Identifier
Values
0 => [2] => [1] => [1,0] => 1
1 => [1,1] => [2] => [1,1,0,0] => 2
00 => [3] => [1] => [1,0] => 1
01 => [2,1] => [1,1] => [1,0,1,0] => 2
10 => [1,2] => [1,1] => [1,0,1,0] => 2
11 => [1,1,1] => [3] => [1,1,1,0,0,0] => 3
000 => [4] => [1] => [1,0] => 1
001 => [3,1] => [1,1] => [1,0,1,0] => 2
010 => [2,2] => [2] => [1,1,0,0] => 2
011 => [2,1,1] => [1,2] => [1,0,1,1,0,0] => 3
100 => [1,3] => [1,1] => [1,0,1,0] => 2
101 => [1,2,1] => [1,1,1] => [1,0,1,0,1,0] => 3
110 => [1,1,2] => [2,1] => [1,1,0,0,1,0] => 3
111 => [1,1,1,1] => [4] => [1,1,1,1,0,0,0,0] => 4
0000 => [5] => [1] => [1,0] => 1
0001 => [4,1] => [1,1] => [1,0,1,0] => 2
0010 => [3,2] => [1,1] => [1,0,1,0] => 2
0011 => [3,1,1] => [1,2] => [1,0,1,1,0,0] => 3
0100 => [2,3] => [1,1] => [1,0,1,0] => 2
0101 => [2,2,1] => [2,1] => [1,1,0,0,1,0] => 3
0110 => [2,1,2] => [1,1,1] => [1,0,1,0,1,0] => 3
0111 => [2,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 4
1000 => [1,4] => [1,1] => [1,0,1,0] => 2
1001 => [1,3,1] => [1,1,1] => [1,0,1,0,1,0] => 3
1010 => [1,2,2] => [1,2] => [1,0,1,1,0,0] => 3
1011 => [1,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
1100 => [1,1,3] => [2,1] => [1,1,0,0,1,0] => 3
1101 => [1,1,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
1110 => [1,1,1,2] => [3,1] => [1,1,1,0,0,0,1,0] => 4
1111 => [1,1,1,1,1] => [5] => [1,1,1,1,1,0,0,0,0,0] => 5
00000 => [6] => [1] => [1,0] => 1
00001 => [5,1] => [1,1] => [1,0,1,0] => 2
00010 => [4,2] => [1,1] => [1,0,1,0] => 2
00011 => [4,1,1] => [1,2] => [1,0,1,1,0,0] => 3
00100 => [3,3] => [2] => [1,1,0,0] => 2
00101 => [3,2,1] => [1,1,1] => [1,0,1,0,1,0] => 3
00110 => [3,1,2] => [1,1,1] => [1,0,1,0,1,0] => 3
00111 => [3,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 4
01000 => [2,4] => [1,1] => [1,0,1,0] => 2
01001 => [2,3,1] => [1,1,1] => [1,0,1,0,1,0] => 3
01010 => [2,2,2] => [3] => [1,1,1,0,0,0] => 3
01011 => [2,2,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => 4
01100 => [2,1,3] => [1,1,1] => [1,0,1,0,1,0] => 3
01101 => [2,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
01110 => [2,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
01111 => [2,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 5
10000 => [1,5] => [1,1] => [1,0,1,0] => 2
10001 => [1,4,1] => [1,1,1] => [1,0,1,0,1,0] => 3
10010 => [1,3,2] => [1,1,1] => [1,0,1,0,1,0] => 3
10011 => [1,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
10100 => [1,2,3] => [1,1,1] => [1,0,1,0,1,0] => 3
10101 => [1,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
10110 => [1,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
10111 => [1,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 5
11000 => [1,1,4] => [2,1] => [1,1,0,0,1,0] => 3
11001 => [1,1,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
11010 => [1,1,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 4
11011 => [1,1,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 5
11100 => [1,1,1,3] => [3,1] => [1,1,1,0,0,0,1,0] => 4
11101 => [1,1,1,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 5
11110 => [1,1,1,1,2] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 5
11111 => [1,1,1,1,1,1] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 6
000000 => [7] => [1] => [1,0] => 1
000001 => [6,1] => [1,1] => [1,0,1,0] => 2
000010 => [5,2] => [1,1] => [1,0,1,0] => 2
000011 => [5,1,1] => [1,2] => [1,0,1,1,0,0] => 3
000100 => [4,3] => [1,1] => [1,0,1,0] => 2
000101 => [4,2,1] => [1,1,1] => [1,0,1,0,1,0] => 3
000110 => [4,1,2] => [1,1,1] => [1,0,1,0,1,0] => 3
000111 => [4,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 4
001000 => [3,4] => [1,1] => [1,0,1,0] => 2
001001 => [3,3,1] => [2,1] => [1,1,0,0,1,0] => 3
001010 => [3,2,2] => [1,2] => [1,0,1,1,0,0] => 3
001011 => [3,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
001100 => [3,1,3] => [1,1,1] => [1,0,1,0,1,0] => 3
001101 => [3,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
001110 => [3,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
001111 => [3,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 5
010000 => [2,5] => [1,1] => [1,0,1,0] => 2
010001 => [2,4,1] => [1,1,1] => [1,0,1,0,1,0] => 3
010010 => [2,3,2] => [1,1,1] => [1,0,1,0,1,0] => 3
010011 => [2,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
010100 => [2,2,3] => [2,1] => [1,1,0,0,1,0] => 3
010101 => [2,2,2,1] => [3,1] => [1,1,1,0,0,0,1,0] => 4
010110 => [2,2,1,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
010111 => [2,2,1,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 5
011000 => [2,1,4] => [1,1,1] => [1,0,1,0,1,0] => 3
011001 => [2,1,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
011010 => [2,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
011011 => [2,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
011100 => [2,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
011101 => [2,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
011110 => [2,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 5
011111 => [2,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
100000 => [1,6] => [1,1] => [1,0,1,0] => 2
100001 => [1,5,1] => [1,1,1] => [1,0,1,0,1,0] => 3
100010 => [1,4,2] => [1,1,1] => [1,0,1,0,1,0] => 3
100011 => [1,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
100100 => [1,3,3] => [1,2] => [1,0,1,1,0,0] => 3
100101 => [1,3,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
100110 => [1,3,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
>>> Load all 1163 entries. <<<
100111 => [1,3,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 5
101000 => [1,2,4] => [1,1,1] => [1,0,1,0,1,0] => 3
101001 => [1,2,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
101010 => [1,2,2,2] => [1,3] => [1,0,1,1,1,0,0,0] => 4
101011 => [1,2,2,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 5
101100 => [1,2,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
101101 => [1,2,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
101110 => [1,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
101111 => [1,2,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 6
110000 => [1,1,5] => [2,1] => [1,1,0,0,1,0] => 3
110001 => [1,1,4,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
110010 => [1,1,3,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
110011 => [1,1,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 5
110100 => [1,1,2,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
110101 => [1,1,2,2,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 5
110110 => [1,1,2,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
110111 => [1,1,2,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 6
111000 => [1,1,1,4] => [3,1] => [1,1,1,0,0,0,1,0] => 4
111001 => [1,1,1,3,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 5
111010 => [1,1,1,2,2] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 5
111011 => [1,1,1,2,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 6
111100 => [1,1,1,1,3] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 5
111101 => [1,1,1,1,2,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
111110 => [1,1,1,1,1,2] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
0000000 => [8] => [1] => [1,0] => 1
0000001 => [7,1] => [1,1] => [1,0,1,0] => 2
0000010 => [6,2] => [1,1] => [1,0,1,0] => 2
0000011 => [6,1,1] => [1,2] => [1,0,1,1,0,0] => 3
0000100 => [5,3] => [1,1] => [1,0,1,0] => 2
0000101 => [5,2,1] => [1,1,1] => [1,0,1,0,1,0] => 3
0000110 => [5,1,2] => [1,1,1] => [1,0,1,0,1,0] => 3
0000111 => [5,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 4
0001000 => [4,4] => [2] => [1,1,0,0] => 2
0001001 => [4,3,1] => [1,1,1] => [1,0,1,0,1,0] => 3
0001010 => [4,2,2] => [1,2] => [1,0,1,1,0,0] => 3
0001011 => [4,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
0001100 => [4,1,3] => [1,1,1] => [1,0,1,0,1,0] => 3
0001101 => [4,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
0001110 => [4,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
0001111 => [4,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 5
0010000 => [3,5] => [1,1] => [1,0,1,0] => 2
0010001 => [3,4,1] => [1,1,1] => [1,0,1,0,1,0] => 3
0010010 => [3,3,2] => [2,1] => [1,1,0,0,1,0] => 3
0010011 => [3,3,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => 4
0010100 => [3,2,3] => [1,1,1] => [1,0,1,0,1,0] => 3
0010101 => [3,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
0010110 => [3,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
0010111 => [3,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 5
0011000 => [3,1,4] => [1,1,1] => [1,0,1,0,1,0] => 3
0011001 => [3,1,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
0011010 => [3,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
0011011 => [3,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
0011100 => [3,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
0011101 => [3,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
0011110 => [3,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 5
0011111 => [3,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
0100000 => [2,6] => [1,1] => [1,0,1,0] => 2
0100001 => [2,5,1] => [1,1,1] => [1,0,1,0,1,0] => 3
0100010 => [2,4,2] => [1,1,1] => [1,0,1,0,1,0] => 3
0100011 => [2,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
0100100 => [2,3,3] => [1,2] => [1,0,1,1,0,0] => 3
0100101 => [2,3,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
0100110 => [2,3,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
0100111 => [2,3,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 5
0101000 => [2,2,4] => [2,1] => [1,1,0,0,1,0] => 3
0101001 => [2,2,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
0101010 => [2,2,2,2] => [4] => [1,1,1,1,0,0,0,0] => 4
0101011 => [2,2,2,1,1] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 5
0101100 => [2,2,1,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
0101101 => [2,2,1,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
0101110 => [2,2,1,1,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 5
0101111 => [2,2,1,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 6
0110000 => [2,1,5] => [1,1,1] => [1,0,1,0,1,0] => 3
0110001 => [2,1,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
0110010 => [2,1,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
0110011 => [2,1,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
0110100 => [2,1,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
