Identifier
-
Mp00097:
Binary words
—delta morphism⟶
Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
Mp00045: Integer partitions —reading tableau⟶ Standard tableaux
St000157: Standard tableaux ⟶ ℤ
Values
0 => [1] => [1] => [[1]] => 0
1 => [1] => [1] => [[1]] => 0
00 => [2] => [2] => [[1,2]] => 0
01 => [1,1] => [1,1] => [[1],[2]] => 1
10 => [1,1] => [1,1] => [[1],[2]] => 1
11 => [2] => [2] => [[1,2]] => 0
000 => [3] => [3] => [[1,2,3]] => 0
001 => [2,1] => [2,1] => [[1,3],[2]] => 1
010 => [1,1,1] => [1,1,1] => [[1],[2],[3]] => 2
011 => [1,2] => [2,1] => [[1,3],[2]] => 1
100 => [1,2] => [2,1] => [[1,3],[2]] => 1
101 => [1,1,1] => [1,1,1] => [[1],[2],[3]] => 2
110 => [2,1] => [2,1] => [[1,3],[2]] => 1
111 => [3] => [3] => [[1,2,3]] => 0
0000 => [4] => [4] => [[1,2,3,4]] => 0
0001 => [3,1] => [3,1] => [[1,3,4],[2]] => 1
0010 => [2,1,1] => [2,1,1] => [[1,4],[2],[3]] => 2
0011 => [2,2] => [2,2] => [[1,2],[3,4]] => 1
0100 => [1,1,2] => [2,1,1] => [[1,4],[2],[3]] => 2
0101 => [1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 3
0110 => [1,2,1] => [2,1,1] => [[1,4],[2],[3]] => 2
0111 => [1,3] => [3,1] => [[1,3,4],[2]] => 1
1000 => [1,3] => [3,1] => [[1,3,4],[2]] => 1
1001 => [1,2,1] => [2,1,1] => [[1,4],[2],[3]] => 2
1010 => [1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 3
1011 => [1,1,2] => [2,1,1] => [[1,4],[2],[3]] => 2
1100 => [2,2] => [2,2] => [[1,2],[3,4]] => 1
1101 => [2,1,1] => [2,1,1] => [[1,4],[2],[3]] => 2
1110 => [3,1] => [3,1] => [[1,3,4],[2]] => 1
1111 => [4] => [4] => [[1,2,3,4]] => 0
00000 => [5] => [5] => [[1,2,3,4,5]] => 0
00001 => [4,1] => [4,1] => [[1,3,4,5],[2]] => 1
00010 => [3,1,1] => [3,1,1] => [[1,4,5],[2],[3]] => 2
00011 => [3,2] => [3,2] => [[1,2,5],[3,4]] => 1
00100 => [2,1,2] => [2,2,1] => [[1,3],[2,5],[4]] => 2
00101 => [2,1,1,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 3
00110 => [2,2,1] => [2,2,1] => [[1,3],[2,5],[4]] => 2
00111 => [2,3] => [3,2] => [[1,2,5],[3,4]] => 1
01000 => [1,1,3] => [3,1,1] => [[1,4,5],[2],[3]] => 2
01001 => [1,1,2,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 3
01010 => [1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 4
01011 => [1,1,1,2] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 3
01100 => [1,2,2] => [2,2,1] => [[1,3],[2,5],[4]] => 2
01101 => [1,2,1,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 3
01110 => [1,3,1] => [3,1,1] => [[1,4,5],[2],[3]] => 2
01111 => [1,4] => [4,1] => [[1,3,4,5],[2]] => 1
10000 => [1,4] => [4,1] => [[1,3,4,5],[2]] => 1
10001 => [1,3,1] => [3,1,1] => [[1,4,5],[2],[3]] => 2
10010 => [1,2,1,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 3
10011 => [1,2,2] => [2,2,1] => [[1,3],[2,5],[4]] => 2
10100 => [1,1,1,2] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 3
10101 => [1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 4
10110 => [1,1,2,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 3
10111 => [1,1,3] => [3,1,1] => [[1,4,5],[2],[3]] => 2
11000 => [2,3] => [3,2] => [[1,2,5],[3,4]] => 1
11001 => [2,2,1] => [2,2,1] => [[1,3],[2,5],[4]] => 2
11010 => [2,1,1,1] => [2,1,1,1] => [[1,5],[2],[3],[4]] => 3
11011 => [2,1,2] => [2,2,1] => [[1,3],[2,5],[4]] => 2
11100 => [3,2] => [3,2] => [[1,2,5],[3,4]] => 1
11101 => [3,1,1] => [3,1,1] => [[1,4,5],[2],[3]] => 2
11110 => [4,1] => [4,1] => [[1,3,4,5],[2]] => 1
11111 => [5] => [5] => [[1,2,3,4,5]] => 0
000000 => [6] => [6] => [[1,2,3,4,5,6]] => 0
000001 => [5,1] => [5,1] => [[1,3,4,5,6],[2]] => 1
000010 => [4,1,1] => [4,1,1] => [[1,4,5,6],[2],[3]] => 2
000011 => [4,2] => [4,2] => [[1,2,5,6],[3,4]] => 1
000100 => [3,1,2] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
000101 => [3,1,1,1] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 3
000110 => [3,2,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
000111 => [3,3] => [3,3] => [[1,2,3],[4,5,6]] => 1
001000 => [2,1,3] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
001001 => [2,1,2,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 3
001010 => [2,1,1,1,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 4
001011 => [2,1,1,2] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 3
001100 => [2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 2
001101 => [2,2,1,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 3
001110 => [2,3,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
001111 => [2,4] => [4,2] => [[1,2,5,6],[3,4]] => 1
010000 => [1,1,4] => [4,1,1] => [[1,4,5,6],[2],[3]] => 2
010001 => [1,1,3,1] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 3
010010 => [1,1,2,1,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 4
010011 => [1,1,2,2] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 3
010100 => [1,1,1,1,2] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 4
010101 => [1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 5
010110 => [1,1,1,2,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 4
010111 => [1,1,1,3] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 3
011000 => [1,2,3] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
011001 => [1,2,2,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 3
011010 => [1,2,1,1,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 4
011011 => [1,2,1,2] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 3
011100 => [1,3,2] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
011101 => [1,3,1,1] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 3
011110 => [1,4,1] => [4,1,1] => [[1,4,5,6],[2],[3]] => 2
011111 => [1,5] => [5,1] => [[1,3,4,5,6],[2]] => 1
100000 => [1,5] => [5,1] => [[1,3,4,5,6],[2]] => 1
100001 => [1,4,1] => [4,1,1] => [[1,4,5,6],[2],[3]] => 2
100010 => [1,3,1,1] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 3
100011 => [1,3,2] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
100100 => [1,2,1,2] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 3
100101 => [1,2,1,1,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 4
100110 => [1,2,2,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 3
>>> Load all 1816 entries. <<<100111 => [1,2,3] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
101000 => [1,1,1,3] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 3
101001 => [1,1,1,2,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 4
101010 => [1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 5
101011 => [1,1,1,1,2] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 4
101100 => [1,1,2,2] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 3
101101 => [1,1,2,1,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 4
101110 => [1,1,3,1] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 3
101111 => [1,1,4] => [4,1,1] => [[1,4,5,6],[2],[3]] => 2
110000 => [2,4] => [4,2] => [[1,2,5,6],[3,4]] => 1
110001 => [2,3,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
110010 => [2,2,1,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 3
110011 => [2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 2
110100 => [2,1,1,2] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 3
110101 => [2,1,1,1,1] => [2,1,1,1,1] => [[1,6],[2],[3],[4],[5]] => 4
110110 => [2,1,2,1] => [2,2,1,1] => [[1,4],[2,6],[3],[5]] => 3
110111 => [2,1,3] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
111000 => [3,3] => [3,3] => [[1,2,3],[4,5,6]] => 1
111001 => [3,2,1] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
111010 => [3,1,1,1] => [3,1,1,1] => [[1,5,6],[2],[3],[4]] => 3
111011 => [3,1,2] => [3,2,1] => [[1,3,6],[2,5],[4]] => 2
111100 => [4,2] => [4,2] => [[1,2,5,6],[3,4]] => 1
111101 => [4,1,1] => [4,1,1] => [[1,4,5,6],[2],[3]] => 2
111110 => [5,1] => [5,1] => [[1,3,4,5,6],[2]] => 1
111111 => [6] => [6] => [[1,2,3,4,5,6]] => 0
0000000 => [7] => [7] => [[1,2,3,4,5,6,7]] => 0
0000001 => [6,1] => [6,1] => [[1,3,4,5,6,7],[2]] => 1
0000010 => [5,1,1] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 2
0000011 => [5,2] => [5,2] => [[1,2,5,6,7],[3,4]] => 1
0000100 => [4,1,2] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 2
0000101 => [4,1,1,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
0000110 => [4,2,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 2
0000111 => [4,3] => [4,3] => [[1,2,3,7],[4,5,6]] => 1
0001000 => [3,1,3] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 2
0001001 => [3,1,2,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 3
0001010 => [3,1,1,1,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 4
0001011 => [3,1,1,2] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 3
0001100 => [3,2,2] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 2
0001101 => [3,2,1,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 3
0001110 => [3,3,1] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 2
0001111 => [3,4] => [4,3] => [[1,2,3,7],[4,5,6]] => 1
0010000 => [2,1,4] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 2
0010001 => [2,1,3,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 3
0010010 => [2,1,2,1,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 4
0010011 => [2,1,2,2] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
0010100 => [2,1,1,1,2] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 4
0010101 => [2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 5
0010110 => [2,1,1,2,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 4
0010111 => [2,1,1,3] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 3
0011000 => [2,2,3] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 2
0011001 => [2,2,2,1] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
0011010 => [2,2,1,1,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 4
0011011 => [2,2,1,2] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
0011100 => [2,3,2] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 2
0011101 => [2,3,1,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 3
0011110 => [2,4,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 2
0011111 => [2,5] => [5,2] => [[1,2,5,6,7],[3,4]] => 1
0100000 => [1,1,5] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 2
0100001 => [1,1,4,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
0100010 => [1,1,3,1,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 4
0100011 => [1,1,3,2] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 3
0100100 => [1,1,2,1,2] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 4
0100101 => [1,1,2,1,1,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 5
0100110 => [1,1,2,2,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 4
0100111 => [1,1,2,3] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 3
0101000 => [1,1,1,1,3] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 4
0101001 => [1,1,1,1,2,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 5
0101010 => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 6
0101011 => [1,1,1,1,1,2] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 5
0101100 => [1,1,1,2,2] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 4
0101101 => [1,1,1,2,1,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 5
0101110 => [1,1,1,3,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 4
0101111 => [1,1,1,4] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
0110000 => [1,2,4] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 2
0110001 => [1,2,3,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 3
0110010 => [1,2,2,1,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 4
0110011 => [1,2,2,2] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
0110100 => [1,2,1,1,2] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 4
0110101 => [1,2,1,1,1,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 5
0110110 => [1,2,1,2,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 4
0110111 => [1,2,1,3] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 3
0111000 => [1,3,3] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 2
0111001 => [1,3,2,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 3
0111010 => [1,3,1,1,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 4
0111011 => [1,3,1,2] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 3
0111100 => [1,4,2] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 2
0111101 => [1,4,1,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
0111110 => [1,5,1] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 2
0111111 => [1,6] => [6,1] => [[1,3,4,5,6,7],[2]] => 1
1000000 => [1,6] => [6,1] => [[1,3,4,5,6,7],[2]] => 1
1000001 => [1,5,1] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 2
1000010 => [1,4,1,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
1000011 => [1,4,2] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 2
1000100 => [1,3,1,2] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 3
1000101 => [1,3,1,1,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 4
1000110 => [1,3,2,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 3
1000111 => [1,3,3] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 2
1001000 => [1,2,1,3] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 3
1001001 => [1,2,1,2,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 4
1001010 => [1,2,1,1,1,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 5
1001011 => [1,2,1,1,2] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 4
1001100 => [1,2,2,2] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
1001101 => [1,2,2,1,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 4
1001110 => [1,2,3,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 3
1001111 => [1,2,4] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 2
1010000 => [1,1,1,4] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
1010001 => [1,1,1,3,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 4
1010010 => [1,1,1,2,1,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 5
1010011 => [1,1,1,2,2] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 4
1010100 => [1,1,1,1,1,2] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 5
1010101 => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 6
1010110 => [1,1,1,1,2,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 5
1010111 => [1,1,1,1,3] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 4
1011000 => [1,1,2,3] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 3
1011001 => [1,1,2,2,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 4
1011010 => [1,1,2,1,1,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 5
1011011 => [1,1,2,1,2] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 4
1011100 => [1,1,3,2] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 3
1011101 => [1,1,3,1,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 4
1011110 => [1,1,4,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
1011111 => [1,1,5] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 2
1100000 => [2,5] => [5,2] => [[1,2,5,6,7],[3,4]] => 1
1100001 => [2,4,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 2
1100010 => [2,3,1,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 3
1100011 => [2,3,2] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 2
1100100 => [2,2,1,2] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
1100101 => [2,2,1,1,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 4
1100110 => [2,2,2,1] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
1100111 => [2,2,3] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 2
1101000 => [2,1,1,3] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 3
1101001 => [2,1,1,2,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 4
1101010 => [2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,7],[2],[3],[4],[5],[6]] => 5
1101011 => [2,1,1,1,2] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 4
1101100 => [2,1,2,2] => [2,2,2,1] => [[1,3],[2,5],[4,7],[6]] => 3
1101101 => [2,1,2,1,1] => [2,2,1,1,1] => [[1,5],[2,7],[3],[4],[6]] => 4
1101110 => [2,1,3,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 3
1101111 => [2,1,4] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 2
1110000 => [3,4] => [4,3] => [[1,2,3,7],[4,5,6]] => 1
1110001 => [3,3,1] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 2
1110010 => [3,2,1,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 3
1110011 => [3,2,2] => [3,2,2] => [[1,2,7],[3,4],[5,6]] => 2
1110100 => [3,1,1,2] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 3
1110101 => [3,1,1,1,1] => [3,1,1,1,1] => [[1,6,7],[2],[3],[4],[5]] => 4
1110110 => [3,1,2,1] => [3,2,1,1] => [[1,4,7],[2,6],[3],[5]] => 3
1110111 => [3,1,3] => [3,3,1] => [[1,3,4],[2,6,7],[5]] => 2
1111000 => [4,3] => [4,3] => [[1,2,3,7],[4,5,6]] => 1
1111001 => [4,2,1] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 2
1111010 => [4,1,1,1] => [4,1,1,1] => [[1,5,6,7],[2],[3],[4]] => 3
1111011 => [4,1,2] => [4,2,1] => [[1,3,6,7],[2,5],[4]] => 2
1111100 => [5,2] => [5,2] => [[1,2,5,6,7],[3,4]] => 1
1111101 => [5,1,1] => [5,1,1] => [[1,4,5,6,7],[2],[3]] => 2
1111110 => [6,1] => [6,1] => [[1,3,4,5,6,7],[2]] => 1
1111111 => [7] => [7] => [[1,2,3,4,5,6,7]] => 0
00000000 => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 0
00000001 => [7,1] => [7,1] => [[1,3,4,5,6,7,8],[2]] => 1
00000010 => [6,1,1] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 2
00000011 => [6,2] => [6,2] => [[1,2,5,6,7,8],[3,4]] => 1
00000100 => [5,1,2] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 2
00000101 => [5,1,1,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 3
00000110 => [5,2,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 2
00000111 => [5,3] => [5,3] => [[1,2,3,7,8],[4,5,6]] => 1
00001000 => [4,1,3] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 2
00001001 => [4,1,2,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
