Identifier
Values
[1] => [1] => 1 => 1
[1,2] => [2] => 10 => 1
[2,1] => [2] => 10 => 1
[1,2,3] => [3] => 100 => 1
[1,3,2] => [1,2] => 110 => 2
[2,1,3] => [3] => 100 => 1
[2,3,1] => [3] => 100 => 1
[3,1,2] => [3] => 100 => 1
[3,2,1] => [2,1] => 101 => 2
[1,2,3,4] => [4] => 1000 => 1
[1,2,4,3] => [2,2] => 1010 => 2
[1,3,2,4] => [1,3] => 1100 => 2
[1,3,4,2] => [1,3] => 1100 => 2
[1,4,2,3] => [1,3] => 1100 => 2
[1,4,3,2] => [1,2,1] => 1101 => 3
[2,1,3,4] => [4] => 1000 => 1
[2,1,4,3] => [2,2] => 1010 => 2
[2,3,1,4] => [4] => 1000 => 1
[2,3,4,1] => [4] => 1000 => 1
[2,4,1,3] => [4] => 1000 => 1
[2,4,3,1] => [3,1] => 1001 => 2
[3,1,2,4] => [4] => 1000 => 1
[3,1,4,2] => [2,2] => 1010 => 2
[3,2,1,4] => [2,2] => 1010 => 2
[3,2,4,1] => [2,2] => 1010 => 2
[3,4,1,2] => [4] => 1000 => 1
[3,4,2,1] => [3,1] => 1001 => 2
[4,1,2,3] => [4] => 1000 => 1
[4,1,3,2] => [3,1] => 1001 => 2
[4,2,1,3] => [2,2] => 1010 => 2
[4,2,3,1] => [3,1] => 1001 => 2
[4,3,1,2] => [1,3] => 1100 => 2
[4,3,2,1] => [1,2,1] => 1101 => 3
[1,2,3,4,5] => [5] => 10000 => 1
[1,2,3,5,4] => [3,2] => 10010 => 2
[1,2,4,3,5] => [2,3] => 10100 => 2
[1,2,4,5,3] => [2,3] => 10100 => 2
[1,2,5,3,4] => [2,3] => 10100 => 2
[1,2,5,4,3] => [2,2,1] => 10101 => 3
[1,3,2,4,5] => [1,4] => 11000 => 2
[1,3,2,5,4] => [1,2,2] => 11010 => 3
[1,3,4,2,5] => [1,4] => 11000 => 2
[1,3,4,5,2] => [1,4] => 11000 => 2
[1,3,5,2,4] => [1,4] => 11000 => 2
[1,3,5,4,2] => [1,3,1] => 11001 => 3
[1,4,2,3,5] => [1,4] => 11000 => 2
[1,4,2,5,3] => [1,2,2] => 11010 => 3
[1,4,3,2,5] => [1,2,2] => 11010 => 3
[1,4,3,5,2] => [1,2,2] => 11010 => 3
[1,4,5,2,3] => [1,4] => 11000 => 2
[1,4,5,3,2] => [1,3,1] => 11001 => 3
[1,5,2,3,4] => [1,4] => 11000 => 2
[1,5,2,4,3] => [1,3,1] => 11001 => 3
[1,5,3,2,4] => [1,2,2] => 11010 => 3
[1,5,3,4,2] => [1,3,1] => 11001 => 3
[1,5,4,2,3] => [1,1,3] => 11100 => 3
[1,5,4,3,2] => [1,1,2,1] => 11101 => 4
[2,1,3,4,5] => [5] => 10000 => 1
[2,1,3,5,4] => [3,2] => 10010 => 2
[2,1,4,3,5] => [2,3] => 10100 => 2
[2,1,4,5,3] => [2,3] => 10100 => 2
[2,1,5,3,4] => [2,3] => 10100 => 2
[2,1,5,4,3] => [2,2,1] => 10101 => 3
[2,3,1,4,5] => [5] => 10000 => 1
[2,3,1,5,4] => [3,2] => 10010 => 2
[2,3,4,1,5] => [5] => 10000 => 1
[2,3,4,5,1] => [5] => 10000 => 1
[2,3,5,1,4] => [5] => 10000 => 1
[2,3,5,4,1] => [4,1] => 10001 => 2
[2,4,1,3,5] => [5] => 10000 => 1
[2,4,1,5,3] => [3,2] => 10010 => 2
[2,4,3,1,5] => [3,2] => 10010 => 2
[2,4,3,5,1] => [3,2] => 10010 => 2
[2,4,5,1,3] => [5] => 10000 => 1
[2,4,5,3,1] => [4,1] => 10001 => 2
[2,5,1,3,4] => [5] => 10000 => 1
[2,5,1,4,3] => [4,1] => 10001 => 2
[2,5,3,1,4] => [3,2] => 10010 => 2
[2,5,3,4,1] => [4,1] => 10001 => 2
[2,5,4,1,3] => [2,3] => 10100 => 2
[2,5,4,3,1] => [2,2,1] => 10101 => 3
[3,1,2,4,5] => [5] => 10000 => 1
[3,1,2,5,4] => [3,2] => 10010 => 2
[3,1,4,2,5] => [2,3] => 10100 => 2
[3,1,4,5,2] => [2,3] => 10100 => 2
[3,1,5,2,4] => [2,3] => 10100 => 2
[3,1,5,4,2] => [2,2,1] => 10101 => 3
[3,2,1,4,5] => [2,3] => 10100 => 2
[3,2,1,5,4] => [2,1,2] => 10110 => 3
[3,2,4,1,5] => [2,3] => 10100 => 2
[3,2,4,5,1] => [2,3] => 10100 => 2
[3,2,5,1,4] => [2,3] => 10100 => 2
[3,2,5,4,1] => [2,2,1] => 10101 => 3
[3,4,1,2,5] => [5] => 10000 => 1
[3,4,1,5,2] => [3,2] => 10010 => 2
[3,4,2,1,5] => [3,2] => 10010 => 2
[3,4,2,5,1] => [3,2] => 10010 => 2
[3,4,5,1,2] => [5] => 10000 => 1
[3,4,5,2,1] => [4,1] => 10001 => 2
[3,5,1,2,4] => [5] => 10000 => 1
[3,5,1,4,2] => [4,1] => 10001 => 2
>>> Load all 13101 entries. <<<
[3,5,2,1,4] => [3,2] => 10010 => 2
[3,5,2,4,1] => [4,1] => 10001 => 2
[3,5,4,1,2] => [2,3] => 10100 => 2
[3,5,4,2,1] => [2,2,1] => 10101 => 3
[4,1,2,3,5] => [5] => 10000 => 1
[4,1,2,5,3] => [3,2] => 10010 => 2
[4,1,3,2,5] => [3,2] => 10010 => 2
[4,1,3,5,2] => [3,2] => 10010 => 2
[4,1,5,2,3] => [2,3] => 10100 => 2
[4,1,5,3,2] => [2,2,1] => 10101 => 3
[4,2,1,3,5] => [2,3] => 10100 => 2
[4,2,1,5,3] => [2,1,2] => 10110 => 3
[4,2,3,1,5] => [3,2] => 10010 => 2
[4,2,3,5,1] => [3,2] => 10010 => 2
[4,2,5,1,3] => [2,3] => 10100 => 2
[4,2,5,3,1] => [2,2,1] => 10101 => 3
[4,3,1,2,5] => [1,4] => 11000 => 2
[4,3,1,5,2] => [1,2,2] => 11010 => 3
[4,3,2,1,5] => [1,2,2] => 11010 => 3
[4,3,2,5,1] => [1,2,2] => 11010 => 3
[4,3,5,1,2] => [1,4] => 11000 => 2
[4,3,5,2,1] => [1,3,1] => 11001 => 3
[4,5,1,2,3] => [5] => 10000 => 1
[4,5,1,3,2] => [4,1] => 10001 => 2
[4,5,2,1,3] => [3,2] => 10010 => 2
[4,5,2,3,1] => [4,1] => 10001 => 2
[4,5,3,1,2] => [3,2] => 10010 => 2
[4,5,3,2,1] => [3,1,1] => 10011 => 3
[5,1,2,3,4] => [5] => 10000 => 1
[5,1,2,4,3] => [4,1] => 10001 => 2
[5,1,3,2,4] => [3,2] => 10010 => 2
[5,1,3,4,2] => [4,1] => 10001 => 2
[5,1,4,2,3] => [2,3] => 10100 => 2
[5,1,4,3,2] => [2,2,1] => 10101 => 3
[5,2,1,3,4] => [2,3] => 10100 => 2
[5,2,1,4,3] => [2,2,1] => 10101 => 3
[5,2,3,1,4] => [3,2] => 10010 => 2
[5,2,3,4,1] => [4,1] => 10001 => 2
[5,2,4,1,3] => [2,3] => 10100 => 2
[5,2,4,3,1] => [2,2,1] => 10101 => 3
[5,3,1,2,4] => [1,4] => 11000 => 2
[5,3,1,4,2] => [1,3,1] => 11001 => 3
[5,3,2,1,4] => [1,2,2] => 11010 => 3
[5,3,2,4,1] => [1,3,1] => 11001 => 3
[5,3,4,1,2] => [1,4] => 11000 => 2
[5,3,4,2,1] => [1,3,1] => 11001 => 3
[5,4,1,2,3] => [1,4] => 11000 => 2
[5,4,1,3,2] => [1,3,1] => 11001 => 3
[5,4,2,1,3] => [1,2,2] => 11010 => 3
[5,4,2,3,1] => [1,3,1] => 11001 => 3
[5,4,3,1,2] => [1,2,2] => 11010 => 3
[5,4,3,2,1] => [1,2,1,1] => 11011 => 4
[1,2,3,4,5,6] => [6] => 100000 => 1
[1,2,3,4,6,5] => [4,2] => 100010 => 2
[1,2,3,5,4,6] => [3,3] => 100100 => 2
[1,2,3,5,6,4] => [3,3] => 100100 => 2
[1,2,3,6,4,5] => [3,3] => 100100 => 2
[1,2,3,6,5,4] => [3,2,1] => 100101 => 3
[1,2,4,3,5,6] => [2,4] => 101000 => 2
[1,2,4,3,6,5] => [2,2,2] => 101010 => 3
[1,2,4,5,3,6] => [2,4] => 101000 => 2
[1,2,4,5,6,3] => [2,4] => 101000 => 2
[1,2,4,6,3,5] => [2,4] => 101000 => 2
[1,2,4,6,5,3] => [2,3,1] => 101001 => 3
[1,2,5,3,4,6] => [2,4] => 101000 => 2
[1,2,5,3,6,4] => [2,2,2] => 101010 => 3
[1,2,5,4,3,6] => [2,2,2] => 101010 => 3
[1,2,5,4,6,3] => [2,2,2] => 101010 => 3
[1,2,5,6,3,4] => [2,4] => 101000 => 2
[1,2,5,6,4,3] => [2,3,1] => 101001 => 3
[1,2,6,3,4,5] => [2,4] => 101000 => 2
[1,2,6,3,5,4] => [2,3,1] => 101001 => 3
[1,2,6,4,3,5] => [2,2,2] => 101010 => 3
[1,2,6,4,5,3] => [2,3,1] => 101001 => 3
[1,2,6,5,3,4] => [2,1,3] => 101100 => 3
[1,2,6,5,4,3] => [2,1,2,1] => 101101 => 4
[1,3,2,4,5,6] => [1,5] => 110000 => 2
[1,3,2,4,6,5] => [1,3,2] => 110010 => 3
[1,3,2,5,4,6] => [1,2,3] => 110100 => 3
[1,3,2,5,6,4] => [1,2,3] => 110100 => 3
[1,3,2,6,4,5] => [1,2,3] => 110100 => 3
[1,3,2,6,5,4] => [1,2,2,1] => 110101 => 4
[1,3,4,2,5,6] => [1,5] => 110000 => 2
[1,3,4,2,6,5] => [1,3,2] => 110010 => 3
[1,3,4,5,2,6] => [1,5] => 110000 => 2
[1,3,4,5,6,2] => [1,5] => 110000 => 2
[1,3,4,6,2,5] => [1,5] => 110000 => 2
[1,3,4,6,5,2] => [1,4,1] => 110001 => 3
[1,3,5,2,4,6] => [1,5] => 110000 => 2
[1,3,5,2,6,4] => [1,3,2] => 110010 => 3
[1,3,5,4,2,6] => [1,3,2] => 110010 => 3
[1,3,5,4,6,2] => [1,3,2] => 110010 => 3
[1,3,5,6,2,4] => [1,5] => 110000 => 2
[1,3,5,6,4,2] => [1,4,1] => 110001 => 3
[1,3,6,2,4,5] => [1,5] => 110000 => 2
[1,3,6,2,5,4] => [1,4,1] => 110001 => 3
[1,3,6,4,2,5] => [1,3,2] => 110010 => 3
[1,3,6,4,5,2] => [1,4,1] => 110001 => 3
[1,3,6,5,2,4] => [1,2,3] => 110100 => 3
[1,3,6,5,4,2] => [1,2,2,1] => 110101 => 4
[1,4,2,3,5,6] => [1,5] => 110000 => 2
[1,4,2,3,6,5] => [1,3,2] => 110010 => 3
[1,4,2,5,3,6] => [1,2,3] => 110100 => 3
[1,4,2,5,6,3] => [1,2,3] => 110100 => 3
[1,4,2,6,3,5] => [1,2,3] => 110100 => 3
[1,4,2,6,5,3] => [1,2,2,1] => 110101 => 4
[1,4,3,2,5,6] => [1,2,3] => 110100 => 3
[1,4,3,2,6,5] => [1,2,1,2] => 110110 => 4
[1,4,3,5,2,6] => [1,2,3] => 110100 => 3
[1,4,3,5,6,2] => [1,2,3] => 110100 => 3
[1,4,3,6,2,5] => [1,2,3] => 110100 => 3
[1,4,3,6,5,2] => [1,2,2,1] => 110101 => 4
[1,4,5,2,3,6] => [1,5] => 110000 => 2
[1,4,5,2,6,3] => [1,3,2] => 110010 => 3
[1,4,5,3,2,6] => [1,3,2] => 110010 => 3
[1,4,5,3,6,2] => [1,3,2] => 110010 => 3
[1,4,5,6,2,3] => [1,5] => 110000 => 2
[1,4,5,6,3,2] => [1,4,1] => 110001 => 3
[1,4,6,2,3,5] => [1,5] => 110000 => 2
[1,4,6,2,5,3] => [1,4,1] => 110001 => 3
[1,4,6,3,2,5] => [1,3,2] => 110010 => 3
[1,4,6,3,5,2] => [1,4,1] => 110001 => 3
[1,4,6,5,2,3] => [1,2,3] => 110100 => 3
[1,4,6,5,3,2] => [1,2,2,1] => 110101 => 4
[1,5,2,3,4,6] => [1,5] => 110000 => 2
[1,5,2,3,6,4] => [1,3,2] => 110010 => 3
[1,5,2,4,3,6] => [1,3,2] => 110010 => 3
[1,5,2,4,6,3] => [1,3,2] => 110010 => 3
[1,5,2,6,3,4] => [1,2,3] => 110100 => 3
[1,5,2,6,4,3] => [1,2,2,1] => 110101 => 4
[1,5,3,2,4,6] => [1,2,3] => 110100 => 3
[1,5,3,2,6,4] => [1,2,1,2] => 110110 => 4
[1,5,3,4,2,6] => [1,3,2] => 110010 => 3
[1,5,3,4,6,2] => [1,3,2] => 110010 => 3
[1,5,3,6,2,4] => [1,2,3] => 110100 => 3
[1,5,3,6,4,2] => [1,2,2,1] => 110101 => 4
[1,5,4,2,3,6] => [1,1,4] => 111000 => 3
[1,5,4,2,6,3] => [1,1,2,2] => 111010 => 4
[1,5,4,3,2,6] => [1,1,2,2] => 111010 => 4
[1,5,4,3,6,2] => [1,1,2,2] => 111010 => 4
[1,5,4,6,2,3] => [1,1,4] => 111000 => 3
[1,5,4,6,3,2] => [1,1,3,1] => 111001 => 4
[1,5,6,2,3,4] => [1,5] => 110000 => 2
[1,5,6,2,4,3] => [1,4,1] => 110001 => 3
[1,5,6,3,2,4] => [1,3,2] => 110010 => 3
[1,5,6,3,4,2] => [1,4,1] => 110001 => 3
[1,5,6,4,2,3] => [1,3,2] => 110010 => 3
[1,5,6,4,3,2] => [1,3,1,1] => 110011 => 4
[1,6,2,3,4,5] => [1,5] => 110000 => 2
[1,6,2,3,5,4] => [1,4,1] => 110001 => 3
[1,6,2,4,3,5] => [1,3,2] => 110010 => 3
[1,6,2,4,5,3] => [1,4,1] => 110001 => 3
[1,6,2,5,3,4] => [1,2,3] => 110100 => 3
[1,6,2,5,4,3] => [1,2,2,1] => 110101 => 4
[1,6,3,2,4,5] => [1,2,3] => 110100 => 3
[1,6,3,2,5,4] => [1,2,2,1] => 110101 => 4
[1,6,3,4,2,5] => [1,3,2] => 110010 => 3
[1,6,3,4,5,2] => [1,4,1] => 110001 => 3
[1,6,3,5,2,4] => [1,2,3] => 110100 => 3
[1,6,3,5,4,2] => [1,2,2,1] => 110101 => 4
[1,6,4,2,3,5] => [1,1,4] => 111000 => 3
[1,6,4,2,5,3] => [1,1,3,1] => 111001 => 4
[1,6,4,3,2,5] => [1,1,2,2] => 111010 => 4
[1,6,4,3,5,2] => [1,1,3,1] => 111001 => 4
[1,6,4,5,2,3] => [1,1,4] => 111000 => 3
[1,6,4,5,3,2] => [1,1,3,1] => 111001 => 4
[1,6,5,2,3,4] => [1,1,4] => 111000 => 3
[1,6,5,2,4,3] => [1,1,3,1] => 111001 => 4
[1,6,5,3,2,4] => [1,1,2,2] => 111010 => 4
[1,6,5,3,4,2] => [1,1,3,1] => 111001 => 4
[1,6,5,4,2,3] => [1,1,2,2] => 111010 => 4
[1,6,5,4,3,2] => [1,1,2,1,1] => 111011 => 5
[2,1,3,4,5,6] => [6] => 100000 => 1
[2,1,3,4,6,5] => [4,2] => 100010 => 2
[2,1,3,5,4,6] => [3,3] => 100100 => 2
[2,1,3,5,6,4] => [3,3] => 100100 => 2
[2,1,3,6,4,5] => [3,3] => 100100 => 2
[2,1,3,6,5,4] => [3,2,1] => 100101 => 3
[2,1,4,3,5,6] => [2,4] => 101000 => 2
[2,1,4,3,6,5] => [2,2,2] => 101010 => 3
[2,1,4,5,3,6] => [2,4] => 101000 => 2
[2,1,4,5,6,3] => [2,4] => 101000 => 2
[2,1,4,6,3,5] => [2,4] => 101000 => 2
[2,1,4,6,5,3] => [2,3,1] => 101001 => 3
[2,1,5,3,4,6] => [2,4] => 101000 => 2
[2,1,5,3,6,4] => [2,2,2] => 101010 => 3
[2,1,5,4,3,6] => [2,2,2] => 101010 => 3
[2,1,5,4,6,3] => [2,2,2] => 101010 => 3
[2,1,5,6,3,4] => [2,4] => 101000 => 2
[2,1,5,6,4,3] => [2,3,1] => 101001 => 3
[2,1,6,3,4,5] => [2,4] => 101000 => 2
[2,1,6,3,5,4] => [2,3,1] => 101001 => 3
[2,1,6,4,3,5] => [2,2,2] => 101010 => 3
[2,1,6,4,5,3] => [2,3,1] => 101001 => 3
[2,1,6,5,3,4] => [2,1,3] => 101100 => 3
[2,1,6,5,4,3] => [2,1,2,1] => 101101 => 4
[2,3,1,4,5,6] => [6] => 100000 => 1
[2,3,1,4,6,5] => [4,2] => 100010 => 2
[2,3,1,5,4,6] => [3,3] => 100100 => 2
[2,3,1,5,6,4] => [3,3] => 100100 => 2
[2,3,1,6,4,5] => [3,3] => 100100 => 2
[2,3,1,6,5,4] => [3,2,1] => 100101 => 3
[2,3,4,1,5,6] => [6] => 100000 => 1
[2,3,4,1,6,5] => [4,2] => 100010 => 2
[2,3,4,5,1,6] => [6] => 100000 => 1
[2,3,4,5,6,1] => [6] => 100000 => 1
[2,3,4,6,1,5] => [6] => 100000 => 1
[2,3,4,6,5,1] => [5,1] => 100001 => 2
[2,3,5,1,4,6] => [6] => 100000 => 1
[2,3,5,1,6,4] => [4,2] => 100010 => 2
[2,3,5,4,1,6] => [4,2] => 100010 => 2
[2,3,5,4,6,1] => [4,2] => 100010 => 2
[2,3,5,6,1,4] => [6] => 100000 => 1
[2,3,5,6,4,1] => [5,1] => 100001 => 2
[2,3,6,1,4,5] => [6] => 100000 => 1
[2,3,6,1,5,4] => [5,1] => 100001 => 2
[2,3,6,4,1,5] => [4,2] => 100010 => 2
[2,3,6,4,5,1] => [5,1] => 100001 => 2
[2,3,6,5,1,4] => [3,3] => 100100 => 2
[2,3,6,5,4,1] => [3,2,1] => 100101 => 3
[2,4,1,3,5,6] => [6] => 100000 => 1
[2,4,1,3,6,5] => [4,2] => 100010 => 2
[2,4,1,5,3,6] => [3,3] => 100100 => 2
[2,4,1,5,6,3] => [3,3] => 100100 => 2
[2,4,1,6,3,5] => [3,3] => 100100 => 2
[2,4,1,6,5,3] => [3,2,1] => 100101 => 3
[2,4,3,1,5,6] => [3,3] => 100100 => 2
[2,4,3,1,6,5] => [3,1,2] => 100110 => 3
[2,4,3,5,1,6] => [3,3] => 100100 => 2
[2,4,3,5,6,1] => [3,3] => 100100 => 2
[2,4,3,6,1,5] => [3,3] => 100100 => 2
[2,4,3,6,5,1] => [3,2,1] => 100101 => 3
[2,4,5,1,3,6] => [6] => 100000 => 1
[2,4,5,1,6,3] => [4,2] => 100010 => 2
[2,4,5,3,1,6] => [4,2] => 100010 => 2
[2,4,5,3,6,1] => [4,2] => 100010 => 2
[2,4,5,6,1,3] => [6] => 100000 => 1
[2,4,5,6,3,1] => [5,1] => 100001 => 2
[2,4,6,1,3,5] => [6] => 100000 => 1
[2,4,6,1,5,3] => [5,1] => 100001 => 2
[2,4,6,3,1,5] => [4,2] => 100010 => 2
[2,4,6,3,5,1] => [5,1] => 100001 => 2
[2,4,6,5,1,3] => [3,3] => 100100 => 2
[2,4,6,5,3,1] => [3,2,1] => 100101 => 3
[2,5,1,3,4,6] => [6] => 100000 => 1
[2,5,1,3,6,4] => [4,2] => 100010 => 2
[2,5,1,4,3,6] => [4,2] => 100010 => 2
[2,5,1,4,6,3] => [4,2] => 100010 => 2
[2,5,1,6,3,4] => [3,3] => 100100 => 2
[2,5,1,6,4,3] => [3,2,1] => 100101 => 3
[2,5,3,1,4,6] => [3,3] => 100100 => 2
[2,5,3,1,6,4] => [3,1,2] => 100110 => 3
[2,5,3,4,1,6] => [4,2] => 100010 => 2
[2,5,3,4,6,1] => [4,2] => 100010 => 2
[2,5,3,6,1,4] => [3,3] => 100100 => 2
[2,5,3,6,4,1] => [3,2,1] => 100101 => 3
[2,5,4,1,3,6] => [2,4] => 101000 => 2
[2,5,4,1,6,3] => [2,2,2] => 101010 => 3
[2,5,4,3,1,6] => [2,2,2] => 101010 => 3
[2,5,4,3,6,1] => [2,2,2] => 101010 => 3
[2,5,4,6,1,3] => [2,4] => 101000 => 2
[2,5,4,6,3,1] => [2,3,1] => 101001 => 3
[2,5,6,1,3,4] => [6] => 100000 => 1
[2,5,6,1,4,3] => [5,1] => 100001 => 2
[2,5,6,3,1,4] => [4,2] => 100010 => 2
[2,5,6,3,4,1] => [5,1] => 100001 => 2
[2,5,6,4,1,3] => [4,2] => 100010 => 2
[2,5,6,4,3,1] => [4,1,1] => 100011 => 3
[2,6,1,3,4,5] => [6] => 100000 => 1
[2,6,1,3,5,4] => [5,1] => 100001 => 2
[2,6,1,4,3,5] => [4,2] => 100010 => 2
[2,6,1,4,5,3] => [5,1] => 100001 => 2
[2,6,1,5,3,4] => [3,3] => 100100 => 2
[2,6,1,5,4,3] => [3,2,1] => 100101 => 3
[2,6,3,1,4,5] => [3,3] => 100100 => 2
[2,6,3,1,5,4] => [3,2,1] => 100101 => 3
[2,6,3,4,1,5] => [4,2] => 100010 => 2
[2,6,3,4,5,1] => [5,1] => 100001 => 2
[2,6,3,5,1,4] => [3,3] => 100100 => 2
[2,6,3,5,4,1] => [3,2,1] => 100101 => 3
[2,6,4,1,3,5] => [2,4] => 101000 => 2
[2,6,4,1,5,3] => [2,3,1] => 101001 => 3
[2,6,4,3,1,5] => [2,2,2] => 101010 => 3
[2,6,4,3,5,1] => [2,3,1] => 101001 => 3
[2,6,4,5,1,3] => [2,4] => 101000 => 2
[2,6,4,5,3,1] => [2,3,1] => 101001 => 3
[2,6,5,1,3,4] => [2,4] => 101000 => 2
[2,6,5,1,4,3] => [2,3,1] => 101001 => 3
[2,6,5,3,1,4] => [2,2,2] => 101010 => 3
[2,6,5,3,4,1] => [2,3,1] => 101001 => 3
[2,6,5,4,1,3] => [2,2,2] => 101010 => 3
[2,6,5,4,3,1] => [2,2,1,1] => 101011 => 4
[3,1,2,4,5,6] => [6] => 100000 => 1
[3,1,2,4,6,5] => [4,2] => 100010 => 2
[3,1,2,5,4,6] => [3,3] => 100100 => 2
[3,1,2,5,6,4] => [3,3] => 100100 => 2
[3,1,2,6,4,5] => [3,3] => 100100 => 2
[3,1,2,6,5,4] => [3,2,1] => 100101 => 3
[3,1,4,2,5,6] => [2,4] => 101000 => 2
[3,1,4,2,6,5] => [2,2,2] => 101010 => 3
[3,1,4,5,2,6] => [2,4] => 101000 => 2
[3,1,4,5,6,2] => [2,4] => 101000 => 2
[3,1,4,6,2,5] => [2,4] => 101000 => 2
[3,1,4,6,5,2] => [2,3,1] => 101001 => 3
[3,1,5,2,4,6] => [2,4] => 101000 => 2
[3,1,5,2,6,4] => [2,2,2] => 101010 => 3
[3,1,5,4,2,6] => [2,2,2] => 101010 => 3
[3,1,5,4,6,2] => [2,2,2] => 101010 => 3
[3,1,5,6,2,4] => [2,4] => 101000 => 2
[3,1,5,6,4,2] => [2,3,1] => 101001 => 3
[3,1,6,2,4,5] => [2,4] => 101000 => 2
[3,1,6,2,5,4] => [2,3,1] => 101001 => 3
[3,1,6,4,2,5] => [2,2,2] => 101010 => 3
[3,1,6,4,5,2] => [2,3,1] => 101001 => 3
[3,1,6,5,2,4] => [2,1,3] => 101100 => 3
[3,1,6,5,4,2] => [2,1,2,1] => 101101 => 4
[3,2,1,4,5,6] => [2,4] => 101000 => 2
[3,2,1,4,6,5] => [2,2,2] => 101010 => 3
[3,2,1,5,4,6] => [2,1,3] => 101100 => 3
[3,2,1,5,6,4] => [2,1,3] => 101100 => 3
[3,2,1,6,4,5] => [2,1,3] => 101100 => 3
[3,2,1,6,5,4] => [2,1,2,1] => 101101 => 4
[3,2,4,1,5,6] => [2,4] => 101000 => 2
[3,2,4,1,6,5] => [2,2,2] => 101010 => 3
[3,2,4,5,1,6] => [2,4] => 101000 => 2
[3,2,4,5,6,1] => [2,4] => 101000 => 2
[3,2,4,6,1,5] => [2,4] => 101000 => 2
[3,2,4,6,5,1] => [2,3,1] => 101001 => 3
[3,2,5,1,4,6] => [2,4] => 101000 => 2
[3,2,5,1,6,4] => [2,2,2] => 101010 => 3
[3,2,5,4,1,6] => [2,2,2] => 101010 => 3
[3,2,5,4,6,1] => [2,2,2] => 101010 => 3
[3,2,5,6,1,4] => [2,4] => 101000 => 2
[3,2,5,6,4,1] => [2,3,1] => 101001 => 3
[3,2,6,1,4,5] => [2,4] => 101000 => 2
[3,2,6,1,5,4] => [2,3,1] => 101001 => 3
[3,2,6,4,1,5] => [2,2,2] => 101010 => 3
[3,2,6,4,5,1] => [2,3,1] => 101001 => 3
[3,2,6,5,1,4] => [2,1,3] => 101100 => 3
[3,2,6,5,4,1] => [2,1,2,1] => 101101 => 4
[3,4,1,2,5,6] => [6] => 100000 => 1
[3,4,1,2,6,5] => [4,2] => 100010 => 2
[3,4,1,5,2,6] => [3,3] => 100100 => 2
[3,4,1,5,6,2] => [3,3] => 100100 => 2
[3,4,1,6,2,5] => [3,3] => 100100 => 2
[3,4,1,6,5,2] => [3,2,1] => 100101 => 3
[3,4,2,1,5,6] => [3,3] => 100100 => 2
[3,4,2,1,6,5] => [3,1,2] => 100110 => 3
[3,4,2,5,1,6] => [3,3] => 100100 => 2
[3,4,2,5,6,1] => [3,3] => 100100 => 2
[3,4,2,6,1,5] => [3,3] => 100100 => 2
[3,4,2,6,5,1] => [3,2,1] => 100101 => 3
[3,4,5,1,2,6] => [6] => 100000 => 1
[3,4,5,1,6,2] => [4,2] => 100010 => 2
[3,4,5,2,1,6] => [4,2] => 100010 => 2
[3,4,5,2,6,1] => [4,2] => 100010 => 2
[3,4,5,6,1,2] => [6] => 100000 => 1
[3,4,5,6,2,1] => [5,1] => 100001 => 2
[3,4,6,1,2,5] => [6] => 100000 => 1
[3,4,6,1,5,2] => [5,1] => 100001 => 2
[3,4,6,2,1,5] => [4,2] => 100010 => 2
[3,4,6,2,5,1] => [5,1] => 100001 => 2
[3,4,6,5,1,2] => [3,3] => 100100 => 2
[3,4,6,5,2,1] => [3,2,1] => 100101 => 3
[3,5,1,2,4,6] => [6] => 100000 => 1
[3,5,1,2,6,4] => [4,2] => 100010 => 2
[3,5,1,4,2,6] => [4,2] => 100010 => 2
[3,5,1,4,6,2] => [4,2] => 100010 => 2
[3,5,1,6,2,4] => [3,3] => 100100 => 2
[3,5,1,6,4,2] => [3,2,1] => 100101 => 3
[3,5,2,1,4,6] => [3,3] => 100100 => 2
[3,5,2,1,6,4] => [3,1,2] => 100110 => 3
[3,5,2,4,1,6] => [4,2] => 100010 => 2
[3,5,2,4,6,1] => [4,2] => 100010 => 2
[3,5,2,6,1,4] => [3,3] => 100100 => 2
[3,5,2,6,4,1] => [3,2,1] => 100101 => 3
[3,5,4,1,2,6] => [2,4] => 101000 => 2
[3,5,4,1,6,2] => [2,2,2] => 101010 => 3
[3,5,4,2,1,6] => [2,2,2] => 101010 => 3
[3,5,4,2,6,1] => [2,2,2] => 101010 => 3
[3,5,4,6,1,2] => [2,4] => 101000 => 2
[3,5,4,6,2,1] => [2,3,1] => 101001 => 3
[3,5,6,1,2,4] => [6] => 100000 => 1
[3,5,6,1,4,2] => [5,1] => 100001 => 2
[3,5,6,2,1,4] => [4,2] => 100010 => 2
[3,5,6,2,4,1] => [5,1] => 100001 => 2
[3,5,6,4,1,2] => [4,2] => 100010 => 2
[3,5,6,4,2,1] => [4,1,1] => 100011 => 3
[3,6,1,2,4,5] => [6] => 100000 => 1
[3,6,1,2,5,4] => [5,1] => 100001 => 2
[3,6,1,4,2,5] => [4,2] => 100010 => 2
[3,6,1,4,5,2] => [5,1] => 100001 => 2
[3,6,1,5,2,4] => [3,3] => 100100 => 2
[3,6,1,5,4,2] => [3,2,1] => 100101 => 3
[3,6,2,1,4,5] => [3,3] => 100100 => 2
[3,6,2,1,5,4] => [3,2,1] => 100101 => 3
[3,6,2,4,1,5] => [4,2] => 100010 => 2
[3,6,2,4,5,1] => [5,1] => 100001 => 2
[3,6,2,5,1,4] => [3,3] => 100100 => 2
[3,6,2,5,4,1] => [3,2,1] => 100101 => 3
[3,6,4,1,2,5] => [2,4] => 101000 => 2
[3,6,4,1,5,2] => [2,3,1] => 101001 => 3
[3,6,4,2,1,5] => [2,2,2] => 101010 => 3
[3,6,4,2,5,1] => [2,3,1] => 101001 => 3
[3,6,4,5,1,2] => [2,4] => 101000 => 2
[3,6,4,5,2,1] => [2,3,1] => 101001 => 3
[3,6,5,1,2,4] => [2,4] => 101000 => 2
[3,6,5,1,4,2] => [2,3,1] => 101001 => 3
[3,6,5,2,1,4] => [2,2,2] => 101010 => 3
[3,6,5,2,4,1] => [2,3,1] => 101001 => 3
[3,6,5,4,1,2] => [2,2,2] => 101010 => 3
[3,6,5,4,2,1] => [2,2,1,1] => 101011 => 4
[4,1,2,3,5,6] => [6] => 100000 => 1
[4,1,2,3,6,5] => [4,2] => 100010 => 2
[4,1,2,5,3,6] => [3,3] => 100100 => 2
[4,1,2,5,6,3] => [3,3] => 100100 => 2
[4,1,2,6,3,5] => [3,3] => 100100 => 2
[4,1,2,6,5,3] => [3,2,1] => 100101 => 3
[4,1,3,2,5,6] => [3,3] => 100100 => 2
[4,1,3,2,6,5] => [3,1,2] => 100110 => 3
[4,1,3,5,2,6] => [3,3] => 100100 => 2
[4,1,3,5,6,2] => [3,3] => 100100 => 2
[4,1,3,6,2,5] => [3,3] => 100100 => 2
[4,1,3,6,5,2] => [3,2,1] => 100101 => 3
[4,1,5,2,3,6] => [2,4] => 101000 => 2
[4,1,5,2,6,3] => [2,2,2] => 101010 => 3
[4,1,5,3,2,6] => [2,2,2] => 101010 => 3
[4,1,5,3,6,2] => [2,2,2] => 101010 => 3
[4,1,5,6,2,3] => [2,4] => 101000 => 2
[4,1,5,6,3,2] => [2,3,1] => 101001 => 3
[4,1,6,2,3,5] => [2,4] => 101000 => 2
[4,1,6,2,5,3] => [2,3,1] => 101001 => 3
[4,1,6,3,2,5] => [2,2,2] => 101010 => 3
[4,1,6,3,5,2] => [2,3,1] => 101001 => 3
[4,1,6,5,2,3] => [2,1,3] => 101100 => 3
[4,1,6,5,3,2] => [2,1,2,1] => 101101 => 4
[4,2,1,3,5,6] => [2,4] => 101000 => 2
[4,2,1,3,6,5] => [2,2,2] => 101010 => 3
[4,2,1,5,3,6] => [2,1,3] => 101100 => 3
[4,2,1,5,6,3] => [2,1,3] => 101100 => 3
[4,2,1,6,3,5] => [2,1,3] => 101100 => 3
[4,2,1,6,5,3] => [2,1,2,1] => 101101 => 4
[4,2,3,1,5,6] => [3,3] => 100100 => 2
[4,2,3,1,6,5] => [3,1,2] => 100110 => 3
[4,2,3,5,1,6] => [3,3] => 100100 => 2
[4,2,3,5,6,1] => [3,3] => 100100 => 2
[4,2,3,6,1,5] => [3,3] => 100100 => 2
[4,2,3,6,5,1] => [3,2,1] => 100101 => 3
[4,2,5,1,3,6] => [2,4] => 101000 => 2
[4,2,5,1,6,3] => [2,2,2] => 101010 => 3
[4,2,5,3,1,6] => [2,2,2] => 101010 => 3
[4,2,5,3,6,1] => [2,2,2] => 101010 => 3
[4,2,5,6,1,3] => [2,4] => 101000 => 2
[4,2,5,6,3,1] => [2,3,1] => 101001 => 3
[4,2,6,1,3,5] => [2,4] => 101000 => 2
[4,2,6,1,5,3] => [2,3,1] => 101001 => 3
[4,2,6,3,1,5] => [2,2,2] => 101010 => 3
[4,2,6,3,5,1] => [2,3,1] => 101001 => 3
[4,2,6,5,1,3] => [2,1,3] => 101100 => 3
[4,2,6,5,3,1] => [2,1,2,1] => 101101 => 4
[4,3,1,2,5,6] => [1,5] => 110000 => 2
[4,3,1,2,6,5] => [1,3,2] => 110010 => 3
[4,3,1,5,2,6] => [1,2,3] => 110100 => 3
[4,3,1,5,6,2] => [1,2,3] => 110100 => 3
[4,3,1,6,2,5] => [1,2,3] => 110100 => 3
[4,3,1,6,5,2] => [1,2,2,1] => 110101 => 4
[4,3,2,1,5,6] => [1,2,3] => 110100 => 3
[4,3,2,1,6,5] => [1,2,1,2] => 110110 => 4
[4,3,2,5,1,6] => [1,2,3] => 110100 => 3
[4,3,2,5,6,1] => [1,2,3] => 110100 => 3
[4,3,2,6,1,5] => [1,2,3] => 110100 => 3
[4,3,2,6,5,1] => [1,2,2,1] => 110101 => 4
[4,3,5,1,2,6] => [1,5] => 110000 => 2
[4,3,5,1,6,2] => [1,3,2] => 110010 => 3
[4,3,5,2,1,6] => [1,3,2] => 110010 => 3
[4,3,5,2,6,1] => [1,3,2] => 110010 => 3
[4,3,5,6,1,2] => [1,5] => 110000 => 2
[4,3,5,6,2,1] => [1,4,1] => 110001 => 3
[4,3,6,1,2,5] => [1,5] => 110000 => 2
[4,3,6,1,5,2] => [1,4,1] => 110001 => 3
[4,3,6,2,1,5] => [1,3,2] => 110010 => 3
[4,3,6,2,5,1] => [1,4,1] => 110001 => 3
[4,3,6,5,1,2] => [1,2,3] => 110100 => 3
[4,3,6,5,2,1] => [1,2,2,1] => 110101 => 4
[4,5,1,2,3,6] => [6] => 100000 => 1
[4,5,1,2,6,3] => [4,2] => 100010 => 2
[4,5,1,3,2,6] => [4,2] => 100010 => 2
[4,5,1,3,6,2] => [4,2] => 100010 => 2
[4,5,1,6,2,3] => [3,3] => 100100 => 2
[4,5,1,6,3,2] => [3,2,1] => 100101 => 3
[4,5,2,1,3,6] => [3,3] => 100100 => 2
[4,5,2,1,6,3] => [3,1,2] => 100110 => 3
[4,5,2,3,1,6] => [4,2] => 100010 => 2
[4,5,2,3,6,1] => [4,2] => 100010 => 2
[4,5,2,6,1,3] => [3,3] => 100100 => 2
[4,5,2,6,3,1] => [3,2,1] => 100101 => 3
[4,5,3,1,2,6] => [3,3] => 100100 => 2
[4,5,3,1,6,2] => [3,1,2] => 100110 => 3
[4,5,3,2,1,6] => [3,1,2] => 100110 => 3
[4,5,3,2,6,1] => [3,1,2] => 100110 => 3
[4,5,3,6,1,2] => [3,3] => 100100 => 2
[4,5,3,6,2,1] => [3,2,1] => 100101 => 3
[4,5,6,1,2,3] => [6] => 100000 => 1
[4,5,6,1,3,2] => [5,1] => 100001 => 2
[4,5,6,2,1,3] => [4,2] => 100010 => 2
[4,5,6,2,3,1] => [5,1] => 100001 => 2
[4,5,6,3,1,2] => [4,2] => 100010 => 2
[4,5,6,3,2,1] => [4,1,1] => 100011 => 3
[4,6,1,2,3,5] => [6] => 100000 => 1
[4,6,1,2,5,3] => [5,1] => 100001 => 2
[4,6,1,3,2,5] => [4,2] => 100010 => 2
[4,6,1,3,5,2] => [5,1] => 100001 => 2
[4,6,1,5,2,3] => [3,3] => 100100 => 2
[4,6,1,5,3,2] => [3,2,1] => 100101 => 3
[4,6,2,1,3,5] => [3,3] => 100100 => 2
[4,6,2,1,5,3] => [3,2,1] => 100101 => 3
[4,6,2,3,1,5] => [4,2] => 100010 => 2
[4,6,2,3,5,1] => [5,1] => 100001 => 2
[4,6,2,5,1,3] => [3,3] => 100100 => 2
[4,6,2,5,3,1] => [3,2,1] => 100101 => 3
[4,6,3,1,2,5] => [3,3] => 100100 => 2
[4,6,3,1,5,2] => [3,2,1] => 100101 => 3
[4,6,3,2,1,5] => [3,1,2] => 100110 => 3
[4,6,3,2,5,1] => [3,2,1] => 100101 => 3
[4,6,3,5,1,2] => [3,3] => 100100 => 2
[4,6,3,5,2,1] => [3,2,1] => 100101 => 3
[4,6,5,1,2,3] => [2,4] => 101000 => 2
[4,6,5,1,3,2] => [2,3,1] => 101001 => 3
[4,6,5,2,1,3] => [2,2,2] => 101010 => 3
[4,6,5,2,3,1] => [2,3,1] => 101001 => 3
[4,6,5,3,1,2] => [2,2,2] => 101010 => 3
[4,6,5,3,2,1] => [2,2,1,1] => 101011 => 4
[5,1,2,3,4,6] => [6] => 100000 => 1
[5,1,2,3,6,4] => [4,2] => 100010 => 2
[5,1,2,4,3,6] => [4,2] => 100010 => 2
[5,1,2,4,6,3] => [4,2] => 100010 => 2
[5,1,2,6,3,4] => [3,3] => 100100 => 2
[5,1,2,6,4,3] => [3,2,1] => 100101 => 3
[5,1,3,2,4,6] => [3,3] => 100100 => 2
[5,1,3,2,6,4] => [3,1,2] => 100110 => 3
[5,1,3,4,2,6] => [4,2] => 100010 => 2
[5,1,3,4,6,2] => [4,2] => 100010 => 2
[5,1,3,6,2,4] => [3,3] => 100100 => 2
[5,1,3,6,4,2] => [3,2,1] => 100101 => 3
[5,1,4,2,3,6] => [2,4] => 101000 => 2
[5,1,4,2,6,3] => [2,2,2] => 101010 => 3
[5,1,4,3,2,6] => [2,2,2] => 101010 => 3
[5,1,4,3,6,2] => [2,2,2] => 101010 => 3
[5,1,4,6,2,3] => [2,4] => 101000 => 2
[5,1,4,6,3,2] => [2,3,1] => 101001 => 3
[5,1,6,2,3,4] => [2,4] => 101000 => 2
[5,1,6,2,4,3] => [2,3,1] => 101001 => 3
[5,1,6,3,2,4] => [2,2,2] => 101010 => 3
[5,1,6,3,4,2] => [2,3,1] => 101001 => 3
[5,1,6,4,2,3] => [2,2,2] => 101010 => 3
[5,1,6,4,3,2] => [2,2,1,1] => 101011 => 4
[5,2,1,3,4,6] => [2,4] => 101000 => 2
[5,2,1,3,6,4] => [2,2,2] => 101010 => 3
[5,2,1,4,3,6] => [2,2,2] => 101010 => 3
[5,2,1,4,6,3] => [2,2,2] => 101010 => 3
[5,2,1,6,3,4] => [2,1,3] => 101100 => 3
[5,2,1,6,4,3] => [2,1,2,1] => 101101 => 4
[5,2,3,1,4,6] => [3,3] => 100100 => 2
[5,2,3,1,6,4] => [3,1,2] => 100110 => 3
[5,2,3,4,1,6] => [4,2] => 100010 => 2
[5,2,3,4,6,1] => [4,2] => 100010 => 2
[5,2,3,6,1,4] => [3,3] => 100100 => 2
[5,2,3,6,4,1] => [3,2,1] => 100101 => 3
[5,2,4,1,3,6] => [2,4] => 101000 => 2
[5,2,4,1,6,3] => [2,2,2] => 101010 => 3
[5,2,4,3,1,6] => [2,2,2] => 101010 => 3
[5,2,4,3,6,1] => [2,2,2] => 101010 => 3
[5,2,4,6,1,3] => [2,4] => 101000 => 2
[5,2,4,6,3,1] => [2,3,1] => 101001 => 3
[5,2,6,1,3,4] => [2,4] => 101000 => 2
[5,2,6,1,4,3] => [2,3,1] => 101001 => 3
[5,2,6,3,1,4] => [2,2,2] => 101010 => 3
[5,2,6,3,4,1] => [2,3,1] => 101001 => 3
[5,2,6,4,1,3] => [2,2,2] => 101010 => 3
[5,2,6,4,3,1] => [2,2,1,1] => 101011 => 4
[5,3,1,2,4,6] => [1,5] => 110000 => 2
[5,3,1,2,6,4] => [1,3,2] => 110010 => 3
[5,3,1,4,2,6] => [1,3,2] => 110010 => 3
[5,3,1,4,6,2] => [1,3,2] => 110010 => 3
[5,3,1,6,2,4] => [1,2,3] => 110100 => 3
[5,3,1,6,4,2] => [1,2,2,1] => 110101 => 4
[5,3,2,1,4,6] => [1,2,3] => 110100 => 3
[5,3,2,1,6,4] => [1,2,1,2] => 110110 => 4
[5,3,2,4,1,6] => [1,3,2] => 110010 => 3
[5,3,2,4,6,1] => [1,3,2] => 110010 => 3
[5,3,2,6,1,4] => [1,2,3] => 110100 => 3
[5,3,2,6,4,1] => [1,2,2,1] => 110101 => 4
[5,3,4,1,2,6] => [1,5] => 110000 => 2
[5,3,4,1,6,2] => [1,3,2] => 110010 => 3
[5,3,4,2,1,6] => [1,3,2] => 110010 => 3
[5,3,4,2,6,1] => [1,3,2] => 110010 => 3
[5,3,4,6,1,2] => [1,5] => 110000 => 2
[5,3,4,6,2,1] => [1,4,1] => 110001 => 3
[5,3,6,1,2,4] => [1,5] => 110000 => 2
[5,3,6,1,4,2] => [1,4,1] => 110001 => 3
[5,3,6,2,1,4] => [1,3,2] => 110010 => 3
[5,3,6,2,4,1] => [1,4,1] => 110001 => 3
[5,3,6,4,1,2] => [1,3,2] => 110010 => 3
[5,3,6,4,2,1] => [1,3,1,1] => 110011 => 4
[5,4,1,2,3,6] => [1,5] => 110000 => 2
[5,4,1,2,6,3] => [1,3,2] => 110010 => 3
[5,4,1,3,2,6] => [1,3,2] => 110010 => 3
[5,4,1,3,6,2] => [1,3,2] => 110010 => 3
[5,4,1,6,2,3] => [1,2,3] => 110100 => 3
[5,4,1,6,3,2] => [1,2,2,1] => 110101 => 4
[5,4,2,1,3,6] => [1,2,3] => 110100 => 3
[5,4,2,1,6,3] => [1,2,1,2] => 110110 => 4
[5,4,2,3,1,6] => [1,3,2] => 110010 => 3
[5,4,2,3,6,1] => [1,3,2] => 110010 => 3
[5,4,2,6,1,3] => [1,2,3] => 110100 => 3
[5,4,2,6,3,1] => [1,2,2,1] => 110101 => 4
[5,4,3,1,2,6] => [1,2,3] => 110100 => 3
[5,4,3,1,6,2] => [1,2,1,2] => 110110 => 4
[5,4,3,2,1,6] => [1,2,1,2] => 110110 => 4
[5,4,3,2,6,1] => [1,2,1,2] => 110110 => 4
[5,4,3,6,1,2] => [1,2,3] => 110100 => 3
[5,4,3,6,2,1] => [1,2,2,1] => 110101 => 4
[5,4,6,1,2,3] => [1,5] => 110000 => 2
[5,4,6,1,3,2] => [1,4,1] => 110001 => 3
[5,4,6,2,1,3] => [1,3,2] => 110010 => 3
[5,4,6,2,3,1] => [1,4,1] => 110001 => 3
[5,4,6,3,1,2] => [1,3,2] => 110010 => 3
[5,4,6,3,2,1] => [1,3,1,1] => 110011 => 4
[5,6,1,2,3,4] => [6] => 100000 => 1
[5,6,1,2,4,3] => [5,1] => 100001 => 2
[5,6,1,3,2,4] => [4,2] => 100010 => 2
[5,6,1,3,4,2] => [5,1] => 100001 => 2
[5,6,1,4,2,3] => [4,2] => 100010 => 2
[5,6,1,4,3,2] => [4,1,1] => 100011 => 3
[5,6,2,1,3,4] => [3,3] => 100100 => 2
[5,6,2,1,4,3] => [3,2,1] => 100101 => 3
[5,6,2,3,1,4] => [4,2] => 100010 => 2
[5,6,2,3,4,1] => [5,1] => 100001 => 2
[5,6,2,4,1,3] => [4,2] => 100010 => 2
[5,6,2,4,3,1] => [4,1,1] => 100011 => 3
[5,6,3,1,2,4] => [3,3] => 100100 => 2
[5,6,3,1,4,2] => [3,2,1] => 100101 => 3
[5,6,3,2,1,4] => [3,1,2] => 100110 => 3
[5,6,3,2,4,1] => [3,2,1] => 100101 => 3
[5,6,3,4,1,2] => [4,2] => 100010 => 2
[5,6,3,4,2,1] => [4,1,1] => 100011 => 3
[5,6,4,1,2,3] => [2,4] => 101000 => 2
[5,6,4,1,3,2] => [2,3,1] => 101001 => 3
[5,6,4,2,1,3] => [2,2,2] => 101010 => 3
[5,6,4,2,3,1] => [2,3,1] => 101001 => 3
[5,6,4,3,1,2] => [2,2,2] => 101010 => 3
[5,6,4,3,2,1] => [2,2,1,1] => 101011 => 4
[6,1,2,3,4,5] => [6] => 100000 => 1
[6,1,2,3,5,4] => [5,1] => 100001 => 2
[6,1,2,4,3,5] => [4,2] => 100010 => 2
[6,1,2,4,5,3] => [5,1] => 100001 => 2
[6,1,2,5,3,4] => [3,3] => 100100 => 2
[6,1,2,5,4,3] => [3,2,1] => 100101 => 3
[6,1,3,2,4,5] => [3,3] => 100100 => 2
[6,1,3,2,5,4] => [3,2,1] => 100101 => 3
[6,1,3,4,2,5] => [4,2] => 100010 => 2
[6,1,3,4,5,2] => [5,1] => 100001 => 2
[6,1,3,5,2,4] => [3,3] => 100100 => 2
[6,1,3,5,4,2] => [3,2,1] => 100101 => 3
[6,1,4,2,3,5] => [2,4] => 101000 => 2
[6,1,4,2,5,3] => [2,3,1] => 101001 => 3
[6,1,4,3,2,5] => [2,2,2] => 101010 => 3
[6,1,4,3,5,2] => [2,3,1] => 101001 => 3
[6,1,4,5,2,3] => [2,4] => 101000 => 2
[6,1,4,5,3,2] => [2,3,1] => 101001 => 3
[6,1,5,2,3,4] => [2,4] => 101000 => 2
[6,1,5,2,4,3] => [2,3,1] => 101001 => 3
[6,1,5,3,2,4] => [2,2,2] => 101010 => 3
[6,1,5,3,4,2] => [2,3,1] => 101001 => 3
[6,1,5,4,2,3] => [2,2,2] => 101010 => 3
[6,1,5,4,3,2] => [2,2,1,1] => 101011 => 4
[6,2,1,3,4,5] => [2,4] => 101000 => 2
[6,2,1,3,5,4] => [2,3,1] => 101001 => 3
[6,2,1,4,3,5] => [2,2,2] => 101010 => 3
[6,2,1,4,5,3] => [2,3,1] => 101001 => 3
[6,2,1,5,3,4] => [2,1,3] => 101100 => 3
[6,2,1,5,4,3] => [2,1,2,1] => 101101 => 4
[6,2,3,1,4,5] => [3,3] => 100100 => 2
[6,2,3,1,5,4] => [3,2,1] => 100101 => 3
[6,2,3,4,1,5] => [4,2] => 100010 => 2
[6,2,3,4,5,1] => [5,1] => 100001 => 2
[6,2,3,5,1,4] => [3,3] => 100100 => 2
[6,2,3,5,4,1] => [3,2,1] => 100101 => 3
[6,2,4,1,3,5] => [2,4] => 101000 => 2
[6,2,4,1,5,3] => [2,3,1] => 101001 => 3
[6,2,4,3,1,5] => [2,2,2] => 101010 => 3
[6,2,4,3,5,1] => [2,3,1] => 101001 => 3
[6,2,4,5,1,3] => [2,4] => 101000 => 2
[6,2,4,5,3,1] => [2,3,1] => 101001 => 3
[6,2,5,1,3,4] => [2,4] => 101000 => 2
[6,2,5,1,4,3] => [2,3,1] => 101001 => 3
[6,2,5,3,1,4] => [2,2,2] => 101010 => 3
[6,2,5,3,4,1] => [2,3,1] => 101001 => 3
[6,2,5,4,1,3] => [2,2,2] => 101010 => 3
[6,2,5,4,3,1] => [2,2,1,1] => 101011 => 4
[6,3,1,2,4,5] => [1,5] => 110000 => 2
[6,3,1,2,5,4] => [1,4,1] => 110001 => 3
[6,3,1,4,2,5] => [1,3,2] => 110010 => 3
[6,3,1,4,5,2] => [1,4,1] => 110001 => 3
[6,3,1,5,2,4] => [1,2,3] => 110100 => 3
[6,3,1,5,4,2] => [1,2,2,1] => 110101 => 4
[6,3,2,1,4,5] => [1,2,3] => 110100 => 3
[6,3,2,1,5,4] => [1,2,2,1] => 110101 => 4
[6,3,2,4,1,5] => [1,3,2] => 110010 => 3
[6,3,2,4,5,1] => [1,4,1] => 110001 => 3
[6,3,2,5,1,4] => [1,2,3] => 110100 => 3
[6,3,2,5,4,1] => [1,2,2,1] => 110101 => 4
[6,3,4,1,2,5] => [1,5] => 110000 => 2
[6,3,4,1,5,2] => [1,4,1] => 110001 => 3
[6,3,4,2,1,5] => [1,3,2] => 110010 => 3
[6,3,4,2,5,1] => [1,4,1] => 110001 => 3
[6,3,4,5,1,2] => [1,5] => 110000 => 2
[6,3,4,5,2,1] => [1,4,1] => 110001 => 3
[6,3,5,1,2,4] => [1,5] => 110000 => 2
[6,3,5,1,4,2] => [1,4,1] => 110001 => 3
[6,3,5,2,1,4] => [1,3,2] => 110010 => 3
[6,3,5,2,4,1] => [1,4,1] => 110001 => 3
[6,3,5,4,1,2] => [1,3,2] => 110010 => 3
[6,3,5,4,2,1] => [1,3,1,1] => 110011 => 4
[6,4,1,2,3,5] => [1,5] => 110000 => 2
[6,4,1,2,5,3] => [1,4,1] => 110001 => 3
[6,4,1,3,2,5] => [1,3,2] => 110010 => 3
[6,4,1,3,5,2] => [1,4,1] => 110001 => 3
[6,4,1,5,2,3] => [1,2,3] => 110100 => 3
[6,4,1,5,3,2] => [1,2,2,1] => 110101 => 4
[6,4,2,1,3,5] => [1,2,3] => 110100 => 3
[6,4,2,1,5,3] => [1,2,2,1] => 110101 => 4
[6,4,2,3,1,5] => [1,3,2] => 110010 => 3
[6,4,2,3,5,1] => [1,4,1] => 110001 => 3
[6,4,2,5,1,3] => [1,2,3] => 110100 => 3
[6,4,2,5,3,1] => [1,2,2,1] => 110101 => 4
[6,4,3,1,2,5] => [1,2,3] => 110100 => 3
[6,4,3,1,5,2] => [1,2,2,1] => 110101 => 4
[6,4,3,2,1,5] => [1,2,1,2] => 110110 => 4
[6,4,3,2,5,1] => [1,2,2,1] => 110101 => 4
[6,4,3,5,1,2] => [1,2,3] => 110100 => 3
[6,4,3,5,2,1] => [1,2,2,1] => 110101 => 4
[6,4,5,1,2,3] => [1,5] => 110000 => 2
[6,4,5,1,3,2] => [1,4,1] => 110001 => 3
[6,4,5,2,1,3] => [1,3,2] => 110010 => 3
[6,4,5,2,3,1] => [1,4,1] => 110001 => 3
[6,4,5,3,1,2] => [1,3,2] => 110010 => 3
[6,4,5,3,2,1] => [1,3,1,1] => 110011 => 4
[6,5,1,2,3,4] => [1,5] => 110000 => 2
[6,5,1,2,4,3] => [1,4,1] => 110001 => 3
[6,5,1,3,2,4] => [1,3,2] => 110010 => 3
[6,5,1,3,4,2] => [1,4,1] => 110001 => 3
[6,5,1,4,2,3] => [1,3,2] => 110010 => 3
[6,5,1,4,3,2] => [1,3,1,1] => 110011 => 4
[6,5,2,1,3,4] => [1,2,3] => 110100 => 3
[6,5,2,1,4,3] => [1,2,2,1] => 110101 => 4
[6,5,2,3,1,4] => [1,3,2] => 110010 => 3
[6,5,2,3,4,1] => [1,4,1] => 110001 => 3
[6,5,2,4,1,3] => [1,3,2] => 110010 => 3
[6,5,2,4,3,1] => [1,3,1,1] => 110011 => 4
[6,5,3,1,2,4] => [1,2,3] => 110100 => 3
[6,5,3,1,4,2] => [1,2,2,1] => 110101 => 4
[6,5,3,2,1,4] => [1,2,1,2] => 110110 => 4
[6,5,3,2,4,1] => [1,2,2,1] => 110101 => 4
[6,5,3,4,1,2] => [1,3,2] => 110010 => 3
[6,5,3,4,2,1] => [1,3,1,1] => 110011 => 4
[6,5,4,1,2,3] => [1,1,4] => 111000 => 3
[6,5,4,1,3,2] => [1,1,3,1] => 111001 => 4
[6,5,4,2,1,3] => [1,1,2,2] => 111010 => 4
[6,5,4,2,3,1] => [1,1,3,1] => 111001 => 4
[6,5,4,3,1,2] => [1,1,2,2] => 111010 => 4
[6,5,4,3,2,1] => [1,1,2,1,1] => 111011 => 5
[1,2,3,4,5,6,7] => [7] => 1000000 => 1
[1,2,3,4,5,7,6] => [5,2] => 1000010 => 2
[1,2,3,4,6,5,7] => [4,3] => 1000100 => 2
[1,2,3,4,6,7,5] => [4,3] => 1000100 => 2
[1,2,3,4,7,5,6] => [4,3] => 1000100 => 2
[1,2,3,4,7,6,5] => [4,2,1] => 1000101 => 3
[1,2,3,5,4,6,7] => [3,4] => 1001000 => 2
[1,2,3,5,4,7,6] => [3,2,2] => 1001010 => 3
[1,2,3,5,6,4,7] => [3,4] => 1001000 => 2
[1,2,3,5,6,7,4] => [3,4] => 1001000 => 2
[1,2,3,5,7,4,6] => [3,4] => 1001000 => 2
[1,2,3,5,7,6,4] => [3,3,1] => 1001001 => 3
[1,2,3,6,4,5,7] => [3,4] => 1001000 => 2
[1,2,3,6,4,7,5] => [3,2,2] => 1001010 => 3
[1,2,3,6,5,4,7] => [3,2,2] => 1001010 => 3
[1,2,3,6,5,7,4] => [3,2,2] => 1001010 => 3
[1,2,3,6,7,4,5] => [3,4] => 1001000 => 2
[1,2,3,6,7,5,4] => [3,3,1] => 1001001 => 3
[1,2,3,7,4,5,6] => [3,4] => 1001000 => 2
[1,2,3,7,4,6,5] => [3,3,1] => 1001001 => 3
[1,2,3,7,5,4,6] => [3,2,2] => 1001010 => 3
[1,2,3,7,5,6,4] => [3,3,1] => 1001001 => 3
[1,2,3,7,6,4,5] => [3,1,3] => 1001100 => 3
[1,2,3,7,6,5,4] => [3,1,2,1] => 1001101 => 4
[1,2,4,3,5,6,7] => [2,5] => 1010000 => 2
[1,2,4,3,5,7,6] => [2,3,2] => 1010010 => 3
[1,2,4,3,6,5,7] => [2,2,3] => 1010100 => 3
[1,2,4,3,6,7,5] => [2,2,3] => 1010100 => 3
[1,2,4,3,7,5,6] => [2,2,3] => 1010100 => 3
[1,2,4,3,7,6,5] => [2,2,2,1] => 1010101 => 4
[1,2,4,5,3,6,7] => [2,5] => 1010000 => 2
[1,2,4,5,3,7,6] => [2,3,2] => 1010010 => 3
[1,2,4,5,6,3,7] => [2,5] => 1010000 => 2
[1,2,4,5,6,7,3] => [2,5] => 1010000 => 2
[1,2,4,5,7,3,6] => [2,5] => 1010000 => 2
[1,2,4,5,7,6,3] => [2,4,1] => 1010001 => 3
[1,2,4,6,3,5,7] => [2,5] => 1010000 => 2
[1,2,4,6,3,7,5] => [2,3,2] => 1010010 => 3
[1,2,4,6,5,3,7] => [2,3,2] => 1010010 => 3
[1,2,4,6,5,7,3] => [2,3,2] => 1010010 => 3
[1,2,4,6,7,3,5] => [2,5] => 1010000 => 2
[1,2,4,6,7,5,3] => [2,4,1] => 1010001 => 3
[1,2,4,7,3,5,6] => [2,5] => 1010000 => 2
[1,2,4,7,3,6,5] => [2,4,1] => 1010001 => 3
[1,2,4,7,5,3,6] => [2,3,2] => 1010010 => 3
[1,2,4,7,5,6,3] => [2,4,1] => 1010001 => 3
[1,2,4,7,6,3,5] => [2,2,3] => 1010100 => 3
[1,2,4,7,6,5,3] => [2,2,2,1] => 1010101 => 4
[1,2,5,3,4,6,7] => [2,5] => 1010000 => 2
[1,2,5,3,4,7,6] => [2,3,2] => 1010010 => 3
[1,2,5,3,6,4,7] => [2,2,3] => 1010100 => 3
[1,2,5,3,6,7,4] => [2,2,3] => 1010100 => 3
[1,2,5,3,7,4,6] => [2,2,3] => 1010100 => 3
[1,2,5,3,7,6,4] => [2,2,2,1] => 1010101 => 4
[1,2,5,4,3,6,7] => [2,2,3] => 1010100 => 3
[1,2,5,4,3,7,6] => [2,2,1,2] => 1010110 => 4
[1,2,5,4,6,3,7] => [2,2,3] => 1010100 => 3
[1,2,5,4,6,7,3] => [2,2,3] => 1010100 => 3
[1,2,5,4,7,3,6] => [2,2,3] => 1010100 => 3
[1,2,5,4,7,6,3] => [2,2,2,1] => 1010101 => 4
[1,2,5,6,3,4,7] => [2,5] => 1010000 => 2
[1,2,5,6,3,7,4] => [2,3,2] => 1010010 => 3
[1,2,5,6,4,3,7] => [2,3,2] => 1010010 => 3
[1,2,5,6,4,7,3] => [2,3,2] => 1010010 => 3
[1,2,5,6,7,3,4] => [2,5] => 1010000 => 2
[1,2,5,6,7,4,3] => [2,4,1] => 1010001 => 3
[1,2,5,7,3,4,6] => [2,5] => 1010000 => 2
[1,2,5,7,3,6,4] => [2,4,1] => 1010001 => 3
[1,2,5,7,4,3,6] => [2,3,2] => 1010010 => 3
[1,2,5,7,4,6,3] => [2,4,1] => 1010001 => 3
[1,2,5,7,6,3,4] => [2,2,3] => 1010100 => 3
[1,2,5,7,6,4,3] => [2,2,2,1] => 1010101 => 4
[1,2,6,3,4,5,7] => [2,5] => 1010000 => 2
[1,2,6,3,4,7,5] => [2,3,2] => 1010010 => 3
[1,2,6,3,5,4,7] => [2,3,2] => 1010010 => 3
[1,2,6,3,5,7,4] => [2,3,2] => 1010010 => 3
[1,2,6,3,7,4,5] => [2,2,3] => 1010100 => 3
[1,2,6,3,7,5,4] => [2,2,2,1] => 1010101 => 4
[1,2,6,4,3,5,7] => [2,2,3] => 1010100 => 3
[1,2,6,4,3,7,5] => [2,2,1,2] => 1010110 => 4
[1,2,6,4,5,3,7] => [2,3,2] => 1010010 => 3
[1,2,6,4,5,7,3] => [2,3,2] => 1010010 => 3
[1,2,6,4,7,3,5] => [2,2,3] => 1010100 => 3
[1,2,6,4,7,5,3] => [2,2,2,1] => 1010101 => 4
[1,2,6,5,3,4,7] => [2,1,4] => 1011000 => 3
[1,2,6,5,3,7,4] => [2,1,2,2] => 1011010 => 4
[1,2,6,5,4,3,7] => [2,1,2,2] => 1011010 => 4
[1,2,6,5,4,7,3] => [2,1,2,2] => 1011010 => 4
[1,2,6,5,7,3,4] => [2,1,4] => 1011000 => 3
[1,2,6,5,7,4,3] => [2,1,3,1] => 1011001 => 4
[1,2,6,7,3,4,5] => [2,5] => 1010000 => 2
[1,2,6,7,3,5,4] => [2,4,1] => 1010001 => 3
[1,2,6,7,4,3,5] => [2,3,2] => 1010010 => 3
[1,2,6,7,4,5,3] => [2,4,1] => 1010001 => 3
[1,2,6,7,5,3,4] => [2,3,2] => 1010010 => 3
[1,2,6,7,5,4,3] => [2,3,1,1] => 1010011 => 4
[1,2,7,3,4,5,6] => [2,5] => 1010000 => 2
[1,2,7,3,4,6,5] => [2,4,1] => 1010001 => 3
[1,2,7,3,5,4,6] => [2,3,2] => 1010010 => 3
[1,2,7,3,5,6,4] => [2,4,1] => 1010001 => 3
[1,2,7,3,6,4,5] => [2,2,3] => 1010100 => 3
[1,2,7,3,6,5,4] => [2,2,2,1] => 1010101 => 4
[1,2,7,4,3,5,6] => [2,2,3] => 1010100 => 3
[1,2,7,4,3,6,5] => [2,2,2,1] => 1010101 => 4
[1,2,7,4,5,3,6] => [2,3,2] => 1010010 => 3
[1,2,7,4,5,6,3] => [2,4,1] => 1010001 => 3
[1,2,7,4,6,3,5] => [2,2,3] => 1010100 => 3
[1,2,7,4,6,5,3] => [2,2,2,1] => 1010101 => 4
[1,2,7,5,3,4,6] => [2,1,4] => 1011000 => 3
[1,2,7,5,3,6,4] => [2,1,3,1] => 1011001 => 4
[1,2,7,5,4,3,6] => [2,1,2,2] => 1011010 => 4
[1,2,7,5,4,6,3] => [2,1,3,1] => 1011001 => 4
[1,2,7,5,6,3,4] => [2,1,4] => 1011000 => 3
[1,2,7,5,6,4,3] => [2,1,3,1] => 1011001 => 4
[1,2,7,6,3,4,5] => [2,1,4] => 1011000 => 3
[1,2,7,6,3,5,4] => [2,1,3,1] => 1011001 => 4
[1,2,7,6,4,3,5] => [2,1,2,2] => 1011010 => 4
[1,2,7,6,4,5,3] => [2,1,3,1] => 1011001 => 4
[1,2,7,6,5,3,4] => [2,1,2,2] => 1011010 => 4
[1,2,7,6,5,4,3] => [2,1,2,1,1] => 1011011 => 5
[1,3,2,4,5,6,7] => [1,6] => 1100000 => 2
[1,3,2,4,5,7,6] => [1,4,2] => 1100010 => 3
[1,3,2,4,6,5,7] => [1,3,3] => 1100100 => 3
[1,3,2,4,6,7,5] => [1,3,3] => 1100100 => 3
[1,3,2,4,7,5,6] => [1,3,3] => 1100100 => 3
[1,3,2,4,7,6,5] => [1,3,2,1] => 1100101 => 4
[1,3,2,5,4,6,7] => [1,2,4] => 1101000 => 3
[1,3,2,5,4,7,6] => [1,2,2,2] => 1101010 => 4
[1,3,2,5,6,4,7] => [1,2,4] => 1101000 => 3
[1,3,2,5,6,7,4] => [1,2,4] => 1101000 => 3
[1,3,2,5,7,4,6] => [1,2,4] => 1101000 => 3
[1,3,2,5,7,6,4] => [1,2,3,1] => 1101001 => 4
[1,3,2,6,4,5,7] => [1,2,4] => 1101000 => 3
[1,3,2,6,4,7,5] => [1,2,2,2] => 1101010 => 4
[1,3,2,6,5,4,7] => [1,2,2,2] => 1101010 => 4
[1,3,2,6,5,7,4] => [1,2,2,2] => 1101010 => 4
[1,3,2,6,7,4,5] => [1,2,4] => 1101000 => 3
[1,3,2,6,7,5,4] => [1,2,3,1] => 1101001 => 4
[1,3,2,7,4,5,6] => [1,2,4] => 1101000 => 3
[1,3,2,7,4,6,5] => [1,2,3,1] => 1101001 => 4
[1,3,2,7,5,4,6] => [1,2,2,2] => 1101010 => 4
[1,3,2,7,5,6,4] => [1,2,3,1] => 1101001 => 4
[1,3,2,7,6,4,5] => [1,2,1,3] => 1101100 => 4
[1,3,2,7,6,5,4] => [1,2,1,2,1] => 1101101 => 5
[1,3,4,2,5,6,7] => [1,6] => 1100000 => 2
[1,3,4,2,5,7,6] => [1,4,2] => 1100010 => 3
[1,3,4,2,6,5,7] => [1,3,3] => 1100100 => 3
[1,3,4,2,6,7,5] => [1,3,3] => 1100100 => 3
[1,3,4,2,7,5,6] => [1,3,3] => 1100100 => 3
[1,3,4,2,7,6,5] => [1,3,2,1] => 1100101 => 4
[1,3,4,5,2,6,7] => [1,6] => 1100000 => 2
[1,3,4,5,2,7,6] => [1,4,2] => 1100010 => 3
[1,3,4,5,6,2,7] => [1,6] => 1100000 => 2
[1,3,4,5,6,7,2] => [1,6] => 1100000 => 2
[1,3,4,5,7,2,6] => [1,6] => 1100000 => 2
[1,3,4,5,7,6,2] => [1,5,1] => 1100001 => 3
[1,3,4,6,2,5,7] => [1,6] => 1100000 => 2
[1,3,4,6,2,7,5] => [1,4,2] => 1100010 => 3
[1,3,4,6,5,2,7] => [1,4,2] => 1100010 => 3
[1,3,4,6,5,7,2] => [1,4,2] => 1100010 => 3
[1,3,4,6,7,2,5] => [1,6] => 1100000 => 2
[1,3,4,6,7,5,2] => [1,5,1] => 1100001 => 3
[1,3,4,7,2,5,6] => [1,6] => 1100000 => 2
[1,3,4,7,2,6,5] => [1,5,1] => 1100001 => 3
[1,3,4,7,5,2,6] => [1,4,2] => 1100010 => 3
[1,3,4,7,5,6,2] => [1,5,1] => 1100001 => 3
[1,3,4,7,6,2,5] => [1,3,3] => 1100100 => 3
[1,3,4,7,6,5,2] => [1,3,2,1] => 1100101 => 4
[1,3,5,2,4,6,7] => [1,6] => 1100000 => 2
[1,3,5,2,4,7,6] => [1,4,2] => 1100010 => 3
[1,3,5,2,6,4,7] => [1,3,3] => 1100100 => 3
[1,3,5,2,6,7,4] => [1,3,3] => 1100100 => 3
[1,3,5,2,7,4,6] => [1,3,3] => 1100100 => 3
[1,3,5,2,7,6,4] => [1,3,2,1] => 1100101 => 4
[1,3,5,4,2,6,7] => [1,3,3] => 1100100 => 3
[1,3,5,4,2,7,6] => [1,3,1,2] => 1100110 => 4
[1,3,5,4,6,2,7] => [1,3,3] => 1100100 => 3
[1,3,5,4,6,7,2] => [1,3,3] => 1100100 => 3
[1,3,5,4,7,2,6] => [1,3,3] => 1100100 => 3
[1,3,5,4,7,6,2] => [1,3,2,1] => 1100101 => 4
[1,3,5,6,2,4,7] => [1,6] => 1100000 => 2
[1,3,5,6,2,7,4] => [1,4,2] => 1100010 => 3
[1,3,5,6,4,2,7] => [1,4,2] => 1100010 => 3
[1,3,5,6,4,7,2] => [1,4,2] => 1100010 => 3
[1,3,5,6,7,2,4] => [1,6] => 1100000 => 2
[1,3,5,6,7,4,2] => [1,5,1] => 1100001 => 3
[1,3,5,7,2,4,6] => [1,6] => 1100000 => 2
[1,3,5,7,2,6,4] => [1,5,1] => 1100001 => 3
[1,3,5,7,4,2,6] => [1,4,2] => 1100010 => 3
[1,3,5,7,4,6,2] => [1,5,1] => 1100001 => 3
[1,3,5,7,6,2,4] => [1,3,3] => 1100100 => 3
[1,3,5,7,6,4,2] => [1,3,2,1] => 1100101 => 4
[1,3,6,2,4,5,7] => [1,6] => 1100000 => 2
[1,3,6,2,4,7,5] => [1,4,2] => 1100010 => 3
[1,3,6,2,5,4,7] => [1,4,2] => 1100010 => 3
[1,3,6,2,5,7,4] => [1,4,2] => 1100010 => 3
[1,3,6,2,7,4,5] => [1,3,3] => 1100100 => 3
[1,3,6,2,7,5,4] => [1,3,2,1] => 1100101 => 4
[1,3,6,4,2,5,7] => [1,3,3] => 1100100 => 3
[1,3,6,4,2,7,5] => [1,3,1,2] => 1100110 => 4
[1,3,6,4,5,2,7] => [1,4,2] => 1100010 => 3
[1,3,6,4,5,7,2] => [1,4,2] => 1100010 => 3
[1,3,6,4,7,2,5] => [1,3,3] => 1100100 => 3
[1,3,6,4,7,5,2] => [1,3,2,1] => 1100101 => 4
[1,3,6,5,2,4,7] => [1,2,4] => 1101000 => 3
[1,3,6,5,2,7,4] => [1,2,2,2] => 1101010 => 4
[1,3,6,5,4,2,7] => [1,2,2,2] => 1101010 => 4
[1,3,6,5,4,7,2] => [1,2,2,2] => 1101010 => 4
[1,3,6,5,7,2,4] => [1,2,4] => 1101000 => 3
[1,3,6,5,7,4,2] => [1,2,3,1] => 1101001 => 4
[1,3,6,7,2,4,5] => [1,6] => 1100000 => 2
[1,3,6,7,2,5,4] => [1,5,1] => 1100001 => 3
[1,3,6,7,4,2,5] => [1,4,2] => 1100010 => 3
[1,3,6,7,4,5,2] => [1,5,1] => 1100001 => 3
[1,3,6,7,5,2,4] => [1,4,2] => 1100010 => 3
[1,3,6,7,5,4,2] => [1,4,1,1] => 1100011 => 4
[1,3,7,2,4,5,6] => [1,6] => 1100000 => 2
[1,3,7,2,4,6,5] => [1,5,1] => 1100001 => 3
[1,3,7,2,5,4,6] => [1,4,2] => 1100010 => 3
[1,3,7,2,5,6,4] => [1,5,1] => 1100001 => 3
[1,3,7,2,6,4,5] => [1,3,3] => 1100100 => 3
[1,3,7,2,6,5,4] => [1,3,2,1] => 1100101 => 4
[1,3,7,4,2,5,6] => [1,3,3] => 1100100 => 3
[1,3,7,4,2,6,5] => [1,3,2,1] => 1100101 => 4
[1,3,7,4,5,2,6] => [1,4,2] => 1100010 => 3
[1,3,7,4,5,6,2] => [1,5,1] => 1100001 => 3
[1,3,7,4,6,2,5] => [1,3,3] => 1100100 => 3
[1,3,7,4,6,5,2] => [1,3,2,1] => 1100101 => 4
[1,3,7,5,2,4,6] => [1,2,4] => 1101000 => 3
[1,3,7,5,2,6,4] => [1,2,3,1] => 1101001 => 4
[1,3,7,5,4,2,6] => [1,2,2,2] => 1101010 => 4
[1,3,7,5,4,6,2] => [1,2,3,1] => 1101001 => 4
[1,3,7,5,6,2,4] => [1,2,4] => 1101000 => 3
[1,3,7,5,6,4,2] => [1,2,3,1] => 1101001 => 4
[1,3,7,6,2,4,5] => [1,2,4] => 1101000 => 3
[1,3,7,6,2,5,4] => [1,2,3,1] => 1101001 => 4
[1,3,7,6,4,2,5] => [1,2,2,2] => 1101010 => 4
[1,3,7,6,4,5,2] => [1,2,3,1] => 1101001 => 4
[1,3,7,6,5,2,4] => [1,2,2,2] => 1101010 => 4
[1,3,7,6,5,4,2] => [1,2,2,1,1] => 1101011 => 5
[1,4,2,3,5,6,7] => [1,6] => 1100000 => 2
[1,4,2,3,5,7,6] => [1,4,2] => 1100010 => 3
[1,4,2,3,6,5,7] => [1,3,3] => 1100100 => 3
[1,4,2,3,6,7,5] => [1,3,3] => 1100100 => 3
[1,4,2,3,7,5,6] => [1,3,3] => 1100100 => 3
[1,4,2,3,7,6,5] => [1,3,2,1] => 1100101 => 4
[1,4,2,5,3,6,7] => [1,2,4] => 1101000 => 3
[1,4,2,5,3,7,6] => [1,2,2,2] => 1101010 => 4
[1,4,2,5,6,3,7] => [1,2,4] => 1101000 => 3
[1,4,2,5,6,7,3] => [1,2,4] => 1101000 => 3
[1,4,2,5,7,3,6] => [1,2,4] => 1101000 => 3
[1,4,2,5,7,6,3] => [1,2,3,1] => 1101001 => 4
[1,4,2,6,3,5,7] => [1,2,4] => 1101000 => 3
[1,4,2,6,3,7,5] => [1,2,2,2] => 1101010 => 4
[1,4,2,6,5,3,7] => [1,2,2,2] => 1101010 => 4
[1,4,2,6,5,7,3] => [1,2,2,2] => 1101010 => 4
[1,4,2,6,7,3,5] => [1,2,4] => 1101000 => 3
[1,4,2,6,7,5,3] => [1,2,3,1] => 1101001 => 4
[1,4,2,7,3,5,6] => [1,2,4] => 1101000 => 3
[1,4,2,7,3,6,5] => [1,2,3,1] => 1101001 => 4
[1,4,2,7,5,3,6] => [1,2,2,2] => 1101010 => 4
[1,4,2,7,5,6,3] => [1,2,3,1] => 1101001 => 4
[1,4,2,7,6,3,5] => [1,2,1,3] => 1101100 => 4
[1,4,2,7,6,5,3] => [1,2,1,2,1] => 1101101 => 5
[1,4,3,2,5,6,7] => [1,2,4] => 1101000 => 3
[1,4,3,2,5,7,6] => [1,2,2,2] => 1101010 => 4
[1,4,3,2,6,5,7] => [1,2,1,3] => 1101100 => 4
[1,4,3,2,6,7,5] => [1,2,1,3] => 1101100 => 4
[1,4,3,2,7,5,6] => [1,2,1,3] => 1101100 => 4
[1,4,3,2,7,6,5] => [1,2,1,2,1] => 1101101 => 5
[1,4,3,5,2,6,7] => [1,2,4] => 1101000 => 3
[1,4,3,5,2,7,6] => [1,2,2,2] => 1101010 => 4
[1,4,3,5,6,2,7] => [1,2,4] => 1101000 => 3
[1,4,3,5,6,7,2] => [1,2,4] => 1101000 => 3
[1,4,3,5,7,2,6] => [1,2,4] => 1101000 => 3
[1,4,3,5,7,6,2] => [1,2,3,1] => 1101001 => 4
[1,4,3,6,2,5,7] => [1,2,4] => 1101000 => 3
[1,4,3,6,2,7,5] => [1,2,2,2] => 1101010 => 4
[1,4,3,6,5,2,7] => [1,2,2,2] => 1101010 => 4
[1,4,3,6,5,7,2] => [1,2,2,2] => 1101010 => 4
[1,4,3,6,7,2,5] => [1,2,4] => 1101000 => 3
[1,4,3,6,7,5,2] => [1,2,3,1] => 1101001 => 4
[1,4,3,7,2,5,6] => [1,2,4] => 1101000 => 3
[1,4,3,7,2,6,5] => [1,2,3,1] => 1101001 => 4
[1,4,3,7,5,2,6] => [1,2,2,2] => 1101010 => 4
[1,4,3,7,5,6,2] => [1,2,3,1] => 1101001 => 4
[1,4,3,7,6,2,5] => [1,2,1,3] => 1101100 => 4
[1,4,3,7,6,5,2] => [1,2,1,2,1] => 1101101 => 5
[1,4,5,2,3,6,7] => [1,6] => 1100000 => 2
[1,4,5,2,3,7,6] => [1,4,2] => 1100010 => 3
[1,4,5,2,6,3,7] => [1,3,3] => 1100100 => 3
[1,4,5,2,6,7,3] => [1,3,3] => 1100100 => 3
[1,4,5,2,7,3,6] => [1,3,3] => 1100100 => 3
[1,4,5,2,7,6,3] => [1,3,2,1] => 1100101 => 4
[1,4,5,3,2,6,7] => [1,3,3] => 1100100 => 3
[1,4,5,3,2,7,6] => [1,3,1,2] => 1100110 => 4
[1,4,5,3,6,2,7] => [1,3,3] => 1100100 => 3
[1,4,5,3,6,7,2] => [1,3,3] => 1100100 => 3
[1,4,5,3,7,2,6] => [1,3,3] => 1100100 => 3
[1,4,5,3,7,6,2] => [1,3,2,1] => 1100101 => 4
[1,4,5,6,2,3,7] => [1,6] => 1100000 => 2
[1,4,5,6,2,7,3] => [1,4,2] => 1100010 => 3
[1,4,5,6,3,2,7] => [1,4,2] => 1100010 => 3
[1,4,5,6,3,7,2] => [1,4,2] => 1100010 => 3
[1,4,5,6,7,2,3] => [1,6] => 1100000 => 2
[1,4,5,6,7,3,2] => [1,5,1] => 1100001 => 3
[1,4,5,7,2,3,6] => [1,6] => 1100000 => 2
[1,4,5,7,2,6,3] => [1,5,1] => 1100001 => 3
[1,4,5,7,3,2,6] => [1,4,2] => 1100010 => 3
[1,4,5,7,3,6,2] => [1,5,1] => 1100001 => 3
[1,4,5,7,6,2,3] => [1,3,3] => 1100100 => 3
[1,4,5,7,6,3,2] => [1,3,2,1] => 1100101 => 4
[1,4,6,2,3,5,7] => [1,6] => 1100000 => 2
[1,4,6,2,3,7,5] => [1,4,2] => 1100010 => 3
[1,4,6,2,5,3,7] => [1,4,2] => 1100010 => 3
[1,4,6,2,5,7,3] => [1,4,2] => 1100010 => 3
[1,4,6,2,7,3,5] => [1,3,3] => 1100100 => 3
[1,4,6,2,7,5,3] => [1,3,2,1] => 1100101 => 4
[1,4,6,3,2,5,7] => [1,3,3] => 1100100 => 3
[1,4,6,3,2,7,5] => [1,3,1,2] => 1100110 => 4
[1,4,6,3,5,2,7] => [1,4,2] => 1100010 => 3
[1,4,6,3,5,7,2] => [1,4,2] => 1100010 => 3
[1,4,6,3,7,2,5] => [1,3,3] => 1100100 => 3
[1,4,6,3,7,5,2] => [1,3,2,1] => 1100101 => 4
[1,4,6,5,2,3,7] => [1,2,4] => 1101000 => 3
[1,4,6,5,2,7,3] => [1,2,2,2] => 1101010 => 4
[1,4,6,5,3,2,7] => [1,2,2,2] => 1101010 => 4
[1,4,6,5,3,7,2] => [1,2,2,2] => 1101010 => 4
[1,4,6,5,7,2,3] => [1,2,4] => 1101000 => 3
[1,4,6,5,7,3,2] => [1,2,3,1] => 1101001 => 4
[1,4,6,7,2,3,5] => [1,6] => 1100000 => 2
[1,4,6,7,2,5,3] => [1,5,1] => 1100001 => 3
[1,4,6,7,3,2,5] => [1,4,2] => 1100010 => 3
[1,4,6,7,3,5,2] => [1,5,1] => 1100001 => 3
[1,4,6,7,5,2,3] => [1,4,2] => 1100010 => 3
[1,4,6,7,5,3,2] => [1,4,1,1] => 1100011 => 4
[1,4,7,2,3,5,6] => [1,6] => 1100000 => 2
[1,4,7,2,3,6,5] => [1,5,1] => 1100001 => 3
[1,4,7,2,5,3,6] => [1,4,2] => 1100010 => 3
[1,4,7,2,5,6,3] => [1,5,1] => 1100001 => 3
[1,4,7,2,6,3,5] => [1,3,3] => 1100100 => 3
[1,4,7,2,6,5,3] => [1,3,2,1] => 1100101 => 4
[1,4,7,3,2,5,6] => [1,3,3] => 1100100 => 3
[1,4,7,3,2,6,5] => [1,3,2,1] => 1100101 => 4
[1,4,7,3,5,2,6] => [1,4,2] => 1100010 => 3
[1,4,7,3,5,6,2] => [1,5,1] => 1100001 => 3
[1,4,7,3,6,2,5] => [1,3,3] => 1100100 => 3
[1,4,7,3,6,5,2] => [1,3,2,1] => 1100101 => 4
[1,4,7,5,2,3,6] => [1,2,4] => 1101000 => 3
[1,4,7,5,2,6,3] => [1,2,3,1] => 1101001 => 4
[1,4,7,5,3,2,6] => [1,2,2,2] => 1101010 => 4
[1,4,7,5,3,6,2] => [1,2,3,1] => 1101001 => 4
[1,4,7,5,6,2,3] => [1,2,4] => 1101000 => 3
[1,4,7,5,6,3,2] => [1,2,3,1] => 1101001 => 4
[1,4,7,6,2,3,5] => [1,2,4] => 1101000 => 3
[1,4,7,6,2,5,3] => [1,2,3,1] => 1101001 => 4
[1,4,7,6,3,2,5] => [1,2,2,2] => 1101010 => 4
[1,4,7,6,3,5,2] => [1,2,3,1] => 1101001 => 4
[1,4,7,6,5,2,3] => [1,2,2,2] => 1101010 => 4
[1,4,7,6,5,3,2] => [1,2,2,1,1] => 1101011 => 5
[1,5,2,3,4,6,7] => [1,6] => 1100000 => 2
[1,5,2,3,4,7,6] => [1,4,2] => 1100010 => 3
[1,5,2,3,6,4,7] => [1,3,3] => 1100100 => 3
[1,5,2,3,6,7,4] => [1,3,3] => 1100100 => 3
[1,5,2,3,7,4,6] => [1,3,3] => 1100100 => 3
[1,5,2,3,7,6,4] => [1,3,2,1] => 1100101 => 4
[1,5,2,4,3,6,7] => [1,3,3] => 1100100 => 3
[1,5,2,4,3,7,6] => [1,3,1,2] => 1100110 => 4
[1,5,2,4,6,3,7] => [1,3,3] => 1100100 => 3
[1,5,2,4,6,7,3] => [1,3,3] => 1100100 => 3
[1,5,2,4,7,3,6] => [1,3,3] => 1100100 => 3
[1,5,2,4,7,6,3] => [1,3,2,1] => 1100101 => 4
[1,5,2,6,3,4,7] => [1,2,4] => 1101000 => 3
[1,5,2,6,3,7,4] => [1,2,2,2] => 1101010 => 4
[1,5,2,6,4,3,7] => [1,2,2,2] => 1101010 => 4
[1,5,2,6,4,7,3] => [1,2,2,2] => 1101010 => 4
[1,5,2,6,7,3,4] => [1,2,4] => 1101000 => 3
[1,5,2,6,7,4,3] => [1,2,3,1] => 1101001 => 4
[1,5,2,7,3,4,6] => [1,2,4] => 1101000 => 3
[1,5,2,7,3,6,4] => [1,2,3,1] => 1101001 => 4
[1,5,2,7,4,3,6] => [1,2,2,2] => 1101010 => 4
[1,5,2,7,4,6,3] => [1,2,3,1] => 1101001 => 4
[1,5,2,7,6,3,4] => [1,2,1,3] => 1101100 => 4
[1,5,2,7,6,4,3] => [1,2,1,2,1] => 1101101 => 5
[1,5,3,2,4,6,7] => [1,2,4] => 1101000 => 3
[1,5,3,2,4,7,6] => [1,2,2,2] => 1101010 => 4
[1,5,3,2,6,4,7] => [1,2,1,3] => 1101100 => 4
[1,5,3,2,6,7,4] => [1,2,1,3] => 1101100 => 4
[1,5,3,2,7,4,6] => [1,2,1,3] => 1101100 => 4
[1,5,3,2,7,6,4] => [1,2,1,2,1] => 1101101 => 5
[1,5,3,4,2,6,7] => [1,3,3] => 1100100 => 3
[1,5,3,4,2,7,6] => [1,3,1,2] => 1100110 => 4
[1,5,3,4,6,2,7] => [1,3,3] => 1100100 => 3
[1,5,3,4,6,7,2] => [1,3,3] => 1100100 => 3
[1,5,3,4,7,2,6] => [1,3,3] => 1100100 => 3
[1,5,3,4,7,6,2] => [1,3,2,1] => 1100101 => 4
[1,5,3,6,2,4,7] => [1,2,4] => 1101000 => 3
[1,5,3,6,2,7,4] => [1,2,2,2] => 1101010 => 4
[1,5,3,6,4,2,7] => [1,2,2,2] => 1101010 => 4
[1,5,3,6,4,7,2] => [1,2,2,2] => 1101010 => 4
[1,5,3,6,7,2,4] => [1,2,4] => 1101000 => 3
[1,5,3,6,7,4,2] => [1,2,3,1] => 1101001 => 4
