Identifier
-
Mp00202:
Integer partitions
—first row removal⟶
Integer partitions
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
Mp00134: Standard tableaux —descent word⟶ Binary words
St000629: Binary words ⟶ ℤ
Values
[1,1,1] => [1,1] => [[1],[2]] => 1 => 0
[2,2] => [2] => [[1,2]] => 0 => 0
[2,1,1] => [1,1] => [[1],[2]] => 1 => 0
[1,1,1,1] => [1,1,1] => [[1],[2],[3]] => 11 => 0
[3,2] => [2] => [[1,2]] => 0 => 0
[3,1,1] => [1,1] => [[1],[2]] => 1 => 0
[2,2,1] => [2,1] => [[1,3],[2]] => 10 => 0
[2,1,1,1] => [1,1,1] => [[1],[2],[3]] => 11 => 0
[1,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 111 => 0
[4,2] => [2] => [[1,2]] => 0 => 0
[4,1,1] => [1,1] => [[1],[2]] => 1 => 0
[3,3] => [3] => [[1,2,3]] => 00 => 0
[3,2,1] => [2,1] => [[1,3],[2]] => 10 => 0
[3,1,1,1] => [1,1,1] => [[1],[2],[3]] => 11 => 0
[2,2,2] => [2,2] => [[1,2],[3,4]] => 010 => 0
[2,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => 110 => 0
[2,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 111 => 0
[1,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1111 => 0
[5,2] => [2] => [[1,2]] => 0 => 0
[5,1,1] => [1,1] => [[1],[2]] => 1 => 0
[4,3] => [3] => [[1,2,3]] => 00 => 0
[4,2,1] => [2,1] => [[1,3],[2]] => 10 => 0
[4,1,1,1] => [1,1,1] => [[1],[2],[3]] => 11 => 0
[3,3,1] => [3,1] => [[1,3,4],[2]] => 100 => 0
[3,2,2] => [2,2] => [[1,2],[3,4]] => 010 => 0
[3,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => 110 => 0
[3,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 111 => 0
[2,2,2,1] => [2,2,1] => [[1,3],[2,5],[4]] => 1010 => 0
[2,2,1,1,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 1110 => 0
[2,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1111 => 0
[1,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 11111 => 0
[6,2] => [2] => [[1,2]] => 0 => 0
[6,1,1] => [1,1] => [[1],[2]] => 1 => 0
[5,3] => [3] => [[1,2,3]] => 00 => 0
[5,2,1] => [2,1] => [[1,3],[2]] => 10 => 0
[5,1,1,1] => [1,1,1] => [[1],[2],[3]] => 11 => 0
[4,4] => [4] => [[1,2,3,4]] => 000 => 0
[4,3,1] => [3,1] => [[1,3,4],[2]] => 100 => 0
[4,2,2] => [2,2] => [[1,2],[3,4]] => 010 => 0
[4,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => 110 => 0
[4,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 111 => 0
[3,3,2] => [3,2] => [[1,2,5],[3,4]] => 0100 => 0
[3,3,1,1] => [3,1,1] => [[1,4,5],[2],[3]] => 1100 => 0
[3,2,2,1] => [2,2,1] => [[1,3],[2,5],[4]] => 1010 => 0
[3,2,1,1,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 1110 => 0
[3,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1111 => 0
[2,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 01010 => 0
[2,2,2,1,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 11010 => 0
[2,2,1,1,1,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 11110 => 0
[2,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 11111 => 0
[1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 111111 => 0
[7,2] => [2] => [[1,2]] => 0 => 0
[7,1,1] => [1,1] => [[1],[2]] => 1 => 0
[6,3] => [3] => [[1,2,3]] => 00 => 0
[6,2,1] => [2,1] => [[1,3],[2]] => 10 => 0
[6,1,1,1] => [1,1,1] => [[1],[2],[3]] => 11 => 0
[5,4] => [4] => [[1,2,3,4]] => 000 => 0
[5,3,1] => [3,1] => [[1,3,4],[2]] => 100 => 0
[5,2,2] => [2,2] => [[1,2],[3,4]] => 010 => 0
[5,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => 110 => 0
[5,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 111 => 0
[4,4,1] => [4,1] => [[1,3,4,5],[2]] => 1000 => 0
[4,3,2] => [3,2] => [[1,2,5],[3,4]] => 0100 => 0
[4,3,1,1] => [3,1,1] => [[1,4,5],[2],[3]] => 1100 => 0
[4,2,2,1] => [2,2,1] => [[1,3],[2,5],[4]] => 1010 => 0
[4,2,1,1,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 1110 => 0
[4,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1111 => 0
[3,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 00100 => 0
[3,3,2,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => 10100 => 0
[3,3,1,1,1] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 11100 => 0
[3,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 01010 => 0
[3,2,2,1,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 11010 => 0
[3,2,1,1,1,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 11110 => 0
[3,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 11111 => 0
[2,2,2,2,1] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 101010 => 0
[2,2,2,1,1,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 111010 => 0
[2,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 111110 => 0
[2,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 111111 => 0
[1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 1111111 => 0
[8,2] => [2] => [[1,2]] => 0 => 0
[8,1,1] => [1,1] => [[1],[2]] => 1 => 0
[7,3] => [3] => [[1,2,3]] => 00 => 0
[7,2,1] => [2,1] => [[1,3],[2]] => 10 => 0
[7,1,1,1] => [1,1,1] => [[1],[2],[3]] => 11 => 0
[6,4] => [4] => [[1,2,3,4]] => 000 => 0
[6,3,1] => [3,1] => [[1,3,4],[2]] => 100 => 0
[6,2,2] => [2,2] => [[1,2],[3,4]] => 010 => 0
[6,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => 110 => 0
[6,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 111 => 0
[5,5] => [5] => [[1,2,3,4,5]] => 0000 => 0
[5,4,1] => [4,1] => [[1,3,4,5],[2]] => 1000 => 0
[5,3,2] => [3,2] => [[1,2,5],[3,4]] => 0100 => 0
[5,3,1,1] => [3,1,1] => [[1,4,5],[2],[3]] => 1100 => 0
[5,2,2,1] => [2,2,1] => [[1,3],[2,5],[4]] => 1010 => 0
[5,2,1,1,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 1110 => 0
[5,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1111 => 0
[4,4,2] => [4,2] => [[1,2,5,6],[3,4]] => 01000 => 0
[4,4,1,1] => [4,1,1] => [[1,4,5,6],[2],[3]] => 11000 => 0
[4,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 00100 => 0
[4,3,2,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => 10100 => 0
[4,3,1,1,1] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 11100 => 0
>>> Load all 868 entries. <<<[4,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 01010 => 0
[4,2,2,1,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 11010 => 0
[4,2,1,1,1,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 11110 => 0
[4,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 11111 => 0
[3,3,3,1] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 100100 => 0
[3,3,2,2] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 010100 => 0
[3,3,2,1,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 110100 => 0
[3,3,1,1,1,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 111100 => 0
[3,2,2,2,1] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 101010 => 0
[3,2,2,1,1,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 111010 => 0
[3,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 111110 => 0
[3,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 111111 => 0
[2,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0101010 => 0
[2,2,2,2,1,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010 => 0
[2,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 1111010 => 0
[2,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1111110 => 0
[2,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 1111111 => 0
[1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 11111111 => 0
[9,2] => [2] => [[1,2]] => 0 => 0
[9,1,1] => [1,1] => [[1],[2]] => 1 => 0
[8,3] => [3] => [[1,2,3]] => 00 => 0
[8,2,1] => [2,1] => [[1,3],[2]] => 10 => 0
[8,1,1,1] => [1,1,1] => [[1],[2],[3]] => 11 => 0
[7,4] => [4] => [[1,2,3,4]] => 000 => 0
[7,3,1] => [3,1] => [[1,3,4],[2]] => 100 => 0
[7,2,2] => [2,2] => [[1,2],[3,4]] => 010 => 0
[7,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => 110 => 0
