Identifier
-
Mp00097:
Binary words
—delta morphism⟶
Integer compositions
Mp00040: Integer compositions —to partition⟶ Integer partitions
Mp00042: Integer partitions —initial tableau⟶ Standard tableaux
St000734: Standard tableaux ⟶ ℤ
Values
0 => [1] => [1] => [[1]] => 1
1 => [1] => [1] => [[1]] => 1
00 => [2] => [2] => [[1,2]] => 2
01 => [1,1] => [1,1] => [[1],[2]] => 1
10 => [1,1] => [1,1] => [[1],[2]] => 1
11 => [2] => [2] => [[1,2]] => 2
000 => [3] => [3] => [[1,2,3]] => 3
001 => [2,1] => [2,1] => [[1,2],[3]] => 2
010 => [1,1,1] => [1,1,1] => [[1],[2],[3]] => 1
011 => [1,2] => [2,1] => [[1,2],[3]] => 2
100 => [1,2] => [2,1] => [[1,2],[3]] => 2
101 => [1,1,1] => [1,1,1] => [[1],[2],[3]] => 1
110 => [2,1] => [2,1] => [[1,2],[3]] => 2
111 => [3] => [3] => [[1,2,3]] => 3
0000 => [4] => [4] => [[1,2,3,4]] => 4
0001 => [3,1] => [3,1] => [[1,2,3],[4]] => 3
0010 => [2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 2
0011 => [2,2] => [2,2] => [[1,2],[3,4]] => 2
0100 => [1,1,2] => [2,1,1] => [[1,2],[3],[4]] => 2
0101 => [1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 1
0110 => [1,2,1] => [2,1,1] => [[1,2],[3],[4]] => 2
0111 => [1,3] => [3,1] => [[1,2,3],[4]] => 3
1000 => [1,3] => [3,1] => [[1,2,3],[4]] => 3
1001 => [1,2,1] => [2,1,1] => [[1,2],[3],[4]] => 2
1010 => [1,1,1,1] => [1,1,1,1] => [[1],[2],[3],[4]] => 1
1011 => [1,1,2] => [2,1,1] => [[1,2],[3],[4]] => 2
1100 => [2,2] => [2,2] => [[1,2],[3,4]] => 2
1101 => [2,1,1] => [2,1,1] => [[1,2],[3],[4]] => 2
1110 => [3,1] => [3,1] => [[1,2,3],[4]] => 3
1111 => [4] => [4] => [[1,2,3,4]] => 4
00000 => [5] => [5] => [[1,2,3,4,5]] => 5
00001 => [4,1] => [4,1] => [[1,2,3,4],[5]] => 4
00010 => [3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 3
00011 => [3,2] => [3,2] => [[1,2,3],[4,5]] => 3
00100 => [2,1,2] => [2,2,1] => [[1,2],[3,4],[5]] => 2
00101 => [2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
00110 => [2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 2
00111 => [2,3] => [3,2] => [[1,2,3],[4,5]] => 3
01000 => [1,1,3] => [3,1,1] => [[1,2,3],[4],[5]] => 3
01001 => [1,1,2,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
01010 => [1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1
01011 => [1,1,1,2] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
01100 => [1,2,2] => [2,2,1] => [[1,2],[3,4],[5]] => 2
01101 => [1,2,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
01110 => [1,3,1] => [3,1,1] => [[1,2,3],[4],[5]] => 3
01111 => [1,4] => [4,1] => [[1,2,3,4],[5]] => 4
10000 => [1,4] => [4,1] => [[1,2,3,4],[5]] => 4
10001 => [1,3,1] => [3,1,1] => [[1,2,3],[4],[5]] => 3
10010 => [1,2,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
10011 => [1,2,2] => [2,2,1] => [[1,2],[3,4],[5]] => 2
10100 => [1,1,1,2] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
10101 => [1,1,1,1,1] => [1,1,1,1,1] => [[1],[2],[3],[4],[5]] => 1
10110 => [1,1,2,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
10111 => [1,1,3] => [3,1,1] => [[1,2,3],[4],[5]] => 3
11000 => [2,3] => [3,2] => [[1,2,3],[4,5]] => 3
11001 => [2,2,1] => [2,2,1] => [[1,2],[3,4],[5]] => 2
11010 => [2,1,1,1] => [2,1,1,1] => [[1,2],[3],[4],[5]] => 2
11011 => [2,1,2] => [2,2,1] => [[1,2],[3,4],[5]] => 2
11100 => [3,2] => [3,2] => [[1,2,3],[4,5]] => 3
11101 => [3,1,1] => [3,1,1] => [[1,2,3],[4],[5]] => 3
11110 => [4,1] => [4,1] => [[1,2,3,4],[5]] => 4
11111 => [5] => [5] => [[1,2,3,4,5]] => 5
000000 => [6] => [6] => [[1,2,3,4,5,6]] => 6
000001 => [5,1] => [5,1] => [[1,2,3,4,5],[6]] => 5
000010 => [4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
000011 => [4,2] => [4,2] => [[1,2,3,4],[5,6]] => 4
000100 => [3,1,2] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
000101 => [3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
000110 => [3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
000111 => [3,3] => [3,3] => [[1,2,3],[4,5,6]] => 3
001000 => [2,1,3] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
001001 => [2,1,2,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
001010 => [2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
001011 => [2,1,1,2] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
001100 => [2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 2
001101 => [2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
001110 => [2,3,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
001111 => [2,4] => [4,2] => [[1,2,3,4],[5,6]] => 4
010000 => [1,1,4] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
010001 => [1,1,3,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
010010 => [1,1,2,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
010011 => [1,1,2,2] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
010100 => [1,1,1,1,2] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
010101 => [1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 1
010110 => [1,1,1,2,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
010111 => [1,1,1,3] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
011000 => [1,2,3] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
011001 => [1,2,2,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
011010 => [1,2,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
011011 => [1,2,1,2] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
011100 => [1,3,2] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
011101 => [1,3,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
011110 => [1,4,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
011111 => [1,5] => [5,1] => [[1,2,3,4,5],[6]] => 5
100000 => [1,5] => [5,1] => [[1,2,3,4,5],[6]] => 5
100001 => [1,4,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
100010 => [1,3,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
100011 => [1,3,2] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
100100 => [1,2,1,2] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
100101 => [1,2,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
100110 => [1,2,2,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
>>> Load all 1830 entries. <<<100111 => [1,2,3] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
101000 => [1,1,1,3] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
101001 => [1,1,1,2,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
101010 => [1,1,1,1,1,1] => [1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6]] => 1
101011 => [1,1,1,1,2] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
101100 => [1,1,2,2] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
101101 => [1,1,2,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
101110 => [1,1,3,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
101111 => [1,1,4] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
110000 => [2,4] => [4,2] => [[1,2,3,4],[5,6]] => 4
110001 => [2,3,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
110010 => [2,2,1,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
110011 => [2,2,2] => [2,2,2] => [[1,2],[3,4],[5,6]] => 2
110100 => [2,1,1,2] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
110101 => [2,1,1,1,1] => [2,1,1,1,1] => [[1,2],[3],[4],[5],[6]] => 2
110110 => [2,1,2,1] => [2,2,1,1] => [[1,2],[3,4],[5],[6]] => 2
110111 => [2,1,3] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
111000 => [3,3] => [3,3] => [[1,2,3],[4,5,6]] => 3
111001 => [3,2,1] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
111010 => [3,1,1,1] => [3,1,1,1] => [[1,2,3],[4],[5],[6]] => 3
111011 => [3,1,2] => [3,2,1] => [[1,2,3],[4,5],[6]] => 3
111100 => [4,2] => [4,2] => [[1,2,3,4],[5,6]] => 4
111101 => [4,1,1] => [4,1,1] => [[1,2,3,4],[5],[6]] => 4
111110 => [5,1] => [5,1] => [[1,2,3,4,5],[6]] => 5
111111 => [6] => [6] => [[1,2,3,4,5,6]] => 6
0000000 => [7] => [7] => [[1,2,3,4,5,6,7]] => 7
0000001 => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 6
0000010 => [5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
0000011 => [5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 5
0000100 => [4,1,2] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
0000101 => [4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
0000110 => [4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
0000111 => [4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 4
0001000 => [3,1,3] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
0001001 => [3,1,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
0001010 => [3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
0001011 => [3,1,1,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
0001100 => [3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
0001101 => [3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
0001110 => [3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
0001111 => [3,4] => [4,3] => [[1,2,3,4],[5,6,7]] => 4
0010000 => [2,1,4] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
0010001 => [2,1,3,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
0010010 => [2,1,2,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
0010011 => [2,1,2,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
0010100 => [2,1,1,1,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
0010101 => [2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
0010110 => [2,1,1,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
0010111 => [2,1,1,3] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
0011000 => [2,2,3] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
0011001 => [2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
0011010 => [2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
0011011 => [2,2,1,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
0011100 => [2,3,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
0011101 => [2,3,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
0011110 => [2,4,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
0011111 => [2,5] => [5,2] => [[1,2,3,4,5],[6,7]] => 5
0100000 => [1,1,5] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
0100001 => [1,1,4,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
0100010 => [1,1,3,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
0100011 => [1,1,3,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
0100100 => [1,1,2,1,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
0100101 => [1,1,2,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
0100110 => [1,1,2,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
0100111 => [1,1,2,3] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
0101000 => [1,1,1,1,3] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
0101001 => [1,1,1,1,2,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
0101010 => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 1
0101011 => [1,1,1,1,1,2] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
0101100 => [1,1,1,2,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
0101101 => [1,1,1,2,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
0101110 => [1,1,1,3,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
0101111 => [1,1,1,4] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
0110000 => [1,2,4] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
0110001 => [1,2,3,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
0110010 => [1,2,2,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
0110011 => [1,2,2,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
0110100 => [1,2,1,1,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
0110101 => [1,2,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
0110110 => [1,2,1,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
0110111 => [1,2,1,3] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
0111000 => [1,3,3] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
0111001 => [1,3,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
0111010 => [1,3,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
0111011 => [1,3,1,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
0111100 => [1,4,2] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
0111101 => [1,4,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
0111110 => [1,5,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
0111111 => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 6
1000000 => [1,6] => [6,1] => [[1,2,3,4,5,6],[7]] => 6
1000001 => [1,5,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
1000010 => [1,4,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
1000011 => [1,4,2] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
1000100 => [1,3,1,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
1000101 => [1,3,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
1000110 => [1,3,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
1000111 => [1,3,3] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
1001000 => [1,2,1,3] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
1001001 => [1,2,1,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
1001010 => [1,2,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
1001011 => [1,2,1,1,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
1001100 => [1,2,2,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
1001101 => [1,2,2,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
1001110 => [1,2,3,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
1001111 => [1,2,4] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
1010000 => [1,1,1,4] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
1010001 => [1,1,1,3,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
1010010 => [1,1,1,2,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
1010011 => [1,1,1,2,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
1010100 => [1,1,1,1,1,2] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
1010101 => [1,1,1,1,1,1,1] => [1,1,1,1,1,1,1] => [[1],[2],[3],[4],[5],[6],[7]] => 1
1010110 => [1,1,1,1,2,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
1010111 => [1,1,1,1,3] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
1011000 => [1,1,2,3] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
1011001 => [1,1,2,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
1011010 => [1,1,2,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
1011011 => [1,1,2,1,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
1011100 => [1,1,3,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
1011101 => [1,1,3,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
1011110 => [1,1,4,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
1011111 => [1,1,5] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
1100000 => [2,5] => [5,2] => [[1,2,3,4,5],[6,7]] => 5
1100001 => [2,4,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
1100010 => [2,3,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
1100011 => [2,3,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
1100100 => [2,2,1,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
1100101 => [2,2,1,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
1100110 => [2,2,2,1] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
1100111 => [2,2,3] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
1101000 => [2,1,1,3] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
1101001 => [2,1,1,2,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
1101010 => [2,1,1,1,1,1] => [2,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7]] => 2
1101011 => [2,1,1,1,2] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
1101100 => [2,1,2,2] => [2,2,2,1] => [[1,2],[3,4],[5,6],[7]] => 2
1101101 => [2,1,2,1,1] => [2,2,1,1,1] => [[1,2],[3,4],[5],[6],[7]] => 2
1101110 => [2,1,3,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
1101111 => [2,1,4] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
1110000 => [3,4] => [4,3] => [[1,2,3,4],[5,6,7]] => 4
1110001 => [3,3,1] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
1110010 => [3,2,1,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
1110011 => [3,2,2] => [3,2,2] => [[1,2,3],[4,5],[6,7]] => 3
1110100 => [3,1,1,2] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
1110101 => [3,1,1,1,1] => [3,1,1,1,1] => [[1,2,3],[4],[5],[6],[7]] => 3
1110110 => [3,1,2,1] => [3,2,1,1] => [[1,2,3],[4,5],[6],[7]] => 3
1110111 => [3,1,3] => [3,3,1] => [[1,2,3],[4,5,6],[7]] => 3
1111000 => [4,3] => [4,3] => [[1,2,3,4],[5,6,7]] => 4
1111001 => [4,2,1] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
1111010 => [4,1,1,1] => [4,1,1,1] => [[1,2,3,4],[5],[6],[7]] => 4
1111011 => [4,1,2] => [4,2,1] => [[1,2,3,4],[5,6],[7]] => 4
1111100 => [5,2] => [5,2] => [[1,2,3,4,5],[6,7]] => 5
1111101 => [5,1,1] => [5,1,1] => [[1,2,3,4,5],[6],[7]] => 5
1111110 => [6,1] => [6,1] => [[1,2,3,4,5,6],[7]] => 6
1111111 => [7] => [7] => [[1,2,3,4,5,6,7]] => 7
00000000 => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 8
00000001 => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 7
00000010 => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
00000011 => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 6
00000100 => [5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
00000101 => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
00000110 => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
00000111 => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 5
00001000 => [4,1,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
00001001 => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
00001010 => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
