Identifier
-
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00070: Permutations —Robinson-Schensted recording tableau⟶ Standard tableaux
Mp00207: Standard tableaux —horizontal strip sizes⟶ Integer compositions
St000008: Integer compositions ⟶ ℤ
Values
[1,0] => [1] => [[1]] => [1] => 0
[1,0,1,0] => [2,1] => [[1],[2]] => [1,1] => 1
[1,1,0,0] => [1,2] => [[1,2]] => [2] => 0
[1,0,1,0,1,0] => [3,2,1] => [[1],[2],[3]] => [1,1,1] => 3
[1,0,1,1,0,0] => [2,3,1] => [[1,2],[3]] => [2,1] => 2
[1,1,0,0,1,0] => [3,1,2] => [[1,3],[2]] => [1,2] => 1
[1,1,0,1,0,0] => [2,1,3] => [[1,3],[2]] => [1,2] => 1
[1,1,1,0,0,0] => [1,2,3] => [[1,2,3]] => [3] => 0
[1,0,1,0,1,0,1,0] => [4,3,2,1] => [[1],[2],[3],[4]] => [1,1,1,1] => 6
[1,0,1,0,1,1,0,0] => [3,4,2,1] => [[1,2],[3],[4]] => [2,1,1] => 5
[1,0,1,1,0,0,1,0] => [4,2,3,1] => [[1,3],[2],[4]] => [1,2,1] => 4
[1,0,1,1,0,1,0,0] => [3,2,4,1] => [[1,3],[2],[4]] => [1,2,1] => 4
[1,0,1,1,1,0,0,0] => [2,3,4,1] => [[1,2,3],[4]] => [3,1] => 3
[1,1,0,0,1,0,1,0] => [4,3,1,2] => [[1,4],[2],[3]] => [1,1,2] => 3
[1,1,0,0,1,1,0,0] => [3,4,1,2] => [[1,2],[3,4]] => [2,2] => 2
[1,1,0,1,0,0,1,0] => [4,2,1,3] => [[1,4],[2],[3]] => [1,1,2] => 3
[1,1,0,1,0,1,0,0] => [3,2,1,4] => [[1,4],[2],[3]] => [1,1,2] => 3
[1,1,0,1,1,0,0,0] => [2,3,1,4] => [[1,2,4],[3]] => [2,2] => 2
[1,1,1,0,0,0,1,0] => [4,1,2,3] => [[1,3,4],[2]] => [1,3] => 1
[1,1,1,0,0,1,0,0] => [3,1,2,4] => [[1,3,4],[2]] => [1,3] => 1
[1,1,1,0,1,0,0,0] => [2,1,3,4] => [[1,3,4],[2]] => [1,3] => 1
[1,1,1,1,0,0,0,0] => [1,2,3,4] => [[1,2,3,4]] => [4] => 0
[1,0,1,0,1,0,1,0,1,0] => [5,4,3,2,1] => [[1],[2],[3],[4],[5]] => [1,1,1,1,1] => 10
[1,0,1,0,1,0,1,1,0,0] => [4,5,3,2,1] => [[1,2],[3],[4],[5]] => [2,1,1,1] => 9
[1,0,1,0,1,1,0,0,1,0] => [5,3,4,2,1] => [[1,3],[2],[4],[5]] => [1,2,1,1] => 8
[1,0,1,0,1,1,0,1,0,0] => [4,3,5,2,1] => [[1,3],[2],[4],[5]] => [1,2,1,1] => 8
[1,0,1,0,1,1,1,0,0,0] => [3,4,5,2,1] => [[1,2,3],[4],[5]] => [3,1,1] => 7
[1,0,1,1,0,0,1,0,1,0] => [5,4,2,3,1] => [[1,4],[2],[3],[5]] => [1,1,2,1] => 7
[1,0,1,1,0,0,1,1,0,0] => [4,5,2,3,1] => [[1,2],[3,4],[5]] => [2,2,1] => 6
[1,0,1,1,0,1,0,0,1,0] => [5,3,2,4,1] => [[1,4],[2],[3],[5]] => [1,1,2,1] => 7
[1,0,1,1,0,1,0,1,0,0] => [4,3,2,5,1] => [[1,4],[2],[3],[5]] => [1,1,2,1] => 7
[1,0,1,1,0,1,1,0,0,0] => [3,4,2,5,1] => [[1,2,4],[3],[5]] => [2,2,1] => 6
[1,0,1,1,1,0,0,0,1,0] => [5,2,3,4,1] => [[1,3,4],[2],[5]] => [1,3,1] => 5
[1,0,1,1,1,0,0,1,0,0] => [4,2,3,5,1] => [[1,3,4],[2],[5]] => [1,3,1] => 5
[1,0,1,1,1,0,1,0,0,0] => [3,2,4,5,1] => [[1,3,4],[2],[5]] => [1,3,1] => 5
[1,0,1,1,1,1,0,0,0,0] => [2,3,4,5,1] => [[1,2,3,4],[5]] => [4,1] => 4
[1,1,0,0,1,0,1,0,1,0] => [5,4,3,1,2] => [[1,5],[2],[3],[4]] => [1,1,1,2] => 6
[1,1,0,0,1,0,1,1,0,0] => [4,5,3,1,2] => [[1,2],[3,5],[4]] => [2,1,2] => 5
[1,1,0,0,1,1,0,0,1,0] => [5,3,4,1,2] => [[1,3],[2,5],[4]] => [1,2,2] => 4
[1,1,0,0,1,1,0,1,0,0] => [4,3,5,1,2] => [[1,3],[2,5],[4]] => [1,2,2] => 4
[1,1,0,0,1,1,1,0,0,0] => [3,4,5,1,2] => [[1,2,3],[4,5]] => [3,2] => 3
[1,1,0,1,0,0,1,0,1,0] => [5,4,2,1,3] => [[1,5],[2],[3],[4]] => [1,1,1,2] => 6
[1,1,0,1,0,0,1,1,0,0] => [4,5,2,1,3] => [[1,2],[3,5],[4]] => [2,1,2] => 5
[1,1,0,1,0,1,0,0,1,0] => [5,3,2,1,4] => [[1,5],[2],[3],[4]] => [1,1,1,2] => 6
[1,1,0,1,0,1,0,1,0,0] => [4,3,2,1,5] => [[1,5],[2],[3],[4]] => [1,1,1,2] => 6
[1,1,0,1,0,1,1,0,0,0] => [3,4,2,1,5] => [[1,2,5],[3],[4]] => [2,1,2] => 5
[1,1,0,1,1,0,0,0,1,0] => [5,2,3,1,4] => [[1,3,5],[2],[4]] => [1,2,2] => 4
[1,1,0,1,1,0,0,1,0,0] => [4,2,3,1,5] => [[1,3,5],[2],[4]] => [1,2,2] => 4
[1,1,0,1,1,0,1,0,0,0] => [3,2,4,1,5] => [[1,3,5],[2],[4]] => [1,2,2] => 4
[1,1,0,1,1,1,0,0,0,0] => [2,3,4,1,5] => [[1,2,3,5],[4]] => [3,2] => 3
[1,1,1,0,0,0,1,0,1,0] => [5,4,1,2,3] => [[1,4,5],[2],[3]] => [1,1,3] => 3
[1,1,1,0,0,0,1,1,0,0] => [4,5,1,2,3] => [[1,2,5],[3,4]] => [2,3] => 2
[1,1,1,0,0,1,0,0,1,0] => [5,3,1,2,4] => [[1,4,5],[2],[3]] => [1,1,3] => 3
[1,1,1,0,0,1,0,1,0,0] => [4,3,1,2,5] => [[1,4,5],[2],[3]] => [1,1,3] => 3
[1,1,1,0,0,1,1,0,0,0] => [3,4,1,2,5] => [[1,2,5],[3,4]] => [2,3] => 2
[1,1,1,0,1,0,0,0,1,0] => [5,2,1,3,4] => [[1,4,5],[2],[3]] => [1,1,3] => 3
[1,1,1,0,1,0,0,1,0,0] => [4,2,1,3,5] => [[1,4,5],[2],[3]] => [1,1,3] => 3
[1,1,1,0,1,0,1,0,0,0] => [3,2,1,4,5] => [[1,4,5],[2],[3]] => [1,1,3] => 3
[1,1,1,0,1,1,0,0,0,0] => [2,3,1,4,5] => [[1,2,4,5],[3]] => [2,3] => 2
[1,1,1,1,0,0,0,0,1,0] => [5,1,2,3,4] => [[1,3,4,5],[2]] => [1,4] => 1
[1,1,1,1,0,0,0,1,0,0] => [4,1,2,3,5] => [[1,3,4,5],[2]] => [1,4] => 1
[1,1,1,1,0,0,1,0,0,0] => [3,1,2,4,5] => [[1,3,4,5],[2]] => [1,4] => 1
[1,1,1,1,0,1,0,0,0,0] => [2,1,3,4,5] => [[1,3,4,5],[2]] => [1,4] => 1
[1,1,1,1,1,0,0,0,0,0] => [1,2,3,4,5] => [[1,2,3,4,5]] => [5] => 0
[1,0,1,0,1,0,1,0,1,0,1,0] => [6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6]] => [1,1,1,1,1,1] => 15
[1,0,1,0,1,0,1,0,1,1,0,0] => [5,6,4,3,2,1] => [[1,2],[3],[4],[5],[6]] => [2,1,1,1,1] => 14
[1,0,1,0,1,0,1,1,0,0,1,0] => [6,4,5,3,2,1] => [[1,3],[2],[4],[5],[6]] => [1,2,1,1,1] => 13
[1,0,1,0,1,0,1,1,0,1,0,0] => [5,4,6,3,2,1] => [[1,3],[2],[4],[5],[6]] => [1,2,1,1,1] => 13
[1,0,1,0,1,0,1,1,1,0,0,0] => [4,5,6,3,2,1] => [[1,2,3],[4],[5],[6]] => [3,1,1,1] => 12
[1,0,1,0,1,1,0,0,1,0,1,0] => [6,5,3,4,2,1] => [[1,4],[2],[3],[5],[6]] => [1,1,2,1,1] => 12
[1,0,1,0,1,1,0,0,1,1,0,0] => [5,6,3,4,2,1] => [[1,2],[3,4],[5],[6]] => [2,2,1,1] => 11
[1,0,1,0,1,1,0,1,0,0,1,0] => [6,4,3,5,2,1] => [[1,4],[2],[3],[5],[6]] => [1,1,2,1,1] => 12
[1,0,1,0,1,1,0,1,0,1,0,0] => [5,4,3,6,2,1] => [[1,4],[2],[3],[5],[6]] => [1,1,2,1,1] => 12
[1,0,1,0,1,1,0,1,1,0,0,0] => [4,5,3,6,2,1] => [[1,2,4],[3],[5],[6]] => [2,2,1,1] => 11
[1,0,1,0,1,1,1,0,0,0,1,0] => [6,3,4,5,2,1] => [[1,3,4],[2],[5],[6]] => [1,3,1,1] => 10
[1,0,1,0,1,1,1,0,0,1,0,0] => [5,3,4,6,2,1] => [[1,3,4],[2],[5],[6]] => [1,3,1,1] => 10
[1,0,1,0,1,1,1,0,1,0,0,0] => [4,3,5,6,2,1] => [[1,3,4],[2],[5],[6]] => [1,3,1,1] => 10
[1,0,1,0,1,1,1,1,0,0,0,0] => [3,4,5,6,2,1] => [[1,2,3,4],[5],[6]] => [4,1,1] => 9
[1,0,1,1,0,0,1,0,1,0,1,0] => [6,5,4,2,3,1] => [[1,5],[2],[3],[4],[6]] => [1,1,1,2,1] => 11
[1,0,1,1,0,0,1,0,1,1,0,0] => [5,6,4,2,3,1] => [[1,2],[3,5],[4],[6]] => [2,1,2,1] => 10
[1,0,1,1,0,0,1,1,0,0,1,0] => [6,4,5,2,3,1] => [[1,3],[2,5],[4],[6]] => [1,2,2,1] => 9
[1,0,1,1,0,0,1,1,0,1,0,0] => [5,4,6,2,3,1] => [[1,3],[2,5],[4],[6]] => [1,2,2,1] => 9
[1,0,1,1,0,0,1,1,1,0,0,0] => [4,5,6,2,3,1] => [[1,2,3],[4,5],[6]] => [3,2,1] => 8
[1,0,1,1,0,1,0,0,1,0,1,0] => [6,5,3,2,4,1] => [[1,5],[2],[3],[4],[6]] => [1,1,1,2,1] => 11
[1,0,1,1,0,1,0,0,1,1,0,0] => [5,6,3,2,4,1] => [[1,2],[3,5],[4],[6]] => [2,1,2,1] => 10
[1,0,1,1,0,1,0,1,0,0,1,0] => [6,4,3,2,5,1] => [[1,5],[2],[3],[4],[6]] => [1,1,1,2,1] => 11
[1,0,1,1,0,1,0,1,0,1,0,0] => [5,4,3,2,6,1] => [[1,5],[2],[3],[4],[6]] => [1,1,1,2,1] => 11
[1,0,1,1,0,1,0,1,1,0,0,0] => [4,5,3,2,6,1] => [[1,2,5],[3],[4],[6]] => [2,1,2,1] => 10
[1,0,1,1,0,1,1,0,0,0,1,0] => [6,3,4,2,5,1] => [[1,3,5],[2],[4],[6]] => [1,2,2,1] => 9
[1,0,1,1,0,1,1,0,0,1,0,0] => [5,3,4,2,6,1] => [[1,3,5],[2],[4],[6]] => [1,2,2,1] => 9
[1,0,1,1,0,1,1,0,1,0,0,0] => [4,3,5,2,6,1] => [[1,3,5],[2],[4],[6]] => [1,2,2,1] => 9
[1,0,1,1,0,1,1,1,0,0,0,0] => [3,4,5,2,6,1] => [[1,2,3,5],[4],[6]] => [3,2,1] => 8
[1,0,1,1,1,0,0,0,1,0,1,0] => [6,5,2,3,4,1] => [[1,4,5],[2],[3],[6]] => [1,1,3,1] => 8
[1,0,1,1,1,0,0,0,1,1,0,0] => [5,6,2,3,4,1] => [[1,2,5],[3,4],[6]] => [2,3,1] => 7
[1,0,1,1,1,0,0,1,0,0,1,0] => [6,4,2,3,5,1] => [[1,4,5],[2],[3],[6]] => [1,1,3,1] => 8
[1,0,1,1,1,0,0,1,0,1,0,0] => [5,4,2,3,6,1] => [[1,4,5],[2],[3],[6]] => [1,1,3,1] => 8
[1,0,1,1,1,0,0,1,1,0,0,0] => [4,5,2,3,6,1] => [[1,2,5],[3,4],[6]] => [2,3,1] => 7
[1,0,1,1,1,0,1,0,0,0,1,0] => [6,3,2,4,5,1] => [[1,4,5],[2],[3],[6]] => [1,1,3,1] => 8
[1,0,1,1,1,0,1,0,0,1,0,0] => [5,3,2,4,6,1] => [[1,4,5],[2],[3],[6]] => [1,1,3,1] => 8
[1,0,1,1,1,0,1,0,1,0,0,0] => [4,3,2,5,6,1] => [[1,4,5],[2],[3],[6]] => [1,1,3,1] => 8
[1,0,1,1,1,0,1,1,0,0,0,0] => [3,4,2,5,6,1] => [[1,2,4,5],[3],[6]] => [2,3,1] => 7
>>> Load all 1675 entries. <<<[1,0,1,1,1,1,0,0,0,0,1,0] => [6,2,3,4,5,1] => [[1,3,4,5],[2],[6]] => [1,4,1] => 6
[1,0,1,1,1,1,0,0,0,1,0,0] => [5,2,3,4,6,1] => [[1,3,4,5],[2],[6]] => [1,4,1] => 6
[1,0,1,1,1,1,0,0,1,0,0,0] => [4,2,3,5,6,1] => [[1,3,4,5],[2],[6]] => [1,4,1] => 6
[1,0,1,1,1,1,0,1,0,0,0,0] => [3,2,4,5,6,1] => [[1,3,4,5],[2],[6]] => [1,4,1] => 6
[1,0,1,1,1,1,1,0,0,0,0,0] => [2,3,4,5,6,1] => [[1,2,3,4,5],[6]] => [5,1] => 5
[1,1,0,0,1,0,1,0,1,0,1,0] => [6,5,4,3,1,2] => [[1,6],[2],[3],[4],[5]] => [1,1,1,1,2] => 10
[1,1,0,0,1,0,1,0,1,1,0,0] => [5,6,4,3,1,2] => [[1,2],[3,6],[4],[5]] => [2,1,1,2] => 9
[1,1,0,0,1,0,1,1,0,0,1,0] => [6,4,5,3,1,2] => [[1,3],[2,6],[4],[5]] => [1,2,1,2] => 8
[1,1,0,0,1,0,1,1,0,1,0,0] => [5,4,6,3,1,2] => [[1,3],[2,6],[4],[5]] => [1,2,1,2] => 8
[1,1,0,0,1,0,1,1,1,0,0,0] => [4,5,6,3,1,2] => [[1,2,3],[4,6],[5]] => [3,1,2] => 7
[1,1,0,0,1,1,0,0,1,0,1,0] => [6,5,3,4,1,2] => [[1,4],[2,6],[3],[5]] => [1,1,2,2] => 7
[1,1,0,0,1,1,0,0,1,1,0,0] => [5,6,3,4,1,2] => [[1,2],[3,4],[5,6]] => [2,2,2] => 6
[1,1,0,0,1,1,0,1,0,0,1,0] => [6,4,3,5,1,2] => [[1,4],[2,6],[3],[5]] => [1,1,2,2] => 7
[1,1,0,0,1,1,0,1,0,1,0,0] => [5,4,3,6,1,2] => [[1,4],[2,6],[3],[5]] => [1,1,2,2] => 7
[1,1,0,0,1,1,0,1,1,0,0,0] => [4,5,3,6,1,2] => [[1,2,4],[3,6],[5]] => [2,2,2] => 6
[1,1,0,0,1,1,1,0,0,0,1,0] => [6,3,4,5,1,2] => [[1,3,4],[2,6],[5]] => [1,3,2] => 5
[1,1,0,0,1,1,1,0,0,1,0,0] => [5,3,4,6,1,2] => [[1,3,4],[2,6],[5]] => [1,3,2] => 5
[1,1,0,0,1,1,1,0,1,0,0,0] => [4,3,5,6,1,2] => [[1,3,4],[2,6],[5]] => [1,3,2] => 5
[1,1,0,0,1,1,1,1,0,0,0,0] => [3,4,5,6,1,2] => [[1,2,3,4],[5,6]] => [4,2] => 4
[1,1,0,1,0,0,1,0,1,0,1,0] => [6,5,4,2,1,3] => [[1,6],[2],[3],[4],[5]] => [1,1,1,1,2] => 10
[1,1,0,1,0,0,1,0,1,1,0,0] => [5,6,4,2,1,3] => [[1,2],[3,6],[4],[5]] => [2,1,1,2] => 9
[1,1,0,1,0,0,1,1,0,0,1,0] => [6,4,5,2,1,3] => [[1,3],[2,6],[4],[5]] => [1,2,1,2] => 8
[1,1,0,1,0,0,1,1,0,1,0,0] => [5,4,6,2,1,3] => [[1,3],[2,6],[4],[5]] => [1,2,1,2] => 8
[1,1,0,1,0,0,1,1,1,0,0,0] => [4,5,6,2,1,3] => [[1,2,3],[4,6],[5]] => [3,1,2] => 7
[1,1,0,1,0,1,0,0,1,0,1,0] => [6,5,3,2,1,4] => [[1,6],[2],[3],[4],[5]] => [1,1,1,1,2] => 10
[1,1,0,1,0,1,0,0,1,1,0,0] => [5,6,3,2,1,4] => [[1,2],[3,6],[4],[5]] => [2,1,1,2] => 9
[1,1,0,1,0,1,0,1,0,0,1,0] => [6,4,3,2,1,5] => [[1,6],[2],[3],[4],[5]] => [1,1,1,1,2] => 10
[1,1,0,1,0,1,0,1,0,1,0,0] => [5,4,3,2,1,6] => [[1,6],[2],[3],[4],[5]] => [1,1,1,1,2] => 10
[1,1,0,1,0,1,0,1,1,0,0,0] => [4,5,3,2,1,6] => [[1,2,6],[3],[4],[5]] => [2,1,1,2] => 9
[1,1,0,1,0,1,1,0,0,0,1,0] => [6,3,4,2,1,5] => [[1,3,6],[2],[4],[5]] => [1,2,1,2] => 8
[1,1,0,1,0,1,1,0,0,1,0,0] => [5,3,4,2,1,6] => [[1,3,6],[2],[4],[5]] => [1,2,1,2] => 8
[1,1,0,1,0,1,1,0,1,0,0,0] => [4,3,5,2,1,6] => [[1,3,6],[2],[4],[5]] => [1,2,1,2] => 8
[1,1,0,1,0,1,1,1,0,0,0,0] => [3,4,5,2,1,6] => [[1,2,3,6],[4],[5]] => [3,1,2] => 7
[1,1,0,1,1,0,0,0,1,0,1,0] => [6,5,2,3,1,4] => [[1,4,6],[2],[3],[5]] => [1,1,2,2] => 7
[1,1,0,1,1,0,0,0,1,1,0,0] => [5,6,2,3,1,4] => [[1,2,6],[3,4],[5]] => [2,2,2] => 6
[1,1,0,1,1,0,0,1,0,0,1,0] => [6,4,2,3,1,5] => [[1,4,6],[2],[3],[5]] => [1,1,2,2] => 7
[1,1,0,1,1,0,0,1,0,1,0,0] => [5,4,2,3,1,6] => [[1,4,6],[2],[3],[5]] => [1,1,2,2] => 7
[1,1,0,1,1,0,0,1,1,0,0,0] => [4,5,2,3,1,6] => [[1,2,6],[3,4],[5]] => [2,2,2] => 6
[1,1,0,1,1,0,1,0,0,0,1,0] => [6,3,2,4,1,5] => [[1,4,6],[2],[3],[5]] => [1,1,2,2] => 7
[1,1,0,1,1,0,1,0,0,1,0,0] => [5,3,2,4,1,6] => [[1,4,6],[2],[3],[5]] => [1,1,2,2] => 7
[1,1,0,1,1,0,1,0,1,0,0,0] => [4,3,2,5,1,6] => [[1,4,6],[2],[3],[5]] => [1,1,2,2] => 7
[1,1,0,1,1,0,1,1,0,0,0,0] => [3,4,2,5,1,6] => [[1,2,4,6],[3],[5]] => [2,2,2] => 6
[1,1,0,1,1,1,0,0,0,0,1,0] => [6,2,3,4,1,5] => [[1,3,4,6],[2],[5]] => [1,3,2] => 5
[1,1,0,1,1,1,0,0,0,1,0,0] => [5,2,3,4,1,6] => [[1,3,4,6],[2],[5]] => [1,3,2] => 5
[1,1,0,1,1,1,0,0,1,0,0,0] => [4,2,3,5,1,6] => [[1,3,4,6],[2],[5]] => [1,3,2] => 5
[1,1,0,1,1,1,0,1,0,0,0,0] => [3,2,4,5,1,6] => [[1,3,4,6],[2],[5]] => [1,3,2] => 5
[1,1,0,1,1,1,1,0,0,0,0,0] => [2,3,4,5,1,6] => [[1,2,3,4,6],[5]] => [4,2] => 4
[1,1,1,0,0,0,1,0,1,0,1,0] => [6,5,4,1,2,3] => [[1,5,6],[2],[3],[4]] => [1,1,1,3] => 6
[1,1,1,0,0,0,1,0,1,1,0,0] => [5,6,4,1,2,3] => [[1,2,6],[3,5],[4]] => [2,1,3] => 5
[1,1,1,0,0,0,1,1,0,0,1,0] => [6,4,5,1,2,3] => [[1,3,6],[2,5],[4]] => [1,2,3] => 4
[1,1,1,0,0,0,1,1,0,1,0,0] => [5,4,6,1,2,3] => [[1,3,6],[2,5],[4]] => [1,2,3] => 4
[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
[1,1,1,0,0,1,0,0,1,0,1,0] => [6,5,3,1,2,4] => [[1,5,6],[2],[3],[4]] => [1,1,1,3] => 6
[1,1,1,0,0,1,0,0,1,1,0,0] => [5,6,3,1,2,4] => [[1,2,6],[3,5],[4]] => [2,1,3] => 5
[1,1,1,0,0,1,0,1,0,0,1,0] => [6,4,3,1,2,5] => [[1,5,6],[2],[3],[4]] => [1,1,1,3] => 6
[1,1,1,0,0,1,0,1,0,1,0,0] => [5,4,3,1,2,6] => [[1,5,6],[2],[3],[4]] => [1,1,1,3] => 6
[1,1,1,0,0,1,0,1,1,0,0,0] => [4,5,3,1,2,6] => [[1,2,6],[3,5],[4]] => [2,1,3] => 5
[1,1,1,0,0,1,1,0,0,0,1,0] => [6,3,4,1,2,5] => [[1,3,6],[2,5],[4]] => [1,2,3] => 4
[1,1,1,0,0,1,1,0,0,1,0,0] => [5,3,4,1,2,6] => [[1,3,6],[2,5],[4]] => [1,2,3] => 4
[1,1,1,0,0,1,1,0,1,0,0,0] => [4,3,5,1,2,6] => [[1,3,6],[2,5],[4]] => [1,2,3] => 4
[1,1,1,0,0,1,1,1,0,0,0,0] => [3,4,5,1,2,6] => [[1,2,3,6],[4,5]] => [3,3] => 3
[1,1,1,0,1,0,0,0,1,0,1,0] => [6,5,2,1,3,4] => [[1,5,6],[2],[3],[4]] => [1,1,1,3] => 6
[1,1,1,0,1,0,0,0,1,1,0,0] => [5,6,2,1,3,4] => [[1,2,6],[3,5],[4]] => [2,1,3] => 5
[1,1,1,0,1,0,0,1,0,0,1,0] => [6,4,2,1,3,5] => [[1,5,6],[2],[3],[4]] => [1,1,1,3] => 6
[1,1,1,0,1,0,0,1,0,1,0,0] => [5,4,2,1,3,6] => [[1,5,6],[2],[3],[4]] => [1,1,1,3] => 6
[1,1,1,0,1,0,0,1,1,0,0,0] => [4,5,2,1,3,6] => [[1,2,6],[3,5],[4]] => [2,1,3] => 5
[1,1,1,0,1,0,1,0,0,0,1,0] => [6,3,2,1,4,5] => [[1,5,6],[2],[3],[4]] => [1,1,1,3] => 6
[1,1,1,0,1,0,1,0,0,1,0,0] => [5,3,2,1,4,6] => [[1,5,6],[2],[3],[4]] => [1,1,1,3] => 6
[1,1,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1,5,6] => [[1,5,6],[2],[3],[4]] => [1,1,1,3] => 6
[1,1,1,0,1,0,1,1,0,0,0,0] => [3,4,2,1,5,6] => [[1,2,5,6],[3],[4]] => [2,1,3] => 5
[1,1,1,0,1,1,0,0,0,0,1,0] => [6,2,3,1,4,5] => [[1,3,5,6],[2],[4]] => [1,2,3] => 4
[1,1,1,0,1,1,0,0,0,1,0,0] => [5,2,3,1,4,6] => [[1,3,5,6],[2],[4]] => [1,2,3] => 4
[1,1,1,0,1,1,0,0,1,0,0,0] => [4,2,3,1,5,6] => [[1,3,5,6],[2],[4]] => [1,2,3] => 4
[1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,4,1,5,6] => [[1,3,5,6],[2],[4]] => [1,2,3] => 4
[1,1,1,0,1,1,1,0,0,0,0,0] => [2,3,4,1,5,6] => [[1,2,3,5,6],[4]] => [3,3] => 3
[1,1,1,1,0,0,0,0,1,0,1,0] => [6,5,1,2,3,4] => [[1,4,5,6],[2],[3]] => [1,1,4] => 3
[1,1,1,1,0,0,0,0,1,1,0,0] => [5,6,1,2,3,4] => [[1,2,5,6],[3,4]] => [2,4] => 2
[1,1,1,1,0,0,0,1,0,0,1,0] => [6,4,1,2,3,5] => [[1,4,5,6],[2],[3]] => [1,1,4] => 3
[1,1,1,1,0,0,0,1,0,1,0,0] => [5,4,1,2,3,6] => [[1,4,5,6],[2],[3]] => [1,1,4] => 3
[1,1,1,1,0,0,0,1,1,0,0,0] => [4,5,1,2,3,6] => [[1,2,5,6],[3,4]] => [2,4] => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [6,3,1,2,4,5] => [[1,4,5,6],[2],[3]] => [1,1,4] => 3
[1,1,1,1,0,0,1,0,0,1,0,0] => [5,3,1,2,4,6] => [[1,4,5,6],[2],[3]] => [1,1,4] => 3
[1,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,2,5,6] => [[1,4,5,6],[2],[3]] => [1,1,4] => 3
[1,1,1,1,0,0,1,1,0,0,0,0] => [3,4,1,2,5,6] => [[1,2,5,6],[3,4]] => [2,4] => 2
[1,1,1,1,0,1,0,0,0,0,1,0] => [6,2,1,3,4,5] => [[1,4,5,6],[2],[3]] => [1,1,4] => 3
[1,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,3,4,6] => [[1,4,5,6],[2],[3]] => [1,1,4] => 3
[1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,3,5,6] => [[1,4,5,6],[2],[3]] => [1,1,4] => 3
[1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,4,5,6] => [[1,4,5,6],[2],[3]] => [1,1,4] => 3
[1,1,1,1,0,1,1,0,0,0,0,0] => [2,3,1,4,5,6] => [[1,2,4,5,6],[3]] => [2,4] => 2
[1,1,1,1,1,0,0,0,0,0,1,0] => [6,1,2,3,4,5] => [[1,3,4,5,6],[2]] => [1,5] => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,2,3,4,6] => [[1,3,4,5,6],[2]] => [1,5] => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,2,3,5,6] => [[1,3,4,5,6],[2]] => [1,5] => 1
[1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,2,4,5,6] => [[1,3,4,5,6],[2]] => [1,5] => 1
[1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,3,4,5,6] => [[1,3,4,5,6],[2]] => [1,5] => 1
[1,1,1,1,1,1,0,0,0,0,0,0] => [1,2,3,4,5,6] => [[1,2,3,4,5,6]] => [6] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7]] => [1,1,1,1,1,1,1] => 21
[1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7]] => [2,1,1,1,1,1] => 20
[1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,2,1] => [[1,3],[2],[4],[5],[6],[7]] => [1,2,1,1,1,1] => 19
[1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,2,1] => [[1,3],[2],[4],[5],[6],[7]] => [1,2,1,1,1,1] => 19
[1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,2,1] => [[1,2,3],[4],[5],[6],[7]] => [3,1,1,1,1] => 18
[1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,2,1] => [[1,4],[2],[3],[5],[6],[7]] => [1,1,2,1,1,1] => 18
[1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,2,1] => [[1,2],[3,4],[5],[6],[7]] => [2,2,1,1,1] => 17
[1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,2,1] => [[1,4],[2],[3],[5],[6],[7]] => [1,1,2,1,1,1] => 18
[1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,2,1] => [[1,4],[2],[3],[5],[6],[7]] => [1,1,2,1,1,1] => 18
[1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,2,1] => [[1,2,4],[3],[5],[6],[7]] => [2,2,1,1,1] => 17
[1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,2,1] => [[1,3,4],[2],[5],[6],[7]] => [1,3,1,1,1] => 16
[1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,2,1] => [[1,3,4],[2],[5],[6],[7]] => [1,3,1,1,1] => 16
[1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,2,1] => [[1,3,4],[2],[5],[6],[7]] => [1,3,1,1,1] => 16
[1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,2,1] => [[1,2,3,4],[5],[6],[7]] => [4,1,1,1] => 15
[1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,2,1] => [[1,5],[2],[3],[4],[6],[7]] => [1,1,1,2,1,1] => 17
[1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,2,1] => [[1,2],[3,5],[4],[6],[7]] => [2,1,2,1,1] => 16
[1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,2,1] => [[1,3],[2,5],[4],[6],[7]] => [1,2,2,1,1] => 15
[1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,2,1] => [[1,3],[2,5],[4],[6],[7]] => [1,2,2,1,1] => 15
[1,0,1,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,2,1] => [[1,2,3],[4,5],[6],[7]] => [3,2,1,1] => 14
[1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,2,1] => [[1,5],[2],[3],[4],[6],[7]] => [1,1,1,2,1,1] => 17
[1,0,1,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,2,1] => [[1,2],[3,5],[4],[6],[7]] => [2,1,2,1,1] => 16
[1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,2,1] => [[1,5],[2],[3],[4],[6],[7]] => [1,1,1,2,1,1] => 17
[1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,2,1] => [[1,5],[2],[3],[4],[6],[7]] => [1,1,1,2,1,1] => 17
[1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,2,1] => [[1,2,5],[3],[4],[6],[7]] => [2,1,2,1,1] => 16
[1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,2,1] => [[1,3,5],[2],[4],[6],[7]] => [1,2,2,1,1] => 15
[1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,2,1] => [[1,3,5],[2],[4],[6],[7]] => [1,2,2,1,1] => 15
[1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,2,1] => [[1,3,5],[2],[4],[6],[7]] => [1,2,2,1,1] => 15
[1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,2,1] => [[1,2,3,5],[4],[6],[7]] => [3,2,1,1] => 14
[1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,2,1] => [[1,4,5],[2],[3],[6],[7]] => [1,1,3,1,1] => 14
[1,0,1,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,2,1] => [[1,2,5],[3,4],[6],[7]] => [2,3,1,1] => 13
[1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,2,1] => [[1,4,5],[2],[3],[6],[7]] => [1,1,3,1,1] => 14
[1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,2,1] => [[1,4,5],[2],[3],[6],[7]] => [1,1,3,1,1] => 14
[1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,2,1] => [[1,2,5],[3,4],[6],[7]] => [2,3,1,1] => 13
[1,0,1,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,2,1] => [[1,4,5],[2],[3],[6],[7]] => [1,1,3,1,1] => 14
[1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,2,1] => [[1,4,5],[2],[3],[6],[7]] => [1,1,3,1,1] => 14
[1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,2,1] => [[1,4,5],[2],[3],[6],[7]] => [1,1,3,1,1] => 14
[1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,2,1] => [[1,2,4,5],[3],[6],[7]] => [2,3,1,1] => 13
[1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,2,1] => [[1,3,4,5],[2],[6],[7]] => [1,4,1,1] => 12
[1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,2,1] => [[1,3,4,5],[2],[6],[7]] => [1,4,1,1] => 12
[1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,2,1] => [[1,3,4,5],[2],[6],[7]] => [1,4,1,1] => 12
[1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,2,1] => [[1,3,4,5],[2],[6],[7]] => [1,4,1,1] => 12
[1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,2,1] => [[1,2,3,4,5],[6],[7]] => [5,1,1] => 11
[1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,3,1] => [[1,6],[2],[3],[4],[5],[7]] => [1,1,1,1,2,1] => 16
[1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,3,1] => [[1,2],[3,6],[4],[5],[7]] => [2,1,1,2,1] => 15
[1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,3,1] => [[1,3],[2,6],[4],[5],[7]] => [1,2,1,2,1] => 14
[1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,3,1] => [[1,3],[2,6],[4],[5],[7]] => [1,2,1,2,1] => 14
[1,0,1,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,3,1] => [[1,2,3],[4,6],[5],[7]] => [3,1,2,1] => 13
[1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,3,1] => [[1,4],[2,6],[3],[5],[7]] => [1,1,2,2,1] => 13
[1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,3,1] => [[1,2],[3,4],[5,6],[7]] => [2,2,2,1] => 12
[1,0,1,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,3,1] => [[1,4],[2,6],[3],[5],[7]] => [1,1,2,2,1] => 13
[1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,3,1] => [[1,4],[2,6],[3],[5],[7]] => [1,1,2,2,1] => 13
[1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,3,1] => [[1,2,4],[3,6],[5],[7]] => [2,2,2,1] => 12
[1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,3,1] => [[1,3,4],[2,6],[5],[7]] => [1,3,2,1] => 11
[1,0,1,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,3,1] => [[1,3,4],[2,6],[5],[7]] => [1,3,2,1] => 11
[1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,3,1] => [[1,3,4],[2,6],[5],[7]] => [1,3,2,1] => 11
[1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,3,1] => [[1,2,3,4],[5,6],[7]] => [4,2,1] => 10
[1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,4,1] => [[1,6],[2],[3],[4],[5],[7]] => [1,1,1,1,2,1] => 16
[1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,4,1] => [[1,2],[3,6],[4],[5],[7]] => [2,1,1,2,1] => 15
[1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,4,1] => [[1,3],[2,6],[4],[5],[7]] => [1,2,1,2,1] => 14
[1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,4,1] => [[1,3],[2,6],[4],[5],[7]] => [1,2,1,2,1] => 14
[1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,4,1] => [[1,2,3],[4,6],[5],[7]] => [3,1,2,1] => 13
[1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,5,1] => [[1,6],[2],[3],[4],[5],[7]] => [1,1,1,1,2,1] => 16
[1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,5,1] => [[1,2],[3,6],[4],[5],[7]] => [2,1,1,2,1] => 15
[1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,6,1] => [[1,6],[2],[3],[4],[5],[7]] => [1,1,1,1,2,1] => 16
[1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,7,1] => [[1,6],[2],[3],[4],[5],[7]] => [1,1,1,1,2,1] => 16
