Identifier
-
Mp00043:
Integer partitions
—to Dyck path⟶
Dyck paths
Mp00024: Dyck paths —to 321-avoiding permutation⟶ Permutations
Mp00059: Permutations —Robinson-Schensted insertion tableau⟶ Standard tableaux
St000336: Standard tableaux ⟶ ℤ
Values
[1] => [1,0,1,0] => [2,1] => [[1],[2]] => 1
[2] => [1,1,0,0,1,0] => [3,1,2] => [[1,2],[3]] => 1
[1,1] => [1,0,1,1,0,0] => [2,3,1] => [[1,3],[2]] => 1
[3] => [1,1,1,0,0,0,1,0] => [4,1,2,3] => [[1,2,3],[4]] => 1
[2,1] => [1,0,1,0,1,0] => [2,1,3] => [[1,3],[2]] => 1
[1,1,1] => [1,0,1,1,1,0,0,0] => [2,3,4,1] => [[1,3,4],[2]] => 1
[4] => [1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [[1,2,3,4],[5]] => 1
[3,1] => [1,1,0,1,0,0,1,0] => [3,1,2,4] => [[1,2,4],[3]] => 1
[2,2] => [1,1,0,0,1,1,0,0] => [3,4,1,2] => [[1,2],[3,4]] => 2
[2,1,1] => [1,0,1,1,0,1,0,0] => [2,3,1,4] => [[1,3,4],[2]] => 1
[1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [[1,3,4,5],[2]] => 1
[5] => [1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [[1,2,3,4,5],[6]] => 1
[4,1] => [1,1,1,0,1,0,0,0,1,0] => [4,1,2,3,5] => [[1,2,3,5],[4]] => 1
[3,2] => [1,1,0,0,1,0,1,0] => [3,1,4,2] => [[1,2],[3,4]] => 2
[3,1,1] => [1,0,1,1,0,0,1,0] => [2,1,3,4] => [[1,3,4],[2]] => 1
[2,2,1] => [1,0,1,0,1,1,0,0] => [2,4,1,3] => [[1,3],[2,4]] => 2
[2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => [2,3,4,1,5] => [[1,3,4,5],[2]] => 1
[1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [[1,3,4,5,6],[2]] => 1
[6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [[1,2,3,4,5,6],[7]] => 1
[5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,4,6] => [[1,2,3,4,6],[5]] => 1
[4,2] => [1,1,1,0,0,1,0,0,1,0] => [4,1,2,5,3] => [[1,2,3],[4,5]] => 2
[4,1,1] => [1,1,0,1,1,0,0,0,1,0] => [3,1,2,4,5] => [[1,2,4,5],[3]] => 1
[3,3] => [1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [[1,2,3],[4,5]] => 2
[3,2,1] => [1,0,1,0,1,0,1,0] => [2,1,4,3] => [[1,3],[2,4]] => 2
[3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => [2,3,1,4,5] => [[1,3,4,5],[2]] => 1
[2,2,2] => [1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [[1,2,5],[3,4]] => 2
[2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => [2,3,5,1,4] => [[1,3,4],[2,5]] => 2
[2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => [2,3,4,5,1,6] => [[1,3,4,5,6],[2]] => 1
[1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [[1,3,4,5,6,7],[2]] => 1
[7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8]] => 1
[6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7] => [[1,2,3,4,5,7],[6]] => 1
[5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => [5,1,2,3,6,4] => [[1,2,3,4],[5,6]] => 2
[5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,5,6] => [[1,2,3,5,6],[4]] => 1
[4,3] => [1,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3] => [[1,2,3],[4,5]] => 2
[4,2,1] => [1,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4] => [[1,2,4],[3,5]] => 2
[4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => [2,1,3,4,5] => [[1,3,4,5],[2]] => 1
[3,3,1] => [1,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4] => [[1,2,4],[3,5]] => 2
[3,2,2] => [1,1,0,0,1,1,0,1,0,0] => [3,4,1,5,2] => [[1,2,5],[3,4]] => 2
[3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => [2,3,1,5,4] => [[1,3,4],[2,5]] => 2
[3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => [2,3,4,1,5,6] => [[1,3,4,5,6],[2]] => 1
[2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => [2,4,5,1,3] => [[1,3,5],[2,4]] => 2
[2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => [2,3,4,6,1,5] => [[1,3,4,5],[2,6]] => 2
[2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,3,4,5,6,1,7] => [[1,3,4,5,6,7],[2]] => 1
[1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [[1,3,4,5,6,7,8],[2]] => 1
[8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8],[9]] => 1
[7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,8] => [[1,2,3,4,5,6,8],[7]] => 1
[6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,1,2,3,4,7,5] => [[1,2,3,4,5],[6,7]] => 2
[6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7] => [[1,2,3,4,6,7],[5]] => 1
[5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,4] => [[1,2,3,4],[5,6]] => 2
[5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5] => [[1,2,3,5],[4,6]] => 2
[5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,4,5,6] => [[1,2,4,5,6],[3]] => 1
[4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [[1,2,3,4],[5,6]] => 2
[4,3,1] => [1,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4] => [[1,2,4],[3,5]] => 2
[4,2,2] => [1,1,0,0,1,1,0,0,1,0] => [3,1,4,5,2] => [[1,2,5],[3,4]] => 2
[4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => [2,1,3,5,4] => [[1,3,4],[2,5]] => 2
[4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => [2,3,1,4,5,6] => [[1,3,4,5,6],[2]] => 1
[3,3,2] => [1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,5] => [[1,2,5],[3,4]] => 2
[3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => [2,5,1,3,4] => [[1,3,4],[2,5]] => 2
[3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => [2,4,1,5,3] => [[1,3,5],[2,4]] => 2
[3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5] => [[1,3,4,5],[2,6]] => 2
[3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,3,4,5,1,6,7] => [[1,3,4,5,6,7],[2]] => 1
[2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [[1,2,5,6],[3,4]] => 2
[2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => [2,3,5,6,1,4] => [[1,3,4,6],[2,5]] => 2
[2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,4,5,7,1,6] => [[1,3,4,5,6],[2,7]] => 2
[2,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => [[1,3,4,5,6,7,8],[2]] => 1
[1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1] => [[1,3,4,5,6,7,8,9],[2]] => 1
[9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [10,1,2,3,4,5,6,7,8,9] => [[1,2,3,4,5,6,7,8,9],[10]] => 1
[7,2] => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,6] => [[1,2,3,4,5,6],[7,8]] => 2
[7,1,1] => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7,8] => [[1,2,3,4,5,7,8],[6]] => 1
[6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,1,2,3,7,4,5] => [[1,2,3,4,5],[6,7]] => 2
[6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [5,1,2,3,4,7,6] => [[1,2,3,4,6],[5,7]] => 2
[6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,6,7] => [[1,2,3,5,6,7],[4]] => 1
[5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => [5,1,6,2,3,4] => [[1,2,3,4],[5,6]] => 2
[5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => [4,1,2,6,3,5] => [[1,2,3,5],[4,6]] => 2
[5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => [4,1,2,5,6,3] => [[1,2,3,6],[4,5]] => 2
[5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5] => [[1,2,4,5],[3,6]] => 2
[5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,3,4,5,6] => [[1,3,4,5,6],[2]] => 1
[4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5] => [[1,2,3,5],[4,6]] => 2
[4,3,2] => [1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,5] => [[1,2,5],[3,4]] => 2
[4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => [2,1,5,3,4] => [[1,3,4],[2,5]] => 2
[4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => [2,1,4,5,3] => [[1,3,5],[2,4]] => 2
[4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5] => [[1,3,4,5],[2,6]] => 2
[4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,3,4,1,5,6,7] => [[1,3,4,5,6,7],[2]] => 1
[3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => [4,5,6,1,2,3] => [[1,2,3],[4,5,6]] => 3
[3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,5] => [[1,3,5],[2,4]] => 2
[3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5] => [[1,3,4,5],[2,6]] => 2
[3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => [3,4,5,1,6,2] => [[1,2,5,6],[3,4]] => 2
[3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => [2,3,5,1,6,4] => [[1,3,4,6],[2,5]] => 2
[3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,3,4,5,1,7,6] => [[1,3,4,5,6],[2,7]] => 2
[3,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => [[1,3,4,5,6,7,8],[2]] => 1
[2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,5,6,1,3] => [[1,3,5,6],[2,4]] => 2
[2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,6,7,1,5] => [[1,3,4,5,7],[2,6]] => 2
[2,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,4,5,6,8,1,7] => [[1,3,4,5,6,7],[2,8]] => 2
[2,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9] => [[1,3,4,5,6,7,8,9],[2]] => 1
[1,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,10,1] => [[1,3,4,5,6,7,8,9,10],[2]] => 1
[9,1] => [1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,8,10] => [[1,2,3,4,5,6,7,8,10],[9]] => 1
[8,2] => [1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,9,7] => [[1,2,3,4,5,6,7],[8,9]] => 2
[7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,1,2,3,4,8,5,6] => [[1,2,3,4,5,6],[7,8]] => 2
[7,2,1] => [1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5,8,7] => [[1,2,3,4,5,7],[6,8]] => 2
[7,1,1,1] => [1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7,8] => [[1,2,3,4,6,7,8],[5]] => 1
[6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,1,2,7,3,4,5] => [[1,2,3,4,5],[6,7]] => 2
>>> Load all 880 entries. <<<[6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [5,1,2,3,7,4,6] => [[1,2,3,4,6],[5,7]] => 2
[6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [5,1,2,3,6,7,4] => [[1,2,3,4,7],[5,6]] => 2
[6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [4,1,2,3,5,7,6] => [[1,2,3,5,6],[4,7]] => 2
[6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7] => [[1,2,4,5,6,7],[3]] => 1
[5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => [[1,2,3,4,5],[6,7]] => 2
[5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5] => [[1,2,3,5],[4,6]] => 2
[5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => [4,1,2,5,3,6] => [[1,2,3,6],[4,5]] => 2
[5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,6,4,5] => [[1,2,4,5],[3,6]] => 2
[5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,6,4] => [[1,2,4,6],[3,5]] => 2
[5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5] => [[1,3,4,5],[2,6]] => 2
[5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,3,1,4,5,6,7] => [[1,3,4,5,6,7],[2]] => 1
[4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => [4,5,1,2,3,6] => [[1,2,3,6],[4,5]] => 2
[4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5] => [[1,2,4,5],[3,6]] => 2
[4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => [4,5,1,6,2,3] => [[1,2,3],[4,5,6]] => 3
[4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,5] => [[1,3,5],[2,4]] => 2
[4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => [2,3,1,6,4,5] => [[1,3,4,5],[2,6]] => 2
[4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => [3,4,1,5,6,2] => [[1,2,5,6],[3,4]] => 2
[4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => [2,3,1,5,6,4] => [[1,3,4,6],[2,5]] => 2
[4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [2,3,4,1,5,7,6] => [[1,3,4,5,6],[2,7]] => 2
[4,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [2,3,4,5,1,6,7,8] => [[1,3,4,5,6,7,8],[2]] => 1
[3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => [3,5,6,1,2,4] => [[1,2,4],[3,5,6]] => 3
[3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => [3,4,5,1,2,6] => [[1,2,5,6],[3,4]] => 2
[3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,6] => [[1,3,4,6],[2,5]] => 2
[3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,3,4,7,1,5,6] => [[1,3,4,5,6],[2,7]] => 2
[3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,5,1,6,3] => [[1,3,5,6],[2,4]] => 2
[3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,3,4,6,1,7,5] => [[1,3,4,5,7],[2,6]] => 2
[3,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,3,4,5,6,1,8,7] => [[1,3,4,5,6,7],[2,8]] => 2
