Identifier
Values
[1,0,1,0,1,0] => [2,1] => [[1,3],[2]] => 10 => 0
[1,0,1,1,0,0] => [1,1] => [[1],[2]] => 1 => 0
[1,1,0,0,1,0] => [2] => [[1,2]] => 0 => 0
[1,0,1,0,1,0,1,0] => [3,2,1] => [[1,3,6],[2,5],[4]] => 10100 => 1
[1,0,1,0,1,1,0,0] => [2,2,1] => [[1,3],[2,5],[4]] => 1010 => 1
[1,0,1,1,0,0,1,0] => [3,1,1] => [[1,4,5],[2],[3]] => 1100 => 0
[1,0,1,1,0,1,0,0] => [2,1,1] => [[1,4],[2],[3]] => 110 => 0
[1,0,1,1,1,0,0,0] => [1,1,1] => [[1],[2],[3]] => 11 => 0
[1,1,0,0,1,0,1,0] => [3,2] => [[1,2,5],[3,4]] => 0100 => 1
[1,1,0,0,1,1,0,0] => [2,2] => [[1,2],[3,4]] => 010 => 1
[1,1,0,1,0,0,1,0] => [3,1] => [[1,3,4],[2]] => 100 => 0
[1,1,0,1,0,1,0,0] => [2,1] => [[1,3],[2]] => 10 => 0
[1,1,0,1,1,0,0,0] => [1,1] => [[1],[2]] => 1 => 0
[1,1,1,0,0,0,1,0] => [3] => [[1,2,3]] => 00 => 0
[1,1,1,0,0,1,0,0] => [2] => [[1,2]] => 0 => 0
[1,0,1,0,1,0,1,0,1,0] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000 => 1
[1,0,1,0,1,0,1,1,0,0] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 10100100 => 1
[1,0,1,0,1,1,0,0,1,0] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 10101000 => 2
[1,0,1,0,1,1,0,1,0,0] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 1010100 => 2
[1,0,1,0,1,1,1,0,0,0] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 101010 => 2
[1,0,1,1,0,0,1,0,1,0] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 11001000 => 0
[1,0,1,1,0,0,1,1,0,0] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 1100100 => 0
[1,0,1,1,0,1,0,0,1,0] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 1101000 => 0
[1,0,1,1,0,1,0,1,0,0] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 110100 => 0
[1,0,1,1,0,1,1,0,0,0] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 11010 => 0
[1,0,1,1,1,0,0,0,1,0] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 111000 => 1
[1,0,1,1,1,0,0,1,0,0] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 11100 => 1
[1,0,1,1,1,0,1,0,0,0] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 1110 => 1
[1,0,1,1,1,1,0,0,0,0] => [1,1,1,1] => [[1],[2],[3],[4]] => 111 => 1
[1,1,0,0,1,0,1,0,1,0] => [4,3,2] => [[1,2,5,9],[3,4,8],[6,7]] => 01001000 => 1
[1,1,0,0,1,0,1,1,0,0] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 0100100 => 1
[1,1,0,0,1,1,0,0,1,0] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 0101000 => 2
[1,1,0,0,1,1,0,1,0,0] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 010100 => 2
[1,1,0,0,1,1,1,0,0,0] => [2,2,2] => [[1,2],[3,4],[5,6]] => 01010 => 2
[1,1,0,1,0,0,1,0,1,0] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 1001000 => 0
[1,1,0,1,0,0,1,1,0,0] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 100100 => 0
[1,1,0,1,0,1,0,0,1,0] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 101000 => 1
[1,1,0,1,0,1,0,1,0,0] => [3,2,1] => [[1,3,6],[2,5],[4]] => 10100 => 1
[1,1,0,1,0,1,1,0,0,0] => [2,2,1] => [[1,3],[2,5],[4]] => 1010 => 1
[1,1,0,1,1,0,0,0,1,0] => [4,1,1] => [[1,4,5,6],[2],[3]] => 11000 => 0
[1,1,0,1,1,0,0,1,0,0] => [3,1,1] => [[1,4,5],[2],[3]] => 1100 => 0
[1,1,0,1,1,0,1,0,0,0] => [2,1,1] => [[1,4],[2],[3]] => 110 => 0
[1,1,0,1,1,1,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => 11 => 0
[1,1,1,0,0,0,1,0,1,0] => [4,3] => [[1,2,3,7],[4,5,6]] => 001000 => 2
[1,1,1,0,0,0,1,1,0,0] => [3,3] => [[1,2,3],[4,5,6]] => 00100 => 2
[1,1,1,0,0,1,0,0,1,0] => [4,2] => [[1,2,5,6],[3,4]] => 01000 => 1
[1,1,1,0,0,1,0,1,0,0] => [3,2] => [[1,2,5],[3,4]] => 0100 => 1
[1,1,1,0,0,1,1,0,0,0] => [2,2] => [[1,2],[3,4]] => 010 => 1
[1,1,1,0,1,0,0,0,1,0] => [4,1] => [[1,3,4,5],[2]] => 1000 => 0
[1,1,1,0,1,0,0,1,0,0] => [3,1] => [[1,3,4],[2]] => 100 => 0
[1,1,1,0,1,0,1,0,0,0] => [2,1] => [[1,3],[2]] => 10 => 0
[1,1,1,0,1,1,0,0,0,0] => [1,1] => [[1],[2]] => 1 => 0
[1,1,1,1,0,0,0,0,1,0] => [4] => [[1,2,3,4]] => 000 => 1
[1,1,1,1,0,0,0,1,0,0] => [3] => [[1,2,3]] => 00 => 0
[1,1,1,1,0,0,1,0,0,0] => [2] => [[1,2]] => 0 => 0
[1,0,1,0,1,1,1,0,1,0,0,0] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 101010100 => 3
[1,0,1,0,1,1,1,1,0,0,0,0] => [2,2,2,2,1] => [[1,3],[2,5],[4,7],[6,9],[8]] => 10101010 => 3
[1,0,1,1,0,1,0,1,1,0,0,0] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 110100100 => 0
[1,0,1,1,0,1,1,0,0,1,0,0] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 110101000 => 0
[1,0,1,1,0,1,1,0,1,0,0,0] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 11010100 => 0
[1,0,1,1,0,1,1,1,0,0,0,0] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010 => 0
[1,0,1,1,1,0,0,1,0,1,0,0] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 111001000 => 1
[1,0,1,1,1,0,0,1,1,0,0,0] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 11100100 => 1
[1,0,1,1,1,0,1,0,0,0,1,0] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 111010000 => 1
[1,0,1,1,1,0,1,0,0,1,0,0] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 11101000 => 1
[1,0,1,1,1,0,1,0,1,0,0,0] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100 => 1
[1,0,1,1,1,0,1,1,0,0,0,0] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 111010 => 1
[1,0,1,1,1,1,0,0,0,0,1,0] => [5,1,1,1,1] => [[1,6,7,8,9],[2],[3],[4],[5]] => 11110000 => 1
[1,0,1,1,1,1,0,0,0,1,0,0] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000 => 1
[1,0,1,1,1,1,0,0,1,0,0,0] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 111100 => 1
[1,0,1,1,1,1,0,1,0,0,0,0] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 11110 => 1
[1,0,1,1,1,1,1,0,0,0,0,0] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1111 => 1
[1,1,0,0,1,1,0,1,1,0,0,0] => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 010100100 => 2
[1,1,0,0,1,1,1,0,0,1,0,0] => [4,2,2,2] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 010101000 => 3
[1,1,0,0,1,1,1,0,1,0,0,0] => [3,2,2,2] => [[1,2,9],[3,4],[5,6],[7,8]] => 01010100 => 3
[1,1,0,0,1,1,1,1,0,0,0,0] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0101010 => 3
[1,1,0,1,0,0,1,1,1,0,0,0] => [3,3,3,1] => [[1,3,4],[2,6,7],[5,9,10],[8]] => 100100100 => 3
[1,1,0,1,0,1,0,1,0,1,0,0] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000 => 1
[1,1,0,1,0,1,0,1,1,0,0,0] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 10100100 => 1
[1,1,0,1,0,1,1,0,0,0,1,0] => [5,2,2,1] => [[1,3,8,9,10],[2,5],[4,7],[6]] => 101010000 => 2
