Identifier
Values
0 => [1] => [1] => [1,0,1,0] => 2
1 => [1] => [1] => [1,0,1,0] => 2
00 => [2] => [2] => [1,1,0,0,1,0] => 3
01 => [1,1] => [1,1] => [1,0,1,1,0,0] => 2
10 => [1,1] => [1,1] => [1,0,1,1,0,0] => 2
11 => [2] => [2] => [1,1,0,0,1,0] => 3
000 => [3] => [3] => [1,1,1,0,0,0,1,0] => 4
001 => [2,1] => [2,1] => [1,0,1,0,1,0] => 3
010 => [1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 2
011 => [1,2] => [2,1] => [1,0,1,0,1,0] => 3
100 => [1,2] => [2,1] => [1,0,1,0,1,0] => 3
101 => [1,1,1] => [1,1,1] => [1,0,1,1,1,0,0,0] => 2
110 => [2,1] => [2,1] => [1,0,1,0,1,0] => 3
111 => [3] => [3] => [1,1,1,0,0,0,1,0] => 4
0000 => [4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 5
0001 => [3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 4
0010 => [2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 3
0011 => [2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 3
0100 => [1,1,2] => [2,1,1] => [1,0,1,1,0,1,0,0] => 3
0101 => [1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 2
0110 => [1,2,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 3
0111 => [1,3] => [3,1] => [1,1,0,1,0,0,1,0] => 4
1000 => [1,3] => [3,1] => [1,1,0,1,0,0,1,0] => 4
1001 => [1,2,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 3
1010 => [1,1,1,1] => [1,1,1,1] => [1,0,1,1,1,1,0,0,0,0] => 2
1011 => [1,1,2] => [2,1,1] => [1,0,1,1,0,1,0,0] => 3
1100 => [2,2] => [2,2] => [1,1,0,0,1,1,0,0] => 3
1101 => [2,1,1] => [2,1,1] => [1,0,1,1,0,1,0,0] => 3
1110 => [3,1] => [3,1] => [1,1,0,1,0,0,1,0] => 4
1111 => [4] => [4] => [1,1,1,1,0,0,0,0,1,0] => 5
00000 => [5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
00001 => [4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 5
00010 => [3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 4
00011 => [3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 4
00100 => [2,1,2] => [2,2,1] => [1,0,1,0,1,1,0,0] => 3
00101 => [2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 3
00110 => [2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 3
00111 => [2,3] => [3,2] => [1,1,0,0,1,0,1,0] => 4
01000 => [1,1,3] => [3,1,1] => [1,0,1,1,0,0,1,0] => 4
01001 => [1,1,2,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 3
01010 => [1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
01011 => [1,1,1,2] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 3
01100 => [1,2,2] => [2,2,1] => [1,0,1,0,1,1,0,0] => 3
01101 => [1,2,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 3
01110 => [1,3,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 4
01111 => [1,4] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 5
10000 => [1,4] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 5
10001 => [1,3,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 4
10010 => [1,2,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 3
10011 => [1,2,2] => [2,2,1] => [1,0,1,0,1,1,0,0] => 3
10100 => [1,1,1,2] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 3
10101 => [1,1,1,1,1] => [1,1,1,1,1] => [1,0,1,1,1,1,1,0,0,0,0,0] => 2
10110 => [1,1,2,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 3
10111 => [1,1,3] => [3,1,1] => [1,0,1,1,0,0,1,0] => 4
11000 => [2,3] => [3,2] => [1,1,0,0,1,0,1,0] => 4
11001 => [2,2,1] => [2,2,1] => [1,0,1,0,1,1,0,0] => 3
11010 => [2,1,1,1] => [2,1,1,1] => [1,0,1,1,1,0,1,0,0,0] => 3
11011 => [2,1,2] => [2,2,1] => [1,0,1,0,1,1,0,0] => 3
11100 => [3,2] => [3,2] => [1,1,0,0,1,0,1,0] => 4
11101 => [3,1,1] => [3,1,1] => [1,0,1,1,0,0,1,0] => 4
11110 => [4,1] => [4,1] => [1,1,1,0,1,0,0,0,1,0] => 5
11111 => [5] => [5] => [1,1,1,1,1,0,0,0,0,0,1,0] => 6
000001 => [5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 6
000010 => [4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
000011 => [4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 5
000100 => [3,1,2] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
000101 => [3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 4
000110 => [3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
000111 => [3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 4
001000 => [2,1,3] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
001001 => [2,1,2,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
001010 => [2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
001011 => [2,1,1,2] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
001100 => [2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 3
001101 => [2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
001110 => [2,3,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
001111 => [2,4] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 5
010000 => [1,1,4] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
010001 => [1,1,3,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 4
010010 => [1,1,2,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
010011 => [1,1,2,2] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
010100 => [1,1,1,1,2] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
010110 => [1,1,1,2,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
010111 => [1,1,1,3] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 4
011000 => [1,2,3] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
011001 => [1,2,2,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
011010 => [1,2,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
011011 => [1,2,1,2] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
011100 => [1,3,2] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
011101 => [1,3,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 4
011110 => [1,4,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
011111 => [1,5] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 6
100000 => [1,5] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 6
100001 => [1,4,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
100010 => [1,3,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 4
100011 => [1,3,2] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
100100 => [1,2,1,2] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
100101 => [1,2,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
100110 => [1,2,2,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
100111 => [1,2,3] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
101000 => [1,1,1,3] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 4
>>> Load all 1046 entries. <<<
101001 => [1,1,1,2,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
101011 => [1,1,1,1,2] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
101100 => [1,1,2,2] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
101101 => [1,1,2,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
101110 => [1,1,3,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 4
101111 => [1,1,4] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
110000 => [2,4] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 5
110001 => [2,3,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
110010 => [2,2,1,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
110011 => [2,2,2] => [2,2,2] => [1,1,0,0,1,1,1,0,0,0] => 3
110100 => [2,1,1,2] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
110101 => [2,1,1,1,1] => [2,1,1,1,1] => [1,0,1,1,1,1,0,1,0,0,0,0] => 3
110110 => [2,1,2,1] => [2,2,1,1] => [1,0,1,1,0,1,1,0,0,0] => 3
110111 => [2,1,3] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
111000 => [3,3] => [3,3] => [1,1,1,0,0,0,1,1,0,0] => 4
111001 => [3,2,1] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
111010 => [3,1,1,1] => [3,1,1,1] => [1,0,1,1,1,0,0,1,0,0] => 4
111011 => [3,1,2] => [3,2,1] => [1,0,1,0,1,0,1,0] => 4
111100 => [4,2] => [4,2] => [1,1,1,0,0,1,0,0,1,0] => 5
111101 => [4,1,1] => [4,1,1] => [1,1,0,1,1,0,0,0,1,0] => 5
111110 => [5,1] => [5,1] => [1,1,1,1,0,1,0,0,0,0,1,0] => 6
0000010 => [5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
0000011 => [5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 6
0000100 => [4,1,2] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
0000101 => [4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
0000110 => [4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
0000111 => [4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 5
0001000 => [3,1,3] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 4
0001001 => [3,1,2,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
0001010 => [3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
0001011 => [3,1,1,2] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
0001100 => [3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 4
0001101 => [3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
0001110 => [3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 4
0001111 => [3,4] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 5
0010000 => [2,1,4] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
0010001 => [2,1,3,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
0010010 => [2,1,2,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
0010011 => [2,1,2,2] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
0010100 => [2,1,1,1,2] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
0010110 => [2,1,1,2,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
0010111 => [2,1,1,3] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
0011000 => [2,2,3] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 4
0011001 => [2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
0011010 => [2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
0011011 => [2,2,1,2] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
0011100 => [2,3,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 4
0011101 => [2,3,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
0011110 => [2,4,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