[1,5,3,7,2,4,6] => [1,2,4] => 1101000 => 3
[1,5,3,7,2,6,4] => [1,2,3,1] => 1101001 => 4
[1,5,3,7,4,2,6] => [1,2,2,2] => 1101010 => 4
[1,5,3,7,4,6,2] => [1,2,3,1] => 1101001 => 4
[1,5,3,7,6,2,4] => [1,2,1,3] => 1101100 => 4
[1,5,3,7,6,4,2] => [1,2,1,2,1] => 1101101 => 5
[1,5,4,2,3,6,7] => [1,1,5] => 1110000 => 3
[1,5,4,2,3,7,6] => [1,1,3,2] => 1110010 => 4
[1,5,4,2,6,3,7] => [1,1,2,3] => 1110100 => 4
[1,5,4,2,6,7,3] => [1,1,2,3] => 1110100 => 4
[1,5,4,2,7,3,6] => [1,1,2,3] => 1110100 => 4
[1,5,4,2,7,6,3] => [1,1,2,2,1] => 1110101 => 5
[1,5,4,3,2,6,7] => [1,1,2,3] => 1110100 => 4
[1,5,4,3,2,7,6] => [1,1,2,1,2] => 1110110 => 5
[1,5,4,3,6,2,7] => [1,1,2,3] => 1110100 => 4
[1,5,4,3,6,7,2] => [1,1,2,3] => 1110100 => 4
[1,5,4,3,7,2,6] => [1,1,2,3] => 1110100 => 4
[1,5,4,3,7,6,2] => [1,1,2,2,1] => 1110101 => 5
[1,5,4,6,2,3,7] => [1,1,5] => 1110000 => 3
[1,5,4,6,2,7,3] => [1,1,3,2] => 1110010 => 4
[1,5,4,6,3,2,7] => [1,1,3,2] => 1110010 => 4
[1,5,4,6,3,7,2] => [1,1,3,2] => 1110010 => 4
[1,5,4,6,7,2,3] => [1,1,5] => 1110000 => 3
[1,5,4,6,7,3,2] => [1,1,4,1] => 1110001 => 4
[1,5,4,7,2,3,6] => [1,1,5] => 1110000 => 3
[1,5,4,7,2,6,3] => [1,1,4,1] => 1110001 => 4
[1,5,4,7,3,2,6] => [1,1,3,2] => 1110010 => 4
[1,5,4,7,3,6,2] => [1,1,4,1] => 1110001 => 4
[1,5,4,7,6,2,3] => [1,1,2,3] => 1110100 => 4
[1,5,4,7,6,3,2] => [1,1,2,2,1] => 1110101 => 5
[1,5,6,2,3,4,7] => [1,6] => 1100000 => 2
[1,5,6,2,3,7,4] => [1,4,2] => 1100010 => 3
[1,5,6,2,4,3,7] => [1,4,2] => 1100010 => 3
[1,5,6,2,4,7,3] => [1,4,2] => 1100010 => 3
[1,5,6,2,7,3,4] => [1,3,3] => 1100100 => 3
[1,5,6,2,7,4,3] => [1,3,2,1] => 1100101 => 4
[1,5,6,3,2,4,7] => [1,3,3] => 1100100 => 3
[1,5,6,3,2,7,4] => [1,3,1,2] => 1100110 => 4
[1,5,6,3,4,2,7] => [1,4,2] => 1100010 => 3
[1,5,6,3,4,7,2] => [1,4,2] => 1100010 => 3
[1,5,6,3,7,2,4] => [1,3,3] => 1100100 => 3
[1,5,6,3,7,4,2] => [1,3,2,1] => 1100101 => 4
[1,5,6,4,2,3,7] => [1,3,3] => 1100100 => 3
[1,5,6,4,2,7,3] => [1,3,1,2] => 1100110 => 4
[1,5,6,4,3,2,7] => [1,3,1,2] => 1100110 => 4
[1,5,6,4,3,7,2] => [1,3,1,2] => 1100110 => 4
[1,5,6,4,7,2,3] => [1,3,3] => 1100100 => 3
[1,5,6,4,7,3,2] => [1,3,2,1] => 1100101 => 4
[1,5,6,7,2,3,4] => [1,6] => 1100000 => 2
[1,5,6,7,2,4,3] => [1,5,1] => 1100001 => 3
[1,5,6,7,3,2,4] => [1,4,2] => 1100010 => 3
[1,5,6,7,3,4,2] => [1,5,1] => 1100001 => 3
[1,5,6,7,4,2,3] => [1,4,2] => 1100010 => 3
[1,5,6,7,4,3,2] => [1,4,1,1] => 1100011 => 4
[1,5,7,2,3,4,6] => [1,6] => 1100000 => 2
[1,5,7,2,3,6,4] => [1,5,1] => 1100001 => 3
[1,5,7,2,4,3,6] => [1,4,2] => 1100010 => 3
[1,5,7,2,4,6,3] => [1,5,1] => 1100001 => 3
[1,5,7,2,6,3,4] => [1,3,3] => 1100100 => 3
[1,5,7,2,6,4,3] => [1,3,2,1] => 1100101 => 4
[1,5,7,3,2,4,6] => [1,3,3] => 1100100 => 3
[1,5,7,3,2,6,4] => [1,3,2,1] => 1100101 => 4
[1,5,7,3,4,2,6] => [1,4,2] => 1100010 => 3
[1,5,7,3,4,6,2] => [1,5,1] => 1100001 => 3
[1,5,7,3,6,2,4] => [1,3,3] => 1100100 => 3
[1,5,7,3,6,4,2] => [1,3,2,1] => 1100101 => 4
[1,5,7,4,2,3,6] => [1,3,3] => 1100100 => 3
[1,5,7,4,2,6,3] => [1,3,2,1] => 1100101 => 4
[1,5,7,4,3,2,6] => [1,3,1,2] => 1100110 => 4
[1,5,7,4,3,6,2] => [1,3,2,1] => 1100101 => 4
[1,5,7,4,6,2,3] => [1,3,3] => 1100100 => 3
[1,5,7,4,6,3,2] => [1,3,2,1] => 1100101 => 4
[1,5,7,6,2,3,4] => [1,2,4] => 1101000 => 3
[1,5,7,6,2,4,3] => [1,2,3,1] => 1101001 => 4
[1,5,7,6,3,2,4] => [1,2,2,2] => 1101010 => 4
[1,5,7,6,3,4,2] => [1,2,3,1] => 1101001 => 4
[1,5,7,6,4,2,3] => [1,2,2,2] => 1101010 => 4
[1,5,7,6,4,3,2] => [1,2,2,1,1] => 1101011 => 5
[1,6,2,3,4,5,7] => [1,6] => 1100000 => 2
[1,6,2,3,4,7,5] => [1,4,2] => 1100010 => 3
[1,6,2,3,5,4,7] => [1,4,2] => 1100010 => 3
[1,6,2,3,5,7,4] => [1,4,2] => 1100010 => 3
[1,6,2,3,7,4,5] => [1,3,3] => 1100100 => 3
[1,6,2,3,7,5,4] => [1,3,2,1] => 1100101 => 4
[1,6,2,4,3,5,7] => [1,3,3] => 1100100 => 3
[1,6,2,4,3,7,5] => [1,3,1,2] => 1100110 => 4
[1,6,2,4,5,3,7] => [1,4,2] => 1100010 => 3
[1,6,2,4,5,7,3] => [1,4,2] => 1100010 => 3
[1,6,2,4,7,3,5] => [1,3,3] => 1100100 => 3
[1,6,2,4,7,5,3] => [1,3,2,1] => 1100101 => 4
[1,6,2,5,3,4,7] => [1,2,4] => 1101000 => 3
[1,6,2,5,3,7,4] => [1,2,2,2] => 1101010 => 4
[1,6,2,5,4,3,7] => [1,2,2,2] => 1101010 => 4
[1,6,2,5,4,7,3] => [1,2,2,2] => 1101010 => 4
[1,6,2,5,7,3,4] => [1,2,4] => 1101000 => 3
[1,6,2,5,7,4,3] => [1,2,3,1] => 1101001 => 4
[1,6,2,7,3,4,5] => [1,2,4] => 1101000 => 3
[1,6,2,7,3,5,4] => [1,2,3,1] => 1101001 => 4
[1,6,2,7,4,3,5] => [1,2,2,2] => 1101010 => 4
[1,6,2,7,4,5,3] => [1,2,3,1] => 1101001 => 4
[1,6,2,7,5,3,4] => [1,2,2,2] => 1101010 => 4
[1,6,2,7,5,4,3] => [1,2,2,1,1] => 1101011 => 5
[1,6,3,2,4,5,7] => [1,2,4] => 1101000 => 3
[1,6,3,2,4,7,5] => [1,2,2,2] => 1101010 => 4
[1,6,3,2,5,4,7] => [1,2,2,2] => 1101010 => 4
[1,6,3,2,5,7,4] => [1,2,2,2] => 1101010 => 4
[1,6,3,2,7,4,5] => [1,2,1,3] => 1101100 => 4
[1,6,3,2,7,5,4] => [1,2,1,2,1] => 1101101 => 5
[1,6,3,4,2,5,7] => [1,3,3] => 1100100 => 3
[1,6,3,4,2,7,5] => [1,3,1,2] => 1100110 => 4
[1,6,3,4,5,2,7] => [1,4,2] => 1100010 => 3
[1,6,3,4,5,7,2] => [1,4,2] => 1100010 => 3
[1,6,3,4,7,2,5] => [1,3,3] => 1100100 => 3
[1,6,3,4,7,5,2] => [1,3,2,1] => 1100101 => 4
[1,6,3,5,2,4,7] => [1,2,4] => 1101000 => 3
[1,6,3,5,2,7,4] => [1,2,2,2] => 1101010 => 4
[1,6,3,5,4,2,7] => [1,2,2,2] => 1101010 => 4
[1,6,3,5,4,7,2] => [1,2,2,2] => 1101010 => 4
[1,6,3,5,7,2,4] => [1,2,4] => 1101000 => 3
[1,6,3,5,7,4,2] => [1,2,3,1] => 1101001 => 4
[1,6,3,7,2,4,5] => [1,2,4] => 1101000 => 3
[1,6,3,7,2,5,4] => [1,2,3,1] => 1101001 => 4
[1,6,3,7,4,2,5] => [1,2,2,2] => 1101010 => 4
[1,6,3,7,4,5,2] => [1,2,3,1] => 1101001 => 4
[1,6,3,7,5,2,4] => [1,2,2,2] => 1101010 => 4
[1,6,3,7,5,4,2] => [1,2,2,1,1] => 1101011 => 5
[1,6,4,2,3,5,7] => [1,1,5] => 1110000 => 3
[1,6,4,2,3,7,5] => [1,1,3,2] => 1110010 => 4
[1,6,4,2,5,3,7] => [1,1,3,2] => 1110010 => 4
[1,6,4,2,5,7,3] => [1,1,3,2] => 1110010 => 4
[1,6,4,2,7,3,5] => [1,1,2,3] => 1110100 => 4
[1,6,4,2,7,5,3] => [1,1,2,2,1] => 1110101 => 5
[1,6,4,3,2,5,7] => [1,1,2,3] => 1110100 => 4
[1,6,4,3,2,7,5] => [1,1,2,1,2] => 1110110 => 5
[1,6,4,3,5,2,7] => [1,1,3,2] => 1110010 => 4
[1,6,4,3,5,7,2] => [1,1,3,2] => 1110010 => 4
[1,6,4,3,7,2,5] => [1,1,2,3] => 1110100 => 4
[1,6,4,3,7,5,2] => [1,1,2,2,1] => 1110101 => 5
[1,6,4,5,2,3,7] => [1,1,5] => 1110000 => 3
[1,6,4,5,2,7,3] => [1,1,3,2] => 1110010 => 4
[1,6,4,5,3,2,7] => [1,1,3,2] => 1110010 => 4
[1,6,4,5,3,7,2] => [1,1,3,2] => 1110010 => 4
[1,6,4,5,7,2,3] => [1,1,5] => 1110000 => 3
[1,6,4,5,7,3,2] => [1,1,4,1] => 1110001 => 4
[1,6,4,7,2,3,5] => [1,1,5] => 1110000 => 3
[1,6,4,7,2,5,3] => [1,1,4,1] => 1110001 => 4
[1,6,4,7,3,2,5] => [1,1,3,2] => 1110010 => 4
[1,6,4,7,3,5,2] => [1,1,4,1] => 1110001 => 4
[1,6,4,7,5,2,3] => [1,1,3,2] => 1110010 => 4
[1,6,4,7,5,3,2] => [1,1,3,1,1] => 1110011 => 5
[1,6,5,2,3,4,7] => [1,1,5] => 1110000 => 3
[1,6,5,2,3,7,4] => [1,1,3,2] => 1110010 => 4
[1,6,5,2,4,3,7] => [1,1,3,2] => 1110010 => 4
[1,6,5,2,4,7,3] => [1,1,3,2] => 1110010 => 4
[1,6,5,2,7,3,4] => [1,1,2,3] => 1110100 => 4
[1,6,5,2,7,4,3] => [1,1,2,2,1] => 1110101 => 5
[1,6,5,3,2,4,7] => [1,1,2,3] => 1110100 => 4
[1,6,5,3,2,7,4] => [1,1,2,1,2] => 1110110 => 5
[1,6,5,3,4,2,7] => [1,1,3,2] => 1110010 => 4
[1,6,5,3,4,7,2] => [1,1,3,2] => 1110010 => 4
[1,6,5,3,7,2,4] => [1,1,2,3] => 1110100 => 4
[1,6,5,3,7,4,2] => [1,1,2,2,1] => 1110101 => 5
[1,6,5,4,2,3,7] => [1,1,2,3] => 1110100 => 4
[1,6,5,4,2,7,3] => [1,1,2,1,2] => 1110110 => 5
[1,6,5,4,3,2,7] => [1,1,2,1,2] => 1110110 => 5
[1,6,5,4,3,7,2] => [1,1,2,1,2] => 1110110 => 5
[1,6,5,4,7,2,3] => [1,1,2,3] => 1110100 => 4
[1,6,5,4,7,3,2] => [1,1,2,2,1] => 1110101 => 5
[1,6,5,7,2,3,4] => [1,1,5] => 1110000 => 3
[1,6,5,7,2,4,3] => [1,1,4,1] => 1110001 => 4
[1,6,5,7,3,2,4] => [1,1,3,2] => 1110010 => 4
[1,6,5,7,3,4,2] => [1,1,4,1] => 1110001 => 4
[1,6,5,7,4,2,3] => [1,1,3,2] => 1110010 => 4
[1,6,5,7,4,3,2] => [1,1,3,1,1] => 1110011 => 5
[1,6,7,2,3,4,5] => [1,6] => 1100000 => 2
[1,6,7,2,3,5,4] => [1,5,1] => 1100001 => 3
[1,6,7,2,4,3,5] => [1,4,2] => 1100010 => 3
[1,6,7,2,4,5,3] => [1,5,1] => 1100001 => 3
[1,6,7,2,5,3,4] => [1,4,2] => 1100010 => 3
[1,6,7,2,5,4,3] => [1,4,1,1] => 1100011 => 4
[1,6,7,3,2,4,5] => [1,3,3] => 1100100 => 3
[1,6,7,3,2,5,4] => [1,3,2,1] => 1100101 => 4
[1,6,7,3,4,2,5] => [1,4,2] => 1100010 => 3
[1,6,7,3,4,5,2] => [1,5,1] => 1100001 => 3
[1,6,7,3,5,2,4] => [1,4,2] => 1100010 => 3
[1,6,7,3,5,4,2] => [1,4,1,1] => 1100011 => 4
[1,6,7,4,2,3,5] => [1,3,3] => 1100100 => 3
[1,6,7,4,2,5,3] => [1,3,2,1] => 1100101 => 4
[1,6,7,4,3,2,5] => [1,3,1,2] => 1100110 => 4
[1,6,7,4,3,5,2] => [1,3,2,1] => 1100101 => 4
[1,6,7,4,5,2,3] => [1,4,2] => 1100010 => 3
[1,6,7,4,5,3,2] => [1,4,1,1] => 1100011 => 4
[1,6,7,5,2,3,4] => [1,2,4] => 1101000 => 3
[1,6,7,5,2,4,3] => [1,2,3,1] => 1101001 => 4
[1,6,7,5,3,2,4] => [1,2,2,2] => 1101010 => 4
[1,6,7,5,3,4,2] => [1,2,3,1] => 1101001 => 4
[1,6,7,5,4,2,3] => [1,2,2,2] => 1101010 => 4
[1,6,7,5,4,3,2] => [1,2,2,1,1] => 1101011 => 5
[1,7,2,3,4,5,6] => [1,6] => 1100000 => 2
[1,7,2,3,4,6,5] => [1,5,1] => 1100001 => 3
[1,7,2,3,5,4,6] => [1,4,2] => 1100010 => 3
[1,7,2,3,5,6,4] => [1,5,1] => 1100001 => 3
[1,7,2,3,6,4,5] => [1,3,3] => 1100100 => 3
[1,7,2,3,6,5,4] => [1,3,2,1] => 1100101 => 4
[1,7,2,4,3,5,6] => [1,3,3] => 1100100 => 3
[1,7,2,4,3,6,5] => [1,3,2,1] => 1100101 => 4
[1,7,2,4,5,3,6] => [1,4,2] => 1100010 => 3
[1,7,2,4,5,6,3] => [1,5,1] => 1100001 => 3
[1,7,2,4,6,3,5] => [1,3,3] => 1100100 => 3
[1,7,2,4,6,5,3] => [1,3,2,1] => 1100101 => 4
[1,7,2,5,3,4,6] => [1,2,4] => 1101000 => 3
[1,7,2,5,3,6,4] => [1,2,3,1] => 1101001 => 4
[1,7,2,5,4,3,6] => [1,2,2,2] => 1101010 => 4
[1,7,2,5,4,6,3] => [1,2,3,1] => 1101001 => 4
[1,7,2,5,6,3,4] => [1,2,4] => 1101000 => 3
[1,7,2,5,6,4,3] => [1,2,3,1] => 1101001 => 4
[1,7,2,6,3,4,5] => [1,2,4] => 1101000 => 3
[1,7,2,6,3,5,4] => [1,2,3,1] => 1101001 => 4
[1,7,2,6,4,3,5] => [1,2,2,2] => 1101010 => 4
[1,7,2,6,4,5,3] => [1,2,3,1] => 1101001 => 4
[1,7,2,6,5,3,4] => [1,2,2,2] => 1101010 => 4
[1,7,2,6,5,4,3] => [1,2,2,1,1] => 1101011 => 5
[1,7,3,2,4,5,6] => [1,2,4] => 1101000 => 3
[1,7,3,2,4,6,5] => [1,2,3,1] => 1101001 => 4
[1,7,3,2,5,4,6] => [1,2,2,2] => 1101010 => 4
[1,7,3,2,5,6,4] => [1,2,3,1] => 1101001 => 4
[1,7,3,2,6,4,5] => [1,2,1,3] => 1101100 => 4
[1,7,3,2,6,5,4] => [1,2,1,2,1] => 1101101 => 5
[1,7,3,4,2,5,6] => [1,3,3] => 1100100 => 3
[1,7,3,4,2,6,5] => [1,3,2,1] => 1100101 => 4
[1,7,3,4,5,2,6] => [1,4,2] => 1100010 => 3
[1,7,3,4,5,6,2] => [1,5,1] => 1100001 => 3
[1,7,3,4,6,2,5] => [1,3,3] => 1100100 => 3
[1,7,3,4,6,5,2] => [1,3,2,1] => 1100101 => 4
[1,7,3,5,2,4,6] => [1,2,4] => 1101000 => 3
[1,7,3,5,2,6,4] => [1,2,3,1] => 1101001 => 4
[1,7,3,5,4,2,6] => [1,2,2,2] => 1101010 => 4
[1,7,3,5,4,6,2] => [1,2,3,1] => 1101001 => 4
[1,7,3,5,6,2,4] => [1,2,4] => 1101000 => 3
[1,7,3,5,6,4,2] => [1,2,3,1] => 1101001 => 4
[1,7,3,6,2,4,5] => [1,2,4] => 1101000 => 3
[1,7,3,6,2,5,4] => [1,2,3,1] => 1101001 => 4
[1,7,3,6,4,2,5] => [1,2,2,2] => 1101010 => 4
[1,7,3,6,4,5,2] => [1,2,3,1] => 1101001 => 4
[1,7,3,6,5,2,4] => [1,2,2,2] => 1101010 => 4
[1,7,3,6,5,4,2] => [1,2,2,1,1] => 1101011 => 5
[1,7,4,2,3,5,6] => [1,1,5] => 1110000 => 3
[1,7,4,2,3,6,5] => [1,1,4,1] => 1110001 => 4
[1,7,4,2,5,3,6] => [1,1,3,2] => 1110010 => 4
[1,7,4,2,5,6,3] => [1,1,4,1] => 1110001 => 4
[1,7,4,2,6,3,5] => [1,1,2,3] => 1110100 => 4
[1,7,4,2,6,5,3] => [1,1,2,2,1] => 1110101 => 5
[1,7,4,3,2,5,6] => [1,1,2,3] => 1110100 => 4
[1,7,4,3,2,6,5] => [1,1,2,2,1] => 1110101 => 5
[1,7,4,3,5,2,6] => [1,1,3,2] => 1110010 => 4
[1,7,4,3,5,6,2] => [1,1,4,1] => 1110001 => 4
[1,7,4,3,6,2,5] => [1,1,2,3] => 1110100 => 4
[1,7,4,3,6,5,2] => [1,1,2,2,1] => 1110101 => 5
[1,7,4,5,2,3,6] => [1,1,5] => 1110000 => 3
[1,7,4,5,2,6,3] => [1,1,4,1] => 1110001 => 4
[1,7,4,5,3,2,6] => [1,1,3,2] => 1110010 => 4
[1,7,4,5,3,6,2] => [1,1,4,1] => 1110001 => 4
[1,7,4,5,6,2,3] => [1,1,5] => 1110000 => 3
[1,7,4,5,6,3,2] => [1,1,4,1] => 1110001 => 4
[1,7,4,6,2,3,5] => [1,1,5] => 1110000 => 3
[1,7,4,6,2,5,3] => [1,1,4,1] => 1110001 => 4
[1,7,4,6,3,2,5] => [1,1,3,2] => 1110010 => 4
[1,7,4,6,3,5,2] => [1,1,4,1] => 1110001 => 4
[1,7,4,6,5,2,3] => [1,1,3,2] => 1110010 => 4
[1,7,4,6,5,3,2] => [1,1,3,1,1] => 1110011 => 5
[1,7,5,2,3,4,6] => [1,1,5] => 1110000 => 3
[1,7,5,2,3,6,4] => [1,1,4,1] => 1110001 => 4
[1,7,5,2,4,3,6] => [1,1,3,2] => 1110010 => 4
[1,7,5,2,4,6,3] => [1,1,4,1] => 1110001 => 4
[1,7,5,2,6,3,4] => [1,1,2,3] => 1110100 => 4
[1,7,5,2,6,4,3] => [1,1,2,2,1] => 1110101 => 5
[1,7,5,3,2,4,6] => [1,1,2,3] => 1110100 => 4
[1,7,5,3,2,6,4] => [1,1,2,2,1] => 1110101 => 5
[1,7,5,3,4,2,6] => [1,1,3,2] => 1110010 => 4
[1,7,5,3,4,6,2] => [1,1,4,1] => 1110001 => 4
[1,7,5,3,6,2,4] => [1,1,2,3] => 1110100 => 4
[1,7,5,3,6,4,2] => [1,1,2,2,1] => 1110101 => 5
[1,7,5,4,2,3,6] => [1,1,2,3] => 1110100 => 4
[1,7,5,4,2,6,3] => [1,1,2,2,1] => 1110101 => 5
[1,7,5,4,3,2,6] => [1,1,2,1,2] => 1110110 => 5
[1,7,5,4,3,6,2] => [1,1,2,2,1] => 1110101 => 5
[1,7,5,4,6,2,3] => [1,1,2,3] => 1110100 => 4
[1,7,5,4,6,3,2] => [1,1,2,2,1] => 1110101 => 5
[1,7,5,6,2,3,4] => [1,1,5] => 1110000 => 3
[1,7,5,6,2,4,3] => [1,1,4,1] => 1110001 => 4
[1,7,5,6,3,2,4] => [1,1,3,2] => 1110010 => 4
[1,7,5,6,3,4,2] => [1,1,4,1] => 1110001 => 4
[1,7,5,6,4,2,3] => [1,1,3,2] => 1110010 => 4
[1,7,5,6,4,3,2] => [1,1,3,1,1] => 1110011 => 5
[1,7,6,2,3,4,5] => [1,1,5] => 1110000 => 3
[1,7,6,2,3,5,4] => [1,1,4,1] => 1110001 => 4
[1,7,6,2,4,3,5] => [1,1,3,2] => 1110010 => 4
[1,7,6,2,4,5,3] => [1,1,4,1] => 1110001 => 4
[1,7,6,2,5,3,4] => [1,1,3,2] => 1110010 => 4
[1,7,6,2,5,4,3] => [1,1,3,1,1] => 1110011 => 5
[1,7,6,3,2,4,5] => [1,1,2,3] => 1110100 => 4
[1,7,6,3,2,5,4] => [1,1,2,2,1] => 1110101 => 5
[1,7,6,3,4,2,5] => [1,1,3,2] => 1110010 => 4
[1,7,6,3,4,5,2] => [1,1,4,1] => 1110001 => 4
[1,7,6,3,5,2,4] => [1,1,3,2] => 1110010 => 4
[1,7,6,3,5,4,2] => [1,1,3,1,1] => 1110011 => 5
[1,7,6,4,2,3,5] => [1,1,2,3] => 1110100 => 4
[1,7,6,4,2,5,3] => [1,1,2,2,1] => 1110101 => 5
[1,7,6,4,3,2,5] => [1,1,2,1,2] => 1110110 => 5
[1,7,6,4,3,5,2] => [1,1,2,2,1] => 1110101 => 5
[1,7,6,4,5,2,3] => [1,1,3,2] => 1110010 => 4
[1,7,6,4,5,3,2] => [1,1,3,1,1] => 1110011 => 5
[1,7,6,5,2,3,4] => [1,1,1,4] => 1111000 => 4
[1,7,6,5,2,4,3] => [1,1,1,3,1] => 1111001 => 5
[1,7,6,5,3,2,4] => [1,1,1,2,2] => 1111010 => 5
[1,7,6,5,3,4,2] => [1,1,1,3,1] => 1111001 => 5
[1,7,6,5,4,2,3] => [1,1,1,2,2] => 1111010 => 5
[1,7,6,5,4,3,2] => [1,1,1,2,1,1] => 1111011 => 6
[2,1,3,4,5,6,7] => [7] => 1000000 => 1
[2,1,3,4,5,7,6] => [5,2] => 1000010 => 2
[2,1,3,4,6,5,7] => [4,3] => 1000100 => 2
[2,1,3,4,6,7,5] => [4,3] => 1000100 => 2
[2,1,3,4,7,5,6] => [4,3] => 1000100 => 2
[2,1,3,4,7,6,5] => [4,2,1] => 1000101 => 3
[2,1,3,5,4,6,7] => [3,4] => 1001000 => 2
[2,1,3,5,4,7,6] => [3,2,2] => 1001010 => 3
[2,1,3,5,6,4,7] => [3,4] => 1001000 => 2
[2,1,3,5,6,7,4] => [3,4] => 1001000 => 2
[2,1,3,5,7,4,6] => [3,4] => 1001000 => 2
[2,1,3,5,7,6,4] => [3,3,1] => 1001001 => 3
[2,1,3,6,4,5,7] => [3,4] => 1001000 => 2
[2,1,3,6,4,7,5] => [3,2,2] => 1001010 => 3
[2,1,3,6,5,4,7] => [3,2,2] => 1001010 => 3
[2,1,3,6,5,7,4] => [3,2,2] => 1001010 => 3
[2,1,3,6,7,4,5] => [3,4] => 1001000 => 2
[2,1,3,6,7,5,4] => [3,3,1] => 1001001 => 3
[2,1,3,7,4,5,6] => [3,4] => 1001000 => 2
[2,1,3,7,4,6,5] => [3,3,1] => 1001001 => 3
[2,1,3,7,5,4,6] => [3,2,2] => 1001010 => 3
[2,1,3,7,5,6,4] => [3,3,1] => 1001001 => 3
[2,1,3,7,6,4,5] => [3,1,3] => 1001100 => 3
[2,1,3,7,6,5,4] => [3,1,2,1] => 1001101 => 4
[2,1,4,3,5,6,7] => [2,5] => 1010000 => 2
[2,1,4,3,5,7,6] => [2,3,2] => 1010010 => 3
[2,1,4,3,6,5,7] => [2,2,3] => 1010100 => 3
[2,1,4,3,6,7,5] => [2,2,3] => 1010100 => 3
[2,1,4,3,7,5,6] => [2,2,3] => 1010100 => 3
[2,1,4,3,7,6,5] => [2,2,2,1] => 1010101 => 4
[2,1,4,5,3,6,7] => [2,5] => 1010000 => 2
[2,1,4,5,3,7,6] => [2,3,2] => 1010010 => 3
[2,1,4,5,6,3,7] => [2,5] => 1010000 => 2
[2,1,4,5,6,7,3] => [2,5] => 1010000 => 2
[2,1,4,5,7,3,6] => [2,5] => 1010000 => 2
[2,1,4,5,7,6,3] => [2,4,1] => 1010001 => 3
[2,1,4,6,3,5,7] => [2,5] => 1010000 => 2
[2,1,4,6,3,7,5] => [2,3,2] => 1010010 => 3
[2,1,4,6,5,3,7] => [2,3,2] => 1010010 => 3
[2,1,4,6,5,7,3] => [2,3,2] => 1010010 => 3
[2,1,4,6,7,3,5] => [2,5] => 1010000 => 2
[2,1,4,6,7,5,3] => [2,4,1] => 1010001 => 3
[2,1,4,7,3,5,6] => [2,5] => 1010000 => 2
[2,1,4,7,3,6,5] => [2,4,1] => 1010001 => 3
[2,1,4,7,5,3,6] => [2,3,2] => 1010010 => 3
[2,1,4,7,5,6,3] => [2,4,1] => 1010001 => 3
[2,1,4,7,6,3,5] => [2,2,3] => 1010100 => 3
[2,1,4,7,6,5,3] => [2,2,2,1] => 1010101 => 4
[2,1,5,3,4,6,7] => [2,5] => 1010000 => 2
[2,1,5,3,4,7,6] => [2,3,2] => 1010010 => 3
[2,1,5,3,6,4,7] => [2,2,3] => 1010100 => 3
[2,1,5,3,6,7,4] => [2,2,3] => 1010100 => 3
[2,1,5,3,7,4,6] => [2,2,3] => 1010100 => 3
[2,1,5,3,7,6,4] => [2,2,2,1] => 1010101 => 4
[2,1,5,4,3,6,7] => [2,2,3] => 1010100 => 3
[2,1,5,4,3,7,6] => [2,2,1,2] => 1010110 => 4
[2,1,5,4,6,3,7] => [2,2,3] => 1010100 => 3
[2,1,5,4,6,7,3] => [2,2,3] => 1010100 => 3
[2,1,5,4,7,3,6] => [2,2,3] => 1010100 => 3
[2,1,5,4,7,6,3] => [2,2,2,1] => 1010101 => 4
[2,1,5,6,3,4,7] => [2,5] => 1010000 => 2
[2,1,5,6,3,7,4] => [2,3,2] => 1010010 => 3
[2,1,5,6,4,3,7] => [2,3,2] => 1010010 => 3
[2,1,5,6,4,7,3] => [2,3,2] => 1010010 => 3
[2,1,5,6,7,3,4] => [2,5] => 1010000 => 2
[2,1,5,6,7,4,3] => [2,4,1] => 1010001 => 3
[2,1,5,7,3,4,6] => [2,5] => 1010000 => 2
[2,1,5,7,3,6,4] => [2,4,1] => 1010001 => 3
[2,1,5,7,4,3,6] => [2,3,2] => 1010010 => 3
[2,1,5,7,4,6,3] => [2,4,1] => 1010001 => 3
[2,1,5,7,6,3,4] => [2,2,3] => 1010100 => 3
[2,1,5,7,6,4,3] => [2,2,2,1] => 1010101 => 4
[2,1,6,3,4,5,7] => [2,5] => 1010000 => 2
[2,1,6,3,4,7,5] => [2,3,2] => 1010010 => 3
[2,1,6,3,5,4,7] => [2,3,2] => 1010010 => 3
[2,1,6,3,5,7,4] => [2,3,2] => 1010010 => 3
[2,1,6,3,7,4,5] => [2,2,3] => 1010100 => 3
[2,1,6,3,7,5,4] => [2,2,2,1] => 1010101 => 4
[2,1,6,4,3,5,7] => [2,2,3] => 1010100 => 3
[2,1,6,4,3,7,5] => [2,2,1,2] => 1010110 => 4
[2,1,6,4,5,3,7] => [2,3,2] => 1010010 => 3
[2,1,6,4,5,7,3] => [2,3,2] => 1010010 => 3
[2,1,6,4,7,3,5] => [2,2,3] => 1010100 => 3
[2,1,6,4,7,5,3] => [2,2,2,1] => 1010101 => 4
[2,1,6,5,3,4,7] => [2,1,4] => 1011000 => 3
[2,1,6,5,3,7,4] => [2,1,2,2] => 1011010 => 4
[2,1,6,5,4,3,7] => [2,1,2,2] => 1011010 => 4
[2,1,6,5,4,7,3] => [2,1,2,2] => 1011010 => 4
[2,1,6,5,7,3,4] => [2,1,4] => 1011000 => 3
[2,1,6,5,7,4,3] => [2,1,3,1] => 1011001 => 4
[2,1,6,7,3,4,5] => [2,5] => 1010000 => 2
[2,1,6,7,3,5,4] => [2,4,1] => 1010001 => 3
[2,1,6,7,4,3,5] => [2,3,2] => 1010010 => 3
[2,1,6,7,4,5,3] => [2,4,1] => 1010001 => 3
[2,1,6,7,5,3,4] => [2,3,2] => 1010010 => 3
[2,1,6,7,5,4,3] => [2,3,1,1] => 1010011 => 4
[2,1,7,3,4,5,6] => [2,5] => 1010000 => 2
[2,1,7,3,4,6,5] => [2,4,1] => 1010001 => 3
[2,1,7,3,5,4,6] => [2,3,2] => 1010010 => 3
[2,1,7,3,5,6,4] => [2,4,1] => 1010001 => 3
[2,1,7,3,6,4,5] => [2,2,3] => 1010100 => 3
[2,1,7,3,6,5,4] => [2,2,2,1] => 1010101 => 4
[2,1,7,4,3,5,6] => [2,2,3] => 1010100 => 3
[2,1,7,4,3,6,5] => [2,2,2,1] => 1010101 => 4
[2,1,7,4,5,3,6] => [2,3,2] => 1010010 => 3
[2,1,7,4,5,6,3] => [2,4,1] => 1010001 => 3
[2,1,7,4,6,3,5] => [2,2,3] => 1010100 => 3
[2,1,7,4,6,5,3] => [2,2,2,1] => 1010101 => 4
[2,1,7,5,3,4,6] => [2,1,4] => 1011000 => 3
[2,1,7,5,3,6,4] => [2,1,3,1] => 1011001 => 4
[2,1,7,5,4,3,6] => [2,1,2,2] => 1011010 => 4
[2,1,7,5,4,6,3] => [2,1,3,1] => 1011001 => 4
[2,1,7,5,6,3,4] => [2,1,4] => 1011000 => 3
[2,1,7,5,6,4,3] => [2,1,3,1] => 1011001 => 4
[2,1,7,6,3,4,5] => [2,1,4] => 1011000 => 3
[2,1,7,6,3,5,4] => [2,1,3,1] => 1011001 => 4
[2,1,7,6,4,3,5] => [2,1,2,2] => 1011010 => 4
[2,1,7,6,4,5,3] => [2,1,3,1] => 1011001 => 4
[2,1,7,6,5,3,4] => [2,1,2,2] => 1011010 => 4
[2,1,7,6,5,4,3] => [2,1,2,1,1] => 1011011 => 5
[2,3,1,4,5,6,7] => [7] => 1000000 => 1
[2,3,1,4,5,7,6] => [5,2] => 1000010 => 2
[2,3,1,4,6,5,7] => [4,3] => 1000100 => 2
[2,3,1,4,6,7,5] => [4,3] => 1000100 => 2
[2,3,1,4,7,5,6] => [4,3] => 1000100 => 2
[2,3,1,4,7,6,5] => [4,2,1] => 1000101 => 3
[2,3,1,5,4,6,7] => [3,4] => 1001000 => 2
[2,3,1,5,4,7,6] => [3,2,2] => 1001010 => 3
[2,3,1,5,6,4,7] => [3,4] => 1001000 => 2
[2,3,1,5,6,7,4] => [3,4] => 1001000 => 2
[2,3,1,5,7,4,6] => [3,4] => 1001000 => 2
[2,3,1,5,7,6,4] => [3,3,1] => 1001001 => 3
[2,3,1,6,4,5,7] => [3,4] => 1001000 => 2
[2,3,1,6,4,7,5] => [3,2,2] => 1001010 => 3
[2,3,1,6,5,4,7] => [3,2,2] => 1001010 => 3
[2,3,1,6,5,7,4] => [3,2,2] => 1001010 => 3
[2,3,1,6,7,4,5] => [3,4] => 1001000 => 2
[2,3,1,6,7,5,4] => [3,3,1] => 1001001 => 3
[2,3,1,7,4,5,6] => [3,4] => 1001000 => 2
[2,3,1,7,4,6,5] => [3,3,1] => 1001001 => 3
[2,3,1,7,5,4,6] => [3,2,2] => 1001010 => 3
[2,3,1,7,5,6,4] => [3,3,1] => 1001001 => 3
[2,3,1,7,6,4,5] => [3,1,3] => 1001100 => 3
[2,3,1,7,6,5,4] => [3,1,2,1] => 1001101 => 4
[2,3,4,1,5,6,7] => [7] => 1000000 => 1
[2,3,4,1,5,7,6] => [5,2] => 1000010 => 2
[2,3,4,1,6,5,7] => [4,3] => 1000100 => 2
[2,3,4,1,6,7,5] => [4,3] => 1000100 => 2
[2,3,4,1,7,5,6] => [4,3] => 1000100 => 2
[2,3,4,1,7,6,5] => [4,2,1] => 1000101 => 3
[2,3,4,5,1,6,7] => [7] => 1000000 => 1
[2,3,4,5,1,7,6] => [5,2] => 1000010 => 2
[2,3,4,5,6,1,7] => [7] => 1000000 => 1
[2,3,4,5,6,7,1] => [7] => 1000000 => 1
[2,3,4,5,7,1,6] => [7] => 1000000 => 1
[2,3,4,5,7,6,1] => [6,1] => 1000001 => 2
[2,3,4,6,1,5,7] => [7] => 1000000 => 1
[2,3,4,6,1,7,5] => [5,2] => 1000010 => 2
[2,3,4,6,5,1,7] => [5,2] => 1000010 => 2
[2,3,4,6,5,7,1] => [5,2] => 1000010 => 2
[2,3,4,6,7,1,5] => [7] => 1000000 => 1
[2,3,4,6,7,5,1] => [6,1] => 1000001 => 2
[2,3,4,7,1,5,6] => [7] => 1000000 => 1
[2,3,4,7,1,6,5] => [6,1] => 1000001 => 2
[2,3,4,7,5,1,6] => [5,2] => 1000010 => 2
[2,3,4,7,5,6,1] => [6,1] => 1000001 => 2
[2,3,4,7,6,1,5] => [4,3] => 1000100 => 2
[2,3,4,7,6,5,1] => [4,2,1] => 1000101 => 3
[2,3,5,1,4,6,7] => [7] => 1000000 => 1
[2,3,5,1,4,7,6] => [5,2] => 1000010 => 2
[2,3,5,1,6,4,7] => [4,3] => 1000100 => 2
[2,3,5,1,6,7,4] => [4,3] => 1000100 => 2
[2,3,5,1,7,4,6] => [4,3] => 1000100 => 2
[2,3,5,1,7,6,4] => [4,2,1] => 1000101 => 3
[2,3,5,4,1,6,7] => [4,3] => 1000100 => 2
[2,3,5,4,1,7,6] => [4,1,2] => 1000110 => 3
[2,3,5,4,6,1,7] => [4,3] => 1000100 => 2
[2,3,5,4,6,7,1] => [4,3] => 1000100 => 2
[2,3,5,4,7,1,6] => [4,3] => 1000100 => 2
[2,3,5,4,7,6,1] => [4,2,1] => 1000101 => 3
[2,3,5,6,1,4,7] => [7] => 1000000 => 1
[2,3,5,6,1,7,4] => [5,2] => 1000010 => 2
[2,3,5,6,4,1,7] => [5,2] => 1000010 => 2
[2,3,5,6,4,7,1] => [5,2] => 1000010 => 2
[2,3,5,6,7,1,4] => [7] => 1000000 => 1
[2,3,5,6,7,4,1] => [6,1] => 1000001 => 2
[2,3,5,7,1,4,6] => [7] => 1000000 => 1
[2,3,5,7,1,6,4] => [6,1] => 1000001 => 2
[2,3,5,7,4,1,6] => [5,2] => 1000010 => 2
[2,3,5,7,4,6,1] => [6,1] => 1000001 => 2
[2,3,5,7,6,1,4] => [4,3] => 1000100 => 2
[2,3,5,7,6,4,1] => [4,2,1] => 1000101 => 3
[2,3,6,1,4,5,7] => [7] => 1000000 => 1
[2,3,6,1,4,7,5] => [5,2] => 1000010 => 2
[2,3,6,1,5,4,7] => [5,2] => 1000010 => 2
[2,3,6,1,5,7,4] => [5,2] => 1000010 => 2
[2,3,6,1,7,4,5] => [4,3] => 1000100 => 2
[2,3,6,1,7,5,4] => [4,2,1] => 1000101 => 3
[2,3,6,4,1,5,7] => [4,3] => 1000100 => 2
[2,3,6,4,1,7,5] => [4,1,2] => 1000110 => 3
[2,3,6,4,5,1,7] => [5,2] => 1000010 => 2
[2,3,6,4,5,7,1] => [5,2] => 1000010 => 2
[2,3,6,4,7,1,5] => [4,3] => 1000100 => 2
[2,3,6,4,7,5,1] => [4,2,1] => 1000101 => 3
[2,3,6,5,1,4,7] => [3,4] => 1001000 => 2
[2,3,6,5,1,7,4] => [3,2,2] => 1001010 => 3
[2,3,6,5,4,1,7] => [3,2,2] => 1001010 => 3
[2,3,6,5,4,7,1] => [3,2,2] => 1001010 => 3
[2,3,6,5,7,1,4] => [3,4] => 1001000 => 2
[2,3,6,5,7,4,1] => [3,3,1] => 1001001 => 3
[2,3,6,7,1,4,5] => [7] => 1000000 => 1
[2,3,6,7,1,5,4] => [6,1] => 1000001 => 2
[2,3,6,7,4,1,5] => [5,2] => 1000010 => 2
[2,3,6,7,4,5,1] => [6,1] => 1000001 => 2
[2,3,6,7,5,1,4] => [5,2] => 1000010 => 2
[2,3,6,7,5,4,1] => [5,1,1] => 1000011 => 3
[2,3,7,1,4,5,6] => [7] => 1000000 => 1
[2,3,7,1,4,6,5] => [6,1] => 1000001 => 2
[2,3,7,1,5,4,6] => [5,2] => 1000010 => 2
[2,3,7,1,5,6,4] => [6,1] => 1000001 => 2
[2,3,7,1,6,4,5] => [4,3] => 1000100 => 2
[2,3,7,1,6,5,4] => [4,2,1] => 1000101 => 3
[2,3,7,4,1,5,6] => [4,3] => 1000100 => 2
[2,3,7,4,1,6,5] => [4,2,1] => 1000101 => 3
[2,3,7,4,5,1,6] => [5,2] => 1000010 => 2
[2,3,7,4,5,6,1] => [6,1] => 1000001 => 2
[2,3,7,4,6,1,5] => [4,3] => 1000100 => 2
[2,3,7,4,6,5,1] => [4,2,1] => 1000101 => 3
[2,3,7,5,1,4,6] => [3,4] => 1001000 => 2
[2,3,7,5,1,6,4] => [3,3,1] => 1001001 => 3
[2,3,7,5,4,1,6] => [3,2,2] => 1001010 => 3
[2,3,7,5,4,6,1] => [3,3,1] => 1001001 => 3
[2,3,7,5,6,1,4] => [3,4] => 1001000 => 2
[2,3,7,5,6,4,1] => [3,3,1] => 1001001 => 3
[2,3,7,6,1,4,5] => [3,4] => 1001000 => 2
[2,3,7,6,1,5,4] => [3,3,1] => 1001001 => 3
[2,3,7,6,4,1,5] => [3,2,2] => 1001010 => 3
[2,3,7,6,4,5,1] => [3,3,1] => 1001001 => 3
[2,3,7,6,5,1,4] => [3,2,2] => 1001010 => 3
[2,3,7,6,5,4,1] => [3,2,1,1] => 1001011 => 4
[2,4,1,3,5,6,7] => [7] => 1000000 => 1
[2,4,1,3,5,7,6] => [5,2] => 1000010 => 2
[2,4,1,3,6,5,7] => [4,3] => 1000100 => 2
[2,4,1,3,6,7,5] => [4,3] => 1000100 => 2
[2,4,1,3,7,5,6] => [4,3] => 1000100 => 2
[2,4,1,3,7,6,5] => [4,2,1] => 1000101 => 3
[2,4,1,5,3,6,7] => [3,4] => 1001000 => 2
[2,4,1,5,3,7,6] => [3,2,2] => 1001010 => 3
[2,4,1,5,6,3,7] => [3,4] => 1001000 => 2
[2,4,1,5,6,7,3] => [3,4] => 1001000 => 2
[2,4,1,5,7,3,6] => [3,4] => 1001000 => 2
[2,4,1,5,7,6,3] => [3,3,1] => 1001001 => 3
[2,4,1,6,3,5,7] => [3,4] => 1001000 => 2
[2,4,1,6,3,7,5] => [3,2,2] => 1001010 => 3
[2,4,1,6,5,3,7] => [3,2,2] => 1001010 => 3
[2,4,1,6,5,7,3] => [3,2,2] => 1001010 => 3
[2,4,1,6,7,3,5] => [3,4] => 1001000 => 2
[2,4,1,6,7,5,3] => [3,3,1] => 1001001 => 3
[2,4,1,7,3,5,6] => [3,4] => 1001000 => 2
[2,4,1,7,3,6,5] => [3,3,1] => 1001001 => 3
[2,4,1,7,5,3,6] => [3,2,2] => 1001010 => 3
[2,4,1,7,5,6,3] => [3,3,1] => 1001001 => 3
[2,4,1,7,6,3,5] => [3,1,3] => 1001100 => 3
[2,4,1,7,6,5,3] => [3,1,2,1] => 1001101 => 4
[2,4,3,1,5,6,7] => [3,4] => 1001000 => 2
[2,4,3,1,5,7,6] => [3,2,2] => 1001010 => 3
[2,4,3,1,6,5,7] => [3,1,3] => 1001100 => 3
[2,4,3,1,6,7,5] => [3,1,3] => 1001100 => 3
[2,4,3,1,7,5,6] => [3,1,3] => 1001100 => 3
[2,4,3,1,7,6,5] => [3,1,2,1] => 1001101 => 4
[2,4,3,5,1,6,7] => [3,4] => 1001000 => 2
[2,4,3,5,1,7,6] => [3,2,2] => 1001010 => 3
[2,4,3,5,6,1,7] => [3,4] => 1001000 => 2
[2,4,3,5,6,7,1] => [3,4] => 1001000 => 2
[2,4,3,5,7,1,6] => [3,4] => 1001000 => 2
[2,4,3,5,7,6,1] => [3,3,1] => 1001001 => 3
[2,4,3,6,1,5,7] => [3,4] => 1001000 => 2
[2,4,3,6,1,7,5] => [3,2,2] => 1001010 => 3
[2,4,3,6,5,1,7] => [3,2,2] => 1001010 => 3
[2,4,3,6,5,7,1] => [3,2,2] => 1001010 => 3
[2,4,3,6,7,1,5] => [3,4] => 1001000 => 2
[2,4,3,6,7,5,1] => [3,3,1] => 1001001 => 3
[2,4,3,7,1,5,6] => [3,4] => 1001000 => 2
[2,4,3,7,1,6,5] => [3,3,1] => 1001001 => 3
[2,4,3,7,5,1,6] => [3,2,2] => 1001010 => 3
[2,4,3,7,5,6,1] => [3,3,1] => 1001001 => 3
[2,4,3,7,6,1,5] => [3,1,3] => 1001100 => 3
[2,4,3,7,6,5,1] => [3,1,2,1] => 1001101 => 4
[2,4,5,1,3,6,7] => [7] => 1000000 => 1
[2,4,5,1,3,7,6] => [5,2] => 1000010 => 2
[2,4,5,1,6,3,7] => [4,3] => 1000100 => 2
[2,4,5,1,6,7,3] => [4,3] => 1000100 => 2
[2,4,5,1,7,3,6] => [4,3] => 1000100 => 2
[2,4,5,1,7,6,3] => [4,2,1] => 1000101 => 3
[2,4,5,3,1,6,7] => [4,3] => 1000100 => 2
[2,4,5,3,1,7,6] => [4,1,2] => 1000110 => 3
[2,4,5,3,6,1,7] => [4,3] => 1000100 => 2
[2,4,5,3,6,7,1] => [4,3] => 1000100 => 2
[2,4,5,3,7,1,6] => [4,3] => 1000100 => 2
[2,4,5,3,7,6,1] => [4,2,1] => 1000101 => 3
[2,4,5,6,1,3,7] => [7] => 1000000 => 1
[2,4,5,6,1,7,3] => [5,2] => 1000010 => 2
[2,4,5,6,3,1,7] => [5,2] => 1000010 => 2
[2,4,5,6,3,7,1] => [5,2] => 1000010 => 2
[2,4,5,6,7,1,3] => [7] => 1000000 => 1
[2,4,5,6,7,3,1] => [6,1] => 1000001 => 2
[2,4,5,7,1,3,6] => [7] => 1000000 => 1
[2,4,5,7,1,6,3] => [6,1] => 1000001 => 2
[2,4,5,7,3,1,6] => [5,2] => 1000010 => 2
[2,4,5,7,3,6,1] => [6,1] => 1000001 => 2
[2,4,5,7,6,1,3] => [4,3] => 1000100 => 2
[2,4,5,7,6,3,1] => [4,2,1] => 1000101 => 3
[2,4,6,1,3,5,7] => [7] => 1000000 => 1
[2,4,6,1,3,7,5] => [5,2] => 1000010 => 2
[2,4,6,1,5,3,7] => [5,2] => 1000010 => 2
[2,4,6,1,5,7,3] => [5,2] => 1000010 => 2
[2,4,6,1,7,3,5] => [4,3] => 1000100 => 2
[2,4,6,1,7,5,3] => [4,2,1] => 1000101 => 3
[2,4,6,3,1,5,7] => [4,3] => 1000100 => 2
[2,4,6,3,1,7,5] => [4,1,2] => 1000110 => 3
[2,4,6,3,5,1,7] => [5,2] => 1000010 => 2
[2,4,6,3,5,7,1] => [5,2] => 1000010 => 2
[2,4,6,3,7,1,5] => [4,3] => 1000100 => 2
[2,4,6,3,7,5,1] => [4,2,1] => 1000101 => 3
[2,4,6,5,1,3,7] => [3,4] => 1001000 => 2
[2,4,6,5,1,7,3] => [3,2,2] => 1001010 => 3
[2,4,6,5,3,1,7] => [3,2,2] => 1001010 => 3
[2,4,6,5,3,7,1] => [3,2,2] => 1001010 => 3
[2,4,6,5,7,1,3] => [3,4] => 1001000 => 2
[2,4,6,5,7,3,1] => [3,3,1] => 1001001 => 3
[2,4,6,7,1,3,5] => [7] => 1000000 => 1
[2,4,6,7,1,5,3] => [6,1] => 1000001 => 2
[2,4,6,7,3,1,5] => [5,2] => 1000010 => 2
[2,4,6,7,3,5,1] => [6,1] => 1000001 => 2
[2,4,6,7,5,1,3] => [5,2] => 1000010 => 2
[2,4,6,7,5,3,1] => [5,1,1] => 1000011 => 3
[2,4,7,1,3,5,6] => [7] => 1000000 => 1
[2,4,7,1,3,6,5] => [6,1] => 1000001 => 2
[2,4,7,1,5,3,6] => [5,2] => 1000010 => 2
[2,4,7,1,5,6,3] => [6,1] => 1000001 => 2
[2,4,7,1,6,3,5] => [4,3] => 1000100 => 2
[2,4,7,1,6,5,3] => [4,2,1] => 1000101 => 3
[2,4,7,3,1,5,6] => [4,3] => 1000100 => 2
[2,4,7,3,1,6,5] => [4,2,1] => 1000101 => 3
[2,4,7,3,5,1,6] => [5,2] => 1000010 => 2
[2,4,7,3,5,6,1] => [6,1] => 1000001 => 2
[2,4,7,3,6,1,5] => [4,3] => 1000100 => 2
[2,4,7,3,6,5,1] => [4,2,1] => 1000101 => 3
[2,4,7,5,1,3,6] => [3,4] => 1001000 => 2
[2,4,7,5,1,6,3] => [3,3,1] => 1001001 => 3
[2,4,7,5,3,1,6] => [3,2,2] => 1001010 => 3
[2,4,7,5,3,6,1] => [3,3,1] => 1001001 => 3
[2,4,7,5,6,1,3] => [3,4] => 1001000 => 2
[2,4,7,5,6,3,1] => [3,3,1] => 1001001 => 3
[2,4,7,6,1,3,5] => [3,4] => 1001000 => 2
[2,4,7,6,1,5,3] => [3,3,1] => 1001001 => 3
[2,4,7,6,3,1,5] => [3,2,2] => 1001010 => 3
[2,4,7,6,3,5,1] => [3,3,1] => 1001001 => 3
[2,4,7,6,5,1,3] => [3,2,2] => 1001010 => 3
[2,4,7,6,5,3,1] => [3,2,1,1] => 1001011 => 4
[2,5,1,3,4,6,7] => [7] => 1000000 => 1
[2,5,1,3,4,7,6] => [5,2] => 1000010 => 2
[2,5,1,3,6,4,7] => [4,3] => 1000100 => 2
[2,5,1,3,6,7,4] => [4,3] => 1000100 => 2
[2,5,1,3,7,4,6] => [4,3] => 1000100 => 2
[2,5,1,3,7,6,4] => [4,2,1] => 1000101 => 3
[2,5,1,4,3,6,7] => [4,3] => 1000100 => 2
[2,5,1,4,3,7,6] => [4,1,2] => 1000110 => 3
[2,5,1,4,6,3,7] => [4,3] => 1000100 => 2
[2,5,1,4,6,7,3] => [4,3] => 1000100 => 2
[2,5,1,4,7,3,6] => [4,3] => 1000100 => 2
[2,5,1,4,7,6,3] => [4,2,1] => 1000101 => 3
[2,5,1,6,3,4,7] => [3,4] => 1001000 => 2
[2,5,1,6,3,7,4] => [3,2,2] => 1001010 => 3
[2,5,1,6,4,3,7] => [3,2,2] => 1001010 => 3
[2,5,1,6,4,7,3] => [3,2,2] => 1001010 => 3
[2,5,1,6,7,3,4] => [3,4] => 1001000 => 2
[2,5,1,6,7,4,3] => [3,3,1] => 1001001 => 3
[2,5,1,7,3,4,6] => [3,4] => 1001000 => 2
[2,5,1,7,3,6,4] => [3,3,1] => 1001001 => 3
[2,5,1,7,4,3,6] => [3,2,2] => 1001010 => 3
[2,5,1,7,4,6,3] => [3,3,1] => 1001001 => 3
[2,5,1,7,6,3,4] => [3,1,3] => 1001100 => 3
[2,5,1,7,6,4,3] => [3,1,2,1] => 1001101 => 4
[2,5,3,1,4,6,7] => [3,4] => 1001000 => 2
[2,5,3,1,4,7,6] => [3,2,2] => 1001010 => 3
[2,5,3,1,6,4,7] => [3,1,3] => 1001100 => 3
[2,5,3,1,6,7,4] => [3,1,3] => 1001100 => 3
[2,5,3,1,7,4,6] => [3,1,3] => 1001100 => 3
[2,5,3,1,7,6,4] => [3,1,2,1] => 1001101 => 4
[2,5,3,4,1,6,7] => [4,3] => 1000100 => 2
[2,5,3,4,1,7,6] => [4,1,2] => 1000110 => 3
[2,5,3,4,6,1,7] => [4,3] => 1000100 => 2
[2,5,3,4,6,7,1] => [4,3] => 1000100 => 2
[2,5,3,4,7,1,6] => [4,3] => 1000100 => 2
[2,5,3,4,7,6,1] => [4,2,1] => 1000101 => 3
[2,5,3,6,1,4,7] => [3,4] => 1001000 => 2
[2,5,3,6,1,7,4] => [3,2,2] => 1001010 => 3
[2,5,3,6,4,1,7] => [3,2,2] => 1001010 => 3
[2,5,3,6,4,7,1] => [3,2,2] => 1001010 => 3
[2,5,3,6,7,1,4] => [3,4] => 1001000 => 2
[2,5,3,6,7,4,1] => [3,3,1] => 1001001 => 3
[2,5,3,7,1,4,6] => [3,4] => 1001000 => 2
[2,5,3,7,1,6,4] => [3,3,1] => 1001001 => 3
[2,5,3,7,4,1,6] => [3,2,2] => 1001010 => 3
[2,5,3,7,4,6,1] => [3,3,1] => 1001001 => 3
[2,5,3,7,6,1,4] => [3,1,3] => 1001100 => 3
[2,5,3,7,6,4,1] => [3,1,2,1] => 1001101 => 4
[2,5,4,1,3,6,7] => [2,5] => 1010000 => 2
[2,5,4,1,3,7,6] => [2,3,2] => 1010010 => 3
[2,5,4,1,6,3,7] => [2,2,3] => 1010100 => 3
[2,5,4,1,6,7,3] => [2,2,3] => 1010100 => 3
[2,5,4,1,7,3,6] => [2,2,3] => 1010100 => 3
[2,5,4,1,7,6,3] => [2,2,2,1] => 1010101 => 4
[2,5,4,3,1,6,7] => [2,2,3] => 1010100 => 3
[2,5,4,3,1,7,6] => [2,2,1,2] => 1010110 => 4
[2,5,4,3,6,1,7] => [2,2,3] => 1010100 => 3
[2,5,4,3,6,7,1] => [2,2,3] => 1010100 => 3
[2,5,4,3,7,1,6] => [2,2,3] => 1010100 => 3
[2,5,4,3,7,6,1] => [2,2,2,1] => 1010101 => 4
[2,5,4,6,1,3,7] => [2,5] => 1010000 => 2
[2,5,4,6,1,7,3] => [2,3,2] => 1010010 => 3
[2,5,4,6,3,1,7] => [2,3,2] => 1010010 => 3
[2,5,4,6,3,7,1] => [2,3,2] => 1010010 => 3
[2,5,4,6,7,1,3] => [2,5] => 1010000 => 2
[2,5,4,6,7,3,1] => [2,4,1] => 1010001 => 3
[2,5,4,7,1,3,6] => [2,5] => 1010000 => 2
[2,5,4,7,1,6,3] => [2,4,1] => 1010001 => 3
[2,5,4,7,3,1,6] => [2,3,2] => 1010010 => 3
[2,5,4,7,3,6,1] => [2,4,1] => 1010001 => 3
[2,5,4,7,6,1,3] => [2,2,3] => 1010100 => 3
[2,5,4,7,6,3,1] => [2,2,2,1] => 1010101 => 4
[2,5,6,1,3,4,7] => [7] => 1000000 => 1
[2,5,6,1,3,7,4] => [5,2] => 1000010 => 2
[2,5,6,1,4,3,7] => [5,2] => 1000010 => 2
[2,5,6,1,4,7,3] => [5,2] => 1000010 => 2
[2,5,6,1,7,3,4] => [4,3] => 1000100 => 2
[2,5,6,1,7,4,3] => [4,2,1] => 1000101 => 3
[2,5,6,3,1,4,7] => [4,3] => 1000100 => 2
[2,5,6,3,1,7,4] => [4,1,2] => 1000110 => 3
[2,5,6,3,4,1,7] => [5,2] => 1000010 => 2
[2,5,6,3,4,7,1] => [5,2] => 1000010 => 2
[2,5,6,3,7,1,4] => [4,3] => 1000100 => 2
[2,5,6,3,7,4,1] => [4,2,1] => 1000101 => 3
[2,5,6,4,1,3,7] => [4,3] => 1000100 => 2
[2,5,6,4,1,7,3] => [4,1,2] => 1000110 => 3
[2,5,6,4,3,1,7] => [4,1,2] => 1000110 => 3
[2,5,6,4,3,7,1] => [4,1,2] => 1000110 => 3
[2,5,6,4,7,1,3] => [4,3] => 1000100 => 2
[2,5,6,4,7,3,1] => [4,2,1] => 1000101 => 3
[2,5,6,7,1,3,4] => [7] => 1000000 => 1
[2,5,6,7,1,4,3] => [6,1] => 1000001 => 2
[2,5,6,7,3,1,4] => [5,2] => 1000010 => 2
[2,5,6,7,3,4,1] => [6,1] => 1000001 => 2
[2,5,6,7,4,1,3] => [5,2] => 1000010 => 2
[2,5,6,7,4,3,1] => [5,1,1] => 1000011 => 3
[2,5,7,1,3,4,6] => [7] => 1000000 => 1
[2,5,7,1,3,6,4] => [6,1] => 1000001 => 2
[2,5,7,1,4,3,6] => [5,2] => 1000010 => 2
[2,5,7,1,4,6,3] => [6,1] => 1000001 => 2
[2,5,7,1,6,3,4] => [4,3] => 1000100 => 2
[2,5,7,1,6,4,3] => [4,2,1] => 1000101 => 3
[2,5,7,3,1,4,6] => [4,3] => 1000100 => 2
[2,5,7,3,1,6,4] => [4,2,1] => 1000101 => 3
[2,5,7,3,4,1,6] => [5,2] => 1000010 => 2
[2,5,7,3,4,6,1] => [6,1] => 1000001 => 2
[2,5,7,3,6,1,4] => [4,3] => 1000100 => 2
[2,5,7,3,6,4,1] => [4,2,1] => 1000101 => 3
[2,5,7,4,1,3,6] => [4,3] => 1000100 => 2
[2,5,7,4,1,6,3] => [4,2,1] => 1000101 => 3
[2,5,7,4,3,1,6] => [4,1,2] => 1000110 => 3
[2,5,7,4,3,6,1] => [4,2,1] => 1000101 => 3
[2,5,7,4,6,1,3] => [4,3] => 1000100 => 2
[2,5,7,4,6,3,1] => [4,2,1] => 1000101 => 3
[2,5,7,6,1,3,4] => [3,4] => 1001000 => 2
[2,5,7,6,1,4,3] => [3,3,1] => 1001001 => 3
[2,5,7,6,3,1,4] => [3,2,2] => 1001010 => 3
[2,5,7,6,3,4,1] => [3,3,1] => 1001001 => 3
[2,5,7,6,4,1,3] => [3,2,2] => 1001010 => 3
[2,5,7,6,4,3,1] => [3,2,1,1] => 1001011 => 4
[2,6,1,3,4,5,7] => [7] => 1000000 => 1
[2,6,1,3,4,7,5] => [5,2] => 1000010 => 2
[2,6,1,3,5,4,7] => [5,2] => 1000010 => 2
[2,6,1,3,5,7,4] => [5,2] => 1000010 => 2
[2,6,1,3,7,4,5] => [4,3] => 1000100 => 2
[2,6,1,3,7,5,4] => [4,2,1] => 1000101 => 3
[2,6,1,4,3,5,7] => [4,3] => 1000100 => 2
[2,6,1,4,3,7,5] => [4,1,2] => 1000110 => 3
[2,6,1,4,5,3,7] => [5,2] => 1000010 => 2
[2,6,1,4,5,7,3] => [5,2] => 1000010 => 2
[2,6,1,4,7,3,5] => [4,3] => 1000100 => 2
[2,6,1,4,7,5,3] => [4,2,1] => 1000101 => 3
[2,6,1,5,3,4,7] => [3,4] => 1001000 => 2
[2,6,1,5,3,7,4] => [3,2,2] => 1001010 => 3
[2,6,1,5,4,3,7] => [3,2,2] => 1001010 => 3
[2,6,1,5,4,7,3] => [3,2,2] => 1001010 => 3
[2,6,1,5,7,3,4] => [3,4] => 1001000 => 2
[2,6,1,5,7,4,3] => [3,3,1] => 1001001 => 3
[2,6,1,7,3,4,5] => [3,4] => 1001000 => 2
[2,6,1,7,3,5,4] => [3,3,1] => 1001001 => 3
[2,6,1,7,4,3,5] => [3,2,2] => 1001010 => 3
[2,6,1,7,4,5,3] => [3,3,1] => 1001001 => 3
[2,6,1,7,5,3,4] => [3,2,2] => 1001010 => 3
[2,6,1,7,5,4,3] => [3,2,1,1] => 1001011 => 4
[2,6,3,1,4,5,7] => [3,4] => 1001000 => 2
[2,6,3,1,4,7,5] => [3,2,2] => 1001010 => 3
[2,6,3,1,5,4,7] => [3,2,2] => 1001010 => 3
[2,6,3,1,5,7,4] => [3,2,2] => 1001010 => 3
[2,6,3,1,7,4,5] => [3,1,3] => 1001100 => 3
[2,6,3,1,7,5,4] => [3,1,2,1] => 1001101 => 4
[2,6,3,4,1,5,7] => [4,3] => 1000100 => 2
[2,6,3,4,1,7,5] => [4,1,2] => 1000110 => 3
[2,6,3,4,5,1,7] => [5,2] => 1000010 => 2
[2,6,3,4,5,7,1] => [5,2] => 1000010 => 2
[2,6,3,4,7,1,5] => [4,3] => 1000100 => 2
[2,6,3,4,7,5,1] => [4,2,1] => 1000101 => 3
[2,6,3,5,1,4,7] => [3,4] => 1001000 => 2
[2,6,3,5,1,7,4] => [3,2,2] => 1001010 => 3
[2,6,3,5,4,1,7] => [3,2,2] => 1001010 => 3
[2,6,3,5,4,7,1] => [3,2,2] => 1001010 => 3
[2,6,3,5,7,1,4] => [3,4] => 1001000 => 2
[2,6,3,5,7,4,1] => [3,3,1] => 1001001 => 3
[2,6,3,7,1,4,5] => [3,4] => 1001000 => 2
[2,6,3,7,1,5,4] => [3,3,1] => 1001001 => 3
[2,6,3,7,4,1,5] => [3,2,2] => 1001010 => 3
[2,6,3,7,4,5,1] => [3,3,1] => 1001001 => 3
[2,6,3,7,5,1,4] => [3,2,2] => 1001010 => 3
[2,6,3,7,5,4,1] => [3,2,1,1] => 1001011 => 4
[2,6,4,1,3,5,7] => [2,5] => 1010000 => 2
[2,6,4,1,3,7,5] => [2,3,2] => 1010010 => 3
[2,6,4,1,5,3,7] => [2,3,2] => 1010010 => 3
[2,6,4,1,5,7,3] => [2,3,2] => 1010010 => 3
[2,6,4,1,7,3,5] => [2,2,3] => 1010100 => 3
[2,6,4,1,7,5,3] => [2,2,2,1] => 1010101 => 4
[2,6,4,3,1,5,7] => [2,2,3] => 1010100 => 3
[2,6,4,3,1,7,5] => [2,2,1,2] => 1010110 => 4
[2,6,4,3,5,1,7] => [2,3,2] => 1010010 => 3
[2,6,4,3,5,7,1] => [2,3,2] => 1010010 => 3
[2,6,4,3,7,1,5] => [2,2,3] => 1010100 => 3
[2,6,4,3,7,5,1] => [2,2,2,1] => 1010101 => 4
[2,6,4,5,1,3,7] => [2,5] => 1010000 => 2
[2,6,4,5,1,7,3] => [2,3,2] => 1010010 => 3
[2,6,4,5,3,1,7] => [2,3,2] => 1010010 => 3
[2,6,4,5,3,7,1] => [2,3,2] => 1010010 => 3
[2,6,4,5,7,1,3] => [2,5] => 1010000 => 2
[2,6,4,5,7,3,1] => [2,4,1] => 1010001 => 3
[2,6,4,7,1,3,5] => [2,5] => 1010000 => 2
[2,6,4,7,1,5,3] => [2,4,1] => 1010001 => 3
[2,6,4,7,3,1,5] => [2,3,2] => 1010010 => 3
[2,6,4,7,3,5,1] => [2,4,1] => 1010001 => 3
[2,6,4,7,5,1,3] => [2,3,2] => 1010010 => 3
[2,6,4,7,5,3,1] => [2,3,1,1] => 1010011 => 4
[2,6,5,1,3,4,7] => [2,5] => 1010000 => 2
[2,6,5,1,3,7,4] => [2,3,2] => 1010010 => 3
[2,6,5,1,4,3,7] => [2,3,2] => 1010010 => 3
[2,6,5,1,4,7,3] => [2,3,2] => 1010010 => 3
[2,6,5,1,7,3,4] => [2,2,3] => 1010100 => 3
[2,6,5,1,7,4,3] => [2,2,2,1] => 1010101 => 4
[2,6,5,3,1,4,7] => [2,2,3] => 1010100 => 3
[2,6,5,3,1,7,4] => [2,2,1,2] => 1010110 => 4
[2,6,5,3,4,1,7] => [2,3,2] => 1010010 => 3
[2,6,5,3,4,7,1] => [2,3,2] => 1010010 => 3
[2,6,5,3,7,1,4] => [2,2,3] => 1010100 => 3
[2,6,5,3,7,4,1] => [2,2,2,1] => 1010101 => 4
[2,6,5,4,1,3,7] => [2,2,3] => 1010100 => 3
[2,6,5,4,1,7,3] => [2,2,1,2] => 1010110 => 4
[2,6,5,4,3,1,7] => [2,2,1,2] => 1010110 => 4
[2,6,5,4,3,7,1] => [2,2,1,2] => 1010110 => 4
[2,6,5,4,7,1,3] => [2,2,3] => 1010100 => 3
[2,6,5,4,7,3,1] => [2,2,2,1] => 1010101 => 4
[2,6,5,7,1,3,4] => [2,5] => 1010000 => 2
[2,6,5,7,1,4,3] => [2,4,1] => 1010001 => 3
[2,6,5,7,3,1,4] => [2,3,2] => 1010010 => 3
[2,6,5,7,3,4,1] => [2,4,1] => 1010001 => 3
[2,6,5,7,4,1,3] => [2,3,2] => 1010010 => 3
[2,6,5,7,4,3,1] => [2,3,1,1] => 1010011 => 4
[2,6,7,1,3,4,5] => [7] => 1000000 => 1
[2,6,7,1,3,5,4] => [6,1] => 1000001 => 2
[2,6,7,1,4,3,5] => [5,2] => 1000010 => 2
[2,6,7,1,4,5,3] => [6,1] => 1000001 => 2
[2,6,7,1,5,3,4] => [5,2] => 1000010 => 2
[2,6,7,1,5,4,3] => [5,1,1] => 1000011 => 3
[2,6,7,3,1,4,5] => [4,3] => 1000100 => 2
[2,6,7,3,1,5,4] => [4,2,1] => 1000101 => 3
[2,6,7,3,4,1,5] => [5,2] => 1000010 => 2
[2,6,7,3,4,5,1] => [6,1] => 1000001 => 2
[2,6,7,3,5,1,4] => [5,2] => 1000010 => 2
[2,6,7,3,5,4,1] => [5,1,1] => 1000011 => 3
[2,6,7,4,1,3,5] => [4,3] => 1000100 => 2
[2,6,7,4,1,5,3] => [4,2,1] => 1000101 => 3
[2,6,7,4,3,1,5] => [4,1,2] => 1000110 => 3
[2,6,7,4,3,5,1] => [4,2,1] => 1000101 => 3
[2,6,7,4,5,1,3] => [5,2] => 1000010 => 2
[2,6,7,4,5,3,1] => [5,1,1] => 1000011 => 3
[2,6,7,5,1,3,4] => [3,4] => 1001000 => 2
[2,6,7,5,1,4,3] => [3,3,1] => 1001001 => 3
[2,6,7,5,3,1,4] => [3,2,2] => 1001010 => 3
[2,6,7,5,3,4,1] => [3,3,1] => 1001001 => 3
[2,6,7,5,4,1,3] => [3,2,2] => 1001010 => 3
[2,6,7,5,4,3,1] => [3,2,1,1] => 1001011 => 4
[2,7,1,3,4,5,6] => [7] => 1000000 => 1
[2,7,1,3,4,6,5] => [6,1] => 1000001 => 2
[2,7,1,3,5,4,6] => [5,2] => 1000010 => 2
[2,7,1,3,5,6,4] => [6,1] => 1000001 => 2
[2,7,1,3,6,4,5] => [4,3] => 1000100 => 2
[2,7,1,3,6,5,4] => [4,2,1] => 1000101 => 3
[2,7,1,4,3,5,6] => [4,3] => 1000100 => 2
[2,7,1,4,3,6,5] => [4,2,1] => 1000101 => 3
[2,7,1,4,5,3,6] => [5,2] => 1000010 => 2
[2,7,1,4,5,6,3] => [6,1] => 1000001 => 2
[2,7,1,4,6,3,5] => [4,3] => 1000100 => 2
[2,7,1,4,6,5,3] => [4,2,1] => 1000101 => 3
[2,7,1,5,3,4,6] => [3,4] => 1001000 => 2
[2,7,1,5,3,6,4] => [3,3,1] => 1001001 => 3
[2,7,1,5,4,3,6] => [3,2,2] => 1001010 => 3
[2,7,1,5,4,6,3] => [3,3,1] => 1001001 => 3
[2,7,1,5,6,3,4] => [3,4] => 1001000 => 2
[2,7,1,5,6,4,3] => [3,3,1] => 1001001 => 3
[2,7,1,6,3,4,5] => [3,4] => 1001000 => 2
[2,7,1,6,3,5,4] => [3,3,1] => 1001001 => 3
[2,7,1,6,4,3,5] => [3,2,2] => 1001010 => 3
[2,7,1,6,4,5,3] => [3,3,1] => 1001001 => 3
[2,7,1,6,5,3,4] => [3,2,2] => 1001010 => 3
[2,7,1,6,5,4,3] => [3,2,1,1] => 1001011 => 4
[2,7,3,1,4,5,6] => [3,4] => 1001000 => 2
[2,7,3,1,4,6,5] => [3,3,1] => 1001001 => 3
[2,7,3,1,5,4,6] => [3,2,2] => 1001010 => 3
[2,7,3,1,5,6,4] => [3,3,1] => 1001001 => 3
[2,7,3,1,6,4,5] => [3,1,3] => 1001100 => 3
[2,7,3,1,6,5,4] => [3,1,2,1] => 1001101 => 4
[2,7,3,4,1,5,6] => [4,3] => 1000100 => 2
[2,7,3,4,1,6,5] => [4,2,1] => 1000101 => 3
[2,7,3,4,5,1,6] => [5,2] => 1000010 => 2
[2,7,3,4,5,6,1] => [6,1] => 1000001 => 2
[2,7,3,4,6,1,5] => [4,3] => 1000100 => 2
[2,7,3,4,6,5,1] => [4,2,1] => 1000101 => 3
[2,7,3,5,1,4,6] => [3,4] => 1001000 => 2
[2,7,3,5,1,6,4] => [3,3,1] => 1001001 => 3
[2,7,3,5,4,1,6] => [3,2,2] => 1001010 => 3
[2,7,3,5,4,6,1] => [3,3,1] => 1001001 => 3
[2,7,3,5,6,1,4] => [3,4] => 1001000 => 2
[2,7,3,5,6,4,1] => [3,3,1] => 1001001 => 3
[2,7,3,6,1,4,5] => [3,4] => 1001000 => 2
[2,7,3,6,1,5,4] => [3,3,1] => 1001001 => 3
[2,7,3,6,4,1,5] => [3,2,2] => 1001010 => 3
[2,7,3,6,4,5,1] => [3,3,1] => 1001001 => 3
[2,7,3,6,5,1,4] => [3,2,2] => 1001010 => 3
[2,7,3,6,5,4,1] => [3,2,1,1] => 1001011 => 4
[2,7,4,1,3,5,6] => [2,5] => 1010000 => 2
[2,7,4,1,3,6,5] => [2,4,1] => 1010001 => 3
[2,7,4,1,5,3,6] => [2,3,2] => 1010010 => 3
[2,7,4,1,5,6,3] => [2,4,1] => 1010001 => 3
[2,7,4,1,6,3,5] => [2,2,3] => 1010100 => 3
[2,7,4,1,6,5,3] => [2,2,2,1] => 1010101 => 4
[2,7,4,3,1,5,6] => [2,2,3] => 1010100 => 3
[2,7,4,3,1,6,5] => [2,2,2,1] => 1010101 => 4
[2,7,4,3,5,1,6] => [2,3,2] => 1010010 => 3
[2,7,4,3,5,6,1] => [2,4,1] => 1010001 => 3
[2,7,4,3,6,1,5] => [2,2,3] => 1010100 => 3
[2,7,4,3,6,5,1] => [2,2,2,1] => 1010101 => 4
[2,7,4,5,1,3,6] => [2,5] => 1010000 => 2
[2,7,4,5,1,6,3] => [2,4,1] => 1010001 => 3
[2,7,4,5,3,1,6] => [2,3,2] => 1010010 => 3
[2,7,4,5,3,6,1] => [2,4,1] => 1010001 => 3
[2,7,4,5,6,1,3] => [2,5] => 1010000 => 2
[2,7,4,5,6,3,1] => [2,4,1] => 1010001 => 3
[2,7,4,6,1,3,5] => [2,5] => 1010000 => 2
[2,7,4,6,1,5,3] => [2,4,1] => 1010001 => 3
[2,7,4,6,3,1,5] => [2,3,2] => 1010010 => 3
[2,7,4,6,3,5,1] => [2,4,1] => 1010001 => 3
[2,7,4,6,5,1,3] => [2,3,2] => 1010010 => 3
[2,7,4,6,5,3,1] => [2,3,1,1] => 1010011 => 4
[2,7,5,1,3,4,6] => [2,5] => 1010000 => 2
[2,7,5,1,3,6,4] => [2,4,1] => 1010001 => 3
[2,7,5,1,4,3,6] => [2,3,2] => 1010010 => 3
[2,7,5,1,4,6,3] => [2,4,1] => 1010001 => 3
[2,7,5,1,6,3,4] => [2,2,3] => 1010100 => 3
[2,7,5,1,6,4,3] => [2,2,2,1] => 1010101 => 4
[2,7,5,3,1,4,6] => [2,2,3] => 1010100 => 3
[2,7,5,3,1,6,4] => [2,2,2,1] => 1010101 => 4
[2,7,5,3,4,1,6] => [2,3,2] => 1010010 => 3
[2,7,5,3,4,6,1] => [2,4,1] => 1010001 => 3
[2,7,5,3,6,1,4] => [2,2,3] => 1010100 => 3
[2,7,5,3,6,4,1] => [2,2,2,1] => 1010101 => 4
[2,7,5,4,1,3,6] => [2,2,3] => 1010100 => 3
[2,7,5,4,1,6,3] => [2,2,2,1] => 1010101 => 4
[2,7,5,4,3,1,6] => [2,2,1,2] => 1010110 => 4
[2,7,5,4,3,6,1] => [2,2,2,1] => 1010101 => 4
[2,7,5,4,6,1,3] => [2,2,3] => 1010100 => 3
[2,7,5,4,6,3,1] => [2,2,2,1] => 1010101 => 4
[2,7,5,6,1,3,4] => [2,5] => 1010000 => 2
[2,7,5,6,1,4,3] => [2,4,1] => 1010001 => 3
[2,7,5,6,3,1,4] => [2,3,2] => 1010010 => 3
[2,7,5,6,3,4,1] => [2,4,1] => 1010001 => 3
[2,7,5,6,4,1,3] => [2,3,2] => 1010010 => 3
[2,7,5,6,4,3,1] => [2,3,1,1] => 1010011 => 4
[2,7,6,1,3,4,5] => [2,5] => 1010000 => 2
[2,7,6,1,3,5,4] => [2,4,1] => 1010001 => 3
[2,7,6,1,4,3,5] => [2,3,2] => 1010010 => 3
[2,7,6,1,4,5,3] => [2,4,1] => 1010001 => 3
[2,7,6,1,5,3,4] => [2,3,2] => 1010010 => 3
[2,7,6,1,5,4,3] => [2,3,1,1] => 1010011 => 4
[2,7,6,3,1,4,5] => [2,2,3] => 1010100 => 3
[2,7,6,3,1,5,4] => [2,2,2,1] => 1010101 => 4
[2,7,6,3,4,1,5] => [2,3,2] => 1010010 => 3
[2,7,6,3,4,5,1] => [2,4,1] => 1010001 => 3
[2,7,6,3,5,1,4] => [2,3,2] => 1010010 => 3
[2,7,6,3,5,4,1] => [2,3,1,1] => 1010011 => 4
[2,7,6,4,1,3,5] => [2,2,3] => 1010100 => 3
[2,7,6,4,1,5,3] => [2,2,2,1] => 1010101 => 4
[2,7,6,4,3,1,5] => [2,2,1,2] => 1010110 => 4
[2,7,6,4,3,5,1] => [2,2,2,1] => 1010101 => 4
[2,7,6,4,5,1,3] => [2,3,2] => 1010010 => 3
[2,7,6,4,5,3,1] => [2,3,1,1] => 1010011 => 4
[2,7,6,5,1,3,4] => [2,1,4] => 1011000 => 3
[2,7,6,5,1,4,3] => [2,1,3,1] => 1011001 => 4
[2,7,6,5,3,1,4] => [2,1,2,2] => 1011010 => 4
[2,7,6,5,3,4,1] => [2,1,3,1] => 1011001 => 4
[2,7,6,5,4,1,3] => [2,1,2,2] => 1011010 => 4
[2,7,6,5,4,3,1] => [2,1,2,1,1] => 1011011 => 5
[3,1,2,4,5,6,7] => [7] => 1000000 => 1
[3,1,2,4,5,7,6] => [5,2] => 1000010 => 2
[3,1,2,4,6,5,7] => [4,3] => 1000100 => 2
[3,1,2,4,6,7,5] => [4,3] => 1000100 => 2
[3,1,2,4,7,5,6] => [4,3] => 1000100 => 2
[3,1,2,4,7,6,5] => [4,2,1] => 1000101 => 3
[3,1,2,5,4,6,7] => [3,4] => 1001000 => 2
[3,1,2,5,4,7,6] => [3,2,2] => 1001010 => 3
[3,1,2,5,6,4,7] => [3,4] => 1001000 => 2
[3,1,2,5,6,7,4] => [3,4] => 1001000 => 2
[3,1,2,5,7,4,6] => [3,4] => 1001000 => 2
[3,1,2,5,7,6,4] => [3,3,1] => 1001001 => 3
[3,1,2,6,4,5,7] => [3,4] => 1001000 => 2
[3,1,2,6,4,7,5] => [3,2,2] => 1001010 => 3
[3,1,2,6,5,4,7] => [3,2,2] => 1001010 => 3
[3,1,2,6,5,7,4] => [3,2,2] => 1001010 => 3
[3,1,2,6,7,4,5] => [3,4] => 1001000 => 2
[3,1,2,6,7,5,4] => [3,3,1] => 1001001 => 3
[3,1,2,7,4,5,6] => [3,4] => 1001000 => 2
[3,1,2,7,4,6,5] => [3,3,1] => 1001001 => 3
[3,1,2,7,5,4,6] => [3,2,2] => 1001010 => 3
[3,1,2,7,5,6,4] => [3,3,1] => 1001001 => 3
[3,1,2,7,6,4,5] => [3,1,3] => 1001100 => 3
[3,1,2,7,6,5,4] => [3,1,2,1] => 1001101 => 4
[3,1,4,2,5,6,7] => [2,5] => 1010000 => 2
[3,1,4,2,5,7,6] => [2,3,2] => 1010010 => 3
[3,1,4,2,6,5,7] => [2,2,3] => 1010100 => 3
[3,1,4,2,6,7,5] => [2,2,3] => 1010100 => 3
[3,1,4,2,7,5,6] => [2,2,3] => 1010100 => 3
[3,1,4,2,7,6,5] => [2,2,2,1] => 1010101 => 4
[3,1,4,5,2,6,7] => [2,5] => 1010000 => 2
[3,1,4,5,2,7,6] => [2,3,2] => 1010010 => 3
[3,1,4,5,6,2,7] => [2,5] => 1010000 => 2
[3,1,4,5,6,7,2] => [2,5] => 1010000 => 2
[3,1,4,5,7,2,6] => [2,5] => 1010000 => 2
[3,1,4,5,7,6,2] => [2,4,1] => 1010001 => 3
[3,1,4,6,2,5,7] => [2,5] => 1010000 => 2
[3,1,4,6,2,7,5] => [2,3,2] => 1010010 => 3
[3,1,4,6,5,2,7] => [2,3,2] => 1010010 => 3
[3,1,4,6,5,7,2] => [2,3,2] => 1010010 => 3
[3,1,4,6,7,2,5] => [2,5] => 1010000 => 2
[3,1,4,6,7,5,2] => [2,4,1] => 1010001 => 3
[3,1,4,7,2,5,6] => [2,5] => 1010000 => 2
[3,1,4,7,2,6,5] => [2,4,1] => 1010001 => 3
[3,1,4,7,5,2,6] => [2,3,2] => 1010010 => 3
[3,1,4,7,5,6,2] => [2,4,1] => 1010001 => 3
[3,1,4,7,6,2,5] => [2,2,3] => 1010100 => 3
[3,1,4,7,6,5,2] => [2,2,2,1] => 1010101 => 4
[3,1,5,2,4,6,7] => [2,5] => 1010000 => 2
[3,1,5,2,4,7,6] => [2,3,2] => 1010010 => 3
[3,1,5,2,6,4,7] => [2,2,3] => 1010100 => 3
[3,1,5,2,6,7,4] => [2,2,3] => 1010100 => 3
[3,1,5,2,7,4,6] => [2,2,3] => 1010100 => 3
[3,1,5,2,7,6,4] => [2,2,2,1] => 1010101 => 4
[3,1,5,4,2,6,7] => [2,2,3] => 1010100 => 3
[3,1,5,4,2,7,6] => [2,2,1,2] => 1010110 => 4
[3,1,5,4,6,2,7] => [2,2,3] => 1010100 => 3
[3,1,5,4,6,7,2] => [2,2,3] => 1010100 => 3
[3,1,5,4,7,2,6] => [2,2,3] => 1010100 => 3
[3,1,5,4,7,6,2] => [2,2,2,1] => 1010101 => 4
[3,1,5,6,2,4,7] => [2,5] => 1010000 => 2
[3,1,5,6,2,7,4] => [2,3,2] => 1010010 => 3
[3,1,5,6,4,2,7] => [2,3,2] => 1010010 => 3
[3,1,5,6,4,7,2] => [2,3,2] => 1010010 => 3
[3,1,5,6,7,2,4] => [2,5] => 1010000 => 2
[3,1,5,6,7,4,2] => [2,4,1] => 1010001 => 3
[3,1,5,7,2,4,6] => [2,5] => 1010000 => 2
[3,1,5,7,2,6,4] => [2,4,1] => 1010001 => 3
[3,1,5,7,4,2,6] => [2,3,2] => 1010010 => 3
[3,1,5,7,4,6,2] => [2,4,1] => 1010001 => 3
[3,1,5,7,6,2,4] => [2,2,3] => 1010100 => 3
[3,1,5,7,6,4,2] => [2,2,2,1] => 1010101 => 4
[3,1,6,2,4,5,7] => [2,5] => 1010000 => 2
[3,1,6,2,4,7,5] => [2,3,2] => 1010010 => 3
[3,1,6,2,5,4,7] => [2,3,2] => 1010010 => 3
[3,1,6,2,5,7,4] => [2,3,2] => 1010010 => 3
[3,1,6,2,7,4,5] => [2,2,3] => 1010100 => 3
[3,1,6,2,7,5,4] => [2,2,2,1] => 1010101 => 4
[3,1,6,4,2,5,7] => [2,2,3] => 1010100 => 3
[3,1,6,4,2,7,5] => [2,2,1,2] => 1010110 => 4
[3,1,6,4,5,2,7] => [2,3,2] => 1010010 => 3
[3,1,6,4,5,7,2] => [2,3,2] => 1010010 => 3
[3,1,6,4,7,2,5] => [2,2,3] => 1010100 => 3
[3,1,6,4,7,5,2] => [2,2,2,1] => 1010101 => 4
[3,1,6,5,2,4,7] => [2,1,4] => 1011000 => 3
[3,1,6,5,2,7,4] => [2,1,2,2] => 1011010 => 4
[3,1,6,5,4,2,7] => [2,1,2,2] => 1011010 => 4
[3,1,6,5,4,7,2] => [2,1,2,2] => 1011010 => 4
[3,1,6,5,7,2,4] => [2,1,4] => 1011000 => 3
[3,1,6,5,7,4,2] => [2,1,3,1] => 1011001 => 4
[3,1,6,7,2,4,5] => [2,5] => 1010000 => 2
[3,1,6,7,2,5,4] => [2,4,1] => 1010001 => 3
[3,1,6,7,4,2,5] => [2,3,2] => 1010010 => 3
[3,1,6,7,4,5,2] => [2,4,1] => 1010001 => 3
[3,1,6,7,5,2,4] => [2,3,2] => 1010010 => 3
[3,1,6,7,5,4,2] => [2,3,1,1] => 1010011 => 4
[3,1,7,2,4,5,6] => [2,5] => 1010000 => 2
[3,1,7,2,4,6,5] => [2,4,1] => 1010001 => 3
[3,1,7,2,5,4,6] => [2,3,2] => 1010010 => 3
[3,1,7,2,5,6,4] => [2,4,1] => 1010001 => 3
[3,1,7,2,6,4,5] => [2,2,3] => 1010100 => 3
[3,1,7,2,6,5,4] => [2,2,2,1] => 1010101 => 4
[3,1,7,4,2,5,6] => [2,2,3] => 1010100 => 3
[3,1,7,4,2,6,5] => [2,2,2,1] => 1010101 => 4
[3,1,7,4,5,2,6] => [2,3,2] => 1010010 => 3
[3,1,7,4,5,6,2] => [2,4,1] => 1010001 => 3
[3,1,7,4,6,2,5] => [2,2,3] => 1010100 => 3
[3,1,7,4,6,5,2] => [2,2,2,1] => 1010101 => 4
[3,1,7,5,2,4,6] => [2,1,4] => 1011000 => 3
[3,1,7,5,2,6,4] => [2,1,3,1] => 1011001 => 4
[3,1,7,5,4,2,6] => [2,1,2,2] => 1011010 => 4
[3,1,7,5,4,6,2] => [2,1,3,1] => 1011001 => 4
[3,1,7,5,6,2,4] => [2,1,4] => 1011000 => 3
[3,1,7,5,6,4,2] => [2,1,3,1] => 1011001 => 4
[3,1,7,6,2,4,5] => [2,1,4] => 1011000 => 3
[3,1,7,6,2,5,4] => [2,1,3,1] => 1011001 => 4
[3,1,7,6,4,2,5] => [2,1,2,2] => 1011010 => 4
[3,1,7,6,4,5,2] => [2,1,3,1] => 1011001 => 4
[3,1,7,6,5,2,4] => [2,1,2,2] => 1011010 => 4
[3,1,7,6,5,4,2] => [2,1,2,1,1] => 1011011 => 5
[3,2,1,4,5,6,7] => [2,5] => 1010000 => 2
[3,2,1,4,5,7,6] => [2,3,2] => 1010010 => 3
[3,2,1,4,6,5,7] => [2,2,3] => 1010100 => 3
[3,2,1,4,6,7,5] => [2,2,3] => 1010100 => 3
[3,2,1,4,7,5,6] => [2,2,3] => 1010100 => 3
[3,2,1,4,7,6,5] => [2,2,2,1] => 1010101 => 4
[3,2,1,5,4,6,7] => [2,1,4] => 1011000 => 3
[3,2,1,5,4,7,6] => [2,1,2,2] => 1011010 => 4
[3,2,1,5,6,4,7] => [2,1,4] => 1011000 => 3
[3,2,1,5,6,7,4] => [2,1,4] => 1011000 => 3
[3,2,1,5,7,4,6] => [2,1,4] => 1011000 => 3
[3,2,1,5,7,6,4] => [2,1,3,1] => 1011001 => 4
[3,2,1,6,4,5,7] => [2,1,4] => 1011000 => 3
[3,2,1,6,4,7,5] => [2,1,2,2] => 1011010 => 4
[3,2,1,6,5,4,7] => [2,1,2,2] => 1011010 => 4
[3,2,1,6,5,7,4] => [2,1,2,2] => 1011010 => 4
[3,2,1,6,7,4,5] => [2,1,4] => 1011000 => 3
[3,2,1,6,7,5,4] => [2,1,3,1] => 1011001 => 4
[3,2,1,7,4,5,6] => [2,1,4] => 1011000 => 3
[3,2,1,7,4,6,5] => [2,1,3,1] => 1011001 => 4
[3,2,1,7,5,4,6] => [2,1,2,2] => 1011010 => 4
[3,2,1,7,5,6,4] => [2,1,3,1] => 1011001 => 4
[3,2,1,7,6,4,5] => [2,1,1,3] => 1011100 => 4
[3,2,1,7,6,5,4] => [2,1,1,2,1] => 1011101 => 5
[3,2,4,1,5,6,7] => [2,5] => 1010000 => 2
[3,2,4,1,5,7,6] => [2,3,2] => 1010010 => 3
[3,2,4,1,6,5,7] => [2,2,3] => 1010100 => 3
[3,2,4,1,6,7,5] => [2,2,3] => 1010100 => 3