00001011 => [4,1,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
00001100 => [4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
00001101 => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
00001110 => [4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
00001111 => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
00010000 => [3,1,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
00010001 => [3,1,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
00010010 => [3,1,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
00010011 => [3,1,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
00010100 => [3,1,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
00010101 => [3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
00010110 => [3,1,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
00010111 => [3,1,1,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
00011000 => [3,2,3] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
00011001 => [3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
00011010 => [3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
00011011 => [3,2,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
00011100 => [3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
00011101 => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
00011110 => [3,4,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
00011111 => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 5
00100000 => [2,1,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
00100001 => [2,1,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
00100010 => [2,1,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
00100011 => [2,1,3,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
00100100 => [2,1,2,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
00100101 => [2,1,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
00100110 => [2,1,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
00100111 => [2,1,2,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
00101000 => [2,1,1,1,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
00101001 => [2,1,1,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
00101010 => [2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
00101011 => [2,1,1,1,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
00101100 => [2,1,1,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
00101101 => [2,1,1,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
00101110 => [2,1,1,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
00101111 => [2,1,1,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
00110000 => [2,2,4] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
00110001 => [2,2,3,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
00110010 => [2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
00110011 => [2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 2
00110100 => [2,2,1,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
00110101 => [2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
00110110 => [2,2,1,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
00110111 => [2,2,1,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
00111000 => [2,3,3] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
00111001 => [2,3,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
00111010 => [2,3,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
00111011 => [2,3,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
00111100 => [2,4,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
00111101 => [2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
00111110 => [2,5,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
00111111 => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 6
01000000 => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
01000001 => [1,1,5,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
01000010 => [1,1,4,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
01000011 => [1,1,4,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
01000100 => [1,1,3,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
01000101 => [1,1,3,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
01000110 => [1,1,3,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
01000111 => [1,1,3,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
01001000 => [1,1,2,1,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
01001001 => [1,1,2,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
01001010 => [1,1,2,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
01001011 => [1,1,2,1,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
01001100 => [1,1,2,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
01001101 => [1,1,2,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
01001110 => [1,1,2,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
01001111 => [1,1,2,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
01010000 => [1,1,1,1,4] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
01010001 => [1,1,1,1,3,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
01010010 => [1,1,1,1,2,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
01010011 => [1,1,1,1,2,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
01010100 => [1,1,1,1,1,1,2] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
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]] => 1
01010110 => [1,1,1,1,1,2,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
01010111 => [1,1,1,1,1,3] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
01011000 => [1,1,1,2,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
01011001 => [1,1,1,2,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
01011010 => [1,1,1,2,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
01011011 => [1,1,1,2,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
01011100 => [1,1,1,3,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
01011101 => [1,1,1,3,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
01011110 => [1,1,1,4,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
01011111 => [1,1,1,5] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
01100000 => [1,2,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
01100001 => [1,2,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
01100010 => [1,2,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
01100011 => [1,2,3,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
01100100 => [1,2,2,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
01100101 => [1,2,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
01100110 => [1,2,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
01100111 => [1,2,2,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
01101000 => [1,2,1,1,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
01101001 => [1,2,1,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
01101010 => [1,2,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
01101011 => [1,2,1,1,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
01101100 => [1,2,1,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
01101101 => [1,2,1,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
01101110 => [1,2,1,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
01101111 => [1,2,1,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
01110000 => [1,3,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
01110001 => [1,3,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
01110010 => [1,3,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
01110011 => [1,3,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
01110100 => [1,3,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
01110101 => [1,3,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
01110110 => [1,3,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
01110111 => [1,3,1,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
01111000 => [1,4,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
01111001 => [1,4,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
01111010 => [1,4,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
01111011 => [1,4,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
01111100 => [1,5,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
01111101 => [1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
01111110 => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
01111111 => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 7
10000000 => [1,7] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 7
10000001 => [1,6,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
10000010 => [1,5,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
10000011 => [1,5,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
10000100 => [1,4,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
10000101 => [1,4,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
10000110 => [1,4,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
10000111 => [1,4,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
10001000 => [1,3,1,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
10001001 => [1,3,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
10001010 => [1,3,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
10001011 => [1,3,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
10001100 => [1,3,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
10001101 => [1,3,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
10001110 => [1,3,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
10001111 => [1,3,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
10010000 => [1,2,1,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
10010001 => [1,2,1,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
10010010 => [1,2,1,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
10010011 => [1,2,1,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
10010100 => [1,2,1,1,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
10010101 => [1,2,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
10010110 => [1,2,1,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
10010111 => [1,2,1,1,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
10011000 => [1,2,2,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
10011001 => [1,2,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
10011010 => [1,2,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
10011011 => [1,2,2,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
10011100 => [1,2,3,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
10011101 => [1,2,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
10011110 => [1,2,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
10011111 => [1,2,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
10100000 => [1,1,1,5] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
10100001 => [1,1,1,4,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
10100010 => [1,1,1,3,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
10100011 => [1,1,1,3,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
10100100 => [1,1,1,2,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
10100101 => [1,1,1,2,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
10100110 => [1,1,1,2,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
10100111 => [1,1,1,2,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
10101000 => [1,1,1,1,1,3] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
10101001 => [1,1,1,1,1,2,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
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]] => 1
10101011 => [1,1,1,1,1,1,2] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
10101100 => [1,1,1,1,2,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
10101101 => [1,1,1,1,2,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
10101110 => [1,1,1,1,3,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
10101111 => [1,1,1,1,4] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
10110000 => [1,1,2,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
10110001 => [1,1,2,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
10110010 => [1,1,2,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
10110011 => [1,1,2,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
10110100 => [1,1,2,1,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
10110101 => [1,1,2,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
10110110 => [1,1,2,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
10110111 => [1,1,2,1,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
10111000 => [1,1,3,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
10111001 => [1,1,3,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
10111010 => [1,1,3,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
10111011 => [1,1,3,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
10111100 => [1,1,4,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
10111101 => [1,1,4,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
10111110 => [1,1,5,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
10111111 => [1,1,6] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
11000000 => [2,6] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 6
11000001 => [2,5,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
11000010 => [2,4,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
11000011 => [2,4,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
11000100 => [2,3,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
11000101 => [2,3,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
11000110 => [2,3,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
11000111 => [2,3,3] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
11001000 => [2,2,1,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
11001001 => [2,2,1,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
11001010 => [2,2,1,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
11001011 => [2,2,1,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
11001100 => [2,2,2,2] => [2,2,2,2] => [[1,2],[3,4],[5,6],[7,8]] => 2
11001101 => [2,2,2,1,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
11001110 => [2,2,3,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
11001111 => [2,2,4] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
11010000 => [2,1,1,4] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
11010001 => [2,1,1,3,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
11010010 => [2,1,1,2,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
11010011 => [2,1,1,2,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
11010100 => [2,1,1,1,1,2] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
11010101 => [2,1,1,1,1,1,1] => [2,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8]] => 2
11010110 => [2,1,1,1,2,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
11010111 => [2,1,1,1,3] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
11011000 => [2,1,2,3] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
11011001 => [2,1,2,2,1] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
11011010 => [2,1,2,1,1,1] => [2,2,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8]] => 2
11011011 => [2,1,2,1,2] => [2,2,2,1,1] => [[1,2],[3,4],[5,6],[7],[8]] => 2
11011100 => [2,1,3,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
11011101 => [2,1,3,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
11011110 => [2,1,4,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
11011111 => [2,1,5] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
11100000 => [3,5] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 5
11100001 => [3,4,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
11100010 => [3,3,1,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
11100011 => [3,3,2] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
11100100 => [3,2,1,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
11100101 => [3,2,1,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
11100110 => [3,2,2,1] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
11100111 => [3,2,3] => [3,3,2] => [[1,2,3],[4,5,6],[7,8]] => 3
11101000 => [3,1,1,3] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
11101001 => [3,1,1,2,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
11101010 => [3,1,1,1,1,1] => [3,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8]] => 3
11101011 => [3,1,1,1,2] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
11101100 => [3,1,2,2] => [3,2,2,1] => [[1,2,3],[4,5],[6,7],[8]] => 3
11101101 => [3,1,2,1,1] => [3,2,1,1,1] => [[1,2,3],[4,5],[6],[7],[8]] => 3
11101110 => [3,1,3,1] => [3,3,1,1] => [[1,2,3],[4,5,6],[7],[8]] => 3
11101111 => [3,1,4] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
11110000 => [4,4] => [4,4] => [[1,2,3,4],[5,6,7,8]] => 4
11110001 => [4,3,1] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
11110010 => [4,2,1,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
11110011 => [4,2,2] => [4,2,2] => [[1,2,3,4],[5,6],[7,8]] => 4
11110100 => [4,1,1,2] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
11110101 => [4,1,1,1,1] => [4,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8]] => 4
11110110 => [4,1,2,1] => [4,2,1,1] => [[1,2,3,4],[5,6],[7],[8]] => 4
11110111 => [4,1,3] => [4,3,1] => [[1,2,3,4],[5,6,7],[8]] => 4
11111000 => [5,3] => [5,3] => [[1,2,3,4,5],[6,7,8]] => 5
11111001 => [5,2,1] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