00001010 => [4,1,1,1,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 4
00001011 => [4,1,1,2] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
00001100 => [4,2,2] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 2
00001101 => [4,2,1,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
00001110 => [4,3,1] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 2
00001111 => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 1
00010000 => [3,1,4] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 2
00010001 => [3,1,3,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
00010010 => [3,1,2,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
00010011 => [3,1,2,2] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 3
00010100 => [3,1,1,1,2] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
00010101 => [3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 5
00010110 => [3,1,1,2,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
00010111 => [3,1,1,3] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
00011000 => [3,2,3] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 2
00011001 => [3,2,2,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 3
00011010 => [3,2,1,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
00011011 => [3,2,1,2] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 3
00011100 => [3,3,2] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 2
00011101 => [3,3,1,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
00011110 => [3,4,1] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 2
00011111 => [3,5] => [5,3] => [[1,2,3,7,8],[4,5,6]] => 1
00100000 => [2,1,5] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 2
00100001 => [2,1,4,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
00100010 => [2,1,3,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
00100011 => [2,1,3,2] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 3
00100100 => [2,1,2,1,2] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 4
00100101 => [2,1,2,1,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 5
00100110 => [2,1,2,2,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 4
00100111 => [2,1,2,3] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 3
00101000 => [2,1,1,1,3] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
00101001 => [2,1,1,1,2,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 5
00101010 => [2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 6
00101011 => [2,1,1,1,1,2] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 5
00101100 => [2,1,1,2,2] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 4
00101101 => [2,1,1,2,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 5
00101110 => [2,1,1,3,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
00101111 => [2,1,1,4] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
00110000 => [2,2,4] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 2
00110001 => [2,2,3,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 3
00110010 => [2,2,2,1,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 4
00110011 => [2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 3
00110100 => [2,2,1,1,2] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 4
00110101 => [2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 5
00110110 => [2,2,1,2,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 4
00110111 => [2,2,1,3] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 3
00111000 => [2,3,3] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 2
00111001 => [2,3,2,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 3
00111010 => [2,3,1,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
00111011 => [2,3,1,2] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 3
00111100 => [2,4,2] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 2
00111101 => [2,4,1,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
00111110 => [2,5,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 2
00111111 => [2,6] => [6,2] => [[1,2,5,6,7,8],[3,4]] => 1
01000000 => [1,1,6] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 2
01000001 => [1,1,5,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 3
01000010 => [1,1,4,1,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 4
01000011 => [1,1,4,2] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
01000100 => [1,1,3,1,2] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
01000101 => [1,1,3,1,1,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 5
01000110 => [1,1,3,2,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
01000111 => [1,1,3,3] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
01001000 => [1,1,2,1,3] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
01001001 => [1,1,2,1,2,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 5
01001010 => [1,1,2,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 6
01001011 => [1,1,2,1,1,2] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 5
01001100 => [1,1,2,2,2] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 4
01001101 => [1,1,2,2,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 5
01001110 => [1,1,2,3,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
01001111 => [1,1,2,4] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
01010000 => [1,1,1,1,4] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 4
01010001 => [1,1,1,1,3,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 5
01010010 => [1,1,1,1,2,1,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 6
01010011 => [1,1,1,1,2,2] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 5
01010100 => [1,1,1,1,1,1,2] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 6
01010101 => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 7
01010110 => [1,1,1,1,1,2,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 6
01010111 => [1,1,1,1,1,3] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 5
01011000 => [1,1,1,2,3] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
01011001 => [1,1,1,2,2,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 5
01011010 => [1,1,1,2,1,1,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 6
01011011 => [1,1,1,2,1,2] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 5
01011100 => [1,1,1,3,2] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
01011101 => [1,1,1,3,1,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 5
01011110 => [1,1,1,4,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 4
01011111 => [1,1,1,5] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 3
01100000 => [1,2,5] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 2
01100001 => [1,2,4,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
01100010 => [1,2,3,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
01100011 => [1,2,3,2] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 3
01100100 => [1,2,2,1,2] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 4
01100101 => [1,2,2,1,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 5
01100110 => [1,2,2,2,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 4
01100111 => [1,2,2,3] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 3
01101000 => [1,2,1,1,3] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
01101001 => [1,2,1,1,2,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 5
01101010 => [1,2,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 6
01101011 => [1,2,1,1,1,2] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 5
01101100 => [1,2,1,2,2] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 4
01101101 => [1,2,1,2,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 5
01101110 => [1,2,1,3,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
01101111 => [1,2,1,4] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
01110000 => [1,3,4] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 2
01110001 => [1,3,3,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
01110010 => [1,3,2,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
01110011 => [1,3,2,2] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 3
01110100 => [1,3,1,1,2] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
01110101 => [1,3,1,1,1,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 5
01110110 => [1,3,1,2,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
01110111 => [1,3,1,3] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
01111000 => [1,4,3] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 2
01111001 => [1,4,2,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
01111010 => [1,4,1,1,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 4
01111011 => [1,4,1,2] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
01111100 => [1,5,2] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 2
01111101 => [1,5,1,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 3
01111110 => [1,6,1] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 2
01111111 => [1,7] => [7,1] => [[1,3,4,5,6,7,8],[2]] => 1
10000000 => [1,7] => [7,1] => [[1,3,4,5,6,7,8],[2]] => 1
10000001 => [1,6,1] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 2
10000010 => [1,5,1,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 3
10000011 => [1,5,2] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 2
10000100 => [1,4,1,2] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
10000101 => [1,4,1,1,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 4
10000110 => [1,4,2,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
10000111 => [1,4,3] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 2
10001000 => [1,3,1,3] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
10001001 => [1,3,1,2,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
10001010 => [1,3,1,1,1,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 5
10001011 => [1,3,1,1,2] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
10001100 => [1,3,2,2] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 3
10001101 => [1,3,2,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
10001110 => [1,3,3,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
10001111 => [1,3,4] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 2
10010000 => [1,2,1,4] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
10010001 => [1,2,1,3,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
10010010 => [1,2,1,2,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 5
10010011 => [1,2,1,2,2] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 4
10010100 => [1,2,1,1,1,2] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 5
10010101 => [1,2,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 6
10010110 => [1,2,1,1,2,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 5
10010111 => [1,2,1,1,3] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
10011000 => [1,2,2,3] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 3
10011001 => [1,2,2,2,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 4
10011010 => [1,2,2,1,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 5
10011011 => [1,2,2,1,2] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 4
10011100 => [1,2,3,2] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 3
10011101 => [1,2,3,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
10011110 => [1,2,4,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
10011111 => [1,2,5] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 2
10100000 => [1,1,1,5] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 3
10100001 => [1,1,1,4,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 4
10100010 => [1,1,1,3,1,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 5
10100011 => [1,1,1,3,2] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
10100100 => [1,1,1,2,1,2] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 5
10100101 => [1,1,1,2,1,1,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 6
10100110 => [1,1,1,2,2,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 5
10100111 => [1,1,1,2,3] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
10101000 => [1,1,1,1,1,3] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 5
10101001 => [1,1,1,1,1,2,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 6
10101010 => [1,1,1,1,1,1,1,1] => [1,1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7],[8]] => 7
10101011 => [1,1,1,1,1,1,2] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 6
10101100 => [1,1,1,1,2,2] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 5
10101101 => [1,1,1,1,2,1,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 6
10101110 => [1,1,1,1,3,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 5
10101111 => [1,1,1,1,4] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 4
10110000 => [1,1,2,4] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
10110001 => [1,1,2,3,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
10110010 => [1,1,2,2,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 5
10110011 => [1,1,2,2,2] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 4
10110100 => [1,1,2,1,1,2] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 5
10110101 => [1,1,2,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 6
10110110 => [1,1,2,1,2,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 5
10110111 => [1,1,2,1,3] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
10111000 => [1,1,3,3] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
10111001 => [1,1,3,2,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
10111010 => [1,1,3,1,1,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 5
10111011 => [1,1,3,1,2] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
10111100 => [1,1,4,2] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
10111101 => [1,1,4,1,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 4
10111110 => [1,1,5,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 3
10111111 => [1,1,6] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 2
11000000 => [2,6] => [6,2] => [[1,2,5,6,7,8],[3,4]] => 1
11000001 => [2,5,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 2
11000010 => [2,4,1,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
11000011 => [2,4,2] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 2
11000100 => [2,3,1,2] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 3
11000101 => [2,3,1,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
11000110 => [2,3,2,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 3
11000111 => [2,3,3] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 2
11001000 => [2,2,1,3] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 3
11001001 => [2,2,1,2,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 4
11001010 => [2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 5
11001011 => [2,2,1,1,2] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 4
11001100 => [2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 3
11001101 => [2,2,2,1,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 4
11001110 => [2,2,3,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 3
11001111 => [2,2,4] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 2
11010000 => [2,1,1,4] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
11010001 => [2,1,1,3,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
11010010 => [2,1,1,2,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 5
11010011 => [2,1,1,2,2] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 4
11010100 => [2,1,1,1,1,2] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 5
11010101 => [2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,8],[2],[3],[4],[5],[6],[7]] => 6
11010110 => [2,1,1,1,2,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 5
11010111 => [2,1,1,1,3] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
11011000 => [2,1,2,3] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 3
11011001 => [2,1,2,2,1] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 4
11011010 => [2,1,2,1,1,1] => [2,2,1,1,1,1] => [[1,6],[2,8],[3],[4],[5],[7]] => 5
11011011 => [2,1,2,1,2] => [2,2,2,1,1] => [[1,4],[2,6],[3,8],[5],[7]] => 4
11011100 => [2,1,3,2] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 3
11011101 => [2,1,3,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
11011110 => [2,1,4,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
11011111 => [2,1,5] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 2
11100000 => [3,5] => [5,3] => [[1,2,3,7,8],[4,5,6]] => 1
11100001 => [3,4,1] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 2
11100010 => [3,3,1,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
11100011 => [3,3,2] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 2
11100100 => [3,2,1,2] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 3
11100101 => [3,2,1,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
11100110 => [3,2,2,1] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 3
11100111 => [3,2,3] => [3,3,2] => [[1,2,5],[3,4,8],[6,7]] => 2
11101000 => [3,1,1,3] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
11101001 => [3,1,1,2,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
11101010 => [3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,7,8],[2],[3],[4],[5],[6]] => 5
11101011 => [3,1,1,1,2] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
11101100 => [3,1,2,2] => [3,2,2,1] => [[1,3,8],[2,5],[4,7],[6]] => 3
11101101 => [3,1,2,1,1] => [3,2,1,1,1] => [[1,5,8],[2,7],[3],[4],[6]] => 4
11101110 => [3,1,3,1] => [3,3,1,1] => [[1,4,5],[2,7,8],[3],[6]] => 3
11101111 => [3,1,4] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 2
11110000 => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 1
