Identifier
Values
[1] => [1] => [1] => 1 => 1
[1,1] => [1,1] => [1,1] => 11 => 2
[1,2] => [1,2] => [1,2] => 110 => 3
[2,1] => [1,2] => [1,2] => 110 => 3
[1,1,1] => [1,1,1] => [1,1,1] => 111 => 3
[1,1,2] => [1,1,2] => [1,1,2] => 1110 => 4
[1,2,1] => [1,1,2] => [1,1,2] => 1110 => 4
[2,1,1] => [1,1,2] => [1,1,2] => 1110 => 4
[1,1,3] => [1,1,3] => [1,1,3] => 11100 => 5
[1,3,1] => [1,1,3] => [1,1,3] => 11100 => 5
[3,1,1] => [1,1,3] => [1,1,3] => 11100 => 5
[1,2,2] => [1,2,2] => [1,2,2] => 11010 => 5
[2,1,2] => [1,2,2] => [1,2,2] => 11010 => 5
[2,2,1] => [1,2,2] => [1,2,2] => 11010 => 5
[1,2,3] => [1,2,3] => [1,2,3] => 110100 => 6
[1,3,2] => [1,2,3] => [1,2,3] => 110100 => 6
[2,1,3] => [1,2,3] => [1,2,3] => 110100 => 6
[2,3,1] => [1,2,3] => [1,2,3] => 110100 => 6
[3,1,2] => [1,2,3] => [1,2,3] => 110100 => 6
[3,2,1] => [1,2,3] => [1,2,3] => 110100 => 6
[1,1,1,1] => [1,1,1,1] => [1,1,1,1] => 1111 => 4
[1,1,1,2] => [1,1,1,2] => [1,1,1,2] => 11110 => 5
[1,1,2,1] => [1,1,1,2] => [1,1,1,2] => 11110 => 5
[1,2,1,1] => [1,1,1,2] => [1,1,1,2] => 11110 => 5
[2,1,1,1] => [1,1,1,2] => [1,1,1,2] => 11110 => 5
[1,1,1,3] => [1,1,1,3] => [1,1,1,3] => 111100 => 6
[1,1,3,1] => [1,1,1,3] => [1,1,1,3] => 111100 => 6
[1,3,1,1] => [1,1,1,3] => [1,1,1,3] => 111100 => 6
[3,1,1,1] => [1,1,1,3] => [1,1,1,3] => 111100 => 6
[1,1,1,4] => [1,1,1,4] => [1,1,1,4] => 1111000 => 7
[1,1,4,1] => [1,1,1,4] => [1,1,1,4] => 1111000 => 7
[1,4,1,1] => [1,1,1,4] => [1,1,1,4] => 1111000 => 7
[4,1,1,1] => [1,1,1,4] => [1,1,1,4] => 1111000 => 7
[1,1,2,2] => [1,1,2,2] => [1,1,2,2] => 111010 => 6
[1,2,1,2] => [1,1,2,2] => [1,1,2,2] => 111010 => 6
[1,2,2,1] => [1,1,2,2] => [1,1,2,2] => 111010 => 6
[2,1,1,2] => [1,1,2,2] => [1,1,2,2] => 111010 => 6
[2,1,2,1] => [1,1,2,2] => [1,1,2,2] => 111010 => 6
[2,2,1,1] => [1,1,2,2] => [1,1,2,2] => 111010 => 6
[1,1,2,3] => [1,1,2,3] => [1,1,2,3] => 1110100 => 7
[1,1,3,2] => [1,1,2,3] => [1,1,2,3] => 1110100 => 7
[1,2,1,3] => [1,1,2,3] => [1,1,2,3] => 1110100 => 7
[1,2,3,1] => [1,1,2,3] => [1,1,2,3] => 1110100 => 7
[1,3,1,2] => [1,1,2,3] => [1,1,2,3] => 1110100 => 7
[1,3,2,1] => [1,1,2,3] => [1,1,2,3] => 1110100 => 7
[2,1,1,3] => [1,1,2,3] => [1,1,2,3] => 1110100 => 7
[2,1,3,1] => [1,1,2,3] => [1,1,2,3] => 1110100 => 7
[2,3,1,1] => [1,1,2,3] => [1,1,2,3] => 1110100 => 7
[3,1,1,2] => [1,1,2,3] => [1,1,2,3] => 1110100 => 7
[3,1,2,1] => [1,1,2,3] => [1,1,2,3] => 1110100 => 7
[3,2,1,1] => [1,1,2,3] => [1,1,2,3] => 1110100 => 7
[1,1,2,4] => [1,1,2,4] => [1,1,2,4] => 11101000 => 8
[1,1,4,2] => [1,1,2,4] => [1,1,2,4] => 11101000 => 8
[1,2,1,4] => [1,1,2,4] => [1,1,2,4] => 11101000 => 8
[1,2,4,1] => [1,1,2,4] => [1,1,2,4] => 11101000 => 8
[1,4,1,2] => [1,1,2,4] => [1,1,2,4] => 11101000 => 8
[1,4,2,1] => [1,1,2,4] => [1,1,2,4] => 11101000 => 8
[2,1,1,4] => [1,1,2,4] => [1,1,2,4] => 11101000 => 8
[2,1,4,1] => [1,1,2,4] => [1,1,2,4] => 11101000 => 8
[2,4,1,1] => [1,1,2,4] => [1,1,2,4] => 11101000 => 8
[4,1,1,2] => [1,1,2,4] => [1,1,2,4] => 11101000 => 8
[4,1,2,1] => [1,1,2,4] => [1,1,2,4] => 11101000 => 8
[4,2,1,1] => [1,1,2,4] => [1,1,2,4] => 11101000 => 8
[1,1,3,3] => [1,1,3,3] => [1,1,3,3] => 11100100 => 8
[1,3,1,3] => [1,1,3,3] => [1,1,3,3] => 11100100 => 8
[1,3,3,1] => [1,1,3,3] => [1,1,3,3] => 11100100 => 8
[3,1,1,3] => [1,1,3,3] => [1,1,3,3] => 11100100 => 8
[3,1,3,1] => [1,1,3,3] => [1,1,3,3] => 11100100 => 8
[3,3,1,1] => [1,1,3,3] => [1,1,3,3] => 11100100 => 8
[1,1,3,4] => [1,1,3,4] => [1,1,3,4] => 111001000 => 9
[1,1,4,3] => [1,1,3,4] => [1,1,3,4] => 111001000 => 9
[1,3,1,4] => [1,1,3,4] => [1,1,3,4] => 111001000 => 9
[1,3,4,1] => [1,1,3,4] => [1,1,3,4] => 111001000 => 9
[1,4,1,3] => [1,1,3,4] => [1,1,3,4] => 111001000 => 9
[1,4,3,1] => [1,1,3,4] => [1,1,3,4] => 111001000 => 9
[3,1,1,4] => [1,1,3,4] => [1,1,3,4] => 111001000 => 9
[3,1,4,1] => [1,1,3,4] => [1,1,3,4] => 111001000 => 9
[3,4,1,1] => [1,1,3,4] => [1,1,3,4] => 111001000 => 9
[4,1,1,3] => [1,1,3,4] => [1,1,3,4] => 111001000 => 9
[4,1,3,1] => [1,1,3,4] => [1,1,3,4] => 111001000 => 9
[4,3,1,1] => [1,1,3,4] => [1,1,3,4] => 111001000 => 9
[1,2,2,2] => [1,2,2,2] => [1,2,2,2] => 1101010 => 7
[2,1,2,2] => [1,2,2,2] => [1,2,2,2] => 1101010 => 7
[2,2,1,2] => [1,2,2,2] => [1,2,2,2] => 1101010 => 7
[2,2,2,1] => [1,2,2,2] => [1,2,2,2] => 1101010 => 7
[1,2,2,3] => [1,2,2,3] => [1,2,2,3] => 11010100 => 8
[1,2,3,2] => [1,2,2,3] => [1,2,2,3] => 11010100 => 8
[1,3,2,2] => [1,2,2,3] => [1,2,2,3] => 11010100 => 8
[2,1,2,3] => [1,2,2,3] => [1,2,2,3] => 11010100 => 8
[2,1,3,2] => [1,2,2,3] => [1,2,2,3] => 11010100 => 8
[2,2,1,3] => [1,2,2,3] => [1,2,2,3] => 11010100 => 8
[2,2,3,1] => [1,2,2,3] => [1,2,2,3] => 11010100 => 8
[2,3,1,2] => [1,2,2,3] => [1,2,2,3] => 11010100 => 8
[2,3,2,1] => [1,2,2,3] => [1,2,2,3] => 11010100 => 8
[3,1,2,2] => [1,2,2,3] => [1,2,2,3] => 11010100 => 8
[3,2,1,2] => [1,2,2,3] => [1,2,2,3] => 11010100 => 8
[3,2,2,1] => [1,2,2,3] => [1,2,2,3] => 11010100 => 8
[1,2,2,4] => [1,2,2,4] => [1,2,2,4] => 110101000 => 9
[1,2,4,2] => [1,2,2,4] => [1,2,2,4] => 110101000 => 9
[1,4,2,2] => [1,2,2,4] => [1,2,2,4] => 110101000 => 9
[2,1,2,4] => [1,2,2,4] => [1,2,2,4] => 110101000 => 9
>>> Load all 646 entries. <<<
[2,1,4,2] => [1,2,2,4] => [1,2,2,4] => 110101000 => 9