[1,1,0,1,0,1,1,0,0,1,0,0] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 10101000 => 2
[1,1,0,1,0,1,1,0,1,0,0,0] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 1010100 => 2
[1,1,0,1,0,1,1,1,0,0,0,0] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 101010 => 2
[1,1,0,1,1,0,0,0,1,1,0,0] => [4,4,1,1] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 110001000 => 0
[1,1,0,1,1,0,0,1,0,0,1,0] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 110010000 => 0
[1,1,0,1,1,0,0,1,0,1,0,0] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 11001000 => 0
[1,1,0,1,1,0,0,1,1,0,0,0] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 1100100 => 0
[1,1,0,1,1,0,1,0,0,0,1,0] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 11010000 => 0
[1,1,0,1,1,0,1,0,0,1,0,0] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 1101000 => 0
[1,1,0,1,1,0,1,0,1,0,0,0] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 110100 => 0
[1,1,0,1,1,0,1,1,0,0,0,0] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 11010 => 0
[1,1,0,1,1,1,0,0,0,0,1,0] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 1110000 => 1
[1,1,0,1,1,1,0,0,0,1,0,0] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 111000 => 1
[1,1,0,1,1,1,0,0,1,0,0,0] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 11100 => 1
[1,1,0,1,1,1,0,1,0,0,0,0] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 1110 => 1
[1,1,0,1,1,1,1,0,0,0,0,0] => [1,1,1,1] => [[1],[2],[3],[4]] => 111 => 1
[1,1,1,0,0,0,1,1,0,1,0,0] => [4,3,3] => [[1,2,3,10],[4,5,6],[7,8,9]] => 001001000 => 2
[1,1,1,0,0,0,1,1,1,0,0,0] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 00100100 => 2
[1,1,1,0,0,1,0,0,1,1,0,0] => [4,4,2] => [[1,2,5,6],[3,4,9,10],[7,8]] => 010001000 => 3
[1,1,1,0,0,1,0,1,0,0,1,0] => [5,3,2] => [[1,2,5,9,10],[3,4,8],[6,7]] => 010010000 => 1
[1,1,1,0,0,1,0,1,0,1,0,0] => [4,3,2] => [[1,2,5,9],[3,4,8],[6,7]] => 01001000 => 1
>>> Load all 559 entries. <<<
[1,1,1,0,0,1,0,1,1,0,0,0] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 0100100 => 1
[1,1,1,0,0,1,1,0,0,0,1,0] => [5,2,2] => [[1,2,7,8,9],[3,4],[5,6]] => 01010000 => 2
[1,1,1,0,0,1,1,0,0,1,0,0] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 0101000 => 2
[1,1,1,0,0,1,1,0,1,0,0,0] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 010100 => 2
[1,1,1,0,0,1,1,1,0,0,0,0] => [2,2,2] => [[1,2],[3,4],[5,6]] => 01010 => 2
[1,1,1,0,1,0,0,0,1,0,1,0] => [5,4,1] => [[1,3,4,5,10],[2,7,8,9],[6]] => 100010000 => 2
[1,1,1,0,1,0,0,0,1,1,0,0] => [4,4,1] => [[1,3,4,5],[2,7,8,9],[6]] => 10001000 => 2
[1,1,1,0,1,0,0,1,0,0,1,0] => [5,3,1] => [[1,3,4,8,9],[2,6,7],[5]] => 10010000 => 0
[1,1,1,0,1,0,0,1,0,1,0,0] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 1001000 => 0
[1,1,1,0,1,0,0,1,1,0,0,0] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 100100 => 0
[1,1,1,0,1,0,1,0,0,0,1,0] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 1010000 => 1
[1,1,1,0,1,0,1,0,0,1,0,0] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 101000 => 1
[1,1,1,0,1,0,1,0,1,0,0,0] => [3,2,1] => [[1,3,6],[2,5],[4]] => 10100 => 1
[1,1,1,0,1,0,1,1,0,0,0,0] => [2,2,1] => [[1,3],[2,5],[4]] => 1010 => 1
[1,1,1,0,1,1,0,0,0,0,1,0] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 110000 => 0
[1,1,1,0,1,1,0,0,0,1,0,0] => [4,1,1] => [[1,4,5,6],[2],[3]] => 11000 => 0
[1,1,1,0,1,1,0,0,1,0,0,0] => [3,1,1] => [[1,4,5],[2],[3]] => 1100 => 0
[1,1,1,0,1,1,0,1,0,0,0,0] => [2,1,1] => [[1,4],[2],[3]] => 110 => 0
[1,1,1,0,1,1,1,0,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => 11 => 0
[1,1,1,1,0,0,0,0,1,0,1,0] => [5,4] => [[1,2,3,4,9],[5,6,7,8]] => 00010000 => 3
[1,1,1,1,0,0,0,0,1,1,0,0] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0001000 => 3
[1,1,1,1,0,0,0,1,0,0,1,0] => [5,3] => [[1,2,3,7,8],[4,5,6]] => 0010000 => 2
[1,1,1,1,0,0,0,1,0,1,0,0] => [4,3] => [[1,2,3,7],[4,5,6]] => 001000 => 2
[1,1,1,1,0,0,0,1,1,0,0,0] => [3,3] => [[1,2,3],[4,5,6]] => 00100 => 2
[1,1,1,1,0,0,1,0,0,0,1,0] => [5,2] => [[1,2,5,6,7],[3,4]] => 010000 => 1
[1,1,1,1,0,0,1,0,0,1,0,0] => [4,2] => [[1,2,5,6],[3,4]] => 01000 => 1
[1,1,1,1,0,0,1,0,1,0,0,0] => [3,2] => [[1,2,5],[3,4]] => 0100 => 1
[1,1,1,1,0,0,1,1,0,0,0,0] => [2,2] => [[1,2],[3,4]] => 010 => 1
[1,1,1,1,0,1,0,0,0,0,1,0] => [5,1] => [[1,3,4,5,6],[2]] => 10000 => 0
[1,1,1,1,0,1,0,0,0,1,0,0] => [4,1] => [[1,3,4,5],[2]] => 1000 => 0
[1,1,1,1,0,1,0,0,1,0,0,0] => [3,1] => [[1,3,4],[2]] => 100 => 0
[1,1,1,1,0,1,0,1,0,0,0,0] => [2,1] => [[1,3],[2]] => 10 => 0
[1,1,1,1,0,1,1,0,0,0,0,0] => [1,1] => [[1],[2]] => 1 => 0
[1,1,1,1,1,0,0,0,0,0,1,0] => [5] => [[1,2,3,4,5]] => 0000 => 1
[1,1,1,1,1,0,0,0,0,1,0,0] => [4] => [[1,2,3,4]] => 000 => 1
[1,1,1,1,1,0,0,0,1,0,0,0] => [3] => [[1,2,3]] => 00 => 0
[1,1,1,1,1,0,0,1,0,0,0,0] => [2] => [[1,2]] => 0 => 0
[1,0,1,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 110101010 => 0
[1,0,1,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 111010100 => 1
[1,0,1,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 11101010 => 1
[1,0,1,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 111100100 => 1
[1,0,1,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 111101000 => 1
[1,0,1,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 11110100 => 1
[1,0,1,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 1111010 => 1
[1,0,1,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 111110000 => 2
[1,0,1,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1,1] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 11111000 => 2
[1,0,1,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100 => 2
[1,0,1,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 111110 => 2
[1,0,1,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 11111 => 2
[1,1,0,0,1,1,1,1,1,0,0,0,0,0] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 010101010 => 4
[1,1,0,1,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 101010100 => 3
[1,1,0,1,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2,1] => [[1,3],[2,5],[4,7],[6,9],[8]] => 10101010 => 3
[1,1,0,1,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 110100100 => 0
[1,1,0,1,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 110101000 => 0
[1,1,0,1,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 11010100 => 0