[7,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 111 => 0
[6,5] => [5] => [[1,2,3,4,5]] => 0000 => 0
[6,4,1] => [4,1] => [[1,3,4,5],[2]] => 1000 => 0
[6,3,2] => [3,2] => [[1,2,5],[3,4]] => 0100 => 0
[6,3,1,1] => [3,1,1] => [[1,4,5],[2],[3]] => 1100 => 0
[6,2,2,1] => [2,2,1] => [[1,3],[2,5],[4]] => 1010 => 0
[6,2,1,1,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 1110 => 0
[6,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1111 => 0
[5,5,1] => [5,1] => [[1,3,4,5,6],[2]] => 10000 => 0
[5,4,2] => [4,2] => [[1,2,5,6],[3,4]] => 01000 => 0
[5,4,1,1] => [4,1,1] => [[1,4,5,6],[2],[3]] => 11000 => 0
[5,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 00100 => 0
[5,3,2,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => 10100 => 0
[5,3,1,1,1] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 11100 => 0
[5,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 01010 => 0
[5,2,2,1,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 11010 => 0
[5,2,1,1,1,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 11110 => 0
[5,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 11111 => 0
[4,4,3] => [4,3] => [[1,2,3,7],[4,5,6]] => 001000 => 0
[4,4,2,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 101000 => 0
[4,4,1,1,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 111000 => 0
[4,3,3,1] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 100100 => 0
[4,3,2,2] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 010100 => 0
[4,3,2,1,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 110100 => 0
[4,3,1,1,1,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 111100 => 0
[4,2,2,2,1] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 101010 => 0
[4,2,2,1,1,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 111010 => 0
[4,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 111110 => 0
[4,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 111111 => 0
[3,3,3,2] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 0100100 => 0
[3,3,3,1,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 1100100 => 0
[3,3,2,2,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 1010100 => 0
[3,3,2,1,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100 => 0
[3,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100 => 0
[3,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0101010 => 0
[3,2,2,2,1,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010 => 0
[3,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 1111010 => 0
[3,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1111110 => 0
[3,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 1111111 => 0
[2,2,2,2,2,1] => [2,2,2,2,1] => [[1,3],[2,5],[4,7],[6,9],[8]] => 10101010 => 0
[2,2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 11101010 => 0
[2,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 11111010 => 0
[2,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 11111110 => 0
[2,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 11111111 => 0
[1,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => 111111111 => 0
[10,2] => [2] => [[1,2]] => 0 => 0
[10,1,1] => [1,1] => [[1],[2]] => 1 => 0
[9,3] => [3] => [[1,2,3]] => 00 => 0
[9,2,1] => [2,1] => [[1,3],[2]] => 10 => 0
[9,1,1,1] => [1,1,1] => [[1],[2],[3]] => 11 => 0
[8,4] => [4] => [[1,2,3,4]] => 000 => 0
[8,3,1] => [3,1] => [[1,3,4],[2]] => 100 => 0
[8,2,2] => [2,2] => [[1,2],[3,4]] => 010 => 0
[8,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => 110 => 0
[8,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 111 => 0
[7,5] => [5] => [[1,2,3,4,5]] => 0000 => 0
[7,4,1] => [4,1] => [[1,3,4,5],[2]] => 1000 => 0
[7,3,2] => [3,2] => [[1,2,5],[3,4]] => 0100 => 0
[7,3,1,1] => [3,1,1] => [[1,4,5],[2],[3]] => 1100 => 0
[7,2,2,1] => [2,2,1] => [[1,3],[2,5],[4]] => 1010 => 0
[7,2,1,1,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 1110 => 0
[7,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1111 => 0
[6,6] => [6] => [[1,2,3,4,5,6]] => 00000 => 0
[6,5,1] => [5,1] => [[1,3,4,5,6],[2]] => 10000 => 0
[6,4,2] => [4,2] => [[1,2,5,6],[3,4]] => 01000 => 0
[6,4,1,1] => [4,1,1] => [[1,4,5,6],[2],[3]] => 11000 => 0
[6,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 00100 => 0
[6,3,2,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => 10100 => 0
[6,3,1,1,1] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 11100 => 0
[6,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 01010 => 0
[6,2,2,1,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 11010 => 0
[6,2,1,1,1,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 11110 => 0
[6,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 11111 => 0
[5,5,2] => [5,2] => [[1,2,5,6,7],[3,4]] => 010000 => 0
[5,5,1,1] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 110000 => 0
[5,4,3] => [4,3] => [[1,2,3,7],[4,5,6]] => 001000 => 0
[5,4,2,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 101000 => 0
[5,4,1,1,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 111000 => 0
[5,3,3,1] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 100100 => 0
[5,3,2,2] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 010100 => 0
[5,3,2,1,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 110100 => 0
[5,3,1,1,1,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 111100 => 0
[5,2,2,2,1] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 101010 => 0
[5,2,2,1,1,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 111010 => 0
[5,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 111110 => 0
[5,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 111111 => 0
[4,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0001000 => 0
[4,4,3,1] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 1001000 => 0
[4,4,2,2] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 0101000 => 0
[4,4,2,1,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 1101000 => 0
[4,4,1,1,1,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000 => 0
[4,3,3,2] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 0100100 => 0
[4,3,3,1,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 1100100 => 0
[4,3,2,2,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 1010100 => 0
[4,3,2,1,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100 => 0
[4,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100 => 0
[4,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0101010 => 0
[4,2,2,2,1,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010 => 0
[4,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 1111010 => 0
[4,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1111110 => 0
[4,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 1111111 => 0
[3,3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 00100100 => 0
[3,3,3,2,1] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 10100100 => 0
[3,3,3,1,1,1] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 11100100 => 0
[3,3,2,2,2] => [3,2,2,2] => [[1,2,9],[3,4],[5,6],[7,8]] => 01010100 => 0
[3,3,2,2,1,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 11010100 => 0
[3,3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 11110100 => 0
[3,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 11111100 => 0
[3,2,2,2,2,1] => [2,2,2,2,1] => [[1,3],[2,5],[4,7],[6,9],[8]] => 10101010 => 0
[3,2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 11101010 => 0
[3,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 11111010 => 0
[3,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 11111110 => 0