[2,2,1,4] => [1,2,2,4] => [1,2,2,4] => 110101000 => 9
[2,2,4,1] => [1,2,2,4] => [1,2,2,4] => 110101000 => 9
[2,4,1,2] => [1,2,2,4] => [1,2,2,4] => 110101000 => 9
[2,4,2,1] => [1,2,2,4] => [1,2,2,4] => 110101000 => 9
[4,1,2,2] => [1,2,2,4] => [1,2,2,4] => 110101000 => 9
[4,2,1,2] => [1,2,2,4] => [1,2,2,4] => 110101000 => 9
[4,2,2,1] => [1,2,2,4] => [1,2,2,4] => 110101000 => 9
[1,2,3,3] => [1,2,3,3] => [1,2,3,3] => 110100100 => 9
[1,3,2,3] => [1,2,3,3] => [1,2,3,3] => 110100100 => 9
[1,3,3,2] => [1,2,3,3] => [1,2,3,3] => 110100100 => 9
[2,1,3,3] => [1,2,3,3] => [1,2,3,3] => 110100100 => 9
[2,3,1,3] => [1,2,3,3] => [1,2,3,3] => 110100100 => 9
[2,3,3,1] => [1,2,3,3] => [1,2,3,3] => 110100100 => 9
[3,1,2,3] => [1,2,3,3] => [1,2,3,3] => 110100100 => 9
[3,1,3,2] => [1,2,3,3] => [1,2,3,3] => 110100100 => 9
[3,2,1,3] => [1,2,3,3] => [1,2,3,3] => 110100100 => 9
[3,2,3,1] => [1,2,3,3] => [1,2,3,3] => 110100100 => 9
[3,3,1,2] => [1,2,3,3] => [1,2,3,3] => 110100100 => 9
[3,3,2,1] => [1,2,3,3] => [1,2,3,3] => 110100100 => 9
[1,1,1,1,1] => [1,1,1,1,1] => [1,1,1,1,1] => 11111 => 5
[1,1,1,1,2] => [1,1,1,1,2] => [1,1,1,1,2] => 111110 => 6
[1,1,1,2,1] => [1,1,1,1,2] => [1,1,1,1,2] => 111110 => 6
[1,1,2,1,1] => [1,1,1,1,2] => [1,1,1,1,2] => 111110 => 6
[1,2,1,1,1] => [1,1,1,1,2] => [1,1,1,1,2] => 111110 => 6
[2,1,1,1,1] => [1,1,1,1,2] => [1,1,1,1,2] => 111110 => 6
[1,1,1,1,3] => [1,1,1,1,3] => [1,1,1,1,3] => 1111100 => 7
[1,1,1,3,1] => [1,1,1,1,3] => [1,1,1,1,3] => 1111100 => 7
[1,1,3,1,1] => [1,1,1,1,3] => [1,1,1,1,3] => 1111100 => 7
[1,3,1,1,1] => [1,1,1,1,3] => [1,1,1,1,3] => 1111100 => 7
[3,1,1,1,1] => [1,1,1,1,3] => [1,1,1,1,3] => 1111100 => 7
[1,1,1,1,4] => [1,1,1,1,4] => [1,1,1,1,4] => 11111000 => 8
[1,1,1,4,1] => [1,1,1,1,4] => [1,1,1,1,4] => 11111000 => 8
[1,1,4,1,1] => [1,1,1,1,4] => [1,1,1,1,4] => 11111000 => 8
[1,4,1,1,1] => [1,1,1,1,4] => [1,1,1,1,4] => 11111000 => 8
[4,1,1,1,1] => [1,1,1,1,4] => [1,1,1,1,4] => 11111000 => 8
[1,1,1,1,5] => [1,1,1,1,5] => [1,1,1,1,5] => 111110000 => 9
[1,1,1,5,1] => [1,1,1,1,5] => [1,1,1,1,5] => 111110000 => 9
[1,1,5,1,1] => [1,1,1,1,5] => [1,1,1,1,5] => 111110000 => 9
[1,5,1,1,1] => [1,1,1,1,5] => [1,1,1,1,5] => 111110000 => 9
[5,1,1,1,1] => [1,1,1,1,5] => [1,1,1,1,5] => 111110000 => 9
[1,1,1,2,2] => [1,1,1,2,2] => [1,1,1,2,2] => 1111010 => 7
[1,1,2,1,2] => [1,1,1,2,2] => [1,1,1,2,2] => 1111010 => 7
[1,1,2,2,1] => [1,1,1,2,2] => [1,1,1,2,2] => 1111010 => 7
[1,2,1,1,2] => [1,1,1,2,2] => [1,1,1,2,2] => 1111010 => 7
[1,2,1,2,1] => [1,1,1,2,2] => [1,1,1,2,2] => 1111010 => 7
[1,2,2,1,1] => [1,1,1,2,2] => [1,1,1,2,2] => 1111010 => 7
[2,1,1,1,2] => [1,1,1,2,2] => [1,1,1,2,2] => 1111010 => 7
[2,1,1,2,1] => [1,1,1,2,2] => [1,1,1,2,2] => 1111010 => 7
[2,1,2,1,1] => [1,1,1,2,2] => [1,1,1,2,2] => 1111010 => 7
[2,2,1,1,1] => [1,1,1,2,2] => [1,1,1,2,2] => 1111010 => 7
[1,1,1,2,3] => [1,1,1,2,3] => [1,1,1,2,3] => 11110100 => 8
[1,1,1,3,2] => [1,1,1,2,3] => [1,1,1,2,3] => 11110100 => 8
[1,1,2,1,3] => [1,1,1,2,3] => [1,1,1,2,3] => 11110100 => 8
[1,1,2,3,1] => [1,1,1,2,3] => [1,1,1,2,3] => 11110100 => 8
[1,1,3,1,2] => [1,1,1,2,3] => [1,1,1,2,3] => 11110100 => 8
[1,1,3,2,1] => [1,1,1,2,3] => [1,1,1,2,3] => 11110100 => 8
[1,2,1,1,3] => [1,1,1,2,3] => [1,1,1,2,3] => 11110100 => 8
[1,2,1,3,1] => [1,1,1,2,3] => [1,1,1,2,3] => 11110100 => 8
[1,2,3,1,1] => [1,1,1,2,3] => [1,1,1,2,3] => 11110100 => 8
[1,3,1,1,2] => [1,1,1,2,3] => [1,1,1,2,3] => 11110100 => 8
[1,3,1,2,1] => [1,1,1,2,3] => [1,1,1,2,3] => 11110100 => 8
[1,3,2,1,1] => [1,1,1,2,3] => [1,1,1,2,3] => 11110100 => 8
[2,1,1,1,3] => [1,1,1,2,3] => [1,1,1,2,3] => 11110100 => 8
[2,1,1,3,1] => [1,1,1,2,3] => [1,1,1,2,3] => 11110100 => 8
[2,1,3,1,1] => [1,1,1,2,3] => [1,1,1,2,3] => 11110100 => 8
[2,3,1,1,1] => [1,1,1,2,3] => [1,1,1,2,3] => 11110100 => 8
[3,1,1,1,2] => [1,1,1,2,3] => [1,1,1,2,3] => 11110100 => 8
[3,1,1,2,1] => [1,1,1,2,3] => [1,1,1,2,3] => 11110100 => 8
[3,1,2,1,1] => [1,1,1,2,3] => [1,1,1,2,3] => 11110100 => 8
[3,2,1,1,1] => [1,1,1,2,3] => [1,1,1,2,3] => 11110100 => 8
[1,1,1,2,4] => [1,1,1,2,4] => [1,1,1,2,4] => 111101000 => 9
[1,1,1,4,2] => [1,1,1,2,4] => [1,1,1,2,4] => 111101000 => 9
[1,1,2,1,4] => [1,1,1,2,4] => [1,1,1,2,4] => 111101000 => 9
[1,1,2,4,1] => [1,1,1,2,4] => [1,1,1,2,4] => 111101000 => 9
[1,1,4,1,2] => [1,1,1,2,4] => [1,1,1,2,4] => 111101000 => 9
[1,1,4,2,1] => [1,1,1,2,4] => [1,1,1,2,4] => 111101000 => 9
[1,2,1,1,4] => [1,1,1,2,4] => [1,1,1,2,4] => 111101000 => 9
[1,2,1,4,1] => [1,1,1,2,4] => [1,1,1,2,4] => 111101000 => 9
[1,2,4,1,1] => [1,1,1,2,4] => [1,1,1,2,4] => 111101000 => 9
[1,4,1,1,2] => [1,1,1,2,4] => [1,1,1,2,4] => 111101000 => 9
[1,4,1,2,1] => [1,1,1,2,4] => [1,1,1,2,4] => 111101000 => 9
[1,4,2,1,1] => [1,1,1,2,4] => [1,1,1,2,4] => 111101000 => 9
[2,1,1,1,4] => [1,1,1,2,4] => [1,1,1,2,4] => 111101000 => 9
[2,1,1,4,1] => [1,1,1,2,4] => [1,1,1,2,4] => 111101000 => 9
[2,1,4,1,1] => [1,1,1,2,4] => [1,1,1,2,4] => 111101000 => 9
[2,4,1,1,1] => [1,1,1,2,4] => [1,1,1,2,4] => 111101000 => 9
[4,1,1,1,2] => [1,1,1,2,4] => [1,1,1,2,4] => 111101000 => 9
[4,1,1,2,1] => [1,1,1,2,4] => [1,1,1,2,4] => 111101000 => 9
[4,1,2,1,1] => [1,1,1,2,4] => [1,1,1,2,4] => 111101000 => 9
[4,2,1,1,1] => [1,1,1,2,4] => [1,1,1,2,4] => 111101000 => 9