[3,2,4,1,7,5,6] => [2,2,3] => 1010100 => 3
[3,2,4,1,7,6,5] => [2,2,2,1] => 1010101 => 4
[3,2,4,5,1,6,7] => [2,5] => 1010000 => 2
[3,2,4,5,1,7,6] => [2,3,2] => 1010010 => 3
[3,2,4,5,6,1,7] => [2,5] => 1010000 => 2
[3,2,4,5,6,7,1] => [2,5] => 1010000 => 2
[3,2,4,5,7,1,6] => [2,5] => 1010000 => 2
[3,2,4,5,7,6,1] => [2,4,1] => 1010001 => 3
[3,2,4,6,1,5,7] => [2,5] => 1010000 => 2
[3,2,4,6,1,7,5] => [2,3,2] => 1010010 => 3
[3,2,4,6,5,1,7] => [2,3,2] => 1010010 => 3
[3,2,4,6,5,7,1] => [2,3,2] => 1010010 => 3
[3,2,4,6,7,1,5] => [2,5] => 1010000 => 2
[3,2,4,6,7,5,1] => [2,4,1] => 1010001 => 3
[3,2,4,7,1,5,6] => [2,5] => 1010000 => 2
[3,2,4,7,1,6,5] => [2,4,1] => 1010001 => 3
[3,2,4,7,5,1,6] => [2,3,2] => 1010010 => 3
[3,2,4,7,5,6,1] => [2,4,1] => 1010001 => 3
[3,2,4,7,6,1,5] => [2,2,3] => 1010100 => 3
[3,2,4,7,6,5,1] => [2,2,2,1] => 1010101 => 4
[3,2,5,1,4,6,7] => [2,5] => 1010000 => 2
[3,2,5,1,4,7,6] => [2,3,2] => 1010010 => 3
[3,2,5,1,6,4,7] => [2,2,3] => 1010100 => 3
[3,2,5,1,6,7,4] => [2,2,3] => 1010100 => 3
[3,2,5,1,7,4,6] => [2,2,3] => 1010100 => 3
[3,2,5,1,7,6,4] => [2,2,2,1] => 1010101 => 4
[3,2,5,4,1,6,7] => [2,2,3] => 1010100 => 3
[3,2,5,4,1,7,6] => [2,2,1,2] => 1010110 => 4
[3,2,5,4,6,1,7] => [2,2,3] => 1010100 => 3
[3,2,5,4,6,7,1] => [2,2,3] => 1010100 => 3
[3,2,5,4,7,1,6] => [2,2,3] => 1010100 => 3
[3,2,5,4,7,6,1] => [2,2,2,1] => 1010101 => 4
[3,2,5,6,1,4,7] => [2,5] => 1010000 => 2
[3,2,5,6,1,7,4] => [2,3,2] => 1010010 => 3
[3,2,5,6,4,1,7] => [2,3,2] => 1010010 => 3
[3,2,5,6,4,7,1] => [2,3,2] => 1010010 => 3
[3,2,5,6,7,1,4] => [2,5] => 1010000 => 2
[3,2,5,6,7,4,1] => [2,4,1] => 1010001 => 3
[3,2,5,7,1,4,6] => [2,5] => 1010000 => 2
[3,2,5,7,1,6,4] => [2,4,1] => 1010001 => 3
[3,2,5,7,4,1,6] => [2,3,2] => 1010010 => 3
[3,2,5,7,4,6,1] => [2,4,1] => 1010001 => 3
[3,2,5,7,6,1,4] => [2,2,3] => 1010100 => 3
[3,2,5,7,6,4,1] => [2,2,2,1] => 1010101 => 4
[3,2,6,1,4,5,7] => [2,5] => 1010000 => 2
[3,2,6,1,4,7,5] => [2,3,2] => 1010010 => 3
[3,2,6,1,5,4,7] => [2,3,2] => 1010010 => 3
[3,2,6,1,5,7,4] => [2,3,2] => 1010010 => 3
[3,2,6,1,7,4,5] => [2,2,3] => 1010100 => 3
[3,2,6,1,7,5,4] => [2,2,2,1] => 1010101 => 4
[3,2,6,4,1,5,7] => [2,2,3] => 1010100 => 3
[3,2,6,4,1,7,5] => [2,2,1,2] => 1010110 => 4
[3,2,6,4,5,1,7] => [2,3,2] => 1010010 => 3
[3,2,6,4,5,7,1] => [2,3,2] => 1010010 => 3
[3,2,6,4,7,1,5] => [2,2,3] => 1010100 => 3
[3,2,6,4,7,5,1] => [2,2,2,1] => 1010101 => 4
[3,2,6,5,1,4,7] => [2,1,4] => 1011000 => 3
[3,2,6,5,1,7,4] => [2,1,2,2] => 1011010 => 4
[3,2,6,5,4,1,7] => [2,1,2,2] => 1011010 => 4
[3,2,6,5,4,7,1] => [2,1,2,2] => 1011010 => 4
[3,2,6,5,7,1,4] => [2,1,4] => 1011000 => 3
[3,2,6,5,7,4,1] => [2,1,3,1] => 1011001 => 4
[3,2,6,7,1,4,5] => [2,5] => 1010000 => 2
[3,2,6,7,1,5,4] => [2,4,1] => 1010001 => 3
[3,2,6,7,4,1,5] => [2,3,2] => 1010010 => 3
[3,2,6,7,4,5,1] => [2,4,1] => 1010001 => 3
[3,2,6,7,5,1,4] => [2,3,2] => 1010010 => 3
[3,2,6,7,5,4,1] => [2,3,1,1] => 1010011 => 4
[3,2,7,1,4,5,6] => [2,5] => 1010000 => 2
[3,2,7,1,4,6,5] => [2,4,1] => 1010001 => 3
[3,2,7,1,5,4,6] => [2,3,2] => 1010010 => 3
[3,2,7,1,5,6,4] => [2,4,1] => 1010001 => 3
[3,2,7,1,6,4,5] => [2,2,3] => 1010100 => 3
[3,2,7,1,6,5,4] => [2,2,2,1] => 1010101 => 4
[3,2,7,4,1,5,6] => [2,2,3] => 1010100 => 3
[3,2,7,4,1,6,5] => [2,2,2,1] => 1010101 => 4
[3,2,7,4,5,1,6] => [2,3,2] => 1010010 => 3
[3,2,7,4,5,6,1] => [2,4,1] => 1010001 => 3
[3,2,7,4,6,1,5] => [2,2,3] => 1010100 => 3
[3,2,7,4,6,5,1] => [2,2,2,1] => 1010101 => 4
[3,2,7,5,1,4,6] => [2,1,4] => 1011000 => 3
[3,2,7,5,1,6,4] => [2,1,3,1] => 1011001 => 4
[3,2,7,5,4,1,6] => [2,1,2,2] => 1011010 => 4
[3,2,7,5,4,6,1] => [2,1,3,1] => 1011001 => 4
[3,2,7,5,6,1,4] => [2,1,4] => 1011000 => 3
[3,2,7,5,6,4,1] => [2,1,3,1] => 1011001 => 4
[3,2,7,6,1,4,5] => [2,1,4] => 1011000 => 3
[3,2,7,6,1,5,4] => [2,1,3,1] => 1011001 => 4
[3,2,7,6,4,1,5] => [2,1,2,2] => 1011010 => 4
[3,2,7,6,4,5,1] => [2,1,3,1] => 1011001 => 4
[3,2,7,6,5,1,4] => [2,1,2,2] => 1011010 => 4
[3,2,7,6,5,4,1] => [2,1,2,1,1] => 1011011 => 5
[3,4,1,2,5,6,7] => [7] => 1000000 => 1
[3,4,1,2,5,7,6] => [5,2] => 1000010 => 2
[3,4,1,2,6,5,7] => [4,3] => 1000100 => 2
[3,4,1,2,6,7,5] => [4,3] => 1000100 => 2
[3,4,1,2,7,5,6] => [4,3] => 1000100 => 2
[3,4,1,2,7,6,5] => [4,2,1] => 1000101 => 3
[3,4,1,5,2,6,7] => [3,4] => 1001000 => 2
[3,4,1,5,2,7,6] => [3,2,2] => 1001010 => 3
[3,4,1,5,6,2,7] => [3,4] => 1001000 => 2
[3,4,1,5,6,7,2] => [3,4] => 1001000 => 2
[3,4,1,5,7,2,6] => [3,4] => 1001000 => 2
[3,4,1,5,7,6,2] => [3,3,1] => 1001001 => 3
[3,4,1,6,2,5,7] => [3,4] => 1001000 => 2
[3,4,1,6,2,7,5] => [3,2,2] => 1001010 => 3
[3,4,1,6,5,2,7] => [3,2,2] => 1001010 => 3
[3,4,1,6,5,7,2] => [3,2,2] => 1001010 => 3
[3,4,1,6,7,2,5] => [3,4] => 1001000 => 2
[3,4,1,6,7,5,2] => [3,3,1] => 1001001 => 3
[3,4,1,7,2,5,6] => [3,4] => 1001000 => 2
[3,4,1,7,2,6,5] => [3,3,1] => 1001001 => 3
[3,4,1,7,5,2,6] => [3,2,2] => 1001010 => 3
[3,4,1,7,5,6,2] => [3,3,1] => 1001001 => 3
[3,4,1,7,6,2,5] => [3,1,3] => 1001100 => 3
[3,4,1,7,6,5,2] => [3,1,2,1] => 1001101 => 4
[3,4,2,1,5,6,7] => [3,4] => 1001000 => 2
[3,4,2,1,5,7,6] => [3,2,2] => 1001010 => 3
[3,4,2,1,6,5,7] => [3,1,3] => 1001100 => 3
[3,4,2,1,6,7,5] => [3,1,3] => 1001100 => 3
[3,4,2,1,7,5,6] => [3,1,3] => 1001100 => 3
[3,4,2,1,7,6,5] => [3,1,2,1] => 1001101 => 4
[3,4,2,5,1,6,7] => [3,4] => 1001000 => 2
[3,4,2,5,1,7,6] => [3,2,2] => 1001010 => 3
[3,4,2,5,6,1,7] => [3,4] => 1001000 => 2
[3,4,2,5,6,7,1] => [3,4] => 1001000 => 2
[3,4,2,5,7,1,6] => [3,4] => 1001000 => 2
[3,4,2,5,7,6,1] => [3,3,1] => 1001001 => 3
[3,4,2,6,1,5,7] => [3,4] => 1001000 => 2
[3,4,2,6,1,7,5] => [3,2,2] => 1001010 => 3
[3,4,2,6,5,1,7] => [3,2,2] => 1001010 => 3
[3,4,2,6,5,7,1] => [3,2,2] => 1001010 => 3
[3,4,2,6,7,1,5] => [3,4] => 1001000 => 2
[3,4,2,6,7,5,1] => [3,3,1] => 1001001 => 3
[3,4,2,7,1,5,6] => [3,4] => 1001000 => 2
[3,4,2,7,1,6,5] => [3,3,1] => 1001001 => 3
[3,4,2,7,5,1,6] => [3,2,2] => 1001010 => 3
[3,4,2,7,5,6,1] => [3,3,1] => 1001001 => 3
[3,4,2,7,6,1,5] => [3,1,3] => 1001100 => 3
[3,4,2,7,6,5,1] => [3,1,2,1] => 1001101 => 4
[3,4,5,1,2,6,7] => [7] => 1000000 => 1
[3,4,5,1,2,7,6] => [5,2] => 1000010 => 2
[3,4,5,1,6,2,7] => [4,3] => 1000100 => 2
[3,4,5,1,6,7,2] => [4,3] => 1000100 => 2
[3,4,5,1,7,2,6] => [4,3] => 1000100 => 2
[3,4,5,1,7,6,2] => [4,2,1] => 1000101 => 3
[3,4,5,2,1,6,7] => [4,3] => 1000100 => 2
[3,4,5,2,1,7,6] => [4,1,2] => 1000110 => 3
[3,4,5,2,6,1,7] => [4,3] => 1000100 => 2
[3,4,5,2,6,7,1] => [4,3] => 1000100 => 2
[3,4,5,2,7,1,6] => [4,3] => 1000100 => 2
[3,4,5,2,7,6,1] => [4,2,1] => 1000101 => 3
[3,4,5,6,1,2,7] => [7] => 1000000 => 1
[3,4,5,6,1,7,2] => [5,2] => 1000010 => 2
[3,4,5,6,2,1,7] => [5,2] => 1000010 => 2
[3,4,5,6,2,7,1] => [5,2] => 1000010 => 2
[3,4,5,6,7,1,2] => [7] => 1000000 => 1
[3,4,5,6,7,2,1] => [6,1] => 1000001 => 2
[3,4,5,7,1,2,6] => [7] => 1000000 => 1
[3,4,5,7,1,6,2] => [6,1] => 1000001 => 2
[3,4,5,7,2,1,6] => [5,2] => 1000010 => 2
[3,4,5,7,2,6,1] => [6,1] => 1000001 => 2
[3,4,5,7,6,1,2] => [4,3] => 1000100 => 2
[3,4,5,7,6,2,1] => [4,2,1] => 1000101 => 3
[3,4,6,1,2,5,7] => [7] => 1000000 => 1
[3,4,6,1,2,7,5] => [5,2] => 1000010 => 2
[3,4,6,1,5,2,7] => [5,2] => 1000010 => 2
[3,4,6,1,5,7,2] => [5,2] => 1000010 => 2
[3,4,6,1,7,2,5] => [4,3] => 1000100 => 2
[3,4,6,1,7,5,2] => [4,2,1] => 1000101 => 3
[3,4,6,2,1,5,7] => [4,3] => 1000100 => 2
[3,4,6,2,1,7,5] => [4,1,2] => 1000110 => 3
[3,4,6,2,5,1,7] => [5,2] => 1000010 => 2
[3,4,6,2,5,7,1] => [5,2] => 1000010 => 2
[3,4,6,2,7,1,5] => [4,3] => 1000100 => 2
[3,4,6,2,7,5,1] => [4,2,1] => 1000101 => 3
[3,4,6,5,1,2,7] => [3,4] => 1001000 => 2
[3,4,6,5,1,7,2] => [3,2,2] => 1001010 => 3
[3,4,6,5,2,1,7] => [3,2,2] => 1001010 => 3
[3,4,6,5,2,7,1] => [3,2,2] => 1001010 => 3
[3,4,6,5,7,1,2] => [3,4] => 1001000 => 2
[3,4,6,5,7,2,1] => [3,3,1] => 1001001 => 3
[3,4,6,7,1,2,5] => [7] => 1000000 => 1
[3,4,6,7,1,5,2] => [6,1] => 1000001 => 2
[3,4,6,7,2,1,5] => [5,2] => 1000010 => 2
[3,4,6,7,2,5,1] => [6,1] => 1000001 => 2
[3,4,6,7,5,1,2] => [5,2] => 1000010 => 2
[3,4,6,7,5,2,1] => [5,1,1] => 1000011 => 3
[3,4,7,1,2,5,6] => [7] => 1000000 => 1
[3,4,7,1,2,6,5] => [6,1] => 1000001 => 2
[3,4,7,1,5,2,6] => [5,2] => 1000010 => 2
[3,4,7,1,5,6,2] => [6,1] => 1000001 => 2
[3,4,7,1,6,2,5] => [4,3] => 1000100 => 2
[3,4,7,1,6,5,2] => [4,2,1] => 1000101 => 3
[3,4,7,2,1,5,6] => [4,3] => 1000100 => 2
[3,4,7,2,1,6,5] => [4,2,1] => 1000101 => 3
[3,4,7,2,5,1,6] => [5,2] => 1000010 => 2
[3,4,7,2,5,6,1] => [6,1] => 1000001 => 2
[3,4,7,2,6,1,5] => [4,3] => 1000100 => 2
[3,4,7,2,6,5,1] => [4,2,1] => 1000101 => 3
[3,4,7,5,1,2,6] => [3,4] => 1001000 => 2
[3,4,7,5,1,6,2] => [3,3,1] => 1001001 => 3
[3,4,7,5,2,1,6] => [3,2,2] => 1001010 => 3
[3,4,7,5,2,6,1] => [3,3,1] => 1001001 => 3
[3,4,7,5,6,1,2] => [3,4] => 1001000 => 2
[3,4,7,5,6,2,1] => [3,3,1] => 1001001 => 3
[3,4,7,6,1,2,5] => [3,4] => 1001000 => 2
[3,4,7,6,1,5,2] => [3,3,1] => 1001001 => 3
[3,4,7,6,2,1,5] => [3,2,2] => 1001010 => 3
[3,4,7,6,2,5,1] => [3,3,1] => 1001001 => 3
[3,4,7,6,5,1,2] => [3,2,2] => 1001010 => 3
[3,4,7,6,5,2,1] => [3,2,1,1] => 1001011 => 4
[3,5,1,2,4,6,7] => [7] => 1000000 => 1
[3,5,1,2,4,7,6] => [5,2] => 1000010 => 2
[3,5,1,2,6,4,7] => [4,3] => 1000100 => 2
[3,5,1,2,6,7,4] => [4,3] => 1000100 => 2
[3,5,1,2,7,4,6] => [4,3] => 1000100 => 2
[3,5,1,2,7,6,4] => [4,2,1] => 1000101 => 3
[3,5,1,4,2,6,7] => [4,3] => 1000100 => 2
[3,5,1,4,2,7,6] => [4,1,2] => 1000110 => 3
[3,5,1,4,6,2,7] => [4,3] => 1000100 => 2
[3,5,1,4,6,7,2] => [4,3] => 1000100 => 2
[3,5,1,4,7,2,6] => [4,3] => 1000100 => 2
[3,5,1,4,7,6,2] => [4,2,1] => 1000101 => 3
[3,5,1,6,2,4,7] => [3,4] => 1001000 => 2
[3,5,1,6,2,7,4] => [3,2,2] => 1001010 => 3
[3,5,1,6,4,2,7] => [3,2,2] => 1001010 => 3
[3,5,1,6,4,7,2] => [3,2,2] => 1001010 => 3
[3,5,1,6,7,2,4] => [3,4] => 1001000 => 2
[3,5,1,6,7,4,2] => [3,3,1] => 1001001 => 3
[3,5,1,7,2,4,6] => [3,4] => 1001000 => 2
[3,5,1,7,2,6,4] => [3,3,1] => 1001001 => 3
[3,5,1,7,4,2,6] => [3,2,2] => 1001010 => 3
[3,5,1,7,4,6,2] => [3,3,1] => 1001001 => 3
[3,5,1,7,6,2,4] => [3,1,3] => 1001100 => 3
[3,5,1,7,6,4,2] => [3,1,2,1] => 1001101 => 4
[3,5,2,1,4,6,7] => [3,4] => 1001000 => 2
[3,5,2,1,4,7,6] => [3,2,2] => 1001010 => 3
[3,5,2,1,6,4,7] => [3,1,3] => 1001100 => 3
[3,5,2,1,6,7,4] => [3,1,3] => 1001100 => 3
[3,5,2,1,7,4,6] => [3,1,3] => 1001100 => 3
[3,5,2,1,7,6,4] => [3,1,2,1] => 1001101 => 4
[3,5,2,4,1,6,7] => [4,3] => 1000100 => 2
[3,5,2,4,1,7,6] => [4,1,2] => 1000110 => 3
[3,5,2,4,6,1,7] => [4,3] => 1000100 => 2
[3,5,2,4,6,7,1] => [4,3] => 1000100 => 2
[3,5,2,4,7,1,6] => [4,3] => 1000100 => 2
[3,5,2,4,7,6,1] => [4,2,1] => 1000101 => 3
[3,5,2,6,1,4,7] => [3,4] => 1001000 => 2
[3,5,2,6,1,7,4] => [3,2,2] => 1001010 => 3
[3,5,2,6,4,1,7] => [3,2,2] => 1001010 => 3
[3,5,2,6,4,7,1] => [3,2,2] => 1001010 => 3
[3,5,2,6,7,1,4] => [3,4] => 1001000 => 2
[3,5,2,6,7,4,1] => [3,3,1] => 1001001 => 3
[3,5,2,7,1,4,6] => [3,4] => 1001000 => 2
[3,5,2,7,1,6,4] => [3,3,1] => 1001001 => 3
[3,5,2,7,4,1,6] => [3,2,2] => 1001010 => 3
[3,5,2,7,4,6,1] => [3,3,1] => 1001001 => 3
[3,5,2,7,6,1,4] => [3,1,3] => 1001100 => 3
[3,5,2,7,6,4,1] => [3,1,2,1] => 1001101 => 4
[3,5,4,1,2,6,7] => [2,5] => 1010000 => 2
[3,5,4,1,2,7,6] => [2,3,2] => 1010010 => 3
[3,5,4,1,6,2,7] => [2,2,3] => 1010100 => 3
[3,5,4,1,6,7,2] => [2,2,3] => 1010100 => 3
[3,5,4,1,7,2,6] => [2,2,3] => 1010100 => 3
[3,5,4,1,7,6,2] => [2,2,2,1] => 1010101 => 4
[3,5,4,2,1,6,7] => [2,2,3] => 1010100 => 3
[3,5,4,2,1,7,6] => [2,2,1,2] => 1010110 => 4
[3,5,4,2,6,1,7] => [2,2,3] => 1010100 => 3
[3,5,4,2,6,7,1] => [2,2,3] => 1010100 => 3
[3,5,4,2,7,1,6] => [2,2,3] => 1010100 => 3
[3,5,4,2,7,6,1] => [2,2,2,1] => 1010101 => 4
[3,5,4,6,1,2,7] => [2,5] => 1010000 => 2
[3,5,4,6,1,7,2] => [2,3,2] => 1010010 => 3
[3,5,4,6,2,1,7] => [2,3,2] => 1010010 => 3
[3,5,4,6,2,7,1] => [2,3,2] => 1010010 => 3
[3,5,4,6,7,1,2] => [2,5] => 1010000 => 2
[3,5,4,6,7,2,1] => [2,4,1] => 1010001 => 3
[3,5,4,7,1,2,6] => [2,5] => 1010000 => 2
[3,5,4,7,1,6,2] => [2,4,1] => 1010001 => 3
[3,5,4,7,2,1,6] => [2,3,2] => 1010010 => 3
[3,5,4,7,2,6,1] => [2,4,1] => 1010001 => 3
[3,5,4,7,6,1,2] => [2,2,3] => 1010100 => 3
[3,5,4,7,6,2,1] => [2,2,2,1] => 1010101 => 4
[3,5,6,1,2,4,7] => [7] => 1000000 => 1
[3,5,6,1,2,7,4] => [5,2] => 1000010 => 2
[3,5,6,1,4,2,7] => [5,2] => 1000010 => 2
[3,5,6,1,4,7,2] => [5,2] => 1000010 => 2
[3,5,6,1,7,2,4] => [4,3] => 1000100 => 2
[3,5,6,1,7,4,2] => [4,2,1] => 1000101 => 3
[3,5,6,2,1,4,7] => [4,3] => 1000100 => 2
[3,5,6,2,1,7,4] => [4,1,2] => 1000110 => 3
[3,5,6,2,4,1,7] => [5,2] => 1000010 => 2
[3,5,6,2,4,7,1] => [5,2] => 1000010 => 2
[3,5,6,2,7,1,4] => [4,3] => 1000100 => 2
[3,5,6,2,7,4,1] => [4,2,1] => 1000101 => 3
[3,5,6,4,1,2,7] => [4,3] => 1000100 => 2
[3,5,6,4,1,7,2] => [4,1,2] => 1000110 => 3
[3,5,6,4,2,1,7] => [4,1,2] => 1000110 => 3
[3,5,6,4,2,7,1] => [4,1,2] => 1000110 => 3
[3,5,6,4,7,1,2] => [4,3] => 1000100 => 2
[3,5,6,4,7,2,1] => [4,2,1] => 1000101 => 3
[3,5,6,7,1,2,4] => [7] => 1000000 => 1
[3,5,6,7,1,4,2] => [6,1] => 1000001 => 2
[3,5,6,7,2,1,4] => [5,2] => 1000010 => 2
[3,5,6,7,2,4,1] => [6,1] => 1000001 => 2
[3,5,6,7,4,1,2] => [5,2] => 1000010 => 2
[3,5,6,7,4,2,1] => [5,1,1] => 1000011 => 3
[3,5,7,1,2,4,6] => [7] => 1000000 => 1
[3,5,7,1,2,6,4] => [6,1] => 1000001 => 2
[3,5,7,1,4,2,6] => [5,2] => 1000010 => 2
[3,5,7,1,4,6,2] => [6,1] => 1000001 => 2
[3,5,7,1,6,2,4] => [4,3] => 1000100 => 2
[3,5,7,1,6,4,2] => [4,2,1] => 1000101 => 3
[3,5,7,2,1,4,6] => [4,3] => 1000100 => 2
[3,5,7,2,1,6,4] => [4,2,1] => 1000101 => 3
[3,5,7,2,4,1,6] => [5,2] => 1000010 => 2
[3,5,7,2,4,6,1] => [6,1] => 1000001 => 2
[3,5,7,2,6,1,4] => [4,3] => 1000100 => 2
[3,5,7,2,6,4,1] => [4,2,1] => 1000101 => 3
[3,5,7,4,1,2,6] => [4,3] => 1000100 => 2
[3,5,7,4,1,6,2] => [4,2,1] => 1000101 => 3
[3,5,7,4,2,1,6] => [4,1,2] => 1000110 => 3
[3,5,7,4,2,6,1] => [4,2,1] => 1000101 => 3
[3,5,7,4,6,1,2] => [4,3] => 1000100 => 2
[3,5,7,4,6,2,1] => [4,2,1] => 1000101 => 3
[3,5,7,6,1,2,4] => [3,4] => 1001000 => 2
[3,5,7,6,1,4,2] => [3,3,1] => 1001001 => 3
[3,5,7,6,2,1,4] => [3,2,2] => 1001010 => 3
[3,5,7,6,2,4,1] => [3,3,1] => 1001001 => 3
[3,5,7,6,4,1,2] => [3,2,2] => 1001010 => 3
[3,5,7,6,4,2,1] => [3,2,1,1] => 1001011 => 4
[3,6,1,2,4,5,7] => [7] => 1000000 => 1
[3,6,1,2,4,7,5] => [5,2] => 1000010 => 2
[3,6,1,2,5,4,7] => [5,2] => 1000010 => 2
[3,6,1,2,5,7,4] => [5,2] => 1000010 => 2
[3,6,1,2,7,4,5] => [4,3] => 1000100 => 2
[3,6,1,2,7,5,4] => [4,2,1] => 1000101 => 3
[3,6,1,4,2,5,7] => [4,3] => 1000100 => 2
[3,6,1,4,2,7,5] => [4,1,2] => 1000110 => 3
[3,6,1,4,5,2,7] => [5,2] => 1000010 => 2
[3,6,1,4,5,7,2] => [5,2] => 1000010 => 2
[3,6,1,4,7,2,5] => [4,3] => 1000100 => 2
[3,6,1,4,7,5,2] => [4,2,1] => 1000101 => 3
[3,6,1,5,2,4,7] => [3,4] => 1001000 => 2
[3,6,1,5,2,7,4] => [3,2,2] => 1001010 => 3
[3,6,1,5,4,2,7] => [3,2,2] => 1001010 => 3
[3,6,1,5,4,7,2] => [3,2,2] => 1001010 => 3
[3,6,1,5,7,2,4] => [3,4] => 1001000 => 2
[3,6,1,5,7,4,2] => [3,3,1] => 1001001 => 3
[3,6,1,7,2,4,5] => [3,4] => 1001000 => 2
[3,6,1,7,2,5,4] => [3,3,1] => 1001001 => 3
[3,6,1,7,4,2,5] => [3,2,2] => 1001010 => 3
[3,6,1,7,4,5,2] => [3,3,1] => 1001001 => 3
[3,6,1,7,5,2,4] => [3,2,2] => 1001010 => 3
[3,6,1,7,5,4,2] => [3,2,1,1] => 1001011 => 4
[3,6,2,1,4,5,7] => [3,4] => 1001000 => 2
[3,6,2,1,4,7,5] => [3,2,2] => 1001010 => 3
[3,6,2,1,5,4,7] => [3,2,2] => 1001010 => 3
[3,6,2,1,5,7,4] => [3,2,2] => 1001010 => 3
[3,6,2,1,7,4,5] => [3,1,3] => 1001100 => 3
[3,6,2,1,7,5,4] => [3,1,2,1] => 1001101 => 4
[3,6,2,4,1,5,7] => [4,3] => 1000100 => 2
[3,6,2,4,1,7,5] => [4,1,2] => 1000110 => 3
[3,6,2,4,5,1,7] => [5,2] => 1000010 => 2
[3,6,2,4,5,7,1] => [5,2] => 1000010 => 2
[3,6,2,4,7,1,5] => [4,3] => 1000100 => 2
[3,6,2,4,7,5,1] => [4,2,1] => 1000101 => 3
[3,6,2,5,1,4,7] => [3,4] => 1001000 => 2
[3,6,2,5,1,7,4] => [3,2,2] => 1001010 => 3
[3,6,2,5,4,1,7] => [3,2,2] => 1001010 => 3
[3,6,2,5,4,7,1] => [3,2,2] => 1001010 => 3
[3,6,2,5,7,1,4] => [3,4] => 1001000 => 2
[3,6,2,5,7,4,1] => [3,3,1] => 1001001 => 3
[3,6,2,7,1,4,5] => [3,4] => 1001000 => 2
[3,6,2,7,1,5,4] => [3,3,1] => 1001001 => 3
[3,6,2,7,4,1,5] => [3,2,2] => 1001010 => 3
[3,6,2,7,4,5,1] => [3,3,1] => 1001001 => 3
[3,6,2,7,5,1,4] => [3,2,2] => 1001010 => 3
[3,6,2,7,5,4,1] => [3,2,1,1] => 1001011 => 4
[3,6,4,1,2,5,7] => [2,5] => 1010000 => 2
[3,6,4,1,2,7,5] => [2,3,2] => 1010010 => 3
[3,6,4,1,5,2,7] => [2,3,2] => 1010010 => 3
[3,6,4,1,5,7,2] => [2,3,2] => 1010010 => 3
[3,6,4,1,7,2,5] => [2,2,3] => 1010100 => 3
[3,6,4,1,7,5,2] => [2,2,2,1] => 1010101 => 4
[3,6,4,2,1,5,7] => [2,2,3] => 1010100 => 3
[3,6,4,2,1,7,5] => [2,2,1,2] => 1010110 => 4
[3,6,4,2,5,1,7] => [2,3,2] => 1010010 => 3
[3,6,4,2,5,7,1] => [2,3,2] => 1010010 => 3
[3,6,4,2,7,1,5] => [2,2,3] => 1010100 => 3
[3,6,4,2,7,5,1] => [2,2,2,1] => 1010101 => 4
[3,6,4,5,1,2,7] => [2,5] => 1010000 => 2
[3,6,4,5,1,7,2] => [2,3,2] => 1010010 => 3
[3,6,4,5,2,1,7] => [2,3,2] => 1010010 => 3
[3,6,4,5,2,7,1] => [2,3,2] => 1010010 => 3
[3,6,4,5,7,1,2] => [2,5] => 1010000 => 2
[3,6,4,5,7,2,1] => [2,4,1] => 1010001 => 3
[3,6,4,7,1,2,5] => [2,5] => 1010000 => 2
[3,6,4,7,1,5,2] => [2,4,1] => 1010001 => 3
[3,6,4,7,2,1,5] => [2,3,2] => 1010010 => 3
[3,6,4,7,2,5,1] => [2,4,1] => 1010001 => 3
[3,6,4,7,5,1,2] => [2,3,2] => 1010010 => 3
[3,6,4,7,5,2,1] => [2,3,1,1] => 1010011 => 4
[3,6,5,1,2,4,7] => [2,5] => 1010000 => 2
[3,6,5,1,2,7,4] => [2,3,2] => 1010010 => 3
[3,6,5,1,4,2,7] => [2,3,2] => 1010010 => 3
[3,6,5,1,4,7,2] => [2,3,2] => 1010010 => 3
[3,6,5,1,7,2,4] => [2,2,3] => 1010100 => 3
[3,6,5,1,7,4,2] => [2,2,2,1] => 1010101 => 4
[3,6,5,2,1,4,7] => [2,2,3] => 1010100 => 3
[3,6,5,2,1,7,4] => [2,2,1,2] => 1010110 => 4
[3,6,5,2,4,1,7] => [2,3,2] => 1010010 => 3
[3,6,5,2,4,7,1] => [2,3,2] => 1010010 => 3
[3,6,5,2,7,1,4] => [2,2,3] => 1010100 => 3
[3,6,5,2,7,4,1] => [2,2,2,1] => 1010101 => 4
[3,6,5,4,1,2,7] => [2,2,3] => 1010100 => 3
[3,6,5,4,1,7,2] => [2,2,1,2] => 1010110 => 4
[3,6,5,4,2,1,7] => [2,2,1,2] => 1010110 => 4
[3,6,5,4,2,7,1] => [2,2,1,2] => 1010110 => 4
[3,6,5,4,7,1,2] => [2,2,3] => 1010100 => 3
[3,6,5,4,7,2,1] => [2,2,2,1] => 1010101 => 4
[3,6,5,7,1,2,4] => [2,5] => 1010000 => 2
[3,6,5,7,1,4,2] => [2,4,1] => 1010001 => 3
[3,6,5,7,2,1,4] => [2,3,2] => 1010010 => 3
[3,6,5,7,2,4,1] => [2,4,1] => 1010001 => 3
[3,6,5,7,4,1,2] => [2,3,2] => 1010010 => 3
[3,6,5,7,4,2,1] => [2,3,1,1] => 1010011 => 4
[3,6,7,1,2,4,5] => [7] => 1000000 => 1
[3,6,7,1,2,5,4] => [6,1] => 1000001 => 2
[3,6,7,1,4,2,5] => [5,2] => 1000010 => 2
[3,6,7,1,4,5,2] => [6,1] => 1000001 => 2
[3,6,7,1,5,2,4] => [5,2] => 1000010 => 2
[3,6,7,1,5,4,2] => [5,1,1] => 1000011 => 3
[3,6,7,2,1,4,5] => [4,3] => 1000100 => 2
[3,6,7,2,1,5,4] => [4,2,1] => 1000101 => 3
[3,6,7,2,4,1,5] => [5,2] => 1000010 => 2
[3,6,7,2,4,5,1] => [6,1] => 1000001 => 2
[3,6,7,2,5,1,4] => [5,2] => 1000010 => 2
[3,6,7,2,5,4,1] => [5,1,1] => 1000011 => 3
[3,6,7,4,1,2,5] => [4,3] => 1000100 => 2
[3,6,7,4,1,5,2] => [4,2,1] => 1000101 => 3
[3,6,7,4,2,1,5] => [4,1,2] => 1000110 => 3
[3,6,7,4,2,5,1] => [4,2,1] => 1000101 => 3
[3,6,7,4,5,1,2] => [5,2] => 1000010 => 2
[3,6,7,4,5,2,1] => [5,1,1] => 1000011 => 3
[3,6,7,5,1,2,4] => [3,4] => 1001000 => 2
[3,6,7,5,1,4,2] => [3,3,1] => 1001001 => 3
[3,6,7,5,2,1,4] => [3,2,2] => 1001010 => 3
[3,6,7,5,2,4,1] => [3,3,1] => 1001001 => 3
[3,6,7,5,4,1,2] => [3,2,2] => 1001010 => 3
[3,6,7,5,4,2,1] => [3,2,1,1] => 1001011 => 4
[3,7,1,2,4,5,6] => [7] => 1000000 => 1
[3,7,1,2,4,6,5] => [6,1] => 1000001 => 2
[3,7,1,2,5,4,6] => [5,2] => 1000010 => 2
[3,7,1,2,5,6,4] => [6,1] => 1000001 => 2
[3,7,1,2,6,4,5] => [4,3] => 1000100 => 2
[3,7,1,2,6,5,4] => [4,2,1] => 1000101 => 3
[3,7,1,4,2,5,6] => [4,3] => 1000100 => 2
[3,7,1,4,2,6,5] => [4,2,1] => 1000101 => 3
[3,7,1,4,5,2,6] => [5,2] => 1000010 => 2
[3,7,1,4,5,6,2] => [6,1] => 1000001 => 2
[3,7,1,4,6,2,5] => [4,3] => 1000100 => 2
[3,7,1,4,6,5,2] => [4,2,1] => 1000101 => 3
[3,7,1,5,2,4,6] => [3,4] => 1001000 => 2
[3,7,1,5,2,6,4] => [3,3,1] => 1001001 => 3
[3,7,1,5,4,2,6] => [3,2,2] => 1001010 => 3
[3,7,1,5,4,6,2] => [3,3,1] => 1001001 => 3
[3,7,1,5,6,2,4] => [3,4] => 1001000 => 2
[3,7,1,5,6,4,2] => [3,3,1] => 1001001 => 3
[3,7,1,6,2,4,5] => [3,4] => 1001000 => 2
[3,7,1,6,2,5,4] => [3,3,1] => 1001001 => 3
[3,7,1,6,4,2,5] => [3,2,2] => 1001010 => 3
[3,7,1,6,4,5,2] => [3,3,1] => 1001001 => 3
[3,7,1,6,5,2,4] => [3,2,2] => 1001010 => 3
[3,7,1,6,5,4,2] => [3,2,1,1] => 1001011 => 4
[3,7,2,1,4,5,6] => [3,4] => 1001000 => 2
[3,7,2,1,4,6,5] => [3,3,1] => 1001001 => 3
[3,7,2,1,5,4,6] => [3,2,2] => 1001010 => 3
[3,7,2,1,5,6,4] => [3,3,1] => 1001001 => 3
[3,7,2,1,6,4,5] => [3,1,3] => 1001100 => 3
[3,7,2,1,6,5,4] => [3,1,2,1] => 1001101 => 4
[3,7,2,4,1,5,6] => [4,3] => 1000100 => 2
[3,7,2,4,1,6,5] => [4,2,1] => 1000101 => 3
[3,7,2,4,5,1,6] => [5,2] => 1000010 => 2
[3,7,2,4,5,6,1] => [6,1] => 1000001 => 2
[3,7,2,4,6,1,5] => [4,3] => 1000100 => 2
[3,7,2,4,6,5,1] => [4,2,1] => 1000101 => 3
[3,7,2,5,1,4,6] => [3,4] => 1001000 => 2
[3,7,2,5,1,6,4] => [3,3,1] => 1001001 => 3
[3,7,2,5,4,1,6] => [3,2,2] => 1001010 => 3
[3,7,2,5,4,6,1] => [3,3,1] => 1001001 => 3
[3,7,2,5,6,1,4] => [3,4] => 1001000 => 2
[3,7,2,5,6,4,1] => [3,3,1] => 1001001 => 3
[3,7,2,6,1,4,5] => [3,4] => 1001000 => 2
[3,7,2,6,1,5,4] => [3,3,1] => 1001001 => 3
[3,7,2,6,4,1,5] => [3,2,2] => 1001010 => 3
[3,7,2,6,4,5,1] => [3,3,1] => 1001001 => 3
[3,7,2,6,5,1,4] => [3,2,2] => 1001010 => 3
[3,7,2,6,5,4,1] => [3,2,1,1] => 1001011 => 4
[3,7,4,1,2,5,6] => [2,5] => 1010000 => 2
[3,7,4,1,2,6,5] => [2,4,1] => 1010001 => 3
[3,7,4,1,5,2,6] => [2,3,2] => 1010010 => 3
[3,7,4,1,5,6,2] => [2,4,1] => 1010001 => 3
[3,7,4,1,6,2,5] => [2,2,3] => 1010100 => 3
[3,7,4,1,6,5,2] => [2,2,2,1] => 1010101 => 4
[3,7,4,2,1,5,6] => [2,2,3] => 1010100 => 3
[3,7,4,2,1,6,5] => [2,2,2,1] => 1010101 => 4
[3,7,4,2,5,1,6] => [2,3,2] => 1010010 => 3
[3,7,4,2,5,6,1] => [2,4,1] => 1010001 => 3
[3,7,4,2,6,1,5] => [2,2,3] => 1010100 => 3
[3,7,4,2,6,5,1] => [2,2,2,1] => 1010101 => 4
[3,7,4,5,1,2,6] => [2,5] => 1010000 => 2
[3,7,4,5,1,6,2] => [2,4,1] => 1010001 => 3
[3,7,4,5,2,1,6] => [2,3,2] => 1010010 => 3
[3,7,4,5,2,6,1] => [2,4,1] => 1010001 => 3
[3,7,4,5,6,1,2] => [2,5] => 1010000 => 2
[3,7,4,5,6,2,1] => [2,4,1] => 1010001 => 3
[3,7,4,6,1,2,5] => [2,5] => 1010000 => 2
[3,7,4,6,1,5,2] => [2,4,1] => 1010001 => 3
[3,7,4,6,2,1,5] => [2,3,2] => 1010010 => 3
[3,7,4,6,2,5,1] => [2,4,1] => 1010001 => 3
[3,7,4,6,5,1,2] => [2,3,2] => 1010010 => 3
[3,7,4,6,5,2,1] => [2,3,1,1] => 1010011 => 4
[3,7,5,1,2,4,6] => [2,5] => 1010000 => 2
[3,7,5,1,2,6,4] => [2,4,1] => 1010001 => 3
[3,7,5,1,4,2,6] => [2,3,2] => 1010010 => 3
[3,7,5,1,4,6,2] => [2,4,1] => 1010001 => 3
[3,7,5,1,6,2,4] => [2,2,3] => 1010100 => 3
[3,7,5,1,6,4,2] => [2,2,2,1] => 1010101 => 4
[3,7,5,2,1,4,6] => [2,2,3] => 1010100 => 3
[3,7,5,2,1,6,4] => [2,2,2,1] => 1010101 => 4
[3,7,5,2,4,1,6] => [2,3,2] => 1010010 => 3
[3,7,5,2,4,6,1] => [2,4,1] => 1010001 => 3
[3,7,5,2,6,1,4] => [2,2,3] => 1010100 => 3
[3,7,5,2,6,4,1] => [2,2,2,1] => 1010101 => 4
[3,7,5,4,1,2,6] => [2,2,3] => 1010100 => 3
[3,7,5,4,1,6,2] => [2,2,2,1] => 1010101 => 4
[3,7,5,4,2,1,6] => [2,2,1,2] => 1010110 => 4
[3,7,5,4,2,6,1] => [2,2,2,1] => 1010101 => 4
[3,7,5,4,6,1,2] => [2,2,3] => 1010100 => 3
[3,7,5,4,6,2,1] => [2,2,2,1] => 1010101 => 4
[3,7,5,6,1,2,4] => [2,5] => 1010000 => 2
[3,7,5,6,1,4,2] => [2,4,1] => 1010001 => 3
[3,7,5,6,2,1,4] => [2,3,2] => 1010010 => 3
[3,7,5,6,2,4,1] => [2,4,1] => 1010001 => 3
[3,7,5,6,4,1,2] => [2,3,2] => 1010010 => 3
[3,7,5,6,4,2,1] => [2,3,1,1] => 1010011 => 4
[3,7,6,1,2,4,5] => [2,5] => 1010000 => 2
[3,7,6,1,2,5,4] => [2,4,1] => 1010001 => 3
[3,7,6,1,4,2,5] => [2,3,2] => 1010010 => 3
[3,7,6,1,4,5,2] => [2,4,1] => 1010001 => 3
[3,7,6,1,5,2,4] => [2,3,2] => 1010010 => 3
[3,7,6,1,5,4,2] => [2,3,1,1] => 1010011 => 4
[3,7,6,2,1,4,5] => [2,2,3] => 1010100 => 3
[3,7,6,2,1,5,4] => [2,2,2,1] => 1010101 => 4
[3,7,6,2,4,1,5] => [2,3,2] => 1010010 => 3
[3,7,6,2,4,5,1] => [2,4,1] => 1010001 => 3
[3,7,6,2,5,1,4] => [2,3,2] => 1010010 => 3
[3,7,6,2,5,4,1] => [2,3,1,1] => 1010011 => 4
[3,7,6,4,1,2,5] => [2,2,3] => 1010100 => 3
[3,7,6,4,1,5,2] => [2,2,2,1] => 1010101 => 4
[3,7,6,4,2,1,5] => [2,2,1,2] => 1010110 => 4
[3,7,6,4,2,5,1] => [2,2,2,1] => 1010101 => 4
[3,7,6,4,5,1,2] => [2,3,2] => 1010010 => 3
[3,7,6,4,5,2,1] => [2,3,1,1] => 1010011 => 4
[3,7,6,5,1,2,4] => [2,1,4] => 1011000 => 3
[3,7,6,5,1,4,2] => [2,1,3,1] => 1011001 => 4
[3,7,6,5,2,1,4] => [2,1,2,2] => 1011010 => 4
[3,7,6,5,2,4,1] => [2,1,3,1] => 1011001 => 4
[3,7,6,5,4,1,2] => [2,1,2,2] => 1011010 => 4
[3,7,6,5,4,2,1] => [2,1,2,1,1] => 1011011 => 5
[4,1,2,3,5,6,7] => [7] => 1000000 => 1
[4,1,2,3,5,7,6] => [5,2] => 1000010 => 2
[4,1,2,3,6,5,7] => [4,3] => 1000100 => 2
[4,1,2,3,6,7,5] => [4,3] => 1000100 => 2
[4,1,2,3,7,5,6] => [4,3] => 1000100 => 2
[4,1,2,3,7,6,5] => [4,2,1] => 1000101 => 3
[4,1,2,5,3,6,7] => [3,4] => 1001000 => 2
[4,1,2,5,3,7,6] => [3,2,2] => 1001010 => 3
[4,1,2,5,6,3,7] => [3,4] => 1001000 => 2
[4,1,2,5,6,7,3] => [3,4] => 1001000 => 2
[4,1,2,5,7,3,6] => [3,4] => 1001000 => 2
[4,1,2,5,7,6,3] => [3,3,1] => 1001001 => 3
[4,1,2,6,3,5,7] => [3,4] => 1001000 => 2
[4,1,2,6,3,7,5] => [3,2,2] => 1001010 => 3
[4,1,2,6,5,3,7] => [3,2,2] => 1001010 => 3
[4,1,2,6,5,7,3] => [3,2,2] => 1001010 => 3
[4,1,2,6,7,3,5] => [3,4] => 1001000 => 2
[4,1,2,6,7,5,3] => [3,3,1] => 1001001 => 3
[4,1,2,7,3,5,6] => [3,4] => 1001000 => 2
[4,1,2,7,3,6,5] => [3,3,1] => 1001001 => 3
[4,1,2,7,5,3,6] => [3,2,2] => 1001010 => 3
[4,1,2,7,5,6,3] => [3,3,1] => 1001001 => 3
[4,1,2,7,6,3,5] => [3,1,3] => 1001100 => 3
[4,1,2,7,6,5,3] => [3,1,2,1] => 1001101 => 4
[4,1,3,2,5,6,7] => [3,4] => 1001000 => 2
[4,1,3,2,5,7,6] => [3,2,2] => 1001010 => 3
[4,1,3,2,6,5,7] => [3,1,3] => 1001100 => 3
[4,1,3,2,6,7,5] => [3,1,3] => 1001100 => 3
[4,1,3,2,7,5,6] => [3,1,3] => 1001100 => 3
[4,1,3,2,7,6,5] => [3,1,2,1] => 1001101 => 4
[4,1,3,5,2,6,7] => [3,4] => 1001000 => 2
[4,1,3,5,2,7,6] => [3,2,2] => 1001010 => 3
[4,1,3,5,6,2,7] => [3,4] => 1001000 => 2
[4,1,3,5,6,7,2] => [3,4] => 1001000 => 2
[4,1,3,5,7,2,6] => [3,4] => 1001000 => 2
[4,1,3,5,7,6,2] => [3,3,1] => 1001001 => 3
[4,1,3,6,2,5,7] => [3,4] => 1001000 => 2
[4,1,3,6,2,7,5] => [3,2,2] => 1001010 => 3
[4,1,3,6,5,2,7] => [3,2,2] => 1001010 => 3
[4,1,3,6,5,7,2] => [3,2,2] => 1001010 => 3
[4,1,3,6,7,2,5] => [3,4] => 1001000 => 2
[4,1,3,6,7,5,2] => [3,3,1] => 1001001 => 3
[4,1,3,7,2,5,6] => [3,4] => 1001000 => 2
[4,1,3,7,2,6,5] => [3,3,1] => 1001001 => 3
[4,1,3,7,5,2,6] => [3,2,2] => 1001010 => 3
[4,1,3,7,5,6,2] => [3,3,1] => 1001001 => 3
[4,1,3,7,6,2,5] => [3,1,3] => 1001100 => 3
[4,1,3,7,6,5,2] => [3,1,2,1] => 1001101 => 4
[4,1,5,2,3,6,7] => [2,5] => 1010000 => 2
[4,1,5,2,3,7,6] => [2,3,2] => 1010010 => 3
[4,1,5,2,6,3,7] => [2,2,3] => 1010100 => 3
[4,1,5,2,6,7,3] => [2,2,3] => 1010100 => 3
[4,1,5,2,7,3,6] => [2,2,3] => 1010100 => 3
[4,1,5,2,7,6,3] => [2,2,2,1] => 1010101 => 4
[4,1,5,3,2,6,7] => [2,2,3] => 1010100 => 3
[4,1,5,3,2,7,6] => [2,2,1,2] => 1010110 => 4
[4,1,5,3,6,2,7] => [2,2,3] => 1010100 => 3
[4,1,5,3,6,7,2] => [2,2,3] => 1010100 => 3
[4,1,5,3,7,2,6] => [2,2,3] => 1010100 => 3
[4,1,5,3,7,6,2] => [2,2,2,1] => 1010101 => 4
[4,1,5,6,2,3,7] => [2,5] => 1010000 => 2
[4,1,5,6,2,7,3] => [2,3,2] => 1010010 => 3
[4,1,5,6,3,2,7] => [2,3,2] => 1010010 => 3
[4,1,5,6,3,7,2] => [2,3,2] => 1010010 => 3
[4,1,5,6,7,2,3] => [2,5] => 1010000 => 2
[4,1,5,6,7,3,2] => [2,4,1] => 1010001 => 3
[4,1,5,7,2,3,6] => [2,5] => 1010000 => 2
[4,1,5,7,2,6,3] => [2,4,1] => 1010001 => 3
[4,1,5,7,3,2,6] => [2,3,2] => 1010010 => 3
[4,1,5,7,3,6,2] => [2,4,1] => 1010001 => 3
[4,1,5,7,6,2,3] => [2,2,3] => 1010100 => 3
[4,1,5,7,6,3,2] => [2,2,2,1] => 1010101 => 4
[4,1,6,2,3,5,7] => [2,5] => 1010000 => 2
[4,1,6,2,3,7,5] => [2,3,2] => 1010010 => 3
[4,1,6,2,5,3,7] => [2,3,2] => 1010010 => 3
[4,1,6,2,5,7,3] => [2,3,2] => 1010010 => 3
[4,1,6,2,7,3,5] => [2,2,3] => 1010100 => 3
[4,1,6,2,7,5,3] => [2,2,2,1] => 1010101 => 4
[4,1,6,3,2,5,7] => [2,2,3] => 1010100 => 3
[4,1,6,3,2,7,5] => [2,2,1,2] => 1010110 => 4
[4,1,6,3,5,2,7] => [2,3,2] => 1010010 => 3
[4,1,6,3,5,7,2] => [2,3,2] => 1010010 => 3
[4,1,6,3,7,2,5] => [2,2,3] => 1010100 => 3
[4,1,6,3,7,5,2] => [2,2,2,1] => 1010101 => 4
[4,1,6,5,2,3,7] => [2,1,4] => 1011000 => 3
[4,1,6,5,2,7,3] => [2,1,2,2] => 1011010 => 4
[4,1,6,5,3,2,7] => [2,1,2,2] => 1011010 => 4
[4,1,6,5,3,7,2] => [2,1,2,2] => 1011010 => 4
[4,1,6,5,7,2,3] => [2,1,4] => 1011000 => 3
[4,1,6,5,7,3,2] => [2,1,3,1] => 1011001 => 4
[4,1,6,7,2,3,5] => [2,5] => 1010000 => 2
[4,1,6,7,2,5,3] => [2,4,1] => 1010001 => 3
[4,1,6,7,3,2,5] => [2,3,2] => 1010010 => 3
[4,1,6,7,3,5,2] => [2,4,1] => 1010001 => 3
[4,1,6,7,5,2,3] => [2,3,2] => 1010010 => 3
[4,1,6,7,5,3,2] => [2,3,1,1] => 1010011 => 4
[4,1,7,2,3,5,6] => [2,5] => 1010000 => 2
[4,1,7,2,3,6,5] => [2,4,1] => 1010001 => 3
[4,1,7,2,5,3,6] => [2,3,2] => 1010010 => 3
[4,1,7,2,5,6,3] => [2,4,1] => 1010001 => 3
[4,1,7,2,6,3,5] => [2,2,3] => 1010100 => 3
[4,1,7,2,6,5,3] => [2,2,2,1] => 1010101 => 4
[4,1,7,3,2,5,6] => [2,2,3] => 1010100 => 3
[4,1,7,3,2,6,5] => [2,2,2,1] => 1010101 => 4
[4,1,7,3,5,2,6] => [2,3,2] => 1010010 => 3
[4,1,7,3,5,6,2] => [2,4,1] => 1010001 => 3
[4,1,7,3,6,2,5] => [2,2,3] => 1010100 => 3
[4,1,7,3,6,5,2] => [2,2,2,1] => 1010101 => 4
[4,1,7,5,2,3,6] => [2,1,4] => 1011000 => 3
[4,1,7,5,2,6,3] => [2,1,3,1] => 1011001 => 4
[4,1,7,5,3,2,6] => [2,1,2,2] => 1011010 => 4
[4,1,7,5,3,6,2] => [2,1,3,1] => 1011001 => 4
[4,1,7,5,6,2,3] => [2,1,4] => 1011000 => 3
[4,1,7,5,6,3,2] => [2,1,3,1] => 1011001 => 4
[4,1,7,6,2,3,5] => [2,1,4] => 1011000 => 3
[4,1,7,6,2,5,3] => [2,1,3,1] => 1011001 => 4
[4,1,7,6,3,2,5] => [2,1,2,2] => 1011010 => 4
[4,1,7,6,3,5,2] => [2,1,3,1] => 1011001 => 4
[4,1,7,6,5,2,3] => [2,1,2,2] => 1011010 => 4
[4,1,7,6,5,3,2] => [2,1,2,1,1] => 1011011 => 5
[4,2,1,3,5,6,7] => [2,5] => 1010000 => 2
[4,2,1,3,5,7,6] => [2,3,2] => 1010010 => 3
[4,2,1,3,6,5,7] => [2,2,3] => 1010100 => 3
[4,2,1,3,6,7,5] => [2,2,3] => 1010100 => 3
[4,2,1,3,7,5,6] => [2,2,3] => 1010100 => 3
[4,2,1,3,7,6,5] => [2,2,2,1] => 1010101 => 4
[4,2,1,5,3,6,7] => [2,1,4] => 1011000 => 3
[4,2,1,5,3,7,6] => [2,1,2,2] => 1011010 => 4
[4,2,1,5,6,3,7] => [2,1,4] => 1011000 => 3
[4,2,1,5,6,7,3] => [2,1,4] => 1011000 => 3
[4,2,1,5,7,3,6] => [2,1,4] => 1011000 => 3
[4,2,1,5,7,6,3] => [2,1,3,1] => 1011001 => 4
[4,2,1,6,3,5,7] => [2,1,4] => 1011000 => 3
[4,2,1,6,3,7,5] => [2,1,2,2] => 1011010 => 4
[4,2,1,6,5,3,7] => [2,1,2,2] => 1011010 => 4
[4,2,1,6,5,7,3] => [2,1,2,2] => 1011010 => 4
[4,2,1,6,7,3,5] => [2,1,4] => 1011000 => 3
[4,2,1,6,7,5,3] => [2,1,3,1] => 1011001 => 4
[4,2,1,7,3,5,6] => [2,1,4] => 1011000 => 3
[4,2,1,7,3,6,5] => [2,1,3,1] => 1011001 => 4
[4,2,1,7,5,3,6] => [2,1,2,2] => 1011010 => 4
[4,2,1,7,5,6,3] => [2,1,3,1] => 1011001 => 4
[4,2,1,7,6,3,5] => [2,1,1,3] => 1011100 => 4
[4,2,1,7,6,5,3] => [2,1,1,2,1] => 1011101 => 5
[4,2,3,1,5,6,7] => [3,4] => 1001000 => 2
[4,2,3,1,5,7,6] => [3,2,2] => 1001010 => 3
[4,2,3,1,6,5,7] => [3,1,3] => 1001100 => 3
[4,2,3,1,6,7,5] => [3,1,3] => 1001100 => 3
[4,2,3,1,7,5,6] => [3,1,3] => 1001100 => 3
[4,2,3,1,7,6,5] => [3,1,2,1] => 1001101 => 4
[4,2,3,5,1,6,7] => [3,4] => 1001000 => 2
[4,2,3,5,1,7,6] => [3,2,2] => 1001010 => 3
[4,2,3,5,6,1,7] => [3,4] => 1001000 => 2
[4,2,3,5,6,7,1] => [3,4] => 1001000 => 2
[4,2,3,5,7,1,6] => [3,4] => 1001000 => 2
[4,2,3,5,7,6,1] => [3,3,1] => 1001001 => 3
[4,2,3,6,1,5,7] => [3,4] => 1001000 => 2
[4,2,3,6,1,7,5] => [3,2,2] => 1001010 => 3
[4,2,3,6,5,1,7] => [3,2,2] => 1001010 => 3
[4,2,3,6,5,7,1] => [3,2,2] => 1001010 => 3
[4,2,3,6,7,1,5] => [3,4] => 1001000 => 2
[4,2,3,6,7,5,1] => [3,3,1] => 1001001 => 3
[4,2,3,7,1,5,6] => [3,4] => 1001000 => 2
[4,2,3,7,1,6,5] => [3,3,1] => 1001001 => 3
[4,2,3,7,5,1,6] => [3,2,2] => 1001010 => 3
[4,2,3,7,5,6,1] => [3,3,1] => 1001001 => 3
[4,2,3,7,6,1,5] => [3,1,3] => 1001100 => 3
[4,2,3,7,6,5,1] => [3,1,2,1] => 1001101 => 4
[4,2,5,1,3,6,7] => [2,5] => 1010000 => 2
[4,2,5,1,3,7,6] => [2,3,2] => 1010010 => 3
[4,2,5,1,6,3,7] => [2,2,3] => 1010100 => 3
[4,2,5,1,6,7,3] => [2,2,3] => 1010100 => 3
[4,2,5,1,7,3,6] => [2,2,3] => 1010100 => 3
[4,2,5,1,7,6,3] => [2,2,2,1] => 1010101 => 4
[4,2,5,3,1,6,7] => [2,2,3] => 1010100 => 3
[4,2,5,3,1,7,6] => [2,2,1,2] => 1010110 => 4
[4,2,5,3,6,1,7] => [2,2,3] => 1010100 => 3
[4,2,5,3,6,7,1] => [2,2,3] => 1010100 => 3
[4,2,5,3,7,1,6] => [2,2,3] => 1010100 => 3
[4,2,5,3,7,6,1] => [2,2,2,1] => 1010101 => 4
[4,2,5,6,1,3,7] => [2,5] => 1010000 => 2
[4,2,5,6,1,7,3] => [2,3,2] => 1010010 => 3
[4,2,5,6,3,1,7] => [2,3,2] => 1010010 => 3
[4,2,5,6,3,7,1] => [2,3,2] => 1010010 => 3
[4,2,5,6,7,1,3] => [2,5] => 1010000 => 2
[4,2,5,6,7,3,1] => [2,4,1] => 1010001 => 3
[4,2,5,7,1,3,6] => [2,5] => 1010000 => 2
[4,2,5,7,1,6,3] => [2,4,1] => 1010001 => 3
[4,2,5,7,3,1,6] => [2,3,2] => 1010010 => 3
[4,2,5,7,3,6,1] => [2,4,1] => 1010001 => 3
[4,2,5,7,6,1,3] => [2,2,3] => 1010100 => 3
[4,2,5,7,6,3,1] => [2,2,2,1] => 1010101 => 4
[4,2,6,1,3,5,7] => [2,5] => 1010000 => 2
[4,2,6,1,3,7,5] => [2,3,2] => 1010010 => 3
[4,2,6,1,5,3,7] => [2,3,2] => 1010010 => 3
[4,2,6,1,5,7,3] => [2,3,2] => 1010010 => 3
[4,2,6,1,7,3,5] => [2,2,3] => 1010100 => 3
[4,2,6,1,7,5,3] => [2,2,2,1] => 1010101 => 4
[4,2,6,3,1,5,7] => [2,2,3] => 1010100 => 3
[4,2,6,3,1,7,5] => [2,2,1,2] => 1010110 => 4
[4,2,6,3,5,1,7] => [2,3,2] => 1010010 => 3
[4,2,6,3,5,7,1] => [2,3,2] => 1010010 => 3
[4,2,6,3,7,1,5] => [2,2,3] => 1010100 => 3
[4,2,6,3,7,5,1] => [2,2,2,1] => 1010101 => 4
[4,2,6,5,1,3,7] => [2,1,4] => 1011000 => 3
[4,2,6,5,1,7,3] => [2,1,2,2] => 1011010 => 4
[4,2,6,5,3,1,7] => [2,1,2,2] => 1011010 => 4
[4,2,6,5,3,7,1] => [2,1,2,2] => 1011010 => 4
[4,2,6,5,7,1,3] => [2,1,4] => 1011000 => 3
[4,2,6,5,7,3,1] => [2,1,3,1] => 1011001 => 4
[4,2,6,7,1,3,5] => [2,5] => 1010000 => 2
[4,2,6,7,1,5,3] => [2,4,1] => 1010001 => 3
[4,2,6,7,3,1,5] => [2,3,2] => 1010010 => 3
[4,2,6,7,3,5,1] => [2,4,1] => 1010001 => 3
[4,2,6,7,5,1,3] => [2,3,2] => 1010010 => 3
[4,2,6,7,5,3,1] => [2,3,1,1] => 1010011 => 4
[4,2,7,1,3,5,6] => [2,5] => 1010000 => 2
[4,2,7,1,3,6,5] => [2,4,1] => 1010001 => 3
[4,2,7,1,5,3,6] => [2,3,2] => 1010010 => 3
[4,2,7,1,5,6,3] => [2,4,1] => 1010001 => 3
[4,2,7,1,6,3,5] => [2,2,3] => 1010100 => 3
[4,2,7,1,6,5,3] => [2,2,2,1] => 1010101 => 4
[4,2,7,3,1,5,6] => [2,2,3] => 1010100 => 3
[4,2,7,3,1,6,5] => [2,2,2,1] => 1010101 => 4
[4,2,7,3,5,1,6] => [2,3,2] => 1010010 => 3
[4,2,7,3,5,6,1] => [2,4,1] => 1010001 => 3
[4,2,7,3,6,1,5] => [2,2,3] => 1010100 => 3
[4,2,7,3,6,5,1] => [2,2,2,1] => 1010101 => 4
[4,2,7,5,1,3,6] => [2,1,4] => 1011000 => 3
[4,2,7,5,1,6,3] => [2,1,3,1] => 1011001 => 4
[4,2,7,5,3,1,6] => [2,1,2,2] => 1011010 => 4
[4,2,7,5,3,6,1] => [2,1,3,1] => 1011001 => 4
[4,2,7,5,6,1,3] => [2,1,4] => 1011000 => 3
[4,2,7,5,6,3,1] => [2,1,3,1] => 1011001 => 4
[4,2,7,6,1,3,5] => [2,1,4] => 1011000 => 3
[4,2,7,6,1,5,3] => [2,1,3,1] => 1011001 => 4
[4,2,7,6,3,1,5] => [2,1,2,2] => 1011010 => 4
[4,2,7,6,3,5,1] => [2,1,3,1] => 1011001 => 4
[4,2,7,6,5,1,3] => [2,1,2,2] => 1011010 => 4
[4,2,7,6,5,3,1] => [2,1,2,1,1] => 1011011 => 5
[4,3,1,2,5,6,7] => [1,6] => 1100000 => 2
[4,3,1,2,5,7,6] => [1,4,2] => 1100010 => 3
[4,3,1,2,6,5,7] => [1,3,3] => 1100100 => 3
[4,3,1,2,6,7,5] => [1,3,3] => 1100100 => 3
[4,3,1,2,7,5,6] => [1,3,3] => 1100100 => 3
[4,3,1,2,7,6,5] => [1,3,2,1] => 1100101 => 4
[4,3,1,5,2,6,7] => [1,2,4] => 1101000 => 3
[4,3,1,5,2,7,6] => [1,2,2,2] => 1101010 => 4
[4,3,1,5,6,2,7] => [1,2,4] => 1101000 => 3
[4,3,1,5,6,7,2] => [1,2,4] => 1101000 => 3
[4,3,1,5,7,2,6] => [1,2,4] => 1101000 => 3
[4,3,1,5,7,6,2] => [1,2,3,1] => 1101001 => 4
[4,3,1,6,2,5,7] => [1,2,4] => 1101000 => 3
[4,3,1,6,2,7,5] => [1,2,2,2] => 1101010 => 4
[4,3,1,6,5,2,7] => [1,2,2,2] => 1101010 => 4
[4,3,1,6,5,7,2] => [1,2,2,2] => 1101010 => 4
[4,3,1,6,7,2,5] => [1,2,4] => 1101000 => 3
[4,3,1,6,7,5,2] => [1,2,3,1] => 1101001 => 4
[4,3,1,7,2,5,6] => [1,2,4] => 1101000 => 3
[4,3,1,7,2,6,5] => [1,2,3,1] => 1101001 => 4
[4,3,1,7,5,2,6] => [1,2,2,2] => 1101010 => 4
[4,3,1,7,5,6,2] => [1,2,3,1] => 1101001 => 4
[4,3,1,7,6,2,5] => [1,2,1,3] => 1101100 => 4
[4,3,1,7,6,5,2] => [1,2,1,2,1] => 1101101 => 5
[4,3,2,1,5,6,7] => [1,2,4] => 1101000 => 3
[4,3,2,1,5,7,6] => [1,2,2,2] => 1101010 => 4
[4,3,2,1,6,5,7] => [1,2,1,3] => 1101100 => 4
[4,3,2,1,6,7,5] => [1,2,1,3] => 1101100 => 4
[4,3,2,1,7,5,6] => [1,2,1,3] => 1101100 => 4
[4,3,2,1,7,6,5] => [1,2,1,2,1] => 1101101 => 5
[4,3,2,5,1,6,7] => [1,2,4] => 1101000 => 3
[4,3,2,5,1,7,6] => [1,2,2,2] => 1101010 => 4
[4,3,2,5,6,1,7] => [1,2,4] => 1101000 => 3
[4,3,2,5,6,7,1] => [1,2,4] => 1101000 => 3
[4,3,2,5,7,1,6] => [1,2,4] => 1101000 => 3
[4,3,2,5,7,6,1] => [1,2,3,1] => 1101001 => 4
[4,3,2,6,1,5,7] => [1,2,4] => 1101000 => 3
[4,3,2,6,1,7,5] => [1,2,2,2] => 1101010 => 4
[4,3,2,6,5,1,7] => [1,2,2,2] => 1101010 => 4
[4,3,2,6,5,7,1] => [1,2,2,2] => 1101010 => 4
[4,3,2,6,7,1,5] => [1,2,4] => 1101000 => 3
[4,3,2,6,7,5,1] => [1,2,3,1] => 1101001 => 4
[4,3,2,7,1,5,6] => [1,2,4] => 1101000 => 3
[4,3,2,7,1,6,5] => [1,2,3,1] => 1101001 => 4
[4,3,2,7,5,1,6] => [1,2,2,2] => 1101010 => 4
[4,3,2,7,5,6,1] => [1,2,3,1] => 1101001 => 4
[4,3,2,7,6,1,5] => [1,2,1,3] => 1101100 => 4
[4,3,2,7,6,5,1] => [1,2,1,2,1] => 1101101 => 5
[4,3,5,1,2,6,7] => [1,6] => 1100000 => 2
[4,3,5,1,2,7,6] => [1,4,2] => 1100010 => 3
[4,3,5,1,6,2,7] => [1,3,3] => 1100100 => 3
[4,3,5,1,6,7,2] => [1,3,3] => 1100100 => 3
[4,3,5,1,7,2,6] => [1,3,3] => 1100100 => 3
[4,3,5,1,7,6,2] => [1,3,2,1] => 1100101 => 4
[4,3,5,2,1,6,7] => [1,3,3] => 1100100 => 3
[4,3,5,2,1,7,6] => [1,3,1,2] => 1100110 => 4
[4,3,5,2,6,1,7] => [1,3,3] => 1100100 => 3
[4,3,5,2,6,7,1] => [1,3,3] => 1100100 => 3
[4,3,5,2,7,1,6] => [1,3,3] => 1100100 => 3
[4,3,5,2,7,6,1] => [1,3,2,1] => 1100101 => 4
[4,3,5,6,1,2,7] => [1,6] => 1100000 => 2
[4,3,5,6,1,7,2] => [1,4,2] => 1100010 => 3
[4,3,5,6,2,1,7] => [1,4,2] => 1100010 => 3
[4,3,5,6,2,7,1] => [1,4,2] => 1100010 => 3
[4,3,5,6,7,1,2] => [1,6] => 1100000 => 2
[4,3,5,6,7,2,1] => [1,5,1] => 1100001 => 3
[4,3,5,7,1,2,6] => [1,6] => 1100000 => 2
[4,3,5,7,1,6,2] => [1,5,1] => 1100001 => 3
[4,3,5,7,2,1,6] => [1,4,2] => 1100010 => 3
[4,3,5,7,2,6,1] => [1,5,1] => 1100001 => 3
[4,3,5,7,6,1,2] => [1,3,3] => 1100100 => 3
[4,3,5,7,6,2,1] => [1,3,2,1] => 1100101 => 4
[4,3,6,1,2,5,7] => [1,6] => 1100000 => 2
[4,3,6,1,2,7,5] => [1,4,2] => 1100010 => 3
[4,3,6,1,5,2,7] => [1,4,2] => 1100010 => 3
[4,3,6,1,5,7,2] => [1,4,2] => 1100010 => 3
[4,3,6,1,7,2,5] => [1,3,3] => 1100100 => 3
[4,3,6,1,7,5,2] => [1,3,2,1] => 1100101 => 4
[4,3,6,2,1,5,7] => [1,3,3] => 1100100 => 3
[4,3,6,2,1,7,5] => [1,3,1,2] => 1100110 => 4
[4,3,6,2,5,1,7] => [1,4,2] => 1100010 => 3
[4,3,6,2,5,7,1] => [1,4,2] => 1100010 => 3
[4,3,6,2,7,1,5] => [1,3,3] => 1100100 => 3
[4,3,6,2,7,5,1] => [1,3,2,1] => 1100101 => 4
[4,3,6,5,1,2,7] => [1,2,4] => 1101000 => 3
[4,3,6,5,1,7,2] => [1,2,2,2] => 1101010 => 4
[4,3,6,5,2,1,7] => [1,2,2,2] => 1101010 => 4
[4,3,6,5,2,7,1] => [1,2,2,2] => 1101010 => 4
[4,3,6,5,7,1,2] => [1,2,4] => 1101000 => 3
[4,3,6,5,7,2,1] => [1,2,3,1] => 1101001 => 4
[4,3,6,7,1,2,5] => [1,6] => 1100000 => 2
[4,3,6,7,1,5,2] => [1,5,1] => 1100001 => 3
[4,3,6,7,2,1,5] => [1,4,2] => 1100010 => 3
[4,3,6,7,2,5,1] => [1,5,1] => 1100001 => 3
[4,3,6,7,5,1,2] => [1,4,2] => 1100010 => 3
[4,3,6,7,5,2,1] => [1,4,1,1] => 1100011 => 4
[4,3,7,1,2,5,6] => [1,6] => 1100000 => 2
[4,3,7,1,2,6,5] => [1,5,1] => 1100001 => 3
[4,3,7,1,5,2,6] => [1,4,2] => 1100010 => 3
[4,3,7,1,5,6,2] => [1,5,1] => 1100001 => 3
[4,3,7,1,6,2,5] => [1,3,3] => 1100100 => 3
[4,3,7,1,6,5,2] => [1,3,2,1] => 1100101 => 4
[4,3,7,2,1,5,6] => [1,3,3] => 1100100 => 3
[4,3,7,2,1,6,5] => [1,3,2,1] => 1100101 => 4
[4,3,7,2,5,1,6] => [1,4,2] => 1100010 => 3
[4,3,7,2,5,6,1] => [1,5,1] => 1100001 => 3
[4,3,7,2,6,1,5] => [1,3,3] => 1100100 => 3
[4,3,7,2,6,5,1] => [1,3,2,1] => 1100101 => 4
[4,3,7,5,1,2,6] => [1,2,4] => 1101000 => 3
[4,3,7,5,1,6,2] => [1,2,3,1] => 1101001 => 4
[4,3,7,5,2,1,6] => [1,2,2,2] => 1101010 => 4
[4,3,7,5,2,6,1] => [1,2,3,1] => 1101001 => 4
[4,3,7,5,6,1,2] => [1,2,4] => 1101000 => 3
[4,3,7,5,6,2,1] => [1,2,3,1] => 1101001 => 4
[4,3,7,6,1,2,5] => [1,2,4] => 1101000 => 3
[4,3,7,6,1,5,2] => [1,2,3,1] => 1101001 => 4
[4,3,7,6,2,1,5] => [1,2,2,2] => 1101010 => 4
[4,3,7,6,2,5,1] => [1,2,3,1] => 1101001 => 4
[4,3,7,6,5,1,2] => [1,2,2,2] => 1101010 => 4
[4,3,7,6,5,2,1] => [1,2,2,1,1] => 1101011 => 5
[4,5,1,2,3,6,7] => [7] => 1000000 => 1
[4,5,1,2,3,7,6] => [5,2] => 1000010 => 2
[4,5,1,2,6,3,7] => [4,3] => 1000100 => 2
[4,5,1,2,6,7,3] => [4,3] => 1000100 => 2
[4,5,1,2,7,3,6] => [4,3] => 1000100 => 2
[4,5,1,2,7,6,3] => [4,2,1] => 1000101 => 3
[4,5,1,3,2,6,7] => [4,3] => 1000100 => 2
[4,5,1,3,2,7,6] => [4,1,2] => 1000110 => 3
[4,5,1,3,6,2,7] => [4,3] => 1000100 => 2
[4,5,1,3,6,7,2] => [4,3] => 1000100 => 2
[4,5,1,3,7,2,6] => [4,3] => 1000100 => 2
[4,5,1,3,7,6,2] => [4,2,1] => 1000101 => 3
[4,5,1,6,2,3,7] => [3,4] => 1001000 => 2
[4,5,1,6,2,7,3] => [3,2,2] => 1001010 => 3
[4,5,1,6,3,2,7] => [3,2,2] => 1001010 => 3
[4,5,1,6,3,7,2] => [3,2,2] => 1001010 => 3
[4,5,1,6,7,2,3] => [3,4] => 1001000 => 2
[4,5,1,6,7,3,2] => [3,3,1] => 1001001 => 3
[4,5,1,7,2,3,6] => [3,4] => 1001000 => 2
[4,5,1,7,2,6,3] => [3,3,1] => 1001001 => 3
[4,5,1,7,3,2,6] => [3,2,2] => 1001010 => 3
[4,5,1,7,3,6,2] => [3,3,1] => 1001001 => 3
[4,5,1,7,6,2,3] => [3,1,3] => 1001100 => 3
[4,5,1,7,6,3,2] => [3,1,2,1] => 1001101 => 4
[4,5,2,1,3,6,7] => [3,4] => 1001000 => 2
[4,5,2,1,3,7,6] => [3,2,2] => 1001010 => 3
[4,5,2,1,6,3,7] => [3,1,3] => 1001100 => 3
[4,5,2,1,6,7,3] => [3,1,3] => 1001100 => 3
[4,5,2,1,7,3,6] => [3,1,3] => 1001100 => 3
[4,5,2,1,7,6,3] => [3,1,2,1] => 1001101 => 4
[4,5,2,3,1,6,7] => [4,3] => 1000100 => 2
[4,5,2,3,1,7,6] => [4,1,2] => 1000110 => 3
[4,5,2,3,6,1,7] => [4,3] => 1000100 => 2
[4,5,2,3,6,7,1] => [4,3] => 1000100 => 2
[4,5,2,3,7,1,6] => [4,3] => 1000100 => 2
[4,5,2,3,7,6,1] => [4,2,1] => 1000101 => 3
[4,5,2,6,1,3,7] => [3,4] => 1001000 => 2
[4,5,2,6,1,7,3] => [3,2,2] => 1001010 => 3
[4,5,2,6,3,1,7] => [3,2,2] => 1001010 => 3
[4,5,2,6,3,7,1] => [3,2,2] => 1001010 => 3
[4,5,2,6,7,1,3] => [3,4] => 1001000 => 2
[4,5,2,6,7,3,1] => [3,3,1] => 1001001 => 3
[4,5,2,7,1,3,6] => [3,4] => 1001000 => 2
[4,5,2,7,1,6,3] => [3,3,1] => 1001001 => 3
[4,5,2,7,3,1,6] => [3,2,2] => 1001010 => 3
[4,5,2,7,3,6,1] => [3,3,1] => 1001001 => 3
[4,5,2,7,6,1,3] => [3,1,3] => 1001100 => 3
[4,5,2,7,6,3,1] => [3,1,2,1] => 1001101 => 4
[4,5,3,1,2,6,7] => [3,4] => 1001000 => 2
[4,5,3,1,2,7,6] => [3,2,2] => 1001010 => 3
[4,5,3,1,6,2,7] => [3,1,3] => 1001100 => 3
[4,5,3,1,6,7,2] => [3,1,3] => 1001100 => 3
[4,5,3,1,7,2,6] => [3,1,3] => 1001100 => 3
[4,5,3,1,7,6,2] => [3,1,2,1] => 1001101 => 4
[4,5,3,2,1,6,7] => [3,1,3] => 1001100 => 3
[4,5,3,2,1,7,6] => [3,1,1,2] => 1001110 => 4
[4,5,3,2,6,1,7] => [3,1,3] => 1001100 => 3
[4,5,3,2,6,7,1] => [3,1,3] => 1001100 => 3
[4,5,3,2,7,1,6] => [3,1,3] => 1001100 => 3
[4,5,3,2,7,6,1] => [3,1,2,1] => 1001101 => 4
[4,5,3,6,1,2,7] => [3,4] => 1001000 => 2
[4,5,3,6,1,7,2] => [3,2,2] => 1001010 => 3
[4,5,3,6,2,1,7] => [3,2,2] => 1001010 => 3
[4,5,3,6,2,7,1] => [3,2,2] => 1001010 => 3
[4,5,3,6,7,1,2] => [3,4] => 1001000 => 2
[4,5,3,6,7,2,1] => [3,3,1] => 1001001 => 3
[4,5,3,7,1,2,6] => [3,4] => 1001000 => 2
[4,5,3,7,1,6,2] => [3,3,1] => 1001001 => 3
[4,5,3,7,2,1,6] => [3,2,2] => 1001010 => 3
[4,5,3,7,2,6,1] => [3,3,1] => 1001001 => 3
[4,5,3,7,6,1,2] => [3,1,3] => 1001100 => 3
[4,5,3,7,6,2,1] => [3,1,2,1] => 1001101 => 4
[4,5,6,1,2,3,7] => [7] => 1000000 => 1
[4,5,6,1,2,7,3] => [5,2] => 1000010 => 2
[4,5,6,1,3,2,7] => [5,2] => 1000010 => 2
[4,5,6,1,3,7,2] => [5,2] => 1000010 => 2
[4,5,6,1,7,2,3] => [4,3] => 1000100 => 2
[4,5,6,1,7,3,2] => [4,2,1] => 1000101 => 3
[4,5,6,2,1,3,7] => [4,3] => 1000100 => 2
[4,5,6,2,1,7,3] => [4,1,2] => 1000110 => 3
[4,5,6,2,3,1,7] => [5,2] => 1000010 => 2
[4,5,6,2,3,7,1] => [5,2] => 1000010 => 2
[4,5,6,2,7,1,3] => [4,3] => 1000100 => 2
[4,5,6,2,7,3,1] => [4,2,1] => 1000101 => 3
[4,5,6,3,1,2,7] => [4,3] => 1000100 => 2
[4,5,6,3,1,7,2] => [4,1,2] => 1000110 => 3
[4,5,6,3,2,1,7] => [4,1,2] => 1000110 => 3
[4,5,6,3,2,7,1] => [4,1,2] => 1000110 => 3
[4,5,6,3,7,1,2] => [4,3] => 1000100 => 2
[4,5,6,3,7,2,1] => [4,2,1] => 1000101 => 3
[4,5,6,7,1,2,3] => [7] => 1000000 => 1
[4,5,6,7,1,3,2] => [6,1] => 1000001 => 2
[4,5,6,7,2,1,3] => [5,2] => 1000010 => 2
[4,5,6,7,2,3,1] => [6,1] => 1000001 => 2
[4,5,6,7,3,1,2] => [5,2] => 1000010 => 2
[4,5,6,7,3,2,1] => [5,1,1] => 1000011 => 3
[4,5,7,1,2,3,6] => [7] => 1000000 => 1
[4,5,7,1,2,6,3] => [6,1] => 1000001 => 2
[4,5,7,1,3,2,6] => [5,2] => 1000010 => 2
[4,5,7,1,3,6,2] => [6,1] => 1000001 => 2
[4,5,7,1,6,2,3] => [4,3] => 1000100 => 2
[4,5,7,1,6,3,2] => [4,2,1] => 1000101 => 3
[4,5,7,2,1,3,6] => [4,3] => 1000100 => 2
[4,5,7,2,1,6,3] => [4,2,1] => 1000101 => 3
[4,5,7,2,3,1,6] => [5,2] => 1000010 => 2
[4,5,7,2,3,6,1] => [6,1] => 1000001 => 2
[4,5,7,2,6,1,3] => [4,3] => 1000100 => 2
[4,5,7,2,6,3,1] => [4,2,1] => 1000101 => 3
[4,5,7,3,1,2,6] => [4,3] => 1000100 => 2
[4,5,7,3,1,6,2] => [4,2,1] => 1000101 => 3
[4,5,7,3,2,1,6] => [4,1,2] => 1000110 => 3
[4,5,7,3,2,6,1] => [4,2,1] => 1000101 => 3
[4,5,7,3,6,1,2] => [4,3] => 1000100 => 2
[4,5,7,3,6,2,1] => [4,2,1] => 1000101 => 3
[4,5,7,6,1,2,3] => [3,4] => 1001000 => 2
[4,5,7,6,1,3,2] => [3,3,1] => 1001001 => 3
[4,5,7,6,2,1,3] => [3,2,2] => 1001010 => 3
[4,5,7,6,2,3,1] => [3,3,1] => 1001001 => 3
[4,5,7,6,3,1,2] => [3,2,2] => 1001010 => 3
[4,5,7,6,3,2,1] => [3,2,1,1] => 1001011 => 4
[4,6,1,2,3,5,7] => [7] => 1000000 => 1
[4,6,1,2,3,7,5] => [5,2] => 1000010 => 2
[4,6,1,2,5,3,7] => [5,2] => 1000010 => 2
[4,6,1,2,5,7,3] => [5,2] => 1000010 => 2
[4,6,1,2,7,3,5] => [4,3] => 1000100 => 2
[4,6,1,2,7,5,3] => [4,2,1] => 1000101 => 3
[4,6,1,3,2,5,7] => [4,3] => 1000100 => 2
[4,6,1,3,2,7,5] => [4,1,2] => 1000110 => 3
[4,6,1,3,5,2,7] => [5,2] => 1000010 => 2
[4,6,1,3,5,7,2] => [5,2] => 1000010 => 2
[4,6,1,3,7,2,5] => [4,3] => 1000100 => 2
[4,6,1,3,7,5,2] => [4,2,1] => 1000101 => 3
[4,6,1,5,2,3,7] => [3,4] => 1001000 => 2
[4,6,1,5,2,7,3] => [3,2,2] => 1001010 => 3
[4,6,1,5,3,2,7] => [3,2,2] => 1001010 => 3
[4,6,1,5,3,7,2] => [3,2,2] => 1001010 => 3
[4,6,1,5,7,2,3] => [3,4] => 1001000 => 2
[4,6,1,5,7,3,2] => [3,3,1] => 1001001 => 3
[4,6,1,7,2,3,5] => [3,4] => 1001000 => 2
[4,6,1,7,2,5,3] => [3,3,1] => 1001001 => 3
[4,6,1,7,3,2,5] => [3,2,2] => 1001010 => 3
[4,6,1,7,3,5,2] => [3,3,1] => 1001001 => 3
[4,6,1,7,5,2,3] => [3,2,2] => 1001010 => 3
[4,6,1,7,5,3,2] => [3,2,1,1] => 1001011 => 4
[4,6,2,1,3,5,7] => [3,4] => 1001000 => 2
[4,6,2,1,3,7,5] => [3,2,2] => 1001010 => 3
[4,6,2,1,5,3,7] => [3,2,2] => 1001010 => 3
[4,6,2,1,5,7,3] => [3,2,2] => 1001010 => 3
[4,6,2,1,7,3,5] => [3,1,3] => 1001100 => 3
[4,6,2,1,7,5,3] => [3,1,2,1] => 1001101 => 4
[4,6,2,3,1,5,7] => [4,3] => 1000100 => 2
[4,6,2,3,1,7,5] => [4,1,2] => 1000110 => 3
[4,6,2,3,5,1,7] => [5,2] => 1000010 => 2
[4,6,2,3,5,7,1] => [5,2] => 1000010 => 2
[4,6,2,3,7,1,5] => [4,3] => 1000100 => 2
[4,6,2,3,7,5,1] => [4,2,1] => 1000101 => 3
[4,6,2,5,1,3,7] => [3,4] => 1001000 => 2
[4,6,2,5,1,7,3] => [3,2,2] => 1001010 => 3
[4,6,2,5,3,1,7] => [3,2,2] => 1001010 => 3
[4,6,2,5,3,7,1] => [3,2,2] => 1001010 => 3
[4,6,2,5,7,1,3] => [3,4] => 1001000 => 2
[4,6,2,5,7,3,1] => [3,3,1] => 1001001 => 3
[4,6,2,7,1,3,5] => [3,4] => 1001000 => 2
[4,6,2,7,1,5,3] => [3,3,1] => 1001001 => 3
[4,6,2,7,3,1,5] => [3,2,2] => 1001010 => 3
[4,6,2,7,3,5,1] => [3,3,1] => 1001001 => 3
[4,6,2,7,5,1,3] => [3,2,2] => 1001010 => 3
[4,6,2,7,5,3,1] => [3,2,1,1] => 1001011 => 4
[4,6,3,1,2,5,7] => [3,4] => 1001000 => 2
[4,6,3,1,2,7,5] => [3,2,2] => 1001010 => 3
[4,6,3,1,5,2,7] => [3,2,2] => 1001010 => 3
[4,6,3,1,5,7,2] => [3,2,2] => 1001010 => 3
[4,6,3,1,7,2,5] => [3,1,3] => 1001100 => 3
[4,6,3,1,7,5,2] => [3,1,2,1] => 1001101 => 4
[4,6,3,2,1,5,7] => [3,1,3] => 1001100 => 3
[4,6,3,2,1,7,5] => [3,1,1,2] => 1001110 => 4
[4,6,3,2,5,1,7] => [3,2,2] => 1001010 => 3
[4,6,3,2,5,7,1] => [3,2,2] => 1001010 => 3
[4,6,3,2,7,1,5] => [3,1,3] => 1001100 => 3
[4,6,3,2,7,5,1] => [3,1,2,1] => 1001101 => 4
[4,6,3,5,1,2,7] => [3,4] => 1001000 => 2
[4,6,3,5,1,7,2] => [3,2,2] => 1001010 => 3
[4,6,3,5,2,1,7] => [3,2,2] => 1001010 => 3
[4,6,3,5,2,7,1] => [3,2,2] => 1001010 => 3
[4,6,3,5,7,1,2] => [3,4] => 1001000 => 2
[4,6,3,5,7,2,1] => [3,3,1] => 1001001 => 3
[4,6,3,7,1,2,5] => [3,4] => 1001000 => 2
[4,6,3,7,1,5,2] => [3,3,1] => 1001001 => 3
[4,6,3,7,2,1,5] => [3,2,2] => 1001010 => 3
[4,6,3,7,2,5,1] => [3,3,1] => 1001001 => 3
[4,6,3,7,5,1,2] => [3,2,2] => 1001010 => 3
[4,6,3,7,5,2,1] => [3,2,1,1] => 1001011 => 4
[4,6,5,1,2,3,7] => [2,5] => 1010000 => 2
[4,6,5,1,2,7,3] => [2,3,2] => 1010010 => 3
[4,6,5,1,3,2,7] => [2,3,2] => 1010010 => 3
[4,6,5,1,3,7,2] => [2,3,2] => 1010010 => 3
[4,6,5,1,7,2,3] => [2,2,3] => 1010100 => 3
[4,6,5,1,7,3,2] => [2,2,2,1] => 1010101 => 4
[4,6,5,2,1,3,7] => [2,2,3] => 1010100 => 3
[4,6,5,2,1,7,3] => [2,2,1,2] => 1010110 => 4
[4,6,5,2,3,1,7] => [2,3,2] => 1010010 => 3
[4,6,5,2,3,7,1] => [2,3,2] => 1010010 => 3
[4,6,5,2,7,1,3] => [2,2,3] => 1010100 => 3
[4,6,5,2,7,3,1] => [2,2,2,1] => 1010101 => 4
[4,6,5,3,1,2,7] => [2,2,3] => 1010100 => 3
[4,6,5,3,1,7,2] => [2,2,1,2] => 1010110 => 4
[4,6,5,3,2,1,7] => [2,2,1,2] => 1010110 => 4
[4,6,5,3,2,7,1] => [2,2,1,2] => 1010110 => 4
[4,6,5,3,7,1,2] => [2,2,3] => 1010100 => 3
[4,6,5,3,7,2,1] => [2,2,2,1] => 1010101 => 4
[4,6,5,7,1,2,3] => [2,5] => 1010000 => 2
[4,6,5,7,1,3,2] => [2,4,1] => 1010001 => 3
[4,6,5,7,2,1,3] => [2,3,2] => 1010010 => 3
[4,6,5,7,2,3,1] => [2,4,1] => 1010001 => 3
[4,6,5,7,3,1,2] => [2,3,2] => 1010010 => 3
[4,6,5,7,3,2,1] => [2,3,1,1] => 1010011 => 4
[4,6,7,1,2,3,5] => [7] => 1000000 => 1
[4,6,7,1,2,5,3] => [6,1] => 1000001 => 2
[4,6,7,1,3,2,5] => [5,2] => 1000010 => 2
[4,6,7,1,3,5,2] => [6,1] => 1000001 => 2
[4,6,7,1,5,2,3] => [5,2] => 1000010 => 2
[4,6,7,1,5,3,2] => [5,1,1] => 1000011 => 3
[4,6,7,2,1,3,5] => [4,3] => 1000100 => 2
[4,6,7,2,1,5,3] => [4,2,1] => 1000101 => 3
[4,6,7,2,3,1,5] => [5,2] => 1000010 => 2
[4,6,7,2,3,5,1] => [6,1] => 1000001 => 2
[4,6,7,2,5,1,3] => [5,2] => 1000010 => 2
[4,6,7,2,5,3,1] => [5,1,1] => 1000011 => 3
[4,6,7,3,1,2,5] => [4,3] => 1000100 => 2
[4,6,7,3,1,5,2] => [4,2,1] => 1000101 => 3
[4,6,7,3,2,1,5] => [4,1,2] => 1000110 => 3
[4,6,7,3,2,5,1] => [4,2,1] => 1000101 => 3
[4,6,7,3,5,1,2] => [5,2] => 1000010 => 2
[4,6,7,3,5,2,1] => [5,1,1] => 1000011 => 3
[4,6,7,5,1,2,3] => [3,4] => 1001000 => 2
[4,6,7,5,1,3,2] => [3,3,1] => 1001001 => 3
[4,6,7,5,2,1,3] => [3,2,2] => 1001010 => 3
[4,6,7,5,2,3,1] => [3,3,1] => 1001001 => 3
[4,6,7,5,3,1,2] => [3,2,2] => 1001010 => 3
[4,6,7,5,3,2,1] => [3,2,1,1] => 1001011 => 4
[4,7,1,2,3,5,6] => [7] => 1000000 => 1
[4,7,1,2,3,6,5] => [6,1] => 1000001 => 2
[4,7,1,2,5,3,6] => [5,2] => 1000010 => 2
[4,7,1,2,5,6,3] => [6,1] => 1000001 => 2
[4,7,1,2,6,3,5] => [4,3] => 1000100 => 2
[4,7,1,2,6,5,3] => [4,2,1] => 1000101 => 3
[4,7,1,3,2,5,6] => [4,3] => 1000100 => 2
[4,7,1,3,2,6,5] => [4,2,1] => 1000101 => 3
[4,7,1,3,5,2,6] => [5,2] => 1000010 => 2
[4,7,1,3,5,6,2] => [6,1] => 1000001 => 2
[4,7,1,3,6,2,5] => [4,3] => 1000100 => 2
[4,7,1,3,6,5,2] => [4,2,1] => 1000101 => 3
[4,7,1,5,2,3,6] => [3,4] => 1001000 => 2
[4,7,1,5,2,6,3] => [3,3,1] => 1001001 => 3
[4,7,1,5,3,2,6] => [3,2,2] => 1001010 => 3
[4,7,1,5,3,6,2] => [3,3,1] => 1001001 => 3
[4,7,1,5,6,2,3] => [3,4] => 1001000 => 2
[4,7,1,5,6,3,2] => [3,3,1] => 1001001 => 3
[4,7,1,6,2,3,5] => [3,4] => 1001000 => 2
[4,7,1,6,2,5,3] => [3,3,1] => 1001001 => 3
[4,7,1,6,3,2,5] => [3,2,2] => 1001010 => 3
[4,7,1,6,3,5,2] => [3,3,1] => 1001001 => 3