[1,1,0,1,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010 => 0
[1,1,0,1,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 111001000 => 1
[1,1,0,1,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 11100100 => 1
[1,1,0,1,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 111010000 => 1
[1,1,0,1,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 11101000 => 1
[1,1,0,1,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100 => 1
[1,1,0,1,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 111010 => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1,1] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 111100000 => 1
[1,1,0,1,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1,1] => [[1,6,7,8,9],[2],[3],[4],[5]] => 11110000 => 1
[1,1,0,1,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000 => 1
[1,1,0,1,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 111100 => 1
[1,1,0,1,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 11110 => 1
[1,1,0,1,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1111 => 1
[1,1,1,0,0,1,1,0,1,1,0,0,0,0] => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 010100100 => 2
[1,1,1,0,0,1,1,1,0,0,1,0,0,0] => [4,2,2,2] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 010101000 => 3
[1,1,1,0,0,1,1,1,0,1,0,0,0,0] => [3,2,2,2] => [[1,2,9],[3,4],[5,6],[7,8]] => 01010100 => 3
[1,1,1,0,0,1,1,1,1,0,0,0,0,0] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0101010 => 3
[1,1,1,0,1,0,0,1,1,1,0,0,0,0] => [3,3,3,1] => [[1,3,4],[2,6,7],[5,9,10],[8]] => 100100100 => 3
[1,1,1,0,1,0,1,0,1,0,1,0,0,0] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000 => 1
[1,1,1,0,1,0,1,0,1,1,0,0,0,0] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 10100100 => 1
[1,1,1,0,1,0,1,1,0,0,0,1,0,0] => [5,2,2,1] => [[1,3,8,9,10],[2,5],[4,7],[6]] => 101010000 => 2
[1,1,1,0,1,0,1,1,0,0,1,0,0,0] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 10101000 => 2
[1,1,1,0,1,0,1,1,0,1,0,0,0,0] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 1010100 => 2
[1,1,1,0,1,0,1,1,1,0,0,0,0,0] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 101010 => 2
[1,1,1,0,1,1,0,0,0,1,1,0,0,0] => [4,4,1,1] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 110001000 => 0
[1,1,1,0,1,1,0,0,1,0,0,1,0,0] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 110010000 => 0
[1,1,1,0,1,1,0,0,1,0,1,0,0,0] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 11001000 => 0
[1,1,1,0,1,1,0,0,1,1,0,0,0,0] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 1100100 => 0
[1,1,1,0,1,1,0,1,0,0,0,0,1,0] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 110100000 => 0
[1,1,1,0,1,1,0,1,0,0,0,1,0,0] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 11010000 => 0
[1,1,1,0,1,1,0,1,0,0,1,0,0,0] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 1101000 => 0
[1,1,1,0,1,1,0,1,0,1,0,0,0,0] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 110100 => 0
[1,1,1,0,1,1,0,1,1,0,0,0,0,0] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 11010 => 0
[1,1,1,0,1,1,1,0,0,0,0,0,1,0] => [6,1,1,1] => [[1,5,6,7,8,9],[2],[3],[4]] => 11100000 => 1
[1,1,1,0,1,1,1,0,0,0,0,1,0,0] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 1110000 => 1
[1,1,1,0,1,1,1,0,0,0,1,0,0,0] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 111000 => 1
[1,1,1,0,1,1,1,0,0,1,0,0,0,0] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 11100 => 1
[1,1,1,0,1,1,1,0,1,0,0,0,0,0] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 1110 => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,0] => [1,1,1,1] => [[1],[2],[3],[4]] => 111 => 1
[1,1,1,1,0,0,0,1,1,0,1,0,0,0] => [4,3,3] => [[1,2,3,10],[4,5,6],[7,8,9]] => 001001000 => 2
[1,1,1,1,0,0,0,1,1,1,0,0,0,0] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 00100100 => 2
[1,1,1,1,0,0,1,0,0,1,1,0,0,0] => [4,4,2] => [[1,2,5,6],[3,4,9,10],[7,8]] => 010001000 => 3
[1,1,1,1,0,0,1,0,1,0,0,1,0,0] => [5,3,2] => [[1,2,5,9,10],[3,4,8],[6,7]] => 010010000 => 1
[1,1,1,1,0,0,1,0,1,0,1,0,0,0] => [4,3,2] => [[1,2,5,9],[3,4,8],[6,7]] => 01001000 => 1
[1,1,1,1,0,0,1,0,1,1,0,0,0,0] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 0100100 => 1
[1,1,1,1,0,0,1,1,0,0,0,0,1,0] => [6,2,2] => [[1,2,7,8,9,10],[3,4],[5,6]] => 010100000 => 2
[1,1,1,1,0,0,1,1,0,0,0,1,0,0] => [5,2,2] => [[1,2,7,8,9],[3,4],[5,6]] => 01010000 => 2
[1,1,1,1,0,0,1,1,0,0,1,0,0,0] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 0101000 => 2
[1,1,1,1,0,0,1,1,0,1,0,0,0,0] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 010100 => 2
[1,1,1,1,0,0,1,1,1,0,0,0,0,0] => [2,2,2] => [[1,2],[3,4],[5,6]] => 01010 => 2
[1,1,1,1,0,1,0,0,0,1,0,1,0,0] => [5,4,1] => [[1,3,4,5,10],[2,7,8,9],[6]] => 100010000 => 2
[1,1,1,1,0,1,0,0,0,1,1,0,0,0] => [4,4,1] => [[1,3,4,5],[2,7,8,9],[6]] => 10001000 => 2
[1,1,1,1,0,1,0,0,1,0,0,0,1,0] => [6,3,1] => [[1,3,4,8,9,10],[2,6,7],[5]] => 100100000 => 0
[1,1,1,1,0,1,0,0,1,0,0,1,0,0] => [5,3,1] => [[1,3,4,8,9],[2,6,7],[5]] => 10010000 => 0
[1,1,1,1,0,1,0,0,1,0,1,0,0,0] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 1001000 => 0
[1,1,1,1,0,1,0,0,1,1,0,0,0,0] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 100100 => 0
[1,1,1,1,0,1,0,1,0,0,0,0,1,0] => [6,2,1] => [[1,3,6,7,8,9],[2,5],[4]] => 10100000 => 1
[1,1,1,1,0,1,0,1,0,0,0,1,0,0] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 1010000 => 1
[1,1,1,1,0,1,0,1,0,0,1,0,0,0] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 101000 => 1
[1,1,1,1,0,1,0,1,0,1,0,0,0,0] => [3,2,1] => [[1,3,6],[2,5],[4]] => 10100 => 1
[1,1,1,1,0,1,0,1,1,0,0,0,0,0] => [2,2,1] => [[1,3],[2,5],[4]] => 1010 => 1
[1,1,1,1,0,1,1,0,0,0,0,0,1,0] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 1100000 => 0
[1,1,1,1,0,1,1,0,0,0,0,1,0,0] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 110000 => 0
[1,1,1,1,0,1,1,0,0,0,1,0,0,0] => [4,1,1] => [[1,4,5,6],[2],[3]] => 11000 => 0
[1,1,1,1,0,1,1,0,0,1,0,0,0,0] => [3,1,1] => [[1,4,5],[2],[3]] => 1100 => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,0] => [2,1,1] => [[1,4],[2],[3]] => 110 => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => 11 => 0
[1,1,1,1,1,0,0,0,0,0,1,1,0,0] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000 => 4
