Values
0 => [2] => [2] => [[1,2]] => 2
1 => [1,1] => [1,1] => [[1],[2]] => 1
00 => [3] => [3] => [[1,2,3]] => 3
01 => [2,1] => [2,1] => [[1,3],[2]] => 2
10 => [1,2] => [2,1] => [[1,3],[2]] => 2
11 => [1,1,1] => [1,1,1] => [[1],[2],[3]] => 1
000 => [4] => [4] => [[1,2,3,4]] => 4
001 => [3,1] => [3,1] => [[1,3,4],[2]] => 3
010 => [2,2] => [2,2] => [[1,2],[3,4]] => 3
011 => [2,1,1] => [2,1,1] => [[1,4],[2],[3]] => 2
100 => [1,3] => [3,1] => [[1,3,4],[2]] => 3
101 => [1,2,1] => [2,1,1] => [[1,4],[2],[3]] => 2
110 => [1,1,2] => [2,1,1] => [[1,4],[2],[3]] => 2
111 => [1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 1
0000 => [5] => [5] => [[1,2,3,4,5]] => 5
0001 => [4,1] => [4,1] => [[1,3,4,5],[2]] => 4
0010 => [3,2] => [3,2] => [[1,2,5],[3,4]] => 4
0011 => [3,1,1] => [3,1,1] => [[1,4,5],[2],[3]] => 3
0100 => [2,3] => [3,2] => [[1,2,5],[3,4]] => 4
0101 => [2,2,1] => [2,2,1] => [[1,3],[2,5],[4]] => 3
0110 => [2,1,2] => [2,2,1] => [[1,3],[2,5],[4]] => 3
0111 => [2,1,1,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 2
1000 => [1,4] => [4,1] => [[1,3,4,5],[2]] => 4
1001 => [1,3,1] => [3,1,1] => [[1,4,5],[2],[3]] => 3
1010 => [1,2,2] => [2,2,1] => [[1,3],[2,5],[4]] => 3
1011 => [1,2,1,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 2
1100 => [1,1,3] => [3,1,1] => [[1,4,5],[2],[3]] => 3
1101 => [1,1,2,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 2
1110 => [1,1,1,2] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 2
1111 => [1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1
00000 => [6] => [6] => [[1,2,3,4,5,6]] => 6
00001 => [5,1] => [5,1] => [[1,3,4,5,6],[2]] => 5
00010 => [4,2] => [4,2] => [[1,2,5,6],[3,4]] => 5
00011 => [4,1,1] => [4,1,1] => [[1,4,5,6],[2],[3]] => 4
00100 => [3,3] => [3,3] => [[1,2,3],[4,5,6]] => 5
00101 => [3,2,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => 4
00110 => [3,1,2] => [3,2,1] => [[1,3,6],[2,5],[4]] => 4
00111 => [3,1,1,1] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 3
01000 => [2,4] => [4,2] => [[1,2,5,6],[3,4]] => 5
01001 => [2,3,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => 4
01010 => [2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 4
01011 => [2,2,1,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 3
01100 => [2,1,3] => [3,2,1] => [[1,3,6],[2,5],[4]] => 4
01101 => [2,1,2,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 3
01110 => [2,1,1,2] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 3
01111 => [2,1,1,1,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 2
10000 => [1,5] => [5,1] => [[1,3,4,5,6],[2]] => 5
10001 => [1,4,1] => [4,1,1] => [[1,4,5,6],[2],[3]] => 4
10010 => [1,3,2] => [3,2,1] => [[1,3,6],[2,5],[4]] => 4
10011 => [1,3,1,1] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 3
10100 => [1,2,3] => [3,2,1] => [[1,3,6],[2,5],[4]] => 4
10101 => [1,2,2,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 3
10110 => [1,2,1,2] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 3
10111 => [1,2,1,1,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 2
11000 => [1,1,4] => [4,1,1] => [[1,4,5,6],[2],[3]] => 4
11001 => [1,1,3,1] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 3
11010 => [1,1,2,2] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 3
11011 => [1,1,2,1,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 2
11100 => [1,1,1,3] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 3
11101 => [1,1,1,2,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 2
11110 => [1,1,1,1,2] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 2
11111 => [1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 1
000000 => [7] => [7] => [[1,2,3,4,5,6,7]] => 7
000001 => [6,1] => [6,1] => [[1,3,4,5,6,7],[2]] => 6
000010 => [5,2] => [5,2] => [[1,2,5,6,7],[3,4]] => 6
000011 => [5,1,1] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 5
000100 => [4,3] => [4,3] => [[1,2,3,7],[4,5,6]] => 6
000101 => [4,2,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 5
000110 => [4,1,2] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 5
000111 => [4,1,1,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 4
001000 => [3,4] => [4,3] => [[1,2,3,7],[4,5,6]] => 6
001001 => [3,3,1] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 5
001010 => [3,2,2] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 5
001011 => [3,2,1,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 4
001100 => [3,1,3] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 5
001101 => [3,1,2,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 4
001110 => [3,1,1,2] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 4
001111 => [3,1,1,1,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 3
010000 => [2,5] => [5,2] => [[1,2,5,6,7],[3,4]] => 6
010001 => [2,4,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 5
010010 => [2,3,2] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 5
010011 => [2,3,1,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 4
010100 => [2,2,3] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 5
010101 => [2,2,2,1] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 4
010110 => [2,2,1,2] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 4
010111 => [2,2,1,1,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 3
011000 => [2,1,4] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 5
011001 => [2,1,3,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 4
011010 => [2,1,2,2] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 4
011011 => [2,1,2,1,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 3
011100 => [2,1,1,3] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 4
011101 => [2,1,1,2,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 3
011110 => [2,1,1,1,2] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 3
011111 => [2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 2
100000 => [1,6] => [6,1] => [[1,3,4,5,6,7],[2]] => 6
100001 => [1,5,1] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 5
100010 => [1,4,2] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 5
100011 => [1,4,1,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 4
100100 => [1,3,3] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 5
100101 => [1,3,2,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 4
100110 => [1,3,1,2] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 4
>>> Load all 1136 entries. <<<
100111 => [1,3,1,1,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 3
101000 => [1,2,4] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 5
101001 => [1,2,3,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 4
101010 => [1,2,2,2] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 4
101011 => [1,2,2,1,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 3
101100 => [1,2,1,3] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 4
101101 => [1,2,1,2,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 3
101110 => [1,2,1,1,2] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 3
101111 => [1,2,1,1,1,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 2
110000 => [1,1,5] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 5
110001 => [1,1,4,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 4
110010 => [1,1,3,2] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 4
110011 => [1,1,3,1,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 3
110100 => [1,1,2,3] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 4
110101 => [1,1,2,2,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 3
110110 => [1,1,2,1,2] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 3
110111 => [1,1,2,1,1,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 2
111000 => [1,1,1,4] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 4
111001 => [1,1,1,3,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 3
111010 => [1,1,1,2,2] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 3
111011 => [1,1,1,2,1,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 2
111100 => [1,1,1,1,3] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 3
111101 => [1,1,1,1,2,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 2
111110 => [1,1,1,1,1,2] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 2
111111 => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 1
0000000 => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 8
0000001 => [7,1] => [7,1] => [[1,3,4,5,6,7,8],[2]] => 7
0000010 => [6,2] => [6,2] => [[1,2,5,6,7,8],[3,4]] => 7
0000011 => [6,1,1] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 6
0000100 => [5,3] => [5,3] => [[1,2,3,7,8],[4,5,6]] => 7
0000101 => [5,2,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 6
0000110 => [5,1,2] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 6
0000111 => [5,1,1,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 5
0001000 => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 7
0001001 => [4,3,1] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 6
0001010 => [4,2,2] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 6
0001011 => [4,2,1,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 5
0001100 => [4,1,3] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 6
0001101 => [4,1,2,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 5
0001110 => [4,1,1,2] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 5
0001111 => [4,1,1,1,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 4
0010000 => [3,5] => [5,3] => [[1,2,3,7,8],[4,5,6]] => 7
0010001 => [3,4,1] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 6
0010010 => [3,3,2] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 6
0010011 => [3,3,1,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 5
0010100 => [3,2,3] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 6
0010101 => [3,2,2,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 5
0010110 => [3,2,1,2] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 5
0010111 => [3,2,1,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
0011000 => [3,1,4] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 6
0011001 => [3,1,3,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 5
0011010 => [3,1,2,2] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 5
0011011 => [3,1,2,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
0011100 => [3,1,1,3] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 5
0011101 => [3,1,1,2,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
0011110 => [3,1,1,1,2] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
0011111 => [3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 3
0100000 => [2,6] => [6,2] => [[1,2,5,6,7,8],[3,4]] => 7
0100001 => [2,5,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 6
0100010 => [2,4,2] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 6
0100011 => [2,4,1,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 5
0100100 => [2,3,3] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 6
0100101 => [2,3,2,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 5