[1,1,1,2,5] => [1,1,1,2,5] => [1,1,1,2,5] => 1111010000 => 10
[1,1,1,5,2] => [1,1,1,2,5] => [1,1,1,2,5] => 1111010000 => 10
[1,1,2,1,5] => [1,1,1,2,5] => [1,1,1,2,5] => 1111010000 => 10
[1,1,2,5,1] => [1,1,1,2,5] => [1,1,1,2,5] => 1111010000 => 10
[1,1,5,1,2] => [1,1,1,2,5] => [1,1,1,2,5] => 1111010000 => 10
[1,1,5,2,1] => [1,1,1,2,5] => [1,1,1,2,5] => 1111010000 => 10
[1,2,1,1,5] => [1,1,1,2,5] => [1,1,1,2,5] => 1111010000 => 10
[1,2,1,5,1] => [1,1,1,2,5] => [1,1,1,2,5] => 1111010000 => 10
[1,2,5,1,1] => [1,1,1,2,5] => [1,1,1,2,5] => 1111010000 => 10
[1,5,1,1,2] => [1,1,1,2,5] => [1,1,1,2,5] => 1111010000 => 10
[1,5,1,2,1] => [1,1,1,2,5] => [1,1,1,2,5] => 1111010000 => 10
[1,5,2,1,1] => [1,1,1,2,5] => [1,1,1,2,5] => 1111010000 => 10
[2,1,1,1,5] => [1,1,1,2,5] => [1,1,1,2,5] => 1111010000 => 10
[2,1,1,5,1] => [1,1,1,2,5] => [1,1,1,2,5] => 1111010000 => 10
[2,1,5,1,1] => [1,1,1,2,5] => [1,1,1,2,5] => 1111010000 => 10
[2,5,1,1,1] => [1,1,1,2,5] => [1,1,1,2,5] => 1111010000 => 10
[5,1,1,1,2] => [1,1,1,2,5] => [1,1,1,2,5] => 1111010000 => 10
[5,1,1,2,1] => [1,1,1,2,5] => [1,1,1,2,5] => 1111010000 => 10
[5,1,2,1,1] => [1,1,1,2,5] => [1,1,1,2,5] => 1111010000 => 10
[5,2,1,1,1] => [1,1,1,2,5] => [1,1,1,2,5] => 1111010000 => 10
[1,1,1,3,3] => [1,1,1,3,3] => [1,1,1,3,3] => 111100100 => 9
[1,1,3,1,3] => [1,1,1,3,3] => [1,1,1,3,3] => 111100100 => 9
[1,1,3,3,1] => [1,1,1,3,3] => [1,1,1,3,3] => 111100100 => 9
[1,3,1,1,3] => [1,1,1,3,3] => [1,1,1,3,3] => 111100100 => 9
[1,3,1,3,1] => [1,1,1,3,3] => [1,1,1,3,3] => 111100100 => 9
[1,3,3,1,1] => [1,1,1,3,3] => [1,1,1,3,3] => 111100100 => 9
[3,1,1,1,3] => [1,1,1,3,3] => [1,1,1,3,3] => 111100100 => 9
[3,1,1,3,1] => [1,1,1,3,3] => [1,1,1,3,3] => 111100100 => 9
[3,1,3,1,1] => [1,1,1,3,3] => [1,1,1,3,3] => 111100100 => 9
[3,3,1,1,1] => [1,1,1,3,3] => [1,1,1,3,3] => 111100100 => 9
[1,1,1,3,4] => [1,1,1,3,4] => [1,1,1,3,4] => 1111001000 => 10
[1,1,1,4,3] => [1,1,1,3,4] => [1,1,1,3,4] => 1111001000 => 10
[1,1,3,1,4] => [1,1,1,3,4] => [1,1,1,3,4] => 1111001000 => 10
[1,1,3,4,1] => [1,1,1,3,4] => [1,1,1,3,4] => 1111001000 => 10
[1,1,4,1,3] => [1,1,1,3,4] => [1,1,1,3,4] => 1111001000 => 10
[1,1,4,3,1] => [1,1,1,3,4] => [1,1,1,3,4] => 1111001000 => 10
[1,3,1,1,4] => [1,1,1,3,4] => [1,1,1,3,4] => 1111001000 => 10
[1,3,1,4,1] => [1,1,1,3,4] => [1,1,1,3,4] => 1111001000 => 10
[1,3,4,1,1] => [1,1,1,3,4] => [1,1,1,3,4] => 1111001000 => 10
[1,4,1,1,3] => [1,1,1,3,4] => [1,1,1,3,4] => 1111001000 => 10
[1,4,1,3,1] => [1,1,1,3,4] => [1,1,1,3,4] => 1111001000 => 10
[1,4,3,1,1] => [1,1,1,3,4] => [1,1,1,3,4] => 1111001000 => 10
[3,1,1,1,4] => [1,1,1,3,4] => [1,1,1,3,4] => 1111001000 => 10
[3,1,1,4,1] => [1,1,1,3,4] => [1,1,1,3,4] => 1111001000 => 10
[3,1,4,1,1] => [1,1,1,3,4] => [1,1,1,3,4] => 1111001000 => 10
[3,4,1,1,1] => [1,1,1,3,4] => [1,1,1,3,4] => 1111001000 => 10
[4,1,1,1,3] => [1,1,1,3,4] => [1,1,1,3,4] => 1111001000 => 10
[4,1,1,3,1] => [1,1,1,3,4] => [1,1,1,3,4] => 1111001000 => 10
[4,1,3,1,1] => [1,1,1,3,4] => [1,1,1,3,4] => 1111001000 => 10
[4,3,1,1,1] => [1,1,1,3,4] => [1,1,1,3,4] => 1111001000 => 10
[1,1,2,2,2] => [1,1,2,2,2] => [1,1,2,2,2] => 11101010 => 8
[1,2,1,2,2] => [1,1,2,2,2] => [1,1,2,2,2] => 11101010 => 8
[1,2,2,1,2] => [1,1,2,2,2] => [1,1,2,2,2] => 11101010 => 8
[1,2,2,2,1] => [1,1,2,2,2] => [1,1,2,2,2] => 11101010 => 8
[2,1,1,2,2] => [1,1,2,2,2] => [1,1,2,2,2] => 11101010 => 8
[2,1,2,1,2] => [1,1,2,2,2] => [1,1,2,2,2] => 11101010 => 8
[2,1,2,2,1] => [1,1,2,2,2] => [1,1,2,2,2] => 11101010 => 8
[2,2,1,1,2] => [1,1,2,2,2] => [1,1,2,2,2] => 11101010 => 8
[2,2,1,2,1] => [1,1,2,2,2] => [1,1,2,2,2] => 11101010 => 8
[2,2,2,1,1] => [1,1,2,2,2] => [1,1,2,2,2] => 11101010 => 8
[1,1,2,2,3] => [1,1,2,2,3] => [1,1,2,2,3] => 111010100 => 9
[1,1,2,3,2] => [1,1,2,2,3] => [1,1,2,2,3] => 111010100 => 9
[1,1,3,2,2] => [1,1,2,2,3] => [1,1,2,2,3] => 111010100 => 9
[1,2,1,2,3] => [1,1,2,2,3] => [1,1,2,2,3] => 111010100 => 9
[1,2,1,3,2] => [1,1,2,2,3] => [1,1,2,2,3] => 111010100 => 9
[1,2,2,1,3] => [1,1,2,2,3] => [1,1,2,2,3] => 111010100 => 9
[1,2,2,3,1] => [1,1,2,2,3] => [1,1,2,2,3] => 111010100 => 9
[1,2,3,1,2] => [1,1,2,2,3] => [1,1,2,2,3] => 111010100 => 9
[1,2,3,2,1] => [1,1,2,2,3] => [1,1,2,2,3] => 111010100 => 9
[1,3,1,2,2] => [1,1,2,2,3] => [1,1,2,2,3] => 111010100 => 9
[1,3,2,1,2] => [1,1,2,2,3] => [1,1,2,2,3] => 111010100 => 9
[1,3,2,2,1] => [1,1,2,2,3] => [1,1,2,2,3] => 111010100 => 9
[2,1,1,2,3] => [1,1,2,2,3] => [1,1,2,2,3] => 111010100 => 9
[2,1,1,3,2] => [1,1,2,2,3] => [1,1,2,2,3] => 111010100 => 9
[2,1,2,1,3] => [1,1,2,2,3] => [1,1,2,2,3] => 111010100 => 9
[2,1,2,3,1] => [1,1,2,2,3] => [1,1,2,2,3] => 111010100 => 9
[2,1,3,1,2] => [1,1,2,2,3] => [1,1,2,2,3] => 111010100 => 9
[2,1,3,2,1] => [1,1,2,2,3] => [1,1,2,2,3] => 111010100 => 9
[2,2,1,1,3] => [1,1,2,2,3] => [1,1,2,2,3] => 111010100 => 9
[2,2,1,3,1] => [1,1,2,2,3] => [1,1,2,2,3] => 111010100 => 9
[2,2,3,1,1] => [1,1,2,2,3] => [1,1,2,2,3] => 111010100 => 9
[2,3,1,1,2] => [1,1,2,2,3] => [1,1,2,2,3] => 111010100 => 9
[2,3,1,2,1] => [1,1,2,2,3] => [1,1,2,2,3] => 111010100 => 9
[2,3,2,1,1] => [1,1,2,2,3] => [1,1,2,2,3] => 111010100 => 9
[3,1,1,2,2] => [1,1,2,2,3] => [1,1,2,2,3] => 111010100 => 9
[3,1,2,1,2] => [1,1,2,2,3] => [1,1,2,2,3] => 111010100 => 9