[1,1,1,1,1,0,0,0,0,1,0,0,1,0] => [6,4] => [[1,2,3,4,9,10],[5,6,7,8]] => 000100000 => 3
[1,1,1,1,1,0,0,0,0,1,0,1,0,0] => [5,4] => [[1,2,3,4,9],[5,6,7,8]] => 00010000 => 3
[1,1,1,1,1,0,0,0,0,1,1,0,0,0] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0001000 => 3
[1,1,1,1,1,0,0,0,1,0,0,0,1,0] => [6,3] => [[1,2,3,7,8,9],[4,5,6]] => 00100000 => 2
[1,1,1,1,1,0,0,0,1,0,0,1,0,0] => [5,3] => [[1,2,3,7,8],[4,5,6]] => 0010000 => 2
[1,1,1,1,1,0,0,0,1,0,1,0,0,0] => [4,3] => [[1,2,3,7],[4,5,6]] => 001000 => 2
[1,1,1,1,1,0,0,0,1,1,0,0,0,0] => [3,3] => [[1,2,3],[4,5,6]] => 00100 => 2
[1,1,1,1,1,0,0,1,0,0,0,0,1,0] => [6,2] => [[1,2,5,6,7,8],[3,4]] => 0100000 => 1
[1,1,1,1,1,0,0,1,0,0,0,1,0,0] => [5,2] => [[1,2,5,6,7],[3,4]] => 010000 => 1
[1,1,1,1,1,0,0,1,0,0,1,0,0,0] => [4,2] => [[1,2,5,6],[3,4]] => 01000 => 1
[1,1,1,1,1,0,0,1,0,1,0,0,0,0] => [3,2] => [[1,2,5],[3,4]] => 0100 => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,0] => [2,2] => [[1,2],[3,4]] => 010 => 1
[1,1,1,1,1,0,1,0,0,0,0,0,1,0] => [6,1] => [[1,3,4,5,6,7],[2]] => 100000 => 0
[1,1,1,1,1,0,1,0,0,0,0,1,0,0] => [5,1] => [[1,3,4,5,6],[2]] => 10000 => 0
[1,1,1,1,1,0,1,0,0,0,1,0,0,0] => [4,1] => [[1,3,4,5],[2]] => 1000 => 0
[1,1,1,1,1,0,1,0,0,1,0,0,0,0] => [3,1] => [[1,3,4],[2]] => 100 => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [2,1] => [[1,3],[2]] => 10 => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [1,1] => [[1],[2]] => 1 => 0
[1,1,1,1,1,1,0,0,0,0,0,0,1,0] => [6] => [[1,2,3,4,5,6]] => 00000 => 2
[1,1,1,1,1,1,0,0,0,0,0,1,0,0] => [5] => [[1,2,3,4,5]] => 0000 => 1
[1,1,1,1,1,1,0,0,0,0,1,0,0,0] => [4] => [[1,2,3,4]] => 000 => 1
[1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [3] => [[1,2,3]] => 00 => 0
[1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [2] => [[1,2]] => 0 => 0
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 111101010 => 1
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 111110100 => 2
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 11111010 => 2
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1,1] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => 111111000 => 2
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 11111100 => 2
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1111110 => 2
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 111111 => 2
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 110101010 => 0
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 111010100 => 1
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 11101010 => 1
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 111100100 => 1
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 111101000 => 1
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 11110100 => 1
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 1111010 => 1
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 111110000 => 2
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1,1] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 11111000 => 2
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100 => 2
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 111110 => 2
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 11111 => 2
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 010101010 => 4
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 101010100 => 3
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2,1] => [[1,3],[2,5],[4,7],[6,9],[8]] => 10101010 => 3
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 110100100 => 0
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 110101000 => 0
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 11010100 => 0
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010 => 0
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 111001000 => 1
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 11100100 => 1
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 111010000 => 1
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 11101000 => 1
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100 => 1
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 111010 => 1
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1,1] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 111100000 => 1
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1,1] => [[1,6,7,8,9],[2],[3],[4],[5]] => 11110000 => 1
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 1111000 => 1
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 111100 => 1
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 11110 => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1111 => 1
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0] => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 010100100 => 2
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0] => [4,2,2,2] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 010101000 => 3
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0] => [3,2,2,2] => [[1,2,9],[3,4],[5,6],[7,8]] => 01010100 => 3
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 0101010 => 3
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0] => [3,3,3,1] => [[1,3,4],[2,6,7],[5,9,10],[8]] => 100100100 => 3
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000 => 1
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 10100100 => 1
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0] => [5,2,2,1] => [[1,3,8,9,10],[2,5],[4,7],[6]] => 101010000 => 2
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 10101000 => 2
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 1010100 => 2
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 101010 => 2
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0] => [4,4,1,1] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 110001000 => 0
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 110010000 => 0
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 11001000 => 0
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 1100100 => 0
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 110100000 => 0
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 11010000 => 0
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 1101000 => 0