[3,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 11111111 => 0
[2,2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 010101010 => 0
[2,2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 110101010 => 0
[2,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 111101010 => 0
[2,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 111111010 => 0
[2,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 111111110 => 0
[2,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => 111111111 => 0
[11,2] => [2] => [[1,2]] => 0 => 0
[11,1,1] => [1,1] => [[1],[2]] => 1 => 0
[10,3] => [3] => [[1,2,3]] => 00 => 0
[10,2,1] => [2,1] => [[1,3],[2]] => 10 => 0
[10,1,1,1] => [1,1,1] => [[1],[2],[3]] => 11 => 0
[9,4] => [4] => [[1,2,3,4]] => 000 => 0
[9,3,1] => [3,1] => [[1,3,4],[2]] => 100 => 0
[9,2,2] => [2,2] => [[1,2],[3,4]] => 010 => 0
[9,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => 110 => 0
[9,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 111 => 0
[8,5] => [5] => [[1,2,3,4,5]] => 0000 => 0
[8,4,1] => [4,1] => [[1,3,4,5],[2]] => 1000 => 0
[8,3,2] => [3,2] => [[1,2,5],[3,4]] => 0100 => 0
[8,3,1,1] => [3,1,1] => [[1,4,5],[2],[3]] => 1100 => 0
[8,2,2,1] => [2,2,1] => [[1,3],[2,5],[4]] => 1010 => 0
[8,2,1,1,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 1110 => 0
[8,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1111 => 0
[7,6] => [6] => [[1,2,3,4,5,6]] => 00000 => 0
[7,5,1] => [5,1] => [[1,3,4,5,6],[2]] => 10000 => 0
[7,4,2] => [4,2] => [[1,2,5,6],[3,4]] => 01000 => 0
[7,4,1,1] => [4,1,1] => [[1,4,5,6],[2],[3]] => 11000 => 0
[7,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 00100 => 0
[7,3,2,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => 10100 => 0
[7,3,1,1,1] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 11100 => 0
[7,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 01010 => 0
[7,2,2,1,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 11010 => 0
[7,2,1,1,1,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 11110 => 0
[7,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 11111 => 0
[6,6,1] => [6,1] => [[1,3,4,5,6,7],[2]] => 100000 => 0
[6,5,2] => [5,2] => [[1,2,5,6,7],[3,4]] => 010000 => 0
[6,5,1,1] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 110000 => 0
[6,4,3] => [4,3] => [[1,2,3,7],[4,5,6]] => 001000 => 0
[6,4,2,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 101000 => 0
[6,4,1,1,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 111000 => 0
[6,3,3,1] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 100100 => 0
[6,3,2,2] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 010100 => 0
[6,3,2,1,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 110100 => 0
[6,3,1,1,1,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 111100 => 0
[6,2,2,2,1] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 101010 => 0
[6,2,2,1,1,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 111010 => 0
[6,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 111110 => 0
[6,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 111111 => 0
[5,5,3] => [5,3] => [[1,2,3,7,8],[4,5,6]] => 0010000 => 0
[5,5,2,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 1010000 => 0
[5,5,1,1,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 1110000 => 0
[5,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0001000 => 0
[5,4,3,1] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 1001000 => 0
[5,4,2,2] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 0101000 => 0
[5,4,2,1,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 1101000 => 0
[5,4,1,1,1,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000 => 0
[5,3,3,2] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 0100100 => 0
[5,3,3,1,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 1100100 => 0
[5,3,2,2,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 1010100 => 0
[5,3,2,1,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100 => 0
[5,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100 => 0
[5,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0101010 => 0
[5,2,2,2,1,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010 => 0
[5,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 1111010 => 0
[5,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1111110 => 0
[5,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 1111111 => 0
[4,4,4,1] => [4,4,1] => [[1,3,4,5],[2,7,8,9],[6]] => 10001000 => 0
[4,4,3,2] => [4,3,2] => [[1,2,5,9],[3,4,8],[6,7]] => 01001000 => 0
[4,4,3,1,1] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 11001000 => 0
[4,4,2,2,1] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 10101000 => 0
[4,4,2,1,1,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 11101000 => 0
[4,4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 11111000 => 0
[4,3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 00100100 => 0
[4,3,3,2,1] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 10100100 => 0
[4,3,3,1,1,1] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 11100100 => 0
[4,3,2,2,2] => [3,2,2,2] => [[1,2,9],[3,4],[5,6],[7,8]] => 01010100 => 0
[4,3,2,2,1,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 11010100 => 0
[4,3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 11110100 => 0
[4,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 11111100 => 0
[4,2,2,2,2,1] => [2,2,2,2,1] => [[1,3],[2,5],[4,7],[6,9],[8]] => 10101010 => 0
[4,2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 11101010 => 0
[4,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 11111010 => 0
[4,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 11111110 => 0
[4,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 11111111 => 0
[3,3,3,3,1] => [3,3,3,1] => [[1,3,4],[2,6,7],[5,9,10],[8]] => 100100100 => 0
[3,3,3,2,2] => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 010100100 => 0
[3,3,3,2,1,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 110100100 => 0
[3,3,3,1,1,1,1] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 111100100 => 0
[3,3,2,2,2,1] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 101010100 => 0
[3,3,2,2,1,1,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 111010100 => 0
[3,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 111110100 => 0
[3,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 111111100 => 0
[3,2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 010101010 => 0
[3,2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 110101010 => 0
[3,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 111101010 => 0
[3,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 111111010 => 0
[3,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 111111110 => 0
[3,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => 111111111 => 0
[12,2] => [2] => [[1,2]] => 0 => 0
[12,1,1] => [1,1] => [[1],[2]] => 1 => 0
[11,3] => [3] => [[1,2,3]] => 00 => 0
[11,2,1] => [2,1] => [[1,3],[2]] => 10 => 0
[11,1,1,1] => [1,1,1] => [[1],[2],[3]] => 11 => 0
[10,4] => [4] => [[1,2,3,4]] => 000 => 0
[10,3,1] => [3,1] => [[1,3,4],[2]] => 100 => 0
[10,2,2] => [2,2] => [[1,2],[3,4]] => 010 => 0
[10,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => 110 => 0
[10,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 111 => 0
[9,5] => [5] => [[1,2,3,4,5]] => 0000 => 0
[9,4,1] => [4,1] => [[1,3,4,5],[2]] => 1000 => 0
[9,3,2] => [3,2] => [[1,2,5],[3,4]] => 0100 => 0
[9,3,1,1] => [3,1,1] => [[1,4,5],[2],[3]] => 1100 => 0
[9,2,2,1] => [2,2,1] => [[1,3],[2,5],[4]] => 1010 => 0