0011111 => [2,5] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 6
0100000 => [1,1,5] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
0100001 => [1,1,4,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
0100010 => [1,1,3,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
0100011 => [1,1,3,2] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
0100100 => [1,1,2,1,2] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
0100110 => [1,1,2,2,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
0100111 => [1,1,2,3] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
0101000 => [1,1,1,1,3] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
0101100 => [1,1,1,2,2] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
0101110 => [1,1,1,3,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
0101111 => [1,1,1,4] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
0110000 => [1,2,4] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
0110001 => [1,2,3,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
0110010 => [1,2,2,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
0110011 => [1,2,2,2] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
0110100 => [1,2,1,1,2] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
0110110 => [1,2,1,2,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
0110111 => [1,2,1,3] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
0111000 => [1,3,3] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 4
0111001 => [1,3,2,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
0111010 => [1,3,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
0111011 => [1,3,1,2] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
0111100 => [1,4,2] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
0111101 => [1,4,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
0111110 => [1,5,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
1000001 => [1,5,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
1000010 => [1,4,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
1000011 => [1,4,2] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
1000100 => [1,3,1,2] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
1000101 => [1,3,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
1000110 => [1,3,2,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
1000111 => [1,3,3] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 4
1001000 => [1,2,1,3] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
1001001 => [1,2,1,2,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
1001011 => [1,2,1,1,2] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
1001100 => [1,2,2,2] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
1001101 => [1,2,2,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
1001110 => [1,2,3,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
1001111 => [1,2,4] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
1010000 => [1,1,1,4] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
1010001 => [1,1,1,3,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
1010011 => [1,1,1,2,2] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
1010111 => [1,1,1,1,3] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
1011000 => [1,1,2,3] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
1011001 => [1,1,2,2,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
1011011 => [1,1,2,1,2] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
1011100 => [1,1,3,2] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
1011101 => [1,1,3,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
1011110 => [1,1,4,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
1011111 => [1,1,5] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
1100000 => [2,5] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 6
1100001 => [2,4,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
1100010 => [2,3,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
1100011 => [2,3,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 4
1100100 => [2,2,1,2] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
1100101 => [2,2,1,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
1100110 => [2,2,2,1] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
1100111 => [2,2,3] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 4
1101000 => [2,1,1,3] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
1101001 => [2,1,1,2,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
1101011 => [2,1,1,1,2] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
1101100 => [2,1,2,2] => [2,2,2,1] => [1,0,1,0,1,1,1,0,0,0] => 3
1101101 => [2,1,2,1,1] => [2,2,1,1,1] => [1,0,1,1,1,0,1,1,0,0,0,0] => 3
1101110 => [2,1,3,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
1101111 => [2,1,4] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
1110000 => [3,4] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 5
1110001 => [3,3,1] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 4
1110010 => [3,2,1,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
1110011 => [3,2,2] => [3,2,2] => [1,1,0,0,1,1,0,1,0,0] => 4
1110100 => [3,1,1,2] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
1110101 => [3,1,1,1,1] => [3,1,1,1,1] => [1,0,1,1,1,1,0,0,1,0,0,0] => 4
1110110 => [3,1,2,1] => [3,2,1,1] => [1,0,1,1,0,1,0,1,0,0] => 4
1110111 => [3,1,3] => [3,3,1] => [1,1,0,1,0,0,1,1,0,0] => 4
1111000 => [4,3] => [4,3] => [1,1,1,0,0,0,1,0,1,0] => 5
1111001 => [4,2,1] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
1111010 => [4,1,1,1] => [4,1,1,1] => [1,0,1,1,1,0,0,0,1,0] => 5
1111011 => [4,1,2] => [4,2,1] => [1,1,0,1,0,1,0,0,1,0] => 5
1111100 => [5,2] => [5,2] => [1,1,1,1,0,0,1,0,0,0,1,0] => 6
1111101 => [5,1,1] => [5,1,1] => [1,1,1,0,1,1,0,0,0,0,1,0] => 6
00000100 => [5,1,2] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
00000101 => [5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
00000110 => [5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
00000111 => [5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 6
00001000 => [4,1,3] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
00001001 => [4,1,2,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
00001010 => [4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
00001011 => [4,1,1,2] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
00001100 => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 5
00001101 => [4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
00001110 => [4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
00001111 => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 5
00010000 => [3,1,4] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
00010001 => [3,1,3,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
00010010 => [3,1,2,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
00010011 => [3,1,2,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
00010100 => [3,1,1,1,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
00010110 => [3,1,1,2,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
00010111 => [3,1,1,3] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
00011000 => [3,2,3] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 4
00011001 => [3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
00011010 => [3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
00011011 => [3,2,1,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
00011100 => [3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 4
00011101 => [3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
00011110 => [3,4,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
00011111 => [3,5] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 6
00100000 => [2,1,5] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
00100001 => [2,1,4,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
00100010 => [2,1,3,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
00100011 => [2,1,3,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
00100100 => [2,1,2,1,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
00100110 => [2,1,2,2,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
00100111 => [2,1,2,3] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
00101000 => [2,1,1,1,3] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
00101100 => [2,1,1,2,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
00101110 => [2,1,1,3,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
00101111 => [2,1,1,4] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
00110000 => [2,2,4] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 5
00110001 => [2,2,3,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
00110010 => [2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
00110011 => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
00110100 => [2,2,1,1,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
00110110 => [2,2,1,2,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
00110111 => [2,2,1,3] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
00111000 => [2,3,3] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 4
00111001 => [2,3,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
00111010 => [2,3,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
00111011 => [2,3,1,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
00111100 => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 5
00111101 => [2,4,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
00111110 => [2,5,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
01000001 => [1,1,5,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
01000010 => [1,1,4,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
01000011 => [1,1,4,2] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
01000100 => [1,1,3,1,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