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 110100 => 0
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 11010 => 0
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0] => [7,1,1,1] => [[1,5,6,7,8,9,10],[2],[3],[4]] => 111000000 => 1
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0] => [6,1,1,1] => [[1,5,6,7,8,9],[2],[3],[4]] => 11100000 => 1
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 1110000 => 1
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 111000 => 1
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 11100 => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 1110 => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [1,1,1,1] => [[1],[2],[3],[4]] => 111 => 1
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0] => [4,3,3] => [[1,2,3,10],[4,5,6],[7,8,9]] => 001001000 => 2
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 00100100 => 2
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0] => [4,4,2] => [[1,2,5,6],[3,4,9,10],[7,8]] => 010001000 => 3
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0] => [5,3,2] => [[1,2,5,9,10],[3,4,8],[6,7]] => 010010000 => 1
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0] => [4,3,2] => [[1,2,5,9],[3,4,8],[6,7]] => 01001000 => 1
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 0100100 => 1
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0] => [6,2,2] => [[1,2,7,8,9,10],[3,4],[5,6]] => 010100000 => 2
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0] => [5,2,2] => [[1,2,7,8,9],[3,4],[5,6]] => 01010000 => 2
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 0101000 => 2
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 010100 => 2
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0] => [2,2,2] => [[1,2],[3,4],[5,6]] => 01010 => 2
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0] => [5,4,1] => [[1,3,4,5,10],[2,7,8,9],[6]] => 100010000 => 2
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0] => [4,4,1] => [[1,3,4,5],[2,7,8,9],[6]] => 10001000 => 2
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0] => [6,3,1] => [[1,3,4,8,9,10],[2,6,7],[5]] => 100100000 => 0
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0] => [5,3,1] => [[1,3,4,8,9],[2,6,7],[5]] => 10010000 => 0
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 1001000 => 0
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 100100 => 0
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0] => [7,2,1] => [[1,3,6,7,8,9,10],[2,5],[4]] => 101000000 => 1
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0] => [6,2,1] => [[1,3,6,7,8,9],[2,5],[4]] => 10100000 => 1
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 1010000 => 1
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 101000 => 1
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0] => [3,2,1] => [[1,3,6],[2,5],[4]] => 10100 => 1
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0] => [2,2,1] => [[1,3],[2,5],[4]] => 1010 => 1
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0] => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 11000000 => 0
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 1100000 => 0
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 110000 => 0
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0] => [4,1,1] => [[1,4,5,6],[2],[3]] => 11000 => 0
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0] => [3,1,1] => [[1,4,5],[2],[3]] => 1100 => 0
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0] => [2,1,1] => [[1,4],[2],[3]] => 110 => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => 11 => 0
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000 => 4
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0] => [6,4] => [[1,2,3,4,9,10],[5,6,7,8]] => 000100000 => 3
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0] => [5,4] => [[1,2,3,4,9],[5,6,7,8]] => 00010000 => 3
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0001000 => 3
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0] => [7,3] => [[1,2,3,7,8,9,10],[4,5,6]] => 001000000 => 2
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0] => [6,3] => [[1,2,3,7,8,9],[4,5,6]] => 00100000 => 2
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0] => [5,3] => [[1,2,3,7,8],[4,5,6]] => 0010000 => 2
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0] => [4,3] => [[1,2,3,7],[4,5,6]] => 001000 => 2
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0] => [3,3] => [[1,2,3],[4,5,6]] => 00100 => 2
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0] => [7,2] => [[1,2,5,6,7,8,9],[3,4]] => 01000000 => 1
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0] => [6,2] => [[1,2,5,6,7,8],[3,4]] => 0100000 => 1
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0] => [5,2] => [[1,2,5,6,7],[3,4]] => 010000 => 1
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0] => [4,2] => [[1,2,5,6],[3,4]] => 01000 => 1
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0] => [3,2] => [[1,2,5],[3,4]] => 0100 => 1
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0] => [2,2] => [[1,2],[3,4]] => 010 => 1
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0] => [7,1] => [[1,3,4,5,6,7,8],[2]] => 1000000 => 0
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0] => [6,1] => [[1,3,4,5,6,7],[2]] => 100000 => 0
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0] => [5,1] => [[1,3,4,5,6],[2]] => 10000 => 0
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0] => [4,1] => [[1,3,4,5],[2]] => 1000 => 0
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0] => [3,1] => [[1,3,4],[2]] => 100 => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [2,1] => [[1,3],[2]] => 10 => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [1,1] => [[1],[2]] => 1 => 0
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => [7] => [[1,2,3,4,5,6,7]] => 000000 => 2
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0] => [6] => [[1,2,3,4,5,6]] => 00000 => 2
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0] => [5] => [[1,2,3,4,5]] => 0000 => 1
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [4] => [[1,2,3,4]] => 000 => 1