[9,2,1,1,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 1110 => 0
[9,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1111 => 0
[8,6] => [6] => [[1,2,3,4,5,6]] => 00000 => 0
[8,5,1] => [5,1] => [[1,3,4,5,6],[2]] => 10000 => 0
[8,4,2] => [4,2] => [[1,2,5,6],[3,4]] => 01000 => 0
[8,4,1,1] => [4,1,1] => [[1,4,5,6],[2],[3]] => 11000 => 0
[8,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 00100 => 0
[8,3,2,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => 10100 => 0
[8,3,1,1,1] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 11100 => 0
[8,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 01010 => 0
[8,2,2,1,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 11010 => 0
[8,2,1,1,1,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 11110 => 0
[8,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 11111 => 0
[7,7] => [7] => [[1,2,3,4,5,6,7]] => 000000 => 0
[7,6,1] => [6,1] => [[1,3,4,5,6,7],[2]] => 100000 => 0
[7,5,2] => [5,2] => [[1,2,5,6,7],[3,4]] => 010000 => 0
[7,5,1,1] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 110000 => 0
[7,4,3] => [4,3] => [[1,2,3,7],[4,5,6]] => 001000 => 0
[7,4,2,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 101000 => 0
[7,4,1,1,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 111000 => 0
[7,3,3,1] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 100100 => 0
[7,3,2,2] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 010100 => 0
[7,3,2,1,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 110100 => 0
[7,3,1,1,1,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 111100 => 0
[7,2,2,2,1] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 101010 => 0
[7,2,2,1,1,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 111010 => 0
[7,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 111110 => 0
[7,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 111111 => 0
[6,6,2] => [6,2] => [[1,2,5,6,7,8],[3,4]] => 0100000 => 0
[6,6,1,1] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 1100000 => 0
[6,5,3] => [5,3] => [[1,2,3,7,8],[4,5,6]] => 0010000 => 0
[6,5,2,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 1010000 => 0
[6,5,1,1,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 1110000 => 0
[6,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0001000 => 0
[6,4,3,1] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 1001000 => 0
[6,4,2,2] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 0101000 => 0
[6,4,2,1,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 1101000 => 0
[6,4,1,1,1,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000 => 0
[6,3,3,2] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 0100100 => 0
[6,3,3,1,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 1100100 => 0
[6,3,2,2,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 1010100 => 0
[6,3,2,1,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100 => 0
[6,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100 => 0
[6,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0101010 => 0
[6,2,2,2,1,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010 => 0
[6,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 1111010 => 0
[6,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1111110 => 0
[6,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 1111111 => 0
[5,5,4] => [5,4] => [[1,2,3,4,9],[5,6,7,8]] => 00010000 => 0
[5,5,3,1] => [5,3,1] => [[1,3,4,8,9],[2,6,7],[5]] => 10010000 => 0
[5,5,2,2] => [5,2,2] => [[1,2,7,8,9],[3,4],[5,6]] => 01010000 => 0
[5,5,2,1,1] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 11010000 => 0
[5,5,1,1,1,1] => [5,1,1,1,1] => [[1,6,7,8,9],[2],[3],[4],[5]] => 11110000 => 0
[5,4,4,1] => [4,4,1] => [[1,3,4,5],[2,7,8,9],[6]] => 10001000 => 0
[5,4,3,2] => [4,3,2] => [[1,2,5,9],[3,4,8],[6,7]] => 01001000 => 0
[5,4,3,1,1] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 11001000 => 0
[5,4,2,2,1] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 10101000 => 0
[5,4,2,1,1,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 11101000 => 0
[5,4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 11111000 => 0
[5,3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 00100100 => 0
[5,3,3,2,1] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 10100100 => 0
[5,3,3,1,1,1] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 11100100 => 0
[5,3,2,2,2] => [3,2,2,2] => [[1,2,9],[3,4],[5,6],[7,8]] => 01010100 => 0
[5,3,2,2,1,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 11010100 => 0
[5,3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 11110100 => 0
[5,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 11111100 => 0
[5,2,2,2,2,1] => [2,2,2,2,1] => [[1,3],[2,5],[4,7],[6,9],[8]] => 10101010 => 0
[5,2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 11101010 => 0
[5,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 11111010 => 0
[5,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 11111110 => 0
[5,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 11111111 => 0
[4,4,4,2] => [4,4,2] => [[1,2,5,6],[3,4,9,10],[7,8]] => 010001000 => 0
[4,4,4,1,1] => [4,4,1,1] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 110001000 => 0
[4,4,3,3] => [4,3,3] => [[1,2,3,10],[4,5,6],[7,8,9]] => 001001000 => 0
[4,4,3,2,1] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000 => 0
[4,4,3,1,1,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 111001000 => 0
[4,4,2,2,2] => [4,2,2,2] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 010101000 => 0
[4,4,2,2,1,1] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 110101000 => 0
[4,4,2,1,1,1,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 111101000 => 0
[4,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => 111111000 => 0
[4,3,3,3,1] => [3,3,3,1] => [[1,3,4],[2,6,7],[5,9,10],[8]] => 100100100 => 0
[4,3,3,2,2] => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 010100100 => 0
[4,3,3,2,1,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 110100100 => 0
[4,3,3,1,1,1,1] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 111100100 => 0
[4,3,2,2,2,1] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 101010100 => 0
[4,3,2,2,1,1,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 111010100 => 0
[4,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 111110100 => 0
[4,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 111111100 => 0
[4,2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 010101010 => 0
[4,2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 110101010 => 0
[4,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 111101010 => 0
[4,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 111111010 => 0
[4,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 111111110 => 0
[4,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => 111111111 => 0
[2,2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 01010101010 => 0
[13,2] => [2] => [[1,2]] => 0 => 0
[13,1,1] => [1,1] => [[1],[2]] => 1 => 0
[12,3] => [3] => [[1,2,3]] => 00 => 0
[12,2,1] => [2,1] => [[1,3],[2]] => 10 => 0
[12,1,1,1] => [1,1,1] => [[1],[2],[3]] => 11 => 0
[11,4] => [4] => [[1,2,3,4]] => 000 => 0
[11,3,1] => [3,1] => [[1,3,4],[2]] => 100 => 0
[11,2,2] => [2,2] => [[1,2],[3,4]] => 010 => 0
[11,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => 110 => 0
[11,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 111 => 0
[10,5] => [5] => [[1,2,3,4,5]] => 0000 => 0
[10,4,1] => [4,1] => [[1,3,4,5],[2]] => 1000 => 0
[10,3,2] => [3,2] => [[1,2,5],[3,4]] => 0100 => 0
[10,3,1,1] => [3,1,1] => [[1,4,5],[2],[3]] => 1100 => 0