11110001 => [4,3,1] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 2
11110010 => [4,2,1,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
11110011 => [4,2,2] => [4,2,2] => [[1,2,7,8],[3,4],[5,6]] => 2
11110100 => [4,1,1,2] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
11110101 => [4,1,1,1,1] => [4,1,1,1,1] => [[1,6,7,8],[2],[3],[4],[5]] => 4
11110110 => [4,1,2,1] => [4,2,1,1] => [[1,4,7,8],[2,6],[3],[5]] => 3
11110111 => [4,1,3] => [4,3,1] => [[1,3,4,8],[2,6,7],[5]] => 2
11111000 => [5,3] => [5,3] => [[1,2,3,7,8],[4,5,6]] => 1
11111001 => [5,2,1] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 2
11111010 => [5,1,1,1] => [5,1,1,1] => [[1,5,6,7,8],[2],[3],[4]] => 3
11111011 => [5,1,2] => [5,2,1] => [[1,3,6,7,8],[2,5],[4]] => 2
11111100 => [6,2] => [6,2] => [[1,2,5,6,7,8],[3,4]] => 1
11111101 => [6,1,1] => [6,1,1] => [[1,4,5,6,7,8],[2],[3]] => 2
11111110 => [7,1] => [7,1] => [[1,3,4,5,6,7,8],[2]] => 1
11111111 => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 0
000000000 => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 0
000000001 => [8,1] => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 1
000000010 => [7,1,1] => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 2
000000011 => [7,2] => [7,2] => [[1,2,5,6,7,8,9],[3,4]] => 1
000000100 => [6,1,2] => [6,2,1] => [[1,3,6,7,8,9],[2,5],[4]] => 2
000000101 => [6,1,1,1] => [6,1,1,1] => [[1,5,6,7,8,9],[2],[3],[4]] => 3
000000110 => [6,2,1] => [6,2,1] => [[1,3,6,7,8,9],[2,5],[4]] => 2
000000111 => [6,3] => [6,3] => [[1,2,3,7,8,9],[4,5,6]] => 1
000001000 => [5,1,3] => [5,3,1] => [[1,3,4,8,9],[2,6,7],[5]] => 2
000001001 => [5,1,2,1] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 3
000001010 => [5,1,1,1,1] => [5,1,1,1,1] => [[1,6,7,8,9],[2],[3],[4],[5]] => 4
000001011 => [5,1,1,2] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 3
000001100 => [5,2,2] => [5,2,2] => [[1,2,7,8,9],[3,4],[5,6]] => 2
000001101 => [5,2,1,1] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 3
000001110 => [5,3,1] => [5,3,1] => [[1,3,4,8,9],[2,6,7],[5]] => 2
000001111 => [5,4] => [5,4] => [[1,2,3,4,9],[5,6,7,8]] => 1
000010000 => [4,1,4] => [4,4,1] => [[1,3,4,5],[2,7,8,9],[6]] => 2
000010001 => [4,1,3,1] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 3
000010010 => [4,1,2,1,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
000010011 => [4,1,2,2] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 3
000010100 => [4,1,1,1,2] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
000010101 => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 5
000010110 => [4,1,1,2,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
000010111 => [4,1,1,3] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 3
000011000 => [4,2,3] => [4,3,2] => [[1,2,5,9],[3,4,8],[6,7]] => 2
000011001 => [4,2,2,1] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 3
000011010 => [4,2,1,1,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
000011011 => [4,2,1,2] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 3
000011100 => [4,3,2] => [4,3,2] => [[1,2,5,9],[3,4,8],[6,7]] => 2
000011101 => [4,3,1,1] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 3
000011110 => [4,4,1] => [4,4,1] => [[1,3,4,5],[2,7,8,9],[6]] => 2
000011111 => [4,5] => [5,4] => [[1,2,3,4,9],[5,6,7,8]] => 1
000100000 => [3,1,5] => [5,3,1] => [[1,3,4,8,9],[2,6,7],[5]] => 2
000100001 => [3,1,4,1] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 3
000100010 => [3,1,3,1,1] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 4
000100011 => [3,1,3,2] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 3
000100100 => [3,1,2,1,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
000100101 => [3,1,2,1,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
000100110 => [3,1,2,2,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
000100111 => [3,1,2,3] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 3
000101000 => [3,1,1,1,3] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 4
000101001 => [3,1,1,1,2,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
000101010 => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 6
000101011 => [3,1,1,1,1,2] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
000101100 => [3,1,1,2,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
000101101 => [3,1,1,2,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
000101110 => [3,1,1,3,1] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 4
000101111 => [3,1,1,4] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 3
000110000 => [3,2,4] => [4,3,2] => [[1,2,5,9],[3,4,8],[6,7]] => 2
000110001 => [3,2,3,1] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 3
000110010 => [3,2,2,1,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
000110011 => [3,2,2,2] => [3,2,2,2] => [[1,2,9],[3,4],[5,6],[7,8]] => 3
000110100 => [3,2,1,1,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
000110101 => [3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
000110110 => [3,2,1,2,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
000110111 => [3,2,1,3] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 3
000111000 => [3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 2
000111001 => [3,3,2,1] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 3
000111010 => [3,3,1,1,1] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 4
000111011 => [3,3,1,2] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 3
000111100 => [3,4,2] => [4,3,2] => [[1,2,5,9],[3,4,8],[6,7]] => 2
000111101 => [3,4,1,1] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 3
000111110 => [3,5,1] => [5,3,1] => [[1,3,4,8,9],[2,6,7],[5]] => 2
000111111 => [3,6] => [6,3] => [[1,2,3,7,8,9],[4,5,6]] => 1
001000000 => [2,1,6] => [6,2,1] => [[1,3,6,7,8,9],[2,5],[4]] => 2
001000001 => [2,1,5,1] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 3
001000010 => [2,1,4,1,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
001000011 => [2,1,4,2] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 3
001000100 => [2,1,3,1,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
001000101 => [2,1,3,1,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
001000110 => [2,1,3,2,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
001000111 => [2,1,3,3] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 3
001001000 => [2,1,2,1,3] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
001001001 => [2,1,2,1,2,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
001001010 => [2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
001001011 => [2,1,2,1,1,2] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
001001100 => [2,1,2,2,2] => [2,2,2,2,1] => [[1,3],[2,5],[4,7],[6,9],[8]] => 4
001001101 => [2,1,2,2,1,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
001001110 => [2,1,2,3,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
001001111 => [2,1,2,4] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 3
001010000 => [2,1,1,1,4] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
001010001 => [2,1,1,1,3,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
001010010 => [2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
001010011 => [2,1,1,1,2,2] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
001010100 => [2,1,1,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
001010101 => [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]] => 7
001010110 => [2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
001010111 => [2,1,1,1,1,3] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
001011000 => [2,1,1,2,3] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
001011001 => [2,1,1,2,2,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
001011010 => [2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
001011011 => [2,1,1,2,1,2] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
001011100 => [2,1,1,3,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
001011101 => [2,1,1,3,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
001011110 => [2,1,1,4,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
001011111 => [2,1,1,5] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 3
001100000 => [2,2,5] => [5,2,2] => [[1,2,7,8,9],[3,4],[5,6]] => 2
001100001 => [2,2,4,1] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 3
001100010 => [2,2,3,1,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
001100011 => [2,2,3,2] => [3,2,2,2] => [[1,2,9],[3,4],[5,6],[7,8]] => 3
001100100 => [2,2,2,1,2] => [2,2,2,2,1] => [[1,3],[2,5],[4,7],[6,9],[8]] => 4
001100101 => [2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
001100110 => [2,2,2,2,1] => [2,2,2,2,1] => [[1,3],[2,5],[4,7],[6,9],[8]] => 4
001100111 => [2,2,2,3] => [3,2,2,2] => [[1,2,9],[3,4],[5,6],[7,8]] => 3
001101000 => [2,2,1,1,3] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
001101001 => [2,2,1,1,2,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
001101010 => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
001101011 => [2,2,1,1,1,2] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
001101100 => [2,2,1,2,2] => [2,2,2,2,1] => [[1,3],[2,5],[4,7],[6,9],[8]] => 4
001101101 => [2,2,1,2,1,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
001101110 => [2,2,1,3,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
001101111 => [2,2,1,4] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 3
001110000 => [2,3,4] => [4,3,2] => [[1,2,5,9],[3,4,8],[6,7]] => 2
001110001 => [2,3,3,1] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 3
001110010 => [2,3,2,1,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
001110011 => [2,3,2,2] => [3,2,2,2] => [[1,2,9],[3,4],[5,6],[7,8]] => 3
001110100 => [2,3,1,1,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
001110101 => [2,3,1,1,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
001110110 => [2,3,1,2,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
001110111 => [2,3,1,3] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 3
001111000 => [2,4,3] => [4,3,2] => [[1,2,5,9],[3,4,8],[6,7]] => 2
001111001 => [2,4,2,1] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 3
001111010 => [2,4,1,1,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
001111011 => [2,4,1,2] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 3
001111100 => [2,5,2] => [5,2,2] => [[1,2,7,8,9],[3,4],[5,6]] => 2
001111101 => [2,5,1,1] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 3
001111110 => [2,6,1] => [6,2,1] => [[1,3,6,7,8,9],[2,5],[4]] => 2
001111111 => [2,7] => [7,2] => [[1,2,5,6,7,8,9],[3,4]] => 1
010000000 => [1,1,7] => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 2
010000001 => [1,1,6,1] => [6,1,1,1] => [[1,5,6,7,8,9],[2],[3],[4]] => 3
010000010 => [1,1,5,1,1] => [5,1,1,1,1] => [[1,6,7,8,9],[2],[3],[4],[5]] => 4
010000011 => [1,1,5,2] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 3
010000100 => [1,1,4,1,2] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
010000101 => [1,1,4,1,1,1] => [4,1,1,1,1,1] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 5
010000110 => [1,1,4,2,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
010000111 => [1,1,4,3] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 3
010001000 => [1,1,3,1,3] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 4
010001001 => [1,1,3,1,2,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
010001010 => [1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 6
010001011 => [1,1,3,1,1,2] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
010001100 => [1,1,3,2,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
010001101 => [1,1,3,2,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
010001110 => [1,1,3,3,1] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 4
010001111 => [1,1,3,4] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 3
010010000 => [1,1,2,1,4] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
010010001 => [1,1,2,1,3,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
010010010 => [1,1,2,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
010010011 => [1,1,2,1,2,2] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
010010100 => [1,1,2,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
010010101 => [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]] => 7
010010110 => [1,1,2,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
010010111 => [1,1,2,1,1,3] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
010011000 => [1,1,2,2,3] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
010011001 => [1,1,2,2,2,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
010011010 => [1,1,2,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
010011011 => [1,1,2,2,1,2] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
010011100 => [1,1,2,3,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
010011101 => [1,1,2,3,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
010011110 => [1,1,2,4,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
010011111 => [1,1,2,5] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 3
010100000 => [1,1,1,1,5] => [5,1,1,1,1] => [[1,6,7,8,9],[2],[3],[4],[5]] => 4
010100001 => [1,1,1,1,4,1] => [4,1,1,1,1,1] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 5
010100010 => [1,1,1,1,3,1,1] => [3,1,1,1,1,1,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 6
010100011 => [1,1,1,1,3,2] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
010100100 => [1,1,1,1,2,1,2] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
010100101 => [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]] => 7
010100110 => [1,1,1,1,2,2,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
010100111 => [1,1,1,1,2,3] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
010101000 => [1,1,1,1,1,1,3] => [3,1,1,1,1,1,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 6
010101001 => [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]] => 7
010101010 => [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]] => 8
010101011 => [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]] => 7
010101100 => [1,1,1,1,1,2,2] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
010101101 => [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]] => 7
010101110 => [1,1,1,1,1,3,1] => [3,1,1,1,1,1,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 6
010101111 => [1,1,1,1,1,4] => [4,1,1,1,1,1] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 5
010110000 => [1,1,1,2,4] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
010110001 => [1,1,1,2,3,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
010110010 => [1,1,1,2,2,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
010110011 => [1,1,1,2,2,2] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
010110100 => [1,1,1,2,1,1,2] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
010110101 => [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]] => 7
010110110 => [1,1,1,2,1,2,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
010110111 => [1,1,1,2,1,3] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
010111000 => [1,1,1,3,3] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 4
010111001 => [1,1,1,3,2,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
010111010 => [1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 6
010111011 => [1,1,1,3,1,2] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
010111100 => [1,1,1,4,2] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
010111101 => [1,1,1,4,1,1] => [4,1,1,1,1,1] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 5
010111110 => [1,1,1,5,1] => [5,1,1,1,1] => [[1,6,7,8,9],[2],[3],[4],[5]] => 4
010111111 => [1,1,1,6] => [6,1,1,1] => [[1,5,6,7,8,9],[2],[3],[4]] => 3
011000000 => [1,2,6] => [6,2,1] => [[1,3,6,7,8,9],[2,5],[4]] => 2
011000001 => [1,2,5,1] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 3
011000010 => [1,2,4,1,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
011000011 => [1,2,4,2] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 3
011000100 => [1,2,3,1,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
011000101 => [1,2,3,1,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
011000110 => [1,2,3,2,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
011000111 => [1,2,3,3] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 3
011001000 => [1,2,2,1,3] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
011001001 => [1,2,2,1,2,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
011001010 => [1,2,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
011001011 => [1,2,2,1,1,2] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
011001100 => [1,2,2,2,2] => [2,2,2,2,1] => [[1,3],[2,5],[4,7],[6,9],[8]] => 4
011001101 => [1,2,2,2,1,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
011001110 => [1,2,2,3,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
011001111 => [1,2,2,4] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 3
011010000 => [1,2,1,1,4] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
011010001 => [1,2,1,1,3,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
011010010 => [1,2,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
011010011 => [1,2,1,1,2,2] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
011010100 => [1,2,1,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
011010101 => [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]] => 7
011010110 => [1,2,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
011010111 => [1,2,1,1,1,3] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
011011000 => [1,2,1,2,3] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