01000110 => [1,1,3,2,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
01000111 => [1,1,3,3] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
01001000 => [1,1,2,1,3] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
01001100 => [1,1,2,2,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
01001110 => [1,1,2,3,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
01001111 => [1,1,2,4] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
01010000 => [1,1,1,1,4] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
01011000 => [1,1,1,2,3] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
01011100 => [1,1,1,3,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
01011110 => [1,1,1,4,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
01011111 => [1,1,1,5] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
01100000 => [1,2,5] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
01100001 => [1,2,4,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
01100010 => [1,2,3,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
01100011 => [1,2,3,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
01100100 => [1,2,2,1,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
01100110 => [1,2,2,2,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
01100111 => [1,2,2,3] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
01101000 => [1,2,1,1,3] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
01101100 => [1,2,1,2,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
01101110 => [1,2,1,3,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
01101111 => [1,2,1,4] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
01110000 => [1,3,4] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
01110001 => [1,3,3,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
01110010 => [1,3,2,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
01110011 => [1,3,2,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
01110100 => [1,3,1,1,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
01110110 => [1,3,1,2,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
01110111 => [1,3,1,3] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
01111000 => [1,4,3] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
01111001 => [1,4,2,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
01111010 => [1,4,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
01111011 => [1,4,1,2] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
01111100 => [1,5,2] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
01111101 => [1,5,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
10000010 => [1,5,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
10000011 => [1,5,2] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
10000100 => [1,4,1,2] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
10000101 => [1,4,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
10000110 => [1,4,2,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
10000111 => [1,4,3] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
10001000 => [1,3,1,3] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
10001001 => [1,3,1,2,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
10001011 => [1,3,1,1,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
10001100 => [1,3,2,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
10001101 => [1,3,2,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
10001110 => [1,3,3,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
10001111 => [1,3,4] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
10010000 => [1,2,1,4] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
10010001 => [1,2,1,3,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
10010011 => [1,2,1,2,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
10010111 => [1,2,1,1,3] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
10011000 => [1,2,2,3] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
10011001 => [1,2,2,2,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
10011011 => [1,2,2,1,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
10011100 => [1,2,3,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
10011101 => [1,2,3,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
10011110 => [1,2,4,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
10011111 => [1,2,5] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
10100000 => [1,1,1,5] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
10100001 => [1,1,1,4,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
10100011 => [1,1,1,3,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
10100111 => [1,1,1,2,3] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
10101111 => [1,1,1,1,4] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
10110000 => [1,1,2,4] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
10110001 => [1,1,2,3,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
10110011 => [1,1,2,2,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
10110111 => [1,1,2,1,3] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
10111000 => [1,1,3,3] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
10111001 => [1,1,3,2,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
10111011 => [1,1,3,1,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
10111100 => [1,1,4,2] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
10111101 => [1,1,4,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
10111110 => [1,1,5,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
11000001 => [2,5,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
11000010 => [2,4,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
11000011 => [2,4,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 5
11000100 => [2,3,1,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
11000101 => [2,3,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
11000110 => [2,3,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
11000111 => [2,3,3] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 4
11001000 => [2,2,1,3] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
11001001 => [2,2,1,2,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
11001011 => [2,2,1,1,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
11001100 => [2,2,2,2] => [2,2,2,2] => [1,1,0,0,1,1,1,1,0,0,0,0] => 3
11001101 => [2,2,2,1,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
11001110 => [2,2,3,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
11001111 => [2,2,4] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 5
11010000 => [2,1,1,4] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
11010001 => [2,1,1,3,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
11010011 => [2,1,1,2,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
11010111 => [2,1,1,1,3] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
11011000 => [2,1,2,3] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
11011001 => [2,1,2,2,1] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
11011011 => [2,1,2,1,2] => [2,2,2,1,1] => [1,0,1,1,0,1,1,1,0,0,0,0] => 3
11011100 => [2,1,3,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
11011101 => [2,1,3,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
11011110 => [2,1,4,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
11011111 => [2,1,5] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
11100000 => [3,5] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 6
11100001 => [3,4,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
11100010 => [3,3,1,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
11100011 => [3,3,2] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 4
11100100 => [3,2,1,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
11100101 => [3,2,1,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
11100110 => [3,2,2,1] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
11100111 => [3,2,3] => [3,3,2] => [1,1,0,0,1,0,1,1,0,0] => 4
11101000 => [3,1,1,3] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
11101001 => [3,1,1,2,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
11101011 => [3,1,1,1,2] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
11101100 => [3,1,2,2] => [3,2,2,1] => [1,0,1,0,1,1,0,1,0,0] => 4
11101101 => [3,1,2,1,1] => [3,2,1,1,1] => [1,0,1,1,1,0,1,0,1,0,0,0] => 4
11101110 => [3,1,3,1] => [3,3,1,1] => [1,0,1,1,0,0,1,1,0,0] => 4
11101111 => [3,1,4] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
11110000 => [4,4] => [4,4] => [1,1,1,1,0,0,0,0,1,1,0,0] => 5
11110001 => [4,3,1] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
11110010 => [4,2,1,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
11110011 => [4,2,2] => [4,2,2] => [1,1,0,0,1,1,0,0,1,0] => 5
11110100 => [4,1,1,2] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
11110101 => [4,1,1,1,1] => [4,1,1,1,1] => [1,0,1,1,1,1,0,0,0,1,0,0] => 5
11110110 => [4,1,2,1] => [4,2,1,1] => [1,0,1,1,0,1,0,0,1,0] => 5
11110111 => [4,1,3] => [4,3,1] => [1,1,0,1,0,0,1,0,1,0] => 5
11111000 => [5,3] => [5,3] => [1,1,1,1,0,0,0,1,0,0,1,0] => 6
11111001 => [5,2,1] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
11111010 => [5,1,1,1] => [5,1,1,1] => [1,1,0,1,1,1,0,0,0,0,1,0] => 6
11111011 => [5,1,2] => [5,2,1] => [1,1,1,0,1,0,1,0,0,0,1,0] => 6
000001000 => [5,1,3] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 6
000001001 => [5,1,2,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
000001010 => [5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
000001011 => [5,1,1,2] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
000001100 => [5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 6
000001101 => [5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
000001110 => [5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 6