[3,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9] => [[1,3,4,5,6,7,8,9],[2]] => 1
[2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [[1,2,5,6,7],[3,4]] => 2
[2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,5,6,7,1,4] => [[1,3,4,6,7],[2,5]] => 2
[2,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,5,7,8,1,6] => [[1,3,4,5,6,8],[2,7]] => 2
[2,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,9,1,10] => [[1,3,4,5,6,7,8,9,10],[2]] => 1
[9,2] => [1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,7,10,8] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[9,1,1] => [1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7,9,10] => [[1,2,3,4,5,6,7,9,10],[8]] => 1
[8,3] => [1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0] => [8,1,2,3,4,5,9,6,7] => [[1,2,3,4,5,6,7],[8,9]] => 2
[8,2,1] => [1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,9,8] => [[1,2,3,4,5,6,8],[7,9]] => 2
[7,4] => [1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [7,1,2,3,8,4,5,6] => [[1,2,3,4,5,6],[7,8]] => 2
[7,3,1] => [1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [6,1,2,3,4,8,5,7] => [[1,2,3,4,5,7],[6,8]] => 2
[7,2,2] => [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,7,8,5] => [[1,2,3,4,5,8],[6,7]] => 2
[7,2,1,1] => [1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0] => [5,1,2,3,4,6,8,7] => [[1,2,3,4,6,7],[5,8]] => 2
[7,1,1,1,1] => [1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [4,1,2,3,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => 1
[6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [6,1,7,2,3,4,5] => [[1,2,3,4,5],[6,7]] => 2
[6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,7,3,4,6] => [[1,2,3,4,6],[5,7]] => 2
[6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [5,1,2,3,6,4,7] => [[1,2,3,4,7],[5,6]] => 2
[6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [4,1,2,3,7,5,6] => [[1,2,3,5,6],[4,7]] => 2
[6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,7,5] => [[1,2,3,5,7],[4,6]] => 2
[6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,1,2,4,5,7,6] => [[1,2,4,5,6],[3,7]] => 2
[6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7] => [[1,3,4,5,6,7],[2]] => 1
[5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [5,7,1,2,3,4,6] => [[1,2,3,4,6],[5,7]] => 2
[5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0] => [4,1,5,2,3,6] => [[1,2,3,6],[4,5]] => 2
[5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5] => [[1,2,4,5],[3,6]] => 2
[5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0] => [4,1,5,6,2,3] => [[1,2,3],[4,5,6]] => 3
[5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,6] => [[1,2,4,6],[3,5]] => 2
[5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5] => [[1,3,4,5],[2,6]] => 2
[5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0] => [3,1,4,5,6,2] => [[1,2,5,6],[3,4]] => 2
[5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,3,5,6,4] => [[1,3,4,6],[2,5]] => 2
[5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [2,3,1,4,5,7,6] => [[1,3,4,5,6],[2,7]] => 2
[5,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [2,3,4,1,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => 1
[4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0] => [4,5,1,2,6,3] => [[1,2,3],[4,5,6]] => 3
[4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,6] => [[1,2,4,6],[3,5]] => 2
[4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => [2,6,1,3,4,5] => [[1,3,4,5],[2,6]] => 2
[4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,6,2,4] => [[1,2,4],[3,5,6]] => 3
[4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0] => [3,4,1,5,2,6] => [[1,2,5,6],[3,4]] => 2
[4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,6] => [[1,3,4,6],[2,5]] => 2
[4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [2,3,4,1,7,5,6] => [[1,3,4,5,6],[2,7]] => 2
[4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,5,6,3] => [[1,3,5,6],[2,4]] => 2
[4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [2,3,4,1,6,7,5] => [[1,3,4,5,7],[2,6]] => 2
[4,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [2,3,4,5,1,6,8,7] => [[1,3,4,5,6,7],[2,8]] => 2
[4,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => 1
[3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5] => [[1,2,5],[3,4,6]] => 3
[3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0] => [2,5,6,1,3,4] => [[1,3,4],[2,5,6]] => 3
[3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,5,1,3,6] => [[1,3,5,6],[2,4]] => 2
[3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [2,3,4,6,1,5,7] => [[1,3,4,5,7],[2,6]] => 2
[3,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,3,4,5,8,1,6,7] => [[1,3,4,5,6,7],[2,8]] => 2
[3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,4,5,6,1,7,2] => [[1,2,5,6,7],[3,4]] => 2
[3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [2,3,5,6,1,7,4] => [[1,3,4,6,7],[2,5]] => 2
[3,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,3,4,5,7,1,8,6] => [[1,3,4,5,6,8],[2,7]] => 2
[3,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => 1
[2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,4,5,6,7,1,3] => [[1,3,5,6,7],[2,4]] => 2
[2,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,6,7,8,1,5] => [[1,3,4,5,7,8],[2,6]] => 2
[9,3] => [1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0] => [9,1,2,3,4,5,6,10,7,8] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[9,2,1] => [1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7,10,9] => [[1,2,3,4,5,6,7,9],[8,10]] => 2
[9,1,1,1] => [1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6,8,9,10] => [[1,2,3,4,5,6,8,9,10],[7]] => 1
[8,4] => [1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,1,0] => [8,1,2,3,4,9,5,6,7] => [[1,2,3,4,5,6,7],[8,9]] => 2
[8,3,1] => [1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0] => [7,1,2,3,4,5,9,6,8] => [[1,2,3,4,5,6,8],[7,9]] => 2
[7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [7,1,2,8,3,4,5,6] => [[1,2,3,4,5,6],[7,8]] => 2
[7,4,1] => [1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [6,1,2,3,8,4,5,7] => [[1,2,3,4,5,7],[6,8]] => 2
[7,3,2] => [1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0] => [6,1,2,3,4,7,5,8] => [[1,2,3,4,5,8],[6,7]] => 2
[7,3,1,1] => [1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [5,1,2,3,4,8,6,7] => [[1,2,3,4,6,7],[5,8]] => 2
[7,2,2,1] => [1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [5,1,2,3,4,7,8,6] => [[1,2,3,4,6,8],[5,7]] => 2
[7,2,1,1,1] => [1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0] => [4,1,2,3,5,6,8,7] => [[1,2,3,5,6,7],[4,8]] => 2
[7,1,1,1,1,1] => [1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => 1
[6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => [[1,2,3,4,5,6],[7,8]] => 2
[6,5,1] => [1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [5,1,7,2,3,4,6] => [[1,2,3,4,6],[5,7]] => 2
[6,4,2] => [1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [5,1,2,6,3,4,7] => [[1,2,3,4,7],[5,6]] => 2
[6,4,1,1] => [1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [4,1,2,7,3,5,6] => [[1,2,3,5,6],[4,7]] => 2
[6,3,3] => [1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [5,1,2,6,7,3,4] => [[1,2,3,4],[5,6,7]] => 3
[6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5,7] => [[1,2,3,5,7],[4,6]] => 2
[6,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [3,1,2,4,7,5,6] => [[1,2,4,5,6],[3,7]] => 2
[6,2,2,2] => [1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [4,1,2,5,6,7,3] => [[1,2,3,6,7],[4,5]] => 2
[6,2,2,1,1] => [1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [3,1,2,4,6,7,5] => [[1,2,4,5,7],[3,6]] => 2
[6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [2,1,3,4,5,7,6] => [[1,3,4,5,6],[2,7]] => 2
[6,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [2,3,1,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => 1
[5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [5,6,1,2,3,4,7] => [[1,2,3,4,7],[5,6]] => 2
[5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [4,7,1,2,3,5,6] => [[1,2,3,5,6],[4,7]] => 2
[5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => [4,1,5,2,6,3] => [[1,2,3],[4,5,6]] => 3
[5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,6] => [[1,2,4,6],[3,5]] => 2
[5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5] => [[1,3,4,5],[2,6]] => 2
[5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,6,2,4] => [[1,2,4],[3,5,6]] => 3
[5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => [3,1,4,5,2,6] => [[1,2,5,6],[3,4]] => 2
[5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,3,5,4,6] => [[1,3,4,6],[2,5]] => 2
[5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [2,3,1,4,7,5,6] => [[1,3,4,5,6],[2,7]] => 2
[5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,5,6,3] => [[1,3,5,6],[2,4]] => 2
[5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [2,3,1,4,6,7,5] => [[1,3,4,5,7],[2,6]] => 2
[5,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [2,3,4,1,5,6,8,7] => [[1,3,4,5,6,7],[2,8]] => 2
[5,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [2,3,4,5,1,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => 1
[4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [[1,2,3,4],[5,6,7]] => 3
[4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,6,4] => [[1,2,4],[3,5,6]] => 3
[4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => [3,4,1,2,5,6] => [[1,2,5,6],[3,4]] => 2
[4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => [2,5,1,3,4,6] => [[1,3,4,6],[2,5]] => 2
[4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [2,3,7,1,4,5,6] => [[1,3,4,5,6],[2,7]] => 2
[4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5] => [[1,2,5],[3,4,6]] => 3
[4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => [2,5,1,6,3,4] => [[1,3,4],[2,5,6]] => 3
[4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,5,3,6] => [[1,3,5,6],[2,4]] => 2
[4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5,7] => [[1,3,4,5,7],[2,6]] => 2
[4,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [2,3,4,5,1,8,6,7] => [[1,3,4,5,6,7],[2,8]] => 2
[4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [3,4,5,1,6,7,2] => [[1,2,5,6,7],[3,4]] => 2
[4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [2,3,5,1,6,7,4] => [[1,3,4,6,7],[2,5]] => 2
[4,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [2,3,4,5,1,7,8,6] => [[1,3,4,5,6,8],[2,7]] => 2
[4,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => 1
[3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [[1,2,3,7],[4,5,6]] => 3
[3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5] => [[1,3,5],[2,4,6]] => 3
[3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [2,3,6,7,1,4,5] => [[1,3,4,5],[2,6,7]] => 3
[3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [3,4,5,6,1,2,7] => [[1,2,5,6,7],[3,4]] => 2
[3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [2,3,5,6,1,4,7] => [[1,3,4,6,7],[2,5]] => 2
[3,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,3,4,5,7,1,6,8] => [[1,3,4,5,6,8],[2,7]] => 2
[3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [2,4,5,6,1,7,3] => [[1,3,5,6,7],[2,4]] => 2
[2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => [[1,2,5,6,7,8],[3,4]] => 2
[2,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,5,6,7,8,1,4] => [[1,3,4,6,7,8],[2,5]] => 2
[9,1,1,1,1] => [1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [6,1,2,3,4,5,7,8,9,10] => [[1,2,3,4,5,7,8,9,10],[6]] => 1
[8,5] => [1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0] => [8,1,2,3,9,4,5,6,7] => [[1,2,3,4,5,6,7],[8,9]] => 2
[7,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [7,1,8,2,3,4,5,6] => [[1,2,3,4,5,6],[7,8]] => 2
[7,5,1] => [1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0] => [6,1,2,8,3,4,5,7] => [[1,2,3,4,5,7],[6,8]] => 2