11111010 => [5,1,1,1] => [5,1,1,1] => [[1,2,3,4,5],[6],[7],[8]] => 5
11111011 => [5,1,2] => [5,2,1] => [[1,2,3,4,5],[6,7],[8]] => 5
11111100 => [6,2] => [6,2] => [[1,2,3,4,5,6],[7,8]] => 6
11111101 => [6,1,1] => [6,1,1] => [[1,2,3,4,5,6],[7],[8]] => 6
11111110 => [7,1] => [7,1] => [[1,2,3,4,5,6,7],[8]] => 7
11111111 => [8] => [8] => [[1,2,3,4,5,6,7,8]] => 8
000000000 => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 9
000000001 => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 8
000000010 => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
000000011 => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 7
000000100 => [6,1,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
000000101 => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
000000110 => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
000000111 => [6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 6
000001000 => [5,1,3] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
000001001 => [5,1,2,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
000001010 => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
000001011 => [5,1,1,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
000001100 => [5,2,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 5
000001101 => [5,2,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
000001110 => [5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
000001111 => [5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 5
000010000 => [4,1,4] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
000010001 => [4,1,3,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
000010010 => [4,1,2,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
000010011 => [4,1,2,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
000010100 => [4,1,1,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
000010101 => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
000010110 => [4,1,1,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
000010111 => [4,1,1,3] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
000011000 => [4,2,3] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
000011001 => [4,2,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
000011010 => [4,2,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
000011011 => [4,2,1,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
000011100 => [4,3,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
000011101 => [4,3,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
000011110 => [4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
000011111 => [4,5] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 5
000100000 => [3,1,5] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
000100001 => [3,1,4,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
000100010 => [3,1,3,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
000100011 => [3,1,3,2] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
000100100 => [3,1,2,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
000100101 => [3,1,2,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
000100110 => [3,1,2,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
000100111 => [3,1,2,3] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
000101000 => [3,1,1,1,3] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
000101001 => [3,1,1,1,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
000101010 => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
000101011 => [3,1,1,1,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
000101100 => [3,1,1,2,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
000101101 => [3,1,1,2,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
000101110 => [3,1,1,3,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
000101111 => [3,1,1,4] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
000110000 => [3,2,4] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
000110001 => [3,2,3,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
000110010 => [3,2,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
000110011 => [3,2,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
000110100 => [3,2,1,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
000110101 => [3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
000110110 => [3,2,1,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
000110111 => [3,2,1,3] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
000111000 => [3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 3
000111001 => [3,3,2,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
000111010 => [3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
000111011 => [3,3,1,2] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
000111100 => [3,4,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
000111101 => [3,4,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
000111110 => [3,5,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
000111111 => [3,6] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 6
001000000 => [2,1,6] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
001000001 => [2,1,5,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
001000010 => [2,1,4,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
001000011 => [2,1,4,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
001000100 => [2,1,3,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
001000101 => [2,1,3,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
001000110 => [2,1,3,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
001000111 => [2,1,3,3] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
001001000 => [2,1,2,1,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
001001001 => [2,1,2,1,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
001001010 => [2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
001001011 => [2,1,2,1,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
001001100 => [2,1,2,2,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
001001101 => [2,1,2,2,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
001001110 => [2,1,2,3,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
001001111 => [2,1,2,4] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
001010000 => [2,1,1,1,4] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
001010001 => [2,1,1,1,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
001010010 => [2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
001010011 => [2,1,1,1,2,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
001010100 => [2,1,1,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
001010101 => [2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
001010110 => [2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
001010111 => [2,1,1,1,1,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
001011000 => [2,1,1,2,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
001011001 => [2,1,1,2,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
001011010 => [2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
001011011 => [2,1,1,2,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
001011100 => [2,1,1,3,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
001011101 => [2,1,1,3,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
001011110 => [2,1,1,4,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
001011111 => [2,1,1,5] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
001100000 => [2,2,5] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 5
001100001 => [2,2,4,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
001100010 => [2,2,3,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
001100011 => [2,2,3,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
001100100 => [2,2,2,1,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
001100101 => [2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
001100110 => [2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
001100111 => [2,2,2,3] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
001101000 => [2,2,1,1,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
001101001 => [2,2,1,1,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
001101010 => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
001101011 => [2,2,1,1,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
001101100 => [2,2,1,2,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
001101101 => [2,2,1,2,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
001101110 => [2,2,1,3,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
001101111 => [2,2,1,4] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
001110000 => [2,3,4] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
001110001 => [2,3,3,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
001110010 => [2,3,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
001110011 => [2,3,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
001110100 => [2,3,1,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
001110101 => [2,3,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
001110110 => [2,3,1,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
001110111 => [2,3,1,3] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
001111000 => [2,4,3] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
001111001 => [2,4,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
001111010 => [2,4,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
001111011 => [2,4,1,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
001111100 => [2,5,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 5
001111101 => [2,5,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
001111110 => [2,6,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
001111111 => [2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 7
010000000 => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
010000001 => [1,1,6,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
010000010 => [1,1,5,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
010000011 => [1,1,5,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
010000100 => [1,1,4,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
010000101 => [1,1,4,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
010000110 => [1,1,4,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
010000111 => [1,1,4,3] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
010001000 => [1,1,3,1,3] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
010001001 => [1,1,3,1,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
010001010 => [1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
010001011 => [1,1,3,1,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
010001100 => [1,1,3,2,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
010001101 => [1,1,3,2,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
010001110 => [1,1,3,3,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
010001111 => [1,1,3,4] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
010010000 => [1,1,2,1,4] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
010010001 => [1,1,2,1,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
010010010 => [1,1,2,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
010010011 => [1,1,2,1,2,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
010010100 => [1,1,2,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
010010101 => [1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
010010110 => [1,1,2,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
010010111 => [1,1,2,1,1,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
010011000 => [1,1,2,2,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
010011001 => [1,1,2,2,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
010011010 => [1,1,2,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
010011011 => [1,1,2,2,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
010011100 => [1,1,2,3,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
010011101 => [1,1,2,3,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
010011110 => [1,1,2,4,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
010011111 => [1,1,2,5] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
010100000 => [1,1,1,1,5] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
010100001 => [1,1,1,1,4,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
010100010 => [1,1,1,1,3,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
010100011 => [1,1,1,1,3,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
010100100 => [1,1,1,1,2,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
010100101 => [1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
010100110 => [1,1,1,1,2,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
010100111 => [1,1,1,1,2,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
010101000 => [1,1,1,1,1,1,3] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
010101001 => [1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
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]] => 1
010101011 => [1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
010101100 => [1,1,1,1,1,2,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
010101101 => [1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
010101110 => [1,1,1,1,1,3,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
010101111 => [1,1,1,1,1,4] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
010110000 => [1,1,1,2,4] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
010110001 => [1,1,1,2,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
010110010 => [1,1,1,2,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
010110011 => [1,1,1,2,2,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
010110100 => [1,1,1,2,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
010110101 => [1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
010110110 => [1,1,1,2,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
010110111 => [1,1,1,2,1,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
010111000 => [1,1,1,3,3] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
010111001 => [1,1,1,3,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
010111010 => [1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
010111011 => [1,1,1,3,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
010111100 => [1,1,1,4,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
010111101 => [1,1,1,4,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
010111110 => [1,1,1,5,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
010111111 => [1,1,1,6] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
011000000 => [1,2,6] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
011000001 => [1,2,5,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
011000010 => [1,2,4,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
011000011 => [1,2,4,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
011000100 => [1,2,3,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
011000101 => [1,2,3,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
011000110 => [1,2,3,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
011000111 => [1,2,3,3] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
011001000 => [1,2,2,1,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
011001001 => [1,2,2,1,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
011001010 => [1,2,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
011001011 => [1,2,2,1,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
011001100 => [1,2,2,2,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
011001101 => [1,2,2,2,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
011001110 => [1,2,2,3,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
011001111 => [1,2,2,4] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
011010000 => [1,2,1,1,4] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
011010001 => [1,2,1,1,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
011010010 => [1,2,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
011010011 => [1,2,1,1,2,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
011010100 => [1,2,1,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
011010101 => [1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
011010110 => [1,2,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
011010111 => [1,2,1,1,1,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
011011000 => [1,2,1,2,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
011011001 => [1,2,1,2,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
011011010 => [1,2,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
011011011 => [1,2,1,2,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
011011100 => [1,2,1,3,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
011011101 => [1,2,1,3,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
011011110 => [1,2,1,4,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
011011111 => [1,2,1,5] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
011100000 => [1,3,5] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
011100001 => [1,3,4,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
011100010 => [1,3,3,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
011100011 => [1,3,3,2] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
011100100 => [1,3,2,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