[1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,7,1] => [[1,2,6],[3],[4],[5],[7]] => [2,1,1,2,1] => 15
[1,0,1,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,6,1] => [[1,3,6],[2],[4],[5],[7]] => [1,2,1,2,1] => 14
[1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,7,1] => [[1,3,6],[2],[4],[5],[7]] => [1,2,1,2,1] => 14
[1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,7,1] => [[1,3,6],[2],[4],[5],[7]] => [1,2,1,2,1] => 14
[1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,7,1] => [[1,2,3,6],[4],[5],[7]] => [3,1,2,1] => 13
[1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,5,1] => [[1,4,6],[2],[3],[5],[7]] => [1,1,2,2,1] => 13
[1,0,1,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,5,1] => [[1,2,6],[3,4],[5],[7]] => [2,2,2,1] => 12
[1,0,1,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,6,1] => [[1,4,6],[2],[3],[5],[7]] => [1,1,2,2,1] => 13
[1,0,1,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,7,1] => [[1,4,6],[2],[3],[5],[7]] => [1,1,2,2,1] => 13
[1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,7,1] => [[1,2,6],[3,4],[5],[7]] => [2,2,2,1] => 12
[1,0,1,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,6,1] => [[1,4,6],[2],[3],[5],[7]] => [1,1,2,2,1] => 13
[1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,7,1] => [[1,4,6],[2],[3],[5],[7]] => [1,1,2,2,1] => 13
[1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,7,1] => [[1,4,6],[2],[3],[5],[7]] => [1,1,2,2,1] => 13
[1,0,1,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,7,1] => [[1,2,4,6],[3],[5],[7]] => [2,2,2,1] => 12
[1,0,1,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,6,1] => [[1,3,4,6],[2],[5],[7]] => [1,3,2,1] => 11
[1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,7,1] => [[1,3,4,6],[2],[5],[7]] => [1,3,2,1] => 11
[1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,7,1] => [[1,3,4,6],[2],[5],[7]] => [1,3,2,1] => 11
[1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,7,1] => [[1,3,4,6],[2],[5],[7]] => [1,3,2,1] => 11
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,7,1] => [[1,2,3,4,6],[5],[7]] => [4,2,1] => 10
[1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,4,1] => [[1,5,6],[2],[3],[4],[7]] => [1,1,1,3,1] => 12
[1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,4,1] => [[1,2,6],[3,5],[4],[7]] => [2,1,3,1] => 11
[1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,4,1] => [[1,3,6],[2,5],[4],[7]] => [1,2,3,1] => 10
[1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,4,1] => [[1,3,6],[2,5],[4],[7]] => [1,2,3,1] => 10
[1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,4,1] => [[1,2,3],[4,5,6],[7]] => [3,3,1] => 9
[1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,5,1] => [[1,5,6],[2],[3],[4],[7]] => [1,1,1,3,1] => 12
[1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,5,1] => [[1,2,6],[3,5],[4],[7]] => [2,1,3,1] => 11
[1,0,1,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,6,1] => [[1,5,6],[2],[3],[4],[7]] => [1,1,1,3,1] => 12
[1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,7,1] => [[1,5,6],[2],[3],[4],[7]] => [1,1,1,3,1] => 12
[1,0,1,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,7,1] => [[1,2,6],[3,5],[4],[7]] => [2,1,3,1] => 11
[1,0,1,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,6,1] => [[1,3,6],[2,5],[4],[7]] => [1,2,3,1] => 10
[1,0,1,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,7,1] => [[1,3,6],[2,5],[4],[7]] => [1,2,3,1] => 10
[1,0,1,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,7,1] => [[1,3,6],[2,5],[4],[7]] => [1,2,3,1] => 10
[1,0,1,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,7,1] => [[1,2,3,6],[4,5],[7]] => [3,3,1] => 9
[1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,5,1] => [[1,5,6],[2],[3],[4],[7]] => [1,1,1,3,1] => 12
[1,0,1,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,5,1] => [[1,2,6],[3,5],[4],[7]] => [2,1,3,1] => 11
[1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,6,1] => [[1,5,6],[2],[3],[4],[7]] => [1,1,1,3,1] => 12
[1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,7,1] => [[1,5,6],[2],[3],[4],[7]] => [1,1,1,3,1] => 12
[1,0,1,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,7,1] => [[1,2,6],[3,5],[4],[7]] => [2,1,3,1] => 11
[1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,6,1] => [[1,5,6],[2],[3],[4],[7]] => [1,1,1,3,1] => 12
[1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,7,1] => [[1,5,6],[2],[3],[4],[7]] => [1,1,1,3,1] => 12
[1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,7,1] => [[1,5,6],[2],[3],[4],[7]] => [1,1,1,3,1] => 12
[1,0,1,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,7,1] => [[1,2,5,6],[3],[4],[7]] => [2,1,3,1] => 11
[1,0,1,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,6,1] => [[1,3,5,6],[2],[4],[7]] => [1,2,3,1] => 10
[1,0,1,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,7,1] => [[1,3,5,6],[2],[4],[7]] => [1,2,3,1] => 10
[1,0,1,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,7,1] => [[1,3,5,6],[2],[4],[7]] => [1,2,3,1] => 10
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,7,1] => [[1,3,5,6],[2],[4],[7]] => [1,2,3,1] => 10
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,7,1] => [[1,2,3,5,6],[4],[7]] => [3,3,1] => 9
[1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,5,1] => [[1,4,5,6],[2],[3],[7]] => [1,1,4,1] => 9
[1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,5,1] => [[1,2,5,6],[3,4],[7]] => [2,4,1] => 8
[1,0,1,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,6,1] => [[1,4,5,6],[2],[3],[7]] => [1,1,4,1] => 9
[1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,7,1] => [[1,4,5,6],[2],[3],[7]] => [1,1,4,1] => 9
[1,0,1,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,7,1] => [[1,2,5,6],[3,4],[7]] => [2,4,1] => 8
[1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,6,1] => [[1,4,5,6],[2],[3],[7]] => [1,1,4,1] => 9
[1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,7,1] => [[1,4,5,6],[2],[3],[7]] => [1,1,4,1] => 9
[1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,7,1] => [[1,4,5,6],[2],[3],[7]] => [1,1,4,1] => 9
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,7,1] => [[1,2,5,6],[3,4],[7]] => [2,4,1] => 8
[1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,6,1] => [[1,4,5,6],[2],[3],[7]] => [1,1,4,1] => 9
[1,0,1,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,7,1] => [[1,4,5,6],[2],[3],[7]] => [1,1,4,1] => 9
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,7,1] => [[1,4,5,6],[2],[3],[7]] => [1,1,4,1] => 9
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,7,1] => [[1,4,5,6],[2],[3],[7]] => [1,1,4,1] => 9
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,7,1] => [[1,2,4,5,6],[3],[7]] => [2,4,1] => 8
[1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,6,1] => [[1,3,4,5,6],[2],[7]] => [1,5,1] => 7
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,7,1] => [[1,3,4,5,6],[2],[7]] => [1,5,1] => 7
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,7,1] => [[1,3,4,5,6],[2],[7]] => [1,5,1] => 7
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,7,1] => [[1,3,4,5,6],[2],[7]] => [1,5,1] => 7
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,7,1] => [[1,3,4,5,6],[2],[7]] => [1,5,1] => 7
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,7,1] => [[1,2,3,4,5,6],[7]] => [6,1] => 6
[1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [7,6,5,4,3,1,2] => [[1,7],[2],[3],[4],[5],[6]] => [1,1,1,1,1,2] => 15
[1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [6,7,5,4,3,1,2] => [[1,2],[3,7],[4],[5],[6]] => [2,1,1,1,2] => 14
[1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [7,5,6,4,3,1,2] => [[1,3],[2,7],[4],[5],[6]] => [1,2,1,1,2] => 13
[1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [6,5,7,4,3,1,2] => [[1,3],[2,7],[4],[5],[6]] => [1,2,1,1,2] => 13
[1,1,0,0,1,0,1,0,1,1,1,0,0,0] => [5,6,7,4,3,1,2] => [[1,2,3],[4,7],[5],[6]] => [3,1,1,2] => 12
[1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [7,6,4,5,3,1,2] => [[1,4],[2,7],[3],[5],[6]] => [1,1,2,1,2] => 12
[1,1,0,0,1,0,1,1,0,0,1,1,0,0] => [6,7,4,5,3,1,2] => [[1,2],[3,4],[5,7],[6]] => [2,2,1,2] => 11
[1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [7,5,4,6,3,1,2] => [[1,4],[2,7],[3],[5],[6]] => [1,1,2,1,2] => 12
[1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [6,5,4,7,3,1,2] => [[1,4],[2,7],[3],[5],[6]] => [1,1,2,1,2] => 12
[1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [5,6,4,7,3,1,2] => [[1,2,4],[3,7],[5],[6]] => [2,2,1,2] => 11
[1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [7,4,5,6,3,1,2] => [[1,3,4],[2,7],[5],[6]] => [1,3,1,2] => 10
[1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [6,4,5,7,3,1,2] => [[1,3,4],[2,7],[5],[6]] => [1,3,1,2] => 10
[1,1,0,0,1,0,1,1,1,0,1,0,0,0] => [5,4,6,7,3,1,2] => [[1,3,4],[2,7],[5],[6]] => [1,3,1,2] => 10
[1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [4,5,6,7,3,1,2] => [[1,2,3,4],[5,7],[6]] => [4,1,2] => 9
[1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [7,6,5,3,4,1,2] => [[1,5],[2,7],[3],[4],[6]] => [1,1,1,2,2] => 11
[1,1,0,0,1,1,0,0,1,0,1,1,0,0] => [6,7,5,3,4,1,2] => [[1,2],[3,5],[4,7],[6]] => [2,1,2,2] => 10
[1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [7,5,6,3,4,1,2] => [[1,3],[2,5],[4,7],[6]] => [1,2,2,2] => 9
[1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [6,5,7,3,4,1,2] => [[1,3],[2,5],[4,7],[6]] => [1,2,2,2] => 9
[1,1,0,0,1,1,0,0,1,1,1,0,0,0] => [5,6,7,3,4,1,2] => [[1,2,3],[4,5],[6,7]] => [3,2,2] => 8
[1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [7,6,4,3,5,1,2] => [[1,5],[2,7],[3],[4],[6]] => [1,1,1,2,2] => 11
[1,1,0,0,1,1,0,1,0,0,1,1,0,0] => [6,7,4,3,5,1,2] => [[1,2],[3,5],[4,7],[6]] => [2,1,2,2] => 10
[1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [7,5,4,3,6,1,2] => [[1,5],[2,7],[3],[4],[6]] => [1,1,1,2,2] => 11
[1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [6,5,4,3,7,1,2] => [[1,5],[2,7],[3],[4],[6]] => [1,1,1,2,2] => 11
[1,1,0,0,1,1,0,1,0,1,1,0,0,0] => [5,6,4,3,7,1,2] => [[1,2,5],[3,7],[4],[6]] => [2,1,2,2] => 10
[1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [7,4,5,3,6,1,2] => [[1,3,5],[2,7],[4],[6]] => [1,2,2,2] => 9
[1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [6,4,5,3,7,1,2] => [[1,3,5],[2,7],[4],[6]] => [1,2,2,2] => 9
[1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [5,4,6,3,7,1,2] => [[1,3,5],[2,7],[4],[6]] => [1,2,2,2] => 9
[1,1,0,0,1,1,0,1,1,1,0,0,0,0] => [4,5,6,3,7,1,2] => [[1,2,3,5],[4,7],[6]] => [3,2,2] => 8
[1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [7,6,3,4,5,1,2] => [[1,4,5],[2,7],[3],[6]] => [1,1,3,2] => 8
[1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [6,7,3,4,5,1,2] => [[1,2,5],[3,4],[6,7]] => [2,3,2] => 7
[1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [7,5,3,4,6,1,2] => [[1,4,5],[2,7],[3],[6]] => [1,1,3,2] => 8
[1,1,0,0,1,1,1,0,0,1,0,1,0,0] => [6,5,3,4,7,1,2] => [[1,4,5],[2,7],[3],[6]] => [1,1,3,2] => 8
[1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [5,6,3,4,7,1,2] => [[1,2,5],[3,4],[6,7]] => [2,3,2] => 7
[1,1,0,0,1,1,1,0,1,0,0,0,1,0] => [7,4,3,5,6,1,2] => [[1,4,5],[2,7],[3],[6]] => [1,1,3,2] => 8
[1,1,0,0,1,1,1,0,1,0,0,1,0,0] => [6,4,3,5,7,1,2] => [[1,4,5],[2,7],[3],[6]] => [1,1,3,2] => 8
[1,1,0,0,1,1,1,0,1,0,1,0,0,0] => [5,4,3,6,7,1,2] => [[1,4,5],[2,7],[3],[6]] => [1,1,3,2] => 8
[1,1,0,0,1,1,1,0,1,1,0,0,0,0] => [4,5,3,6,7,1,2] => [[1,2,4,5],[3,7],[6]] => [2,3,2] => 7
[1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [7,3,4,5,6,1,2] => [[1,3,4,5],[2,7],[6]] => [1,4,2] => 6
[1,1,0,0,1,1,1,1,0,0,0,1,0,0] => [6,3,4,5,7,1,2] => [[1,3,4,5],[2,7],[6]] => [1,4,2] => 6
[1,1,0,0,1,1,1,1,0,0,1,0,0,0] => [5,3,4,6,7,1,2] => [[1,3,4,5],[2,7],[6]] => [1,4,2] => 6
[1,1,0,0,1,1,1,1,0,1,0,0,0,0] => [4,3,5,6,7,1,2] => [[1,3,4,5],[2,7],[6]] => [1,4,2] => 6
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [3,4,5,6,7,1,2] => [[1,2,3,4,5],[6,7]] => [5,2] => 5
[1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,2,1,3] => [[1,7],[2],[3],[4],[5],[6]] => [1,1,1,1,1,2] => 15
[1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,2,1,3] => [[1,2],[3,7],[4],[5],[6]] => [2,1,1,1,2] => 14
[1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,2,1,3] => [[1,3],[2,7],[4],[5],[6]] => [1,2,1,1,2] => 13
[1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,2,1,3] => [[1,3],[2,7],[4],[5],[6]] => [1,2,1,1,2] => 13
[1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,2,1,3] => [[1,2,3],[4,7],[5],[6]] => [3,1,1,2] => 12
[1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,2,1,3] => [[1,4],[2,7],[3],[5],[6]] => [1,1,2,1,2] => 12
[1,1,0,1,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,2,1,3] => [[1,2],[3,4],[5,7],[6]] => [2,2,1,2] => 11
[1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,2,1,3] => [[1,4],[2,7],[3],[5],[6]] => [1,1,2,1,2] => 12
[1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,2,1,3] => [[1,4],[2,7],[3],[5],[6]] => [1,1,2,1,2] => 12
[1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,2,1,3] => [[1,2,4],[3,7],[5],[6]] => [2,2,1,2] => 11
[1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,2,1,3] => [[1,3,4],[2,7],[5],[6]] => [1,3,1,2] => 10
[1,1,0,1,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,2,1,3] => [[1,3,4],[2,7],[5],[6]] => [1,3,1,2] => 10
[1,1,0,1,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,2,1,3] => [[1,3,4],[2,7],[5],[6]] => [1,3,1,2] => 10
[1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,2,1,3] => [[1,2,3,4],[5,7],[6]] => [4,1,2] => 9
[1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,2,1,4] => [[1,7],[2],[3],[4],[5],[6]] => [1,1,1,1,1,2] => 15
[1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,2,1,4] => [[1,2],[3,7],[4],[5],[6]] => [2,1,1,1,2] => 14
[1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,2,1,4] => [[1,3],[2,7],[4],[5],[6]] => [1,2,1,1,2] => 13
[1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,2,1,4] => [[1,3],[2,7],[4],[5],[6]] => [1,2,1,1,2] => 13
[1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,2,1,4] => [[1,2,3],[4,7],[5],[6]] => [3,1,1,2] => 12
[1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,2,1,5] => [[1,7],[2],[3],[4],[5],[6]] => [1,1,1,1,1,2] => 15
[1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,2,1,5] => [[1,2],[3,7],[4],[5],[6]] => [2,1,1,1,2] => 14
[1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,2,1,6] => [[1,7],[2],[3],[4],[5],[6]] => [1,1,1,1,1,2] => 15
[1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,2,1,7] => [[1,7],[2],[3],[4],[5],[6]] => [1,1,1,1,1,2] => 15
[1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,2,1,7] => [[1,2,7],[3],[4],[5],[6]] => [2,1,1,1,2] => 14
[1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,2,1,6] => [[1,3,7],[2],[4],[5],[6]] => [1,2,1,1,2] => 13
[1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,2,1,7] => [[1,3,7],[2],[4],[5],[6]] => [1,2,1,1,2] => 13
[1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,2,1,7] => [[1,3,7],[2],[4],[5],[6]] => [1,2,1,1,2] => 13
[1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,2,1,7] => [[1,2,3,7],[4],[5],[6]] => [3,1,1,2] => 12
[1,1,0,1,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,2,1,5] => [[1,4,7],[2],[3],[5],[6]] => [1,1,2,1,2] => 12
[1,1,0,1,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,2,1,5] => [[1,2,7],[3,4],[5],[6]] => [2,2,1,2] => 11
[1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,2,1,6] => [[1,4,7],[2],[3],[5],[6]] => [1,1,2,1,2] => 12
[1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,2,1,7] => [[1,4,7],[2],[3],[5],[6]] => [1,1,2,1,2] => 12
[1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,2,1,7] => [[1,2,7],[3,4],[5],[6]] => [2,2,1,2] => 11
[1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,2,1,6] => [[1,4,7],[2],[3],[5],[6]] => [1,1,2,1,2] => 12
[1,1,0,1,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,2,1,7] => [[1,4,7],[2],[3],[5],[6]] => [1,1,2,1,2] => 12
[1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,2,1,7] => [[1,4,7],[2],[3],[5],[6]] => [1,1,2,1,2] => 12
[1,1,0,1,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,2,1,7] => [[1,2,4,7],[3],[5],[6]] => [2,2,1,2] => 11
[1,1,0,1,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,2,1,6] => [[1,3,4,7],[2],[5],[6]] => [1,3,1,2] => 10
[1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,2,1,7] => [[1,3,4,7],[2],[5],[6]] => [1,3,1,2] => 10
[1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,2,1,7] => [[1,3,4,7],[2],[5],[6]] => [1,3,1,2] => 10
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,2,1,7] => [[1,3,4,7],[2],[5],[6]] => [1,3,1,2] => 10
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,2,1,7] => [[1,2,3,4,7],[5],[6]] => [4,1,2] => 9
[1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,3,1,4] => [[1,5,7],[2],[3],[4],[6]] => [1,1,1,2,2] => 11
[1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,3,1,4] => [[1,2,7],[3,5],[4],[6]] => [2,1,2,2] => 10
[1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,3,1,4] => [[1,3,7],[2,5],[4],[6]] => [1,2,2,2] => 9
[1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,3,1,4] => [[1,3,7],[2,5],[4],[6]] => [1,2,2,2] => 9
[1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,3,1,4] => [[1,2,3],[4,5,7],[6]] => [3,2,2] => 8
[1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,3,1,5] => [[1,5,7],[2],[3],[4],[6]] => [1,1,1,2,2] => 11
[1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,3,1,5] => [[1,2,7],[3,5],[4],[6]] => [2,1,2,2] => 10
[1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,3,1,6] => [[1,5,7],[2],[3],[4],[6]] => [1,1,1,2,2] => 11
[1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,3,1,7] => [[1,5,7],[2],[3],[4],[6]] => [1,1,1,2,2] => 11
[1,1,0,1,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,3,1,7] => [[1,2,7],[3,5],[4],[6]] => [2,1,2,2] => 10
[1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,3,1,6] => [[1,3,7],[2,5],[4],[6]] => [1,2,2,2] => 9
[1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,3,1,7] => [[1,3,7],[2,5],[4],[6]] => [1,2,2,2] => 9
[1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,3,1,7] => [[1,3,7],[2,5],[4],[6]] => [1,2,2,2] => 9
[1,1,0,1,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,3,1,7] => [[1,2,3,7],[4,5],[6]] => [3,2,2] => 8
[1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,4,1,5] => [[1,5,7],[2],[3],[4],[6]] => [1,1,1,2,2] => 11
[1,1,0,1,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,4,1,5] => [[1,2,7],[3,5],[4],[6]] => [2,1,2,2] => 10
[1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,4,1,6] => [[1,5,7],[2],[3],[4],[6]] => [1,1,1,2,2] => 11
[1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,4,1,7] => [[1,5,7],[2],[3],[4],[6]] => [1,1,1,2,2] => 11
[1,1,0,1,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,4,1,7] => [[1,2,7],[3,5],[4],[6]] => [2,1,2,2] => 10
[1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,5,1,6] => [[1,5,7],[2],[3],[4],[6]] => [1,1,1,2,2] => 11
[1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,5,1,7] => [[1,5,7],[2],[3],[4],[6]] => [1,1,1,2,2] => 11
[1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,6,1,7] => [[1,5,7],[2],[3],[4],[6]] => [1,1,1,2,2] => 11
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,6,1,7] => [[1,2,5,7],[3],[4],[6]] => [2,1,2,2] => 10
[1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,5,1,6] => [[1,3,5,7],[2],[4],[6]] => [1,2,2,2] => 9
[1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,5,1,7] => [[1,3,5,7],[2],[4],[6]] => [1,2,2,2] => 9
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,6,1,7] => [[1,3,5,7],[2],[4],[6]] => [1,2,2,2] => 9
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,6,1,7] => [[1,3,5,7],[2],[4],[6]] => [1,2,2,2] => 9
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,6,1,7] => [[1,2,3,5,7],[4],[6]] => [3,2,2] => 8
[1,1,0,1,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,4,1,5] => [[1,4,5,7],[2],[3],[6]] => [1,1,3,2] => 8
[1,1,0,1,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,4,1,5] => [[1,2,5,7],[3,4],[6]] => [2,3,2] => 7
[1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,4,1,6] => [[1,4,5,7],[2],[3],[6]] => [1,1,3,2] => 8
[1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,4,1,7] => [[1,4,5,7],[2],[3],[6]] => [1,1,3,2] => 8
[1,1,0,1,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,4,1,7] => [[1,2,5,7],[3,4],[6]] => [2,3,2] => 7
[1,1,0,1,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,5,1,6] => [[1,4,5,7],[2],[3],[6]] => [1,1,3,2] => 8
[1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,5,1,7] => [[1,4,5,7],[2],[3],[6]] => [1,1,3,2] => 8
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,6,1,7] => [[1,4,5,7],[2],[3],[6]] => [1,1,3,2] => 8
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,6,1,7] => [[1,2,5,7],[3,4],[6]] => [2,3,2] => 7
[1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,5,1,6] => [[1,4,5,7],[2],[3],[6]] => [1,1,3,2] => 8
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,5,1,7] => [[1,4,5,7],[2],[3],[6]] => [1,1,3,2] => 8
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,6,1,7] => [[1,4,5,7],[2],[3],[6]] => [1,1,3,2] => 8
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,6,1,7] => [[1,4,5,7],[2],[3],[6]] => [1,1,3,2] => 8
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,6,1,7] => [[1,2,4,5,7],[3],[6]] => [2,3,2] => 7
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,5,1,6] => [[1,3,4,5,7],[2],[6]] => [1,4,2] => 6
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,5,1,7] => [[1,3,4,5,7],[2],[6]] => [1,4,2] => 6
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,6,1,7] => [[1,3,4,5,7],[2],[6]] => [1,4,2] => 6
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,6,1,7] => [[1,3,4,5,7],[2],[6]] => [1,4,2] => 6
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,6,1,7] => [[1,3,4,5,7],[2],[6]] => [1,4,2] => 6
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,6,1,7] => [[1,2,3,4,5,7],[6]] => [5,2] => 5
[1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [7,6,5,4,1,2,3] => [[1,6,7],[2],[3],[4],[5]] => [1,1,1,1,3] => 10
[1,1,1,0,0,0,1,0,1,0,1,1,0,0] => [6,7,5,4,1,2,3] => [[1,2,7],[3,6],[4],[5]] => [2,1,1,3] => 9
[1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [7,5,6,4,1,2,3] => [[1,3,7],[2,6],[4],[5]] => [1,2,1,3] => 8
[1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [6,5,7,4,1,2,3] => [[1,3,7],[2,6],[4],[5]] => [1,2,1,3] => 8
[1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [5,6,7,4,1,2,3] => [[1,2,3],[4,6,7],[5]] => [3,1,3] => 7
[1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [7,6,4,5,1,2,3] => [[1,4,7],[2,6],[3],[5]] => [1,1,2,3] => 7
[1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [6,7,4,5,1,2,3] => [[1,2,7],[3,4],[5,6]] => [2,2,3] => 6
[1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [7,5,4,6,1,2,3] => [[1,4,7],[2,6],[3],[5]] => [1,1,2,3] => 7
[1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [6,5,4,7,1,2,3] => [[1,4,7],[2,6],[3],[5]] => [1,1,2,3] => 7
[1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [5,6,4,7,1,2,3] => [[1,2,4],[3,6,7],[5]] => [2,2,3] => 6
[1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [7,4,5,6,1,2,3] => [[1,3,4],[2,6,7],[5]] => [1,3,3] => 5
[1,1,1,0,0,0,1,1,1,0,0,1,0,0] => [6,4,5,7,1,2,3] => [[1,3,4],[2,6,7],[5]] => [1,3,3] => 5
[1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [5,4,6,7,1,2,3] => [[1,3,4],[2,6,7],[5]] => [1,3,3] => 5
[1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [4,5,6,7,1,2,3] => [[1,2,3,4],[5,6,7]] => [4,3] => 4