[4,7,1,6,5,2,3] => [3,2,2] => 1001010 => 3
[4,7,1,6,5,3,2] => [3,2,1,1] => 1001011 => 4
[4,7,2,1,3,5,6] => [3,4] => 1001000 => 2
[4,7,2,1,3,6,5] => [3,3,1] => 1001001 => 3
[4,7,2,1,5,3,6] => [3,2,2] => 1001010 => 3
[4,7,2,1,5,6,3] => [3,3,1] => 1001001 => 3
[4,7,2,1,6,3,5] => [3,1,3] => 1001100 => 3
[4,7,2,1,6,5,3] => [3,1,2,1] => 1001101 => 4
[4,7,2,3,1,5,6] => [4,3] => 1000100 => 2
[4,7,2,3,1,6,5] => [4,2,1] => 1000101 => 3
[4,7,2,3,5,1,6] => [5,2] => 1000010 => 2
[4,7,2,3,5,6,1] => [6,1] => 1000001 => 2
[4,7,2,3,6,1,5] => [4,3] => 1000100 => 2
[4,7,2,3,6,5,1] => [4,2,1] => 1000101 => 3
[4,7,2,5,1,3,6] => [3,4] => 1001000 => 2
[4,7,2,5,1,6,3] => [3,3,1] => 1001001 => 3
[4,7,2,5,3,1,6] => [3,2,2] => 1001010 => 3
[4,7,2,5,3,6,1] => [3,3,1] => 1001001 => 3
[4,7,2,5,6,1,3] => [3,4] => 1001000 => 2
[4,7,2,5,6,3,1] => [3,3,1] => 1001001 => 3
[4,7,2,6,1,3,5] => [3,4] => 1001000 => 2
[4,7,2,6,1,5,3] => [3,3,1] => 1001001 => 3
[4,7,2,6,3,1,5] => [3,2,2] => 1001010 => 3
[4,7,2,6,3,5,1] => [3,3,1] => 1001001 => 3
[4,7,2,6,5,1,3] => [3,2,2] => 1001010 => 3
[4,7,2,6,5,3,1] => [3,2,1,1] => 1001011 => 4
[4,7,3,1,2,5,6] => [3,4] => 1001000 => 2
[4,7,3,1,2,6,5] => [3,3,1] => 1001001 => 3
[4,7,3,1,5,2,6] => [3,2,2] => 1001010 => 3
[4,7,3,1,5,6,2] => [3,3,1] => 1001001 => 3
[4,7,3,1,6,2,5] => [3,1,3] => 1001100 => 3
[4,7,3,1,6,5,2] => [3,1,2,1] => 1001101 => 4
[4,7,3,2,1,5,6] => [3,1,3] => 1001100 => 3
[4,7,3,2,1,6,5] => [3,1,2,1] => 1001101 => 4
[4,7,3,2,5,1,6] => [3,2,2] => 1001010 => 3
[4,7,3,2,5,6,1] => [3,3,1] => 1001001 => 3
[4,7,3,2,6,1,5] => [3,1,3] => 1001100 => 3
[4,7,3,2,6,5,1] => [3,1,2,1] => 1001101 => 4
[4,7,3,5,1,2,6] => [3,4] => 1001000 => 2
[4,7,3,5,1,6,2] => [3,3,1] => 1001001 => 3
[4,7,3,5,2,1,6] => [3,2,2] => 1001010 => 3
[4,7,3,5,2,6,1] => [3,3,1] => 1001001 => 3
[4,7,3,5,6,1,2] => [3,4] => 1001000 => 2
[4,7,3,5,6,2,1] => [3,3,1] => 1001001 => 3
[4,7,3,6,1,2,5] => [3,4] => 1001000 => 2
[4,7,3,6,1,5,2] => [3,3,1] => 1001001 => 3
[4,7,3,6,2,1,5] => [3,2,2] => 1001010 => 3
[4,7,3,6,2,5,1] => [3,3,1] => 1001001 => 3
[4,7,3,6,5,1,2] => [3,2,2] => 1001010 => 3
[4,7,3,6,5,2,1] => [3,2,1,1] => 1001011 => 4
[4,7,5,1,2,3,6] => [2,5] => 1010000 => 2
[4,7,5,1,2,6,3] => [2,4,1] => 1010001 => 3
[4,7,5,1,3,2,6] => [2,3,2] => 1010010 => 3
[4,7,5,1,3,6,2] => [2,4,1] => 1010001 => 3
[4,7,5,1,6,2,3] => [2,2,3] => 1010100 => 3
[4,7,5,1,6,3,2] => [2,2,2,1] => 1010101 => 4
[4,7,5,2,1,3,6] => [2,2,3] => 1010100 => 3
[4,7,5,2,1,6,3] => [2,2,2,1] => 1010101 => 4
[4,7,5,2,3,1,6] => [2,3,2] => 1010010 => 3
[4,7,5,2,3,6,1] => [2,4,1] => 1010001 => 3
[4,7,5,2,6,1,3] => [2,2,3] => 1010100 => 3
[4,7,5,2,6,3,1] => [2,2,2,1] => 1010101 => 4
[4,7,5,3,1,2,6] => [2,2,3] => 1010100 => 3
[4,7,5,3,1,6,2] => [2,2,2,1] => 1010101 => 4
[4,7,5,3,2,1,6] => [2,2,1,2] => 1010110 => 4
[4,7,5,3,2,6,1] => [2,2,2,1] => 1010101 => 4
[4,7,5,3,6,1,2] => [2,2,3] => 1010100 => 3
[4,7,5,3,6,2,1] => [2,2,2,1] => 1010101 => 4
[4,7,5,6,1,2,3] => [2,5] => 1010000 => 2
[4,7,5,6,1,3,2] => [2,4,1] => 1010001 => 3
[4,7,5,6,2,1,3] => [2,3,2] => 1010010 => 3
[4,7,5,6,2,3,1] => [2,4,1] => 1010001 => 3
[4,7,5,6,3,1,2] => [2,3,2] => 1010010 => 3
[4,7,5,6,3,2,1] => [2,3,1,1] => 1010011 => 4
[4,7,6,1,2,3,5] => [2,5] => 1010000 => 2
[4,7,6,1,2,5,3] => [2,4,1] => 1010001 => 3
[4,7,6,1,3,2,5] => [2,3,2] => 1010010 => 3
[4,7,6,1,3,5,2] => [2,4,1] => 1010001 => 3
[4,7,6,1,5,2,3] => [2,3,2] => 1010010 => 3
[4,7,6,1,5,3,2] => [2,3,1,1] => 1010011 => 4
[4,7,6,2,1,3,5] => [2,2,3] => 1010100 => 3
[4,7,6,2,1,5,3] => [2,2,2,1] => 1010101 => 4
[4,7,6,2,3,1,5] => [2,3,2] => 1010010 => 3
[4,7,6,2,3,5,1] => [2,4,1] => 1010001 => 3
[4,7,6,2,5,1,3] => [2,3,2] => 1010010 => 3
[4,7,6,2,5,3,1] => [2,3,1,1] => 1010011 => 4
[4,7,6,3,1,2,5] => [2,2,3] => 1010100 => 3
[4,7,6,3,1,5,2] => [2,2,2,1] => 1010101 => 4
[4,7,6,3,2,1,5] => [2,2,1,2] => 1010110 => 4
[4,7,6,3,2,5,1] => [2,2,2,1] => 1010101 => 4
[4,7,6,3,5,1,2] => [2,3,2] => 1010010 => 3
[4,7,6,3,5,2,1] => [2,3,1,1] => 1010011 => 4
[4,7,6,5,1,2,3] => [2,1,4] => 1011000 => 3
[4,7,6,5,1,3,2] => [2,1,3,1] => 1011001 => 4
[4,7,6,5,2,1,3] => [2,1,2,2] => 1011010 => 4
[4,7,6,5,2,3,1] => [2,1,3,1] => 1011001 => 4
[4,7,6,5,3,1,2] => [2,1,2,2] => 1011010 => 4
[4,7,6,5,3,2,1] => [2,1,2,1,1] => 1011011 => 5
[5,1,2,3,4,6,7] => [7] => 1000000 => 1
[5,1,2,3,4,7,6] => [5,2] => 1000010 => 2
[5,1,2,3,6,4,7] => [4,3] => 1000100 => 2
[5,1,2,3,6,7,4] => [4,3] => 1000100 => 2
[5,1,2,3,7,4,6] => [4,3] => 1000100 => 2
[5,1,2,3,7,6,4] => [4,2,1] => 1000101 => 3
[5,1,2,4,3,6,7] => [4,3] => 1000100 => 2
[5,1,2,4,3,7,6] => [4,1,2] => 1000110 => 3
[5,1,2,4,6,3,7] => [4,3] => 1000100 => 2
[5,1,2,4,6,7,3] => [4,3] => 1000100 => 2
[5,1,2,4,7,3,6] => [4,3] => 1000100 => 2
[5,1,2,4,7,6,3] => [4,2,1] => 1000101 => 3
[5,1,2,6,3,4,7] => [3,4] => 1001000 => 2
[5,1,2,6,3,7,4] => [3,2,2] => 1001010 => 3
[5,1,2,6,4,3,7] => [3,2,2] => 1001010 => 3
[5,1,2,6,4,7,3] => [3,2,2] => 1001010 => 3
[5,1,2,6,7,3,4] => [3,4] => 1001000 => 2
[5,1,2,6,7,4,3] => [3,3,1] => 1001001 => 3
[5,1,2,7,3,4,6] => [3,4] => 1001000 => 2
[5,1,2,7,3,6,4] => [3,3,1] => 1001001 => 3
[5,1,2,7,4,3,6] => [3,2,2] => 1001010 => 3
[5,1,2,7,4,6,3] => [3,3,1] => 1001001 => 3
[5,1,2,7,6,3,4] => [3,1,3] => 1001100 => 3
[5,1,2,7,6,4,3] => [3,1,2,1] => 1001101 => 4
[5,1,3,2,4,6,7] => [3,4] => 1001000 => 2
[5,1,3,2,4,7,6] => [3,2,2] => 1001010 => 3
[5,1,3,2,6,4,7] => [3,1,3] => 1001100 => 3
[5,1,3,2,6,7,4] => [3,1,3] => 1001100 => 3
[5,1,3,2,7,4,6] => [3,1,3] => 1001100 => 3
[5,1,3,2,7,6,4] => [3,1,2,1] => 1001101 => 4
[5,1,3,4,2,6,7] => [4,3] => 1000100 => 2
[5,1,3,4,2,7,6] => [4,1,2] => 1000110 => 3
[5,1,3,4,6,2,7] => [4,3] => 1000100 => 2
[5,1,3,4,6,7,2] => [4,3] => 1000100 => 2
[5,1,3,4,7,2,6] => [4,3] => 1000100 => 2
[5,1,3,4,7,6,2] => [4,2,1] => 1000101 => 3
[5,1,3,6,2,4,7] => [3,4] => 1001000 => 2
[5,1,3,6,2,7,4] => [3,2,2] => 1001010 => 3
[5,1,3,6,4,2,7] => [3,2,2] => 1001010 => 3
[5,1,3,6,4,7,2] => [3,2,2] => 1001010 => 3
[5,1,3,6,7,2,4] => [3,4] => 1001000 => 2
[5,1,3,6,7,4,2] => [3,3,1] => 1001001 => 3
[5,1,3,7,2,4,6] => [3,4] => 1001000 => 2
[5,1,3,7,2,6,4] => [3,3,1] => 1001001 => 3
[5,1,3,7,4,2,6] => [3,2,2] => 1001010 => 3
[5,1,3,7,4,6,2] => [3,3,1] => 1001001 => 3
[5,1,3,7,6,2,4] => [3,1,3] => 1001100 => 3
[5,1,3,7,6,4,2] => [3,1,2,1] => 1001101 => 4
[5,1,4,2,3,6,7] => [2,5] => 1010000 => 2
[5,1,4,2,3,7,6] => [2,3,2] => 1010010 => 3
[5,1,4,2,6,3,7] => [2,2,3] => 1010100 => 3
[5,1,4,2,6,7,3] => [2,2,3] => 1010100 => 3
[5,1,4,2,7,3,6] => [2,2,3] => 1010100 => 3
[5,1,4,2,7,6,3] => [2,2,2,1] => 1010101 => 4
[5,1,4,3,2,6,7] => [2,2,3] => 1010100 => 3
[5,1,4,3,2,7,6] => [2,2,1,2] => 1010110 => 4
[5,1,4,3,6,2,7] => [2,2,3] => 1010100 => 3
[5,1,4,3,6,7,2] => [2,2,3] => 1010100 => 3
[5,1,4,3,7,2,6] => [2,2,3] => 1010100 => 3
[5,1,4,3,7,6,2] => [2,2,2,1] => 1010101 => 4
[5,1,4,6,2,3,7] => [2,5] => 1010000 => 2
[5,1,4,6,2,7,3] => [2,3,2] => 1010010 => 3
[5,1,4,6,3,2,7] => [2,3,2] => 1010010 => 3
[5,1,4,6,3,7,2] => [2,3,2] => 1010010 => 3
[5,1,4,6,7,2,3] => [2,5] => 1010000 => 2
[5,1,4,6,7,3,2] => [2,4,1] => 1010001 => 3
[5,1,4,7,2,3,6] => [2,5] => 1010000 => 2
[5,1,4,7,2,6,3] => [2,4,1] => 1010001 => 3
[5,1,4,7,3,2,6] => [2,3,2] => 1010010 => 3
[5,1,4,7,3,6,2] => [2,4,1] => 1010001 => 3
[5,1,4,7,6,2,3] => [2,2,3] => 1010100 => 3
[5,1,4,7,6,3,2] => [2,2,2,1] => 1010101 => 4
[5,1,6,2,3,4,7] => [2,5] => 1010000 => 2
[5,1,6,2,3,7,4] => [2,3,2] => 1010010 => 3
[5,1,6,2,4,3,7] => [2,3,2] => 1010010 => 3
[5,1,6,2,4,7,3] => [2,3,2] => 1010010 => 3
[5,1,6,2,7,3,4] => [2,2,3] => 1010100 => 3
[5,1,6,2,7,4,3] => [2,2,2,1] => 1010101 => 4
[5,1,6,3,2,4,7] => [2,2,3] => 1010100 => 3
[5,1,6,3,2,7,4] => [2,2,1,2] => 1010110 => 4
[5,1,6,3,4,2,7] => [2,3,2] => 1010010 => 3
[5,1,6,3,4,7,2] => [2,3,2] => 1010010 => 3
[5,1,6,3,7,2,4] => [2,2,3] => 1010100 => 3
[5,1,6,3,7,4,2] => [2,2,2,1] => 1010101 => 4
[5,1,6,4,2,3,7] => [2,2,3] => 1010100 => 3
[5,1,6,4,2,7,3] => [2,2,1,2] => 1010110 => 4
[5,1,6,4,3,2,7] => [2,2,1,2] => 1010110 => 4
[5,1,6,4,3,7,2] => [2,2,1,2] => 1010110 => 4
[5,1,6,4,7,2,3] => [2,2,3] => 1010100 => 3
[5,1,6,4,7,3,2] => [2,2,2,1] => 1010101 => 4
[5,1,6,7,2,3,4] => [2,5] => 1010000 => 2
[5,1,6,7,2,4,3] => [2,4,1] => 1010001 => 3
[5,1,6,7,3,2,4] => [2,3,2] => 1010010 => 3
[5,1,6,7,3,4,2] => [2,4,1] => 1010001 => 3
[5,1,6,7,4,2,3] => [2,3,2] => 1010010 => 3
[5,1,6,7,4,3,2] => [2,3,1,1] => 1010011 => 4
[5,1,7,2,3,4,6] => [2,5] => 1010000 => 2
[5,1,7,2,3,6,4] => [2,4,1] => 1010001 => 3
[5,1,7,2,4,3,6] => [2,3,2] => 1010010 => 3
[5,1,7,2,4,6,3] => [2,4,1] => 1010001 => 3
[5,1,7,2,6,3,4] => [2,2,3] => 1010100 => 3
[5,1,7,2,6,4,3] => [2,2,2,1] => 1010101 => 4
[5,1,7,3,2,4,6] => [2,2,3] => 1010100 => 3
[5,1,7,3,2,6,4] => [2,2,2,1] => 1010101 => 4
[5,1,7,3,4,2,6] => [2,3,2] => 1010010 => 3
[5,1,7,3,4,6,2] => [2,4,1] => 1010001 => 3
[5,1,7,3,6,2,4] => [2,2,3] => 1010100 => 3
[5,1,7,3,6,4,2] => [2,2,2,1] => 1010101 => 4
[5,1,7,4,2,3,6] => [2,2,3] => 1010100 => 3
[5,1,7,4,2,6,3] => [2,2,2,1] => 1010101 => 4
[5,1,7,4,3,2,6] => [2,2,1,2] => 1010110 => 4
[5,1,7,4,3,6,2] => [2,2,2,1] => 1010101 => 4
[5,1,7,4,6,2,3] => [2,2,3] => 1010100 => 3
[5,1,7,4,6,3,2] => [2,2,2,1] => 1010101 => 4
[5,1,7,6,2,3,4] => [2,1,4] => 1011000 => 3
[5,1,7,6,2,4,3] => [2,1,3,1] => 1011001 => 4
[5,1,7,6,3,2,4] => [2,1,2,2] => 1011010 => 4
[5,1,7,6,3,4,2] => [2,1,3,1] => 1011001 => 4
[5,1,7,6,4,2,3] => [2,1,2,2] => 1011010 => 4
[5,1,7,6,4,3,2] => [2,1,2,1,1] => 1011011 => 5
[5,2,1,3,4,6,7] => [2,5] => 1010000 => 2
[5,2,1,3,4,7,6] => [2,3,2] => 1010010 => 3
[5,2,1,3,6,4,7] => [2,2,3] => 1010100 => 3
[5,2,1,3,6,7,4] => [2,2,3] => 1010100 => 3
[5,2,1,3,7,4,6] => [2,2,3] => 1010100 => 3
[5,2,1,3,7,6,4] => [2,2,2,1] => 1010101 => 4
[5,2,1,4,3,6,7] => [2,2,3] => 1010100 => 3
[5,2,1,4,3,7,6] => [2,2,1,2] => 1010110 => 4
[5,2,1,4,6,3,7] => [2,2,3] => 1010100 => 3
[5,2,1,4,6,7,3] => [2,2,3] => 1010100 => 3
[5,2,1,4,7,3,6] => [2,2,3] => 1010100 => 3
[5,2,1,4,7,6,3] => [2,2,2,1] => 1010101 => 4
[5,2,1,6,3,4,7] => [2,1,4] => 1011000 => 3
[5,2,1,6,3,7,4] => [2,1,2,2] => 1011010 => 4
[5,2,1,6,4,3,7] => [2,1,2,2] => 1011010 => 4
[5,2,1,6,4,7,3] => [2,1,2,2] => 1011010 => 4
[5,2,1,6,7,3,4] => [2,1,4] => 1011000 => 3
[5,2,1,6,7,4,3] => [2,1,3,1] => 1011001 => 4
[5,2,1,7,3,4,6] => [2,1,4] => 1011000 => 3
[5,2,1,7,3,6,4] => [2,1,3,1] => 1011001 => 4
[5,2,1,7,4,3,6] => [2,1,2,2] => 1011010 => 4
[5,2,1,7,4,6,3] => [2,1,3,1] => 1011001 => 4
[5,2,1,7,6,3,4] => [2,1,1,3] => 1011100 => 4
[5,2,1,7,6,4,3] => [2,1,1,2,1] => 1011101 => 5
[5,2,3,1,4,6,7] => [3,4] => 1001000 => 2
[5,2,3,1,4,7,6] => [3,2,2] => 1001010 => 3
[5,2,3,1,6,4,7] => [3,1,3] => 1001100 => 3
[5,2,3,1,6,7,4] => [3,1,3] => 1001100 => 3
[5,2,3,1,7,4,6] => [3,1,3] => 1001100 => 3
[5,2,3,1,7,6,4] => [3,1,2,1] => 1001101 => 4
[5,2,3,4,1,6,7] => [4,3] => 1000100 => 2
[5,2,3,4,1,7,6] => [4,1,2] => 1000110 => 3
[5,2,3,4,6,1,7] => [4,3] => 1000100 => 2
[5,2,3,4,6,7,1] => [4,3] => 1000100 => 2
[5,2,3,4,7,1,6] => [4,3] => 1000100 => 2
[5,2,3,4,7,6,1] => [4,2,1] => 1000101 => 3
[5,2,3,6,1,4,7] => [3,4] => 1001000 => 2
[5,2,3,6,1,7,4] => [3,2,2] => 1001010 => 3
[5,2,3,6,4,1,7] => [3,2,2] => 1001010 => 3
[5,2,3,6,4,7,1] => [3,2,2] => 1001010 => 3
[5,2,3,6,7,1,4] => [3,4] => 1001000 => 2
[5,2,3,6,7,4,1] => [3,3,1] => 1001001 => 3
[5,2,3,7,1,4,6] => [3,4] => 1001000 => 2
[5,2,3,7,1,6,4] => [3,3,1] => 1001001 => 3
[5,2,3,7,4,1,6] => [3,2,2] => 1001010 => 3
[5,2,3,7,4,6,1] => [3,3,1] => 1001001 => 3
[5,2,3,7,6,1,4] => [3,1,3] => 1001100 => 3
[5,2,3,7,6,4,1] => [3,1,2,1] => 1001101 => 4
[5,2,4,1,3,6,7] => [2,5] => 1010000 => 2
[5,2,4,1,3,7,6] => [2,3,2] => 1010010 => 3
[5,2,4,1,6,3,7] => [2,2,3] => 1010100 => 3
[5,2,4,1,6,7,3] => [2,2,3] => 1010100 => 3
[5,2,4,1,7,3,6] => [2,2,3] => 1010100 => 3
[5,2,4,1,7,6,3] => [2,2,2,1] => 1010101 => 4
[5,2,4,3,1,6,7] => [2,2,3] => 1010100 => 3
[5,2,4,3,1,7,6] => [2,2,1,2] => 1010110 => 4
[5,2,4,3,6,1,7] => [2,2,3] => 1010100 => 3
[5,2,4,3,6,7,1] => [2,2,3] => 1010100 => 3
[5,2,4,3,7,1,6] => [2,2,3] => 1010100 => 3
[5,2,4,3,7,6,1] => [2,2,2,1] => 1010101 => 4
[5,2,4,6,1,3,7] => [2,5] => 1010000 => 2
[5,2,4,6,1,7,3] => [2,3,2] => 1010010 => 3
[5,2,4,6,3,1,7] => [2,3,2] => 1010010 => 3
[5,2,4,6,3,7,1] => [2,3,2] => 1010010 => 3
[5,2,4,6,7,1,3] => [2,5] => 1010000 => 2
[5,2,4,6,7,3,1] => [2,4,1] => 1010001 => 3
[5,2,4,7,1,3,6] => [2,5] => 1010000 => 2
[5,2,4,7,1,6,3] => [2,4,1] => 1010001 => 3
[5,2,4,7,3,1,6] => [2,3,2] => 1010010 => 3
[5,2,4,7,3,6,1] => [2,4,1] => 1010001 => 3
[5,2,4,7,6,1,3] => [2,2,3] => 1010100 => 3
[5,2,4,7,6,3,1] => [2,2,2,1] => 1010101 => 4
[5,2,6,1,3,4,7] => [2,5] => 1010000 => 2
[5,2,6,1,3,7,4] => [2,3,2] => 1010010 => 3
[5,2,6,1,4,3,7] => [2,3,2] => 1010010 => 3
[5,2,6,1,4,7,3] => [2,3,2] => 1010010 => 3
[5,2,6,1,7,3,4] => [2,2,3] => 1010100 => 3
[5,2,6,1,7,4,3] => [2,2,2,1] => 1010101 => 4
[5,2,6,3,1,4,7] => [2,2,3] => 1010100 => 3
[5,2,6,3,1,7,4] => [2,2,1,2] => 1010110 => 4
[5,2,6,3,4,1,7] => [2,3,2] => 1010010 => 3
[5,2,6,3,4,7,1] => [2,3,2] => 1010010 => 3
[5,2,6,3,7,1,4] => [2,2,3] => 1010100 => 3
[5,2,6,3,7,4,1] => [2,2,2,1] => 1010101 => 4
[5,2,6,4,1,3,7] => [2,2,3] => 1010100 => 3
[5,2,6,4,1,7,3] => [2,2,1,2] => 1010110 => 4
[5,2,6,4,3,1,7] => [2,2,1,2] => 1010110 => 4
[5,2,6,4,3,7,1] => [2,2,1,2] => 1010110 => 4
[5,2,6,4,7,1,3] => [2,2,3] => 1010100 => 3
[5,2,6,4,7,3,1] => [2,2,2,1] => 1010101 => 4
[5,2,6,7,1,3,4] => [2,5] => 1010000 => 2
[5,2,6,7,1,4,3] => [2,4,1] => 1010001 => 3
[5,2,6,7,3,1,4] => [2,3,2] => 1010010 => 3
[5,2,6,7,3,4,1] => [2,4,1] => 1010001 => 3
[5,2,6,7,4,1,3] => [2,3,2] => 1010010 => 3
[5,2,6,7,4,3,1] => [2,3,1,1] => 1010011 => 4
[5,2,7,1,3,4,6] => [2,5] => 1010000 => 2
[5,2,7,1,3,6,4] => [2,4,1] => 1010001 => 3
[5,2,7,1,4,3,6] => [2,3,2] => 1010010 => 3
[5,2,7,1,4,6,3] => [2,4,1] => 1010001 => 3
[5,2,7,1,6,3,4] => [2,2,3] => 1010100 => 3
[5,2,7,1,6,4,3] => [2,2,2,1] => 1010101 => 4
[5,2,7,3,1,4,6] => [2,2,3] => 1010100 => 3
[5,2,7,3,1,6,4] => [2,2,2,1] => 1010101 => 4
[5,2,7,3,4,1,6] => [2,3,2] => 1010010 => 3
[5,2,7,3,4,6,1] => [2,4,1] => 1010001 => 3
[5,2,7,3,6,1,4] => [2,2,3] => 1010100 => 3
[5,2,7,3,6,4,1] => [2,2,2,1] => 1010101 => 4
[5,2,7,4,1,3,6] => [2,2,3] => 1010100 => 3
[5,2,7,4,1,6,3] => [2,2,2,1] => 1010101 => 4
[5,2,7,4,3,1,6] => [2,2,1,2] => 1010110 => 4
[5,2,7,4,3,6,1] => [2,2,2,1] => 1010101 => 4
[5,2,7,4,6,1,3] => [2,2,3] => 1010100 => 3
[5,2,7,4,6,3,1] => [2,2,2,1] => 1010101 => 4
[5,2,7,6,1,3,4] => [2,1,4] => 1011000 => 3
[5,2,7,6,1,4,3] => [2,1,3,1] => 1011001 => 4
[5,2,7,6,3,1,4] => [2,1,2,2] => 1011010 => 4
[5,2,7,6,3,4,1] => [2,1,3,1] => 1011001 => 4
[5,2,7,6,4,1,3] => [2,1,2,2] => 1011010 => 4
[5,2,7,6,4,3,1] => [2,1,2,1,1] => 1011011 => 5
[5,3,1,2,4,6,7] => [1,6] => 1100000 => 2
[5,3,1,2,4,7,6] => [1,4,2] => 1100010 => 3
[5,3,1,2,6,4,7] => [1,3,3] => 1100100 => 3
[5,3,1,2,6,7,4] => [1,3,3] => 1100100 => 3
[5,3,1,2,7,4,6] => [1,3,3] => 1100100 => 3
[5,3,1,2,7,6,4] => [1,3,2,1] => 1100101 => 4
[5,3,1,4,2,6,7] => [1,3,3] => 1100100 => 3
[5,3,1,4,2,7,6] => [1,3,1,2] => 1100110 => 4
[5,3,1,4,6,2,7] => [1,3,3] => 1100100 => 3
[5,3,1,4,6,7,2] => [1,3,3] => 1100100 => 3
[5,3,1,4,7,2,6] => [1,3,3] => 1100100 => 3
[5,3,1,4,7,6,2] => [1,3,2,1] => 1100101 => 4
[5,3,1,6,2,4,7] => [1,2,4] => 1101000 => 3
[5,3,1,6,2,7,4] => [1,2,2,2] => 1101010 => 4
[5,3,1,6,4,2,7] => [1,2,2,2] => 1101010 => 4
[5,3,1,6,4,7,2] => [1,2,2,2] => 1101010 => 4
[5,3,1,6,7,2,4] => [1,2,4] => 1101000 => 3
[5,3,1,6,7,4,2] => [1,2,3,1] => 1101001 => 4
[5,3,1,7,2,4,6] => [1,2,4] => 1101000 => 3
[5,3,1,7,2,6,4] => [1,2,3,1] => 1101001 => 4
[5,3,1,7,4,2,6] => [1,2,2,2] => 1101010 => 4
[5,3,1,7,4,6,2] => [1,2,3,1] => 1101001 => 4
[5,3,1,7,6,2,4] => [1,2,1,3] => 1101100 => 4
[5,3,1,7,6,4,2] => [1,2,1,2,1] => 1101101 => 5
[5,3,2,1,4,6,7] => [1,2,4] => 1101000 => 3
[5,3,2,1,4,7,6] => [1,2,2,2] => 1101010 => 4
[5,3,2,1,6,4,7] => [1,2,1,3] => 1101100 => 4
[5,3,2,1,6,7,4] => [1,2,1,3] => 1101100 => 4
[5,3,2,1,7,4,6] => [1,2,1,3] => 1101100 => 4
[5,3,2,1,7,6,4] => [1,2,1,2,1] => 1101101 => 5
[5,3,2,4,1,6,7] => [1,3,3] => 1100100 => 3
[5,3,2,4,1,7,6] => [1,3,1,2] => 1100110 => 4
[5,3,2,4,6,1,7] => [1,3,3] => 1100100 => 3
[5,3,2,4,6,7,1] => [1,3,3] => 1100100 => 3
[5,3,2,4,7,1,6] => [1,3,3] => 1100100 => 3
[5,3,2,4,7,6,1] => [1,3,2,1] => 1100101 => 4
[5,3,2,6,1,4,7] => [1,2,4] => 1101000 => 3
[5,3,2,6,1,7,4] => [1,2,2,2] => 1101010 => 4
[5,3,2,6,4,1,7] => [1,2,2,2] => 1101010 => 4
[5,3,2,6,4,7,1] => [1,2,2,2] => 1101010 => 4
[5,3,2,6,7,1,4] => [1,2,4] => 1101000 => 3
[5,3,2,6,7,4,1] => [1,2,3,1] => 1101001 => 4
[5,3,2,7,1,4,6] => [1,2,4] => 1101000 => 3
[5,3,2,7,1,6,4] => [1,2,3,1] => 1101001 => 4
[5,3,2,7,4,1,6] => [1,2,2,2] => 1101010 => 4
[5,3,2,7,4,6,1] => [1,2,3,1] => 1101001 => 4
[5,3,2,7,6,1,4] => [1,2,1,3] => 1101100 => 4
[5,3,2,7,6,4,1] => [1,2,1,2,1] => 1101101 => 5
[5,3,4,1,2,6,7] => [1,6] => 1100000 => 2
[5,3,4,1,2,7,6] => [1,4,2] => 1100010 => 3
[5,3,4,1,6,2,7] => [1,3,3] => 1100100 => 3
[5,3,4,1,6,7,2] => [1,3,3] => 1100100 => 3
[5,3,4,1,7,2,6] => [1,3,3] => 1100100 => 3
[5,3,4,1,7,6,2] => [1,3,2,1] => 1100101 => 4
[5,3,4,2,1,6,7] => [1,3,3] => 1100100 => 3
[5,3,4,2,1,7,6] => [1,3,1,2] => 1100110 => 4
[5,3,4,2,6,1,7] => [1,3,3] => 1100100 => 3
[5,3,4,2,6,7,1] => [1,3,3] => 1100100 => 3
[5,3,4,2,7,1,6] => [1,3,3] => 1100100 => 3
[5,3,4,2,7,6,1] => [1,3,2,1] => 1100101 => 4
[5,3,4,6,1,2,7] => [1,6] => 1100000 => 2
[5,3,4,6,1,7,2] => [1,4,2] => 1100010 => 3
[5,3,4,6,2,1,7] => [1,4,2] => 1100010 => 3
[5,3,4,6,2,7,1] => [1,4,2] => 1100010 => 3
[5,3,4,6,7,1,2] => [1,6] => 1100000 => 2
[5,3,4,6,7,2,1] => [1,5,1] => 1100001 => 3
[5,3,4,7,1,2,6] => [1,6] => 1100000 => 2
[5,3,4,7,1,6,2] => [1,5,1] => 1100001 => 3
[5,3,4,7,2,1,6] => [1,4,2] => 1100010 => 3
[5,3,4,7,2,6,1] => [1,5,1] => 1100001 => 3
[5,3,4,7,6,1,2] => [1,3,3] => 1100100 => 3
[5,3,4,7,6,2,1] => [1,3,2,1] => 1100101 => 4
[5,3,6,1,2,4,7] => [1,6] => 1100000 => 2
[5,3,6,1,2,7,4] => [1,4,2] => 1100010 => 3
[5,3,6,1,4,2,7] => [1,4,2] => 1100010 => 3
[5,3,6,1,4,7,2] => [1,4,2] => 1100010 => 3
[5,3,6,1,7,2,4] => [1,3,3] => 1100100 => 3
[5,3,6,1,7,4,2] => [1,3,2,1] => 1100101 => 4
[5,3,6,2,1,4,7] => [1,3,3] => 1100100 => 3
[5,3,6,2,1,7,4] => [1,3,1,2] => 1100110 => 4
[5,3,6,2,4,1,7] => [1,4,2] => 1100010 => 3
[5,3,6,2,4,7,1] => [1,4,2] => 1100010 => 3
[5,3,6,2,7,1,4] => [1,3,3] => 1100100 => 3
[5,3,6,2,7,4,1] => [1,3,2,1] => 1100101 => 4
[5,3,6,4,1,2,7] => [1,3,3] => 1100100 => 3
[5,3,6,4,1,7,2] => [1,3,1,2] => 1100110 => 4
[5,3,6,4,2,1,7] => [1,3,1,2] => 1100110 => 4
[5,3,6,4,2,7,1] => [1,3,1,2] => 1100110 => 4
[5,3,6,4,7,1,2] => [1,3,3] => 1100100 => 3
[5,3,6,4,7,2,1] => [1,3,2,1] => 1100101 => 4
[5,3,6,7,1,2,4] => [1,6] => 1100000 => 2
[5,3,6,7,1,4,2] => [1,5,1] => 1100001 => 3
[5,3,6,7,2,1,4] => [1,4,2] => 1100010 => 3
[5,3,6,7,2,4,1] => [1,5,1] => 1100001 => 3
[5,3,6,7,4,1,2] => [1,4,2] => 1100010 => 3
[5,3,6,7,4,2,1] => [1,4,1,1] => 1100011 => 4
[5,3,7,1,2,4,6] => [1,6] => 1100000 => 2
[5,3,7,1,2,6,4] => [1,5,1] => 1100001 => 3
[5,3,7,1,4,2,6] => [1,4,2] => 1100010 => 3
[5,3,7,1,4,6,2] => [1,5,1] => 1100001 => 3
[5,3,7,1,6,2,4] => [1,3,3] => 1100100 => 3
[5,3,7,1,6,4,2] => [1,3,2,1] => 1100101 => 4
[5,3,7,2,1,4,6] => [1,3,3] => 1100100 => 3
[5,3,7,2,1,6,4] => [1,3,2,1] => 1100101 => 4
[5,3,7,2,4,1,6] => [1,4,2] => 1100010 => 3
[5,3,7,2,4,6,1] => [1,5,1] => 1100001 => 3
[5,3,7,2,6,1,4] => [1,3,3] => 1100100 => 3
[5,3,7,2,6,4,1] => [1,3,2,1] => 1100101 => 4
[5,3,7,4,1,2,6] => [1,3,3] => 1100100 => 3
[5,3,7,4,1,6,2] => [1,3,2,1] => 1100101 => 4
[5,3,7,4,2,1,6] => [1,3,1,2] => 1100110 => 4
[5,3,7,4,2,6,1] => [1,3,2,1] => 1100101 => 4
[5,3,7,4,6,1,2] => [1,3,3] => 1100100 => 3
[5,3,7,4,6,2,1] => [1,3,2,1] => 1100101 => 4
[5,3,7,6,1,2,4] => [1,2,4] => 1101000 => 3
[5,3,7,6,1,4,2] => [1,2,3,1] => 1101001 => 4
[5,3,7,6,2,1,4] => [1,2,2,2] => 1101010 => 4
[5,3,7,6,2,4,1] => [1,2,3,1] => 1101001 => 4
[5,3,7,6,4,1,2] => [1,2,2,2] => 1101010 => 4
[5,3,7,6,4,2,1] => [1,2,2,1,1] => 1101011 => 5
[5,4,1,2,3,6,7] => [1,6] => 1100000 => 2
[5,4,1,2,3,7,6] => [1,4,2] => 1100010 => 3
[5,4,1,2,6,3,7] => [1,3,3] => 1100100 => 3
[5,4,1,2,6,7,3] => [1,3,3] => 1100100 => 3
[5,4,1,2,7,3,6] => [1,3,3] => 1100100 => 3
[5,4,1,2,7,6,3] => [1,3,2,1] => 1100101 => 4
[5,4,1,3,2,6,7] => [1,3,3] => 1100100 => 3
[5,4,1,3,2,7,6] => [1,3,1,2] => 1100110 => 4
[5,4,1,3,6,2,7] => [1,3,3] => 1100100 => 3
[5,4,1,3,6,7,2] => [1,3,3] => 1100100 => 3
[5,4,1,3,7,2,6] => [1,3,3] => 1100100 => 3
[5,4,1,3,7,6,2] => [1,3,2,1] => 1100101 => 4
[5,4,1,6,2,3,7] => [1,2,4] => 1101000 => 3
[5,4,1,6,2,7,3] => [1,2,2,2] => 1101010 => 4
[5,4,1,6,3,2,7] => [1,2,2,2] => 1101010 => 4
[5,4,1,6,3,7,2] => [1,2,2,2] => 1101010 => 4
[5,4,1,6,7,2,3] => [1,2,4] => 1101000 => 3
[5,4,1,6,7,3,2] => [1,2,3,1] => 1101001 => 4
[5,4,1,7,2,3,6] => [1,2,4] => 1101000 => 3
[5,4,1,7,2,6,3] => [1,2,3,1] => 1101001 => 4
[5,4,1,7,3,2,6] => [1,2,2,2] => 1101010 => 4
[5,4,1,7,3,6,2] => [1,2,3,1] => 1101001 => 4
[5,4,1,7,6,2,3] => [1,2,1,3] => 1101100 => 4
[5,4,1,7,6,3,2] => [1,2,1,2,1] => 1101101 => 5
[5,4,2,1,3,6,7] => [1,2,4] => 1101000 => 3
[5,4,2,1,3,7,6] => [1,2,2,2] => 1101010 => 4
[5,4,2,1,6,3,7] => [1,2,1,3] => 1101100 => 4
[5,4,2,1,6,7,3] => [1,2,1,3] => 1101100 => 4
[5,4,2,1,7,3,6] => [1,2,1,3] => 1101100 => 4
[5,4,2,1,7,6,3] => [1,2,1,2,1] => 1101101 => 5
[5,4,2,3,1,6,7] => [1,3,3] => 1100100 => 3
[5,4,2,3,1,7,6] => [1,3,1,2] => 1100110 => 4
[5,4,2,3,6,1,7] => [1,3,3] => 1100100 => 3
[5,4,2,3,6,7,1] => [1,3,3] => 1100100 => 3
[5,4,2,3,7,1,6] => [1,3,3] => 1100100 => 3
[5,4,2,3,7,6,1] => [1,3,2,1] => 1100101 => 4
[5,4,2,6,1,3,7] => [1,2,4] => 1101000 => 3
[5,4,2,6,1,7,3] => [1,2,2,2] => 1101010 => 4
[5,4,2,6,3,1,7] => [1,2,2,2] => 1101010 => 4
[5,4,2,6,3,7,1] => [1,2,2,2] => 1101010 => 4
[5,4,2,6,7,1,3] => [1,2,4] => 1101000 => 3
[5,4,2,6,7,3,1] => [1,2,3,1] => 1101001 => 4
[5,4,2,7,1,3,6] => [1,2,4] => 1101000 => 3
[5,4,2,7,1,6,3] => [1,2,3,1] => 1101001 => 4
[5,4,2,7,3,1,6] => [1,2,2,2] => 1101010 => 4
[5,4,2,7,3,6,1] => [1,2,3,1] => 1101001 => 4
[5,4,2,7,6,1,3] => [1,2,1,3] => 1101100 => 4
[5,4,2,7,6,3,1] => [1,2,1,2,1] => 1101101 => 5
[5,4,3,1,2,6,7] => [1,2,4] => 1101000 => 3
[5,4,3,1,2,7,6] => [1,2,2,2] => 1101010 => 4
[5,4,3,1,6,2,7] => [1,2,1,3] => 1101100 => 4
[5,4,3,1,6,7,2] => [1,2,1,3] => 1101100 => 4
[5,4,3,1,7,2,6] => [1,2,1,3] => 1101100 => 4
[5,4,3,1,7,6,2] => [1,2,1,2,1] => 1101101 => 5
[5,4,3,2,1,6,7] => [1,2,1,3] => 1101100 => 4
[5,4,3,2,1,7,6] => [1,2,1,1,2] => 1101110 => 5
[5,4,3,2,6,1,7] => [1,2,1,3] => 1101100 => 4
[5,4,3,2,6,7,1] => [1,2,1,3] => 1101100 => 4
[5,4,3,2,7,1,6] => [1,2,1,3] => 1101100 => 4
[5,4,3,2,7,6,1] => [1,2,1,2,1] => 1101101 => 5
[5,4,3,6,1,2,7] => [1,2,4] => 1101000 => 3
[5,4,3,6,1,7,2] => [1,2,2,2] => 1101010 => 4
[5,4,3,6,2,1,7] => [1,2,2,2] => 1101010 => 4
[5,4,3,6,2,7,1] => [1,2,2,2] => 1101010 => 4
[5,4,3,6,7,1,2] => [1,2,4] => 1101000 => 3
[5,4,3,6,7,2,1] => [1,2,3,1] => 1101001 => 4
[5,4,3,7,1,2,6] => [1,2,4] => 1101000 => 3
[5,4,3,7,1,6,2] => [1,2,3,1] => 1101001 => 4
[5,4,3,7,2,1,6] => [1,2,2,2] => 1101010 => 4
[5,4,3,7,2,6,1] => [1,2,3,1] => 1101001 => 4
[5,4,3,7,6,1,2] => [1,2,1,3] => 1101100 => 4
[5,4,3,7,6,2,1] => [1,2,1,2,1] => 1101101 => 5
[5,4,6,1,2,3,7] => [1,6] => 1100000 => 2
[5,4,6,1,2,7,3] => [1,4,2] => 1100010 => 3
[5,4,6,1,3,2,7] => [1,4,2] => 1100010 => 3
[5,4,6,1,3,7,2] => [1,4,2] => 1100010 => 3
[5,4,6,1,7,2,3] => [1,3,3] => 1100100 => 3
[5,4,6,1,7,3,2] => [1,3,2,1] => 1100101 => 4
[5,4,6,2,1,3,7] => [1,3,3] => 1100100 => 3
[5,4,6,2,1,7,3] => [1,3,1,2] => 1100110 => 4
[5,4,6,2,3,1,7] => [1,4,2] => 1100010 => 3
[5,4,6,2,3,7,1] => [1,4,2] => 1100010 => 3
[5,4,6,2,7,1,3] => [1,3,3] => 1100100 => 3
[5,4,6,2,7,3,1] => [1,3,2,1] => 1100101 => 4
[5,4,6,3,1,2,7] => [1,3,3] => 1100100 => 3
[5,4,6,3,1,7,2] => [1,3,1,2] => 1100110 => 4
[5,4,6,3,2,1,7] => [1,3,1,2] => 1100110 => 4
[5,4,6,3,2,7,1] => [1,3,1,2] => 1100110 => 4
[5,4,6,3,7,1,2] => [1,3,3] => 1100100 => 3
[5,4,6,3,7,2,1] => [1,3,2,1] => 1100101 => 4
[5,4,6,7,1,2,3] => [1,6] => 1100000 => 2
[5,4,6,7,1,3,2] => [1,5,1] => 1100001 => 3
[5,4,6,7,2,1,3] => [1,4,2] => 1100010 => 3
[5,4,6,7,2,3,1] => [1,5,1] => 1100001 => 3
[5,4,6,7,3,1,2] => [1,4,2] => 1100010 => 3
[5,4,6,7,3,2,1] => [1,4,1,1] => 1100011 => 4
[5,4,7,1,2,3,6] => [1,6] => 1100000 => 2
[5,4,7,1,2,6,3] => [1,5,1] => 1100001 => 3
[5,4,7,1,3,2,6] => [1,4,2] => 1100010 => 3
[5,4,7,1,3,6,2] => [1,5,1] => 1100001 => 3
[5,4,7,1,6,2,3] => [1,3,3] => 1100100 => 3
[5,4,7,1,6,3,2] => [1,3,2,1] => 1100101 => 4
[5,4,7,2,1,3,6] => [1,3,3] => 1100100 => 3
[5,4,7,2,1,6,3] => [1,3,2,1] => 1100101 => 4
[5,4,7,2,3,1,6] => [1,4,2] => 1100010 => 3
[5,4,7,2,3,6,1] => [1,5,1] => 1100001 => 3
[5,4,7,2,6,1,3] => [1,3,3] => 1100100 => 3
[5,4,7,2,6,3,1] => [1,3,2,1] => 1100101 => 4
[5,4,7,3,1,2,6] => [1,3,3] => 1100100 => 3
[5,4,7,3,1,6,2] => [1,3,2,1] => 1100101 => 4
[5,4,7,3,2,1,6] => [1,3,1,2] => 1100110 => 4
[5,4,7,3,2,6,1] => [1,3,2,1] => 1100101 => 4
[5,4,7,3,6,1,2] => [1,3,3] => 1100100 => 3
[5,4,7,3,6,2,1] => [1,3,2,1] => 1100101 => 4
[5,4,7,6,1,2,3] => [1,2,4] => 1101000 => 3
[5,4,7,6,1,3,2] => [1,2,3,1] => 1101001 => 4
[5,4,7,6,2,1,3] => [1,2,2,2] => 1101010 => 4
[5,4,7,6,2,3,1] => [1,2,3,1] => 1101001 => 4
[5,4,7,6,3,1,2] => [1,2,2,2] => 1101010 => 4
[5,4,7,6,3,2,1] => [1,2,2,1,1] => 1101011 => 5
[5,6,1,2,3,4,7] => [7] => 1000000 => 1
[5,6,1,2,3,7,4] => [5,2] => 1000010 => 2
[5,6,1,2,4,3,7] => [5,2] => 1000010 => 2
[5,6,1,2,4,7,3] => [5,2] => 1000010 => 2
[5,6,1,2,7,3,4] => [4,3] => 1000100 => 2
[5,6,1,2,7,4,3] => [4,2,1] => 1000101 => 3
[5,6,1,3,2,4,7] => [4,3] => 1000100 => 2
[5,6,1,3,2,7,4] => [4,1,2] => 1000110 => 3
[5,6,1,3,4,2,7] => [5,2] => 1000010 => 2
[5,6,1,3,4,7,2] => [5,2] => 1000010 => 2
[5,6,1,3,7,2,4] => [4,3] => 1000100 => 2
[5,6,1,3,7,4,2] => [4,2,1] => 1000101 => 3
[5,6,1,4,2,3,7] => [4,3] => 1000100 => 2
[5,6,1,4,2,7,3] => [4,1,2] => 1000110 => 3
[5,6,1,4,3,2,7] => [4,1,2] => 1000110 => 3
[5,6,1,4,3,7,2] => [4,1,2] => 1000110 => 3
[5,6,1,4,7,2,3] => [4,3] => 1000100 => 2
[5,6,1,4,7,3,2] => [4,2,1] => 1000101 => 3
[5,6,1,7,2,3,4] => [3,4] => 1001000 => 2
[5,6,1,7,2,4,3] => [3,3,1] => 1001001 => 3
[5,6,1,7,3,2,4] => [3,2,2] => 1001010 => 3
[5,6,1,7,3,4,2] => [3,3,1] => 1001001 => 3
[5,6,1,7,4,2,3] => [3,2,2] => 1001010 => 3
[5,6,1,7,4,3,2] => [3,2,1,1] => 1001011 => 4
[5,6,2,1,3,4,7] => [3,4] => 1001000 => 2
[5,6,2,1,3,7,4] => [3,2,2] => 1001010 => 3
[5,6,2,1,4,3,7] => [3,2,2] => 1001010 => 3
[5,6,2,1,4,7,3] => [3,2,2] => 1001010 => 3
[5,6,2,1,7,3,4] => [3,1,3] => 1001100 => 3
[5,6,2,1,7,4,3] => [3,1,2,1] => 1001101 => 4
[5,6,2,3,1,4,7] => [4,3] => 1000100 => 2
[5,6,2,3,1,7,4] => [4,1,2] => 1000110 => 3
[5,6,2,3,4,1,7] => [5,2] => 1000010 => 2
[5,6,2,3,4,7,1] => [5,2] => 1000010 => 2
[5,6,2,3,7,1,4] => [4,3] => 1000100 => 2
[5,6,2,3,7,4,1] => [4,2,1] => 1000101 => 3
[5,6,2,4,1,3,7] => [4,3] => 1000100 => 2
[5,6,2,4,1,7,3] => [4,1,2] => 1000110 => 3
[5,6,2,4,3,1,7] => [4,1,2] => 1000110 => 3
[5,6,2,4,3,7,1] => [4,1,2] => 1000110 => 3
[5,6,2,4,7,1,3] => [4,3] => 1000100 => 2
[5,6,2,4,7,3,1] => [4,2,1] => 1000101 => 3
[5,6,2,7,1,3,4] => [3,4] => 1001000 => 2
[5,6,2,7,1,4,3] => [3,3,1] => 1001001 => 3
[5,6,2,7,3,1,4] => [3,2,2] => 1001010 => 3
[5,6,2,7,3,4,1] => [3,3,1] => 1001001 => 3
[5,6,2,7,4,1,3] => [3,2,2] => 1001010 => 3
[5,6,2,7,4,3,1] => [3,2,1,1] => 1001011 => 4
[5,6,3,1,2,4,7] => [3,4] => 1001000 => 2
[5,6,3,1,2,7,4] => [3,2,2] => 1001010 => 3
[5,6,3,1,4,2,7] => [3,2,2] => 1001010 => 3
[5,6,3,1,4,7,2] => [3,2,2] => 1001010 => 3
[5,6,3,1,7,2,4] => [3,1,3] => 1001100 => 3
[5,6,3,1,7,4,2] => [3,1,2,1] => 1001101 => 4
[5,6,3,2,1,4,7] => [3,1,3] => 1001100 => 3
[5,6,3,2,1,7,4] => [3,1,1,2] => 1001110 => 4
[5,6,3,2,4,1,7] => [3,2,2] => 1001010 => 3
[5,6,3,2,4,7,1] => [3,2,2] => 1001010 => 3
[5,6,3,2,7,1,4] => [3,1,3] => 1001100 => 3
[5,6,3,2,7,4,1] => [3,1,2,1] => 1001101 => 4
[5,6,3,4,1,2,7] => [4,3] => 1000100 => 2
[5,6,3,4,1,7,2] => [4,1,2] => 1000110 => 3
[5,6,3,4,2,1,7] => [4,1,2] => 1000110 => 3
[5,6,3,4,2,7,1] => [4,1,2] => 1000110 => 3
[5,6,3,4,7,1,2] => [4,3] => 1000100 => 2
[5,6,3,4,7,2,1] => [4,2,1] => 1000101 => 3
[5,6,3,7,1,2,4] => [3,4] => 1001000 => 2
[5,6,3,7,1,4,2] => [3,3,1] => 1001001 => 3
[5,6,3,7,2,1,4] => [3,2,2] => 1001010 => 3
[5,6,3,7,2,4,1] => [3,3,1] => 1001001 => 3
[5,6,3,7,4,1,2] => [3,2,2] => 1001010 => 3
[5,6,3,7,4,2,1] => [3,2,1,1] => 1001011 => 4
[5,6,4,1,2,3,7] => [2,5] => 1010000 => 2
[5,6,4,1,2,7,3] => [2,3,2] => 1010010 => 3
[5,6,4,1,3,2,7] => [2,3,2] => 1010010 => 3
[5,6,4,1,3,7,2] => [2,3,2] => 1010010 => 3
[5,6,4,1,7,2,3] => [2,2,3] => 1010100 => 3
[5,6,4,1,7,3,2] => [2,2,2,1] => 1010101 => 4
[5,6,4,2,1,3,7] => [2,2,3] => 1010100 => 3
[5,6,4,2,1,7,3] => [2,2,1,2] => 1010110 => 4
[5,6,4,2,3,1,7] => [2,3,2] => 1010010 => 3
[5,6,4,2,3,7,1] => [2,3,2] => 1010010 => 3
[5,6,4,2,7,1,3] => [2,2,3] => 1010100 => 3
[5,6,4,2,7,3,1] => [2,2,2,1] => 1010101 => 4
[5,6,4,3,1,2,7] => [2,2,3] => 1010100 => 3
[5,6,4,3,1,7,2] => [2,2,1,2] => 1010110 => 4
[5,6,4,3,2,1,7] => [2,2,1,2] => 1010110 => 4
[5,6,4,3,2,7,1] => [2,2,1,2] => 1010110 => 4
[5,6,4,3,7,1,2] => [2,2,3] => 1010100 => 3
[5,6,4,3,7,2,1] => [2,2,2,1] => 1010101 => 4
[5,6,4,7,1,2,3] => [2,5] => 1010000 => 2
[5,6,4,7,1,3,2] => [2,4,1] => 1010001 => 3
[5,6,4,7,2,1,3] => [2,3,2] => 1010010 => 3
[5,6,4,7,2,3,1] => [2,4,1] => 1010001 => 3
[5,6,4,7,3,1,2] => [2,3,2] => 1010010 => 3
[5,6,4,7,3,2,1] => [2,3,1,1] => 1010011 => 4
[5,6,7,1,2,3,4] => [7] => 1000000 => 1
[5,6,7,1,2,4,3] => [6,1] => 1000001 => 2
[5,6,7,1,3,2,4] => [5,2] => 1000010 => 2
[5,6,7,1,3,4,2] => [6,1] => 1000001 => 2
[5,6,7,1,4,2,3] => [5,2] => 1000010 => 2
[5,6,7,1,4,3,2] => [5,1,1] => 1000011 => 3
[5,6,7,2,1,3,4] => [4,3] => 1000100 => 2
[5,6,7,2,1,4,3] => [4,2,1] => 1000101 => 3
[5,6,7,2,3,1,4] => [5,2] => 1000010 => 2
[5,6,7,2,3,4,1] => [6,1] => 1000001 => 2
[5,6,7,2,4,1,3] => [5,2] => 1000010 => 2
[5,6,7,2,4,3,1] => [5,1,1] => 1000011 => 3
[5,6,7,3,1,2,4] => [4,3] => 1000100 => 2
[5,6,7,3,1,4,2] => [4,2,1] => 1000101 => 3
[5,6,7,3,2,1,4] => [4,1,2] => 1000110 => 3
[5,6,7,3,2,4,1] => [4,2,1] => 1000101 => 3
[5,6,7,3,4,1,2] => [5,2] => 1000010 => 2
[5,6,7,3,4,2,1] => [5,1,1] => 1000011 => 3
[5,6,7,4,1,2,3] => [4,3] => 1000100 => 2
[5,6,7,4,1,3,2] => [4,2,1] => 1000101 => 3
[5,6,7,4,2,1,3] => [4,1,2] => 1000110 => 3
[5,6,7,4,2,3,1] => [4,2,1] => 1000101 => 3
[5,6,7,4,3,1,2] => [4,1,2] => 1000110 => 3
[5,6,7,4,3,2,1] => [4,1,1,1] => 1000111 => 4
[5,7,1,2,3,4,6] => [7] => 1000000 => 1
[5,7,1,2,3,6,4] => [6,1] => 1000001 => 2
[5,7,1,2,4,3,6] => [5,2] => 1000010 => 2
[5,7,1,2,4,6,3] => [6,1] => 1000001 => 2
[5,7,1,2,6,3,4] => [4,3] => 1000100 => 2
[5,7,1,2,6,4,3] => [4,2,1] => 1000101 => 3
[5,7,1,3,2,4,6] => [4,3] => 1000100 => 2
[5,7,1,3,2,6,4] => [4,2,1] => 1000101 => 3
[5,7,1,3,4,2,6] => [5,2] => 1000010 => 2
[5,7,1,3,4,6,2] => [6,1] => 1000001 => 2
[5,7,1,3,6,2,4] => [4,3] => 1000100 => 2
[5,7,1,3,6,4,2] => [4,2,1] => 1000101 => 3
[5,7,1,4,2,3,6] => [4,3] => 1000100 => 2
[5,7,1,4,2,6,3] => [4,2,1] => 1000101 => 3
[5,7,1,4,3,2,6] => [4,1,2] => 1000110 => 3
[5,7,1,4,3,6,2] => [4,2,1] => 1000101 => 3
[5,7,1,4,6,2,3] => [4,3] => 1000100 => 2
[5,7,1,4,6,3,2] => [4,2,1] => 1000101 => 3
[5,7,1,6,2,3,4] => [3,4] => 1001000 => 2
[5,7,1,6,2,4,3] => [3,3,1] => 1001001 => 3
[5,7,1,6,3,2,4] => [3,2,2] => 1001010 => 3
[5,7,1,6,3,4,2] => [3,3,1] => 1001001 => 3
[5,7,1,6,4,2,3] => [3,2,2] => 1001010 => 3
[5,7,1,6,4,3,2] => [3,2,1,1] => 1001011 => 4
[5,7,2,1,3,4,6] => [3,4] => 1001000 => 2
[5,7,2,1,3,6,4] => [3,3,1] => 1001001 => 3
[5,7,2,1,4,3,6] => [3,2,2] => 1001010 => 3
[5,7,2,1,4,6,3] => [3,3,1] => 1001001 => 3
[5,7,2,1,6,3,4] => [3,1,3] => 1001100 => 3
[5,7,2,1,6,4,3] => [3,1,2,1] => 1001101 => 4
[5,7,2,3,1,4,6] => [4,3] => 1000100 => 2
[5,7,2,3,1,6,4] => [4,2,1] => 1000101 => 3
[5,7,2,3,4,1,6] => [5,2] => 1000010 => 2
[5,7,2,3,4,6,1] => [6,1] => 1000001 => 2
[5,7,2,3,6,1,4] => [4,3] => 1000100 => 2
[5,7,2,3,6,4,1] => [4,2,1] => 1000101 => 3
[5,7,2,4,1,3,6] => [4,3] => 1000100 => 2
[5,7,2,4,1,6,3] => [4,2,1] => 1000101 => 3
[5,7,2,4,3,1,6] => [4,1,2] => 1000110 => 3
[5,7,2,4,3,6,1] => [4,2,1] => 1000101 => 3
[5,7,2,4,6,1,3] => [4,3] => 1000100 => 2
[5,7,2,4,6,3,1] => [4,2,1] => 1000101 => 3
[5,7,2,6,1,3,4] => [3,4] => 1001000 => 2
[5,7,2,6,1,4,3] => [3,3,1] => 1001001 => 3
[5,7,2,6,3,1,4] => [3,2,2] => 1001010 => 3
[5,7,2,6,3,4,1] => [3,3,1] => 1001001 => 3
[5,7,2,6,4,1,3] => [3,2,2] => 1001010 => 3
[5,7,2,6,4,3,1] => [3,2,1,1] => 1001011 => 4
[5,7,3,1,2,4,6] => [3,4] => 1001000 => 2
[5,7,3,1,2,6,4] => [3,3,1] => 1001001 => 3
[5,7,3,1,4,2,6] => [3,2,2] => 1001010 => 3
[5,7,3,1,4,6,2] => [3,3,1] => 1001001 => 3
[5,7,3,1,6,2,4] => [3,1,3] => 1001100 => 3
[5,7,3,1,6,4,2] => [3,1,2,1] => 1001101 => 4
[5,7,3,2,1,4,6] => [3,1,3] => 1001100 => 3
[5,7,3,2,1,6,4] => [3,1,2,1] => 1001101 => 4
[5,7,3,2,4,1,6] => [3,2,2] => 1001010 => 3
[5,7,3,2,4,6,1] => [3,3,1] => 1001001 => 3
[5,7,3,2,6,1,4] => [3,1,3] => 1001100 => 3
[5,7,3,2,6,4,1] => [3,1,2,1] => 1001101 => 4
[5,7,3,4,1,2,6] => [4,3] => 1000100 => 2
[5,7,3,4,1,6,2] => [4,2,1] => 1000101 => 3
[5,7,3,4,2,1,6] => [4,1,2] => 1000110 => 3
[5,7,3,4,2,6,1] => [4,2,1] => 1000101 => 3
[5,7,3,4,6,1,2] => [4,3] => 1000100 => 2
[5,7,3,4,6,2,1] => [4,2,1] => 1000101 => 3
[5,7,3,6,1,2,4] => [3,4] => 1001000 => 2
[5,7,3,6,1,4,2] => [3,3,1] => 1001001 => 3
[5,7,3,6,2,1,4] => [3,2,2] => 1001010 => 3
[5,7,3,6,2,4,1] => [3,3,1] => 1001001 => 3
[5,7,3,6,4,1,2] => [3,2,2] => 1001010 => 3
[5,7,3,6,4,2,1] => [3,2,1,1] => 1001011 => 4
[5,7,4,1,2,3,6] => [2,5] => 1010000 => 2
[5,7,4,1,2,6,3] => [2,4,1] => 1010001 => 3
[5,7,4,1,3,2,6] => [2,3,2] => 1010010 => 3
[5,7,4,1,3,6,2] => [2,4,1] => 1010001 => 3
[5,7,4,1,6,2,3] => [2,2,3] => 1010100 => 3
[5,7,4,1,6,3,2] => [2,2,2,1] => 1010101 => 4
[5,7,4,2,1,3,6] => [2,2,3] => 1010100 => 3
[5,7,4,2,1,6,3] => [2,2,2,1] => 1010101 => 4
[5,7,4,2,3,1,6] => [2,3,2] => 1010010 => 3
[5,7,4,2,3,6,1] => [2,4,1] => 1010001 => 3
[5,7,4,2,6,1,3] => [2,2,3] => 1010100 => 3
[5,7,4,2,6,3,1] => [2,2,2,1] => 1010101 => 4
[5,7,4,3,1,2,6] => [2,2,3] => 1010100 => 3
[5,7,4,3,1,6,2] => [2,2,2,1] => 1010101 => 4
[5,7,4,3,2,1,6] => [2,2,1,2] => 1010110 => 4
[5,7,4,3,2,6,1] => [2,2,2,1] => 1010101 => 4
[5,7,4,3,6,1,2] => [2,2,3] => 1010100 => 3
[5,7,4,3,6,2,1] => [2,2,2,1] => 1010101 => 4
[5,7,4,6,1,2,3] => [2,5] => 1010000 => 2
[5,7,4,6,1,3,2] => [2,4,1] => 1010001 => 3
[5,7,4,6,2,1,3] => [2,3,2] => 1010010 => 3
[5,7,4,6,2,3,1] => [2,4,1] => 1010001 => 3
[5,7,4,6,3,1,2] => [2,3,2] => 1010010 => 3
[5,7,4,6,3,2,1] => [2,3,1,1] => 1010011 => 4
[5,7,6,1,2,3,4] => [2,5] => 1010000 => 2
[5,7,6,1,2,4,3] => [2,4,1] => 1010001 => 3
[5,7,6,1,3,2,4] => [2,3,2] => 1010010 => 3
[5,7,6,1,3,4,2] => [2,4,1] => 1010001 => 3
[5,7,6,1,4,2,3] => [2,3,2] => 1010010 => 3
[5,7,6,1,4,3,2] => [2,3,1,1] => 1010011 => 4
[5,7,6,2,1,3,4] => [2,2,3] => 1010100 => 3
[5,7,6,2,1,4,3] => [2,2,2,1] => 1010101 => 4
[5,7,6,2,3,1,4] => [2,3,2] => 1010010 => 3
[5,7,6,2,3,4,1] => [2,4,1] => 1010001 => 3
[5,7,6,2,4,1,3] => [2,3,2] => 1010010 => 3
[5,7,6,2,4,3,1] => [2,3,1,1] => 1010011 => 4
[5,7,6,3,1,2,4] => [2,2,3] => 1010100 => 3
[5,7,6,3,1,4,2] => [2,2,2,1] => 1010101 => 4
[5,7,6,3,2,1,4] => [2,2,1,2] => 1010110 => 4
[5,7,6,3,2,4,1] => [2,2,2,1] => 1010101 => 4
[5,7,6,3,4,1,2] => [2,3,2] => 1010010 => 3
[5,7,6,3,4,2,1] => [2,3,1,1] => 1010011 => 4
[5,7,6,4,1,2,3] => [2,2,3] => 1010100 => 3
[5,7,6,4,1,3,2] => [2,2,2,1] => 1010101 => 4
[5,7,6,4,2,1,3] => [2,2,1,2] => 1010110 => 4
[5,7,6,4,2,3,1] => [2,2,2,1] => 1010101 => 4
[5,7,6,4,3,1,2] => [2,2,1,2] => 1010110 => 4
[5,7,6,4,3,2,1] => [2,2,1,1,1] => 1010111 => 5
[6,1,2,3,4,5,7] => [7] => 1000000 => 1
[6,1,2,3,4,7,5] => [5,2] => 1000010 => 2
[6,1,2,3,5,4,7] => [5,2] => 1000010 => 2
[6,1,2,3,5,7,4] => [5,2] => 1000010 => 2
[6,1,2,3,7,4,5] => [4,3] => 1000100 => 2
[6,1,2,3,7,5,4] => [4,2,1] => 1000101 => 3
[6,1,2,4,3,5,7] => [4,3] => 1000100 => 2
[6,1,2,4,3,7,5] => [4,1,2] => 1000110 => 3
[6,1,2,4,5,3,7] => [5,2] => 1000010 => 2
[6,1,2,4,5,7,3] => [5,2] => 1000010 => 2
[6,1,2,4,7,3,5] => [4,3] => 1000100 => 2
[6,1,2,4,7,5,3] => [4,2,1] => 1000101 => 3
[6,1,2,5,3,4,7] => [3,4] => 1001000 => 2
[6,1,2,5,3,7,4] => [3,2,2] => 1001010 => 3
[6,1,2,5,4,3,7] => [3,2,2] => 1001010 => 3
[6,1,2,5,4,7,3] => [3,2,2] => 1001010 => 3
[6,1,2,5,7,3,4] => [3,4] => 1001000 => 2
[6,1,2,5,7,4,3] => [3,3,1] => 1001001 => 3
[6,1,2,7,3,4,5] => [3,4] => 1001000 => 2
[6,1,2,7,3,5,4] => [3,3,1] => 1001001 => 3
[6,1,2,7,4,3,5] => [3,2,2] => 1001010 => 3
[6,1,2,7,4,5,3] => [3,3,1] => 1001001 => 3
[6,1,2,7,5,3,4] => [3,2,2] => 1001010 => 3
[6,1,2,7,5,4,3] => [3,2,1,1] => 1001011 => 4
[6,1,3,2,4,5,7] => [3,4] => 1001000 => 2
[6,1,3,2,4,7,5] => [3,2,2] => 1001010 => 3
[6,1,3,2,5,4,7] => [3,2,2] => 1001010 => 3
[6,1,3,2,5,7,4] => [3,2,2] => 1001010 => 3
[6,1,3,2,7,4,5] => [3,1,3] => 1001100 => 3
[6,1,3,2,7,5,4] => [3,1,2,1] => 1001101 => 4
[6,1,3,4,2,5,7] => [4,3] => 1000100 => 2
[6,1,3,4,2,7,5] => [4,1,2] => 1000110 => 3
[6,1,3,4,5,2,7] => [5,2] => 1000010 => 2
[6,1,3,4,5,7,2] => [5,2] => 1000010 => 2
[6,1,3,4,7,2,5] => [4,3] => 1000100 => 2
[6,1,3,4,7,5,2] => [4,2,1] => 1000101 => 3
[6,1,3,5,2,4,7] => [3,4] => 1001000 => 2
[6,1,3,5,2,7,4] => [3,2,2] => 1001010 => 3
[6,1,3,5,4,2,7] => [3,2,2] => 1001010 => 3
[6,1,3,5,4,7,2] => [3,2,2] => 1001010 => 3
[6,1,3,5,7,2,4] => [3,4] => 1001000 => 2
[6,1,3,5,7,4,2] => [3,3,1] => 1001001 => 3
[6,1,3,7,2,4,5] => [3,4] => 1001000 => 2
[6,1,3,7,2,5,4] => [3,3,1] => 1001001 => 3
[6,1,3,7,4,2,5] => [3,2,2] => 1001010 => 3
[6,1,3,7,4,5,2] => [3,3,1] => 1001001 => 3
[6,1,3,7,5,2,4] => [3,2,2] => 1001010 => 3
[6,1,3,7,5,4,2] => [3,2,1,1] => 1001011 => 4
[6,1,4,2,3,5,7] => [2,5] => 1010000 => 2
[6,1,4,2,3,7,5] => [2,3,2] => 1010010 => 3
[6,1,4,2,5,3,7] => [2,3,2] => 1010010 => 3
[6,1,4,2,5,7,3] => [2,3,2] => 1010010 => 3
[6,1,4,2,7,3,5] => [2,2,3] => 1010100 => 3
[6,1,4,2,7,5,3] => [2,2,2,1] => 1010101 => 4
[6,1,4,3,2,5,7] => [2,2,3] => 1010100 => 3
[6,1,4,3,2,7,5] => [2,2,1,2] => 1010110 => 4
[6,1,4,3,5,2,7] => [2,3,2] => 1010010 => 3
[6,1,4,3,5,7,2] => [2,3,2] => 1010010 => 3
[6,1,4,3,7,2,5] => [2,2,3] => 1010100 => 3
[6,1,4,3,7,5,2] => [2,2,2,1] => 1010101 => 4
[6,1,4,5,2,3,7] => [2,5] => 1010000 => 2
[6,1,4,5,2,7,3] => [2,3,2] => 1010010 => 3
[6,1,4,5,3,2,7] => [2,3,2] => 1010010 => 3
[6,1,4,5,3,7,2] => [2,3,2] => 1010010 => 3
[6,1,4,5,7,2,3] => [2,5] => 1010000 => 2
[6,1,4,5,7,3,2] => [2,4,1] => 1010001 => 3
[6,1,4,7,2,3,5] => [2,5] => 1010000 => 2
[6,1,4,7,2,5,3] => [2,4,1] => 1010001 => 3
[6,1,4,7,3,2,5] => [2,3,2] => 1010010 => 3
[6,1,4,7,3,5,2] => [2,4,1] => 1010001 => 3
[6,1,4,7,5,2,3] => [2,3,2] => 1010010 => 3
[6,1,4,7,5,3,2] => [2,3,1,1] => 1010011 => 4
[6,1,5,2,3,4,7] => [2,5] => 1010000 => 2
[6,1,5,2,3,7,4] => [2,3,2] => 1010010 => 3
[6,1,5,2,4,3,7] => [2,3,2] => 1010010 => 3
[6,1,5,2,4,7,3] => [2,3,2] => 1010010 => 3
[6,1,5,2,7,3,4] => [2,2,3] => 1010100 => 3
[6,1,5,2,7,4,3] => [2,2,2,1] => 1010101 => 4
[6,1,5,3,2,4,7] => [2,2,3] => 1010100 => 3
[6,1,5,3,2,7,4] => [2,2,1,2] => 1010110 => 4
[6,1,5,3,4,2,7] => [2,3,2] => 1010010 => 3
[6,1,5,3,4,7,2] => [2,3,2] => 1010010 => 3
[6,1,5,3,7,2,4] => [2,2,3] => 1010100 => 3
[6,1,5,3,7,4,2] => [2,2,2,1] => 1010101 => 4
[6,1,5,4,2,3,7] => [2,2,3] => 1010100 => 3
[6,1,5,4,2,7,3] => [2,2,1,2] => 1010110 => 4
[6,1,5,4,3,2,7] => [2,2,1,2] => 1010110 => 4
[6,1,5,4,3,7,2] => [2,2,1,2] => 1010110 => 4
[6,1,5,4,7,2,3] => [2,2,3] => 1010100 => 3
[6,1,5,4,7,3,2] => [2,2,2,1] => 1010101 => 4
[6,1,5,7,2,3,4] => [2,5] => 1010000 => 2
[6,1,5,7,2,4,3] => [2,4,1] => 1010001 => 3
[6,1,5,7,3,2,4] => [2,3,2] => 1010010 => 3
[6,1,5,7,3,4,2] => [2,4,1] => 1010001 => 3
[6,1,5,7,4,2,3] => [2,3,2] => 1010010 => 3
[6,1,5,7,4,3,2] => [2,3,1,1] => 1010011 => 4
[6,1,7,2,3,4,5] => [2,5] => 1010000 => 2
[6,1,7,2,3,5,4] => [2,4,1] => 1010001 => 3
[6,1,7,2,4,3,5] => [2,3,2] => 1010010 => 3
[6,1,7,2,4,5,3] => [2,4,1] => 1010001 => 3
[6,1,7,2,5,3,4] => [2,3,2] => 1010010 => 3
[6,1,7,2,5,4,3] => [2,3,1,1] => 1010011 => 4
[6,1,7,3,2,4,5] => [2,2,3] => 1010100 => 3
[6,1,7,3,2,5,4] => [2,2,2,1] => 1010101 => 4
[6,1,7,3,4,2,5] => [2,3,2] => 1010010 => 3
[6,1,7,3,4,5,2] => [2,4,1] => 1010001 => 3
[6,1,7,3,5,2,4] => [2,3,2] => 1010010 => 3
[6,1,7,3,5,4,2] => [2,3,1,1] => 1010011 => 4
[6,1,7,4,2,3,5] => [2,2,3] => 1010100 => 3
[6,1,7,4,2,5,3] => [2,2,2,1] => 1010101 => 4
[6,1,7,4,3,2,5] => [2,2,1,2] => 1010110 => 4
[6,1,7,4,3,5,2] => [2,2,2,1] => 1010101 => 4
[6,1,7,4,5,2,3] => [2,3,2] => 1010010 => 3
[6,1,7,4,5,3,2] => [2,3,1,1] => 1010011 => 4
[6,1,7,5,2,3,4] => [2,1,4] => 1011000 => 3
[6,1,7,5,2,4,3] => [2,1,3,1] => 1011001 => 4
[6,1,7,5,3,2,4] => [2,1,2,2] => 1011010 => 4
[6,1,7,5,3,4,2] => [2,1,3,1] => 1011001 => 4
[6,1,7,5,4,2,3] => [2,1,2,2] => 1011010 => 4
[6,1,7,5,4,3,2] => [2,1,2,1,1] => 1011011 => 5
[6,2,1,3,4,5,7] => [2,5] => 1010000 => 2
[6,2,1,3,4,7,5] => [2,3,2] => 1010010 => 3
[6,2,1,3,5,4,7] => [2,3,2] => 1010010 => 3
[6,2,1,3,5,7,4] => [2,3,2] => 1010010 => 3
[6,2,1,3,7,4,5] => [2,2,3] => 1010100 => 3
[6,2,1,3,7,5,4] => [2,2,2,1] => 1010101 => 4
[6,2,1,4,3,5,7] => [2,2,3] => 1010100 => 3
[6,2,1,4,3,7,5] => [2,2,1,2] => 1010110 => 4
[6,2,1,4,5,3,7] => [2,3,2] => 1010010 => 3
[6,2,1,4,5,7,3] => [2,3,2] => 1010010 => 3
[6,2,1,4,7,3,5] => [2,2,3] => 1010100 => 3
[6,2,1,4,7,5,3] => [2,2,2,1] => 1010101 => 4
[6,2,1,5,3,4,7] => [2,1,4] => 1011000 => 3
[6,2,1,5,3,7,4] => [2,1,2,2] => 1011010 => 4
[6,2,1,5,4,3,7] => [2,1,2,2] => 1011010 => 4
[6,2,1,5,4,7,3] => [2,1,2,2] => 1011010 => 4
[6,2,1,5,7,3,4] => [2,1,4] => 1011000 => 3
[6,2,1,5,7,4,3] => [2,1,3,1] => 1011001 => 4
[6,2,1,7,3,4,5] => [2,1,4] => 1011000 => 3
[6,2,1,7,3,5,4] => [2,1,3,1] => 1011001 => 4
[6,2,1,7,4,3,5] => [2,1,2,2] => 1011010 => 4
[6,2,1,7,4,5,3] => [2,1,3,1] => 1011001 => 4
[6,2,1,7,5,3,4] => [2,1,2,2] => 1011010 => 4
[6,2,1,7,5,4,3] => [2,1,2,1,1] => 1011011 => 5
[6,2,3,1,4,5,7] => [3,4] => 1001000 => 2
[6,2,3,1,4,7,5] => [3,2,2] => 1001010 => 3
[6,2,3,1,5,4,7] => [3,2,2] => 1001010 => 3
[6,2,3,1,5,7,4] => [3,2,2] => 1001010 => 3
[6,2,3,1,7,4,5] => [3,1,3] => 1001100 => 3
[6,2,3,1,7,5,4] => [3,1,2,1] => 1001101 => 4
[6,2,3,4,1,5,7] => [4,3] => 1000100 => 2
[6,2,3,4,1,7,5] => [4,1,2] => 1000110 => 3
[6,2,3,4,5,1,7] => [5,2] => 1000010 => 2
[6,2,3,4,5,7,1] => [5,2] => 1000010 => 2
[6,2,3,4,7,1,5] => [4,3] => 1000100 => 2
[6,2,3,4,7,5,1] => [4,2,1] => 1000101 => 3
[6,2,3,5,1,4,7] => [3,4] => 1001000 => 2
[6,2,3,5,1,7,4] => [3,2,2] => 1001010 => 3
[6,2,3,5,4,1,7] => [3,2,2] => 1001010 => 3
[6,2,3,5,4,7,1] => [3,2,2] => 1001010 => 3
[6,2,3,5,7,1,4] => [3,4] => 1001000 => 2
[6,2,3,5,7,4,1] => [3,3,1] => 1001001 => 3
[6,2,3,7,1,4,5] => [3,4] => 1001000 => 2
[6,2,3,7,1,5,4] => [3,3,1] => 1001001 => 3
[6,2,3,7,4,1,5] => [3,2,2] => 1001010 => 3
[6,2,3,7,4,5,1] => [3,3,1] => 1001001 => 3
[6,2,3,7,5,1,4] => [3,2,2] => 1001010 => 3
[6,2,3,7,5,4,1] => [3,2,1,1] => 1001011 => 4
[6,2,4,1,3,5,7] => [2,5] => 1010000 => 2
[6,2,4,1,3,7,5] => [2,3,2] => 1010010 => 3
[6,2,4,1,5,3,7] => [2,3,2] => 1010010 => 3
[6,2,4,1,5,7,3] => [2,3,2] => 1010010 => 3
[6,2,4,1,7,3,5] => [2,2,3] => 1010100 => 3
[6,2,4,1,7,5,3] => [2,2,2,1] => 1010101 => 4
[6,2,4,3,1,5,7] => [2,2,3] => 1010100 => 3
[6,2,4,3,1,7,5] => [2,2,1,2] => 1010110 => 4
[6,2,4,3,5,1,7] => [2,3,2] => 1010010 => 3
[6,2,4,3,5,7,1] => [2,3,2] => 1010010 => 3
[6,2,4,3,7,1,5] => [2,2,3] => 1010100 => 3
[6,2,4,3,7,5,1] => [2,2,2,1] => 1010101 => 4
[6,2,4,5,1,3,7] => [2,5] => 1010000 => 2
[6,2,4,5,1,7,3] => [2,3,2] => 1010010 => 3
[6,2,4,5,3,1,7] => [2,3,2] => 1010010 => 3
[6,2,4,5,3,7,1] => [2,3,2] => 1010010 => 3
[6,2,4,5,7,1,3] => [2,5] => 1010000 => 2
[6,2,4,5,7,3,1] => [2,4,1] => 1010001 => 3
[6,2,4,7,1,3,5] => [2,5] => 1010000 => 2
[6,2,4,7,1,5,3] => [2,4,1] => 1010001 => 3
[6,2,4,7,3,1,5] => [2,3,2] => 1010010 => 3
[6,2,4,7,3,5,1] => [2,4,1] => 1010001 => 3
[6,2,4,7,5,1,3] => [2,3,2] => 1010010 => 3
[6,2,4,7,5,3,1] => [2,3,1,1] => 1010011 => 4
[6,2,5,1,3,4,7] => [2,5] => 1010000 => 2
[6,2,5,1,3,7,4] => [2,3,2] => 1010010 => 3
[6,2,5,1,4,3,7] => [2,3,2] => 1010010 => 3
[6,2,5,1,4,7,3] => [2,3,2] => 1010010 => 3
[6,2,5,1,7,3,4] => [2,2,3] => 1010100 => 3
[6,2,5,1,7,4,3] => [2,2,2,1] => 1010101 => 4
[6,2,5,3,1,4,7] => [2,2,3] => 1010100 => 3
[6,2,5,3,1,7,4] => [2,2,1,2] => 1010110 => 4
[6,2,5,3,4,1,7] => [2,3,2] => 1010010 => 3
[6,2,5,3,4,7,1] => [2,3,2] => 1010010 => 3
[6,2,5,3,7,1,4] => [2,2,3] => 1010100 => 3
[6,2,5,3,7,4,1] => [2,2,2,1] => 1010101 => 4
[6,2,5,4,1,3,7] => [2,2,3] => 1010100 => 3
[6,2,5,4,1,7,3] => [2,2,1,2] => 1010110 => 4
[6,2,5,4,3,1,7] => [2,2,1,2] => 1010110 => 4
[6,2,5,4,3,7,1] => [2,2,1,2] => 1010110 => 4
[6,2,5,4,7,1,3] => [2,2,3] => 1010100 => 3
[6,2,5,4,7,3,1] => [2,2,2,1] => 1010101 => 4
[6,2,5,7,1,3,4] => [2,5] => 1010000 => 2
[6,2,5,7,1,4,3] => [2,4,1] => 1010001 => 3
[6,2,5,7,3,1,4] => [2,3,2] => 1010010 => 3
[6,2,5,7,3,4,1] => [2,4,1] => 1010001 => 3
[6,2,5,7,4,1,3] => [2,3,2] => 1010010 => 3
[6,2,5,7,4,3,1] => [2,3,1,1] => 1010011 => 4
[6,2,7,1,3,4,5] => [2,5] => 1010000 => 2
[6,2,7,1,3,5,4] => [2,4,1] => 1010001 => 3
[6,2,7,1,4,3,5] => [2,3,2] => 1010010 => 3
[6,2,7,1,4,5,3] => [2,4,1] => 1010001 => 3
[6,2,7,1,5,3,4] => [2,3,2] => 1010010 => 3
[6,2,7,1,5,4,3] => [2,3,1,1] => 1010011 => 4
[6,2,7,3,1,4,5] => [2,2,3] => 1010100 => 3
[6,2,7,3,1,5,4] => [2,2,2,1] => 1010101 => 4
[6,2,7,3,4,1,5] => [2,3,2] => 1010010 => 3
[6,2,7,3,4,5,1] => [2,4,1] => 1010001 => 3
[6,2,7,3,5,1,4] => [2,3,2] => 1010010 => 3
[6,2,7,3,5,4,1] => [2,3,1,1] => 1010011 => 4
[6,2,7,4,1,3,5] => [2,2,3] => 1010100 => 3
[6,2,7,4,1,5,3] => [2,2,2,1] => 1010101 => 4
[6,2,7,4,3,1,5] => [2,2,1,2] => 1010110 => 4
[6,2,7,4,3,5,1] => [2,2,2,1] => 1010101 => 4
[6,2,7,4,5,1,3] => [2,3,2] => 1010010 => 3
[6,2,7,4,5,3,1] => [2,3,1,1] => 1010011 => 4
[6,2,7,5,1,3,4] => [2,1,4] => 1011000 => 3
[6,2,7,5,1,4,3] => [2,1,3,1] => 1011001 => 4
[6,2,7,5,3,1,4] => [2,1,2,2] => 1011010 => 4
[6,2,7,5,3,4,1] => [2,1,3,1] => 1011001 => 4
[6,2,7,5,4,1,3] => [2,1,2,2] => 1011010 => 4
[6,2,7,5,4,3,1] => [2,1,2,1,1] => 1011011 => 5
[6,3,1,2,4,5,7] => [1,6] => 1100000 => 2
[6,3,1,2,4,7,5] => [1,4,2] => 1100010 => 3
[6,3,1,2,5,4,7] => [1,4,2] => 1100010 => 3
[6,3,1,2,5,7,4] => [1,4,2] => 1100010 => 3
[6,3,1,2,7,4,5] => [1,3,3] => 1100100 => 3
[6,3,1,2,7,5,4] => [1,3,2,1] => 1100101 => 4
[6,3,1,4,2,5,7] => [1,3,3] => 1100100 => 3
[6,3,1,4,2,7,5] => [1,3,1,2] => 1100110 => 4
[6,3,1,4,5,2,7] => [1,4,2] => 1100010 => 3
[6,3,1,4,5,7,2] => [1,4,2] => 1100010 => 3
[6,3,1,4,7,2,5] => [1,3,3] => 1100100 => 3
[6,3,1,4,7,5,2] => [1,3,2,1] => 1100101 => 4
[6,3,1,5,2,4,7] => [1,2,4] => 1101000 => 3
[6,3,1,5,2,7,4] => [1,2,2,2] => 1101010 => 4
[6,3,1,5,4,2,7] => [1,2,2,2] => 1101010 => 4
[6,3,1,5,4,7,2] => [1,2,2,2] => 1101010 => 4
[6,3,1,5,7,2,4] => [1,2,4] => 1101000 => 3
[6,3,1,5,7,4,2] => [1,2,3,1] => 1101001 => 4
[6,3,1,7,2,4,5] => [1,2,4] => 1101000 => 3
[6,3,1,7,2,5,4] => [1,2,3,1] => 1101001 => 4
[6,3,1,7,4,2,5] => [1,2,2,2] => 1101010 => 4
[6,3,1,7,4,5,2] => [1,2,3,1] => 1101001 => 4
[6,3,1,7,5,2,4] => [1,2,2,2] => 1101010 => 4
[6,3,1,7,5,4,2] => [1,2,2,1,1] => 1101011 => 5
[6,3,2,1,4,5,7] => [1,2,4] => 1101000 => 3
[6,3,2,1,4,7,5] => [1,2,2,2] => 1101010 => 4
[6,3,2,1,5,4,7] => [1,2,2,2] => 1101010 => 4
[6,3,2,1,5,7,4] => [1,2,2,2] => 1101010 => 4
[6,3,2,1,7,4,5] => [1,2,1,3] => 1101100 => 4
[6,3,2,1,7,5,4] => [1,2,1,2,1] => 1101101 => 5
[6,3,2,4,1,5,7] => [1,3,3] => 1100100 => 3
[6,3,2,4,1,7,5] => [1,3,1,2] => 1100110 => 4
[6,3,2,4,5,1,7] => [1,4,2] => 1100010 => 3
[6,3,2,4,5,7,1] => [1,4,2] => 1100010 => 3
[6,3,2,4,7,1,5] => [1,3,3] => 1100100 => 3
[6,3,2,4,7,5,1] => [1,3,2,1] => 1100101 => 4
[6,3,2,5,1,4,7] => [1,2,4] => 1101000 => 3
[6,3,2,5,1,7,4] => [1,2,2,2] => 1101010 => 4
[6,3,2,5,4,1,7] => [1,2,2,2] => 1101010 => 4
[6,3,2,5,4,7,1] => [1,2,2,2] => 1101010 => 4
[6,3,2,5,7,1,4] => [1,2,4] => 1101000 => 3
[6,3,2,5,7,4,1] => [1,2,3,1] => 1101001 => 4
[6,3,2,7,1,4,5] => [1,2,4] => 1101000 => 3
[6,3,2,7,1,5,4] => [1,2,3,1] => 1101001 => 4
[6,3,2,7,4,1,5] => [1,2,2,2] => 1101010 => 4
[6,3,2,7,4,5,1] => [1,2,3,1] => 1101001 => 4
[6,3,2,7,5,1,4] => [1,2,2,2] => 1101010 => 4
[6,3,2,7,5,4,1] => [1,2,2,1,1] => 1101011 => 5
[6,3,4,1,2,5,7] => [1,6] => 1100000 => 2
[6,3,4,1,2,7,5] => [1,4,2] => 1100010 => 3
[6,3,4,1,5,2,7] => [1,4,2] => 1100010 => 3
[6,3,4,1,5,7,2] => [1,4,2] => 1100010 => 3
[6,3,4,1,7,2,5] => [1,3,3] => 1100100 => 3
[6,3,4,1,7,5,2] => [1,3,2,1] => 1100101 => 4
[6,3,4,2,1,5,7] => [1,3,3] => 1100100 => 3
[6,3,4,2,1,7,5] => [1,3,1,2] => 1100110 => 4
[6,3,4,2,5,1,7] => [1,4,2] => 1100010 => 3
[6,3,4,2,5,7,1] => [1,4,2] => 1100010 => 3
[6,3,4,2,7,1,5] => [1,3,3] => 1100100 => 3
[6,3,4,2,7,5,1] => [1,3,2,1] => 1100101 => 4
[6,3,4,5,1,2,7] => [1,6] => 1100000 => 2
[6,3,4,5,1,7,2] => [1,4,2] => 1100010 => 3
[6,3,4,5,2,1,7] => [1,4,2] => 1100010 => 3
[6,3,4,5,2,7,1] => [1,4,2] => 1100010 => 3
[6,3,4,5,7,1,2] => [1,6] => 1100000 => 2
[6,3,4,5,7,2,1] => [1,5,1] => 1100001 => 3
[6,3,4,7,1,2,5] => [1,6] => 1100000 => 2
[6,3,4,7,1,5,2] => [1,5,1] => 1100001 => 3
[6,3,4,7,2,1,5] => [1,4,2] => 1100010 => 3
[6,3,4,7,2,5,1] => [1,5,1] => 1100001 => 3
[6,3,4,7,5,1,2] => [1,4,2] => 1100010 => 3
[6,3,4,7,5,2,1] => [1,4,1,1] => 1100011 => 4
[6,3,5,1,2,4,7] => [1,6] => 1100000 => 2
[6,3,5,1,2,7,4] => [1,4,2] => 1100010 => 3
[6,3,5,1,4,2,7] => [1,4,2] => 1100010 => 3
[6,3,5,1,4,7,2] => [1,4,2] => 1100010 => 3
[6,3,5,1,7,2,4] => [1,3,3] => 1100100 => 3
[6,3,5,1,7,4,2] => [1,3,2,1] => 1100101 => 4
[6,3,5,2,1,4,7] => [1,3,3] => 1100100 => 3
[6,3,5,2,1,7,4] => [1,3,1,2] => 1100110 => 4
[6,3,5,2,4,1,7] => [1,4,2] => 1100010 => 3
[6,3,5,2,4,7,1] => [1,4,2] => 1100010 => 3
[6,3,5,2,7,1,4] => [1,3,3] => 1100100 => 3
[6,3,5,2,7,4,1] => [1,3,2,1] => 1100101 => 4
[6,3,5,4,1,2,7] => [1,3,3] => 1100100 => 3
[6,3,5,4,1,7,2] => [1,3,1,2] => 1100110 => 4
[6,3,5,4,2,1,7] => [1,3,1,2] => 1100110 => 4
[6,3,5,4,2,7,1] => [1,3,1,2] => 1100110 => 4
[6,3,5,4,7,1,2] => [1,3,3] => 1100100 => 3
[6,3,5,4,7,2,1] => [1,3,2,1] => 1100101 => 4
[6,3,5,7,1,2,4] => [1,6] => 1100000 => 2
[6,3,5,7,1,4,2] => [1,5,1] => 1100001 => 3
[6,3,5,7,2,1,4] => [1,4,2] => 1100010 => 3
[6,3,5,7,2,4,1] => [1,5,1] => 1100001 => 3
[6,3,5,7,4,1,2] => [1,4,2] => 1100010 => 3
[6,3,5,7,4,2,1] => [1,4,1,1] => 1100011 => 4
[6,3,7,1,2,4,5] => [1,6] => 1100000 => 2
[6,3,7,1,2,5,4] => [1,5,1] => 1100001 => 3
[6,3,7,1,4,2,5] => [1,4,2] => 1100010 => 3
[6,3,7,1,4,5,2] => [1,5,1] => 1100001 => 3
[6,3,7,1,5,2,4] => [1,4,2] => 1100010 => 3
[6,3,7,1,5,4,2] => [1,4,1,1] => 1100011 => 4
[6,3,7,2,1,4,5] => [1,3,3] => 1100100 => 3
[6,3,7,2,1,5,4] => [1,3,2,1] => 1100101 => 4
[6,3,7,2,4,1,5] => [1,4,2] => 1100010 => 3
[6,3,7,2,4,5,1] => [1,5,1] => 1100001 => 3
[6,3,7,2,5,1,4] => [1,4,2] => 1100010 => 3
[6,3,7,2,5,4,1] => [1,4,1,1] => 1100011 => 4
[6,3,7,4,1,2,5] => [1,3,3] => 1100100 => 3
[6,3,7,4,1,5,2] => [1,3,2,1] => 1100101 => 4
[6,3,7,4,2,1,5] => [1,3,1,2] => 1100110 => 4
[6,3,7,4,2,5,1] => [1,3,2,1] => 1100101 => 4
[6,3,7,4,5,1,2] => [1,4,2] => 1100010 => 3
[6,3,7,4,5,2,1] => [1,4,1,1] => 1100011 => 4
[6,3,7,5,1,2,4] => [1,2,4] => 1101000 => 3
[6,3,7,5,1,4,2] => [1,2,3,1] => 1101001 => 4
[6,3,7,5,2,1,4] => [1,2,2,2] => 1101010 => 4
[6,3,7,5,2,4,1] => [1,2,3,1] => 1101001 => 4
[6,3,7,5,4,1,2] => [1,2,2,2] => 1101010 => 4
[6,3,7,5,4,2,1] => [1,2,2,1,1] => 1101011 => 5