[10,2,2,1] => [2,2,1] => [[1,3],[2,5],[4]] => 1010 => 0
[10,2,1,1,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 1110 => 0
[10,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1111 => 0
[9,6] => [6] => [[1,2,3,4,5,6]] => 00000 => 0
[9,5,1] => [5,1] => [[1,3,4,5,6],[2]] => 10000 => 0
[9,4,2] => [4,2] => [[1,2,5,6],[3,4]] => 01000 => 0
[9,4,1,1] => [4,1,1] => [[1,4,5,6],[2],[3]] => 11000 => 0
[9,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 00100 => 0
[9,3,2,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => 10100 => 0
[9,3,1,1,1] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 11100 => 0
[9,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 01010 => 0
[9,2,2,1,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 11010 => 0
[9,2,1,1,1,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 11110 => 0
[9,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 11111 => 0
[8,7] => [7] => [[1,2,3,4,5,6,7]] => 000000 => 0
[8,6,1] => [6,1] => [[1,3,4,5,6,7],[2]] => 100000 => 0
[8,5,2] => [5,2] => [[1,2,5,6,7],[3,4]] => 010000 => 0
[8,5,1,1] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 110000 => 0
[8,4,3] => [4,3] => [[1,2,3,7],[4,5,6]] => 001000 => 0
[8,4,2,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 101000 => 0
[8,4,1,1,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 111000 => 0
[8,3,3,1] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 100100 => 0
[8,3,2,2] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 010100 => 0
[8,3,2,1,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 110100 => 0
[8,3,1,1,1,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 111100 => 0
[8,2,2,2,1] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 101010 => 0
[8,2,2,1,1,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 111010 => 0
[8,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 111110 => 0
[8,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 111111 => 0
[7,7,1] => [7,1] => [[1,3,4,5,6,7,8],[2]] => 1000000 => 0
[7,6,2] => [6,2] => [[1,2,5,6,7,8],[3,4]] => 0100000 => 0
[7,6,1,1] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 1100000 => 0
[7,5,3] => [5,3] => [[1,2,3,7,8],[4,5,6]] => 0010000 => 0
[7,5,2,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 1010000 => 0
[7,5,1,1,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 1110000 => 0
[7,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0001000 => 0
[7,4,3,1] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 1001000 => 0
[7,4,2,2] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 0101000 => 0
[7,4,2,1,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 1101000 => 0
[7,4,1,1,1,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000 => 0
[7,3,3,2] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 0100100 => 0
[7,3,3,1,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 1100100 => 0
[7,3,2,2,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 1010100 => 0
[7,3,2,1,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100 => 0
[7,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100 => 0
[7,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0101010 => 0
[7,2,2,2,1,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010 => 0
[7,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 1111010 => 0
[7,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1111110 => 0
[7,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 1111111 => 0
[6,6,3] => [6,3] => [[1,2,3,7,8,9],[4,5,6]] => 00100000 => 0
[6,6,2,1] => [6,2,1] => [[1,3,6,7,8,9],[2,5],[4]] => 10100000 => 0
[6,6,1,1,1] => [6,1,1,1] => [[1,5,6,7,8,9],[2],[3],[4]] => 11100000 => 0
[6,5,4] => [5,4] => [[1,2,3,4,9],[5,6,7,8]] => 00010000 => 0
[6,5,3,1] => [5,3,1] => [[1,3,4,8,9],[2,6,7],[5]] => 10010000 => 0
[6,5,2,2] => [5,2,2] => [[1,2,7,8,9],[3,4],[5,6]] => 01010000 => 0
[6,5,2,1,1] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 11010000 => 0
[6,5,1,1,1,1] => [5,1,1,1,1] => [[1,6,7,8,9],[2],[3],[4],[5]] => 11110000 => 0
[6,4,4,1] => [4,4,1] => [[1,3,4,5],[2,7,8,9],[6]] => 10001000 => 0
[6,4,3,2] => [4,3,2] => [[1,2,5,9],[3,4,8],[6,7]] => 01001000 => 0
[6,4,3,1,1] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 11001000 => 0
[6,4,2,2,1] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 10101000 => 0
[6,4,2,1,1,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 11101000 => 0
[6,4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 11111000 => 0
[6,3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 00100100 => 0
[6,3,3,2,1] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 10100100 => 0
[6,3,3,1,1,1] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 11100100 => 0
[6,3,2,2,2] => [3,2,2,2] => [[1,2,9],[3,4],[5,6],[7,8]] => 01010100 => 0
[6,3,2,2,1,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 11010100 => 0
[6,3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 11110100 => 0
[6,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 11111100 => 0
[6,2,2,2,2,1] => [2,2,2,2,1] => [[1,3],[2,5],[4,7],[6,9],[8]] => 10101010 => 0
[6,2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 11101010 => 0
[6,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 11111010 => 0
[6,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 11111110 => 0
[6,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 11111111 => 0
[5,5,5] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000 => 0
[5,5,4,1] => [5,4,1] => [[1,3,4,5,10],[2,7,8,9],[6]] => 100010000 => 0
[5,5,3,2] => [5,3,2] => [[1,2,5,9,10],[3,4,8],[6,7]] => 010010000 => 0
[5,5,3,1,1] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 110010000 => 0
[5,5,2,2,1] => [5,2,2,1] => [[1,3,8,9,10],[2,5],[4,7],[6]] => 101010000 => 0
[5,5,2,1,1,1] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 111010000 => 0
[5,5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 111110000 => 0
[5,4,4,2] => [4,4,2] => [[1,2,5,6],[3,4,9,10],[7,8]] => 010001000 => 0
[5,4,4,1,1] => [4,4,1,1] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 110001000 => 0
[5,4,3,3] => [4,3,3] => [[1,2,3,10],[4,5,6],[7,8,9]] => 001001000 => 0
[5,4,3,2,1] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000 => 0
[5,4,3,1,1,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 111001000 => 0
[5,4,2,2,2] => [4,2,2,2] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 010101000 => 0
[5,4,2,2,1,1] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 110101000 => 0
[5,4,2,1,1,1,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 111101000 => 0
[5,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => 111111000 => 0
[5,3,3,3,1] => [3,3,3,1] => [[1,3,4],[2,6,7],[5,9,10],[8]] => 100100100 => 0
[5,3,3,2,2] => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 010100100 => 0
[5,3,3,2,1,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 110100100 => 0
[5,3,3,1,1,1,1] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 111100100 => 0
[5,3,2,2,2,1] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 101010100 => 0
[5,3,2,2,1,1,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 111010100 => 0
[5,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 111110100 => 0
[5,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 111111100 => 0
[5,2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 010101010 => 0
[5,2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 110101010 => 0
[5,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 111101010 => 0
[5,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 111111010 => 0