011011001 => [1,2,1,2,2,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
011011010 => [1,2,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
011011011 => [1,2,1,2,1,2] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
011011100 => [1,2,1,3,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
011011101 => [1,2,1,3,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
011011110 => [1,2,1,4,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
011011111 => [1,2,1,5] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 3
011100000 => [1,3,5] => [5,3,1] => [[1,3,4,8,9],[2,6,7],[5]] => 2
011100001 => [1,3,4,1] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 3
011100010 => [1,3,3,1,1] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 4
011100011 => [1,3,3,2] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 3
011100100 => [1,3,2,1,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
011100101 => [1,3,2,1,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
011100110 => [1,3,2,2,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
011100111 => [1,3,2,3] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 3
011101000 => [1,3,1,1,3] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 4
011101001 => [1,3,1,1,2,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
011101010 => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 6
011101011 => [1,3,1,1,1,2] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
011101100 => [1,3,1,2,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
011101101 => [1,3,1,2,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
011101110 => [1,3,1,3,1] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 4
011101111 => [1,3,1,4] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 3
011110000 => [1,4,4] => [4,4,1] => [[1,3,4,5],[2,7,8,9],[6]] => 2
011110001 => [1,4,3,1] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 3
011110010 => [1,4,2,1,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
011110011 => [1,4,2,2] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 3
011110100 => [1,4,1,1,2] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
011110101 => [1,4,1,1,1,1] => [4,1,1,1,1,1] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 5
011110110 => [1,4,1,2,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
011110111 => [1,4,1,3] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 3
011111000 => [1,5,3] => [5,3,1] => [[1,3,4,8,9],[2,6,7],[5]] => 2
011111001 => [1,5,2,1] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 3
011111010 => [1,5,1,1,1] => [5,1,1,1,1] => [[1,6,7,8,9],[2],[3],[4],[5]] => 4
011111011 => [1,5,1,2] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 3
011111100 => [1,6,2] => [6,2,1] => [[1,3,6,7,8,9],[2,5],[4]] => 2
011111101 => [1,6,1,1] => [6,1,1,1] => [[1,5,6,7,8,9],[2],[3],[4]] => 3
011111110 => [1,7,1] => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 2
011111111 => [1,8] => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 1
100000000 => [1,8] => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 1
100000001 => [1,7,1] => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 2
100000010 => [1,6,1,1] => [6,1,1,1] => [[1,5,6,7,8,9],[2],[3],[4]] => 3
100000011 => [1,6,2] => [6,2,1] => [[1,3,6,7,8,9],[2,5],[4]] => 2
100000100 => [1,5,1,2] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 3
100000101 => [1,5,1,1,1] => [5,1,1,1,1] => [[1,6,7,8,9],[2],[3],[4],[5]] => 4
100000110 => [1,5,2,1] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 3
100000111 => [1,5,3] => [5,3,1] => [[1,3,4,8,9],[2,6,7],[5]] => 2
100001000 => [1,4,1,3] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 3
100001001 => [1,4,1,2,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
100001010 => [1,4,1,1,1,1] => [4,1,1,1,1,1] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 5
100001011 => [1,4,1,1,2] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
100001100 => [1,4,2,2] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 3
100001101 => [1,4,2,1,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
100001110 => [1,4,3,1] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 3
100001111 => [1,4,4] => [4,4,1] => [[1,3,4,5],[2,7,8,9],[6]] => 2
100010000 => [1,3,1,4] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 3
100010001 => [1,3,1,3,1] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 4
100010010 => [1,3,1,2,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
100010011 => [1,3,1,2,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
100010100 => [1,3,1,1,1,2] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
100010101 => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 6
100010110 => [1,3,1,1,2,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
100010111 => [1,3,1,1,3] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 4
100011000 => [1,3,2,3] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 3
100011001 => [1,3,2,2,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
100011010 => [1,3,2,1,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
100011011 => [1,3,2,1,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
100011100 => [1,3,3,2] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 3
100011101 => [1,3,3,1,1] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 4
100011110 => [1,3,4,1] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 3
100011111 => [1,3,5] => [5,3,1] => [[1,3,4,8,9],[2,6,7],[5]] => 2
100100000 => [1,2,1,5] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 3
100100001 => [1,2,1,4,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
100100010 => [1,2,1,3,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
100100011 => [1,2,1,3,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
100100100 => [1,2,1,2,1,2] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
100100101 => [1,2,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
100100110 => [1,2,1,2,2,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
100100111 => [1,2,1,2,3] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
100101000 => [1,2,1,1,1,3] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
100101001 => [1,2,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
100101010 => [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]] => 7
100101011 => [1,2,1,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
100101100 => [1,2,1,1,2,2] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
100101101 => [1,2,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
100101110 => [1,2,1,1,3,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
100101111 => [1,2,1,1,4] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
100110000 => [1,2,2,4] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 3
100110001 => [1,2,2,3,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
100110010 => [1,2,2,2,1,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
100110011 => [1,2,2,2,2] => [2,2,2,2,1] => [[1,3],[2,5],[4,7],[6,9],[8]] => 4
100110100 => [1,2,2,1,1,2] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
100110101 => [1,2,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
100110110 => [1,2,2,1,2,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
100110111 => [1,2,2,1,3] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
100111000 => [1,2,3,3] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 3
100111001 => [1,2,3,2,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
100111010 => [1,2,3,1,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
100111011 => [1,2,3,1,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
100111100 => [1,2,4,2] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 3
100111101 => [1,2,4,1,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
100111110 => [1,2,5,1] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 3
100111111 => [1,2,6] => [6,2,1] => [[1,3,6,7,8,9],[2,5],[4]] => 2
101000000 => [1,1,1,6] => [6,1,1,1] => [[1,5,6,7,8,9],[2],[3],[4]] => 3
101000001 => [1,1,1,5,1] => [5,1,1,1,1] => [[1,6,7,8,9],[2],[3],[4],[5]] => 4
101000010 => [1,1,1,4,1,1] => [4,1,1,1,1,1] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 5
101000011 => [1,1,1,4,2] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
101000100 => [1,1,1,3,1,2] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
101000101 => [1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 6
101000110 => [1,1,1,3,2,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
101000111 => [1,1,1,3,3] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 4
101001000 => [1,1,1,2,1,3] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
101001001 => [1,1,1,2,1,2,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
101001010 => [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]] => 7
101001011 => [1,1,1,2,1,1,2] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
101001100 => [1,1,1,2,2,2] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
101001101 => [1,1,1,2,2,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
101001110 => [1,1,1,2,3,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
101001111 => [1,1,1,2,4] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
101010000 => [1,1,1,1,1,4] => [4,1,1,1,1,1] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 5
101010001 => [1,1,1,1,1,3,1] => [3,1,1,1,1,1,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 6
101010010 => [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]] => 7
101010011 => [1,1,1,1,1,2,2] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
101010100 => [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]] => 7
101010101 => [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]] => 8
101010110 => [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]] => 7
101010111 => [1,1,1,1,1,1,3] => [3,1,1,1,1,1,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 6
101011000 => [1,1,1,1,2,3] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
101011001 => [1,1,1,1,2,2,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
101011010 => [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]] => 7
101011011 => [1,1,1,1,2,1,2] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
101011100 => [1,1,1,1,3,2] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
101011101 => [1,1,1,1,3,1,1] => [3,1,1,1,1,1,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 6
101011110 => [1,1,1,1,4,1] => [4,1,1,1,1,1] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 5
101011111 => [1,1,1,1,5] => [5,1,1,1,1] => [[1,6,7,8,9],[2],[3],[4],[5]] => 4
101100000 => [1,1,2,5] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 3
101100001 => [1,1,2,4,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
101100010 => [1,1,2,3,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
101100011 => [1,1,2,3,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
101100100 => [1,1,2,2,1,2] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
101100101 => [1,1,2,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
101100110 => [1,1,2,2,2,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
101100111 => [1,1,2,2,3] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
101101000 => [1,1,2,1,1,3] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
101101001 => [1,1,2,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
101101010 => [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]] => 7
101101011 => [1,1,2,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
101101100 => [1,1,2,1,2,2] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
101101101 => [1,1,2,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
101101110 => [1,1,2,1,3,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
101101111 => [1,1,2,1,4] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
101110000 => [1,1,3,4] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 3
101110001 => [1,1,3,3,1] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 4
101110010 => [1,1,3,2,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
101110011 => [1,1,3,2,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
101110100 => [1,1,3,1,1,2] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
101110101 => [1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 6
101110110 => [1,1,3,1,2,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
101110111 => [1,1,3,1,3] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 4
101111000 => [1,1,4,3] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 3
101111001 => [1,1,4,2,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
101111010 => [1,1,4,1,1,1] => [4,1,1,1,1,1] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 5
101111011 => [1,1,4,1,2] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
101111100 => [1,1,5,2] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 3
101111101 => [1,1,5,1,1] => [5,1,1,1,1] => [[1,6,7,8,9],[2],[3],[4],[5]] => 4
101111110 => [1,1,6,1] => [6,1,1,1] => [[1,5,6,7,8,9],[2],[3],[4]] => 3
101111111 => [1,1,7] => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 2
110000000 => [2,7] => [7,2] => [[1,2,5,6,7,8,9],[3,4]] => 1
110000001 => [2,6,1] => [6,2,1] => [[1,3,6,7,8,9],[2,5],[4]] => 2
110000010 => [2,5,1,1] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 3
110000011 => [2,5,2] => [5,2,2] => [[1,2,7,8,9],[3,4],[5,6]] => 2
110000100 => [2,4,1,2] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 3
110000101 => [2,4,1,1,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
110000110 => [2,4,2,1] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 3
110000111 => [2,4,3] => [4,3,2] => [[1,2,5,9],[3,4,8],[6,7]] => 2
110001000 => [2,3,1,3] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 3
110001001 => [2,3,1,2,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
110001010 => [2,3,1,1,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
110001011 => [2,3,1,1,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
110001100 => [2,3,2,2] => [3,2,2,2] => [[1,2,9],[3,4],[5,6],[7,8]] => 3
110001101 => [2,3,2,1,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
110001110 => [2,3,3,1] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 3
110001111 => [2,3,4] => [4,3,2] => [[1,2,5,9],[3,4,8],[6,7]] => 2
110010000 => [2,2,1,4] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 3
110010001 => [2,2,1,3,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
110010010 => [2,2,1,2,1,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
110010011 => [2,2,1,2,2] => [2,2,2,2,1] => [[1,3],[2,5],[4,7],[6,9],[8]] => 4
110010100 => [2,2,1,1,1,2] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
110010101 => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
110010110 => [2,2,1,1,2,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
110010111 => [2,2,1,1,3] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
110011000 => [2,2,2,3] => [3,2,2,2] => [[1,2,9],[3,4],[5,6],[7,8]] => 3
110011001 => [2,2,2,2,1] => [2,2,2,2,1] => [[1,3],[2,5],[4,7],[6,9],[8]] => 4
110011010 => [2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
110011011 => [2,2,2,1,2] => [2,2,2,2,1] => [[1,3],[2,5],[4,7],[6,9],[8]] => 4
110011100 => [2,2,3,2] => [3,2,2,2] => [[1,2,9],[3,4],[5,6],[7,8]] => 3
110011101 => [2,2,3,1,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
110011110 => [2,2,4,1] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 3
110011111 => [2,2,5] => [5,2,2] => [[1,2,7,8,9],[3,4],[5,6]] => 2
110100000 => [2,1,1,5] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 3
110100001 => [2,1,1,4,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
110100010 => [2,1,1,3,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
110100011 => [2,1,1,3,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
110100100 => [2,1,1,2,1,2] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
110100101 => [2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
110100110 => [2,1,1,2,2,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
110100111 => [2,1,1,2,3] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
110101000 => [2,1,1,1,1,3] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
110101001 => [2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
110101010 => [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]] => 7
110101011 => [2,1,1,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
110101100 => [2,1,1,1,2,2] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
110101101 => [2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
110101110 => [2,1,1,1,3,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
110101111 => [2,1,1,1,4] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
110110000 => [2,1,2,4] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 3
110110001 => [2,1,2,3,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
110110010 => [2,1,2,2,1,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
110110011 => [2,1,2,2,2] => [2,2,2,2,1] => [[1,3],[2,5],[4,7],[6,9],[8]] => 4
110110100 => [2,1,2,1,1,2] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
110110101 => [2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,7],[2,9],[3],[4],[5],[6],[8]] => 6
110110110 => [2,1,2,1,2,1] => [2,2,2,1,1,1] => [[1,5],[2,7],[3,9],[4],[6],[8]] => 5
110110111 => [2,1,2,1,3] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
110111000 => [2,1,3,3] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 3
110111001 => [2,1,3,2,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
110111010 => [2,1,3,1,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
110111011 => [2,1,3,1,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