[7,4,2] => [1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [6,1,2,3,7,4,5,8] => [[1,2,3,4,5,8],[6,7]] => 2
[7,4,1,1] => [1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0] => [5,1,2,3,8,4,6,7] => [[1,2,3,4,6,7],[5,8]] => 2
[7,3,3] => [1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [6,1,2,3,7,8,4,5] => [[1,2,3,4,5],[6,7,8]] => 3
[7,3,1,1,1] => [1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [4,1,2,3,5,8,6,7] => [[1,2,3,5,6,7],[4,8]] => 2
[7,2,2,2] => [1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [5,1,2,3,6,7,8,4] => [[1,2,3,4,7,8],[5,6]] => 2
[7,2,2,1,1] => [1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0] => [4,1,2,3,5,7,8,6] => [[1,2,3,5,6,8],[4,7]] => 2
[7,2,1,1,1,1] => [1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [3,1,2,4,5,6,8,7] => [[1,2,4,5,6,7],[3,8]] => 2
[7,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => 1
[6,6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [6,8,1,2,3,4,5,7] => [[1,2,3,4,5,7],[6,8]] => 2
[6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [5,1,6,2,3,4,7] => [[1,2,3,4,7],[5,6]] => 2
[6,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [4,1,7,2,3,5,6] => [[1,2,3,5,6],[4,7]] => 2
[6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [5,1,2,6,3,7,4] => [[1,2,3,4],[5,6,7]] => 3
[6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [4,1,2,6,3,5,7] => [[1,2,3,5,7],[4,6]] => 2
[6,4,1,1,1] => [1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [3,1,2,7,4,5,6] => [[1,2,4,5,6],[3,7]] => 2
[6,3,3,1] => [1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [4,1,2,6,7,3,5] => [[1,2,3,5],[4,6,7]] => 3
[6,3,2,2] => [1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [4,1,2,5,6,3,7] => [[1,2,3,6,7],[4,5]] => 2
[6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5,7] => [[1,2,4,5,7],[3,6]] => 2
[6,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [2,1,3,4,7,5,6] => [[1,3,4,5,6],[2,7]] => 2
[6,2,2,2,1] => [1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [3,1,2,5,6,7,4] => [[1,2,4,6,7],[3,5]] => 2
[6,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [2,1,3,4,6,7,5] => [[1,3,4,5,7],[2,6]] => 2
[6,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [2,3,1,4,5,6,8,7] => [[1,3,4,5,6,7],[2,8]] => 2
[6,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [2,3,4,1,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => 1
[5,5,3] => [1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [5,6,1,2,3,7,4] => [[1,2,3,4],[5,6,7]] => 3
[5,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5,7] => [[1,2,3,5,7],[4,6]] => 2
[5,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [3,7,1,2,4,5,6] => [[1,2,4,5,6],[3,7]] => 2
[5,4,4] => [1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [5,6,1,7,2,3,4] => [[1,2,3,4],[5,6,7]] => 3
[5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,6,4] => [[1,2,4],[3,5,6]] => 3
[5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0] => [3,1,4,2,5,6] => [[1,2,5,6],[3,4]] => 2
[5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,6] => [[1,3,4,6],[2,5]] => 2
[5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,3,1,7,4,5,6] => [[1,3,4,5,6],[2,7]] => 2
[5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5] => [[1,2,5],[3,4,6]] => 3
[5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,5,6,3,4] => [[1,3,4],[2,5,6]] => 3
[5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,5,3,6] => [[1,3,5,6],[2,4]] => 2
[5,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5,7] => [[1,3,4,5,7],[2,6]] => 2
[5,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [2,3,4,1,5,8,6,7] => [[1,3,4,5,6,7],[2,8]] => 2
[5,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [3,4,1,5,6,7,2] => [[1,2,5,6,7],[3,4]] => 2
[5,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [2,3,1,5,6,7,4] => [[1,3,4,6,7],[2,5]] => 2
[5,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [2,3,4,1,5,7,8,6] => [[1,3,4,5,6,8],[2,7]] => 2
[5,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => 1
[4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [4,6,7,1,2,3,5] => [[1,2,3,5],[4,6,7]] => 3
[4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5] => [[1,2,5],[3,4,6]] => 3
[4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0] => [2,5,1,3,6,4] => [[1,3,4],[2,5,6]] => 3
[4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,5,6] => [[1,3,5,6],[2,4]] => 2
[4,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [2,3,6,1,4,5,7] => [[1,3,4,5,7],[2,6]] => 2
[4,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [2,3,4,8,1,5,6,7] => [[1,3,4,5,6,7],[2,8]] => 2
[4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [4,5,6,1,7,2,3] => [[1,2,3,7],[4,5,6]] => 3
[4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5] => [[1,3,5],[2,4,6]] => 3
[4,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [2,3,6,1,7,4,5] => [[1,3,4,5],[2,6,7]] => 3
[4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [3,4,5,1,6,2,7] => [[1,2,5,6,7],[3,4]] => 2
[4,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [2,3,5,1,6,4,7] => [[1,3,4,6,7],[2,5]] => 2
[4,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [2,3,4,5,1,7,6,8] => [[1,3,4,5,6,8],[2,7]] => 2
[4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [2,4,5,1,6,7,3] => [[1,3,5,6,7],[2,4]] => 2
[4,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [2,3,4,6,1,7,8,5] => [[1,3,4,5,7,8],[2,6]] => 2
[3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,5,6,7,1,2,4] => [[1,2,4,7],[3,5,6]] => 3
[3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,7,1,2,6] => [[1,2,5,6],[3,4,7]] => 3
[3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [2,3,5,7,1,4,6] => [[1,3,4,6],[2,5,7]] => 3
[3,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,3,4,7,8,1,5,6] => [[1,3,4,5,6],[2,7,8]] => 3
[3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [2,4,5,6,1,3,7] => [[1,3,5,6,7],[2,4]] => 2
[3,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,3,4,6,7,1,5,8] => [[1,3,4,5,7,8],[2,6]] => 2
[3,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,4,5,6,7,1,8,2] => [[1,2,5,6,7,8],[3,4]] => 2
[2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,4,5,6,7,8,1,3] => [[1,3,5,6,7,8],[2,4]] => 2
[9,5] => [1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0] => [9,1,2,3,4,10,5,6,7,8] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[9,1,1,1,1,1] => [1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [5,1,2,3,4,6,7,8,9,10] => [[1,2,3,4,6,7,8,9,10],[5]] => 1
[8,6] => [1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0] => [8,1,2,9,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8,9]] => 2
[8,1,1,1,1,1,1] => [1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7,8,9] => [[1,2,4,5,6,7,8,9],[3]] => 1
[7,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => [8,9,1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8,9]] => 2
[7,6,1] => [1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [6,1,8,2,3,4,5,7] => [[1,2,3,4,5,7],[6,8]] => 2
[7,5,2] => [1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0] => [6,1,2,7,3,4,5,8] => [[1,2,3,4,5,8],[6,7]] => 2
[7,5,1,1] => [1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0] => [5,1,2,8,3,4,6,7] => [[1,2,3,4,6,7],[5,8]] => 2
[7,4,3] => [1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [6,1,2,3,7,4,8,5] => [[1,2,3,4,5],[6,7,8]] => 3
[7,4,1,1,1] => [1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [4,1,2,3,8,5,6,7] => [[1,2,3,5,6,7],[4,8]] => 2
[7,3,3,1] => [1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0] => [5,1,2,3,7,8,4,6] => [[1,2,3,4,6],[5,7,8]] => 3
[7,3,2,2] => [1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0] => [5,1,2,3,6,7,4,8] => [[1,2,3,4,7,8],[5,6]] => 2
[7,3,2,1,1] => [1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0] => [4,1,2,3,5,7,6,8] => [[1,2,3,5,6,8],[4,7]] => 2
[7,3,1,1,1,1] => [1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0] => [3,1,2,4,5,8,6,7] => [[1,2,4,5,6,7],[3,8]] => 2
[7,2,2,2,1] => [1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [4,1,2,3,6,7,8,5] => [[1,2,3,5,7,8],[4,6]] => 2
[7,2,2,1,1,1] => [1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [3,1,2,4,5,7,8,6] => [[1,2,4,5,6,8],[3,7]] => 2
[7,2,1,1,1,1,1] => [1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [2,1,3,4,5,6,8,7] => [[1,3,4,5,6,7],[2,8]] => 2
[7,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [2,3,1,4,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => 1
[6,6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5,8] => [[1,2,3,4,5,8],[6,7]] => 2
[6,6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [5,8,1,2,3,4,6,7] => [[1,2,3,4,6,7],[5,8]] => 2
[6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [5,1,6,2,3,7,4] => [[1,2,3,4],[5,6,7]] => 3
[6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5,7] => [[1,2,3,5,7],[4,6]] => 2
[6,5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [3,1,7,2,4,5,6] => [[1,2,4,5,6],[3,7]] => 2
[6,4,4] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [5,1,6,7,2,3,4] => [[1,2,3,4],[5,6,7]] => 3
[6,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,2,6,3,7,5] => [[1,2,3,5],[4,6,7]] => 3
[6,4,2,2] => [1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [4,1,2,5,3,6,7] => [[1,2,3,6,7],[4,5]] => 2
[6,4,2,1,1] => [1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [3,1,2,6,4,5,7] => [[1,2,4,5,7],[3,6]] => 2
[6,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [2,1,3,7,4,5,6] => [[1,3,4,5,6],[2,7]] => 2
[6,3,3,2] => [1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [4,1,2,5,7,3,6] => [[1,2,3,6],[4,5,7]] => 3
[6,3,3,1,1] => [1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [3,1,2,6,7,4,5] => [[1,2,4,5],[3,6,7]] => 3
[6,3,2,2,1] => [1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [3,1,2,5,6,4,7] => [[1,2,4,6,7],[3,5]] => 2
[6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5,7] => [[1,3,4,5,7],[2,6]] => 2
[6,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [2,3,1,4,5,8,6,7] => [[1,3,4,5,6,7],[2,8]] => 2
[6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [3,1,4,5,6,7,2] => [[1,2,5,6,7],[3,4]] => 2
[6,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [2,1,3,5,6,7,4] => [[1,3,4,6,7],[2,5]] => 2
[6,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [2,3,1,4,5,7,8,6] => [[1,3,4,5,6,8],[2,7]] => 2
[6,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [2,3,4,5,1,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => 1
[5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [5,6,1,2,7,3,4] => [[1,2,3,4],[5,6,7]] => 3
[5,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [4,6,1,2,3,7,5] => [[1,2,3,5],[4,6,7]] => 3
[5,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3,6,7] => [[1,2,3,6,7],[4,5]] => 2
[5,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [3,6,1,2,4,5,7] => [[1,2,4,5,7],[3,6]] => 2
[5,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [2,7,1,3,4,5,6] => [[1,3,4,5,6],[2,7]] => 2
[5,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [4,6,1,7,2,3,5] => [[1,2,3,5],[4,6,7]] => 3
[5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5] => [[1,2,5],[3,4,6]] => 3
[5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,5,3,6,4] => [[1,3,4],[2,5,6]] => 3
[5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,5,6] => [[1,3,5,6],[2,4]] => 2
[5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,3,1,6,4,5,7] => [[1,3,4,5,7],[2,6]] => 2
[5,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [2,3,4,1,8,5,6,7] => [[1,3,4,5,6,7],[2,8]] => 2
[5,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [4,5,1,6,7,2,3] => [[1,2,3,7],[4,5,6]] => 3
[5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5] => [[1,3,5],[2,4,6]] => 3