0110101 => [2,1,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
0110110 => [2,1,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
0110111 => [2,1,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
0111000 => [2,1,1,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
0111001 => [2,1,1,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
0111010 => [2,1,1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 5
0111011 => [2,1,1,2,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 6
0111100 => [2,1,1,1,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 5
0111101 => [2,1,1,1,2,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 6
0111110 => [2,1,1,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
1000000 => [1,7] => [1,1] => [1,0,1,0] => 2
1000001 => [1,6,1] => [1,1,1] => [1,0,1,0,1,0] => 3
1000010 => [1,5,2] => [1,1,1] => [1,0,1,0,1,0] => 3
1000011 => [1,5,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
1000100 => [1,4,3] => [1,1,1] => [1,0,1,0,1,0] => 3
1000101 => [1,4,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
1000110 => [1,4,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
1000111 => [1,4,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 5
1001000 => [1,3,4] => [1,1,1] => [1,0,1,0,1,0] => 3
1001001 => [1,3,3,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
1001010 => [1,3,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
1001011 => [1,3,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
1001100 => [1,3,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
1001101 => [1,3,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
1001110 => [1,3,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
1001111 => [1,3,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 6
1010000 => [1,2,5] => [1,1,1] => [1,0,1,0,1,0] => 3
1010001 => [1,2,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
1010010 => [1,2,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
1010011 => [1,2,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
1010100 => [1,2,2,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
1010101 => [1,2,2,2,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 5
1010110 => [1,2,2,1,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
1010111 => [1,2,2,1,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 6
1011000 => [1,2,1,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
1011001 => [1,2,1,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
1011010 => [1,2,1,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
1011011 => [1,2,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 6
1011100 => [1,2,1,1,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
1011101 => [1,2,1,1,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 6
1011110 => [1,2,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 6
1100000 => [1,1,6] => [2,1] => [1,1,0,0,1,0] => 3
1100001 => [1,1,5,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
1100010 => [1,1,4,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
1100011 => [1,1,4,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 5
1100100 => [1,1,3,3] => [2,2] => [1,1,0,0,1,1,0,0] => 4
1100101 => [1,1,3,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
1100110 => [1,1,3,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
1100111 => [1,1,3,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 6
1101000 => [1,1,2,4] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
1101001 => [1,1,2,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
1101010 => [1,1,2,2,2] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 5
1101011 => [1,1,2,2,1,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 6
1101100 => [1,1,2,1,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
1101101 => [1,1,2,1,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 6
1101110 => [1,1,2,1,1,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 6
1110000 => [1,1,1,5] => [3,1] => [1,1,1,0,0,0,1,0] => 4
1110001 => [1,1,1,4,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 5
1110010 => [1,1,1,3,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 5
1110011 => [1,1,1,3,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 6
1110100 => [1,1,1,2,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 5
1110101 => [1,1,1,2,2,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 6
1110110 => [1,1,1,2,1,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
1111000 => [1,1,1,1,4] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 5
1111001 => [1,1,1,1,3,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
1111010 => [1,1,1,1,2,2] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 6
1111100 => [1,1,1,1,1,3] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
00000000 => [9] => [1] => [1,0] => 1
00000001 => [8,1] => [1,1] => [1,0,1,0] => 2
00000010 => [7,2] => [1,1] => [1,0,1,0] => 2
00000011 => [7,1,1] => [1,2] => [1,0,1,1,0,0] => 3
00000100 => [6,3] => [1,1] => [1,0,1,0] => 2
00000101 => [6,2,1] => [1,1,1] => [1,0,1,0,1,0] => 3
00000110 => [6,1,2] => [1,1,1] => [1,0,1,0,1,0] => 3
00000111 => [6,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 4
00001000 => [5,4] => [1,1] => [1,0,1,0] => 2
00001001 => [5,3,1] => [1,1,1] => [1,0,1,0,1,0] => 3
00001010 => [5,2,2] => [1,2] => [1,0,1,1,0,0] => 3
00001011 => [5,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
00001100 => [5,1,3] => [1,1,1] => [1,0,1,0,1,0] => 3
00001101 => [5,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
00001110 => [5,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
00001111 => [5,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 5
00010000 => [4,5] => [1,1] => [1,0,1,0] => 2
00010001 => [4,4,1] => [2,1] => [1,1,0,0,1,0] => 3
00010010 => [4,3,2] => [1,1,1] => [1,0,1,0,1,0] => 3
00010011 => [4,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
00010100 => [4,2,3] => [1,1,1] => [1,0,1,0,1,0] => 3
00010101 => [4,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
00010110 => [4,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
00010111 => [4,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 5
00011000 => [4,1,4] => [1,1,1] => [1,0,1,0,1,0] => 3
00011001 => [4,1,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
00011010 => [4,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
00011011 => [4,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
00011100 => [4,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
00011101 => [4,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
00011110 => [4,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 5
00011111 => [4,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
00100000 => [3,6] => [1,1] => [1,0,1,0] => 2
00100001 => [3,5,1] => [1,1,1] => [1,0,1,0,1,0] => 3
00100010 => [3,4,2] => [1,1,1] => [1,0,1,0,1,0] => 3
00100011 => [3,4,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
00100100 => [3,3,3] => [3] => [1,1,1,0,0,0] => 3
00100101 => [3,3,2,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
00100110 => [3,3,1,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
00100111 => [3,3,1,1,1] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 5
00101000 => [3,2,4] => [1,1,1] => [1,0,1,0,1,0] => 3
00101001 => [3,2,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
00101010 => [3,2,2,2] => [1,3] => [1,0,1,1,1,0,0,0] => 4
00101011 => [3,2,2,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 5
00101100 => [3,2,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
00101101 => [3,2,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
00101110 => [3,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
00101111 => [3,2,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 6
00110000 => [3,1,5] => [1,1,1] => [1,0,1,0,1,0] => 3
00110001 => [3,1,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
00110010 => [3,1,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
00110011 => [3,1,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
00110100 => [3,1,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
00110101 => [3,1,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
00110110 => [3,1,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
00110111 => [3,1,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
00111000 => [3,1,1,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
00111001 => [3,1,1,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
00111010 => [3,1,1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 5
00111011 => [3,1,1,2,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 6
00111100 => [3,1,1,1,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 5
00111101 => [3,1,1,1,2,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 6
00111110 => [3,1,1,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
01000000 => [2,7] => [1,1] => [1,0,1,0] => 2
01000001 => [2,6,1] => [1,1,1] => [1,0,1,0,1,0] => 3
01000010 => [2,5,2] => [1,1,1] => [1,0,1,0,1,0] => 3
01000011 => [2,5,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
01000100 => [2,4,3] => [1,1,1] => [1,0,1,0,1,0] => 3
01000101 => [2,4,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
01000110 => [2,4,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
01000111 => [2,4,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 5
01001000 => [2,3,4] => [1,1,1] => [1,0,1,0,1,0] => 3
01001001 => [2,3,3,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
01001010 => [2,3,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
01001011 => [2,3,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
01001100 => [2,3,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
01001101 => [2,3,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
01001110 => [2,3,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
01001111 => [2,3,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 6
01010000 => [2,2,5] => [2,1] => [1,1,0,0,1,0] => 3
01010001 => [2,2,4,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
01010010 => [2,2,3,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
01010011 => [2,2,3,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 5
01010100 => [2,2,2,3] => [3,1] => [1,1,1,0,0,0,1,0] => 4
01010101 => [2,2,2,2,1] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 5
01010110 => [2,2,2,1,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 5
01010111 => [2,2,2,1,1,1] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 6