0100110 => [2,3,1,2] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 5
0100111 => [2,3,1,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
0101000 => [2,2,4] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 6
0101001 => [2,2,3,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 5
0101010 => [2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 5
0101011 => [2,2,2,1,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 4
0101100 => [2,2,1,3] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 5
0101101 => [2,2,1,2,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 4
0101110 => [2,2,1,1,2] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 4
0101111 => [2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 3
0110000 => [2,1,5] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 6
0110001 => [2,1,4,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 5
0110010 => [2,1,3,2] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 5
0110011 => [2,1,3,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
0110100 => [2,1,2,3] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 5
0110101 => [2,1,2,2,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 4
0110110 => [2,1,2,1,2] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 4
0110111 => [2,1,2,1,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 3
0111000 => [2,1,1,4] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 5
0111001 => [2,1,1,3,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
0111010 => [2,1,1,2,2] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 4
0111011 => [2,1,1,2,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 3
0111100 => [2,1,1,1,3] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
0111101 => [2,1,1,1,2,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 3
0111110 => [2,1,1,1,1,2] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 3
0111111 => [2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 2
1000000 => [1,7] => [7,1] => [[1,3,4,5,6,7,8],[2]] => 7
1000001 => [1,6,1] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 6
1000010 => [1,5,2] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 6
1000011 => [1,5,1,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 5
1000100 => [1,4,3] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 6
1000101 => [1,4,2,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 5
1000110 => [1,4,1,2] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 5
1000111 => [1,4,1,1,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 4
1001000 => [1,3,4] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 6
1001001 => [1,3,3,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 5
1001010 => [1,3,2,2] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 5
1001011 => [1,3,2,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
1001100 => [1,3,1,3] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 5
1001101 => [1,3,1,2,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
1001110 => [1,3,1,1,2] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
1001111 => [1,3,1,1,1,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 3
1010000 => [1,2,5] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 6
1010001 => [1,2,4,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 5
1010010 => [1,2,3,2] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 5
1010011 => [1,2,3,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
1010100 => [1,2,2,3] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 5
1010101 => [1,2,2,2,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 4
1010110 => [1,2,2,1,2] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 4
1010111 => [1,2,2,1,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 3
1011000 => [1,2,1,4] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 5
1011001 => [1,2,1,3,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
1011010 => [1,2,1,2,2] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 4
1011011 => [1,2,1,2,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 3
1011100 => [1,2,1,1,3] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
1011101 => [1,2,1,1,2,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 3
1011110 => [1,2,1,1,1,2] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 3
1011111 => [1,2,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 2
1100000 => [1,1,6] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 6
1100001 => [1,1,5,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 5
1100010 => [1,1,4,2] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 5
1100011 => [1,1,4,1,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 4
1100100 => [1,1,3,3] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 5
1100101 => [1,1,3,2,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
1100110 => [1,1,3,1,2] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
1100111 => [1,1,3,1,1,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 3
1101000 => [1,1,2,4] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 5
1101001 => [1,1,2,3,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
1101010 => [1,1,2,2,2] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 4
1101011 => [1,1,2,2,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 3
1101100 => [1,1,2,1,3] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
1101101 => [1,1,2,1,2,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 3
1101110 => [1,1,2,1,1,2] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 3
1101111 => [1,1,2,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 2
1110000 => [1,1,1,5] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 5
1110001 => [1,1,1,4,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 4
1110010 => [1,1,1,3,2] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
1110011 => [1,1,1,3,1,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 3
1110100 => [1,1,1,2,3] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
1110101 => [1,1,1,2,2,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 3
1110110 => [1,1,1,2,1,2] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 3
1110111 => [1,1,1,2,1,1,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 2
1111000 => [1,1,1,1,4] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 4
1111001 => [1,1,1,1,3,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 3
1111010 => [1,1,1,1,2,2] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 3
1111011 => [1,1,1,1,2,1,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 2
1111100 => [1,1,1,1,1,3] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 3
1111101 => [1,1,1,1,1,2,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 2
1111110 => [1,1,1,1,1,1,2] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 2
1111111 => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 1
00000000 => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 9
00000001 => [8,1] => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 8
00000010 => [7,2] => [7,2] => [[1,2,5,6,7,8,9],[3,4]] => 8
00000011 => [7,1,1] => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 7
00000100 => [6,3] => [6,3] => [[1,2,3,7,8,9],[4,5,6]] => 8
00000101 => [6,2,1] => [6,2,1] => [[1,3,6,7,8,9],[2,5],[4]] => 7
00000110 => [6,1,2] => [6,2,1] => [[1,3,6,7,8,9],[2,5],[4]] => 7
00000111 => [6,1,1,1] => [6,1,1,1] => [[1,5,6,7,8,9],[2],[3],[4]] => 6
00001000 => [5,4] => [5,4] => [[1,2,3,4,9],[5,6,7,8]] => 8
00001001 => [5,3,1] => [5,3,1] => [[1,3,4,8,9],[2,6,7],[5]] => 7
00001010 => [5,2,2] => [5,2,2] => [[1,2,7,8,9],[3,4],[5,6]] => 7
00001011 => [5,2,1,1] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 6
00001100 => [5,1,3] => [5,3,1] => [[1,3,4,8,9],[2,6,7],[5]] => 7
00001101 => [5,1,2,1] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 6
00001110 => [5,1,1,2] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 6
00001111 => [5,1,1,1,1] => [5,1,1,1,1] => [[1,6,7,8,9],[2],[3],[4],[5]] => 5
00010000 => [4,5] => [5,4] => [[1,2,3,4,9],[5,6,7,8]] => 8
00010001 => [4,4,1] => [4,4,1] => [[1,3,4,5],[2,7,8,9],[6]] => 7
00010010 => [4,3,2] => [4,3,2] => [[1,2,5,9],[3,4,8],[6,7]] => 7
00010011 => [4,3,1,1] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 6
00010100 => [4,2,3] => [4,3,2] => [[1,2,5,9],[3,4,8],[6,7]] => 7
00010101 => [4,2,2,1] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 6
00010110 => [4,2,1,2] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 6
00010111 => [4,2,1,1,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 5
00011000 => [4,1,4] => [4,4,1] => [[1,3,4,5],[2,7,8,9],[6]] => 7
00011001 => [4,1,3,1] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 6
00011010 => [4,1,2,2] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 6
00011011 => [4,1,2,1,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 5
00011100 => [4,1,1,3] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 6
00011101 => [4,1,1,2,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 5
00011110 => [4,1,1,1,2] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 5
00011111 => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 4
00100000 => [3,6] => [6,3] => [[1,2,3,7,8,9],[4,5,6]] => 8
00100001 => [3,5,1] => [5,3,1] => [[1,3,4,8,9],[2,6,7],[5]] => 7
00100010 => [3,4,2] => [4,3,2] => [[1,2,5,9],[3,4,8],[6,7]] => 7
00100011 => [3,4,1,1] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 6
00100100 => [3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 7
00100101 => [3,3,2,1] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 6
00100110 => [3,3,1,2] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 6
00100111 => [3,3,1,1,1] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 5
00101000 => [3,2,4] => [4,3,2] => [[1,2,5,9],[3,4,8],[6,7]] => 7
00101001 => [3,2,3,1] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 6
00101010 => [3,2,2,2] => [3,2,2,2] => [[1,2,9],[3,4],[5,6],[7,8]] => 6
00101011 => [3,2,2,1,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 5
00101100 => [3,2,1,3] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 6
00101101 => [3,2,1,2,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 5
00101110 => [3,2,1,1,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 5
00101111 => [3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 4
00110000 => [3,1,5] => [5,3,1] => [[1,3,4,8,9],[2,6,7],[5]] => 7
00110001 => [3,1,4,1] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 6
00110010 => [3,1,3,2] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 6
00110011 => [3,1,3,1,1] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 5
00110100 => [3,1,2,3] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 6
00110101 => [3,1,2,2,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 5
00110110 => [3,1,2,1,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 5
00110111 => [3,1,2,1,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 4
00111000 => [3,1,1,4] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 6
00111001 => [3,1,1,3,1] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 5