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [3] => [[1,2,3]] => 00 => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [2] => [[1,2]] => 0 => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => [8] => [[1,2,3,4,5,6,7,8]] => 0000000 => 3
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 1111111 => 3
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => [9] => [[1,2,3,4,5,6,7,8,9]] => 00000000 => 3
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0] => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 10000000 => 0
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 11111110 => 3
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 11111111 => 3
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 000000000 => 4
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0] => [9,1] => [[1,3,4,5,6,7,8,9,10],[2]] => 100000000 => 0
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0] => [8,2] => [[1,2,5,6,7,8,9,10],[3,4]] => 010000000 => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0] => [8,1,1] => [[1,4,5,6,7,8,9,10],[2],[3]] => 110000000 => 0
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 111111100 => 3
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 111111010 => 2
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 111111110 => 3
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => 111111111 => 4
[1,1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 111101010 => 1
[1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 111110100 => 2
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 11111010 => 2
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1,1] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => 111111000 => 2
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 11111100 => 2
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1111110 => 2
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 111111 => 2
[1,1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 110101010 => 0
[1,1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 11101010 => 1
[1,1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 11110100 => 1
[1,1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 1111010 => 1
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 111110000 => 2
[1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1,1,1] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 11111000 => 2
[1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100 => 2
[1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 111110 => 2
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 11111 => 2
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 010101010 => 4
[1,1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0,0] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 101010100 => 3
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0] => [2,2,2,2,1] => [[1,3],[2,5],[4,7],[6,9],[8]] => 10101010 => 3
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 11010100 => 0
[1,1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 1101010 => 0
[1,1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 111001000 => 1
[1,1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 11100100 => 1
[1,1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 111010000 => 1
[1,1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 1110100 => 1
[1,1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 111010 => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1,1] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 111100000 => 1
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1,1] => [[1,6,7,8,9],[2],[3],[4],[5]] => 11110000 => 1
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 11110 => 1
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1111 => 1
[1,1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0,0] => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 010100100 => 2
[1,1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3,1] => [[1,3,4],[2,6,7],[5,9,10],[8]] => 100100100 => 3
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000 => 1
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 10100100 => 1
[1,1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 10101000 => 2
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 1010100 => 2
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 101010 => 2
[1,1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 11001000 => 0
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 1100100 => 0
[1,1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 1101000 => 0
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 110100 => 0
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 11010 => 0
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1,1] => [[1,5,6,7,8,9,10],[2],[3],[4]] => 111000000 => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1,1] => [[1,5,6,7,8,9],[2],[3],[4]] => 11100000 => 1
[1,1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0,0] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 1110000 => 1
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 111000 => 1
[1,1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 11100 => 1
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 1110 => 1
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1,1] => [[1],[2],[3],[4]] => 111 => 1
[1,1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0,0] => [4,3,3] => [[1,2,3,10],[4,5,6],[7,8,9]] => 001001000 => 2
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 00100100 => 2
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0,0] => [4,4,2] => [[1,2,5,6],[3,4,9,10],[7,8]] => 010001000 => 3
[1,1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0,0] => [5,3,2] => [[1,2,5,9,10],[3,4,8],[6,7]] => 010010000 => 1
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0] => [4,3,2] => [[1,2,5,9],[3,4,8],[6,7]] => 01001000 => 1
[1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 0100100 => 1
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 0101000 => 2
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 010100 => 2
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0] => [2,2,2] => [[1,2],[3,4],[5,6]] => 01010 => 2
[1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0] => [5,4,1] => [[1,3,4,5,10],[2,7,8,9],[6]] => 100010000 => 2