[1,1,1,0,0,1,0,0,1,0,1,0,1,0] => [7,6,5,3,1,2,4] => [[1,6,7],[2],[3],[4],[5]] => [1,1,1,1,3] => 10
[1,1,1,0,0,1,0,0,1,0,1,1,0,0] => [6,7,5,3,1,2,4] => [[1,2,7],[3,6],[4],[5]] => [2,1,1,3] => 9
[1,1,1,0,0,1,0,0,1,1,0,0,1,0] => [7,5,6,3,1,2,4] => [[1,3,7],[2,6],[4],[5]] => [1,2,1,3] => 8
[1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [6,5,7,3,1,2,4] => [[1,3,7],[2,6],[4],[5]] => [1,2,1,3] => 8
[1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [5,6,7,3,1,2,4] => [[1,2,3],[4,6,7],[5]] => [3,1,3] => 7
[1,1,1,0,0,1,0,1,0,0,1,0,1,0] => [7,6,4,3,1,2,5] => [[1,6,7],[2],[3],[4],[5]] => [1,1,1,1,3] => 10
[1,1,1,0,0,1,0,1,0,0,1,1,0,0] => [6,7,4,3,1,2,5] => [[1,2,7],[3,6],[4],[5]] => [2,1,1,3] => 9
[1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [7,5,4,3,1,2,6] => [[1,6,7],[2],[3],[4],[5]] => [1,1,1,1,3] => 10
[1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [6,5,4,3,1,2,7] => [[1,6,7],[2],[3],[4],[5]] => [1,1,1,1,3] => 10
[1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [5,6,4,3,1,2,7] => [[1,2,7],[3,6],[4],[5]] => [2,1,1,3] => 9
[1,1,1,0,0,1,0,1,1,0,0,0,1,0] => [7,4,5,3,1,2,6] => [[1,3,7],[2,6],[4],[5]] => [1,2,1,3] => 8
[1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [6,4,5,3,1,2,7] => [[1,3,7],[2,6],[4],[5]] => [1,2,1,3] => 8
[1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [5,4,6,3,1,2,7] => [[1,3,7],[2,6],[4],[5]] => [1,2,1,3] => 8
[1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [4,5,6,3,1,2,7] => [[1,2,3,7],[4,6],[5]] => [3,1,3] => 7
[1,1,1,0,0,1,1,0,0,0,1,0,1,0] => [7,6,3,4,1,2,5] => [[1,4,7],[2,6],[3],[5]] => [1,1,2,3] => 7
[1,1,1,0,0,1,1,0,0,0,1,1,0,0] => [6,7,3,4,1,2,5] => [[1,2,7],[3,4],[5,6]] => [2,2,3] => 6
[1,1,1,0,0,1,1,0,0,1,0,0,1,0] => [7,5,3,4,1,2,6] => [[1,4,7],[2,6],[3],[5]] => [1,1,2,3] => 7
[1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [6,5,3,4,1,2,7] => [[1,4,7],[2,6],[3],[5]] => [1,1,2,3] => 7
[1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [5,6,3,4,1,2,7] => [[1,2,7],[3,4],[5,6]] => [2,2,3] => 6
[1,1,1,0,0,1,1,0,1,0,0,0,1,0] => [7,4,3,5,1,2,6] => [[1,4,7],[2,6],[3],[5]] => [1,1,2,3] => 7
[1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [6,4,3,5,1,2,7] => [[1,4,7],[2,6],[3],[5]] => [1,1,2,3] => 7
[1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [5,4,3,6,1,2,7] => [[1,4,7],[2,6],[3],[5]] => [1,1,2,3] => 7
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [4,5,3,6,1,2,7] => [[1,2,4,7],[3,6],[5]] => [2,2,3] => 6
[1,1,1,0,0,1,1,1,0,0,0,0,1,0] => [7,3,4,5,1,2,6] => [[1,3,4,7],[2,6],[5]] => [1,3,3] => 5
[1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [6,3,4,5,1,2,7] => [[1,3,4,7],[2,6],[5]] => [1,3,3] => 5
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [5,3,4,6,1,2,7] => [[1,3,4,7],[2,6],[5]] => [1,3,3] => 5
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [4,3,5,6,1,2,7] => [[1,3,4,7],[2,6],[5]] => [1,3,3] => 5
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [3,4,5,6,1,2,7] => [[1,2,3,4,7],[5,6]] => [4,3] => 4
[1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [7,6,5,2,1,3,4] => [[1,6,7],[2],[3],[4],[5]] => [1,1,1,1,3] => 10
[1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [6,7,5,2,1,3,4] => [[1,2,7],[3,6],[4],[5]] => [2,1,1,3] => 9
[1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [7,5,6,2,1,3,4] => [[1,3,7],[2,6],[4],[5]] => [1,2,1,3] => 8
[1,1,1,0,1,0,0,0,1,1,0,1,0,0] => [6,5,7,2,1,3,4] => [[1,3,7],[2,6],[4],[5]] => [1,2,1,3] => 8
[1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [5,6,7,2,1,3,4] => [[1,2,3],[4,6,7],[5]] => [3,1,3] => 7
[1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [7,6,4,2,1,3,5] => [[1,6,7],[2],[3],[4],[5]] => [1,1,1,1,3] => 10
[1,1,1,0,1,0,0,1,0,0,1,1,0,0] => [6,7,4,2,1,3,5] => [[1,2,7],[3,6],[4],[5]] => [2,1,1,3] => 9
[1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [7,5,4,2,1,3,6] => [[1,6,7],[2],[3],[4],[5]] => [1,1,1,1,3] => 10
[1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [6,5,4,2,1,3,7] => [[1,6,7],[2],[3],[4],[5]] => [1,1,1,1,3] => 10
[1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [5,6,4,2,1,3,7] => [[1,2,7],[3,6],[4],[5]] => [2,1,1,3] => 9
[1,1,1,0,1,0,0,1,1,0,0,0,1,0] => [7,4,5,2,1,3,6] => [[1,3,7],[2,6],[4],[5]] => [1,2,1,3] => 8
[1,1,1,0,1,0,0,1,1,0,0,1,0,0] => [6,4,5,2,1,3,7] => [[1,3,7],[2,6],[4],[5]] => [1,2,1,3] => 8
[1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [5,4,6,2,1,3,7] => [[1,3,7],[2,6],[4],[5]] => [1,2,1,3] => 8
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [4,5,6,2,1,3,7] => [[1,2,3,7],[4,6],[5]] => [3,1,3] => 7
[1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [7,6,3,2,1,4,5] => [[1,6,7],[2],[3],[4],[5]] => [1,1,1,1,3] => 10
[1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [6,7,3,2,1,4,5] => [[1,2,7],[3,6],[4],[5]] => [2,1,1,3] => 9
[1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [7,5,3,2,1,4,6] => [[1,6,7],[2],[3],[4],[5]] => [1,1,1,1,3] => 10
[1,1,1,0,1,0,1,0,0,1,0,1,0,0] => [6,5,3,2,1,4,7] => [[1,6,7],[2],[3],[4],[5]] => [1,1,1,1,3] => 10
[1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [5,6,3,2,1,4,7] => [[1,2,7],[3,6],[4],[5]] => [2,1,1,3] => 9
[1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [7,4,3,2,1,5,6] => [[1,6,7],[2],[3],[4],[5]] => [1,1,1,1,3] => 10
[1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [6,4,3,2,1,5,7] => [[1,6,7],[2],[3],[4],[5]] => [1,1,1,1,3] => 10
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [5,4,3,2,1,6,7] => [[1,6,7],[2],[3],[4],[5]] => [1,1,1,1,3] => 10
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [4,5,3,2,1,6,7] => [[1,2,6,7],[3],[4],[5]] => [2,1,1,3] => 9
[1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [7,3,4,2,1,5,6] => [[1,3,6,7],[2],[4],[5]] => [1,2,1,3] => 8
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [6,3,4,2,1,5,7] => [[1,3,6,7],[2],[4],[5]] => [1,2,1,3] => 8
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [5,3,4,2,1,6,7] => [[1,3,6,7],[2],[4],[5]] => [1,2,1,3] => 8
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [4,3,5,2,1,6,7] => [[1,3,6,7],[2],[4],[5]] => [1,2,1,3] => 8
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [3,4,5,2,1,6,7] => [[1,2,3,6,7],[4],[5]] => [3,1,3] => 7
[1,1,1,0,1,1,0,0,0,0,1,0,1,0] => [7,6,2,3,1,4,5] => [[1,4,6,7],[2],[3],[5]] => [1,1,2,3] => 7
[1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [6,7,2,3,1,4,5] => [[1,2,6,7],[3,4],[5]] => [2,2,3] => 6
[1,1,1,0,1,1,0,0,0,1,0,0,1,0] => [7,5,2,3,1,4,6] => [[1,4,6,7],[2],[3],[5]] => [1,1,2,3] => 7
[1,1,1,0,1,1,0,0,0,1,0,1,0,0] => [6,5,2,3,1,4,7] => [[1,4,6,7],[2],[3],[5]] => [1,1,2,3] => 7
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [5,6,2,3,1,4,7] => [[1,2,6,7],[3,4],[5]] => [2,2,3] => 6
[1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [7,4,2,3,1,5,6] => [[1,4,6,7],[2],[3],[5]] => [1,1,2,3] => 7
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [6,4,2,3,1,5,7] => [[1,4,6,7],[2],[3],[5]] => [1,1,2,3] => 7
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [5,4,2,3,1,6,7] => [[1,4,6,7],[2],[3],[5]] => [1,1,2,3] => 7
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [4,5,2,3,1,6,7] => [[1,2,6,7],[3,4],[5]] => [2,2,3] => 6
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [7,3,2,4,1,5,6] => [[1,4,6,7],[2],[3],[5]] => [1,1,2,3] => 7
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [6,3,2,4,1,5,7] => [[1,4,6,7],[2],[3],[5]] => [1,1,2,3] => 7
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [5,3,2,4,1,6,7] => [[1,4,6,7],[2],[3],[5]] => [1,1,2,3] => 7
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [4,3,2,5,1,6,7] => [[1,4,6,7],[2],[3],[5]] => [1,1,2,3] => 7
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [3,4,2,5,1,6,7] => [[1,2,4,6,7],[3],[5]] => [2,2,3] => 6
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [7,2,3,4,1,5,6] => [[1,3,4,6,7],[2],[5]] => [1,3,3] => 5
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [6,2,3,4,1,5,7] => [[1,3,4,6,7],[2],[5]] => [1,3,3] => 5
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [5,2,3,4,1,6,7] => [[1,3,4,6,7],[2],[5]] => [1,3,3] => 5
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [4,2,3,5,1,6,7] => [[1,3,4,6,7],[2],[5]] => [1,3,3] => 5
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,4,5,1,6,7] => [[1,3,4,6,7],[2],[5]] => [1,3,3] => 5
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,3,4,5,1,6,7] => [[1,2,3,4,6,7],[5]] => [4,3] => 4
[1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [7,6,5,1,2,3,4] => [[1,5,6,7],[2],[3],[4]] => [1,1,1,4] => 6
[1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [6,7,5,1,2,3,4] => [[1,2,6,7],[3,5],[4]] => [2,1,4] => 5
[1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [7,5,6,1,2,3,4] => [[1,3,6,7],[2,5],[4]] => [1,2,4] => 4
[1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [6,5,7,1,2,3,4] => [[1,3,6,7],[2,5],[4]] => [1,2,4] => 4
[1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [5,6,7,1,2,3,4] => [[1,2,3,7],[4,5,6]] => [3,4] => 3
[1,1,1,1,0,0,0,1,0,0,1,0,1,0] => [7,6,4,1,2,3,5] => [[1,5,6,7],[2],[3],[4]] => [1,1,1,4] => 6
[1,1,1,1,0,0,0,1,0,0,1,1,0,0] => [6,7,4,1,2,3,5] => [[1,2,6,7],[3,5],[4]] => [2,1,4] => 5
[1,1,1,1,0,0,0,1,0,1,0,0,1,0] => [7,5,4,1,2,3,6] => [[1,5,6,7],[2],[3],[4]] => [1,1,1,4] => 6
[1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [6,5,4,1,2,3,7] => [[1,5,6,7],[2],[3],[4]] => [1,1,1,4] => 6
[1,1,1,1,0,0,0,1,0,1,1,0,0,0] => [5,6,4,1,2,3,7] => [[1,2,6,7],[3,5],[4]] => [2,1,4] => 5
[1,1,1,1,0,0,0,1,1,0,0,0,1,0] => [7,4,5,1,2,3,6] => [[1,3,6,7],[2,5],[4]] => [1,2,4] => 4
[1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [6,4,5,1,2,3,7] => [[1,3,6,7],[2,5],[4]] => [1,2,4] => 4
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [5,4,6,1,2,3,7] => [[1,3,6,7],[2,5],[4]] => [1,2,4] => 4
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [4,5,6,1,2,3,7] => [[1,2,3,7],[4,5,6]] => [3,4] => 3
[1,1,1,1,0,0,1,0,0,0,1,0,1,0] => [7,6,3,1,2,4,5] => [[1,5,6,7],[2],[3],[4]] => [1,1,1,4] => 6
[1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [6,7,3,1,2,4,5] => [[1,2,6,7],[3,5],[4]] => [2,1,4] => 5
[1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [7,5,3,1,2,4,6] => [[1,5,6,7],[2],[3],[4]] => [1,1,1,4] => 6
[1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [6,5,3,1,2,4,7] => [[1,5,6,7],[2],[3],[4]] => [1,1,1,4] => 6
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [5,6,3,1,2,4,7] => [[1,2,6,7],[3,5],[4]] => [2,1,4] => 5
[1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [7,4,3,1,2,5,6] => [[1,5,6,7],[2],[3],[4]] => [1,1,1,4] => 6
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [6,4,3,1,2,5,7] => [[1,5,6,7],[2],[3],[4]] => [1,1,1,4] => 6
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [5,4,3,1,2,6,7] => [[1,5,6,7],[2],[3],[4]] => [1,1,1,4] => 6
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [4,5,3,1,2,6,7] => [[1,2,6,7],[3,5],[4]] => [2,1,4] => 5
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [7,3,4,1,2,5,6] => [[1,3,6,7],[2,5],[4]] => [1,2,4] => 4
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [6,3,4,1,2,5,7] => [[1,3,6,7],[2,5],[4]] => [1,2,4] => 4
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [5,3,4,1,2,6,7] => [[1,3,6,7],[2,5],[4]] => [1,2,4] => 4
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [4,3,5,1,2,6,7] => [[1,3,6,7],[2,5],[4]] => [1,2,4] => 4
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [3,4,5,1,2,6,7] => [[1,2,3,6,7],[4,5]] => [3,4] => 3
[1,1,1,1,0,1,0,0,0,0,1,0,1,0] => [7,6,2,1,3,4,5] => [[1,5,6,7],[2],[3],[4]] => [1,1,1,4] => 6
[1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [6,7,2,1,3,4,5] => [[1,2,6,7],[3,5],[4]] => [2,1,4] => 5
[1,1,1,1,0,1,0,0,0,1,0,0,1,0] => [7,5,2,1,3,4,6] => [[1,5,6,7],[2],[3],[4]] => [1,1,1,4] => 6
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [6,5,2,1,3,4,7] => [[1,5,6,7],[2],[3],[4]] => [1,1,1,4] => 6
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [5,6,2,1,3,4,7] => [[1,2,6,7],[3,5],[4]] => [2,1,4] => 5
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [7,4,2,1,3,5,6] => [[1,5,6,7],[2],[3],[4]] => [1,1,1,4] => 6
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [6,4,2,1,3,5,7] => [[1,5,6,7],[2],[3],[4]] => [1,1,1,4] => 6
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [5,4,2,1,3,6,7] => [[1,5,6,7],[2],[3],[4]] => [1,1,1,4] => 6
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [4,5,2,1,3,6,7] => [[1,2,6,7],[3,5],[4]] => [2,1,4] => 5
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [7,3,2,1,4,5,6] => [[1,5,6,7],[2],[3],[4]] => [1,1,1,4] => 6
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [6,3,2,1,4,5,7] => [[1,5,6,7],[2],[3],[4]] => [1,1,1,4] => 6
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [5,3,2,1,4,6,7] => [[1,5,6,7],[2],[3],[4]] => [1,1,1,4] => 6
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1,5,6,7] => [[1,5,6,7],[2],[3],[4]] => [1,1,1,4] => 6
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [3,4,2,1,5,6,7] => [[1,2,5,6,7],[3],[4]] => [2,1,4] => 5
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [7,2,3,1,4,5,6] => [[1,3,5,6,7],[2],[4]] => [1,2,4] => 4
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [6,2,3,1,4,5,7] => [[1,3,5,6,7],[2],[4]] => [1,2,4] => 4
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [5,2,3,1,4,6,7] => [[1,3,5,6,7],[2],[4]] => [1,2,4] => 4
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,3,1,5,6,7] => [[1,3,5,6,7],[2],[4]] => [1,2,4] => 4
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,4,1,5,6,7] => [[1,3,5,6,7],[2],[4]] => [1,2,4] => 4
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,3,4,1,5,6,7] => [[1,2,3,5,6,7],[4]] => [3,4] => 3
[1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [7,6,1,2,3,4,5] => [[1,4,5,6,7],[2],[3]] => [1,1,5] => 3
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [6,7,1,2,3,4,5] => [[1,2,5,6,7],[3,4]] => [2,5] => 2
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [7,5,1,2,3,4,6] => [[1,4,5,6,7],[2],[3]] => [1,1,5] => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [6,5,1,2,3,4,7] => [[1,4,5,6,7],[2],[3]] => [1,1,5] => 3
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [5,6,1,2,3,4,7] => [[1,2,5,6,7],[3,4]] => [2,5] => 2
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [7,4,1,2,3,5,6] => [[1,4,5,6,7],[2],[3]] => [1,1,5] => 3
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [6,4,1,2,3,5,7] => [[1,4,5,6,7],[2],[3]] => [1,1,5] => 3
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [5,4,1,2,3,6,7] => [[1,4,5,6,7],[2],[3]] => [1,1,5] => 3
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [4,5,1,2,3,6,7] => [[1,2,5,6,7],[3,4]] => [2,5] => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [7,3,1,2,4,5,6] => [[1,4,5,6,7],[2],[3]] => [1,1,5] => 3
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [6,3,1,2,4,5,7] => [[1,4,5,6,7],[2],[3]] => [1,1,5] => 3
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,2,4,6,7] => [[1,4,5,6,7],[2],[3]] => [1,1,5] => 3
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,2,5,6,7] => [[1,4,5,6,7],[2],[3]] => [1,1,5] => 3
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,4,1,2,5,6,7] => [[1,2,5,6,7],[3,4]] => [2,5] => 2
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [7,2,1,3,4,5,6] => [[1,4,5,6,7],[2],[3]] => [1,1,5] => 3
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,3,4,5,7] => [[1,4,5,6,7],[2],[3]] => [1,1,5] => 3
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,3,4,6,7] => [[1,4,5,6,7],[2],[3]] => [1,1,5] => 3
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,3,5,6,7] => [[1,4,5,6,7],[2],[3]] => [1,1,5] => 3
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,4,5,6,7] => [[1,4,5,6,7],[2],[3]] => [1,1,5] => 3
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,3,1,4,5,6,7] => [[1,2,4,5,6,7],[3]] => [2,5] => 2
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [7,1,2,3,4,5,6] => [[1,3,4,5,6,7],[2]] => [1,6] => 1
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,2,3,4,5,7] => [[1,3,4,5,6,7],[2]] => [1,6] => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,2,3,4,6,7] => [[1,3,4,5,6,7],[2]] => [1,6] => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,2,3,5,6,7] => [[1,3,4,5,6,7],[2]] => [1,6] => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,2,4,5,6,7] => [[1,3,4,5,6,7],[2]] => [1,6] => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,3,4,5,6,7] => [[1,3,4,5,6,7],[2]] => [1,6] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7] => [[1,2,3,4,5,6,7]] => [7] => 0
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => [1,1,1,1,1,1,1,1] => 28
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,2,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => [2,1,1,1,1,1,1] => 27
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,2,1] => [[1,3],[2],[4],[5],[6],[7],[8]] => [1,2,1,1,1,1,1] => 26
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,2,1] => [[1,3],[2],[4],[5],[6],[7],[8]] => [1,2,1,1,1,1,1] => 26
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,2,1] => [[1,2,3],[4],[5],[6],[7],[8]] => [3,1,1,1,1,1] => 25
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,2,1] => [[1,4],[2],[3],[5],[6],[7],[8]] => [1,1,2,1,1,1,1] => 25
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,2,1] => [[1,2],[3,4],[5],[6],[7],[8]] => [2,2,1,1,1,1] => 24
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,2,1] => [[1,4],[2],[3],[5],[6],[7],[8]] => [1,1,2,1,1,1,1] => 25
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,2,1] => [[1,4],[2],[3],[5],[6],[7],[8]] => [1,1,2,1,1,1,1] => 25
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,2,1] => [[1,2,4],[3],[5],[6],[7],[8]] => [2,2,1,1,1,1] => 24
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,3,2,1] => [[1,3,4],[2],[5],[6],[7],[8]] => [1,3,1,1,1,1] => 23
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,2,1] => [[1,3,4],[2],[5],[6],[7],[8]] => [1,3,1,1,1,1] => 23
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,2,1] => [[1,3,4],[2],[5],[6],[7],[8]] => [1,3,1,1,1,1] => 23
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,2,1] => [[1,2,3,4],[5],[6],[7],[8]] => [4,1,1,1,1] => 22
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,2,1] => [[1,5],[2],[3],[4],[6],[7],[8]] => [1,1,1,2,1,1,1] => 24
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,2,1] => [[1,2],[3,5],[4],[6],[7],[8]] => [2,1,2,1,1,1] => 23
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,2,1] => [[1,3],[2,5],[4],[6],[7],[8]] => [1,2,2,1,1,1] => 22
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,3,2,1] => [[1,3],[2,5],[4],[6],[7],[8]] => [1,2,2,1,1,1] => 22
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,3,2,1] => [[1,5],[2],[3],[4],[6],[7],[8]] => [1,1,1,2,1,1,1] => 24
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,3,2,1] => [[1,5],[2],[3],[4],[6],[7],[8]] => [1,1,1,2,1,1,1] => 24
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,2,1] => [[1,5],[2],[3],[4],[6],[7],[8]] => [1,1,1,2,1,1,1] => 24
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,3,2,1] => [[1,2,5],[3],[4],[6],[7],[8]] => [2,1,2,1,1,1] => 23
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,3,2,1] => [[1,3,5],[2],[4],[6],[7],[8]] => [1,2,2,1,1,1] => 22
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,2,1] => [[1,3,5],[2],[4],[6],[7],[8]] => [1,2,2,1,1,1] => 22
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,2,1] => [[1,3,5],[2],[4],[6],[7],[8]] => [1,2,2,1,1,1] => 22
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,3,2,1] => [[1,2,3,5],[4],[6],[7],[8]] => [3,2,1,1,1] => 21
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,3,2,1] => [[1,4,5],[2],[3],[6],[7],[8]] => [1,1,3,1,1,1] => 21
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,3,2,1] => [[1,4,5],[2],[3],[6],[7],[8]] => [1,1,3,1,1,1] => 21
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,2,1] => [[1,4,5],[2],[3],[6],[7],[8]] => [1,1,3,1,1,1] => 21
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,3,2,1] => [[1,2,5],[3,4],[6],[7],[8]] => [2,3,1,1,1] => 20
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,3,2,1] => [[1,4,5],[2],[3],[6],[7],[8]] => [1,1,3,1,1,1] => 21
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,2,1] => [[1,4,5],[2],[3],[6],[7],[8]] => [1,1,3,1,1,1] => 21
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,2,1] => [[1,2,4,5],[3],[6],[7],[8]] => [2,3,1,1,1] => 20
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,3,2,1] => [[1,3,4,5],[2],[6],[7],[8]] => [1,4,1,1,1] => 19
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,3,2,1] => [[1,3,4,5],[2],[6],[7],[8]] => [1,4,1,1,1] => 19
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0] => [6,4,5,7,8,3,2,1] => [[1,3,4,5],[2],[6],[7],[8]] => [1,4,1,1,1] => 19
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,2,1] => [[1,3,4,5],[2],[6],[7],[8]] => [1,4,1,1,1] => 19
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,2,1] => [[1,2,3,4,5],[6],[7],[8]] => [5,1,1,1] => 18
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,2,1] => [[1,6],[2],[3],[4],[5],[7],[8]] => [1,1,1,1,2,1,1] => 23
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,2,1] => [[1,2],[3,6],[4],[5],[7],[8]] => [2,1,1,2,1,1] => 22
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,4,2,1] => [[1,3],[2,6],[4],[5],[7],[8]] => [1,2,1,2,1,1] => 21
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,2,1] => [[1,3],[2,6],[4],[5],[7],[8]] => [1,2,1,2,1,1] => 21
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,2,1] => [[1,4],[2,6],[3],[5],[7],[8]] => [1,1,2,2,1,1] => 20
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,2,1] => [[1,2],[3,4],[5,6],[7],[8]] => [2,2,2,1,1] => 19
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,2,1] => [[1,4],[2,6],[3],[5],[7],[8]] => [1,1,2,2,1,1] => 20
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,2,1] => [[1,2,4],[3,6],[5],[7],[8]] => [2,2,2,1,1] => 19
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,2,1] => [[1,3,4],[2,6],[5],[7],[8]] => [1,3,2,1,1] => 18
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,2,1] => [[1,3,4],[2,6],[5],[7],[8]] => [1,3,2,1,1] => 18
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,2,1] => [[1,2,3,4],[5,6],[7],[8]] => [4,2,1,1] => 17
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,5,2,1] => [[1,6],[2],[3],[4],[5],[7],[8]] => [1,1,1,1,2,1,1] => 23
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,5,2,1] => [[1,2],[3,6],[4],[5],[7],[8]] => [2,1,1,2,1,1] => 22
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,5,2,1] => [[1,3],[2,6],[4],[5],[7],[8]] => [1,2,1,2,1,1] => 21
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,5,2,1] => [[1,3],[2,6],[4],[5],[7],[8]] => [1,2,1,2,1,1] => 21
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,5,2,1] => [[1,2,3],[4,6],[5],[7],[8]] => [3,1,2,1,1] => 20
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,6,2,1] => [[1,6],[2],[3],[4],[5],[7],[8]] => [1,1,1,1,2,1,1] => 23
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,2,1] => [[1,2],[3,6],[4],[5],[7],[8]] => [2,1,1,2,1,1] => 22
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,2,1] => [[1,6],[2],[3],[4],[5],[7],[8]] => [1,1,1,1,2,1,1] => 23
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,2,1] => [[1,6],[2],[3],[4],[5],[7],[8]] => [1,1,1,1,2,1,1] => 23
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,8,2,1] => [[1,2,6],[3],[4],[5],[7],[8]] => [2,1,1,2,1,1] => 22
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,8,2,1] => [[1,3,6],[2],[4],[5],[7],[8]] => [1,2,1,2,1,1] => 21