00111010 => [3,1,1,2,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 5
00111011 => [3,1,1,2,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 4
00111100 => [3,1,1,1,3] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 5
00111101 => [3,1,1,1,2,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 4
00111110 => [3,1,1,1,1,2] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 4
00111111 => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 3
01000000 => [2,7] => [7,2] => [[1,2,5,6,7,8,9],[3,4]] => 8
01000001 => [2,6,1] => [6,2,1] => [[1,3,6,7,8,9],[2,5],[4]] => 7
01000010 => [2,5,2] => [5,2,2] => [[1,2,7,8,9],[3,4],[5,6]] => 7
01000011 => [2,5,1,1] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 6
01000100 => [2,4,3] => [4,3,2] => [[1,2,5,9],[3,4,8],[6,7]] => 7
01000101 => [2,4,2,1] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 6
01000110 => [2,4,1,2] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 6
01000111 => [2,4,1,1,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 5
01001000 => [2,3,4] => [4,3,2] => [[1,2,5,9],[3,4,8],[6,7]] => 7
01001001 => [2,3,3,1] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 6
01001010 => [2,3,2,2] => [3,2,2,2] => [[1,2,9],[3,4],[5,6],[7,8]] => 6
01001011 => [2,3,2,1,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 5
01001100 => [2,3,1,3] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 6
01001101 => [2,3,1,2,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 5
01001110 => [2,3,1,1,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 5
01001111 => [2,3,1,1,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 4
01010000 => [2,2,5] => [5,2,2] => [[1,2,7,8,9],[3,4],[5,6]] => 7
01010001 => [2,2,4,1] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 6
01010010 => [2,2,3,2] => [3,2,2,2] => [[1,2,9],[3,4],[5,6],[7,8]] => 6
01010011 => [2,2,3,1,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 5
01010100 => [2,2,2,3] => [3,2,2,2] => [[1,2,9],[3,4],[5,6],[7,8]] => 6
01010101 => [2,2,2,2,1] => [2,2,2,2,1] => [[1,3],[2,5],[4,7],[6,9],[8]] => 5
01010110 => [2,2,2,1,2] => [2,2,2,2,1] => [[1,3],[2,5],[4,7],[6,9],[8]] => 5
01010111 => [2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 4
01011000 => [2,2,1,4] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 6
01011001 => [2,2,1,3,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 5
01011010 => [2,2,1,2,2] => [2,2,2,2,1] => [[1,3],[2,5],[4,7],[6,9],[8]] => 5
01011011 => [2,2,1,2,1,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 4
01011100 => [2,2,1,1,3] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 5
01011101 => [2,2,1,1,2,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 4
01011110 => [2,2,1,1,1,2] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 4
01011111 => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 3
01100000 => [2,1,6] => [6,2,1] => [[1,3,6,7,8,9],[2,5],[4]] => 7
01100001 => [2,1,5,1] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 6
01100010 => [2,1,4,2] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 6
01100011 => [2,1,4,1,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 5
01100100 => [2,1,3,3] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 6
01100101 => [2,1,3,2,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 5
01100110 => [2,1,3,1,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 5
01100111 => [2,1,3,1,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 4
01101000 => [2,1,2,4] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 6
01101001 => [2,1,2,3,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 5
01101010 => [2,1,2,2,2] => [2,2,2,2,1] => [[1,3],[2,5],[4,7],[6,9],[8]] => 5
01101011 => [2,1,2,2,1,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 4
01101100 => [2,1,2,1,3] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 5
01101101 => [2,1,2,1,2,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 4
01101110 => [2,1,2,1,1,2] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 4
01101111 => [2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 3
01110000 => [2,1,1,5] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 6
01110001 => [2,1,1,4,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 5
01110010 => [2,1,1,3,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 5
01110011 => [2,1,1,3,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 4
01110100 => [2,1,1,2,3] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 5
01110101 => [2,1,1,2,2,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 4
01110110 => [2,1,1,2,1,2] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 4
01110111 => [2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 3
01111000 => [2,1,1,1,4] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 5
01111001 => [2,1,1,1,3,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 4
01111010 => [2,1,1,1,2,2] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 4
01111011 => [2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 3
01111100 => [2,1,1,1,1,3] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 4
01111101 => [2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 3
01111110 => [2,1,1,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 3
01111111 => [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]] => 2
10000000 => [1,8] => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 8
10000001 => [1,7,1] => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 7
10000010 => [1,6,2] => [6,2,1] => [[1,3,6,7,8,9],[2,5],[4]] => 7
10000011 => [1,6,1,1] => [6,1,1,1] => [[1,5,6,7,8,9],[2],[3],[4]] => 6
10000100 => [1,5,3] => [5,3,1] => [[1,3,4,8,9],[2,6,7],[5]] => 7
10000101 => [1,5,2,1] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 6
10000110 => [1,5,1,2] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 6
10000111 => [1,5,1,1,1] => [5,1,1,1,1] => [[1,6,7,8,9],[2],[3],[4],[5]] => 5
10001000 => [1,4,4] => [4,4,1] => [[1,3,4,5],[2,7,8,9],[6]] => 7
10001001 => [1,4,3,1] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 6
10001010 => [1,4,2,2] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 6
10001011 => [1,4,2,1,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 5
10001100 => [1,4,1,3] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 6
10001101 => [1,4,1,2,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 5
10001110 => [1,4,1,1,2] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 5
10001111 => [1,4,1,1,1,1] => [4,1,1,1,1,1] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 4
10010000 => [1,3,5] => [5,3,1] => [[1,3,4,8,9],[2,6,7],[5]] => 7
10010001 => [1,3,4,1] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 6
10010010 => [1,3,3,2] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 6
10010011 => [1,3,3,1,1] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 5
10010100 => [1,3,2,3] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 6
10010101 => [1,3,2,2,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 5
10010110 => [1,3,2,1,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 5
10010111 => [1,3,2,1,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 4
10011000 => [1,3,1,4] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 6
10011001 => [1,3,1,3,1] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 5
10011010 => [1,3,1,2,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 5
10011011 => [1,3,1,2,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 4
10011100 => [1,3,1,1,3] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 5
10011101 => [1,3,1,1,2,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 4
10011110 => [1,3,1,1,1,2] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 4
10011111 => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 3
10100000 => [1,2,6] => [6,2,1] => [[1,3,6,7,8,9],[2,5],[4]] => 7
10100001 => [1,2,5,1] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 6
10100010 => [1,2,4,2] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 6
10100011 => [1,2,4,1,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 5
10100100 => [1,2,3,3] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 6
10100101 => [1,2,3,2,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 5
10100110 => [1,2,3,1,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 5
10100111 => [1,2,3,1,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 4
10101000 => [1,2,2,4] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 6
10101001 => [1,2,2,3,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 5
10101010 => [1,2,2,2,2] => [2,2,2,2,1] => [[1,3],[2,5],[4,7],[6,9],[8]] => 5
10101011 => [1,2,2,2,1,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 4
10101100 => [1,2,2,1,3] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 5
10101101 => [1,2,2,1,2,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 4
10101110 => [1,2,2,1,1,2] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 4
10101111 => [1,2,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 3
10110000 => [1,2,1,5] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 6
10110001 => [1,2,1,4,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 5
10110010 => [1,2,1,3,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 5
10110011 => [1,2,1,3,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 4
10110100 => [1,2,1,2,3] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 5
10110101 => [1,2,1,2,2,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 4
10110110 => [1,2,1,2,1,2] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 4
10110111 => [1,2,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 3
10111000 => [1,2,1,1,4] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 5
10111001 => [1,2,1,1,3,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 4
10111010 => [1,2,1,1,2,2] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 4
10111011 => [1,2,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 3
10111100 => [1,2,1,1,1,3] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 4
10111101 => [1,2,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 3
10111110 => [1,2,1,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 3
10111111 => [1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 2
11000000 => [1,1,7] => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 7
11000001 => [1,1,6,1] => [6,1,1,1] => [[1,5,6,7,8,9],[2],[3],[4]] => 6
11000010 => [1,1,5,2] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 6
11000011 => [1,1,5,1,1] => [5,1,1,1,1] => [[1,6,7,8,9],[2],[3],[4],[5]] => 5
11000100 => [1,1,4,3] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 6
11000101 => [1,1,4,2,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 5
11000110 => [1,1,4,1,2] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 5
11000111 => [1,1,4,1,1,1] => [4,1,1,1,1,1] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 4
11001000 => [1,1,3,4] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 6