011100101 => [1,3,2,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
011100110 => [1,3,2,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
011100111 => [1,3,2,3] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
011101000 => [1,3,1,1,3] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
011101001 => [1,3,1,1,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
011101010 => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
011101011 => [1,3,1,1,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
011101100 => [1,3,1,2,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
011101101 => [1,3,1,2,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
011101110 => [1,3,1,3,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
011101111 => [1,3,1,4] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
011110000 => [1,4,4] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
011110001 => [1,4,3,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
011110010 => [1,4,2,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
011110011 => [1,4,2,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
011110100 => [1,4,1,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
011110101 => [1,4,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
011110110 => [1,4,1,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
011110111 => [1,4,1,3] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
011111000 => [1,5,3] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
011111001 => [1,5,2,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
011111010 => [1,5,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
011111011 => [1,5,1,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
011111100 => [1,6,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
011111101 => [1,6,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
011111110 => [1,7,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
011111111 => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 8
100000000 => [1,8] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 8
100000001 => [1,7,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
100000010 => [1,6,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
100000011 => [1,6,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
100000100 => [1,5,1,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
100000101 => [1,5,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
100000110 => [1,5,2,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
100000111 => [1,5,3] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
100001000 => [1,4,1,3] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
100001001 => [1,4,1,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
100001010 => [1,4,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
100001011 => [1,4,1,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
100001100 => [1,4,2,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
100001101 => [1,4,2,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
100001110 => [1,4,3,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
100001111 => [1,4,4] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
100010000 => [1,3,1,4] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
100010001 => [1,3,1,3,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
100010010 => [1,3,1,2,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
100010011 => [1,3,1,2,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
100010100 => [1,3,1,1,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
100010101 => [1,3,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
100010110 => [1,3,1,1,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
100010111 => [1,3,1,1,3] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
100011000 => [1,3,2,3] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
100011001 => [1,3,2,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
100011010 => [1,3,2,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
100011011 => [1,3,2,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
100011100 => [1,3,3,2] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
100011101 => [1,3,3,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
100011110 => [1,3,4,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
100011111 => [1,3,5] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
100100000 => [1,2,1,5] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
100100001 => [1,2,1,4,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
100100010 => [1,2,1,3,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
100100011 => [1,2,1,3,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
100100100 => [1,2,1,2,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
100100101 => [1,2,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
100100110 => [1,2,1,2,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
100100111 => [1,2,1,2,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
100101000 => [1,2,1,1,1,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
100101001 => [1,2,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
100101010 => [1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
100101011 => [1,2,1,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
100101100 => [1,2,1,1,2,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
100101101 => [1,2,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
100101110 => [1,2,1,1,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
100101111 => [1,2,1,1,4] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
100110000 => [1,2,2,4] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
100110001 => [1,2,2,3,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
100110010 => [1,2,2,2,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
100110011 => [1,2,2,2,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
100110100 => [1,2,2,1,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
100110101 => [1,2,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
100110110 => [1,2,2,1,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
100110111 => [1,2,2,1,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
100111000 => [1,2,3,3] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
100111001 => [1,2,3,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
100111010 => [1,2,3,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
100111011 => [1,2,3,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
100111100 => [1,2,4,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
100111101 => [1,2,4,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
100111110 => [1,2,5,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
100111111 => [1,2,6] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
101000000 => [1,1,1,6] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
101000001 => [1,1,1,5,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
101000010 => [1,1,1,4,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
101000011 => [1,1,1,4,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
101000100 => [1,1,1,3,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
101000101 => [1,1,1,3,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
101000110 => [1,1,1,3,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
101000111 => [1,1,1,3,3] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
101001000 => [1,1,1,2,1,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
101001001 => [1,1,1,2,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
101001010 => [1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
101001011 => [1,1,1,2,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
101001100 => [1,1,1,2,2,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
101001101 => [1,1,1,2,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
101001110 => [1,1,1,2,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
101001111 => [1,1,1,2,4] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
101010000 => [1,1,1,1,1,4] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
101010001 => [1,1,1,1,1,3,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
101010010 => [1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
101010011 => [1,1,1,1,1,2,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
101010100 => [1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
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]] => 1
101010110 => [1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
101010111 => [1,1,1,1,1,1,3] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
101011000 => [1,1,1,1,2,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
101011001 => [1,1,1,1,2,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
101011010 => [1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
101011011 => [1,1,1,1,2,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
101011100 => [1,1,1,1,3,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
101011101 => [1,1,1,1,3,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
101011110 => [1,1,1,1,4,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
101011111 => [1,1,1,1,5] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
101100000 => [1,1,2,5] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
101100001 => [1,1,2,4,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
101100010 => [1,1,2,3,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
101100011 => [1,1,2,3,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
101100100 => [1,1,2,2,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
101100101 => [1,1,2,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
101100110 => [1,1,2,2,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
101100111 => [1,1,2,2,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
101101000 => [1,1,2,1,1,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
101101001 => [1,1,2,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
101101010 => [1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
101101011 => [1,1,2,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
101101100 => [1,1,2,1,2,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
101101101 => [1,1,2,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
101101110 => [1,1,2,1,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
101101111 => [1,1,2,1,4] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
101110000 => [1,1,3,4] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
101110001 => [1,1,3,3,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
101110010 => [1,1,3,2,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
101110011 => [1,1,3,2,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
101110100 => [1,1,3,1,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
101110101 => [1,1,3,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
101110110 => [1,1,3,1,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
101110111 => [1,1,3,1,3] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
101111000 => [1,1,4,3] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
101111001 => [1,1,4,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
101111010 => [1,1,4,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
101111011 => [1,1,4,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
101111100 => [1,1,5,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
101111101 => [1,1,5,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
101111110 => [1,1,6,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
101111111 => [1,1,7] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
110000000 => [2,7] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 7
110000001 => [2,6,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
110000010 => [2,5,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
110000011 => [2,5,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 5
110000100 => [2,4,1,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
110000101 => [2,4,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
110000110 => [2,4,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
110000111 => [2,4,3] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
110001000 => [2,3,1,3] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
110001001 => [2,3,1,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
110001010 => [2,3,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
110001011 => [2,3,1,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
110001100 => [2,3,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
110001101 => [2,3,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
110001110 => [2,3,3,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
110001111 => [2,3,4] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
110010000 => [2,2,1,4] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
110010001 => [2,2,1,3,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
110010010 => [2,2,1,2,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
110010011 => [2,2,1,2,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
110010100 => [2,2,1,1,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
110010101 => [2,2,1,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
110010110 => [2,2,1,1,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
110010111 => [2,2,1,1,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
110011000 => [2,2,2,3] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
110011001 => [2,2,2,2,1] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
110011010 => [2,2,2,1,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
110011011 => [2,2,2,1,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
110011100 => [2,2,3,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
110011101 => [2,2,3,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
110011110 => [2,2,4,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
110011111 => [2,2,5] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 5
110100000 => [2,1,1,5] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
110100001 => [2,1,1,4,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
110100010 => [2,1,1,3,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
110100011 => [2,1,1,3,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
110100100 => [2,1,1,2,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
110100101 => [2,1,1,2,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
110100110 => [2,1,1,2,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
110100111 => [2,1,1,2,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
110101000 => [2,1,1,1,1,3] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
110101001 => [2,1,1,1,1,2,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
110101010 => [2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9]] => 2
110101011 => [2,1,1,1,1,1,2] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
110101100 => [2,1,1,1,2,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
110101101 => [2,1,1,1,2,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
110101110 => [2,1,1,1,3,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
110101111 => [2,1,1,1,4] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
110110000 => [2,1,2,4] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
110110001 => [2,1,2,3,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
110110010 => [2,1,2,2,1,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
110110011 => [2,1,2,2,2] => [2,2,2,2,1] => [[1,2],[3,4],[5,6],[7,8],[9]] => 2
110110100 => [2,1,2,1,1,2] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
110110101 => [2,1,2,1,1,1,1] => [2,2,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9]] => 2
110110110 => [2,1,2,1,2,1] => [2,2,2,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9]] => 2
110110111 => [2,1,2,1,3] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
110111000 => [2,1,3,3] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
110111001 => [2,1,3,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
110111010 => [2,1,3,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
110111011 => [2,1,3,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
110111100 => [2,1,4,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
110111101 => [2,1,4,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
110111110 => [2,1,5,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
110111111 => [2,1,6] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
111000000 => [3,6] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 6
111000001 => [3,5,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
111000010 => [3,4,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
111000011 => [3,4,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
111000100 => [3,3,1,2] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
111000101 => [3,3,1,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
111000110 => [3,3,2,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
111000111 => [3,3,3] => [3,3,3] => [[1,2,3],[4,5,6],[7,8,9]] => 3
111001000 => [3,2,1,3] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
111001001 => [3,2,1,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
111001010 => [3,2,1,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
111001011 => [3,2,1,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