01011000 => [2,2,1,4] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
01011001 => [2,2,1,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
01011010 => [2,2,1,2,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 5
01011011 => [2,2,1,2,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 6
01011100 => [2,2,1,1,3] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 5
01011101 => [2,2,1,1,2,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 6
01011110 => [2,2,1,1,1,2] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 6
01100000 => [2,1,6] => [1,1,1] => [1,0,1,0,1,0] => 3
01100001 => [2,1,5,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
01100010 => [2,1,4,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
01100011 => [2,1,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
01100100 => [2,1,3,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
01100101 => [2,1,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
01100110 => [2,1,3,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
01100111 => [2,1,3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
01101000 => [2,1,2,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
01101001 => [2,1,2,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
01101010 => [2,1,2,2,2] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 5
01101011 => [2,1,2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 6
01101100 => [2,1,2,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
01101101 => [2,1,2,1,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
01101110 => [2,1,2,1,1,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 6
01110000 => [2,1,1,5] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
01110001 => [2,1,1,4,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
01110010 => [2,1,1,3,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
01110011 => [2,1,1,3,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 6
01110100 => [2,1,1,2,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
01110101 => [2,1,1,2,2,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 6
01110110 => [2,1,1,2,1,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 6
01111000 => [2,1,1,1,4] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 5
01111001 => [2,1,1,1,3,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 6
01111010 => [2,1,1,1,2,2] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 6
01111100 => [2,1,1,1,1,3] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
10000000 => [1,8] => [1,1] => [1,0,1,0] => 2
10000001 => [1,7,1] => [1,1,1] => [1,0,1,0,1,0] => 3
10000010 => [1,6,2] => [1,1,1] => [1,0,1,0,1,0] => 3
10000011 => [1,6,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
10000100 => [1,5,3] => [1,1,1] => [1,0,1,0,1,0] => 3
10000101 => [1,5,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
10000110 => [1,5,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
10000111 => [1,5,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 5
10001000 => [1,4,4] => [1,2] => [1,0,1,1,0,0] => 3
10001001 => [1,4,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
10001010 => [1,4,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
10001011 => [1,4,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
10001100 => [1,4,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
10001101 => [1,4,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
10001110 => [1,4,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
10001111 => [1,4,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 6
10010000 => [1,3,5] => [1,1,1] => [1,0,1,0,1,0] => 3
10010001 => [1,3,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
10010010 => [1,3,3,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
10010011 => [1,3,3,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 5
10010100 => [1,3,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
10010101 => [1,3,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
10010110 => [1,3,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
10010111 => [1,3,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
10011000 => [1,3,1,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
10011001 => [1,3,1,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
10011010 => [1,3,1,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
10011011 => [1,3,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 6
10011100 => [1,3,1,1,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
10011101 => [1,3,1,1,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 6
10011110 => [1,3,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 6
10100000 => [1,2,6] => [1,1,1] => [1,0,1,0,1,0] => 3
10100001 => [1,2,5,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
10100010 => [1,2,4,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
10100011 => [1,2,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
10100100 => [1,2,3,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
10100101 => [1,2,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
10100110 => [1,2,3,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
10100111 => [1,2,3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
10101000 => [1,2,2,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
10101001 => [1,2,2,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
10101010 => [1,2,2,2,2] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 5
10101011 => [1,2,2,2,1,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 6
10101100 => [1,2,2,1,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
10101101 => [1,2,2,1,2,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 6
10101110 => [1,2,2,1,1,2] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 6
10110000 => [1,2,1,5] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
10110001 => [1,2,1,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
10110010 => [1,2,1,3,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
10110011 => [1,2,1,3,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 6
10110100 => [1,2,1,2,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
10110101 => [1,2,1,2,2,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 6
10110110 => [1,2,1,2,1,2] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
10111000 => [1,2,1,1,4] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
10111001 => [1,2,1,1,3,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 6
10111010 => [1,2,1,1,2,2] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 6
10111100 => [1,2,1,1,1,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 6
11000000 => [1,1,7] => [2,1] => [1,1,0,0,1,0] => 3
11000001 => [1,1,6,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
11000010 => [1,1,5,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
11000011 => [1,1,5,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 5
11000100 => [1,1,4,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
11000101 => [1,1,4,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
11000110 => [1,1,4,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
11000111 => [1,1,4,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 6
11001000 => [1,1,3,4] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
11001001 => [1,1,3,3,1] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 5
11001010 => [1,1,3,2,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 5
11001011 => [1,1,3,2,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 6
11001100 => [1,1,3,1,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
11001101 => [1,1,3,1,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 6
11001110 => [1,1,3,1,1,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 6
11010000 => [1,1,2,5] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
11010001 => [1,1,2,4,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
11010010 => [1,1,2,3,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
11010011 => [1,1,2,3,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 6
11010100 => [1,1,2,2,3] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 5
11010101 => [1,1,2,2,2,1] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 6
11010110 => [1,1,2,2,1,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 6
11011000 => [1,1,2,1,4] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
11011001 => [1,1,2,1,3,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 6
11011010 => [1,1,2,1,2,2] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 6
11011100 => [1,1,2,1,1,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 6
11100000 => [1,1,1,6] => [3,1] => [1,1,1,0,0,0,1,0] => 4
11100001 => [1,1,1,5,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 5
11100010 => [1,1,1,4,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 5
11100011 => [1,1,1,4,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 6
11100100 => [1,1,1,3,3] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 5
11100101 => [1,1,1,3,2,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
11100110 => [1,1,1,3,1,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
11101000 => [1,1,1,2,4] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 5
11101001 => [1,1,1,2,3,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
11101010 => [1,1,1,2,2,2] => [3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 6
11101100 => [1,1,1,2,1,3] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
11110000 => [1,1,1,1,5] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 5
11110001 => [1,1,1,1,4,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
11110010 => [1,1,1,1,3,2] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
11110100 => [1,1,1,1,2,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
11111000 => [1,1,1,1,1,4] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
000000000 => [10] => [1] => [1,0] => 1
000000001 => [9,1] => [1,1] => [1,0,1,0] => 2
000000010 => [8,2] => [1,1] => [1,0,1,0] => 2
000000011 => [8,1,1] => [1,2] => [1,0,1,1,0,0] => 3
000000100 => [7,3] => [1,1] => [1,0,1,0] => 2
000000101 => [7,2,1] => [1,1,1] => [1,0,1,0,1,0] => 3
000000110 => [7,1,2] => [1,1,1] => [1,0,1,0,1,0] => 3
000000111 => [7,1,1,1] => [1,3] => [1,0,1,1,1,0,0,0] => 4
000001000 => [6,4] => [1,1] => [1,0,1,0] => 2
000001001 => [6,3,1] => [1,1,1] => [1,0,1,0,1,0] => 3
000001010 => [6,2,2] => [1,2] => [1,0,1,1,0,0] => 3