11001001 => [1,1,3,3,1] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 5
11001010 => [1,1,3,2,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 5
11001011 => [1,1,3,2,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 4
11001100 => [1,1,3,1,3] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 5
11001101 => [1,1,3,1,2,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 4
11001110 => [1,1,3,1,1,2] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 4
11001111 => [1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 3
11010000 => [1,1,2,5] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 6
11010001 => [1,1,2,4,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 5
11010010 => [1,1,2,3,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 5
11010011 => [1,1,2,3,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 4
11010100 => [1,1,2,2,3] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 5
11010101 => [1,1,2,2,2,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 4
11010110 => [1,1,2,2,1,2] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 4
11010111 => [1,1,2,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 3
11011000 => [1,1,2,1,4] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 5
11011001 => [1,1,2,1,3,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 4
11011010 => [1,1,2,1,2,2] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 4
11011011 => [1,1,2,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 3
11011100 => [1,1,2,1,1,3] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 4
11011101 => [1,1,2,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 3
11011110 => [1,1,2,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 3
11011111 => [1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 2
11100000 => [1,1,1,6] => [6,1,1,1] => [[1,5,6,7,8,9],[2],[3],[4]] => 6
11100001 => [1,1,1,5,1] => [5,1,1,1,1] => [[1,6,7,8,9],[2],[3],[4],[5]] => 5
11100010 => [1,1,1,4,2] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 5
11100011 => [1,1,1,4,1,1] => [4,1,1,1,1,1] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 4
11100100 => [1,1,1,3,3] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 5
11100101 => [1,1,1,3,2,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 4
11100110 => [1,1,1,3,1,2] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 4
11100111 => [1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 3
11101000 => [1,1,1,2,4] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 5
11101001 => [1,1,1,2,3,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 4
11101010 => [1,1,1,2,2,2] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 4
11101011 => [1,1,1,2,2,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 3
11101100 => [1,1,1,2,1,3] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 4
11101101 => [1,1,1,2,1,2,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 3
11101110 => [1,1,1,2,1,1,2] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 3
11101111 => [1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 2
11110000 => [1,1,1,1,5] => [5,1,1,1,1] => [[1,6,7,8,9],[2],[3],[4],[5]] => 5
11110001 => [1,1,1,1,4,1] => [4,1,1,1,1,1] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 4
11110010 => [1,1,1,1,3,2] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 4
11110011 => [1,1,1,1,3,1,1] => [3,1,1,1,1,1,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 3
11110100 => [1,1,1,1,2,3] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 4
11110101 => [1,1,1,1,2,2,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 3
11110110 => [1,1,1,1,2,1,2] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 3
11110111 => [1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 2
11111000 => [1,1,1,1,1,4] => [4,1,1,1,1,1] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 4
11111001 => [1,1,1,1,1,3,1] => [3,1,1,1,1,1,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 3
11111010 => [1,1,1,1,1,2,2] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 3
11111011 => [1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 2
11111100 => [1,1,1,1,1,1,3] => [3,1,1,1,1,1,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 3
11111101 => [1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 2
11111110 => [1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1] => [[1,9],[2],[3],[4],[5],[6],[7],[8]] => 2
11111111 => [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]] => 1
000000000 => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 10
000000001 => [9,1] => [9,1] => [[1,3,4,5,6,7,8,9,10],[2]] => 9
000000010 => [8,2] => [8,2] => [[1,2,5,6,7,8,9,10],[3,4]] => 9
000000011 => [8,1,1] => [8,1,1] => [[1,4,5,6,7,8,9,10],[2],[3]] => 8
000000100 => [7,3] => [7,3] => [[1,2,3,7,8,9,10],[4,5,6]] => 9
000000101 => [7,2,1] => [7,2,1] => [[1,3,6,7,8,9,10],[2,5],[4]] => 8
000000110 => [7,1,2] => [7,2,1] => [[1,3,6,7,8,9,10],[2,5],[4]] => 8
000000111 => [7,1,1,1] => [7,1,1,1] => [[1,5,6,7,8,9,10],[2],[3],[4]] => 7
000001000 => [6,4] => [6,4] => [[1,2,3,4,9,10],[5,6,7,8]] => 9
000001001 => [6,3,1] => [6,3,1] => [[1,3,4,8,9,10],[2,6,7],[5]] => 8
000001010 => [6,2,2] => [6,2,2] => [[1,2,7,8,9,10],[3,4],[5,6]] => 8
000001011 => [6,2,1,1] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 7
000001100 => [6,1,3] => [6,3,1] => [[1,3,4,8,9,10],[2,6,7],[5]] => 8
000001101 => [6,1,2,1] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 7
000001110 => [6,1,1,2] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 7
000001111 => [6,1,1,1,1] => [6,1,1,1,1] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 6
000010000 => [5,5] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 9
000010001 => [5,4,1] => [5,4,1] => [[1,3,4,5,10],[2,7,8,9],[6]] => 8
000010010 => [5,3,2] => [5,3,2] => [[1,2,5,9,10],[3,4,8],[6,7]] => 8
000010011 => [5,3,1,1] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 7
000010100 => [5,2,3] => [5,3,2] => [[1,2,5,9,10],[3,4,8],[6,7]] => 8
000010101 => [5,2,2,1] => [5,2,2,1] => [[1,3,8,9,10],[2,5],[4,7],[6]] => 7
000010110 => [5,2,1,2] => [5,2,2,1] => [[1,3,8,9,10],[2,5],[4,7],[6]] => 7
000010111 => [5,2,1,1,1] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 6
000011000 => [5,1,4] => [5,4,1] => [[1,3,4,5,10],[2,7,8,9],[6]] => 8
000011001 => [5,1,3,1] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 7
000011010 => [5,1,2,2] => [5,2,2,1] => [[1,3,8,9,10],[2,5],[4,7],[6]] => 7
000011011 => [5,1,2,1,1] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 6
000011100 => [5,1,1,3] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 7
000011101 => [5,1,1,2,1] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 6
000011110 => [5,1,1,1,2] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 6
000011111 => [5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 5
000100000 => [4,6] => [6,4] => [[1,2,3,4,9,10],[5,6,7,8]] => 9
000100001 => [4,5,1] => [5,4,1] => [[1,3,4,5,10],[2,7,8,9],[6]] => 8
000100010 => [4,4,2] => [4,4,2] => [[1,2,5,6],[3,4,9,10],[7,8]] => 8
000100011 => [4,4,1,1] => [4,4,1,1] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 7
000100100 => [4,3,3] => [4,3,3] => [[1,2,3,10],[4,5,6],[7,8,9]] => 8
000100101 => [4,3,2,1] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 7
000100110 => [4,3,1,2] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 7
000100111 => [4,3,1,1,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 6
000101000 => [4,2,4] => [4,4,2] => [[1,2,5,6],[3,4,9,10],[7,8]] => 8
000101001 => [4,2,3,1] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 7
000101010 => [4,2,2,2] => [4,2,2,2] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 7
000101011 => [4,2,2,1,1] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 6
000101100 => [4,2,1,3] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 7
000101101 => [4,2,1,2,1] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 6
000101110 => [4,2,1,1,2] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 6
000101111 => [4,2,1,1,1,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
000110000 => [4,1,5] => [5,4,1] => [[1,3,4,5,10],[2,7,8,9],[6]] => 8
000110001 => [4,1,4,1] => [4,4,1,1] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 7
000110010 => [4,1,3,2] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 7
000110011 => [4,1,3,1,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 6
000110100 => [4,1,2,3] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 7
000110101 => [4,1,2,2,1] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 6
000110110 => [4,1,2,1,2] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 6
000110111 => [4,1,2,1,1,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
000111000 => [4,1,1,4] => [4,4,1,1] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 7
000111001 => [4,1,1,3,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 6
000111010 => [4,1,1,2,2] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 6
000111011 => [4,1,1,2,1,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
000111100 => [4,1,1,1,3] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 6
000111101 => [4,1,1,1,2,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
000111110 => [4,1,1,1,1,2] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
000111111 => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => 4
001000000 => [3,7] => [7,3] => [[1,2,3,7,8,9,10],[4,5,6]] => 9
001000001 => [3,6,1] => [6,3,1] => [[1,3,4,8,9,10],[2,6,7],[5]] => 8
001000010 => [3,5,2] => [5,3,2] => [[1,2,5,9,10],[3,4,8],[6,7]] => 8
001000011 => [3,5,1,1] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 7
001000100 => [3,4,3] => [4,3,3] => [[1,2,3,10],[4,5,6],[7,8,9]] => 8
001000101 => [3,4,2,1] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 7
001000110 => [3,4,1,2] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 7
001000111 => [3,4,1,1,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 6
001001000 => [3,3,4] => [4,3,3] => [[1,2,3,10],[4,5,6],[7,8,9]] => 8
001001001 => [3,3,3,1] => [3,3,3,1] => [[1,3,4],[2,6,7],[5,9,10],[8]] => 7
001001010 => [3,3,2,2] => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 7
001001011 => [3,3,2,1,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 6
001001100 => [3,3,1,3] => [3,3,3,1] => [[1,3,4],[2,6,7],[5,9,10],[8]] => 7
001001101 => [3,3,1,2,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 6
001001110 => [3,3,1,1,2] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 6
001001111 => [3,3,1,1,1,1] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
001010000 => [3,2,5] => [5,3,2] => [[1,2,5,9,10],[3,4,8],[6,7]] => 8
001010001 => [3,2,4,1] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 7
001010010 => [3,2,3,2] => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 7
001010011 => [3,2,3,1,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 6
001010100 => [3,2,2,3] => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 7
001010101 => [3,2,2,2,1] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 6
001010110 => [3,2,2,1,2] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 6