[6,4,1,2,3,5,7] => [1,6] => 1100000 => 2
[6,4,1,2,3,7,5] => [1,4,2] => 1100010 => 3
[6,4,1,2,5,3,7] => [1,4,2] => 1100010 => 3
[6,4,1,2,5,7,3] => [1,4,2] => 1100010 => 3
[6,4,1,2,7,3,5] => [1,3,3] => 1100100 => 3
[6,4,1,2,7,5,3] => [1,3,2,1] => 1100101 => 4
[6,4,1,3,2,5,7] => [1,3,3] => 1100100 => 3
[6,4,1,3,2,7,5] => [1,3,1,2] => 1100110 => 4
[6,4,1,3,5,2,7] => [1,4,2] => 1100010 => 3
[6,4,1,3,5,7,2] => [1,4,2] => 1100010 => 3
[6,4,1,3,7,2,5] => [1,3,3] => 1100100 => 3
[6,4,1,3,7,5,2] => [1,3,2,1] => 1100101 => 4
[6,4,1,5,2,3,7] => [1,2,4] => 1101000 => 3
[6,4,1,5,2,7,3] => [1,2,2,2] => 1101010 => 4
[6,4,1,5,3,2,7] => [1,2,2,2] => 1101010 => 4
[6,4,1,5,3,7,2] => [1,2,2,2] => 1101010 => 4
[6,4,1,5,7,2,3] => [1,2,4] => 1101000 => 3
[6,4,1,5,7,3,2] => [1,2,3,1] => 1101001 => 4
[6,4,1,7,2,3,5] => [1,2,4] => 1101000 => 3
[6,4,1,7,2,5,3] => [1,2,3,1] => 1101001 => 4
[6,4,1,7,3,2,5] => [1,2,2,2] => 1101010 => 4
[6,4,1,7,3,5,2] => [1,2,3,1] => 1101001 => 4
[6,4,1,7,5,2,3] => [1,2,2,2] => 1101010 => 4
[6,4,1,7,5,3,2] => [1,2,2,1,1] => 1101011 => 5
[6,4,2,1,3,5,7] => [1,2,4] => 1101000 => 3
[6,4,2,1,3,7,5] => [1,2,2,2] => 1101010 => 4
[6,4,2,1,5,3,7] => [1,2,2,2] => 1101010 => 4
[6,4,2,1,5,7,3] => [1,2,2,2] => 1101010 => 4
[6,4,2,1,7,3,5] => [1,2,1,3] => 1101100 => 4
[6,4,2,1,7,5,3] => [1,2,1,2,1] => 1101101 => 5
[6,4,2,3,1,5,7] => [1,3,3] => 1100100 => 3
[6,4,2,3,1,7,5] => [1,3,1,2] => 1100110 => 4
[6,4,2,3,5,1,7] => [1,4,2] => 1100010 => 3
[6,4,2,3,5,7,1] => [1,4,2] => 1100010 => 3
[6,4,2,3,7,1,5] => [1,3,3] => 1100100 => 3
[6,4,2,3,7,5,1] => [1,3,2,1] => 1100101 => 4
[6,4,2,5,1,3,7] => [1,2,4] => 1101000 => 3
[6,4,2,5,1,7,3] => [1,2,2,2] => 1101010 => 4
[6,4,2,5,3,1,7] => [1,2,2,2] => 1101010 => 4
[6,4,2,5,3,7,1] => [1,2,2,2] => 1101010 => 4
[6,4,2,5,7,1,3] => [1,2,4] => 1101000 => 3
[6,4,2,5,7,3,1] => [1,2,3,1] => 1101001 => 4
[6,4,2,7,1,3,5] => [1,2,4] => 1101000 => 3
[6,4,2,7,1,5,3] => [1,2,3,1] => 1101001 => 4
[6,4,2,7,3,1,5] => [1,2,2,2] => 1101010 => 4
[6,4,2,7,3,5,1] => [1,2,3,1] => 1101001 => 4
[6,4,2,7,5,1,3] => [1,2,2,2] => 1101010 => 4
[6,4,2,7,5,3,1] => [1,2,2,1,1] => 1101011 => 5
[6,4,3,1,2,5,7] => [1,2,4] => 1101000 => 3
[6,4,3,1,2,7,5] => [1,2,2,2] => 1101010 => 4
[6,4,3,1,5,2,7] => [1,2,2,2] => 1101010 => 4
[6,4,3,1,5,7,2] => [1,2,2,2] => 1101010 => 4
[6,4,3,1,7,2,5] => [1,2,1,3] => 1101100 => 4
[6,4,3,1,7,5,2] => [1,2,1,2,1] => 1101101 => 5
[6,4,3,2,1,5,7] => [1,2,1,3] => 1101100 => 4
[6,4,3,2,1,7,5] => [1,2,1,1,2] => 1101110 => 5
[6,4,3,2,5,1,7] => [1,2,2,2] => 1101010 => 4
[6,4,3,2,5,7,1] => [1,2,2,2] => 1101010 => 4
[6,4,3,2,7,1,5] => [1,2,1,3] => 1101100 => 4
[6,4,3,2,7,5,1] => [1,2,1,2,1] => 1101101 => 5
[6,4,3,5,1,2,7] => [1,2,4] => 1101000 => 3
[6,4,3,5,1,7,2] => [1,2,2,2] => 1101010 => 4
[6,4,3,5,2,1,7] => [1,2,2,2] => 1101010 => 4
[6,4,3,5,2,7,1] => [1,2,2,2] => 1101010 => 4
[6,4,3,5,7,1,2] => [1,2,4] => 1101000 => 3
[6,4,3,5,7,2,1] => [1,2,3,1] => 1101001 => 4
[6,4,3,7,1,2,5] => [1,2,4] => 1101000 => 3
[6,4,3,7,1,5,2] => [1,2,3,1] => 1101001 => 4
[6,4,3,7,2,1,5] => [1,2,2,2] => 1101010 => 4
[6,4,3,7,2,5,1] => [1,2,3,1] => 1101001 => 4
[6,4,3,7,5,1,2] => [1,2,2,2] => 1101010 => 4
[6,4,3,7,5,2,1] => [1,2,2,1,1] => 1101011 => 5
[6,4,5,1,2,3,7] => [1,6] => 1100000 => 2
[6,4,5,1,2,7,3] => [1,4,2] => 1100010 => 3
[6,4,5,1,3,2,7] => [1,4,2] => 1100010 => 3
[6,4,5,1,3,7,2] => [1,4,2] => 1100010 => 3
[6,4,5,1,7,2,3] => [1,3,3] => 1100100 => 3
[6,4,5,1,7,3,2] => [1,3,2,1] => 1100101 => 4
[6,4,5,2,1,3,7] => [1,3,3] => 1100100 => 3
[6,4,5,2,1,7,3] => [1,3,1,2] => 1100110 => 4
[6,4,5,2,3,1,7] => [1,4,2] => 1100010 => 3
[6,4,5,2,3,7,1] => [1,4,2] => 1100010 => 3
[6,4,5,2,7,1,3] => [1,3,3] => 1100100 => 3
[6,4,5,2,7,3,1] => [1,3,2,1] => 1100101 => 4
[6,4,5,3,1,2,7] => [1,3,3] => 1100100 => 3
[6,4,5,3,1,7,2] => [1,3,1,2] => 1100110 => 4
[6,4,5,3,2,1,7] => [1,3,1,2] => 1100110 => 4
[6,4,5,3,2,7,1] => [1,3,1,2] => 1100110 => 4
[6,4,5,3,7,1,2] => [1,3,3] => 1100100 => 3
[6,4,5,3,7,2,1] => [1,3,2,1] => 1100101 => 4
[6,4,5,7,1,2,3] => [1,6] => 1100000 => 2
[6,4,5,7,1,3,2] => [1,5,1] => 1100001 => 3
[6,4,5,7,2,1,3] => [1,4,2] => 1100010 => 3
[6,4,5,7,2,3,1] => [1,5,1] => 1100001 => 3
[6,4,5,7,3,1,2] => [1,4,2] => 1100010 => 3
[6,4,5,7,3,2,1] => [1,4,1,1] => 1100011 => 4
[6,4,7,1,2,3,5] => [1,6] => 1100000 => 2
[6,4,7,1,2,5,3] => [1,5,1] => 1100001 => 3
[6,4,7,1,3,2,5] => [1,4,2] => 1100010 => 3
[6,4,7,1,3,5,2] => [1,5,1] => 1100001 => 3
[6,4,7,1,5,2,3] => [1,4,2] => 1100010 => 3
[6,4,7,1,5,3,2] => [1,4,1,1] => 1100011 => 4
[6,4,7,2,1,3,5] => [1,3,3] => 1100100 => 3
[6,4,7,2,1,5,3] => [1,3,2,1] => 1100101 => 4
[6,4,7,2,3,1,5] => [1,4,2] => 1100010 => 3
[6,4,7,2,3,5,1] => [1,5,1] => 1100001 => 3
[6,4,7,2,5,1,3] => [1,4,2] => 1100010 => 3
[6,4,7,2,5,3,1] => [1,4,1,1] => 1100011 => 4
[6,4,7,3,1,2,5] => [1,3,3] => 1100100 => 3
[6,4,7,3,1,5,2] => [1,3,2,1] => 1100101 => 4
[6,4,7,3,2,1,5] => [1,3,1,2] => 1100110 => 4
[6,4,7,3,2,5,1] => [1,3,2,1] => 1100101 => 4
[6,4,7,3,5,1,2] => [1,4,2] => 1100010 => 3
[6,4,7,3,5,2,1] => [1,4,1,1] => 1100011 => 4
[6,4,7,5,1,2,3] => [1,2,4] => 1101000 => 3
[6,4,7,5,1,3,2] => [1,2,3,1] => 1101001 => 4
[6,4,7,5,2,1,3] => [1,2,2,2] => 1101010 => 4
[6,4,7,5,2,3,1] => [1,2,3,1] => 1101001 => 4
[6,4,7,5,3,1,2] => [1,2,2,2] => 1101010 => 4
[6,4,7,5,3,2,1] => [1,2,2,1,1] => 1101011 => 5
[6,5,1,2,3,4,7] => [1,6] => 1100000 => 2
[6,5,1,2,3,7,4] => [1,4,2] => 1100010 => 3
[6,5,1,2,4,3,7] => [1,4,2] => 1100010 => 3
[6,5,1,2,4,7,3] => [1,4,2] => 1100010 => 3
[6,5,1,2,7,3,4] => [1,3,3] => 1100100 => 3
[6,5,1,2,7,4,3] => [1,3,2,1] => 1100101 => 4
[6,5,1,3,2,4,7] => [1,3,3] => 1100100 => 3
[6,5,1,3,2,7,4] => [1,3,1,2] => 1100110 => 4
[6,5,1,3,4,2,7] => [1,4,2] => 1100010 => 3
[6,5,1,3,4,7,2] => [1,4,2] => 1100010 => 3
[6,5,1,3,7,2,4] => [1,3,3] => 1100100 => 3
[6,5,1,3,7,4,2] => [1,3,2,1] => 1100101 => 4
[6,5,1,4,2,3,7] => [1,3,3] => 1100100 => 3
[6,5,1,4,2,7,3] => [1,3,1,2] => 1100110 => 4
[6,5,1,4,3,2,7] => [1,3,1,2] => 1100110 => 4
[6,5,1,4,3,7,2] => [1,3,1,2] => 1100110 => 4
[6,5,1,4,7,2,3] => [1,3,3] => 1100100 => 3
[6,5,1,4,7,3,2] => [1,3,2,1] => 1100101 => 4
[6,5,1,7,2,3,4] => [1,2,4] => 1101000 => 3
[6,5,1,7,2,4,3] => [1,2,3,1] => 1101001 => 4
[6,5,1,7,3,2,4] => [1,2,2,2] => 1101010 => 4
[6,5,1,7,3,4,2] => [1,2,3,1] => 1101001 => 4
[6,5,1,7,4,2,3] => [1,2,2,2] => 1101010 => 4
[6,5,1,7,4,3,2] => [1,2,2,1,1] => 1101011 => 5
[6,5,2,1,3,4,7] => [1,2,4] => 1101000 => 3
[6,5,2,1,3,7,4] => [1,2,2,2] => 1101010 => 4
[6,5,2,1,4,3,7] => [1,2,2,2] => 1101010 => 4
[6,5,2,1,4,7,3] => [1,2,2,2] => 1101010 => 4
[6,5,2,1,7,3,4] => [1,2,1,3] => 1101100 => 4
[6,5,2,1,7,4,3] => [1,2,1,2,1] => 1101101 => 5
[6,5,2,3,1,4,7] => [1,3,3] => 1100100 => 3
[6,5,2,3,1,7,4] => [1,3,1,2] => 1100110 => 4
[6,5,2,3,4,1,7] => [1,4,2] => 1100010 => 3
[6,5,2,3,4,7,1] => [1,4,2] => 1100010 => 3
[6,5,2,3,7,1,4] => [1,3,3] => 1100100 => 3
[6,5,2,3,7,4,1] => [1,3,2,1] => 1100101 => 4
[6,5,2,4,1,3,7] => [1,3,3] => 1100100 => 3
[6,5,2,4,1,7,3] => [1,3,1,2] => 1100110 => 4
[6,5,2,4,3,1,7] => [1,3,1,2] => 1100110 => 4
[6,5,2,4,3,7,1] => [1,3,1,2] => 1100110 => 4
[6,5,2,4,7,1,3] => [1,3,3] => 1100100 => 3
[6,5,2,4,7,3,1] => [1,3,2,1] => 1100101 => 4
[6,5,2,7,1,3,4] => [1,2,4] => 1101000 => 3
[6,5,2,7,1,4,3] => [1,2,3,1] => 1101001 => 4
[6,5,2,7,3,1,4] => [1,2,2,2] => 1101010 => 4
[6,5,2,7,3,4,1] => [1,2,3,1] => 1101001 => 4
[6,5,2,7,4,1,3] => [1,2,2,2] => 1101010 => 4
[6,5,2,7,4,3,1] => [1,2,2,1,1] => 1101011 => 5
[6,5,3,1,2,4,7] => [1,2,4] => 1101000 => 3
[6,5,3,1,2,7,4] => [1,2,2,2] => 1101010 => 4
[6,5,3,1,4,2,7] => [1,2,2,2] => 1101010 => 4
[6,5,3,1,4,7,2] => [1,2,2,2] => 1101010 => 4
[6,5,3,1,7,2,4] => [1,2,1,3] => 1101100 => 4
[6,5,3,1,7,4,2] => [1,2,1,2,1] => 1101101 => 5
[6,5,3,2,1,4,7] => [1,2,1,3] => 1101100 => 4
[6,5,3,2,1,7,4] => [1,2,1,1,2] => 1101110 => 5
[6,5,3,2,4,1,7] => [1,2,2,2] => 1101010 => 4
[6,5,3,2,4,7,1] => [1,2,2,2] => 1101010 => 4
[6,5,3,2,7,1,4] => [1,2,1,3] => 1101100 => 4
[6,5,3,2,7,4,1] => [1,2,1,2,1] => 1101101 => 5
[6,5,3,4,1,2,7] => [1,3,3] => 1100100 => 3
[6,5,3,4,1,7,2] => [1,3,1,2] => 1100110 => 4
[6,5,3,4,2,1,7] => [1,3,1,2] => 1100110 => 4
[6,5,3,4,2,7,1] => [1,3,1,2] => 1100110 => 4
[6,5,3,4,7,1,2] => [1,3,3] => 1100100 => 3
[6,5,3,4,7,2,1] => [1,3,2,1] => 1100101 => 4
[6,5,3,7,1,2,4] => [1,2,4] => 1101000 => 3
[6,5,3,7,1,4,2] => [1,2,3,1] => 1101001 => 4
[6,5,3,7,2,1,4] => [1,2,2,2] => 1101010 => 4
[6,5,3,7,2,4,1] => [1,2,3,1] => 1101001 => 4
[6,5,3,7,4,1,2] => [1,2,2,2] => 1101010 => 4
[6,5,3,7,4,2,1] => [1,2,2,1,1] => 1101011 => 5
[6,5,4,1,2,3,7] => [1,1,5] => 1110000 => 3
[6,5,4,1,2,7,3] => [1,1,3,2] => 1110010 => 4
[6,5,4,1,3,2,7] => [1,1,3,2] => 1110010 => 4
[6,5,4,1,3,7,2] => [1,1,3,2] => 1110010 => 4
[6,5,4,1,7,2,3] => [1,1,2,3] => 1110100 => 4
[6,5,4,1,7,3,2] => [1,1,2,2,1] => 1110101 => 5
[6,5,4,2,1,3,7] => [1,1,2,3] => 1110100 => 4
[6,5,4,2,1,7,3] => [1,1,2,1,2] => 1110110 => 5
[6,5,4,2,3,1,7] => [1,1,3,2] => 1110010 => 4
[6,5,4,2,3,7,1] => [1,1,3,2] => 1110010 => 4
[6,5,4,2,7,1,3] => [1,1,2,3] => 1110100 => 4
[6,5,4,2,7,3,1] => [1,1,2,2,1] => 1110101 => 5
[6,5,4,3,1,2,7] => [1,1,2,3] => 1110100 => 4
[6,5,4,3,1,7,2] => [1,1,2,1,2] => 1110110 => 5
[6,5,4,3,2,1,7] => [1,1,2,1,2] => 1110110 => 5
[6,5,4,3,2,7,1] => [1,1,2,1,2] => 1110110 => 5
[6,5,4,3,7,1,2] => [1,1,2,3] => 1110100 => 4
[6,5,4,3,7,2,1] => [1,1,2,2,1] => 1110101 => 5
[6,5,4,7,1,2,3] => [1,1,5] => 1110000 => 3
[6,5,4,7,1,3,2] => [1,1,4,1] => 1110001 => 4
[6,5,4,7,2,1,3] => [1,1,3,2] => 1110010 => 4
[6,5,4,7,2,3,1] => [1,1,4,1] => 1110001 => 4
[6,5,4,7,3,1,2] => [1,1,3,2] => 1110010 => 4
[6,5,4,7,3,2,1] => [1,1,3,1,1] => 1110011 => 5
[6,5,7,1,2,3,4] => [1,6] => 1100000 => 2
[6,5,7,1,2,4,3] => [1,5,1] => 1100001 => 3
[6,5,7,1,3,2,4] => [1,4,2] => 1100010 => 3
[6,5,7,1,3,4,2] => [1,5,1] => 1100001 => 3
[6,5,7,1,4,2,3] => [1,4,2] => 1100010 => 3
[6,5,7,1,4,3,2] => [1,4,1,1] => 1100011 => 4
[6,5,7,2,1,3,4] => [1,3,3] => 1100100 => 3
[6,5,7,2,1,4,3] => [1,3,2,1] => 1100101 => 4
[6,5,7,2,3,1,4] => [1,4,2] => 1100010 => 3
[6,5,7,2,3,4,1] => [1,5,1] => 1100001 => 3
[6,5,7,2,4,1,3] => [1,4,2] => 1100010 => 3
[6,5,7,2,4,3,1] => [1,4,1,1] => 1100011 => 4
[6,5,7,3,1,2,4] => [1,3,3] => 1100100 => 3
[6,5,7,3,1,4,2] => [1,3,2,1] => 1100101 => 4
[6,5,7,3,2,1,4] => [1,3,1,2] => 1100110 => 4
[6,5,7,3,2,4,1] => [1,3,2,1] => 1100101 => 4
[6,5,7,3,4,1,2] => [1,4,2] => 1100010 => 3
[6,5,7,3,4,2,1] => [1,4,1,1] => 1100011 => 4
[6,5,7,4,1,2,3] => [1,3,3] => 1100100 => 3
[6,5,7,4,1,3,2] => [1,3,2,1] => 1100101 => 4
[6,5,7,4,2,1,3] => [1,3,1,2] => 1100110 => 4
[6,5,7,4,2,3,1] => [1,3,2,1] => 1100101 => 4
[6,5,7,4,3,1,2] => [1,3,1,2] => 1100110 => 4
[6,5,7,4,3,2,1] => [1,3,1,1,1] => 1100111 => 5
[6,7,1,2,3,4,5] => [7] => 1000000 => 1
[6,7,1,2,3,5,4] => [6,1] => 1000001 => 2
[6,7,1,2,4,3,5] => [5,2] => 1000010 => 2
[6,7,1,2,4,5,3] => [6,1] => 1000001 => 2
[6,7,1,2,5,3,4] => [5,2] => 1000010 => 2
[6,7,1,2,5,4,3] => [5,1,1] => 1000011 => 3
[6,7,1,3,2,4,5] => [4,3] => 1000100 => 2
[6,7,1,3,2,5,4] => [4,2,1] => 1000101 => 3
[6,7,1,3,4,2,5] => [5,2] => 1000010 => 2
[6,7,1,3,4,5,2] => [6,1] => 1000001 => 2
[6,7,1,3,5,2,4] => [5,2] => 1000010 => 2
[6,7,1,3,5,4,2] => [5,1,1] => 1000011 => 3
[6,7,1,4,2,3,5] => [4,3] => 1000100 => 2
[6,7,1,4,2,5,3] => [4,2,1] => 1000101 => 3
[6,7,1,4,3,2,5] => [4,1,2] => 1000110 => 3
[6,7,1,4,3,5,2] => [4,2,1] => 1000101 => 3
[6,7,1,4,5,2,3] => [5,2] => 1000010 => 2
[6,7,1,4,5,3,2] => [5,1,1] => 1000011 => 3
[6,7,1,5,2,3,4] => [3,4] => 1001000 => 2
[6,7,1,5,2,4,3] => [3,3,1] => 1001001 => 3
[6,7,1,5,3,2,4] => [3,2,2] => 1001010 => 3
[6,7,1,5,3,4,2] => [3,3,1] => 1001001 => 3
[6,7,1,5,4,2,3] => [3,2,2] => 1001010 => 3
[6,7,1,5,4,3,2] => [3,2,1,1] => 1001011 => 4
[6,7,2,1,3,4,5] => [3,4] => 1001000 => 2
[6,7,2,1,3,5,4] => [3,3,1] => 1001001 => 3
[6,7,2,1,4,3,5] => [3,2,2] => 1001010 => 3
[6,7,2,1,4,5,3] => [3,3,1] => 1001001 => 3
[6,7,2,1,5,3,4] => [3,2,2] => 1001010 => 3
[6,7,2,1,5,4,3] => [3,2,1,1] => 1001011 => 4
[6,7,2,3,1,4,5] => [4,3] => 1000100 => 2
[6,7,2,3,1,5,4] => [4,2,1] => 1000101 => 3
[6,7,2,3,4,1,5] => [5,2] => 1000010 => 2
[6,7,2,3,4,5,1] => [6,1] => 1000001 => 2
[6,7,2,3,5,1,4] => [5,2] => 1000010 => 2
[6,7,2,3,5,4,1] => [5,1,1] => 1000011 => 3
[6,7,2,4,1,3,5] => [4,3] => 1000100 => 2
[6,7,2,4,1,5,3] => [4,2,1] => 1000101 => 3
[6,7,2,4,3,1,5] => [4,1,2] => 1000110 => 3
[6,7,2,4,3,5,1] => [4,2,1] => 1000101 => 3
[6,7,2,4,5,1,3] => [5,2] => 1000010 => 2
[6,7,2,4,5,3,1] => [5,1,1] => 1000011 => 3
[6,7,2,5,1,3,4] => [3,4] => 1001000 => 2
[6,7,2,5,1,4,3] => [3,3,1] => 1001001 => 3
[6,7,2,5,3,1,4] => [3,2,2] => 1001010 => 3
[6,7,2,5,3,4,1] => [3,3,1] => 1001001 => 3
[6,7,2,5,4,1,3] => [3,2,2] => 1001010 => 3
[6,7,2,5,4,3,1] => [3,2,1,1] => 1001011 => 4
[6,7,3,1,2,4,5] => [3,4] => 1001000 => 2
[6,7,3,1,2,5,4] => [3,3,1] => 1001001 => 3
[6,7,3,1,4,2,5] => [3,2,2] => 1001010 => 3
[6,7,3,1,4,5,2] => [3,3,1] => 1001001 => 3
[6,7,3,1,5,2,4] => [3,2,2] => 1001010 => 3
[6,7,3,1,5,4,2] => [3,2,1,1] => 1001011 => 4
[6,7,3,2,1,4,5] => [3,1,3] => 1001100 => 3
[6,7,3,2,1,5,4] => [3,1,2,1] => 1001101 => 4
[6,7,3,2,4,1,5] => [3,2,2] => 1001010 => 3
[6,7,3,2,4,5,1] => [3,3,1] => 1001001 => 3
[6,7,3,2,5,1,4] => [3,2,2] => 1001010 => 3
[6,7,3,2,5,4,1] => [3,2,1,1] => 1001011 => 4
[6,7,3,4,1,2,5] => [4,3] => 1000100 => 2
[6,7,3,4,1,5,2] => [4,2,1] => 1000101 => 3
[6,7,3,4,2,1,5] => [4,1,2] => 1000110 => 3
[6,7,3,4,2,5,1] => [4,2,1] => 1000101 => 3
[6,7,3,4,5,1,2] => [5,2] => 1000010 => 2
[6,7,3,4,5,2,1] => [5,1,1] => 1000011 => 3
[6,7,3,5,1,2,4] => [3,4] => 1001000 => 2
[6,7,3,5,1,4,2] => [3,3,1] => 1001001 => 3
[6,7,3,5,2,1,4] => [3,2,2] => 1001010 => 3
[6,7,3,5,2,4,1] => [3,3,1] => 1001001 => 3
[6,7,3,5,4,1,2] => [3,2,2] => 1001010 => 3
[6,7,3,5,4,2,1] => [3,2,1,1] => 1001011 => 4
[6,7,4,1,2,3,5] => [2,5] => 1010000 => 2
[6,7,4,1,2,5,3] => [2,4,1] => 1010001 => 3
[6,7,4,1,3,2,5] => [2,3,2] => 1010010 => 3
[6,7,4,1,3,5,2] => [2,4,1] => 1010001 => 3
[6,7,4,1,5,2,3] => [2,3,2] => 1010010 => 3
[6,7,4,1,5,3,2] => [2,3,1,1] => 1010011 => 4
[6,7,4,2,1,3,5] => [2,2,3] => 1010100 => 3
[6,7,4,2,1,5,3] => [2,2,2,1] => 1010101 => 4
[6,7,4,2,3,1,5] => [2,3,2] => 1010010 => 3
[6,7,4,2,3,5,1] => [2,4,1] => 1010001 => 3
[6,7,4,2,5,1,3] => [2,3,2] => 1010010 => 3
[6,7,4,2,5,3,1] => [2,3,1,1] => 1010011 => 4
[6,7,4,3,1,2,5] => [2,2,3] => 1010100 => 3
[6,7,4,3,1,5,2] => [2,2,2,1] => 1010101 => 4
[6,7,4,3,2,1,5] => [2,2,1,2] => 1010110 => 4
[6,7,4,3,2,5,1] => [2,2,2,1] => 1010101 => 4
[6,7,4,3,5,1,2] => [2,3,2] => 1010010 => 3
[6,7,4,3,5,2,1] => [2,3,1,1] => 1010011 => 4
[6,7,4,5,1,2,3] => [2,5] => 1010000 => 2
[6,7,4,5,1,3,2] => [2,4,1] => 1010001 => 3
[6,7,4,5,2,1,3] => [2,3,2] => 1010010 => 3
[6,7,4,5,2,3,1] => [2,4,1] => 1010001 => 3
[6,7,4,5,3,1,2] => [2,3,2] => 1010010 => 3
[6,7,4,5,3,2,1] => [2,3,1,1] => 1010011 => 4
[6,7,5,1,2,3,4] => [2,5] => 1010000 => 2
[6,7,5,1,2,4,3] => [2,4,1] => 1010001 => 3
[6,7,5,1,3,2,4] => [2,3,2] => 1010010 => 3
[6,7,5,1,3,4,2] => [2,4,1] => 1010001 => 3
[6,7,5,1,4,2,3] => [2,3,2] => 1010010 => 3
[6,7,5,1,4,3,2] => [2,3,1,1] => 1010011 => 4
[6,7,5,2,1,3,4] => [2,2,3] => 1010100 => 3
[6,7,5,2,1,4,3] => [2,2,2,1] => 1010101 => 4
[6,7,5,2,3,1,4] => [2,3,2] => 1010010 => 3
[6,7,5,2,3,4,1] => [2,4,1] => 1010001 => 3
[6,7,5,2,4,1,3] => [2,3,2] => 1010010 => 3
[6,7,5,2,4,3,1] => [2,3,1,1] => 1010011 => 4
[6,7,5,3,1,2,4] => [2,2,3] => 1010100 => 3
[6,7,5,3,1,4,2] => [2,2,2,1] => 1010101 => 4
[6,7,5,3,2,1,4] => [2,2,1,2] => 1010110 => 4
[6,7,5,3,2,4,1] => [2,2,2,1] => 1010101 => 4
[6,7,5,3,4,1,2] => [2,3,2] => 1010010 => 3
[6,7,5,3,4,2,1] => [2,3,1,1] => 1010011 => 4
[6,7,5,4,1,2,3] => [2,2,3] => 1010100 => 3
[6,7,5,4,1,3,2] => [2,2,2,1] => 1010101 => 4
[6,7,5,4,2,1,3] => [2,2,1,2] => 1010110 => 4
[6,7,5,4,2,3,1] => [2,2,2,1] => 1010101 => 4
[6,7,5,4,3,1,2] => [2,2,1,2] => 1010110 => 4
[6,7,5,4,3,2,1] => [2,2,1,1,1] => 1010111 => 5
[7,1,2,3,4,5,6] => [7] => 1000000 => 1
[7,1,2,3,4,6,5] => [6,1] => 1000001 => 2
[7,1,2,3,5,4,6] => [5,2] => 1000010 => 2
[7,1,2,3,5,6,4] => [6,1] => 1000001 => 2
[7,1,2,3,6,4,5] => [4,3] => 1000100 => 2
[7,1,2,3,6,5,4] => [4,2,1] => 1000101 => 3
[7,1,2,4,3,5,6] => [4,3] => 1000100 => 2
[7,1,2,4,3,6,5] => [4,2,1] => 1000101 => 3
[7,1,2,4,5,3,6] => [5,2] => 1000010 => 2
[7,1,2,4,5,6,3] => [6,1] => 1000001 => 2
[7,1,2,4,6,3,5] => [4,3] => 1000100 => 2
[7,1,2,4,6,5,3] => [4,2,1] => 1000101 => 3
[7,1,2,5,3,4,6] => [3,4] => 1001000 => 2
[7,1,2,5,3,6,4] => [3,3,1] => 1001001 => 3
[7,1,2,5,4,3,6] => [3,2,2] => 1001010 => 3
[7,1,2,5,4,6,3] => [3,3,1] => 1001001 => 3
[7,1,2,5,6,3,4] => [3,4] => 1001000 => 2
[7,1,2,5,6,4,3] => [3,3,1] => 1001001 => 3
[7,1,2,6,3,4,5] => [3,4] => 1001000 => 2
[7,1,2,6,3,5,4] => [3,3,1] => 1001001 => 3
[7,1,2,6,4,3,5] => [3,2,2] => 1001010 => 3
[7,1,2,6,4,5,3] => [3,3,1] => 1001001 => 3
[7,1,2,6,5,3,4] => [3,2,2] => 1001010 => 3
[7,1,2,6,5,4,3] => [3,2,1,1] => 1001011 => 4
[7,1,3,2,4,5,6] => [3,4] => 1001000 => 2
[7,1,3,2,4,6,5] => [3,3,1] => 1001001 => 3
[7,1,3,2,5,4,6] => [3,2,2] => 1001010 => 3
[7,1,3,2,5,6,4] => [3,3,1] => 1001001 => 3
[7,1,3,2,6,4,5] => [3,1,3] => 1001100 => 3
[7,1,3,2,6,5,4] => [3,1,2,1] => 1001101 => 4
[7,1,3,4,2,5,6] => [4,3] => 1000100 => 2
[7,1,3,4,2,6,5] => [4,2,1] => 1000101 => 3
[7,1,3,4,5,2,6] => [5,2] => 1000010 => 2
[7,1,3,4,5,6,2] => [6,1] => 1000001 => 2
[7,1,3,4,6,2,5] => [4,3] => 1000100 => 2
[7,1,3,4,6,5,2] => [4,2,1] => 1000101 => 3
[7,1,3,5,2,4,6] => [3,4] => 1001000 => 2
[7,1,3,5,2,6,4] => [3,3,1] => 1001001 => 3
[7,1,3,5,4,2,6] => [3,2,2] => 1001010 => 3
[7,1,3,5,4,6,2] => [3,3,1] => 1001001 => 3
[7,1,3,5,6,2,4] => [3,4] => 1001000 => 2
[7,1,3,5,6,4,2] => [3,3,1] => 1001001 => 3
[7,1,3,6,2,4,5] => [3,4] => 1001000 => 2
[7,1,3,6,2,5,4] => [3,3,1] => 1001001 => 3
[7,1,3,6,4,2,5] => [3,2,2] => 1001010 => 3
[7,1,3,6,4,5,2] => [3,3,1] => 1001001 => 3
[7,1,3,6,5,2,4] => [3,2,2] => 1001010 => 3
[7,1,3,6,5,4,2] => [3,2,1,1] => 1001011 => 4
[7,1,4,2,3,5,6] => [2,5] => 1010000 => 2
[7,1,4,2,3,6,5] => [2,4,1] => 1010001 => 3
[7,1,4,2,5,3,6] => [2,3,2] => 1010010 => 3
[7,1,4,2,5,6,3] => [2,4,1] => 1010001 => 3
[7,1,4,2,6,3,5] => [2,2,3] => 1010100 => 3
[7,1,4,2,6,5,3] => [2,2,2,1] => 1010101 => 4
[7,1,4,3,2,5,6] => [2,2,3] => 1010100 => 3
[7,1,4,3,2,6,5] => [2,2,2,1] => 1010101 => 4
[7,1,4,3,5,2,6] => [2,3,2] => 1010010 => 3
[7,1,4,3,5,6,2] => [2,4,1] => 1010001 => 3
[7,1,4,3,6,2,5] => [2,2,3] => 1010100 => 3
[7,1,4,3,6,5,2] => [2,2,2,1] => 1010101 => 4
[7,1,4,5,2,3,6] => [2,5] => 1010000 => 2
[7,1,4,5,2,6,3] => [2,4,1] => 1010001 => 3
[7,1,4,5,3,2,6] => [2,3,2] => 1010010 => 3
[7,1,4,5,3,6,2] => [2,4,1] => 1010001 => 3
[7,1,4,5,6,2,3] => [2,5] => 1010000 => 2
[7,1,4,5,6,3,2] => [2,4,1] => 1010001 => 3
[7,1,4,6,2,3,5] => [2,5] => 1010000 => 2
[7,1,4,6,2,5,3] => [2,4,1] => 1010001 => 3
[7,1,4,6,3,2,5] => [2,3,2] => 1010010 => 3
[7,1,4,6,3,5,2] => [2,4,1] => 1010001 => 3
[7,1,4,6,5,2,3] => [2,3,2] => 1010010 => 3
[7,1,4,6,5,3,2] => [2,3,1,1] => 1010011 => 4
[7,1,5,2,3,4,6] => [2,5] => 1010000 => 2
[7,1,5,2,3,6,4] => [2,4,1] => 1010001 => 3
[7,1,5,2,4,3,6] => [2,3,2] => 1010010 => 3
[7,1,5,2,4,6,3] => [2,4,1] => 1010001 => 3
[7,1,5,2,6,3,4] => [2,2,3] => 1010100 => 3
[7,1,5,2,6,4,3] => [2,2,2,1] => 1010101 => 4
[7,1,5,3,2,4,6] => [2,2,3] => 1010100 => 3
[7,1,5,3,2,6,4] => [2,2,2,1] => 1010101 => 4
[7,1,5,3,4,2,6] => [2,3,2] => 1010010 => 3
[7,1,5,3,4,6,2] => [2,4,1] => 1010001 => 3
[7,1,5,3,6,2,4] => [2,2,3] => 1010100 => 3
[7,1,5,3,6,4,2] => [2,2,2,1] => 1010101 => 4
[7,1,5,4,2,3,6] => [2,2,3] => 1010100 => 3
[7,1,5,4,2,6,3] => [2,2,2,1] => 1010101 => 4
[7,1,5,4,3,2,6] => [2,2,1,2] => 1010110 => 4
[7,1,5,4,3,6,2] => [2,2,2,1] => 1010101 => 4
[7,1,5,4,6,2,3] => [2,2,3] => 1010100 => 3
[7,1,5,4,6,3,2] => [2,2,2,1] => 1010101 => 4
[7,1,5,6,2,3,4] => [2,5] => 1010000 => 2
[7,1,5,6,2,4,3] => [2,4,1] => 1010001 => 3
[7,1,5,6,3,2,4] => [2,3,2] => 1010010 => 3
[7,1,5,6,3,4,2] => [2,4,1] => 1010001 => 3
[7,1,5,6,4,2,3] => [2,3,2] => 1010010 => 3
[7,1,5,6,4,3,2] => [2,3,1,1] => 1010011 => 4
[7,1,6,2,3,4,5] => [2,5] => 1010000 => 2
[7,1,6,2,3,5,4] => [2,4,1] => 1010001 => 3
[7,1,6,2,4,3,5] => [2,3,2] => 1010010 => 3
[7,1,6,2,4,5,3] => [2,4,1] => 1010001 => 3
[7,1,6,2,5,3,4] => [2,3,2] => 1010010 => 3
[7,1,6,2,5,4,3] => [2,3,1,1] => 1010011 => 4
[7,1,6,3,2,4,5] => [2,2,3] => 1010100 => 3
[7,1,6,3,2,5,4] => [2,2,2,1] => 1010101 => 4
[7,1,6,3,4,2,5] => [2,3,2] => 1010010 => 3
[7,1,6,3,4,5,2] => [2,4,1] => 1010001 => 3
[7,1,6,3,5,2,4] => [2,3,2] => 1010010 => 3
[7,1,6,3,5,4,2] => [2,3,1,1] => 1010011 => 4
[7,1,6,4,2,3,5] => [2,2,3] => 1010100 => 3
[7,1,6,4,2,5,3] => [2,2,2,1] => 1010101 => 4
[7,1,6,4,3,2,5] => [2,2,1,2] => 1010110 => 4
[7,1,6,4,3,5,2] => [2,2,2,1] => 1010101 => 4
[7,1,6,4,5,2,3] => [2,3,2] => 1010010 => 3
[7,1,6,4,5,3,2] => [2,3,1,1] => 1010011 => 4
[7,1,6,5,2,3,4] => [2,1,4] => 1011000 => 3
[7,1,6,5,2,4,3] => [2,1,3,1] => 1011001 => 4
[7,1,6,5,3,2,4] => [2,1,2,2] => 1011010 => 4
[7,1,6,5,3,4,2] => [2,1,3,1] => 1011001 => 4
[7,1,6,5,4,2,3] => [2,1,2,2] => 1011010 => 4
[7,1,6,5,4,3,2] => [2,1,2,1,1] => 1011011 => 5
[7,2,1,3,4,5,6] => [2,5] => 1010000 => 2
[7,2,1,3,4,6,5] => [2,4,1] => 1010001 => 3
[7,2,1,3,5,4,6] => [2,3,2] => 1010010 => 3
[7,2,1,3,5,6,4] => [2,4,1] => 1010001 => 3
[7,2,1,3,6,4,5] => [2,2,3] => 1010100 => 3
[7,2,1,3,6,5,4] => [2,2,2,1] => 1010101 => 4
[7,2,1,4,3,5,6] => [2,2,3] => 1010100 => 3
[7,2,1,4,3,6,5] => [2,2,2,1] => 1010101 => 4
[7,2,1,4,5,3,6] => [2,3,2] => 1010010 => 3
[7,2,1,4,5,6,3] => [2,4,1] => 1010001 => 3
[7,2,1,4,6,3,5] => [2,2,3] => 1010100 => 3
[7,2,1,4,6,5,3] => [2,2,2,1] => 1010101 => 4
[7,2,1,5,3,4,6] => [2,1,4] => 1011000 => 3
[7,2,1,5,3,6,4] => [2,1,3,1] => 1011001 => 4
[7,2,1,5,4,3,6] => [2,1,2,2] => 1011010 => 4
[7,2,1,5,4,6,3] => [2,1,3,1] => 1011001 => 4
[7,2,1,5,6,3,4] => [2,1,4] => 1011000 => 3
[7,2,1,5,6,4,3] => [2,1,3,1] => 1011001 => 4
[7,2,1,6,3,4,5] => [2,1,4] => 1011000 => 3
[7,2,1,6,3,5,4] => [2,1,3,1] => 1011001 => 4
[7,2,1,6,4,3,5] => [2,1,2,2] => 1011010 => 4
[7,2,1,6,4,5,3] => [2,1,3,1] => 1011001 => 4
[7,2,1,6,5,3,4] => [2,1,2,2] => 1011010 => 4
[7,2,1,6,5,4,3] => [2,1,2,1,1] => 1011011 => 5
[7,2,3,1,4,5,6] => [3,4] => 1001000 => 2
[7,2,3,1,4,6,5] => [3,3,1] => 1001001 => 3
[7,2,3,1,5,4,6] => [3,2,2] => 1001010 => 3
[7,2,3,1,5,6,4] => [3,3,1] => 1001001 => 3
[7,2,3,1,6,4,5] => [3,1,3] => 1001100 => 3
[7,2,3,1,6,5,4] => [3,1,2,1] => 1001101 => 4
[7,2,3,4,1,5,6] => [4,3] => 1000100 => 2
[7,2,3,4,1,6,5] => [4,2,1] => 1000101 => 3
[7,2,3,4,5,1,6] => [5,2] => 1000010 => 2
[7,2,3,4,5,6,1] => [6,1] => 1000001 => 2
[7,2,3,4,6,1,5] => [4,3] => 1000100 => 2
[7,2,3,4,6,5,1] => [4,2,1] => 1000101 => 3
[7,2,3,5,1,4,6] => [3,4] => 1001000 => 2
[7,2,3,5,1,6,4] => [3,3,1] => 1001001 => 3
[7,2,3,5,4,1,6] => [3,2,2] => 1001010 => 3
[7,2,3,5,4,6,1] => [3,3,1] => 1001001 => 3
[7,2,3,5,6,1,4] => [3,4] => 1001000 => 2
[7,2,3,5,6,4,1] => [3,3,1] => 1001001 => 3
[7,2,3,6,1,4,5] => [3,4] => 1001000 => 2
[7,2,3,6,1,5,4] => [3,3,1] => 1001001 => 3
[7,2,3,6,4,1,5] => [3,2,2] => 1001010 => 3
[7,2,3,6,4,5,1] => [3,3,1] => 1001001 => 3
[7,2,3,6,5,1,4] => [3,2,2] => 1001010 => 3
[7,2,3,6,5,4,1] => [3,2,1,1] => 1001011 => 4
[7,2,4,1,3,5,6] => [2,5] => 1010000 => 2
[7,2,4,1,3,6,5] => [2,4,1] => 1010001 => 3
[7,2,4,1,5,3,6] => [2,3,2] => 1010010 => 3
[7,2,4,1,5,6,3] => [2,4,1] => 1010001 => 3
[7,2,4,1,6,3,5] => [2,2,3] => 1010100 => 3
[7,2,4,1,6,5,3] => [2,2,2,1] => 1010101 => 4
[7,2,4,3,1,5,6] => [2,2,3] => 1010100 => 3
[7,2,4,3,1,6,5] => [2,2,2,1] => 1010101 => 4
[7,2,4,3,5,1,6] => [2,3,2] => 1010010 => 3
[7,2,4,3,5,6,1] => [2,4,1] => 1010001 => 3
[7,2,4,3,6,1,5] => [2,2,3] => 1010100 => 3
[7,2,4,3,6,5,1] => [2,2,2,1] => 1010101 => 4
[7,2,4,5,1,3,6] => [2,5] => 1010000 => 2
[7,2,4,5,1,6,3] => [2,4,1] => 1010001 => 3
[7,2,4,5,3,1,6] => [2,3,2] => 1010010 => 3
[7,2,4,5,3,6,1] => [2,4,1] => 1010001 => 3
[7,2,4,5,6,1,3] => [2,5] => 1010000 => 2
[7,2,4,5,6,3,1] => [2,4,1] => 1010001 => 3
[7,2,4,6,1,3,5] => [2,5] => 1010000 => 2
[7,2,4,6,1,5,3] => [2,4,1] => 1010001 => 3
[7,2,4,6,3,1,5] => [2,3,2] => 1010010 => 3
[7,2,4,6,3,5,1] => [2,4,1] => 1010001 => 3
[7,2,4,6,5,1,3] => [2,3,2] => 1010010 => 3
[7,2,4,6,5,3,1] => [2,3,1,1] => 1010011 => 4
[7,2,5,1,3,4,6] => [2,5] => 1010000 => 2
[7,2,5,1,3,6,4] => [2,4,1] => 1010001 => 3
[7,2,5,1,4,3,6] => [2,3,2] => 1010010 => 3
[7,2,5,1,4,6,3] => [2,4,1] => 1010001 => 3
[7,2,5,1,6,3,4] => [2,2,3] => 1010100 => 3
[7,2,5,1,6,4,3] => [2,2,2,1] => 1010101 => 4
[7,2,5,3,1,4,6] => [2,2,3] => 1010100 => 3
[7,2,5,3,1,6,4] => [2,2,2,1] => 1010101 => 4
[7,2,5,3,4,1,6] => [2,3,2] => 1010010 => 3
[7,2,5,3,4,6,1] => [2,4,1] => 1010001 => 3
[7,2,5,3,6,1,4] => [2,2,3] => 1010100 => 3
[7,2,5,3,6,4,1] => [2,2,2,1] => 1010101 => 4
[7,2,5,4,1,3,6] => [2,2,3] => 1010100 => 3
[7,2,5,4,1,6,3] => [2,2,2,1] => 1010101 => 4
[7,2,5,4,3,1,6] => [2,2,1,2] => 1010110 => 4
[7,2,5,4,3,6,1] => [2,2,2,1] => 1010101 => 4
[7,2,5,4,6,1,3] => [2,2,3] => 1010100 => 3
[7,2,5,4,6,3,1] => [2,2,2,1] => 1010101 => 4
[7,2,5,6,1,3,4] => [2,5] => 1010000 => 2
[7,2,5,6,1,4,3] => [2,4,1] => 1010001 => 3
[7,2,5,6,3,1,4] => [2,3,2] => 1010010 => 3
[7,2,5,6,3,4,1] => [2,4,1] => 1010001 => 3
[7,2,5,6,4,1,3] => [2,3,2] => 1010010 => 3
[7,2,5,6,4,3,1] => [2,3,1,1] => 1010011 => 4
[7,2,6,1,3,4,5] => [2,5] => 1010000 => 2
[7,2,6,1,3,5,4] => [2,4,1] => 1010001 => 3
[7,2,6,1,4,3,5] => [2,3,2] => 1010010 => 3
[7,2,6,1,4,5,3] => [2,4,1] => 1010001 => 3
[7,2,6,1,5,3,4] => [2,3,2] => 1010010 => 3
[7,2,6,1,5,4,3] => [2,3,1,1] => 1010011 => 4
[7,2,6,3,1,4,5] => [2,2,3] => 1010100 => 3
[7,2,6,3,1,5,4] => [2,2,2,1] => 1010101 => 4
[7,2,6,3,4,1,5] => [2,3,2] => 1010010 => 3
[7,2,6,3,4,5,1] => [2,4,1] => 1010001 => 3
[7,2,6,3,5,1,4] => [2,3,2] => 1010010 => 3
[7,2,6,3,5,4,1] => [2,3,1,1] => 1010011 => 4
[7,2,6,4,1,3,5] => [2,2,3] => 1010100 => 3
[7,2,6,4,1,5,3] => [2,2,2,1] => 1010101 => 4
[7,2,6,4,3,1,5] => [2,2,1,2] => 1010110 => 4
[7,2,6,4,3,5,1] => [2,2,2,1] => 1010101 => 4
[7,2,6,4,5,1,3] => [2,3,2] => 1010010 => 3
[7,2,6,4,5,3,1] => [2,3,1,1] => 1010011 => 4
[7,2,6,5,1,3,4] => [2,1,4] => 1011000 => 3
[7,2,6,5,1,4,3] => [2,1,3,1] => 1011001 => 4
[7,2,6,5,3,1,4] => [2,1,2,2] => 1011010 => 4
[7,2,6,5,3,4,1] => [2,1,3,1] => 1011001 => 4
[7,2,6,5,4,1,3] => [2,1,2,2] => 1011010 => 4
[7,2,6,5,4,3,1] => [2,1,2,1,1] => 1011011 => 5
[7,3,1,2,4,5,6] => [1,6] => 1100000 => 2
[7,3,1,2,4,6,5] => [1,5,1] => 1100001 => 3
[7,3,1,2,5,4,6] => [1,4,2] => 1100010 => 3
[7,3,1,2,5,6,4] => [1,5,1] => 1100001 => 3
[7,3,1,2,6,4,5] => [1,3,3] => 1100100 => 3
[7,3,1,2,6,5,4] => [1,3,2,1] => 1100101 => 4
[7,3,1,4,2,5,6] => [1,3,3] => 1100100 => 3
[7,3,1,4,2,6,5] => [1,3,2,1] => 1100101 => 4
[7,3,1,4,5,2,6] => [1,4,2] => 1100010 => 3
[7,3,1,4,5,6,2] => [1,5,1] => 1100001 => 3
[7,3,1,4,6,2,5] => [1,3,3] => 1100100 => 3
[7,3,1,4,6,5,2] => [1,3,2,1] => 1100101 => 4
[7,3,1,5,2,4,6] => [1,2,4] => 1101000 => 3
[7,3,1,5,2,6,4] => [1,2,3,1] => 1101001 => 4
[7,3,1,5,4,2,6] => [1,2,2,2] => 1101010 => 4
[7,3,1,5,4,6,2] => [1,2,3,1] => 1101001 => 4
[7,3,1,5,6,2,4] => [1,2,4] => 1101000 => 3
[7,3,1,5,6,4,2] => [1,2,3,1] => 1101001 => 4
[7,3,1,6,2,4,5] => [1,2,4] => 1101000 => 3
[7,3,1,6,2,5,4] => [1,2,3,1] => 1101001 => 4
[7,3,1,6,4,2,5] => [1,2,2,2] => 1101010 => 4
[7,3,1,6,4,5,2] => [1,2,3,1] => 1101001 => 4
[7,3,1,6,5,2,4] => [1,2,2,2] => 1101010 => 4
[7,3,1,6,5,4,2] => [1,2,2,1,1] => 1101011 => 5
[7,3,2,1,4,5,6] => [1,2,4] => 1101000 => 3
[7,3,2,1,4,6,5] => [1,2,3,1] => 1101001 => 4
[7,3,2,1,5,4,6] => [1,2,2,2] => 1101010 => 4
[7,3,2,1,5,6,4] => [1,2,3,1] => 1101001 => 4
[7,3,2,1,6,4,5] => [1,2,1,3] => 1101100 => 4
[7,3,2,1,6,5,4] => [1,2,1,2,1] => 1101101 => 5
[7,3,2,4,1,5,6] => [1,3,3] => 1100100 => 3
[7,3,2,4,1,6,5] => [1,3,2,1] => 1100101 => 4
[7,3,2,4,5,1,6] => [1,4,2] => 1100010 => 3
[7,3,2,4,5,6,1] => [1,5,1] => 1100001 => 3
[7,3,2,4,6,1,5] => [1,3,3] => 1100100 => 3
[7,3,2,4,6,5,1] => [1,3,2,1] => 1100101 => 4
[7,3,2,5,1,4,6] => [1,2,4] => 1101000 => 3
[7,3,2,5,1,6,4] => [1,2,3,1] => 1101001 => 4
[7,3,2,5,4,1,6] => [1,2,2,2] => 1101010 => 4
[7,3,2,5,4,6,1] => [1,2,3,1] => 1101001 => 4
[7,3,2,5,6,1,4] => [1,2,4] => 1101000 => 3
[7,3,2,5,6,4,1] => [1,2,3,1] => 1101001 => 4
[7,3,2,6,1,4,5] => [1,2,4] => 1101000 => 3
[7,3,2,6,1,5,4] => [1,2,3,1] => 1101001 => 4
[7,3,2,6,4,1,5] => [1,2,2,2] => 1101010 => 4
[7,3,2,6,4,5,1] => [1,2,3,1] => 1101001 => 4
[7,3,2,6,5,1,4] => [1,2,2,2] => 1101010 => 4
[7,3,2,6,5,4,1] => [1,2,2,1,1] => 1101011 => 5
[7,3,4,1,2,5,6] => [1,6] => 1100000 => 2
[7,3,4,1,2,6,5] => [1,5,1] => 1100001 => 3
[7,3,4,1,5,2,6] => [1,4,2] => 1100010 => 3
[7,3,4,1,5,6,2] => [1,5,1] => 1100001 => 3
[7,3,4,1,6,2,5] => [1,3,3] => 1100100 => 3
[7,3,4,1,6,5,2] => [1,3,2,1] => 1100101 => 4
[7,3,4,2,1,5,6] => [1,3,3] => 1100100 => 3
[7,3,4,2,1,6,5] => [1,3,2,1] => 1100101 => 4
[7,3,4,2,5,1,6] => [1,4,2] => 1100010 => 3
[7,3,4,2,5,6,1] => [1,5,1] => 1100001 => 3
[7,3,4,2,6,1,5] => [1,3,3] => 1100100 => 3
[7,3,4,2,6,5,1] => [1,3,2,1] => 1100101 => 4
[7,3,4,5,1,2,6] => [1,6] => 1100000 => 2
[7,3,4,5,1,6,2] => [1,5,1] => 1100001 => 3
[7,3,4,5,2,1,6] => [1,4,2] => 1100010 => 3
[7,3,4,5,2,6,1] => [1,5,1] => 1100001 => 3
[7,3,4,5,6,1,2] => [1,6] => 1100000 => 2
[7,3,4,5,6,2,1] => [1,5,1] => 1100001 => 3
[7,3,4,6,1,2,5] => [1,6] => 1100000 => 2
[7,3,4,6,1,5,2] => [1,5,1] => 1100001 => 3
[7,3,4,6,2,1,5] => [1,4,2] => 1100010 => 3
[7,3,4,6,2,5,1] => [1,5,1] => 1100001 => 3
[7,3,4,6,5,1,2] => [1,4,2] => 1100010 => 3
[7,3,4,6,5,2,1] => [1,4,1,1] => 1100011 => 4
[7,3,5,1,2,4,6] => [1,6] => 1100000 => 2
[7,3,5,1,2,6,4] => [1,5,1] => 1100001 => 3
[7,3,5,1,4,2,6] => [1,4,2] => 1100010 => 3
[7,3,5,1,4,6,2] => [1,5,1] => 1100001 => 3
[7,3,5,1,6,2,4] => [1,3,3] => 1100100 => 3
[7,3,5,1,6,4,2] => [1,3,2,1] => 1100101 => 4
[7,3,5,2,1,4,6] => [1,3,3] => 1100100 => 3
[7,3,5,2,1,6,4] => [1,3,2,1] => 1100101 => 4
[7,3,5,2,4,1,6] => [1,4,2] => 1100010 => 3
[7,3,5,2,4,6,1] => [1,5,1] => 1100001 => 3
[7,3,5,2,6,1,4] => [1,3,3] => 1100100 => 3
[7,3,5,2,6,4,1] => [1,3,2,1] => 1100101 => 4
[7,3,5,4,1,2,6] => [1,3,3] => 1100100 => 3
[7,3,5,4,1,6,2] => [1,3,2,1] => 1100101 => 4
[7,3,5,4,2,1,6] => [1,3,1,2] => 1100110 => 4
[7,3,5,4,2,6,1] => [1,3,2,1] => 1100101 => 4
[7,3,5,4,6,1,2] => [1,3,3] => 1100100 => 3
[7,3,5,4,6,2,1] => [1,3,2,1] => 1100101 => 4
[7,3,5,6,1,2,4] => [1,6] => 1100000 => 2
[7,3,5,6,1,4,2] => [1,5,1] => 1100001 => 3
[7,3,5,6,2,1,4] => [1,4,2] => 1100010 => 3
[7,3,5,6,2,4,1] => [1,5,1] => 1100001 => 3
[7,3,5,6,4,1,2] => [1,4,2] => 1100010 => 3
[7,3,5,6,4,2,1] => [1,4,1,1] => 1100011 => 4
[7,3,6,1,2,4,5] => [1,6] => 1100000 => 2
[7,3,6,1,2,5,4] => [1,5,1] => 1100001 => 3
[7,3,6,1,4,2,5] => [1,4,2] => 1100010 => 3
[7,3,6,1,4,5,2] => [1,5,1] => 1100001 => 3
[7,3,6,1,5,2,4] => [1,4,2] => 1100010 => 3
[7,3,6,1,5,4,2] => [1,4,1,1] => 1100011 => 4
[7,3,6,2,1,4,5] => [1,3,3] => 1100100 => 3
[7,3,6,2,1,5,4] => [1,3,2,1] => 1100101 => 4
[7,3,6,2,4,1,5] => [1,4,2] => 1100010 => 3
[7,3,6,2,4,5,1] => [1,5,1] => 1100001 => 3
[7,3,6,2,5,1,4] => [1,4,2] => 1100010 => 3
[7,3,6,2,5,4,1] => [1,4,1,1] => 1100011 => 4
[7,3,6,4,1,2,5] => [1,3,3] => 1100100 => 3
[7,3,6,4,1,5,2] => [1,3,2,1] => 1100101 => 4
[7,3,6,4,2,1,5] => [1,3,1,2] => 1100110 => 4
[7,3,6,4,2,5,1] => [1,3,2,1] => 1100101 => 4
[7,3,6,4,5,1,2] => [1,4,2] => 1100010 => 3
[7,3,6,4,5,2,1] => [1,4,1,1] => 1100011 => 4
[7,3,6,5,1,2,4] => [1,2,4] => 1101000 => 3
[7,3,6,5,1,4,2] => [1,2,3,1] => 1101001 => 4
[7,3,6,5,2,1,4] => [1,2,2,2] => 1101010 => 4
[7,3,6,5,2,4,1] => [1,2,3,1] => 1101001 => 4
[7,3,6,5,4,1,2] => [1,2,2,2] => 1101010 => 4
[7,3,6,5,4,2,1] => [1,2,2,1,1] => 1101011 => 5
[7,4,1,2,3,5,6] => [1,6] => 1100000 => 2
[7,4,1,2,3,6,5] => [1,5,1] => 1100001 => 3
[7,4,1,2,5,3,6] => [1,4,2] => 1100010 => 3
[7,4,1,2,5,6,3] => [1,5,1] => 1100001 => 3
[7,4,1,2,6,3,5] => [1,3,3] => 1100100 => 3
[7,4,1,2,6,5,3] => [1,3,2,1] => 1100101 => 4
[7,4,1,3,2,5,6] => [1,3,3] => 1100100 => 3
[7,4,1,3,2,6,5] => [1,3,2,1] => 1100101 => 4
[7,4,1,3,5,2,6] => [1,4,2] => 1100010 => 3
[7,4,1,3,5,6,2] => [1,5,1] => 1100001 => 3
[7,4,1,3,6,2,5] => [1,3,3] => 1100100 => 3
[7,4,1,3,6,5,2] => [1,3,2,1] => 1100101 => 4
[7,4,1,5,2,3,6] => [1,2,4] => 1101000 => 3
[7,4,1,5,2,6,3] => [1,2,3,1] => 1101001 => 4
[7,4,1,5,3,2,6] => [1,2,2,2] => 1101010 => 4
[7,4,1,5,3,6,2] => [1,2,3,1] => 1101001 => 4
[7,4,1,5,6,2,3] => [1,2,4] => 1101000 => 3
[7,4,1,5,6,3,2] => [1,2,3,1] => 1101001 => 4
[7,4,1,6,2,3,5] => [1,2,4] => 1101000 => 3
[7,4,1,6,2,5,3] => [1,2,3,1] => 1101001 => 4
[7,4,1,6,3,2,5] => [1,2,2,2] => 1101010 => 4
[7,4,1,6,3,5,2] => [1,2,3,1] => 1101001 => 4
[7,4,1,6,5,2,3] => [1,2,2,2] => 1101010 => 4
[7,4,1,6,5,3,2] => [1,2,2,1,1] => 1101011 => 5
[7,4,2,1,3,5,6] => [1,2,4] => 1101000 => 3
[7,4,2,1,3,6,5] => [1,2,3,1] => 1101001 => 4
[7,4,2,1,5,3,6] => [1,2,2,2] => 1101010 => 4
[7,4,2,1,5,6,3] => [1,2,3,1] => 1101001 => 4
[7,4,2,1,6,3,5] => [1,2,1,3] => 1101100 => 4
[7,4,2,1,6,5,3] => [1,2,1,2,1] => 1101101 => 5
[7,4,2,3,1,5,6] => [1,3,3] => 1100100 => 3
[7,4,2,3,1,6,5] => [1,3,2,1] => 1100101 => 4
[7,4,2,3,5,1,6] => [1,4,2] => 1100010 => 3
[7,4,2,3,5,6,1] => [1,5,1] => 1100001 => 3
[7,4,2,3,6,1,5] => [1,3,3] => 1100100 => 3
[7,4,2,3,6,5,1] => [1,3,2,1] => 1100101 => 4
[7,4,2,5,1,3,6] => [1,2,4] => 1101000 => 3
[7,4,2,5,1,6,3] => [1,2,3,1] => 1101001 => 4
[7,4,2,5,3,1,6] => [1,2,2,2] => 1101010 => 4
[7,4,2,5,3,6,1] => [1,2,3,1] => 1101001 => 4
[7,4,2,5,6,1,3] => [1,2,4] => 1101000 => 3
[7,4,2,5,6,3,1] => [1,2,3,1] => 1101001 => 4
[7,4,2,6,1,3,5] => [1,2,4] => 1101000 => 3
[7,4,2,6,1,5,3] => [1,2,3,1] => 1101001 => 4
[7,4,2,6,3,1,5] => [1,2,2,2] => 1101010 => 4
[7,4,2,6,3,5,1] => [1,2,3,1] => 1101001 => 4
[7,4,2,6,5,1,3] => [1,2,2,2] => 1101010 => 4
[7,4,2,6,5,3,1] => [1,2,2,1,1] => 1101011 => 5
[7,4,3,1,2,5,6] => [1,2,4] => 1101000 => 3
[7,4,3,1,2,6,5] => [1,2,3,1] => 1101001 => 4
[7,4,3,1,5,2,6] => [1,2,2,2] => 1101010 => 4
[7,4,3,1,5,6,2] => [1,2,3,1] => 1101001 => 4
[7,4,3,1,6,2,5] => [1,2,1,3] => 1101100 => 4
[7,4,3,1,6,5,2] => [1,2,1,2,1] => 1101101 => 5
[7,4,3,2,1,5,6] => [1,2,1,3] => 1101100 => 4
[7,4,3,2,1,6,5] => [1,2,1,2,1] => 1101101 => 5
[7,4,3,2,5,1,6] => [1,2,2,2] => 1101010 => 4
[7,4,3,2,5,6,1] => [1,2,3,1] => 1101001 => 4
[7,4,3,2,6,1,5] => [1,2,1,3] => 1101100 => 4
[7,4,3,2,6,5,1] => [1,2,1,2,1] => 1101101 => 5
[7,4,3,5,1,2,6] => [1,2,4] => 1101000 => 3
[7,4,3,5,1,6,2] => [1,2,3,1] => 1101001 => 4
[7,4,3,5,2,1,6] => [1,2,2,2] => 1101010 => 4
[7,4,3,5,2,6,1] => [1,2,3,1] => 1101001 => 4
[7,4,3,5,6,1,2] => [1,2,4] => 1101000 => 3
[7,4,3,5,6,2,1] => [1,2,3,1] => 1101001 => 4
[7,4,3,6,1,2,5] => [1,2,4] => 1101000 => 3
[7,4,3,6,1,5,2] => [1,2,3,1] => 1101001 => 4
[7,4,3,6,2,1,5] => [1,2,2,2] => 1101010 => 4
[7,4,3,6,2,5,1] => [1,2,3,1] => 1101001 => 4
[7,4,3,6,5,1,2] => [1,2,2,2] => 1101010 => 4
[7,4,3,6,5,2,1] => [1,2,2,1,1] => 1101011 => 5
[7,4,5,1,2,3,6] => [1,6] => 1100000 => 2
[7,4,5,1,2,6,3] => [1,5,1] => 1100001 => 3
[7,4,5,1,3,2,6] => [1,4,2] => 1100010 => 3
[7,4,5,1,3,6,2] => [1,5,1] => 1100001 => 3
[7,4,5,1,6,2,3] => [1,3,3] => 1100100 => 3
[7,4,5,1,6,3,2] => [1,3,2,1] => 1100101 => 4
[7,4,5,2,1,3,6] => [1,3,3] => 1100100 => 3
[7,4,5,2,1,6,3] => [1,3,2,1] => 1100101 => 4
[7,4,5,2,3,1,6] => [1,4,2] => 1100010 => 3
[7,4,5,2,3,6,1] => [1,5,1] => 1100001 => 3
[7,4,5,2,6,1,3] => [1,3,3] => 1100100 => 3
[7,4,5,2,6,3,1] => [1,3,2,1] => 1100101 => 4
[7,4,5,3,1,2,6] => [1,3,3] => 1100100 => 3
[7,4,5,3,1,6,2] => [1,3,2,1] => 1100101 => 4
[7,4,5,3,2,1,6] => [1,3,1,2] => 1100110 => 4
[7,4,5,3,2,6,1] => [1,3,2,1] => 1100101 => 4
[7,4,5,3,6,1,2] => [1,3,3] => 1100100 => 3
[7,4,5,3,6,2,1] => [1,3,2,1] => 1100101 => 4
[7,4,5,6,1,2,3] => [1,6] => 1100000 => 2
[7,4,5,6,1,3,2] => [1,5,1] => 1100001 => 3
[7,4,5,6,2,1,3] => [1,4,2] => 1100010 => 3
[7,4,5,6,2,3,1] => [1,5,1] => 1100001 => 3
[7,4,5,6,3,1,2] => [1,4,2] => 1100010 => 3
[7,4,5,6,3,2,1] => [1,4,1,1] => 1100011 => 4
[7,4,6,1,2,3,5] => [1,6] => 1100000 => 2
[7,4,6,1,2,5,3] => [1,5,1] => 1100001 => 3
[7,4,6,1,3,2,5] => [1,4,2] => 1100010 => 3
[7,4,6,1,3,5,2] => [1,5,1] => 1100001 => 3
[7,4,6,1,5,2,3] => [1,4,2] => 1100010 => 3
[7,4,6,1,5,3,2] => [1,4,1,1] => 1100011 => 4
[7,4,6,2,1,3,5] => [1,3,3] => 1100100 => 3
[7,4,6,2,1,5,3] => [1,3,2,1] => 1100101 => 4
[7,4,6,2,3,1,5] => [1,4,2] => 1100010 => 3
[7,4,6,2,3,5,1] => [1,5,1] => 1100001 => 3
[7,4,6,2,5,1,3] => [1,4,2] => 1100010 => 3
[7,4,6,2,5,3,1] => [1,4,1,1] => 1100011 => 4
[7,4,6,3,1,2,5] => [1,3,3] => 1100100 => 3
[7,4,6,3,1,5,2] => [1,3,2,1] => 1100101 => 4
[7,4,6,3,2,1,5] => [1,3,1,2] => 1100110 => 4
[7,4,6,3,2,5,1] => [1,3,2,1] => 1100101 => 4
[7,4,6,3,5,1,2] => [1,4,2] => 1100010 => 3
[7,4,6,3,5,2,1] => [1,4,1,1] => 1100011 => 4
[7,4,6,5,1,2,3] => [1,2,4] => 1101000 => 3
[7,4,6,5,1,3,2] => [1,2,3,1] => 1101001 => 4
[7,4,6,5,2,1,3] => [1,2,2,2] => 1101010 => 4
[7,4,6,5,2,3,1] => [1,2,3,1] => 1101001 => 4
[7,4,6,5,3,1,2] => [1,2,2,2] => 1101010 => 4
[7,4,6,5,3,2,1] => [1,2,2,1,1] => 1101011 => 5
[7,5,1,2,3,4,6] => [1,6] => 1100000 => 2
[7,5,1,2,3,6,4] => [1,5,1] => 1100001 => 3
[7,5,1,2,4,3,6] => [1,4,2] => 1100010 => 3
[7,5,1,2,4,6,3] => [1,5,1] => 1100001 => 3
[7,5,1,2,6,3,4] => [1,3,3] => 1100100 => 3
[7,5,1,2,6,4,3] => [1,3,2,1] => 1100101 => 4
[7,5,1,3,2,4,6] => [1,3,3] => 1100100 => 3
[7,5,1,3,2,6,4] => [1,3,2,1] => 1100101 => 4
[7,5,1,3,4,2,6] => [1,4,2] => 1100010 => 3
[7,5,1,3,4,6,2] => [1,5,1] => 1100001 => 3
[7,5,1,3,6,2,4] => [1,3,3] => 1100100 => 3
[7,5,1,3,6,4,2] => [1,3,2,1] => 1100101 => 4
[7,5,1,4,2,3,6] => [1,3,3] => 1100100 => 3
[7,5,1,4,2,6,3] => [1,3,2,1] => 1100101 => 4
[7,5,1,4,3,2,6] => [1,3,1,2] => 1100110 => 4
[7,5,1,4,3,6,2] => [1,3,2,1] => 1100101 => 4
[7,5,1,4,6,2,3] => [1,3,3] => 1100100 => 3
[7,5,1,4,6,3,2] => [1,3,2,1] => 1100101 => 4
[7,5,1,6,2,3,4] => [1,2,4] => 1101000 => 3
[7,5,1,6,2,4,3] => [1,2,3,1] => 1101001 => 4
[7,5,1,6,3,2,4] => [1,2,2,2] => 1101010 => 4
[7,5,1,6,3,4,2] => [1,2,3,1] => 1101001 => 4
[7,5,1,6,4,2,3] => [1,2,2,2] => 1101010 => 4
[7,5,1,6,4,3,2] => [1,2,2,1,1] => 1101011 => 5
[7,5,2,1,3,4,6] => [1,2,4] => 1101000 => 3
[7,5,2,1,3,6,4] => [1,2,3,1] => 1101001 => 4
[7,5,2,1,4,3,6] => [1,2,2,2] => 1101010 => 4
[7,5,2,1,4,6,3] => [1,2,3,1] => 1101001 => 4
[7,5,2,1,6,3,4] => [1,2,1,3] => 1101100 => 4
[7,5,2,1,6,4,3] => [1,2,1,2,1] => 1101101 => 5
[7,5,2,3,1,4,6] => [1,3,3] => 1100100 => 3
[7,5,2,3,1,6,4] => [1,3,2,1] => 1100101 => 4
[7,5,2,3,4,1,6] => [1,4,2] => 1100010 => 3
[7,5,2,3,4,6,1] => [1,5,1] => 1100001 => 3
[7,5,2,3,6,1,4] => [1,3,3] => 1100100 => 3
[7,5,2,3,6,4,1] => [1,3,2,1] => 1100101 => 4
[7,5,2,4,1,3,6] => [1,3,3] => 1100100 => 3
[7,5,2,4,1,6,3] => [1,3,2,1] => 1100101 => 4
[7,5,2,4,3,1,6] => [1,3,1,2] => 1100110 => 4
[7,5,2,4,3,6,1] => [1,3,2,1] => 1100101 => 4
[7,5,2,4,6,1,3] => [1,3,3] => 1100100 => 3
[7,5,2,4,6,3,1] => [1,3,2,1] => 1100101 => 4
[7,5,2,6,1,3,4] => [1,2,4] => 1101000 => 3
[7,5,2,6,1,4,3] => [1,2,3,1] => 1101001 => 4
[7,5,2,6,3,1,4] => [1,2,2,2] => 1101010 => 4
[7,5,2,6,3,4,1] => [1,2,3,1] => 1101001 => 4
[7,5,2,6,4,1,3] => [1,2,2,2] => 1101010 => 4
[7,5,2,6,4,3,1] => [1,2,2,1,1] => 1101011 => 5
[7,5,3,1,2,4,6] => [1,2,4] => 1101000 => 3
[7,5,3,1,2,6,4] => [1,2,3,1] => 1101001 => 4
[7,5,3,1,4,2,6] => [1,2,2,2] => 1101010 => 4
[7,5,3,1,4,6,2] => [1,2,3,1] => 1101001 => 4
[7,5,3,1,6,2,4] => [1,2,1,3] => 1101100 => 4
[7,5,3,1,6,4,2] => [1,2,1,2,1] => 1101101 => 5
[7,5,3,2,1,4,6] => [1,2,1,3] => 1101100 => 4
[7,5,3,2,1,6,4] => [1,2,1,2,1] => 1101101 => 5
[7,5,3,2,4,1,6] => [1,2,2,2] => 1101010 => 4
[7,5,3,2,4,6,1] => [1,2,3,1] => 1101001 => 4
[7,5,3,2,6,1,4] => [1,2,1,3] => 1101100 => 4
[7,5,3,2,6,4,1] => [1,2,1,2,1] => 1101101 => 5
[7,5,3,4,1,2,6] => [1,3,3] => 1100100 => 3
[7,5,3,4,1,6,2] => [1,3,2,1] => 1100101 => 4
[7,5,3,4,2,1,6] => [1,3,1,2] => 1100110 => 4
[7,5,3,4,2,6,1] => [1,3,2,1] => 1100101 => 4
[7,5,3,4,6,1,2] => [1,3,3] => 1100100 => 3
[7,5,3,4,6,2,1] => [1,3,2,1] => 1100101 => 4
[7,5,3,6,1,2,4] => [1,2,4] => 1101000 => 3
[7,5,3,6,1,4,2] => [1,2,3,1] => 1101001 => 4
[7,5,3,6,2,1,4] => [1,2,2,2] => 1101010 => 4
[7,5,3,6,2,4,1] => [1,2,3,1] => 1101001 => 4
[7,5,3,6,4,1,2] => [1,2,2,2] => 1101010 => 4
[7,5,3,6,4,2,1] => [1,2,2,1,1] => 1101011 => 5
[7,5,4,1,2,3,6] => [1,1,5] => 1110000 => 3
[7,5,4,1,2,6,3] => [1,1,4,1] => 1110001 => 4
[7,5,4,1,3,2,6] => [1,1,3,2] => 1110010 => 4
[7,5,4,1,3,6,2] => [1,1,4,1] => 1110001 => 4
[7,5,4,1,6,2,3] => [1,1,2,3] => 1110100 => 4
[7,5,4,1,6,3,2] => [1,1,2,2,1] => 1110101 => 5
[7,5,4,2,1,3,6] => [1,1,2,3] => 1110100 => 4
[7,5,4,2,1,6,3] => [1,1,2,2,1] => 1110101 => 5
[7,5,4,2,3,1,6] => [1,1,3,2] => 1110010 => 4
[7,5,4,2,3,6,1] => [1,1,4,1] => 1110001 => 4
[7,5,4,2,6,1,3] => [1,1,2,3] => 1110100 => 4
[7,5,4,2,6,3,1] => [1,1,2,2,1] => 1110101 => 5
[7,5,4,3,1,2,6] => [1,1,2,3] => 1110100 => 4
[7,5,4,3,1,6,2] => [1,1,2,2,1] => 1110101 => 5
[7,5,4,3,2,1,6] => [1,1,2,1,2] => 1110110 => 5
[7,5,4,3,2,6,1] => [1,1,2,2,1] => 1110101 => 5
[7,5,4,3,6,1,2] => [1,1,2,3] => 1110100 => 4
[7,5,4,3,6,2,1] => [1,1,2,2,1] => 1110101 => 5
[7,5,4,6,1,2,3] => [1,1,5] => 1110000 => 3
[7,5,4,6,1,3,2] => [1,1,4,1] => 1110001 => 4
[7,5,4,6,2,1,3] => [1,1,3,2] => 1110010 => 4
[7,5,4,6,2,3,1] => [1,1,4,1] => 1110001 => 4
[7,5,4,6,3,1,2] => [1,1,3,2] => 1110010 => 4
[7,5,4,6,3,2,1] => [1,1,3,1,1] => 1110011 => 5
[7,5,6,1,2,3,4] => [1,6] => 1100000 => 2
[7,5,6,1,2,4,3] => [1,5,1] => 1100001 => 3
[7,5,6,1,3,2,4] => [1,4,2] => 1100010 => 3
[7,5,6,1,3,4,2] => [1,5,1] => 1100001 => 3
[7,5,6,1,4,2,3] => [1,4,2] => 1100010 => 3
[7,5,6,1,4,3,2] => [1,4,1,1] => 1100011 => 4
[7,5,6,2,1,3,4] => [1,3,3] => 1100100 => 3
[7,5,6,2,1,4,3] => [1,3,2,1] => 1100101 => 4
[7,5,6,2,3,1,4] => [1,4,2] => 1100010 => 3
[7,5,6,2,3,4,1] => [1,5,1] => 1100001 => 3
[7,5,6,2,4,1,3] => [1,4,2] => 1100010 => 3
[7,5,6,2,4,3,1] => [1,4,1,1] => 1100011 => 4
[7,5,6,3,1,2,4] => [1,3,3] => 1100100 => 3
[7,5,6,3,1,4,2] => [1,3,2,1] => 1100101 => 4
[7,5,6,3,2,1,4] => [1,3,1,2] => 1100110 => 4
[7,5,6,3,2,4,1] => [1,3,2,1] => 1100101 => 4
[7,5,6,3,4,1,2] => [1,4,2] => 1100010 => 3
[7,5,6,3,4,2,1] => [1,4,1,1] => 1100011 => 4
[7,5,6,4,1,2,3] => [1,3,3] => 1100100 => 3
[7,5,6,4,1,3,2] => [1,3,2,1] => 1100101 => 4
[7,5,6,4,2,1,3] => [1,3,1,2] => 1100110 => 4
[7,5,6,4,2,3,1] => [1,3,2,1] => 1100101 => 4
[7,5,6,4,3,1,2] => [1,3,1,2] => 1100110 => 4
[7,5,6,4,3,2,1] => [1,3,1,1,1] => 1100111 => 5
[7,6,1,2,3,4,5] => [1,6] => 1100000 => 2
[7,6,1,2,3,5,4] => [1,5,1] => 1100001 => 3
[7,6,1,2,4,3,5] => [1,4,2] => 1100010 => 3
[7,6,1,2,4,5,3] => [1,5,1] => 1100001 => 3
[7,6,1,2,5,3,4] => [1,4,2] => 1100010 => 3
[7,6,1,2,5,4,3] => [1,4,1,1] => 1100011 => 4
[7,6,1,3,2,4,5] => [1,3,3] => 1100100 => 3
[7,6,1,3,2,5,4] => [1,3,2,1] => 1100101 => 4
[7,6,1,3,4,2,5] => [1,4,2] => 1100010 => 3
[7,6,1,3,4,5,2] => [1,5,1] => 1100001 => 3
[7,6,1,3,5,2,4] => [1,4,2] => 1100010 => 3
[7,6,1,3,5,4,2] => [1,4,1,1] => 1100011 => 4
[7,6,1,4,2,3,5] => [1,3,3] => 1100100 => 3
[7,6,1,4,2,5,3] => [1,3,2,1] => 1100101 => 4
[7,6,1,4,3,2,5] => [1,3,1,2] => 1100110 => 4
[7,6,1,4,3,5,2] => [1,3,2,1] => 1100101 => 4
[7,6,1,4,5,2,3] => [1,4,2] => 1100010 => 3
[7,6,1,4,5,3,2] => [1,4,1,1] => 1100011 => 4
[7,6,1,5,2,3,4] => [1,2,4] => 1101000 => 3
[7,6,1,5,2,4,3] => [1,2,3,1] => 1101001 => 4
[7,6,1,5,3,2,4] => [1,2,2,2] => 1101010 => 4
[7,6,1,5,3,4,2] => [1,2,3,1] => 1101001 => 4
[7,6,1,5,4,2,3] => [1,2,2,2] => 1101010 => 4
[7,6,1,5,4,3,2] => [1,2,2,1,1] => 1101011 => 5
[7,6,2,1,3,4,5] => [1,2,4] => 1101000 => 3
[7,6,2,1,3,5,4] => [1,2,3,1] => 1101001 => 4
[7,6,2,1,4,3,5] => [1,2,2,2] => 1101010 => 4
[7,6,2,1,4,5,3] => [1,2,3,1] => 1101001 => 4
[7,6,2,1,5,3,4] => [1,2,2,2] => 1101010 => 4
[7,6,2,1,5,4,3] => [1,2,2,1,1] => 1101011 => 5
[7,6,2,3,1,4,5] => [1,3,3] => 1100100 => 3
[7,6,2,3,1,5,4] => [1,3,2,1] => 1100101 => 4
[7,6,2,3,4,1,5] => [1,4,2] => 1100010 => 3
[7,6,2,3,4,5,1] => [1,5,1] => 1100001 => 3
[7,6,2,3,5,1,4] => [1,4,2] => 1100010 => 3
[7,6,2,3,5,4,1] => [1,4,1,1] => 1100011 => 4
[7,6,2,4,1,3,5] => [1,3,3] => 1100100 => 3
[7,6,2,4,1,5,3] => [1,3,2,1] => 1100101 => 4
[7,6,2,4,3,1,5] => [1,3,1,2] => 1100110 => 4
[7,6,2,4,3,5,1] => [1,3,2,1] => 1100101 => 4
[7,6,2,4,5,1,3] => [1,4,2] => 1100010 => 3
[7,6,2,4,5,3,1] => [1,4,1,1] => 1100011 => 4
[7,6,2,5,1,3,4] => [1,2,4] => 1101000 => 3
[7,6,2,5,1,4,3] => [1,2,3,1] => 1101001 => 4
[7,6,2,5,3,1,4] => [1,2,2,2] => 1101010 => 4
[7,6,2,5,3,4,1] => [1,2,3,1] => 1101001 => 4
[7,6,2,5,4,1,3] => [1,2,2,2] => 1101010 => 4
[7,6,2,5,4,3,1] => [1,2,2,1,1] => 1101011 => 5
[7,6,3,1,2,4,5] => [1,2,4] => 1101000 => 3
[7,6,3,1,2,5,4] => [1,2,3,1] => 1101001 => 4
[7,6,3,1,4,2,5] => [1,2,2,2] => 1101010 => 4
[7,6,3,1,4,5,2] => [1,2,3,1] => 1101001 => 4
[7,6,3,1,5,2,4] => [1,2,2,2] => 1101010 => 4
[7,6,3,1,5,4,2] => [1,2,2,1,1] => 1101011 => 5
[7,6,3,2,1,4,5] => [1,2,1,3] => 1101100 => 4
[7,6,3,2,1,5,4] => [1,2,1,2,1] => 1101101 => 5
[7,6,3,2,4,1,5] => [1,2,2,2] => 1101010 => 4
[7,6,3,2,4,5,1] => [1,2,3,1] => 1101001 => 4
[7,6,3,2,5,1,4] => [1,2,2,2] => 1101010 => 4
[7,6,3,2,5,4,1] => [1,2,2,1,1] => 1101011 => 5
[7,6,3,4,1,2,5] => [1,3,3] => 1100100 => 3
[7,6,3,4,1,5,2] => [1,3,2,1] => 1100101 => 4
[7,6,3,4,2,1,5] => [1,3,1,2] => 1100110 => 4
[7,6,3,4,2,5,1] => [1,3,2,1] => 1100101 => 4
[7,6,3,4,5,1,2] => [1,4,2] => 1100010 => 3
[7,6,3,4,5,2,1] => [1,4,1,1] => 1100011 => 4
[7,6,3,5,1,2,4] => [1,2,4] => 1101000 => 3
[7,6,3,5,1,4,2] => [1,2,3,1] => 1101001 => 4
[7,6,3,5,2,1,4] => [1,2,2,2] => 1101010 => 4
[7,6,3,5,2,4,1] => [1,2,3,1] => 1101001 => 4
[7,6,3,5,4,1,2] => [1,2,2,2] => 1101010 => 4
[7,6,3,5,4,2,1] => [1,2,2,1,1] => 1101011 => 5
[7,6,4,1,2,3,5] => [1,1,5] => 1110000 => 3
[7,6,4,1,2,5,3] => [1,1,4,1] => 1110001 => 4
[7,6,4,1,3,2,5] => [1,1,3,2] => 1110010 => 4
[7,6,4,1,3,5,2] => [1,1,4,1] => 1110001 => 4
[7,6,4,1,5,2,3] => [1,1,3,2] => 1110010 => 4
[7,6,4,1,5,3,2] => [1,1,3,1,1] => 1110011 => 5
[7,6,4,2,1,3,5] => [1,1,2,3] => 1110100 => 4
[7,6,4,2,1,5,3] => [1,1,2,2,1] => 1110101 => 5
[7,6,4,2,3,1,5] => [1,1,3,2] => 1110010 => 4
[7,6,4,2,3,5,1] => [1,1,4,1] => 1110001 => 4
[7,6,4,2,5,1,3] => [1,1,3,2] => 1110010 => 4
[7,6,4,2,5,3,1] => [1,1,3,1,1] => 1110011 => 5
[7,6,4,3,1,2,5] => [1,1,2,3] => 1110100 => 4
[7,6,4,3,1,5,2] => [1,1,2,2,1] => 1110101 => 5
[7,6,4,3,2,1,5] => [1,1,2,1,2] => 1110110 => 5
[7,6,4,3,2,5,1] => [1,1,2,2,1] => 1110101 => 5
[7,6,4,3,5,1,2] => [1,1,3,2] => 1110010 => 4
[7,6,4,3,5,2,1] => [1,1,3,1,1] => 1110011 => 5
[7,6,4,5,1,2,3] => [1,1,5] => 1110000 => 3
[7,6,4,5,1,3,2] => [1,1,4,1] => 1110001 => 4
[7,6,4,5,2,1,3] => [1,1,3,2] => 1110010 => 4
[7,6,4,5,2,3,1] => [1,1,4,1] => 1110001 => 4
[7,6,4,5,3,1,2] => [1,1,3,2] => 1110010 => 4
[7,6,4,5,3,2,1] => [1,1,3,1,1] => 1110011 => 5
[7,6,5,1,2,3,4] => [1,1,5] => 1110000 => 3
[7,6,5,1,2,4,3] => [1,1,4,1] => 1110001 => 4
[7,6,5,1,3,2,4] => [1,1,3,2] => 1110010 => 4
[7,6,5,1,3,4,2] => [1,1,4,1] => 1110001 => 4
[7,6,5,1,4,2,3] => [1,1,3,2] => 1110010 => 4
[7,6,5,1,4,3,2] => [1,1,3,1,1] => 1110011 => 5
[7,6,5,2,1,3,4] => [1,1,2,3] => 1110100 => 4
[7,6,5,2,1,4,3] => [1,1,2,2,1] => 1110101 => 5
[7,6,5,2,3,1,4] => [1,1,3,2] => 1110010 => 4
[7,6,5,2,3,4,1] => [1,1,4,1] => 1110001 => 4
[7,6,5,2,4,1,3] => [1,1,3,2] => 1110010 => 4
[7,6,5,2,4,3,1] => [1,1,3,1,1] => 1110011 => 5
[7,6,5,3,1,2,4] => [1,1,2,3] => 1110100 => 4
[7,6,5,3,1,4,2] => [1,1,2,2,1] => 1110101 => 5
[7,6,5,3,2,1,4] => [1,1,2,1,2] => 1110110 => 5
[7,6,5,3,2,4,1] => [1,1,2,2,1] => 1110101 => 5
[7,6,5,3,4,1,2] => [1,1,3,2] => 1110010 => 4
[7,6,5,3,4,2,1] => [1,1,3,1,1] => 1110011 => 5
[7,6,5,4,1,2,3] => [1,1,2,3] => 1110100 => 4
[7,6,5,4,1,3,2] => [1,1,2,2,1] => 1110101 => 5
[7,6,5,4,2,1,3] => [1,1,2,1,2] => 1110110 => 5
[7,6,5,4,2,3,1] => [1,1,2,2,1] => 1110101 => 5
[7,6,5,4,3,1,2] => [1,1,2,1,2] => 1110110 => 5
[7,6,5,4,3,2,1] => [1,1,2,1,1,1] => 1110111 => 6
[8,7,6,5,4,3,2,1] => [1,1,1,2,1,1,1] => 11110111 => 7
[7,8,6,5,4,3,2,1] => [2,1,2,1,1,1] => 10110111 => 6
[7,6,8,5,4,3,2,1] => [1,2,2,1,1,1] => 11010111 => 6
[6,7,8,5,4,3,2,1] => [3,2,1,1,1] => 10010111 => 5
[7,8,5,6,4,3,2,1] => [2,3,1,1,1] => 10100111 => 5
[7,6,5,8,4,3,2,1] => [1,1,3,1,1,1] => 11100111 => 6
[7,5,6,8,4,3,2,1] => [1,4,1,1,1] => 11000111 => 5
[6,5,7,8,4,3,2,1] => [1,4,1,1,1] => 11000111 => 5
[5,6,7,8,4,3,2,1] => [5,1,1,1] => 10000111 => 4
[8,7,6,4,5,3,2,1] => [1,1,3,1,1,1] => 11100111 => 6
[7,8,6,4,5,3,2,1] => [2,3,1,1,1] => 10100111 => 5
[8,6,7,4,5,3,2,1] => [1,4,1,1,1] => 11000111 => 5
[7,6,5,4,8,3,2,1] => [1,1,2,2,1,1] => 11101011 => 6
[6,5,7,4,8,3,2,1] => [1,3,2,1,1] => 11001011 => 5
[7,6,4,5,8,3,2,1] => [1,1,4,1,1] => 11100011 => 5
[7,5,4,6,8,3,2,1] => [1,1,4,1,1] => 11100011 => 5
[7,4,5,6,8,3,2,1] => [1,5,1,1] => 11000011 => 4
[4,5,6,7,8,3,2,1] => [6,1,1] => 10000011 => 3
[8,7,6,5,3,4,2,1] => [1,1,1,3,1,1] => 11110011 => 6
[7,8,6,5,3,4,2,1] => [2,1,3,1,1] => 10110011 => 5
[8,6,7,5,3,4,2,1] => [1,2,3,1,1] => 11010011 => 5
[8,7,5,6,3,4,2,1] => [1,1,4,1,1] => 11100011 => 5
[5,6,7,8,3,4,2,1] => [6,1,1] => 10000011 => 3
[6,7,8,3,4,5,2,1] => [6,1,1] => 10000011 => 3
[8,7,5,4,3,6,2,1] => [1,1,2,2,1,1] => 11101011 => 6
[7,6,5,4,3,8,2,1] => [1,1,2,1,2,1] => 11101101 => 6
[6,4,5,7,3,8,2,1] => [1,4,2,1] => 11000101 => 4
[5,4,6,7,3,8,2,1] => [1,4,2,1] => 11000101 => 4
[4,5,6,7,3,8,2,1] => [5,2,1] => 10000101 => 3
[7,6,5,3,4,8,2,1] => [1,1,3,2,1] => 11100101 => 5
[7,6,4,3,5,8,2,1] => [1,1,3,2,1] => 11100101 => 5
[7,6,3,4,5,8,2,1] => [1,4,2,1] => 11000101 => 4
[6,3,4,5,7,8,2,1] => [1,6,1] => 11000001 => 3
[4,3,5,6,7,8,2,1] => [1,6,1] => 11000001 => 3
[8,7,6,5,4,2,3,1] => [1,1,1,2,2,1] => 11110101 => 6
[7,8,6,5,4,2,3,1] => [2,1,2,2,1] => 10110101 => 5
[8,6,7,5,4,2,3,1] => [1,2,2,2,1] => 11010101 => 5
[8,7,5,6,4,2,3,1] => [1,1,3,2,1] => 11100101 => 5
[5,6,7,8,4,2,3,1] => [5,2,1] => 10000101 => 3
[8,7,6,4,5,2,3,1] => [1,1,3,2,1] => 11100101 => 5
[8,6,7,4,5,2,3,1] => [1,4,2,1] => 11000101 => 4
[4,5,6,7,8,2,3,1] => [7,1] => 10000001 => 2
[8,7,6,5,3,2,4,1] => [1,1,1,2,2,1] => 11110101 => 6
[8,6,5,7,3,2,4,1] => [1,1,3,2,1] => 11100101 => 5
[5,6,7,8,3,2,4,1] => [5,2,1] => 10000101 => 3
[8,7,6,5,2,3,4,1] => [1,1,1,4,1] => 11110001 => 5
[6,7,8,5,2,3,4,1] => [3,4,1] => 10010001 => 3
[8,5,6,7,2,3,4,1] => [1,6,1] => 11000001 => 3
[5,6,7,8,2,3,4,1] => [7,1] => 10000001 => 2
[7,8,3,2,4,5,6,1] => [3,4,1] => 10010001 => 3
[7,6,5,4,3,2,8,1] => [1,1,2,1,1,2] => 11101110 => 6
[6,7,5,4,3,2,8,1] => [2,2,1,1,2] => 10101110 => 5
[6,5,7,4,3,2,8,1] => [1,3,1,1,2] => 11001110 => 5
[6,4,5,7,3,2,8,1] => [1,4,1,2] => 11000110 => 4
[4,5,6,7,3,2,8,1] => [5,1,2] => 10000110 => 3
[6,5,4,3,7,2,8,1] => [1,1,2,2,2] => 11101010 => 5
[5,4,6,3,7,2,8,1] => [1,3,2,2] => 11001010 => 4
[6,5,3,4,7,2,8,1] => [1,3,2,2] => 11001010 => 4
[7,6,5,4,2,3,8,1] => [1,1,2,2,2] => 11101010 => 5
[6,7,4,5,2,3,8,1] => [2,4,2] => 10100010 => 3
[6,4,5,7,2,3,8,1] => [1,5,2] => 11000010 => 3
[4,5,6,7,2,3,8,1] => [6,2] => 10000010 => 2
[7,6,5,3,2,4,8,1] => [1,1,2,2,2] => 11101010 => 5
[7,6,5,2,3,4,8,1] => [1,1,4,2] => 11100010 => 4
[6,7,2,3,4,5,8,1] => [6,2] => 10000010 => 2
[5,4,3,2,6,7,8,1] => [1,2,1,4] => 11011000 => 4
[3,4,5,2,6,7,8,1] => [4,4] => 10001000 => 2
[5,2,3,4,6,7,8,1] => [4,4] => 10001000 => 2
[4,3,2,5,6,7,8,1] => [1,2,5] => 11010000 => 3
[3,4,2,5,6,7,8,1] => [3,5] => 10010000 => 2
[4,2,3,5,6,7,8,1] => [3,5] => 10010000 => 2
[3,2,4,5,6,7,8,1] => [2,6] => 10100000 => 2
[2,3,4,5,6,7,8,1] => [8] => 10000000 => 1
[8,7,6,5,4,3,1,2] => [1,1,1,2,1,2] => 11110110 => 6