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,8,2,1] => [[1,3,6],[2],[4],[5],[7],[8]] => [1,2,1,2,1,1] => 21
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,2,1] => [[1,2,3,6],[4],[5],[7],[8]] => [3,1,2,1,1] => 20
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,6,2,1] => [[1,4,6],[2],[3],[5],[7],[8]] => [1,1,2,2,1,1] => 20
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,2,1] => [[1,2,6],[3,4],[5],[7],[8]] => [2,2,2,1,1] => 19
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,8,2,1] => [[1,4,6],[2],[3],[5],[7],[8]] => [1,1,2,2,1,1] => 20
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,8,2,1] => [[1,4,6],[2],[3],[5],[7],[8]] => [1,1,2,2,1,1] => 20
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,8,2,1] => [[1,3,4,6],[2],[5],[7],[8]] => [1,3,2,1,1] => 18
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,8,2,1] => [[1,3,4,6],[2],[5],[7],[8]] => [1,3,2,1,1] => 18
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,8,2,1] => [[1,3,4,6],[2],[5],[7],[8]] => [1,3,2,1,1] => 18
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,2,1] => [[1,2,3,4,6],[5],[7],[8]] => [4,2,1,1] => 17
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => [1,1,1,3,1,1] => 19
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,5,2,1] => [[1,2,6],[3,5],[4],[7],[8]] => [2,1,3,1,1] => 18
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,2,1] => [[1,3,6],[2,5],[4],[7],[8]] => [1,2,3,1,1] => 17
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,5,2,1] => [[1,3,6],[2,5],[4],[7],[8]] => [1,2,3,1,1] => 17
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,5,2,1] => [[1,2,3],[4,5,6],[7],[8]] => [3,3,1,1] => 16
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,6,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => [1,1,1,3,1,1] => 19
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,2,1] => [[1,2,6],[3,5],[4],[7],[8]] => [2,1,3,1,1] => 18
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => [1,1,1,3,1,1] => 19
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => [1,1,1,3,1,1] => 19
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,7,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => [1,1,1,3,1,1] => 19
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => [1,1,1,3,1,1] => 19
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,7,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => [1,1,1,3,1,1] => 19
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,8,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => [1,1,1,3,1,1] => 19
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,2,1] => [[1,5,6],[2],[3],[4],[7],[8]] => [1,1,1,3,1,1] => 19
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => [1,1,4,1,1] => 16
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,2,1] => [[1,2,5,6],[3,4],[7],[8]] => [2,4,1,1] => 15
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => [1,1,4,1,1] => 16
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,7,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => [1,1,4,1,1] => 16
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,8,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => [1,1,4,1,1] => 16
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,8,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => [1,1,4,1,1] => 16
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => [1,1,4,1,1] => 16
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,2,1] => [[1,4,5,6],[2],[3],[7],[8]] => [1,1,4,1,1] => 16
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,2,1] => [[1,3,4,5,6],[2],[7],[8]] => [1,5,1,1] => 14
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,2,1] => [[1,3,4,5,6],[2],[7],[8]] => [1,5,1,1] => 14
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,2,1] => [[1,3,4,5,6],[2],[7],[8]] => [1,5,1,1] => 14
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,2,1] => [[1,3,4,5,6],[2],[7],[8]] => [1,5,1,1] => 14
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,2,1] => [[1,3,4,5,6],[2],[7],[8]] => [1,5,1,1] => 14
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,2,1] => [[1,2,3,4,5,6],[7],[8]] => [6,1,1] => 13
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,3,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => [1,1,1,1,1,2,1] => 22
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,3,1] => [[1,2],[3,7],[4],[5],[6],[8]] => [2,1,1,1,2,1] => 21
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,3,1] => [[1,3],[2,7],[4],[5],[6],[8]] => [1,2,1,1,2,1] => 20
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,3,1] => [[1,3],[2,7],[4],[5],[6],[8]] => [1,2,1,1,2,1] => 20
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,3,1] => [[1,4],[2,7],[3],[5],[6],[8]] => [1,1,2,1,2,1] => 19
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,2,3,1] => [[1,4],[2,7],[3],[5],[6],[8]] => [1,1,2,1,2,1] => 19
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,3,1] => [[1,4],[2,7],[3],[5],[6],[8]] => [1,1,2,1,2,1] => 19
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,3,1] => [[1,2,4],[3,7],[5],[6],[8]] => [2,2,1,2,1] => 18
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,2,3,1] => [[1,3,4],[2,7],[5],[6],[8]] => [1,3,1,2,1] => 17
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,2,3,1] => [[1,3,4],[2,7],[5],[6],[8]] => [1,3,1,2,1] => 17
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,3,1] => [[1,2,3,4],[5,7],[6],[8]] => [4,1,2,1] => 16
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,3,1] => [[1,5],[2,7],[3],[4],[6],[8]] => [1,1,1,2,2,1] => 18
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,2,3,1] => [[1,3],[2,5],[4,7],[6],[8]] => [1,2,2,2,1] => 16
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0] => [7,6,8,4,5,2,3,1] => [[1,3],[2,5],[4,7],[6],[8]] => [1,2,2,2,1] => 16
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,2,3,1] => [[1,5],[2,7],[3],[4],[6],[8]] => [1,1,1,2,2,1] => 18
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,2,3,1] => [[1,5],[2,7],[3],[4],[6],[8]] => [1,1,1,2,2,1] => 18
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,2,3,1] => [[1,5],[2,7],[3],[4],[6],[8]] => [1,1,1,2,2,1] => 18
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,2,3,1] => [[1,3,5],[2,7],[4],[6],[8]] => [1,2,2,2,1] => 16
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,2,3,1] => [[1,3,5],[2,7],[4],[6],[8]] => [1,2,2,2,1] => 16
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,3,1] => [[1,3,5],[2,7],[4],[6],[8]] => [1,2,2,2,1] => 16
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,2,3,1] => [[1,4,5],[2,7],[3],[6],[8]] => [1,1,3,2,1] => 15
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,2,3,1] => [[1,2,5],[3,4],[6,7],[8]] => [2,3,2,1] => 14
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,2,3,1] => [[1,4,5],[2,7],[3],[6],[8]] => [1,1,3,2,1] => 15
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,2,3,1] => [[1,2,5],[3,4],[6,7],[8]] => [2,3,2,1] => 14
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,3,1] => [[1,3,4,5],[2,7],[6],[8]] => [1,4,2,1] => 13
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,3,1] => [[1,2,3,4,5],[6,7],[8]] => [5,2,1] => 12
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,4,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => [1,1,1,1,1,2,1] => 22
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,2,4,1] => [[1,2],[3,7],[4],[5],[6],[8]] => [2,1,1,1,2,1] => 21
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,4,1] => [[1,3],[2,7],[4],[5],[6],[8]] => [1,2,1,1,2,1] => 20
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,4,1] => [[1,3],[2,7],[4],[5],[6],[8]] => [1,2,1,1,2,1] => 20
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,4,1] => [[1,2,3],[4,7],[5],[6],[8]] => [3,1,1,2,1] => 19
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,2,4,1] => [[1,4],[2,7],[3],[5],[6],[8]] => [1,1,2,1,2,1] => 19
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,4,1] => [[1,4],[2,7],[3],[5],[6],[8]] => [1,1,2,1,2,1] => 19
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,4,1] => [[1,4],[2,7],[3],[5],[6],[8]] => [1,1,2,1,2,1] => 19
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,4,1] => [[1,2,4],[3,7],[5],[6],[8]] => [2,2,1,2,1] => 18
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,2,4,1] => [[1,3,4],[2,7],[5],[6],[8]] => [1,3,1,2,1] => 17
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,4,1] => [[1,2,3,4],[5,7],[6],[8]] => [4,1,2,1] => 16
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,5,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => [1,1,1,1,1,2,1] => 22
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,2,5,1] => [[1,2],[3,7],[4],[5],[6],[8]] => [2,1,1,1,2,1] => 21
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,2,5,1] => [[1,3],[2,7],[4],[5],[6],[8]] => [1,2,1,1,2,1] => 20
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,5,1] => [[1,3],[2,7],[4],[5],[6],[8]] => [1,2,1,1,2,1] => 20
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,5,1] => [[1,2,3],[4,7],[5],[6],[8]] => [3,1,1,2,1] => 19
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,6,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => [1,1,1,1,1,2,1] => 22
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,6,1] => [[1,2],[3,7],[4],[5],[6],[8]] => [2,1,1,1,2,1] => 21
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,7,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => [1,1,1,1,1,2,1] => 22
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,8,1] => [[1,7],[2],[3],[4],[5],[6],[8]] => [1,1,1,1,1,2,1] => 22
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,8,1] => [[1,2,7],[3],[4],[5],[6],[8]] => [2,1,1,1,2,1] => 21
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,7,1] => [[1,3,7],[2],[4],[5],[6],[8]] => [1,2,1,1,2,1] => 20
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,2,8,1] => [[1,3,7],[2],[4],[5],[6],[8]] => [1,2,1,1,2,1] => 20
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,8,1] => [[1,3,7],[2],[4],[5],[6],[8]] => [1,2,1,1,2,1] => 20
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,8,1] => [[1,2,3,7],[4],[5],[6],[8]] => [3,1,1,2,1] => 19
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,2,7,1] => [[1,4,7],[2],[3],[5],[6],[8]] => [1,1,2,1,2,1] => 19
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,8,1] => [[1,4,7],[2],[3],[5],[6],[8]] => [1,1,2,1,2,1] => 19
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,2,8,1] => [[1,2,7],[3,4],[5],[6],[8]] => [2,2,1,2,1] => 18
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,2,7,1] => [[1,4,7],[2],[3],[5],[6],[8]] => [1,1,2,1,2,1] => 19
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,8,1] => [[1,4,7],[2],[3],[5],[6],[8]] => [1,1,2,1,2,1] => 19
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,8,1] => [[1,3,4,7],[2],[5],[6],[8]] => [1,3,1,2,1] => 17
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0] => [6,4,5,7,3,2,8,1] => [[1,3,4,7],[2],[5],[6],[8]] => [1,3,1,2,1] => 17
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,8,1] => [[1,2,3,4,7],[5],[6],[8]] => [4,1,2,1] => 16
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,5,1] => [[1,5,7],[2],[3],[4],[6],[8]] => [1,1,1,2,2,1] => 18
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,2,5,1] => [[1,2,7],[3,5],[4],[6],[8]] => [2,1,2,2,1] => 17
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,2,5,1] => [[1,3,7],[2,5],[4],[6],[8]] => [1,2,2,2,1] => 16
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,4,2,5,1] => [[1,3,7],[2,5],[4],[6],[8]] => [1,2,2,2,1] => 16
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,5,1] => [[1,2,3],[4,5,7],[6],[8]] => [3,2,2,1] => 15
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,2,6,1] => [[1,5,7],[2],[3],[4],[6],[8]] => [1,1,1,2,2,1] => 18
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,2,6,1] => [[1,2,7],[3,5],[4],[6],[8]] => [2,1,2,2,1] => 17
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,2,7,1] => [[1,5,7],[2],[3],[4],[6],[8]] => [1,1,1,2,2,1] => 18
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,8,1] => [[1,5,7],[2],[3],[4],[6],[8]] => [1,1,1,2,2,1] => 18
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,7,1] => [[1,3,7],[2,5],[4],[6],[8]] => [1,2,2,2,1] => 16
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,8,1] => [[1,3,7],[2,5],[4],[6],[8]] => [1,2,2,2,1] => 16
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,2,8,1] => [[1,3,7],[2,5],[4],[6],[8]] => [1,2,2,2,1] => 16
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,2,6,1] => [[1,5,7],[2],[3],[4],[6],[8]] => [1,1,1,2,2,1] => 18
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,5,2,7,1] => [[1,5,7],[2],[3],[4],[6],[8]] => [1,1,1,2,2,1] => 18
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,8,1] => [[1,5,7],[2],[3],[4],[6],[8]] => [1,1,1,2,2,1] => 18
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,2,7,1] => [[1,5,7],[2],[3],[4],[6],[8]] => [1,1,1,2,2,1] => 18
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,8,1] => [[1,5,7],[2],[3],[4],[6],[8]] => [1,1,1,2,2,1] => 18
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,8,1] => [[1,5,7],[2],[3],[4],[6],[8]] => [1,1,1,2,2,1] => 18
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,7,1] => [[1,3,5,7],[2],[4],[6],[8]] => [1,2,2,2,1] => 16
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,2,8,1] => [[1,3,5,7],[2],[4],[6],[8]] => [1,2,2,2,1] => 16
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,2,8,1] => [[1,3,5,7],[2],[4],[6],[8]] => [1,2,2,2,1] => 16
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,8,1] => [[1,3,5,7],[2],[4],[6],[8]] => [1,2,2,2,1] => 16
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,2,8,1] => [[1,2,3,5,7],[4],[6],[8]] => [3,2,2,1] => 15
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,2,7,1] => [[1,4,5,7],[2],[3],[6],[8]] => [1,1,3,2,1] => 15
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,8,1] => [[1,4,5,7],[2],[3],[6],[8]] => [1,1,3,2,1] => 15
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,2,8,1] => [[1,4,5,7],[2],[3],[6],[8]] => [1,1,3,2,1] => 15
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,7,2,8,1] => [[1,4,5,7],[2],[3],[6],[8]] => [1,1,3,2,1] => 15
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,2,8,1] => [[1,2,5,7],[3,4],[6],[8]] => [2,3,2,1] => 14
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,2,7,1] => [[1,4,5,7],[2],[3],[6],[8]] => [1,1,3,2,1] => 15
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,2,8,1] => [[1,4,5,7],[2],[3],[6],[8]] => [1,1,3,2,1] => 15
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,2,8,1] => [[1,4,5,7],[2],[3],[6],[8]] => [1,1,3,2,1] => 15
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,2,8,1] => [[1,2,4,5,7],[3],[6],[8]] => [2,3,2,1] => 14
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,7,1] => [[1,3,4,5,7],[2],[6],[8]] => [1,4,2,1] => 13
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,8,1] => [[1,3,4,5,7],[2],[6],[8]] => [1,4,2,1] => 13
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,2,8,1] => [[1,3,4,5,7],[2],[6],[8]] => [1,4,2,1] => 13
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,2,8,1] => [[1,3,4,5,7],[2],[6],[8]] => [1,4,2,1] => 13
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,8,1] => [[1,2,3,4,5,7],[6],[8]] => [5,2,1] => 12
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,4,1] => [[1,6,7],[2],[3],[4],[5],[8]] => [1,1,1,1,3,1] => 17
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,4,1] => [[1,3,7],[2,6],[4],[5],[8]] => [1,2,1,3,1] => 15
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,3,4,1] => [[1,3,7],[2,6],[4],[5],[8]] => [1,2,1,3,1] => 15
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,4,1] => [[1,2,3],[4,6,7],[5],[8]] => [3,1,3,1] => 14
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,4,1] => [[1,4,7],[2,6],[3],[5],[8]] => [1,1,2,3,1] => 14
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,4,1] => [[1,2,7],[3,4],[5,6],[8]] => [2,2,3,1] => 13
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,3,4,1] => [[1,4,7],[2,6],[3],[5],[8]] => [1,1,2,3,1] => 14
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,4,1] => [[1,4,7],[2,6],[3],[5],[8]] => [1,1,2,3,1] => 14
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,4,1] => [[1,2,4],[3,6,7],[5],[8]] => [2,2,3,1] => 13
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,4,1] => [[1,3,4],[2,6,7],[5],[8]] => [1,3,3,1] => 12
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,3,4,1] => [[1,3,4],[2,6,7],[5],[8]] => [1,3,3,1] => 12
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,4,1] => [[1,2,3,4],[5,6,7],[8]] => [4,3,1] => 11
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,2,3,5,1] => [[1,3,7],[2,6],[4],[5],[8]] => [1,2,1,3,1] => 15
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,5,1] => [[1,2,3],[4,6,7],[5],[8]] => [3,1,3,1] => 14
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,7,1] => [[1,6,7],[2],[3],[4],[5],[8]] => [1,1,1,1,3,1] => 17
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,8,1] => [[1,6,7],[2],[3],[4],[5],[8]] => [1,1,1,1,3,1] => 17
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,8,1] => [[1,2,7],[3,6],[4],[5],[8]] => [2,1,1,3,1] => 16
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,8,1] => [[1,3,7],[2,6],[4],[5],[8]] => [1,2,1,3,1] => 15
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,3,8,1] => [[1,3,7],[2,6],[4],[5],[8]] => [1,2,1,3,1] => 15
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,8,1] => [[1,2,3,7],[4,6],[5],[8]] => [3,1,3,1] => 14
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,8,1] => [[1,4,7],[2,6],[3],[5],[8]] => [1,1,2,3,1] => 14
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,8,1] => [[1,2,7],[3,4],[5,6],[8]] => [2,2,3,1] => 13
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,3,8,1] => [[1,4,7],[2,6],[3],[5],[8]] => [1,1,2,3,1] => 14
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,8,1] => [[1,4,7],[2,6],[3],[5],[8]] => [1,1,2,3,1] => 14
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,8,1] => [[1,2,4,7],[3,6],[5],[8]] => [2,2,3,1] => 13
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,2,3,8,1] => [[1,3,4,7],[2,6],[5],[8]] => [1,3,3,1] => 12
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,8,1] => [[1,3,4,7],[2,6],[5],[8]] => [1,3,3,1] => 12
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,8,1] => [[1,2,3,4,7],[5,6],[8]] => [4,3,1] => 11
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,5,1] => [[1,6,7],[2],[3],[4],[5],[8]] => [1,1,1,1,3,1] => 17
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,4,5,1] => [[1,2,7],[3,6],[4],[5],[8]] => [2,1,1,3,1] => 16
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,5,1] => [[1,3,7],[2,6],[4],[5],[8]] => [1,2,1,3,1] => 15
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,5,1] => [[1,2,3],[4,6,7],[5],[8]] => [3,1,3,1] => 14
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,6,1] => [[1,6,7],[2],[3],[4],[5],[8]] => [1,1,1,1,3,1] => 17
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,7,1] => [[1,6,7],[2],[3],[4],[5],[8]] => [1,1,1,1,3,1] => 17
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,8,1] => [[1,6,7],[2],[3],[4],[5],[8]] => [1,1,1,1,3,1] => 17
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,2,4,8,1] => [[1,2,7],[3,6],[4],[5],[8]] => [2,1,1,3,1] => 16
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,8,1] => [[1,3,7],[2,6],[4],[5],[8]] => [1,2,1,3,1] => 15
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,6,1] => [[1,6,7],[2],[3],[4],[5],[8]] => [1,1,1,1,3,1] => 17
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,6,1] => [[1,2,7],[3,6],[4],[5],[8]] => [2,1,1,3,1] => 16
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,5,7,1] => [[1,6,7],[2],[3],[4],[5],[8]] => [1,1,1,1,3,1] => 17
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,8,1] => [[1,2,7],[3,6],[4],[5],[8]] => [2,1,1,3,1] => 16
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,7,1] => [[1,6,7],[2],[3],[4],[5],[8]] => [1,1,1,1,3,1] => 17
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,8,1] => [[1,6,7],[2],[3],[4],[5],[8]] => [1,1,1,1,3,1] => 17
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,8,1] => [[1,6,7],[2],[3],[4],[5],[8]] => [1,1,1,1,3,1] => 17
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,6,7,1] => [[1,3,6,7],[2],[4],[5],[8]] => [1,2,1,3,1] => 15
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,7,8,1] => [[1,3,6,7],[2],[4],[5],[8]] => [1,2,1,3,1] => 15
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,7,8,1] => [[1,2,3,6,7],[4],[5],[8]] => [3,1,3,1] => 14
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,5,6,1] => [[1,2,6,7],[3,4],[5],[8]] => [2,2,3,1] => 13
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,2,6,7,1] => [[1,4,6,7],[2],[3],[5],[8]] => [1,1,2,3,1] => 14
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,7,8,1] => [[1,4,6,7],[2],[3],[5],[8]] => [1,1,2,3,1] => 14
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,8,1] => [[1,4,6,7],[2],[3],[5],[8]] => [1,1,2,3,1] => 14
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,8,1] => [[1,4,6,7],[2],[3],[5],[8]] => [1,1,2,3,1] => 14
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,6,7,1] => [[1,3,4,6,7],[2],[5],[8]] => [1,3,3,1] => 12
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,8,1] => [[1,3,4,6,7],[2],[5],[8]] => [1,3,3,1] => 12
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,8,1] => [[1,3,4,6,7],[2],[5],[8]] => [1,3,3,1] => 12
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,8,1] => [[1,2,3,4,6,7],[5],[8]] => [4,3,1] => 11
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,5,1] => [[1,5,6,7],[2],[3],[4],[8]] => [1,1,1,4,1] => 13
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,4,5,1] => [[1,2,6,7],[3,5],[4],[8]] => [2,1,4,1] => 12
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,5,1] => [[1,3,6,7],[2,5],[4],[8]] => [1,2,4,1] => 11
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,4,5,1] => [[1,3,6,7],[2,5],[4],[8]] => [1,2,4,1] => 11
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,5,1] => [[1,2,3,7],[4,5,6],[8]] => [3,4,1] => 10
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,8,1] => [[1,5,6,7],[2],[3],[4],[8]] => [1,1,1,4,1] => 13
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,8,1] => [[1,3,6,7],[2,5],[4],[8]] => [1,2,4,1] => 11
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,8,1] => [[1,2,3,7],[4,5,6],[8]] => [3,4,1] => 10
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,5,6,1] => [[1,2,6,7],[3,5],[4],[8]] => [2,1,4,1] => 12
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,7,1] => [[1,5,6,7],[2],[3],[4],[8]] => [1,1,1,4,1] => 13
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,8,1] => [[1,5,6,7],[2],[3],[4],[8]] => [1,1,1,4,1] => 13
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,3,6,7,1] => [[1,5,6,7],[2],[3],[4],[8]] => [1,1,1,4,1] => 13
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,6,8,1] => [[1,5,6,7],[2],[3],[4],[8]] => [1,1,1,4,1] => 13
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,3,7,8,1] => [[1,5,6,7],[2],[3],[4],[8]] => [1,1,1,4,1] => 13
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,3,7,8,1] => [[1,2,6,7],[3,5],[4],[8]] => [2,1,4,1] => 12
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,6,7,1] => [[1,3,6,7],[2,5],[4],[8]] => [1,2,4,1] => 11
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,8,1] => [[1,3,6,7],[2,5],[4],[8]] => [1,2,4,1] => 11