001010111 => [3,2,2,1,1,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
001011000 => [3,2,1,4] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 7
001011001 => [3,2,1,3,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 6
001011010 => [3,2,1,2,2] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 6
001011011 => [3,2,1,2,1,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
001011100 => [3,2,1,1,3] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 6
001011101 => [3,2,1,1,2,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
001011110 => [3,2,1,1,1,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
001011111 => [3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
001100000 => [3,1,6] => [6,3,1] => [[1,3,4,8,9,10],[2,6,7],[5]] => 8
001100001 => [3,1,5,1] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 7
001100010 => [3,1,4,2] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 7
001100011 => [3,1,4,1,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 6
001100100 => [3,1,3,3] => [3,3,3,1] => [[1,3,4],[2,6,7],[5,9,10],[8]] => 7
001100101 => [3,1,3,2,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 6
001100110 => [3,1,3,1,2] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 6
001100111 => [3,1,3,1,1,1] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
001101000 => [3,1,2,4] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 7
001101001 => [3,1,2,3,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 6
001101010 => [3,1,2,2,2] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 6
001101011 => [3,1,2,2,1,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
001101100 => [3,1,2,1,3] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 6
001101101 => [3,1,2,1,2,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
001101110 => [3,1,2,1,1,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
001101111 => [3,1,2,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
001110000 => [3,1,1,5] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 7
001110001 => [3,1,1,4,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 6
001110010 => [3,1,1,3,2] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 6
001110011 => [3,1,1,3,1,1] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
001110100 => [3,1,1,2,3] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 6
001110101 => [3,1,1,2,2,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
001110110 => [3,1,1,2,1,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
001110111 => [3,1,1,2,1,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
001111000 => [3,1,1,1,4] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 6
001111001 => [3,1,1,1,3,1] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
001111010 => [3,1,1,1,2,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
001111011 => [3,1,1,1,2,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
001111100 => [3,1,1,1,1,3] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
001111101 => [3,1,1,1,1,2,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
001111110 => [3,1,1,1,1,1,2] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
001111111 => [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]] => 3
010000000 => [2,8] => [8,2] => [[1,2,5,6,7,8,9,10],[3,4]] => 9
010000001 => [2,7,1] => [7,2,1] => [[1,3,6,7,8,9,10],[2,5],[4]] => 8
010000010 => [2,6,2] => [6,2,2] => [[1,2,7,8,9,10],[3,4],[5,6]] => 8
010000011 => [2,6,1,1] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 7
010000100 => [2,5,3] => [5,3,2] => [[1,2,5,9,10],[3,4,8],[6,7]] => 8
010000101 => [2,5,2,1] => [5,2,2,1] => [[1,3,8,9,10],[2,5],[4,7],[6]] => 7
010000110 => [2,5,1,2] => [5,2,2,1] => [[1,3,8,9,10],[2,5],[4,7],[6]] => 7
010000111 => [2,5,1,1,1] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 6
010001000 => [2,4,4] => [4,4,2] => [[1,2,5,6],[3,4,9,10],[7,8]] => 8
010001001 => [2,4,3,1] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 7
010001010 => [2,4,2,2] => [4,2,2,2] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 7
010001011 => [2,4,2,1,1] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 6
010001100 => [2,4,1,3] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 7
010001101 => [2,4,1,2,1] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 6
010001110 => [2,4,1,1,2] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 6
010001111 => [2,4,1,1,1,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
010010000 => [2,3,5] => [5,3,2] => [[1,2,5,9,10],[3,4,8],[6,7]] => 8
010010001 => [2,3,4,1] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 7
010010010 => [2,3,3,2] => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 7
010010011 => [2,3,3,1,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 6
010010100 => [2,3,2,3] => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 7
010010101 => [2,3,2,2,1] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 6
010010110 => [2,3,2,1,2] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 6
010010111 => [2,3,2,1,1,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
010011000 => [2,3,1,4] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 7
010011001 => [2,3,1,3,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 6
010011010 => [2,3,1,2,2] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 6
010011011 => [2,3,1,2,1,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
010011100 => [2,3,1,1,3] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 6
010011101 => [2,3,1,1,2,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
010011110 => [2,3,1,1,1,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
010011111 => [2,3,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
010100000 => [2,2,6] => [6,2,2] => [[1,2,7,8,9,10],[3,4],[5,6]] => 8
010100001 => [2,2,5,1] => [5,2,2,1] => [[1,3,8,9,10],[2,5],[4,7],[6]] => 7
010100010 => [2,2,4,2] => [4,2,2,2] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 7
010100011 => [2,2,4,1,1] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 6
010100100 => [2,2,3,3] => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 7
010100101 => [2,2,3,2,1] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 6
010100110 => [2,2,3,1,2] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 6
010100111 => [2,2,3,1,1,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
010101000 => [2,2,2,4] => [4,2,2,2] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 7
010101001 => [2,2,2,3,1] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 6
010101010 => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 6
010101011 => [2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
010101100 => [2,2,2,1,3] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 6
010101101 => [2,2,2,1,2,1] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
010101110 => [2,2,2,1,1,2] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
010101111 => [2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
010110000 => [2,2,1,5] => [5,2,2,1] => [[1,3,8,9,10],[2,5],[4,7],[6]] => 7
010110001 => [2,2,1,4,1] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 6
010110010 => [2,2,1,3,2] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 6
010110011 => [2,2,1,3,1,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
010110100 => [2,2,1,2,3] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 6
010110101 => [2,2,1,2,2,1] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
010110110 => [2,2,1,2,1,2] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
010110111 => [2,2,1,2,1,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
010111000 => [2,2,1,1,4] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 6
010111001 => [2,2,1,1,3,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
010111010 => [2,2,1,1,2,2] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
010111011 => [2,2,1,1,2,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
010111100 => [2,2,1,1,1,3] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
010111101 => [2,2,1,1,1,2,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
010111110 => [2,2,1,1,1,1,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
010111111 => [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]] => 3
011000000 => [2,1,7] => [7,2,1] => [[1,3,6,7,8,9,10],[2,5],[4]] => 8
011000001 => [2,1,6,1] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 7
011000010 => [2,1,5,2] => [5,2,2,1] => [[1,3,8,9,10],[2,5],[4,7],[6]] => 7
011000011 => [2,1,5,1,1] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 6
011000100 => [2,1,4,3] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 7
011000101 => [2,1,4,2,1] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 6
011000110 => [2,1,4,1,2] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 6
011000111 => [2,1,4,1,1,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
011001000 => [2,1,3,4] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 7
011001001 => [2,1,3,3,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 6
011001010 => [2,1,3,2,2] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 6
011001011 => [2,1,3,2,1,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
011001100 => [2,1,3,1,3] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 6
011001101 => [2,1,3,1,2,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
011001110 => [2,1,3,1,1,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
011001111 => [2,1,3,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
011010000 => [2,1,2,5] => [5,2,2,1] => [[1,3,8,9,10],[2,5],[4,7],[6]] => 7
011010001 => [2,1,2,4,1] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 6
011010010 => [2,1,2,3,2] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 6
011010011 => [2,1,2,3,1,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
011010100 => [2,1,2,2,3] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 6
011010101 => [2,1,2,2,2,1] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
011010110 => [2,1,2,2,1,2] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
011010111 => [2,1,2,2,1,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
011011000 => [2,1,2,1,4] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 6
011011001 => [2,1,2,1,3,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
011011010 => [2,1,2,1,2,2] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
011011011 => [2,1,2,1,2,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
011011100 => [2,1,2,1,1,3] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
011011101 => [2,1,2,1,1,2,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
011011110 => [2,1,2,1,1,1,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
011011111 => [2,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 3
011100000 => [2,1,1,6] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 7
011100001 => [2,1,1,5,1] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 6
011100010 => [2,1,1,4,2] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 6