[1,1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0,0] => [4,4,1] => [[1,3,4,5],[2,7,8,9],[6]] => 10001000 => 2
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0,0] => [6,3,1] => [[1,3,4,8,9,10],[2,6,7],[5]] => 100100000 => 0
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0] => [5,3,1] => [[1,3,4,8,9],[2,6,7],[5]] => 10010000 => 0
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 1001000 => 0
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 100100 => 0
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0] => [7,2,1] => [[1,3,6,7,8,9,10],[2,5],[4]] => 101000000 => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0,0] => [6,2,1] => [[1,3,6,7,8,9],[2,5],[4]] => 10100000 => 1
[1,1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0,0] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 1010000 => 1
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 101000 => 1
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0] => [3,2,1] => [[1,3,6],[2,5],[4]] => 10100 => 1
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0] => [2,2,1] => [[1,3],[2,5],[4]] => 1010 => 1
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0] => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 11000000 => 0
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0,0] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 1100000 => 0
[1,1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0,0] => [4,1,1] => [[1,4,5,6],[2],[3]] => 11000 => 0
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0] => [3,1,1] => [[1,4,5],[2],[3]] => 1100 => 0
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0] => [2,1,1] => [[1,4],[2],[3]] => 110 => 0
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => 11 => 0
[1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000 => 4
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0001000 => 3
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,0] => [7,3] => [[1,2,3,7,8,9,10],[4,5,6]] => 001000000 => 2
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0] => [4,3] => [[1,2,3,7],[4,5,6]] => 001000 => 2
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0] => [3,3] => [[1,2,3],[4,5,6]] => 00100 => 2
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0] => [7,2] => [[1,2,5,6,7,8,9],[3,4]] => 01000000 => 1
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0] => [4,2] => [[1,2,5,6],[3,4]] => 01000 => 1
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0] => [3,2] => [[1,2,5],[3,4]] => 0100 => 1
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0] => [2,2] => [[1,2],[3,4]] => 010 => 1
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0] => [7,1] => [[1,3,4,5,6,7,8],[2]] => 1000000 => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0] => [6,1] => [[1,3,4,5,6,7],[2]] => 100000 => 0
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0] => [5,1] => [[1,3,4,5,6],[2]] => 10000 => 0
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0] => [4,1] => [[1,3,4,5],[2]] => 1000 => 0
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0] => [3,1] => [[1,3,4],[2]] => 100 => 0
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [2,1] => [[1,3],[2]] => 10 => 0
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [1,1] => [[1],[2]] => 1 => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0] => [7] => [[1,2,3,4,5,6,7]] => 000000 => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0] => [6] => [[1,2,3,4,5,6]] => 00000 => 2
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0] => [5] => [[1,2,3,4,5]] => 0000 => 1
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [4] => [[1,2,3,4]] => 000 => 1
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [3] => [[1,2,3]] => 00 => 0
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [2] => [[1,2]] => 0 => 0
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0] => [1,1] => [[1],[2]] => 1 => 0
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0] => [2] => [[1,2]] => 0 => 0
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1] => [[1],[2]] => 1 => 0
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1] => [[1,3],[2,5],[4]] => 1010 => 1
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0] => [3,2] => [[1,2,5],[3,4]] => 0100 => 1
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0] => [2] => [[1,2]] => 0 => 0
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 1111111 => 3
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0] => [8] => [[1,2,3,4,5,6,7,8]] => 0000000 => 3
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0] => [9] => [[1,2,3,4,5,6,7,8,9]] => 00000000 => 3
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0] => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 10000000 => 0
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => 11 => 0
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1] => [[1],[2],[3],[4]] => 111 => 1
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1111 => 1
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 11111 => 2
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 111111 => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0] => [7] => [[1,2,3,4,5,6,7]] => 000000 => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0] => [6] => [[1,2,3,4,5,6]] => 00000 => 2
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0] => [5] => [[1,2,3,4,5]] => 0000 => 1
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0] => [4] => [[1,2,3,4]] => 000 => 1
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0] => [3] => [[1,2,3]] => 00 => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0,0] => [9,1] => [[1,3,4,5,6,7,8,9,10],[2]] => 100000000 => 0
[1,1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1,1] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 111111110 => 3
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0] => [2,2] => [[1,2],[3,4]] => 010 => 1
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0] => [3,3] => [[1,2,3],[4,5,6]] => 00100 => 2
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 00100100 => 2
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1] => [[1,4],[2],[3]] => 110 => 0