[3,1,2,2,1] => [1,1,2,2,3] => [1,1,2,2,3] => 111010100 => 9
[3,2,1,1,2] => [1,1,2,2,3] => [1,1,2,2,3] => 111010100 => 9
[3,2,1,2,1] => [1,1,2,2,3] => [1,1,2,2,3] => 111010100 => 9
[3,2,2,1,1] => [1,1,2,2,3] => [1,1,2,2,3] => 111010100 => 9
[1,1,2,2,4] => [1,1,2,2,4] => [1,1,2,2,4] => 1110101000 => 10
[1,1,2,4,2] => [1,1,2,2,4] => [1,1,2,2,4] => 1110101000 => 10
[1,1,4,2,2] => [1,1,2,2,4] => [1,1,2,2,4] => 1110101000 => 10
[1,2,1,2,4] => [1,1,2,2,4] => [1,1,2,2,4] => 1110101000 => 10
[1,2,1,4,2] => [1,1,2,2,4] => [1,1,2,2,4] => 1110101000 => 10
[1,2,2,1,4] => [1,1,2,2,4] => [1,1,2,2,4] => 1110101000 => 10
[1,2,2,4,1] => [1,1,2,2,4] => [1,1,2,2,4] => 1110101000 => 10
[1,2,4,1,2] => [1,1,2,2,4] => [1,1,2,2,4] => 1110101000 => 10
[1,2,4,2,1] => [1,1,2,2,4] => [1,1,2,2,4] => 1110101000 => 10
[1,4,1,2,2] => [1,1,2,2,4] => [1,1,2,2,4] => 1110101000 => 10
[1,4,2,1,2] => [1,1,2,2,4] => [1,1,2,2,4] => 1110101000 => 10
[1,4,2,2,1] => [1,1,2,2,4] => [1,1,2,2,4] => 1110101000 => 10
[2,1,1,2,4] => [1,1,2,2,4] => [1,1,2,2,4] => 1110101000 => 10
[2,1,1,4,2] => [1,1,2,2,4] => [1,1,2,2,4] => 1110101000 => 10
[2,1,2,1,4] => [1,1,2,2,4] => [1,1,2,2,4] => 1110101000 => 10
[2,1,2,4,1] => [1,1,2,2,4] => [1,1,2,2,4] => 1110101000 => 10
[2,1,4,1,2] => [1,1,2,2,4] => [1,1,2,2,4] => 1110101000 => 10
[2,1,4,2,1] => [1,1,2,2,4] => [1,1,2,2,4] => 1110101000 => 10
[2,2,1,1,4] => [1,1,2,2,4] => [1,1,2,2,4] => 1110101000 => 10
[2,2,1,4,1] => [1,1,2,2,4] => [1,1,2,2,4] => 1110101000 => 10
[2,2,4,1,1] => [1,1,2,2,4] => [1,1,2,2,4] => 1110101000 => 10
[2,4,1,1,2] => [1,1,2,2,4] => [1,1,2,2,4] => 1110101000 => 10
[2,4,1,2,1] => [1,1,2,2,4] => [1,1,2,2,4] => 1110101000 => 10
[2,4,2,1,1] => [1,1,2,2,4] => [1,1,2,2,4] => 1110101000 => 10
[4,1,1,2,2] => [1,1,2,2,4] => [1,1,2,2,4] => 1110101000 => 10
[4,1,2,1,2] => [1,1,2,2,4] => [1,1,2,2,4] => 1110101000 => 10
[4,1,2,2,1] => [1,1,2,2,4] => [1,1,2,2,4] => 1110101000 => 10
[4,2,1,1,2] => [1,1,2,2,4] => [1,1,2,2,4] => 1110101000 => 10
[4,2,1,2,1] => [1,1,2,2,4] => [1,1,2,2,4] => 1110101000 => 10
[4,2,2,1,1] => [1,1,2,2,4] => [1,1,2,2,4] => 1110101000 => 10
[1,1,2,3,3] => [1,1,2,3,3] => [1,1,2,3,3] => 1110100100 => 10
[1,1,3,2,3] => [1,1,2,3,3] => [1,1,2,3,3] => 1110100100 => 10
[1,1,3,3,2] => [1,1,2,3,3] => [1,1,2,3,3] => 1110100100 => 10
[1,2,1,3,3] => [1,1,2,3,3] => [1,1,2,3,3] => 1110100100 => 10
[1,2,3,1,3] => [1,1,2,3,3] => [1,1,2,3,3] => 1110100100 => 10
[1,2,3,3,1] => [1,1,2,3,3] => [1,1,2,3,3] => 1110100100 => 10
[1,3,1,2,3] => [1,1,2,3,3] => [1,1,2,3,3] => 1110100100 => 10
[1,3,1,3,2] => [1,1,2,3,3] => [1,1,2,3,3] => 1110100100 => 10
[1,3,2,1,3] => [1,1,2,3,3] => [1,1,2,3,3] => 1110100100 => 10
[1,3,2,3,1] => [1,1,2,3,3] => [1,1,2,3,3] => 1110100100 => 10
[1,3,3,1,2] => [1,1,2,3,3] => [1,1,2,3,3] => 1110100100 => 10
[1,3,3,2,1] => [1,1,2,3,3] => [1,1,2,3,3] => 1110100100 => 10
[2,1,1,3,3] => [1,1,2,3,3] => [1,1,2,3,3] => 1110100100 => 10
[2,1,3,1,3] => [1,1,2,3,3] => [1,1,2,3,3] => 1110100100 => 10
[2,1,3,3,1] => [1,1,2,3,3] => [1,1,2,3,3] => 1110100100 => 10
[2,3,1,1,3] => [1,1,2,3,3] => [1,1,2,3,3] => 1110100100 => 10
[2,3,1,3,1] => [1,1,2,3,3] => [1,1,2,3,3] => 1110100100 => 10
[2,3,3,1,1] => [1,1,2,3,3] => [1,1,2,3,3] => 1110100100 => 10
[3,1,1,2,3] => [1,1,2,3,3] => [1,1,2,3,3] => 1110100100 => 10
[3,1,1,3,2] => [1,1,2,3,3] => [1,1,2,3,3] => 1110100100 => 10
[3,1,2,1,3] => [1,1,2,3,3] => [1,1,2,3,3] => 1110100100 => 10
[3,1,2,3,1] => [1,1,2,3,3] => [1,1,2,3,3] => 1110100100 => 10
[3,1,3,1,2] => [1,1,2,3,3] => [1,1,2,3,3] => 1110100100 => 10
[3,1,3,2,1] => [1,1,2,3,3] => [1,1,2,3,3] => 1110100100 => 10
[3,2,1,1,3] => [1,1,2,3,3] => [1,1,2,3,3] => 1110100100 => 10
[3,2,1,3,1] => [1,1,2,3,3] => [1,1,2,3,3] => 1110100100 => 10
[3,2,3,1,1] => [1,1,2,3,3] => [1,1,2,3,3] => 1110100100 => 10
[3,3,1,1,2] => [1,1,2,3,3] => [1,1,2,3,3] => 1110100100 => 10
[3,3,1,2,1] => [1,1,2,3,3] => [1,1,2,3,3] => 1110100100 => 10
[3,3,2,1,1] => [1,1,2,3,3] => [1,1,2,3,3] => 1110100100 => 10
[1,2,2,2,2] => [1,2,2,2,2] => [1,2,2,2,2] => 110101010 => 9
[2,1,2,2,2] => [1,2,2,2,2] => [1,2,2,2,2] => 110101010 => 9
[2,2,1,2,2] => [1,2,2,2,2] => [1,2,2,2,2] => 110101010 => 9
[2,2,2,1,2] => [1,2,2,2,2] => [1,2,2,2,2] => 110101010 => 9
[2,2,2,2,1] => [1,2,2,2,2] => [1,2,2,2,2] => 110101010 => 9
[1,2,2,2,3] => [1,2,2,2,3] => [1,2,2,2,3] => 1101010100 => 10
[1,2,2,3,2] => [1,2,2,2,3] => [1,2,2,2,3] => 1101010100 => 10
[1,2,3,2,2] => [1,2,2,2,3] => [1,2,2,2,3] => 1101010100 => 10
[1,3,2,2,2] => [1,2,2,2,3] => [1,2,2,2,3] => 1101010100 => 10
[2,1,2,2,3] => [1,2,2,2,3] => [1,2,2,2,3] => 1101010100 => 10
[2,1,2,3,2] => [1,2,2,2,3] => [1,2,2,2,3] => 1101010100 => 10
[2,1,3,2,2] => [1,2,2,2,3] => [1,2,2,2,3] => 1101010100 => 10
[2,2,1,2,3] => [1,2,2,2,3] => [1,2,2,2,3] => 1101010100 => 10
[2,2,1,3,2] => [1,2,2,2,3] => [1,2,2,2,3] => 1101010100 => 10
[2,2,2,1,3] => [1,2,2,2,3] => [1,2,2,2,3] => 1101010100 => 10
[2,2,2,3,1] => [1,2,2,2,3] => [1,2,2,2,3] => 1101010100 => 10
[2,2,3,1,2] => [1,2,2,2,3] => [1,2,2,2,3] => 1101010100 => 10
[2,2,3,2,1] => [1,2,2,2,3] => [1,2,2,2,3] => 1101010100 => 10
[2,3,1,2,2] => [1,2,2,2,3] => [1,2,2,2,3] => 1101010100 => 10
[2,3,2,1,2] => [1,2,2,2,3] => [1,2,2,2,3] => 1101010100 => 10
[2,3,2,2,1] => [1,2,2,2,3] => [1,2,2,2,3] => 1101010100 => 10
