Identifier
Values
0 => [1] => [1] => [1,0] => 1
1 => [1] => [1] => [1,0] => 1
00 => [2] => [1,1] => [1,0,1,0] => 1
01 => [1,1] => [2] => [1,1,0,0] => 2
10 => [1,1] => [2] => [1,1,0,0] => 2
11 => [2] => [1,1] => [1,0,1,0] => 1
000 => [3] => [1,1,1] => [1,0,1,0,1,0] => 1
001 => [2,1] => [2,1] => [1,1,0,0,1,0] => 2
010 => [1,1,1] => [3] => [1,1,1,0,0,0] => 3
011 => [1,2] => [1,2] => [1,0,1,1,0,0] => 2
100 => [1,2] => [1,2] => [1,0,1,1,0,0] => 2
101 => [1,1,1] => [3] => [1,1,1,0,0,0] => 3
110 => [2,1] => [2,1] => [1,1,0,0,1,0] => 2
111 => [3] => [1,1,1] => [1,0,1,0,1,0] => 1
0000 => [4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 1
0001 => [3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
0010 => [2,1,1] => [3,1] => [1,1,1,0,0,0,1,0] => 3
0011 => [2,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
0100 => [1,1,2] => [1,3] => [1,0,1,1,1,0,0,0] => 3
0101 => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 4
0110 => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 2
0111 => [1,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
1000 => [1,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => 2
1001 => [1,2,1] => [2,2] => [1,1,0,0,1,1,0,0] => 2
1010 => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 4
1011 => [1,1,2] => [1,3] => [1,0,1,1,1,0,0,0] => 3
1100 => [2,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 2
1101 => [2,1,1] => [3,1] => [1,1,1,0,0,0,1,0] => 3
1110 => [3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 2
1111 => [4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 1
00000 => [5] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 1
00001 => [4,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
00010 => [3,1,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 3
00011 => [3,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
00100 => [2,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 3
00101 => [2,1,1,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 4
00110 => [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
00111 => [2,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
01000 => [1,1,3] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 3
01001 => [1,1,2,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 3
01010 => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 5
01011 => [1,1,1,2] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 4
01100 => [1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
01101 => [1,2,1,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 3
01110 => [1,3,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
01111 => [1,4] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
10000 => [1,4] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 2
10001 => [1,3,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 2
10010 => [1,2,1,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 3
10011 => [1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 2
10100 => [1,1,1,2] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 4
10101 => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 5
10110 => [1,1,2,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 3
10111 => [1,1,3] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 3
11000 => [2,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 2
11001 => [2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 2
11010 => [2,1,1,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 4
11011 => [2,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 3
11100 => [3,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 2
11101 => [3,1,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 3
11110 => [4,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 2
11111 => [5] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 1
000000 => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
000001 => [5,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 2
000010 => [4,1,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
000011 => [4,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 2
000100 => [3,1,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
000101 => [3,1,1,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
000110 => [3,2,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
000111 => [3,3] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
001000 => [2,1,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 3
001001 => [2,1,2,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 3
001010 => [2,1,1,1,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
001011 => [2,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 4
001100 => [2,2,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
001101 => [2,2,1,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
001110 => [2,3,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
001111 => [2,4] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
010000 => [1,1,4] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
010001 => [1,1,3,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
010010 => [1,1,2,1,1] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
010011 => [1,1,2,2] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 3
010100 => [1,1,1,1,2] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
010101 => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 6
010110 => [1,1,1,2,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
010111 => [1,1,1,3] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
011000 => [1,2,3] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
011001 => [1,2,2,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
011010 => [1,2,1,1,1] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
011011 => [1,2,1,2] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 3
011100 => [1,3,2] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
011101 => [1,3,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 3
011110 => [1,4,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
011111 => [1,5] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 2
100000 => [1,5] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 2
100001 => [1,4,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 2
100010 => [1,3,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 3
100011 => [1,3,2] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 2
100100 => [1,2,1,2] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 3
100101 => [1,2,1,1,1] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 4
100110 => [1,2,2,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 2
>>> Load all 673 entries. <<<
100111 => [1,2,3] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 2
101000 => [1,1,1,3] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 4
101001 => [1,1,1,2,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 4
101010 => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 6
101011 => [1,1,1,1,2] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 5
101100 => [1,1,2,2] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 3
101101 => [1,1,2,1,1] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 3
101110 => [1,1,3,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 3