000001111 => [5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
000010000 => [4,1,4] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 5
000010001 => [4,1,3,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
000010010 => [4,1,2,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
000010011 => [4,1,2,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
000010100 => [4,1,1,1,2] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
000010110 => [4,1,1,2,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
000010111 => [4,1,1,3] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
000011000 => [4,2,3] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 5
000011001 => [4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
000011010 => [4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
000011011 => [4,2,1,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
000011100 => [4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 5
000011101 => [4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
000011110 => [4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 5
000011111 => [4,5] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
000100000 => [3,1,5] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 6
000100001 => [3,1,4,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
000100010 => [3,1,3,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 4
000100011 => [3,1,3,2] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
000100100 => [3,1,2,1,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
000100110 => [3,1,2,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
000100111 => [3,1,2,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
000101000 => [3,1,1,1,3] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 4
000101100 => [3,1,1,2,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
000101110 => [3,1,1,3,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 4
000101111 => [3,1,1,4] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
000110000 => [3,2,4] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 5
000110001 => [3,2,3,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
000110010 => [3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
000110011 => [3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 4
000110100 => [3,2,1,1,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
000110110 => [3,2,1,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
000110111 => [3,2,1,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
000111000 => [3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 4
000111001 => [3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
000111010 => [3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 4
000111011 => [3,3,1,2] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
000111100 => [3,4,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 5
000111101 => [3,4,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
000111110 => [3,5,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 6
001000001 => [2,1,5,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
001000010 => [2,1,4,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
001000011 => [2,1,4,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
001000100 => [2,1,3,1,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
001000110 => [2,1,3,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
001000111 => [2,1,3,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
001001000 => [2,1,2,1,3] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
001001100 => [2,1,2,2,2] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
001001110 => [2,1,2,3,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
001001111 => [2,1,2,4] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
001010000 => [2,1,1,1,4] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
001011000 => [2,1,1,2,3] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
001011100 => [2,1,1,3,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
001011110 => [2,1,1,4,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
001011111 => [2,1,1,5] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
001100000 => [2,2,5] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 6
001100001 => [2,2,4,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
001100010 => [2,2,3,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
001100011 => [2,2,3,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 4
001100100 => [2,2,2,1,2] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
001100110 => [2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
001100111 => [2,2,2,3] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 4
001101000 => [2,2,1,1,3] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
001101100 => [2,2,1,2,2] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
001101110 => [2,2,1,3,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
001101111 => [2,2,1,4] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
001110000 => [2,3,4] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 5
001110001 => [2,3,3,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
001110010 => [2,3,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
001110011 => [2,3,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 4
001110100 => [2,3,1,1,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
001110110 => [2,3,1,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
001110111 => [2,3,1,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
001111000 => [2,4,3] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 5
001111001 => [2,4,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
001111010 => [2,4,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
001111011 => [2,4,1,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
001111100 => [2,5,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 6
001111101 => [2,5,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
010000010 => [1,1,5,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
010000011 => [1,1,5,2] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
010000100 => [1,1,4,1,2] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
010000110 => [1,1,4,2,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
010000111 => [1,1,4,3] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
010001000 => [1,1,3,1,3] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 4
010001100 => [1,1,3,2,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
010001110 => [1,1,3,3,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 4
010001111 => [1,1,3,4] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
010010000 => [1,1,2,1,4] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
010011000 => [1,1,2,2,3] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
010011100 => [1,1,2,3,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
010011110 => [1,1,2,4,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
010011111 => [1,1,2,5] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
010100000 => [1,1,1,1,5] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
010110000 => [1,1,1,2,4] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
010111000 => [1,1,1,3,3] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 4
010111100 => [1,1,1,4,2] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
010111110 => [1,1,1,5,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
011000001 => [1,2,5,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
011000010 => [1,2,4,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
011000011 => [1,2,4,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
011000100 => [1,2,3,1,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
011000110 => [1,2,3,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
011000111 => [1,2,3,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
011001000 => [1,2,2,1,3] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
011001100 => [1,2,2,2,2] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
011001110 => [1,2,2,3,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
011001111 => [1,2,2,4] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
011010000 => [1,2,1,1,4] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
011011000 => [1,2,1,2,3] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
011011100 => [1,2,1,3,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
011011110 => [1,2,1,4,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
011011111 => [1,2,1,5] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
011100000 => [1,3,5] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 6
011100001 => [1,3,4,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
011100010 => [1,3,3,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 4
011100011 => [1,3,3,2] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
011100100 => [1,3,2,1,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
011100110 => [1,3,2,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
011100111 => [1,3,2,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
011101000 => [1,3,1,1,3] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 4
011101100 => [1,3,1,2,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
011101110 => [1,3,1,3,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 4
011101111 => [1,3,1,4] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
011110000 => [1,4,4] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 5
011110001 => [1,4,3,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
011110010 => [1,4,2,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
011110011 => [1,4,2,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
011110100 => [1,4,1,1,2] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