000001011 => [6,2,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
000001100 => [6,1,3] => [1,1,1] => [1,0,1,0,1,0] => 3
000001101 => [6,1,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
000001110 => [6,1,1,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
000001111 => [6,1,1,1,1] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 5
000010000 => [5,5] => [2] => [1,1,0,0] => 2
000010001 => [5,4,1] => [1,1,1] => [1,0,1,0,1,0] => 3
000010010 => [5,3,2] => [1,1,1] => [1,0,1,0,1,0] => 3
000010011 => [5,3,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
000010100 => [5,2,3] => [1,1,1] => [1,0,1,0,1,0] => 3
000010101 => [5,2,2,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
000010110 => [5,2,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
000010111 => [5,2,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 5
000011000 => [5,1,4] => [1,1,1] => [1,0,1,0,1,0] => 3
000011001 => [5,1,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
000011010 => [5,1,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
000011011 => [5,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
000011100 => [5,1,1,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
000011101 => [5,1,1,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
000011110 => [5,1,1,1,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 5
000011111 => [5,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
000100000 => [4,6] => [1,1] => [1,0,1,0] => 2
000100001 => [4,5,1] => [1,1,1] => [1,0,1,0,1,0] => 3
000100010 => [4,4,2] => [2,1] => [1,1,0,0,1,0] => 3
000100011 => [4,4,1,1] => [2,2] => [1,1,0,0,1,1,0,0] => 4
000100100 => [4,3,3] => [1,2] => [1,0,1,1,0,0] => 3
000100101 => [4,3,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
000100110 => [4,3,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
000100111 => [4,3,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 5
000101000 => [4,2,4] => [1,1,1] => [1,0,1,0,1,0] => 3
000101001 => [4,2,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
000101010 => [4,2,2,2] => [1,3] => [1,0,1,1,1,0,0,0] => 4
000101011 => [4,2,2,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 5
000101100 => [4,2,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
000101101 => [4,2,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
000101110 => [4,2,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
000101111 => [4,2,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 6
000110000 => [4,1,5] => [1,1,1] => [1,0,1,0,1,0] => 3
000110001 => [4,1,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
000110010 => [4,1,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
000110011 => [4,1,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
000110100 => [4,1,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
000110101 => [4,1,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
000110110 => [4,1,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
000110111 => [4,1,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
000111000 => [4,1,1,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
000111001 => [4,1,1,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
000111010 => [4,1,1,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 5
000111011 => [4,1,1,2,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 6
000111100 => [4,1,1,1,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 5
000111101 => [4,1,1,1,2,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 6
000111110 => [4,1,1,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
001000000 => [3,7] => [1,1] => [1,0,1,0] => 2
001000001 => [3,6,1] => [1,1,1] => [1,0,1,0,1,0] => 3
001000010 => [3,5,2] => [1,1,1] => [1,0,1,0,1,0] => 3
001000011 => [3,5,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
001000100 => [3,4,3] => [1,1,1] => [1,0,1,0,1,0] => 3
001000101 => [3,4,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
001000110 => [3,4,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
001000111 => [3,4,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 5
001001000 => [3,3,4] => [2,1] => [1,1,0,0,1,0] => 3
001001001 => [3,3,3,1] => [3,1] => [1,1,1,0,0,0,1,0] => 4
001001010 => [3,3,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 4
001001011 => [3,3,2,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 5
001001100 => [3,3,1,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
001001101 => [3,3,1,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
001001110 => [3,3,1,1,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 5
001001111 => [3,3,1,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 6
001010000 => [3,2,5] => [1,1,1] => [1,0,1,0,1,0] => 3
001010001 => [3,2,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
001010010 => [3,2,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
001010011 => [3,2,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
001010100 => [3,2,2,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
001010101 => [3,2,2,2,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 5
001010110 => [3,2,2,1,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
001010111 => [3,2,2,1,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 6
001011000 => [3,2,1,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
001011001 => [3,2,1,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
001011010 => [3,2,1,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
001011011 => [3,2,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 6
001011100 => [3,2,1,1,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
001011101 => [3,2,1,1,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 6
001011110 => [3,2,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 6
001100000 => [3,1,6] => [1,1,1] => [1,0,1,0,1,0] => 3
001100001 => [3,1,5,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
001100010 => [3,1,4,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
001100011 => [3,1,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
001100100 => [3,1,3,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
001100101 => [3,1,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
001100110 => [3,1,3,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
001100111 => [3,1,3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
001101000 => [3,1,2,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
001101001 => [3,1,2,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
001101010 => [3,1,2,2,2] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 5
001101011 => [3,1,2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 6
001101100 => [3,1,2,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
001101101 => [3,1,2,1,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
001101110 => [3,1,2,1,1,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 6
001110000 => [3,1,1,5] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
001110001 => [3,1,1,4,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
001110010 => [3,1,1,3,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
001110011 => [3,1,1,3,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 6
001110100 => [3,1,1,2,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
001110101 => [3,1,1,2,2,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 6
001110110 => [3,1,1,2,1,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 6
001111000 => [3,1,1,1,4] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 5
001111001 => [3,1,1,1,3,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 6
001111010 => [3,1,1,1,2,2] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 6
001111100 => [3,1,1,1,1,3] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
010000000 => [2,8] => [1,1] => [1,0,1,0] => 2
010000001 => [2,7,1] => [1,1,1] => [1,0,1,0,1,0] => 3
010000010 => [2,6,2] => [1,1,1] => [1,0,1,0,1,0] => 3
010000011 => [2,6,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
010000100 => [2,5,3] => [1,1,1] => [1,0,1,0,1,0] => 3
010000101 => [2,5,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
010000110 => [2,5,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
010000111 => [2,5,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 5
010001000 => [2,4,4] => [1,2] => [1,0,1,1,0,0] => 3
010001001 => [2,4,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
010001010 => [2,4,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
010001011 => [2,4,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
010001100 => [2,4,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
010001101 => [2,4,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
010001110 => [2,4,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
010001111 => [2,4,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 6
010010000 => [2,3,5] => [1,1,1] => [1,0,1,0,1,0] => 3
010010001 => [2,3,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
010010010 => [2,3,3,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
010010011 => [2,3,3,1,1] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 5
010010100 => [2,3,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
010010101 => [2,3,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
010010110 => [2,3,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
010010111 => [2,3,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
010011000 => [2,3,1,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
010011001 => [2,3,1,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
010011010 => [2,3,1,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
010011011 => [2,3,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 6
010011100 => [2,3,1,1,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
010011101 => [2,3,1,1,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 6
010011110 => [2,3,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 6
010100000 => [2,2,6] => [2,1] => [1,1,0,0,1,0] => 3
010100001 => [2,2,5,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
010100010 => [2,2,4,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
010100011 => [2,2,4,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 5
010100100 => [2,2,3,3] => [2,2] => [1,1,0,0,1,1,0,0] => 4
010100101 => [2,2,3,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
010100110 => [2,2,3,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
010100111 => [2,2,3,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 6