101111 => [1,1,4] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 3
110000 => [2,4] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 2
110001 => [2,3,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 2
110010 => [2,2,1,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 3
110011 => [2,2,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 2
110100 => [2,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 4
110101 => [2,1,1,1,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 5
110110 => [2,1,2,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 3
110111 => [2,1,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 3
111000 => [3,3] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 2
111001 => [3,2,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 2
111010 => [3,1,1,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 4
111011 => [3,1,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 3
111100 => [4,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 2
111101 => [4,1,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 3
111110 => [5,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 2
111111 => [6] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 1
0000000 => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
0000001 => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
0000010 => [5,1,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3
0000011 => [5,2] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
0000100 => [4,1,2] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
0000101 => [4,1,1,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
0000110 => [4,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
0000111 => [4,3] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
0001000 => [3,1,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
0001001 => [3,1,2,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
0001010 => [3,1,1,1,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
0001011 => [3,1,1,2] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
0001100 => [3,2,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
0001101 => [3,2,1,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3
0001110 => [3,3,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
0001111 => [3,4] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
0010000 => [2,1,4] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
0010001 => [2,1,3,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3
0010010 => [2,1,2,1,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
0010011 => [2,1,2,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
0010100 => [2,1,1,1,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
0010101 => [2,1,1,1,1,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
0010110 => [2,1,1,2,1] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
0010111 => [2,1,1,3] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
0011000 => [2,2,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
0011001 => [2,2,2,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
0011010 => [2,2,1,1,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
0011011 => [2,2,1,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
0011100 => [2,3,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
0011101 => [2,3,1,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3
0011110 => [2,4,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
0011111 => [2,5] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
0100000 => [1,1,5] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
0100001 => [1,1,4,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
0100010 => [1,1,3,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
0100011 => [1,1,3,2] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
0100100 => [1,1,2,1,2] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
0100101 => [1,1,2,1,1,1] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
0100110 => [1,1,2,2,1] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 3
0100111 => [1,1,2,3] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
0101000 => [1,1,1,1,3] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
0101001 => [1,1,1,1,2,1] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
0101010 => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
0101011 => [1,1,1,1,1,2] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
0101100 => [1,1,1,2,2] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
0101101 => [1,1,1,2,1,1] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
0101110 => [1,1,1,3,1] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
0101111 => [1,1,1,4] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
0110000 => [1,2,4] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
0110001 => [1,2,3,1] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
0110010 => [1,2,2,1,1] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3
0110011 => [1,2,2,2] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
0110100 => [1,2,1,1,2] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
0110101 => [1,2,1,1,1,1] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
0110110 => [1,2,1,2,1] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 3
0110111 => [1,2,1,3] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
0111000 => [1,3,3] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
0111001 => [1,3,2,1] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2
0111010 => [1,3,1,1,1] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
0111011 => [1,3,1,2] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
0111100 => [1,4,2] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
0111101 => [1,4,1,1] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
0111110 => [1,5,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
0111111 => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
1000000 => [1,6] => [1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
1000001 => [1,5,1] => [2,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
1000010 => [1,4,1,1] => [3,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,1,0,0] => 3
1000011 => [1,4,2] => [1,2,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
1000100 => [1,3,1,2] => [1,3,1,2] => [1,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
1000101 => [1,3,1,1,1] => [4,1,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
1000110 => [1,3,2,1] => [2,2,1,2] => [1,1,0,0,1,1,0,0,1,0,1,1,0,0] => 2
1000111 => [1,3,3] => [1,1,2,1,2] => [1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
1001000 => [1,2,1,3] => [1,1,3,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
1001001 => [1,2,1,2,1] => [2,3,2] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 3
1001010 => [1,2,1,1,1,1] => [5,2] => [1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
1001011 => [1,2,1,1,2] => [1,4,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
1001100 => [1,2,2,2] => [1,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
1001101 => [1,2,2,1,1] => [3,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3
1001110 => [1,2,3,1] => [2,1,2,2] => [1,1,0,0,1,0,1,1,0,0,1,1,0,0] => 2