011110110 => [1,4,1,2,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
011110111 => [1,4,1,3] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
011111000 => [1,5,3] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 6
011111001 => [1,5,2,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
011111010 => [1,5,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
011111011 => [1,5,1,2] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
100000100 => [1,5,1,2] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
100000101 => [1,5,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
100000110 => [1,5,2,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
100000111 => [1,5,3] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 6
100001000 => [1,4,1,3] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
100001001 => [1,4,1,2,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
100001011 => [1,4,1,1,2] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
100001100 => [1,4,2,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
100001101 => [1,4,2,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
100001110 => [1,4,3,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
100001111 => [1,4,4] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 5
100010000 => [1,3,1,4] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
100010001 => [1,3,1,3,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 4
100010011 => [1,3,1,2,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
100010111 => [1,3,1,1,3] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 4
100011000 => [1,3,2,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
100011001 => [1,3,2,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
100011011 => [1,3,2,1,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
100011100 => [1,3,3,2] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
100011101 => [1,3,3,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 4
100011110 => [1,3,4,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
100011111 => [1,3,5] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 6
100100000 => [1,2,1,5] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
100100001 => [1,2,1,4,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
100100011 => [1,2,1,3,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
100100111 => [1,2,1,2,3] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
100101111 => [1,2,1,1,4] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
100110000 => [1,2,2,4] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
100110001 => [1,2,2,3,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
100110011 => [1,2,2,2,2] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
100110111 => [1,2,2,1,3] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
100111000 => [1,2,3,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
100111001 => [1,2,3,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
100111011 => [1,2,3,1,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
100111100 => [1,2,4,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
100111101 => [1,2,4,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
100111110 => [1,2,5,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
101000001 => [1,1,1,5,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
101000011 => [1,1,1,4,2] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
101000111 => [1,1,1,3,3] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 4
101001111 => [1,1,1,2,4] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
101011111 => [1,1,1,1,5] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
101100000 => [1,1,2,5] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
101100001 => [1,1,2,4,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
101100011 => [1,1,2,3,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
101100111 => [1,1,2,2,3] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
101101111 => [1,1,2,1,4] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
101110000 => [1,1,3,4] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
101110001 => [1,1,3,3,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 4
101110011 => [1,1,3,2,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
101110111 => [1,1,3,1,3] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 4
101111000 => [1,1,4,3] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
101111001 => [1,1,4,2,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
101111011 => [1,1,4,1,2] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
101111100 => [1,1,5,2] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
101111101 => [1,1,5,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
110000010 => [2,5,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
110000011 => [2,5,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 6
110000100 => [2,4,1,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
110000101 => [2,4,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
110000110 => [2,4,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
110000111 => [2,4,3] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 5
110001000 => [2,3,1,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
110001001 => [2,3,1,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
110001011 => [2,3,1,1,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
110001100 => [2,3,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 4
110001101 => [2,3,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
110001110 => [2,3,3,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
110001111 => [2,3,4] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 5
110010000 => [2,2,1,4] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
110010001 => [2,2,1,3,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
110010011 => [2,2,1,2,2] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
110010111 => [2,2,1,1,3] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
110011000 => [2,2,2,3] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 4
110011001 => [2,2,2,2,1] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
110011011 => [2,2,2,1,2] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
110011100 => [2,2,3,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 4
110011101 => [2,2,3,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
110011110 => [2,2,4,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
110011111 => [2,2,5] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 6
110100000 => [2,1,1,5] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
110100001 => [2,1,1,4,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
110100011 => [2,1,1,3,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
110100111 => [2,1,1,2,3] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
110101111 => [2,1,1,1,4] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
110110000 => [2,1,2,4] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
110110001 => [2,1,2,3,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
110110011 => [2,1,2,2,2] => [2,2,2,2,1] => [1,0,1,0,1,1,1,1,0,0,0,0] => 3
110110111 => [2,1,2,1,3] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
110111000 => [2,1,3,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
110111001 => [2,1,3,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
110111011 => [2,1,3,1,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
110111100 => [2,1,4,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
110111101 => [2,1,4,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
110111110 => [2,1,5,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
111000001 => [3,5,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 6
111000010 => [3,4,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
111000011 => [3,4,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 5
111000100 => [3,3,1,2] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
111000101 => [3,3,1,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 4
111000110 => [3,3,2,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
111000111 => [3,3,3] => [3,3,3] => [1,1,1,0,0,0,1,1,1,0,0,0] => 4
111001000 => [3,2,1,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
111001001 => [3,2,1,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
111001011 => [3,2,1,1,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
111001100 => [3,2,2,2] => [3,2,2,2] => [1,1,0,0,1,1,1,0,1,0,0,0] => 4
111001101 => [3,2,2,1,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
111001110 => [3,2,3,1] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
111001111 => [3,2,4] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 5
111010000 => [3,1,1,4] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
111010001 => [3,1,1,3,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 4
111010011 => [3,1,1,2,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
111010111 => [3,1,1,1,3] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 4
111011000 => [3,1,2,3] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
111011001 => [3,1,2,2,1] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
111011011 => [3,1,2,1,2] => [3,2,2,1,1] => [1,0,1,1,0,1,1,0,1,0,0,0] => 4
111011100 => [3,1,3,2] => [3,3,2,1] => [1,0,1,0,1,0,1,1,0,0] => 4
111011101 => [3,1,3,1,1] => [3,3,1,1,1] => [1,0,1,1,1,0,0,1,1,0,0,0] => 4
111011110 => [3,1,4,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
111011111 => [3,1,5] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 6
111100000 => [4,5] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
111100001 => [4,4,1] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 5
111100010 => [4,3,1,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