010101000 => [2,2,2,4] => [3,1] => [1,1,1,0,0,0,1,0] => 4
010101001 => [2,2,2,3,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 5
010101010 => [2,2,2,2,2] => [5] => [1,1,1,1,1,0,0,0,0,0] => 5
010101011 => [2,2,2,2,1,1] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 6
010101100 => [2,2,2,1,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 5
010101101 => [2,2,2,1,2,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
010101110 => [2,2,2,1,1,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 6
010110000 => [2,2,1,5] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
010110001 => [2,2,1,4,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
010110010 => [2,2,1,3,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
010110011 => [2,2,1,3,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 6
010110100 => [2,2,1,2,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
010110101 => [2,2,1,2,2,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 6
010110110 => [2,2,1,2,1,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 6
010111000 => [2,2,1,1,4] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 5
010111001 => [2,2,1,1,3,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 6
010111010 => [2,2,1,1,2,2] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 6
010111100 => [2,2,1,1,1,3] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 6
011000000 => [2,1,7] => [1,1,1] => [1,0,1,0,1,0] => 3
011000001 => [2,1,6,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
011000010 => [2,1,5,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
011000011 => [2,1,5,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
011000100 => [2,1,4,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
011000101 => [2,1,4,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
011000110 => [2,1,4,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
011000111 => [2,1,4,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
011001000 => [2,1,3,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
011001001 => [2,1,3,3,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
011001010 => [2,1,3,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
011001011 => [2,1,3,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 6
011001100 => [2,1,3,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
011001101 => [2,1,3,1,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
011001110 => [2,1,3,1,1,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 6
011010000 => [2,1,2,5] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
011010001 => [2,1,2,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
011010010 => [2,1,2,3,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
011010011 => [2,1,2,3,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 6
011010100 => [2,1,2,2,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
011010101 => [2,1,2,2,2,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 6
011010110 => [2,1,2,2,1,2] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 6
011011000 => [2,1,2,1,4] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
011011001 => [2,1,2,1,3,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
011011010 => [2,1,2,1,2,2] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 6
011011100 => [2,1,2,1,1,3] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 6
011100000 => [2,1,1,6] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
011100001 => [2,1,1,5,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
011100010 => [2,1,1,4,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
011100011 => [2,1,1,4,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 6
011100100 => [2,1,1,3,3] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 5
011100101 => [2,1,1,3,2,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 6
011100110 => [2,1,1,3,1,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 6
011101000 => [2,1,1,2,4] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
011101001 => [2,1,1,2,3,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 6
011101010 => [2,1,1,2,2,2] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 6
011101100 => [2,1,1,2,1,3] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 6
011110000 => [2,1,1,1,5] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 5
011110001 => [2,1,1,1,4,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 6
011110010 => [2,1,1,1,3,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 6
011110100 => [2,1,1,1,2,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 6
011111000 => [2,1,1,1,1,4] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
100000000 => [1,9] => [1,1] => [1,0,1,0] => 2
100000001 => [1,8,1] => [1,1,1] => [1,0,1,0,1,0] => 3
100000010 => [1,7,2] => [1,1,1] => [1,0,1,0,1,0] => 3
100000011 => [1,7,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
100000100 => [1,6,3] => [1,1,1] => [1,0,1,0,1,0] => 3
100000101 => [1,6,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
100000110 => [1,6,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
100000111 => [1,6,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 5
100001000 => [1,5,4] => [1,1,1] => [1,0,1,0,1,0] => 3
100001001 => [1,5,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
100001010 => [1,5,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
100001011 => [1,5,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
100001100 => [1,5,1,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
100001101 => [1,5,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
100001110 => [1,5,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
100001111 => [1,5,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 6
100010000 => [1,4,5] => [1,1,1] => [1,0,1,0,1,0] => 3
100010001 => [1,4,4,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
100010010 => [1,4,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
100010011 => [1,4,3,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
100010100 => [1,4,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
100010101 => [1,4,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
100010110 => [1,4,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
100010111 => [1,4,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
100011000 => [1,4,1,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
100011001 => [1,4,1,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
100011010 => [1,4,1,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
100011011 => [1,4,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 6
100011100 => [1,4,1,1,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
100011101 => [1,4,1,1,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 6
100011110 => [1,4,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 6
100100000 => [1,3,6] => [1,1,1] => [1,0,1,0,1,0] => 3
100100001 => [1,3,5,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
100100010 => [1,3,4,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
100100011 => [1,3,4,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
100100100 => [1,3,3,3] => [1,3] => [1,0,1,1,1,0,0,0] => 4
100100101 => [1,3,3,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
100100110 => [1,3,3,1,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
100100111 => [1,3,3,1,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 6
100101000 => [1,3,2,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
100101001 => [1,3,2,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
100101010 => [1,3,2,2,2] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 5
100101011 => [1,3,2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 6
100101100 => [1,3,2,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
100101101 => [1,3,2,1,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
100101110 => [1,3,2,1,1,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 6
100110000 => [1,3,1,5] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
100110001 => [1,3,1,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
100110010 => [1,3,1,3,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
100110011 => [1,3,1,3,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 6
100110100 => [1,3,1,2,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
100110101 => [1,3,1,2,2,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 6
100110110 => [1,3,1,2,1,2] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
100111000 => [1,3,1,1,4] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
100111001 => [1,3,1,1,3,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 6
100111010 => [1,3,1,1,2,2] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 6
100111100 => [1,3,1,1,1,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 6
101000000 => [1,2,7] => [1,1,1] => [1,0,1,0,1,0] => 3
101000001 => [1,2,6,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
101000010 => [1,2,5,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
101000011 => [1,2,5,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
101000100 => [1,2,4,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
101000101 => [1,2,4,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
101000110 => [1,2,4,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
101000111 => [1,2,4,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
101001000 => [1,2,3,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
101001001 => [1,2,3,3,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
101001010 => [1,2,3,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
101001011 => [1,2,3,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 6
101001100 => [1,2,3,1,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
101001101 => [1,2,3,1,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
101001110 => [1,2,3,1,1,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 6
101010000 => [1,2,2,5] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
101010001 => [1,2,2,4,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
101010010 => [1,2,2,3,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
101010011 => [1,2,2,3,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 6
101010100 => [1,2,2,2,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 5
101010101 => [1,2,2,2,2,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