1001111 => [1,2,4] => [1,1,1,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
1010000 => [1,1,1,4] => [1,1,1,4] => [1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
1010001 => [1,1,1,3,1] => [2,1,4] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
1010010 => [1,1,1,2,1,1] => [3,4] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
1010011 => [1,1,1,2,2] => [1,2,4] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
1010100 => [1,1,1,1,1,2] => [1,6] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
1010101 => [1,1,1,1,1,1,1] => [7] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
1010110 => [1,1,1,1,2,1] => [2,5] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
1010111 => [1,1,1,1,3] => [1,1,5] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
1011000 => [1,1,2,3] => [1,1,2,3] => [1,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
1011001 => [1,1,2,2,1] => [2,2,3] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 3
1011010 => [1,1,2,1,1,1] => [4,3] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
1011011 => [1,1,2,1,2] => [1,3,3] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
1011100 => [1,1,3,2] => [1,2,1,3] => [1,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
1011101 => [1,1,3,1,1] => [3,1,3] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
1011110 => [1,1,4,1] => [2,1,1,3] => [1,1,0,0,1,0,1,0,1,1,1,0,0,0] => 3
1011111 => [1,1,5] => [1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
1100000 => [2,5] => [1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
1100001 => [2,4,1] => [2,1,1,2,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0] => 2
1100010 => [2,3,1,1] => [3,1,2,1] => [1,1,1,0,0,0,1,0,1,1,0,0,1,0] => 3
1100011 => [2,3,2] => [1,2,1,2,1] => [1,0,1,1,0,0,1,0,1,1,0,0,1,0] => 2
1100100 => [2,2,1,2] => [1,3,2,1] => [1,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
1100101 => [2,2,1,1,1] => [4,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
1100110 => [2,2,2,1] => [2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
1100111 => [2,2,3] => [1,1,2,2,1] => [1,0,1,0,1,1,0,0,1,1,0,0,1,0] => 2
1101000 => [2,1,1,3] => [1,1,4,1] => [1,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
1101001 => [2,1,1,2,1] => [2,4,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
1101010 => [2,1,1,1,1,1] => [6,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
1101011 => [2,1,1,1,2] => [1,5,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
1101100 => [2,1,2,2] => [1,2,3,1] => [1,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
1101101 => [2,1,2,1,1] => [3,3,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
1101110 => [2,1,3,1] => [2,1,3,1] => [1,1,0,0,1,0,1,1,1,0,0,0,1,0] => 3
1101111 => [2,1,4] => [1,1,1,3,1] => [1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
1110000 => [3,4] => [1,1,1,2,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
1110001 => [3,3,1] => [2,1,2,1,1] => [1,1,0,0,1,0,1,1,0,0,1,0,1,0] => 2
1110010 => [3,2,1,1] => [3,2,1,1] => [1,1,1,0,0,0,1,1,0,0,1,0,1,0] => 3
1110011 => [3,2,2] => [1,2,2,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0] => 2
1110100 => [3,1,1,2] => [1,4,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
1110101 => [3,1,1,1,1] => [5,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
1110110 => [3,1,2,1] => [2,3,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0] => 3
1110111 => [3,1,3] => [1,1,3,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0] => 3
1111000 => [4,3] => [1,1,2,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
1111001 => [4,2,1] => [2,2,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0] => 2
1111010 => [4,1,1,1] => [4,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0] => 4
1111011 => [4,1,2] => [1,3,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
1111100 => [5,2] => [1,2,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
1111101 => [5,1,1] => [3,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3
1111110 => [6,1] => [2,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
1111111 => [7] => [1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
00000000 => [8] => [1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
00000001 => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
00000010 => [6,1,1] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 3
00000011 => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
00000100 => [5,1,2] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3
00000101 => [5,1,1,1] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 4
00000110 => [5,2,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
00000111 => [5,3] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
00001000 => [4,1,3] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
00001001 => [4,1,2,1] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
00001010 => [4,1,1,1,1] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 5
00001111 => [4,4] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
00010010 => [3,1,2,1,1] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 3
00010100 => [3,1,1,1,2] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
00010101 => [3,1,1,1,1,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 6
00010110 => [3,1,1,2,1] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
00011010 => [3,2,1,1,1] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 4
00011110 => [3,4,1] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
00011111 => [3,5] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
00100000 => [2,1,5] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
00100010 => [2,1,3,1,1] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => 3
00100100 => [2,1,2,1,2] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
00100110 => [2,1,2,2,1] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
00101000 => [2,1,1,1,3] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
00101001 => [2,1,1,1,2,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
00101010 => [2,1,1,1,1,1,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 7
00101011 => [2,1,1,1,1,2] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
00101100 => [2,1,1,2,2] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
00101101 => [2,1,1,2,1,1] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 4
00101110 => [2,1,1,3,1] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
00110010 => [2,2,2,1,1] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 3
00110011 => [2,2,2,2] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
00110100 => [2,2,1,1,2] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
00110110 => [2,2,1,2,1] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
00111010 => [2,3,1,1,1] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 4
00111110 => [2,5,1] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
00111111 => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
01000000 => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
01000001 => [1,1,5,1] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
01000010 => [1,1,4,1,1] => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => 3