011100011 => [2,1,1,4,1,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
011100100 => [2,1,1,3,3] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 6
011100101 => [2,1,1,3,2,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
011100110 => [2,1,1,3,1,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
011100111 => [2,1,1,3,1,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
011101000 => [2,1,1,2,4] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 6
011101001 => [2,1,1,2,3,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
011101010 => [2,1,1,2,2,2] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
011101011 => [2,1,1,2,2,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
011101100 => [2,1,1,2,1,3] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
011101101 => [2,1,1,2,1,2,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
011101110 => [2,1,1,2,1,1,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
011101111 => [2,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 3
011110000 => [2,1,1,1,5] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 6
011110001 => [2,1,1,1,4,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
011110010 => [2,1,1,1,3,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
011110011 => [2,1,1,1,3,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
011110100 => [2,1,1,1,2,3] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
011110101 => [2,1,1,1,2,2,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
011110110 => [2,1,1,1,2,1,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
011110111 => [2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 3
011111000 => [2,1,1,1,1,4] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
011111001 => [2,1,1,1,1,3,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
011111010 => [2,1,1,1,1,2,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
011111011 => [2,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 3
011111100 => [2,1,1,1,1,1,3] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
011111101 => [2,1,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 3
011111110 => [2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 3
011111111 => [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]] => 2
100000000 => [1,9] => [9,1] => [[1,3,4,5,6,7,8,9,10],[2]] => 9
100000001 => [1,8,1] => [8,1,1] => [[1,4,5,6,7,8,9,10],[2],[3]] => 8
100000010 => [1,7,2] => [7,2,1] => [[1,3,6,7,8,9,10],[2,5],[4]] => 8
100000011 => [1,7,1,1] => [7,1,1,1] => [[1,5,6,7,8,9,10],[2],[3],[4]] => 7
100000100 => [1,6,3] => [6,3,1] => [[1,3,4,8,9,10],[2,6,7],[5]] => 8
100000101 => [1,6,2,1] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 7
100000110 => [1,6,1,2] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 7
100000111 => [1,6,1,1,1] => [6,1,1,1,1] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 6
100001000 => [1,5,4] => [5,4,1] => [[1,3,4,5,10],[2,7,8,9],[6]] => 8
100001001 => [1,5,3,1] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 7
100001010 => [1,5,2,2] => [5,2,2,1] => [[1,3,8,9,10],[2,5],[4,7],[6]] => 7
100001011 => [1,5,2,1,1] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 6
100001100 => [1,5,1,3] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 7
100001101 => [1,5,1,2,1] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 6
100001110 => [1,5,1,1,2] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 6
100001111 => [1,5,1,1,1,1] => [5,1,1,1,1,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 5
100010000 => [1,4,5] => [5,4,1] => [[1,3,4,5,10],[2,7,8,9],[6]] => 8
100010001 => [1,4,4,1] => [4,4,1,1] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 7
100010010 => [1,4,3,2] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 7
100010011 => [1,4,3,1,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 6
100010100 => [1,4,2,3] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 7
100010101 => [1,4,2,2,1] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 6
100010110 => [1,4,2,1,2] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 6
100010111 => [1,4,2,1,1,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
100011000 => [1,4,1,4] => [4,4,1,1] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 7
100011001 => [1,4,1,3,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 6
100011010 => [1,4,1,2,2] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 6
100011011 => [1,4,1,2,1,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
100011100 => [1,4,1,1,3] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 6
100011101 => [1,4,1,1,2,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
100011110 => [1,4,1,1,1,2] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
100011111 => [1,4,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => 4
100100000 => [1,3,6] => [6,3,1] => [[1,3,4,8,9,10],[2,6,7],[5]] => 8
100100001 => [1,3,5,1] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 7
100100010 => [1,3,4,2] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 7
100100011 => [1,3,4,1,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 6
100100100 => [1,3,3,3] => [3,3,3,1] => [[1,3,4],[2,6,7],[5,9,10],[8]] => 7
100100101 => [1,3,3,2,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 6
100100110 => [1,3,3,1,2] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 6
100100111 => [1,3,3,1,1,1] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
100101000 => [1,3,2,4] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 7
100101001 => [1,3,2,3,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 6
100101010 => [1,3,2,2,2] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 6
100101011 => [1,3,2,2,1,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
100101100 => [1,3,2,1,3] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 6
100101101 => [1,3,2,1,2,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
100101110 => [1,3,2,1,1,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
100101111 => [1,3,2,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
100110000 => [1,3,1,5] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 7
100110001 => [1,3,1,4,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 6
100110010 => [1,3,1,3,2] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 6
100110011 => [1,3,1,3,1,1] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
100110100 => [1,3,1,2,3] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 6
100110101 => [1,3,1,2,2,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
100110110 => [1,3,1,2,1,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
100110111 => [1,3,1,2,1,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
100111000 => [1,3,1,1,4] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 6
100111001 => [1,3,1,1,3,1] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
100111010 => [1,3,1,1,2,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
100111011 => [1,3,1,1,2,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
100111100 => [1,3,1,1,1,3] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
100111101 => [1,3,1,1,1,2,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
100111110 => [1,3,1,1,1,1,2] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
100111111 => [1,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 3
101000000 => [1,2,7] => [7,2,1] => [[1,3,6,7,8,9,10],[2,5],[4]] => 8
101000001 => [1,2,6,1] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 7
101000010 => [1,2,5,2] => [5,2,2,1] => [[1,3,8,9,10],[2,5],[4,7],[6]] => 7
101000011 => [1,2,5,1,1] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 6
101000100 => [1,2,4,3] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 7
101000101 => [1,2,4,2,1] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 6
101000110 => [1,2,4,1,2] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 6
101000111 => [1,2,4,1,1,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
101001000 => [1,2,3,4] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 7
101001001 => [1,2,3,3,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 6
101001010 => [1,2,3,2,2] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 6
101001011 => [1,2,3,2,1,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
101001100 => [1,2,3,1,3] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 6
101001101 => [1,2,3,1,2,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
101001110 => [1,2,3,1,1,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
101001111 => [1,2,3,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
101010000 => [1,2,2,5] => [5,2,2,1] => [[1,3,8,9,10],[2,5],[4,7],[6]] => 7
101010001 => [1,2,2,4,1] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 6
101010010 => [1,2,2,3,2] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 6
101010011 => [1,2,2,3,1,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
101010100 => [1,2,2,2,3] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 6
101010101 => [1,2,2,2,2,1] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
101010110 => [1,2,2,2,1,2] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
101010111 => [1,2,2,2,1,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
101011000 => [1,2,2,1,4] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 6
101011001 => [1,2,2,1,3,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
101011010 => [1,2,2,1,2,2] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
101011011 => [1,2,2,1,2,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
101011100 => [1,2,2,1,1,3] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
101011101 => [1,2,2,1,1,2,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
101011110 => [1,2,2,1,1,1,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
101011111 => [1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 3
101100000 => [1,2,1,6] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 7
101100001 => [1,2,1,5,1] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 6
101100010 => [1,2,1,4,2] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 6
101100011 => [1,2,1,4,1,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
101100100 => [1,2,1,3,3] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 6
101100101 => [1,2,1,3,2,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
101100110 => [1,2,1,3,1,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
101100111 => [1,2,1,3,1,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
101101000 => [1,2,1,2,4] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 6
101101001 => [1,2,1,2,3,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
101101010 => [1,2,1,2,2,2] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
101101011 => [1,2,1,2,2,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
101101100 => [1,2,1,2,1,3] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
101101101 => [1,2,1,2,1,2,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
101101110 => [1,2,1,2,1,1,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