111001100 => [3,2,2,2] => [3,2,2,2] => [[1,2,3],[4,5],[6,7],[8,9]] => 3
111001101 => [3,2,2,1,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
111001110 => [3,2,3,1] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
111001111 => [3,2,4] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
111010000 => [3,1,1,4] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
111010001 => [3,1,1,3,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
111010010 => [3,1,1,2,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
111010011 => [3,1,1,2,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
111010100 => [3,1,1,1,1,2] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
111010101 => [3,1,1,1,1,1,1] => [3,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9]] => 3
111010110 => [3,1,1,1,2,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
111010111 => [3,1,1,1,3] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
111011000 => [3,1,2,3] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
111011001 => [3,1,2,2,1] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
111011010 => [3,1,2,1,1,1] => [3,2,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9]] => 3
111011011 => [3,1,2,1,2] => [3,2,2,1,1] => [[1,2,3],[4,5],[6,7],[8],[9]] => 3
111011100 => [3,1,3,2] => [3,3,2,1] => [[1,2,3],[4,5,6],[7,8],[9]] => 3
111011101 => [3,1,3,1,1] => [3,3,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9]] => 3
111011110 => [3,1,4,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
111011111 => [3,1,5] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
111100000 => [4,5] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 5
111100001 => [4,4,1] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
111100010 => [4,3,1,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
111100011 => [4,3,2] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
111100100 => [4,2,1,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
111100101 => [4,2,1,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
111100110 => [4,2,2,1] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
111100111 => [4,2,3] => [4,3,2] => [[1,2,3,4],[5,6,7],[8,9]] => 4
111101000 => [4,1,1,3] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
111101001 => [4,1,1,2,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
111101010 => [4,1,1,1,1,1] => [4,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9]] => 4
111101011 => [4,1,1,1,2] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
111101100 => [4,1,2,2] => [4,2,2,1] => [[1,2,3,4],[5,6],[7,8],[9]] => 4
111101101 => [4,1,2,1,1] => [4,2,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9]] => 4
111101110 => [4,1,3,1] => [4,3,1,1] => [[1,2,3,4],[5,6,7],[8],[9]] => 4
111101111 => [4,1,4] => [4,4,1] => [[1,2,3,4],[5,6,7,8],[9]] => 4
111110000 => [5,4] => [5,4] => [[1,2,3,4,5],[6,7,8,9]] => 5
111110001 => [5,3,1] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
111110010 => [5,2,1,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
111110011 => [5,2,2] => [5,2,2] => [[1,2,3,4,5],[6,7],[8,9]] => 5
111110100 => [5,1,1,2] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
111110101 => [5,1,1,1,1] => [5,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9]] => 5
111110110 => [5,1,2,1] => [5,2,1,1] => [[1,2,3,4,5],[6,7],[8],[9]] => 5
111110111 => [5,1,3] => [5,3,1] => [[1,2,3,4,5],[6,7,8],[9]] => 5
111111000 => [6,3] => [6,3] => [[1,2,3,4,5,6],[7,8,9]] => 6
111111001 => [6,2,1] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
111111010 => [6,1,1,1] => [6,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9]] => 6
111111011 => [6,1,2] => [6,2,1] => [[1,2,3,4,5,6],[7,8],[9]] => 6
111111100 => [7,2] => [7,2] => [[1,2,3,4,5,6,7],[8,9]] => 7
111111101 => [7,1,1] => [7,1,1] => [[1,2,3,4,5,6,7],[8],[9]] => 7
111111110 => [8,1] => [8,1] => [[1,2,3,4,5,6,7,8],[9]] => 8
111111111 => [9] => [9] => [[1,2,3,4,5,6,7,8,9]] => 9
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]] => 1
1010101100 => [1,1,1,1,1,1,2,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
1010110010 => [1,1,1,1,2,2,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
1010110100 => [1,1,1,1,2,1,1,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
1010111000 => [1,1,1,1,3,3] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
1011001010 => [1,1,2,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
1011001100 => [1,1,2,2,2,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
1011010010 => [1,1,2,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
1011010100 => [1,1,2,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
1011011000 => [1,1,2,1,2,3] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
1011100010 => [1,1,3,3,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
1011100100 => [1,1,3,2,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
1011101000 => [1,1,3,1,1,3] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
1011110000 => [1,1,4,4] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
1100101010 => [2,2,1,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
1100101100 => [2,2,1,1,2,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
1100110010 => [2,2,2,2,1,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
1100110100 => [2,2,2,1,1,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
1100111000 => [2,2,3,3] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => 3
1101001010 => [2,1,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
1101001100 => [2,1,1,2,2,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
1101010010 => [2,1,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
1101010100 => [2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
1101011000 => [2,1,1,1,2,3] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
1101100010 => [2,1,2,3,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
1101100100 => [2,1,2,2,1,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
1101101000 => [2,1,2,1,1,3] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
1101110000 => [2,1,3,4] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
1110001010 => [3,3,1,1,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
1110001100 => [3,3,2,2] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => 3
1110010010 => [3,2,1,2,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
1110010100 => [3,2,1,1,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
1110011000 => [3,2,2,3] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => 3
1110100010 => [3,1,1,3,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
1110100100 => [3,1,1,2,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
1110101000 => [3,1,1,1,1,3] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
1110110000 => [3,1,2,4] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
1111000010 => [4,4,1,1] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
1111000100 => [4,3,1,2] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
1111001000 => [4,2,1,3] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
1111010000 => [4,1,1,4] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
1111100000 => [5,5] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 5
101100111000 => [1,1,2,2,3,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
101110001100 => [1,1,3,3,2,2] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
101110011000 => [1,1,3,2,2,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
110010111000 => [2,2,1,1,3,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
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]] => 2
110011100010 => [2,2,3,3,1,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
110011101000 => [2,2,3,1,1,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
110011110000 => [2,2,4,4] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
110100111000 => [2,1,1,2,3,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
110111000100 => [2,1,3,3,1,2] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
110111001000 => [2,1,3,2,1,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
110111100000 => [2,1,4,5] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 5
111000101100 => [3,3,1,1,2,2] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
111000110010 => [3,3,2,2,1,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
111000110100 => [3,3,2,1,1,2] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
111000111000 => [3,3,3,3] => [3,3,3,3] => [[1,2,3],[4,5,6],[7,8,9],[10,11,12]] => 3
111001011000 => [3,2,1,1,2,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
111001100010 => [3,2,2,3,1,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
111001101000 => [3,2,2,1,1,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
111001110000 => [3,2,3,4] => [4,3,3,2] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12]] => 4
111010001100 => [3,1,1,3,2,2] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
111010011000 => [3,1,1,2,2,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
111011000100 => [3,1,2,3,1,2] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
111011001000 => [3,1,2,2,1,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
111011100000 => [3,1,3,5] => [5,3,3,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12]] => 5
111100001100 => [4,4,2,2] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
111100011000 => [4,3,2,3] => [4,3,3,2] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12]] => 4
111100110000 => [4,2,2,4] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
111101100000 => [4,1,2,5] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 5
111110000100 => [5,4,1,2] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 5
111110001000 => [5,3,1,3] => [5,3,3,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12]] => 5
111110010000 => [5,2,1,4] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 5
111111000000 => [6,6] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 6
1111111111 => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 10
1111111110 => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 9
1111111101 => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
1111111100 => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 8
1111111011 => [7,1,2] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
1111111010 => [7,1,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
1111111001 => [7,2,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
1111110110 => [6,1,2,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
1111110101 => [6,1,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
1111110011 => [6,2,2] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 6
1111110010 => [6,2,1,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
1111110001 => [6,3,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
1111110000 => [6,4] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 6
1111101010 => [5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
1111101001 => [5,1,1,2,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
1111101000 => [5,1,1,3] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
1111100100 => [5,2,1,2] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 5
1111100011 => [5,3,2] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => 5
1111100010 => [5,3,1,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
1111100001 => [5,4,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
1111011110 => [4,1,4,1] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
1111011101 => [4,1,3,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
1111011011 => [4,1,2,1,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
1111011000 => [4,1,2,3] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
1111010111 => [4,1,1,1,3] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
1111010101 => [4,1,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
1111010100 => [4,1,1,1,1,2] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
1111010011 => [4,1,1,2,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
1111010010 => [4,1,1,2,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
1111010001 => [4,1,1,3,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
1111001111 => [4,2,4] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => 4
1111001100 => [4,2,2,2] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
1111001011 => [4,2,1,1,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
1111001010 => [4,2,1,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
1111001001 => [4,2,1,2,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
1111000111 => [4,3,3] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => 4
1111000110 => [4,3,2,1] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
1111000101 => [4,3,1,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
1111000011 => [4,4,2] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => 4
1111000001 => [4,5,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
1111000000 => [4,6] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 6
1110111111 => [3,1,6] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
1110111110 => [3,1,5,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
1110111101 => [3,1,4,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
1110111011 => [3,1,3,1,2] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
1110111000 => [3,1,3,3] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => 3
1110110101 => [3,1,2,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
1110110100 => [3,1,2,1,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
1110110010 => [3,1,2,2,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
1110110001 => [3,1,2,3,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
1110101111 => [3,1,1,1,4] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
1110101101 => [3,1,1,1,2,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
1110101100 => [3,1,1,1,2,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
1110101011 => [3,1,1,1,1,1,2] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
1110101010 => [3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 3
1110101001 => [3,1,1,1,1,2,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
1110100101 => [3,1,1,2,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
1110100011 => [3,1,1,3,2] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
1110100001 => [3,1,1,4,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
1110011111 => [3,2,5] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => 5
1110011110 => [3,2,4,1] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
1110011001 => [3,2,2,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
1110010101 => [3,2,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
1110010011 => [3,2,1,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
1110010001 => [3,2,1,3,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
1110001101 => [3,3,2,1,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
1110001001 => [3,3,1,2,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
1110000111 => [3,4,3] => [4,3,3] => [[1,2,3,4],[5,6,7],[8,9,10]] => 4
1110000101 => [3,4,1,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
1110000011 => [3,5,2] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => 5
1110000010 => [3,5,1,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
1110000001 => [3,6,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
1101111111 => [2,1,7] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
1101111110 => [2,1,6,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
1101111101 => [2,1,5,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
1101111011 => [2,1,4,1,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
1101111001 => [2,1,4,2,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
1101111000 => [2,1,4,3] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
1101110111 => [2,1,3,1,3] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
1101110010 => [2,1,3,2,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
1101110001 => [2,1,3,3,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
1101101111 => [2,1,2,1,4] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
1101101100 => [2,1,2,1,2,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
1101101001 => [2,1,2,1,1,2,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
1101100110 => [2,1,2,2,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
1101100101 => [2,1,2,2,1,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
1101100011 => [2,1,2,3,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
1101100001 => [2,1,2,4,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
1101100000 => [2,1,2,5] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 5
1101011111 => [2,1,1,1,5] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
1101011010 => [2,1,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
1101011001 => [2,1,1,1,2,2,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
1101010111 => [2,1,1,1,1,1,3] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
1101010101 => [2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
1101010011 => [2,1,1,1,1,2,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
1101010001 => [2,1,1,1,1,3,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
1101001111 => [2,1,1,2,4] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
1101001110 => [2,1,1,2,3,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
