2,2,2,2,2] => [2,1,2,2,2,2,2,2,2,2,1]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [[1,2,4,6,8,10,12,14,16,18],[3,5,7,9,11,13,15,17,19,20]] => [2,2,2,2,2,2,2,2,2,2] => [1,2,2,2,2,2,2,2,2,2,1]
Map
to two-row standard tableau
Description
Return a standard tableau of shape $(n,n)$ where $n$ is the semilength of the Dyck path.
Given a Dyck path $D$, its image is given by recording the positions of the up-steps in the first row and the positions of the down-steps in the second row.
Map
horizontal strip sizes
Description
The composition of horizontal strip sizes.
We associate to a standard Young tableau $T$ the composition $(c_1,\dots,c_k)$, such that $k$ is minimal and the numbers $c_1+\dots+c_i + 1,\dots,c_1+\dots+c_{i+1}$ form a horizontal strip in $T$ for all $i$.
Map
complement
Description
The complement of a composition.
The complement of a composition $I$ is defined as follows:
If $I$ is the empty composition, then the complement is also the empty composition. Otherwise, let $S$ be the descent set corresponding to $I=(i_1,\dots,i_k)$, that is, the subset
$$\{ i_1, i_1 + i_2, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$$
of $\{ 1, 2, \ldots, |I|-1 \}$. Then, the complement of $I$ is the composition of the same size as $I$, whose descent set is $\{ 1, 2, \ldots, |I|-1 \} \setminus S$.
The complement of a composition $I$ coincides with the reversal (Mp00038reverse) of the composition conjugate (Mp00041conjugate) to $I$.