111100011 => [4,3,2] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 5
111100100 => [4,2,1,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
111100101 => [4,2,1,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
111100110 => [4,2,2,1] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
111100111 => [4,2,3] => [4,3,2] => [1,1,0,0,1,0,1,0,1,0] => 5
111101000 => [4,1,1,3] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
111101001 => [4,1,1,2,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
111101011 => [4,1,1,1,2] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
111101100 => [4,1,2,2] => [4,2,2,1] => [1,0,1,0,1,1,0,0,1,0] => 5
111101101 => [4,1,2,1,1] => [4,2,1,1,1] => [1,0,1,1,1,0,1,0,0,1,0,0] => 5
111101110 => [4,1,3,1] => [4,3,1,1] => [1,0,1,1,0,0,1,0,1,0] => 5
111101111 => [4,1,4] => [4,4,1] => [1,1,1,0,1,0,0,0,1,1,0,0] => 5
111110000 => [5,4] => [5,4] => [1,1,1,1,0,0,0,0,1,0,1,0] => 6
111110001 => [5,3,1] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 6
111110010 => [5,2,1,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
111110011 => [5,2,2] => [5,2,2] => [1,1,1,0,0,1,1,0,0,0,1,0] => 6
111110100 => [5,1,1,2] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
111110101 => [5,1,1,1,1] => [5,1,1,1,1] => [1,0,1,1,1,1,0,0,0,0,1,0] => 6
111110110 => [5,1,2,1] => [5,2,1,1] => [1,1,0,1,1,0,1,0,0,0,1,0] => 6
111110111 => [5,1,3] => [5,3,1] => [1,1,1,0,1,0,0,1,0,0,1,0] => 6
1011110000 => [1,1,4,4] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 5
1100111000 => [2,2,3,3] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 4
1101110000 => [2,1,3,4] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 5
1110001100 => [3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 4
1110011000 => [3,2,2,3] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 4
1110110000 => [3,1,2,4] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 5
1111000010 => [4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 5
1111000100 => [4,3,1,2] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 5
1111001000 => [4,2,1,3] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 5
1111010000 => [4,1,1,4] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 5
110011110000 => [2,2,4,4] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 5
110111100000 => [2,1,4,5] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 6
111001110000 => [3,2,3,4] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 5
111011100000 => [3,1,3,5] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 6
111100001100 => [4,4,2,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 5
111100011000 => [4,3,2,3] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 5
111100110000 => [4,2,2,4] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 5
111101100000 => [4,1,2,5] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 6
111110000100 => [5,4,1,2] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 6
111110001000 => [5,3,1,3] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 6
111110010000 => [5,2,1,4] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 6
1111101001 => [5,1,1,2,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 6
1111101000 => [5,1,1,3] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 6
1111100100 => [5,2,1,2] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 6
1111100011 => [5,3,2] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 6
1111100010 => [5,3,1,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 6
1111100001 => [5,4,1] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 6
1111011110 => [4,1,4,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 5
1111011101 => [4,1,3,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
1111011011 => [4,1,2,1,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 5
1111011000 => [4,1,2,3] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 5
1111010111 => [4,1,1,1,3] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
1111010011 => [4,1,1,2,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 5
1111010001 => [4,1,1,3,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
1111001111 => [4,2,4] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 5
1111001100 => [4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
1111001011 => [4,2,1,1,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 5
1111001001 => [4,2,1,2,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 5
1111000111 => [4,3,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 5
1111000110 => [4,3,2,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 5
1111000101 => [4,3,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
1111000011 => [4,4,2] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 5
1111000001 => [4,5,1] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 6
1110111110 => [3,1,5,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 6
1110111101 => [3,1,4,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
1110111011 => [3,1,3,1,2] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
1110111000 => [3,1,3,3] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 4
1110110001 => [3,1,2,3,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
1110101111 => [3,1,1,1,4] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
1110100011 => [3,1,1,3,2] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
1110100001 => [3,1,1,4,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
1110011111 => [3,2,5] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 6
1110011110 => [3,2,4,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 5
1110011001 => [3,2,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
1110010011 => [3,2,1,2,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
1110010001 => [3,2,1,3,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
1110001101 => [3,3,2,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
1110001001 => [3,3,1,2,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
1110000111 => [3,4,3] => [4,3,3] => [1,1,1,0,0,0,1,1,0,1,0,0] => 5
1110000101 => [3,4,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
1110000011 => [3,5,2] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 6
1110000010 => [3,5,1,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 6
1101111101 => [2,1,5,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 6
1101111011 => [2,1,4,1,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 5
1101111001 => [2,1,4,2,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 5
1101111000 => [2,1,4,3] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 5
1101110111 => [2,1,3,1,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
1101110001 => [2,1,3,3,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
1101101111 => [2,1,2,1,4] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 5
1101100011 => [2,1,2,3,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
1101100001 => [2,1,2,4,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 5
1101100000 => [2,1,2,5] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 6
1101011111 => [2,1,1,1,5] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 6
1101001111 => [2,1,1,2,4] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 5
1101000111 => [2,1,1,3,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
1101000011 => [2,1,1,4,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 5
1101000001 => [2,1,1,5,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 6
1100111100 => [2,2,4,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
1100111001 => [2,2,3,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
1100110001 => [2,2,2,3,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
1100110000 => [2,2,2,4] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
1100100111 => [2,2,1,2,3] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
1100100011 => [2,2,1,3,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
1100011110 => [2,3,4,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 5
1100011101 => [2,3,3,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
1100011100 => [2,3,3,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 4
1100011011 => [2,3,2,1,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
1100011001 => [2,3,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
1100011000 => [2,3,2,3] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 4
1100010111 => [2,3,1,1,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
1100010011 => [2,3,1,2,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
1100001111 => [2,4,4] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 5
1100001101 => [2,4,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 5
1100001100 => [2,4,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
1100001011 => [2,4,1,1,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 5
1100001000 => [2,4,1,3] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 5
1100000111 => [2,5,3] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 6
1100000110 => [2,5,2,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 6
1011111011 => [1,1,5,1,2] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 6
1011111000 => [1,1,5,3] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 6
1011110111 => [1,1,4,1,3] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
1011110001 => [1,1,4,3,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
1011100011 => [1,1,3,3,2] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
1011100001 => [1,1,3,4,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
1011100000 => [1,1,3,5] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 6
1011000111 => [1,1,2,3,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
1011000011 => [1,1,2,4,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 5
1010001111 => [1,1,1,3,4] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