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,3,7,8,1] => [[1,3,6,7],[2,5],[4],[8]] => [1,2,4,1] => 11
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,7,8,1] => [[1,3,6,7],[2,5],[4],[8]] => [1,2,4,1] => 11
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,3,7,8,1] => [[1,2,3,6,7],[4,5],[8]] => [3,4,1] => 10
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,5,6,1] => [[1,2,6,7],[3,5],[4],[8]] => [2,1,4,1] => 12
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,8,1] => [[1,5,6,7],[2],[3],[4],[8]] => [1,1,1,4,1] => 13
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,8,1] => [[1,2,6,7],[3,5],[4],[8]] => [2,1,4,1] => 12
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,8,1] => [[1,5,6,7],[2],[3],[4],[8]] => [1,1,1,4,1] => 13
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,7,8,1] => [[1,5,6,7],[2],[3],[4],[8]] => [1,1,1,4,1] => 13
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,5,6,7,1] => [[1,5,6,7],[2],[3],[4],[8]] => [1,1,1,4,1] => 13
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,5,6,8,1] => [[1,5,6,7],[2],[3],[4],[8]] => [1,1,1,4,1] => 13
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,8,1] => [[1,5,6,7],[2],[3],[4],[8]] => [1,1,1,4,1] => 13
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,7,8,1] => [[1,2,5,6,7],[3],[4],[8]] => [2,1,4,1] => 12
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,6,7,1] => [[1,3,5,6,7],[2],[4],[8]] => [1,2,4,1] => 11
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,6,7,8,1] => [[1,3,5,6,7],[2],[4],[8]] => [1,2,4,1] => 11
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,7,8,1] => [[1,3,5,6,7],[2],[4],[8]] => [1,2,4,1] => 11
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,8,1] => [[1,2,3,5,6,7],[4],[8]] => [3,4,1] => 10
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,6,1] => [[1,4,5,6,7],[2],[3],[8]] => [1,1,5,1] => 10
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,6,1] => [[1,2,5,6,7],[3,4],[8]] => [2,5,1] => 9
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,4,5,7,1] => [[1,4,5,6,7],[2],[3],[8]] => [1,1,5,1] => 10
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,8,1] => [[1,4,5,6,7],[2],[3],[8]] => [1,1,5,1] => 10
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,8,1] => [[1,2,5,6,7],[3,4],[8]] => [2,5,1] => 9
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,6,8,1] => [[1,4,5,6,7],[2],[3],[8]] => [1,1,5,1] => 10
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,7,8,1] => [[1,4,5,6,7],[2],[3],[8]] => [1,1,5,1] => 10
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,6,7,1] => [[1,4,5,6,7],[2],[3],[8]] => [1,1,5,1] => 10
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,8,1] => [[1,4,5,6,7],[2],[3],[8]] => [1,1,5,1] => 10
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,7,8,1] => [[1,2,5,6,7],[3,4],[8]] => [2,5,1] => 9
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,7,1] => [[1,4,5,6,7],[2],[3],[8]] => [1,1,5,1] => 10
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [7,3,2,4,5,6,8,1] => [[1,4,5,6,7],[2],[3],[8]] => [1,1,5,1] => 10
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,7,8,1] => [[1,4,5,6,7],[2],[3],[8]] => [1,1,5,1] => 10
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,8,1] => [[1,4,5,6,7],[2],[3],[8]] => [1,1,5,1] => 10
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,8,1] => [[1,2,4,5,6,7],[3],[8]] => [2,5,1] => 9
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,7,1] => [[1,3,4,5,6,7],[2],[8]] => [1,6,1] => 8
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,8,1] => [[1,3,4,5,6,7],[2],[8]] => [1,6,1] => 8
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,7,8,1] => [[1,3,4,5,6,7],[2],[8]] => [1,6,1] => 8
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,8,1] => [[1,3,4,5,6,7],[2],[8]] => [1,6,1] => 8
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,8,1] => [[1,3,4,5,6,7],[2],[8]] => [1,6,1] => 8
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,8,1] => [[1,3,4,5,6,7],[2],[8]] => [1,6,1] => 8
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,8,1] => [[1,2,3,4,5,6,7],[8]] => [7,1] => 7
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,3,1,2] => [[1,8],[2],[3],[4],[5],[6],[7]] => [1,1,1,1,1,1,2] => 21
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,3,1,2] => [[1,2],[3,8],[4],[5],[6],[7]] => [2,1,1,1,1,2] => 20
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,3,1,2] => [[1,3],[2,8],[4],[5],[6],[7]] => [1,2,1,1,1,2] => 19
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,3,1,2] => [[1,3],[2,8],[4],[5],[6],[7]] => [1,2,1,1,1,2] => 19
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,3,1,2] => [[1,2,3],[4,8],[5],[6],[7]] => [3,1,1,1,2] => 18
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,3,1,2] => [[1,4],[2,8],[3],[5],[6],[7]] => [1,1,2,1,1,2] => 18
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,3,1,2] => [[1,2],[3,4],[5,8],[6],[7]] => [2,2,1,1,2] => 17
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,3,1,2] => [[1,4],[2,8],[3],[5],[6],[7]] => [1,1,2,1,1,2] => 18
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,3,1,2] => [[1,4],[2,8],[3],[5],[6],[7]] => [1,1,2,1,1,2] => 18
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,3,1,2] => [[1,2,4],[3,8],[5],[6],[7]] => [2,2,1,1,2] => 17
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,3,1,2] => [[1,3,4],[2,8],[5],[6],[7]] => [1,3,1,1,2] => 16
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,3,1,2] => [[1,3,4],[2,8],[5],[6],[7]] => [1,3,1,1,2] => 16
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,3,1,2] => [[1,2,3,4],[5,8],[6],[7]] => [4,1,1,2] => 15
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,3,1,2] => [[1,5],[2,8],[3],[4],[6],[7]] => [1,1,1,2,1,2] => 17
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0] => [7,8,6,4,5,3,1,2] => [[1,2],[3,5],[4,8],[6],[7]] => [2,1,2,1,2] => 16
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,3,1,2] => [[1,3],[2,5],[4,8],[6],[7]] => [1,2,2,1,2] => 15
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,3,1,2] => [[1,2,3],[4,5],[6,8],[7]] => [3,2,1,2] => 14
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,3,1,2] => [[1,5],[2,8],[3],[4],[6],[7]] => [1,1,1,2,1,2] => 17
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,3,1,2] => [[1,5],[2,8],[3],[4],[6],[7]] => [1,1,1,2,1,2] => 17
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,3,1,2] => [[1,3,5],[2,8],[4],[6],[7]] => [1,2,2,1,2] => 15
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0] => [7,5,6,4,8,3,1,2] => [[1,3,5],[2,8],[4],[6],[7]] => [1,2,2,1,2] => 15
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,3,1,2] => [[1,3,5],[2,8],[4],[6],[7]] => [1,2,2,1,2] => 15
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,3,1,2] => [[1,4,5],[2,8],[3],[6],[7]] => [1,1,3,1,2] => 14
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,3,1,2] => [[1,4,5],[2,8],[3],[6],[7]] => [1,1,3,1,2] => 14
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,3,1,2] => [[1,2,5],[3,4],[6,8],[7]] => [2,3,1,2] => 13
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,3,1,2] => [[1,4,5],[2,8],[3],[6],[7]] => [1,1,3,1,2] => 14
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,3,1,2] => [[1,4,5],[2,8],[3],[6],[7]] => [1,1,3,1,2] => 14
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,3,1,2] => [[1,2,4,5],[3,8],[6],[7]] => [2,3,1,2] => 13
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,3,1,2] => [[1,3,4,5],[2,8],[6],[7]] => [1,4,1,2] => 12
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,3,1,2] => [[1,2,3,4,5],[6,8],[7]] => [5,1,2] => 11
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,4,1,2] => [[1,6],[2,8],[3],[4],[5],[7]] => [1,1,1,1,2,2] => 16
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,4,1,2] => [[1,2],[3,6],[4,8],[5],[7]] => [2,1,1,2,2] => 15
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,4,1,2] => [[1,3],[2,6],[4,8],[5],[7]] => [1,2,1,2,2] => 14
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,4,1,2] => [[1,2,3],[4,6],[5,8],[7]] => [3,1,2,2] => 13
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,4,1,2] => [[1,4],[2,6],[3,8],[5],[7]] => [1,1,2,2,2] => 13
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,4,1,2] => [[1,2],[3,4],[5,6],[7,8]] => [2,2,2,2] => 12
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,4,1,2] => [[1,4],[2,6],[3,8],[5],[7]] => [1,1,2,2,2] => 13
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,4,1,2] => [[1,4],[2,6],[3,8],[5],[7]] => [1,1,2,2,2] => 13
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,4,1,2] => [[1,2,4],[3,6],[5,8],[7]] => [2,2,2,2] => 12
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,4,1,2] => [[1,3,4],[2,6],[5,8],[7]] => [1,3,2,2] => 11
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,4,1,2] => [[1,3,4],[2,6],[5,8],[7]] => [1,3,2,2] => 11
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,4,1,2] => [[1,3,4],[2,6],[5,8],[7]] => [1,3,2,2] => 11
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,4,1,2] => [[1,2,3,4],[5,6],[7,8]] => [4,2,2] => 10
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,5,1,2] => [[1,2,3],[4,6],[5,8],[7]] => [3,1,2,2] => 13
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,6,1,2] => [[1,2],[3,6],[4,8],[5],[7]] => [2,1,1,2,2] => 15
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,7,1,2] => [[1,6],[2,8],[3],[4],[5],[7]] => [1,1,1,1,2,2] => 16
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,8,1,2] => [[1,6],[2,8],[3],[4],[5],[7]] => [1,1,1,1,2,2] => 16
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,8,1,2] => [[1,3,6],[2,8],[4],[5],[7]] => [1,2,1,2,2] => 14
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,8,1,2] => [[1,2,3,6],[4,8],[5],[7]] => [3,1,2,2] => 13
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,6,1,2] => [[1,4,6],[2,8],[3],[5],[7]] => [1,1,2,2,2] => 13
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,6,1,2] => [[1,2,6],[3,4],[5,8],[7]] => [2,2,2,2] => 12
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,8,1,2] => [[1,2,6],[3,4],[5,8],[7]] => [2,2,2,2] => 12
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0] => [8,5,4,6,3,7,1,2] => [[1,4,6],[2,8],[3],[5],[7]] => [1,1,2,2,2] => 13
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,8,1,2] => [[1,4,6],[2,8],[3],[5],[7]] => [1,1,2,2,2] => 13
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,8,1,2] => [[1,4,6],[2,8],[3],[5],[7]] => [1,1,2,2,2] => 13
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,8,1,2] => [[1,2,4,6],[3,8],[5],[7]] => [2,2,2,2] => 12
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,8,1,2] => [[1,2,3,4,6],[5,8],[7]] => [4,2,2] => 10
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,5,1,2] => [[1,5,6],[2,8],[3],[4],[7]] => [1,1,1,3,2] => 12
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,5,1,2] => [[1,3,6],[2,5],[4,8],[7]] => [1,2,3,2] => 10
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,4,6,1,2] => [[1,2,6],[3,5],[4,8],[7]] => [2,1,3,2] => 11
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,8,1,2] => [[1,5,6],[2,8],[3],[4],[7]] => [1,1,1,3,2] => 12
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,5,6,1,2] => [[1,5,6],[2,8],[3],[4],[7]] => [1,1,1,3,2] => 12
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,5,6,1,2] => [[1,2,6],[3,5],[4,8],[7]] => [2,1,3,2] => 11
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,8,1,2] => [[1,5,6],[2,8],[3],[4],[7]] => [1,1,1,3,2] => 12
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,7,1,2] => [[1,5,6],[2,8],[3],[4],[7]] => [1,1,1,3,2] => 12
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,8,1,2] => [[1,5,6],[2,8],[3],[4],[7]] => [1,1,1,3,2] => 12
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,8,1,2] => [[1,5,6],[2,8],[3],[4],[7]] => [1,1,1,3,2] => 12
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,8,1,2] => [[1,2,5,6],[3,8],[4],[7]] => [2,1,3,2] => 11
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,6,8,1,2] => [[1,3,5,6],[2,8],[4],[7]] => [1,2,3,2] => 10
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,8,1,2] => [[1,3,5,6],[2,8],[4],[7]] => [1,2,3,2] => 10
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,7,8,1,2] => [[1,2,3,5,6],[4,8],[7]] => [3,3,2] => 9
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,6,1,2] => [[1,4,5,6],[2,8],[3],[7]] => [1,1,4,2] => 9
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,6,1,2] => [[1,2,5,6],[3,4],[7,8]] => [2,4,2] => 8
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,8,1,2] => [[1,4,5,6],[2,8],[3],[7]] => [1,1,4,2] => 9
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,7,1,2] => [[1,4,5,6],[2,8],[3],[7]] => [1,1,4,2] => 9
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,6,8,1,2] => [[1,4,5,6],[2,8],[3],[7]] => [1,1,4,2] => 9
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,8,1,2] => [[1,2,5,6],[3,4],[7,8]] => [2,4,2] => 8
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,7,1,2] => [[1,4,5,6],[2,8],[3],[7]] => [1,1,4,2] => 9
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0] => [6,4,3,5,7,8,1,2] => [[1,4,5,6],[2,8],[3],[7]] => [1,1,4,2] => 9
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,8,1,2] => [[1,4,5,6],[2,8],[3],[7]] => [1,1,4,2] => 9
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,7,8,1,2] => [[1,2,4,5,6],[3,8],[7]] => [2,4,2] => 8
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,7,1,2] => [[1,3,4,5,6],[2,8],[7]] => [1,5,2] => 7
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,8,1,2] => [[1,3,4,5,6],[2,8],[7]] => [1,5,2] => 7
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,8,1,2] => [[1,3,4,5,6],[2,8],[7]] => [1,5,2] => 7
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,7,8,1,2] => [[1,3,4,5,6],[2,8],[7]] => [1,5,2] => 7
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,8,1,2] => [[1,3,4,5,6],[2,8],[7]] => [1,5,2] => 7
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,8,1,2] => [[1,2,3,4,5,6],[7,8]] => [6,2] => 6
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,2,1,3] => [[1,8],[2],[3],[4],[5],[6],[7]] => [1,1,1,1,1,1,2] => 21
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,2,1,3] => [[1,2],[3,8],[4],[5],[6],[7]] => [2,1,1,1,1,2] => 20
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0] => [8,6,7,5,4,2,1,3] => [[1,3],[2,8],[4],[5],[6],[7]] => [1,2,1,1,1,2] => 19
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,2,1,3] => [[1,3],[2,8],[4],[5],[6],[7]] => [1,2,1,1,1,2] => 19
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,2,1,3] => [[1,2,3],[4,8],[5],[6],[7]] => [3,1,1,1,2] => 18
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0] => [8,7,5,6,4,2,1,3] => [[1,4],[2,8],[3],[5],[6],[7]] => [1,1,2,1,1,2] => 18
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,2,1,3] => [[1,2],[3,4],[5,8],[6],[7]] => [2,2,1,1,2] => 17
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,2,1,3] => [[1,4],[2,8],[3],[5],[6],[7]] => [1,1,2,1,1,2] => 18
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,2,1,3] => [[1,2,4],[3,8],[5],[6],[7]] => [2,2,1,1,2] => 17
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,2,1,3] => [[1,3,4],[2,8],[5],[6],[7]] => [1,3,1,1,2] => 16
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,2,1,3] => [[1,3,4],[2,8],[5],[6],[7]] => [1,3,1,1,2] => 16
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,2,1,3] => [[1,2,3,4],[5,8],[6],[7]] => [4,1,1,2] => 15
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,2,1,3] => [[1,5],[2,8],[3],[4],[6],[7]] => [1,1,1,2,1,2] => 17
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,2,1,3] => [[1,5],[2,8],[3],[4],[6],[7]] => [1,1,1,2,1,2] => 17
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,2,1,3] => [[1,2,5],[3,8],[4],[6],[7]] => [2,1,2,1,2] => 16
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,2,1,3] => [[1,3,5],[2,8],[4],[6],[7]] => [1,2,2,1,2] => 15
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,2,1,3] => [[1,2,3,5],[4,8],[6],[7]] => [3,2,1,2] => 14
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0] => [7,6,4,5,8,2,1,3] => [[1,4,5],[2,8],[3],[6],[7]] => [1,1,3,1,2] => 14
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,2,1,3] => [[1,3,4,5],[2,8],[6],[7]] => [1,4,1,2] => 12
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0] => [7,4,5,6,8,2,1,3] => [[1,3,4,5],[2,8],[6],[7]] => [1,4,1,2] => 12
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,2,1,3] => [[1,3,4,5],[2,8],[6],[7]] => [1,4,1,2] => 12
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,2,1,3] => [[1,2,3,4,5],[6,8],[7]] => [5,1,2] => 11
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,2,1,4] => [[1,8],[2],[3],[4],[5],[6],[7]] => [1,1,1,1,1,1,2] => 21
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,2,1,4] => [[1,2],[3,8],[4],[5],[6],[7]] => [2,1,1,1,1,2] => 20
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,2,1,4] => [[1,3],[2,8],[4],[5],[6],[7]] => [1,2,1,1,1,2] => 19
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,2,1,4] => [[1,3],[2,8],[4],[5],[6],[7]] => [1,2,1,1,1,2] => 19
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,3,2,1,4] => [[1,2,3],[4,8],[5],[6],[7]] => [3,1,1,1,2] => 18
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,2,1,4] => [[1,4],[2,8],[3],[5],[6],[7]] => [1,1,2,1,1,2] => 18
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,2,1,4] => [[1,2],[3,4],[5,8],[6],[7]] => [2,2,1,1,2] => 17
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,3,2,1,4] => [[1,4],[2,8],[3],[5],[6],[7]] => [1,1,2,1,1,2] => 18
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,2,1,4] => [[1,4],[2,8],[3],[5],[6],[7]] => [1,1,2,1,1,2] => 18
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,2,1,4] => [[1,2,4],[3,8],[5],[6],[7]] => [2,2,1,1,2] => 17
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,3,2,1,4] => [[1,3,4],[2,8],[5],[6],[7]] => [1,3,1,1,2] => 16
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,2,1,4] => [[1,3,4],[2,8],[5],[6],[7]] => [1,3,1,1,2] => 16
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,2,1,4] => [[1,3,4],[2,8],[5],[6],[7]] => [1,3,1,1,2] => 16
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,2,1,4] => [[1,2,3,4],[5,8],[6],[7]] => [4,1,1,2] => 15
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,2,1,5] => [[1,8],[2],[3],[4],[5],[6],[7]] => [1,1,1,1,1,1,2] => 21
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,3,2,1,5] => [[1,2],[3,8],[4],[5],[6],[7]] => [2,1,1,1,1,2] => 20
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,3,2,1,5] => [[1,3],[2,8],[4],[5],[6],[7]] => [1,2,1,1,1,2] => 19
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,3,2,1,5] => [[1,3],[2,8],[4],[5],[6],[7]] => [1,2,1,1,1,2] => 19
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,2,1,5] => [[1,2,3],[4,8],[5],[6],[7]] => [3,1,1,1,2] => 18
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,2,1,6] => [[1,8],[2],[3],[4],[5],[6],[7]] => [1,1,1,1,1,1,2] => 21
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,2,1,6] => [[1,2],[3,8],[4],[5],[6],[7]] => [2,1,1,1,1,2] => 20
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,2,1,7] => [[1,8],[2],[3],[4],[5],[6],[7]] => [1,1,1,1,1,1,2] => 21
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,2,1,8] => [[1,8],[2],[3],[4],[5],[6],[7]] => [1,1,1,1,1,1,2] => 21
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,2,1,8] => [[1,2,8],[3],[4],[5],[6],[7]] => [2,1,1,1,1,2] => 20
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,3,2,1,7] => [[1,3,8],[2],[4],[5],[6],[7]] => [1,2,1,1,1,2] => 19
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,2,1,8] => [[1,3,8],[2],[4],[5],[6],[7]] => [1,2,1,1,1,2] => 19
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,3,2,1,8] => [[1,3,8],[2],[4],[5],[6],[7]] => [1,2,1,1,1,2] => 19
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,3,2,1,8] => [[1,2,3,8],[4],[5],[6],[7]] => [3,1,1,1,2] => 18
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,3,2,1,6] => [[1,4,8],[2],[3],[5],[6],[7]] => [1,1,2,1,1,2] => 18
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,3,2,1,6] => [[1,2,8],[3,4],[5],[6],[7]] => [2,2,1,1,2] => 17
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,2,1,7] => [[1,4,8],[2],[3],[5],[6],[7]] => [1,1,2,1,1,2] => 18
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,2,1,8] => [[1,4,8],[2],[3],[5],[6],[7]] => [1,1,2,1,1,2] => 18
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,3,2,1,8] => [[1,2,8],[3,4],[5],[6],[7]] => [2,2,1,1,2] => 17
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,3,2,1,8] => [[1,4,8],[2],[3],[5],[6],[7]] => [1,1,2,1,1,2] => 18
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,3,2,1,8] => [[1,4,8],[2],[3],[5],[6],[7]] => [1,1,2,1,1,2] => 18
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,3,2,1,8] => [[1,2,4,8],[3],[5],[6],[7]] => [2,2,1,1,2] => 17
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,3,2,1,7] => [[1,3,4,8],[2],[5],[6],[7]] => [1,3,1,1,2] => 16
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,3,2,1,8] => [[1,3,4,8],[2],[5],[6],[7]] => [1,3,1,1,2] => 16
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,2,1,8] => [[1,3,4,8],[2],[5],[6],[7]] => [1,3,1,1,2] => 16
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,2,1,8] => [[1,2,3,4,8],[5],[6],[7]] => [4,1,1,2] => 15
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,2,1,5] => [[1,5,8],[2],[3],[4],[6],[7]] => [1,1,1,2,1,2] => 17
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,2,1,5] => [[1,2,8],[3,5],[4],[6],[7]] => [2,1,2,1,2] => 16
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,2,1,5] => [[1,2,3],[4,5,8],[6],[7]] => [3,2,1,2] => 14
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,2,1,6] => [[1,5,8],[2],[3],[4],[6],[7]] => [1,1,1,2,1,2] => 17
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,2,1,7] => [[1,5,8],[2],[3],[4],[6],[7]] => [1,1,1,2,1,2] => 17
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,2,1,8] => [[1,5,8],[2],[3],[4],[6],[7]] => [1,1,1,2,1,2] => 17
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0] => [6,7,5,3,4,2,1,8] => [[1,2,8],[3,5],[4],[6],[7]] => [2,1,2,1,2] => 16
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,2,1,7] => [[1,3,8],[2,5],[4],[6],[7]] => [1,2,2,1,2] => 15
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0] => [7,5,6,3,4,2,1,8] => [[1,3,8],[2,5],[4],[6],[7]] => [1,2,2,1,2] => 15
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,4,2,1,8] => [[1,3,8],[2,5],[4],[6],[7]] => [1,2,2,1,2] => 15
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,4,2,1,8] => [[1,2,3,8],[4,5],[6],[7]] => [3,2,1,2] => 14
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,5,2,1,8] => [[1,5,8],[2],[3],[4],[6],[7]] => [1,1,1,2,1,2] => 17
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,5,2,1,8] => [[1,2,8],[3,5],[4],[6],[7]] => [2,1,2,1,2] => 16
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,6,2,1,8] => [[1,5,8],[2],[3],[4],[6],[7]] => [1,1,1,2,1,2] => 17
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,2,1,8] => [[1,5,8],[2],[3],[4],[6],[7]] => [1,1,1,2,1,2] => 17
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,7,2,1,8] => [[1,2,5,8],[3],[4],[6],[7]] => [2,1,2,1,2] => 16
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,2,1,7] => [[1,3,5,8],[2],[4],[6],[7]] => [1,2,2,1,2] => 15
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,7,2,1,8] => [[1,3,5,8],[2],[4],[6],[7]] => [1,2,2,1,2] => 15
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,2,1,6] => [[1,4,5,8],[2],[3],[6],[7]] => [1,1,3,1,2] => 14