[7,8,6,5,4,3,1,2] => [2,1,2,1,2] => 10110110 => 5
[8,6,7,5,4,3,1,2] => [1,2,2,1,2] => 11010110 => 5
[8,7,5,6,4,3,1,2] => [1,1,3,1,2] => 11100110 => 5
[6,5,7,8,4,3,1,2] => [1,4,1,2] => 11000110 => 4
[5,6,7,8,4,3,1,2] => [5,1,2] => 10000110 => 3
[8,7,6,4,5,3,1,2] => [1,1,3,1,2] => 11100110 => 5
[7,8,6,4,5,3,1,2] => [2,3,1,2] => 10100110 => 4
[4,5,6,7,8,3,1,2] => [6,2] => 10000010 => 2
[8,7,6,5,3,4,1,2] => [1,1,1,3,2] => 11110010 => 5
[8,7,5,6,3,4,1,2] => [1,1,4,2] => 11100010 => 4
[7,8,5,6,3,4,1,2] => [2,4,2] => 10100010 => 3
[7,6,5,8,3,4,1,2] => [1,1,4,2] => 11100010 => 4
[6,7,5,8,3,4,1,2] => [2,4,2] => 10100010 => 3
[7,5,6,8,3,4,1,2] => [1,5,2] => 11000010 => 3
[6,5,7,8,3,4,1,2] => [1,5,2] => 11000010 => 3
[5,6,7,8,3,4,1,2] => [6,2] => 10000010 => 2
[7,8,5,4,3,6,1,2] => [2,2,2,2] => 10101010 => 4
[7,8,4,5,3,6,1,2] => [2,4,2] => 10100010 => 3
[7,8,5,3,4,6,1,2] => [2,4,2] => 10100010 => 3
[7,8,4,3,5,6,1,2] => [2,4,2] => 10100010 => 3
[7,8,3,4,5,6,1,2] => [6,2] => 10000010 => 2
[8,4,3,5,6,7,1,2] => [1,2,5] => 11010000 => 3
[8,3,4,5,6,7,1,2] => [1,7] => 11000000 => 2
[7,6,5,4,3,8,1,2] => [1,1,2,1,3] => 11101100 => 5
[6,5,7,4,3,8,1,2] => [1,3,1,3] => 11001100 => 4
[5,6,7,4,3,8,1,2] => [4,1,3] => 10001100 => 3
[6,7,4,5,3,8,1,2] => [2,3,3] => 10100100 => 3
[5,6,4,7,3,8,1,2] => [2,3,3] => 10100100 => 3
[5,4,6,7,3,8,1,2] => [1,4,3] => 11000100 => 3
[4,5,6,7,3,8,1,2] => [5,3] => 10000100 => 2
[5,4,6,3,7,8,1,2] => [1,3,4] => 11001000 => 3
[5,6,3,4,7,8,1,2] => [4,4] => 10001000 => 2
[6,4,3,5,7,8,1,2] => [1,2,5] => 11010000 => 3
[6,3,4,5,7,8,1,2] => [1,7] => 11000000 => 2
[5,4,3,6,7,8,1,2] => [1,2,5] => 11010000 => 3
[4,5,3,6,7,8,1,2] => [3,5] => 10010000 => 2
[4,3,5,6,7,8,1,2] => [1,7] => 11000000 => 2
[3,4,5,6,7,8,1,2] => [8] => 10000000 => 1
[8,7,6,5,4,2,1,3] => [1,1,1,2,1,2] => 11110110 => 6
[7,6,8,5,4,2,1,3] => [1,2,2,1,2] => 11010110 => 5
[5,6,7,8,4,2,1,3] => [5,1,2] => 10000110 => 3
[4,5,6,7,8,2,1,3] => [6,2] => 10000010 => 2
[8,7,6,5,4,1,2,3] => [1,1,1,2,3] => 11110100 => 5
[6,7,8,5,4,1,2,3] => [3,2,3] => 10010100 => 3
[8,5,6,7,4,1,2,3] => [1,4,3] => 11000100 => 3
[6,5,7,8,4,1,2,3] => [1,4,3] => 11000100 => 3
[5,6,7,8,4,1,2,3] => [5,3] => 10000100 => 2
[8,7,6,4,5,1,2,3] => [1,1,3,3] => 11100100 => 4
[8,6,7,4,5,1,2,3] => [1,4,3] => 11000100 => 3
[8,7,4,5,6,1,2,3] => [1,1,6] => 11100000 => 3
[7,8,4,5,6,1,2,3] => [2,6] => 10100000 => 2
[6,7,4,5,8,1,2,3] => [2,6] => 10100000 => 2
[6,5,4,7,8,1,2,3] => [1,1,6] => 11100000 => 3
[4,5,6,7,8,1,2,3] => [8] => 10000000 => 1
[8,7,6,5,3,2,1,4] => [1,1,1,2,1,2] => 11110110 => 6
[7,8,5,6,3,2,1,4] => [2,3,1,2] => 10100110 => 4
[7,6,5,8,3,2,1,4] => [1,1,3,1,2] => 11100110 => 5
[5,6,7,8,3,2,1,4] => [5,1,2] => 10000110 => 3
[8,7,6,5,2,3,1,4] => [1,1,1,3,2] => 11110010 => 5
[7,8,5,6,2,3,1,4] => [2,4,2] => 10100010 => 3
[6,7,5,8,2,3,1,4] => [2,4,2] => 10100010 => 3
[7,5,6,8,2,3,1,4] => [1,5,2] => 11000010 => 3
[5,6,7,8,2,3,1,4] => [6,2] => 10000010 => 2
[8,7,6,5,3,1,2,4] => [1,1,1,2,3] => 11110100 => 5
[7,8,5,6,3,1,2,4] => [2,3,3] => 10100100 => 3
[6,7,5,8,3,1,2,4] => [2,3,3] => 10100100 => 3
[7,5,6,8,3,1,2,4] => [1,4,3] => 11000100 => 3
[5,6,7,8,3,1,2,4] => [5,3] => 10000100 => 2
[8,7,6,5,2,1,3,4] => [1,1,1,2,3] => 11110100 => 5
[7,8,6,5,2,1,3,4] => [2,1,2,3] => 10110100 => 4
[6,7,8,5,2,1,3,4] => [3,2,3] => 10010100 => 3
[7,8,5,6,2,1,3,4] => [2,3,3] => 10100100 => 3
[6,5,7,8,2,1,3,4] => [1,4,3] => 11000100 => 3
[5,6,7,8,2,1,3,4] => [5,3] => 10000100 => 2
[8,7,6,5,1,2,3,4] => [1,1,1,5] => 11110000 => 4
[7,8,6,5,1,2,3,4] => [2,1,5] => 10110000 => 3
[8,6,7,5,1,2,3,4] => [1,2,5] => 11010000 => 3
[7,6,8,5,1,2,3,4] => [1,2,5] => 11010000 => 3
[6,7,8,5,1,2,3,4] => [3,5] => 10010000 => 2
[8,7,5,6,1,2,3,4] => [1,1,6] => 11100000 => 3
[7,8,5,6,1,2,3,4] => [2,6] => 10100000 => 2
[8,6,5,7,1,2,3,4] => [1,1,6] => 11100000 => 3
[8,5,6,7,1,2,3,4] => [1,7] => 11000000 => 2
[7,6,5,8,1,2,3,4] => [1,1,6] => 11100000 => 3
[6,7,5,8,1,2,3,4] => [2,6] => 10100000 => 2
[7,5,6,8,1,2,3,4] => [1,7] => 11000000 => 2
[6,5,7,8,1,2,3,4] => [1,7] => 11000000 => 2
[5,6,7,8,1,2,3,4] => [8] => 10000000 => 1
[8,7,6,4,3,2,1,5] => [1,1,2,1,1,2] => 11101110 => 6
[6,7,8,4,3,2,1,5] => [4,1,1,2] => 10001110 => 4
[8,7,6,3,4,2,1,5] => [1,1,3,1,2] => 11100110 => 5
[6,7,8,3,4,2,1,5] => [5,1,2] => 10000110 => 3
[8,7,6,4,2,3,1,5] => [1,1,2,2,2] => 11101010 => 5
[6,7,8,4,2,3,1,5] => [4,2,2] => 10001010 => 3
[8,7,6,3,2,4,1,5] => [1,1,2,2,2] => 11101010 => 5
[6,7,8,3,2,4,1,5] => [4,2,2] => 10001010 => 3
[8,7,6,2,3,4,1,5] => [1,1,4,2] => 11100010 => 4
[6,7,8,2,3,4,1,5] => [6,2] => 10000010 => 2
[8,7,6,4,3,1,2,5] => [1,1,2,1,3] => 11101100 => 5
[6,7,8,4,3,1,2,5] => [4,1,3] => 10001100 => 3
[8,7,6,3,4,1,2,5] => [1,1,3,3] => 11100100 => 4
[6,7,8,3,4,1,2,5] => [5,3] => 10000100 => 2
[8,7,6,4,2,1,3,5] => [1,1,2,1,3] => 11101100 => 5
[6,7,8,4,2,1,3,5] => [4,1,3] => 10001100 => 3
[8,7,6,4,1,2,3,5] => [1,1,2,4] => 11101000 => 4
[6,7,8,4,1,2,3,5] => [4,4] => 10001000 => 2
[8,7,6,3,2,1,4,5] => [1,1,2,1,3] => 11101100 => 5
[6,7,8,3,2,1,4,5] => [4,1,3] => 10001100 => 3
[8,7,6,2,3,1,4,5] => [1,1,3,3] => 11100100 => 4
[6,7,8,2,3,1,4,5] => [5,3] => 10000100 => 2
[8,7,6,3,1,2,4,5] => [1,1,2,4] => 11101000 => 4
[6,7,8,3,1,2,4,5] => [4,4] => 10001000 => 2
[8,7,6,2,1,3,4,5] => [1,1,2,4] => 11101000 => 4
[6,7,8,2,1,3,4,5] => [4,4] => 10001000 => 2
[8,7,6,1,2,3,4,5] => [1,1,6] => 11100000 => 3
[7,8,6,1,2,3,4,5] => [2,6] => 10100000 => 2
[8,6,7,1,2,3,4,5] => [1,7] => 11000000 => 2
[7,6,8,1,2,3,4,5] => [1,7] => 11000000 => 2
[6,7,8,1,2,3,4,5] => [8] => 10000000 => 1
[7,8,5,4,3,2,1,6] => [2,2,1,1,2] => 10101110 => 5
[7,8,4,5,2,3,1,6] => [2,4,2] => 10100010 => 3
[7,8,3,4,2,5,1,6] => [4,2,2] => 10001010 => 3
[7,8,5,4,2,1,3,6] => [2,2,1,3] => 10101100 => 4
[7,8,5,4,1,2,3,6] => [2,2,4] => 10101000 => 3
[7,8,4,5,1,2,3,6] => [2,6] => 10100000 => 2
[8,7,5,2,1,3,4,6] => [1,1,2,4] => 11101000 => 4
[7,8,5,2,1,3,4,6] => [2,2,4] => 10101000 => 3
[8,7,5,1,2,3,4,6] => [1,1,6] => 11100000 => 3
[7,8,5,1,2,3,4,6] => [2,6] => 10100000 => 2
[8,7,4,3,2,1,5,6] => [1,1,2,1,3] => 11101100 => 5
[7,8,4,3,2,1,5,6] => [2,2,1,3] => 10101100 => 4
[7,8,3,2,4,1,5,6] => [3,2,3] => 10010100 => 3
[7,8,2,3,4,1,5,6] => [5,3] => 10000100 => 2
[7,8,3,4,1,2,5,6] => [4,4] => 10001000 => 2
[7,8,4,2,1,3,5,6] => [2,2,4] => 10101000 => 3
[8,7,4,1,2,3,5,6] => [1,1,6] => 11100000 => 3
[8,7,3,2,1,4,5,6] => [1,2,1,4] => 11011000 => 4
[7,8,3,2,1,4,5,6] => [3,1,4] => 10011000 => 3
[7,8,2,1,3,4,5,6] => [3,5] => 10010000 => 2
[8,7,1,2,3,4,5,6] => [1,7] => 11000000 => 2
[7,8,1,2,3,4,5,6] => [8] => 10000000 => 1
[8,6,5,4,3,2,1,7] => [1,1,2,1,1,2] => 11101110 => 6
[8,4,5,6,3,2,1,7] => [1,4,1,2] => 11000110 => 4
[8,6,5,4,3,1,2,7] => [1,1,2,1,3] => 11101100 => 5
[8,5,6,3,4,1,2,7] => [1,4,3] => 11000100 => 3
[8,4,3,5,6,1,2,7] => [1,2,5] => 11010000 => 3
[8,3,4,5,6,1,2,7] => [1,7] => 11000000 => 2
[8,6,5,4,2,1,3,7] => [1,1,2,1,3] => 11101100 => 5
[8,6,4,5,1,2,3,7] => [1,1,6] => 11100000 => 3
[8,6,5,2,3,1,4,7] => [1,1,3,3] => 11100100 => 4
[8,5,6,2,3,1,4,7] => [1,4,3] => 11000100 => 3
[8,5,6,2,1,3,4,7] => [1,3,4] => 11001000 => 3
[8,6,5,1,2,3,4,7] => [1,1,6] => 11100000 => 3
[8,5,6,1,2,3,4,7] => [1,7] => 11000000 => 2
[8,6,4,3,2,1,5,7] => [1,1,2,1,3] => 11101100 => 5
[8,6,3,4,2,1,5,7] => [1,3,1,3] => 11001100 => 4
[8,6,4,2,1,3,5,7] => [1,1,2,4] => 11101000 => 4
[8,4,3,2,1,5,6,7] => [1,2,1,4] => 11011000 => 4
[8,2,3,4,1,5,6,7] => [4,4] => 10001000 => 2
[8,4,1,2,3,5,6,7] => [1,7] => 11000000 => 2
[8,3,2,1,4,5,6,7] => [1,2,5] => 11010000 => 3
[8,2,3,1,4,5,6,7] => [3,5] => 10010000 => 2
[8,3,1,2,4,5,6,7] => [1,7] => 11000000 => 2
[8,2,1,3,4,5,6,7] => [2,6] => 10100000 => 2
[8,1,2,3,4,5,6,7] => [8] => 10000000 => 1
[7,6,5,4,3,2,1,8] => [1,1,2,1,1,2] => 11101110 => 6
[6,7,5,4,3,2,1,8] => [2,2,1,1,2] => 10101110 => 5
[6,5,7,4,3,2,1,8] => [1,3,1,1,2] => 11001110 => 5
[5,6,7,4,3,2,1,8] => [4,1,1,2] => 10001110 => 4
[7,6,4,5,3,2,1,8] => [1,1,3,1,2] => 11100110 => 5
[7,4,5,6,3,2,1,8] => [1,4,1,2] => 11000110 => 4
[6,5,4,7,3,2,1,8] => [1,1,3,1,2] => 11100110 => 5
[4,5,6,7,3,2,1,8] => [5,1,2] => 10000110 => 3
[7,5,6,3,4,2,1,8] => [1,4,1,2] => 11000110 => 4
[5,6,7,3,4,2,1,8] => [5,1,2] => 10000110 => 3
[7,6,4,3,5,2,1,8] => [1,1,3,1,2] => 11100110 => 5
[7,6,3,4,5,2,1,8] => [1,4,1,2] => 11000110 => 4
[7,5,4,3,6,2,1,8] => [1,1,2,2,2] => 11101010 => 5
[6,7,5,4,2,3,1,8] => [2,2,2,2] => 10101010 => 4
[5,6,7,4,2,3,1,8] => [4,2,2] => 10001010 => 3
[7,6,4,5,2,3,1,8] => [1,1,4,2] => 11100010 => 4
[6,7,4,5,2,3,1,8] => [2,4,2] => 10100010 => 3
[7,4,5,6,2,3,1,8] => [1,5,2] => 11000010 => 3
[5,6,4,7,2,3,1,8] => [2,4,2] => 10100010 => 3
[4,5,6,7,2,3,1,8] => [6,2] => 10000010 => 2
[6,5,7,3,2,4,1,8] => [1,3,2,2] => 11001010 => 4
[5,6,7,3,2,4,1,8] => [4,2,2] => 10001010 => 3
[7,6,5,2,3,4,1,8] => [1,1,4,2] => 11100010 => 4
[6,7,5,2,3,4,1,8] => [2,4,2] => 10100010 => 3
[7,5,6,2,3,4,1,8] => [1,5,2] => 11000010 => 3
[6,5,7,2,3,4,1,8] => [1,5,2] => 11000010 => 3
[5,6,7,2,3,4,1,8] => [6,2] => 10000010 => 2
[6,7,3,4,2,5,1,8] => [4,2,2] => 10001010 => 3
[7,4,5,2,3,6,1,8] => [1,5,2] => 11000010 => 3
[5,6,3,4,2,7,1,8] => [4,1,3] => 10001100 => 3
[4,5,3,6,2,7,1,8] => [3,2,3] => 10010100 => 3
[5,4,3,2,6,7,1,8] => [1,2,1,4] => 11011000 => 4
[3,2,4,5,6,7,1,8] => [2,6] => 10100000 => 2
[2,3,4,5,6,7,1,8] => [8] => 10000000 => 1
[7,6,5,4,3,1,2,8] => [1,1,2,1,3] => 11101100 => 5
[7,5,6,4,3,1,2,8] => [1,3,1,3] => 11001100 => 4
[7,4,5,6,3,1,2,8] => [1,4,3] => 11000100 => 3
[4,5,6,7,3,1,2,8] => [5,3] => 10000100 => 2
[7,6,5,4,2,1,3,8] => [1,1,2,1,3] => 11101100 => 5
[6,5,7,4,2,1,3,8] => [1,3,1,3] => 11001100 => 4
[7,5,4,6,2,1,3,8] => [1,1,3,3] => 11100100 => 4
[7,4,5,6,2,1,3,8] => [1,4,3] => 11000100 => 3
[4,5,6,7,2,1,3,8] => [5,3] => 10000100 => 2
[7,6,5,4,1,2,3,8] => [1,1,2,4] => 11101000 => 4
[5,6,7,4,1,2,3,8] => [4,4] => 10001000 => 2
[7,4,5,6,1,2,3,8] => [1,7] => 11000000 => 2
[5,6,4,7,1,2,3,8] => [2,6] => 10100000 => 2
[5,4,6,7,1,2,3,8] => [1,7] => 11000000 => 2
[4,5,6,7,1,2,3,8] => [8] => 10000000 => 1
[5,6,7,3,1,2,4,8] => [4,4] => 10001000 => 2
[5,6,7,2,1,3,4,8] => [4,4] => 10001000 => 2
[7,6,5,1,2,3,4,8] => [1,1,6] => 11100000 => 3
[6,7,5,1,2,3,4,8] => [2,6] => 10100000 => 2
[7,5,6,1,2,3,4,8] => [1,7] => 11000000 => 2
[6,5,7,1,2,3,4,8] => [1,7] => 11000000 => 2
[5,6,7,1,2,3,4,8] => [8] => 10000000 => 1
[7,6,4,3,2,1,5,8] => [1,1,2,1,3] => 11101100 => 5
[7,6,4,3,1,2,5,8] => [1,1,2,4] => 11101000 => 4
[6,7,1,2,3,4,5,8] => [8] => 10000000 => 1
[7,5,3,1,2,4,6,8] => [1,2,5] => 11010000 => 3
[7,5,1,2,3,4,6,8] => [1,7] => 11000000 => 2
[7,4,3,2,1,5,6,8] => [1,2,1,4] => 11011000 => 4
[7,3,1,2,4,5,6,8] => [1,7] => 11000000 => 2
[7,2,1,3,4,5,6,8] => [2,6] => 10100000 => 2
[7,1,2,3,4,5,6,8] => [8] => 10000000 => 1
[6,5,4,3,2,1,7,8] => [1,1,2,1,3] => 11101100 => 5
[5,4,3,2,6,1,7,8] => [1,2,1,4] => 11011000 => 4
[4,5,3,2,6,1,7,8] => [3,1,4] => 10011000 => 3
[4,2,3,5,6,1,7,8] => [3,5] => 10010000 => 2
[2,3,4,5,6,1,7,8] => [8] => 10000000 => 1
[5,6,4,3,1,2,7,8] => [2,2,4] => 10101000 => 3
[5,4,6,3,1,2,7,8] => [1,3,4] => 11001000 => 3
[5,6,3,4,1,2,7,8] => [4,4] => 10001000 => 2
[5,4,3,6,1,2,7,8] => [1,2,5] => 11010000 => 3
[5,6,4,2,1,3,7,8] => [2,2,4] => 10101000 => 3
[5,4,6,2,1,3,7,8] => [1,3,4] => 11001000 => 3
[4,5,6,1,2,3,7,8] => [8] => 10000000 => 1
[5,6,3,2,1,4,7,8] => [3,1,4] => 10011000 => 3
[6,4,3,2,1,5,7,8] => [1,2,1,4] => 11011000 => 4
[6,4,3,1,2,5,7,8] => [1,2,5] => 11010000 => 3
[6,4,1,2,3,5,7,8] => [1,7] => 11000000 => 2
[6,2,3,1,4,5,7,8] => [3,5] => 10010000 => 2
[6,1,2,3,4,5,7,8] => [8] => 10000000 => 1
[5,4,3,2,1,6,7,8] => [1,2,1,4] => 11011000 => 4
[4,5,2,3,1,6,7,8] => [4,4] => 10001000 => 2
[5,2,3,4,1,6,7,8] => [4,4] => 10001000 => 2
[2,3,4,5,1,6,7,8] => [8] => 10000000 => 1
[5,3,1,2,4,6,7,8] => [1,7] => 11000000 => 2
[5,1,2,3,4,6,7,8] => [8] => 10000000 => 1
[4,3,2,1,5,6,7,8] => [1,2,5] => 11010000 => 3
[3,2,4,1,5,6,7,8] => [2,6] => 10100000 => 2
[2,3,4,1,5,6,7,8] => [8] => 10000000 => 1
[3,4,1,2,5,6,7,8] => [8] => 10000000 => 1
[4,1,2,3,5,6,7,8] => [8] => 10000000 => 1
[3,2,1,4,5,6,7,8] => [2,6] => 10100000 => 2
[3,1,2,4,5,6,7,8] => [8] => 10000000 => 1
[2,1,3,4,5,6,7,8] => [8] => 10000000 => 1
[1,2,3,4,5,6,7,8] => [8] => 10000000 => 1
[5,8,7,6,4,3,2,1] => [2,1,2,1,1,1] => 10110111 => 6
[6,5,8,7,4,3,2,1] => [1,2,2,1,1,1] => 11010111 => 6
[4,8,7,6,5,3,2,1] => [2,1,2,1,1,1] => 10110111 => 6
[4,7,6,5,8,3,2,1] => [2,1,3,1,1] => 10110011 => 5
[3,7,6,8,5,4,2,1] => [2,3,1,1,1] => 10100111 => 5
[3,5,8,7,6,4,2,1] => [3,1,2,1,1] => 10011011 => 5
[3,5,6,8,7,4,2,1] => [4,2,1,1] => 10001011 => 4
[3,5,6,7,8,4,2,1] => [6,1,1] => 10000011 => 3
[3,4,8,7,6,5,2,1] => [3,1,2,1,1] => 10011011 => 5
[3,4,5,8,7,6,2,1] => [4,2,1,1] => 10001011 => 4
[4,3,6,5,8,7,2,1] => [1,2,2,2,1] => 11010101 => 5
[5,7,6,4,3,8,2,1] => [2,2,1,2,1] => 10101101 => 5
[2,7,8,6,5,4,3,1] => [3,2,1,1,1] => 10010111 => 5
[2,6,8,7,5,4,3,1] => [3,2,1,1,1] => 10010111 => 5
[2,5,6,7,8,4,3,1] => [6,1,1] => 10000011 => 3
[2,4,8,7,6,5,3,1] => [3,1,2,1,1] => 10011011 => 5
[2,4,6,8,7,5,3,1] => [4,2,1,1] => 10001011 => 4
[2,7,6,5,4,8,3,1] => [2,1,2,2,1] => 10110101 => 5
[2,3,5,6,8,7,4,1] => [5,2,1] => 10000101 => 3
[2,3,5,6,7,8,4,1] => [7,1] => 10000001 => 2
[4,3,2,8,7,6,5,1] => [1,2,1,2,1,1] => 11011011 => 6
[3,4,2,8,7,6,5,1] => [3,1,2,1,1] => 10011011 => 5
[2,4,3,8,7,6,5,1] => [3,1,2,1,1] => 10011011 => 5
[3,2,4,8,7,6,5,1] => [2,2,2,1,1] => 10101011 => 5
[2,3,4,8,7,6,5,1] => [4,2,1,1] => 10001011 => 4
[5,4,3,2,8,7,6,1] => [1,2,1,1,2,1] => 11011101 => 6
[5,4,3,2,7,8,6,1] => [1,2,1,3,1] => 11011001 => 5
[2,5,4,3,8,7,6,1] => [2,2,1,2,1] => 10101101 => 5
[2,5,4,3,7,8,6,1] => [2,2,3,1] => 10101001 => 4
[2,4,5,3,7,8,6,1] => [4,3,1] => 10001001 => 3
[3,4,2,5,7,8,6,1] => [3,4,1] => 10010001 => 3
[4,3,6,5,2,8,7,1] => [1,2,2,2,1] => 11010101 => 5
[3,2,6,5,4,8,7,1] => [2,1,2,2,1] => 10110101 => 5
[2,4,3,6,5,8,7,1] => [3,2,2,1] => 10010101 => 4
[5,4,3,2,6,8,7,1] => [1,2,1,3,1] => 11011001 => 5
[2,5,4,3,6,8,7,1] => [2,2,3,1] => 10101001 => 4
[2,4,3,5,6,8,7,1] => [3,4,1] => 10010001 => 3
[2,3,4,5,6,8,7,1] => [7,1] => 10000001 => 2
[4,3,6,5,7,2,8,1] => [1,2,3,2] => 11010010 => 4
[2,5,4,7,6,3,8,1] => [2,2,2,2] => 10101010 => 4
[2,5,4,6,7,3,8,1] => [2,4,2] => 10100010 => 3
[3,2,6,5,7,4,8,1] => [2,1,3,2] => 10110010 => 4
[4,3,2,7,6,5,8,1] => [1,2,1,2,2] => 11011010 => 5
[3,4,2,7,6,5,8,1] => [3,1,2,2] => 10011010 => 4
[3,4,2,6,7,5,8,1] => [3,3,2] => 10010010 => 3
[2,4,3,7,6,5,8,1] => [3,1,2,2] => 10011010 => 4
[3,2,4,7,6,5,8,1] => [2,2,2,2] => 10101010 => 4
[2,3,4,7,6,5,8,1] => [4,2,2] => 10001010 => 3
[5,4,3,2,7,6,8,1] => [1,2,1,2,2] => 11011010 => 5
[4,3,5,2,7,6,8,1] => [1,3,2,2] => 11001010 => 4
[2,5,4,3,7,6,8,1] => [2,2,2,2] => 10101010 => 4
[3,2,5,4,7,6,8,1] => [2,2,2,2] => 10101010 => 4
[2,3,5,4,7,6,8,1] => [4,2,2] => 10001010 => 3
[3,2,4,5,7,6,8,1] => [2,4,2] => 10100010 => 3
[2,4,3,6,5,7,8,1] => [3,2,3] => 10010100 => 3
[2,5,4,3,6,7,8,1] => [2,2,4] => 10101000 => 3
[1,8,7,6,5,4,3,2] => [1,1,1,2,1,1,1] => 11110111 => 7
[1,7,8,6,5,4,3,2] => [1,2,2,1,1,1] => 11010111 => 6
[1,6,8,7,5,4,3,2] => [1,2,2,1,1,1] => 11010111 => 6
[1,7,6,8,5,4,3,2] => [1,1,3,1,1,1] => 11100111 => 6
[1,6,7,8,5,4,3,2] => [1,4,1,1,1] => 11000111 => 5
[1,5,8,7,6,4,3,2] => [1,2,1,2,1,1] => 11011011 => 6
[1,7,6,5,8,4,3,2] => [1,1,1,3,1,1] => 11110011 => 6
[1,5,6,7,8,4,3,2] => [1,5,1,1] => 11000011 => 4
[1,4,8,7,6,5,3,2] => [1,2,1,2,1,1] => 11011011 => 6
[1,4,7,8,6,5,3,2] => [1,3,2,1,1] => 11001011 => 5
[1,3,5,7,8,6,4,2] => [1,5,1,1] => 11000011 => 4
[1,3,6,5,7,8,4,2] => [1,2,4,1] => 11010001 => 4
[1,3,5,6,7,8,4,2] => [1,6,1] => 11000001 => 3
[1,4,3,8,7,6,5,2] => [1,2,1,2,1,1] => 11011011 => 6
[1,4,3,7,8,6,5,2] => [1,2,3,1,1] => 11010011 => 5
[1,4,3,7,6,8,5,2] => [1,2,1,3,1] => 11011001 => 5
[1,3,4,8,7,6,5,2] => [1,3,2,1,1] => 11001011 => 5
[1,3,4,7,6,8,5,2] => [1,3,3,1] => 11001001 => 4
[1,3,4,5,7,8,6,2] => [1,6,1] => 11000001 => 3
[1,6,5,4,3,8,7,2] => [1,1,2,1,2,1] => 11101101 => 6
[1,5,6,4,3,8,7,2] => [1,3,1,2,1] => 11001101 => 5
[1,4,3,6,5,8,7,2] => [1,2,2,2,1] => 11010101 => 5
[1,3,4,5,6,8,7,2] => [1,6,1] => 11000001 => 3
[1,5,4,3,6,7,8,2] => [1,1,2,4] => 11101000 => 4
[1,4,5,3,6,7,8,2] => [1,3,4] => 11001000 => 3
[1,4,3,5,6,7,8,2] => [1,2,5] => 11010000 => 3
[1,3,4,5,6,7,8,2] => [1,7] => 11000000 => 2
[2,1,8,7,6,5,4,3] => [2,1,1,2,1,1] => 10111011 => 6
[2,1,6,7,8,5,4,3] => [2,4,1,1] => 10100011 => 4
[2,1,6,5,8,7,4,3] => [2,1,2,2,1] => 10110101 => 5
[2,1,7,6,5,8,4,3] => [2,1,2,2,1] => 10110101 => 5
[2,1,6,7,5,8,4,3] => [2,3,2,1] => 10100101 => 4
[2,1,6,5,7,8,4,3] => [2,1,4,1] => 10110001 => 4
[2,1,5,6,7,8,4,3] => [2,5,1] => 10100001 => 3
[2,1,4,8,7,6,5,3] => [2,2,2,1,1] => 10101011 => 5
[2,1,4,7,8,6,5,3] => [2,4,1,1] => 10100011 => 4
[2,1,4,5,8,7,6,3] => [2,3,2,1] => 10100101 => 4
[2,1,4,5,7,8,6,3] => [2,5,1] => 10100001 => 3
[2,1,4,6,5,8,7,3] => [2,3,2,1] => 10100101 => 4
[2,1,6,5,7,4,8,3] => [2,1,3,2] => 10110010 => 4
[2,1,5,4,7,6,8,3] => [2,2,2,2] => 10101010 => 4
[2,1,4,5,6,7,8,3] => [2,6] => 10100000 => 2
[1,2,6,7,8,5,4,3] => [2,4,1,1] => 10100011 => 4
[1,2,5,6,7,8,4,3] => [2,5,1] => 10100001 => 3
[1,2,4,8,7,6,5,3] => [2,2,2,1,1] => 10101011 => 5
[1,2,4,7,8,6,5,3] => [2,4,1,1] => 10100011 => 4
[1,2,4,6,7,8,5,3] => [2,5,1] => 10100001 => 3
[1,2,6,5,4,7,8,3] => [2,1,2,3] => 10110100 => 4
[1,2,5,6,4,7,8,3] => [2,3,3] => 10100100 => 3
[1,2,5,4,6,7,8,3] => [2,2,4] => 10101000 => 3
[1,2,4,5,6,7,8,3] => [2,6] => 10100000 => 2
[3,2,1,8,7,6,5,4] => [2,1,1,2,1,1] => 10111011 => 6
[3,2,1,7,8,6,5,4] => [2,1,3,1,1] => 10110011 => 5
[3,2,1,6,8,7,5,4] => [2,1,2,2,1] => 10110101 => 5
[3,2,1,7,6,8,5,4] => [2,1,1,3,1] => 10111001 => 5
[3,2,1,6,7,8,5,4] => [2,1,4,1] => 10110001 => 4
[3,2,1,5,8,7,6,4] => [2,1,2,2,1] => 10110101 => 5
[3,2,1,5,7,8,6,4] => [2,1,4,1] => 10110001 => 4
[3,2,1,6,5,8,7,4] => [2,1,2,2,1] => 10110101 => 5
[3,2,1,5,6,8,7,4] => [2,1,4,1] => 10110001 => 4
[3,2,1,7,6,5,8,4] => [2,1,1,2,2] => 10111010 => 5
[3,2,1,6,7,5,8,4] => [2,1,3,2] => 10110010 => 4
[3,2,1,5,7,6,8,4] => [2,1,3,2] => 10110010 => 4
[3,2,1,6,5,7,8,4] => [2,1,2,3] => 10110100 => 4
[3,2,1,5,6,7,8,4] => [2,1,5] => 10110000 => 3
[2,3,1,8,7,6,5,4] => [3,1,2,1,1] => 10011011 => 5
[1,3,2,8,7,6,5,4] => [1,2,1,2,1,1] => 11011011 => 6
[2,1,3,8,7,6,5,4] => [3,1,2,1,1] => 10011011 => 5
[1,2,3,8,7,6,5,4] => [3,1,2,1,1] => 10011011 => 5
[1,2,3,7,8,6,5,4] => [3,3,1,1] => 10010011 => 4
[1,2,3,6,8,7,5,4] => [3,2,2,1] => 10010101 => 4
[1,2,3,7,6,8,5,4] => [3,1,3,1] => 10011001 => 4
[1,2,3,6,7,8,5,4] => [3,4,1] => 10010001 => 3
[1,2,3,5,8,7,6,4] => [3,2,2,1] => 10010101 => 4
[1,2,3,5,7,8,6,4] => [3,4,1] => 10010001 => 3
[1,2,3,6,5,8,7,4] => [3,2,2,1] => 10010101 => 4
[1,2,3,5,6,8,7,4] => [3,4,1] => 10010001 => 3
[1,2,3,7,6,5,8,4] => [3,1,2,2] => 10011010 => 4
[1,2,3,6,7,5,8,4] => [3,3,2] => 10010010 => 3
[1,2,3,5,7,6,8,4] => [3,3,2] => 10010010 => 3
[1,2,3,6,5,7,8,4] => [3,2,3] => 10010100 => 3
[1,2,3,5,6,7,8,4] => [3,5] => 10010000 => 2
[4,3,2,1,8,7,6,5] => [1,2,1,1,2,1] => 11011101 => 6
[4,3,2,1,7,8,6,5] => [1,2,1,3,1] => 11011001 => 5
[4,3,2,1,6,8,7,5] => [1,2,1,3,1] => 11011001 => 5
[4,3,2,1,7,6,8,5] => [1,2,1,2,2] => 11011010 => 5
[4,3,2,1,6,7,8,5] => [1,2,1,4] => 11011000 => 4
[3,4,2,1,8,7,6,5] => [3,1,1,2,1] => 10011101 => 5
[3,4,2,1,7,8,6,5] => [3,1,3,1] => 10011001 => 4
[3,4,2,1,6,8,7,5] => [3,1,3,1] => 10011001 => 4
[3,4,2,1,7,6,8,5] => [3,1,2,2] => 10011010 => 4
[3,4,2,1,6,7,8,5] => [3,1,4] => 10011000 => 3
[2,4,3,1,8,7,6,5] => [3,1,1,2,1] => 10011101 => 5
[2,4,3,1,7,8,6,5] => [3,1,3,1] => 10011001 => 4
[2,4,3,1,6,8,7,5] => [3,1,3,1] => 10011001 => 4
[2,4,3,1,7,6,8,5] => [3,1,2,2] => 10011010 => 4
[2,4,3,1,6,7,8,5] => [3,1,4] => 10011000 => 3
[3,2,4,1,8,7,6,5] => [2,2,1,2,1] => 10101101 => 5
[3,2,4,1,7,8,6,5] => [2,2,3,1] => 10101001 => 4
[3,2,4,1,6,8,7,5] => [2,2,3,1] => 10101001 => 4
[3,2,4,1,7,6,8,5] => [2,2,2,2] => 10101010 => 4
[3,2,4,1,6,7,8,5] => [2,2,4] => 10101000 => 3
[2,3,4,1,8,7,6,5] => [4,1,2,1] => 10001101 => 4
[2,3,4,1,7,8,6,5] => [4,3,1] => 10001001 => 3
[2,3,4,1,6,8,7,5] => [4,3,1] => 10001001 => 3
[2,3,4,1,7,6,8,5] => [4,2,2] => 10001010 => 3
[2,3,4,1,6,7,8,5] => [4,4] => 10001000 => 2
[1,4,3,2,8,7,6,5] => [1,2,1,1,2,1] => 11011101 => 6
[1,4,3,2,7,6,8,5] => [1,2,1,2,2] => 11011010 => 5
[1,4,3,2,6,7,8,5] => [1,2,1,4] => 11011000 => 4
[1,3,4,2,8,7,6,5] => [1,3,1,2,1] => 11001101 => 5
[1,3,4,2,7,6,8,5] => [1,3,2,2] => 11001010 => 4
[1,3,4,2,6,7,8,5] => [1,3,4] => 11001000 => 3
[2,1,4,3,8,7,6,5] => [2,2,1,2,1] => 10101101 => 5
[2,1,4,3,7,8,6,5] => [2,2,3,1] => 10101001 => 4
[2,1,4,3,6,8,7,5] => [2,2,3,1] => 10101001 => 4
[2,1,4,3,7,6,8,5] => [2,2,2,2] => 10101010 => 4
[2,1,4,3,6,7,8,5] => [2,2,4] => 10101000 => 3
[1,2,4,3,8,7,6,5] => [2,2,1,2,1] => 10101101 => 5
[1,2,4,3,7,6,8,5] => [2,2,2,2] => 10101010 => 4
[1,2,4,3,6,7,8,5] => [2,2,4] => 10101000 => 3
[3,2,1,4,8,7,6,5] => [2,2,1,2,1] => 10101101 => 5
[3,2,1,4,7,8,6,5] => [2,2,3,1] => 10101001 => 4
[3,2,1,4,7,6,8,5] => [2,2,2,2] => 10101010 => 4
[3,2,1,4,6,7,8,5] => [2,2,4] => 10101000 => 3
[2,3,1,4,8,7,6,5] => [4,1,2,1] => 10001101 => 4
[2,3,1,4,7,6,8,5] => [4,2,2] => 10001010 => 3
[2,3,1,4,6,7,8,5] => [4,4] => 10001000 => 2
[1,3,2,4,8,7,6,5] => [1,3,1,2,1] => 11001101 => 5
[1,3,2,4,7,6,8,5] => [1,3,2,2] => 11001010 => 4
[1,3,2,4,6,7,8,5] => [1,3,4] => 11001000 => 3
[2,1,3,4,8,7,6,5] => [4,1,2,1] => 10001101 => 4
[2,1,3,4,7,8,6,5] => [4,3,1] => 10001001 => 3
[2,1,3,4,7,6,8,5] => [4,2,2] => 10001010 => 3
[2,1,3,4,6,7,8,5] => [4,4] => 10001000 => 2
[1,2,3,4,8,7,6,5] => [4,1,2,1] => 10001101 => 4
[1,2,3,4,7,8,6,5] => [4,3,1] => 10001001 => 3
[1,2,3,4,7,6,8,5] => [4,2,2] => 10001010 => 3
[1,2,3,4,6,7,8,5] => [4,4] => 10001000 => 2
[5,4,3,2,1,8,7,6] => [1,2,1,1,2,1] => 11011101 => 6
[5,4,3,2,1,7,8,6] => [1,2,1,1,3] => 11011100 => 5
[4,5,3,2,1,8,7,6] => [3,1,1,2,1] => 10011101 => 5
[3,5,4,2,1,8,7,6] => [2,2,1,2,1] => 10101101 => 5
[4,3,5,2,1,8,7,6] => [1,3,1,2,1] => 11001101 => 5
[3,4,5,2,1,8,7,6] => [4,1,2,1] => 10001101 => 4
[2,5,4,3,1,8,7,6] => [2,2,1,2,1] => 10101101 => 5
[2,4,5,3,1,8,7,6] => [4,1,2,1] => 10001101 => 4
[3,2,5,4,1,8,7,6] => [2,2,1,2,1] => 10101101 => 5
[2,3,5,4,1,8,7,6] => [4,1,2,1] => 10001101 => 4
[4,3,2,5,1,8,7,6] => [1,2,2,2,1] => 11010101 => 5
[3,4,2,5,1,8,7,6] => [3,2,2,1] => 10010101 => 4
[2,4,3,5,1,8,7,6] => [3,2,2,1] => 10010101 => 4
[3,2,4,5,1,8,7,6] => [2,3,2,1] => 10100101 => 4
[2,3,4,5,1,8,7,6] => [5,2,1] => 10000101 => 3
[4,3,2,1,5,8,7,6] => [1,2,2,2,1] => 11010101 => 5
[4,3,2,1,5,7,8,6] => [1,2,2,3] => 11010100 => 4
[3,2,4,1,5,8,7,6] => [2,3,2,1] => 10100101 => 4
[3,2,4,1,5,7,8,6] => [2,3,3] => 10100100 => 3
[2,3,4,1,5,8,7,6] => [5,2,1] => 10000101 => 3
[2,3,4,1,5,7,8,6] => [5,3] => 10000100 => 2
[3,2,1,4,5,8,7,6] => [2,3,2,1] => 10100101 => 4
[2,3,1,4,5,7,8,6] => [5,3] => 10000100 => 2
[1,2,3,4,5,8,7,6] => [5,2,1] => 10000101 => 3
[1,2,3,4,5,7,8,6] => [5,3] => 10000100 => 2
[6,5,4,3,2,1,8,7] => [1,1,2,1,1,2] => 11101110 => 6
[5,6,4,3,2,1,8,7] => [2,2,1,1,2] => 10101110 => 5
[4,5,6,3,2,1,8,7] => [4,1,1,2] => 10001110 => 4
[3,6,5,4,2,1,8,7] => [2,2,1,1,2] => 10101110 => 5
[4,3,6,5,2,1,8,7] => [1,2,2,1,2] => 11010110 => 5
[5,4,3,6,2,1,8,7] => [1,2,2,1,2] => 11010110 => 5
[4,5,3,6,2,1,8,7] => [3,2,1,2] => 10010110 => 4
[4,3,5,6,2,1,8,7] => [1,4,1,2] => 11000110 => 4
[2,3,6,5,4,1,8,7] => [3,2,1,2] => 10010110 => 4
[2,4,3,6,5,1,8,7] => [3,2,1,2] => 10010110 => 4
[5,4,3,2,6,1,8,7] => [1,2,1,2,2] => 11011010 => 5
[4,5,3,2,6,1,8,7] => [3,1,2,2] => 10011010 => 4
[4,3,5,2,6,1,8,7] => [1,3,2,2] => 11001010 => 4
[3,2,5,4,6,1,8,7] => [2,2,2,2] => 10101010 => 4
[4,3,2,5,6,1,8,7] => [1,2,3,2] => 11010010 => 4
[2,3,4,5,6,1,8,7] => [6,2] => 10000010 => 2
[1,5,6,4,3,2,8,7] => [1,3,1,1,2] => 11001110 => 5
[2,1,6,5,4,3,8,7] => [2,1,2,1,2] => 10110110 => 5
[2,1,5,6,4,3,8,7] => [2,3,1,2] => 10100110 => 4
[2,1,4,6,5,3,8,7] => [2,3,1,2] => 10100110 => 4
[2,1,5,4,6,3,8,7] => [2,2,2,2] => 10101010 => 4
[2,1,4,5,6,3,8,7] => [2,4,2] => 10100010 => 3
[4,3,2,1,6,5,8,7] => [1,2,1,2,2] => 11011010 => 5
[3,4,2,1,6,5,8,7] => [3,1,2,2] => 10011010 => 4
[2,4,3,1,6,5,8,7] => [3,1,2,2] => 10011010 => 4
[3,2,4,1,6,5,8,7] => [2,2,2,2] => 10101010 => 4
[2,3,4,1,6,5,8,7] => [4,2,2] => 10001010 => 3
[2,1,4,3,6,5,8,7] => [2,2,2,2] => 10101010 => 4
[5,4,3,2,1,6,8,7] => [1,2,1,2,2] => 11011010 => 5
[2,1,5,4,3,6,8,7] => [2,2,2,2] => 10101010 => 4
[4,3,2,1,5,6,8,7] => [1,2,3,2] => 11010010 => 4
[3,2,4,1,5,6,8,7] => [2,4,2] => 10100010 => 3
[2,3,4,1,5,6,8,7] => [6,2] => 10000010 => 2
[2,1,3,4,5,6,8,7] => [6,2] => 10000010 => 2
[1,2,3,4,5,6,8,7] => [6,2] => 10000010 => 2
[5,7,6,4,3,2,1,8] => [2,2,1,1,2] => 10101110 => 5
[4,7,6,5,3,2,1,8] => [2,1,2,1,2] => 10110110 => 5
[3,4,7,6,5,2,1,8] => [3,2,1,2] => 10010110 => 4
[3,2,7,6,5,4,1,8] => [2,1,2,1,2] => 10110110 => 5
[3,2,6,7,5,4,1,8] => [2,3,1,2] => 10100110 => 4
[5,4,3,2,7,6,1,8] => [1,2,1,2,2] => 11011010 => 5
[4,5,3,2,7,6,1,8] => [3,1,2,2] => 10011010 => 4
[3,5,4,2,7,6,1,8] => [2,2,2,2] => 10101010 => 4
[3,2,5,4,7,6,1,8] => [2,2,2,2] => 10101010 => 4
[2,3,4,5,7,6,1,8] => [6,2] => 10000010 => 2
[3,5,4,2,6,7,1,8] => [2,2,4] => 10101000 => 3
[1,3,4,6,7,5,2,8] => [1,5,2] => 11000010 => 3
[1,3,4,5,7,6,2,8] => [1,5,2] => 11000010 => 3
[2,1,6,7,5,4,3,8] => [2,3,1,2] => 10100110 => 4
[2,3,1,5,6,7,4,8] => [3,5] => 10010000 => 2
[4,3,2,1,7,6,5,8] => [1,2,1,2,2] => 11011010 => 5
[4,3,2,1,6,7,5,8] => [1,2,1,4] => 11011000 => 4
[3,2,4,1,7,6,5,8] => [2,2,2,2] => 10101010 => 4
[3,2,4,1,6,7,5,8] => [2,2,4] => 10101000 => 3
[2,3,4,1,7,6,5,8] => [4,2,2] => 10001010 => 3
[2,3,4,1,6,7,5,8] => [4,4] => 10001000 => 2
[1,4,3,2,7,6,5,8] => [1,2,1,2,2] => 11011010 => 5
[1,3,4,2,6,7,5,8] => [1,3,4] => 11001000 => 3
[3,2,1,4,7,6,5,8] => [2,2,2,2] => 10101010 => 4
[5,4,3,2,1,7,6,8] => [1,2,1,1,3] => 11011100 => 5
[3,2,1,5,4,7,6,8] => [2,1,2,3] => 10110100 => 4
[2,3,1,5,4,7,6,8] => [3,2,3] => 10010100 => 3
[1,3,2,5,4,7,6,8] => [1,2,2,3] => 11010100 => 4
[1,2,3,5,4,7,6,8] => [3,2,3] => 10010100 => 3
[4,3,2,1,5,7,6,8] => [1,2,2,3] => 11010100 => 4
[3,2,4,1,5,7,6,8] => [2,3,3] => 10100100 => 3
[2,3,4,1,5,7,6,8] => [5,3] => 10000100 => 2
[1,3,2,4,5,7,6,8] => [1,4,3] => 11000100 => 3
[1,2,3,4,5,7,6,8] => [5,3] => 10000100 => 2
[2,3,4,6,5,1,7,8] => [5,3] => 10000100 => 2
[1,2,4,6,5,3,7,8] => [2,3,3] => 10100100 => 3
[4,3,2,1,6,5,7,8] => [1,2,1,4] => 11011000 => 4
[3,2,4,1,6,5,7,8] => [2,2,4] => 10101000 => 3
[2,3,4,1,6,5,7,8] => [4,4] => 10001000 => 2
[1,2,4,3,6,5,7,8] => [2,2,4] => 10101000 => 3
[3,2,5,4,1,6,7,8] => [2,2,4] => 10101000 => 3
[1,3,2,5,4,6,7,8] => [1,2,5] => 11010000 => 3
[1,2,3,5,4,6,7,8] => [3,5] => 10010000 => 2
[1,3,2,4,5,6,7,8] => [1,7] => 11000000 => 2
[1,2,3,4,8,6,7,5] => [4,3,1] => 10001001 => 3
[1,2,3,5,8,6,7,4] => [3,4,1] => 10010001 => 3
[1,2,3,7,5,6,8,4] => [3,3,2] => 10010010 => 3
[1,2,3,8,5,6,7,4] => [3,4,1] => 10010001 => 3
[1,2,3,8,5,7,6,4] => [3,2,2,1] => 10010101 => 4
[1,2,3,8,6,5,7,4] => [3,1,3,1] => 10011001 => 4
[1,2,3,8,6,7,5,4] => [3,1,3,1] => 10011001 => 4
[1,2,4,5,8,6,7,3] => [2,5,1] => 10100001 => 3
[1,2,4,8,6,5,7,3] => [2,2,3,1] => 10101001 => 4
[1,2,6,4,5,7,8,3] => [2,3,3] => 10100100 => 3
[1,2,8,5,4,6,7,3] => [2,1,4,1] => 10110001 => 4
[1,3,2,8,6,5,7,4] => [1,2,1,3,1] => 11011001 => 5
[1,3,7,4,5,6,2,8] => [1,5,2] => 11000010 => 3
[1,3,8,5,4,6,7,2] => [1,2,4,1] => 11010001 => 4
[1,3,8,5,6,7,4,2] => [1,2,4,1] => 11010001 => 4
[1,3,8,6,5,7,4,2] => [1,2,2,2,1] => 11010101 => 5
[1,5,3,4,6,7,8,2] => [1,3,4] => 11001000 => 3
[1,6,3,5,4,8,7,2] => [1,2,2,2,1] => 11010101 => 5
[1,8,4,3,5,6,7,2] => [1,1,5,1] => 11100001 => 4
[1,8,4,7,6,5,3,2] => [1,1,2,2,1,1] => 11101011 => 6
[1,7,5,4,3,6,8,2] => [1,1,2,2,2] => 11101010 => 5
[1,8,5,4,3,6,7,2] => [1,1,2,3,1] => 11101001 => 5
[1,8,5,4,7,6,3,2] => [1,1,2,2,1,1] => 11101011 => 6
[1,8,7,4,5,6,3,2] => [1,1,4,1,1] => 11100011 => 5
[1,8,7,4,6,5,3,2] => [1,1,2,2,1,1] => 11101011 => 6
[1,8,6,5,4,7,3,2] => [1,1,1,2,2,1] => 11110101 => 6
[1,8,7,5,4,6,3,2] => [1,1,1,3,1,1] => 11110011 => 6
[1,8,7,5,6,4,3,2] => [1,1,1,3,1,1] => 11110011 => 6
[2,1,3,8,5,7,6,4] => [3,2,2,1] => 10010101 => 4
[2,1,4,3,8,6,7,5] => [2,2,3,1] => 10101001 => 4
[2,1,4,5,8,6,7,3] => [2,5,1] => 10100001 => 3
[2,1,6,4,5,3,8,7] => [2,3,1,2] => 10100110 => 4
[2,1,7,4,6,5,8,3] => [2,2,2,2] => 10101010 => 4
[2,1,8,5,4,7,6,3] => [2,1,2,2,1] => 10110101 => 5
[2,1,8,7,5,6,4,3] => [2,1,3,1,1] => 10110011 => 5
[2,3,1,8,6,7,5,4] => [3,1,3,1] => 10011001 => 4
[2,3,4,1,8,6,7,5] => [4,3,1] => 10001001 => 3
[2,3,4,8,5,6,7,1] => [7,1] => 10000001 => 2
[2,3,4,8,5,7,6,1] => [5,2,1] => 10000101 => 3
[2,3,4,8,6,5,7,1] => [4,3,1] => 10001001 => 3
[2,3,4,8,6,7,5,1] => [4,3,1] => 10001001 => 3
[2,3,6,4,5,1,8,7] => [5,1,2] => 10000110 => 3
[2,3,7,4,5,6,8,1] => [6,2] => 10000010 => 2
[2,5,3,4,1,8,7,6] => [4,1,2,1] => 10001101 => 4
[2,5,3,4,8,6,7,1] => [4,3,1] => 10001001 => 3
[2,8,3,4,5,6,7,1] => [7,1] => 10000001 => 2
[2,8,3,5,4,7,6,1] => [3,2,2,1] => 10010101 => 4
[2,8,3,5,7,6,4,1] => [3,3,1,1] => 10010011 => 4
[2,5,4,3,8,6,7,1] => [2,2,3,1] => 10101001 => 4
[2,8,4,3,5,7,6,1] => [2,3,2,1] => 10100101 => 4
[3,2,1,5,8,6,7,4] => [2,1,4,1] => 10110001 => 4
[3,2,1,7,5,6,4,8] => [2,1,3,2] => 10110010 => 4
[3,2,1,7,5,6,8,4] => [2,1,3,2] => 10110010 => 4
[3,2,1,8,5,6,7,4] => [2,1,4,1] => 10110001 => 4
[3,2,1,8,5,7,6,4] => [2,1,2,2,1] => 10110101 => 5
[3,2,1,8,6,5,7,4] => [2,1,1,3,1] => 10111001 => 5
[3,2,1,8,6,7,5,4] => [2,1,1,3,1] => 10111001 => 5
[3,2,4,1,8,6,7,5] => [2,2,3,1] => 10101001 => 4
[3,2,7,4,6,5,8,1] => [2,2,2,2] => 10101010 => 4
[3,2,7,5,4,6,1,8] => [2,1,3,2] => 10110010 => 4
[4,2,3,1,6,5,8,7] => [3,1,2,2] => 10011010 => 4
[4,2,3,1,6,7,8,5] => [3,1,4] => 10011000 => 3
[4,2,3,1,7,6,8,5] => [3,1,2,2] => 10011010 => 4
[4,2,3,1,8,6,7,5] => [3,1,3,1] => 10011001 => 4
[4,2,3,1,8,7,6,5] => [3,1,1,2,1] => 10011101 => 5
[4,2,3,5,1,8,7,6] => [3,2,2,1] => 10010101 => 4
[4,2,3,7,5,6,8,1] => [3,3,2] => 10010010 => 3
[4,2,3,7,6,5,8,1] => [3,1,2,2] => 10011010 => 4
[4,2,3,8,7,6,5,1] => [3,1,2,1,1] => 10011011 => 5
[5,2,3,4,1,8,7,6] => [4,1,2,1] => 10001101 => 4
[7,2,3,4,6,5,1,8] => [4,2,2] => 10001010 => 3
[6,2,3,5,4,1,7,8] => [3,2,3] => 10010100 => 3
[7,2,3,6,5,4,1,8] => [3,2,1,2] => 10010110 => 4
[5,2,4,3,1,6,7,8] => [2,2,4] => 10101000 => 3
[5,2,4,3,1,7,6,8] => [2,2,1,3] => 10101100 => 4
[5,2,4,3,1,8,7,6] => [2,2,1,2,1] => 10101101 => 5
[5,2,4,3,6,1,7,8] => [2,2,4] => 10101000 => 3
[5,2,4,3,6,1,8,7] => [2,2,2,2] => 10101010 => 4
[5,2,4,3,7,6,8,1] => [2,2,2,2] => 10101010 => 4
[7,2,4,3,6,5,8,1] => [2,2,2,2] => 10101010 => 4
[8,2,7,4,6,5,3,1] => [2,2,2,1,1] => 10101011 => 5
[4,3,2,1,8,6,7,5] => [1,2,1,3,1] => 11011001 => 5
[4,3,2,7,5,6,8,1] => [1,2,3,2] => 11010010 => 4
[4,3,2,8,5,7,6,1] => [1,2,2,2,1] => 11010101 => 5
[5,3,2,4,1,6,8,7] => [1,3,2,2] => 11001010 => 4
[5,3,2,4,1,8,7,6] => [1,3,1,2,1] => 11001101 => 5
[6,3,2,5,4,1,8,7] => [1,2,2,1,2] => 11010110 => 5
[8,3,2,5,4,7,6,1] => [1,2,2,2,1] => 11010101 => 5
[8,3,2,7,6,5,4,1] => [1,2,1,2,1,1] => 11011011 => 6
[5,3,4,2,1,7,8,6] => [1,3,1,3] => 11001100 => 4
[5,3,4,2,1,8,7,6] => [1,3,1,2,1] => 11001101 => 5
[8,3,7,4,6,5,2,1] => [1,3,2,1,1] => 11001011 => 5
[7,3,6,5,4,2,1,8] => [1,2,2,1,2] => 11010110 => 5
[5,4,3,2,8,6,7,1] => [1,2,1,3,1] => 11011001 => 5
[7,4,3,6,5,2,1,8] => [1,2,2,1,2] => 11010110 => 5
[6,5,3,4,2,1,8,7] => [1,3,1,1,2] => 11001110 => 5
[7,6,3,5,4,2,1,8] => [1,2,2,1,2] => 11010110 => 5
[8,7,3,5,4,6,2,1] => [1,2,3,1,1] => 11010011 => 5
[8,7,3,6,5,4,2,1] => [1,2,2,1,1,1] => 11010111 => 6
[8,5,4,3,2,7,6,1] => [1,1,2,1,2,1] => 11101101 => 6
[8,7,4,3,6,5,2,1] => [1,1,2,2,1,1] => 11101011 => 6
[2,4,1,3,6,5,8,7] => [4,2,2] => 10001010 => 3
[2,1,4,6,3,5,8,7] => [2,4,2] => 10100010 => 3
[2,4,1,6,3,5,8,7] => [3,3,2] => 10010010 => 3
[2,4,6,1,3,5,8,7] => [6,2] => 10000010 => 2
[2,1,4,3,6,8,5,7] => [2,2,4] => 10101000 => 3
[2,4,1,3,6,8,5,7] => [4,4] => 10001000 => 2
[2,1,4,6,3,8,5,7] => [2,3,3] => 10100100 => 3
[2,4,1,6,3,8,5,7] => [3,2,3] => 10010100 => 3
[2,4,6,1,3,8,5,7] => [5,3] => 10000100 => 2
[2,1,4,6,8,3,5,7] => [2,6] => 10100000 => 2
[2,4,1,6,8,3,5,7] => [3,5] => 10010000 => 2
[2,4,6,1,8,3,5,7] => [4,4] => 10001000 => 2
[2,4,6,8,1,3,5,7] => [8] => 10000000 => 1
[2,4,1,6,3,7,5,8] => [3,2,3] => 10010100 => 3
[2,4,1,3,6,7,8,5] => [4,4] => 10001000 => 2
[2,4,1,6,3,7,8,5] => [3,2,3] => 10010100 => 3
[2,4,1,6,7,3,8,5] => [3,3,2] => 10010010 => 3
[2,4,6,1,7,3,8,5] => [4,2,2] => 10001010 => 3
[2,4,1,6,7,8,3,5] => [3,5] => 10010000 => 2
[2,4,6,7,1,8,3,5] => [5,3] => 10000100 => 2
[2,1,4,3,7,5,8,6] => [2,2,2,2] => 10101010 => 4
[2,4,1,3,7,5,8,6] => [4,2,2] => 10001010 => 3
[2,4,7,1,3,5,8,6] => [6,2] => 10000010 => 2
[2,1,4,3,7,8,5,6] => [2,2,4] => 10101000 => 3
[2,4,1,3,7,8,5,6] => [4,4] => 10001000 => 2
[2,4,7,1,3,8,5,6] => [5,3] => 10000100 => 2
[2,4,7,8,1,3,5,6] => [8] => 10000000 => 1
[2,4,1,5,3,7,6,8] => [3,2,3] => 10010100 => 3
[2,1,4,5,7,3,8,6] => [2,4,2] => 10100010 => 3
[2,4,5,7,1,3,8,6] => [6,2] => 10000010 => 2
[2,1,4,3,8,5,6,7] => [2,2,4] => 10101000 => 3
[2,4,1,3,8,5,6,7] => [4,4] => 10001000 => 2
[2,4,1,5,3,8,6,7] => [3,2,3] => 10010100 => 3
[2,1,4,5,8,3,6,7] => [2,6] => 10100000 => 2
[2,4,5,1,8,3,6,7] => [4,4] => 10001000 => 2
[2,4,1,5,3,6,8,7] => [3,3,2] => 10010010 => 3
[2,4,1,5,6,3,8,7] => [3,3,2] => 10010010 => 3
[2,4,1,5,3,6,7,8] => [3,5] => 10010000 => 2
[2,4,1,5,6,3,7,8] => [3,5] => 10010000 => 2
[2,4,1,5,6,7,8,3] => [3,5] => 10010000 => 2
[2,4,5,6,1,7,8,3] => [5,3] => 10000100 => 2
[2,4,5,6,7,1,8,3] => [6,2] => 10000010 => 2
[2,4,5,6,7,8,1,3] => [8] => 10000000 => 1
[2,1,5,3,6,4,8,7] => [2,2,2,2] => 10101010 => 4
[2,1,5,6,3,4,8,7] => [2,4,2] => 10100010 => 3
[2,5,6,8,1,3,4,7] => [8] => 10000000 => 1
[2,5,1,6,7,3,4,8] => [3,5] => 10010000 => 2
[2,5,1,6,7,3,8,4] => [3,3,2] => 10010010 => 3
[2,1,5,6,7,8,3,4] => [2,6] => 10100000 => 2
[2,5,1,6,7,8,3,4] => [3,5] => 10010000 => 2
[2,5,6,1,7,8,3,4] => [4,4] => 10001000 => 2
[2,5,6,7,8,1,3,4] => [8] => 10000000 => 1
[2,1,5,3,7,4,8,6] => [2,2,2,2] => 10101010 => 4
[2,5,1,7,3,4,8,6] => [3,3,2] => 10010010 => 3
[2,5,1,3,7,8,4,6] => [4,4] => 10001000 => 2
[2,1,5,7,3,8,4,6] => [2,3,3] => 10100100 => 3
[2,1,5,7,8,3,4,6] => [2,6] => 10100000 => 2
[2,5,7,1,8,3,4,6] => [4,4] => 10001000 => 2
[2,5,7,8,1,3,4,6] => [8] => 10000000 => 1
[2,3,5,1,7,4,8,6] => [4,2,2] => 10001010 => 3
[2,3,5,1,6,4,7,8] => [4,4] => 10001000 => 2
[2,3,5,1,6,7,8,4] => [4,4] => 10001000 => 2
[2,3,5,6,1,7,8,4] => [5,3] => 10000100 => 2
[2,3,5,6,7,8,1,4] => [8] => 10000000 => 1
[2,1,6,3,7,4,8,5] => [2,2,2,2] => 10101010 => 4
[2,6,1,3,7,4,8,5] => [4,2,2] => 10001010 => 3
[2,6,7,1,3,4,8,5] => [6,2] => 10000010 => 2
[2,1,6,3,7,8,4,5] => [2,2,4] => 10101000 => 3
[2,6,1,7,3,8,4,5] => [3,2,3] => 10010100 => 3
[2,1,6,7,8,3,4,5] => [2,6] => 10100000 => 2
[2,6,7,8,1,3,4,5] => [8] => 10000000 => 1
[2,1,6,3,7,4,5,8] => [2,2,4] => 10101000 => 3
[2,3,1,6,4,7,5,8] => [3,2,3] => 10010100 => 3
[2,3,6,1,4,7,5,8] => [5,3] => 10000100 => 2
[2,1,6,3,4,7,8,5] => [2,3,3] => 10100100 => 3
[2,1,3,6,7,8,4,5] => [3,5] => 10010000 => 2
[2,3,1,6,7,8,4,5] => [3,5] => 10010000 => 2
[2,3,6,1,7,8,4,5] => [4,4] => 10001000 => 2
[2,1,6,3,4,8,5,7] => [2,3,3] => 10100100 => 3
[2,3,1,6,4,8,5,7] => [3,2,3] => 10010100 => 3
[2,3,1,6,8,4,5,7] => [3,5] => 10010000 => 2
[2,3,6,1,8,4,5,7] => [4,4] => 10001000 => 2
[2,1,6,3,4,5,8,7] => [2,4,2] => 10100010 => 3
[2,3,6,1,4,5,8,7] => [6,2] => 10000010 => 2
[2,3,4,1,6,8,5,7] => [4,4] => 10001000 => 2
[2,6,1,3,4,5,7,8] => [8] => 10000000 => 1
[2,3,4,6,1,7,5,8] => [5,3] => 10000100 => 2
[2,3,4,6,7,8,1,5] => [8] => 10000000 => 1
[2,1,7,8,3,4,5,6] => [2,6] => 10100000 => 2
[2,7,1,8,3,4,5,6] => [3,5] => 10010000 => 2
[2,7,8,1,3,4,5,6] => [8] => 10000000 => 1
[2,3,1,7,4,8,5,6] => [3,2,3] => 10010100 => 3
[2,3,7,1,4,8,5,6] => [5,3] => 10000100 => 2
[2,3,7,8,1,4,5,6] => [8] => 10000000 => 1
[2,3,4,1,7,5,8,6] => [4,2,2] => 10001010 => 3
[2,3,1,4,7,8,5,6] => [4,4] => 10001000 => 2
[2,3,4,1,7,8,5,6] => [4,4] => 10001000 => 2
[2,3,4,7,1,8,5,6] => [5,3] => 10000100 => 2
[2,7,1,3,4,5,6,8] => [8] => 10000000 => 1
[2,3,4,1,7,5,6,8] => [4,4] => 10001000 => 2
[2,3,4,5,7,1,8,6] => [6,2] => 10000010 => 2
[2,3,4,5,7,8,1,6] => [8] => 10000000 => 1
[2,1,8,3,4,5,6,7] => [2,6] => 10100000 => 2
[2,8,1,3,4,5,6,7] => [8] => 10000000 => 1
[2,1,3,8,4,5,6,7] => [3,5] => 10010000 => 2
[2,1,3,4,8,5,6,7] => [4,4] => 10001000 => 2
[2,3,1,4,8,5,6,7] => [4,4] => 10001000 => 2
[2,3,4,1,8,5,6,7] => [4,4] => 10001000 => 2
[2,3,4,8,1,5,6,7] => [8] => 10000000 => 1
[2,3,4,1,5,8,6,7] => [5,3] => 10000100 => 2
[2,3,4,5,1,8,6,7] => [5,3] => 10000100 => 2
[2,3,4,5,8,1,6,7] => [8] => 10000000 => 1
[2,3,4,5,6,8,1,7] => [8] => 10000000 => 1
[3,1,4,2,6,5,8,7] => [2,2,2,2] => 10101010 => 4
[3,4,1,2,6,5,8,7] => [4,2,2] => 10001010 => 3
[3,1,4,2,6,8,5,7] => [2,2,4] => 10101000 => 3
[3,4,1,2,6,8,5,7] => [4,4] => 10001000 => 2
[3,1,4,6,8,2,5,7] => [2,6] => 10100000 => 2
[3,4,6,8,1,2,5,7] => [8] => 10000000 => 1
[3,4,6,1,2,7,5,8] => [5,3] => 10000100 => 2
[3,4,6,7,1,2,5,8] => [8] => 10000000 => 1
[3,1,4,2,6,7,8,5] => [2,2,4] => 10101000 => 3
[3,4,1,2,6,7,8,5] => [4,4] => 10001000 => 2
[3,4,6,1,2,7,8,5] => [5,3] => 10000100 => 2
[3,4,6,1,7,2,8,5] => [4,2,2] => 10001010 => 3
[3,4,6,7,1,2,8,5] => [6,2] => 10000010 => 2
[3,4,6,1,7,8,2,5] => [4,4] => 10001000 => 2
[3,4,6,7,1,8,2,5] => [5,3] => 10000100 => 2
[3,1,4,2,7,5,8,6] => [2,2,2,2] => 10101010 => 4
[3,4,1,2,7,8,5,6] => [4,4] => 10001000 => 2
[3,4,7,1,8,2,5,6] => [4,4] => 10001000 => 2
[3,4,7,8,1,2,5,6] => [8] => 10000000 => 1
[3,4,5,7,1,2,8,6] => [6,2] => 10000010 => 2
[3,1,4,2,8,5,6,7] => [2,2,4] => 10101000 => 3
[3,4,1,2,8,5,6,7] => [4,4] => 10001000 => 2
[3,4,1,5,8,2,6,7] => [3,5] => 10010000 => 2
[3,4,5,8,1,2,6,7] => [8] => 10000000 => 1
[3,1,4,2,5,6,7,8] => [2,6] => 10100000 => 2
[3,1,4,5,6,7,8,2] => [2,6] => 10100000 => 2
[3,4,1,5,6,7,8,2] => [3,5] => 10010000 => 2
[3,4,5,6,7,1,8,2] => [6,2] => 10000010 => 2
[3,1,5,2,6,4,8,7] => [2,2,2,2] => 10101010 => 4
[3,5,1,6,2,4,8,7] => [3,3,2] => 10010010 => 3
[3,5,6,1,2,4,8,7] => [6,2] => 10000010 => 2
[3,5,1,2,6,8,4,7] => [4,4] => 10001000 => 2
[3,1,5,6,2,8,4,7] => [2,3,3] => 10100100 => 3
[3,5,6,1,8,2,4,7] => [4,4] => 10001000 => 2
[3,5,6,8,1,2,4,7] => [8] => 10000000 => 1
[3,5,6,1,7,2,4,8] => [4,4] => 10001000 => 2
[3,5,6,1,7,2,8,4] => [4,2,2] => 10001010 => 3
[3,5,6,1,7,8,2,4] => [4,4] => 10001000 => 2
[3,5,6,7,8,1,2,4] => [8] => 10000000 => 1
[3,1,5,2,7,4,8,6] => [2,2,2,2] => 10101010 => 4
[3,1,5,7,2,4,8,6] => [2,4,2] => 10100010 => 3
[3,1,5,7,2,8,4,6] => [2,3,3] => 10100100 => 3
[3,5,1,7,2,8,4,6] => [3,2,3] => 10010100 => 3
[3,5,1,7,8,2,4,6] => [3,5] => 10010000 => 2
[3,5,7,8,1,2,4,6] => [8] => 10000000 => 1
[3,1,5,2,7,4,6,8] => [2,2,4] => 10101000 => 3
[1,3,5,2,7,4,8,6] => [1,3,2,2] => 11001010 => 4
[3,1,5,2,8,4,6,7] => [2,2,4] => 10101000 => 3
[1,3,2,5,4,8,6,7] => [1,2,2,3] => 11010100 => 4
[1,3,2,5,8,4,6,7] => [1,2,5] => 11010000 => 3
[1,3,5,8,2,4,6,7] => [1,7] => 11000000 => 2
[1,3,5,2,6,8,4,7] => [1,3,4] => 11001000 => 3
[1,3,5,2,6,7,4,8] => [1,3,4] => 11001000 => 3
[1,3,5,6,2,7,4,8] => [1,4,3] => 11000100 => 3
[1,3,5,6,7,8,2,4] => [1,7] => 11000000 => 2
[3,1,6,2,7,4,8,5] => [2,2,2,2] => 10101010 => 4
[3,6,1,7,2,4,8,5] => [3,3,2] => 10010010 => 3
[3,6,1,7,2,8,4,5] => [3,2,3] => 10010100 => 3
[3,6,7,1,2,8,4,5] => [5,3] => 10000100 => 2
[3,6,1,7,8,2,4,5] => [3,5] => 10010000 => 2
[3,6,7,8,1,2,4,5] => [8] => 10000000 => 1
[3,1,6,2,7,4,5,8] => [2,2,4] => 10101000 => 3
[3,1,6,7,2,4,5,8] => [2,6] => 10100000 => 2
[3,6,1,2,4,7,5,8] => [5,3] => 10000100 => 2
[1,3,2,6,4,7,5,8] => [1,2,2,3] => 11010100 => 4
[1,3,6,2,4,7,8,5] => [1,4,3] => 11000100 => 3
[3,1,2,6,7,4,8,5] => [3,3,2] => 10010010 => 3
[1,3,6,2,7,8,4,5] => [1,3,4] => 11001000 => 3
[3,1,6,2,8,4,5,7] => [2,2,4] => 10101000 => 3
[3,1,6,8,2,4,5,7] => [2,6] => 10100000 => 2
[1,3,2,6,4,8,5,7] => [1,2,2,3] => 11010100 => 4
[3,1,6,2,4,5,8,7] => [2,4,2] => 10100010 => 3
[3,1,6,2,4,5,7,8] => [2,6] => 10100000 => 2
[1,3,2,6,4,5,7,8] => [1,2,5] => 11010000 => 3
[3,1,2,4,6,7,8,5] => [4,4] => 10001000 => 2
[1,3,4,6,7,2,8,5] => [1,5,2] => 11000010 => 3
[3,1,7,8,2,4,5,6] => [2,6] => 10100000 => 2
[1,3,2,7,4,8,5,6] => [1,2,2,3] => 11010100 => 4
[1,3,7,2,8,4,5,6] => [1,3,4] => 11001000 => 3
[3,7,1,2,4,5,6,8] => [8] => 10000000 => 1
[1,3,2,7,4,5,6,8] => [1,2,5] => 11010000 => 3
[1,3,4,5,7,8,2,6] => [1,7] => 11000000 => 2
[3,1,8,2,4,5,6,7] => [2,6] => 10100000 => 2
[1,3,2,8,4,5,6,7] => [1,2,5] => 11010000 => 3
[3,1,2,4,8,5,6,7] => [4,4] => 10001000 => 2
[1,3,2,4,8,5,6,7] => [1,3,4] => 11001000 => 3
[1,3,4,2,8,5,6,7] => [1,3,4] => 11001000 => 3
[3,1,2,4,5,8,6,7] => [5,3] => 10000100 => 2
[1,3,2,4,5,8,6,7] => [1,4,3] => 11000100 => 3
[4,1,5,2,6,3,8,7] => [2,2,2,2] => 10101010 => 4
[4,5,1,2,6,3,8,7] => [4,2,2] => 10001010 => 3
[4,5,6,1,2,3,8,7] => [6,2] => 10000010 => 2
[4,1,5,2,6,8,3,7] => [2,2,4] => 10101000 => 3
[4,5,1,6,2,8,3,7] => [3,2,3] => 10010100 => 3
[4,5,6,1,2,8,3,7] => [5,3] => 10000100 => 2
[4,1,5,6,8,2,3,7] => [2,6] => 10100000 => 2
[4,5,6,8,1,2,3,7] => [8] => 10000000 => 1
[4,5,1,6,2,7,3,8] => [3,2,3] => 10010100 => 3
[4,5,6,1,7,2,3,8] => [4,4] => 10001000 => 2
[4,5,6,7,1,2,8,3] => [6,2] => 10000010 => 2
[4,1,5,6,7,8,2,3] => [2,6] => 10100000 => 2
[4,5,6,7,1,8,2,3] => [5,3] => 10000100 => 2
[4,1,5,2,7,3,8,6] => [2,2,2,2] => 10101010 => 4
[4,5,1,7,2,3,8,6] => [3,3,2] => 10010010 => 3
[4,1,5,2,7,8,3,6] => [2,2,4] => 10101000 => 3
[4,1,5,7,2,8,3,6] => [2,3,3] => 10100100 => 3
[4,5,1,7,2,8,3,6] => [3,2,3] => 10010100 => 3
[4,5,7,1,2,8,3,6] => [5,3] => 10000100 => 2
[4,5,1,7,8,2,3,6] => [3,5] => 10010000 => 2
[4,5,7,8,1,2,3,6] => [8] => 10000000 => 1
[4,5,1,2,7,3,6,8] => [4,4] => 10001000 => 2
[1,4,2,5,3,7,6,8] => [1,2,2,3] => 11010100 => 4
[4,1,2,5,7,3,6,8] => [3,5] => 10010000 => 2
[1,4,2,5,7,3,8,6] => [1,2,3,2] => 11010010 => 4
[1,4,5,2,7,3,8,6] => [1,3,2,2] => 11001010 => 4
[1,4,5,7,2,3,8,6] => [1,5,2] => 11000010 => 3
[1,4,2,5,7,8,3,6] => [1,2,5] => 11010000 => 3
[4,5,1,2,8,3,6,7] => [4,4] => 10001000 => 2
[1,4,2,5,3,8,6,7] => [1,2,2,3] => 11010100 => 4
[1,4,2,5,8,3,6,7] => [1,2,5] => 11010000 => 3
[4,1,2,5,6,3,8,7] => [3,3,2] => 10010010 => 3
[1,4,5,2,6,3,8,7] => [1,3,2,2] => 11001010 => 4
[1,4,2,5,3,6,7,8] => [1,2,5] => 11010000 => 3
[1,4,5,2,6,3,7,8] => [1,3,4] => 11001000 => 3
[1,4,2,5,6,7,3,8] => [1,2,5] => 11010000 => 3
[1,4,5,6,2,7,3,8] => [1,4,3] => 11000100 => 3
[1,4,5,6,7,2,3,8] => [1,7] => 11000000 => 2
[4,1,2,5,6,7,8,3] => [3,5] => 10010000 => 2
[1,4,2,5,6,7,8,3] => [1,2,5] => 11010000 => 3
[1,4,5,2,6,7,8,3] => [1,3,4] => 11001000 => 3
[1,4,5,6,7,8,2,3] => [1,7] => 11000000 => 2
[4,1,6,2,7,3,8,5] => [2,2,2,2] => 10101010 => 4
[4,6,1,2,7,8,3,5] => [4,4] => 10001000 => 2
[4,6,7,1,8,2,3,5] => [4,4] => 10001000 => 2
[4,6,7,8,1,2,3,5] => [8] => 10000000 => 1
[4,6,1,7,2,3,5,8] => [3,5] => 10010000 => 2
[4,6,1,2,3,7,5,8] => [5,3] => 10000100 => 2
[1,4,2,6,3,7,5,8] => [1,2,2,3] => 11010100 => 4
[4,1,6,2,3,7,8,5] => [2,3,3] => 10100100 => 3
[4,1,2,6,7,3,8,5] => [3,3,2] => 10010010 => 3
[1,4,6,2,7,3,8,5] => [1,3,2,2] => 11001010 => 4
[1,4,2,6,7,8,3,5] => [1,2,5] => 11010000 => 3
[1,4,6,2,7,8,3,5] => [1,3,4] => 11001000 => 3
[1,4,6,7,2,8,3,5] => [1,4,3] => 11000100 => 3
[4,1,6,2,8,3,5,7] => [2,2,4] => 10101000 => 3
[4,6,1,8,2,3,5,7] => [3,5] => 10010000 => 2
[4,1,2,6,3,8,5,7] => [3,2,3] => 10010100 => 3
[1,4,2,6,3,8,5,7] => [1,2,2,3] => 11010100 => 4
[4,1,2,3,6,5,8,7] => [4,2,2] => 10001010 => 3
[4,1,2,3,6,8,5,7] => [4,4] => 10001000 => 2
[4,6,1,2,3,5,7,8] => [8] => 10000000 => 1
[1,4,2,6,3,5,7,8] => [1,2,5] => 11010000 => 3
[4,1,2,3,6,5,7,8] => [4,4] => 10001000 => 2
[4,1,2,3,6,7,5,8] => [4,4] => 10001000 => 2
[4,1,2,3,6,7,8,5] => [4,4] => 10001000 => 2
[1,4,2,3,6,7,8,5] => [1,3,4] => 11001000 => 3
[1,2,4,6,7,8,3,5] => [2,6] => 10100000 => 2
[4,1,7,2,8,3,5,6] => [2,2,4] => 10101000 => 3
[4,7,1,2,8,3,5,6] => [4,4] => 10001000 => 2
[4,1,7,8,2,3,5,6] => [2,6] => 10100000 => 2
[4,7,1,8,2,3,5,6] => [3,5] => 10010000 => 2
[1,4,2,7,3,8,5,6] => [1,2,2,3] => 11010100 => 4
[4,1,2,7,8,3,5,6] => [3,5] => 10010000 => 2
[1,4,2,7,8,3,5,6] => [1,2,5] => 11010000 => 3
[1,4,7,8,2,3,5,6] => [1,7] => 11000000 => 2
[4,1,2,3,7,5,8,6] => [4,2,2] => 10001010 => 3
[4,1,2,3,7,8,5,6] => [4,4] => 10001000 => 2
[4,1,7,2,3,5,6,8] => [2,6] => 10100000 => 2
[4,7,1,2,3,5,6,8] => [8] => 10000000 => 1
[1,4,2,7,3,5,6,8] => [1,2,5] => 11010000 => 3
[4,1,2,3,7,5,6,8] => [4,4] => 10001000 => 2
[1,4,2,3,7,5,6,8] => [1,3,4] => 11001000 => 3
[4,1,2,3,5,7,6,8] => [5,3] => 10000100 => 2
[1,4,2,3,5,7,6,8] => [1,4,3] => 11000100 => 3
[4,1,2,3,5,7,8,6] => [5,3] => 10000100 => 2
[1,2,4,5,7,3,8,6] => [2,4,2] => 10100010 => 3
[4,8,1,2,3,5,6,7] => [8] => 10000000 => 1
[1,4,2,8,3,5,6,7] => [1,2,5] => 11010000 => 3
[4,1,2,3,8,5,6,7] => [4,4] => 10001000 => 2
[1,4,2,3,8,5,6,7] => [1,3,4] => 11001000 => 3
[1,2,4,3,8,5,6,7] => [2,2,4] => 10101000 => 3
[4,1,2,3,5,8,6,7] => [5,3] => 10000100 => 2
[1,4,2,3,5,8,6,7] => [1,4,3] => 11000100 => 3
[4,1,2,3,5,6,8,7] => [6,2] => 10000010 => 2
[1,4,2,3,5,6,7,8] => [1,7] => 11000000 => 2
[5,1,6,2,7,3,8,4] => [2,2,2,2] => 10101010 => 4
[5,6,1,2,7,8,3,4] => [4,4] => 10001000 => 2
[1,5,2,6,3,7,4,8] => [1,2,2,3] => 11010100 => 4
[5,6,1,2,3,7,8,4] => [5,3] => 10000100 => 2
[1,5,6,7,8,2,3,4] => [1,7] => 11000000 => 2
[5,6,1,2,8,3,4,7] => [4,4] => 10001000 => 2
[5,6,8,1,2,3,4,7] => [8] => 10000000 => 1
[5,1,6,2,3,8,4,7] => [2,3,3] => 10100100 => 3
[5,6,1,2,3,8,4,7] => [5,3] => 10000100 => 2
[1,5,2,6,3,8,4,7] => [1,2,2,3] => 11010100 => 4
[1,5,6,2,3,8,4,7] => [1,4,3] => 11000100 => 3
[5,1,6,2,3,4,7,8] => [2,6] => 10100000 => 2
[1,5,2,6,3,4,7,8] => [1,2,5] => 11010000 => 3
[1,5,2,3,6,4,7,8] => [1,3,4] => 11001000 => 3
[1,2,5,3,6,4,7,8] => [2,2,4] => 10101000 => 3
[1,2,5,6,3,4,7,8] => [2,6] => 10100000 => 2
[1,2,5,3,6,7,4,8] => [2,2,4] => 10101000 => 3
[5,1,2,3,6,7,8,4] => [4,4] => 10001000 => 2
[1,5,2,3,6,7,8,4] => [1,3,4] => 11001000 => 3
[1,2,5,3,6,7,8,4] => [2,2,4] => 10101000 => 3
[1,2,5,6,3,7,8,4] => [2,3,3] => 10100100 => 3
[1,2,5,6,7,3,8,4] => [2,4,2] => 10100010 => 3
[1,2,5,6,7,8,3,4] => [2,6] => 10100000 => 2
[5,1,7,2,8,3,4,6] => [2,2,4] => 10101000 => 3
[5,7,1,2,8,3,4,6] => [4,4] => 10001000 => 2
[5,7,8,1,2,3,4,6] => [8] => 10000000 => 1
[1,5,2,7,3,8,4,6] => [1,2,2,3] => 11010100 => 4
[1,5,7,2,8,3,4,6] => [1,3,4] => 11001000 => 3
[5,1,2,7,3,4,8,6] => [3,3,2] => 10010010 => 3
[5,7,1,2,3,4,6,8] => [8] => 10000000 => 1
[1,5,2,7,3,4,6,8] => [1,2,5] => 11010000 => 3
[1,5,2,3,7,4,6,8] => [1,3,4] => 11001000 => 3
[1,5,2,3,4,7,6,8] => [1,4,3] => 11000100 => 3
[5,1,2,8,3,4,6,7] => [3,5] => 10010000 => 2
[1,5,2,8,3,4,6,7] => [1,2,5] => 11010000 => 3
[1,5,8,2,3,4,6,7] => [1,7] => 11000000 => 2
[5,1,2,3,8,4,6,7] => [4,4] => 10001000 => 2
[1,2,5,3,8,4,6,7] => [2,2,4] => 10101000 => 3
[1,5,2,3,4,8,6,7] => [1,4,3] => 11000100 => 3
[1,2,3,5,4,8,6,7] => [3,2,3] => 10010100 => 3
[5,1,2,3,4,6,8,7] => [6,2] => 10000010 => 2
[1,5,2,3,4,6,7,8] => [1,7] => 11000000 => 2
[6,1,7,8,2,3,4,5] => [2,6] => 10100000 => 2
[6,7,1,8,2,3,4,5] => [3,5] => 10010000 => 2
[1,6,2,7,3,8,4,5] => [1,2,2,3] => 11010100 => 4
[1,6,7,2,8,3,4,5] => [1,3,4] => 11001000 => 3
[1,6,7,8,2,3,4,5] => [1,7] => 11000000 => 2
[6,7,1,2,3,4,8,5] => [6,2] => 10000010 => 2
[6,1,2,3,7,8,4,5] => [4,4] => 10001000 => 2
[6,1,7,2,3,4,5,8] => [2,6] => 10100000 => 2
[6,1,2,7,3,4,5,8] => [3,5] => 10010000 => 2
[1,6,2,7,3,4,5,8] => [1,2,5] => 11010000 => 3
[1,6,7,2,3,4,5,8] => [1,7] => 11000000 => 2
[1,2,6,3,7,4,5,8] => [2,2,4] => 10101000 => 3
[1,6,2,3,4,7,5,8] => [1,4,3] => 11000100 => 3
[1,2,3,6,4,7,5,8] => [3,2,3] => 10010100 => 3
[6,1,2,3,4,7,8,5] => [5,3] => 10000100 => 2
[1,2,6,3,4,7,8,5] => [2,3,3] => 10100100 => 3
[1,2,3,6,4,7,8,5] => [3,2,3] => 10010100 => 3
[1,2,3,6,7,4,8,5] => [3,3,2] => 10010010 => 3
[6,1,8,2,3,4,5,7] => [2,6] => 10100000 => 2
[6,1,2,8,3,4,5,7] => [3,5] => 10010000 => 2
[1,6,2,8,3,4,5,7] => [1,2,5] => 11010000 => 3
[1,6,8,2,3,4,5,7] => [1,7] => 11000000 => 2
[1,6,2,3,4,8,5,7] => [1,4,3] => 11000100 => 3
[1,2,6,3,4,8,5,7] => [2,3,3] => 10100100 => 3
[1,2,3,6,4,8,5,7] => [3,2,3] => 10010100 => 3
[6,1,2,3,4,5,8,7] => [6,2] => 10000010 => 2
[1,6,2,3,4,5,7,8] => [1,7] => 11000000 => 2
[1,2,3,6,4,5,7,8] => [3,5] => 10010000 => 2
[7,1,8,2,3,4,5,6] => [2,6] => 10100000 => 2
[7,1,2,8,3,4,5,6] => [3,5] => 10010000 => 2
[1,7,2,8,3,4,5,6] => [1,2,5] => 11010000 => 3
[1,7,8,2,3,4,5,6] => [1,7] => 11000000 => 2
[1,7,2,3,8,4,5,6] => [1,3,4] => 11001000 => 3
[7,1,2,3,4,8,5,6] => [5,3] => 10000100 => 2
[1,7,2,3,4,8,5,6] => [1,4,3] => 11000100 => 3
[1,2,3,7,4,8,5,6] => [3,2,3] => 10010100 => 3
[7,1,2,3,4,5,8,6] => [6,2] => 10000010 => 2
[1,7,2,3,4,5,8,6] => [1,5,2] => 11000010 => 3
[1,2,7,3,4,5,8,6] => [2,4,2] => 10100010 => 3
[1,2,3,7,4,5,8,6] => [3,3,2] => 10010010 => 3
[1,2,3,4,7,5,8,6] => [4,2,2] => 10001010 => 3
[1,2,3,4,7,8,5,6] => [4,4] => 10001000 => 2
[1,7,2,3,4,5,6,8] => [1,7] => 11000000 => 2
[1,2,3,7,4,5,6,8] => [3,5] => 10010000 => 2
[1,8,2,3,4,5,6,7] => [1,7] => 11000000 => 2
[1,2,3,8,4,5,6,7] => [3,5] => 10010000 => 2
[1,2,3,4,8,5,6,7] => [4,4] => 10001000 => 2
[1,2,3,4,5,8,6,7] => [5,3] => 10000100 => 2
[5,3,2,6,1,4,8,7] => [1,2,3,2] => 11010010 => 4
[7,3,2,5,4,8,1,6] => [1,2,2,3] => 11010100 => 4
[8,4,5,2,3,7,6,1] => [1,4,2,1] => 11000101 => 4
[7,4,5,2,3,8,1,6] => [1,4,3] => 11000100 => 3
[6,4,5,2,3,1,8,7] => [1,4,1,2] => 11000110 => 4
[5,4,6,2,1,3,8,7] => [1,3,2,2] => 11001010 => 4
[3,6,1,5,4,2,8,7] => [3,2,1,2] => 10010110 => 4
[4,6,5,1,3,2,8,7] => [2,3,1,2] => 10100110 => 4
[5,6,4,3,1,2,8,7] => [2,2,2,2] => 10101010 => 4
[7,5,4,3,2,8,1,6] => [1,1,2,1,3] => 11101100 => 5
[8,6,4,3,7,2,5,1] => [1,1,2,3,1] => 11101001 => 5
[7,6,4,3,8,2,1,5] => [1,1,2,2,2] => 11101010 => 5
[6,7,4,3,8,1,2,5] => [2,2,4] => 10101000 => 3
[5,7,4,3,1,8,2,6] => [2,2,1,3] => 10101100 => 4
[4,7,5,1,3,8,2,6] => [2,3,3] => 10100100 => 3
[3,7,1,5,4,8,2,6] => [3,2,3] => 10010100 => 3
[2,1,7,5,4,8,3,6] => [2,1,2,3] => 10110100 => 4
[3,8,1,5,4,7,6,2] => [3,2,2,1] => 10010101 => 4
[4,8,5,1,3,7,6,2] => [2,3,2,1] => 10100101 => 4
[5,8,4,3,1,7,6,2] => [2,2,1,2,1] => 10101101 => 5
[6,8,4,3,7,1,5,2] => [2,2,3,1] => 10101001 => 4
[7,8,4,3,6,5,1,2] => [2,2,2,2] => 10101010 => 4
[6,8,5,7,3,1,4,2] => [2,3,2,1] => 10100101 => 4
[5,8,6,7,1,3,4,2] => [2,5,1] => 10100001 => 3
[4,8,6,1,7,3,5,2] => [2,2,3,1] => 10101001 => 4
[3,8,1,6,7,4,5,2] => [3,4,1] => 10010001 => 3
[2,1,8,6,7,4,5,3] => [2,1,4,1] => 10110001 => 4
[2,1,7,6,8,4,3,5] => [2,1,3,2] => 10110010 => 4
[3,7,1,6,8,4,2,5] => [3,3,2] => 10010010 => 3
[4,7,6,1,8,3,2,5] => [2,2,2,2] => 10101010 => 4
[5,7,6,8,1,3,2,4] => [2,4,2] => 10100010 => 3
[5,4,7,2,1,8,3,6] => [1,3,1,3] => 11001100 => 4
[6,4,7,2,8,1,3,5] => [1,3,4] => 11001000 => 3
[7,4,6,2,8,3,1,5] => [1,3,2,2] => 11001010 => 4
[8,4,6,2,7,3,5,1] => [1,3,3,1] => 11001001 => 4
[8,3,2,6,7,4,5,1] => [1,2,4,1] => 11010001 => 4
[7,3,2,6,8,4,1,5] => [1,2,3,2] => 11010010 => 4
[6,3,2,7,8,1,4,5] => [1,2,5] => 11010000 => 3
[5,3,2,7,1,8,4,6] => [1,2,2,3] => 11010100 => 4
[4,3,2,1,7,8,5,6] => [1,2,1,4] => 11011000 => 4
[3,4,1,2,8,7,6,5] => [4,1,2,1] => 10001101 => 4
[5,3,2,8,1,7,6,4] => [1,2,2,2,1] => 11010101 => 5
[6,3,2,8,7,1,5,4] => [1,2,1,3,1] => 11011001 => 5
[7,3,2,8,6,5,1,4] => [1,2,1,2,2] => 11011010 => 5
[8,4,7,2,6,5,3,1] => [1,3,2,1,1] => 11001011 => 5
[7,4,8,2,6,5,1,3] => [1,3,2,2] => 11001010 => 4
[6,4,8,2,7,1,5,3] => [1,3,3,1] => 11001001 => 4
[5,4,8,2,1,7,6,3] => [1,3,1,2,1] => 11001101 => 5