1101001101 => [2,1,1,2,2,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
1101001011 => [2,1,1,2,1,1,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
1101001001 => [2,1,1,2,1,2,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
1101001000 => [2,1,1,2,1,3] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
1101000111 => [2,1,1,3,3] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
1101000101 => [2,1,1,3,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
1101000011 => [2,1,1,4,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
1101000010 => [2,1,1,4,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
1101000001 => [2,1,1,5,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
1100111111 => [2,2,6] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 6
1100111100 => [2,2,4,2] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
1100111001 => [2,2,3,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
1100110110 => [2,2,2,1,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
1100110101 => [2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
1100110011 => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
1100110001 => [2,2,2,3,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
1100110000 => [2,2,2,4] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
1100101110 => [2,2,1,1,3,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
1100101101 => [2,2,1,1,2,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
1100101011 => [2,2,1,1,1,1,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
1100101001 => [2,2,1,1,1,2,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
1100100111 => [2,2,1,2,3] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
1100100110 => [2,2,1,2,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
1100100101 => [2,2,1,2,1,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
1100100011 => [2,2,1,3,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
1100011110 => [2,3,4,1] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
1100011101 => [2,3,3,1,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
1100011100 => [2,3,3,2] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => 3
1100011011 => [2,3,2,1,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
1100011001 => [2,3,2,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
1100011000 => [2,3,2,3] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => 3
1100010111 => [2,3,1,1,3] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
1100010101 => [2,3,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
1100010011 => [2,3,1,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
1100010010 => [2,3,1,2,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
1100001111 => [2,4,4] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => 4
1100001101 => [2,4,2,1,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
1100001100 => [2,4,2,2] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
1100001011 => [2,4,1,1,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
1100001010 => [2,4,1,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
1100001000 => [2,4,1,3] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
1100000111 => [2,5,3] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => 5
1100000110 => [2,5,2,1] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 5
1100000011 => [2,6,2] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 6
1100000010 => [2,6,1,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
1100000001 => [2,7,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
1100000000 => [2,8] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 8
1011111111 => [1,1,8] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
1011111110 => [1,1,7,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
1011111101 => [1,1,6,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
1011111100 => [1,1,6,2] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
1011111011 => [1,1,5,1,2] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
1011111010 => [1,1,5,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
1011111000 => [1,1,5,3] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
1011110111 => [1,1,4,1,3] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
1011110100 => [1,1,4,1,1,2] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
1011110001 => [1,1,4,3,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
1011100011 => [1,1,3,3,2] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
1011100001 => [1,1,3,4,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
1011100000 => [1,1,3,5] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
1011011001 => [1,1,2,1,2,2,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
1011010111 => [1,1,2,1,1,1,3] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
1011010101 => [1,1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
1011010011 => [1,1,2,1,1,2,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
1011010001 => [1,1,2,1,1,3,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
1011010000 => [1,1,2,1,1,4] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
1011001101 => [1,1,2,2,2,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
1011001011 => [1,1,2,2,1,1,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
1011001001 => [1,1,2,2,1,2,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
1011001000 => [1,1,2,2,1,3] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
1011000111 => [1,1,2,3,3] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
1011000101 => [1,1,2,3,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
1011000100 => [1,1,2,3,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
1011000011 => [1,1,2,4,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
1011000010 => [1,1,2,4,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
1011000000 => [1,1,2,6] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
1010111111 => [1,1,1,1,6] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
1010111110 => [1,1,1,1,5,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
1010110111 => [1,1,1,1,2,1,3] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
1010110101 => [1,1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
1010110011 => [1,1,1,1,2,2,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
1010110001 => [1,1,1,1,2,3,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
1010110000 => [1,1,1,1,2,4] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
1010101111 => [1,1,1,1,1,1,4] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
1010101101 => [1,1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
1010101011 => [1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
1010101001 => [1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
1010101000 => [1,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 3
1010100111 => [1,1,1,1,1,2,3] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
1010100110 => [1,1,1,1,1,2,2,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
1010100101 => [1,1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
1010100100 => [1,1,1,1,1,2,1,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
1010100011 => [1,1,1,1,1,3,2] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
1010100010 => [1,1,1,1,1,3,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 3
1010100000 => [1,1,1,1,1,5] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
1010011101 => [1,1,1,2,3,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
1010011011 => [1,1,1,2,2,1,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
1010011010 => [1,1,1,2,2,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
1010011001 => [1,1,1,2,2,2,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
1010011000 => [1,1,1,2,2,3] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
1010010111 => [1,1,1,2,1,1,3] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
1010010110 => [1,1,1,2,1,1,2,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
1010010101 => [1,1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
1010010100 => [1,1,1,2,1,1,1,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
1010010011 => [1,1,1,2,1,2,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
1010010010 => [1,1,1,2,1,2,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
1010010001 => [1,1,1,2,1,3,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
1010001111 => [1,1,1,3,4] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
1010001110 => [1,1,1,3,3,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
1010001101 => [1,1,1,3,2,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
1010001100 => [1,1,1,3,2,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
1010001011 => [1,1,1,3,1,1,2] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
1010001010 => [1,1,1,3,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 3
1010000111 => [1,1,1,4,3] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
1010000010 => [1,1,1,5,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
1010000001 => [1,1,1,6,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
1010000000 => [1,1,1,7] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
1001111110 => [1,2,6,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
1001111000 => [1,2,4,3] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
1001110101 => [1,2,3,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
1001110100 => [1,2,3,1,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
1001110011 => [1,2,3,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
1001110001 => [1,2,3,3,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
1001110000 => [1,2,3,4] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
1001101101 => [1,2,2,1,2,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
1001101100 => [1,2,2,1,2,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
1001101011 => [1,2,2,1,1,1,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
1001101010 => [1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
1001101001 => [1,2,2,1,1,2,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
1001101000 => [1,2,2,1,1,3] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
1001100111 => [1,2,2,2,3] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
1001100110 => [1,2,2,2,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
1001100101 => [1,2,2,2,1,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
1001100100 => [1,2,2,2,1,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
1001100011 => [1,2,2,3,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
1001100010 => [1,2,2,3,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
1001011111 => [1,2,1,1,5] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
1001011110 => [1,2,1,1,4,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
1001011101 => [1,2,1,1,3,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
1001011011 => [1,2,1,1,2,1,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
1001011010 => [1,2,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
1001011001 => [1,2,1,1,2,2,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
1001011000 => [1,2,1,1,2,3] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
1001010111 => [1,2,1,1,1,1,3] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
1001010110 => [1,2,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
1001010101 => [1,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
1001010100 => [1,2,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
1001010011 => [1,2,1,1,1,2,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
1001010010 => [1,2,1,1,1,2,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
1001001111 => [1,2,1,2,4] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
1001001110 => [1,2,1,2,3,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
1001001101 => [1,2,1,2,2,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
1001001100 => [1,2,1,2,2,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
1001001011 => [1,2,1,2,1,1,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
1001001010 => [1,2,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
1001000111 => [1,2,1,3,3] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
1001000000 => [1,2,1,6] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
1000111110 => [1,3,5,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
1000111101 => [1,3,4,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
1000111100 => [1,3,4,2] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
1000111011 => [1,3,3,1,2] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
1000111010 => [1,3,3,1,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
1000111001 => [1,3,3,2,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
1000111000 => [1,3,3,3] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => 3
1000110111 => [1,3,2,1,3] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
1000110110 => [1,3,2,1,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
1000110101 => [1,3,2,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
1000110100 => [1,3,2,1,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
1000110011 => [1,3,2,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
1000110010 => [1,3,2,2,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
1000110001 => [1,3,2,3,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
1000101111 => [1,3,1,1,4] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
1000101110 => [1,3,1,1,3,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
1000101101 => [1,3,1,1,2,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
1000101100 => [1,3,1,1,2,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
1000101011 => [1,3,1,1,1,1,2] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
1000101010 => [1,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 3
1000100111 => [1,3,1,2,3] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
1000011111 => [1,4,5] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
1000011110 => [1,4,4,1] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
1000011101 => [1,4,3,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
1000011011 => [1,4,2,1,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
1000010111 => [1,4,1,1,3] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
1000010110 => [1,4,1,1,2,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
1000010101 => [1,4,1,1,1,1,1] => [4,1,1,1,1,1,1] => [[1,2,3,4],[5],[6],[7],[8],[9],[10]] => 4
1000001111 => [1,5,4] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
1000001110 => [1,5,3,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
1000001101 => [1,5,2,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
1000001011 => [1,5,1,1,2] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
1000001010 => [1,5,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
1000001001 => [1,5,1,2,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
1000000110 => [1,6,2,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
1000000101 => [1,6,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
1000000100 => [1,6,1,2] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
1000000011 => [1,7,2] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
1000000010 => [1,7,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
1000000001 => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
1000000000 => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 9
10000011110 => [1,5,4,1] => [5,4,1,1] => [[1,2,3,4,5],[6,7,8,9],[10],[11]] => 5
10000111110 => [1,4,5,1] => [5,4,1,1] => [[1,2,3,4,5],[6,7,8,9],[10],[11]] => 5
100011001110 => [1,3,2,2,3,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
110000011110 => [2,5,4,1] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 5
100001111100 => [1,4,5,2] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 5
100110001110 => [1,2,2,3,3,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
100011100110 => [1,3,3,2,2,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
0111111111 => [1,9] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 9
0111111101 => [1,7,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
0111111001 => [1,6,2,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
0111110001 => [1,5,3,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
0111100001 => [1,4,4,1] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
0100000001 => [1,1,7,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
0000000001 => [9,1] => [9,1] => [[1,2,3,4,5,6,7,8,9],[10]] => 9
0111111011 => [1,6,1,2] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
0111110101 => [1,5,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
0111101001 => [1,4,1,1,2,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
0111010001 => [1,3,1,1,3,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
0110100001 => [1,2,1,1,4,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
0101000001 => [1,1,1,1,5,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 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]] => 1
0101001011 => [1,1,1,1,2,1,1,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
0101000111 => [1,1,1,1,3,3] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
0100110011 => [1,1,2,2,2,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