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,2,1,6] => [[1,2,5,8],[3,4],[6],[7]] => [2,3,1,2] => 13
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,5,2,1,8] => [[1,4,5,8],[2],[3],[6],[7]] => [1,1,3,1,2] => 14
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,2,1,7] => [[1,4,5,8],[2],[3],[6],[7]] => [1,1,3,1,2] => 14
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,7,2,1,8] => [[1,4,5,8],[2],[3],[6],[7]] => [1,1,3,1,2] => 14
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,2,1,7] => [[1,3,4,5,8],[2],[6],[7]] => [1,4,1,2] => 12
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,6,2,1,8] => [[1,3,4,5,8],[2],[6],[7]] => [1,4,1,2] => 12
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,2,1,8] => [[1,2,3,4,5,8],[6],[7]] => [5,1,2] => 11
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,3,1,4] => [[1,6,8],[2],[3],[4],[5],[7]] => [1,1,1,1,2,2] => 16
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,3,1,4] => [[1,2,8],[3,6],[4],[5],[7]] => [2,1,1,2,2] => 15
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,2,3,1,4] => [[1,3,8],[2,6],[4],[5],[7]] => [1,2,1,2,2] => 14
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,3,1,4] => [[1,3,8],[2,6],[4],[5],[7]] => [1,2,1,2,2] => 14
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,3,1,4] => [[1,2,3],[4,6,8],[5],[7]] => [3,1,2,2] => 13
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,3,1,4] => [[1,4,8],[2,6],[3],[5],[7]] => [1,1,2,2,2] => 13
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,3,1,4] => [[1,2,8],[3,4],[5,6],[7]] => [2,2,2,2] => 12
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,3,1,4] => [[1,4,8],[2,6],[3],[5],[7]] => [1,1,2,2,2] => 13
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,3,1,4] => [[1,4,8],[2,6],[3],[5],[7]] => [1,1,2,2,2] => 13
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,3,1,4] => [[1,2,4],[3,6,8],[5],[7]] => [2,2,2,2] => 12
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,3,1,4] => [[1,3,4],[2,6,8],[5],[7]] => [1,3,2,2] => 11
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,3,1,4] => [[1,3,4],[2,6,8],[5],[7]] => [1,3,2,2] => 11
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,3,1,4] => [[1,3,4],[2,6,8],[5],[7]] => [1,3,2,2] => 11
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,3,1,4] => [[1,2,3,4],[5,6,8],[7]] => [4,2,2] => 10
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,3,1,5] => [[1,6,8],[2],[3],[4],[5],[7]] => [1,1,1,1,2,2] => 16
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,2,3,1,5] => [[1,3,8],[2,6],[4],[5],[7]] => [1,2,1,2,2] => 14
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,3,1,5] => [[1,2,3],[4,6,8],[5],[7]] => [3,1,2,2] => 13
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,3,1,7] => [[1,6,8],[2],[3],[4],[5],[7]] => [1,1,1,1,2,2] => 16
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,3,1,8] => [[1,6,8],[2],[3],[4],[5],[7]] => [1,1,1,1,2,2] => 16
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,2,3,1,8] => [[1,2,8],[3,6],[4],[5],[7]] => [2,1,1,2,2] => 15
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,3,1,7] => [[1,3,8],[2,6],[4],[5],[7]] => [1,2,1,2,2] => 14
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,2,3,1,8] => [[1,3,8],[2,6],[4],[5],[7]] => [1,2,1,2,2] => 14
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,2,3,1,8] => [[1,2,3,8],[4,6],[5],[7]] => [3,1,2,2] => 13
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,2,3,1,6] => [[1,4,8],[2,6],[3],[5],[7]] => [1,1,2,2,2] => 13
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,2,3,1,6] => [[1,2,8],[3,4],[5,6],[7]] => [2,2,2,2] => 12
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,3,1,8] => [[1,4,8],[2,6],[3],[5],[7]] => [1,1,2,2,2] => 13
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0] => [6,7,4,5,2,3,1,8] => [[1,2,8],[3,4],[5,6],[7]] => [2,2,2,2] => 12
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,3,1,8] => [[1,4,8],[2,6],[3],[5],[7]] => [1,1,2,2,2] => 13
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0] => [6,5,4,7,2,3,1,8] => [[1,4,8],[2,6],[3],[5],[7]] => [1,1,2,2,2] => 13
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0] => [5,6,4,7,2,3,1,8] => [[1,2,4,8],[3,6],[5],[7]] => [2,2,2,2] => 12
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,2,3,1,7] => [[1,3,4,8],[2,6],[5],[7]] => [1,3,2,2] => 11
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,3,1,8] => [[1,3,4,8],[2,6],[5],[7]] => [1,3,2,2] => 11
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,3,1,8] => [[1,2,3,4,8],[5,6],[7]] => [4,2,2] => 10
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,4,1,5] => [[1,6,8],[2],[3],[4],[5],[7]] => [1,1,1,1,2,2] => 16
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,4,1,5] => [[1,3,8],[2,6],[4],[5],[7]] => [1,2,1,2,2] => 14
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,4,1,5] => [[1,2,3],[4,6,8],[5],[7]] => [3,1,2,2] => 13
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,4,1,6] => [[1,6,8],[2],[3],[4],[5],[7]] => [1,1,1,1,2,2] => 16
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,4,1,7] => [[1,6,8],[2],[3],[4],[5],[7]] => [1,1,1,1,2,2] => 16
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,4,1,8] => [[1,6,8],[2],[3],[4],[5],[7]] => [1,1,1,1,2,2] => 16
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0] => [6,5,7,3,2,4,1,8] => [[1,3,8],[2,6],[4],[5],[7]] => [1,2,1,2,2] => 14
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0] => [5,6,7,3,2,4,1,8] => [[1,2,3,8],[4,6],[5],[7]] => [3,1,2,2] => 13
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,5,1,6] => [[1,6,8],[2],[3],[4],[5],[7]] => [1,1,1,1,2,2] => 16
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,5,1,6] => [[1,2,8],[3,6],[4],[5],[7]] => [2,1,1,2,2] => 15
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,5,1,8] => [[1,6,8],[2],[3],[4],[5],[7]] => [1,1,1,1,2,2] => 16
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,5,1,8] => [[1,2,8],[3,6],[4],[5],[7]] => [2,1,1,2,2] => 15
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,6,1,7] => [[1,6,8],[2],[3],[4],[5],[7]] => [1,1,1,1,2,2] => 16
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,6,1,8] => [[1,6,8],[2],[3],[4],[5],[7]] => [1,1,1,1,2,2] => 16
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,7,1,8] => [[1,6,8],[2],[3],[4],[5],[7]] => [1,1,1,1,2,2] => 16
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,7,1,8] => [[1,2,6,8],[3],[4],[5],[7]] => [2,1,1,2,2] => 15
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,6,1,8] => [[1,3,6,8],[2],[4],[5],[7]] => [1,2,1,2,2] => 14
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,7,1,8] => [[1,3,6,8],[2],[4],[5],[7]] => [1,2,1,2,2] => 14
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,5,1,6] => [[1,4,6,8],[2],[3],[5],[7]] => [1,1,2,2,2] => 13
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,5,1,6] => [[1,2,6,8],[3,4],[5],[7]] => [2,2,2,2] => 12
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,5,1,8] => [[1,2,6,8],[3,4],[5],[7]] => [2,2,2,2] => 12
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0] => [7,5,3,4,2,6,1,8] => [[1,4,6,8],[2],[3],[5],[7]] => [1,1,2,2,2] => 13
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,7,1,8] => [[1,2,6,8],[3,4],[5],[7]] => [2,2,2,2] => 12
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,6,1,7] => [[1,4,6,8],[2],[3],[5],[7]] => [1,1,2,2,2] => 13
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,6,1,8] => [[1,4,6,8],[2],[3],[5],[7]] => [1,1,2,2,2] => 13
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,7,1,8] => [[1,4,6,8],[2],[3],[5],[7]] => [1,1,2,2,2] => 13
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0] => [4,5,3,6,2,7,1,8] => [[1,2,4,6,8],[3],[5],[7]] => [2,2,2,2] => 12
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,2,7,1,8] => [[1,3,4,6,8],[2],[5],[7]] => [1,3,2,2] => 11
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0] => [5,3,4,6,2,7,1,8] => [[1,3,4,6,8],[2],[5],[7]] => [1,3,2,2] => 11
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,2,7,1,8] => [[1,3,4,6,8],[2],[5],[7]] => [1,3,2,2] => 11
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,7,1,8] => [[1,2,3,4,6,8],[5],[7]] => [4,2,2] => 10
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,4,1,5] => [[1,5,6,8],[2],[3],[4],[7]] => [1,1,1,3,2] => 12
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,4,1,5] => [[1,3,6,8],[2,5],[4],[7]] => [1,2,3,2] => 10
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,4,1,5] => [[1,3,6,8],[2,5],[4],[7]] => [1,2,3,2] => 10
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,4,1,5] => [[1,2,3,8],[4,5,6],[7]] => [3,3,2] => 9
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,3,4,1,6] => [[1,2,6,8],[3,5],[4],[7]] => [2,1,3,2] => 11
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,4,1,7] => [[1,5,6,8],[2],[3],[4],[7]] => [1,1,1,3,2] => 12
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,4,1,8] => [[1,5,6,8],[2],[3],[4],[7]] => [1,1,1,3,2] => 12
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,4,1,8] => [[1,2,6,8],[3,5],[4],[7]] => [2,1,3,2] => 11
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,4,1,7] => [[1,3,6,8],[2,5],[4],[7]] => [1,2,3,2] => 10
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,4,1,8] => [[1,3,6,8],[2,5],[4],[7]] => [1,2,3,2] => 10
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,4,1,8] => [[1,3,6,8],[2,5],[4],[7]] => [1,2,3,2] => 10
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,4,1,8] => [[1,2,3,8],[4,5,6],[7]] => [3,3,2] => 9
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,5,1,7] => [[1,5,6,8],[2],[3],[4],[7]] => [1,1,1,3,2] => 12
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,5,1,8] => [[1,5,6,8],[2],[3],[4],[7]] => [1,1,1,3,2] => 12
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0] => [6,7,4,2,3,5,1,8] => [[1,2,6,8],[3,5],[4],[7]] => [2,1,3,2] => 11
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,3,6,1,7] => [[1,5,6,8],[2],[3],[4],[7]] => [1,1,1,3,2] => 12
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,6,1,7] => [[1,3,6,8],[2,5],[4],[7]] => [1,2,3,2] => 10
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,3,6,1,8] => [[1,3,6,8],[2,5],[4],[7]] => [1,2,3,2] => 10
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,7,1,8] => [[1,3,6,8],[2,5],[4],[7]] => [1,2,3,2] => 10
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,5,1,7] => [[1,5,6,8],[2],[3],[4],[7]] => [1,1,1,3,2] => 12
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,5,1,8] => [[1,5,6,8],[2],[3],[4],[7]] => [1,1,1,3,2] => 12
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,5,1,8] => [[1,2,6,8],[3,5],[4],[7]] => [2,1,3,2] => 11
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,4,6,1,7] => [[1,5,6,8],[2],[3],[4],[7]] => [1,1,1,3,2] => 12
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,6,1,8] => [[1,5,6,8],[2],[3],[4],[7]] => [1,1,1,3,2] => 12
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,4,7,1,8] => [[1,5,6,8],[2],[3],[4],[7]] => [1,1,1,3,2] => 12
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,7,1,8] => [[1,5,6,8],[2],[3],[4],[7]] => [1,1,1,3,2] => 12
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,5,6,1,7] => [[1,3,5,6,8],[2],[4],[7]] => [1,2,3,2] => 10
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,7,1,8] => [[1,2,3,5,6,8],[4],[7]] => [3,3,2] => 9
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,5,1,6] => [[1,4,5,6,8],[2],[3],[7]] => [1,1,4,2] => 9
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,5,1,6] => [[1,2,5,6,8],[3,4],[7]] => [2,4,2] => 8
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,5,1,8] => [[1,4,5,6,8],[2],[3],[7]] => [1,1,4,2] => 9
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,5,1,8] => [[1,2,5,6,8],[3,4],[7]] => [2,4,2] => 8
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,6,1,7] => [[1,4,5,6,8],[2],[3],[7]] => [1,1,4,2] => 9
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,6,1,8] => [[1,4,5,6,8],[2],[3],[7]] => [1,1,4,2] => 9
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0] => [6,4,2,3,5,7,1,8] => [[1,4,5,6,8],[2],[3],[7]] => [1,1,4,2] => 9
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,6,7,1,8] => [[1,4,5,6,8],[2],[3],[7]] => [1,1,4,2] => 9
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,6,7,1,8] => [[1,2,5,6,8],[3,4],[7]] => [2,4,2] => 8
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0] => [8,3,2,4,5,6,1,7] => [[1,4,5,6,8],[2],[3],[7]] => [1,1,4,2] => 9
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0] => [6,3,2,4,5,7,1,8] => [[1,4,5,6,8],[2],[3],[7]] => [1,1,4,2] => 9
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,7,1,8] => [[1,4,5,6,8],[2],[3],[7]] => [1,1,4,2] => 9
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,7,1,8] => [[1,2,4,5,6,8],[3],[7]] => [2,4,2] => 8
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,6,1,7] => [[1,3,4,5,6,8],[2],[7]] => [1,5,2] => 7
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,6,1,8] => [[1,3,4,5,6,8],[2],[7]] => [1,5,2] => 7
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,7,1,8] => [[1,3,4,5,6,8],[2],[7]] => [1,5,2] => 7
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,7,1,8] => [[1,3,4,5,6,8],[2],[7]] => [1,5,2] => 7
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,7,1,8] => [[1,3,4,5,6,8],[2],[7]] => [1,5,2] => 7
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,7,1,8] => [[1,3,4,5,6,8],[2],[7]] => [1,5,2] => 7
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,7,1,8] => [[1,2,3,4,5,6,8],[7]] => [6,2] => 6
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => [8,7,6,5,4,1,2,3] => [[1,7,8],[2],[3],[4],[5],[6]] => [1,1,1,1,1,3] => 15
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => [7,8,6,5,4,1,2,3] => [[1,2,8],[3,7],[4],[5],[6]] => [2,1,1,1,3] => 14
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0] => [7,6,8,5,4,1,2,3] => [[1,3,8],[2,7],[4],[5],[6]] => [1,2,1,1,3] => 13
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => [6,7,8,5,4,1,2,3] => [[1,2,3],[4,7,8],[5],[6]] => [3,1,1,3] => 12
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => [7,8,5,6,4,1,2,3] => [[1,2,8],[3,4],[5,7],[6]] => [2,2,1,3] => 11
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0] => [8,6,5,7,4,1,2,3] => [[1,4,8],[2,7],[3],[5],[6]] => [1,1,2,1,3] => 12
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0] => [7,6,5,8,4,1,2,3] => [[1,4,8],[2,7],[3],[5],[6]] => [1,1,2,1,3] => 12
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0] => [6,7,5,8,4,1,2,3] => [[1,2,4],[3,7,8],[5],[6]] => [2,2,1,3] => 11
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => [8,5,6,7,4,1,2,3] => [[1,3,4],[2,7,8],[5],[6]] => [1,3,1,3] => 10
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0] => [7,5,6,8,4,1,2,3] => [[1,3,4],[2,7,8],[5],[6]] => [1,3,1,3] => 10
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0] => [6,5,7,8,4,1,2,3] => [[1,3,4],[2,7,8],[5],[6]] => [1,3,1,3] => 10
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => [5,6,7,8,4,1,2,3] => [[1,2,3,4],[5,7,8],[6]] => [4,1,3] => 9
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0] => [8,7,6,4,5,1,2,3] => [[1,5,8],[2,7],[3],[4],[6]] => [1,1,1,2,3] => 11
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => [8,6,7,4,5,1,2,3] => [[1,3,8],[2,5],[4,7],[6]] => [1,2,2,3] => 9
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => [6,7,8,4,5,1,2,3] => [[1,2,3],[4,5,8],[6,7]] => [3,2,3] => 8
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0] => [8,7,5,4,6,1,2,3] => [[1,5,8],[2,7],[3],[4],[6]] => [1,1,1,2,3] => 11
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0] => [7,8,5,4,6,1,2,3] => [[1,2,8],[3,5],[4,7],[6]] => [2,1,2,3] => 10
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0] => [8,6,5,4,7,1,2,3] => [[1,5,8],[2,7],[3],[4],[6]] => [1,1,1,2,3] => 11
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0] => [7,6,5,4,8,1,2,3] => [[1,5,8],[2,7],[3],[4],[6]] => [1,1,1,2,3] => 11
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0] => [6,7,5,4,8,1,2,3] => [[1,2,5],[3,7,8],[4],[6]] => [2,1,2,3] => 10
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0] => [8,5,6,4,7,1,2,3] => [[1,3,5],[2,7,8],[4],[6]] => [1,2,2,3] => 9
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0] => [6,5,7,4,8,1,2,3] => [[1,3,5],[2,7,8],[4],[6]] => [1,2,2,3] => 9
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0] => [5,6,7,4,8,1,2,3] => [[1,2,3,5],[4,7,8],[6]] => [3,2,3] => 8
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => [8,7,4,5,6,1,2,3] => [[1,4,5],[2,7,8],[3],[6]] => [1,1,3,3] => 8
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => [7,8,4,5,6,1,2,3] => [[1,2,5],[3,4,8],[6,7]] => [2,3,3] => 7
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0] => [8,6,4,5,7,1,2,3] => [[1,4,5],[2,7,8],[3],[6]] => [1,1,3,3] => 8
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0] => [6,7,4,5,8,1,2,3] => [[1,2,5],[3,4,8],[6,7]] => [2,3,3] => 7
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0] => [8,5,4,6,7,1,2,3] => [[1,4,5],[2,7,8],[3],[6]] => [1,1,3,3] => 8
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0] => [7,5,4,6,8,1,2,3] => [[1,4,5],[2,7,8],[3],[6]] => [1,1,3,3] => 8
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0] => [6,5,4,7,8,1,2,3] => [[1,4,5],[2,7,8],[3],[6]] => [1,1,3,3] => 8
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0] => [5,6,4,7,8,1,2,3] => [[1,2,4,5],[3,7,8],[6]] => [2,3,3] => 7
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => [8,4,5,6,7,1,2,3] => [[1,3,4,5],[2,7,8],[6]] => [1,4,3] => 6
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0] => [5,4,6,7,8,1,2,3] => [[1,3,4,5],[2,7,8],[6]] => [1,4,3] => 6
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => [4,5,6,7,8,1,2,3] => [[1,2,3,4,5],[6,7,8]] => [5,3] => 5
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,3,1,2,4] => [[1,7,8],[2],[3],[4],[5],[6]] => [1,1,1,1,1,3] => 15
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,3,1,2,4] => [[1,2,8],[3,7],[4],[5],[6]] => [2,1,1,1,3] => 14
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,3,1,2,4] => [[1,3,8],[2,7],[4],[5],[6]] => [1,2,1,1,3] => 13
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,3,1,2,4] => [[1,3,8],[2,7],[4],[5],[6]] => [1,2,1,1,3] => 13
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,3,1,2,4] => [[1,4,8],[2,7],[3],[5],[6]] => [1,1,2,1,3] => 12
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,3,1,2,4] => [[1,2,8],[3,4],[5,7],[6]] => [2,2,1,3] => 11
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,3,1,2,4] => [[1,4,8],[2,7],[3],[5],[6]] => [1,1,2,1,3] => 12
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,3,1,2,4] => [[1,2,4],[3,7,8],[5],[6]] => [2,2,1,3] => 11
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,3,1,2,4] => [[1,3,4],[2,7,8],[5],[6]] => [1,3,1,3] => 10
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,3,1,2,4] => [[1,3,4],[2,7,8],[5],[6]] => [1,3,1,3] => 10
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,3,1,2,4] => [[1,2,3,4],[5,7,8],[6]] => [4,1,3] => 9
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,3,1,2,5] => [[1,7,8],[2],[3],[4],[5],[6]] => [1,1,1,1,1,3] => 15
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,3,1,2,5] => [[1,2,3],[4,7,8],[5],[6]] => [3,1,1,3] => 12
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,3,1,2,6] => [[1,7,8],[2],[3],[4],[5],[6]] => [1,1,1,1,1,3] => 15
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,3,1,2,6] => [[1,2,8],[3,7],[4],[5],[6]] => [2,1,1,1,3] => 14
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,3,1,2,7] => [[1,7,8],[2],[3],[4],[5],[6]] => [1,1,1,1,1,3] => 15
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,3,1,2,8] => [[1,7,8],[2],[3],[4],[5],[6]] => [1,1,1,1,1,3] => 15
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0] => [6,7,5,4,3,1,2,8] => [[1,2,8],[3,7],[4],[5],[6]] => [2,1,1,1,3] => 14
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0] => [7,5,6,4,3,1,2,8] => [[1,3,8],[2,7],[4],[5],[6]] => [1,2,1,1,3] => 13
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,3,1,2,7] => [[1,4,8],[2,7],[3],[5],[6]] => [1,1,2,1,3] => 12
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,3,1,2,8] => [[1,4,8],[2,7],[3],[5],[6]] => [1,1,2,1,3] => 12
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,3,1,2,8] => [[1,3,4,8],[2,7],[5],[6]] => [1,3,1,3] => 10
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,3,1,2,8] => [[1,2,3,4,8],[5,7],[6]] => [4,1,3] => 9
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,4,1,2,5] => [[1,5,8],[2,7],[3],[4],[6]] => [1,1,1,2,3] => 11
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,4,1,2,5] => [[1,2,8],[3,5],[4,7],[6]] => [2,1,2,3] => 10
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,4,1,2,5] => [[1,3,8],[2,5],[4,7],[6]] => [1,2,2,3] => 9
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,4,1,2,5] => [[1,2,3],[4,5,8],[6,7]] => [3,2,3] => 8
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,4,1,2,6] => [[1,5,8],[2,7],[3],[4],[6]] => [1,1,1,2,3] => 11
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,4,1,2,7] => [[1,5,8],[2,7],[3],[4],[6]] => [1,1,1,2,3] => 11
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,4,1,2,8] => [[1,5,8],[2,7],[3],[4],[6]] => [1,1,1,2,3] => 11
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,4,1,2,7] => [[1,3,8],[2,5],[4,7],[6]] => [1,2,2,3] => 9
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,6,1,2,7] => [[1,5,8],[2,7],[3],[4],[6]] => [1,1,1,2,3] => 11
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,7,1,2,8] => [[1,5,8],[2,7],[3],[4],[6]] => [1,1,1,2,3] => 11
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,6,1,2,7] => [[1,3,5,8],[2,7],[4],[6]] => [1,2,2,3] => 9
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,7,1,2,8] => [[1,3,5,8],[2,7],[4],[6]] => [1,2,2,3] => 9
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,5,1,2,6] => [[1,4,5,8],[2,7],[3],[6]] => [1,1,3,3] => 8
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,5,1,2,6] => [[1,2,5,8],[3,4],[6,7]] => [2,3,3] => 7
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,5,1,2,7] => [[1,4,5,8],[2,7],[3],[6]] => [1,1,3,3] => 8
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,5,1,2,8] => [[1,2,5,8],[3,4],[6,7]] => [2,3,3] => 7
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,6,1,2,7] => [[1,4,5,8],[2,7],[3],[6]] => [1,1,3,3] => 8
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,7,1,2,8] => [[1,2,5,8],[3,4],[6,7]] => [2,3,3] => 7
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,6,1,2,7] => [[1,4,5,8],[2,7],[3],[6]] => [1,1,3,3] => 8
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,6,1,2,7] => [[1,3,4,5,8],[2,7],[6]] => [1,4,3] => 6
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0] => [6,3,4,5,7,1,2,8] => [[1,3,4,5,8],[2,7],[6]] => [1,4,3] => 6
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,7,1,2,8] => [[1,3,4,5,8],[2,7],[6]] => [1,4,3] => 6
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,7,1,2,8] => [[1,2,3,4,5,8],[6,7]] => [5,3] => 5
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,2,1,3,4] => [[1,7,8],[2],[3],[4],[5],[6]] => [1,1,1,1,1,3] => 15
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,2,1,3,4] => [[1,2,8],[3,7],[4],[5],[6]] => [2,1,1,1,3] => 14
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,2,1,3,4] => [[1,3,8],[2,7],[4],[5],[6]] => [1,2,1,1,3] => 13
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,2,1,3,4] => [[1,2,3],[4,7,8],[5],[6]] => [3,1,1,3] => 12