101101111 => [1,2,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 3
101110000 => [1,2,1,1,5] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 6
101110001 => [1,2,1,1,4,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
101110010 => [1,2,1,1,3,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
101110011 => [1,2,1,1,3,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
101110100 => [1,2,1,1,2,3] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
101110101 => [1,2,1,1,2,2,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
101110110 => [1,2,1,1,2,1,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
101110111 => [1,2,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 3
101111000 => [1,2,1,1,1,4] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
101111001 => [1,2,1,1,1,3,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
101111010 => [1,2,1,1,1,2,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
101111011 => [1,2,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 3
101111100 => [1,2,1,1,1,1,3] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
101111101 => [1,2,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 3
101111110 => [1,2,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 3
101111111 => [1,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 2
110000000 => [1,1,8] => [8,1,1] => [[1,4,5,6,7,8,9,10],[2],[3]] => 8
110000001 => [1,1,7,1] => [7,1,1,1] => [[1,5,6,7,8,9,10],[2],[3],[4]] => 7
110000010 => [1,1,6,2] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 7
110000011 => [1,1,6,1,1] => [6,1,1,1,1] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 6
110000100 => [1,1,5,3] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 7
110000101 => [1,1,5,2,1] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 6
110000110 => [1,1,5,1,2] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 6
110000111 => [1,1,5,1,1,1] => [5,1,1,1,1,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 5
110001000 => [1,1,4,4] => [4,4,1,1] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 7
110001001 => [1,1,4,3,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 6
110001010 => [1,1,4,2,2] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 6
110001011 => [1,1,4,2,1,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
110001100 => [1,1,4,1,3] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 6
110001101 => [1,1,4,1,2,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
110001110 => [1,1,4,1,1,2] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
110001111 => [1,1,4,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => 4
110010000 => [1,1,3,5] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 7
110010001 => [1,1,3,4,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 6
110010010 => [1,1,3,3,2] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 6
110010011 => [1,1,3,3,1,1] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
110010100 => [1,1,3,2,3] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 6
110010101 => [1,1,3,2,2,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
110010110 => [1,1,3,2,1,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
110010111 => [1,1,3,2,1,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
110011000 => [1,1,3,1,4] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 6
110011001 => [1,1,3,1,3,1] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
110011010 => [1,1,3,1,2,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
110011011 => [1,1,3,1,2,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
110011100 => [1,1,3,1,1,3] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
110011101 => [1,1,3,1,1,2,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
110011110 => [1,1,3,1,1,1,2] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
110011111 => [1,1,3,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 3
110100000 => [1,1,2,6] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 7
110100001 => [1,1,2,5,1] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 6
110100010 => [1,1,2,4,2] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 6
110100011 => [1,1,2,4,1,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
110100100 => [1,1,2,3,3] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 6
110100101 => [1,1,2,3,2,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
110100110 => [1,1,2,3,1,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
110100111 => [1,1,2,3,1,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
110101000 => [1,1,2,2,4] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 6
110101001 => [1,1,2,2,3,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
110101010 => [1,1,2,2,2,2] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
110101011 => [1,1,2,2,2,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
110101100 => [1,1,2,2,1,3] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
110101101 => [1,1,2,2,1,2,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
110101110 => [1,1,2,2,1,1,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
110101111 => [1,1,2,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 3
110110000 => [1,1,2,1,5] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 6
110110001 => [1,1,2,1,4,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
110110010 => [1,1,2,1,3,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
110110011 => [1,1,2,1,3,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
110110100 => [1,1,2,1,2,3] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
110110101 => [1,1,2,1,2,2,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
110110110 => [1,1,2,1,2,1,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
110110111 => [1,1,2,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 3
110111000 => [1,1,2,1,1,4] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
110111001 => [1,1,2,1,1,3,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
110111010 => [1,1,2,1,1,2,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
110111011 => [1,1,2,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 3
110111100 => [1,1,2,1,1,1,3] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
110111101 => [1,1,2,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 3
110111110 => [1,1,2,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 3
110111111 => [1,1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 2
111000000 => [1,1,1,7] => [7,1,1,1] => [[1,5,6,7,8,9,10],[2],[3],[4]] => 7
111000001 => [1,1,1,6,1] => [6,1,1,1,1] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 6
111000010 => [1,1,1,5,2] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 6
111000011 => [1,1,1,5,1,1] => [5,1,1,1,1,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 5
111000100 => [1,1,1,4,3] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 6
111000101 => [1,1,1,4,2,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
111000110 => [1,1,1,4,1,2] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
111000111 => [1,1,1,4,1,1,1] => [4,1,1,1,1,1,1] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => 4
111001000 => [1,1,1,3,4] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 6
111001001 => [1,1,1,3,3,1] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
111001010 => [1,1,1,3,2,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
111001011 => [1,1,1,3,2,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
111001100 => [1,1,1,3,1,3] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
111001101 => [1,1,1,3,1,2,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
111001110 => [1,1,1,3,1,1,2] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
111001111 => [1,1,1,3,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 3
111010000 => [1,1,1,2,5] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 6
111010001 => [1,1,1,2,4,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
111010010 => [1,1,1,2,3,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
111010011 => [1,1,1,2,3,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
111010100 => [1,1,1,2,2,3] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
111010101 => [1,1,1,2,2,2,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
111010110 => [1,1,1,2,2,1,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
111010111 => [1,1,1,2,2,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 3
111011000 => [1,1,1,2,1,4] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
111011001 => [1,1,1,2,1,3,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
111011010 => [1,1,1,2,1,2,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
111011011 => [1,1,1,2,1,2,1,1] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 3
111011100 => [1,1,1,2,1,1,3] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
111011101 => [1,1,1,2,1,1,2,1] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 3
111011110 => [1,1,1,2,1,1,1,2] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 3
111011111 => [1,1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 2
111100000 => [1,1,1,1,6] => [6,1,1,1,1] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 6
111100001 => [1,1,1,1,5,1] => [5,1,1,1,1,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 5
111100010 => [1,1,1,1,4,2] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
111100011 => [1,1,1,1,4,1,1] => [4,1,1,1,1,1,1] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => 4
111100100 => [1,1,1,1,3,3] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
111100101 => [1,1,1,1,3,2,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
111100110 => [1,1,1,1,3,1,2] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
111100111 => [1,1,1,1,3,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 3
111101000 => [1,1,1,1,2,4] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
111101001 => [1,1,1,1,2,3,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
111101010 => [1,1,1,1,2,2,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 4
111101011 => [1,1,1,1,2,2,1,1] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 3
111101100 => [1,1,1,1,2,1,3] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
111101101 => [1,1,1,1,2,1,2,1] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 3
111101110 => [1,1,1,1,2,1,1,2] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 3
111101111 => [1,1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 2
111110000 => [1,1,1,1,1,5] => [5,1,1,1,1,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 5
111110001 => [1,1,1,1,1,4,1] => [4,1,1,1,1,1,1] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => 4
111110010 => [1,1,1,1,1,3,2] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
111110011 => [1,1,1,1,1,3,1,1] => [3,1,1,1,1,1,1,1] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 3
111110100 => [1,1,1,1,1,2,3] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 4
111110101 => [1,1,1,1,1,2,2,1] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 3