[5,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [2,3,1,6,7,4,5] => [[1,3,4,5],[2,6,7]] => 3
[5,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [3,4,1,5,6,2,7] => [[1,2,5,6,7],[3,4]] => 2
[5,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [2,3,1,5,6,4,7] => [[1,3,4,6,7],[2,5]] => 2
[5,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [2,3,4,1,5,7,6,8] => [[1,3,4,5,6,8],[2,7]] => 2
[5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1,5,6,7,3] => [[1,3,5,6,7],[2,4]] => 2
[5,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [2,3,4,1,6,7,8,5] => [[1,3,4,5,7,8],[2,6]] => 2
[4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [4,5,7,1,2,3,6] => [[1,2,3,6],[4,5,7]] => 3
[4,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [3,6,7,1,2,4,5] => [[1,2,4,5],[3,6,7]] => 3
[4,4,3,3] => [1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [4,5,6,1,2,7,3] => [[1,2,3,7],[4,5,6]] => 3
[4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5] => [[1,3,5],[2,4,6]] => 3
[4,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [2,3,6,1,4,7,5] => [[1,3,4,5],[2,6,7]] => 3
[4,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [3,4,5,1,2,6,7] => [[1,2,5,6,7],[3,4]] => 2
[4,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [2,3,5,1,4,6,7] => [[1,3,4,6,7],[2,5]] => 2
[4,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [2,3,4,7,1,5,6,8] => [[1,3,4,5,6,8],[2,7]] => 2
[4,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [3,5,6,1,7,2,4] => [[1,2,4,7],[3,5,6]] => 3
[4,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [3,4,5,1,7,2,6] => [[1,2,5,6],[3,4,7]] => 3
[4,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [2,3,5,1,7,4,6] => [[1,3,4,6],[2,5,7]] => 3
[4,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [2,3,4,7,1,8,5,6] => [[1,3,4,5,6],[2,7,8]] => 3
[4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,4,5,1,6,3,7] => [[1,3,5,6,7],[2,4]] => 2
[4,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,4,5,6,1,7,8,2] => [[1,2,5,6,7,8],[3,4]] => 2
[4,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [2,3,5,6,1,7,8,4] => [[1,3,4,6,7,8],[2,5]] => 2
[3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,4,6,7,1,2,5] => [[1,2,5,7],[3,4,6]] => 3
[3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [2,5,6,7,1,3,4] => [[1,3,4,7],[2,5,6]] => 3
[3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [2,4,5,7,1,3,6] => [[1,3,5,6],[2,4,7]] => 3
[3,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,3,4,6,8,1,5,7] => [[1,3,4,5,7],[2,6,8]] => 3
[3,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2,8] => [[1,2,5,6,7,8],[3,4]] => 2
[3,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,3,5,6,7,1,4,8] => [[1,3,4,6,7,8],[2,5]] => 2
[3,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,4,5,6,7,1,8,3] => [[1,3,5,6,7,8],[2,4]] => 2
[2,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,2] => [[1,2,5,6,7,8,9],[3,4]] => 2
[9,2,2,2] => [1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,8,9,10,6] => [[1,2,3,4,5,6,9,10],[7,8]] => 2
[9,1,1,1,1,1,1] => [1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [4,1,2,3,5,6,7,8,9,10] => [[1,2,3,5,6,7,8,9,10],[4]] => 1
[8,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [8,1,9,2,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8,9]] => 2
[8,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => 1
[7,7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0] => [7,9,1,2,3,4,5,6,8] => [[1,2,3,4,5,6,8],[7,9]] => 2
[7,6,2] => [1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0] => [6,1,7,2,3,4,5,8] => [[1,2,3,4,5,8],[6,7]] => 2
[7,6,1,1] => [1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [5,1,8,2,3,4,6,7] => [[1,2,3,4,6,7],[5,8]] => 2
[7,5,3] => [1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [6,1,2,7,3,4,8,5] => [[1,2,3,4,5],[6,7,8]] => 3
[7,5,2,1] => [1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [5,1,2,7,3,4,6,8] => [[1,2,3,4,6,8],[5,7]] => 2
[7,5,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [4,1,2,8,3,5,6,7] => [[1,2,3,5,6,7],[4,8]] => 2
[7,4,4] => [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [6,1,2,7,8,3,4,5] => [[1,2,3,4,5],[6,7,8]] => 3
[7,4,3,1] => [1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [5,1,2,3,7,4,8,6] => [[1,2,3,4,6],[5,7,8]] => 3
[7,4,2,2] => [1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [5,1,2,3,6,4,7,8] => [[1,2,3,4,7,8],[5,6]] => 2
[7,4,2,1,1] => [1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0] => [4,1,2,3,7,5,6,8] => [[1,2,3,5,6,8],[4,7]] => 2
[7,4,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [3,1,2,4,8,5,6,7] => [[1,2,4,5,6,7],[3,8]] => 2
[7,3,3,2] => [1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0] => [5,1,2,3,6,8,4,7] => [[1,2,3,4,7],[5,6,8]] => 3
[7,3,3,1,1] => [1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [4,1,2,3,7,8,5,6] => [[1,2,3,5,6],[4,7,8]] => 3
[7,3,2,2,1] => [1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [4,1,2,3,6,7,5,8] => [[1,2,3,5,7,8],[4,6]] => 2
[7,3,2,1,1,1] => [1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0] => [3,1,2,4,5,7,6,8] => [[1,2,4,5,6,8],[3,7]] => 2
[7,3,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [2,1,3,4,5,8,6,7] => [[1,3,4,5,6,7],[2,8]] => 2
[7,2,2,2,2] => [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [4,1,2,5,6,7,8,3] => [[1,2,3,6,7,8],[4,5]] => 2
[7,2,2,2,1,1] => [1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0] => [3,1,2,4,6,7,8,5] => [[1,2,4,5,7,8],[3,6]] => 2
[7,2,2,1,1,1,1] => [1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [2,1,3,4,5,7,8,6] => [[1,3,4,5,6,8],[2,7]] => 2
[7,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [2,3,4,1,5,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => 1
[6,6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [6,7,1,2,3,4,8,5] => [[1,2,3,4,5],[6,7,8]] => 3
[6,6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [5,7,1,2,3,4,6,8] => [[1,2,3,4,6,8],[5,7]] => 2
[6,6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [4,8,1,2,3,5,6,7] => [[1,2,3,5,6,7],[4,8]] => 2
[6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [5,1,6,2,7,3,4] => [[1,2,3,4],[5,6,7]] => 3
[6,5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,6,2,3,7,5] => [[1,2,3,5],[4,6,7]] => 3
[6,5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [4,1,5,2,3,6,7] => [[1,2,3,6,7],[4,5]] => 2
[6,5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5,7] => [[1,2,4,5,7],[3,6]] => 2
[6,5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [2,1,7,3,4,5,6] => [[1,3,4,5,6],[2,7]] => 2
[6,4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [4,1,6,7,2,3,5] => [[1,2,3,5],[4,6,7]] => 3
[6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [4,1,2,5,3,7,6] => [[1,2,3,6],[4,5,7]] => 3
[6,4,3,1,1] => [1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [3,1,2,6,4,7,5] => [[1,2,4,5],[3,6,7]] => 3
[6,4,2,2,1] => [1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [3,1,2,5,4,6,7] => [[1,2,4,6,7],[3,5]] => 2
[6,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [2,1,3,6,4,5,7] => [[1,3,4,5,7],[2,6]] => 2
[6,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [2,3,1,4,8,5,6,7] => [[1,3,4,5,6,7],[2,8]] => 2
[6,3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [4,1,5,6,7,2,3] => [[1,2,3,7],[4,5,6]] => 3
[6,3,3,2,1] => [1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [3,1,2,5,7,4,6] => [[1,2,4,6],[3,5,7]] => 3
[6,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [2,1,3,6,7,4,5] => [[1,3,4,5],[2,6,7]] => 3
[6,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [3,1,4,5,6,2,7] => [[1,2,5,6,7],[3,4]] => 2
[6,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [2,1,3,5,6,4,7] => [[1,3,4,6,7],[2,5]] => 2
[6,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [2,3,1,4,5,7,6,8] => [[1,3,4,5,6,8],[2,7]] => 2
[6,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [2,1,4,5,6,7,3] => [[1,3,5,6,7],[2,4]] => 2
[6,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [2,3,1,4,6,7,8,5] => [[1,3,4,5,7,8],[2,6]] => 2
[5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => [[1,2,3,4,5],[6,7,8]] => 3
[5,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [4,6,1,2,7,3,5] => [[1,2,3,5],[4,6,7]] => 3
[5,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [4,5,1,2,3,7,6] => [[1,2,3,6],[4,5,7]] => 3
[5,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [3,6,1,2,4,7,5] => [[1,2,4,5],[3,6,7]] => 3
[5,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [3,5,1,2,4,6,7] => [[1,2,4,6,7],[3,5]] => 2
[5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [2,6,1,3,4,5,7] => [[1,3,4,5,7],[2,6]] => 2
[5,5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [2,3,8,1,4,5,6,7] => [[1,3,4,5,6,7],[2,8]] => 2
[5,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [4,5,1,7,2,3,6] => [[1,2,3,6],[4,5,7]] => 3
[5,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [3,6,1,7,2,4,5] => [[1,2,4,5],[3,6,7]] => 3
[5,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [4,5,1,6,2,7,3] => [[1,2,3,7],[4,5,6]] => 3
[5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5] => [[1,3,5],[2,4,6]] => 3
[5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,3,1,6,4,7,5] => [[1,3,4,5],[2,6,7]] => 3
[5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [3,4,1,5,2,6,7] => [[1,2,5,6,7],[3,4]] => 2
[5,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [2,3,1,5,4,6,7] => [[1,3,4,6,7],[2,5]] => 2
[5,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [2,3,4,1,7,5,6,8] => [[1,3,4,5,6,8],[2,7]] => 2
[5,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [3,5,1,6,7,2,4] => [[1,2,4,7],[3,5,6]] => 3
[5,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [3,4,1,5,7,2,6] => [[1,2,5,6],[3,4,7]] => 3
[5,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [2,3,1,5,7,4,6] => [[1,3,4,6],[2,5,7]] => 3
[5,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [2,3,4,1,7,8,5,6] => [[1,3,4,5,6],[2,7,8]] => 3
[5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,4,1,5,6,3,7] => [[1,3,5,6,7],[2,4]] => 2
[5,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [2,3,4,1,6,7,5,8] => [[1,3,4,5,7,8],[2,6]] => 2
[5,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [3,4,5,1,6,7,8,2] => [[1,2,5,6,7,8],[3,4]] => 2
[5,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [2,3,5,1,6,7,8,4] => [[1,3,4,6,7,8],[2,5]] => 2
[4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [4,5,6,1,2,3,7] => [[1,2,3,7],[4,5,6]] => 3
[4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,5,7,1,2,4,6] => [[1,2,4,6],[3,5,7]] => 3
[4,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [2,6,7,1,3,4,5] => [[1,3,4,5],[2,6,7]] => 3
[4,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [3,5,6,1,2,7,4] => [[1,2,4,7],[3,5,6]] => 3
[4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [3,4,5,1,2,7,6] => [[1,2,5,6],[3,4,7]] => 3
[4,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,7,6] => [[1,3,4,6],[2,5,7]] => 3
[4,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [2,3,4,7,1,5,8,6] => [[1,3,4,5,6],[2,7,8]] => 3
[4,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [2,4,5,1,3,6,7] => [[1,3,5,6,7],[2,4]] => 2
[4,4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [2,3,4,6,1,5,7,8] => [[1,3,4,5,7,8],[2,6]] => 2
[4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [3,4,6,1,7,2,5] => [[1,2,5,7],[3,4,6]] => 3
[4,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [2,5,6,1,7,3,4] => [[1,3,4,7],[2,5,6]] => 3
[4,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [2,4,5,1,7,3,6] => [[1,3,5,6],[2,4,7]] => 3
[4,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [2,3,4,6,1,8,5,7] => [[1,3,4,5,7],[2,6,8]] => 3