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,2,1,3,4] => [[1,4,8],[2,7],[3],[5],[6]] => [1,1,2,1,3] => 12
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,2,1,3,4] => [[1,2,8],[3,4],[5,7],[6]] => [2,2,1,3] => 11
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,2,1,3,4] => [[1,4,8],[2,7],[3],[5],[6]] => [1,1,2,1,3] => 12
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,2,1,3,4] => [[1,4,8],[2,7],[3],[5],[6]] => [1,1,2,1,3] => 12
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,2,1,3,4] => [[1,2,4],[3,7,8],[5],[6]] => [2,2,1,3] => 11
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,2,1,3,4] => [[1,3,4],[2,7,8],[5],[6]] => [1,3,1,3] => 10
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,2,1,3,4] => [[1,3,4],[2,7,8],[5],[6]] => [1,3,1,3] => 10
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,2,1,3,4] => [[1,3,4],[2,7,8],[5],[6]] => [1,3,1,3] => 10
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0] => [5,6,7,8,2,1,3,4] => [[1,2,3,4],[5,7,8],[6]] => [4,1,3] => 9
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,2,1,3,5] => [[1,7,8],[2],[3],[4],[5],[6]] => [1,1,1,1,1,3] => 15
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,2,1,3,5] => [[1,2,8],[3,7],[4],[5],[6]] => [2,1,1,1,3] => 14
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0] => [8,6,7,4,2,1,3,5] => [[1,3,8],[2,7],[4],[5],[6]] => [1,2,1,1,3] => 13
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,2,1,3,5] => [[1,2,3],[4,7,8],[5],[6]] => [3,1,1,3] => 12
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,2,1,3,6] => [[1,2,8],[3,7],[4],[5],[6]] => [2,1,1,1,3] => 14
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,2,1,3,7] => [[1,7,8],[2],[3],[4],[5],[6]] => [1,1,1,1,1,3] => 15
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,2,1,3,8] => [[1,7,8],[2],[3],[4],[5],[6]] => [1,1,1,1,1,3] => 15
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,2,1,3,7] => [[1,3,8],[2,7],[4],[5],[6]] => [1,2,1,1,3] => 13
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0] => [6,5,7,4,2,1,3,8] => [[1,3,8],[2,7],[4],[5],[6]] => [1,2,1,1,3] => 13
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0] => [7,6,4,5,2,1,3,8] => [[1,4,8],[2,7],[3],[5],[6]] => [1,1,2,1,3] => 12
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0] => [7,5,4,6,2,1,3,8] => [[1,4,8],[2,7],[3],[5],[6]] => [1,1,2,1,3] => 12
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,2,1,3,7] => [[1,3,4,8],[2,7],[5],[6]] => [1,3,1,3] => 10
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,2,1,3,8] => [[1,3,4,8],[2,7],[5],[6]] => [1,3,1,3] => 10
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,2,1,3,8] => [[1,2,3,4,8],[5,7],[6]] => [4,1,3] => 9
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,2,1,4,5] => [[1,7,8],[2],[3],[4],[5],[6]] => [1,1,1,1,1,3] => 15
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,2,1,4,5] => [[1,2,8],[3,7],[4],[5],[6]] => [2,1,1,1,3] => 14
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,2,1,4,5] => [[1,3,8],[2,7],[4],[5],[6]] => [1,2,1,1,3] => 13
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,2,1,4,5] => [[1,3,8],[2,7],[4],[5],[6]] => [1,2,1,1,3] => 13
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,2,1,4,5] => [[1,2,3],[4,7,8],[5],[6]] => [3,1,1,3] => 12
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,2,1,4,6] => [[1,7,8],[2],[3],[4],[5],[6]] => [1,1,1,1,1,3] => 15
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,2,1,4,6] => [[1,2,8],[3,7],[4],[5],[6]] => [2,1,1,1,3] => 14
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0] => [8,6,5,3,2,1,4,7] => [[1,7,8],[2],[3],[4],[5],[6]] => [1,1,1,1,1,3] => 15
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0] => [7,6,5,3,2,1,4,8] => [[1,7,8],[2],[3],[4],[5],[6]] => [1,1,1,1,1,3] => 15
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,2,1,4,7] => [[1,3,8],[2,7],[4],[5],[6]] => [1,2,1,1,3] => 13
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0] => [8,7,4,3,2,1,5,6] => [[1,7,8],[2],[3],[4],[5],[6]] => [1,1,1,1,1,3] => 15
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,2,1,5,6] => [[1,2,8],[3,7],[4],[5],[6]] => [2,1,1,1,3] => 14
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,2,1,5,7] => [[1,7,8],[2],[3],[4],[5],[6]] => [1,1,1,1,1,3] => 15
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,2,1,5,8] => [[1,7,8],[2],[3],[4],[5],[6]] => [1,1,1,1,1,3] => 15
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0] => [6,7,4,3,2,1,5,8] => [[1,2,8],[3,7],[4],[5],[6]] => [2,1,1,1,3] => 14
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0] => [8,5,4,3,2,1,6,7] => [[1,7,8],[2],[3],[4],[5],[6]] => [1,1,1,1,1,3] => 15
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,2,1,6,8] => [[1,7,8],[2],[3],[4],[5],[6]] => [1,1,1,1,1,3] => 15
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,2,1,7,8] => [[1,7,8],[2],[3],[4],[5],[6]] => [1,1,1,1,1,3] => 15
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0] => [5,6,4,3,2,1,7,8] => [[1,2,7,8],[3],[4],[5],[6]] => [2,1,1,1,3] => 14
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0] => [8,4,5,3,2,1,6,7] => [[1,3,7,8],[2],[4],[5],[6]] => [1,2,1,1,3] => 13
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0] => [7,4,5,3,2,1,6,8] => [[1,3,7,8],[2],[4],[5],[6]] => [1,2,1,1,3] => 13
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,2,1,7,8] => [[1,3,7,8],[2],[4],[5],[6]] => [1,2,1,1,3] => 13
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0] => [4,5,6,3,2,1,7,8] => [[1,2,3,7,8],[4],[5],[6]] => [3,1,1,3] => 12
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,2,1,5,6] => [[1,4,7,8],[2],[3],[5],[6]] => [1,1,2,1,3] => 12
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,2,1,5,6] => [[1,2,7,8],[3,4],[5],[6]] => [2,2,1,3] => 11
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,2,1,5,7] => [[1,4,7,8],[2],[3],[5],[6]] => [1,1,2,1,3] => 12
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0] => [7,6,3,4,2,1,5,8] => [[1,4,7,8],[2],[3],[5],[6]] => [1,1,2,1,3] => 12
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,2,1,5,8] => [[1,2,7,8],[3,4],[5],[6]] => [2,2,1,3] => 11
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0] => [6,5,3,4,2,1,7,8] => [[1,4,7,8],[2],[3],[5],[6]] => [1,1,2,1,3] => 12
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,2,1,7,8] => [[1,2,7,8],[3,4],[5],[6]] => [2,2,1,3] => 11
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0] => [8,4,3,5,2,1,6,7] => [[1,4,7,8],[2],[3],[5],[6]] => [1,1,2,1,3] => 12
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0] => [7,4,3,5,2,1,6,8] => [[1,4,7,8],[2],[3],[5],[6]] => [1,1,2,1,3] => 12
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,2,1,7,8] => [[1,4,7,8],[2],[3],[5],[6]] => [1,1,2,1,3] => 12
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,2,1,6,7] => [[1,3,4,7,8],[2],[5],[6]] => [1,3,1,3] => 10
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0] => [7,3,4,5,2,1,6,8] => [[1,3,4,7,8],[2],[5],[6]] => [1,3,1,3] => 10
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,2,1,7,8] => [[1,2,3,4,7,8],[5],[6]] => [4,1,3] => 9
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,3,1,4,5] => [[1,5,7,8],[2],[3],[4],[6]] => [1,1,1,2,3] => 11
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,3,1,4,5] => [[1,2,7,8],[3,5],[4],[6]] => [2,1,2,3] => 10
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,3,1,4,5] => [[1,3,7,8],[2,5],[4],[6]] => [1,2,2,3] => 9
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0] => [7,6,8,2,3,1,4,5] => [[1,3,7,8],[2,5],[4],[6]] => [1,2,2,3] => 9
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,3,1,4,5] => [[1,2,3,8],[4,5,7],[6]] => [3,2,3] => 8
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,3,1,4,7] => [[1,5,7,8],[2],[3],[4],[6]] => [1,1,1,2,3] => 11
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,3,1,4,8] => [[1,5,7,8],[2],[3],[4],[6]] => [1,1,1,2,3] => 11
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,3,1,4,8] => [[1,2,7,8],[3,5],[4],[6]] => [2,1,2,3] => 10
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,3,1,4,7] => [[1,3,7,8],[2,5],[4],[6]] => [1,2,2,3] => 9
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,3,1,4,8] => [[1,3,7,8],[2,5],[4],[6]] => [1,2,2,3] => 9
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0] => [6,5,7,2,3,1,4,8] => [[1,3,7,8],[2,5],[4],[6]] => [1,2,2,3] => 9
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,3,1,4,8] => [[1,2,3,8],[4,5,7],[6]] => [3,2,3] => 8
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,3,1,5,6] => [[1,2,7,8],[3,5],[4],[6]] => [2,1,2,3] => 10
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,3,1,5,7] => [[1,5,7,8],[2],[3],[4],[6]] => [1,1,1,2,3] => 11
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,3,1,5,8] => [[1,5,7,8],[2],[3],[4],[6]] => [1,1,1,2,3] => 11
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0] => [7,5,4,2,3,1,6,8] => [[1,5,7,8],[2],[3],[4],[6]] => [1,1,1,2,3] => 11
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0] => [8,4,5,2,3,1,6,7] => [[1,3,7,8],[2,5],[4],[6]] => [1,2,2,3] => 9
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0] => [5,4,6,2,3,1,7,8] => [[1,3,7,8],[2,5],[4],[6]] => [1,2,2,3] => 9
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,4,1,5,6] => [[1,5,7,8],[2],[3],[4],[6]] => [1,1,1,2,3] => 11
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,4,1,5,6] => [[1,2,7,8],[3,5],[4],[6]] => [2,1,2,3] => 10
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,4,1,5,7] => [[1,5,7,8],[2],[3],[4],[6]] => [1,1,1,2,3] => 11
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,4,1,5,8] => [[1,5,7,8],[2],[3],[4],[6]] => [1,1,1,2,3] => 11
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,4,1,5,8] => [[1,2,7,8],[3,5],[4],[6]] => [2,1,2,3] => 10
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,4,1,6,8] => [[1,5,7,8],[2],[3],[4],[6]] => [1,1,1,2,3] => 11
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,4,1,7,8] => [[1,2,7,8],[3,5],[4],[6]] => [2,1,2,3] => 10
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,5,1,7,8] => [[1,5,7,8],[2],[3],[4],[6]] => [1,1,1,2,3] => 11
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,6,1,7,8] => [[1,5,7,8],[2],[3],[4],[6]] => [1,1,1,2,3] => 11
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,6,1,7,8] => [[1,2,5,7,8],[3],[4],[6]] => [2,1,2,3] => 10
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,6,1,7,8] => [[1,3,5,7,8],[2],[4],[6]] => [1,2,2,3] => 9
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,6,1,7,8] => [[1,2,3,5,7,8],[4],[6]] => [3,2,3] => 8
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,4,1,5,6] => [[1,4,5,7,8],[2],[3],[6]] => [1,1,3,3] => 8
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,4,1,5,6] => [[1,2,5,7,8],[3,4],[6]] => [2,3,3] => 7
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0] => [8,6,2,3,4,1,5,7] => [[1,4,5,7,8],[2],[3],[6]] => [1,1,3,3] => 8
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,4,1,5,8] => [[1,4,5,7,8],[2],[3],[6]] => [1,1,3,3] => 8
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,4,1,5,8] => [[1,2,5,7,8],[3,4],[6]] => [2,3,3] => 7
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0] => [8,5,2,3,4,1,6,7] => [[1,4,5,7,8],[2],[3],[6]] => [1,1,3,3] => 8
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,4,1,6,8] => [[1,4,5,7,8],[2],[3],[6]] => [1,1,3,3] => 8
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0] => [6,5,2,3,4,1,7,8] => [[1,4,5,7,8],[2],[3],[6]] => [1,1,3,3] => 8
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0] => [5,6,2,3,4,1,7,8] => [[1,2,5,7,8],[3,4],[6]] => [2,3,3] => 7
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,5,1,6,7] => [[1,4,5,7,8],[2],[3],[6]] => [1,1,3,3] => 8
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0] => [7,4,2,3,5,1,6,8] => [[1,4,5,7,8],[2],[3],[6]] => [1,1,3,3] => 8
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,6,1,7,8] => [[1,4,5,7,8],[2],[3],[6]] => [1,1,3,3] => 8
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,6,1,7,8] => [[1,4,5,7,8],[2],[3],[6]] => [1,1,3,3] => 8
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,6,1,7,8] => [[1,2,4,5,7,8],[3],[6]] => [2,3,3] => 7
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,5,1,6,7] => [[1,3,4,5,7,8],[2],[6]] => [1,4,3] => 6
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,5,1,6,8] => [[1,3,4,5,7,8],[2],[6]] => [1,4,3] => 6
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [6,2,3,4,5,1,7,8] => [[1,3,4,5,7,8],[2],[6]] => [1,4,3] => 6
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,6,1,7,8] => [[1,3,4,5,7,8],[2],[6]] => [1,4,3] => 6
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,6,1,7,8] => [[1,3,4,5,7,8],[2],[6]] => [1,4,3] => 6
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,6,1,7,8] => [[1,3,4,5,7,8],[2],[6]] => [1,4,3] => 6
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8] => [[1,2,3,4,5,7,8],[6]] => [5,3] => 5
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => [8,7,6,5,1,2,3,4] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 10
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => [7,8,6,5,1,2,3,4] => [[1,2,7,8],[3,6],[4],[5]] => [2,1,1,4] => 9
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => [8,6,7,5,1,2,3,4] => [[1,3,7,8],[2,6],[4],[5]] => [1,2,1,4] => 8
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0] => [7,6,8,5,1,2,3,4] => [[1,3,7,8],[2,6],[4],[5]] => [1,2,1,4] => 8
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => [6,7,8,5,1,2,3,4] => [[1,2,3,8],[4,6,7],[5]] => [3,1,4] => 7
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => [8,7,5,6,1,2,3,4] => [[1,4,7,8],[2,6],[3],[5]] => [1,1,2,4] => 7
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => [7,8,5,6,1,2,3,4] => [[1,2,7,8],[3,4],[5,6]] => [2,2,4] => 6
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0] => [8,6,5,7,1,2,3,4] => [[1,4,7,8],[2,6],[3],[5]] => [1,1,2,4] => 7
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0] => [7,6,5,8,1,2,3,4] => [[1,4,7,8],[2,6],[3],[5]] => [1,1,2,4] => 7
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0] => [6,7,5,8,1,2,3,4] => [[1,2,4,8],[3,6,7],[5]] => [2,2,4] => 6
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => [8,5,6,7,1,2,3,4] => [[1,3,4,8],[2,6,7],[5]] => [1,3,4] => 5
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0] => [7,5,6,8,1,2,3,4] => [[1,3,4,8],[2,6,7],[5]] => [1,3,4] => 5
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0] => [6,5,7,8,1,2,3,4] => [[1,3,4,8],[2,6,7],[5]] => [1,3,4] => 5
[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
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0] => [8,7,6,4,1,2,3,5] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 10
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0] => [7,8,6,4,1,2,3,5] => [[1,2,7,8],[3,6],[4],[5]] => [2,1,1,4] => 9
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0] => [7,6,8,4,1,2,3,5] => [[1,3,7,8],[2,6],[4],[5]] => [1,2,1,4] => 8
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0] => [6,7,8,4,1,2,3,5] => [[1,2,3,8],[4,6,7],[5]] => [3,1,4] => 7
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0] => [8,7,5,4,1,2,3,6] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 10
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0] => [7,8,5,4,1,2,3,6] => [[1,2,7,8],[3,6],[4],[5]] => [2,1,1,4] => 9
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0] => [8,6,5,4,1,2,3,7] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 10
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0] => [7,6,5,4,1,2,3,8] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 10
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0] => [8,5,6,4,1,2,3,7] => [[1,3,7,8],[2,6],[4],[5]] => [1,2,1,4] => 8
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0] => [5,6,7,4,1,2,3,8] => [[1,2,3,8],[4,6,7],[5]] => [3,1,4] => 7
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0] => [8,7,4,5,1,2,3,6] => [[1,4,7,8],[2,6],[3],[5]] => [1,1,2,4] => 7
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0] => [7,8,4,5,1,2,3,6] => [[1,2,7,8],[3,4],[5,6]] => [2,2,4] => 6
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0] => [8,6,4,5,1,2,3,7] => [[1,4,7,8],[2,6],[3],[5]] => [1,1,2,4] => 7
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0] => [8,4,5,6,1,2,3,7] => [[1,3,4,8],[2,6,7],[5]] => [1,3,4] => 5
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0] => [7,4,5,6,1,2,3,8] => [[1,3,4,8],[2,6,7],[5]] => [1,3,4] => 5
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0] => [5,4,6,7,1,2,3,8] => [[1,3,4,8],[2,6,7],[5]] => [1,3,4] => 5
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0] => [4,5,6,7,1,2,3,8] => [[1,2,3,4,8],[5,6,7]] => [4,4] => 4
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0] => [8,7,6,3,1,2,4,5] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 10
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0] => [7,8,6,3,1,2,4,5] => [[1,2,7,8],[3,6],[4],[5]] => [2,1,1,4] => 9
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0] => [8,6,7,3,1,2,4,5] => [[1,3,7,8],[2,6],[4],[5]] => [1,2,1,4] => 8
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0] => [7,6,8,3,1,2,4,5] => [[1,3,7,8],[2,6],[4],[5]] => [1,2,1,4] => 8
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0] => [6,7,8,3,1,2,4,5] => [[1,2,3,8],[4,6,7],[5]] => [3,1,4] => 7
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0] => [8,7,5,3,1,2,4,6] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 10
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0] => [7,8,5,3,1,2,4,6] => [[1,2,7,8],[3,6],[4],[5]] => [2,1,1,4] => 9
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0] => [8,5,6,3,1,2,4,7] => [[1,3,7,8],[2,6],[4],[5]] => [1,2,1,4] => 8
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0] => [7,8,4,3,1,2,5,6] => [[1,2,7,8],[3,6],[4],[5]] => [2,1,1,4] => 9
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0] => [8,6,4,3,1,2,5,7] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 10
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0] => [7,6,4,3,1,2,5,8] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 10
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0] => [7,5,4,3,1,2,6,8] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 10
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [6,5,4,3,1,2,7,8] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 10
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0] => [6,4,5,3,1,2,7,8] => [[1,3,7,8],[2,6],[4],[5]] => [1,2,1,4] => 8
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0] => [5,4,6,3,1,2,7,8] => [[1,3,7,8],[2,6],[4],[5]] => [1,2,1,4] => 8
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0] => [8,7,3,4,1,2,5,6] => [[1,4,7,8],[2,6],[3],[5]] => [1,1,2,4] => 7
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0] => [7,8,3,4,1,2,5,6] => [[1,2,7,8],[3,4],[5,6]] => [2,2,4] => 6
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0] => [8,6,3,4,1,2,5,7] => [[1,4,7,8],[2,6],[3],[5]] => [1,1,2,4] => 7
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0] => [6,7,3,4,1,2,5,8] => [[1,2,7,8],[3,4],[5,6]] => [2,2,4] => 6
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0] => [8,5,3,4,1,2,6,7] => [[1,4,7,8],[2,6],[3],[5]] => [1,1,2,4] => 7
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0] => [5,6,3,4,1,2,7,8] => [[1,2,7,8],[3,4],[5,6]] => [2,2,4] => 6
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0] => [5,4,3,6,1,2,7,8] => [[1,4,7,8],[2,6],[3],[5]] => [1,1,2,4] => 7
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0] => [8,3,4,5,1,2,6,7] => [[1,3,4,7,8],[2,6],[5]] => [1,3,4] => 5
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [4,3,5,6,1,2,7,8] => [[1,3,4,7,8],[2,6],[5]] => [1,3,4] => 5
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [3,4,5,6,1,2,7,8] => [[1,2,3,4,7,8],[5,6]] => [4,4] => 4
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0] => [8,7,6,2,1,3,4,5] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 10
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0] => [7,8,6,2,1,3,4,5] => [[1,2,7,8],[3,6],[4],[5]] => [2,1,1,4] => 9
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0] => [8,6,7,2,1,3,4,5] => [[1,3,7,8],[2,6],[4],[5]] => [1,2,1,4] => 8
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0] => [6,7,8,2,1,3,4,5] => [[1,2,3,8],[4,6,7],[5]] => [3,1,4] => 7
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0] => [8,7,5,2,1,3,4,6] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 10
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0] => [7,8,5,2,1,3,4,6] => [[1,2,7,8],[3,6],[4],[5]] => [2,1,1,4] => 9
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0] => [8,6,5,2,1,3,4,7] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 10
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0] => [7,6,5,2,1,3,4,8] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 10
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0] => [6,7,5,2,1,3,4,8] => [[1,2,7,8],[3,6],[4],[5]] => [2,1,1,4] => 9
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0] => [8,5,6,2,1,3,4,7] => [[1,3,7,8],[2,6],[4],[5]] => [1,2,1,4] => 8
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0] => [7,5,6,2,1,3,4,8] => [[1,3,7,8],[2,6],[4],[5]] => [1,2,1,4] => 8
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0] => [5,6,7,2,1,3,4,8] => [[1,2,3,8],[4,6,7],[5]] => [3,1,4] => 7
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0] => [8,7,4,2,1,3,5,6] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 10
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0] => [7,8,4,2,1,3,5,6] => [[1,2,7,8],[3,6],[4],[5]] => [2,1,1,4] => 9
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0] => [8,6,4,2,1,3,5,7] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 10
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0] => [7,6,4,2,1,3,5,8] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 10
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0] => [8,5,4,2,1,3,6,7] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 10
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0] => [6,5,4,2,1,3,7,8] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 10
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0] => [5,6,4,2,1,3,7,8] => [[1,2,7,8],[3,6],[4],[5]] => [2,1,1,4] => 9
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0] => [7,4,5,2,1,3,6,8] => [[1,3,7,8],[2,6],[4],[5]] => [1,2,1,4] => 8
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0] => [6,4,5,2,1,3,7,8] => [[1,3,7,8],[2,6],[4],[5]] => [1,2,1,4] => 8
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [4,5,6,2,1,3,7,8] => [[1,2,3,7,8],[4,6],[5]] => [3,1,4] => 7
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0] => [8,7,3,2,1,4,5,6] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 10
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0] => [7,8,3,2,1,4,5,6] => [[1,2,7,8],[3,6],[4],[5]] => [2,1,1,4] => 9
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0] => [8,6,3,2,1,4,5,7] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 10
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0] => [7,6,3,2,1,4,5,8] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 10
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0] => [6,7,3,2,1,4,5,8] => [[1,2,7,8],[3,6],[4],[5]] => [2,1,1,4] => 9
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0] => [8,5,3,2,1,4,6,7] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 10