110111100 => [2,1,4,2] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 3
110111101 => [2,1,4,1,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
110111110 => [2,1,5,1] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 3
110111111 => [2,1,6] => [6,2,1] => [[1,3,6,7,8,9],[2,5],[4]] => 2
111000000 => [3,6] => [6,3] => [[1,2,3,7,8,9],[4,5,6]] => 1
111000001 => [3,5,1] => [5,3,1] => [[1,3,4,8,9],[2,6,7],[5]] => 2
111000010 => [3,4,1,1] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 3
111000011 => [3,4,2] => [4,3,2] => [[1,2,5,9],[3,4,8],[6,7]] => 2
111000100 => [3,3,1,2] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 3
111000101 => [3,3,1,1,1] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 4
111000110 => [3,3,2,1] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 3
111000111 => [3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 2
111001000 => [3,2,1,3] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 3
111001001 => [3,2,1,2,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
111001010 => [3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
111001011 => [3,2,1,1,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
111001100 => [3,2,2,2] => [3,2,2,2] => [[1,2,9],[3,4],[5,6],[7,8]] => 3
111001101 => [3,2,2,1,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
111001110 => [3,2,3,1] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 3
111001111 => [3,2,4] => [4,3,2] => [[1,2,5,9],[3,4,8],[6,7]] => 2
111010000 => [3,1,1,4] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 3
111010001 => [3,1,1,3,1] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 4
111010010 => [3,1,1,2,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
111010011 => [3,1,1,2,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
111010100 => [3,1,1,1,1,2] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
111010101 => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,8,9],[2],[3],[4],[5],[6],[7]] => 6
111010110 => [3,1,1,1,2,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
111010111 => [3,1,1,1,3] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 4
111011000 => [3,1,2,3] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 3
111011001 => [3,1,2,2,1] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
111011010 => [3,1,2,1,1,1] => [3,2,1,1,1,1] => [[1,6,9],[2,8],[3],[4],[5],[7]] => 5
111011011 => [3,1,2,1,2] => [3,2,2,1,1] => [[1,4,9],[2,6],[3,8],[5],[7]] => 4
111011100 => [3,1,3,2] => [3,3,2,1] => [[1,3,6],[2,5,9],[4,8],[7]] => 3
111011101 => [3,1,3,1,1] => [3,3,1,1,1] => [[1,5,6],[2,8,9],[3],[4],[7]] => 4
111011110 => [3,1,4,1] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 3
111011111 => [3,1,5] => [5,3,1] => [[1,3,4,8,9],[2,6,7],[5]] => 2
111100000 => [4,5] => [5,4] => [[1,2,3,4,9],[5,6,7,8]] => 1
111100001 => [4,4,1] => [4,4,1] => [[1,3,4,5],[2,7,8,9],[6]] => 2
111100010 => [4,3,1,1] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 3
111100011 => [4,3,2] => [4,3,2] => [[1,2,5,9],[3,4,8],[6,7]] => 2
111100100 => [4,2,1,2] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 3
111100101 => [4,2,1,1,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
111100110 => [4,2,2,1] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 3
111100111 => [4,2,3] => [4,3,2] => [[1,2,5,9],[3,4,8],[6,7]] => 2
111101000 => [4,1,1,3] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 3
111101001 => [4,1,1,2,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
111101010 => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,7,8,9],[2],[3],[4],[5],[6]] => 5
111101011 => [4,1,1,1,2] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
111101100 => [4,1,2,2] => [4,2,2,1] => [[1,3,8,9],[2,5],[4,7],[6]] => 3
111101101 => [4,1,2,1,1] => [4,2,1,1,1] => [[1,5,8,9],[2,7],[3],[4],[6]] => 4
111101110 => [4,1,3,1] => [4,3,1,1] => [[1,4,5,9],[2,7,8],[3],[6]] => 3
111101111 => [4,1,4] => [4,4,1] => [[1,3,4,5],[2,7,8,9],[6]] => 2
111110000 => [5,4] => [5,4] => [[1,2,3,4,9],[5,6,7,8]] => 1
111110001 => [5,3,1] => [5,3,1] => [[1,3,4,8,9],[2,6,7],[5]] => 2
111110010 => [5,2,1,1] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 3
111110011 => [5,2,2] => [5,2,2] => [[1,2,7,8,9],[3,4],[5,6]] => 2
111110100 => [5,1,1,2] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 3
111110101 => [5,1,1,1,1] => [5,1,1,1,1] => [[1,6,7,8,9],[2],[3],[4],[5]] => 4
111110110 => [5,1,2,1] => [5,2,1,1] => [[1,4,7,8,9],[2,6],[3],[5]] => 3
111110111 => [5,1,3] => [5,3,1] => [[1,3,4,8,9],[2,6,7],[5]] => 2
111111000 => [6,3] => [6,3] => [[1,2,3,7,8,9],[4,5,6]] => 1
111111001 => [6,2,1] => [6,2,1] => [[1,3,6,7,8,9],[2,5],[4]] => 2
111111010 => [6,1,1,1] => [6,1,1,1] => [[1,5,6,7,8,9],[2],[3],[4]] => 3
111111011 => [6,1,2] => [6,2,1] => [[1,3,6,7,8,9],[2,5],[4]] => 2
111111100 => [7,2] => [7,2] => [[1,2,5,6,7,8,9],[3,4]] => 1
111111101 => [7,1,1] => [7,1,1] => [[1,4,5,6,7,8,9],[2],[3]] => 2
111111110 => [8,1] => [8,1] => [[1,3,4,5,6,7,8,9],[2]] => 1
111111111 => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 0
1010101010 => [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]] => 9
1010101100 => [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]] => 7
1010110010 => [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]] => 7
1010110100 => [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]] => 7
1010111000 => [1,1,1,1,3,3] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
1011001010 => [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]] => 7
1011001100 => [1,1,2,2,2,2] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
1011010010 => [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]] => 7
1011010100 => [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]] => 7
1011011000 => [1,1,2,1,2,3] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
1011100010 => [1,1,3,3,1,1] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
1011100100 => [1,1,3,2,1,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
1011101000 => [1,1,3,1,1,3] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
1011110000 => [1,1,4,4] => [4,4,1,1] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 3
1100101010 => [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]] => 7
1100101100 => [2,2,1,1,2,2] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
1100110010 => [2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
1100110100 => [2,2,2,1,1,2] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
1100111000 => [2,2,3,3] => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 3
1101001010 => [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]] => 7
1101001100 => [2,1,1,2,2,2] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
1101010010 => [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]] => 7
1101010100 => [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]] => 7
1101011000 => [2,1,1,1,2,3] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
1101100010 => [2,1,2,3,1,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
1101100100 => [2,1,2,2,1,2] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
1101101000 => [2,1,2,1,1,3] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
1101110000 => [2,1,3,4] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 3
1110001010 => [3,3,1,1,1,1] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
1110001100 => [3,3,2,2] => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 3
1110010010 => [3,2,1,2,1,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
1110010100 => [3,2,1,1,1,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
1110011000 => [3,2,2,3] => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 3
1110100010 => [3,1,1,3,1,1] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
1110100100 => [3,1,1,2,1,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
1110101000 => [3,1,1,1,1,3] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
1110110000 => [3,1,2,4] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 3
1111000010 => [4,4,1,1] => [4,4,1,1] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 3
1111000100 => [4,3,1,2] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 3
1111001000 => [4,2,1,3] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 3
1111010000 => [4,1,1,4] => [4,4,1,1] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 3
1111100000 => [5,5] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 1
101100111000 => [1,1,2,2,3,3] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
101110001100 => [1,1,3,3,2,2] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
101110011000 => [1,1,3,2,2,3] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
110010111000 => [2,2,1,1,3,3] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
110011001100 => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 5
110011100010 => [2,2,3,3,1,1] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
110011101000 => [2,2,3,1,1,3] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
110011110000 => [2,2,4,4] => [4,4,2,2] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 3
110100111000 => [2,1,1,2,3,3] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
110111000100 => [2,1,3,3,1,2] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
110111001000 => [2,1,3,2,1,3] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
110111100000 => [2,1,4,5] => [5,4,2,1] => [[1,3,6,7,12],[2,5,10,11],[4,9],[8]] => 3
111000101100 => [3,3,1,1,2,2] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
111000110010 => [3,3,2,2,1,1] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
111000110100 => [3,3,2,1,1,2] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
111001011000 => [3,2,1,1,2,3] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
111001100010 => [3,2,2,3,1,1] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
111001101000 => [3,2,2,1,1,3] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
111001110000 => [3,2,3,4] => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 3
111010001100 => [3,1,1,3,2,2] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
111010011000 => [3,1,1,2,2,3] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
111011000100 => [3,1,2,3,1,2] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
111011001000 => [3,1,2,2,1,3] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
111011100000 => [3,1,3,5] => [5,3,3,1] => [[1,3,4,11,12],[2,6,7],[5,9,10],[8]] => 3
111100001100 => [4,4,2,2] => [4,4,2,2] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 3
111100011000 => [4,3,2,3] => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 3
111100110000 => [4,2,2,4] => [4,4,2,2] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 3
111101100000 => [4,1,2,5] => [5,4,2,1] => [[1,3,6,7,12],[2,5,10,11],[4,9],[8]] => 3
111110000100 => [5,4,1,2] => [5,4,2,1] => [[1,3,6,7,12],[2,5,10,11],[4,9],[8]] => 3
111110001000 => [5,3,1,3] => [5,3,3,1] => [[1,3,4,11,12],[2,6,7],[5,9,10],[8]] => 3
111110010000 => [5,2,1,4] => [5,4,2,1] => [[1,3,6,7,12],[2,5,10,11],[4,9],[8]] => 3
111111000000 => [6,6] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 1
1111111111 => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
1111111110 => [9,1] => [9,1] => [[1,3,4,5,6,7,8,9,10],[2]] => 1
1111111101 => [8,1,1] => [8,1,1] => [[1,4,5,6,7,8,9,10],[2],[3]] => 2
1111111100 => [8,2] => [8,2] => [[1,2,5,6,7,8,9,10],[3,4]] => 1
1111111011 => [7,1,2] => [7,2,1] => [[1,3,6,7,8,9,10],[2,5],[4]] => 2
1111111010 => [7,1,1,1] => [7,1,1,1] => [[1,5,6,7,8,9,10],[2],[3],[4]] => 3
1111111001 => [7,2,1] => [7,2,1] => [[1,3,6,7,8,9,10],[2,5],[4]] => 2
1111110110 => [6,1,2,1] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 3
1111110101 => [6,1,1,1,1] => [6,1,1,1,1] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 4
1111110011 => [6,2,2] => [6,2,2] => [[1,2,7,8,9,10],[3,4],[5,6]] => 2
1111110010 => [6,2,1,1] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 3
1111110001 => [6,3,1] => [6,3,1] => [[1,3,4,8,9,10],[2,6,7],[5]] => 2
1111110000 => [6,4] => [6,4] => [[1,2,3,4,9,10],[5,6,7,8]] => 1
1111101010 => [5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 5
1111101001 => [5,1,1,2,1] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 4
1111101000 => [5,1,1,3] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 3
1111100100 => [5,2,1,2] => [5,2,2,1] => [[1,3,8,9,10],[2,5],[4,7],[6]] => 3
1111100011 => [5,3,2] => [5,3,2] => [[1,2,5,9,10],[3,4,8],[6,7]] => 2
1111100010 => [5,3,1,1] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 3
1111100001 => [5,4,1] => [5,4,1] => [[1,3,4,5,10],[2,7,8,9],[6]] => 2
1111011110 => [4,1,4,1] => [4,4,1,1] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 3
1111011101 => [4,1,3,1,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 4
1111011011 => [4,1,2,1,2] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 4
1111011000 => [4,1,2,3] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 3
1111010111 => [4,1,1,1,3] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 4
1111010101 => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => 6
1111010100 => [4,1,1,1,1,2] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
1111010011 => [4,1,1,2,2] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 4
1111010010 => [4,1,1,2,1,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
1111010001 => [4,1,1,3,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 4
1111001111 => [4,2,4] => [4,4,2] => [[1,2,5,6],[3,4,9,10],[7,8]] => 2
1111001100 => [4,2,2,2] => [4,2,2,2] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 3
1111001011 => [4,2,1,1,2] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 4
1111001010 => [4,2,1,1,1,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
1111001001 => [4,2,1,2,1] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 4
1111000111 => [4,3,3] => [4,3,3] => [[1,2,3,10],[4,5,6],[7,8,9]] => 2
1111000110 => [4,3,2,1] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 3
1111000101 => [4,3,1,1,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 4
1111000011 => [4,4,2] => [4,4,2] => [[1,2,5,6],[3,4,9,10],[7,8]] => 2
1111000001 => [4,5,1] => [5,4,1] => [[1,3,4,5,10],[2,7,8,9],[6]] => 2
1111000000 => [4,6] => [6,4] => [[1,2,3,4,9,10],[5,6,7,8]] => 1
1110111111 => [3,1,6] => [6,3,1] => [[1,3,4,8,9,10],[2,6,7],[5]] => 2
1110111110 => [3,1,5,1] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 3
1110111101 => [3,1,4,1,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 4
1110111011 => [3,1,3,1,2] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
1110111000 => [3,1,3,3] => [3,3,3,1] => [[1,3,4],[2,6,7],[5,9,10],[8]] => 3
1110110101 => [3,1,2,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
1110110100 => [3,1,2,1,1,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
1110110010 => [3,1,2,2,1,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
1110110001 => [3,1,2,3,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
1110101111 => [3,1,1,1,4] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 4
1110101101 => [3,1,1,1,2,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
1110101100 => [3,1,1,1,2,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
1110101011 => [3,1,1,1,1,1,2] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
1110101010 => [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]] => 7
1110101001 => [3,1,1,1,1,2,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
1110100101 => [3,1,1,2,1,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
1110100011 => [3,1,1,3,2] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
1110100001 => [3,1,1,4,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 4
1110011111 => [3,2,5] => [5,3,2] => [[1,2,5,9,10],[3,4,8],[6,7]] => 2
1110011110 => [3,2,4,1] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 3
1110011001 => [3,2,2,2,1] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 4
1110010101 => [3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
1110010011 => [3,2,1,2,2] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 4
1110010001 => [3,2,1,3,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
1110001101 => [3,3,2,1,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
1110001001 => [3,3,1,2,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
1110000111 => [3,4,3] => [4,3,3] => [[1,2,3,10],[4,5,6],[7,8,9]] => 2
1110000101 => [3,4,1,1,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 4
1110000011 => [3,5,2] => [5,3,2] => [[1,2,5,9,10],[3,4,8],[6,7]] => 2
1110000010 => [3,5,1,1] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 3
1110000001 => [3,6,1] => [6,3,1] => [[1,3,4,8,9,10],[2,6,7],[5]] => 2
1101111111 => [2,1,7] => [7,2,1] => [[1,3,6,7,8,9,10],[2,5],[4]] => 2
1101111110 => [2,1,6,1] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 3
1101111101 => [2,1,5,1,1] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 4
1101111011 => [2,1,4,1,2] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 4
1101111001 => [2,1,4,2,1] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 4
1101111000 => [2,1,4,3] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 3
1101110111 => [2,1,3,1,3] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
1101110010 => [2,1,3,2,1,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
1101110001 => [2,1,3,3,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
1101101111 => [2,1,2,1,4] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 4
1101101100 => [2,1,2,1,2,2] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
1101101001 => [2,1,2,1,1,2,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
1101100110 => [2,1,2,2,2,1] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