[4,5,8,1,2,7,6,3] => [5,2,1] => 10000101 => 3
[3,5,1,8,2,7,6,4] => [3,2,2,1] => 10010101 => 4
[2,1,5,8,3,7,6,4] => [2,3,2,1] => 10100101 => 4
[2,1,6,8,7,3,5,4] => [2,2,3,1] => 10101001 => 4
[3,6,1,8,7,2,5,4] => [3,1,3,1] => 10011001 => 4
[4,6,8,1,7,2,5,3] => [4,3,1] => 10001001 => 3
[5,6,8,7,1,2,4,3] => [3,4,1] => 10010001 => 3
[6,5,8,7,2,1,4,3] => [1,2,2,2,1] => 11010101 => 5
[7,5,8,6,2,4,1,3] => [1,2,3,2] => 11010010 => 4
[8,5,7,6,2,4,3,1] => [1,2,3,1,1] => 11010011 => 5
[5,7,8,6,1,4,2,3] => [3,3,2] => 10010010 => 3
[4,7,8,1,6,5,2,3] => [4,2,2] => 10001010 => 3
[3,7,1,8,6,5,2,4] => [3,1,2,2] => 10011010 => 4
[2,1,7,8,6,5,3,4] => [2,2,2,2] => 10101010 => 4
[3,8,1,7,6,5,4,2] => [3,1,2,1,1] => 10011011 => 5
[4,8,7,1,6,5,3,2] => [2,2,2,1,1] => 10101011 => 5
[5,8,7,6,1,4,3,2] => [2,1,3,1,1] => 10110011 => 5
[6,8,7,5,4,1,3,2] => [2,1,2,2,1] => 10110101 => 5
[2,1,4,3,6,5,8,7,10,9] => [2,2,2,2,2] => 1010101010 => 5
[6,7,8,9,10,1,2,3,4,5] => [10] => 1000000000 => 1
[8,5,4,3,2,9,10,1,6,7] => [1,1,2,1,5] => 1110110000 => 5
[9,7,5,10,3,8,2,6,1,4] => [1,1,3,3,2] => 1110010010 => 5
[4,2,5,1,3,6,7,8] => [2,6] => 10100000 => 2
[3,2,6,1,4,5,7,8] => [2,6] => 10100000 => 2
[6,3,5,1,2,4,7,8] => [1,7] => 11000000 => 2
[7,3,5,1,2,4,6,8] => [1,7] => 11000000 => 2
[6,2,8,1,3,4,5,7] => [2,6] => 10100000 => 2
[6,5,8,1,2,3,4,7] => [1,7] => 11000000 => 2
[7,5,8,1,2,3,4,6] => [1,7] => 11000000 => 2
[8,3,5,1,2,4,6,7] => [1,7] => 11000000 => 2
[8,3,7,1,2,4,5,6] => [1,7] => 11000000 => 2
[8,5,7,1,2,3,4,6] => [1,7] => 11000000 => 2
[5,2,6,7,1,3,4,8] => [2,6] => 10100000 => 2
[5,3,6,7,1,2,4,8] => [1,7] => 11000000 => 2
[6,2,5,7,1,3,4,8] => [2,6] => 10100000 => 2
[6,3,5,7,1,2,4,8] => [1,7] => 11000000 => 2
[4,2,6,8,1,3,5,7] => [2,6] => 10100000 => 2
[4,3,6,8,1,2,5,7] => [1,7] => 11000000 => 2
[6,2,4,8,1,3,5,7] => [2,6] => 10100000 => 2
[6,3,5,8,1,2,4,7] => [1,7] => 11000000 => 2
[3,2,7,8,1,4,5,6] => [2,6] => 10100000 => 2
[7,3,4,8,1,2,5,6] => [1,7] => 11000000 => 2
[8,2,4,6,1,3,5,7] => [2,6] => 10100000 => 2
[8,3,5,7,1,2,4,6] => [1,7] => 11000000 => 2
[5,6,2,4,1,3,7,8] => [4,4] => 10001000 => 2
[5,7,2,4,1,3,6,8] => [4,4] => 10001000 => 2
[4,7,3,6,1,2,5,8] => [3,5] => 10010000 => 2
[4,8,2,5,1,3,6,7] => [3,5] => 10010000 => 2
[4,8,2,6,1,3,5,7] => [3,5] => 10010000 => 2
[6,8,2,4,1,3,5,7] => [4,4] => 10001000 => 2
[3,8,2,7,1,4,5,6] => [3,5] => 10010000 => 2
[4,8,2,7,1,3,5,6] => [3,5] => 10010000 => 2
[4,8,3,7,1,2,5,6] => [3,5] => 10010000 => 2
[5,8,2,7,1,3,4,6] => [3,5] => 10010000 => 2
[5,8,3,7,1,2,4,6] => [3,5] => 10010000 => 2
[5,8,4,7,1,2,3,6] => [2,6] => 10100000 => 2
[6,8,5,7,1,2,3,4] => [2,6] => 10100000 => 2
[7,8,2,4,1,3,5,6] => [4,4] => 10001000 => 2
[7,8,3,5,1,2,4,6] => [3,5] => 10010000 => 2
[7,8,4,6,1,2,3,5] => [2,6] => 10100000 => 2
[4,3,2,6,1,5,7,8] => [1,2,5] => 11010000 => 3
[5,3,2,6,1,4,7,8] => [1,2,5] => 11010000 => 3
[5,4,2,6,1,3,7,8] => [1,2,5] => 11010000 => 3
[4,3,2,7,1,5,6,8] => [1,2,5] => 11010000 => 3
[5,3,2,7,1,4,6,8] => [1,2,5] => 11010000 => 3
[6,5,3,7,1,2,4,8] => [1,2,5] => 11010000 => 3
[7,4,2,5,1,3,6,8] => [1,2,5] => 11010000 => 3
[7,4,2,6,1,3,5,8] => [1,2,5] => 11010000 => 3
[4,3,2,8,1,5,6,7] => [1,2,5] => 11010000 => 3
[5,3,2,8,1,4,6,7] => [1,2,5] => 11010000 => 3
[6,4,2,8,1,3,5,7] => [1,2,5] => 11010000 => 3
[6,5,2,8,1,3,4,7] => [1,2,5] => 11010000 => 3
[6,5,3,8,1,2,4,7] => [1,2,5] => 11010000 => 3
[6,5,4,8,1,2,3,7] => [1,1,6] => 11100000 => 3
[7,4,2,8,1,3,5,6] => [1,2,5] => 11010000 => 3
[7,4,3,8,1,2,5,6] => [1,2,5] => 11010000 => 3
[8,4,2,5,1,3,6,7] => [1,2,5] => 11010000 => 3
[8,4,2,6,1,3,5,7] => [1,2,5] => 11010000 => 3
[8,6,2,4,1,3,5,7] => [1,3,4] => 11001000 => 3
[8,4,2,7,1,3,5,6] => [1,2,5] => 11010000 => 3
[8,5,4,7,1,2,3,6] => [1,1,6] => 11100000 => 3
[8,7,2,4,1,3,5,6] => [1,3,4] => 11001000 => 3
[8,7,3,5,1,2,4,6] => [1,2,5] => 11010000 => 3
[8,7,2,6,1,3,4,5] => [1,2,5] => 11010000 => 3
[8,7,3,6,1,2,4,5] => [1,2,5] => 11010000 => 3
[8,7,4,6,1,2,3,5] => [1,1,6] => 11100000 => 3
[5,6,2,4,8,1,3,7] => [4,4] => 10001000 => 2
[4,7,3,5,8,1,2,6] => [3,5] => 10010000 => 2
[5,7,2,4,8,1,3,6] => [4,4] => 10001000 => 2
[4,7,3,6,8,1,2,5] => [3,5] => 10010000 => 2
[6,7,3,4,8,1,2,5] => [4,4] => 10001000 => 2
[4,8,3,5,7,1,2,6] => [3,5] => 10010000 => 2
[5,8,4,6,7,1,2,3] => [2,6] => 10100000 => 2
[6,8,2,5,7,1,3,4] => [3,5] => 10010000 => 2
[7,8,2,4,6,1,3,5] => [4,4] => 10001000 => 2
[4,3,2,6,8,1,5,7] => [1,2,5] => 11010000 => 3
[5,4,2,6,8,1,3,7] => [1,2,5] => 11010000 => 3
[6,3,2,5,8,1,4,7] => [1,2,5] => 11010000 => 3
[6,4,3,5,8,1,2,7] => [1,2,5] => 11010000 => 3
[6,5,2,4,8,1,3,7] => [1,3,4] => 11001000 => 3
[4,3,2,7,8,1,5,6] => [1,2,5] => 11010000 => 3
[5,4,2,7,8,1,3,6] => [1,2,5] => 11010000 => 3
[8,7,2,4,6,1,3,5] => [1,3,4] => 11001000 => 3
[8,7,3,4,6,1,2,5] => [1,3,4] => 11001000 => 3
[4,3,7,2,6,1,5,8] => [1,3,4] => 11001000 => 3
[6,3,7,2,5,1,4,8] => [1,4,3] => 11000100 => 3
[6,4,7,2,5,1,3,8] => [1,4,3] => 11000100 => 3
[4,3,8,2,6,1,5,7] => [1,3,4] => 11001000 => 3
[6,4,8,2,5,1,3,7] => [1,4,3] => 11000100 => 3
[4,3,8,2,7,1,5,6] => [1,3,4] => 11001000 => 3
[6,4,8,2,7,1,3,5] => [1,3,4] => 11001000 => 3
[6,5,8,2,7,1,3,4] => [1,3,4] => 11001000 => 3
[7,5,8,2,4,1,3,6] => [1,4,3] => 11000100 => 3
[7,5,8,2,6,1,3,4] => [1,3,4] => 11001000 => 3
[7,5,8,4,6,1,2,3] => [1,3,4] => 11001000 => 3
[8,3,7,2,6,1,4,5] => [1,3,4] => 11001000 => 3
[8,4,7,2,6,1,3,5] => [1,3,4] => 11001000 => 3
[8,4,7,3,6,1,2,5] => [1,3,4] => 11001000 => 3
[8,5,7,2,6,1,3,4] => [1,3,4] => 11001000 => 3
[8,6,7,2,5,1,3,4] => [1,4,3] => 11000100 => 3
[5,4,3,2,7,1,6,8] => [1,2,1,4] => 11011000 => 4
[6,4,3,2,7,1,5,8] => [1,2,1,4] => 11011000 => 4
[6,5,3,2,7,1,4,8] => [1,2,1,4] => 11011000 => 4
[7,5,3,2,6,1,4,8] => [1,2,1,4] => 11011000 => 4
[5,4,3,2,8,1,6,7] => [1,2,1,4] => 11011000 => 4
[6,5,3,2,8,1,4,7] => [1,2,1,4] => 11011000 => 4
[7,5,3,2,8,1,4,6] => [1,2,1,4] => 11011000 => 4
[7,6,5,3,8,1,2,4] => [1,1,2,4] => 11101000 => 4
[8,5,3,2,6,1,4,7] => [1,2,1,4] => 11011000 => 4
[8,5,3,2,7,1,4,6] => [1,2,1,4] => 11011000 => 4
[8,6,5,3,7,1,2,4] => [1,1,2,4] => 11101000 => 4
[8,7,4,2,6,1,3,5] => [1,1,2,4] => 11101000 => 4
[8,7,4,3,6,1,2,5] => [1,1,2,4] => 11101000 => 4
[8,7,5,2,6,1,3,4] => [1,1,2,4] => 11101000 => 4
[8,7,5,3,6,1,2,4] => [1,1,2,4] => 11101000 => 4
[8,7,6,2,4,1,3,5] => [1,1,3,3] => 11100100 => 4
[4,8,3,7,2,6,1,5] => [3,3,2] => 10010010 => 3
[5,8,3,7,2,6,1,4] => [3,3,2] => 10010010 => 3
[5,8,4,7,2,6,1,3] => [2,4,2] => 10100010 => 3
[5,8,4,7,3,6,1,2] => [2,4,2] => 10100010 => 3
[6,8,3,7,2,5,1,4] => [3,3,2] => 10010010 => 3
[6,8,4,7,2,5,1,3] => [2,4,2] => 10100010 => 3
[6,8,4,7,3,5,1,2] => [2,4,2] => 10100010 => 3
[6,8,5,7,2,4,1,3] => [2,4,2] => 10100010 => 3
[6,8,5,7,3,4,1,2] => [2,4,2] => 10100010 => 3
[7,8,3,6,2,5,1,4] => [3,3,2] => 10010010 => 3
[7,8,4,6,2,5,1,3] => [2,4,2] => 10100010 => 3
[7,8,4,6,3,5,1,2] => [2,4,2] => 10100010 => 3
[7,8,5,6,2,4,1,3] => [2,4,2] => 10100010 => 3
[6,4,3,8,2,7,1,5] => [1,2,2,3] => 11010100 => 4
[6,5,3,8,2,7,1,4] => [1,2,2,3] => 11010100 => 4
[7,5,3,8,2,6,1,4] => [1,2,3,2] => 11010010 => 4
[7,6,4,8,2,5,1,3] => [1,1,4,2] => 11100010 => 4
[8,5,3,7,2,6,1,4] => [1,2,3,2] => 11010010 => 4
[8,5,4,7,2,6,1,3] => [1,1,4,2] => 11100010 => 4
[8,5,4,7,3,6,1,2] => [1,1,4,2] => 11100010 => 4
[8,6,4,7,2,5,1,3] => [1,1,4,2] => 11100010 => 4
[8,7,5,6,2,4,1,3] => [1,1,4,2] => 11100010 => 4
[6,5,4,3,2,8,1,7] => [1,1,2,1,3] => 11101100 => 5
[8,5,4,3,2,7,1,6] => [1,1,2,1,3] => 11101100 => 5
[8,7,5,4,2,6,1,3] => [1,1,2,2,2] => 11101010 => 5
[8,7,6,5,2,4,1,3] => [1,1,1,3,2] => 11110010 => 5
[8,1,2,3,4,7,5,6] => [5,3] => 10000100 => 2
[8,1,2,3,7,4,5,6] => [4,4] => 10001000 => 2
[5,1,2,3,8,7,4,6] => [4,1,3] => 10001100 => 3
[8,1,2,3,6,7,4,5] => [4,4] => 10001000 => 2
[4,1,2,8,7,3,5,6] => [3,1,4] => 10011000 => 3
[4,1,2,7,6,3,8,5] => [3,1,2,2] => 10011010 => 4
[8,1,2,5,6,3,4,7] => [3,5] => 10010000 => 2
[8,1,2,5,7,3,4,6] => [3,5] => 10010000 => 2
[8,1,2,7,6,3,4,5] => [3,1,4] => 10011000 => 3
[7,1,2,5,6,3,8,4] => [3,3,2] => 10010010 => 3
[4,1,2,5,8,7,3,6] => [3,2,3] => 10010100 => 3
[8,1,2,5,6,7,3,4] => [3,5] => 10010000 => 2
[3,1,7,2,6,4,8,5] => [2,2,2,2] => 10101010 => 4
[3,1,8,2,6,7,4,5] => [2,2,4] => 10101000 => 3
[6,1,4,2,3,8,5,7] => [2,3,3] => 10100100 => 3
[8,1,4,2,3,7,5,6] => [2,3,3] => 10100100 => 3
[8,1,7,2,3,4,5,6] => [2,6] => 10100000 => 2
[6,1,5,2,3,8,4,7] => [2,3,3] => 10100100 => 3
[5,1,4,2,8,3,6,7] => [2,2,4] => 10101000 => 3
[5,1,4,2,7,3,8,6] => [2,2,2,2] => 10101010 => 4
[8,1,4,2,6,3,5,7] => [2,2,4] => 10101000 => 3
[7,1,4,2,6,3,8,5] => [2,2,2,2] => 10101010 => 4
[8,1,5,2,7,3,4,6] => [2,2,4] => 10101000 => 3
[7,1,5,2,6,3,8,4] => [2,2,2,2] => 10101010 => 4
[5,1,4,2,8,7,3,6] => [2,2,1,3] => 10101100 => 4
[5,1,4,2,6,7,8,3] => [2,2,4] => 10101000 => 3
[3,1,8,6,2,4,5,7] => [2,1,5] => 10110000 => 3
[3,1,8,6,2,7,4,5] => [2,1,2,3] => 10110100 => 4
[8,1,4,5,2,3,6,7] => [2,6] => 10100000 => 2
[7,1,4,8,2,3,5,6] => [2,6] => 10100000 => 2
[7,1,8,5,2,3,4,6] => [2,1,5] => 10110000 => 3
[7,1,8,6,2,3,4,5] => [2,1,5] => 10110000 => 3
[8,1,4,5,2,7,3,6] => [2,3,3] => 10100100 => 3
[8,1,6,5,2,7,3,4] => [2,1,2,3] => 10110100 => 4
[6,1,4,5,2,7,8,3] => [2,3,3] => 10100100 => 3
[3,1,4,8,7,2,5,6] => [2,2,4] => 10101000 => 3
[3,1,7,5,6,2,8,4] => [2,1,3,2] => 10110010 => 4
[8,1,4,5,7,2,3,6] => [2,6] => 10100000 => 2
[8,1,4,7,6,2,3,5] => [2,2,4] => 10101000 => 3
[8,1,7,5,6,2,3,4] => [2,1,5] => 10110000 => 3
[7,1,4,5,6,2,8,3] => [2,4,2] => 10100010 => 3
[3,1,4,5,8,7,2,6] => [2,3,3] => 10100100 => 3
[3,1,4,8,6,7,2,5] => [2,2,4] => 10101000 => 3
[3,1,8,5,6,7,2,4] => [2,1,5] => 10110000 => 3
[8,1,4,5,6,7,2,3] => [2,6] => 10100000 => 2
[2,8,1,3,4,7,5,6] => [5,3] => 10000100 => 2
[2,4,1,8,6,3,5,7] => [3,1,4] => 10011000 => 3
[7,3,1,2,4,5,8,6] => [1,5,2] => 11000010 => 3
[8,3,1,2,4,7,5,6] => [1,4,3] => 11000100 => 3
[8,3,1,2,6,4,5,7] => [1,3,4] => 11001000 => 3
[7,6,1,2,3,4,8,5] => [1,5,2] => 11000010 => 3
[5,8,1,2,3,7,4,6] => [5,3] => 10000100 => 2
[8,6,1,2,3,7,4,5] => [1,4,3] => 11000100 => 3
[5,4,1,2,8,3,6,7] => [1,3,4] => 11001000 => 3
[8,4,1,2,7,3,5,6] => [1,3,4] => 11001000 => 3
[7,4,1,2,6,3,8,5] => [1,3,2,2] => 11001010 => 4
[5,8,1,2,7,3,4,6] => [4,4] => 10001000 => 2
[8,7,1,2,6,3,4,5] => [1,3,4] => 11001000 => 3
[5,7,1,2,6,3,8,4] => [4,2,2] => 10001010 => 3
[5,4,1,2,8,7,3,6] => [1,3,1,3] => 11001100 => 4
[8,4,1,2,6,7,3,5] => [1,3,4] => 11001000 => 3
[5,8,1,2,6,7,3,4] => [4,4] => 10001000 => 2
[5,4,1,2,6,7,8,3] => [1,3,4] => 11001000 => 3
[4,3,1,6,2,8,5,7] => [1,2,2,3] => 11010100 => 4
[4,3,1,6,2,7,8,5] => [1,2,2,3] => 11010100 => 4
[7,3,1,8,2,4,5,6] => [1,2,5] => 11010000 => 3
[7,3,1,6,2,4,8,5] => [1,2,3,2] => 11010010 => 4
[8,3,1,5,2,7,4,6] => [1,2,2,3] => 11010100 => 4
[8,3,1,6,2,7,4,5] => [1,2,2,3] => 11010100 => 4
[6,3,1,5,2,7,8,4] => [1,2,2,3] => 11010100 => 4
[7,4,1,5,2,3,8,6] => [1,2,3,2] => 11010010 => 4
[8,4,1,6,2,3,5,7] => [1,2,5] => 11010000 => 3
[7,4,1,8,2,3,5,6] => [1,2,5] => 11010000 => 3
[7,4,1,6,2,3,8,5] => [1,2,3,2] => 11010010 => 4
[8,7,1,5,2,3,4,6] => [1,2,5] => 11010000 => 3
[8,7,1,6,2,3,4,5] => [1,2,5] => 11010000 => 3
[6,7,1,5,2,3,8,4] => [3,3,2] => 10010010 => 3
[6,4,1,5,2,8,3,7] => [1,2,2,3] => 11010100 => 4
[8,4,1,5,2,7,3,6] => [1,2,2,3] => 11010100 => 4
[8,4,1,6,2,7,3,5] => [1,2,2,3] => 11010100 => 4
[6,8,1,5,2,7,3,4] => [3,2,3] => 10010100 => 3
[6,4,1,5,2,7,8,3] => [1,2,2,3] => 11010100 => 4
[4,3,1,8,7,2,5,6] => [1,2,1,4] => 11011000 => 4
[4,3,1,7,6,2,8,5] => [1,2,1,2,2] => 11011010 => 5
[8,3,1,5,6,2,4,7] => [1,2,5] => 11010000 => 3
[8,3,1,5,7,2,4,6] => [1,2,5] => 11010000 => 3
[8,3,1,7,6,2,4,5] => [1,2,1,4] => 11011000 => 4
[7,3,1,5,6,2,8,4] => [1,2,3,2] => 11010010 => 4
[8,4,1,5,7,2,3,6] => [1,2,5] => 11010000 => 3
[8,4,1,7,6,2,3,5] => [1,2,1,4] => 11011000 => 4
[7,8,1,5,6,2,3,4] => [3,5] => 10010000 => 2
[7,4,1,5,6,2,8,3] => [1,2,3,2] => 11010010 => 4
[4,3,1,5,6,8,2,7] => [1,2,5] => 11010000 => 3
[4,3,1,5,8,7,2,6] => [1,2,2,3] => 11010100 => 4
[4,3,1,8,6,7,2,5] => [1,2,1,4] => 11011000 => 4
[8,3,1,5,6,7,2,4] => [1,2,5] => 11010000 => 3
[8,4,1,5,6,7,2,3] => [1,2,5] => 11010000 => 3
[4,3,1,5,6,7,8,2] => [1,2,5] => 11010000 => 3
[2,3,8,1,6,7,4,5] => [4,4] => 10001000 => 2
[2,6,4,1,3,8,5,7] => [2,3,3] => 10100100 => 3
[2,6,4,1,3,7,8,5] => [2,3,3] => 10100100 => 3
[2,7,5,1,3,4,8,6] => [2,4,2] => 10100010 => 3
[2,8,7,1,3,4,5,6] => [2,6] => 10100000 => 2
[2,8,5,1,3,7,4,6] => [2,3,3] => 10100100 => 3
[2,6,8,1,3,7,4,5] => [5,3] => 10000100 => 2
[2,6,5,1,3,7,8,4] => [2,3,3] => 10100100 => 3
[2,8,4,1,6,3,5,7] => [2,2,4] => 10101000 => 3
[2,8,4,1,7,3,5,6] => [2,2,4] => 10101000 => 3
[2,7,4,1,6,3,8,5] => [2,2,2,2] => 10101010 => 4
[2,8,5,1,7,3,4,6] => [2,2,4] => 10101000 => 3
[2,7,8,1,6,3,4,5] => [4,4] => 10001000 => 2
[2,7,5,1,6,3,8,4] => [2,2,2,2] => 10101010 => 4
[2,5,4,1,8,7,3,6] => [2,2,1,3] => 10101100 => 4
[2,8,4,1,6,7,3,5] => [2,2,4] => 10101000 => 3
[2,8,5,1,6,7,3,4] => [2,2,4] => 10101000 => 3
[2,5,4,1,6,7,8,3] => [2,2,4] => 10101000 => 3
[6,3,4,1,2,7,8,5] => [1,4,3] => 11000100 => 3
[7,3,5,1,2,4,8,6] => [1,5,2] => 11000010 => 3
[6,3,7,1,2,4,8,5] => [1,5,2] => 11000010 => 3
[8,3,5,1,2,7,4,6] => [1,4,3] => 11000100 => 3
[6,3,8,1,2,7,4,5] => [1,4,3] => 11000100 => 3
[6,3,5,1,2,7,8,4] => [1,4,3] => 11000100 => 3
[7,5,4,1,2,3,8,6] => [1,1,4,2] => 11100010 => 4
[6,7,4,1,2,3,8,5] => [2,4,2] => 10100010 => 3
[6,8,5,1,2,3,4,7] => [2,6] => 10100000 => 2
[6,7,5,1,2,3,8,4] => [2,4,2] => 10100010 => 3
[8,5,4,1,2,7,3,6] => [1,1,3,3] => 11100100 => 4
[6,8,4,1,2,7,3,5] => [2,3,3] => 10100100 => 3
[6,8,5,1,2,7,3,4] => [2,3,3] => 10100100 => 3
[6,5,4,1,2,7,8,3] => [1,1,3,3] => 11100100 => 4
[8,3,4,1,7,2,5,6] => [1,3,4] => 11001000 => 3
[7,3,4,1,6,2,8,5] => [1,3,2,2] => 11001010 => 4
[8,3,5,1,6,2,4,7] => [1,3,4] => 11001000 => 3
[8,3,5,1,7,2,4,6] => [1,3,4] => 11001000 => 3
[7,3,8,1,6,2,4,5] => [1,3,4] => 11001000 => 3
[7,3,5,1,6,2,8,4] => [1,3,2,2] => 11001010 => 4
[8,5,4,1,6,2,3,7] => [1,1,2,4] => 11101000 => 4
[8,5,4,1,7,2,3,6] => [1,1,2,4] => 11101000 => 4
[7,8,4,1,6,2,3,5] => [2,2,4] => 10101000 => 3
[7,8,5,1,6,2,3,4] => [2,2,4] => 10101000 => 3
[7,5,4,1,6,2,8,3] => [1,1,2,2,2] => 11101010 => 5
[5,3,4,1,6,8,2,7] => [1,3,4] => 11001000 => 3
[5,3,4,1,8,7,2,6] => [1,3,1,3] => 11001100 => 4
[8,3,4,1,6,7,2,5] => [1,3,4] => 11001000 => 3
[8,3,5,1,6,7,2,4] => [1,3,4] => 11001000 => 3
[8,5,4,1,6,7,2,3] => [1,1,2,4] => 11101000 => 4
[5,3,4,1,6,7,8,2] => [1,3,4] => 11001000 => 3
[2,3,4,8,1,7,5,6] => [5,3] => 10000100 => 2
[2,3,7,6,1,4,8,5] => [3,3,2] => 10010010 => 3
[2,3,8,5,1,7,4,6] => [3,2,3] => 10010100 => 3
[2,3,8,6,1,7,4,5] => [3,2,3] => 10010100 => 3
[2,3,6,5,1,7,8,4] => [3,2,3] => 10010100 => 3
[2,8,4,6,1,3,5,7] => [2,6] => 10100000 => 2
[2,7,4,8,1,3,5,6] => [2,6] => 10100000 => 2
[2,7,4,6,1,3,8,5] => [2,4,2] => 10100010 => 3
[2,8,6,5,1,3,4,7] => [2,1,5] => 10110000 => 3
[2,7,8,5,1,3,4,6] => [3,5] => 10010000 => 2
[2,7,8,6,1,3,4,5] => [3,5] => 10010000 => 2
[2,7,6,5,1,3,8,4] => [2,1,3,2] => 10110010 => 4
[2,6,4,5,1,8,3,7] => [2,3,3] => 10100100 => 3
[2,8,4,5,1,7,3,6] => [2,3,3] => 10100100 => 3
[2,8,4,6,1,7,3,5] => [2,3,3] => 10100100 => 3
[2,8,6,5,1,7,3,4] => [2,1,2,3] => 10110100 => 4
[2,6,4,5,1,7,8,3] => [2,3,3] => 10100100 => 3
[7,3,4,6,1,2,8,5] => [1,5,2] => 11000010 => 3
[8,3,6,5,1,2,4,7] => [1,2,5] => 11010000 => 3
[7,3,8,5,1,2,4,6] => [1,2,5] => 11010000 => 3
[7,3,8,6,1,2,4,5] => [1,2,5] => 11010000 => 3
[7,3,6,5,1,2,8,4] => [1,2,3,2] => 11010010 => 4
[7,6,4,5,1,2,8,3] => [1,1,4,2] => 11100010 => 4
[6,3,4,5,1,8,2,7] => [1,4,3] => 11000100 => 3
[8,3,4,5,1,7,2,6] => [1,4,3] => 11000100 => 3
[8,3,4,6,1,7,2,5] => [1,4,3] => 11000100 => 3
[8,3,6,5,1,7,2,4] => [1,2,2,3] => 11010100 => 4
[8,6,4,5,1,7,2,3] => [1,1,3,3] => 11100100 => 4
[6,3,4,5,1,7,8,2] => [1,4,3] => 11000100 => 3
[2,3,4,8,6,1,5,7] => [4,4] => 10001000 => 2
[2,3,4,8,7,1,5,6] => [4,4] => 10001000 => 2
[2,3,4,7,6,1,8,5] => [4,2,2] => 10001010 => 3
[2,3,8,5,6,1,4,7] => [3,5] => 10010000 => 2
[2,3,8,5,7,1,4,6] => [3,5] => 10010000 => 2
[2,3,8,7,6,1,4,5] => [3,1,4] => 10011000 => 3
[2,3,7,5,6,1,8,4] => [3,3,2] => 10010010 => 3
[2,8,4,5,6,1,3,7] => [2,6] => 10100000 => 2
[2,8,4,5,7,1,3,6] => [2,6] => 10100000 => 2
[2,8,4,7,6,1,3,5] => [2,2,4] => 10101000 => 3
[2,8,7,5,6,1,3,4] => [2,1,5] => 10110000 => 3
[2,7,4,5,6,1,8,3] => [2,4,2] => 10100010 => 3
[8,3,4,5,7,1,2,6] => [1,7] => 11000000 => 2
[8,3,4,7,6,1,2,5] => [1,3,4] => 11001000 => 3
[8,3,7,5,6,1,2,4] => [1,2,5] => 11010000 => 3
[7,3,4,5,6,1,8,2] => [1,5,2] => 11000010 => 3
[2,3,4,5,8,7,1,6] => [5,3] => 10000100 => 2
[2,3,4,8,6,7,1,5] => [4,4] => 10001000 => 2
[2,3,8,5,6,7,1,4] => [3,5] => 10010000 => 2
[2,8,4,5,6,7,1,3] => [2,6] => 10100000 => 2
[9,1,2,3,4,5,6,7,8] => [9] => 100000000 => 1
[8,1,2,3,4,5,6,9,7] => [7,2] => 100000010 => 2
[9,1,2,3,4,5,8,6,7] => [6,3] => 100000100 => 2
[7,1,2,3,4,5,8,9,6] => [6,3] => 100000100 => 2
[9,1,2,3,4,8,5,6,7] => [5,4] => 100001000 => 2
[6,1,2,3,4,9,8,5,7] => [5,1,3] => 100001100 => 3
[9,1,2,3,4,7,8,5,6] => [5,4] => 100001000 => 2
[6,1,2,3,4,7,8,9,5] => [5,4] => 100001000 => 2
[8,1,2,3,9,4,5,6,7] => [4,5] => 100010000 => 2
[9,1,2,3,6,8,4,5,7] => [4,5] => 100010000 => 2
[5,1,2,3,6,9,8,4,7] => [4,2,3] => 100010100 => 3
[9,1,2,8,3,4,5,6,7] => [3,6] => 100100000 => 2
[4,1,2,8,9,3,5,6,7] => [3,6] => 100100000 => 2
[8,1,2,5,9,3,4,6,7] => [3,6] => 100100000 => 2
[9,1,8,2,3,4,5,6,7] => [2,7] => 101000000 => 2
[9,1,4,8,2,3,5,6,7] => [2,7] => 101000000 => 2
[3,1,4,8,9,2,5,6,7] => [2,7] => 101000000 => 2
[7,1,4,5,6,2,8,9,3] => [2,4,3] => 101000100 => 3
[3,1,4,9,6,7,8,2,5] => [2,2,5] => 101010000 => 3
[9,1,4,5,6,7,8,2,3] => [2,7] => 101000000 => 2
[3,1,4,5,6,7,8,9,2] => [2,7] => 101000000 => 2
[2,9,1,3,4,5,6,7,8] => [9] => 100000000 => 1
[2,4,1,6,3,8,5,9,7] => [3,2,2,2] => 100101010 => 4
[9,3,1,2,4,5,6,7,8] => [1,8] => 110000000 => 2
[8,9,1,2,3,4,5,6,7] => [9] => 100000000 => 1
[2,9,8,1,3,4,5,6,7] => [2,7] => 101000000 => 2
[9,3,8,1,2,4,5,6,7] => [1,8] => 110000000 => 2
[9,7,8,1,2,3,4,5,6] => [1,8] => 110000000 => 2
[2,3,9,8,1,4,5,6,7] => [3,6] => 100100000 => 2
[6,3,4,5,1,7,9,2,8] => [1,4,4] => 110001000 => 3
[9,7,4,5,6,1,2,3,8] => [1,1,7] => 111000000 => 3
[2,3,9,5,6,7,1,4,8] => [3,6] => 100100000 => 2
[2,9,4,5,6,7,1,3,8] => [2,7] => 101000000 => 2
[9,3,4,5,6,7,1,2,8] => [1,8] => 110000000 => 2
[2,3,4,5,6,7,9,1,8] => [9] => 100000000 => 1
[2,3,4,5,6,7,8,9,1] => [9] => 100000000 => 1
[3,5,2,6,1,4,8,7] => [3,3,2] => 10010010 => 3
[3,5,2,6,4,1,8,7] => [3,2,1,2] => 10010110 => 4
[3,5,2,7,4,8,1,6] => [3,2,3] => 10010100 => 3
[3,5,2,7,4,8,6,1] => [3,2,2,1] => 10010101 => 4
[4,5,7,2,3,8,6,1] => [5,2,1] => 10000101 => 3
[4,5,7,2,3,8,1,6] => [5,3] => 10000100 => 2
[4,5,6,2,3,1,8,7] => [5,1,2] => 10000110 => 3
[4,5,6,2,1,3,8,7] => [4,2,2] => 10001010 => 3
[3,5,1,6,4,2,8,7] => [3,2,1,2] => 10010110 => 4
[4,5,6,1,3,2,8,7] => [5,1,2] => 10000110 => 3
[4,5,6,3,1,2,8,7] => [4,2,2] => 10001010 => 3
[4,5,7,3,2,8,1,6] => [4,1,3] => 10001100 => 3
[4,5,7,3,2,8,6,1] => [4,1,2,1] => 10001101 => 4
[4,6,7,3,8,2,5,1] => [4,3,1] => 10001001 => 3
[4,6,7,3,8,2,1,5] => [4,2,2] => 10001010 => 3
[4,6,7,3,8,1,2,5] => [4,4] => 10001000 => 2
[4,5,7,3,1,8,2,6] => [4,1,3] => 10001100 => 3
[4,5,7,1,3,8,2,6] => [5,3] => 10000100 => 2
[3,5,1,7,4,8,2,6] => [3,2,3] => 10010100 => 3
[2,1,5,7,4,8,3,6] => [2,3,3] => 10100100 => 3
[2,1,5,7,4,8,6,3] => [2,3,2,1] => 10100101 => 4
[3,5,1,7,4,8,6,2] => [3,2,2,1] => 10010101 => 4
[4,5,7,1,3,8,6,2] => [5,2,1] => 10000101 => 3
[4,5,7,3,1,8,6,2] => [4,1,2,1] => 10001101 => 4
[4,6,7,3,8,1,5,2] => [4,3,1] => 10001001 => 3
[4,6,7,3,8,5,1,2] => [4,2,2] => 10001010 => 3
[4,6,7,3,8,5,2,1] => [4,2,1,1] => 10001011 => 4
[5,6,7,8,3,1,4,2] => [5,2,1] => 10000101 => 3
[5,6,7,8,1,3,4,2] => [7,1] => 10000001 => 2
[4,6,7,1,8,3,5,2] => [4,3,1] => 10001001 => 3
[3,6,1,7,8,4,5,2] => [3,4,1] => 10010001 => 3
[2,1,6,7,8,4,5,3] => [2,5,1] => 10100001 => 3
[2,1,6,7,8,4,3,5] => [2,4,2] => 10100010 => 3
[3,6,1,7,8,4,2,5] => [3,3,2] => 10010010 => 3
[4,6,7,1,8,3,2,5] => [4,2,2] => 10001010 => 3
[5,6,7,8,1,3,2,4] => [6,2] => 10000010 => 2
[4,5,7,2,1,8,3,6] => [4,1,3] => 10001100 => 3
[4,6,7,2,8,1,3,5] => [4,4] => 10001000 => 2
[4,6,7,2,8,3,1,5] => [4,2,2] => 10001010 => 3
[4,6,7,2,8,3,5,1] => [4,3,1] => 10001001 => 3
[3,6,2,7,8,4,5,1] => [3,4,1] => 10010001 => 3
[3,6,2,7,8,4,1,5] => [3,3,2] => 10010010 => 3
[3,6,2,7,8,1,4,5] => [3,5] => 10010000 => 2
[3,5,2,7,1,8,4,6] => [3,2,3] => 10010100 => 3
[3,4,2,1,7,8,5,6] => [3,1,4] => 10011000 => 3
[3,4,1,2,7,8,6,5] => [4,3,1] => 10001001 => 3
[3,5,2,7,1,8,6,4] => [3,2,2,1] => 10010101 => 4
[3,6,2,7,8,1,5,4] => [3,4,1] => 10010001 => 3
[3,6,2,7,8,5,1,4] => [3,3,2] => 10010010 => 3
[3,6,2,7,8,5,4,1] => [3,3,1,1] => 10010011 => 4
[4,6,7,2,8,5,3,1] => [4,2,1,1] => 10001011 => 4
[4,6,7,2,8,5,1,3] => [4,2,2] => 10001010 => 3
[4,6,7,2,8,1,5,3] => [4,3,1] => 10001001 => 3
[4,5,7,2,1,8,6,3] => [4,1,2,1] => 10001101 => 4
[4,5,7,1,2,8,6,3] => [5,2,1] => 10000101 => 3
[3,5,1,7,2,8,6,4] => [3,2,2,1] => 10010101 => 4
[2,1,5,7,3,8,6,4] => [2,3,2,1] => 10100101 => 4
[2,1,6,7,8,3,5,4] => [2,5,1] => 10100001 => 3
[3,6,1,7,8,2,5,4] => [3,4,1] => 10010001 => 3
[4,6,7,1,8,2,5,3] => [4,3,1] => 10001001 => 3
[5,6,7,8,1,2,4,3] => [7,1] => 10000001 => 2
[5,6,7,8,2,1,4,3] => [5,2,1] => 10000101 => 3
[5,6,7,8,2,4,1,3] => [6,2] => 10000010 => 2
[5,6,7,8,2,4,3,1] => [6,1,1] => 10000011 => 3
[5,6,7,8,1,4,2,3] => [6,2] => 10000010 => 2
[4,6,7,1,8,5,2,3] => [4,2,2] => 10001010 => 3
[3,6,1,7,8,5,2,4] => [3,3,2] => 10010010 => 3
[2,1,6,7,8,5,3,4] => [2,4,2] => 10100010 => 3
[3,6,1,7,8,5,4,2] => [3,3,1,1] => 10010011 => 4
[4,6,7,1,8,5,3,2] => [4,2,1,1] => 10001011 => 4
[5,6,7,8,1,4,3,2] => [6,1,1] => 10000011 => 3
[5,6,7,8,4,1,3,2] => [5,2,1] => 10000101 => 3
[3,4,2,1,6,5,8,7,10,9] => [3,1,2,2,2] => 1001101010 => 5
[3,5,2,6,4,1,8,7,10,9] => [3,2,1,2,2] => 1001011010 => 5
[3,5,2,7,4,8,6,1,10,9] => [3,2,2,1,2] => 1001010110 => 5
[3,5,2,7,4,9,6,10,8,1] => [3,2,2,2,1] => 1001010101 => 5
[2,1,5,6,4,3,8,7,10,9] => [2,3,1,2,2] => 1010011010 => 5
[4,5,6,3,2,1,8,7,10,9] => [4,1,1,2,2] => 1000111010 => 5
[4,5,7,3,2,8,6,1,10,9] => [4,1,2,1,2] => 1000110110 => 5
[2,1,5,7,4,8,6,3,10,9] => [2,3,2,1,2] => 1010010110 => 5
[4,6,7,3,8,5,2,1,10,9] => [4,2,1,1,2] => 1000101110 => 5
[2,1,5,7,4,9,6,10,8,3] => [2,3,2,2,1] => 1010010101 => 5
[2,1,4,3,7,8,6,5,10,9] => [2,2,3,1,2] => 1010100110 => 5
[3,4,2,1,7,8,6,5,10,9] => [3,1,3,1,2] => 1001100110 => 5
[3,6,2,7,8,5,4,1,10,9] => [3,3,1,1,2] => 1001001110 => 5
[2,1,6,7,8,5,4,3,10,9] => [2,4,1,1,2] => 1010001110 => 5
[5,6,7,8,4,3,2,1,10,9] => [5,1,1,1,2] => 1000011110 => 5
[2,1,4,3,7,9,6,10,8,5] => [2,2,3,2,1] => 1010100101 => 5
[3,4,2,1,7,9,6,10,8,5] => [3,1,3,2,1] => 1001100101 => 5
[2,1,4,3,6,5,9,10,8,7] => [2,2,2,3,1] => 1010101001 => 5
[3,4,2,1,6,5,9,10,8,7] => [3,1,2,3,1] => 1001101001 => 5
[3,5,2,6,4,1,9,10,8,7] => [3,2,1,3,1] => 1001011001 => 5
[2,1,5,6,4,3,9,10,8,7] => [2,3,1,3,1] => 1010011001 => 5
[6,5,8,7,3,4,1,2] => [1,2,3,2] => 11010010 => 4
[3,6,7,4,5,8,1,2] => [5,3] => 10000100 => 2
[2,6,7,4,5,1,8,3] => [5,1,2] => 10000110 => 3
[1,6,7,4,5,2,3,8] => [1,4,3] => 11000100 => 3
[1,5,4,7,6,2,3,8] => [1,1,2,4] => 11101000 => 4
[2,5,4,7,6,1,8,3] => [2,2,2,2] => 10101010 => 4
[3,5,4,7,6,8,1,2] => [2,2,4] => 10101000 => 3
[4,5,3,7,8,6,1,2] => [3,3,2] => 10010010 => 3
[5,4,3,8,7,6,1,2] => [1,2,1,2,2] => 11011010 => 5
[6,4,8,3,7,5,1,2] => [1,3,2,2] => 11001010 => 4
[6,3,8,4,5,7,1,2] => [1,4,3] => 11000100 => 3
[5,3,4,8,6,7,1,2] => [1,3,4] => 11001000 => 3
[4,3,5,6,8,7,1,2] => [1,4,3] => 11000100 => 3
[3,2,5,6,1,8,7,4] => [2,3,2,1] => 10100101 => 4
[4,2,5,6,8,1,7,3] => [2,5,1] => 10100001 => 3
[5,2,4,8,6,1,7,3] => [2,2,3,1] => 10101001 => 4
[6,2,8,4,5,1,7,3] => [2,3,2,1] => 10100101 => 4
[7,8,2,4,5,1,6,3] => [5,2,1] => 10000101 => 3
[7,8,1,4,5,2,3,6] => [5,3] => 10000100 => 2
[6,1,8,4,5,2,3,7] => [2,3,3] => 10100100 => 3
[5,1,4,8,6,2,3,7] => [2,2,4] => 10101000 => 3
[4,1,3,2,8,6,5,7] => [3,1,2,2] => 10011010 => 4
[5,1,3,8,2,6,4,7] => [3,3,2] => 10010010 => 3
[6,1,8,3,2,5,4,7] => [2,2,2,2] => 10101010 => 4
[7,8,1,3,2,5,4,6] => [4,2,2] => 10001010 => 3
[7,8,2,3,1,5,6,4] => [4,3,1] => 10001001 => 3
[6,2,8,3,1,5,7,4] => [2,2,3,1] => 10101001 => 4
[5,2,3,8,1,6,7,4] => [3,4,1] => 10010001 => 3
[6,3,8,2,1,7,5,4] => [1,3,1,2,1] => 11001101 => 5
[7,8,3,2,1,6,5,4] => [3,1,2,1,1] => 10011011 => 5
[7,8,4,2,6,1,5,3] => [2,2,3,1] => 10101001 => 4
[5,4,2,8,7,1,6,3] => [1,2,1,3,1] => 11011001 => 5
[4,5,2,7,8,1,6,3] => [3,4,1] => 10010001 => 3
[2,5,3,7,1,6,8,4] => [3,3,2] => 10010010 => 3
[1,5,3,7,2,6,4,8] => [1,2,3,2] => 11010010 => 4
[1,6,7,3,2,5,4,8] => [1,3,2,2] => 11001010 => 4
[2,6,7,3,1,5,8,4] => [4,2,2] => 10001010 => 3
[3,6,7,2,1,8,5,4] => [4,1,2,1] => 10001101 => 4
[7,8,5,6,2,1,4,3] => [2,3,2,1] => 10100101 => 4
[6,5,8,7,1,2,3,4] => [1,2,5] => 11010000 => 3
[5,4,1,8,7,2,3,6] => [1,2,1,4] => 11011000 => 4
[6,4,8,1,7,2,3,5] => [1,3,4] => 11001000 => 3
[7,8,3,1,2,6,4,5] => [3,3,2] => 10010010 => 3
[5,3,1,8,2,7,4,6] => [1,2,2,3] => 11010100 => 4
[4,3,1,2,8,7,5,6] => [1,3,1,3] => 11001100 => 4
[4,2,1,3,8,5,7,6] => [2,2,3,1] => 10101001 => 4
[5,2,1,8,3,4,7,6] => [2,1,4,1] => 10110001 => 4
[6,2,8,1,3,4,7,5] => [2,5,1] => 10100001 => 3
[7,8,2,1,3,4,6,5] => [3,4,1] => 10010001 => 3
[4,3,1,2,6,5,8,7] => [1,3,2,2] => 11001010 => 4
[5,3,1,6,2,4,8,7] => [1,2,3,2] => 11010010 => 4
[6,3,1,5,2,4,8,7] => [1,2,3,2] => 11010010 => 4
[7,3,1,5,2,8,4,6] => [1,2,2,3] => 11010100 => 4
[8,4,5,1,2,7,3,6] => [1,4,3] => 11000100 => 3
[7,4,5,1,2,8,3,6] => [1,4,3] => 11000100 => 3
[6,4,5,1,2,3,8,7] => [1,5,2] => 11000010 => 3
[5,4,6,1,2,3,8,7] => [1,5,2] => 11000010 => 3
[2,1,6,5,3,4,8,7] => [2,1,3,2] => 10110010 => 4
[3,6,1,5,2,4,8,7] => [3,3,2] => 10010010 => 3
[4,6,5,1,2,3,8,7] => [2,4,2] => 10100010 => 3
[5,6,4,1,2,3,8,7] => [2,4,2] => 10100010 => 3
[6,5,4,1,2,3,8,7] => [1,1,4,2] => 11100010 => 4
[7,5,4,1,2,8,3,6] => [1,1,3,3] => 11100100 => 4
[8,6,4,1,7,2,3,5] => [1,1,2,4] => 11101000 => 4
[7,6,4,1,8,2,3,5] => [1,1,2,4] => 11101000 => 4
[6,7,4,1,8,2,3,5] => [2,2,4] => 10101000 => 3
[5,7,4,1,2,8,3,6] => [2,3,3] => 10100100 => 3
[4,7,5,1,2,8,3,6] => [2,3,3] => 10100100 => 3
[3,7,1,5,2,8,4,6] => [3,2,3] => 10010100 => 3
[2,1,7,5,3,8,4,6] => [2,1,2,3] => 10110100 => 4
[2,1,8,5,3,7,4,6] => [2,1,2,3] => 10110100 => 4
[3,8,1,5,2,7,4,6] => [3,2,3] => 10010100 => 3
[4,8,5,1,2,7,3,6] => [2,3,3] => 10100100 => 3
[5,8,4,1,2,7,3,6] => [2,3,3] => 10100100 => 3
[6,8,4,1,7,2,3,5] => [2,2,4] => 10101000 => 3
[8,7,4,1,6,2,3,5] => [1,1,2,4] => 11101000 => 4
[5,8,6,7,1,2,3,4] => [2,6] => 10100000 => 2
[4,8,6,1,7,2,3,5] => [2,2,4] => 10101000 => 3
[3,8,1,6,7,2,4,5] => [3,5] => 10010000 => 2
[2,1,8,6,7,3,4,5] => [2,1,5] => 10110000 => 3
[2,1,7,6,8,3,4,5] => [2,1,5] => 10110000 => 3
[3,7,1,6,8,2,4,5] => [3,5] => 10010000 => 2
[4,7,6,1,8,2,3,5] => [2,2,4] => 10101000 => 3
[5,7,6,8,1,2,3,4] => [2,6] => 10100000 => 2
[5,4,7,1,2,8,3,6] => [1,4,3] => 11000100 => 3
[6,4,7,1,8,2,3,5] => [1,3,4] => 11001000 => 3
[7,4,6,1,8,2,3,5] => [1,3,4] => 11001000 => 3
[8,4,6,1,7,2,3,5] => [1,3,4] => 11001000 => 3
[8,3,1,6,7,2,4,5] => [1,2,5] => 11010000 => 3
[7,3,1,6,8,2,4,5] => [1,2,5] => 11010000 => 3
[6,3,1,7,8,2,4,5] => [1,2,5] => 11010000 => 3
[5,3,1,7,2,8,4,6] => [1,2,2,3] => 11010100 => 4
[4,3,1,2,7,8,5,6] => [1,3,4] => 11001000 => 3
[2,1,4,3,8,7,5,6] => [2,2,1,3] => 10101100 => 4
[3,4,1,2,8,7,5,6] => [4,1,3] => 10001100 => 3
[6,3,1,8,7,2,4,5] => [1,2,1,4] => 11011000 => 4
[7,3,1,8,6,2,4,5] => [1,2,1,4] => 11011000 => 4
[8,4,7,1,6,2,3,5] => [1,3,4] => 11001000 => 3
[7,4,8,1,6,2,3,5] => [1,3,4] => 11001000 => 3
[5,4,8,1,2,7,3,6] => [1,4,3] => 11000100 => 3
[4,5,8,1,2,7,3,6] => [5,3] => 10000100 => 2
[3,5,1,8,2,7,4,6] => [3,2,3] => 10010100 => 3
[2,1,5,8,3,7,4,6] => [2,3,3] => 10100100 => 3
[2,1,6,8,7,3,4,5] => [2,2,4] => 10101000 => 3
[3,6,1,8,7,2,4,5] => [3,1,4] => 10011000 => 3
[4,6,8,1,7,2,3,5] => [4,4] => 10001000 => 2
[5,6,8,7,1,2,3,4] => [3,5] => 10010000 => 2
[7,5,8,6,1,2,3,4] => [1,2,5] => 11010000 => 3
[8,5,7,6,1,2,3,4] => [1,2,5] => 11010000 => 3
[5,7,8,6,1,2,3,4] => [3,5] => 10010000 => 2
[4,7,8,1,6,2,3,5] => [4,4] => 10001000 => 2
[3,7,1,8,6,2,4,5] => [3,1,4] => 10011000 => 3
[2,1,7,8,6,3,4,5] => [2,2,4] => 10101000 => 3
[2,1,8,7,6,3,4,5] => [2,1,1,4] => 10111000 => 4
[3,8,1,7,6,2,4,5] => [3,1,4] => 10011000 => 3
[4,8,7,1,6,2,3,5] => [2,2,4] => 10101000 => 3
[5,8,7,6,1,2,3,4] => [2,1,5] => 10110000 => 3
[6,8,7,5,1,2,3,4] => [2,1,5] => 10110000 => 3
[6,4,7,3,8,5,1,2] => [1,3,2,2] => 11001010 => 4
[6,4,7,3,5,8,1,2] => [1,4,3] => 11000100 => 3
[6,4,7,2,5,1,8,3] => [1,4,1,2] => 11000110 => 4
[5,4,2,7,6,1,3,8] => [1,2,1,4] => 11011000 => 4
[5,4,2,7,6,1,8,3] => [1,2,1,2,2] => 11011010 => 5
[5,4,3,7,6,8,1,2] => [1,2,1,4] => 11011000 => 4
[5,4,3,7,8,6,1,2] => [1,2,3,2] => 11010010 => 4
[6,4,8,3,5,7,1,2] => [1,4,3] => 11000100 => 3
[5,4,3,8,6,7,1,2] => [1,2,1,4] => 11011000 => 4
[5,4,3,6,8,7,1,2] => [1,2,2,3] => 11010100 => 4
[5,4,2,6,7,1,8,3] => [1,2,3,2] => 11010010 => 4
[5,4,2,6,7,1,3,8] => [1,2,5] => 11010000 => 3
[5,3,2,6,1,7,4,8] => [1,2,2,3] => 11010100 => 4
[5,3,2,6,1,7,8,4] => [1,2,2,3] => 11010100 => 4
[5,3,2,6,1,8,7,4] => [1,2,2,2,1] => 11010101 => 5
[5,4,2,6,8,1,7,3] => [1,2,4,1] => 11010001 => 4
[5,4,2,8,6,1,7,3] => [1,2,1,3,1] => 11011001 => 5
[6,4,8,2,5,1,7,3] => [1,4,2,1] => 11000101 => 4
[7,8,4,2,5,1,6,3] => [2,3,2,1] => 10100101 => 4
[7,8,4,2,5,1,3,6] => [2,3,3] => 10100100 => 3
[5,4,2,8,6,1,3,7] => [1,2,1,4] => 11011000 => 4
[5,3,2,6,1,8,4,7] => [1,2,2,3] => 11010100 => 4
[4,3,2,1,6,8,5,7] => [1,2,1,4] => 11011000 => 4
[4,3,2,1,8,6,5,7] => [1,2,1,2,2] => 11011010 => 5
[5,3,2,8,1,6,4,7] => [1,2,3,2] => 11010010 => 4
[6,3,8,2,1,5,4,7] => [1,3,2,2] => 11001010 => 4
[7,8,3,2,1,5,4,6] => [3,1,2,2] => 10011010 => 4
[7,8,3,2,1,5,6,4] => [3,1,3,1] => 10011001 => 4
[6,3,8,2,1,5,7,4] => [1,3,3,1] => 11001001 => 4
[5,3,2,8,1,6,7,4] => [1,2,4,1] => 11010001 => 4
[5,4,2,7,8,1,6,3] => [1,2,4,1] => 11010001 => 4
[5,3,2,7,1,8,6,4] => [1,2,2,2,1] => 11010101 => 5
[5,3,2,7,1,6,8,4] => [1,2,3,2] => 11010010 => 4
[5,3,2,7,1,6,4,8] => [1,2,3,2] => 11010010 => 4
[6,3,7,2,1,5,4,8] => [1,3,2,2] => 11001010 => 4
[6,3,7,2,1,5,8,4] => [1,3,2,2] => 11001010 => 4
[6,3,7,2,1,8,5,4] => [1,3,1,2,1] => 11001101 => 5
[6,4,7,2,8,1,5,3] => [1,3,3,1] => 11001001 => 4
[6,5,7,8,2,1,4,3] => [1,4,2,1] => 11000101 => 4
[6,5,8,7,2,1,3,4] => [1,2,2,3] => 11010100 => 4
[6,3,7,2,1,8,4,5] => [1,3,1,3] => 11001100 => 4
[6,3,7,2,1,4,8,5] => [1,3,2,2] => 11001010 => 4
[6,3,7,2,1,4,5,8] => [1,3,4] => 11001000 => 3
[5,3,2,7,1,4,8,6] => [1,2,3,2] => 11010010 => 4
[5,4,2,8,7,1,3,6] => [1,2,1,4] => 11011000 => 4
[7,8,4,2,6,1,3,5] => [2,2,4] => 10101000 => 3
[7,8,3,2,1,6,4,5] => [3,1,2,2] => 10011010 => 4
[6,3,8,2,1,7,4,5] => [1,3,1,3] => 11001100 => 4
[5,3,2,8,1,7,4,6] => [1,2,2,3] => 11010100 => 4
[4,3,2,1,8,7,5,6] => [1,2,1,1,3] => 11011100 => 5
[4,3,2,1,7,5,8,6] => [1,2,1,2,2] => 11011010 => 5
[4,3,2,1,7,5,6,8] => [1,2,1,4] => 11011000 => 4
[4,3,2,1,8,5,7,6] => [1,2,1,3,1] => 11011001 => 5
[5,3,2,8,1,4,7,6] => [1,2,4,1] => 11010001 => 4
[6,3,8,2,1,4,7,5] => [1,3,3,1] => 11001001 => 4
[7,8,3,2,1,4,6,5] => [3,1,3,1] => 10011001 => 4
[6,3,8,2,1,4,5,7] => [1,3,4] => 11001000 => 3
[4,3,2,1,8,5,6,7] => [1,2,1,4] => 11011000 => 4
[4,3,2,1,5,8,6,7] => [1,2,2,3] => 11010100 => 4
[7,8,5,6,1,2,4,3] => [2,5,1] => 10100001 => 3
[7,8,4,1,6,2,5,3] => [2,2,3,1] => 10101001 => 4
[7,8,1,4,6,2,5,3] => [4,3,1] => 10001001 => 3
[6,1,8,4,7,2,5,3] => [2,2,3,1] => 10101001 => 4
[1,6,8,4,7,2,5,3] => [1,3,3,1] => 11001001 => 4
[1,6,8,3,2,7,5,4] => [1,3,1,2,1] => 11001101 => 5
[6,1,8,3,2,7,5,4] => [2,2,1,2,1] => 10101101 => 5
[7,8,1,3,2,6,5,4] => [4,2,1,1] => 10001011 => 4
[7,8,3,1,2,6,5,4] => [3,3,1,1] => 10010011 => 4
[7,8,3,4,6,5,1,2] => [4,2,2] => 10001010 => 3
[7,8,2,4,6,1,5,3] => [4,3,1] => 10001001 => 3
[7,8,2,3,1,6,5,4] => [4,2,1,1] => 10001011 => 4
[7,8,2,1,3,6,5,4] => [3,3,1,1] => 10010011 => 4
[7,8,1,2,3,6,5,4] => [6,1,1] => 10000011 => 3
[6,1,8,2,3,7,5,4] => [2,3,2,1] => 10100101 => 4
[1,6,8,2,3,7,5,4] => [1,4,2,1] => 11000101 => 4
[1,5,2,8,3,7,6,4] => [1,2,2,2,1] => 11010101 => 5
[5,1,2,8,3,7,6,4] => [3,2,2,1] => 10010101 => 4
[5,2,1,8,3,7,6,4] => [2,1,2,2,1] => 10110101 => 5
[6,2,8,1,3,7,5,4] => [2,3,2,1] => 10100101 => 4
[6,2,8,3,1,7,5,4] => [2,2,1,2,1] => 10101101 => 5
[6,2,8,4,7,1,5,3] => [2,2,3,1] => 10101001 => 4
[6,3,8,4,7,5,1,2] => [1,3,2,2] => 11001010 => 4
[3,6,8,4,7,5,1,2] => [4,2,2] => 10001010 => 3
[2,6,8,4,7,1,5,3] => [4,3,1] => 10001001 => 3
[2,6,8,3,1,7,5,4] => [4,1,2,1] => 10001101 => 4
[2,6,8,1,3,7,5,4] => [5,2,1] => 10000101 => 3
[2,5,1,8,3,7,6,4] => [3,2,2,1] => 10010101 => 4
[1,2,5,8,3,7,6,4] => [2,3,2,1] => 10100101 => 4
[2,4,1,3,8,7,6,5] => [4,1,2,1] => 10001101 => 4
[2,5,3,8,1,7,6,4] => [3,2,2,1] => 10010101 => 4
[2,5,4,8,7,1,6,3] => [2,2,3,1] => 10101001 => 4
[3,5,4,8,7,6,1,2] => [2,2,2,2] => 10101010 => 4
[5,3,4,8,7,6,1,2] => [1,3,2,2] => 11001010 => 4
[5,2,4,8,7,1,6,3] => [2,2,3,1] => 10101001 => 4
[5,2,3,8,1,7,6,4] => [3,2,2,1] => 10010101 => 4
[4,2,1,3,8,7,6,5] => [2,2,1,2,1] => 10101101 => 5
[4,1,2,3,8,7,6,5] => [4,1,2,1] => 10001101 => 4
[1,4,2,3,8,7,6,5] => [1,3,1,2,1] => 11001101 => 5
[4,1,3,2,8,7,6,5] => [3,1,1,2,1] => 10011101 => 5
[4,3,1,2,8,7,6,5] => [1,3,1,2,1] => 11001101 => 5
[6,3,8,1,2,7,5,4] => [1,4,2,1] => 11000101 => 4
[5,3,1,8,2,7,6,4] => [1,2,2,2,1] => 11010101 => 5
[5,1,3,8,2,7,6,4] => [3,2,2,1] => 10010101 => 4
[1,5,3,8,2,7,6,4] => [1,2,2,2,1] => 11010101 => 5
[1,5,4,8,7,2,6,3] => [1,1,2,3,1] => 11101001 => 5
[5,1,4,8,7,2,6,3] => [2,2,3,1] => 10101001 => 4
[5,4,1,8,7,2,6,3] => [1,2,1,3,1] => 11011001 => 5
[6,4,8,1,7,2,5,3] => [1,3,3,1] => 11001001 => 4
[6,5,8,7,1,2,4,3] => [1,2,4,1] => 11010001 => 4
[5,6,8,7,3,4,1,2] => [3,3,2] => 10010010 => 3
[5,6,8,7,2,1,4,3] => [3,2,2,1] => 10010101 => 4
[4,5,1,8,7,2,6,3] => [3,1,3,1] => 10011001 => 4
[4,1,5,8,7,2,6,3] => [2,2,3,1] => 10101001 => 4
[1,4,5,8,7,2,6,3] => [1,3,3,1] => 11001001 => 4
[1,3,5,8,2,7,6,4] => [1,4,2,1] => 11000101 => 4
[3,1,5,8,2,7,6,4] => [2,3,2,1] => 10100101 => 4
[3,6,8,1,2,7,5,4] => [5,2,1] => 10000101 => 3
[3,6,8,2,1,7,5,4] => [4,1,2,1] => 10001101 => 4
[4,6,8,2,7,1,5,3] => [4,3,1] => 10001001 => 3
[4,6,8,3,7,5,1,2] => [4,2,2] => 10001010 => 3
[4,5,3,8,7,6,1,2] => [3,1,2,2] => 10011010 => 4
[4,5,2,8,7,1,6,3] => [3,1,3,1] => 10011001 => 4
[3,5,2,8,1,7,6,4] => [3,2,2,1] => 10010101 => 4
[3,1,4,2,8,7,6,5] => [2,2,1,2,1] => 10101101 => 5
[3,1,2,4,8,7,6,5] => [4,1,2,1] => 10001101 => 4
[3,2,5,8,1,7,6,4] => [2,3,2,1] => 10100101 => 4
[4,2,5,8,7,1,6,3] => [2,2,3,1] => 10101001 => 4
[4,3,5,8,7,6,1,2] => [1,3,2,2] => 11001010 => 4
[3,4,5,8,7,6,1,2] => [4,2,2] => 10001010 => 3
[2,4,5,8,7,1,6,3] => [4,3,1] => 10001001 => 3
[2,3,5,8,1,7,6,4] => [5,2,1] => 10000101 => 3
[4,1,3,2,6,5,8,7] => [3,1,2,2] => 10011010 => 4
[5,1,3,2,6,4,8,7] => [3,1,2,2] => 10011010 => 4
[6,1,3,2,5,4,8,7] => [3,2,1,2] => 10010110 => 4
[7,1,3,2,5,4,8,6] => [3,2,1,2] => 10010110 => 4
[8,1,3,2,5,4,7,6] => [3,2,2,1] => 10010101 => 4
[8,1,4,2,5,3,7,6] => [2,3,2,1] => 10100101 => 4
[7,1,4,2,5,3,8,6] => [2,3,1,2] => 10100110 => 4
[6,1,4,2,5,3,8,7] => [2,3,1,2] => 10100110 => 4
[5,1,4,2,6,3,8,7] => [2,2,2,2] => 10101010 => 4
[2,1,6,3,5,4,8,7] => [2,3,1,2] => 10100110 => 4
[3,1,6,2,5,4,8,7] => [2,3,1,2] => 10100110 => 4
[4,1,6,2,5,3,8,7] => [2,3,1,2] => 10100110 => 4
[6,2,5,1,4,3,8,7] => [2,3,1,2] => 10100110 => 4
[5,2,6,1,4,3,8,7] => [2,3,1,2] => 10100110 => 4
[5,2,7,1,4,3,8,6] => [2,3,1,2] => 10100110 => 4
[5,2,8,1,4,3,7,6] => [2,3,2,1] => 10100101 => 4
[6,2,8,1,4,3,7,5] => [2,3,2,1] => 10100101 => 4
[6,2,7,1,4,3,8,5] => [2,3,1,2] => 10100110 => 4
[7,2,6,1,4,3,8,5] => [2,3,1,2] => 10100110 => 4
[7,2,5,1,4,3,8,6] => [2,3,1,2] => 10100110 => 4
[4,1,7,2,5,3,8,6] => [2,3,1,2] => 10100110 => 4
[3,1,7,2,5,4,8,6] => [2,3,1,2] => 10100110 => 4
[2,1,7,3,5,4,8,6] => [2,3,1,2] => 10100110 => 4
[2,1,8,3,5,4,7,6] => [2,3,2,1] => 10100101 => 4
[3,1,8,2,5,4,7,6] => [2,3,2,1] => 10100101 => 4
[4,1,8,2,5,3,7,6] => [2,3,2,1] => 10100101 => 4
[8,2,5,1,4,3,7,6] => [2,3,2,1] => 10100101 => 4
[8,2,6,1,4,3,7,5] => [2,3,2,1] => 10100101 => 4
[7,1,4,3,8,2,6,5] => [2,2,3,1] => 10101001 => 4
[8,1,4,3,7,2,6,5] => [2,2,3,1] => 10101001 => 4
[8,1,5,3,7,2,6,4] => [2,2,3,1] => 10101001 => 4
[7,1,5,3,8,2,6,4] => [2,2,3,1] => 10101001 => 4
[8,2,6,1,5,3,7,4] => [2,3,2,1] => 10100101 => 4
[5,1,8,2,6,3,7,4] => [2,2,3,1] => 10101001 => 4
[4,1,8,2,6,3,7,5] => [2,2,3,1] => 10101001 => 4
[3,1,8,2,6,4,7,5] => [2,2,3,1] => 10101001 => 4
[2,1,8,3,6,4,7,5] => [2,2,3,1] => 10101001 => 4
[2,1,7,3,6,4,8,5] => [2,2,2,2] => 10101010 => 4
[4,1,7,2,6,3,8,5] => [2,2,2,2] => 10101010 => 4
[5,1,7,2,6,3,8,4] => [2,2,2,2] => 10101010 => 4
[7,2,6,1,5,3,8,4] => [2,3,1,2] => 10100110 => 4
[6,2,7,1,5,3,8,4] => [2,3,1,2] => 10100110 => 4
[6,2,8,1,5,3,7,4] => [2,3,2,1] => 10100101 => 4
[8,1,5,2,6,3,7,4] => [2,2,3,1] => 10101001 => 4
[6,1,5,2,7,3,8,4] => [2,2,2,2] => 10101010 => 4
[6,1,4,2,7,3,8,5] => [2,2,2,2] => 10101010 => 4
[8,1,4,2,6,3,7,5] => [2,2,3,1] => 10101001 => 4
[8,1,3,2,6,4,7,5] => [3,1,3,1] => 10011001 => 4
[7,1,3,2,6,4,8,5] => [3,1,2,2] => 10011010 => 4
[6,1,3,2,7,4,8,5] => [3,1,2,2] => 10011010 => 4
[5,1,3,2,7,4,8,6] => [3,1,2,2] => 10011010 => 4
[4,1,3,2,7,5,8,6] => [3,1,2,2] => 10011010 => 4
[2,1,4,3,8,5,7,6] => [2,2,3,1] => 10101001 => 4
[3,1,4,2,8,5,7,6] => [2,2,3,1] => 10101001 => 4
[4,1,3,2,8,5,7,6] => [3,1,3,1] => 10011001 => 4
[5,1,3,2,8,4,7,6] => [3,1,3,1] => 10011001 => 4
[6,1,3,2,8,4,7,5] => [3,1,3,1] => 10011001 => 4
[8,4,7,1,3,2,6,5] => [1,4,2,1] => 11000101 => 4
[7,4,8,1,3,2,6,5] => [1,4,2,1] => 11000101 => 4
[7,3,8,1,4,2,6,5] => [1,4,2,1] => 11000101 => 4
[8,3,7,1,4,2,6,5] => [1,4,2,1] => 11000101 => 4
[6,1,4,2,8,3,7,5] => [2,2,3,1] => 10101001 => 4
[5,1,4,2,8,3,7,6] => [2,2,3,1] => 10101001 => 4
[4,1,5,2,8,3,7,6] => [2,2,3,1] => 10101001 => 4
[3,1,5,2,8,4,7,6] => [2,2,3,1] => 10101001 => 4
[2,1,5,3,8,4,7,6] => [2,2,3,1] => 10101001 => 4
[2,1,6,3,8,4,7,5] => [2,2,3,1] => 10101001 => 4
[3,1,6,2,8,4,7,5] => [2,2,3,1] => 10101001 => 4
[4,1,6,2,8,3,7,5] => [2,2,3,1] => 10101001 => 4
[5,1,6,2,8,3,7,4] => [2,2,3,1] => 10101001 => 4
[6,1,5,2,8,3,7,4] => [2,2,3,1] => 10101001 => 4
[8,3,7,1,5,2,6,4] => [1,4,2,1] => 11000101 => 4
[7,3,8,1,5,2,6,4] => [1,4,2,1] => 11000101 => 4
[6,2,7,3,8,1,5,4] => [2,2,3,1] => 10101001 => 4
[6,2,8,3,7,1,5,4] => [2,2,3,1] => 10101001 => 4
[8,3,7,2,6,1,5,4] => [1,3,3,1] => 11001001 => 4
[5,1,8,3,7,2,6,4] => [2,2,3,1] => 10101001 => 4
[4,1,8,3,7,2,6,5] => [2,2,3,1] => 10101001 => 4
[3,1,8,4,7,2,6,5] => [2,2,3,1] => 10101001 => 4
[2,1,8,4,7,3,6,5] => [2,2,3,1] => 10101001 => 4
[2,1,7,4,8,3,6,5] => [2,2,3,1] => 10101001 => 4
[3,1,7,4,8,2,6,5] => [2,2,3,1] => 10101001 => 4
[4,1,7,3,8,2,6,5] => [2,2,3,1] => 10101001 => 4
[5,1,7,3,8,2,6,4] => [2,2,3,1] => 10101001 => 4
[7,3,8,2,6,1,5,4] => [1,3,3,1] => 11001001 => 4
[8,2,6,3,7,1,5,4] => [2,2,3,1] => 10101001 => 4
[7,2,6,3,8,1,5,4] => [2,2,3,1] => 10101001 => 4
[3,4,2,6,8,1,5,7] => [3,5] => 10010000 => 2
[5,3,6,2,8,1,4,7] => [1,3,4] => 11001000 => 3
[5,3,6,2,4,8,1,7] => [1,4,3] => 11000100 => 3
[5,7,3,8,2,4,1,6] => [3,3,2] => 10010010 => 3
[5,7,3,8,2,4,6,1] => [3,4,1] => 10010001 => 3
[7,4,2,5,8,3,6,1] => [1,2,4,1] => 11010001 => 4
[7,4,2,5,8,3,1,6] => [1,2,3,2] => 11010010 => 4
[4,5,2,6,3,8,1,7] => [3,2,3] => 10010100 => 3
[4,5,2,1,6,8,3,7] => [3,1,4] => 10011000 => 3
[5,3,1,6,8,2,4,7] => [1,2,5] => 11010000 => 3
[5,6,2,8,1,3,4,7] => [3,5] => 10010000 => 2
[3,5,6,1,4,8,2,7] => [5,3] => 10000100 => 2
[4,1,5,6,3,8,2,7] => [2,3,3] => 10100100 => 3
[4,5,1,6,3,8,2,7] => [3,2,3] => 10010100 => 3
[4,5,6,3,2,8,1,7] => [4,1,3] => 10001100 => 3
[7,4,5,3,8,2,1,6] => [1,3,2,2] => 11001010 => 4
[7,4,5,3,8,2,6,1] => [1,3,3,1] => 11001001 => 4
[6,7,4,8,3,2,5,1] => [2,3,2,1] => 10100101 => 4
[6,7,4,8,3,2,1,5] => [2,3,1,2] => 10100110 => 4
[6,7,4,1,8,3,2,5] => [2,2,2,2] => 10101010 => 4
[7,4,5,3,1,8,2,6] => [1,3,1,3] => 11001100 => 4
[4,7,1,5,8,3,2,6] => [3,3,2] => 10010010 => 3
[5,3,7,8,1,4,2,6] => [1,5,2] => 11000010 => 3
[7,5,8,2,4,6,1,3] => [1,5,2] => 11000010 => 3
[7,3,5,8,1,4,6,2] => [1,6,1] => 11000001 => 3
[4,5,1,7,8,3,6,2] => [3,4,1] => 10010001 => 3
[7,4,1,5,8,3,6,2] => [1,2,4,1] => 11010001 => 4
[6,7,4,3,8,1,5,2] => [2,2,3,1] => 10101001 => 4
[6,7,4,8,3,1,5,2] => [2,3,2,1] => 10100101 => 4
[6,7,4,8,3,5,2,1] => [2,4,1,1] => 10100011 => 4
[5,6,7,3,8,4,2,1] => [4,2,1,1] => 10001011 => 4
[5,6,7,3,1,8,4,2] => [4,1,2,1] => 10001101 => 4
[5,6,1,7,3,8,4,2] => [3,2,2,1] => 10010101 => 4
[5,1,6,7,3,8,4,2] => [2,3,2,1] => 10100101 => 4
[6,4,7,1,8,3,5,2] => [1,3,3,1] => 11001001 => 4
[6,7,8,3,1,4,5,2] => [4,3,1] => 10001001 => 3
[6,7,2,8,4,5,1,3] => [3,3,2] => 10010010 => 3
[6,7,2,8,4,1,3,5] => [3,2,3] => 10010100 => 3
[6,1,7,4,8,3,2,5] => [2,2,2,2] => 10101010 => 4
[5,1,6,7,3,2,8,4] => [2,3,1,2] => 10100110 => 4
[5,6,1,7,3,2,8,4] => [3,2,1,2] => 10010110 => 4
[5,6,7,3,2,1,8,4] => [4,1,1,2] => 10001110 => 4
[5,6,7,3,2,8,4,1] => [4,1,2,1] => 10001101 => 4
[5,6,2,7,3,8,4,1] => [3,2,2,1] => 10010101 => 4
[5,6,2,7,3,1,8,4] => [3,2,1,2] => 10010110 => 4
[5,6,2,1,7,3,8,4] => [3,1,2,2] => 10011010 => 4
[6,1,7,4,2,8,3,5] => [2,2,1,3] => 10101100 => 4
[6,7,2,1,8,3,4,5] => [3,1,4] => 10011000 => 3
[7,5,8,2,1,3,4,6] => [1,3,4] => 11001000 => 3
[5,7,3,1,8,2,4,6] => [3,1,4] => 10011000 => 3
[4,7,1,5,2,8,3,6] => [3,2,3] => 10010100 => 3
[7,4,2,5,1,8,3,6] => [1,2,2,3] => 11010100 => 4
[6,7,4,2,1,8,3,5] => [2,2,1,3] => 10101100 => 4
[6,7,4,2,8,3,1,5] => [2,2,2,2] => 10101010 => 4
[6,7,4,2,8,3,5,1] => [2,2,3,1] => 10101001 => 4
[3,6,7,2,8,4,5,1] => [4,3,1] => 10001001 => 3
[3,6,7,2,8,4,1,5] => [4,2,2] => 10001010 => 3
[3,6,7,2,1,8,4,5] => [4,1,3] => 10001100 => 3
[5,7,3,8,2,1,4,6] => [3,2,3] => 10010100 => 3
[3,4,7,8,2,1,5,6] => [5,3] => 10000100 => 2
[3,7,8,1,4,6,2,5] => [6,2] => 10000010 => 2
[3,4,7,8,2,6,1,5] => [6,2] => 10000010 => 2
[5,7,3,8,2,6,1,4] => [3,3,2] => 10010010 => 3
[3,6,7,2,8,5,1,4] => [4,2,2] => 10001010 => 3
[3,6,7,8,5,2,1,4] => [5,1,2] => 10000110 => 3
[3,6,7,8,5,2,4,1] => [5,2,1] => 10000101 => 3
[6,4,7,8,2,5,3,1] => [1,5,1,1] => 11000011 => 4
[6,4,7,8,2,1,5,3] => [1,4,2,1] => 11000101 => 4
[4,1,5,7,8,2,6,3] => [2,5,1] => 10100001 => 3
[5,3,7,8,1,6,2,4] => [1,5,2] => 11000010 => 3
[6,7,2,8,5,1,3,4] => [3,2,3] => 10010100 => 3
[6,4,1,7,8,2,5,3] => [1,2,4,1] => 11010001 => 4
[5,1,6,2,7,8,4,3] => [2,2,3,1] => 10101001 => 4
[5,6,2,1,7,8,4,3] => [3,1,3,1] => 10011001 => 4
[5,6,2,7,1,8,4,3] => [3,2,2,1] => 10010101 => 4
[5,6,2,7,8,4,3,1] => [3,3,1,1] => 10010011 => 4
[5,6,7,2,8,4,3,1] => [4,2,1,1] => 10001011 => 4
[5,6,7,2,1,8,4,3] => [4,1,2,1] => 10001101 => 4
[5,6,1,7,2,8,4,3] => [3,2,2,1] => 10010101 => 4
[5,1,6,7,2,8,4,3] => [2,3,2,1] => 10100101 => 4
[6,4,7,1,8,2,5,3] => [1,3,3,1] => 11001001 => 4
[3,6,7,1,8,5,2,4] => [4,2,2] => 10001010 => 3
[6,7,8,5,2,4,1,3] => [3,3,2] => 10010010 => 3
[6,7,8,3,5,1,4,2] => [5,2,1] => 10000101 => 3
[4,6,7,8,1,5,3,2] => [6,1,1] => 10000011 => 3
[5,1,6,7,8,4,3,2] => [2,4,1,1] => 10100011 => 4
[5,6,1,7,8,4,3,2] => [3,3,1,1] => 10010011 => 4
[5,6,7,1,8,4,3,2] => [4,2,1,1] => 10001011 => 4
[8,6,1,3,4,2,5,7] => [1,4,3] => 11000100 => 3
[8,3,2,5,1,6,4,7] => [1,2,3,2] => 11010010 => 4
[8,5,3,6,2,4,1,7] => [1,2,3,2] => 11010010 => 4
[5,3,2,7,4,1,8,6] => [1,2,2,1,2] => 11010110 => 5
[7,5,3,8,2,4,6,1] => [1,2,4,1] => 11010001 => 4
[7,2,4,5,8,3,6,1] => [2,5,1] => 10100001 => 3
[2,4,5,3,7,1,8,6] => [4,2,2] => 10001010 => 3
[8,2,4,5,6,3,1,7] => [2,4,2] => 10100010 => 3
[8,2,4,5,6,1,3,7] => [2,6] => 10100000 => 2
[8,1,2,4,5,6,3,7] => [6,2] => 10000010 => 2
[8,2,5,1,3,6,4,7] => [2,4,2] => 10100010 => 3
[8,5,6,2,1,4,3,7] => [1,3,2,2] => 11001010 => 4
[8,5,3,6,4,1,2,7] => [1,2,2,3] => 11010100 => 4
[8,4,1,5,6,3,2,7] => [1,2,3,2] => 11010010 => 4
[8,1,4,5,6,3,2,7] => [2,4,2] => 10100010 => 3
[4,5,3,7,2,1,8,6] => [3,2,1,2] => 10010110 => 4
[7,4,5,8,3,2,6,1] => [1,4,2,1] => 11000101 => 4
[4,3,6,7,2,8,5,1] => [1,4,2,1] => 11000101 => 4
[4,3,6,7,2,8,1,5] => [1,4,3] => 11000100 => 3
[1,4,3,6,7,2,8,5] => [1,2,3,2] => 11010010 => 4
[4,5,3,7,1,8,2,6] => [3,2,3] => 10010100 => 3
[4,1,5,3,7,2,8,6] => [2,2,2,2] => 10101010 => 4
[5,3,4,7,1,2,8,6] => [1,5,2] => 11000010 => 3
[7,5,8,2,1,4,6,3] => [1,3,3,1] => 11001001 => 4
[7,5,3,8,4,1,6,2] => [1,2,2,2,1] => 11010101 => 5
[7,4,5,8,3,6,1,2] => [1,5,2] => 11000010 => 3
[4,3,6,7,8,1,5,2] => [1,6,1] => 11000001 => 3
[1,6,4,7,8,3,5,2] => [1,1,5,1] => 11100001 => 4
[6,4,7,8,3,5,2,1] => [1,5,1,1] => 11000011 => 4
[3,5,6,7,8,4,1,2] => [6,2] => 10000010 => 2
[3,1,5,6,7,8,4,2] => [2,5,1] => 10100001 => 3
[4,6,1,7,8,3,5,2] => [3,4,1] => 10010001 => 3
[3,6,7,1,4,8,5,2] => [5,2,1] => 10000101 => 3
[6,2,4,1,7,8,5,3] => [2,2,3,1] => 10101001 => 4
[2,6,7,1,4,8,3,5] => [5,3] => 10000100 => 2
[4,3,6,7,8,1,2,5] => [1,7] => 11000000 => 2
[1,5,3,6,7,8,2,4] => [1,2,5] => 11010000 => 3
[3,5,6,7,8,2,1,4] => [6,2] => 10000010 => 2
[3,5,6,7,8,2,4,1] => [7,1] => 10000001 => 2
[5,2,7,1,3,8,4,6] => [2,3,3] => 10100100 => 3
[5,3,1,7,8,2,4,6] => [1,2,5] => 11010000 => 3
[4,5,2,7,8,1,3,6] => [3,5] => 10010000 => 2
[4,2,6,7,8,3,1,5] => [2,4,2] => 10100010 => 3
[4,2,6,7,8,3,5,1] => [2,5,1] => 10100001 => 3
[3,6,2,7,4,8,5,1] => [3,2,2,1] => 10010101 => 4
[3,6,2,7,4,8,1,5] => [3,2,3] => 10010100 => 3
[3,2,1,6,4,7,8,5] => [2,1,2,3] => 10110100 => 4
[3,7,4,2,1,5,8,6] => [2,2,2,2] => 10101010 => 4
[1,7,3,4,2,5,8,6] => [1,3,2,2] => 11001010 => 4
[4,7,2,1,3,5,8,6] => [3,3,2] => 10010010 => 3
[7,8,4,2,1,3,6,5] => [2,2,3,1] => 10101001 => 4
[7,8,1,3,4,2,6,5] => [5,2,1] => 10000101 => 3
[7,8,3,4,2,1,6,5] => [4,1,2,1] => 10001101 => 4
[6,3,2,7,1,8,5,4] => [1,2,2,2,1] => 11010101 => 5
[3,6,2,7,1,8,5,4] => [3,2,2,1] => 10010101 => 4
[6,7,3,8,2,5,4,1] => [3,3,1,1] => 10010011 => 4
[6,4,7,8,5,2,3,1] => [1,4,2,1] => 11000101 => 4
[2,6,4,7,8,1,5,3] => [2,5,1] => 10100001 => 3
[4,6,2,7,8,1,5,3] => [3,4,1] => 10010001 => 3
[7,4,5,8,6,2,1,3] => [1,3,2,2] => 11001010 => 4
[7,4,1,5,8,6,2,3] => [1,2,3,2] => 11010010 => 4
[7,5,3,8,6,1,2,4] => [1,2,1,4] => 11011000 => 4
[7,5,8,2,1,6,3,4] => [1,3,2,2] => 11001010 => 4
[6,2,7,1,3,8,5,4] => [2,3,2,1] => 10100101 => 4
[6,3,1,7,8,2,5,4] => [1,2,4,1] => 11010001 => 4
[4,6,1,7,8,5,2,3] => [3,3,2] => 10010010 => 3
[5,1,2,6,7,8,4,3] => [3,4,1] => 10010001 => 3
[5,2,6,7,8,4,1,3] => [2,4,2] => 10100010 => 3
[5,2,6,7,8,4,3,1] => [2,4,1,1] => 10100011 => 4
[2,5,6,7,8,4,1,3] => [6,2] => 10000010 => 2
[1,5,2,6,7,8,4,3] => [1,2,4,1] => 11010001 => 4
[1,6,4,7,8,5,2,3] => [1,1,4,2] => 11100010 => 4
[2,6,7,1,3,8,5,4] => [5,2,1] => 10000101 => 3
[6,7,8,2,1,5,4,3] => [4,2,1,1] => 10001011 => 4
[6,7,3,8,5,1,4,2] => [3,2,2,1] => 10010101 => 4
[6,4,7,8,5,3,1,2] => [1,4,1,2] => 11000110 => 4
[4,5,2,3,7,6,1,8] => [4,2,2] => 10001010 => 3
[6,4,3,7,2,5,1,8] => [1,2,3,2] => 11010010 => 4
[8,4,3,6,5,1,2,7] => [1,2,2,3] => 11010100 => 4
[1,5,6,3,4,8,7,2] => [1,4,2,1] => 11000101 => 4
[4,6,2,7,3,5,1,8] => [3,3,2] => 10010010 => 3
[3,2,6,7,4,5,1,8] => [2,4,2] => 10100010 => 3
[4,7,2,6,5,3,1,8] => [3,2,1,2] => 10010110 => 4
[5,7,6,2,4,3,1,8] => [2,3,1,2] => 10100110 => 4
[1,7,5,4,8,3,6,2] => [1,1,2,3,1] => 11101001 => 5
[8,7,5,4,1,3,2,6] => [1,1,2,2,2] => 11101010 => 5
[6,8,5,4,2,1,3,7] => [2,2,1,3] => 10101100 => 4
[5,8,6,2,4,1,3,7] => [2,3,3] => 10100100 => 3
[4,8,2,6,5,1,3,7] => [3,2,3] => 10010100 => 3
[3,2,8,6,5,1,4,7] => [2,1,2,3] => 10110100 => 4
[4,1,2,6,5,8,7,3] => [3,2,2,1] => 10010101 => 4
[5,1,6,2,4,8,7,3] => [2,3,2,1] => 10100101 => 4
[6,1,5,4,2,8,7,3] => [2,2,1,2,1] => 10101101 => 5
[7,1,5,4,8,2,6,3] => [2,2,3,1] => 10101001 => 4
[8,1,5,4,7,6,2,3] => [2,2,2,2] => 10101010 => 4
[1,8,6,7,4,5,3,2] => [1,1,4,1,1] => 11100011 => 5
[8,1,6,7,4,5,2,3] => [2,4,2] => 10100010 => 3
[7,1,6,8,4,2,5,3] => [2,3,2,1] => 10100101 => 4
[6,1,7,8,2,4,5,3] => [2,5,1] => 10100001 => 3
[5,1,7,2,8,4,6,3] => [2,2,3,1] => 10101001 => 4
[4,1,2,7,8,5,6,3] => [3,4,1] => 10010001 => 3
[3,2,1,7,8,5,6,4] => [2,1,4,1] => 10110001 => 4
[3,2,8,7,1,5,4,6] => [2,1,3,2] => 10110010 => 4
[4,8,2,7,1,5,3,6] => [3,3,2] => 10010010 => 3
[5,8,7,2,1,4,3,6] => [2,2,2,2] => 10101010 => 4
[6,8,7,1,2,4,3,5] => [2,4,2] => 10100010 => 3
[7,8,6,1,4,2,3,5] => [2,3,3] => 10100100 => 3
[8,7,6,1,4,3,2,5] => [1,1,3,1,2] => 11100110 => 5
[1,7,6,8,4,3,5,2] => [1,1,3,2,1] => 11100101 => 5
[1,6,7,8,3,4,5,2] => [1,6,1] => 11000001 => 3
[8,6,7,1,3,4,2,5] => [1,5,2] => 11000010 => 3
[7,6,8,1,3,2,4,5] => [1,4,3] => 11000100 => 3
[5,7,8,2,1,3,4,6] => [4,4] => 10001000 => 2
[4,7,2,8,1,3,5,6] => [3,5] => 10010000 => 2
[3,2,6,8,4,1,5,7] => [2,3,3] => 10100100 => 3
[4,6,2,8,3,1,5,7] => [3,2,3] => 10010100 => 3
[5,6,8,2,3,1,4,7] => [5,3] => 10000100 => 2
[6,5,8,3,2,1,4,7] => [1,3,1,3] => 11001100 => 4
[7,5,8,3,1,2,4,6] => [1,3,4] => 11001000 => 3
[8,5,7,3,1,4,2,6] => [1,3,2,2] => 11001010 => 4
[1,5,7,3,8,4,6,2] => [1,3,3,1] => 11001001 => 4
[1,4,3,7,8,5,6,2] => [1,2,4,1] => 11010001 => 4
[8,4,3,7,1,5,2,6] => [1,2,3,2] => 11010010 => 4
[6,4,3,8,2,1,5,7] => [1,2,2,3] => 11010100 => 4
[4,5,2,3,8,1,6,7] => [4,4] => 10001000 => 2
[3,2,5,4,8,1,6,7] => [2,2,4] => 10101000 => 3
[4,5,2,3,1,8,7,6] => [4,1,2,1] => 10001101 => 4
[6,4,3,1,2,8,7,5] => [1,2,2,2,1] => 11010101 => 5
[7,4,3,1,8,2,6,5] => [1,2,1,3,1] => 11011001 => 5
[8,4,3,1,7,6,2,5] => [1,2,1,2,2] => 11011010 => 5
[1,5,8,3,7,6,4,2] => [1,3,2,1,1] => 11001011 => 5
[8,5,1,3,7,6,2,4] => [1,3,2,2] => 11001010 => 4
[7,5,1,3,8,2,6,4] => [1,3,3,1] => 11001001 => 4
[6,5,1,3,2,8,7,4] => [1,3,1,2,1] => 11001101 => 5
[5,6,1,2,3,8,7,4] => [5,2,1] => 10000101 => 3
[4,6,2,1,3,8,7,5] => [3,2,2,1] => 10010101 => 4
[3,2,6,1,4,8,7,5] => [2,3,2,1] => 10100101 => 4
[3,2,7,1,8,4,6,5] => [2,2,3,1] => 10101001 => 4
[4,7,2,1,8,3,6,5] => [3,1,3,1] => 10011001 => 4
[5,7,1,2,8,3,6,4] => [4,3,1] => 10001001 => 3
[6,7,1,8,2,3,5,4] => [3,4,1] => 10010001 => 3
[7,6,1,8,3,2,5,4] => [1,2,2,2,1] => 11010101 => 5
[8,6,1,7,3,5,2,4] => [1,2,3,2] => 11010010 => 4
[1,6,8,7,3,5,4,2] => [1,2,3,1,1] => 11010011 => 5
[1,7,8,6,5,3,4,2] => [1,2,2,2,1] => 11010101 => 5
[8,7,1,6,5,3,2,4] => [1,2,2,1,2] => 11010110 => 5
[7,8,1,6,5,2,3,4] => [3,2,3] => 10010100 => 3
[6,8,1,7,2,5,3,4] => [3,3,2] => 10010010 => 3
[5,8,1,2,7,6,3,4] => [4,2,2] => 10001010 => 3
[4,8,2,1,7,6,3,5] => [3,1,2,2] => 10011010 => 4
[3,2,8,1,7,6,4,5] => [2,2,2,2] => 10101010 => 4
[4,1,2,8,7,6,5,3] => [3,1,2,1,1] => 10011011 => 5
[5,1,8,2,7,6,4,3] => [2,2,2,1,1] => 10101011 => 5
[6,1,8,7,2,5,4,3] => [2,1,3,1,1] => 10110011 => 5
[7,1,8,6,5,2,4,3] => [2,1,2,2,1] => 10110101 => 5
[8,1,7,6,5,4,2,3] => [2,1,2,1,2] => 10110110 => 5
[3,1,2,6,5,8,7,4] => [3,2,2,1] => 10010101 => 4
[3,1,6,2,4,8,7,5] => [2,3,2,1] => 10100101 => 4
[3,1,5,2,4,8,7,6] => [2,3,2,1] => 10100101 => 4
[4,5,1,2,3,8,7,6] => [5,2,1] => 10000101 => 3
[4,6,1,2,3,8,7,5] => [5,2,1] => 10000101 => 3
[1,6,5,3,4,8,7,2] => [1,1,3,2,1] => 11100101 => 5
[6,1,5,2,4,8,7,3] => [2,3,2,1] => 10100101 => 4
[6,5,1,2,3,8,7,4] => [1,4,2,1] => 11000101 => 4
[6,4,1,2,3,8,7,5] => [1,4,2,1] => 11000101 => 4
[5,4,1,2,3,8,7,6] => [1,4,2,1] => 11000101 => 4
[5,4,1,2,7,3,6,8] => [1,3,4] => 11001000 => 3
[6,4,1,7,2,3,5,8] => [1,2,5] => 11010000 => 3
[6,4,1,8,2,3,5,7] => [1,2,5] => 11010000 => 3
[7,4,1,2,8,3,6,5] => [1,3,3,1] => 11001001 => 4
[7,5,1,2,8,3,6,4] => [1,3,3,1] => 11001001 => 4
[7,1,5,2,8,4,6,3] => [2,2,3,1] => 10101001 => 4
[1,7,5,3,8,4,6,2] => [1,1,2,3,1] => 11101001 => 5
[1,8,5,3,7,4,6,2] => [1,1,2,3,1] => 11101001 => 5