01000100 => [1,1,3,1,2] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
01000110 => [1,1,3,2,1] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
01001000 => [1,1,2,1,3] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
01001010 => [1,1,2,1,1,1,1] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 5
01001100 => [1,1,2,2,2] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 3
01001110 => [1,1,2,3,1] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
01010000 => [1,1,1,1,4] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
01010001 => [1,1,1,1,3,1] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
01010010 => [1,1,1,1,2,1,1] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 5
01010011 => [1,1,1,1,2,2] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
01010100 => [1,1,1,1,1,1,2] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
01010101 => [1,1,1,1,1,1,1,1] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 8
01010110 => [1,1,1,1,1,2,1] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
01010111 => [1,1,1,1,1,3] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
01011000 => [1,1,1,2,3] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
01011001 => [1,1,1,2,2,1] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
01011010 => [1,1,1,2,1,1,1] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 4
01011011 => [1,1,1,2,1,2] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
01011100 => [1,1,1,3,2] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
01011110 => [1,1,1,4,1] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
01011111 => [1,1,1,5] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
01100000 => [1,2,5] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
01100010 => [1,2,3,1,1] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => 3
01100100 => [1,2,2,1,2] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3
01100101 => [1,2,2,1,1,1] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 4
01100110 => [1,2,2,2,1] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
01100111 => [1,2,2,3] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
01101000 => [1,2,1,1,3] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
01101001 => [1,2,1,1,2,1] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
01101010 => [1,2,1,1,1,1,1] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 6
01101011 => [1,2,1,1,1,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
01101100 => [1,2,1,2,2] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 3
01101110 => [1,2,1,3,1] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
01101111 => [1,2,1,4] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
01110000 => [1,3,4] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
01110010 => [1,3,2,1,1] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => 3
01110100 => [1,3,1,1,2] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
01110110 => [1,3,1,2,1] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
01111000 => [1,4,3] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
01111010 => [1,4,1,1,1] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => 4
01111100 => [1,5,2] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
01111101 => [1,5,1,1] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 3
01111110 => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
01111111 => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
10000000 => [1,7] => [1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
10000001 => [1,6,1] => [2,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
10000010 => [1,5,1,1] => [3,1,1,1,2] => [1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0] => 3
10000011 => [1,5,2] => [1,2,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0] => 2
10000101 => [1,4,1,1,1] => [4,1,1,2] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0] => 4
10000111 => [1,4,3] => [1,1,2,1,1,2] => [1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0] => 2
10001001 => [1,3,1,2,1] => [2,3,1,2] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
10001011 => [1,3,1,1,2] => [1,4,1,2] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
10001101 => [1,3,2,1,1] => [3,2,1,2] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0] => 3
10001111 => [1,3,4] => [1,1,1,2,1,2] => [1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0] => 2
10010000 => [1,2,1,4] => [1,1,1,3,2] => [1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
10010001 => [1,2,1,3,1] => [2,1,3,2] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
10010011 => [1,2,1,2,2] => [1,2,3,2] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0] => 3
10010100 => [1,2,1,1,1,2] => [1,5,2] => [1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0] => 5
10010101 => [1,2,1,1,1,1,1] => [6,2] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 6
10010110 => [1,2,1,1,2,1] => [2,4,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
10010111 => [1,2,1,1,3] => [1,1,4,2] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
10011000 => [1,2,2,3] => [1,1,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
10011001 => [1,2,2,2,1] => [2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
10011010 => [1,2,2,1,1,1] => [4,2,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 4
10011011 => [1,2,2,1,2] => [1,3,2,2] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3
10011101 => [1,2,3,1,1] => [3,1,2,2] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0] => 3
10011111 => [1,2,5] => [1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
10100000 => [1,1,1,5] => [1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
10100001 => [1,1,1,4,1] => [2,1,1,4] => [1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
10100011 => [1,1,1,3,2] => [1,2,1,4] => [1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
10100100 => [1,1,1,2,1,2] => [1,3,4] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
10100101 => [1,1,1,2,1,1,1] => [4,4] => [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0] => 4
10100110 => [1,1,1,2,2,1] => [2,2,4] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
10100111 => [1,1,1,2,3] => [1,1,2,4] => [1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
10101000 => [1,1,1,1,1,3] => [1,1,6] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
10101001 => [1,1,1,1,1,2,1] => [2,6] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
10101010 => [1,1,1,1,1,1,1,1] => [8] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 8
10101011 => [1,1,1,1,1,1,2] => [1,7] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
10101100 => [1,1,1,1,2,2] => [1,2,5] => [1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0] => 5
10101101 => [1,1,1,1,2,1,1] => [3,5] => [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0] => 5
10101110 => [1,1,1,1,3,1] => [2,1,5] => [1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
10101111 => [1,1,1,1,4] => [1,1,1,5] => [1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0] => 5
10110001 => [1,1,2,3,1] => [2,1,2,3] => [1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
10110011 => [1,1,2,2,2] => [1,2,2,3] => [1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0] => 3