[3,1,2,2,2] => [1,2,2,2,3] => [1,2,2,2,3] => 1101010100 => 10
[3,2,1,2,2] => [1,2,2,2,3] => [1,2,2,2,3] => 1101010100 => 10
[3,2,2,1,2] => [1,2,2,2,3] => [1,2,2,2,3] => 1101010100 => 10
[3,2,2,2,1] => [1,2,2,2,3] => [1,2,2,2,3] => 1101010100 => 10
[1,1,1,1,1,1] => [1,1,1,1,1,1] => [1,1,1,1,1,1] => 111111 => 6
[1,1,1,1,1,2] => [1,1,1,1,1,2] => [1,1,1,1,1,2] => 1111110 => 7
[1,1,1,1,2,1] => [1,1,1,1,1,2] => [1,1,1,1,1,2] => 1111110 => 7
[1,1,1,2,1,1] => [1,1,1,1,1,2] => [1,1,1,1,1,2] => 1111110 => 7
[1,1,2,1,1,1] => [1,1,1,1,1,2] => [1,1,1,1,1,2] => 1111110 => 7
[1,2,1,1,1,1] => [1,1,1,1,1,2] => [1,1,1,1,1,2] => 1111110 => 7
[2,1,1,1,1,1] => [1,1,1,1,1,2] => [1,1,1,1,1,2] => 1111110 => 7
[1,1,1,1,1,3] => [1,1,1,1,1,3] => [1,1,1,1,1,3] => 11111100 => 8
[1,1,1,1,3,1] => [1,1,1,1,1,3] => [1,1,1,1,1,3] => 11111100 => 8
[1,1,1,3,1,1] => [1,1,1,1,1,3] => [1,1,1,1,1,3] => 11111100 => 8
[1,1,3,1,1,1] => [1,1,1,1,1,3] => [1,1,1,1,1,3] => 11111100 => 8
[1,3,1,1,1,1] => [1,1,1,1,1,3] => [1,1,1,1,1,3] => 11111100 => 8
[3,1,1,1,1,1] => [1,1,1,1,1,3] => [1,1,1,1,1,3] => 11111100 => 8
[1,1,1,1,1,4] => [1,1,1,1,1,4] => [1,1,1,1,1,4] => 111111000 => 9
[1,1,1,1,4,1] => [1,1,1,1,1,4] => [1,1,1,1,1,4] => 111111000 => 9
[1,1,1,4,1,1] => [1,1,1,1,1,4] => [1,1,1,1,1,4] => 111111000 => 9
[1,1,4,1,1,1] => [1,1,1,1,1,4] => [1,1,1,1,1,4] => 111111000 => 9
[1,4,1,1,1,1] => [1,1,1,1,1,4] => [1,1,1,1,1,4] => 111111000 => 9
[4,1,1,1,1,1] => [1,1,1,1,1,4] => [1,1,1,1,1,4] => 111111000 => 9
[1,1,1,1,2,2] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => 11111010 => 8
[1,1,1,2,1,2] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => 11111010 => 8
[1,1,1,2,2,1] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => 11111010 => 8
[1,1,2,1,1,2] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => 11111010 => 8
[1,1,2,1,2,1] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => 11111010 => 8
[1,1,2,2,1,1] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => 11111010 => 8
[1,2,1,1,1,2] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => 11111010 => 8
[1,2,1,1,2,1] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => 11111010 => 8
[1,2,1,2,1,1] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => 11111010 => 8
[1,2,2,1,1,1] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => 11111010 => 8
[2,1,1,1,1,2] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => 11111010 => 8
[2,1,1,1,2,1] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => 11111010 => 8
[2,1,1,2,1,1] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => 11111010 => 8
[2,1,2,1,1,1] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => 11111010 => 8
[2,2,1,1,1,1] => [1,1,1,1,2,2] => [1,1,1,1,2,2] => 11111010 => 8
[1,1,1,1,2,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => 111110100 => 9
[1,1,1,1,3,2] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => 111110100 => 9
[1,1,1,2,1,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => 111110100 => 9
[1,1,1,2,3,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => 111110100 => 9
[1,1,1,3,1,2] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => 111110100 => 9
[1,1,1,3,2,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => 111110100 => 9
[1,1,2,1,1,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => 111110100 => 9
[1,1,2,1,3,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => 111110100 => 9
[1,1,2,3,1,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => 111110100 => 9
[1,1,3,1,1,2] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => 111110100 => 9
[1,1,3,1,2,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => 111110100 => 9
[1,1,3,2,1,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => 111110100 => 9
[1,2,1,1,1,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => 111110100 => 9
[1,2,1,1,3,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => 111110100 => 9
[1,2,1,3,1,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => 111110100 => 9
[1,2,3,1,1,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => 111110100 => 9
[1,3,1,1,1,2] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => 111110100 => 9
[1,3,1,1,2,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => 111110100 => 9
[1,3,1,2,1,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => 111110100 => 9
[1,3,2,1,1,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => 111110100 => 9
[2,1,1,1,1,3] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => 111110100 => 9
[2,1,1,1,3,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => 111110100 => 9
[2,1,1,3,1,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => 111110100 => 9
[2,1,3,1,1,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => 111110100 => 9
[2,3,1,1,1,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => 111110100 => 9
[3,1,1,1,1,2] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => 111110100 => 9
[3,1,1,1,2,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => 111110100 => 9
[3,1,1,2,1,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => 111110100 => 9
[3,1,2,1,1,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => 111110100 => 9
[3,2,1,1,1,1] => [1,1,1,1,2,3] => [1,1,1,1,2,3] => 111110100 => 9