[4,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,4,5,6,1,7,2,8] => [[1,2,5,6,7,8],[3,4]] => 2
[4,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [2,4,5,6,1,7,8,3] => [[1,3,5,6,7,8],[2,4]] => 2
[3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3] => [[1,2,3,7,8],[4,5,6]] => 3
[3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,6,7,1,3,5] => [[1,3,5,7],[2,4,6]] => 3
[3,3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,3,6,7,8,1,4,5] => [[1,3,4,5,8],[2,6,7]] => 3
[3,3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,6,8,1,2,7] => [[1,2,5,6,7],[3,4,8]] => 3
[3,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,3,5,6,8,1,4,7] => [[1,3,4,6,7],[2,5,8]] => 3
[3,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,4,5,6,7,1,3,8] => [[1,3,5,6,7,8],[2,4]] => 2
[3,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,9,2] => [[1,2,5,6,7,8,9],[3,4]] => 2
[2,2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,4,5,6,7,8,9,1,3] => [[1,3,5,6,7,8,9],[2,4]] => 2
[9,1,1,1,1,1,1,1] => [1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [3,1,2,4,5,6,7,8,9,10] => [[1,2,4,5,6,7,8,9,10],[3]] => 1
[8,8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => [9,10,1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[8,7,1] => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0] => [7,1,9,2,3,4,5,6,8] => [[1,2,3,4,5,6,8],[7,9]] => 2
[8,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [2,3,1,4,5,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => 1
[7,6,3] => [1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [6,1,7,2,3,4,8,5] => [[1,2,3,4,5],[6,7,8]] => 3
[7,6,2,1] => [1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [5,1,7,2,3,4,6,8] => [[1,2,3,4,6,8],[5,7]] => 2
[7,6,1,1,1] => [1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [4,1,8,2,3,5,6,7] => [[1,2,3,5,6,7],[4,8]] => 2
[7,5,4] => [1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [6,1,2,7,3,8,4,5] => [[1,2,3,4,5],[6,7,8]] => 3
[7,5,3,1] => [1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [5,1,2,7,3,4,8,6] => [[1,2,3,4,6],[5,7,8]] => 3
[7,5,2,2] => [1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [5,1,2,6,3,4,7,8] => [[1,2,3,4,7,8],[5,6]] => 2
[7,5,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [4,1,2,7,3,5,6,8] => [[1,2,3,5,6,8],[4,7]] => 2
[7,5,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0] => [3,1,2,8,4,5,6,7] => [[1,2,4,5,6,7],[3,8]] => 2
[7,4,4,1] => [1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [5,1,2,7,8,3,4,6] => [[1,2,3,4,6],[5,7,8]] => 3
[7,4,3,1,1] => [1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0] => [4,1,2,3,7,5,8,6] => [[1,2,3,5,6],[4,7,8]] => 3
[7,4,2,2,1] => [1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0] => [4,1,2,3,6,5,7,8] => [[1,2,3,5,7,8],[4,6]] => 2
[7,4,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [3,1,2,4,7,5,6,8] => [[1,2,4,5,6,8],[3,7]] => 2
[7,4,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [2,1,3,4,8,5,6,7] => [[1,3,4,5,6,7],[2,8]] => 2
[7,3,3,3] => [1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [5,1,2,6,7,8,3,4] => [[1,2,3,4,8],[5,6,7]] => 3
[7,3,3,2,1] => [1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [4,1,2,3,6,8,5,7] => [[1,2,3,5,7],[4,6,8]] => 3
[7,3,3,1,1,1] => [1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [3,1,2,4,7,8,5,6] => [[1,2,4,5,6],[3,7,8]] => 3
[7,3,2,2,2] => [1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [4,1,2,5,6,7,3,8] => [[1,2,3,6,7,8],[4,5]] => 2
[7,3,2,2,1,1] => [1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [3,1,2,4,6,7,5,8] => [[1,2,4,5,7,8],[3,6]] => 2
[7,3,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [2,1,3,4,5,7,6,8] => [[1,3,4,5,6,8],[2,7]] => 2
[7,2,2,2,2,1] => [1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [3,1,2,5,6,7,8,4] => [[1,2,4,6,7,8],[3,5]] => 2
[7,2,2,2,1,1,1] => [1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [2,1,3,4,6,7,8,5] => [[1,3,4,5,7,8],[2,6]] => 2
[6,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [6,7,1,2,3,8,4,5] => [[1,2,3,4,5],[6,7,8]] => 3
[6,6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [5,7,1,2,3,4,8,6] => [[1,2,3,4,6],[5,7,8]] => 3
[6,6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [4,7,1,2,3,5,6,8] => [[1,2,3,5,6,8],[4,7]] => 2
[6,6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [3,8,1,2,4,5,6,7] => [[1,2,4,5,6,7],[3,8]] => 2
[6,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [6,7,1,8,2,3,4,5] => [[1,2,3,4,5],[6,7,8]] => 3
[6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,6,2,7,3,5] => [[1,2,3,5],[4,6,7]] => 3
[6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [4,1,5,2,3,7,6] => [[1,2,3,6],[4,5,7]] => 3
[6,5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [3,1,6,2,4,7,5] => [[1,2,4,5],[3,6,7]] => 3
[6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [3,1,5,2,4,6,7] => [[1,2,4,6,7],[3,5]] => 2
[6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5,7] => [[1,3,4,5,7],[2,6]] => 2
[6,5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [2,3,1,8,4,5,6,7] => [[1,3,4,5,6,7],[2,8]] => 2
[6,4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [4,1,5,7,2,3,6] => [[1,2,3,6],[4,5,7]] => 3
[6,4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [3,1,6,7,2,4,5] => [[1,2,4,5],[3,6,7]] => 3
[6,4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [4,1,5,6,2,7,3] => [[1,2,3,7],[4,5,6]] => 3
[6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,7,6] => [[1,2,4,6],[3,5,7]] => 3
[6,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [2,1,3,6,4,7,5] => [[1,3,4,5],[2,6,7]] => 3
[6,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [3,1,4,5,2,6,7] => [[1,2,5,6,7],[3,4]] => 2
[6,4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [2,1,3,5,4,6,7] => [[1,3,4,6,7],[2,5]] => 2
[6,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [2,3,1,4,7,5,6,8] => [[1,3,4,5,6,8],[2,7]] => 2
[6,3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [3,1,5,6,7,2,4] => [[1,2,4,7],[3,5,6]] => 3
[6,3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [3,1,4,5,7,2,6] => [[1,2,5,6],[3,4,7]] => 3
[6,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [2,1,3,5,7,4,6] => [[1,3,4,6],[2,5,7]] => 3
[6,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [2,3,1,4,7,8,5,6] => [[1,3,4,5,6],[2,7,8]] => 3
[6,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [2,1,4,5,6,3,7] => [[1,3,5,6,7],[2,4]] => 2
[6,3,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [2,3,1,4,6,7,5,8] => [[1,3,4,5,7,8],[2,6]] => 2
[6,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [3,4,1,5,6,7,8,2] => [[1,2,5,6,7,8],[3,4]] => 2
[6,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [2,3,1,5,6,7,8,4] => [[1,3,4,6,7,8],[2,5]] => 2
[5,5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [5,7,8,1,2,3,4,6] => [[1,2,3,4,6],[5,7,8]] => 3
[5,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [4,5,1,2,7,3,6] => [[1,2,3,6],[4,5,7]] => 3
[5,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [3,6,1,2,7,4,5] => [[1,2,4,5],[3,6,7]] => 3
[5,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [4,5,1,2,6,7,3] => [[1,2,3,7],[4,5,6]] => 3
[5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,7,6] => [[1,2,4,6],[3,5,7]] => 3
[5,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [2,6,1,3,4,7,5] => [[1,3,4,5],[2,6,7]] => 3
[5,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [3,4,1,2,5,6,7] => [[1,2,5,6,7],[3,4]] => 2
[5,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [2,5,1,3,4,6,7] => [[1,3,4,6,7],[2,5]] => 2
[5,5,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [2,3,7,1,4,5,6,8] => [[1,3,4,5,6,8],[2,7]] => 2
[5,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [4,5,1,6,2,3,7] => [[1,2,3,7],[4,5,6]] => 3
[5,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [3,5,1,7,2,4,6] => [[1,2,4,6],[3,5,7]] => 3
[5,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [2,6,1,7,3,4,5] => [[1,3,4,5],[2,6,7]] => 3
[5,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [3,5,1,6,2,7,4] => [[1,2,4,7],[3,5,6]] => 3
[5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [3,4,1,5,2,7,6] => [[1,2,5,6],[3,4,7]] => 3
[5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,7,6] => [[1,3,4,6],[2,5,7]] => 3
[5,4,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [2,3,4,1,7,5,8,6] => [[1,3,4,5,6],[2,7,8]] => 3
[5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,5,3,6,7] => [[1,3,5,6,7],[2,4]] => 2
[5,4,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [2,3,4,1,6,5,7,8] => [[1,3,4,5,7,8],[2,6]] => 2
[5,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [3,4,1,6,7,2,5] => [[1,2,5,7],[3,4,6]] => 3
[5,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [2,5,1,6,7,3,4] => [[1,3,4,7],[2,5,6]] => 3
[5,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [2,4,1,5,7,3,6] => [[1,3,5,6],[2,4,7]] => 3
[5,3,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [2,3,4,1,6,8,5,7] => [[1,3,4,5,7],[2,6,8]] => 3
[5,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [3,4,5,1,6,7,2,8] => [[1,2,5,6,7,8],[3,4]] => 2
[5,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [2,4,5,1,6,7,8,3] => [[1,3,5,6,7,8],[2,4]] => 2
[4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,1,2,3,4] => [[1,2,3,4],[5,6,7,8]] => 4
[4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,5,6,1,2,4,7] => [[1,2,4,7],[3,5,6]] => 3
[4,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [3,4,7,1,2,5,6] => [[1,2,5,6],[3,4,7]] => 3
[4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [2,5,7,1,3,4,6] => [[1,3,4,6],[2,5,7]] => 3
[4,4,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [2,3,7,8,1,4,5,6] => [[1,3,4,5,6],[2,7,8]] => 3
[4,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [3,4,6,1,2,7,5] => [[1,2,5,7],[3,4,6]] => 3
[4,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [2,5,6,1,3,7,4] => [[1,3,4,7],[2,5,6]] => 3
[4,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,7,6] => [[1,3,5,6],[2,4,7]] => 3
[4,4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,5,6,1,2,7,8] => [[1,2,5,6,7,8],[3,4]] => 2
[4,4,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [2,3,5,6,1,4,7,8] => [[1,3,4,6,7,8],[2,5]] => 2
[4,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [4,5,6,7,1,8,2,3] => [[1,2,3,7,8],[4,5,6]] => 3
[4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,6,1,7,3,5] => [[1,3,5,7],[2,4,6]] => 3
[4,3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [2,3,6,7,1,8,4,5] => [[1,3,4,5,8],[2,6,7]] => 3
[4,3,3,2,2,2] => [1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,4,5,6,1,8,2,7] => [[1,2,5,6,7],[3,4,8]] => 3
[4,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [2,3,5,6,1,8,4,7] => [[1,3,4,6,7],[2,5,8]] => 3
[4,3,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [2,4,5,6,1,7,3,8] => [[1,3,5,6,7,8],[2,4]] => 2
[4,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,4,5,6,7,1,8,9,2] => [[1,2,5,6,7,8,9],[3,4]] => 2
[3,3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,5,6,7,8,1,2,4] => [[1,2,4,7,8],[3,5,6]] => 3
[3,3,3,3,2,2] => [1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,7,8,1,2,6] => [[1,2,5,6,8],[3,4,7]] => 3
[3,3,3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,3,5,7,8,1,4,6] => [[1,3,4,6,8],[2,5,7]] => 3
[3,3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,4,5,6,8,1,3,7] => [[1,3,5,6,7],[2,4,8]] => 3
[3,3,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2,9] => [[1,2,5,6,7,8,9],[3,4]] => 2
[2,2,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,1,2] => [[1,2,5,6,7,8,9,10],[3,4]] => 2
[9,8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => [9,1,10,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8],[9,10]] => 2