10110101 => [1,1,2,1,1,1,1] => [5,3] => [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0] => 5
10110111 => [1,1,2,1,3] => [1,1,3,3] => [1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
10111001 => [1,1,3,2,1] => [2,2,1,3] => [1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
10111011 => [1,1,3,1,2] => [1,3,1,3] => [1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
10111101 => [1,1,4,1,1] => [3,1,1,3] => [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0] => 3
10111110 => [1,1,5,1] => [2,1,1,1,3] => [1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
10111111 => [1,1,6] => [1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
11000000 => [2,6] => [1,1,1,1,1,2,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
11000001 => [2,5,1] => [2,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
11000101 => [2,3,1,1,1] => [4,1,2,1] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0] => 4
11001001 => [2,2,1,2,1] => [2,3,2,1] => [1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
11001011 => [2,2,1,1,2] => [1,4,2,1] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
11001100 => [2,2,2,2] => [1,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
11001101 => [2,2,2,1,1] => [3,2,2,1] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0] => 3
11010001 => [2,1,1,3,1] => [2,1,4,1] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
11010010 => [2,1,1,2,1,1] => [3,4,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 4
11010011 => [2,1,1,2,2] => [1,2,4,1] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
11010100 => [2,1,1,1,1,2] => [1,6,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
11010101 => [2,1,1,1,1,1,1] => [7,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 7
11010110 => [2,1,1,1,2,1] => [2,5,1] => [1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
11010111 => [2,1,1,1,3] => [1,1,5,1] => [1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0] => 5
11011001 => [2,1,2,2,1] => [2,2,3,1] => [1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
11011011 => [2,1,2,1,2] => [1,3,3,1] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
11011101 => [2,1,3,1,1] => [3,1,3,1] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0] => 3
11011111 => [2,1,5] => [1,1,1,1,3,1] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0] => 3
11100000 => [3,5] => [1,1,1,1,2,1,1] => [1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
11100001 => [3,4,1] => [2,1,1,2,1,1] => [1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0] => 2
11100101 => [3,2,1,1,1] => [4,2,1,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0] => 4
11101001 => [3,1,1,2,1] => [2,4,1,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
11101010 => [3,1,1,1,1,1] => [6,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 6
11101011 => [3,1,1,1,2] => [1,5,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0] => 5
11101101 => [3,1,2,1,1] => [3,3,1,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0] => 3
11110000 => [4,4] => [1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
11110101 => [4,1,1,1,1] => [5,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0] => 5
11110110 => [4,1,2,1] => [2,3,1,1,1] => [1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
11110111 => [4,1,3] => [1,1,3,1,1,1] => [1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0] => 3
11111000 => [5,3] => [1,1,2,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
11111001 => [5,2,1] => [2,2,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
11111010 => [5,1,1,1] => [4,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0] => 4
11111011 => [5,1,2] => [1,3,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0] => 3
11111100 => [6,2] => [1,2,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
11111101 => [6,1,1] => [3,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 3
11111110 => [7,1] => [2,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
11111111 => [8] => [1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
000000000 => [9] => [1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
000000001 => [8,1] => [2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
000000010 => [7,1,1] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 3
000000011 => [7,2] => [1,2,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
000000100 => [6,1,2] => [1,3,1,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 3
000000101 => [6,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 4
000000110 => [6,2,1] => [2,2,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
000000111 => [6,3] => [1,1,2,1,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
000001010 => [5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => 5
000001100 => [5,2,2] => [1,2,2,1,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
000001111 => [5,4] => [1,1,1,2,1,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
000010101 => [4,1,1,1,1,1] => [6,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => 6
000100101 => [3,1,2,1,1,1] => [4,3,1,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => 4
000101010 => [3,1,1,1,1,1,1] => [7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 7
000101011 => [3,1,1,1,1,2] => [1,6,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 6
000101101 => [3,1,1,2,1,1] => [3,4,1,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
001000101 => [2,1,3,1,1,1] => [4,1,3,1] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0] => 4
001001001 => [2,1,2,1,2,1] => [2,3,3,1] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
001001011 => [2,1,2,1,1,2] => [1,4,3,1] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => 4
001001101 => [2,1,2,2,1,1] => [3,2,3,1] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
001010100 => [2,1,1,1,1,1,2] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 7
001010101 => [2,1,1,1,1,1,1,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 8
001010110 => [2,1,1,1,1,2,1] => [2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
001010111 => [2,1,1,1,1,3] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
001011001 => [2,1,1,2,2,1] => [2,2,4,1] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
001011011 => [2,1,1,2,1,2] => [1,3,4,1] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 4
001011101 => [2,1,1,3,1,1] => [3,1,4,1] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
001100101 => [2,2,2,1,1,1] => [4,2,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => 4
001100110 => [2,2,2,2,1] => [2,2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
001101001 => [2,2,1,1,2,1] => [2,4,2,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
001101101 => [2,2,1,2,1,1] => [3,3,2,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
001111110 => [2,6,1] => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
010000000 => [1,1,7] => [1,1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
010000101 => [1,1,4,1,1,1] => [4,1,1,3] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0] => 4
010001001 => [1,1,3,1,2,1] => [2,3,1,3] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
010001011 => [1,1,3,1,1,2] => [1,4,1,3] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => 4