0100100111 => [1,1,2,1,2,3] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0100011011 => [1,1,3,2,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0100010111 => [1,1,3,1,1,3] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
0100001111 => [1,1,4,4] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
0011010011 => [2,2,1,1,2,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
0011000111 => [2,2,3,3] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => 3
0010101011 => [2,1,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
0010010111 => [2,1,2,1,1,3] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0010001111 => [2,1,3,4] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
0001110011 => [3,3,2,2] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => 3
0001101011 => [3,2,1,1,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0001100111 => [3,2,2,3] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => 3
0001011101 => [3,1,1,3,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
0001010111 => [3,1,1,1,1,3] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
0001001111 => [3,1,2,4] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
0000111101 => [4,4,1,1] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
0000110111 => [4,2,1,3] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
0000101111 => [4,1,1,4] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
0000011111 => [5,5] => [5,5] => [[1,2,3,4,5],[6,7,8,9,10]] => 5
010011000111 => [1,1,2,2,3,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
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]] => 2
001100010111 => [2,2,3,1,1,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
001100001111 => [2,2,4,4] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
001011000111 => [2,1,1,2,3,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
001000110111 => [2,1,3,2,1,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
001000011111 => [2,1,4,5] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 5
000111010011 => [3,3,1,1,2,2] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
000111001011 => [3,3,2,1,1,2] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
000111000111 => [3,3,3,3] => [3,3,3,3] => [[1,2,3],[4,5,6],[7,8,9],[10,11,12]] => 3
000110010111 => [3,2,2,1,1,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
000110001111 => [3,2,3,4] => [4,3,3,2] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12]] => 4
000100111011 => [3,1,2,3,1,2] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
000100110111 => [3,1,2,2,1,3] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
000100011111 => [3,1,3,5] => [5,3,3,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12]] => 5
000011110011 => [4,4,2,2] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
000011001111 => [4,2,2,4] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
000010011111 => [4,1,2,5] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 5
000001111011 => [5,4,1,2] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 5
000001110111 => [5,3,1,3] => [5,3,3,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12]] => 5
000001101111 => [5,2,1,4] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 5
000000111111 => [6,6] => [6,6] => [[1,2,3,4,5,6],[7,8,9,10,11,12]] => 6
111111111111 => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 12
111001100001 => [3,2,2,4,1] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
111000011001 => [3,4,2,2,1] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
111000001101 => [3,5,2,1,1] => [5,3,2,1,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11],[12]] => 5
111000110001 => [3,3,2,3,1] => [3,3,3,2,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => 3
111011000001 => [3,1,2,5,1] => [5,3,2,1,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11],[12]] => 5
100111100001 => [1,2,4,4,1] => [4,4,2,1,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11],[12]] => 4
100110000111 => [1,2,2,4,3] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
100001111001 => [1,4,4,2,1] => [4,4,2,1,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11],[12]] => 4
100001100111 => [1,4,2,2,3] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
100000110111 => [1,5,2,1,3] => [5,3,2,1,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11],[12]] => 5
100000110001 => [1,5,2,3,1] => [5,3,2,1,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11],[12]] => 5
100000111101 => [1,5,4,1,1] => [5,4,1,1,1] => [[1,2,3,4,5],[6,7,8,9],[10],[11],[12]] => 5
100011000111 => [1,3,2,3,3] => [3,3,3,2,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => 3
100011110001 => [1,3,4,3,1] => [4,3,3,1,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11],[12]] => 4
101100011111 => [1,1,2,3,5] => [5,3,2,1,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11],[12]] => 5
101100000111 => [1,1,2,5,3] => [5,3,2,1,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11],[12]] => 5
101111000111 => [1,1,4,3,3] => [4,3,3,1,1] => [[1,2,3,4],[5,6,7],[8,9,10],[11],[12]] => 4
101111000001 => [1,1,4,5,1] => [5,4,1,1,1] => [[1,2,3,4,5],[6,7,8,9],[10],[11],[12]] => 5
0000000000 => [10] => [10] => [[1,2,3,4,5,6,7,8,9,10]] => 10
0000000110 => [7,2,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
0000011000 => [5,2,3] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => 5
0000011110 => [5,4,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
0001111110 => [3,6,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
0110011000 => [1,2,2,2,3] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
0110010010 => [1,2,2,1,2,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
0111100000 => [1,4,5] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
0111111110 => [1,8,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
0111001000 => [1,3,2,1,3] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
0111000010 => [1,3,4,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
0100111000 => [1,1,2,3,3] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
0100111110 => [1,1,2,5,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
0100110010 => [1,1,2,2,2,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
0100000010 => [1,1,6,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
0101101000 => [1,1,1,2,1,1,3] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
0101100010 => [1,1,1,2,3,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
0101001010 => [1,1,1,1,2,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
000000000000 => [12] => [12] => [[1,2,3,4,5,6,7,8,9,10,11,12]] => 12
000110011110 => [3,2,2,4,1] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
000111100110 => [3,4,2,2,1] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
000111110010 => [3,5,2,1,1] => [5,3,2,1,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11],[12]] => 5
000111001110 => [3,3,2,3,1] => [3,3,3,2,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => 3
000100111110 => [3,1,2,5,1] => [5,3,2,1,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11],[12]] => 5
011000011110 => [1,2,4,4,1] => [4,4,2,1,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11],[12]] => 4
011001111000 => [1,2,2,4,3] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
011110000110 => [1,4,4,2,1] => [4,4,2,1,1] => [[1,2,3,4],[5,6,7,8],[9,10],[11],[12]] => 4
011110011000 => [1,4,2,2,3] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
011111001000 => [1,5,2,1,3] => [5,3,2,1,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11],[12]] => 5
011111000010 => [1,5,4,1,1] => [5,4,1,1,1] => [[1,2,3,4,5],[6,7,8,9],[10],[11],[12]] => 5
011100111000 => [1,3,2,3,3] => [3,3,3,2,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => 3
010011111000 => [1,1,2,5,3] => [5,3,2,1,1] => [[1,2,3,4,5],[6,7,8],[9,10],[11],[12]] => 5
010000111110 => [1,1,4,5,1] => [5,4,1,1,1] => [[1,2,3,4,5],[6,7,8,9],[10],[11],[12]] => 5
0010101010 => [2,1,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
0010101100 => [2,1,1,1,1,2,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
0010110100 => [2,1,1,2,1,1,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
0011010100 => [2,2,1,1,1,1,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
0101010100 => [1,1,1,1,1,1,1,1,2] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
0010101110 => [2,1,1,1,1,3,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
0010111100 => [2,1,1,4,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
0011110100 => [2,4,1,1,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
0000010100 => [5,1,1,1,2] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
0111010100 => [1,3,1,1,1,1,2] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
0000000010 => [8,1,1] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
0000001110 => [6,3,1] => [6,3,1] => [[1,2,3,4,5,6],[7,8,9],[10]] => 6
0000111110 => [4,5,1] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
0011111110 => [2,7,1] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
0000000100 => [7,1,2] => [7,2,1] => [[1,2,3,4,5,6,7],[8,9],[10]] => 7
0000001010 => [6,1,1,1,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
0000010110 => [5,1,1,2,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
0000101110 => [4,1,1,3,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
0001011110 => [3,1,1,4,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
0010111110 => [2,1,1,5,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
0101111110 => [1,1,1,6,1] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
0010110010 => [2,1,1,2,2,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
0010111000 => [2,1,1,3,3] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
0011001010 => [2,2,2,1,1,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
0011001100 => [2,2,2,2,2] => [2,2,2,2,2] => [[1,2],[3,4],[5,6],[7,8],[9,10]] => 2
0011010010 => [2,2,1,1,2,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
0011011000 => [2,2,1,2,3] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
0011100010 => [2,3,3,1,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
0011100100 => [2,3,2,1,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
0011101000 => [2,3,1,1,3] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
0011110000 => [2,4,4] => [4,4,2] => [[1,2,3,4],[5,6,7,8],[9,10]] => 4
0100101010 => [1,1,2,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
0100101100 => [1,1,2,1,1,2,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
0100110100 => [1,1,2,2,1,1,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
0101001100 => [1,1,1,1,2,2,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
0101010010 => [1,1,1,1,1,1,2,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
0101011000 => [1,1,1,1,1,2,3] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
0101100100 => [1,1,1,2,2,1,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
0101110000 => [1,1,1,3,4] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
0110001010 => [1,2,3,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
0110001100 => [1,2,3,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
0110010100 => [1,2,2,1,1,1,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
0110100010 => [1,2,1,1,3,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
0110100100 => [1,2,1,1,2,1,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
0110101000 => [1,2,1,1,1,1,3] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
0110110000 => [1,2,1,2,4] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
0111000100 => [1,3,3,1,2] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
0111010000 => [1,3,1,1,4] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
001100111000 => [2,2,2,3,3] => [3,3,2,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10],[11,12]] => 3
001110001100 => [2,3,3,2,2] => [3,3,2,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10],[11,12]] => 3
001110011000 => [2,3,2,2,3] => [3,3,2,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10],[11,12]] => 3
011000111000 => [1,2,3,3,3] => [3,3,3,2,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => 3
011100001100 => [1,3,4,2,2] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
011100011000 => [1,3,3,2,3] => [3,3,3,2,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => 3
10000100001 => [1,4,1,4,1] => [4,4,1,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10],[11]] => 4
0100000000 => [1,1,8] => [8,1,1] => [[1,2,3,4,5,6,7,8],[9],[10]] => 8
0100000011 => [1,1,6,2] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
0100000111 => [1,1,5,3] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
0100011111 => [1,1,3,5] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
0100111111 => [1,1,2,6] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
0101111111 => [1,1,1,7] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
0100000101 => [1,1,5,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
0100001011 => [1,1,4,1,1,2] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
0100101111 => [1,1,2,1,1,4] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
0101011111 => [1,1,1,1,1,5] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
0110111111 => [1,2,1,6] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
0101010110 => [1,1,1,1,1,1,1,2,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
0101011001 => [1,1,1,1,1,2,2,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
0101011010 => [1,1,1,1,1,2,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
0101011100 => [1,1,1,1,1,3,2] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
0101100101 => [1,1,1,2,2,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
0101100110 => [1,1,1,2,2,2,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
0101101001 => [1,1,1,2,1,1,2,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
0101101010 => [1,1,1,2,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
0101101100 => [1,1,1,2,1,2,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
0101110001 => [1,1,1,3,3,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
0101110010 => [1,1,1,3,2,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
0101110100 => [1,1,1,3,1,1,2] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
0101111000 => [1,1,1,4,3] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
0110010101 => [1,2,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
0110010110 => [1,2,2,1,1,2,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
0110011001 => [1,2,2,2,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
0110011010 => [1,2,2,2,1,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
0110011100 => [1,2,2,3,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
0110100101 => [1,2,1,1,2,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
0110100110 => [1,2,1,1,2,2,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
0110101001 => [1,2,1,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
0110101010 => [1,2,1,1,1,1,1,1,1] => [2,1,1,1,1,1,1,1,1] => [[1,2],[3],[4],[5],[6],[7],[8],[9],[10]] => 2
0110101100 => [1,2,1,1,1,2,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
0110110001 => [1,2,1,2,3,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0110110010 => [1,2,1,2,2,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
0110110100 => [1,2,1,2,1,1,2] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
0110111000 => [1,2,1,3,3] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
0111000101 => [1,3,3,1,1,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
0111000110 => [1,3,3,2,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
0111001001 => [1,3,2,1,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0111001010 => [1,3,2,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
0111001100 => [1,3,2,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
0111010010 => [1,3,1,1,2,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
0111011000 => [1,3,1,2,3] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
0111100010 => [1,4,3,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
0111100100 => [1,4,2,1,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
0111101000 => [1,4,1,1,3] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
0111110000 => [1,5,4] => [5,4,1] => [[1,2,3,4,5],[6,7,8,9],[10]] => 5
011001110001 => [1,2,2,3,3,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
011100011001 => [1,3,3,2,2,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
011100011100 => [1,3,3,3,2] => [3,3,3,2,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => 3
011100110001 => [1,3,2,2,3,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
011110001100 => [1,4,3,2,2] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
0100000100 => [1,1,5,1,2] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
0011100110 => [2,3,2,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
0011101010 => [2,3,1,1,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
0011101100 => [2,3,1,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
0001101110 => [3,2,1,3,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
0010110110 => [2,1,1,2,1,2,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
0011110010 => [2,4,2,1,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
0001110110 => [3,3,1,2,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
0100111010 => [1,1,2,3,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
0010111010 => [2,1,1,3,1,1,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