[9,1,1,1,1,1,1,1,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [2,1,3,4,5,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => 1
[8,8,1] => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,1,0,0] => [8,10,1,2,3,4,5,6,7,9] => [[1,2,3,4,5,6,7,9],[8,10]] => 2
[7,7,3] => [1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,9,6] => [[1,2,3,4,5,6],[7,8,9]] => 3
[7,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [6,1,7,2,3,8,4,5] => [[1,2,3,4,5],[6,7,8]] => 3
[7,6,3,1] => [1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [5,1,7,2,3,4,8,6] => [[1,2,3,4,6],[5,7,8]] => 3
[7,6,2,2] => [1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [5,1,6,2,3,4,7,8] => [[1,2,3,4,7,8],[5,6]] => 2
[7,6,2,1,1] => [1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [4,1,7,2,3,5,6,8] => [[1,2,3,5,6,8],[4,7]] => 2
[7,6,1,1,1,1] => [1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [3,1,8,2,4,5,6,7] => [[1,2,4,5,6,7],[3,8]] => 2
[7,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [6,1,7,8,2,3,4,5] => [[1,2,3,4,5],[6,7,8]] => 3
[7,5,4,1] => [1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [5,1,2,7,3,8,4,6] => [[1,2,3,4,6],[5,7,8]] => 3
[7,5,3,2] => [1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [5,1,2,6,3,4,8,7] => [[1,2,3,4,7],[5,6,8]] => 3
[7,5,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [4,1,2,7,3,5,8,6] => [[1,2,3,5,6],[4,7,8]] => 3
[7,5,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [3,1,2,7,4,5,6,8] => [[1,2,4,5,6,8],[3,7]] => 2
[7,5,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [2,1,3,8,4,5,6,7] => [[1,3,4,5,6,7],[2,8]] => 2
[7,4,4,2] => [1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [5,1,2,6,8,3,4,7] => [[1,2,3,4,7],[5,6,8]] => 3
[7,4,4,1,1] => [1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [4,1,2,7,8,3,5,6] => [[1,2,3,5,6],[4,7,8]] => 3
[7,4,3,3] => [1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0] => [5,1,2,6,7,3,8,4] => [[1,2,3,4,8],[5,6,7]] => 3
[7,4,3,2,1] => [1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [4,1,2,3,6,5,8,7] => [[1,2,3,5,7],[4,6,8]] => 3
[7,4,3,1,1,1] => [1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [3,1,2,4,7,5,8,6] => [[1,2,4,5,6],[3,7,8]] => 3
[7,4,2,2,2] => [1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [4,1,2,5,6,3,7,8] => [[1,2,3,6,7,8],[4,5]] => 2
[7,4,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [2,1,3,4,7,5,6,8] => [[1,3,4,5,6,8],[2,7]] => 2
[7,3,3,2,2] => [1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [4,1,2,5,6,8,3,7] => [[1,2,3,6,7],[4,5,8]] => 3
[7,3,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [2,1,3,4,7,8,5,6] => [[1,3,4,5,6],[2,7,8]] => 3
[7,3,2,2,2,1] => [1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [3,1,2,5,6,7,4,8] => [[1,2,4,6,7,8],[3,5]] => 2
[7,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,2] => [[1,2,5,6,7,8],[3,4]] => 2
[7,2,2,2,2,1,1] => [1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [2,1,3,5,6,7,8,4] => [[1,3,4,6,7,8],[2,5]] => 2
[6,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [6,7,1,2,8,3,4,5] => [[1,2,3,4,5],[6,7,8]] => 3
[6,6,4,1] => [1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [5,7,1,2,3,8,4,6] => [[1,2,3,4,6],[5,7,8]] => 3
[6,6,3,2] => [1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [5,6,1,2,3,4,8,7] => [[1,2,3,4,7],[5,6,8]] => 3
[6,6,3,1,1] => [1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [4,7,1,2,3,5,8,6] => [[1,2,3,5,6],[4,7,8]] => 3
[6,6,2,2,1] => [1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [4,6,1,2,3,5,7,8] => [[1,2,3,5,7,8],[4,6]] => 2
[6,6,2,1,1,1] => [1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0] => [3,7,1,2,4,5,6,8] => [[1,2,4,5,6,8],[3,7]] => 2
[6,6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [2,8,1,3,4,5,6,7] => [[1,3,4,5,6,7],[2,8]] => 2
[6,5,5,1] => [1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0] => [5,7,1,8,2,3,4,6] => [[1,2,3,4,6],[5,7,8]] => 3
[6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [4,1,5,2,7,3,6] => [[1,2,3,6],[4,5,7]] => 3
[6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,6,2,7,4,5] => [[1,2,4,5],[3,6,7]] => 3
[6,5,3,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [4,1,5,2,6,7,3] => [[1,2,3,7],[4,5,6]] => 3
[6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,7,6] => [[1,2,4,6],[3,5,7]] => 3
[6,5,3,1,1,1] => [1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [2,1,6,3,4,7,5] => [[1,3,4,5],[2,6,7]] => 3
[6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [3,1,4,2,5,6,7] => [[1,2,5,6,7],[3,4]] => 2
[6,5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [2,1,5,3,4,6,7] => [[1,3,4,6,7],[2,5]] => 2
[6,4,4,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [4,1,5,6,2,3,7] => [[1,2,3,7],[4,5,6]] => 3
[6,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [3,1,5,7,2,4,6] => [[1,2,4,6],[3,5,7]] => 3
[6,4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [2,1,6,7,3,4,5] => [[1,3,4,5],[2,6,7]] => 3
[6,4,3,3,1] => [1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [3,1,5,6,2,7,4] => [[1,2,4,7],[3,5,6]] => 3
[6,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [3,1,4,5,2,7,6] => [[1,2,5,6],[3,4,7]] => 3
[6,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [2,1,3,5,4,7,6] => [[1,3,4,6],[2,5,7]] => 3
[6,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [2,1,4,5,3,6,7] => [[1,3,5,6,7],[2,4]] => 2
[6,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [3,1,4,6,7,2,5] => [[1,2,5,7],[3,4,6]] => 3
[6,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [2,1,5,6,7,3,4] => [[1,3,4,7],[2,5,6]] => 3
[6,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [2,1,4,5,7,3,6] => [[1,3,5,6],[2,4,7]] => 3
[6,3,2,2,2,2] => [1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0] => [3,4,1,5,6,7,2,8] => [[1,2,5,6,7,8],[3,4]] => 2
[6,3,2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [2,3,1,5,6,7,4,8] => [[1,3,4,6,7,8],[2,5]] => 2
[6,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [2,4,1,5,6,7,8,3] => [[1,3,5,6,7,8],[2,4]] => 2
[5,5,5,2] => [1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [5,6,8,1,2,3,4,7] => [[1,2,3,4,7],[5,6,8]] => 3
[5,5,5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [4,7,8,1,2,3,5,6] => [[1,2,3,5,6],[4,7,8]] => 3
[5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [4,5,1,2,6,3,7] => [[1,2,3,7],[4,5,6]] => 3
[5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,7,4,6] => [[1,2,4,6],[3,5,7]] => 3
[5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [2,6,1,3,7,4,5] => [[1,3,4,5],[2,6,7]] => 3
[5,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [3,5,1,2,6,7,4] => [[1,2,4,7],[3,5,6]] => 3
[5,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [3,4,1,2,5,7,6] => [[1,2,5,6],[3,4,7]] => 3
[5,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [2,5,1,3,4,7,6] => [[1,3,4,6],[2,5,7]] => 3
[5,5,3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [2,3,7,1,4,5,8,6] => [[1,3,4,5,6],[2,7,8]] => 3
[5,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [2,4,1,3,5,6,7] => [[1,3,5,6,7],[2,4]] => 2
[5,5,2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [2,3,6,1,4,5,7,8] => [[1,3,4,5,7,8],[2,6]] => 2
[5,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [5,6,7,1,8,2,3,4] => [[1,2,3,4],[5,6,7,8]] => 4
[5,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [3,5,1,6,2,4,7] => [[1,2,4,7],[3,5,6]] => 3
[5,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [3,4,1,7,2,5,6] => [[1,2,5,6],[3,4,7]] => 3
[5,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [2,5,1,7,3,4,6] => [[1,3,4,6],[2,5,7]] => 3
[5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [3,4,1,6,2,7,5] => [[1,2,5,7],[3,4,6]] => 3
[5,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,5,1,6,3,7,4] => [[1,3,4,7],[2,5,6]] => 3
[5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,1,5,3,7,6] => [[1,3,5,6],[2,4,7]] => 3
[5,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [2,3,4,1,6,5,8,7] => [[1,3,4,5,7],[2,6,8]] => 3
[5,4,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0] => [3,4,5,1,6,2,7,8] => [[1,2,5,6,7,8],[3,4]] => 2
[5,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0] => [4,5,6,1,7,8,2,3] => [[1,2,3,7,8],[4,5,6]] => 3
[5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,6,7,3,5] => [[1,3,5,7],[2,4,6]] => 3
[5,3,3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [2,3,6,1,7,8,4,5] => [[1,3,4,5,8],[2,6,7]] => 3
[5,3,3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [2,3,5,1,6,8,4,7] => [[1,3,4,6,7],[2,5,8]] => 3
[4,4,4,4,1] => [1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [4,6,7,8,1,2,3,5] => [[1,2,3,5],[4,6,7,8]] => 4
[4,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5,7] => [[1,2,5,7],[3,4,6]] => 3
[4,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [2,5,6,1,3,4,7] => [[1,3,4,7],[2,5,6]] => 3
[4,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [2,4,7,1,3,5,6] => [[1,3,5,6],[2,4,7]] => 3
[4,4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,6,7,1,2,8,3] => [[1,2,3,7,8],[4,5,6]] => 3
[4,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,6,1,3,7,5] => [[1,3,5,7],[2,4,6]] => 3
[4,4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,5,6,1,2,8,7] => [[1,2,5,6,7],[3,4,8]] => 3
[4,4,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [2,4,5,6,1,3,7,8] => [[1,3,5,6,7,8],[2,4]] => 2
[4,3,3,3,3,1] => [1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [3,5,6,7,1,8,2,4] => [[1,2,4,7,8],[3,5,6]] => 3
[4,3,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [2,4,5,6,1,8,3,7] => [[1,3,5,6,7],[2,4,8]] => 3
[3,3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,6,7,8,1,2,5] => [[1,2,5,7,8],[3,4,6]] => 3
[3,3,3,3,3,1,1] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,5,6,7,8,1,3,4] => [[1,3,4,7,8],[2,5,6]] => 3
[3,3,3,3,2,2,1] => [1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,4,5,7,8,1,3,6] => [[1,3,5,6,8],[2,4,7]] => 3
[3,3,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,4,5,6,7,8,1,3,9] => [[1,3,5,6,7,8,9],[2,4]] => 2
[3,2,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,1,10,2] => [[1,2,5,6,7,8,9,10],[3,4]] => 2
[2,2,2,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [2,4,5,6,7,8,9,10,1,3] => [[1,3,5,6,7,8,9,10],[2,4]] => 2
[] => [] => [] => [] => 0
[6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,7] => [[1,3,5,7],[2,4,6]] => 3
[5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5,7] => [[1,3,5,7],[2,4,6]] => 3
[6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5,7] => [[1,3,5,7],[2,4,6]] => 3
[5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5,7] => [[1,3,5,7],[2,4,6]] => 3
[4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5,7] => [[1,3,5,7],[2,4,6]] => 3
[6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,7,5] => [[1,3,5,7],[2,4,6]] => 3
[5,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,7,5] => [[1,3,5,7],[2,4,6]] => 3
[6,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,7,5] => [[1,3,5,7],[2,4,6]] => 3
[5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5] => [[1,3,5,7],[2,4,6]] => 3
[6,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,6,7,3,5] => [[1,3,5,7],[2,4,6]] => 3
[6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [2,1,4,3,7,5,6] => [[1,3,5,6],[2,4,7]] => 3
[5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,4,1,3,7,5,6] => [[1,3,5,6],[2,4,7]] => 3
[6,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [2,1,4,7,3,5,6] => [[1,3,5,6],[2,4,7]] => 3
[5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [2,4,1,7,3,5,6] => [[1,3,5,6],[2,4,7]] => 3
[6,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [2,1,4,3,5,7,6] => [[1,3,5,6],[2,4,7]] => 3
[5,5,3,2,2,1] => [1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [2,4,1,3,5,7,6] => [[1,3,5,6],[2,4,7]] => 3