010001101 => [1,1,3,2,1,1] => [3,2,1,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
010010001 => [1,1,2,1,3,1] => [2,1,3,3] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
010010011 => [1,1,2,1,2,2] => [1,2,3,3] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
010010101 => [1,1,2,1,1,1,1,1] => [6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 6
010010111 => [1,1,2,1,1,3] => [1,1,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
010011011 => [1,1,2,2,1,2] => [1,3,2,3] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => 3
010011101 => [1,1,2,3,1,1] => [3,1,2,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
010100101 => [1,1,1,1,2,1,1,1] => [4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 5
010101000 => [1,1,1,1,1,1,3] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
010101001 => [1,1,1,1,1,1,2,1] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
010101010 => [1,1,1,1,1,1,1,1,1] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 9
010101011 => [1,1,1,1,1,1,1,2] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 8
010101100 => [1,1,1,1,1,2,2] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
010101101 => [1,1,1,1,1,2,1,1] => [3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
010101111 => [1,1,1,1,1,4] => [1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
010110001 => [1,1,1,2,3,1] => [2,1,2,4] => [1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
010110011 => [1,1,1,2,2,2] => [1,2,2,4] => [1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
010110101 => [1,1,1,2,1,1,1,1] => [5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 5
010110111 => [1,1,1,2,1,3] => [1,1,3,4] => [1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
010111001 => [1,1,1,3,2,1] => [2,2,1,4] => [1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
010111011 => [1,1,1,3,1,2] => [1,3,1,4] => [1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => 4
010111101 => [1,1,1,4,1,1] => [3,1,1,4] => [1,1,1,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
010111111 => [1,1,1,6] => [1,1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
011000000 => [1,2,6] => [1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
011000101 => [1,2,3,1,1,1] => [4,1,2,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,0,0] => 4
011001000 => [1,2,2,1,3] => [1,1,3,2,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3
011001011 => [1,2,2,1,1,2] => [1,4,2,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 4
011001100 => [1,2,2,2,2] => [1,2,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
011001101 => [1,2,2,2,1,1] => [3,2,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
011001111 => [1,2,2,4] => [1,1,1,2,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
011010001 => [1,2,1,1,3,1] => [2,1,4,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
011010011 => [1,2,1,1,2,2] => [1,2,4,2] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
011010100 => [1,2,1,1,1,1,2] => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 6
011010101 => [1,2,1,1,1,1,1,1] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 7
011011011 => [1,2,1,2,1,2] => [1,3,3,2] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => 3
011011101 => [1,2,1,3,1,1] => [3,1,3,2] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
011011111 => [1,2,1,5] => [1,1,1,1,3,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
011100101 => [1,3,2,1,1,1] => [4,2,1,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,0,0] => 4
011101001 => [1,3,1,1,2,1] => [2,4,1,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
011101101 => [1,3,1,2,1,1] => [3,3,1,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
011111100 => [1,6,2] => [1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
011111110 => [1,7,1] => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
011111111 => [1,8] => [1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
100000000 => [1,8] => [1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
100000001 => [1,7,1] => [2,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
100000011 => [1,6,2] => [1,2,1,1,1,1,2] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
100010010 => [1,3,1,2,1,1] => [3,3,1,2] => [1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,1,0,0] => 3
100010110 => [1,3,1,1,2,1] => [2,4,1,2] => [1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
100011010 => [1,3,2,1,1,1] => [4,2,1,2] => [1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,1,0,0] => 4
100100000 => [1,2,1,5] => [1,1,1,1,3,2] => [1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
100100010 => [1,2,1,3,1,1] => [3,1,3,2] => [1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,1,0,0] => 3
100100100 => [1,2,1,2,1,2] => [1,3,3,2] => [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0] => 3
100101010 => [1,2,1,1,1,1,1,1] => [7,2] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0] => 7
100101011 => [1,2,1,1,1,1,2] => [1,6,2] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0] => 6
100101100 => [1,2,1,1,2,2] => [1,2,4,2] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
100101110 => [1,2,1,1,3,1] => [2,1,4,2] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
100110000 => [1,2,2,4] => [1,1,1,2,2,2] => [1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
100110010 => [1,2,2,2,1,1] => [3,2,2,2] => [1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 3
100110011 => [1,2,2,2,2] => [1,2,2,2,2] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
100110100 => [1,2,2,1,1,2] => [1,4,2,2] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0] => 4
100110111 => [1,2,2,1,3] => [1,1,3,2,2] => [1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0] => 3
100111010 => [1,2,3,1,1,1] => [4,1,2,2] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,0,0] => 4
100111111 => [1,2,6] => [1,1,1,1,1,2,2] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0] => 2
101000000 => [1,1,1,6] => [1,1,1,1,1,4] => [1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
101000010 => [1,1,1,4,1,1] => [3,1,1,4] => [1,1,1,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0] => 4
101000100 => [1,1,1,3,1,2] => [1,3,1,4] => [1,0,1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0] => 4
101000110 => [1,1,1,3,2,1] => [2,2,1,4] => [1,1,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
101001000 => [1,1,1,2,1,3] => [1,1,3,4] => [1,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
101001010 => [1,1,1,2,1,1,1,1] => [5,4] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0] => 5
101001100 => [1,1,1,2,2,2] => [1,2,2,4] => [1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
101001110 => [1,1,1,2,3,1] => [2,1,2,4] => [1,1,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
101010000 => [1,1,1,1,1,4] => [1,1,1,6] => [1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
101010010 => [1,1,1,1,1,2,1,1] => [3,6] => [1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
101010011 => [1,1,1,1,1,2,2] => [1,2,6] => [1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
101010100 => [1,1,1,1,1,1,1,2] => [1,8] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 8
101010101 => [1,1,1,1,1,1,1,1,1] => [9] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 9