[5,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 111111110 => 0
[5,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => 111111111 => 0
[4,4,4,3] => [4,4,3] => [[1,2,3,7],[4,5,6,11],[8,9,10]] => 0010001000 => 0
[3,3,3,3,2,1] => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 10100100100 => 0
[3,2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 01010101010 => 0
[14,2] => [2] => [[1,2]] => 0 => 0
[14,1,1] => [1,1] => [[1],[2]] => 1 => 0
[13,3] => [3] => [[1,2,3]] => 00 => 0
[13,2,1] => [2,1] => [[1,3],[2]] => 10 => 0
[13,1,1,1] => [1,1,1] => [[1],[2],[3]] => 11 => 0
[12,4] => [4] => [[1,2,3,4]] => 000 => 0
[12,3,1] => [3,1] => [[1,3,4],[2]] => 100 => 0
[12,2,2] => [2,2] => [[1,2],[3,4]] => 010 => 0
[12,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => 110 => 0
[12,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 111 => 0
[11,5] => [5] => [[1,2,3,4,5]] => 0000 => 0
[11,4,1] => [4,1] => [[1,3,4,5],[2]] => 1000 => 0
[11,3,2] => [3,2] => [[1,2,5],[3,4]] => 0100 => 0
[11,3,1,1] => [3,1,1] => [[1,4,5],[2],[3]] => 1100 => 0
[11,2,2,1] => [2,2,1] => [[1,3],[2,5],[4]] => 1010 => 0
[11,2,1,1,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 1110 => 0
[11,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1111 => 0
[10,6] => [6] => [[1,2,3,4,5,6]] => 00000 => 0
[10,5,1] => [5,1] => [[1,3,4,5,6],[2]] => 10000 => 0
[10,4,2] => [4,2] => [[1,2,5,6],[3,4]] => 01000 => 0
[10,4,1,1] => [4,1,1] => [[1,4,5,6],[2],[3]] => 11000 => 0
[10,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 00100 => 0
[10,3,2,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => 10100 => 0
[10,3,1,1,1] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 11100 => 0
[10,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 01010 => 0
[10,2,2,1,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 11010 => 0
[10,2,1,1,1,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 11110 => 0
[10,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 11111 => 0
[9,7] => [7] => [[1,2,3,4,5,6,7]] => 000000 => 0
[9,6,1] => [6,1] => [[1,3,4,5,6,7],[2]] => 100000 => 0
[9,5,2] => [5,2] => [[1,2,5,6,7],[3,4]] => 010000 => 0
[9,5,1,1] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 110000 => 0
[9,4,3] => [4,3] => [[1,2,3,7],[4,5,6]] => 001000 => 0
[9,4,2,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 101000 => 0
[9,4,1,1,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 111000 => 0
[9,3,3,1] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 100100 => 0
[9,3,2,2] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 010100 => 0
[9,3,2,1,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 110100 => 0
[9,3,1,1,1,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 111100 => 0
[9,2,2,2,1] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 101010 => 0
[9,2,2,1,1,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 111010 => 0
[9,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 111110 => 0
[9,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 111111 => 0
[8,8] => [8] => [[1,2,3,4,5,6,7,8]] => 0000000 => 0
[8,7,1] => [7,1] => [[1,3,4,5,6,7,8],[2]] => 1000000 => 0
[8,6,2] => [6,2] => [[1,2,5,6,7,8],[3,4]] => 0100000 => 0
[8,6,1,1] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 1100000 => 0
[8,5,3] => [5,3] => [[1,2,3,7,8],[4,5,6]] => 0010000 => 0
[8,5,2,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 1010000 => 0
[8,5,1,1,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 1110000 => 0
[8,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0001000 => 0
[8,4,3,1] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 1001000 => 0
[8,4,2,2] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 0101000 => 0
[8,4,2,1,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 1101000 => 0
[8,4,1,1,1,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000 => 0
[8,3,3,2] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 0100100 => 0
[8,3,3,1,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 1100100 => 0
[8,3,2,2,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 1010100 => 0
[8,3,2,1,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100 => 0
[8,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100 => 0
[8,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0101010 => 0
[8,2,2,2,1,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010 => 0
[8,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 1111010 => 0
[8,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1111110 => 0
[8,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 1111111 => 0
[7,7,2] => [7,2] => [[1,2,5,6,7,8,9],[3,4]] => 01000000 => 0
[7,7,1,1] => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 11000000 => 0
[7,6,3] => [6,3] => [[1,2,3,7,8,9],[4,5,6]] => 00100000 => 0
[7,6,2,1] => [6,2,1] => [[1,3,6,7,8,9],[2,5],[4]] => 10100000 => 0
[7,6,1,1,1] => [6,1,1,1] => [[1,5,6,7,8,9],[2],[3],[4]] => 11100000 => 0
[7,5,4] => [5,4] => [[1,2,3,4,9],[5,6,7,8]] => 00010000 => 0
[7,5,3,1] => [5,3,1] => [[1,3,4,8,9],[2,6,7],[5]] => 10010000 => 0
[7,5,2,2] => [5,2,2] => [[1,2,7,8,9],[3,4],[5,6]] => 01010000 => 0
[7,5,2,1,1] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 11010000 => 0
[7,5,1,1,1,1] => [5,1,1,1,1] => [[1,6,7,8,9],[2],[3],[4],[5]] => 11110000 => 0
[7,4,4,1] => [4,4,1] => [[1,3,4,5],[2,7,8,9],[6]] => 10001000 => 0
[7,4,3,2] => [4,3,2] => [[1,2,5,9],[3,4,8],[6,7]] => 01001000 => 0
[7,4,3,1,1] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 11001000 => 0
[7,4,2,2,1] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 10101000 => 0
[7,4,2,1,1,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 11101000 => 0
[7,4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 11111000 => 0
[7,3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 00100100 => 0
[7,3,3,2,1] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 10100100 => 0
[7,3,3,1,1,1] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 11100100 => 0
[7,3,2,2,2] => [3,2,2,2] => [[1,2,9],[3,4],[5,6],[7,8]] => 01010100 => 0
[7,3,2,2,1,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 11010100 => 0
[7,3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 11110100 => 0
[7,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 11111100 => 0
[7,2,2,2,2,1] => [2,2,2,2,1] => [[1,3],[2,5],[4,7],[6,9],[8]] => 10101010 => 0
[7,2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 11101010 => 0
[7,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 11111010 => 0
[7,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 11111110 => 0
[7,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 11111111 => 0
[6,6,4] => [6,4] => [[1,2,3,4,9,10],[5,6,7,8]] => 000100000 => 0
[6,6,3,1] => [6,3,1] => [[1,3,4,8,9,10],[2,6,7],[5]] => 100100000 => 0
[6,6,2,2] => [6,2,2] => [[1,2,7,8,9,10],[3,4],[5,6]] => 010100000 => 0
[6,6,2,1,1] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 110100000 => 0
[6,6,1,1,1,1] => [6,1,1,1,1] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 111100000 => 0
[6,5,5] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000 => 0
[6,5,4,1] => [5,4,1] => [[1,3,4,5,10],[2,7,8,9],[6]] => 100010000 => 0
[6,5,3,2] => [5,3,2] => [[1,2,5,9,10],[3,4,8],[6,7]] => 010010000 => 0
[6,5,3,1,1] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 110010000 => 0
[6,5,2,2,1] => [5,2,2,1] => [[1,3,8,9,10],[2,5],[4,7],[6]] => 101010000 => 0
[6,5,2,1,1,1] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 111010000 => 0
[6,5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 111110000 => 0