101010110 => [1,2,2,2,1,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 6
101011000 => [1,2,2,1,4] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
101011001 => [1,2,2,1,3,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 6
101011010 => [1,2,2,1,2,2] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 6
101011100 => [1,2,2,1,1,3] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 6
101100000 => [1,2,1,6] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
101100001 => [1,2,1,5,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
101100010 => [1,2,1,4,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
101100011 => [1,2,1,4,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 6
101100100 => [1,2,1,3,3] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
101100101 => [1,2,1,3,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
101100110 => [1,2,1,3,1,2] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
101101000 => [1,2,1,2,4] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
101101001 => [1,2,1,2,3,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
101101010 => [1,2,1,2,2,2] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
101101100 => [1,2,1,2,1,3] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
101110000 => [1,2,1,1,5] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
101110001 => [1,2,1,1,4,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 6
101110010 => [1,2,1,1,3,2] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 6
101110100 => [1,2,1,1,2,3] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 6
101111000 => [1,2,1,1,1,4] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 6
110000000 => [1,1,8] => [2,1] => [1,1,0,0,1,0] => 3
110000001 => [1,1,7,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
110000010 => [1,1,6,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
110000011 => [1,1,6,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 5
110000100 => [1,1,5,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
110000101 => [1,1,5,2,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
110000110 => [1,1,5,1,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
110000111 => [1,1,5,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 6
110001000 => [1,1,4,4] => [2,2] => [1,1,0,0,1,1,0,0] => 4
110001001 => [1,1,4,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
110001010 => [1,1,4,2,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 5
110001011 => [1,1,4,2,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 6
110001100 => [1,1,4,1,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
110001101 => [1,1,4,1,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 6
110001110 => [1,1,4,1,1,2] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 6
110010000 => [1,1,3,5] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
110010001 => [1,1,3,4,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
110010010 => [1,1,3,3,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 5
110010011 => [1,1,3,3,1,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 6
110010100 => [1,1,3,2,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
110010101 => [1,1,3,2,2,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 6
110010110 => [1,1,3,2,1,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 6
110011000 => [1,1,3,1,4] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
110011001 => [1,1,3,1,3,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 6
110011010 => [1,1,3,1,2,2] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 6
110011100 => [1,1,3,1,1,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 6
110100000 => [1,1,2,6] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
110100001 => [1,1,2,5,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
110100010 => [1,1,2,4,2] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
110100011 => [1,1,2,4,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 6
110100100 => [1,1,2,3,3] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 5
110100101 => [1,1,2,3,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 6
110100110 => [1,1,2,3,1,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 6
110101000 => [1,1,2,2,4] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 5
110101001 => [1,1,2,2,3,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 6
110101010 => [1,1,2,2,2,2] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 6
110101100 => [1,1,2,2,1,3] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 6
110110000 => [1,1,2,1,5] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
110110001 => [1,1,2,1,4,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 6
110110010 => [1,1,2,1,3,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 6
110110100 => [1,1,2,1,2,3] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 6
110111000 => [1,1,2,1,1,4] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 6
111000000 => [1,1,1,7] => [3,1] => [1,1,1,0,0,0,1,0] => 4
111000001 => [1,1,1,6,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 5
111000010 => [1,1,1,5,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 5
111000011 => [1,1,1,5,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 6
111000100 => [1,1,1,4,3] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 5
111000101 => [1,1,1,4,2,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
111000110 => [1,1,1,4,1,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
111001000 => [1,1,1,3,4] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 5
111001001 => [1,1,1,3,3,1] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 6
111001010 => [1,1,1,3,2,2] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 6
111001100 => [1,1,1,3,1,3] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
111010000 => [1,1,1,2,5] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 5
111010001 => [1,1,1,2,4,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
111010010 => [1,1,1,2,3,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
111010100 => [1,1,1,2,2,3] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 6
111011000 => [1,1,1,2,1,4] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
111100000 => [1,1,1,1,6] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 5
111100001 => [1,1,1,1,5,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
111100010 => [1,1,1,1,4,2] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
111100100 => [1,1,1,1,3,3] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 6
111101000 => [1,1,1,1,2,4] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
111110000 => [1,1,1,1,1,5] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
1010101010 => [1,2,2,2,2,2] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
1010101100 => [1,2,2,2,1,3] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 6
1010110010 => [1,2,2,1,3,2] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 6
1010110100 => [1,2,2,1,2,3] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 6
1010111000 => [1,2,2,1,1,4] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 6
1011001010 => [1,2,1,3,2,2] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 6
1011001100 => [1,2,1,3,1,3] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
1011010010 => [1,2,1,2,3,2] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
1011010100 => [1,2,1,2,2,3] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 6
1011011000 => [1,2,1,2,1,4] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
1011100010 => [1,2,1,1,4,2] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 6
1011100100 => [1,2,1,1,3,3] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 6
1011101000 => [1,2,1,1,2,4] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 6
1011110000 => [1,2,1,1,1,5] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 6
1100101010 => [1,1,3,2,2,2] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 6
1100101100 => [1,1,3,2,1,3] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 6
1100110010 => [1,1,3,1,3,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 6
1100110100 => [1,1,3,1,2,3] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 6
1100111000 => [1,1,3,1,1,4] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 6
1101001010 => [1,1,2,3,2,2] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 6
1101001100 => [1,1,2,3,1,3] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 6
1101010010 => [1,1,2,2,3,2] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 6
1101010100 => [1,1,2,2,2,3] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 6
1101011000 => [1,1,2,2,1,4] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 6
1101100010 => [1,1,2,1,4,2] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 6
1101100100 => [1,1,2,1,3,3] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 6
1101101000 => [1,1,2,1,2,4] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 6
1101110000 => [1,1,2,1,1,5] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 6
1110001010 => [1,1,1,4,2,2] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 6
1110001100 => [1,1,1,4,1,3] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
1110010010 => [1,1,1,3,3,2] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 6
1110010100 => [1,1,1,3,2,3] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
1110011000 => [1,1,1,3,1,4] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
1110100010 => [1,1,1,2,4,2] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
1110100100 => [1,1,1,2,3,3] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 6
1110101000 => [1,1,1,2,2,4] => [3,2,1] => [1,1,1,0,0,0,1,1,0,0,1,0] => 6
1110110000 => [1,1,1,2,1,5] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
1111000010 => [1,1,1,1,5,2] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
1111000100 => [1,1,1,1,4,3] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
1111001000 => [1,1,1,1,3,4] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
1111010000 => [1,1,1,1,2,5] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
1111100000 => [1,1,1,1,1,6] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
1110000001 => [1,1,1,7,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 5
1101010001 => [1,1,2,2,4,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 6
1101000011 => [1,1,2,5,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 6
1100001011 => [1,1,5,2,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 6