101010110 => [1,1,1,1,1,1,2,1] => [2,7] => [1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
101010111 => [1,1,1,1,1,1,3] => [1,1,7] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
101011010 => [1,1,1,1,2,1,1,1] => [4,5] => [1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 5
101100010 => [1,1,2,3,1,1] => [3,1,2,3] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 3
101100100 => [1,1,2,2,1,2] => [1,3,2,3] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0] => 3
101101000 => [1,1,2,1,1,3] => [1,1,4,3] => [1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
101101010 => [1,1,2,1,1,1,1,1] => [6,3] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0] => 6
101101100 => [1,1,2,1,2,2] => [1,2,3,3] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
101101110 => [1,1,2,1,3,1] => [2,1,3,3] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0] => 3
101110010 => [1,1,3,2,1,1] => [3,2,1,3] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,0,0,0] => 3
101110100 => [1,1,3,1,1,2] => [1,4,1,3] => [1,0,1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0] => 4
101110110 => [1,1,3,1,2,1] => [2,3,1,3] => [1,1,0,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0] => 3
101111010 => [1,1,4,1,1,1] => [4,1,1,3] => [1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,0,0,0] => 4
101111111 => [1,1,7] => [1,1,1,1,1,1,3] => [1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0] => 3
110000001 => [2,6,1] => [2,1,1,1,1,2,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0] => 2
110010010 => [2,2,1,2,1,1] => [3,3,2,1] => [1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 3
110010110 => [2,2,1,1,2,1] => [2,4,2,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
110011001 => [2,2,2,2,1] => [2,2,2,2,1] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
110011010 => [2,2,2,1,1,1] => [4,2,2,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0] => 4
110100010 => [2,1,1,3,1,1] => [3,1,4,1] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,0] => 4
110100100 => [2,1,1,2,1,2] => [1,3,4,1] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 4
110100110 => [2,1,1,2,2,1] => [2,2,4,1] => [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
110101000 => [2,1,1,1,1,3] => [1,1,6,1] => [1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
110101001 => [2,1,1,1,1,2,1] => [2,6,1] => [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0] => 6
110101010 => [2,1,1,1,1,1,1,1] => [8,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 8
110101011 => [2,1,1,1,1,1,2] => [1,7,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 7
110110010 => [2,1,2,2,1,1] => [3,2,3,1] => [1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 3
110110100 => [2,1,2,1,1,2] => [1,4,3,1] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => 4
110110110 => [2,1,2,1,2,1] => [2,3,3,1] => [1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0] => 3
110111010 => [2,1,3,1,1,1] => [4,1,3,1] => [1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0,1,0] => 4
111010010 => [3,1,1,2,1,1] => [3,4,1,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0] => 4
111010100 => [3,1,1,1,1,2] => [1,6,1,1] => [1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0] => 6
111010101 => [3,1,1,1,1,1,1] => [7,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 7
111011010 => [3,1,2,1,1,1] => [4,3,1,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0] => 4
111101010 => [4,1,1,1,1,1] => [6,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0] => 6
111110000 => [5,4] => [1,1,1,2,1,1,1,1] => [1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
111110011 => [5,2,2] => [1,2,2,1,1,1,1] => [1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0] => 2
111110101 => [5,1,1,1,1] => [5,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0] => 5
111111000 => [6,3] => [1,1,2,1,1,1,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
111111001 => [6,2,1] => [2,2,1,1,1,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0] => 2
111111010 => [6,1,1,1] => [4,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 4
111111011 => [6,1,2] => [1,3,1,1,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0] => 3
111111100 => [7,2] => [1,2,1,1,1,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
111111101 => [7,1,1] => [3,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 3
111111110 => [8,1] => [2,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
111111111 => [9] => [1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
1010101010 => [1,1,1,1,1,1,1,1,1,1] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 10
1101010100 => [2,1,1,1,1,1,1,2] => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 8
1111111111 => [10] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
1111111110 => [9,1] => [2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
1111111101 => [8,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 3
1111111010 => [7,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 4
1111110101 => [6,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 5
1111101010 => [5,1,1,1,1,1] => [6,1,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => 6
1111010101 => [4,1,1,1,1,1,1] => [7,1,1,1] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0] => 7
1111000000 => [4,6] => [1,1,1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
1110101011 => [3,1,1,1,1,1,2] => [1,7,1,1] => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0] => 7
1110101010 => [3,1,1,1,1,1,1,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 8
1101101001 => [2,1,2,1,1,2,1] => [2,4,3,1] => [1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0] => 4
1101100101 => [2,1,2,2,1,1,1] => [4,2,3,1] => [1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0,1,0] => 4
1101010111 => [2,1,1,1,1,1,3] => [1,1,7,1] => [1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0] => 7
1101010101 => [2,1,1,1,1,1,1,1,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 9
1101001101 => [2,1,1,2,2,1,1] => [3,2,4,1] => [1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
1101001001 => [2,1,1,2,1,2,1] => [2,3,4,1] => [1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 4
1100110011 => [2,2,2,2,2] => [1,2,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
1100101101 => [2,2,1,1,2,1,1] => [3,4,2,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
1100100101 => [2,2,1,2,1,1,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 4
1011010101 => [1,1,2,1,1,1,1,1,1] => [7,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => 7
1011010011 => [1,1,2,1,1,2,2] => [1,2,4,3] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
1011010001 => [1,1,2,1,1,3,1] => [2,1,4,3] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
1011001011 => [1,1,2,2,1,1,2] => [1,4,2,3] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0] => 4
1011000101 => [1,1,2,3,1,1,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 4
1010110101 => [1,1,1,1,2,1,1,1,1] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 5
1010101101 => [1,1,1,1,1,1,2,1,1] => [3,7] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
1010101011 => [1,1,1,1,1,1,1,1,2] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 9