[6,4,4,2] => [4,4,2] => [[1,2,5,6],[3,4,9,10],[7,8]] => 010001000 => 0
[6,4,4,1,1] => [4,4,1,1] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 110001000 => 0
[6,4,3,3] => [4,3,3] => [[1,2,3,10],[4,5,6],[7,8,9]] => 001001000 => 0
[6,4,3,2,1] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000 => 0
[6,4,3,1,1,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 111001000 => 0
[6,4,2,2,2] => [4,2,2,2] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 010101000 => 0
[6,4,2,2,1,1] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 110101000 => 0
[6,4,2,1,1,1,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 111101000 => 0
[6,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => 111111000 => 0
[6,3,3,3,1] => [3,3,3,1] => [[1,3,4],[2,6,7],[5,9,10],[8]] => 100100100 => 0
[6,3,3,2,2] => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 010100100 => 0
[6,3,3,2,1,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 110100100 => 0
[6,3,3,1,1,1,1] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 111100100 => 0
[6,3,2,2,2,1] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 101010100 => 0
[6,3,2,2,1,1,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 111010100 => 0
[6,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 111110100 => 0
[6,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 111111100 => 0
[6,2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 010101010 => 0
[6,2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 110101010 => 0
[6,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 111101010 => 0
[6,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 111111010 => 0
[6,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 111111110 => 0
[6,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => 111111111 => 0
[5,5,3,3] => [5,3,3] => [[1,2,3,10,11],[4,5,6],[7,8,9]] => 0010010000 => 0
[5,4,4,3] => [4,4,3] => [[1,2,3,7],[4,5,6,11],[8,9,10]] => 0010001000 => 0
[4,4,4,3,1] => [4,4,3,1] => [[1,3,4,8],[2,6,7,12],[5,10,11],[9]] => 10010001000 => 0
[4,4,4,2,2] => [4,4,2,2] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 01010001000 => 0
[4,4,3,3,2] => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 01001001000 => 0
[4,3,3,3,2,1] => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 10100100100 => 0
[4,2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 01010101010 => 0
[15,2] => [2] => [[1,2]] => 0 => 0
[15,1,1] => [1,1] => [[1],[2]] => 1 => 0
[14,3] => [3] => [[1,2,3]] => 00 => 0
[14,2,1] => [2,1] => [[1,3],[2]] => 10 => 0
[14,1,1,1] => [1,1,1] => [[1],[2],[3]] => 11 => 0
[13,4] => [4] => [[1,2,3,4]] => 000 => 0
[13,3,1] => [3,1] => [[1,3,4],[2]] => 100 => 0
[13,2,2] => [2,2] => [[1,2],[3,4]] => 010 => 0
[13,2,1,1] => [2,1,1] => [[1,4],[2],[3]] => 110 => 0
[13,1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 111 => 0
[12,5] => [5] => [[1,2,3,4,5]] => 0000 => 0
[12,4,1] => [4,1] => [[1,3,4,5],[2]] => 1000 => 0
[12,3,2] => [3,2] => [[1,2,5],[3,4]] => 0100 => 0
[12,3,1,1] => [3,1,1] => [[1,4,5],[2],[3]] => 1100 => 0
[12,2,2,1] => [2,2,1] => [[1,3],[2,5],[4]] => 1010 => 0
[12,2,1,1,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 1110 => 0
[12,1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1111 => 0
[11,6] => [6] => [[1,2,3,4,5,6]] => 00000 => 0
[11,5,1] => [5,1] => [[1,3,4,5,6],[2]] => 10000 => 0
[11,4,2] => [4,2] => [[1,2,5,6],[3,4]] => 01000 => 0
[11,4,1,1] => [4,1,1] => [[1,4,5,6],[2],[3]] => 11000 => 0
[11,3,3] => [3,3] => [[1,2,3],[4,5,6]] => 00100 => 0
[11,3,2,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => 10100 => 0
[11,3,1,1,1] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 11100 => 0
[11,2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 01010 => 0
[11,2,2,1,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 11010 => 0
[11,2,1,1,1,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 11110 => 0
[11,1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 11111 => 0
[10,7] => [7] => [[1,2,3,4,5,6,7]] => 000000 => 0
[10,6,1] => [6,1] => [[1,3,4,5,6,7],[2]] => 100000 => 0
[10,5,2] => [5,2] => [[1,2,5,6,7],[3,4]] => 010000 => 0
[10,5,1,1] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 110000 => 0
[10,4,3] => [4,3] => [[1,2,3,7],[4,5,6]] => 001000 => 0
[10,4,2,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 101000 => 0
[10,4,1,1,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 111000 => 0
[10,3,3,1] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 100100 => 0
[10,3,2,2] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 010100 => 0
[10,3,2,1,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 110100 => 0
[10,3,1,1,1,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 111100 => 0
[10,2,2,2,1] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 101010 => 0
[10,2,2,1,1,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 111010 => 0
[10,2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 111110 => 0
[10,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 111111 => 0
[9,8] => [8] => [[1,2,3,4,5,6,7,8]] => 0000000 => 0
[9,7,1] => [7,1] => [[1,3,4,5,6,7,8],[2]] => 1000000 => 0
[9,6,2] => [6,2] => [[1,2,5,6,7,8],[3,4]] => 0100000 => 0
[9,6,1,1] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 1100000 => 0
[9,5,3] => [5,3] => [[1,2,3,7,8],[4,5,6]] => 0010000 => 0
[9,5,2,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 1010000 => 0
[9,5,1,1,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 1110000 => 0
[9,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0001000 => 0
[9,4,3,1] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 1001000 => 0
[9,4,2,2] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 0101000 => 0
[9,4,2,1,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 1101000 => 0
[9,4,1,1,1,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000 => 0
[9,3,3,2] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 0100100 => 0
[9,3,3,1,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 1100100 => 0
[9,3,2,2,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 1010100 => 0
[9,3,2,1,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100 => 0
[9,3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100 => 0
[9,2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0101010 => 0
[9,2,2,2,1,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010 => 0
[9,2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 1111010 => 0
[9,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1111110 => 0
[9,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 1111111 => 0
[8,8,1] => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 10000000 => 0
[8,7,2] => [7,2] => [[1,2,5,6,7,8,9],[3,4]] => 01000000 => 0
[8,7,1,1] => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 11000000 => 0
[8,6,3] => [6,3] => [[1,2,3,7,8,9],[4,5,6]] => 00100000 => 0
[8,6,2,1] => [6,2,1] => [[1,3,6,7,8,9],[2,5],[4]] => 10100000 => 0
[8,6,1,1,1] => [6,1,1,1] => [[1,5,6,7,8,9],[2],[3],[4]] => 11100000 => 0
[8,5,4] => [5,4] => [[1,2,3,4,9],[5,6,7,8]] => 00010000 => 0
[8,5,3,1] => [5,3,1] => [[1,3,4,8,9],[2,6,7],[5]] => 10010000 => 0
[8,5,2,2] => [5,2,2] => [[1,2,7,8,9],[3,4],[5,6]] => 01010000 => 0
[8,5,2,1,1] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 11010000 => 0
[8,5,1,1,1,1] => [5,1,1,1,1] => [[1,6,7,8,9],[2],[3],[4],[5]] => 11110000 => 0
[8,4,4,1] => [4,4,1] => [[1,3,4,5],[2,7,8,9],[6]] => 10001000 => 0
[8,4,3,2] => [4,3,2] => [[1,2,5,9],[3,4,8],[6,7]] => 01001000 => 0
[8,4,3,1,1] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 11001000 => 0