1101100101 => [2,1,2,2,1,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
1101100011 => [2,1,2,3,2] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 4
1101100001 => [2,1,2,4,1] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 4
1101100000 => [2,1,2,5] => [5,2,2,1] => [[1,3,8,9,10],[2,5],[4,7],[6]] => 3
1101011111 => [2,1,1,1,5] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 4
1101011010 => [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]] => 7
1101011001 => [2,1,1,1,2,2,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
1101010111 => [2,1,1,1,1,1,3] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
1101010101 => [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]] => 8
1101010011 => [2,1,1,1,1,2,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
1101010001 => [2,1,1,1,1,3,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
1101001111 => [2,1,1,2,4] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 4
1101001110 => [2,1,1,2,3,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
1101001101 => [2,1,1,2,2,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
1101001011 => [2,1,1,2,1,1,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
1101001001 => [2,1,1,2,1,2,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
1101001000 => [2,1,1,2,1,3] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
1101000111 => [2,1,1,3,3] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
1101000101 => [2,1,1,3,1,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
1101000011 => [2,1,1,4,2] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 4
1101000010 => [2,1,1,4,1,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
1101000001 => [2,1,1,5,1] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 4
1100111111 => [2,2,6] => [6,2,2] => [[1,2,7,8,9,10],[3,4],[5,6]] => 2
1100111100 => [2,2,4,2] => [4,2,2,2] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 3
1100111001 => [2,2,3,2,1] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 4
1100110110 => [2,2,2,1,2,1] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
1100110101 => [2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
1100110011 => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 4
1100110001 => [2,2,2,3,1] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 4
1100110000 => [2,2,2,4] => [4,2,2,2] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 3
1100101110 => [2,2,1,1,3,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
1100101101 => [2,2,1,1,2,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
1100101011 => [2,2,1,1,1,1,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
1100101001 => [2,2,1,1,1,2,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
1100100111 => [2,2,1,2,3] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 4
1100100110 => [2,2,1,2,2,1] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
1100100101 => [2,2,1,2,1,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
1100100011 => [2,2,1,3,2] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 4
1100011110 => [2,3,4,1] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 3
1100011101 => [2,3,3,1,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
1100011100 => [2,3,3,2] => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 3
1100011011 => [2,3,2,1,2] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 4
1100011001 => [2,3,2,2,1] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 4
1100011000 => [2,3,2,3] => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 3
1100010111 => [2,3,1,1,3] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
1100010101 => [2,3,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
1100010011 => [2,3,1,2,2] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 4
1100010010 => [2,3,1,2,1,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
1100001111 => [2,4,4] => [4,4,2] => [[1,2,5,6],[3,4,9,10],[7,8]] => 2
1100001101 => [2,4,2,1,1] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 4
1100001100 => [2,4,2,2] => [4,2,2,2] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 3
1100001011 => [2,4,1,1,2] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 4
1100001010 => [2,4,1,1,1,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
1100001000 => [2,4,1,3] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 3
1100000111 => [2,5,3] => [5,3,2] => [[1,2,5,9,10],[3,4,8],[6,7]] => 2
1100000110 => [2,5,2,1] => [5,2,2,1] => [[1,3,8,9,10],[2,5],[4,7],[6]] => 3
1100000011 => [2,6,2] => [6,2,2] => [[1,2,7,8,9,10],[3,4],[5,6]] => 2
1100000010 => [2,6,1,1] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 3
1100000001 => [2,7,1] => [7,2,1] => [[1,3,6,7,8,9,10],[2,5],[4]] => 2
1100000000 => [2,8] => [8,2] => [[1,2,5,6,7,8,9,10],[3,4]] => 1
1011111111 => [1,1,8] => [8,1,1] => [[1,4,5,6,7,8,9,10],[2],[3]] => 2
1011111110 => [1,1,7,1] => [7,1,1,1] => [[1,5,6,7,8,9,10],[2],[3],[4]] => 3
1011111101 => [1,1,6,1,1] => [6,1,1,1,1] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 4
1011111100 => [1,1,6,2] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 3
1011111011 => [1,1,5,1,2] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 4
1011111010 => [1,1,5,1,1,1] => [5,1,1,1,1,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 5
1011111000 => [1,1,5,3] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 3
1011110111 => [1,1,4,1,3] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 4
1011110100 => [1,1,4,1,1,2] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
1011110001 => [1,1,4,3,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 4
1011100011 => [1,1,3,3,2] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
1011100001 => [1,1,3,4,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 4
1011100000 => [1,1,3,5] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 3
1011011001 => [1,1,2,1,2,2,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
1011010111 => [1,1,2,1,1,1,3] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
1011010101 => [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]] => 8
1011010011 => [1,1,2,1,1,2,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
1011010001 => [1,1,2,1,1,3,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
1011010000 => [1,1,2,1,1,4] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
1011001101 => [1,1,2,2,2,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
1011001011 => [1,1,2,2,1,1,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
1011001001 => [1,1,2,2,1,2,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
1011001000 => [1,1,2,2,1,3] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
1011000111 => [1,1,2,3,3] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
1011000101 => [1,1,2,3,1,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
1011000100 => [1,1,2,3,1,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
1011000011 => [1,1,2,4,2] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 4
1011000010 => [1,1,2,4,1,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
1011000000 => [1,1,2,6] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 3
1010111111 => [1,1,1,1,6] => [6,1,1,1,1] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 4
1010111110 => [1,1,1,1,5,1] => [5,1,1,1,1,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 5
1010110111 => [1,1,1,1,2,1,3] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
1010110101 => [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]] => 8
1010110011 => [1,1,1,1,2,2,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
1010110001 => [1,1,1,1,2,3,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
1010110000 => [1,1,1,1,2,4] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
1010101111 => [1,1,1,1,1,1,4] => [4,1,1,1,1,1,1] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => 6
1010101101 => [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]] => 8
1010101011 => [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]] => 8
1010101001 => [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]] => 8
1010101000 => [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]] => 7
1010100111 => [1,1,1,1,1,2,3] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
1010100110 => [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]] => 7
1010100101 => [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]] => 8
1010100100 => [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]] => 7
1010100011 => [1,1,1,1,1,3,2] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
1010100010 => [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]] => 7
1010100000 => [1,1,1,1,1,5] => [5,1,1,1,1,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 5
1010011101 => [1,1,1,2,3,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
1010011011 => [1,1,1,2,2,1,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
1010011010 => [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]] => 7
1010011001 => [1,1,1,2,2,2,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
1010011000 => [1,1,1,2,2,3] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
1010010111 => [1,1,1,2,1,1,3] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
1010010110 => [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]] => 7
1010010101 => [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]] => 8
1010010100 => [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]] => 7
1010010011 => [1,1,1,2,1,2,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
1010010010 => [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]] => 7
1010010001 => [1,1,1,2,1,3,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
1010001111 => [1,1,1,3,4] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 4
1010001110 => [1,1,1,3,3,1] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
1010001101 => [1,1,1,3,2,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
1010001100 => [1,1,1,3,2,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
1010001011 => [1,1,1,3,1,1,2] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
1010001010 => [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]] => 7
1010000111 => [1,1,1,4,3] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 4
1010000010 => [1,1,1,5,1,1] => [5,1,1,1,1,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 5
1010000001 => [1,1,1,6,1] => [6,1,1,1,1] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 4
1010000000 => [1,1,1,7] => [7,1,1,1] => [[1,5,6,7,8,9,10],[2],[3],[4]] => 3
1001111110 => [1,2,6,1] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 3
1001111000 => [1,2,4,3] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 3
1001110101 => [1,2,3,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
1001110100 => [1,2,3,1,1,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
1001110011 => [1,2,3,2,2] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 4
1001110001 => [1,2,3,3,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
1001110000 => [1,2,3,4] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 3
1001101101 => [1,2,2,1,2,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
1001101100 => [1,2,2,1,2,2] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
1001101011 => [1,2,2,1,1,1,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
1001101010 => [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]] => 7
1001101001 => [1,2,2,1,1,2,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
1001101000 => [1,2,2,1,1,3] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
1001100111 => [1,2,2,2,3] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 4
1001100110 => [1,2,2,2,2,1] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
1001100101 => [1,2,2,2,1,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
1001100100 => [1,2,2,2,1,2] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
1001100011 => [1,2,2,3,2] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 4
1001100010 => [1,2,2,3,1,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
1001011111 => [1,2,1,1,5] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 4
1001011110 => [1,2,1,1,4,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
1001011101 => [1,2,1,1,3,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
1001011011 => [1,2,1,1,2,1,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
1001011010 => [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]] => 7
1001011001 => [1,2,1,1,2,2,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
1001011000 => [1,2,1,1,2,3] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
1001010111 => [1,2,1,1,1,1,3] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
1001010110 => [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]] => 7
1001010101 => [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]] => 8
1001010100 => [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]] => 7
1001010011 => [1,2,1,1,1,2,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
1001010010 => [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]] => 7
1001001111 => [1,2,1,2,4] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 4
1001001110 => [1,2,1,2,3,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
1001001101 => [1,2,1,2,2,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
1001001100 => [1,2,1,2,2,2] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
1001001011 => [1,2,1,2,1,1,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
1001001010 => [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]] => 7
1001000111 => [1,2,1,3,3] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
1001000000 => [1,2,1,6] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 3
1000111110 => [1,3,5,1] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 3
1000111101 => [1,3,4,1,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 4
1000111100 => [1,3,4,2] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 3
1000111011 => [1,3,3,1,2] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
1000111010 => [1,3,3,1,1,1] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
1000111001 => [1,3,3,2,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
1000111000 => [1,3,3,3] => [3,3,3,1] => [[1,3,4],[2,6,7],[5,9,10],[8]] => 3
1000110111 => [1,3,2,1,3] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
1000110110 => [1,3,2,1,2,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
1000110101 => [1,3,2,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
1000110100 => [1,3,2,1,1,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
1000110011 => [1,3,2,2,2] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 4
1000110010 => [1,3,2,2,1,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
1000110001 => [1,3,2,3,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
1000101111 => [1,3,1,1,4] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 4
1000101110 => [1,3,1,1,3,1] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
1000101101 => [1,3,1,1,2,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
1000101100 => [1,3,1,1,2,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
1000101011 => [1,3,1,1,1,1,2] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
1000101010 => [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]] => 7
1000100111 => [1,3,1,2,3] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
1000011111 => [1,4,5] => [5,4,1] => [[1,3,4,5,10],[2,7,8,9],[6]] => 2
1000011110 => [1,4,4,1] => [4,4,1,1] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 3
1000011101 => [1,4,3,1,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 4
1000011011 => [1,4,2,1,2] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 4
1000010111 => [1,4,1,1,3] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 4
1000010110 => [1,4,1,1,2,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
1000010101 => [1,4,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,8,9,10],[2],[3],[4],[5],[6],[7]] => 6
1000001111 => [1,5,4] => [5,4,1] => [[1,3,4,5,10],[2,7,8,9],[6]] => 2
1000001110 => [1,5,3,1] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 3
1000001101 => [1,5,2,1,1] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 4
1000001011 => [1,5,1,1,2] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 4
1000001010 => [1,5,1,1,1,1] => [5,1,1,1,1,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 5
1000001001 => [1,5,1,2,1] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 4
1000000110 => [1,6,2,1] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 3
1000000101 => [1,6,1,1,1] => [6,1,1,1,1] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 4
1000000100 => [1,6,1,2] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 3
1000000011 => [1,7,2] => [7,2,1] => [[1,3,6,7,8,9,10],[2,5],[4]] => 2
1000000010 => [1,7,1,1] => [7,1,1,1] => [[1,5,6,7,8,9,10],[2],[3],[4]] => 3
1000000001 => [1,8,1] => [8,1,1] => [[1,4,5,6,7,8,9,10],[2],[3]] => 2
1000000000 => [1,9] => [9,1] => [[1,3,4,5,6,7,8,9,10],[2]] => 1
10000011110 => [1,5,4,1] => [5,4,1,1] => [[1,4,5,6,11],[2,8,9,10],[3],[7]] => 3
10000111110 => [1,4,5,1] => [5,4,1,1] => [[1,4,5,6,11],[2,8,9,10],[3],[7]] => 3
100011001110 => [1,3,2,2,3,1] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
110000011110 => [2,5,4,1] => [5,4,2,1] => [[1,3,6,7,12],[2,5,10,11],[4,9],[8]] => 3
100001111100 => [1,4,5,2] => [5,4,2,1] => [[1,3,6,7,12],[2,5,10,11],[4,9],[8]] => 3
100110001110 => [1,2,2,3,3,1] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
100011100110 => [1,3,3,2,2,1] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
0111111111 => [1,9] => [9,1] => [[1,3,4,5,6,7,8,9,10],[2]] => 1