[6,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [2,1,4,5,3,7,6] => [[1,3,5,6],[2,4,7]] => 3
[6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [2,1,4,3,5,6,7] => [[1,3,5,6,7],[2,4]] => 2
[6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,7] => [[1,3,4,7],[2,5,6]] => 3
[5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,5,1,3,6,4,7] => [[1,3,4,7],[2,5,6]] => 3
[6,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [2,1,5,6,3,4,7] => [[1,3,4,7],[2,5,6]] => 3
[5,4,4,3,1,1] => [1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,5,1,6,3,4,7] => [[1,3,4,7],[2,5,6]] => 3
[6,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [2,1,5,3,6,7,4] => [[1,3,4,7],[2,5,6]] => 3
[5,5,3,3,1,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [2,5,1,3,6,7,4] => [[1,3,4,7],[2,5,6]] => 3
[6,4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [2,1,5,6,3,7,4] => [[1,3,4,7],[2,5,6]] => 3
[6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [2,1,5,3,7,4,6] => [[1,3,4,6],[2,5,7]] => 3
[5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [2,5,1,3,7,4,6] => [[1,3,4,6],[2,5,7]] => 3
[6,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [2,1,5,7,3,4,6] => [[1,3,4,6],[2,5,7]] => 3
[6,5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [2,1,5,3,4,7,6] => [[1,3,4,6],[2,5,7]] => 3
[6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,6,3,7,4,5] => [[1,3,4,5],[2,6,7]] => 3
[6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,7] => [[1,2,5,7],[3,4,6]] => 3
[5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5,7] => [[1,2,5,7],[3,4,6]] => 3
[6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5,7] => [[1,2,5,7],[3,4,6]] => 3
[5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5,7] => [[1,2,5,7],[3,4,6]] => 3
[6,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,7,5] => [[1,2,5,7],[3,4,6]] => 3
[5,5,3,3,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [3,4,1,2,6,7,5] => [[1,2,5,7],[3,4,6]] => 3
[6,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [3,1,4,6,2,7,5] => [[1,2,5,7],[3,4,6]] => 3
[6,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [3,1,4,2,7,5,6] => [[1,2,5,6],[3,4,7]] => 3
[5,5,4,2,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [3,4,1,2,7,5,6] => [[1,2,5,6],[3,4,7]] => 3
[6,4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [3,1,4,7,2,5,6] => [[1,2,5,6],[3,4,7]] => 3
[6,5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [3,1,4,2,5,7,6] => [[1,2,5,6],[3,4,7]] => 3
[6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,6,4,7] => [[1,2,4,7],[3,5,6]] => 3
[5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [3,5,1,2,6,4,7] => [[1,2,4,7],[3,5,6]] => 3
[6,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [3,1,5,6,2,4,7] => [[1,2,4,7],[3,5,6]] => 3
[6,5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [3,1,5,2,6,7,4] => [[1,2,4,7],[3,5,6]] => 3
[6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,7,4,6] => [[1,2,4,6],[3,5,7]] => 3
[6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,5,2,6,3,7] => [[1,2,3,7],[4,5,6]] => 3
[7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,8,7] => [[1,3,5,7],[2,4,6,8]] => 4
[6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5,8,7] => [[1,3,5,7],[2,4,6,8]] => 4
[7,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [2,1,4,6,3,5,8,7] => [[1,3,5,7],[2,4,6,8]] => 4
[6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5,8,7] => [[1,3,5,7],[2,4,6,8]] => 4
[5,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5,8,7] => [[1,3,5,7],[2,4,6,8]] => 4
[7,6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [2,1,4,3,6,8,5,7] => [[1,3,5,7],[2,4,6,8]] => 4
[6,6,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,8,5,7] => [[1,3,5,7],[2,4,6,8]] => 4
[7,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [2,1,4,6,3,8,5,7] => [[1,3,5,7],[2,4,6,8]] => 4
[6,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,7] => [[1,3,5,7],[2,4,6,8]] => 4
[5,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [2,4,6,1,3,8,5,7] => [[1,3,5,7],[2,4,6,8]] => 4
[7,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [2,1,4,6,8,3,5,7] => [[1,3,5,7],[2,4,6,8]] => 4
[6,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,6,8,3,5,7] => [[1,3,5,7],[2,4,6,8]] => 4
[5,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [2,4,6,1,8,3,5,7] => [[1,3,5,7],[2,4,6,8]] => 4
[4,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [2,4,6,8,1,3,5,7] => [[1,3,5,7],[2,4,6,8]] => 4
[6,6,5,3,3,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [2,4,1,3,6,5,7,8] => [[1,3,5,7,8],[2,4,6]] => 3
[6,5,4,3,3,2,1] => [1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5,8] => [[1,3,5,7,8],[2,4,6]] => 3
[6,5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,6,3,7,8,5] => [[1,3,5,7,8],[2,4,6]] => 3
[6,4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [2,4,1,6,7,3,8,5] => [[1,3,5,7,8],[2,4,6]] => 3
[5,4,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [2,4,6,1,7,3,8,5] => [[1,3,5,7,8],[2,4,6]] => 3
[6,3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [2,4,1,6,7,8,3,5] => [[1,3,5,7,8],[2,4,6]] => 3
[3,3,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [2,4,6,7,8,1,3,5] => [[1,3,5,7,8],[2,4,6]] => 3
[6,6,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [2,4,1,3,7,5,8,6] => [[1,3,5,6],[2,4,7,8]] => 4
[6,5,5,4,2,2,1] => [1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [2,4,1,7,3,5,8,6] => [[1,3,5,6],[2,4,7,8]] => 4
[6,5,4,4,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [2,4,1,7,3,8,5,6] => [[1,3,5,6],[2,4,7,8]] => 4
[6,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,5,3,7,6,8] => [[1,3,5,6,8],[2,4,7]] => 3
[5,5,4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [2,4,5,1,3,7,6,8] => [[1,3,5,6,8],[2,4,7]] => 3
[7,6,5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [2,1,4,3,8,5,6,7] => [[1,3,5,6,7],[2,4,8]] => 3
[6,5,4,2,2,2,1] => [1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,5,3,8,6,7] => [[1,3,5,6,7],[2,4,8]] => 3
[6,5,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [2,4,1,5,3,6,8,7] => [[1,3,5,6,7],[2,4,8]] => 3
[6,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [2,4,1,5,6,3,8,7] => [[1,3,5,6,7],[2,4,8]] => 3
[5,4,3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [2,4,5,1,6,3,8,7] => [[1,3,5,6,7],[2,4,8]] => 3
[6,5,2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [2,4,1,5,3,6,7,8] => [[1,3,5,6,7,8],[2,4]] => 2
[7,2,2,2,2,2,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [2,1,4,5,6,7,8,3] => [[1,3,5,6,7,8],[2,4]] => 2
[7,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [2,1,5,3,6,4,8,7] => [[1,3,4,7],[2,5,6,8]] => 4
[6,6,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [2,5,1,3,6,4,8,7] => [[1,3,4,7],[2,5,6,8]] => 4
[6,5,5,4,3,1,1] => [1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [2,5,1,6,3,4,8,7] => [[1,3,4,7],[2,5,6,8]] => 4
[6,6,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [2,5,1,3,7,4,8,6] => [[1,3,4,6],[2,5,7,8]] => 4
[6,5,5,4,2,1,1] => [1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [2,5,1,7,3,4,8,6] => [[1,3,4,6],[2,5,7,8]] => 4
[4,4,4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [2,5,7,8,1,3,4,6] => [[1,3,4,6],[2,5,7,8]] => 4
[6,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [2,3,1,5,4,7,6,8] => [[1,3,4,6,8],[2,5,7]] => 3
[5,5,4,3,2,1,1] => [1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [2,3,5,1,4,7,6,8] => [[1,3,4,6,8],[2,5,7]] => 3
[7,6,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [2,1,6,3,7,4,8,5] => [[1,3,4,5],[2,6,7,8]] => 4
[6,5,5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [2,6,1,7,3,4,8,5] => [[1,3,4,5],[2,6,7,8]] => 4
[6,5,4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [2,3,1,6,4,7,5,8] => [[1,3,4,5,8],[2,6,7]] => 3
[7,6,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [2,1,6,3,8,4,5,7] => [[1,3,4,5,7],[2,6,8]] => 3
[5,5,5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [2,6,8,1,3,4,5,7] => [[1,3,4,5,7],[2,6,8]] => 3
[6,5,4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [2,3,1,6,4,8,5,7] => [[1,3,4,5,7],[2,6,8]] => 3
[7,6,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [2,1,6,3,4,5,8,7] => [[1,3,4,5,7],[2,6,8]] => 3
[7,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [2,1,3,4,6,5,8,7] => [[1,3,4,5,7],[2,6,8]] => 3
[6,4,3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [2,3,1,4,6,5,8,7] => [[1,3,4,5,7],[2,6,8]] => 3
[6,5,4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [2,3,1,7,4,8,5,6] => [[1,3,4,5,6],[2,7,8]] => 3
[6,6,2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [2,7,1,3,4,5,6,8] => [[1,3,4,5,6,8],[2,7]] => 2
[7,6,1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [2,1,8,3,4,5,6,7] => [[1,3,4,5,6,7],[2,8]] => 2
[7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,8,7] => [[1,2,5,7],[3,4,6,8]] => 4
[6,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5,8,7] => [[1,2,5,7],[3,4,6,8]] => 4
[7,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [3,1,4,6,2,5,8,7] => [[1,2,5,7],[3,4,6,8]] => 4
[6,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5,8,7] => [[1,2,5,7],[3,4,6,8]] => 4
[5,5,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [3,4,6,1,2,5,8,7] => [[1,2,5,7],[3,4,6,8]] => 4
[7,6,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [3,1,4,2,6,8,5,7] => [[1,2,5,7],[3,4,6,8]] => 4
[6,5,4,4,3,2] => [1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [3,4,1,6,2,8,5,7] => [[1,2,5,7],[3,4,6,8]] => 4
[6,5,4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [3,4,1,6,2,7,5,8] => [[1,2,5,7,8],[3,4,6]] => 3
[5,4,3,3,3,2] => [1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [3,4,6,1,7,2,8,5] => [[1,2,5,7,8],[3,4,6]] => 3
[4,3,3,3,3,2] => [1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [3,4,6,7,1,8,2,5] => [[1,2,5,7,8],[3,4,6]] => 3
[6,5,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [3,4,1,5,2,7,6,8] => [[1,2,5,6,8],[3,4,7]] => 3
[4,4,4,3,2,2] => [1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,7,1,2,6,8] => [[1,2,5,6,8],[3,4,7]] => 3
[7,6,5,2,2,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [3,1,4,2,8,5,6,7] => [[1,2,5,6,7],[3,4,8]] => 3
[6,5,4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [3,4,1,5,2,8,6,7] => [[1,2,5,6,7],[3,4,8]] => 3
[5,4,3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [3,4,5,1,6,2,8,7] => [[1,2,5,6,7],[3,4,8]] => 3
[6,6,2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [3,4,1,2,5,6,7,8] => [[1,2,5,6,7,8],[3,4]] => 2
[7,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [3,1,5,2,6,4,8,7] => [[1,2,4,7],[3,5,6,8]] => 4
[6,6,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [3,5,1,2,6,4,8,7] => [[1,2,4,7],[3,5,6,8]] => 4
[6,5,5,4,3,1] => [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [3,5,1,6,2,4,8,7] => [[1,2,4,7],[3,5,6,8]] => 4
[4,4,4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [3,5,6,8,1,2,4,7] => [[1,2,4,7],[3,5,6,8]] => 4
[7,6,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [3,1,5,2,7,4,8,6] => [[1,2,4,6],[3,5,7,8]] => 4
[5,5,5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [3,5,7,1,2,4,8,6] => [[1,2,4,6],[3,5,7,8]] => 4
[4,4,4,4,2,1] => [1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,5,7,8,1,2,4,6] => [[1,2,4,6],[3,5,7,8]] => 4
[7,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [3,1,5,2,7,4,6,8] => [[1,2,4,6,8],[3,5,7]] => 3
[6,6,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [3,5,1,2,7,4,6,8] => [[1,2,4,6,8],[3,5,7]] => 3
[5,5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,5,7,1,2,4,6,8] => [[1,2,4,6,8],[3,5,7]] => 3
[7,6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,7,6,8] => [[1,2,4,6,8],[3,5,7]] => 3