1010000111 => [1,1,1,4,3] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
1001111000 => [1,2,4,3] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 5
1001110011 => [1,2,3,2,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
1001110001 => [1,2,3,3,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
1001110000 => [1,2,3,4] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 5
1001100111 => [1,2,2,2,3] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
1001100011 => [1,2,2,3,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
1001011111 => [1,2,1,1,5] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 6
1001001111 => [1,2,1,2,4] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 5
1001000111 => [1,2,1,3,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
1000111110 => [1,3,5,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 6
1000111101 => [1,3,4,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
1000111100 => [1,3,4,2] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 5
1000111011 => [1,3,3,1,2] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
1000111001 => [1,3,3,2,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
1000111000 => [1,3,3,3] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 4
1000110111 => [1,3,2,1,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
1000110011 => [1,3,2,2,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
1000110001 => [1,3,2,3,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
1000101111 => [1,3,1,1,4] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
1000100111 => [1,3,1,2,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
1000011111 => [1,4,5] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 6
1000011110 => [1,4,4,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 5
1000011101 => [1,4,3,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
1000011011 => [1,4,2,1,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 5
1000010111 => [1,4,1,1,3] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
1000001111 => [1,5,4] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 6
1000001110 => [1,5,3,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 6
1000001101 => [1,5,2,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 6
1000001011 => [1,5,1,1,2] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 6
1000001001 => [1,5,1,2,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 6
10000011110 => [1,5,4,1] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => 6
10000111110 => [1,4,5,1] => [5,4,1,1] => [1,1,0,1,1,0,0,0,1,0,1,0] => 6
110000011110 => [2,5,4,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 6
100001111100 => [1,4,5,2] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 6
0111110001 => [1,5,3,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 6
0111100001 => [1,4,4,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 5
0100001111 => [1,1,4,4] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 5
0011000111 => [2,2,3,3] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 4
0010001111 => [2,1,3,4] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 5
0001110011 => [3,3,2,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 4
0001100111 => [3,2,2,3] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 4
0001001111 => [3,1,2,4] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 5
0000111101 => [4,4,1,1] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 5
0000110111 => [4,2,1,3] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 5
0000101111 => [4,1,1,4] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 5
001100001111 => [2,2,4,4] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 5
001000011111 => [2,1,4,5] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 6
000110001111 => [3,2,3,4] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 5
000100011111 => [3,1,3,5] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 6
000011110011 => [4,4,2,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 5
000011001111 => [4,2,2,4] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 5
000010011111 => [4,1,2,5] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 6
000001111011 => [5,4,1,2] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 6
000001110111 => [5,3,1,3] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 6
000001101111 => [5,2,1,4] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 6
111001100001 => [3,2,2,4,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
111000011001 => [3,4,2,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
111000001101 => [3,5,2,1,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 6
111000110001 => [3,3,2,3,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 4
111011000001 => [3,1,2,5,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 6
100111100001 => [1,2,4,4,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 5
100110000111 => [1,2,2,4,3] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
100001111001 => [1,4,4,2,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 5
100001100111 => [1,4,2,2,3] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
100000110111 => [1,5,2,1,3] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 6
100000110001 => [1,5,2,3,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 6
100000111101 => [1,5,4,1,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 6
100011000111 => [1,3,2,3,3] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 4
100011110001 => [1,3,4,3,1] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 5
101100011111 => [1,1,2,3,5] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 6
101100000111 => [1,1,2,5,3] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 6
101111000111 => [1,1,4,3,3] => [4,3,3,1,1] => [1,0,1,1,0,0,1,1,0,1,0,0] => 5
101111000001 => [1,1,4,5,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 6
0000011000 => [5,2,3] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 6
0000011110 => [5,4,1] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 6
0110011000 => [1,2,2,2,3] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
0111100000 => [1,4,5] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 6
0111001000 => [1,3,2,1,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
0111000010 => [1,3,4,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
0100111000 => [1,1,2,3,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
0100111110 => [1,1,2,5,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 6
000110011110 => [3,2,2,4,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
000111100110 => [3,4,2,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
000111110010 => [3,5,2,1,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 6
000111001110 => [3,3,2,3,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 4
000100111110 => [3,1,2,5,1] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 6
011000011110 => [1,2,4,4,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 5
011001111000 => [1,2,2,4,3] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
011110000110 => [1,4,4,2,1] => [4,4,2,1,1] => [1,0,1,1,0,1,0,0,1,1,0,0] => 5
011110011000 => [1,4,2,2,3] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
011111001000 => [1,5,2,1,3] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 6
011111000010 => [1,5,4,1,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 6
011100111000 => [1,3,2,3,3] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 4
010011111000 => [1,1,2,5,3] => [5,3,2,1,1] => [1,0,1,1,0,1,0,1,0,0,1,0] => 6
010000111110 => [1,1,4,5,1] => [5,4,1,1,1] => [1,0,1,1,1,0,0,0,1,0,1,0] => 6
0010111100 => [2,1,1,4,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 5
0011110100 => [2,4,1,1,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 5
0000010100 => [5,1,1,1,2] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 6
0000111110 => [4,5,1] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 6
0000010110 => [5,1,1,2,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 6
0000101110 => [4,1,1,3,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
0001011110 => [3,1,1,4,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
0010111110 => [2,1,1,5,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 6
0010111000 => [2,1,1,3,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
0011011000 => [2,2,1,2,3] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
0011100010 => [2,3,3,1,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
0011100100 => [2,3,2,1,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
0011101000 => [2,3,1,1,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
0011110000 => [2,4,4] => [4,4,2] => [1,1,1,0,0,1,0,0,1,1,0,0] => 5
0101110000 => [1,1,1,3,4] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
0110001100 => [1,2,3,2,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
0110110000 => [1,2,1,2,4] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 5
0111000100 => [1,3,3,1,2] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
0111010000 => [1,3,1,1,4] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
011000111000 => [1,2,3,3,3] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 4
011100001100 => [1,3,4,2,2] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
011100011000 => [1,3,3,2,3] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 4
10000100001 => [1,4,1,4,1] => [4,4,1,1,1] => [1,0,1,1,1,0,0,0,1,1,0,0] => 5
0100000111 => [1,1,5,3] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 6
0100011111 => [1,1,3,5] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 6
0101111000 => [1,1,1,4,3] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
0110011100 => [1,2,2,3,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