[1,1,1,1,4,4] => [1,1,1,1,4,4] => [1,1,1,1,4,4] => 111110001000 => 12
[1,1,1,4,1,4] => [1,1,1,1,4,4] => [1,1,1,1,4,4] => 111110001000 => 12
[1,1,1,4,4,1] => [1,1,1,1,4,4] => [1,1,1,1,4,4] => 111110001000 => 12
[1,1,4,1,1,4] => [1,1,1,1,4,4] => [1,1,1,1,4,4] => 111110001000 => 12
[1,1,4,1,4,1] => [1,1,1,1,4,4] => [1,1,1,1,4,4] => 111110001000 => 12
[1,1,4,4,1,1] => [1,1,1,1,4,4] => [1,1,1,1,4,4] => 111110001000 => 12
[1,4,1,1,1,4] => [1,1,1,1,4,4] => [1,1,1,1,4,4] => 111110001000 => 12
[1,4,1,1,4,1] => [1,1,1,1,4,4] => [1,1,1,1,4,4] => 111110001000 => 12
[1,4,1,4,1,1] => [1,1,1,1,4,4] => [1,1,1,1,4,4] => 111110001000 => 12
[1,4,4,1,1,1] => [1,1,1,1,4,4] => [1,1,1,1,4,4] => 111110001000 => 12
[4,1,1,1,1,4] => [1,1,1,1,4,4] => [1,1,1,1,4,4] => 111110001000 => 12
[4,1,1,1,4,1] => [1,1,1,1,4,4] => [1,1,1,1,4,4] => 111110001000 => 12
[4,1,1,4,1,1] => [1,1,1,1,4,4] => [1,1,1,1,4,4] => 111110001000 => 12
[4,1,4,1,1,1] => [1,1,1,1,4,4] => [1,1,1,1,4,4] => 111110001000 => 12
[4,4,1,1,1,1] => [1,1,1,1,4,4] => [1,1,1,1,4,4] => 111110001000 => 12
[1,1,1,2,2,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => 111101010 => 9
[1,1,2,1,2,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => 111101010 => 9
[1,1,2,2,1,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => 111101010 => 9
[1,1,2,2,2,1] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => 111101010 => 9
[1,2,1,1,2,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => 111101010 => 9
[1,2,1,2,1,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => 111101010 => 9
[1,2,1,2,2,1] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => 111101010 => 9
[1,2,2,1,1,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => 111101010 => 9
[1,2,2,1,2,1] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => 111101010 => 9
[1,2,2,2,1,1] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => 111101010 => 9
[2,1,1,1,2,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => 111101010 => 9
[2,1,1,2,1,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => 111101010 => 9
[2,1,1,2,2,1] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => 111101010 => 9
[2,1,2,1,1,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => 111101010 => 9
[2,1,2,1,2,1] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => 111101010 => 9
[2,1,2,2,1,1] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => 111101010 => 9
[2,2,1,1,1,2] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => 111101010 => 9
[2,2,1,1,2,1] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => 111101010 => 9
[2,2,1,2,1,1] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => 111101010 => 9
[2,2,2,1,1,1] => [1,1,1,2,2,2] => [1,1,1,2,2,2] => 111101010 => 9
[1,1,2,2,2,4] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[1,1,2,2,4,2] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[1,1,2,4,2,2] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[1,1,4,2,2,2] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[1,2,1,2,2,4] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[1,2,1,2,4,2] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[1,2,1,4,2,2] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[1,2,2,1,2,4] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[1,2,2,1,4,2] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[1,2,2,2,1,4] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[1,2,2,2,4,1] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[1,2,2,4,1,2] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[1,2,2,4,2,1] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[1,2,4,1,2,2] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[1,2,4,2,1,2] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[1,2,4,2,2,1] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[1,4,1,2,2,2] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[1,4,2,1,2,2] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[1,4,2,2,1,2] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[1,4,2,2,2,1] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[2,1,1,2,2,4] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[2,1,1,2,4,2] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[2,1,1,4,2,2] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[2,1,2,1,2,4] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[2,1,2,1,4,2] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[2,1,2,2,1,4] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[2,1,2,2,4,1] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[2,1,2,4,1,2] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[2,1,2,4,2,1] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[2,1,4,1,2,2] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[2,1,4,2,1,2] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[2,1,4,2,2,1] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[2,2,1,1,2,4] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[2,2,1,1,4,2] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[2,2,1,2,1,4] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[2,2,1,2,4,1] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[2,2,1,4,1,2] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[2,2,1,4,2,1] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[2,2,2,1,1,4] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