0111111101 => [1,7,1,1] => [7,1,1,1] => [[1,5,6,7,8,9,10],[2],[3],[4]] => 3
0111111001 => [1,6,2,1] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 3
0111110001 => [1,5,3,1] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 3
0111100001 => [1,4,4,1] => [4,4,1,1] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 3
0100000001 => [1,1,7,1] => [7,1,1,1] => [[1,5,6,7,8,9,10],[2],[3],[4]] => 3
0000000001 => [9,1] => [9,1] => [[1,3,4,5,6,7,8,9,10],[2]] => 1
0111111011 => [1,6,1,2] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 3
0111110101 => [1,5,1,1,1,1] => [5,1,1,1,1,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 5
0111101001 => [1,4,1,1,2,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
0111010001 => [1,3,1,1,3,1] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
0110100001 => [1,2,1,1,4,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
0101000001 => [1,1,1,1,5,1] => [5,1,1,1,1,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 5
0101010101 => [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]] => 9
0101001011 => [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]] => 7
0101000111 => [1,1,1,1,3,3] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
0100110011 => [1,1,2,2,2,2] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
0100100111 => [1,1,2,1,2,3] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0100011011 => [1,1,3,2,1,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0100010111 => [1,1,3,1,1,3] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
0100001111 => [1,1,4,4] => [4,4,1,1] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 3
0011010011 => [2,2,1,1,2,2] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
0011000111 => [2,2,3,3] => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 3
0010101011 => [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]] => 7
0010010111 => [2,1,2,1,1,3] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0010001111 => [2,1,3,4] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 3
0001110011 => [3,3,2,2] => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 3
0001101011 => [3,2,1,1,1,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0001100111 => [3,2,2,3] => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 3
0001011101 => [3,1,1,3,1,1] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
0001010111 => [3,1,1,1,1,3] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
0001001111 => [3,1,2,4] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 3
0000111101 => [4,4,1,1] => [4,4,1,1] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 3
0000110111 => [4,2,1,3] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 3
0000101111 => [4,1,1,4] => [4,4,1,1] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 3
0000011111 => [5,5] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 1
010011000111 => [1,1,2,2,3,3] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
001100110011 => [2,2,2,2,2,2] => [2,2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10],[11,12]] => 5
001100010111 => [2,2,3,1,1,3] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
001100001111 => [2,2,4,4] => [4,4,2,2] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 3
001011000111 => [2,1,1,2,3,3] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
001000110111 => [2,1,3,2,1,3] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
001000011111 => [2,1,4,5] => [5,4,2,1] => [[1,3,6,7,12],[2,5,10,11],[4,9],[8]] => 3
000111010011 => [3,3,1,1,2,2] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
000111001011 => [3,3,2,1,1,2] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
000110010111 => [3,2,2,1,1,3] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
000110001111 => [3,2,3,4] => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 3
000100111011 => [3,1,2,3,1,2] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
000100110111 => [3,1,2,2,1,3] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
000100011111 => [3,1,3,5] => [5,3,3,1] => [[1,3,4,11,12],[2,6,7],[5,9,10],[8]] => 3
000011110011 => [4,4,2,2] => [4,4,2,2] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 3
000011001111 => [4,2,2,4] => [4,4,2,2] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 3
000010011111 => [4,1,2,5] => [5,4,2,1] => [[1,3,6,7,12],[2,5,10,11],[4,9],[8]] => 3
000001111011 => [5,4,1,2] => [5,4,2,1] => [[1,3,6,7,12],[2,5,10,11],[4,9],[8]] => 3
000001110111 => [5,3,1,3] => [5,3,3,1] => [[1,3,4,11,12],[2,6,7],[5,9,10],[8]] => 3
000001101111 => [5,2,1,4] => [5,4,2,1] => [[1,3,6,7,12],[2,5,10,11],[4,9],[8]] => 3
000000111111 => [6,6] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 1
111111111111 => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 0
111001100001 => [3,2,2,4,1] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 4
111000011001 => [3,4,2,2,1] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 4
111000001101 => [3,5,2,1,1] => [5,3,2,1,1] => [[1,4,7,11,12],[2,6,10],[3,9],[5],[8]] => 4
111000110001 => [3,3,2,3,1] => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 4
111011000001 => [3,1,2,5,1] => [5,3,2,1,1] => [[1,4,7,11,12],[2,6,10],[3,9],[5],[8]] => 4
100111100001 => [1,2,4,4,1] => [4,4,2,1,1] => [[1,4,7,8],[2,6,11,12],[3,10],[5],[9]] => 4
100110000111 => [1,2,2,4,3] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 4
100001111001 => [1,4,4,2,1] => [4,4,2,1,1] => [[1,4,7,8],[2,6,11,12],[3,10],[5],[9]] => 4
100001100111 => [1,4,2,2,3] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 4
100000110111 => [1,5,2,1,3] => [5,3,2,1,1] => [[1,4,7,11,12],[2,6,10],[3,9],[5],[8]] => 4
100000110001 => [1,5,2,3,1] => [5,3,2,1,1] => [[1,4,7,11,12],[2,6,10],[3,9],[5],[8]] => 4
100000111101 => [1,5,4,1,1] => [5,4,1,1,1] => [[1,5,6,7,12],[2,9,10,11],[3],[4],[8]] => 4
100011000111 => [1,3,2,3,3] => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 4
100011110001 => [1,3,4,3,1] => [4,3,3,1,1] => [[1,4,5,12],[2,7,8],[3,10,11],[6],[9]] => 4
101100011111 => [1,1,2,3,5] => [5,3,2,1,1] => [[1,4,7,11,12],[2,6,10],[3,9],[5],[8]] => 4
101100000111 => [1,1,2,5,3] => [5,3,2,1,1] => [[1,4,7,11,12],[2,6,10],[3,9],[5],[8]] => 4
101111000111 => [1,1,4,3,3] => [4,3,3,1,1] => [[1,4,5,12],[2,7,8],[3,10,11],[6],[9]] => 4
101111000001 => [1,1,4,5,1] => [5,4,1,1,1] => [[1,5,6,7,12],[2,9,10,11],[3],[4],[8]] => 4
0000000000 => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 0
0000000110 => [7,2,1] => [7,2,1] => [[1,3,6,7,8,9,10],[2,5],[4]] => 2
0000011000 => [5,2,3] => [5,3,2] => [[1,2,5,9,10],[3,4,8],[6,7]] => 2
0000011110 => [5,4,1] => [5,4,1] => [[1,3,4,5,10],[2,7,8,9],[6]] => 2
0001111110 => [3,6,1] => [6,3,1] => [[1,3,4,8,9,10],[2,6,7],[5]] => 2
0110011000 => [1,2,2,2,3] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 4
0110010010 => [1,2,2,1,2,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
0111100000 => [1,4,5] => [5,4,1] => [[1,3,4,5,10],[2,7,8,9],[6]] => 2
0111111110 => [1,8,1] => [8,1,1] => [[1,4,5,6,7,8,9,10],[2],[3]] => 2
0111001000 => [1,3,2,1,3] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
0111000010 => [1,3,4,1,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 4
0100111000 => [1,1,2,3,3] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
0100111110 => [1,1,2,5,1] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 4
0100110010 => [1,1,2,2,2,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
0100000010 => [1,1,6,1,1] => [6,1,1,1,1] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 4
0101101000 => [1,1,1,2,1,1,3] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
0101100010 => [1,1,1,2,3,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
0101001010 => [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]] => 8
000000000000 => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 0
000110011110 => [3,2,2,4,1] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 4
000111100110 => [3,4,2,2,1] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 4
000111110010 => [3,5,2,1,1] => [5,3,2,1,1] => [[1,4,7,11,12],[2,6,10],[3,9],[5],[8]] => 4
000111001110 => [3,3,2,3,1] => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 4
000100111110 => [3,1,2,5,1] => [5,3,2,1,1] => [[1,4,7,11,12],[2,6,10],[3,9],[5],[8]] => 4
011000011110 => [1,2,4,4,1] => [4,4,2,1,1] => [[1,4,7,8],[2,6,11,12],[3,10],[5],[9]] => 4
011001111000 => [1,2,2,4,3] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 4
011110000110 => [1,4,4,2,1] => [4,4,2,1,1] => [[1,4,7,8],[2,6,11,12],[3,10],[5],[9]] => 4
011110011000 => [1,4,2,2,3] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 4
011111001000 => [1,5,2,1,3] => [5,3,2,1,1] => [[1,4,7,11,12],[2,6,10],[3,9],[5],[8]] => 4
011111000010 => [1,5,4,1,1] => [5,4,1,1,1] => [[1,5,6,7,12],[2,9,10,11],[3],[4],[8]] => 4
011100111000 => [1,3,2,3,3] => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 4
010011111000 => [1,1,2,5,3] => [5,3,2,1,1] => [[1,4,7,11,12],[2,6,10],[3,9],[5],[8]] => 4
010000111110 => [1,1,4,5,1] => [5,4,1,1,1] => [[1,5,6,7,12],[2,9,10,11],[3],[4],[8]] => 4
0010101010 => [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]] => 8
0010101100 => [2,1,1,1,1,2,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
0010110100 => [2,1,1,2,1,1,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
0011010100 => [2,2,1,1,1,1,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
0101010100 => [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]] => 8
0010101110 => [2,1,1,1,1,3,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
0010111100 => [2,1,1,4,2] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 4
0011110100 => [2,4,1,1,2] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 4
0000010100 => [5,1,1,1,2] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 4
0111010100 => [1,3,1,1,1,1,2] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
0000000010 => [8,1,1] => [8,1,1] => [[1,4,5,6,7,8,9,10],[2],[3]] => 2
0000001110 => [6,3,1] => [6,3,1] => [[1,3,4,8,9,10],[2,6,7],[5]] => 2
0000111110 => [4,5,1] => [5,4,1] => [[1,3,4,5,10],[2,7,8,9],[6]] => 2
0011111110 => [2,7,1] => [7,2,1] => [[1,3,6,7,8,9,10],[2,5],[4]] => 2
0000000100 => [7,1,2] => [7,2,1] => [[1,3,6,7,8,9,10],[2,5],[4]] => 2
0000001010 => [6,1,1,1,1] => [6,1,1,1,1] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 4
0000010110 => [5,1,1,2,1] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 4
0000101110 => [4,1,1,3,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 4
0001011110 => [3,1,1,4,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 4
0010111110 => [2,1,1,5,1] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 4
0101111110 => [1,1,1,6,1] => [6,1,1,1,1] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 4
0010110010 => [2,1,1,2,2,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
0010111000 => [2,1,1,3,3] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
0011001010 => [2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
0011001100 => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 4
0011010010 => [2,2,1,1,2,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
0011011000 => [2,2,1,2,3] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 4
0011100010 => [2,3,3,1,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
0011100100 => [2,3,2,1,2] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 4
0011101000 => [2,3,1,1,3] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
0011110000 => [2,4,4] => [4,4,2] => [[1,2,5,6],[3,4,9,10],[7,8]] => 2
0100101010 => [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]] => 8
0100101100 => [1,1,2,1,1,2,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
0100110100 => [1,1,2,2,1,1,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
0101001100 => [1,1,1,1,2,2,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
0101010010 => [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]] => 8
0101011000 => [1,1,1,1,1,2,3] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
0101100100 => [1,1,1,2,2,1,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
0101110000 => [1,1,1,3,4] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 4
0110001010 => [1,2,3,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
0110001100 => [1,2,3,2,2] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 4
0110010100 => [1,2,2,1,1,1,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
0110100010 => [1,2,1,1,3,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
0110100100 => [1,2,1,1,2,1,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
0110101000 => [1,2,1,1,1,1,3] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
0110110000 => [1,2,1,2,4] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 4
0111000100 => [1,3,3,1,2] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
0111010000 => [1,3,1,1,4] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 4
011000111000 => [1,2,3,3,3] => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 4
011100001100 => [1,3,4,2,2] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 4
011100011000 => [1,3,3,2,3] => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 4
10000100001 => [1,4,1,4,1] => [4,4,1,1,1] => [[1,5,6,7],[2,9,10,11],[3],[4],[8]] => 4
0100000000 => [1,1,8] => [8,1,1] => [[1,4,5,6,7,8,9,10],[2],[3]] => 2
0100000011 => [1,1,6,2] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 3
0100000111 => [1,1,5,3] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 3
0100011111 => [1,1,3,5] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 3
0100111111 => [1,1,2,6] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 3
0101111111 => [1,1,1,7] => [7,1,1,1] => [[1,5,6,7,8,9,10],[2],[3],[4]] => 3
0100000101 => [1,1,5,1,1,1] => [5,1,1,1,1,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 5
0100001011 => [1,1,4,1,1,2] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
0100101111 => [1,1,2,1,1,4] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
0101011111 => [1,1,1,1,1,5] => [5,1,1,1,1,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 5
0110111111 => [1,2,1,6] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 3
0101010110 => [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]] => 8
0101011001 => [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]] => 7
0101011010 => [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]] => 8
0101011100 => [1,1,1,1,1,3,2] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
0101100101 => [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]] => 7
0101100110 => [1,1,1,2,2,2,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
0101101001 => [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]] => 7
0101101010 => [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]] => 8
0101101100 => [1,1,1,2,1,2,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
0101110001 => [1,1,1,3,3,1] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
0101110010 => [1,1,1,3,2,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
0101110100 => [1,1,1,3,1,1,2] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
0101111000 => [1,1,1,4,3] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 4
0110010101 => [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]] => 7
0110010110 => [1,2,2,1,1,2,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
0110011001 => [1,2,2,2,2,1] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
0110011010 => [1,2,2,2,1,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
0110011100 => [1,2,2,3,2] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 4
0110100101 => [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]] => 7
0110100110 => [1,2,1,1,2,2,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
0110101001 => [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]] => 7
0110101010 => [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]] => 8
0110101100 => [1,2,1,1,1,2,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
0110110001 => [1,2,1,2,3,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0110110010 => [1,2,1,2,2,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
0110110100 => [1,2,1,2,1,1,2] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
0110111000 => [1,2,1,3,3] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
0111000101 => [1,3,3,1,1,1] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
0111000110 => [1,3,3,2,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
0111001001 => [1,3,2,1,2,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0111001010 => [1,3,2,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
0111001100 => [1,3,2,2,2] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 4
0111010010 => [1,3,1,1,2,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
0111011000 => [1,3,1,2,3] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
0111100010 => [1,4,3,1,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 4
0111100100 => [1,4,2,1,2] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 4
0111101000 => [1,4,1,1,3] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 4
0111110000 => [1,5,4] => [5,4,1] => [[1,3,4,5,10],[2,7,8,9],[6]] => 2
011001110001 => [1,2,2,3,3,1] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
011100011001 => [1,3,3,2,2,1] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
011100011100 => [1,3,3,3,2] => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 4
011100110001 => [1,3,2,2,3,1] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
011110001100 => [1,4,3,2,2] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 4
0100000100 => [1,1,5,1,2] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 4