[8,4,2,2,1] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 10101000 => 0
[8,4,2,1,1,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 11101000 => 0
[8,4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 11111000 => 0
[8,3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 00100100 => 0
[8,3,3,2,1] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 10100100 => 0
[8,3,3,1,1,1] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 11100100 => 0
[8,3,2,2,2] => [3,2,2,2] => [[1,2,9],[3,4],[5,6],[7,8]] => 01010100 => 0
[8,3,2,2,1,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 11010100 => 0
[8,3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 11110100 => 0
[8,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 11111100 => 0
[8,2,2,2,2,1] => [2,2,2,2,1] => [[1,3],[2,5],[4,7],[6,9],[8]] => 10101010 => 0
[8,2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 11101010 => 0
[8,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 11111010 => 0
[8,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 11111110 => 0
[8,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 11111111 => 0
[7,7,3] => [7,3] => [[1,2,3,7,8,9,10],[4,5,6]] => 001000000 => 0
[7,7,2,1] => [7,2,1] => [[1,3,6,7,8,9,10],[2,5],[4]] => 101000000 => 0
[7,7,1,1,1] => [7,1,1,1] => [[1,5,6,7,8,9,10],[2],[3],[4]] => 111000000 => 0
[7,6,4] => [6,4] => [[1,2,3,4,9,10],[5,6,7,8]] => 000100000 => 0
[7,6,3,1] => [6,3,1] => [[1,3,4,8,9,10],[2,6,7],[5]] => 100100000 => 0
[7,6,2,2] => [6,2,2] => [[1,2,7,8,9,10],[3,4],[5,6]] => 010100000 => 0
[7,6,2,1,1] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 110100000 => 0
[7,6,1,1,1,1] => [6,1,1,1,1] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 111100000 => 0
[7,5,5] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000 => 0
[7,5,4,1] => [5,4,1] => [[1,3,4,5,10],[2,7,8,9],[6]] => 100010000 => 0
[7,5,3,2] => [5,3,2] => [[1,2,5,9,10],[3,4,8],[6,7]] => 010010000 => 0
[7,5,3,1,1] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 110010000 => 0
[7,5,2,2,1] => [5,2,2,1] => [[1,3,8,9,10],[2,5],[4,7],[6]] => 101010000 => 0
[7,5,2,1,1,1] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 111010000 => 0
[7,5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 111110000 => 0
[7,4,4,2] => [4,4,2] => [[1,2,5,6],[3,4,9,10],[7,8]] => 010001000 => 0
[7,4,4,1,1] => [4,4,1,1] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 110001000 => 0
[7,4,3,3] => [4,3,3] => [[1,2,3,10],[4,5,6],[7,8,9]] => 001001000 => 0
[7,4,3,2,1] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000 => 0
[7,4,3,1,1,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 111001000 => 0
[7,4,2,2,2] => [4,2,2,2] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 010101000 => 0
[7,4,2,2,1,1] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 110101000 => 0
[7,4,2,1,1,1,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 111101000 => 0
[7,4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => 111111000 => 0
[7,3,3,3,1] => [3,3,3,1] => [[1,3,4],[2,6,7],[5,9,10],[8]] => 100100100 => 0
[7,3,3,2,2] => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 010100100 => 0
[7,3,3,2,1,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 110100100 => 0
[7,3,3,1,1,1,1] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 111100100 => 0
[7,3,2,2,2,1] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 101010100 => 0
[7,3,2,2,1,1,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 111010100 => 0
[7,3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 111110100 => 0
[7,3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 111111100 => 0
[7,2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 010101010 => 0
[7,2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 110101010 => 0
[7,2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 111101010 => 0
[7,2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 111111010 => 0
[7,2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 111111110 => 0
[7,1,1,1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => 111111111 => 0
[6,5,3,3] => [5,3,3] => [[1,2,3,10,11],[4,5,6],[7,8,9]] => 0010010000 => 0
[6,4,4,3] => [4,4,3] => [[1,2,3,7],[4,5,6,11],[8,9,10]] => 0010001000 => 0
[5,5,4,3] => [5,4,3] => [[1,2,3,7,12],[4,5,6,11],[8,9,10]] => 00100010000 => 0
[5,4,4,3,1] => [4,4,3,1] => [[1,3,4,8],[2,6,7,12],[5,10,11],[9]] => 10010001000 => 0
[5,4,4,2,2] => [4,4,2,2] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 01010001000 => 0
[5,4,3,3,2] => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 01001001000 => 0
[5,3,3,3,2,1] => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 10100100100 => 0
[5,2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 01010101010 => 0
[6,3,3,3,2,1] => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 10100100100 => 0
[6,4,3,3,2] => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 01001001000 => 0
[6,4,4,2,2] => [4,4,2,2] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 01010001000 => 0
[6,4,4,3,1] => [4,4,3,1] => [[1,3,4,8],[2,6,7,12],[5,10,11],[9]] => 10010001000 => 0
[6,5,4,3] => [5,4,3] => [[1,2,3,7,12],[4,5,6,11],[8,9,10]] => 00100010000 => 0
[7,3,3,3,2,1] => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 10100100100 => 0
[7,5,4,3] => [5,4,3] => [[1,2,3,7,12],[4,5,6,11],[8,9,10]] => 00100010000 => 0
[6,2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 01010101010 => 0
[6,6,6] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000 => 0
[7,6,6] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 00000100000 => 0
[10,4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0001000 => 0
[10,10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 000000000 => 0
[11,7,3] => [7,3] => [[1,2,3,7,8,9,10],[4,5,6]] => 001000000 => 0
[8,2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 01010101010 => 0
[9,6,3] => [6,3] => [[1,2,3,7,8,9],[4,5,6]] => 00100000 => 0
[8,6,4] => [6,4] => [[1,2,3,4,9,10],[5,6,7,8]] => 000100000 => 0
[10,6,4] => [6,4] => [[1,2,3,4,9,10],[5,6,7,8]] => 000100000 => 0
[15,5,5] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000 => 0
[9,6,4] => [6,4] => [[1,2,3,4,9,10],[5,6,7,8]] => 000100000 => 0
[10,7,3] => [7,3] => [[1,2,3,7,8,9,10],[4,5,6]] => 001000000 => 0
[9,9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 00000000 => 0
search for individual values
searching the database for the individual values of this statistic
Description
The defect of a binary word.
The defect of a finite word w is given by the difference between the maximum possible number and the actual number of palindromic factors contained in w. The maximum possible number of palindromic factors in a word w is |w|+1.
The defect of a finite word w is given by the difference between the maximum possible number and the actual number of palindromic factors contained in w. The maximum possible number of palindromic factors in a word w is |w|+1.
Map
first row removal
Description
Removes the first entry of an integer partition
Map
reading tableau
Description
Return the RSK recording tableau of the reading word of the (standard) tableau T labeled down (in English convention) each column to the shape of a partition.
Map
descent word
Description
The descent word of a standard Young tableau.
For a standard Young tableau of size n we set wi=1 if i+1 is in a lower row than i, and 0 otherwise, for 1≤i<n.
For a standard Young tableau of size n we set wi=1 if i+1 is in a lower row than i, and 0 otherwise, for 1≤i<n.
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