1100000001 => [1,1,8,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
1100000000 => [1,1,9] => [2,1] => [1,1,0,0,1,0] => 3
1011000001 => [1,2,1,6,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
1010010001 => [1,2,3,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
1010000101 => [1,2,5,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
1010000001 => [1,2,7,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
1010000000 => [1,2,8] => [1,1,1] => [1,0,1,0,1,0] => 3
1001100001 => [1,3,1,5,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
1001000000 => [1,3,7] => [1,1,1] => [1,0,1,0,1,0] => 3
1000110001 => [1,4,1,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
1000101110 => [1,4,2,1,1,2] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 6
1000101011 => [1,4,2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 6
1000100101 => [1,4,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
1000100000 => [1,4,6] => [1,1,1] => [1,0,1,0,1,0] => 3
1000011110 => [1,5,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 6
1000011001 => [1,5,1,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
1000010110 => [1,5,2,1,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
1000010000 => [1,5,5] => [1,2] => [1,0,1,1,0,0] => 3
1000001110 => [1,6,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
1000001101 => [1,6,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
1000001010 => [1,6,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
1000001001 => [1,6,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
1000000111 => [1,7,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 5
1000000110 => [1,7,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
1000000101 => [1,7,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
1000000100 => [1,7,3] => [1,1,1] => [1,0,1,0,1,0] => 3
1000000011 => [1,8,1,1] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
1000000010 => [1,8,2] => [1,1,1] => [1,0,1,0,1,0] => 3
1000000001 => [1,9,1] => [1,1,1] => [1,0,1,0,1,0] => 3
1000000000 => [1,10] => [1,1] => [1,0,1,0] => 2
10000000000 => [1,11] => [1,1] => [1,0,1,0] => 2
10000000010 => [1,9,2] => [1,1,1] => [1,0,1,0,1,0] => 3
10000000110 => [1,8,1,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
10000001110 => [1,7,1,1,2] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
10000011110 => [1,6,1,1,1,2] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 6
10000000100 => [1,8,3] => [1,1,1] => [1,0,1,0,1,0] => 3
10000010000 => [1,6,5] => [1,1,1] => [1,0,1,0,1,0] => 3
10000100010 => [1,5,4,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
10001000010 => [1,4,5,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
10000100100 => [1,5,3,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
10001001010 => [1,4,3,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
10001000100 => [1,4,4,3] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
10000101000 => [1,5,2,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
10010001010 => [1,3,4,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
10001010010 => [1,4,2,3,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
10010000100 => [1,3,5,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
10001001000 => [1,4,3,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
10010010010 => [1,3,3,3,2] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 5
10001010100 => [1,4,2,2,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
10010101010 => [1,3,2,2,2,2] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 6
10100000000 => [1,2,9] => [1,1,1] => [1,0,1,0,1,0] => 3
10010001000 => [1,3,4,4] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
10100010010 => [1,2,4,3,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
10010100010 => [1,3,2,4,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
10010010100 => [1,3,3,2,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
10100101010 => [1,2,3,2,2,2] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
=> [1] => [1] => [1,0] => 1
0111100001 => [2,1,1,1,5,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 6
0111000001 => [2,1,1,6,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
0110000001 => [2,1,7,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
0100000001 => [2,8,1] => [1,1,1] => [1,0,1,0,1,0] => 3
0000000001 => [10,1] => [1,1] => [1,0,1,0] => 2
0111010001 => [2,1,1,2,4,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 6
01111000001 => [2,1,1,1,6,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 6
0110100001 => [2,1,2,5,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
01110000001 => [2,1,1,7,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
0101000001 => [2,2,6,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
01100000001 => [2,1,8,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
0010000001 => [3,7,1] => [1,1,1] => [1,0,1,0,1,0] => 3
01000000001 => [2,9,1] => [1,1,1] => [1,0,1,0,1,0] => 3
00000000001 => [11,1] => [1,1] => [1,0,1,0] => 2
0101010101 => [2,2,2,2,2,1] => [5,1] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
0101010011 => [2,2,2,3,1,1] => [3,1,2] => [1,1,1,0,0,0,1,0,1,1,0,0] => 6
0101001101 => [2,2,3,1,2,1] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 6
0101001011 => [2,2,3,2,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 6
0101000111 => [2,2,4,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 6
0100110101 => [2,3,1,2,2,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 6
0100110011 => [2,3,1,3,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 6
0100101101 => [2,3,2,1,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
0100101011 => [2,3,2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 6
0100100111 => [2,3,3,1,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 6
0100011101 => [2,4,1,1,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 6
0100011011 => [2,4,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 6
0100010111 => [2,4,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
0100001111 => [2,5,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 6
0011010101 => [3,1,2,2,2,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 6
0011010011 => [3,1,2,3,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 6
0011001101 => [3,1,3,1,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
0011001011 => [3,1,3,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 6
0011000111 => [3,1,4,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
0010110101 => [3,2,1,2,2,1] => [1,1,1,2,1] => [1,0,1,0,1,0,1,1,0,0,1,0] => 6
0010110011 => [3,2,1,3,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 6
0010101101 => [3,2,2,1,2,1] => [1,2,1,1,1] => [1,0,1,1,0,0,1,0,1,0,1,0] => 6
0010101011 => [3,2,2,2,1,1] => [1,3,2] => [1,0,1,1,1,0,0,0,1,1,0,0] => 6
0010100111 => [3,2,3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
0010011101 => [3,3,1,1,2,1] => [2,2,1,1] => [1,1,0,0,1,1,0,0,1,0,1,0] => 6
0010011011 => [3,3,1,2,1,1] => [2,1,1,2] => [1,1,0,0,1,0,1,0,1,1,0,0] => 6
0010010111 => [3,3,2,1,1,1] => [2,1,3] => [1,1,0,0,1,0,1,1,1,0,0,0] => 6
0010001111 => [3,4,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 6
0001110101 => [4,1,1,2,2,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 6
0001110011 => [4,1,1,3,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 6
0001101101 => [4,1,2,1,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
0001101011 => [4,1,2,2,1,1] => [1,1,2,2] => [1,0,1,0,1,1,0,0,1,1,0,0] => 6
0001100111 => [4,1,3,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
0001011101 => [4,2,1,1,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 6
0001011011 => [4,2,1,2,1,1] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 6
0001010111 => [4,2,2,1,1,1] => [1,2,3] => [1,0,1,1,0,0,1,1,1,0,0,0] => 6
0001001111 => [4,3,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 6
0000111101 => [5,1,1,1,2,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 6
0000111011 => [5,1,1,2,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 6
0000110111 => [5,1,2,1,1,1] => [1,1,1,3] => [1,0,1,0,1,0,1,1,1,0,0,0] => 6
0000101111 => [5,2,1,1,1,1] => [1,1,4] => [1,0,1,0,1,1,1,1,0,0,0,0] => 6
0000011111 => [6,1,1,1,1,1] => [1,5] => [1,0,1,1,1,1,1,0,0,0,0,0] => 6
11010101000 => [1,1,2,2,2,4] => [2,3,1] => [1,1,0,0,1,1,1,0,0,0,1,0] => 6
11010100100 => [1,1,2,2,3,3] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 6
11010010100 => [1,1,2,3,2,3] => [2,1,1,1,1] => [1,1,0,0,1,0,1,0,1,0,1,0] => 6
11001010100 => [1,1,3,2,2,3] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 6
10101010100 => [1,2,2,2,2,3] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
111000000001 => [1,1,1,9,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 5
100110000001 => [1,3,1,7,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
100001100001 => [1,5,1,5,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
100000011001 => [1,7,1,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
100000000111 => [1,9,1,1,1] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 5
100000000001 => [1,11,1] => [1,1,1] => [1,0,1,0,1,0] => 3
100000001101 => [1,8,1,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
100000110001 => [1,6,1,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
100000100101 => [1,6,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
100011000001 => [1,4,1,6,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
100010010001 => [1,4,3,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
100010000101 => [1,4,5,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
101100000001 => [1,2,1,8,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
101001000001 => [1,2,3,6,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
101000010001 => [1,2,5,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
101000000101 => [1,2,7,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
0000000000 => [11] => [1] => [1,0] => 1
00101010101 => [3,2,2,2,2,1] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
00101010011 => [3,2,2,3,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 6
00100101011 => [3,3,2,2,1,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 6
0000000010 => [9,2] => [1,1] => [1,0,1,0] => 2
0000111110 => [5,1,1,1,1,2] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
00000000000 => [12] => [1] => [1,0] => 1