111110110 => [1,1,1,1,1,2,1,2] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 3
111110111 => [1,1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 2
111111000 => [1,1,1,1,1,1,4] => [4,1,1,1,1,1,1] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => 4
111111001 => [1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 3
111111010 => [1,1,1,1,1,1,2,2] => [2,2,1,1,1,1,1,1] => [[1,8],[2,10],[3],[4],[5],[6],[7],[9]] => 3
111111011 => [1,1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 2
111111100 => [1,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,1] => [[1,9,10],[2],[3],[4],[5],[6],[7],[8]] => 3
111111101 => [1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 2
111111110 => [1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1] => [[1,10],[2],[3],[4],[5],[6],[7],[8],[9]] => 2
111111111 => [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]] => 1
1010010001 => [1,2,3,4,1] => [4,3,2,1,1] => [[1,4,7,11],[2,6,10],[3,9],[5],[8]] => 7
1010000101 => [1,2,5,2,1] => [5,2,2,1,1] => [[1,4,9,10,11],[2,6],[3,8],[5],[7]] => 7
1001100001 => [1,3,1,5,1] => [5,3,1,1,1] => [[1,5,6,10,11],[2,8,9],[3],[4],[7]] => 7
1000110001 => [1,4,1,4,1] => [4,4,1,1,1] => [[1,5,6,7],[2,9,10,11],[3],[4],[8]] => 7
1000100101 => [1,4,3,2,1] => [4,3,2,1,1] => [[1,4,7,11],[2,6,10],[3,9],[5],[8]] => 7
1000011001 => [1,5,1,3,1] => [5,3,1,1,1] => [[1,5,6,10,11],[2,8,9],[3],[4],[7]] => 7
1000010110 => [1,5,2,1,2] => [5,2,2,1,1] => [[1,4,9,10,11],[2,6],[3,8],[5],[7]] => 7
10000100010 => [1,5,4,2] => [5,4,2,1] => [[1,3,6,7,12],[2,5,10,11],[4,9],[8]] => 9
10001000010 => [1,4,5,2] => [5,4,2,1] => [[1,3,6,7,12],[2,5,10,11],[4,9],[8]] => 9
10000100100 => [1,5,3,3] => [5,3,3,1] => [[1,3,4,11,12],[2,6,7],[5,9,10],[8]] => 9
10001001010 => [1,4,3,2,2] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 8
10001000100 => [1,4,4,3] => [4,4,3,1] => [[1,3,4,8],[2,6,7,12],[5,10,11],[9]] => 9
10000101000 => [1,5,2,4] => [5,4,2,1] => [[1,3,6,7,12],[2,5,10,11],[4,9],[8]] => 9
10010001010 => [1,3,4,2,2] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 8
10001010010 => [1,4,2,3,2] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 8
10010000100 => [1,3,5,3] => [5,3,3,1] => [[1,3,4,11,12],[2,6,7],[5,9,10],[8]] => 9
10001001000 => [1,4,3,4] => [4,4,3,1] => [[1,3,4,8],[2,6,7,12],[5,10,11],[9]] => 9
10010010010 => [1,3,3,3,2] => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 8
10001010100 => [1,4,2,2,3] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 8
10010001000 => [1,3,4,4] => [4,4,3,1] => [[1,3,4,8],[2,6,7,12],[5,10,11],[9]] => 9
10100010010 => [1,2,4,3,2] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 8
10010100010 => [1,3,2,4,2] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 8
10010010100 => [1,3,3,2,3] => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 8
=> [1] => [1] => [[1]] => 1
0110100001 => [2,1,2,5,1] => [5,2,2,1,1] => [[1,4,9,10,11],[2,6],[3,8],[5],[7]] => 7
11010100100 => [1,1,2,2,3,3] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 7
11010010100 => [1,1,2,3,2,3] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 7
11001010100 => [1,1,3,2,2,3] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 7
100010010001 => [1,4,3,4,1] => [4,4,3,1,1] => [[1,4,5,9],[2,7,8,13],[3,11,12],[6],[10]] => 9
100010000101 => [1,4,5,2,1] => [5,4,2,1,1] => [[1,4,7,8,13],[2,6,11,12],[3,10],[5],[9]] => 9
101000010001 => [1,2,5,4,1] => [5,4,2,1,1] => [[1,4,7,8,13],[2,6,11,12],[3,10],[5],[9]] => 9
00101010011 => [3,2,2,3,1,1] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 7
00100101011 => [3,3,2,2,1,1] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 7
00000000000 => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 12
10101001001 => [1,2,2,3,3,1] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 7
10101000100 => [1,2,2,4,3] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 8
10100100101 => [1,2,3,3,2,1] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 7
10100100010 => [1,2,3,4,2] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 8
10100101001 => [1,2,3,2,3,1] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 7
10100100100 => [1,2,3,3,3] => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 8
10100010001 => [1,2,4,4,1] => [4,4,2,1,1] => [[1,4,7,8],[2,6,11,12],[3,10],[5],[9]] => 8
10100010100 => [1,2,4,2,3] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 8
10100001000 => [1,2,5,4] => [5,4,2,1] => [[1,3,6,7,12],[2,5,10,11],[4,9],[8]] => 9
10010010101 => [1,3,3,2,2,1] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 7
10010001001 => [1,3,4,3,1] => [4,3,3,1,1] => [[1,4,5,12],[2,7,8],[3,10,11],[6],[9]] => 8
10010100101 => [1,3,2,3,2,1] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 7
10010101001 => [1,3,2,2,3,1] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 7
10010100100 => [1,3,2,3,3] => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 8
10010010001 => [1,3,3,4,1] => [4,3,3,1,1] => [[1,4,5,12],[2,7,8],[3,10,11],[6],[9]] => 8
10001000101 => [1,4,4,2,1] => [4,4,2,1,1] => [[1,4,7,8],[2,6,11,12],[3,10],[5],[9]] => 8
10001001001 => [1,4,3,3,1] => [4,3,3,1,1] => [[1,4,5,12],[2,7,8],[3,10,11],[6],[9]] => 8
10001010001 => [1,4,2,4,1] => [4,4,2,1,1] => [[1,4,7,8],[2,6,11,12],[3,10],[5],[9]] => 8
01001001001 => [2,3,3,3,1] => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 8
01001000100 => [2,3,4,3] => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 9
01000100101 => [2,4,3,2,1] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 8
01000100010 => [2,4,4,2] => [4,4,2,2] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 9
01000101001 => [2,4,2,3,1] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 8
01000100100 => [2,4,3,3] => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 9
01000010001 => [2,5,4,1] => [5,4,2,1] => [[1,3,6,7,12],[2,5,10,11],[4,9],[8]] => 9
01000010010 => [2,5,3,2] => [5,3,2,2] => [[1,2,7,11,12],[3,4,10],[5,6],[8,9]] => 9
01000010100 => [2,5,2,3] => [5,3,2,2] => [[1,2,7,11,12],[3,4,10],[5,6],[8,9]] => 9
01000001000 => [2,6,4] => [6,4,2] => [[1,2,5,6,11,12],[3,4,9,10],[7,8]] => 10
01010001001 => [2,2,4,3,1] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 8
01010000100 => [2,2,5,3] => [5,3,2,2] => [[1,2,7,11,12],[3,4,10],[5,6],[8,9]] => 9
01010101010 => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 7
01010010001 => [2,2,3,4,1] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 8
01010001000 => [2,2,4,4] => [4,4,2,2] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 9
01001000101 => [2,3,4,2,1] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 8
01001000010 => [2,3,5,2] => [5,3,2,2] => [[1,2,7,11,12],[3,4,10],[5,6],[8,9]] => 9
01001010001 => [2,3,2,4,1] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 8
01001001000 => [2,3,3,4] => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 9
01000100001 => [2,4,5,1] => [5,4,2,1] => [[1,3,6,7,12],[2,5,10,11],[4,9],[8]] => 9
01000101000 => [2,4,2,4] => [4,4,2,2] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 9
00100010101 => [3,4,2,2,1] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 8
00100010010 => [3,4,3,2] => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 9
00100001001 => [3,5,3,1] => [5,3,3,1] => [[1,3,4,11,12],[2,6,7],[5,9,10],[8]] => 9
00100001010 => [3,5,2,2] => [5,3,2,2] => [[1,2,7,11,12],[3,4,10],[5,6],[8,9]] => 9
00100100101 => [3,3,3,2,1] => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 8
00100100010 => [3,3,4,2] => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 9
00100101001 => [3,3,2,3,1] => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 8
00100010001 => [3,4,4,1] => [4,4,3,1] => [[1,3,4,8],[2,6,7,12],[5,10,11],[9]] => 9
00100010100 => [3,4,2,3] => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 9
00100001000 => [3,5,4] => [5,4,3] => [[1,2,3,7,12],[4,5,6,11],[8,9,10]] => 10
00101000101 => [3,2,4,2,1] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 8
00101000010 => [3,2,5,2] => [5,3,2,2] => [[1,2,7,11,12],[3,4,10],[5,6],[8,9]] => 9
00101001001 => [3,2,3,3,1] => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 8
00101000100 => [3,2,4,3] => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 9
00101010001 => [3,2,2,4,1] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 8
00101001000 => [3,2,3,4] => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 9
00100100001 => [3,3,5,1] => [5,3,3,1] => [[1,3,4,11,12],[2,6,7],[5,9,10],[8]] => 9
00100101000 => [3,3,2,4] => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 9
00100010000 => [3,4,5] => [5,4,3] => [[1,2,3,7,12],[4,5,6,11],[8,9,10]] => 10
00010000101 => [4,5,2,1] => [5,4,2,1] => [[1,3,6,7,12],[2,5,10,11],[4,9],[8]] => 9
00010000010 => [4,6,2] => [6,4,2] => [[1,2,5,6,11,12],[3,4,9,10],[7,8]] => 10
00010001001 => [4,4,3,1] => [4,4,3,1] => [[1,3,4,8],[2,6,7,12],[5,10,11],[9]] => 9
00010001010 => [4,4,2,2] => [4,4,2,2] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 9
00010000100 => [4,5,3] => [5,4,3] => [[1,2,3,7,12],[4,5,6,11],[8,9,10]] => 10
00010010001 => [4,3,4,1] => [4,4,3,1] => [[1,3,4,8],[2,6,7,12],[5,10,11],[9]] => 9
00010010010 => [4,3,3,2] => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 9
00010010100 => [4,3,2,3] => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 9
00010100001 => [4,2,5,1] => [5,4,2,1] => [[1,3,6,7,12],[2,5,10,11],[4,9],[8]] => 9
00010100010 => [4,2,4,2] => [4,4,2,2] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 9
00010100100 => [4,2,3,3] => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 9
00010101000 => [4,2,2,4] => [4,4,2,2] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 9
00010010000 => [4,3,5] => [5,4,3] => [[1,2,3,7,12],[4,5,6,11],[8,9,10]] => 10
00001000100 => [5,4,3] => [5,4,3] => [[1,2,3,7,12],[4,5,6,11],[8,9,10]] => 10
00001001000 => [5,3,4] => [5,4,3] => [[1,2,3,7,12],[4,5,6,11],[8,9,10]] => 10
00000100000 => [6,6] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 11
00010010101 => [4,3,2,2,1] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 8
00010100101 => [4,2,3,2,1] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 8
00010101001 => [4,2,2,3,1] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 8
00000100010 => [6,4,2] => [6,4,2] => [[1,2,5,6,11,12],[3,4,9,10],[7,8]] => 10
00001010101 => [5,2,2,2,1] => [5,2,2,2,1] => [[1,3,10,11,12],[2,5],[4,7],[6,9],[8]] => 8
11010000100 => [1,1,2,5,3] => [5,3,2,1,1] => [[1,4,7,11,12],[2,6,10],[3,9],[5],[8]] => 8
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Description
The number of ascents of a standard tableau.
Entry $i$ of a standard Young tableau is an ascent if $i+1$ appears to the right or above $i$ in the tableau (with respect to the English notation for tableaux).
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
to partition
Description
Sends a composition to the partition obtained by sorting the entries.
Map
to composition
Description
The composition corresponding to a binary word.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.