1010101001 => [1,1,1,1,1,1,1,2,1] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 8
1010101000 => [1,1,1,1,1,1,1,3] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 8
1010100101 => [1,1,1,1,1,2,1,1,1] => [4,6] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
1010011101 => [1,1,1,2,3,1,1] => [3,1,2,4] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
1010011011 => [1,1,1,2,2,1,2] => [1,3,2,4] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
1010010101 => [1,1,1,2,1,1,1,1,1] => [6,4] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => 6
1010010011 => [1,1,1,2,1,2,2] => [1,2,3,4] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
1010010001 => [1,1,1,2,1,3,1] => [2,1,3,4] => [1,1,0,0,1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
1010001101 => [1,1,1,3,2,1,1] => [3,2,1,4] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
1001100111 => [1,2,2,2,3] => [1,1,2,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
1001100110 => [1,2,2,2,2,1] => [2,2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
1001011101 => [1,2,1,1,3,1,1] => [3,1,4,2] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
1001011011 => [1,2,1,1,2,1,2] => [1,3,4,2] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
1001010101 => [1,2,1,1,1,1,1,1,1] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 8
1001001011 => [1,2,1,2,1,1,2] => [1,4,3,2] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => 4
1000101101 => [1,3,1,1,2,1,1] => [3,4,1,2] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
1000000001 => [1,8,1] => [2,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
1000000000 => [1,9] => [1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
10000000000 => [1,10] => [1,1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
0111111111 => [1,9] => [1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
0000000001 => [9,1] => [2,1,1,1,1,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 2
01111111111 => [1,10] => [1,1,1,1,1,1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
0101010101 => [1,1,1,1,1,1,1,1,1,1] => [10] => [1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0] => 10
0010101011 => [2,1,1,1,1,1,1,2] => [1,8,1] => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0] => 8
111111111111 => [12] => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
0000000000 => [10] => [1,1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
0110011000 => [1,2,2,2,3] => [1,1,2,2,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
0111111110 => [1,8,1] => [2,1,1,1,1,1,1,2] => [1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0] => 2
0101100010 => [1,1,1,2,3,1,1] => [3,1,2,4] => [1,1,1,0,0,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
0101001010 => [1,1,1,1,2,1,1,1,1] => [5,5] => [1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0] => 5
000000000000 => [12] => [1,1,1,1,1,1,1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 1
0010101010 => [2,1,1,1,1,1,1,1,1] => [9,1] => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0] => 9
0101010100 => [1,1,1,1,1,1,1,1,2] => [1,9] => [1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0] => 9
0000000010 => [8,1,1] => [3,1,1,1,1,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0] => 3
0000001010 => [6,1,1,1,1] => [5,1,1,1,1,1] => [1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0] => 5
0010110010 => [2,1,1,2,2,1,1] => [3,2,4,1] => [1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0] => 4
0011001100 => [2,2,2,2,2] => [1,2,2,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0] => 2
0011010010 => [2,2,1,1,2,1,1] => [3,4,2,1] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0] => 4
0100101010 => [1,1,2,1,1,1,1,1,1] => [7,3] => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0] => 7
0100101100 => [1,1,2,1,1,2,2] => [1,2,4,3] => [1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
0100110100 => [1,1,2,2,1,1,2] => [1,4,2,3] => [1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,0,0,0] => 4
0101010010 => [1,1,1,1,1,1,2,1,1] => [3,7] => [1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0] => 7
0101100100 => [1,1,1,2,2,1,2] => [1,3,2,4] => [1,0,1,1,1,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0] => 4
0110100010 => [1,2,1,1,3,1,1] => [3,1,4,2] => [1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
0110100100 => [1,2,1,1,2,1,2] => [1,3,4,2] => [1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0] => 4
0101010110 => [1,1,1,1,1,1,1,2,1] => [2,8] => [1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 8
0101011010 => [1,1,1,1,1,2,1,1,1] => [4,6] => [1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0] => 6
0101101010 => [1,1,1,2,1,1,1,1,1] => [6,4] => [1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0] => 6
0101101100 => [1,1,1,2,1,2,2] => [1,2,3,4] => [1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0] => 4
0101110010 => [1,1,1,3,2,1,1] => [3,2,1,4] => [1,1,1,0,0,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0] => 4
0110011001 => [1,2,2,2,2,1] => [2,2,2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
0110101010 => [1,2,1,1,1,1,1,1,1] => [8,2] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0] => 8
0110110100 => [1,2,1,2,1,1,2] => [1,4,3,2] => [1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0] => 4
0111010010 => [1,3,1,1,2,1,1] => [3,4,1,2] => [1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0] => 4
0010110110 => [2,1,1,2,1,2,1] => [2,3,4,1] => [1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0] => 4
0100111010 => [1,1,2,3,1,1,1] => [4,1,2,3] => [1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,1,1,0,0,0] => 4
0000000101 => [7,1,1,1] => [4,1,1,1,1,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0] => 4
0000010101 => [5,1,1,1,1,1] => [6,1,1,1,1] => [1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0] => 6
0000111111 => [4,6] => [1,1,1,1,1,2,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0] => 2
0110011111 => [1,2,2,5] => [1,1,1,1,2,2,2] => [1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0] => 2
0011011010 => [2,2,1,2,1,1,1] => [4,3,2,1] => [1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0,1,0] => 4
0100101110 => [1,1,2,1,1,3,1] => [2,1,4,3] => [1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0] => 4
0001010101 => [3,1,1,1,1,1,1,1] => [8,1,1] => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0] => 8
0101010111 => [1,1,1,1,1,1,1,3] => [1,1,8] => [1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0] => 8
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Description
The height of a Dyck path.
The height of a Dyck path $D$ of semilength $n$ is defined as the maximal height of a peak of $D$. The height of $D$ at position $i$ is the number of up-steps minus the number of down-steps before position $i$.
Map
delta morphism
Description
Applies the delta morphism to a binary word.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
conjugate
Description
The conjugate of a composition.
The conjugate of a composition $C$ is defined as the complement (Mp00039complement) of the reversal (Mp00038reverse) of $C$.
Equivalently, the ribbon shape corresponding to the conjugate of $C$ is the conjugate of the ribbon shape of $C$.