0011111000 => [2,5,3] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => 5
0001111010 => [3,4,1,1,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
0100111100 => [1,1,2,4,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
0001111100 => [3,5,2] => [5,3,2] => [[1,2,3,4,5],[6,7,8],[9,10]] => 5
001111000110 => [2,4,3,2,1] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
100111110000 => [1,2,5,4] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 5
001111110000 => [2,6,4] => [6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 6
110001111000 => [2,3,4,3] => [4,3,3,2] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12]] => 4
100011111000 => [1,3,5,3] => [5,3,3,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12]] => 5
000011111100 => [4,6,2] => [6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 6
0000000101 => [7,1,1,1] => [7,1,1,1] => [[1,2,3,4,5,6,7],[8],[9],[10]] => 7
0000001101 => [6,2,1,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
0000011101 => [5,3,1,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
0001111101 => [3,5,1,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
0011111101 => [2,6,1,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
0000001001 => [6,1,2,1] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
0000010101 => [5,1,1,1,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
0000101101 => [4,1,1,2,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
0010111101 => [2,1,1,4,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
0101111101 => [1,1,1,5,1,1] => [5,1,1,1,1,1] => [[1,2,3,4,5],[6],[7],[8],[9],[10]] => 5
110001110001 => [2,3,3,3,1] => [3,3,3,2,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => 3
110011100001 => [2,2,3,4,1] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
0111000011 => [1,3,4,2] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
0011110001 => [2,4,3,1] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
110000111100 => [2,4,4,2] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
110000001111 => [2,6,4] => [6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 6
011100000111 => [1,3,5,3] => [5,3,3,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12]] => 5
111000011100 => [3,4,3,2] => [4,3,3,2] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12]] => 4
001111000011 => [2,4,4,2] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
011110000011 => [1,4,5,2] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 5
111100000011 => [4,6,2] => [6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 6
000111110001 => [3,5,3,1] => [5,3,3,1] => [[1,2,3,4,5],[6,7,8],[9,10,11],[12]] => 5
001111100001 => [2,5,4,1] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 5
0011011001 => [2,2,1,2,2,1] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
0010110001 => [2,1,1,2,3,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0001000001 => [3,1,5,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
0111010101 => [1,3,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 3
0111010011 => [1,3,1,1,2,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0111001101 => [1,3,2,2,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0111011001 => [1,3,1,2,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0111000111 => [1,3,3,3] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => 3
0011110101 => [2,4,1,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
0011110011 => [2,4,2,2] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
0111100101 => [1,4,2,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
0111100011 => [1,4,3,2] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
0011111001 => [2,5,2,1] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 5
0000111111 => [4,6] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 6
110011000111 => [2,2,2,3,3] => [3,3,2,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10],[11,12]] => 3
110001110011 => [2,3,3,2,2] => [3,3,2,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10],[11,12]] => 3
110011100011 => [2,2,3,3,2] => [3,3,2,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10],[11,12]] => 3
110001111001 => [2,3,4,2,1] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
110011110001 => [2,2,4,3,1] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
011100111001 => [1,3,2,3,2,1] => [3,3,2,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9,10],[11],[12]] => 3
011100001111 => [1,3,4,4] => [4,4,3,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12]] => 4
111000110011 => [3,3,2,2,2] => [3,3,2,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10],[11,12]] => 3
111001100011 => [3,2,2,3,2] => [3,3,2,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10],[11,12]] => 3
111000111001 => [3,3,3,2,1] => [3,3,3,2,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => 3
111001110001 => [3,2,3,3,1] => [3,3,3,2,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => 3
111000001111 => [3,5,4] => [5,4,3] => [[1,2,3,4,5],[6,7,8,9],[10,11,12]] => 5
001111000111 => [2,4,3,3] => [4,3,3,2] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12]] => 4
011110000111 => [1,4,4,3] => [4,4,3,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12]] => 4
111100011001 => [4,3,2,2,1] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
111100110001 => [4,2,2,3,1] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
111100000111 => [4,5,3] => [5,4,3] => [[1,2,3,4,5],[6,7,8,9],[10,11,12]] => 5
000111110011 => [3,5,2,2] => [5,3,2,2] => [[1,2,3,4,5],[6,7,8],[9,10],[11,12]] => 5
001111100011 => [2,5,3,2] => [5,3,2,2] => [[1,2,3,4,5],[6,7,8],[9,10],[11,12]] => 5
011111000011 => [1,5,4,2] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 5
0001101100 => [3,2,1,2,2] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
0011000110 => [2,2,3,2,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
0010001110 => [2,1,3,3,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
0110111001 => [1,2,1,3,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0001101001 => [3,2,1,1,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0000110001 => [4,2,3,1] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
0000010001 => [5,1,3,1] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
0100011001 => [1,1,3,2,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0100111001 => [1,1,2,3,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0101111001 => [1,1,1,4,2,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
0110010001 => [1,2,2,1,3,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0100010001 => [1,1,3,1,3,1] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
0100110001 => [1,1,2,2,3,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0100100001 => [1,1,2,1,4,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
0101100001 => [1,1,1,2,4,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
0110011011 => [1,2,2,2,1,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
0110111011 => [1,2,1,3,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0100111011 => [1,1,2,3,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0101111011 => [1,1,1,4,1,2] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
0110010011 => [1,2,2,1,2,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
0100010011 => [1,1,3,1,2,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0110110011 => [1,2,1,2,2,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
0101110011 => [1,1,1,3,2,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0110100011 => [1,2,1,1,3,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0100100011 => [1,1,2,1,3,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0101100011 => [1,1,1,2,3,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0101000011 => [1,1,1,1,4,2] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
0110010111 => [1,2,2,1,1,3] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0110110111 => [1,2,1,2,1,3] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0100110111 => [1,1,2,2,1,3] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0101110111 => [1,1,1,3,1,3] => [3,3,1,1,1,1] => [[1,2,3],[4,5,6],[7],[8],[9],[10]] => 3
0110100111 => [1,2,1,1,2,3] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0101100111 => [1,1,1,2,2,3] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0110101111 => [1,2,1,1,1,4] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
0101101111 => [1,1,1,2,1,4] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
0101001111 => [1,1,1,1,2,4] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
100011100011 => [1,3,3,3,2] => [3,3,3,2,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => 3
100001110011 => [1,4,3,2,2] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
0000001100 => [6,2,2] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 6
0000011001 => [5,2,2,1] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 5
0000110011 => [4,2,2,2] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
0011001111 => [2,2,2,4] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
0110011111 => [1,2,2,5] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 5
0000110100 => [4,2,1,1,2] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
0000000011 => [8,2] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 8
0000011011 => [5,2,1,2] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 5
0001101111 => [3,2,1,4] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
0011011111 => [2,2,1,5] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 5
0000110101 => [4,2,1,1,1,1] => [4,2,1,1,1,1] => [[1,2,3,4],[5,6],[7],[8],[9],[10]] => 4
0011010111 => [2,2,1,1,1,3] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0111001011 => [1,3,2,1,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0111110111 => [1,5,1,3] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
0110001011 => [1,2,3,1,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0110000111 => [1,2,4,3] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
110000111001 => [2,4,3,2,1] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
001110000111 => [2,3,4,3] => [4,3,3,2] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12]] => 4
011000001111 => [1,2,5,4] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 5
0011011010 => [2,2,1,2,1,1,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
0011010110 => [2,2,1,1,1,2,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
0100110110 => [1,1,2,2,1,2,1] => [2,2,2,1,1,1,1] => [[1,2],[3,4],[5,6],[7],[8],[9],[10]] => 2
0110001110 => [1,2,3,3,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
0101001110 => [1,1,1,1,2,3,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
0011001110 => [2,2,2,3,1] => [3,2,2,2,1] => [[1,2,3],[4,5],[6,7],[8,9],[10]] => 3
0100101110 => [1,1,2,1,1,3,1] => [3,2,1,1,1,1,1] => [[1,2,3],[4,5],[6],[7],[8],[9],[10]] => 3
0100011110 => [1,1,3,4,1] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
0010011110 => [2,1,2,4,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
001110001110 => [2,3,3,3,1] => [3,3,3,2,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => 3
001100011110 => [2,2,3,4,1] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
0101000000 => [1,1,1,1,6] => [6,1,1,1,1] => [[1,2,3,4,5,6],[7],[8],[9],[10]] => 6
0001010000 => [3,1,1,1,4] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
0100010000 => [1,1,3,1,4] => [4,3,1,1,1] => [[1,2,3,4],[5,6,7],[8],[9],[10]] => 4
0001000100 => [3,1,3,1,2] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
0111011100 => [1,3,1,3,2] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
0101000101 => [1,1,1,1,3,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 3
0001010101 => [3,1,1,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 3
0100010101 => [1,1,3,1,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 3
0110110101 => [1,2,1,2,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
0101010001 => [1,1,1,1,1,1,3,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 3
0100101001 => [1,1,2,1,1,1,2,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
0110001001 => [1,2,3,1,2,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0101011011 => [1,1,1,1,1,2,1,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
0001001011 => [3,1,2,1,1,2] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0110101011 => [1,2,1,1,1,1,1,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
0001100011 => [3,2,3,2] => [3,3,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10]] => 3
0110000011 => [1,2,5,2] => [5,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10]] => 5
0001110111 => [3,3,1,3] => [3,3,3,1] => [[1,2,3],[4,5,6],[7,8,9],[10]] => 3
0111101111 => [1,4,1,4] => [4,4,1,1] => [[1,2,3,4],[5,6,7,8],[9],[10]] => 4
000110001100 => [3,2,3,2,2] => [3,3,2,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10],[11,12]] => 3
011000001100 => [1,2,5,2,2] => [5,2,2,2,1] => [[1,2,3,4,5],[6,7],[8,9],[10,11],[12]] => 5
000001100011 => [5,2,3,2] => [5,3,2,2] => [[1,2,3,4,5],[6,7,8],[9,10],[11,12]] => 5
000110000011 => [3,2,5,2] => [5,3,2,2] => [[1,2,3,4,5],[6,7,8],[9,10],[11,12]] => 5
011110001111 => [1,4,3,4] => [4,4,3,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12]] => 4
100011110011 => [1,3,4,2,2] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 4
100111000111 => [1,2,3,3,3] => [3,3,3,2,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => 3
110001100111 => [2,3,2,2,3] => [3,3,2,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10],[11,12]] => 3
100011100111 => [1,3,3,2,3] => [3,3,3,2,1] => [[1,2,3],[4,5,6],[7,8,9],[10,11],[12]] => 3
0000000111 => [7,3] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 7
0000001111 => [6,4] => [6,4] => [[1,2,3,4,5,6],[7,8,9,10]] => 6
0001111111 => [3,7] => [7,3] => [[1,2,3,4,5,6,7],[8,9,10]] => 7
0011111111 => [2,8] => [8,2] => [[1,2,3,4,5,6,7,8],[9,10]] => 8
0000001011 => [6,1,1,2] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
0000010111 => [5,1,1,3] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
0001011111 => [3,1,1,5] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
0010111111 => [2,1,1,6] => [6,2,1,1] => [[1,2,3,4,5,6],[7,8],[9],[10]] => 6
0011011110 => [2,2,1,4,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
0011101110 => [2,3,1,3,1] => [3,3,2,1,1] => [[1,2,3],[4,5,6],[7,8],[9],[10]] => 3
0011110110 => [2,4,1,2,1] => [4,2,2,1,1] => [[1,2,3,4],[5,6],[7,8],[9],[10]] => 4
0011111010 => [2,5,1,1,1] => [5,2,1,1,1] => [[1,2,3,4,5],[6,7],[8],[9],[10]] => 5
0011111100 => [2,6,2] => [6,2,2] => [[1,2,3,4,5,6],[7,8],[9,10]] => 6
000111100011 => [3,4,3,2] => [4,3,3,2] => [[1,2,3,4],[5,6,7],[8,9,10],[11,12]] => 4
0010010101 => [2,1,2,1,1,1,1,1] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
0101010111 => [1,1,1,1,1,1,1,3] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 3
0101110101 => [1,1,1,3,1,1,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 3
01111100100 => [1,5,2,1,2] => [5,2,2,1,1] => [[1,2,3,4,5],[6,7],[8,9],[10],[11]] => 5
110000011000 => [2,5,2,3] => [5,3,2,2] => [[1,2,3,4,5],[6,7,8],[9,10],[11,12]] => 5
111100011110 => [4,3,4,1] => [4,4,3,1] => [[1,2,3,4],[5,6,7,8],[9,10,11],[12]] => 4
111100000110 => [4,5,2,1] => [5,4,2,1] => [[1,2,3,4,5],[6,7,8,9],[10,11],[12]] => 5
110001100011 => [2,3,2,3,2] => [3,3,2,2,2] => [[1,2,3],[4,5,6],[7,8],[9,10],[11,12]] => 3
0110001111 => [1,2,3,4] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
0101101011 => [1,1,1,2,1,1,1,2] => [2,2,1,1,1,1,1,1] => [[1,2],[3,4],[5],[6],[7],[8],[9],[10]] => 2
0101011101 => [1,1,1,1,1,3,1,1] => [3,1,1,1,1,1,1,1] => [[1,2,3],[4],[5],[6],[7],[8],[9],[10]] => 3
0011000011 => [2,2,4,2] => [4,2,2,2] => [[1,2,3,4],[5,6],[7,8],[9,10]] => 4
0011011011 => [2,2,1,2,1,2] => [2,2,2,2,1,1] => [[1,2],[3,4],[5,6],[7,8],[9],[10]] => 2
0001111011 => [3,4,1,2] => [4,3,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10]] => 4
111111001111 => [6,2,4] => [6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 6
111111000011 => [6,4,2] => [6,4,2] => [[1,2,3,4,5,6],[7,8,9,10],[11,12]] => 6
111100001111 => [4,4,4] => [4,4,4] => [[1,2,3,4],[5,6,7,8],[9,10,11,12]] => 4
001111001111 => [2,4,2,4] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
000011000011 => [4,2,4,2] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
111100111100 => [4,2,4,2] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
110000110000 => [2,4,2,4] => [4,4,2,2] => [[1,2,3,4],[5,6,7,8],[9,10],[11,12]] => 4
0011011101 => [2,2,1,3,1,1] => [3,2,2,1,1,1] => [[1,2,3],[4,5],[6,7],[8],[9],[10]] => 3
0111011111 => [1,3,1,5] => [5,3,1,1] => [[1,2,3,4,5],[6,7,8],[9],[10]] => 5
111100111001 => [4,2,3,2,1] => [4,3,2,2,1] => [[1,2,3,4],[5,6,7],[8,9],[10,11],[12]] => 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 2,8,4,2 2,14,10,4,2 2,24,22,10,4,2 2,40,46,24,10,4,2 2,66,94,54,24,10,4,2 2,108,188,118,56,24,10,4,2
F1=2 q
F2=2 q+2 q2
F3=2 q+4 q2+2 q3
F4=2 q+8 q2+4 q3+2 q4
F5=2 q+14 q2+10 q3+4 q4+2 q5
F6=2 q+24 q2+22 q3+10 q4+4 q5+2 q6
F7=2 q+40 q2+46 q3+24 q4+10 q5+4 q6+2 q7
F8=2 q+66 q2+94 q3+54 q4+24 q5+10 q6+4 q7+2 q8
F9=2 q+108 q2+188 q3+118 q4+56 q5+24 q6+10 q7+4 q8+2 q9
Description
The last entry in the first row of a standard tableau.
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
initial tableau
Description
Sends an integer partition to the standard tableau obtained by filling the numbers 1 through n row by row.
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