0011100110 => [2,3,2,2,1] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 4
0011101010 => [2,3,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
0011101100 => [2,3,1,2,2] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 4
0001101110 => [3,2,1,3,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
0010110110 => [2,1,1,2,1,2,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
0011110010 => [2,4,2,1,1] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 4
0001110110 => [3,3,1,2,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
0100111010 => [1,1,2,3,1,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
0010111010 => [2,1,1,3,1,1,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
0011111000 => [2,5,3] => [5,3,2] => [[1,2,5,9,10],[3,4,8],[6,7]] => 2
0001111010 => [3,4,1,1,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 4
0100111100 => [1,1,2,4,2] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 4
0001111100 => [3,5,2] => [5,3,2] => [[1,2,5,9,10],[3,4,8],[6,7]] => 2
001111000110 => [2,4,3,2,1] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 4
100111110000 => [1,2,5,4] => [5,4,2,1] => [[1,3,6,7,12],[2,5,10,11],[4,9],[8]] => 3
001111110000 => [2,6,4] => [6,4,2] => [[1,2,5,6,11,12],[3,4,9,10],[7,8]] => 2
110001111000 => [2,3,4,3] => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 3
100011111000 => [1,3,5,3] => [5,3,3,1] => [[1,3,4,11,12],[2,6,7],[5,9,10],[8]] => 3
000011111100 => [4,6,2] => [6,4,2] => [[1,2,5,6,11,12],[3,4,9,10],[7,8]] => 2
0000000101 => [7,1,1,1] => [7,1,1,1] => [[1,5,6,7,8,9,10],[2],[3],[4]] => 3
0000001101 => [6,2,1,1] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 3
0000011101 => [5,3,1,1] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 3
0001111101 => [3,5,1,1] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 3
0011111101 => [2,6,1,1] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 3
0000001001 => [6,1,2,1] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 3
0000010101 => [5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 5
0000101101 => [4,1,1,2,1,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
0010111101 => [2,1,1,4,1,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
0101111101 => [1,1,1,5,1,1] => [5,1,1,1,1,1] => [[1,7,8,9,10],[2],[3],[4],[5],[6]] => 5
110001110001 => [2,3,3,3,1] => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 4
110011100001 => [2,2,3,4,1] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 4
0111000011 => [1,3,4,2] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 3
0011110001 => [2,4,3,1] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 3
110000111100 => [2,4,4,2] => [4,4,2,2] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 3
110000001111 => [2,6,4] => [6,4,2] => [[1,2,5,6,11,12],[3,4,9,10],[7,8]] => 2
011100000111 => [1,3,5,3] => [5,3,3,1] => [[1,3,4,11,12],[2,6,7],[5,9,10],[8]] => 3
111000011100 => [3,4,3,2] => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 3
001111000011 => [2,4,4,2] => [4,4,2,2] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 3
011110000011 => [1,4,5,2] => [5,4,2,1] => [[1,3,6,7,12],[2,5,10,11],[4,9],[8]] => 3
111100000011 => [4,6,2] => [6,4,2] => [[1,2,5,6,11,12],[3,4,9,10],[7,8]] => 2
000111110001 => [3,5,3,1] => [5,3,3,1] => [[1,3,4,11,12],[2,6,7],[5,9,10],[8]] => 3
001111100001 => [2,5,4,1] => [5,4,2,1] => [[1,3,6,7,12],[2,5,10,11],[4,9],[8]] => 3
0011011001 => [2,2,1,2,2,1] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
0010110001 => [2,1,1,2,3,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0001000001 => [3,1,5,1] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 3
0111010101 => [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]] => 7
0111010011 => [1,3,1,1,2,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0111001101 => [1,3,2,2,1,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0111011001 => [1,3,1,2,2,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0111000111 => [1,3,3,3] => [3,3,3,1] => [[1,3,4],[2,6,7],[5,9,10],[8]] => 3
0011110101 => [2,4,1,1,1,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
0011110011 => [2,4,2,2] => [4,2,2,2] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 3
0111100101 => [1,4,2,1,1,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
0111100011 => [1,4,3,2] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 3
0011111001 => [2,5,2,1] => [5,2,2,1] => [[1,3,8,9,10],[2,5],[4,7],[6]] => 3
0000111111 => [4,6] => [6,4] => [[1,2,3,4,9,10],[5,6,7,8]] => 1
110001111001 => [2,3,4,2,1] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 4
110011110001 => [2,2,4,3,1] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 4
011100111001 => [1,3,2,3,2,1] => [3,3,2,2,1,1] => [[1,4,9],[2,6,12],[3,8],[5,11],[7],[10]] => 5
011100001111 => [1,3,4,4] => [4,4,3,1] => [[1,3,4,8],[2,6,7,12],[5,10,11],[9]] => 3
111000111001 => [3,3,3,2,1] => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 4
111001110001 => [3,2,3,3,1] => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 4
111000001111 => [3,5,4] => [5,4,3] => [[1,2,3,7,12],[4,5,6,11],[8,9,10]] => 2
001111000111 => [2,4,3,3] => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 3
011110000111 => [1,4,4,3] => [4,4,3,1] => [[1,3,4,8],[2,6,7,12],[5,10,11],[9]] => 3
111100011001 => [4,3,2,2,1] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 4
111100110001 => [4,2,2,3,1] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 4
111100000111 => [4,5,3] => [5,4,3] => [[1,2,3,7,12],[4,5,6,11],[8,9,10]] => 2
000111110011 => [3,5,2,2] => [5,3,2,2] => [[1,2,7,11,12],[3,4,10],[5,6],[8,9]] => 3
001111100011 => [2,5,3,2] => [5,3,2,2] => [[1,2,7,11,12],[3,4,10],[5,6],[8,9]] => 3
011111000011 => [1,5,4,2] => [5,4,2,1] => [[1,3,6,7,12],[2,5,10,11],[4,9],[8]] => 3
0001101100 => [3,2,1,2,2] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 4
0011000110 => [2,2,3,2,1] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 4
0010001110 => [2,1,3,3,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
0110111001 => [1,2,1,3,2,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0001101001 => [3,2,1,1,2,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0000110001 => [4,2,3,1] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 3
0000010001 => [5,1,3,1] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 3
0100011001 => [1,1,3,2,2,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0100111001 => [1,1,2,3,2,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0101111001 => [1,1,1,4,2,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
0110010001 => [1,2,2,1,3,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0100010001 => [1,1,3,1,3,1] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
0100110001 => [1,1,2,2,3,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0100100001 => [1,1,2,1,4,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
0101100001 => [1,1,1,2,4,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
0110011011 => [1,2,2,2,1,2] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
0110111011 => [1,2,1,3,1,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0100111011 => [1,1,2,3,1,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0101111011 => [1,1,1,4,1,2] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
0110010011 => [1,2,2,1,2,2] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
0100010011 => [1,1,3,1,2,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0110110011 => [1,2,1,2,2,2] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
0101110011 => [1,1,1,3,2,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0110100011 => [1,2,1,1,3,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0100100011 => [1,1,2,1,3,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0101100011 => [1,1,1,2,3,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0101000011 => [1,1,1,1,4,2] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
0110010111 => [1,2,2,1,1,3] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0110110111 => [1,2,1,2,1,3] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0100110111 => [1,1,2,2,1,3] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0101110111 => [1,1,1,3,1,3] => [3,3,1,1,1,1] => [[1,6,7],[2,9,10],[3],[4],[5],[8]] => 5
0110100111 => [1,2,1,1,2,3] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0101100111 => [1,1,1,2,2,3] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0110101111 => [1,2,1,1,1,4] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
0101101111 => [1,1,1,2,1,4] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
0101001111 => [1,1,1,1,2,4] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
100011100011 => [1,3,3,3,2] => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 4
100001110011 => [1,4,3,2,2] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 4
0000001100 => [6,2,2] => [6,2,2] => [[1,2,7,8,9,10],[3,4],[5,6]] => 2
0000011001 => [5,2,2,1] => [5,2,2,1] => [[1,3,8,9,10],[2,5],[4,7],[6]] => 3
0000110011 => [4,2,2,2] => [4,2,2,2] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 3
0011001111 => [2,2,2,4] => [4,2,2,2] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 3
0110011111 => [1,2,2,5] => [5,2,2,1] => [[1,3,8,9,10],[2,5],[4,7],[6]] => 3
0000110100 => [4,2,1,1,2] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 4
0000000011 => [8,2] => [8,2] => [[1,2,5,6,7,8,9,10],[3,4]] => 1
0000011011 => [5,2,1,2] => [5,2,2,1] => [[1,3,8,9,10],[2,5],[4,7],[6]] => 3
0001101111 => [3,2,1,4] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 3
0011011111 => [2,2,1,5] => [5,2,2,1] => [[1,3,8,9,10],[2,5],[4,7],[6]] => 3
0000110101 => [4,2,1,1,1,1] => [4,2,1,1,1,1] => [[1,6,9,10],[2,8],[3],[4],[5],[7]] => 5
0011010111 => [2,2,1,1,1,3] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0111001011 => [1,3,2,1,1,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0111110111 => [1,5,1,3] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 3
0110001011 => [1,2,3,1,1,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0110000111 => [1,2,4,3] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 3
110000111001 => [2,4,3,2,1] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 4
001110000111 => [2,3,4,3] => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 3
011000001111 => [1,2,5,4] => [5,4,2,1] => [[1,3,6,7,12],[2,5,10,11],[4,9],[8]] => 3
0011011010 => [2,2,1,2,1,1,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
0011010110 => [2,2,1,1,1,2,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
0100110110 => [1,1,2,2,1,2,1] => [2,2,2,1,1,1,1] => [[1,6],[2,8],[3,10],[4],[5],[7],[9]] => 6
0110001110 => [1,2,3,3,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
0101001110 => [1,1,1,1,2,3,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
0011001110 => [2,2,2,3,1] => [3,2,2,2,1] => [[1,3,10],[2,5],[4,7],[6,9],[8]] => 4
0100101110 => [1,1,2,1,1,3,1] => [3,2,1,1,1,1,1] => [[1,7,10],[2,9],[3],[4],[5],[6],[8]] => 6
0100011110 => [1,1,3,4,1] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 4
0010011110 => [2,1,2,4,1] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 4
001110001110 => [2,3,3,3,1] => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 4
001100011110 => [2,2,3,4,1] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 4
0101000000 => [1,1,1,1,6] => [6,1,1,1,1] => [[1,6,7,8,9,10],[2],[3],[4],[5]] => 4
0001010000 => [3,1,1,1,4] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 4
0100010000 => [1,1,3,1,4] => [4,3,1,1,1] => [[1,5,6,10],[2,8,9],[3],[4],[7]] => 4
0001000100 => [3,1,3,1,2] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
0111011100 => [1,3,1,3,2] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
0101000101 => [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]] => 7
0001010101 => [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]] => 7
0100010101 => [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]] => 7
0110110101 => [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]] => 7
0101010001 => [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]] => 7
0100101001 => [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]] => 7
0110001001 => [1,2,3,1,2,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0101011011 => [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]] => 7
0001001011 => [3,1,2,1,1,2] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0110101011 => [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]] => 7
0001100011 => [3,2,3,2] => [3,3,2,2] => [[1,2,7],[3,4,10],[5,6],[8,9]] => 3
0110000011 => [1,2,5,2] => [5,2,2,1] => [[1,3,8,9,10],[2,5],[4,7],[6]] => 3
0001110111 => [3,3,1,3] => [3,3,3,1] => [[1,3,4],[2,6,7],[5,9,10],[8]] => 3
0111101111 => [1,4,1,4] => [4,4,1,1] => [[1,4,5,6],[2,8,9,10],[3],[7]] => 3
011000001100 => [1,2,5,2,2] => [5,2,2,2,1] => [[1,3,10,11,12],[2,5],[4,7],[6,9],[8]] => 4
000001100011 => [5,2,3,2] => [5,3,2,2] => [[1,2,7,11,12],[3,4,10],[5,6],[8,9]] => 3
000110000011 => [3,2,5,2] => [5,3,2,2] => [[1,2,7,11,12],[3,4,10],[5,6],[8,9]] => 3
011110001111 => [1,4,3,4] => [4,4,3,1] => [[1,3,4,8],[2,6,7,12],[5,10,11],[9]] => 3
100011110011 => [1,3,4,2,2] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 4
100111000111 => [1,2,3,3,3] => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 4
100011100111 => [1,3,3,2,3] => [3,3,3,2,1] => [[1,3,6],[2,5,9],[4,8,12],[7,11],[10]] => 4
0000000111 => [7,3] => [7,3] => [[1,2,3,7,8,9,10],[4,5,6]] => 1
0000001111 => [6,4] => [6,4] => [[1,2,3,4,9,10],[5,6,7,8]] => 1
0001111111 => [3,7] => [7,3] => [[1,2,3,7,8,9,10],[4,5,6]] => 1
0011111111 => [2,8] => [8,2] => [[1,2,5,6,7,8,9,10],[3,4]] => 1
0000001011 => [6,1,1,2] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 3
0000010111 => [5,1,1,3] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 3
0001011111 => [3,1,1,5] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 3
0010111111 => [2,1,1,6] => [6,2,1,1] => [[1,4,7,8,9,10],[2,6],[3],[5]] => 3
0011011110 => [2,2,1,4,1] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 4
0011101110 => [2,3,1,3,1] => [3,3,2,1,1] => [[1,4,7],[2,6,10],[3,9],[5],[8]] => 4
0011110110 => [2,4,1,2,1] => [4,2,2,1,1] => [[1,4,9,10],[2,6],[3,8],[5],[7]] => 4
0011111010 => [2,5,1,1,1] => [5,2,1,1,1] => [[1,5,8,9,10],[2,7],[3],[4],[6]] => 4
0011111100 => [2,6,2] => [6,2,2] => [[1,2,7,8,9,10],[3,4],[5,6]] => 2
000111100011 => [3,4,3,2] => [4,3,3,2] => [[1,2,5,12],[3,4,8],[6,7,11],[9,10]] => 3
0010010101 => [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]] => 7
0101010111 => [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]] => 7
0101110101 => [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]] => 7
01111100100 => [1,5,2,1,2] => [5,2,2,1,1] => [[1,4,9,10,11],[2,6],[3,8],[5],[7]] => 4
110000011000 => [2,5,2,3] => [5,3,2,2] => [[1,2,7,11,12],[3,4,10],[5,6],[8,9]] => 3
111100011110 => [4,3,4,1] => [4,4,3,1] => [[1,3,4,8],[2,6,7,12],[5,10,11],[9]] => 3
111100000110 => [4,5,2,1] => [5,4,2,1] => [[1,3,6,7,12],[2,5,10,11],[4,9],[8]] => 3
0110001111 => [1,2,3,4] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 3
0101101011 => [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]] => 7
0101011101 => [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]] => 7
0011000011 => [2,2,4,2] => [4,2,2,2] => [[1,2,9,10],[3,4],[5,6],[7,8]] => 3
0011011011 => [2,2,1,2,1,2] => [2,2,2,2,1,1] => [[1,4],[2,6],[3,8],[5,10],[7],[9]] => 5
0001111011 => [3,4,1,2] => [4,3,2,1] => [[1,3,6,10],[2,5,9],[4,8],[7]] => 3
111111001111 => [6,2,4] => [6,4,2] => [[1,2,5,6,11,12],[3,4,9,10],[7,8]] => 2
111111000011 => [6,4,2] => [6,4,2] => [[1,2,5,6,11,12],[3,4,9,10],[7,8]] => 2
001111001111 => [2,4,2,4] => [4,4,2,2] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 3
000011000011 => [4,2,4,2] => [4,4,2,2] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 3
111100111100 => [4,2,4,2] => [4,4,2,2] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 3
110000110000 => [2,4,2,4] => [4,4,2,2] => [[1,2,7,8],[3,4,11,12],[5,6],[9,10]] => 3
0011011101 => [2,2,1,3,1,1] => [3,2,2,1,1,1] => [[1,5,10],[2,7],[3,9],[4],[6],[8]] => 5
0111011111 => [1,3,1,5] => [5,3,1,1] => [[1,4,5,9,10],[2,7,8],[3],[6]] => 3
111100111001 => [4,2,3,2,1] => [4,3,2,2,1] => [[1,3,8,12],[2,5,11],[4,7],[6,10],[9]] => 4
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Generating function
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Sequences for the coefficients of a few of the
first generating functions, in the case at hand:
2,2 2,4,2 2,6,6,2 2,8,12,8,2 2,10,20,20,10,2 2,12,30,40,30,12,2 2,14,42,70,70,42,14,2 2,16,56,112,140,112,56,16,2
$F_{1} = 2$
$F_{2} = 2 + 2\ q$
$F_{3} = 2 + 4\ q + 2\ q^{2}$
$F_{4} = 2 + 6\ q + 6\ q^{2} + 2\ q^{3}$
$F_{5} = 2 + 8\ q + 12\ q^{2} + 8\ q^{3} + 2\ q^{4}$
$F_{6} = 2 + 10\ q + 20\ q^{2} + 20\ q^{3} + 10\ q^{4} + 2\ q^{5}$
$F_{7} = 2 + 12\ q + 30\ q^{2} + 40\ q^{3} + 30\ q^{4} + 12\ q^{5} + 2\ q^{6}$
$F_{8} = 2 + 14\ q + 42\ q^{2} + 70\ q^{3} + 70\ q^{4} + 42\ q^{5} + 14\ q^{6} + 2\ q^{7}$
$F_{9} = 2 + 16\ q + 56\ q^{2} + 112\ q^{3} + 140\ q^{4} + 112\ q^{5} + 56\ q^{6} + 16\ q^{7} + 2\ q^{8}$
Description
The number of descents of a standard tableau.
Entry $i$ of a standard Young tableau is a descent if $i+1$ appears in a row below the row of $i$.
Entry $i$ of a standard Young tableau is a descent if $i+1$ appears in a row below the row of $i$.
Map
delta morphism
Description
Applies the delta morphism to a binary word.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.
Map
to partition
Description
Sends a composition to the partition obtained by sorting the entries.
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.
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