0110111000 => [1,2,1,3,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
0111000110 => [1,3,3,2,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
0111001100 => [1,3,2,2,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
0111011000 => [1,3,1,2,3] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
0111100010 => [1,4,3,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
0111100100 => [1,4,2,1,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 5
0111101000 => [1,4,1,1,3] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
0111110000 => [1,5,4] => [5,4,1] => [1,1,1,0,1,0,0,0,1,0,1,0] => 6
011100011100 => [1,3,3,3,2] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 4
011110001100 => [1,4,3,2,2] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
0100000100 => [1,1,5,1,2] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 6
0011100110 => [2,3,2,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
0011101100 => [2,3,1,2,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
0001101110 => [3,2,1,3,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
0011110010 => [2,4,2,1,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 5
0001110110 => [3,3,1,2,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
0011111000 => [2,5,3] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 6
0001111010 => [3,4,1,1,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
0100111100 => [1,1,2,4,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 5
0001111100 => [3,5,2] => [5,3,2] => [1,1,1,0,0,1,0,1,0,0,1,0] => 6
001111000110 => [2,4,3,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
100111110000 => [1,2,5,4] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 6
110001111000 => [2,3,4,3] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 5
100011111000 => [1,3,5,3] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 6
0000011101 => [5,3,1,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 6
0001111101 => [3,5,1,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 6
110001110001 => [2,3,3,3,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 4
110011100001 => [2,2,3,4,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
0111000011 => [1,3,4,2] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 5
0011110001 => [2,4,3,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 5
110000111100 => [2,4,4,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 5
011100000111 => [1,3,5,3] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 6
111000011100 => [3,4,3,2] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 5
001111000011 => [2,4,4,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 5
011110000011 => [1,4,5,2] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 6
000111110001 => [3,5,3,1] => [5,3,3,1] => [1,1,0,1,0,0,1,1,0,0,1,0] => 6
001111100001 => [2,5,4,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 6
0001000001 => [3,1,5,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 6
0111000111 => [1,3,3,3] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 4
0011110011 => [2,4,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
0111100011 => [1,4,3,2] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 5
0011111001 => [2,5,2,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 6
110001111001 => [2,3,4,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
110011110001 => [2,2,4,3,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
011100001111 => [1,3,4,4] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 5
111000111001 => [3,3,3,2,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 4
111001110001 => [3,2,3,3,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 4
111000001111 => [3,5,4] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
001111000111 => [2,4,3,3] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 5
011110000111 => [1,4,4,3] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 5
111100011001 => [4,3,2,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
111100110001 => [4,2,2,3,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
111100000111 => [4,5,3] => [5,4,3] => [1,1,1,0,0,0,1,0,1,0,1,0] => 6
000111110011 => [3,5,2,2] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 6
001111100011 => [2,5,3,2] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 6
011111000011 => [1,5,4,2] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 6
0001101100 => [3,2,1,2,2] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
0011000110 => [2,2,3,2,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
0010001110 => [2,1,3,3,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
0000110001 => [4,2,3,1] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 5
0000010001 => [5,1,3,1] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 6
100011100011 => [1,3,3,3,2] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 4
100001110011 => [1,4,3,2,2] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
0000011001 => [5,2,2,1] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 6
0000110011 => [4,2,2,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
0011001111 => [2,2,2,4] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
0110011111 => [1,2,2,5] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 6
0000110100 => [4,2,1,1,2] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 5
0000011011 => [5,2,1,2] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 6
0001101111 => [3,2,1,4] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 5
0011011111 => [2,2,1,5] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 6
0111110111 => [1,5,1,3] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 6
0110000111 => [1,2,4,3] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 5
110000111001 => [2,4,3,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
001110000111 => [2,3,4,3] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 5
011000001111 => [1,2,5,4] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 6
0110001110 => [1,2,3,3,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
0011001110 => [2,2,2,3,1] => [3,2,2,2,1] => [1,0,1,0,1,1,1,0,1,0,0,0] => 4
0100011110 => [1,1,3,4,1] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
0010011110 => [2,1,2,4,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 5
001110001110 => [2,3,3,3,1] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 4
001100011110 => [2,2,3,4,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
0001010000 => [3,1,1,1,4] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
0100010000 => [1,1,3,1,4] => [4,3,1,1,1] => [1,0,1,1,1,0,0,1,0,1,0,0] => 5
0001000100 => [3,1,3,1,2] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
0111011100 => [1,3,1,3,2] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
0001100011 => [3,2,3,2] => [3,3,2,2] => [1,1,0,0,1,1,0,1,1,0,0,0] => 4
0110000011 => [1,2,5,2] => [5,2,2,1] => [1,1,0,1,0,1,1,0,0,0,1,0] => 6
0001110111 => [3,3,1,3] => [3,3,3,1] => [1,1,0,1,0,0,1,1,1,0,0,0] => 4
0111101111 => [1,4,1,4] => [4,4,1,1] => [1,1,0,1,1,0,0,0,1,1,0,0] => 5
011000001100 => [1,2,5,2,2] => [5,2,2,2,1] => [1,0,1,0,1,1,1,0,0,0,1,0] => 6
000001100011 => [5,2,3,2] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 6
000110000011 => [3,2,5,2] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 6
011110001111 => [1,4,3,4] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 5
100011110011 => [1,3,4,2,2] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
100111000111 => [1,2,3,3,3] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 4
100011100111 => [1,3,3,2,3] => [3,3,3,2,1] => [1,0,1,0,1,0,1,1,1,0,0,0] => 4
0000010111 => [5,1,1,3] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 6
0001011111 => [3,1,1,5] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 6
0011011110 => [2,2,1,4,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 5
0011101110 => [2,3,1,3,1] => [3,3,2,1,1] => [1,0,1,1,0,1,0,1,1,0,0,0] => 4
0011110110 => [2,4,1,2,1] => [4,2,2,1,1] => [1,0,1,1,0,1,1,0,0,1,0,0] => 5
0011111010 => [2,5,1,1,1] => [5,2,1,1,1] => [1,0,1,1,1,0,1,0,0,0,1,0] => 6
000111100011 => [3,4,3,2] => [4,3,3,2] => [1,1,0,0,1,0,1,1,0,1,0,0] => 5
01111100100 => [1,5,2,1,2] => [5,2,2,1,1] => [1,0,1,1,0,1,1,0,0,0,1,0] => 6
110000011000 => [2,5,2,3] => [5,3,2,2] => [1,1,0,0,1,1,0,1,0,0,1,0] => 6
111100011110 => [4,3,4,1] => [4,4,3,1] => [1,1,0,1,0,0,1,0,1,1,0,0] => 5
111100000110 => [4,5,2,1] => [5,4,2,1] => [1,1,0,1,0,1,0,0,1,0,1,0] => 6
0110001111 => [1,2,3,4] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 5
0011000011 => [2,2,4,2] => [4,2,2,2] => [1,1,0,0,1,1,1,0,0,1,0,0] => 5
0001111011 => [3,4,1,2] => [4,3,2,1] => [1,0,1,0,1,0,1,0,1,0] => 5
001111001111 => [2,4,2,4] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 5
000011000011 => [4,2,4,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 5
111100111100 => [4,2,4,2] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 5
110000110000 => [2,4,2,4] => [4,4,2,2] => [1,1,0,0,1,1,0,0,1,1,0,0] => 5
0111011111 => [1,3,1,5] => [5,3,1,1] => [1,1,0,1,1,0,0,1,0,0,1,0] => 6
111100111001 => [4,2,3,2,1] => [4,3,2,2,1] => [1,0,1,0,1,1,0,1,0,1,0,0] => 5
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Description
The number of indecomposable summands of the tensor product of two copies of the dual of the Nakayama algebra associated to a Dyck path.
Let $A$ be the Nakayama algebra associated to a Dyck path as given in DyckPaths/NakayamaAlgebras. This statistics is the number of indecomposable summands of $D(A) \otimes D(A)$, where $D(A)$ is the natural dual of $A$.
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
to Dyck path
Description
Sends a partition to the shortest Dyck path tracing the shape of its Ferrers diagram.
Map
to partition
Description
Sends a composition to the partition obtained by sorting the entries.