00000000010 => [10,2] => [1,1] => [1,0,1,0] => 2
10101010010 => [1,2,2,2,3,2] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 6
10101001001 => [1,2,2,3,3,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 6
10101001010 => [1,2,2,3,2,2] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 6
10101000100 => [1,2,2,4,3] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
10100100101 => [1,2,3,3,2,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 6
10100100010 => [1,2,3,4,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
10100101001 => [1,2,3,2,3,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
10100100100 => [1,2,3,3,3] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 5
10100010001 => [1,2,4,4,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
10100010100 => [1,2,4,2,3] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
10100001000 => [1,2,5,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
10010010101 => [1,3,3,2,2,1] => [1,2,2,1] => [1,0,1,1,0,0,1,1,0,0,1,0] => 6
10010001001 => [1,3,4,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
10010100101 => [1,3,2,3,2,1] => [1,1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0,1,0] => 6
10010101001 => [1,3,2,2,3,1] => [1,1,2,1,1] => [1,0,1,0,1,1,0,0,1,0,1,0] => 6
10010100100 => [1,3,2,3,3] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
10010010001 => [1,3,3,4,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
10001000101 => [1,4,4,2,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
10001001001 => [1,4,3,3,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
10001010001 => [1,4,2,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
10000100001 => [1,5,5,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
01001010101 => [2,3,2,2,2,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 6
01001010010 => [2,3,2,3,2] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
01001001001 => [2,3,3,3,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 5
01001001010 => [2,3,3,2,2] => [1,2,2] => [1,0,1,1,0,0,1,1,0,0] => 5
01001000100 => [2,3,4,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
01000100101 => [2,4,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
01000100010 => [2,4,4,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
01000101001 => [2,4,2,3,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
01000101010 => [2,4,2,2,2] => [1,1,3] => [1,0,1,0,1,1,1,0,0,0] => 5
01000100100 => [2,4,3,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
01000010001 => [2,5,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
01000010010 => [2,5,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
01000010100 => [2,5,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
01000001000 => [2,6,4] => [1,1,1] => [1,0,1,0,1,0] => 3
01010010101 => [2,2,3,2,2,1] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 6
01010010010 => [2,2,3,3,2] => [2,2,1] => [1,1,0,0,1,1,0,0,1,0] => 5
01010001001 => [2,2,4,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
01010001010 => [2,2,4,2,2] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 5
01010000100 => [2,2,5,3] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
01010100101 => [2,2,2,3,2,1] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
01010100010 => [2,2,2,4,2] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 5
01010101001 => [2,2,2,2,3,1] => [4,1,1] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
01010101010 => [2,2,2,2,2,2] => [6] => [1,1,1,1,1,1,0,0,0,0,0,0] => 6
01010100100 => [2,2,2,3,3] => [3,2] => [1,1,1,0,0,0,1,1,0,0] => 5
01010010001 => [2,2,3,4,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
01010010100 => [2,2,3,2,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
01010001000 => [2,2,4,4] => [2,2] => [1,1,0,0,1,1,0,0] => 4
01001000101 => [2,3,4,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
01001000010 => [2,3,5,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
01001010001 => [2,3,2,4,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
01001010100 => [2,3,2,2,3] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
01001001000 => [2,3,3,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
01000100001 => [2,4,5,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
01000101000 => [2,4,2,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
01000010000 => [2,5,5] => [1,2] => [1,0,1,1,0,0] => 3
00100010101 => [3,4,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
00100010010 => [3,4,3,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
00100001001 => [3,5,3,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
00100001010 => [3,5,2,2] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
00100000100 => [3,6,3] => [1,1,1] => [1,0,1,0,1,0] => 3
00100100101 => [3,3,3,2,1] => [3,1,1] => [1,1,1,0,0,0,1,0,1,0] => 5
00100100010 => [3,3,4,2] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
00100101001 => [3,3,2,3,1] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
00100101010 => [3,3,2,2,2] => [2,3] => [1,1,0,0,1,1,1,0,0,0] => 5
00100100100 => [3,3,3,3] => [4] => [1,1,1,1,0,0,0,0] => 4
00100010001 => [3,4,4,1] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
00100010100 => [3,4,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
00100001000 => [3,5,4] => [1,1,1] => [1,0,1,0,1,0] => 3
00101000101 => [3,2,4,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
00101000010 => [3,2,5,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
00101001001 => [3,2,3,3,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
00101001010 => [3,2,3,2,2] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
00101000100 => [3,2,4,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
00101010001 => [3,2,2,4,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
00101010010 => [3,2,2,3,2] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
00101010100 => [3,2,2,2,3] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 5
00101001000 => [3,2,3,4] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
00100100001 => [3,3,5,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
00100101000 => [3,3,2,4] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
00100010000 => [3,4,5] => [1,1,1] => [1,0,1,0,1,0] => 3
00010000101 => [4,5,2,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
00010000010 => [4,6,2] => [1,1,1] => [1,0,1,0,1,0] => 3
00010001001 => [4,4,3,1] => [2,1,1] => [1,1,0,0,1,0,1,0] => 4
00010001010 => [4,4,2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 4
00010000100 => [4,5,3] => [1,1,1] => [1,0,1,0,1,0] => 3
00010010001 => [4,3,4,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
00010010010 => [4,3,3,2] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
00010010100 => [4,3,2,3] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
00010001000 => [4,4,4] => [3] => [1,1,1,0,0,0] => 3
00010100001 => [4,2,5,1] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
00010100010 => [4,2,4,2] => [1,1,1,1] => [1,0,1,0,1,0,1,0] => 4
00010100100 => [4,2,3,3] => [1,1,2] => [1,0,1,0,1,1,0,0] => 4
00010101000 => [4,2,2,4] => [1,2,1] => [1,0,1,1,0,0,1,0] => 4
00010010000 => [4,3,5] => [1,1,1] => [1,0,1,0,1,0] => 3
00001000001 => [5,6,1] => [1,1,1] => [1,0,1,0,1,0] => 3
00001000010 => [5,5,2] => [2,1] => [1,1,0,0,1,0] => 3
00001000100 => [5,4,3] => [1,1,1] => [1,0,1,0,1,0] => 3
00001001000 => [5,3,4] => [1,1,1] => [1,0,1,0,1,0] => 3
00001010000 => [5,2,5] => [1,1,1] => [1,0,1,0,1,0] => 3
00000100000 => [6,6] => [2] => [1,1,0,0] => 2
0100000000 => [2,9] => [1,1] => [1,0,1,0] => 2
00000000101 => [9,2,1] => [1,1,1] => [1,0,1,0,1,0] => 3
00100000001 => [3,8,1] => [1,1,1] => [1,0,1,0,1,0] => 3
10000000001 => [1,10,1] => [1,1,1] => [1,0,1,0,1,0] => 3
00000011011 => [7,1,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
10001010101 => [1,4,2,2,2,1] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 6
10000010101 => [1,6,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
0001000100 => [4,4,3] => [2,1] => [1,1,0,0,1,0] => 3
10000001011 => [1,7,2,1,1] => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0] => 5
11000000011 => [1,1,8,1,1] => [2,1,2] => [1,1,0,0,1,0,1,1,0,0] => 5
00010010101 => [4,3,2,2,1] => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
00010100101 => [4,2,3,2,1] => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0] => 5
00010101001 => [4,2,2,3,1] => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
00010101010 => [4,2,2,2,2] => [1,4] => [1,0,1,1,1,1,0,0,0,0] => 5
00000100010 => [6,4,2] => [1,1,1] => [1,0,1,0,1,0] => 3
00001010101 => [5,2,2,2,1] => [1,3,1] => [1,0,1,1,1,0,0,0,1,0] => 5
10101010001 => [1,2,2,2,4,1] => [1,3,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 6
01101010100 => [2,1,2,2,2,3] => [1,1,3,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 6
01101001010 => [2,1,2,3,2,2] => [1,1,1,1,2] => [1,0,1,0,1,0,1,0,1,1,0,0] => 6
01010101000 => [2,2,2,2,4] => [4,1] => [1,1,1,1,0,0,0,0,1,0] => 5
11010000100 => [1,1,2,5,3] => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0] => 5
01010110100 => [2,2,2,1,2,3] => [3,1,1,1] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
11110001000 => [1,1,1,1,4,4] => [4,2] => [1,1,1,1,0,0,0,0,1,1,0,0] => 6
11000111000 => [1,1,4,1,1,4] => [2,1,2,1] => [1,1,0,0,1,0,1,1,0,0,1,0] => 6
11000100011 => [1,1,4,4,1,1] => [2,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 6
00011111000 => [4,1,1,1,1,4] => [1,4,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
00011100011 => [4,1,1,4,1,1] => [1,2,1,2] => [1,0,1,1,0,0,1,0,1,1,0,0] => 6
00010001111 => [4,4,1,1,1,1] => [2,4] => [1,1,0,0,1,1,1,1,0,0,0,0] => 6
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Description
Sum of projective dimension of the indecomposable injective modules of the Nakayama algebra corresponding to the Dyck path.
Map
bounce path
Description
The bounce path determined by an integer composition.
Map
delta morphism
Description
Apply the delta morphism to an integer composition.
The delta morphism of a composition $C$ is the compositions composed of the lengths of consecutive runs of the same integer in $C$.
Map
to composition
Description
The composition corresponding to a binary word.
Prepending $1$ to a binary word $w$, the $i$-th part of the composition equals $1$ plus the number of zeros after the $i$-th $1$ in $w$.
This map is not surjective, since the empty composition does not have a preimage.