[2,2,2,1,4,1] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[2,2,2,4,1,1] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[2,2,4,1,1,2] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[2,2,4,1,2,1] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[2,2,4,2,1,1] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[2,4,1,1,2,2] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[2,4,1,2,1,2] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[2,4,1,2,2,1] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[2,4,2,1,1,2] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[2,4,2,1,2,1] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[2,4,2,2,1,1] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[4,1,1,2,2,2] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[4,1,2,1,2,2] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[4,1,2,2,1,2] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[4,1,2,2,2,1] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[4,2,1,1,2,2] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[4,2,1,2,1,2] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[4,2,1,2,2,1] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[4,2,2,1,1,2] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[4,2,2,1,2,1] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[4,2,2,2,1,1] => [1,1,2,2,2,4] => [1,1,2,2,2,4] => 111010101000 => 12
[1,1,2,2,3,3] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[1,1,2,3,2,3] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[1,1,2,3,3,2] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[1,1,3,2,2,3] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[1,1,3,2,3,2] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[1,1,3,3,2,2] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[1,2,1,2,3,3] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[1,2,1,3,2,3] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[1,2,1,3,3,2] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[1,2,2,1,3,3] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[1,2,2,3,1,3] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[1,2,2,3,3,1] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[1,2,3,1,2,3] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[1,2,3,1,3,2] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[1,2,3,2,1,3] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[1,2,3,2,3,1] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[1,2,3,3,1,2] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[1,2,3,3,2,1] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[1,3,1,2,2,3] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[1,3,1,2,3,2] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[1,3,1,3,2,2] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[1,3,2,1,2,3] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[1,3,2,1,3,2] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[1,3,2,2,1,3] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[1,3,2,2,3,1] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[1,3,2,3,1,2] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[1,3,2,3,2,1] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[1,3,3,1,2,2] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[1,3,3,2,1,2] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[1,3,3,2,2,1] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[2,1,1,2,3,3] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[2,1,1,3,2,3] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[2,1,1,3,3,2] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[2,1,2,1,3,3] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[2,1,2,3,1,3] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[2,1,2,3,3,1] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[2,1,3,1,2,3] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[2,1,3,1,3,2] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[2,1,3,2,1,3] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[2,1,3,2,3,1] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[2,1,3,3,1,2] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[2,1,3,3,2,1] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[2,2,1,1,3,3] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[2,2,1,3,1,3] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[2,2,1,3,3,1] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[2,2,3,1,1,3] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[2,2,3,1,3,1] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[2,2,3,3,1,1] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[2,3,1,1,2,3] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[2,3,1,1,3,2] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[2,3,1,2,1,3] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[2,3,1,2,3,1] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[2,3,1,3,1,2] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[2,3,1,3,2,1] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[2,3,2,1,1,3] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[2,3,2,1,3,1] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[2,3,2,3,1,1] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[2,3,3,1,1,2] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