[6,6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,7,6,8] => [[1,2,4,6,8],[3,5,7]] => 3
[7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,7,6,8] => [[1,2,4,6,8],[3,5,7]] => 3
[7,6,5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [3,1,5,2,8,4,6,7] => [[1,2,4,6,7],[3,5,8]] => 3
[7,6,5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [3,1,6,2,7,4,8,5] => [[1,2,4,5],[3,6,7,8]] => 4
[7,6,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [3,1,6,2,4,5,8,7] => [[1,2,4,5,7],[3,6,8]] => 3
[7,4,3,2,1,1] => [1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [3,1,2,4,6,5,8,7] => [[1,2,4,5,7],[3,6,8]] => 3
[7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [4,1,5,2,6,3,8,7] => [[1,2,3,7],[4,5,6,8]] => 4
[6,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [4,5,1,2,6,3,8,7] => [[1,2,3,7],[4,5,6,8]] => 4
[6,5,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [4,5,1,6,2,3,8,7] => [[1,2,3,7],[4,5,6,8]] => 4
[5,4,4,4,3] => [1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [4,5,6,1,8,2,3,7] => [[1,2,3,7],[4,5,6,8]] => 4
[5,4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [4,5,6,1,7,2,8,3] => [[1,2,3,7,8],[4,5,6]] => 3
[7,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [4,1,5,6,7,8,2,3] => [[1,2,3,7,8],[4,5,6]] => 3
[7,6,5,4,2] => [1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [4,1,5,2,7,3,8,6] => [[1,2,3,6],[4,5,7,8]] => 4
[4,4,4,4,2] => [1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,7,8,1,2,3,6] => [[1,2,3,6],[4,5,7,8]] => 4
[7,6,5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [4,1,5,2,7,3,6,8] => [[1,2,3,6,8],[4,5,7]] => 3
[7,6,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [4,1,5,2,3,7,6,8] => [[1,2,3,6,8],[4,5,7]] => 3
[7,5,4,3,2] => [1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [4,1,2,5,3,7,6,8] => [[1,2,3,6,8],[4,5,7]] => 3
[7,6,5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [4,1,6,2,7,3,8,5] => [[1,2,3,5],[4,6,7,8]] => 4
[7,5,4,3,1] => [1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [4,1,2,6,3,7,5,8] => [[1,2,3,5,8],[4,6,7]] => 3
[7,6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [4,1,6,2,8,3,5,7] => [[1,2,3,5,7],[4,6,8]] => 3
[6,6,5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [4,6,1,2,8,3,5,7] => [[1,2,3,5,7],[4,6,8]] => 3
[7,6,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [4,1,6,2,3,8,5,7] => [[1,2,3,5,7],[4,6,8]] => 3
[7,5,4,2,1] => [1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [4,1,2,6,3,8,5,7] => [[1,2,3,5,7],[4,6,8]] => 3
[7,6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [4,1,6,2,3,5,8,7] => [[1,2,3,5,7],[4,6,8]] => 3
[6,6,3,2,1] => [1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [4,6,1,2,3,5,8,7] => [[1,2,3,5,7],[4,6,8]] => 3
[7,6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [5,1,6,2,7,3,8,4] => [[1,2,3,4],[5,6,7,8]] => 4
[6,5,5,4] => [1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [5,6,1,7,2,3,8,4] => [[1,2,3,4],[5,6,7,8]] => 4
[7,6,5,3] => [1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [5,1,6,2,7,3,4,8] => [[1,2,3,4,8],[5,6,7]] => 3
[7,6,4,3] => [1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [5,1,6,2,3,7,4,8] => [[1,2,3,4,8],[5,6,7]] => 3
[7,5,4,3] => [1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [5,1,2,6,3,7,4,8] => [[1,2,3,4,8],[5,6,7]] => 3
[7,6,5,2] => [1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [5,1,6,2,8,3,4,7] => [[1,2,3,4,7],[5,6,8]] => 3
[7,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [6,1,7,2,8,3,4,5] => [[1,2,3,4,5],[6,7,8]] => 3
[3,3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,1,2,3] => [[1,2,3,7,8,9],[4,5,6]] => 3
[3,3,3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [4,5,6,7,8,9,10,1,2,3] => [[1,2,3,7,8,9,10],[4,5,6]] => 3
[4,3,3,3,3,3] => [1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,5,6,7,8,1,9,2,3] => [[1,2,3,7,8,9],[4,5,6]] => 3
[4,4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [5,6,7,8,9,1,2,3,4] => [[1,2,3,4,9],[5,6,7,8]] => 4
[4,4,4,3,3,3] => [1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3,9] => [[1,2,3,7,8,9],[4,5,6]] => 3
[4,4,4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,10,1,2,3,4] => [[1,2,3,4,9,10],[5,6,7,8]] => 4
[5,5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => [6,7,8,9,1,2,3,4,5] => [[1,2,3,4,5],[6,7,8,9]] => 4
[6,6,6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => [7,8,9,10,1,2,3,4,5,6] => [[1,2,3,4,5,6],[7,8,9,10]] => 4
[6,6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => [7,8,9,1,2,3,4,5,6] => [[1,2,3,4,5,6],[7,8,9]] => 3
[7,6,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0] => [7,8,1,9,2,3,4,5,6] => [[1,2,3,4,5,6],[7,8,9]] => 3
[8,2,2,2,2,2,2] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [3,1,4,5,6,7,8,9,2] => [[1,2,5,6,7,8,9],[3,4]] => 2
[8,7,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => [7,1,8,2,9,3,4,5,6] => [[1,2,3,4,5,6],[7,8,9]] => 3
[9,8,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => [8,1,9,2,10,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8,9,10]] => 3
[7,7,7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => [8,9,10,1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7],[8,9,10]] => 3
[8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,8,7,9] => [[1,3,5,7,9],[2,4,6,8]] => 4
[7,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5,8,7,9] => [[1,3,5,7,9],[2,4,6,8]] => 4
[7,6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5,8,7,9] => [[1,3,5,7,9],[2,4,6,8]] => 4
[7,6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,7,9] => [[1,3,5,7,9],[2,4,6,8]] => 4
[7,6,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,9,7] => [[1,3,5,7,9],[2,4,6,8]] => 4
[9,8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [2,1,4,3,6,5,8,7,10,9] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
[8,8,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [2,4,1,3,6,5,8,7,10,9] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
[6,6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [2,4,6,1,3,5,8,7,9] => [[1,3,5,7,9],[2,4,6,8]] => 4
[8,7,7,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [2,4,1,6,3,5,8,7,10,9] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
[7,5,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [2,4,1,6,8,3,5,7,9] => [[1,3,5,7,9],[2,4,6,8]] => 4
[8,7,6,6,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,7,10,9] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
[7,6,4,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [2,4,1,6,3,8,9,5,7] => [[1,3,5,7,9],[2,4,6,8]] => 4
[8,7,6,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,10,7,9] => [[1,3,5,7,9],[2,4,6,8,10]] => 5
[7,6,5,3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [2,4,1,6,3,7,5,8,9] => [[1,3,5,7,8,9],[2,4,6]] => 3
[8,7,6,5,4,4,3,2,1] => [1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [2,4,1,6,3,8,5,9,7,10] => [[1,3,5,7,9,10],[2,4,6,8]] => 4
[8,7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [3,1,5,2,4,7,6,9,8] => [[1,2,4,6,8],[3,5,7,9]] => 4
[8,6,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,7,6,9,8] => [[1,2,4,6,8],[3,5,7,9]] => 4
[9,8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [3,1,4,2,6,5,8,7,10,9] => [[1,2,5,7,9],[3,4,6,8,10]] => 5
[9,7,6,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [3,1,2,5,4,7,6,9,8,10] => [[1,2,4,6,8,10],[3,5,7,9]] => 4
[5,5,5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => [6,7,8,9,10,1,2,3,4,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 5
[6,6,6,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [3,5,7,1,2,4,6,9,8] => [[1,2,4,6,8],[3,5,7,9]] => 4
[5,5,5,5,3,2,1] => [1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [3,5,7,9,1,2,4,6,8] => [[1,2,4,6,8],[3,5,7,9]] => 4
[6,5,5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0] => [6,7,8,1,9,2,3,4,5] => [[1,2,3,4,5],[6,7,8,9]] => 4
[5,4,4,4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0] => [5,6,7,8,1,9,2,3,4] => [[1,2,3,4,9],[5,6,7,8]] => 4
[8,7,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [3,4,1,6,2,5,8,7,10,9] => [[1,2,5,7,9],[3,4,6,8,10]] => 5
[8,8,7,6,5,4,3,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [3,4,1,2,6,5,8,7,10,9] => [[1,2,5,7,9],[3,4,6,8,10]] => 5
[9,8,7,6,5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [4,1,5,2,6,3,8,7,10,9] => [[1,2,3,7,9],[4,5,6,8,10]] => 5
[8,7,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => [6,1,7,2,8,3,9,4,5] => [[1,2,3,4,5],[6,7,8,9]] => 4
[8,7,6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [5,1,6,2,7,3,8,4,9] => [[1,2,3,4,9],[5,6,7,8]] => 4
[8,7,5] => [1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0] => [7,1,8,2,3,9,4,5,6] => [[1,2,3,4,5,6],[7,8,9]] => 3
[9,8,7,6] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => [7,1,8,2,9,3,10,4,5,6] => [[1,2,3,4,5,6],[7,8,9,10]] => 4
[8,7,6,4] => [1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0] => [6,1,7,2,8,3,4,9,5] => [[1,2,3,4,5],[6,7,8,9]] => 4
[9,8,7,6,5] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => [6,1,7,2,8,3,9,4,10,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 5
[9,8,7,6,5,4] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [5,1,6,2,7,3,8,4,10,9] => [[1,2,3,4,9],[5,6,7,8,10]] => 5
[7,7,5,5,4,3,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [2,4,1,3,6,8,5,7,9] => [[1,3,5,7,9],[2,4,6,8]] => 4
[7,7,5,4,3,2,1] => [1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [3,5,1,2,4,7,6,9,8] => [[1,2,4,6,8],[3,5,7,9]] => 4
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Generating function
click to show known generating functions
Search the OEIS for these generating functions
Search the Online Encyclopedia of Integer
Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
4,1 5,2 6,5 7,8 8,14
F1=q
F2=2 q
F3=3 q
F4=4 q+q2
F5=5 q+2 q2
F6=6 q+5 q2
F7=7 q+8 q2
F8=8 q+14 q2
Description
The leg major index of a standard tableau.
The leg length of a cell is the number of cells strictly below in the same column. This statistic is the sum of all leg lengths. Therefore, this is actually a statistic on the underlying integer partition.
It happens to coincide with the (leg) major index of a tabloid restricted to standard Young tableaux, defined as follows: the descent set of a tabloid is the set of cells, not in the top row, whose entry is strictly larger than the entry directly above it. The leg major index is the sum of the leg lengths of the descents plus the number of descents.
The leg length of a cell is the number of cells strictly below in the same column. This statistic is the sum of all leg lengths. Therefore, this is actually a statistic on the underlying integer partition.
It happens to coincide with the (leg) major index of a tabloid restricted to standard Young tableaux, defined as follows: the descent set of a tabloid is the set of cells, not in the top row, whose entry is strictly larger than the entry directly above it. The leg major index is the sum of the leg lengths of the descents plus the number of descents.
Map
Robinson-Schensted insertion tableau
Description
Sends a permutation to its Robinson-Schensted insertion tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length n and pairs of standard Young tableaux of the same shape and of size n, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding insertion tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length n and pairs of standard Young tableaux of the same shape and of size n, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to its corresponding insertion tableau.
Map
to 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
Map
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!