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1,1] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 11111110 => 3
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9]] => 11111111 => 3
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0] => [8,1,1] => [[1,4,5,6,7,8,9,10],[2],[3]] => 110000000 => 0
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1,1,1] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 111111100 => 3
[1,1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 111111010 => 2
[1,1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1,1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8],[9],[10]] => 111111111 => 4
[1,1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2] => [[1,2,5,9],[3,4,8],[6,7]] => 01001000 => 1
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0] => [3,1] => [[1,3,4],[2]] => 100 => 0
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 111110 => 2
[1,1,1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 1111100 => 2
[1,1,1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0] => [4,1,1,1,1,1] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 11111000 => 2
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0] => [5,1,1,1,1,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 111110000 => 2
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0] => [2,1] => [[1,3],[2]] => 10 => 0
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1] => [[1,3],[2]] => 10 => 0
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 101001000 => 1
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1] => [[1,3,6],[2,5],[4]] => 10100 => 1
[1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0] => [3] => [[1,2,3]] => 00 => 0
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0,0] => [7,2,1] => [[1,3,6,7,8,9,10],[2,5],[4]] => 101000000 => 1
[1,1,1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 111110100 => 2
[1,1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0,0] => [3,1] => [[1,3,4],[2]] => 100 => 0
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0] => [4,2] => [[1,2,5,6],[3,4]] => 01000 => 1
[1,1,1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0,0,0] => [5,4,1] => [[1,3,4,5,10],[2,7,8,9],[6]] => 100010000 => 2
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 1001000 => 0
[1,1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2] => [[1,2],[3,4],[5,6]] => 01010 => 2
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0] => [7,1] => [[1,3,4,5,6,7,8],[2]] => 1000000 => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0] => [6,1] => [[1,3,4,5,6,7],[2]] => 100000 => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0] => [5,1] => [[1,3,4,5,6],[2]] => 10000 => 0
[1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0] => [4,1] => [[1,3,4,5],[2]] => 1000 => 0
[1,1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 1110 => 1
[1,1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 11110 => 1
[1,1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 1111110 => 2
[1,1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0,0] => [2,1,1] => [[1,4],[2],[3]] => 110 => 0
[1,1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0,0] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 1010100 => 2
[1,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0,0] => [1,1,1] => [[1],[2],[3]] => 11 => 0
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0] => [3,1,1] => [[1,4,5],[2],[3]] => 1100 => 0
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 11010 => 0
[1,1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0,0] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 110100 => 0
[1,1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0,0] => [2,2] => [[1,2],[3,4]] => 010 => 1
[1,1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0,0] => [3,3] => [[1,2,3],[4,5,6]] => 00100 => 2
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0,0,0] => [3] => [[1,2,3]] => 00 => 0
[1,1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0,0] => [1,1] => [[1],[2]] => 1 => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0,0] => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 10000000 => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,0,0] => [7,1] => [[1,3,4,5,6,7,8],[2]] => 1000000 => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,0,0,0] => [6,1] => [[1,3,4,5,6,7],[2]] => 100000 => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0,0,0] => [5,1] => [[1,3,4,5,6],[2]] => 10000 => 0
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0,0,0,0] => [4,1] => [[1,3,4,5],[2]] => 1000 => 0
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0,0] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 000010000 => 4
[1,1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0,0] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 0001000 => 3
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,0,0] => [5,3,1] => [[1,3,4,8,9],[2,6,7],[5]] => 10010000 => 0
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 101010 => 2
[1,1,1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0,0,0] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 0100100 => 1
search for individual values
searching the database for the individual values of this statistic
Description
Half the length of the longest odd length palindromic prefix of a binary word.
More precisely, this statistic is the largest number $k$ such that the word has a palindromic prefix of length $2k+1$.
Map
to partition
Description
The cut-out partition of a Dyck path.
The partition $\lambda$ associated to a Dyck path is defined to be the complementary partition inside the staircase partition $(n-1,\ldots,2,1)$ when cutting out $D$ considered as a path from $(0,0)$ to $(n,n)$.
In other words, $\lambda_{i}$ is the number of down-steps before the $(n+1-i)$-th up-step of $D$.
This map is a bijection between Dyck paths of size $n$ and partitions inside the staircase partition $(n-1,\ldots,2,1)$.
Map
descent word
Description
The descent word of a standard Young tableau.
For a standard Young tableau of size $n$ we set $w_i=1$ if $i+1$ is in a lower row than $i$, and $0$ otherwise, for $1\leq i < n$.
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.