[2,3,3,1,2,1] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[2,3,3,2,1,1] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[3,1,1,2,2,3] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[3,1,1,2,3,2] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[3,1,1,3,2,2] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[3,1,2,1,2,3] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[3,1,2,1,3,2] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[3,1,2,2,1,3] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[3,1,2,2,3,1] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[3,1,2,3,1,2] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[3,1,2,3,2,1] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[3,1,3,1,2,2] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[3,1,3,2,1,2] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[3,1,3,2,2,1] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[3,2,1,1,2,3] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[3,2,1,1,3,2] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[3,2,1,2,1,3] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[3,2,1,2,3,1] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[3,2,1,3,1,2] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[3,2,1,3,2,1] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[3,2,2,1,1,3] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[3,2,2,1,3,1] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[3,2,2,3,1,1] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[3,2,3,1,1,2] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[3,2,3,1,2,1] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[3,2,3,2,1,1] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[3,3,1,1,2,2] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[3,3,1,2,1,2] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[3,3,1,2,2,1] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[3,3,2,1,1,2] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[3,3,2,1,2,1] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[3,3,2,2,1,1] => [1,1,2,2,3,3] => [1,1,2,2,3,3] => 111010100100 => 12
[1,2,2,2,2,3] => [1,2,2,2,2,3] => [1,2,2,2,2,3] => 110101010100 => 12
[1,2,2,2,3,2] => [1,2,2,2,2,3] => [1,2,2,2,2,3] => 110101010100 => 12
[1,2,2,3,2,2] => [1,2,2,2,2,3] => [1,2,2,2,2,3] => 110101010100 => 12
[1,2,3,2,2,2] => [1,2,2,2,2,3] => [1,2,2,2,2,3] => 110101010100 => 12
[1,3,2,2,2,2] => [1,2,2,2,2,3] => [1,2,2,2,2,3] => 110101010100 => 12
[2,1,2,2,2,3] => [1,2,2,2,2,3] => [1,2,2,2,2,3] => 110101010100 => 12
[2,1,2,2,3,2] => [1,2,2,2,2,3] => [1,2,2,2,2,3] => 110101010100 => 12
[2,1,2,3,2,2] => [1,2,2,2,2,3] => [1,2,2,2,2,3] => 110101010100 => 12
[2,1,3,2,2,2] => [1,2,2,2,2,3] => [1,2,2,2,2,3] => 110101010100 => 12
[2,2,1,2,2,3] => [1,2,2,2,2,3] => [1,2,2,2,2,3] => 110101010100 => 12
[2,2,1,2,3,2] => [1,2,2,2,2,3] => [1,2,2,2,2,3] => 110101010100 => 12
[2,2,1,3,2,2] => [1,2,2,2,2,3] => [1,2,2,2,2,3] => 110101010100 => 12
[2,2,2,1,2,3] => [1,2,2,2,2,3] => [1,2,2,2,2,3] => 110101010100 => 12
[2,2,2,1,3,2] => [1,2,2,2,2,3] => [1,2,2,2,2,3] => 110101010100 => 12
[2,2,2,2,1,3] => [1,2,2,2,2,3] => [1,2,2,2,2,3] => 110101010100 => 12
[2,2,2,2,3,1] => [1,2,2,2,2,3] => [1,2,2,2,2,3] => 110101010100 => 12
[2,2,2,3,1,2] => [1,2,2,2,2,3] => [1,2,2,2,2,3] => 110101010100 => 12
[2,2,2,3,2,1] => [1,2,2,2,2,3] => [1,2,2,2,2,3] => 110101010100 => 12
[2,2,3,1,2,2] => [1,2,2,2,2,3] => [1,2,2,2,2,3] => 110101010100 => 12
[2,2,3,2,1,2] => [1,2,2,2,2,3] => [1,2,2,2,2,3] => 110101010100 => 12
[2,2,3,2,2,1] => [1,2,2,2,2,3] => [1,2,2,2,2,3] => 110101010100 => 12
[2,3,1,2,2,2] => [1,2,2,2,2,3] => [1,2,2,2,2,3] => 110101010100 => 12
[2,3,2,1,2,2] => [1,2,2,2,2,3] => [1,2,2,2,2,3] => 110101010100 => 12
[2,3,2,2,1,2] => [1,2,2,2,2,3] => [1,2,2,2,2,3] => 110101010100 => 12
[2,3,2,2,2,1] => [1,2,2,2,2,3] => [1,2,2,2,2,3] => 110101010100 => 12
[3,1,2,2,2,2] => [1,2,2,2,2,3] => [1,2,2,2,2,3] => 110101010100 => 12
[3,2,1,2,2,2] => [1,2,2,2,2,3] => [1,2,2,2,2,3] => 110101010100 => 12
[3,2,2,1,2,2] => [1,2,2,2,2,3] => [1,2,2,2,2,3] => 110101010100 => 12
[3,2,2,2,1,2] => [1,2,2,2,2,3] => [1,2,2,2,2,3] => 110101010100 => 12
[3,2,2,2,2,1] => [1,2,2,2,2,3] => [1,2,2,2,2,3] => 110101010100 => 12
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Description
The flex of a binary word.
This is the product of the lex statistic (St001436The index of a given binary word in the lex-order among all its cyclic shifts., augmented by 1) and its frequency (St000627The exponent of a binary word.), see [1, §8].
Map
to non-decreasing parking function
Description
Return the non-decreasing parking function which underlies the parking function.
Sorts the parking function into an increasing sequence.
Map
to composition
Description
Return the parking function interpreted as an integer composition.
Map
to binary word
Description
Return the composition as a binary word, treating ones as separators.
Encoding a positive integer $i$ as the word $10\dots 0$ consisting of a one followed by $i-1$ zeros, the binary word of a composition $(i_1,\dots,i_k)$ is the concatenation of of words for $i_1,\dots,i_k$.
The image of this map contains precisely the words which do not begin with a $0$.