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0] => [7,5,3,2,1,4,6,8] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 10
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0] => [6,5,3,2,1,4,7,8] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 10
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0] => [5,6,3,2,1,4,7,8] => [[1,2,7,8],[3,6],[4],[5]] => [2,1,1,4] => 9
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0] => [8,4,3,2,1,5,6,7] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 10
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0] => [7,4,3,2,1,5,6,8] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 10
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0] => [6,4,3,2,1,5,7,8] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 10
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [5,4,3,2,1,6,7,8] => [[1,6,7,8],[2],[3],[4],[5]] => [1,1,1,1,4] => 10
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [4,5,3,2,1,6,7,8] => [[1,2,6,7,8],[3],[4],[5]] => [2,1,1,4] => 9
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0] => [8,3,4,2,1,5,6,7] => [[1,3,6,7,8],[2],[4],[5]] => [1,2,1,4] => 8
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [6,3,4,2,1,5,7,8] => [[1,3,6,7,8],[2],[4],[5]] => [1,2,1,4] => 8
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [5,3,4,2,1,6,7,8] => [[1,3,6,7,8],[2],[4],[5]] => [1,2,1,4] => 8
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [4,3,5,2,1,6,7,8] => [[1,3,6,7,8],[2],[4],[5]] => [1,2,1,4] => 8
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [3,4,5,2,1,6,7,8] => [[1,2,3,6,7,8],[4],[5]] => [3,1,4] => 7
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0] => [8,7,2,3,1,4,5,6] => [[1,4,6,7,8],[2],[3],[5]] => [1,1,2,4] => 7
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0] => [7,8,2,3,1,4,5,6] => [[1,2,6,7,8],[3,4],[5]] => [2,2,4] => 6
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0] => [7,6,2,3,1,4,5,8] => [[1,4,6,7,8],[2],[3],[5]] => [1,1,2,4] => 7
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0] => [6,7,2,3,1,4,5,8] => [[1,2,6,7,8],[3,4],[5]] => [2,2,4] => 6
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0] => [7,5,2,3,1,4,6,8] => [[1,4,6,7,8],[2],[3],[5]] => [1,1,2,4] => 7
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0] => [8,4,2,3,1,5,6,7] => [[1,4,6,7,8],[2],[3],[5]] => [1,1,2,4] => 7
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [5,4,2,3,1,6,7,8] => [[1,4,6,7,8],[2],[3],[5]] => [1,1,2,4] => 7
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [4,5,2,3,1,6,7,8] => [[1,2,6,7,8],[3,4],[5]] => [2,2,4] => 6
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [5,3,2,4,1,6,7,8] => [[1,4,6,7,8],[2],[3],[5]] => [1,1,2,4] => 7
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [4,3,2,5,1,6,7,8] => [[1,4,6,7,8],[2],[3],[5]] => [1,1,2,4] => 7
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [3,4,2,5,1,6,7,8] => [[1,2,4,6,7,8],[3],[5]] => [2,2,4] => 6
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [8,2,3,4,1,5,6,7] => [[1,3,4,6,7,8],[2],[5]] => [1,3,4] => 5
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [7,2,3,4,1,5,6,8] => [[1,3,4,6,7,8],[2],[5]] => [1,3,4] => 5
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [5,2,3,4,1,6,7,8] => [[1,3,4,6,7,8],[2],[5]] => [1,3,4] => 5
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [4,2,3,5,1,6,7,8] => [[1,3,4,6,7,8],[2],[5]] => [1,3,4] => 5
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,4,5,1,6,7,8] => [[1,3,4,6,7,8],[2],[5]] => [1,3,4] => 5
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,3,4,5,1,6,7,8] => [[1,2,3,4,6,7,8],[5]] => [4,4] => 4
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => [8,7,6,1,2,3,4,5] => [[1,5,6,7,8],[2],[3],[4]] => [1,1,1,5] => 6
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0] => [7,8,6,1,2,3,4,5] => [[1,2,6,7,8],[3,5],[4]] => [2,1,5] => 5
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0] => [8,6,7,1,2,3,4,5] => [[1,3,6,7,8],[2,5],[4]] => [1,2,5] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0] => [7,6,8,1,2,3,4,5] => [[1,3,6,7,8],[2,5],[4]] => [1,2,5] => 4
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => [6,7,8,1,2,3,4,5] => [[1,2,3,7,8],[4,5,6]] => [3,5] => 3
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0] => [8,7,5,1,2,3,4,6] => [[1,5,6,7,8],[2],[3],[4]] => [1,1,1,5] => 6
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0] => [7,8,5,1,2,3,4,6] => [[1,2,6,7,8],[3,5],[4]] => [2,1,5] => 5
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0] => [8,6,5,1,2,3,4,7] => [[1,5,6,7,8],[2],[3],[4]] => [1,1,1,5] => 6
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0] => [7,6,5,1,2,3,4,8] => [[1,5,6,7,8],[2],[3],[4]] => [1,1,1,5] => 6
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0] => [6,7,5,1,2,3,4,8] => [[1,2,6,7,8],[3,5],[4]] => [2,1,5] => 5
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0] => [8,5,6,1,2,3,4,7] => [[1,3,6,7,8],[2,5],[4]] => [1,2,5] => 4
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0] => [7,5,6,1,2,3,4,8] => [[1,3,6,7,8],[2,5],[4]] => [1,2,5] => 4
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0] => [6,5,7,1,2,3,4,8] => [[1,3,6,7,8],[2,5],[4]] => [1,2,5] => 4
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0] => [5,6,7,1,2,3,4,8] => [[1,2,3,7,8],[4,5,6]] => [3,5] => 3
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0] => [8,7,4,1,2,3,5,6] => [[1,5,6,7,8],[2],[3],[4]] => [1,1,1,5] => 6
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0] => [7,8,4,1,2,3,5,6] => [[1,2,6,7,8],[3,5],[4]] => [2,1,5] => 5
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0] => [8,6,4,1,2,3,5,7] => [[1,5,6,7,8],[2],[3],[4]] => [1,1,1,5] => 6
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0] => [8,5,4,1,2,3,6,7] => [[1,5,6,7,8],[2],[3],[4]] => [1,1,1,5] => 6
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0] => [6,5,4,1,2,3,7,8] => [[1,5,6,7,8],[2],[3],[4]] => [1,1,1,5] => 6
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0] => [8,4,5,1,2,3,6,7] => [[1,3,6,7,8],[2,5],[4]] => [1,2,5] => 4
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0] => [7,4,5,1,2,3,6,8] => [[1,3,6,7,8],[2,5],[4]] => [1,2,5] => 4
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [4,5,6,1,2,3,7,8] => [[1,2,3,7,8],[4,5,6]] => [3,5] => 3
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0] => [7,8,3,1,2,4,5,6] => [[1,2,6,7,8],[3,5],[4]] => [2,1,5] => 5
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0] => [6,7,3,1,2,4,5,8] => [[1,2,6,7,8],[3,5],[4]] => [2,1,5] => 5
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0] => [8,5,3,1,2,4,6,7] => [[1,5,6,7,8],[2],[3],[4]] => [1,1,1,5] => 6
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0] => [7,5,3,1,2,4,6,8] => [[1,5,6,7,8],[2],[3],[4]] => [1,1,1,5] => 6
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0] => [7,4,3,1,2,5,6,8] => [[1,5,6,7,8],[2],[3],[4]] => [1,1,1,5] => 6
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [6,4,3,1,2,5,7,8] => [[1,5,6,7,8],[2],[3],[4]] => [1,1,1,5] => 6
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [5,4,3,1,2,6,7,8] => [[1,5,6,7,8],[2],[3],[4]] => [1,1,1,5] => 6
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0] => [8,3,4,1,2,5,6,7] => [[1,3,6,7,8],[2,5],[4]] => [1,2,5] => 4
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [7,3,4,1,2,5,6,8] => [[1,3,6,7,8],[2,5],[4]] => [1,2,5] => 4
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [5,3,4,1,2,6,7,8] => [[1,3,6,7,8],[2,5],[4]] => [1,2,5] => 4
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [4,3,5,1,2,6,7,8] => [[1,3,6,7,8],[2,5],[4]] => [1,2,5] => 4
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [3,4,5,1,2,6,7,8] => [[1,2,3,6,7,8],[4,5]] => [3,5] => 3
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0] => [8,7,2,1,3,4,5,6] => [[1,5,6,7,8],[2],[3],[4]] => [1,1,1,5] => 6
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0] => [7,8,2,1,3,4,5,6] => [[1,2,6,7,8],[3,5],[4]] => [2,1,5] => 5
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0] => [8,5,2,1,3,4,6,7] => [[1,5,6,7,8],[2],[3],[4]] => [1,1,1,5] => 6
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [5,6,2,1,3,4,7,8] => [[1,2,6,7,8],[3,5],[4]] => [2,1,5] => 5
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0] => [8,4,2,1,3,5,6,7] => [[1,5,6,7,8],[2],[3],[4]] => [1,1,1,5] => 6
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [6,4,2,1,3,5,7,8] => [[1,5,6,7,8],[2],[3],[4]] => [1,1,1,5] => 6
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [5,4,2,1,3,6,7,8] => [[1,5,6,7,8],[2],[3],[4]] => [1,1,1,5] => 6
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [4,5,2,1,3,6,7,8] => [[1,2,6,7,8],[3,5],[4]] => [2,1,5] => 5
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [8,3,2,1,4,5,6,7] => [[1,5,6,7,8],[2],[3],[4]] => [1,1,1,5] => 6
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [7,3,2,1,4,5,6,8] => [[1,5,6,7,8],[2],[3],[4]] => [1,1,1,5] => 6
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2,1,4,6,7,8] => [[1,5,6,7,8],[2],[3],[4]] => [1,1,1,5] => 6
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1,5,6,7,8] => [[1,5,6,7,8],[2],[3],[4]] => [1,1,1,5] => 6
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [3,4,2,1,5,6,7,8] => [[1,2,5,6,7,8],[3],[4]] => [2,1,5] => 5
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [8,2,3,1,4,5,6,7] => [[1,3,5,6,7,8],[2],[4]] => [1,2,5] => 4
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [7,2,3,1,4,5,6,8] => [[1,3,5,6,7,8],[2],[4]] => [1,2,5] => 4
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [6,2,3,1,4,5,7,8] => [[1,3,5,6,7,8],[2],[4]] => [1,2,5] => 4
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [5,2,3,1,4,6,7,8] => [[1,3,5,6,7,8],[2],[4]] => [1,2,5] => 4
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,3,1,5,6,7,8] => [[1,3,5,6,7,8],[2],[4]] => [1,2,5] => 4
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,4,1,5,6,7,8] => [[1,3,5,6,7,8],[2],[4]] => [1,2,5] => 4
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,3,4,1,5,6,7,8] => [[1,2,3,5,6,7,8],[4]] => [3,5] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [8,7,1,2,3,4,5,6] => [[1,4,5,6,7,8],[2],[3]] => [1,1,6] => 3
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => [7,8,1,2,3,4,5,6] => [[1,2,5,6,7,8],[3,4]] => [2,6] => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0] => [8,6,1,2,3,4,5,7] => [[1,4,5,6,7,8],[2],[3]] => [1,1,6] => 3
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0] => [7,6,1,2,3,4,5,8] => [[1,4,5,6,7,8],[2],[3]] => [1,1,6] => 3
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [6,7,1,2,3,4,5,8] => [[1,2,5,6,7,8],[3,4]] => [2,6] => 2
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0] => [8,5,1,2,3,4,6,7] => [[1,4,5,6,7,8],[2],[3]] => [1,1,6] => 3
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [7,5,1,2,3,4,6,8] => [[1,4,5,6,7,8],[2],[3]] => [1,1,6] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [8,4,1,2,3,5,6,7] => [[1,4,5,6,7,8],[2],[3]] => [1,1,6] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [7,4,1,2,3,5,6,8] => [[1,4,5,6,7,8],[2],[3]] => [1,1,6] => 3
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [6,4,1,2,3,5,7,8] => [[1,4,5,6,7,8],[2],[3]] => [1,1,6] => 3
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1,2,3,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => [1,1,6] => 3
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [4,5,1,2,3,6,7,8] => [[1,2,5,6,7,8],[3,4]] => [2,6] => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [8,3,1,2,4,5,6,7] => [[1,4,5,6,7,8],[2],[3]] => [1,1,6] => 3
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [7,3,1,2,4,5,6,8] => [[1,4,5,6,7,8],[2],[3]] => [1,1,6] => 3
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1,2,4,5,7,8] => [[1,4,5,6,7,8],[2],[3]] => [1,1,6] => 3
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1,2,4,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => [1,1,6] => 3
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,2,5,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => [1,1,6] => 3
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,4,1,2,5,6,7,8] => [[1,2,5,6,7,8],[3,4]] => [2,6] => 2
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [8,2,1,3,4,5,6,7] => [[1,4,5,6,7,8],[2],[3]] => [1,1,6] => 3
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1,3,4,5,6,8] => [[1,4,5,6,7,8],[2],[3]] => [1,1,6] => 3
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,3,4,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => [1,1,6] => 3
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,3,5,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => [1,1,6] => 3
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,4,5,6,7,8] => [[1,4,5,6,7,8],[2],[3]] => [1,1,6] => 3
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,3,1,4,5,6,7,8] => [[1,2,4,5,6,7,8],[3]] => [2,6] => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [8,1,2,3,4,5,6,7] => [[1,3,4,5,6,7,8],[2]] => [1,7] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,2,3,4,5,6,8] => [[1,3,4,5,6,7,8],[2]] => [1,7] => 1
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,2,3,4,5,7,8] => [[1,3,4,5,6,7,8],[2]] => [1,7] => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,2,3,4,6,7,8] => [[1,3,4,5,6,7,8],[2]] => [1,7] => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,2,3,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => [1,7] => 1
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => [1,7] => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8] => [[1,3,4,5,6,7,8],[2]] => [1,7] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,2,3,4,5,6,7,8] => [[1,2,3,4,5,6,7,8]] => [8] => 0
[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] => [[1,3,4,5,6,7,8,9],[2]] => [1,8] => 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] => [[1,2,3,4,5,6,7,8],[9]] => [8,1] => 8
[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] => [[1,3,4,5,6,7,8,9,10],[2]] => [1,9] => 1
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,1] => [[1,3,4,5,6,7,8],[2],[9]] => [1,7,1] => 9
[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] => [[1,2,3,4,5,6,7,8,9],[10]] => [9,1] => 9
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [4,2,3,5,6,7,8,9,1] => [[1,3,4,5,6,7,8],[2],[9]] => [1,7,1] => 9
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [3,2,4,5,6,7,8,9,10,1] => [[1,3,4,5,6,7,8,9],[2],[10]] => [1,8,1] => 10
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,5,6,7,8,9,1] => [[1,4,5,6,7,8],[2],[3],[9]] => [1,1,6,1] => 11
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [4,2,3,5,6,7,8,9,10,1] => [[1,3,4,5,6,7,8,9],[2],[10]] => [1,8,1] => 10
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [4,3,2,5,6,7,8,9,10,1] => [[1,4,5,6,7,8,9],[2],[3],[10]] => [1,1,7,1] => 12
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [6,2,3,4,5,7,8,9,10,1] => [[1,3,4,5,6,7,8,9],[2],[10]] => [1,8,1] => 10
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [5,4,2,3,6,7,8,9,1] => [[1,4,5,6,7,8],[2],[3],[9]] => [1,1,6,1] => 11
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [8,2,3,4,5,6,7,9,1] => [[1,3,4,5,6,7,8],[2],[9]] => [1,7,1] => 9
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,2,9,1] => [[1,2,3,4,5,6,8],[7],[9]] => [6,2,1] => 14
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [9,2,3,4,5,6,7,8,1] => [[1,3,4,5,6,7,8],[2],[9]] => [1,7,1] => 9
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [4,3,5,6,7,8,9,1,2] => [[1,3,4,5,6,7],[2,9],[8]] => [1,6,2] => 8
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,2,1] => [[1,2,3,4,5,6,7],[8],[9]] => [7,1,1] => 15
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [9,3,2,4,5,6,7,8,1] => [[1,4,5,6,7,8],[2],[3],[9]] => [1,1,6,1] => 11
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [9,2,3,4,5,6,7,8,10,1] => [[1,3,4,5,6,7,8,9],[2],[10]] => [1,8,1] => 10
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [5,3,4,6,7,8,9,1,2] => [[1,3,4,5,6,7],[2,9],[8]] => [1,6,2] => 8
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [10,2,3,4,5,6,7,8,9,1] => [[1,3,4,5,6,7,8,9],[2],[10]] => [1,8,1] => 10
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [3,4,5,6,7,8,9,10,2,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => [8,1,1] => 17
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,2,3,4,5,6,7,9] => [[1,3,4,5,6,7,8,9],[2]] => [1,8] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [7,1,2,3,4,5,6,8,9] => [[1,3,4,5,6,7,8,9],[2]] => [1,8] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [6,1,2,3,4,5,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => [1,8] => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => [1,8] => 1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => [1,8] => 1
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => [1,8] => 1
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9] => [[1,3,4,5,6,7,8,9],[2]] => [1,8] => 1
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,4,3,2,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => [1,1,1,1,1,1,1,1,1,1] => 45
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0] => [6,5,7,8,9,4,3,2,1] => [[1,3,4,5],[2],[6],[7],[8],[9]] => [1,4,1,1,1,1] => 27
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [6,5,4,3,2,7,8,9,1] => [[1,6,7,8],[2],[3],[4],[5],[9]] => [1,1,1,1,4,1] => 18
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [6,5,7,8,9,10,4,3,2,1] => [[1,3,4,5,6],[2],[7],[8],[9],[10]] => [1,5,1,1,1,1] => 31
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,8,2,1] => [[1,3,4,5,6,7],[2],[8],[9]] => [1,6,1,1] => 16
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => [4,5,6,7,8,9,2,3,1] => [[1,2,3,4,5,6],[7,8],[9]] => [6,2,1] => 14
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => [9,8,2,3,4,5,6,7,1] => [[1,4,5,6,7,8],[2],[3],[9]] => [1,1,6,1] => 11
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,8,1,2] => [[1,3,4,5,6,7],[2,9],[8]] => [1,6,2] => 8
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [10,3,4,5,6,7,8,9,2,1] => [[1,3,4,5,6,7,8],[2],[9],[10]] => [1,7,1,1] => 18
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => [10,9,2,3,4,5,6,7,8,1] => [[1,4,5,6,7,8,9],[2],[3],[10]] => [1,1,7,1] => 12
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => [9,10,8,7,6,5,4,3,1,2] => [[1,2],[3,10],[4],[5],[6],[7],[8],[9]] => [2,1,1,1,1,1,1,2] => 35
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => [10,9,8,7,6,5,3,4,1,2] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => [1,1,1,1,1,1,2,2] => 29
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0] => [10,9,7,8,5,6,3,4,1,2] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => [1,1,2,2,2,2] => 21
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => [9,10,7,8,4,5,6,1,2,3] => [[1,2,7],[3,4,10],[5,6],[8,9]] => [2,2,3,3] => 13
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => [10,9,5,6,7,8,1,2,3,4] => [[1,4,5,6],[2,8,9,10],[3],[7]] => [1,1,4,4] => 9
[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]] => [5,5] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0] => [8,9,7,6,5,4,3,2,1,10] => [[1,2,10],[3],[4],[5],[6],[7],[8],[9]] => [2,1,1,1,1,1,1,2] => 35
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1,2,4,5,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => [1,9] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1,2,3,4,5,6,7,8,10] => [[1,3,4,5,6,7,8,9,10],[2]] => [1,9] => 1
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,3,4,5,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => [1,9] => 1
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [2,3,4,5,6,1,7,8,9,10] => [[1,2,3,4,5,7,8,9,10],[6]] => [5,5] => 5
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0] => [8,7,6,5,4,3,2,9,1,10] => [[1,8,10],[2],[3],[4],[5],[6],[7],[9]] => [1,1,1,1,1,1,2,2] => 29
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0] => [9,8,7,6,4,3,2,5,1,10] => [[1,8,10],[2],[3],[4],[5],[6],[7],[9]] => [1,1,1,1,1,1,2,2] => 29
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [6,5,4,3,2,7,8,9,10,1] => [[1,6,7,8,9],[2],[3],[4],[5],[10]] => [1,1,1,1,5,1] => 19
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0] => [7,6,5,4,2,3,8,9,1] => [[1,6,7,8],[2],[3],[4],[5],[9]] => [1,1,1,1,4,1] => 18
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [8,1,2,3,4,5,6,7,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => [1,9] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1,2,3,4,5,6,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => [1,9] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1,2,3,4,5,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => [1,9] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1,2,3,4,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => [1,9] => 1
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1,2,3,5,6,7,8,9,10] => [[1,3,4,5,6,7,8,9,10],[2]] => [1,9] => 1
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0] => [5,6,7,8,9,1,2,3,4,10] => [[1,2,3,4,5,10],[6,7,8,9]] => [5,5] => 5
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0] => [9,10,7,6,5,4,3,2,1,8] => [[1,2],[3,10],[4],[5],[6],[7],[8],[9]] => [2,1,1,1,1,1,1,2] => 35
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0] => [9,3,4,5,6,7,2,1,8] => [[1,3,4,5,6,9],[2],[7],[8]] => [1,5,1,2] => 14
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => [11,12,9,10,7,8,5,6,3,4,1,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => [2,2,2,2,2,2] => 30
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [10,3,2,4,5,6,7,8,9,1] => [[1,4,5,6,7,8,9],[2],[3],[10]] => [1,1,7,1] => 12
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
1,1 1,2,1,1 1,3,2,4,2,1,1 1,4,3,8,6,6,6,4,2,1,1 1,5,4,13,11,14,19,15,15,10,11,6,4,2,1,1 1,6,5,19,17,24,39,37,41,40,45,35,35,24,20,16,11,6,4,2,1,1
$F_{1} = 1$
$F_{2} = 1 + q$
$F_{3} = 1 + 2\ q + q^{2} + q^{3}$
$F_{4} = 1 + 3\ q + 2\ q^{2} + 4\ q^{3} + 2\ q^{4} + q^{5} + q^{6}$
$F_{5} = 1 + 4\ q + 3\ q^{2} + 8\ q^{3} + 6\ q^{4} + 6\ q^{5} + 6\ q^{6} + 4\ q^{7} + 2\ q^{8} + q^{9} + q^{10}$
$F_{6} = 1 + 5\ q + 4\ q^{2} + 13\ q^{3} + 11\ q^{4} + 14\ q^{5} + 19\ q^{6} + 15\ q^{7} + 15\ q^{8} + 10\ q^{9} + 11\ q^{10} + 6\ q^{11} + 4\ q^{12} + 2\ q^{13} + q^{14} + q^{15}$
$F_{7} = 1 + 6\ q + 5\ q^{2} + 19\ q^{3} + 17\ q^{4} + 24\ q^{5} + 39\ q^{6} + 37\ q^{7} + 41\ q^{8} + 40\ q^{9} + 45\ q^{10} + 35\ q^{11} + 35\ q^{12} + 24\ q^{13} + 20\ q^{14} + 16\ q^{15} + 11\ q^{16} + 6\ q^{17} + 4\ q^{18} + 2\ q^{19} + q^{20} + q^{21}$
Description
The major index of the composition.
The descents of a composition $[c_1,c_2,\dots,c_k]$ are the partial sums $c_1, c_1+c_2,\dots, c_1+\dots+c_{k-1}$, excluding the sum of all parts. The major index of a composition is the sum of its descents.
For details about the major index see Permutations/Descents-Major.
The descents of a composition $[c_1,c_2,\dots,c_k]$ are the partial sums $c_1, c_1+c_2,\dots, c_1+\dots+c_{k-1}$, excluding the sum of all parts. The major index of a composition is the sum of its descents.
For details about the major index see Permutations/Descents-Major.
Map
Robinson-Schensted recording tableau
Description
Sends a permutation to its Robinson-Schensted recording 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 recording 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 recording tableau.
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 $i$.
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
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
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