[8,1,5,2,7,4,6,3] => [2,2,3,1] => 10101001 => 4
[8,5,1,2,7,3,6,4] => [1,3,3,1] => 11001001 => 4
[8,4,1,2,7,3,6,5] => [1,3,3,1] => 11001001 => 4
[8,4,1,7,2,3,5,6] => [1,2,5] => 11010000 => 3
[7,4,1,6,2,3,5,8] => [1,2,5] => 11010000 => 3
[8,6,1,7,2,3,5,4] => [1,2,4,1] => 11010001 => 4
[8,1,6,7,2,4,5,3] => [2,5,1] => 10100001 => 3
[1,8,6,7,3,4,5,2] => [1,1,5,1] => 11100001 => 4
[1,7,6,8,3,4,5,2] => [1,1,5,1] => 11100001 => 4
[7,1,6,8,2,4,5,3] => [2,5,1] => 10100001 => 3
[7,6,1,8,2,3,5,4] => [1,2,4,1] => 11010001 => 4
[4,7,1,2,8,3,6,5] => [4,3,1] => 10001001 => 3
[3,1,7,2,8,4,6,5] => [2,2,3,1] => 10101001 => 4
[3,1,2,7,8,5,6,4] => [3,4,1] => 10010001 => 3
[1,4,3,8,7,5,6,2] => [1,2,1,3,1] => 11011001 => 5
[4,1,2,8,7,5,6,3] => [3,1,3,1] => 10011001 => 4
[3,1,2,8,7,5,6,4] => [3,1,3,1] => 10011001 => 4
[3,1,8,2,7,4,6,5] => [2,2,3,1] => 10101001 => 4
[3,1,8,7,2,4,5,6] => [2,1,5] => 10110000 => 3
[3,1,7,6,2,4,5,8] => [2,1,5] => 10110000 => 3
[4,7,1,6,2,3,5,8] => [3,5] => 10010000 => 2
[4,8,1,6,2,3,5,7] => [3,5] => 10010000 => 2
[4,8,1,7,2,3,5,6] => [3,5] => 10010000 => 2
[4,8,1,2,7,3,6,5] => [4,3,1] => 10001001 => 3
[5,8,1,2,7,3,6,4] => [4,3,1] => 10001001 => 3
[5,1,8,2,7,4,6,3] => [2,2,3,1] => 10101001 => 4
[1,5,8,3,7,4,6,2] => [1,3,3,1] => 11001001 => 4
[1,6,8,7,3,4,5,2] => [1,2,4,1] => 11010001 => 4
[6,1,8,7,2,4,5,3] => [2,1,4,1] => 10110001 => 4
[6,8,1,7,2,3,5,4] => [3,4,1] => 10010001 => 3
[6,8,7,1,2,3,4,5] => [2,6] => 10100000 => 2
[5,8,7,1,2,3,4,6] => [2,6] => 10100000 => 2
[5,8,6,1,2,3,4,7] => [2,6] => 10100000 => 2
[5,7,6,1,2,3,4,8] => [2,6] => 10100000 => 2
[7,8,1,6,2,3,5,4] => [3,4,1] => 10010001 => 3
[7,1,8,6,2,4,5,3] => [2,1,4,1] => 10110001 => 4
[1,7,8,6,3,4,5,2] => [1,2,4,1] => 11010001 => 4
[1,8,7,6,3,4,5,2] => [1,1,1,4,1] => 11110001 => 5
[8,1,7,6,2,4,5,3] => [2,1,4,1] => 10110001 => 4
[8,7,1,6,2,3,5,4] => [1,2,4,1] => 11010001 => 4
[3,2,5,1,6,4,8,7] => [2,2,2,2] => 10101010 => 4
[3,2,5,4,7,1,8,6] => [2,2,2,2] => 10101010 => 4
[4,2,5,3,7,6,8,1] => [2,2,2,2] => 10101010 => 4
[4,2,5,3,7,1,8,6] => [2,2,2,2] => 10101010 => 4
[4,2,5,3,6,1,8,7] => [2,2,2,2] => 10101010 => 4
[4,2,5,1,6,3,8,7] => [2,2,2,2] => 10101010 => 4
[3,1,5,4,6,2,8,7] => [2,2,2,2] => 10101010 => 4
[4,1,5,3,6,2,8,7] => [2,2,2,2] => 10101010 => 4
[4,3,5,1,6,2,8,7] => [1,3,2,2] => 11001010 => 4
[4,3,5,2,7,1,8,6] => [1,3,2,2] => 11001010 => 4
[4,3,6,2,7,5,8,1] => [1,3,2,2] => 11001010 => 4
[4,3,6,2,7,1,8,5] => [1,3,2,2] => 11001010 => 4
[4,3,6,1,7,2,8,5] => [1,3,2,2] => 11001010 => 4
[4,3,5,1,7,2,8,6] => [1,3,2,2] => 11001010 => 4
[3,1,5,4,7,2,8,6] => [2,2,2,2] => 10101010 => 4
[2,1,5,4,7,3,8,6] => [2,2,2,2] => 10101010 => 4
[3,1,5,4,7,6,8,2] => [2,2,2,2] => 10101010 => 4
[4,1,5,3,7,6,8,2] => [2,2,2,2] => 10101010 => 4
[4,3,5,1,7,6,8,2] => [1,3,2,2] => 11001010 => 4
[4,3,6,1,7,5,8,2] => [1,3,2,2] => 11001010 => 4
[4,3,6,5,7,1,8,2] => [1,2,3,2] => 11010010 => 4
[5,3,6,4,7,2,8,1] => [1,3,2,2] => 11001010 => 4
[5,3,6,4,7,1,8,2] => [1,3,2,2] => 11001010 => 4
[5,3,6,1,7,4,8,2] => [1,3,2,2] => 11001010 => 4
[5,1,6,3,7,4,8,2] => [2,2,2,2] => 10101010 => 4
[4,1,6,3,7,5,8,2] => [2,2,2,2] => 10101010 => 4
[3,1,6,4,7,5,8,2] => [2,2,2,2] => 10101010 => 4
[2,1,6,4,7,5,8,3] => [2,2,2,2] => 10101010 => 4
[2,1,6,4,7,3,8,5] => [2,2,2,2] => 10101010 => 4
[3,1,6,4,7,2,8,5] => [2,2,2,2] => 10101010 => 4
[4,1,6,3,7,2,8,5] => [2,2,2,2] => 10101010 => 4
[5,1,6,3,7,2,8,4] => [2,2,2,2] => 10101010 => 4
[5,3,6,1,7,2,8,4] => [1,3,2,2] => 11001010 => 4
[5,3,6,2,7,1,8,4] => [1,3,2,2] => 11001010 => 4
[5,3,6,2,7,4,8,1] => [1,3,2,2] => 11001010 => 4
[5,2,6,3,7,4,8,1] => [2,2,2,2] => 10101010 => 4
[5,2,6,3,7,1,8,4] => [2,2,2,2] => 10101010 => 4
[5,2,6,1,7,3,8,4] => [2,2,2,2] => 10101010 => 4
[4,2,5,1,7,3,8,6] => [2,2,2,2] => 10101010 => 4
[4,2,6,1,7,3,8,5] => [2,2,2,2] => 10101010 => 4
[4,2,6,3,7,1,8,5] => [2,2,2,2] => 10101010 => 4
[4,2,6,3,7,5,8,1] => [2,2,2,2] => 10101010 => 4
[3,2,6,4,7,5,8,1] => [2,2,2,2] => 10101010 => 4
[3,2,6,4,7,1,8,5] => [2,2,2,2] => 10101010 => 4
[3,2,6,1,7,4,8,5] => [2,2,2,2] => 10101010 => 4
[3,2,5,1,7,4,8,6] => [2,2,2,2] => 10101010 => 4
[3,2,4,1,7,5,8,6] => [2,2,2,2] => 10101010 => 4
[3,1,4,2,7,6,8,5] => [2,2,2,2] => 10101010 => 4
[3,2,5,1,7,6,8,4] => [2,2,2,2] => 10101010 => 4
[3,2,6,1,7,5,8,4] => [2,2,2,2] => 10101010 => 4
[3,2,6,5,7,1,8,4] => [2,1,3,2] => 10110010 => 4
[4,2,6,5,7,3,8,1] => [2,1,3,2] => 10110010 => 4
[4,2,6,5,7,1,8,3] => [2,1,3,2] => 10110010 => 4
[4,2,6,1,7,5,8,3] => [2,2,2,2] => 10101010 => 4
[4,2,5,1,7,6,8,3] => [2,2,2,2] => 10101010 => 4
[4,1,5,2,7,6,8,3] => [2,2,2,2] => 10101010 => 4
[3,1,5,2,7,6,8,4] => [2,2,2,2] => 10101010 => 4
[2,1,5,3,7,6,8,4] => [2,2,2,2] => 10101010 => 4
[2,1,6,3,7,5,8,4] => [2,2,2,2] => 10101010 => 4
[3,1,6,2,7,5,8,4] => [2,2,2,2] => 10101010 => 4
[4,1,6,2,7,5,8,3] => [2,2,2,2] => 10101010 => 4
[5,1,6,2,7,4,8,3] => [2,2,2,2] => 10101010 => 4
[5,2,6,1,7,4,8,3] => [2,2,2,2] => 10101010 => 4
[5,2,6,4,7,1,8,3] => [2,2,2,2] => 10101010 => 4
[5,2,6,4,7,3,8,1] => [2,2,2,2] => 10101010 => 4
[5,4,6,2,7,3,8,1] => [1,3,2,2] => 11001010 => 4
[5,4,6,2,7,1,8,3] => [1,3,2,2] => 11001010 => 4
[5,4,6,1,7,2,8,3] => [1,3,2,2] => 11001010 => 4
[5,1,6,4,7,2,8,3] => [2,2,2,2] => 10101010 => 4
[4,1,6,5,7,2,8,3] => [2,1,3,2] => 10110010 => 4
[3,1,6,5,7,2,8,4] => [2,1,3,2] => 10110010 => 4
[2,1,6,5,7,3,8,4] => [2,1,3,2] => 10110010 => 4
[3,1,6,5,7,4,8,2] => [2,1,3,2] => 10110010 => 4
[4,1,6,5,7,3,8,2] => [2,1,3,2] => 10110010 => 4
[5,1,6,4,7,3,8,2] => [2,2,2,2] => 10101010 => 4
[5,4,6,1,7,3,8,2] => [1,3,2,2] => 11001010 => 4
[5,4,6,3,7,1,8,2] => [1,3,2,2] => 11001010 => 4
[8,3,5,2,1,6,4,7] => [1,3,2,2] => 11001010 => 4
[8,6,3,5,2,4,1,7] => [1,2,3,2] => 11010010 => 4
[3,7,5,2,4,1,8,6] => [2,3,1,2] => 10100110 => 4
[8,3,7,5,2,4,6,1] => [1,2,4,1] => 11010001 => 4
[8,2,4,5,7,3,6,1] => [2,5,1] => 10100001 => 3
[2,4,5,7,3,1,8,6] => [5,1,2] => 10000110 => 3
[8,2,4,6,5,3,1,7] => [2,3,1,2] => 10100110 => 4
[8,2,5,4,6,1,3,7] => [2,2,4] => 10101000 => 3
[8,6,3,5,1,4,2,7] => [1,2,3,2] => 11010010 => 4
[8,6,1,4,5,3,2,7] => [1,4,1,2] => 11000110 => 4
[8,1,5,6,4,3,2,7] => [2,3,1,2] => 10100110 => 4
[5,7,4,3,2,1,8,6] => [2,2,1,1,2] => 10101110 => 5
[8,5,7,4,3,2,6,1] => [1,3,1,2,1] => 11001101 => 5
[4,6,8,3,2,7,5,1] => [4,1,2,1] => 10001101 => 4
[4,7,6,3,2,8,1,5] => [2,2,1,3] => 10101100 => 4
[1,4,6,7,3,2,8,5] => [1,4,1,2] => 11000110 => 4
[5,4,7,3,1,8,2,6] => [1,3,1,3] => 11001100 => 4
[1,7,4,5,3,2,8,6] => [1,1,3,1,2] => 11100110 => 5
[3,7,5,1,4,2,8,6] => [2,3,1,2] => 10100110 => 4
[5,7,4,2,1,3,8,6] => [2,2,2,2] => 10101010 => 4
[8,5,7,4,2,1,6,3] => [1,3,1,2,1] => 11001101 => 5
[8,3,7,5,1,4,6,2] => [1,2,4,1] => 11010001 => 4
[8,4,1,7,5,3,6,2] => [1,2,2,2,1] => 11010101 => 5
[4,6,3,8,7,1,5,2] => [3,1,3,1] => 10011001 => 4
[1,7,4,8,6,3,5,2] => [1,1,2,3,1] => 11101001 => 5
[8,4,7,6,3,5,2,1] => [1,2,3,1,1] => 11010011 => 5
[3,6,5,8,7,4,1,2] => [2,2,2,2] => 10101010 => 4
[3,1,5,8,6,7,4,2] => [2,2,3,1] => 10101001 => 4
[4,8,1,6,7,3,5,2] => [3,4,1] => 10010001 => 3
[3,6,4,1,8,7,5,2] => [2,2,1,2,1] => 10101101 => 5
[8,2,6,1,4,7,5,3] => [2,3,2,1] => 10100101 => 4
[2,7,6,8,1,4,3,5] => [2,4,2] => 10100010 => 3
[3,7,1,6,4,8,2,5] => [3,2,3] => 10010100 => 3
[1,7,3,5,6,8,2,4] => [1,2,5] => 11010000 => 3
[1,3,6,7,5,8,2,4] => [1,4,3] => 11000100 => 3
[3,7,6,5,8,2,1,4] => [2,1,3,2] => 10110010 => 4
[3,6,8,5,7,2,4,1] => [3,4,1] => 10010001 => 3
[2,3,5,7,6,8,1,4] => [4,4] => 10001000 => 2
[2,1,6,5,7,8,3,4] => [2,1,5] => 10110000 => 3
[4,2,7,6,8,3,1,5] => [2,1,3,2] => 10110010 => 4
[4,2,6,8,7,3,5,1] => [2,2,3,1] => 10101001 => 4
[3,8,2,4,6,7,5,1] => [4,3,1] => 10001001 => 3
[3,7,2,6,4,8,1,5] => [3,2,3] => 10010100 => 3
[3,2,6,1,4,7,8,5] => [2,3,3] => 10100100 => 3
[5,3,7,2,1,8,4,6] => [1,3,1,3] => 11001100 => 4
[4,7,3,2,1,5,8,6] => [3,1,2,2] => 10011010 => 4
[8,7,6,1,3,4,2,5] => [1,1,4,2] => 11100010 => 4
[8,5,7,3,2,1,6,4] => [1,3,1,2,1] => 11001101 => 5
[8,3,6,7,2,1,5,4] => [1,4,2,1] => 11000101 => 4
[3,7,8,6,2,1,5,4] => [3,2,2,1] => 10010101 => 4
[8,7,6,3,5,2,4,1] => [1,1,3,2,1] => 11100101 => 5
[2,7,4,8,1,6,5,3] => [2,4,1,1] => 10100011 => 4
[4,6,8,2,1,7,5,3] => [4,1,2,1] => 10001101 => 4
[8,4,1,5,7,2,6,3] => [1,2,4,1] => 11010001 => 4
[8,5,3,7,1,6,2,4] => [1,2,3,2] => 11010010 => 4
[8,5,7,2,1,3,6,4] => [1,3,3,1] => 11001001 => 4
[8,2,6,7,1,3,5,4] => [2,5,1] => 10100001 => 3
[8,3,6,1,7,5,2,4] => [1,3,2,2] => 11001010 => 4
[4,6,1,8,7,2,5,3] => [3,1,3,1] => 10011001 => 4
[8,1,2,5,6,7,4,3] => [3,4,1] => 10010001 => 3
[8,2,6,5,7,4,1,3] => [2,1,3,2] => 10110010 => 4
[2,1,7,8,5,6,4,3] => [2,4,1,1] => 10100011 => 4
[8,2,5,7,6,4,3,1] => [2,2,2,1,1] => 10101011 => 5
[2,7,6,8,5,4,1,3] => [2,3,1,2] => 10100110 => 4
[1,7,2,5,8,6,4,3] => [1,2,3,1,1] => 11010011 => 5
[1,7,4,8,2,6,5,3] => [1,1,4,1,1] => 11100011 => 5
[3,7,8,1,6,5,2,4] => [4,2,2] => 10001010 => 3
[2,7,8,6,1,3,5,4] => [3,4,1] => 10010001 => 3
[8,7,6,3,5,1,4,2] => [1,1,3,2,1] => 11100101 => 5
[8,4,7,6,5,1,3,2] => [1,2,2,2,1] => 11010101 => 5
[8,7,1,5,6,4,3,2] => [1,2,3,1,1] => 11010011 => 5
[8,1,6,7,5,4,3,2] => [2,3,1,1,1] => 10100111 => 5
[6,5,3,1,2,4,8,7] => [1,2,3,2] => 11010010 => 4
[4,6,3,5,1,2,8,7] => [3,3,2] => 10010010 => 3
[8,5,3,7,2,1,4,6] => [1,2,2,3] => 11010100 => 4
[6,8,1,4,5,7,3,2] => [5,2,1] => 10000101 => 3
[8,7,2,4,5,1,3,6] => [1,4,3] => 11000100 => 3
[3,6,2,4,5,1,8,7] => [5,1,2] => 10000110 => 3
[2,6,1,4,5,3,8,7] => [5,1,2] => 10000110 => 3
[6,1,2,4,5,3,8,7] => [5,1,2] => 10000110 => 3
[5,6,3,2,1,4,8,7] => [3,1,2,2] => 10011010 => 4
[5,4,3,6,1,2,8,7] => [1,2,3,2] => 11010010 => 4
[6,3,1,4,5,2,8,7] => [1,4,1,2] => 11000110 => 4
[3,1,6,4,5,2,8,7] => [2,3,1,2] => 10100110 => 4
[8,3,7,4,5,1,2,6] => [1,4,3] => 11000100 => 3
[5,8,7,4,2,6,3,1] => [2,2,2,1,1] => 10101011 => 5
[2,8,7,4,1,6,3,5] => [2,2,2,2] => 10101010 => 4
[8,1,7,4,2,6,3,5] => [2,2,2,2] => 10101010 => 4
[3,7,8,4,5,1,2,6] => [5,3] => 10000100 => 2
[2,1,8,7,5,3,4,6] => [2,1,2,3] => 10110100 => 4
[2,1,6,8,5,7,3,4] => [2,3,3] => 10100100 => 3
[5,6,3,8,1,7,2,4] => [3,2,3] => 10010100 => 3
[7,6,1,4,5,8,3,2] => [1,4,2,1] => 11000101 => 4
[3,7,6,4,5,8,2,1] => [2,3,2,1] => 10100101 => 4
[8,5,7,4,1,6,3,2] => [1,3,2,1,1] => 11001011 => 5
[5,1,8,4,7,6,2,3] => [2,2,2,2] => 10101010 => 4
[2,5,8,4,7,6,1,3] => [4,2,2] => 10001010 => 3
[2,4,8,3,5,6,7,1] => [7,1] => 10000001 => 2
[4,1,8,3,5,6,7,2] => [2,5,1] => 10100001 => 3
[3,8,4,2,5,6,7,1] => [2,5,1] => 10100001 => 3
[8,4,1,3,5,6,7,2] => [1,6,1] => 11000001 => 3
[7,5,8,4,3,6,1,2] => [1,3,2,2] => 11001010 => 4
[6,5,3,8,4,1,7,2] => [1,2,2,2,1] => 11010101 => 5
[2,1,5,8,4,6,7,3] => [2,5,1] => 10100001 => 3
[2,1,4,8,3,6,7,5] => [2,5,1] => 10100001 => 3
[6,4,3,8,2,1,7,5] => [1,2,2,2,1] => 11010101 => 5
[7,3,8,4,2,6,1,5] => [1,3,2,2] => 11001010 => 4
[8,3,1,2,5,6,7,4] => [1,6,1] => 11000001 => 3
[3,1,8,2,5,6,7,4] => [2,5,1] => 10100001 => 3
[2,3,8,1,5,6,7,4] => [7,1] => 10000001 => 2
[4,3,8,2,5,6,7,1] => [1,6,1] => 11000001 => 3
[4,8,2,3,5,6,7,1] => [7,1] => 10000001 => 2
[3,8,2,1,5,6,7,4] => [3,4,1] => 10010001 => 3
[2,8,1,3,5,6,7,4] => [7,1] => 10000001 => 2
[8,1,2,3,5,6,7,4] => [7,1] => 10000001 => 2
[7,8,2,4,3,6,1,5] => [4,2,2] => 10001010 => 3
[6,8,3,2,4,1,7,5] => [3,2,2,1] => 10010101 => 4
[2,1,8,3,4,6,7,5] => [2,5,1] => 10100001 => 3
[2,1,7,8,5,4,3,6] => [2,3,1,2] => 10100110 => 4
[5,7,3,8,1,4,2,6] => [3,3,2] => 10010010 => 3
[7,1,8,4,5,3,2,6] => [2,3,1,2] => 10100110 => 4
[2,7,8,4,5,3,1,6] => [5,1,2] => 10000110 => 3
[8,7,1,4,3,6,2,5] => [1,3,2,2] => 11001010 => 4
[3,8,7,4,2,6,1,5] => [2,2,2,2] => 10101010 => 4
[5,7,8,4,3,6,2,1] => [4,2,1,1] => 10001011 => 4
[5,6,3,8,4,2,7,1] => [3,2,2,1] => 10010101 => 4
[4,8,3,6,2,1,7,5] => [3,2,2,1] => 10010101 => 4
[8,6,3,1,4,2,7,5] => [1,2,2,2,1] => 11010101 => 5
[7,5,3,8,2,4,1,6] => [1,2,3,2] => 11010010 => 4
[2,4,3,1,8,5,7,6] => [3,1,3,1] => 10011001 => 4
[4,1,3,2,6,8,7,5] => [3,1,3,1] => 10011001 => 4
[7,5,3,6,2,8,1,4] => [1,2,2,3] => 11010100 => 4
[8,6,3,5,1,2,7,4] => [1,2,4,1] => 11010001 => 4
[5,8,3,2,6,1,7,4] => [3,1,3,1] => 10011001 => 4
[4,5,3,8,6,2,7,1] => [3,1,3,1] => 10011001 => 4
[3,5,8,4,7,6,2,1] => [4,2,1,1] => 10001011 => 4
[5,8,2,4,7,6,1,3] => [4,2,2] => 10001010 => 3
[8,7,5,4,1,6,2,3] => [1,1,2,2,2] => 11101010 => 5
[2,7,6,4,5,8,1,3] => [2,3,3] => 10100100 => 3
[7,1,6,4,5,8,2,3] => [2,3,3] => 10100100 => 3
[5,7,3,6,1,8,2,4] => [3,2,3] => 10010100 => 3
[2,1,7,6,5,8,3,4] => [2,1,2,3] => 10110100 => 4
[2,1,8,5,3,6,7,4] => [2,1,4,1] => 10110001 => 4
[6,8,3,5,2,1,7,4] => [3,2,2,1] => 10010101 => 4
[7,8,5,4,2,6,1,3] => [2,2,2,2] => 10101010 => 4
[8,1,4,2,5,6,7,3] => [2,5,1] => 10100001 => 3
[2,8,4,1,5,6,7,3] => [2,5,1] => 10100001 => 3
[4,8,1,2,5,6,7,3] => [7,1] => 10000001 => 2
[3,4,8,1,5,6,7,2] => [7,1] => 10000001 => 2
[3,4,2,8,5,6,7,1] => [3,4,1] => 10010001 => 3
[2,4,1,8,5,6,7,3] => [3,4,1] => 10010001 => 3
[4,1,2,8,5,6,7,3] => [3,4,1] => 10010001 => 3
[8,4,2,1,5,6,7,3] => [1,2,4,1] => 11010001 => 4
[7,5,2,4,8,6,1,3] => [1,3,2,2] => 11001010 => 4
[6,5,3,2,8,1,7,4] => [1,2,1,3,1] => 11011001 => 5
[2,1,5,3,8,6,7,4] => [2,2,3,1] => 10101001 => 4
[6,4,3,5,8,1,7,2] => [1,2,4,1] => 11010001 => 4
[7,3,5,4,8,6,1,2] => [1,3,2,2] => 11001010 => 4
[8,3,4,1,5,6,7,2] => [1,6,1] => 11000001 => 3
[4,3,1,8,5,6,7,2] => [1,2,4,1] => 11010001 => 4
[3,1,4,8,5,6,7,2] => [2,5,1] => 10100001 => 3
[6,5,3,7,2,8,4,1] => [1,2,2,2,1] => 11010101 => 5
[6,3,7,4,5,8,2,1] => [1,4,2,1] => 11000101 => 4
[6,7,2,4,5,8,3,1] => [5,2,1] => 10000101 => 3
[5,1,7,4,8,6,3,2] => [2,2,2,1,1] => 10101011 => 5
[2,5,7,4,8,6,3,1] => [4,2,1,1] => 10001011 => 4
[5,6,3,7,1,8,4,2] => [3,2,2,1] => 10010101 => 4
[3,8,7,4,5,2,1,6] => [2,3,1,2] => 10100110 => 4
[3,7,5,4,8,6,2,1] => [2,2,2,1,1] => 10101011 => 5
[5,7,1,4,8,6,2,3] => [4,2,2] => 10001010 => 3
[5,6,3,1,8,2,7,4] => [3,1,3,1] => 10011001 => 4
[4,6,3,5,8,2,7,1] => [3,4,1] => 10010001 => 3
[4,6,3,8,1,2,7,5] => [3,4,1] => 10010001 => 3
[3,7,8,4,1,6,2,5] => [4,2,2] => 10001010 => 3
[3,2,5,1,6,8,4,7] => [2,2,4] => 10101000 => 3
[3,6,2,5,4,8,1,7] => [3,2,3] => 10010100 => 3
[3,5,2,4,7,1,8,6] => [4,2,2] => 10001010 => 3
[3,5,8,2,4,7,6,1] => [5,2,1] => 10000101 => 3
[4,2,5,8,3,7,6,1] => [2,3,2,1] => 10100101 => 4
[4,2,6,5,3,8,1,7] => [2,1,2,3] => 10110100 => 4
[5,4,2,1,6,8,3,7] => [1,2,1,4] => 11011000 => 4
[6,3,5,1,4,8,2,7] => [1,4,3] => 11000100 => 3
[4,6,1,5,3,8,2,7] => [3,2,3] => 10010100 => 3
[5,1,6,4,3,8,2,7] => [2,2,1,3] => 10101100 => 4
[5,4,3,2,7,1,8,6] => [1,2,1,2,2] => 11011010 => 5
[5,4,3,8,2,7,6,1] => [1,2,2,2,1] => 11010101 => 5
[4,3,6,2,8,7,5,1] => [1,3,1,2,1] => 11001101 => 5
[4,3,7,6,2,1,8,5] => [1,2,2,1,2] => 11010110 => 5
[6,4,3,1,7,2,8,5] => [1,2,1,2,2] => 11011010 => 5
[7,5,4,3,1,8,2,6] => [1,1,2,1,3] => 11101100 => 5
[1,4,7,5,8,3,2,6] => [1,2,3,2] => 11010010 => 4
[7,1,3,5,8,4,2,6] => [3,3,2] => 10010010 => 3
[7,2,5,8,4,1,3,6] => [2,3,3] => 10100100 => 3
[2,8,5,7,4,6,1,3] => [2,4,2] => 10100010 => 3
[3,5,8,7,1,4,6,2] => [3,4,1] => 10010001 => 3
[1,4,5,8,7,3,6,2] => [1,3,3,1] => 11001001 => 4
[1,5,4,8,7,3,6,2] => [1,1,2,3,1] => 11101001 => 5
[6,4,3,8,1,7,5,2] => [1,2,2,2,1] => 11010101 => 5
[4,3,7,1,8,6,5,2] => [1,3,2,1,1] => 11001011 => 5
[4,8,3,7,6,5,2,1] => [3,1,2,1,1] => 10011011 => 5
[5,3,8,7,6,4,2,1] => [1,2,1,2,1,1] => 11011011 => 6
[7,5,3,1,8,6,4,2] => [1,2,1,2,1,1] => 11011011 => 6
[1,8,6,5,3,7,4,2] => [1,1,1,2,2,1] => 11110101 => 6
[1,5,8,6,3,7,4,2] => [1,2,2,2,1] => 11010101 => 5
[4,6,1,8,7,3,5,2] => [3,1,3,1] => 10011001 => 4
[6,8,7,3,1,4,5,2] => [2,2,3,1] => 10101001 => 4
[6,2,8,7,4,5,1,3] => [2,1,3,2] => 10110010 => 4
[7,6,2,8,4,1,3,5] => [1,2,2,3] => 11010100 => 4
[7,3,1,6,8,4,2,5] => [1,2,3,2] => 11010010 => 4
[1,7,6,4,8,3,2,5] => [1,1,2,2,2] => 11101010 => 5
[5,7,1,6,3,2,8,4] => [3,2,1,2] => 10010110 => 4
[6,1,7,5,3,2,8,4] => [2,1,2,1,2] => 10110110 => 5
[7,6,5,3,2,1,8,4] => [1,1,2,1,1,2] => 11101110 => 6
[6,5,3,2,8,7,4,1] => [1,2,1,1,2,1] => 11011101 => 6
[5,2,6,3,8,7,4,1] => [2,2,1,2,1] => 10101101 => 5
[5,2,7,6,3,1,8,4] => [2,1,2,1,2] => 10110110 => 5
[6,5,2,1,7,3,8,4] => [1,2,1,2,2] => 11011010 => 5
[5,2,7,4,1,8,3,6] => [2,2,1,3] => 10101100 => 4
[4,7,2,6,3,1,8,5] => [3,2,1,2] => 10010110 => 4
[2,4,8,6,3,7,5,1] => [3,2,2,1] => 10010101 => 4
[3,8,6,2,4,7,5,1] => [2,3,2,1] => 10100101 => 4
[7,3,6,2,4,1,8,5] => [1,4,1,2] => 11000110 => 4
[3,6,7,2,1,4,8,5] => [4,2,2] => 10001010 => 3
[4,3,7,8,2,1,5,6] => [1,4,3] => 11000100 => 3
[8,3,7,1,4,6,2,5] => [1,5,2] => 11000010 => 3
[3,8,2,5,7,1,6,4] => [3,4,1] => 10010001 => 3
[8,3,6,2,7,1,5,4] => [1,3,3,1] => 11001001 => 4
[7,8,3,6,2,1,5,4] => [3,2,2,1] => 10010101 => 4
[8,7,3,6,2,5,4,1] => [1,2,3,1,1] => 11010011 => 5
[4,7,8,2,1,6,5,3] => [4,2,1,1] => 10001011 => 4
[4,2,6,8,1,7,5,3] => [2,3,2,1] => 10100101 => 4
[5,4,8,2,7,1,6,3] => [1,3,3,1] => 11001001 => 4
[4,8,1,5,7,2,6,3] => [3,4,1] => 10010001 => 3
[5,8,3,7,1,6,2,4] => [3,3,2] => 10010010 => 3
[5,8,7,2,6,1,3,4] => [2,2,4] => 10101000 => 3
[8,6,2,7,5,1,3,4] => [1,2,2,3] => 11010100 => 4
[3,6,8,1,7,5,2,4] => [4,2,2] => 10001010 => 3
[5,1,6,8,2,7,4,3] => [2,3,2,1] => 10100101 => 4
[6,5,2,8,1,7,4,3] => [1,2,2,2,1] => 11010101 => 5
[5,2,7,1,8,6,4,3] => [2,2,2,1,1] => 10101011 => 5
[5,8,2,7,6,4,3,1] => [3,1,2,1,1] => 10011011 => 5
[6,2,8,7,5,4,3,1] => [2,1,2,1,1,1] => 10110111 => 6
[7,6,2,1,8,5,4,3] => [1,2,1,2,1,1] => 11011011 => 6
[6,1,7,2,8,5,4,3] => [2,2,2,1,1] => 10101011 => 5
[7,5,1,8,2,6,4,3] => [1,2,3,1,1] => 11010011 => 5
[4,7,1,8,6,2,5,3] => [3,1,3,1] => 10011001 => 4
[7,8,3,1,6,5,2,4] => [3,1,2,2] => 10011010 => 4
[8,7,4,6,1,5,3,2] => [1,1,4,1,1] => 11100011 => 5
[8,5,7,1,6,4,3,2] => [1,3,2,1,1] => 11001011 => 5
[6,8,1,7,5,4,3,2] => [3,2,1,1,1] => 10010111 => 5
[7,1,8,6,5,4,3,2] => [2,1,2,1,1,1] => 10110111 => 6
[5,4,2,3,7,6,1,8] => [1,3,2,2] => 11001010 => 4
[6,4,2,7,3,5,1,8] => [1,2,3,2] => 11010010 => 4
[7,4,2,6,3,5,1,8] => [1,2,3,2] => 11010010 => 4
[8,4,2,6,3,1,5,7] => [1,2,2,3] => 11010100 => 4
[3,2,7,6,4,5,1,8] => [2,1,3,2] => 10110010 => 4
[4,7,2,6,3,5,1,8] => [3,3,2] => 10010010 => 3
[5,7,6,2,3,4,1,8] => [2,4,2] => 10100010 => 3
[1,6,5,2,3,8,4,7] => [1,1,3,3] => 11100100 => 4
[1,7,5,2,8,3,4,6] => [1,1,2,4] => 11101000 => 4
[6,8,5,2,3,1,4,7] => [2,3,3] => 10100100 => 3
[5,8,6,2,3,1,4,7] => [2,3,3] => 10100100 => 3
[4,8,2,6,3,1,5,7] => [3,2,3] => 10010100 => 3
[3,2,8,6,4,1,5,7] => [2,1,2,3] => 10110100 => 4
[3,2,1,6,4,8,5,7] => [2,1,2,3] => 10110100 => 4
[7,1,5,2,8,3,4,6] => [2,2,4] => 10101000 => 3
[1,8,5,2,7,3,4,6] => [1,1,2,4] => 11101000 => 4
[1,8,6,7,2,3,4,5] => [1,1,6] => 11100000 => 3
[8,1,6,7,2,3,4,5] => [2,6] => 10100000 => 2
[7,1,6,8,2,3,4,5] => [2,6] => 10100000 => 2
[3,2,1,7,8,4,5,6] => [2,1,5] => 10110000 => 3
[3,2,8,7,1,4,5,6] => [2,1,5] => 10110000 => 3
[5,8,7,2,1,3,4,6] => [2,2,4] => 10101000 => 3
[1,7,6,8,2,3,4,5] => [1,1,6] => 11100000 => 3
[6,5,8,2,3,1,4,7] => [1,4,3] => 11000100 => 3
[8,5,7,2,1,3,4,6] => [1,3,4] => 11001000 => 3
[6,4,2,8,3,1,5,7] => [1,2,2,3] => 11010100 => 4
[5,4,2,3,8,1,6,7] => [1,3,4] => 11001000 => 3
[3,2,5,4,1,8,6,7] => [2,2,1,3] => 10101100 => 4
[4,5,2,3,1,8,6,7] => [4,1,3] => 10001100 => 3
[5,4,2,3,1,8,6,7] => [1,3,1,3] => 11001100 => 4
[6,4,2,1,3,8,5,7] => [1,2,2,3] => 11010100 => 4
[7,4,2,1,8,3,5,6] => [1,2,1,4] => 11011000 => 4
[8,4,2,1,7,3,5,6] => [1,2,1,4] => 11011000 => 4
[1,4,2,8,7,3,5,6] => [1,2,1,4] => 11011000 => 4
[1,5,8,2,7,3,4,6] => [1,3,4] => 11001000 => 3
[8,5,1,2,7,3,4,6] => [1,3,4] => 11001000 => 3
[7,5,1,2,8,3,4,6] => [1,3,4] => 11001000 => 3
[6,5,1,2,3,8,4,7] => [1,4,3] => 11000100 => 3
[4,6,2,1,3,8,5,7] => [3,2,3] => 10010100 => 3
[3,2,6,1,4,8,5,7] => [2,3,3] => 10100100 => 3
[3,2,7,1,8,4,5,6] => [2,2,4] => 10101000 => 3
[4,7,2,1,8,3,5,6] => [3,1,4] => 10011000 => 3
[7,6,1,8,2,3,4,5] => [1,2,5] => 11010000 => 3
[8,6,1,7,2,3,4,5] => [1,2,5] => 11010000 => 3
[1,6,8,7,2,3,4,5] => [1,2,5] => 11010000 => 3
[1,7,8,6,2,3,4,5] => [1,2,5] => 11010000 => 3
[7,8,1,6,2,3,4,5] => [3,5] => 10010000 => 2
[6,8,1,7,2,3,4,5] => [3,5] => 10010000 => 2
[4,8,2,1,7,3,5,6] => [3,1,4] => 10011000 => 3
[3,2,8,1,7,4,5,6] => [2,2,4] => 10101000 => 3
[3,2,1,8,7,4,5,6] => [2,1,1,4] => 10111000 => 4
[5,1,8,2,7,3,4,6] => [2,2,4] => 10101000 => 3
[6,1,8,7,2,3,4,5] => [2,1,5] => 10110000 => 3
[8,1,7,6,2,3,4,5] => [2,1,5] => 10110000 => 3
[1,8,7,6,2,3,4,5] => [1,1,1,5] => 11110000 => 4
[6,3,5,1,2,4,8,7] => [1,5,2] => 11000010 => 3
[4,3,5,6,1,2,8,7] => [1,5,2] => 11000010 => 3
[8,3,7,5,2,1,4,6] => [1,2,2,3] => 11010100 => 4
[6,3,7,5,1,8,4,2] => [1,2,2,2,1] => 11010101 => 5
[6,5,2,7,1,8,3,4] => [1,2,2,3] => 11010100 => 4
[8,5,2,7,4,1,3,6] => [1,2,2,3] => 11010100 => 4
[2,6,1,5,4,3,8,7] => [3,2,1,2] => 10010110 => 4
[6,4,3,5,1,2,8,7] => [1,2,3,2] => 11010010 => 4
[5,3,1,4,6,2,8,7] => [1,3,2,2] => 11001010 => 4
[3,1,4,6,5,2,8,7] => [2,3,1,2] => 10100110 => 4
[5,7,4,6,2,8,3,1] => [2,3,2,1] => 10100101 => 4
[8,1,4,7,2,6,3,5] => [2,4,2] => 10100010 => 3
[3,4,7,8,5,2,1,6] => [5,1,2] => 10000110 => 3
[2,1,8,5,7,3,4,6] => [2,1,5] => 10110000 => 3
[8,6,3,5,1,7,4,2] => [1,2,2,2,1] => 11010101 => 5
[5,8,2,4,6,7,3,1] => [4,3,1] => 10001001 => 3
[3,4,8,6,5,7,1,2] => [3,2,3] => 10010100 => 3
[7,5,4,8,1,6,3,2] => [1,1,4,1,1] => 11100011 => 5
[5,1,4,6,8,2,7,3] => [2,5,1] => 10100001 => 3
[2,5,4,6,7,1,8,3] => [2,4,2] => 10100010 => 3
[2,4,6,3,7,5,8,1] => [4,2,2] => 10001010 => 3
[4,1,6,3,8,5,7,2] => [2,2,3,1] => 10101001 => 4
[3,7,4,2,8,6,5,1] => [2,2,2,1,1] => 10101011 => 5
[7,4,1,3,5,8,6,2] => [1,4,2,1] => 11000101 => 4
[6,5,8,4,1,7,3,2] => [1,3,1,2,1] => 11001101 => 5
[8,5,3,7,4,1,6,2] => [1,2,2,2,1] => 11010101 => 5
[2,1,4,8,3,7,6,5] => [2,3,2,1] => 10100101 => 4
[7,4,3,8,2,1,6,5] => [1,2,2,2,1] => 11010101 => 5
[6,3,7,4,1,8,2,5] => [1,3,1,3] => 11001100 => 4
[8,3,1,2,5,7,6,4] => [1,4,2,1] => 11000101 => 4
[3,1,8,2,7,6,5,4] => [2,2,2,1,1] => 10101011 => 5
[2,3,8,1,6,7,5,4] => [4,3,1] => 10001001 => 3
[4,3,7,2,6,8,5,1] => [1,3,3,1] => 11001001 => 4
[4,7,2,3,8,5,6,1] => [4,3,1] => 10001001 => 3
[3,8,2,1,7,5,6,4] => [3,1,3,1] => 10011001 => 4
[2,8,1,3,6,5,7,4] => [4,3,1] => 10001001 => 3
[2,7,8,5,4,3,1,6] => [3,2,1,2] => 10010110 => 4
[8,7,1,6,3,4,2,5] => [1,2,3,2] => 11010010 => 4
[3,8,6,7,2,4,1,5] => [2,4,2] => 10100010 => 3
[5,3,8,7,4,2,6,1] => [1,2,2,2,1] => 11010101 => 5
[4,3,8,7,2,1,6,5] => [1,2,2,2,1] => 11010101 => 5
[8,3,6,1,4,2,7,5] => [1,4,2,1] => 11000101 => 4
[7,3,5,8,2,4,1,6] => [1,5,2] => 11000010 => 3
[2,3,4,1,8,5,7,6] => [4,3,1] => 10001001 => 3
[4,1,3,2,6,7,8,5] => [3,1,4] => 10011000 => 3
[8,3,5,6,2,7,1,4] => [1,4,3] => 11000100 => 3
[5,3,6,1,8,7,2,4] => [1,3,1,3] => 11001100 => 4
[5,6,2,8,7,4,1,3] => [3,1,2,2] => 10011010 => 4
[7,8,5,6,1,4,2,3] => [2,4,2] => 10100010 => 3
[2,8,6,5,4,7,1,3] => [2,1,2,3] => 10110100 => 4
[8,1,6,4,5,7,2,3] => [2,3,3] => 10100100 => 3
[5,8,3,6,1,7,2,4] => [3,2,3] => 10010100 => 3
[2,1,8,6,5,7,3,4] => [2,1,2,3] => 10110100 => 4
[2,1,7,5,3,6,8,4] => [2,1,3,2] => 10110010 => 4
[6,7,3,5,2,1,8,4] => [3,2,1,2] => 10010110 => 4
[7,1,4,2,5,6,8,3] => [2,4,2] => 10100010 => 3
[2,7,4,1,6,5,8,3] => [2,2,2,2] => 10101010 => 4
[4,6,1,2,8,7,3,5] => [4,1,3] => 10001100 => 3
[2,4,1,5,8,7,6,3] => [3,2,2,1] => 10010101 => 4
[4,1,2,5,8,6,7,3] => [3,4,1] => 10010001 => 3
[6,4,2,1,5,8,7,3] => [1,2,2,2,1] => 11010101 => 5
[8,5,2,4,6,1,7,3] => [1,3,3,1] => 11001001 => 4
[7,5,3,2,6,8,1,4] => [1,2,1,4] => 11011000 => 4
[2,1,5,3,6,8,7,4] => [2,2,3,1] => 10101001 => 4
[7,3,5,4,6,1,8,2] => [1,3,2,2] => 11001010 => 4
[6,3,4,1,5,7,8,2] => [1,4,3] => 11000100 => 3
[4,3,1,5,7,6,8,2] => [1,2,3,2] => 11010010 => 4
[3,1,4,5,6,8,7,2] => [2,5,1] => 10100001 => 3
[4,5,2,6,3,1,8,7] => [3,2,1,2] => 10010110 => 4
[6,5,2,1,4,3,8,7] => [1,2,2,1,2] => 11010110 => 5
[6,5,2,7,4,8,3,1] => [1,2,2,2,1] => 11010101 => 5
[8,5,2,7,4,1,6,3] => [1,2,2,2,1] => 11010101 => 5
[8,3,7,5,2,1,6,4] => [1,2,2,2,1] => 11010101 => 5
[6,3,7,5,2,8,4,1] => [1,2,2,2,1] => 11010101 => 5
[3,1,6,5,4,2,8,7] => [2,1,2,1,2] => 10110110 => 5
[5,6,3,2,4,1,8,7] => [3,2,1,2] => 10010110 => 4
[3,6,2,4,1,5,8,7] => [4,2,2] => 10001010 => 3
[2,6,1,3,5,4,8,7] => [5,1,2] => 10000110 => 3
[6,7,2,3,4,8,5,1] => [5,2,1] => 10000101 => 3
[8,7,2,3,4,1,6,5] => [1,4,2,1] => 11000101 => 4
[5,1,7,3,8,4,6,2] => [2,2,3,1] => 10101001 => 4
[2,5,7,3,8,6,4,1] => [4,2,1,1] => 10001011 => 4
[7,6,1,3,5,8,4,2] => [1,4,2,1] => 11000101 => 4
[3,6,7,4,1,8,5,2] => [4,1,2,1] => 10001101 => 4
[5,6,3,7,4,8,1,2] => [3,2,3] => 10010100 => 3
[2,1,6,7,4,8,5,3] => [2,3,2,1] => 10100101 => 4
[2,1,8,7,4,3,6,5] => [2,1,2,2,1] => 10110101 => 5
[5,8,3,7,4,2,6,1] => [3,2,2,1] => 10010101 => 4
[3,8,7,4,1,2,6,5] => [2,2,3,1] => 10101001 => 4
[7,8,1,3,5,2,6,4] => [5,2,1] => 10000101 => 3
[5,8,7,3,2,6,1,4] => [2,2,2,2] => 10101010 => 4
[2,8,6,3,1,5,7,4] => [2,2,3,1] => 10101001 => 4
[8,1,6,3,2,5,4,7] => [2,2,2,2] => 10101010 => 4
[2,8,4,1,6,3,7,5] => [2,2,3,1] => 10101001 => 4
[4,8,1,2,7,6,3,5] => [4,2,2] => 10001010 => 3
[3,8,4,2,5,7,1,6] => [2,3,3] => 10100100 => 3
[6,8,3,5,2,7,4,1] => [3,2,2,1] => 10010101 => 4
[2,1,5,3,8,7,6,4] => [2,2,1,2,1] => 10101101 => 5
[6,5,3,2,8,7,1,4] => [1,2,1,1,3] => 11011100 => 5
[7,5,2,4,8,1,6,3] => [1,3,3,1] => 11001001 => 4
[3,4,2,8,5,7,6,1] => [3,2,2,1] => 10010101 => 4
[2,4,1,8,7,6,5,3] => [3,1,2,1,1] => 10011011 => 5
[8,4,2,1,7,5,3,6] => [1,2,1,2,2] => 11011010 => 5
[4,3,1,8,6,7,5,2] => [1,2,1,3,1] => 11011001 => 5
[3,1,4,8,6,5,7,2] => [2,2,3,1] => 10101001 => 4
[7,1,6,5,4,8,2,3] => [2,1,2,3] => 10110100 => 4
[3,7,5,6,8,4,2,1] => [2,4,1,1] => 10100011 => 4
[5,7,1,6,8,2,4,3] => [3,4,1] => 10010001 => 3
[8,6,2,5,1,7,4,3] => [1,2,2,2,1] => 11010101 => 5
[5,6,2,1,8,7,3,4] => [3,1,1,3] => 10011100 => 4
[4,6,2,5,8,3,7,1] => [3,4,1] => 10010001 => 3
[7,5,2,6,3,8,1,4] => [1,2,2,3] => 11010100 => 4
[4,1,2,3,6,8,7,5] => [4,3,1] => 10001001 => 3
[2,4,3,1,8,5,6,7] => [3,1,4] => 10011000 => 3
[7,5,2,8,3,4,6,1] => [1,2,4,1] => 11010001 => 4
[5,6,2,8,4,3,1,7] => [3,2,1,2] => 10010110 => 4
[4,7,2,8,1,5,3,6] => [3,3,2] => 10010010 => 3
[8,7,2,1,4,5,6,3] => [1,2,4,1] => 11010001 => 4
[3,6,8,7,1,5,4,2] => [3,3,1,1] => 10010011 => 4
[5,7,8,6,3,4,1,2] => [3,3,2] => 10010010 => 3
[7,1,8,5,4,3,6,2] => [2,1,2,2,1] => 10110101 => 5
[2,7,8,4,5,3,6,1] => [5,2,1] => 10000101 => 3
[5,7,3,8,1,4,6,2] => [3,4,1] => 10010001 => 3
[2,1,7,8,5,4,6,3] => [2,3,2,1] => 10100101 => 4
[2,1,5,8,4,6,3,7] => [2,4,2] => 10100010 => 3
[6,5,3,8,4,1,2,7] => [1,2,2,3] => 11010100 => 4
[7,5,8,4,3,6,2,1] => [1,3,2,1,1] => 11001011 => 5
[2,4,8,3,5,6,1,7] => [6,2] => 10000010 => 2
[4,1,8,3,6,5,2,7] => [2,2,2,2] => 10101010 => 4
[3,4,8,1,7,2,5,6] => [4,4] => 10001000 => 2
[8,4,1,3,7,2,6,5] => [1,3,3,1] => 11001001 => 4
[3,1,8,2,4,7,6,5] => [2,3,2,1] => 10100101 => 4
[2,3,8,1,4,6,7,5] => [7,1] => 10000001 => 2
[4,3,8,2,5,1,7,6] => [1,4,2,1] => 11000101 => 4
[6,3,8,4,2,5,7,1] => [1,3,3,1] => 11001001 => 4
[7,4,3,8,2,5,1,6] => [1,2,3,2] => 11010010 => 4
[2,1,4,8,3,5,7,6] => [2,5,1] => 10100001 => 3
[6,8,2,4,3,5,1,7] => [4,2,2] => 10001010 => 3
[4,8,2,3,5,1,6,7] => [5,3] => 10000100 => 2
[3,8,2,1,4,6,5,7] => [3,3,2] => 10010010 => 3
[2,8,1,3,4,5,7,6] => [7,1] => 10000001 => 2
[2,8,4,1,6,5,3,7] => [2,2,2,2] => 10101010 => 4
[2,8,4,1,6,5,7,3] => [2,2,3,1] => 10101001 => 4
[2,8,7,6,1,4,3,5] => [2,1,3,2] => 10110010 => 4
[2,8,5,6,7,4,3,1] => [2,4,1,1] => 10100011 => 4
[7,5,8,6,1,4,2,3] => [1,2,3,2] => 11010010 => 4
[3,5,7,6,1,4,2,8] => [3,3,2] => 10010010 => 3
[3,5,7,2,4,1,6,8] => [5,3] => 10000100 => 2
[7,5,8,2,4,1,6,3] => [1,4,2,1] => 11000101 => 4
[2,8,5,3,4,7,6,1] => [2,3,2,1] => 10100101 => 4
[2,8,5,3,4,1,7,6] => [2,3,2,1] => 10100101 => 4
[2,8,5,3,4,1,6,7] => [2,3,3] => 10100100 => 3
[2,8,7,6,1,4,5,3] => [2,1,4,1] => 10110001 => 4
[2,8,5,3,6,1,7,4] => [2,2,3,1] => 10101001 => 4
[2,8,5,6,7,4,1,3] => [2,4,2] => 10100010 => 3
[2,8,5,3,4,7,1,6] => [2,3,3] => 10100100 => 3
[2,8,5,3,4,6,1,7] => [2,4,2] => 10100010 => 3
[2,8,5,3,4,6,7,1] => [2,5,1] => 10100001 => 3
[3,5,7,2,4,6,1,8] => [6,2] => 10000010 => 2
[6,5,2,7,3,1,4,8] => [1,2,2,3] => 11010100 => 4
[6,5,2,8,3,1,7,4] => [1,2,2,2,1] => 11010101 => 5
[6,5,2,8,3,1,4,7] => [1,2,2,3] => 11010100 => 4
[7,5,8,2,4,6,3,1] => [1,5,1,1] => 11000011 => 4
[7,5,8,6,1,4,3,2] => [1,2,3,1,1] => 11010011 => 5
[6,5,8,2,1,3,7,4] => [1,3,3,1] => 11001001 => 4
[3,5,6,2,1,8,7,4] => [4,1,2,1] => 10001101 => 4
[3,5,7,6,1,4,8,2] => [3,3,2] => 10010010 => 3
[3,5,7,2,4,1,8,6] => [5,1,2] => 10000110 => 3
[3,5,7,2,4,6,8,1] => [6,2] => 10000010 => 2
[6,5,2,7,3,1,8,4] => [1,2,2,1,2] => 11010110 => 5
[4,5,2,6,3,1,7,8] => [3,2,3] => 10010100 => 3
[4,1,2,3,7,6,8,5] => [4,2,2] => 10001010 => 3
[6,5,2,7,3,4,8,1] => [1,2,3,2] => 11010010 => 4
[5,1,6,7,4,3,8,2] => [2,3,1,2] => 10100110 => 4
[5,1,2,6,4,8,7,3] => [3,2,2,1] => 10010101 => 4
[5,1,2,8,6,4,7,3] => [3,1,3,1] => 10011001 => 4
[5,1,6,8,7,3,4,2] => [2,2,3,1] => 10101001 => 4
[6,5,2,8,3,7,4,1] => [1,2,2,2,1] => 11010101 => 5
[4,1,2,3,8,7,5,6] => [4,1,3] => 10001100 => 3
[4,1,2,3,8,6,5,7] => [4,2,2] => 10001010 => 3
[4,1,2,3,8,6,7,5] => [4,3,1] => 10001001 => 3
[4,1,2,3,7,6,5,8] => [4,2,2] => 10001010 => 3
[4,1,2,3,8,5,7,6] => [4,3,1] => 10001001 => 3
[7,1,6,8,4,3,5,2] => [2,3,2,1] => 10100101 => 4
[6,1,2,8,4,5,7,3] => [3,4,1] => 10010001 => 3
[5,6,8,2,3,1,7,4] => [5,2,1] => 10000101 => 3
[6,5,8,2,4,3,1,7] => [1,4,1,2] => 11000110 => 4
[6,5,8,2,4,3,7,1] => [1,4,2,1] => 11000101 => 4
[7,5,2,8,3,4,1,6] => [1,2,3,2] => 11010010 => 4
[6,5,2,8,3,7,1,4] => [1,2,2,3] => 11010100 => 4
[6,5,2,7,3,4,1,8] => [1,2,3,2] => 11010010 => 4
[5,1,6,7,4,3,2,8] => [2,3,1,2] => 10100110 => 4
[5,1,6,8,7,3,2,4] => [2,2,2,2] => 10101010 => 4
[7,1,6,8,4,3,2,5] => [2,3,1,2] => 10100110 => 4
[5,7,8,6,3,4,2,1] => [3,3,1,1] => 10010011 => 4
[4,1,8,3,6,5,7,2] => [2,2,3,1] => 10101001 => 4
[4,1,8,3,6,2,7,5] => [2,2,3,1] => 10101001 => 4
[3,1,4,8,6,2,7,5] => [2,2,3,1] => 10101001 => 4
[3,1,4,8,6,5,2,7] => [2,2,2,2] => 10101010 => 4
[7,1,6,5,8,3,2,4] => [2,1,3,2] => 10110010 => 4
[4,1,6,7,8,3,2,5] => [2,4,2] => 10100010 => 3
[4,1,6,5,7,3,2,8] => [2,1,3,2] => 10110010 => 4
[4,5,2,6,3,7,1,8] => [3,2,3] => 10010100 => 3
[4,5,2,7,3,8,1,6] => [3,2,3] => 10010100 => 3
[3,5,6,2,4,8,7,1] => [5,2,1] => 10000101 => 3
[3,5,6,2,4,8,1,7] => [5,3] => 10000100 => 2
[3,7,5,6,8,4,1,2] => [2,4,2] => 10100010 => 3
[3,6,5,2,8,1,7,4] => [2,2,3,1] => 10101001 => 4
[6,1,2,5,8,4,7,3] => [3,4,1] => 10010001 => 3
[7,1,6,5,8,3,4,2] => [2,1,4,1] => 10110001 => 4
[7,5,2,6,3,8,4,1] => [1,2,2,2,1] => 11010101 => 5
[4,1,2,3,5,8,7,6] => [5,2,1] => 10000101 => 3
[4,1,2,3,7,8,6,5] => [4,3,1] => 10001001 => 3
[4,5,2,7,3,8,6,1] => [3,2,2,1] => 10010101 => 4
[4,1,6,7,8,3,5,2] => [2,5,1] => 10100001 => 3
[4,1,2,6,8,5,7,3] => [3,4,1] => 10010001 => 3
[4,1,2,5,6,8,7,3] => [3,4,1] => 10010001 => 3
[4,5,2,6,3,7,8,1] => [3,2,3] => 10010100 => 3
[7,8,5,6,1,4,3,2] => [2,4,1,1] => 10100011 => 4
[7,8,4,2,1,5,3,6] => [2,2,2,2] => 10101010 => 4
[7,8,2,1,6,5,3,4] => [3,1,2,2] => 10011010 => 4
[6,4,1,2,5,7,3,8] => [1,4,3] => 11000100 => 3
[2,4,8,1,5,7,3,6] => [5,3] => 10000100 => 2
[4,3,8,1,7,2,5,6] => [1,3,4] => 11001000 => 3
[6,3,1,4,7,2,5,8] => [1,3,4] => 11001000 => 3
[7,8,3,4,5,1,6,2] => [5,2,1] => 10000101 => 3
[7,8,3,5,4,2,1,6] => [3,2,1,2] => 10010110 => 4
[7,8,4,1,2,3,6,5] => [2,5,1] => 10100001 => 3
[7,8,3,6,5,4,1,2] => [3,2,1,2] => 10010110 => 4
[7,8,2,1,5,3,4,6] => [3,2,3] => 10010100 => 3
[7,8,2,6,4,1,3,5] => [3,2,3] => 10010100 => 3
[7,8,2,5,6,4,1,3] => [3,3,2] => 10010010 => 3
[7,8,1,6,5,4,3,2] => [3,2,1,1,1] => 10010111 => 5
[6,2,1,7,5,4,3,8] => [2,1,2,1,2] => 10110110 => 5
[2,1,8,7,5,4,3,6] => [2,1,2,1,2] => 10110110 => 5
[1,3,8,2,6,4,7,5] => [1,3,3,1] => 11001001 => 4
[5,3,7,1,6,4,8,2] => [1,3,2,2] => 11001010 => 4
[5,3,6,2,7,4,1,8] => [1,3,2,2] => 11001010 => 4
[6,1,2,5,8,7,4,3] => [3,2,2,1] => 10010101 => 4
[6,3,1,8,4,2,7,5] => [1,2,2,2,1] => 11010101 => 5
[6,4,2,1,5,3,8,7] => [1,2,2,1,2] => 11010110 => 5
[6,4,3,7,5,8,1,2] => [1,2,2,3] => 11010100 => 4
[4,3,8,7,5,6,1,2] => [1,2,3,2] => 11010010 => 4
[2,4,7,1,5,3,6,8] => [5,3] => 10000100 => 2
[1,3,7,6,4,2,8,5] => [1,2,2,1,2] => 11010110 => 5
[2,1,7,5,6,8,4,3] => [2,1,4,1] => 10110001 => 4
[3,7,2,8,6,4,1,5] => [3,1,2,2] => 10011010 => 4
[3,8,1,7,6,4,5,2] => [3,1,3,1] => 10011001 => 4
[1,8,5,7,3,6,4,2] => [1,1,4,1,1] => 11100011 => 5
[2,7,5,8,3,6,1,4] => [2,4,2] => 10100010 => 3
[1,5,6,8,2,4,7,3] => [1,6,1] => 11000001 => 3
[2,6,8,5,3,1,4,7] => [3,2,3] => 10010100 => 3
[2,6,1,4,7,3,5,8] => [4,4] => 10001000 => 2
[5,6,7,3,8,4,1,2] => [4,2,2] => 10001010 => 3
[5,2,8,1,4,7,3,6] => [2,3,3] => 10100100 => 3
[4,6,7,5,2,1,3,8] => [3,2,3] => 10010100 => 3
[4,5,6,7,2,8,1,3] => [5,3] => 10000100 => 2
[4,5,7,6,1,8,3,2] => [3,2,2,1] => 10010101 => 4
[1,5,8,6,2,7,3,4] => [1,2,2,3] => 11010100 => 4
[1,6,5,8,3,2,7,4] => [1,1,3,2,1] => 11100101 => 5
[4,6,5,7,1,2,8,3] => [2,4,2] => 10100010 => 3
[4,7,5,6,3,1,8,2] => [2,3,1,2] => 10100110 => 4
[5,1,6,3,4,2,8,7] => [2,3,1,2] => 10100110 => 4
[5,7,1,4,2,3,8,6] => [4,2,2] => 10001010 => 3
[5,7,6,4,3,8,1,2] => [2,2,1,3] => 10101100 => 4
[6,3,4,5,8,7,1,2] => [1,4,3] => 11000100 => 3
[6,2,4,1,8,3,7,5] => [2,2,3,1] => 10101001 => 4
[6,2,3,5,4,8,1,7] => [3,2,3] => 10010100 => 3
[6,1,3,4,5,8,7,2] => [5,2,1] => 10000101 => 3
[5,1,4,2,7,6,8,3] => [2,2,2,2] => 10101010 => 4
[1,6,2,4,7,8,3,5] => [1,3,4] => 11001000 => 3
[5,7,2,4,1,6,3,8] => [4,2,2] => 10001010 => 3
[6,1,4,2,8,5,3,7] => [2,2,2,2] => 10101010 => 4
[6,7,5,8,1,4,3,2] => [2,4,1,1] => 10100011 => 4
[5,8,7,6,3,4,1,2] => [2,1,3,2] => 10110010 => 4
[5,8,7,6,2,3,1,4] => [2,1,3,2] => 10110010 => 4
[4,1,7,2,6,5,3,8] => [2,2,2,2] => 10101010 => 4
[4,8,2,1,5,6,3,7] => [3,3,2] => 10010010 => 3
[4,2,7,8,1,6,3,5] => [2,4,2] => 10100010 => 3
[2,1,8,7,6,5,3,4] => [2,1,1,2,2] => 10111010 => 5
[3,1,4,7,8,2,6,5] => [2,5,1] => 10100001 => 3
[3,1,7,4,5,6,8,2] => [2,4,2] => 10100010 => 3
[4,2,7,1,6,3,8,5] => [2,2,2,2] => 10101010 => 4
[4,3,7,5,6,8,1,2] => [1,2,5] => 11010000 => 3
[4,8,6,3,5,7,1,2] => [2,3,3] => 10100100 => 3
[4,8,1,2,5,3,7,6] => [5,2,1] => 10000101 => 3
[3,8,6,5,2,4,1,7] => [2,1,3,2] => 10110010 => 4
[3,8,5,6,1,4,7,2] => [2,5,1] => 10100001 => 3
[5,3,7,8,2,1,6,4] => [1,4,2,1] => 11000101 => 4
[5,2,8,7,1,6,4,3] => [2,1,3,1,1] => 10110011 => 5
[1,6,8,7,5,2,4,3] => [1,2,2,2,1] => 11010101 => 5
[3,6,7,8,5,1,4,2] => [5,2,1] => 10000101 => 3
[3,7,6,8,5,2,1,4] => [2,3,1,2] => 10100110 => 4
[3,7,8,5,1,2,4,6] => [3,5] => 10010000 => 2
[3,7,1,6,4,2,5,8] => [3,2,3] => 10010100 => 3
[4,1,8,6,2,3,5,7] => [2,1,5] => 10110000 => 3
[4,7,8,6,3,5,1,2] => [3,3,2] => 10010010 => 3
[3,8,7,6,5,4,1,2] => [2,1,2,1,2] => 10110110 => 5
[2,1,7,6,5,3,4,8] => [2,1,2,3] => 10110100 => 4
[2,8,1,6,4,5,3,7] => [3,3,2] => 10010010 => 3
[2,8,7,5,1,4,3,6] => [2,1,3,2] => 10110010 => 4
[2,8,6,7,5,1,3,4] => [2,3,3] => 10100100 => 3
[2,7,8,6,5,4,1,3] => [3,2,1,2] => 10010110 => 4
[6,3,1,2,7,4,8,5] => [1,3,2,2] => 11001010 => 4
[6,4,2,7,1,3,8,5] => [1,2,3,2] => 11010010 => 4
[7,4,2,5,1,3,8,6] => [1,2,3,2] => 11010010 => 4
[7,5,3,6,1,8,2,4] => [1,2,2,3] => 11010100 => 4
[8,5,3,6,1,7,2,4] => [1,2,2,3] => 11010100 => 4
[8,3,6,2,4,7,1,5] => [1,4,3] => 11000100 => 3
[7,3,6,2,4,8,1,5] => [1,4,3] => 11000100 => 3
[4,3,7,1,2,5,8,6] => [1,5,2] => 11000010 => 3
[3,6,2,7,1,4,8,5] => [3,3,2] => 10010010 => 3
[5,3,6,7,1,2,8,4] => [1,5,2] => 11000010 => 3
[6,3,7,4,1,2,8,5] => [1,3,2,2] => 11001010 => 4
[4,7,1,5,2,3,8,6] => [3,3,2] => 10010010 => 3
[3,7,5,1,2,4,8,6] => [2,4,2] => 10100010 => 3
[7,6,4,2,3,8,1,5] => [1,1,3,3] => 11100100 => 4
[8,6,4,2,3,7,1,5] => [1,1,3,3] => 11100100 => 4
[4,7,6,3,8,1,2,5] => [2,2,4] => 10101000 => 3
[5,7,4,2,3,8,1,6] => [2,3,3] => 10100100 => 3
[3,7,6,1,4,8,2,5] => [2,3,3] => 10100100 => 3
[5,7,2,6,1,8,3,4] => [3,2,3] => 10010100 => 3
[6,4,7,5,2,8,1,3] => [1,2,2,3] => 11010100 => 4
[7,4,8,5,2,6,1,3] => [1,2,3,2] => 11010010 => 4
[5,8,2,6,3,7,1,4] => [3,2,3] => 10010100 => 3
[3,8,6,1,2,7,4,5] => [2,3,3] => 10100100 => 3
[3,8,6,2,4,7,1,5] => [2,3,3] => 10100100 => 3
[6,8,4,3,7,1,2,5] => [2,2,4] => 10101000 => 3
[6,8,5,3,7,1,2,4] => [2,2,4] => 10101000 => 3
[3,8,5,7,1,2,4,6] => [2,6] => 10100000 => 2
[2,8,5,7,1,3,4,6] => [2,6] => 10100000 => 2
[4,8,6,2,7,1,3,5] => [2,2,4] => 10101000 => 3
[7,3,8,5,6,1,2,4] => [1,2,5] => 11010000 => 3
[6,3,7,5,8,1,2,4] => [1,2,5] => 11010000 => 3
[2,7,6,4,8,1,3,5] => [2,2,4] => 10101000 => 3
[2,6,5,8,1,3,4,7] => [2,6] => 10100000 => 2
[3,6,5,8,1,2,4,7] => [2,6] => 10100000 => 2
[2,5,7,4,8,1,3,6] => [4,4] => 10001000 => 2
[5,4,6,7,2,8,1,3] => [1,4,3] => 11000100 => 3
[4,6,3,7,1,8,2,5] => [3,2,3] => 10010100 => 3
[3,5,7,1,4,8,2,6] => [5,3] => 10000100 => 2
[5,3,7,2,4,8,1,6] => [1,4,3] => 11000100 => 3
[5,4,7,3,8,1,2,6] => [1,3,4] => 11001000 => 3
[7,4,6,3,8,1,2,5] => [1,3,4] => 11001000 => 3
[8,4,6,3,7,1,2,5] => [1,3,4] => 11001000 => 3
[8,4,1,6,7,2,3,5] => [1,2,5] => 11010000 => 3
[7,4,1,6,8,2,3,5] => [1,2,5] => 11010000 => 3
[5,4,1,7,8,2,3,6] => [1,2,5] => 11010000 => 3
[6,5,3,7,1,8,2,4] => [1,2,2,3] => 11010100 => 4
[6,5,1,2,7,8,3,4] => [1,3,4] => 11001000 => 3
[5,3,6,4,7,8,1,2] => [1,3,4] => 11001000 => 3
[6,3,7,4,8,5,1,2] => [1,3,2,2] => 11001010 => 4
[4,7,1,5,8,6,2,3] => [3,3,2] => 10010010 => 3
[7,5,1,2,8,6,3,4] => [1,3,2,2] => 11001010 => 4
[7,5,3,8,1,6,2,4] => [1,2,3,2] => 11010010 => 4
[7,4,1,8,6,2,3,5] => [1,2,1,4] => 11011000 => 4
[7,6,1,8,5,2,3,4] => [1,2,2,3] => 11010100 => 4
[8,6,1,7,5,2,3,4] => [1,2,2,3] => 11010100 => 4
[5,7,2,8,1,6,3,4] => [3,3,2] => 10010010 => 3
[6,4,7,8,2,5,1,3] => [1,5,2] => 11000010 => 3
[6,3,7,8,5,1,2,4] => [1,4,3] => 11000100 => 3
[3,6,8,2,7,1,4,5] => [4,4] => 10001000 => 2
[2,4,8,7,1,3,5,6] => [3,5] => 10010000 => 2
[4,3,8,7,1,2,5,6] => [1,2,5] => 11010000 => 3
[5,3,8,7,1,2,4,6] => [1,2,5] => 11010000 => 3
[8,3,7,6,1,2,4,5] => [1,2,5] => 11010000 => 3
[8,4,7,6,1,2,3,5] => [1,2,5] => 11010000 => 3
[5,4,8,7,1,2,3,6] => [1,2,5] => 11010000 => 3
[3,5,8,7,1,2,4,6] => [3,5] => 10010000 => 2
[2,5,8,7,1,3,4,6] => [3,5] => 10010000 => 2
[4,6,8,2,7,1,3,5] => [4,4] => 10001000 => 2
[4,7,1,8,6,2,3,5] => [3,1,4] => 10011000 => 3
[7,5,8,6,4,1,2,3] => [1,2,2,3] => 11010100 => 4
[6,8,4,7,5,1,2,3] => [2,3,3] => 10100100 => 3
[5,8,7,1,6,2,3,4] => [2,2,4] => 10101000 => 3
[2,8,7,6,1,3,4,5] => [2,1,5] => 10110000 => 3
[3,8,7,6,1,2,4,5] => [2,1,5] => 10110000 => 3
[4,8,7,6,1,2,3,5] => [2,1,5] => 10110000 => 3
[5,6,3,1,4,2,8,7] => [3,2,1,2] => 10010110 => 4
[7,5,3,8,2,1,6,4] => [1,2,2,2,1] => 11010101 => 5
[3,8,7,4,5,1,6,2] => [2,3,2,1] => 10100101 => 4
[6,7,1,4,5,8,2,3] => [5,3] => 10000100 => 2
[2,1,7,8,5,3,6,4] => [2,3,2,1] => 10100101 => 4
[5,7,3,8,1,2,6,4] => [3,4,1] => 10010001 => 3
[8,7,1,4,5,3,2,6] => [1,4,1,2] => 11000110 => 4
[2,7,8,4,1,6,5,3] => [4,2,1,1] => 10001011 => 4
[7,1,8,4,2,6,5,3] => [2,2,2,1,1] => 10101011 => 5
[7,5,1,4,8,6,3,2] => [1,3,2,1,1] => 11001011 => 5
[6,5,3,1,8,4,7,2] => [1,2,1,3,1] => 11011001 => 5
[6,4,3,8,1,5,7,2] => [1,2,4,1] => 11010001 => 4
[8,6,3,1,2,5,7,4] => [1,2,4,1] => 11010001 => 4
[8,7,1,4,2,6,5,3] => [1,3,2,1,1] => 11001011 => 5
[7,3,8,4,1,6,5,2] => [1,3,2,1,1] => 11001011 => 5
[2,3,4,5,6,7,8,1,9] => [9] => 100000000 => 1
[2,3,4,5,6,8,9,1,7] => [9] => 100000000 => 1
[2,3,4,5,7,8,9,1,6] => [9] => 100000000 => 1
[2,3,4,6,7,8,9,1,5] => [9] => 100000000 => 1
[2,3,5,6,7,8,9,1,4] => [9] => 100000000 => 1
[2,4,5,6,7,8,9,1,3] => [9] => 100000000 => 1
[3,4,5,6,7,8,9,1,2] => [9] => 100000000 => 1
[2,3,4,5,6,7,8,9,10,1] => [10] => 1000000000 => 1
[2,3,4,5,6,7,8,9,1,10] => [10] => 1000000000 => 1
[2,3,4,5,6,7,1,8,9] => [9] => 100000000 => 1
[2,3,4,5,6,7,8,10,1,9] => [10] => 1000000000 => 1
[2,3,4,5,6,1,9,7,8] => [6,3] => 100000100 => 2
[2,3,4,5,6,7,9,10,1,8] => [10] => 1000000000 => 1
[2,3,4,5,1,8,9,6,7] => [5,4] => 100001000 => 2
[2,3,4,5,6,8,9,10,1,7] => [10] => 1000000000 => 1
[2,3,4,1,7,8,9,5,6] => [4,5] => 100010000 => 2
[2,3,4,5,7,8,9,10,1,6] => [10] => 1000000000 => 1
[2,3,1,6,7,8,9,4,5] => [3,6] => 100100000 => 2
[2,3,4,6,7,8,9,10,1,5] => [10] => 1000000000 => 1
[2,1,5,6,7,8,9,3,4] => [2,7] => 101000000 => 2
[2,3,5,6,7,8,9,10,1,4] => [10] => 1000000000 => 1
[1,4,5,6,7,8,9,2,3] => [1,8] => 110000000 => 2
[2,4,5,6,7,8,9,10,1,3] => [10] => 1000000000 => 1
[3,4,5,6,7,8,9,10,1,2] => [10] => 1000000000 => 1
[3,6,4,5,7,2,8,1] => [2,4,2] => 10100010 => 3
[5,3,2,7,4,6,8,1] => [1,2,3,2] => 11010010 => 4
[7,5,3,6,2,4,8,1] => [1,2,3,2] => 11010010 => 4
[6,3,2,5,1,8,4,7] => [1,2,2,3] => 11010100 => 4
[8,5,3,6,2,7,1,4] => [1,2,2,3] => 11010100 => 4
[8,2,6,3,4,7,1,5] => [2,3,3] => 10100100 => 3
[7,2,6,3,4,5,8,1] => [2,4,2] => 10100010 => 3
[6,2,7,3,4,5,8,1] => [2,4,2] => 10100010 => 3
[3,6,2,7,4,5,8,1] => [3,3,2] => 10010010 => 3
[4,2,5,7,3,6,8,1] => [2,4,2] => 10100010 => 3
[5,4,7,6,2,3,8,1] => [1,2,3,2] => 11010010 => 4
[6,7,3,5,2,4,8,1] => [3,3,2] => 10010010 => 3
[3,7,6,2,4,5,8,1] => [2,4,2] => 10100010 => 3
[2,7,6,3,4,5,8,1] => [2,4,2] => 10100010 => 3
[6,5,3,1,2,8,4,7] => [1,2,2,3] => 11010100 => 4
[8,6,5,2,3,7,1,4] => [1,1,3,3] => 11100100 => 4
[8,5,2,1,7,3,4,6] => [1,2,1,4] => 11011000 => 4
[7,5,2,1,8,3,4,6] => [1,2,1,4] => 11011000 => 4
[1,6,3,2,8,4,5,7] => [1,2,1,4] => 11011000 => 4
[5,7,3,1,2,8,4,6] => [3,2,3] => 10010100 => 3
[5,6,2,3,1,8,4,7] => [4,1,3] => 10001100 => 3
[4,2,6,5,1,8,3,7] => [2,1,2,3] => 10110100 => 4
[5,4,8,6,2,7,1,3] => [1,2,2,3] => 11010100 => 4
[6,8,3,5,2,7,1,4] => [3,2,3] => 10010100 => 3
[7,8,5,2,3,6,1,4] => [2,4,2] => 10100010 => 3
[6,8,2,1,7,3,4,5] => [3,1,4] => 10011000 => 3
[1,8,6,3,7,2,4,5] => [1,1,2,4] => 11101000 => 4
[1,8,2,7,3,4,5,6] => [1,2,5] => 11010000 => 3
[2,8,1,7,3,4,5,6] => [3,5] => 10010000 => 2
[3,8,6,1,7,2,4,5] => [2,2,4] => 10101000 => 3
[4,8,1,5,7,2,3,6] => [3,5] => 10010000 => 2
[4,2,8,3,7,1,5,6] => [2,2,4] => 10101000 => 3
[4,1,7,5,8,2,3,6] => [2,1,5] => 10110000 => 3
[1,7,3,8,2,4,5,6] => [1,2,5] => 11010000 => 3
[8,1,2,7,3,4,5,6] => [3,5] => 10010000 => 2
[4,2,5,7,1,8,3,6] => [2,3,3] => 10100100 => 3
[3,6,2,7,1,8,4,5] => [3,2,3] => 10010100 => 3
[6,3,7,1,2,8,4,5] => [1,4,3] => 11000100 => 3
[7,2,6,1,8,3,4,5] => [2,2,4] => 10101000 => 3
[8,2,6,1,7,3,4,5] => [2,2,4] => 10101000 => 3
[7,3,1,5,8,2,4,6] => [1,2,5] => 11010000 => 3
[3,2,1,5,8,4,6,7] => [2,1,5] => 10110000 => 3
[5,4,1,3,6,8,2,7] => [1,3,4] => 11001000 => 3
[1,5,3,4,6,8,2,7] => [1,3,4] => 11001000 => 3
[4,3,5,1,6,8,2,7] => [1,3,4] => 11001000 => 3
[5,4,6,3,8,7,1,2] => [1,3,1,3] => 11001100 => 4
[3,6,4,5,8,7,1,2] => [2,3,3] => 10100100 => 3
[6,5,3,4,8,7,1,2] => [1,3,1,3] => 11001100 => 4
[5,3,2,8,7,1,4,6] => [1,2,1,4] => 11011000 => 4
[5,3,1,8,7,2,4,6] => [1,2,1,4] => 11011000 => 4
[8,5,3,7,6,1,2,4] => [1,2,1,4] => 11011000 => 4
[6,1,8,3,7,2,4,5] => [2,2,4] => 10101000 => 3
[6,3,8,1,7,2,4,5] => [1,3,4] => 11001000 => 3
[7,6,8,2,3,5,1,4] => [1,5,2] => 11000010 => 3
[3,7,8,2,4,6,1,5] => [6,2] => 10000010 => 2
[6,7,3,8,2,5,1,4] => [3,3,2] => 10010010 => 3
[5,4,7,8,2,6,1,3] => [1,5,2] => 11000010 => 3
[4,2,5,8,7,1,3,6] => [2,2,4] => 10101000 => 3
[3,6,2,8,7,1,4,5] => [3,1,4] => 10011000 => 3
[3,7,8,1,6,2,4,5] => [4,4] => 10001000 => 2
[2,3,8,7,1,4,5,6] => [3,5] => 10010000 => 2
[7,2,8,6,1,3,4,5] => [2,1,5] => 10110000 => 3
[2,1,8,7,3,4,5,6] => [2,1,5] => 10110000 => 3
[8,2,7,6,1,3,4,5] => [2,1,5] => 10110000 => 3
[1,2,8,7,3,4,5,6] => [2,1,5] => 10110000 => 3
[1,3,8,7,2,4,5,6] => [1,2,5] => 11010000 => 3
[1,7,8,3,6,2,4,5] => [1,3,4] => 11001000 => 3
[4,1,5,8,7,2,3,6] => [2,2,4] => 10101000 => 3
[5,4,8,7,6,1,2,3] => [1,2,1,4] => 11011000 => 4
[6,8,3,7,5,1,2,4] => [3,2,3] => 10010100 => 3
[7,8,6,2,5,1,3,4] => [2,3,3] => 10100100 => 3
[8,1,6,7,3,2,5,4] => [2,3,2,1] => 10100101 => 4
[8,1,6,7,3,2,4,5] => [2,3,3] => 10100100 => 3
[8,1,5,3,7,2,4,6] => [2,2,4] => 10101000 => 3
[8,1,5,3,6,2,4,7] => [2,2,4] => 10101000 => 3
[7,5,1,3,6,2,4,8] => [1,3,4] => 11001000 => 3
[7,5,8,3,6,2,4,1] => [1,3,3,1] => 11001001 => 4
[7,4,8,3,2,6,5,1] => [1,3,2,1,1] => 11001011 => 5
[7,4,1,3,2,6,5,8] => [1,3,2,2] => 11001010 => 4
[8,1,4,3,2,6,5,7] => [2,2,2,2] => 10101010 => 4
[8,1,4,3,2,7,5,6] => [2,2,1,3] => 10101100 => 4
[8,1,4,3,2,7,6,5] => [2,2,1,2,1] => 10101101 => 5
[8,1,5,4,6,7,2,3] => [2,2,4] => 10101000 => 3
[8,1,5,3,6,2,7,4] => [2,2,3,1] => 10101001 => 4
[8,1,4,3,2,6,7,5] => [2,2,3,1] => 10101001 => 4
[8,1,4,3,2,5,7,6] => [2,2,3,1] => 10101001 => 4
[8,1,4,3,2,5,6,7] => [2,2,4] => 10101000 => 3
[7,4,1,3,2,5,6,8] => [1,3,4] => 11001000 => 3
[7,4,8,3,2,5,6,1] => [1,3,3,1] => 11001001 => 4
[6,4,3,8,2,5,7,1] => [1,2,4,1] => 11010001 => 4
[6,4,3,1,2,5,8,7] => [1,2,3,2] => 11010010 => 4
[7,4,1,3,2,5,8,6] => [1,3,2,2] => 11001010 => 4
[7,4,1,3,2,6,8,5] => [1,3,2,2] => 11001010 => 4
[7,5,1,3,6,2,8,4] => [1,3,2,2] => 11001010 => 4
[7,5,1,4,6,8,2,3] => [1,3,4] => 11001000 => 3
[7,5,8,3,6,2,1,4] => [1,3,2,2] => 11001010 => 4
[7,4,8,3,2,6,1,5] => [1,3,2,2] => 11001010 => 4
[7,4,8,3,2,5,1,6] => [1,3,2,2] => 11001010 => 4
[6,4,3,8,2,5,1,7] => [1,2,3,2] => 11010010 => 4
[6,4,3,7,2,5,8,1] => [1,2,3,2] => 11010010 => 4
[5,4,3,2,8,6,1,7] => [1,2,1,2,2] => 11011010 => 5
[5,4,3,2,8,7,1,6] => [1,2,1,1,3] => 11011100 => 5
[6,5,3,8,7,2,1,4] => [1,2,1,2,2] => 11011010 => 5
[6,5,4,8,7,1,2,3] => [1,1,2,4] => 11101000 => 4
[6,5,4,1,7,8,2,3] => [1,1,2,4] => 11101000 => 4
[6,5,3,1,7,2,8,4] => [1,2,1,2,2] => 11011010 => 5
[6,4,3,1,2,7,8,5] => [1,2,2,3] => 11010100 => 4
[5,4,3,2,1,8,6,7] => [1,2,1,1,3] => 11011100 => 5
[6,5,3,1,8,2,7,4] => [1,2,1,3,1] => 11011001 => 5
[6,5,4,1,8,7,2,3] => [1,1,2,1,3] => 11101100 => 5
[7,5,1,4,8,6,2,3] => [1,3,2,2] => 11001010 => 4
[7,4,1,3,2,8,6,5] => [1,3,1,2,1] => 11001101 => 5
[7,4,1,3,2,8,5,6] => [1,3,1,3] => 11001100 => 4
[6,4,3,1,2,8,5,7] => [1,2,2,3] => 11010100 => 4
[6,4,3,1,2,7,5,8] => [1,2,2,3] => 11010100 => 4
[6,4,3,8,2,7,5,1] => [1,2,2,2,1] => 11010101 => 5
[6,5,3,8,7,2,4,1] => [1,2,1,3,1] => 11011001 => 5
[6,5,3,1,7,2,4,8] => [1,2,1,4] => 11011000 => 4
[6,5,3,1,8,2,4,7] => [1,2,1,4] => 11011000 => 4
[7,5,1,3,8,2,4,6] => [1,3,4] => 11001000 => 3
[7,6,1,8,3,2,4,5] => [1,2,2,3] => 11010100 => 4
[7,6,1,8,4,5,2,3] => [1,2,3,2] => 11010010 => 4
[7,6,8,1,4,5,2,3] => [1,5,2] => 11000010 => 3
[7,6,8,1,3,2,5,4] => [1,4,2,1] => 11000101 => 4
[6,5,3,7,8,2,4,1] => [1,2,4,1] => 11010001 => 4
[6,4,3,7,2,8,5,1] => [1,2,2,2,1] => 11010101 => 5
[6,4,3,7,2,1,5,8] => [1,2,2,3] => 11010100 => 4
[7,4,8,3,2,1,5,6] => [1,3,1,3] => 11001100 => 4
[7,4,8,3,2,1,6,5] => [1,3,1,2,1] => 11001101 => 5
[7,5,8,3,1,2,6,4] => [1,3,3,1] => 11001001 => 4
[7,5,8,4,1,6,2,3] => [1,3,2,2] => 11001010 => 4
[6,5,4,8,1,7,2,3] => [1,1,3,3] => 11100100 => 4
[6,5,3,8,1,2,7,4] => [1,2,4,1] => 11010001 => 4
[5,4,3,2,8,1,7,6] => [1,2,1,3,1] => 11011001 => 5
[6,4,3,7,2,1,8,5] => [1,2,2,1,2] => 11010110 => 5
[6,5,3,7,1,2,8,4] => [1,2,3,2] => 11010010 => 4
[6,5,4,7,1,8,2,3] => [1,1,3,3] => 11100100 => 4
[6,5,3,7,8,2,1,4] => [1,2,3,2] => 11010010 => 4
[6,4,3,7,2,8,1,5] => [1,2,2,3] => 11010100 => 4
[5,4,3,2,7,8,1,6] => [1,2,1,4] => 11011000 => 4
[5,4,3,2,6,8,1,7] => [1,2,1,4] => 11011000 => 4
[5,6,2,1,3,4,8,7] => [3,3,2] => 10010010 => 3
[5,8,2,7,4,1,3,6] => [3,2,3] => 10010100 => 3
[5,3,7,8,2,1,4,6] => [1,4,3] => 11000100 => 3
[7,6,1,2,5,8,3,4] => [1,4,3] => 11000100 => 3
[2,1,7,8,4,3,5,6] => [2,3,3] => 10100100 => 3
[8,3,7,4,1,5,6,2] => [1,3,3,1] => 11001001 => 4
[7,8,1,2,5,4,6,3] => [5,2,1] => 10000101 => 3
[2,6,8,3,1,4,7,5] => [4,3,1] => 10001001 => 3
[6,1,8,3,2,4,5,7] => [2,2,4] => 10101000 => 3
[8,4,1,3,7,6,2,5] => [1,3,2,2] => 11001010 => 4
[5,8,7,4,2,1,6,3] => [2,2,1,2,1] => 10101101 => 5
[7,5,1,6,8,3,4,2] => [1,2,4,1] => 11010001 => 4
[6,5,2,1,8,7,4,3] => [1,2,1,1,2,1] => 11011101 => 6
[4,7,2,8,1,3,6,5] => [3,4,1] => 10010001 => 3
[7,3,8,6,1,2,5,4] => [1,2,4,1] => 11010001 => 4
[3,4,7,1,8,2,6,5] => [4,3,1] => 10001001 => 3
[1,8,2,4,3,5,6,7] => [1,3,4] => 11001000 => 3
[1,7,2,4,3,5,6,8] => [1,3,4] => 11001000 => 3
[1,6,2,4,3,5,7,8] => [1,3,4] => 11001000 => 3
[1,5,2,4,3,6,7,8] => [1,3,4] => 11001000 => 3
[1,6,2,5,3,4,7,8] => [1,2,5] => 11010000 => 3
[1,7,2,5,3,4,6,8] => [1,2,5] => 11010000 => 3
[1,8,2,5,3,4,6,7] => [1,2,5] => 11010000 => 3
[1,8,2,6,3,4,5,7] => [1,2,5] => 11010000 => 3
[1,7,2,6,3,4,5,8] => [1,2,5] => 11010000 => 3
[1,8,2,7,3,5,4,6] => [1,2,3,2] => 11010010 => 4
[1,7,2,8,3,5,4,6] => [1,2,3,2] => 11010010 => 4
[1,6,2,8,3,5,4,7] => [1,2,3,2] => 11010010 => 4
[1,5,2,8,3,6,4,7] => [1,2,3,2] => 11010010 => 4
[1,4,2,8,3,6,5,7] => [1,2,3,2] => 11010010 => 4
[1,3,2,8,4,6,5,7] => [1,2,3,2] => 11010010 => 4
[1,2,3,8,4,6,5,7] => [3,3,2] => 10010010 => 3
[1,2,3,7,4,6,5,8] => [3,3,2] => 10010010 => 3
[1,3,2,7,4,6,5,8] => [1,2,3,2] => 11010010 => 4
[1,4,2,7,3,6,5,8] => [1,2,3,2] => 11010010 => 4
[1,5,2,7,3,6,4,8] => [1,2,3,2] => 11010010 => 4
[1,6,2,7,3,5,4,8] => [1,2,3,2] => 11010010 => 4
[1,7,2,6,3,5,4,8] => [1,2,3,2] => 11010010 => 4
[1,8,2,6,3,5,4,7] => [1,2,3,2] => 11010010 => 4
[1,8,2,5,3,6,4,7] => [1,2,3,2] => 11010010 => 4
[1,7,2,5,3,6,4,8] => [1,2,3,2] => 11010010 => 4
[1,6,2,5,3,7,4,8] => [1,2,2,3] => 11010100 => 4
[1,5,2,4,3,7,6,8] => [1,3,1,3] => 11001100 => 4
[1,6,2,4,3,7,5,8] => [1,3,1,3] => 11001100 => 4
[1,7,2,4,3,6,5,8] => [1,3,2,2] => 11001010 => 4
[1,8,2,4,3,6,5,7] => [1,3,2,2] => 11001010 => 4
[1,8,2,3,4,6,5,7] => [1,5,2] => 11000010 => 3
[1,7,2,3,4,6,5,8] => [1,5,2] => 11000010 => 3
[1,8,2,3,4,7,5,6] => [1,4,3] => 11000100 => 3
[1,8,2,4,3,7,5,6] => [1,3,1,3] => 11001100 => 4
[1,7,2,4,3,8,5,6] => [1,3,1,3] => 11001100 => 4
[1,6,2,4,3,8,5,7] => [1,3,1,3] => 11001100 => 4
[1,5,2,4,3,8,6,7] => [1,3,1,3] => 11001100 => 4
[1,6,2,5,3,8,4,7] => [1,2,2,3] => 11010100 => 4
[1,7,2,5,3,8,4,6] => [1,2,2,3] => 11010100 => 4
[1,8,2,5,3,7,4,6] => [1,2,2,3] => 11010100 => 4
[1,8,2,6,3,7,4,5] => [1,2,2,3] => 11010100 => 4
[1,7,2,6,3,8,4,5] => [1,2,2,3] => 11010100 => 4
[1,2,3,8,4,7,5,6] => [3,2,3] => 10010100 => 3
[1,3,2,8,4,7,5,6] => [1,2,2,3] => 11010100 => 4
[1,4,2,8,3,7,5,6] => [1,2,2,3] => 11010100 => 4
[1,5,2,8,3,7,4,6] => [1,2,2,3] => 11010100 => 4
[1,6,2,8,3,7,4,5] => [1,2,2,3] => 11010100 => 4
[1,7,2,8,3,6,4,5] => [1,2,3,2] => 11010010 => 4
[1,8,2,7,3,6,4,5] => [1,2,3,2] => 11010010 => 4
[4,6,3,7,2,5,1,8] => [3,3,2] => 10010010 => 3
[4,6,3,7,5,2,1,8] => [3,2,1,2] => 10010110 => 4
[4,6,3,8,5,1,7,2] => [3,2,2,1] => 10010101 => 4
[4,6,3,8,5,1,2,7] => [3,2,3] => 10010100 => 3
[5,6,8,3,4,1,2,7] => [5,3] => 10000100 => 2
[5,6,8,3,4,1,7,2] => [5,2,1] => 10000101 => 3
[4,6,2,7,5,3,1,8] => [3,2,1,2] => 10010110 => 4
[5,6,7,2,4,3,1,8] => [5,1,2] => 10000110 => 3
[5,6,8,4,3,1,7,2] => [4,1,2,1] => 10001101 => 4
[5,6,8,4,3,1,2,7] => [4,1,3] => 10001100 => 3
[5,7,8,4,1,6,2,3] => [4,2,2] => 10001010 => 3
[5,7,8,4,1,6,3,2] => [4,2,1,1] => 10001011 => 4
[5,7,8,4,1,3,6,2] => [4,3,1] => 10001001 => 3
[5,6,8,4,2,1,7,3] => [4,1,2,1] => 10001101 => 4
[5,6,8,2,4,1,7,3] => [5,2,1] => 10000101 => 3
[4,6,2,8,5,1,7,3] => [3,2,2,1] => 10010101 => 4
[3,2,6,8,5,1,7,4] => [2,3,2,1] => 10100101 => 4
[3,2,6,8,5,1,4,7] => [2,3,3] => 10100100 => 3
[4,6,2,8,5,1,3,7] => [3,2,3] => 10010100 => 3
[5,6,8,2,4,1,3,7] => [5,3] => 10000100 => 2
[5,6,8,4,2,1,3,7] => [4,1,3] => 10001100 => 3
[5,7,8,4,1,3,2,6] => [4,2,2] => 10001010 => 3
[5,7,8,4,1,2,6,3] => [4,3,1] => 10001001 => 3
[5,7,8,4,1,2,3,6] => [4,4] => 10001000 => 2
[6,7,8,1,5,2,3,4] => [5,3] => 10000100 => 2
[6,7,8,1,5,2,4,3] => [5,2,1] => 10000101 => 3
[6,7,8,1,5,3,2,4] => [5,1,2] => 10000110 => 3
[6,7,8,1,3,5,2,4] => [6,2] => 10000010 => 2
[5,7,8,2,1,6,3,4] => [4,2,2] => 10001010 => 3
[4,7,2,8,1,6,3,5] => [3,3,2] => 10010010 => 3
[3,2,7,8,1,6,4,5] => [2,4,2] => 10100010 => 3
[3,2,7,8,1,6,5,4] => [2,4,1,1] => 10100011 => 4
[4,7,2,8,1,6,5,3] => [3,3,1,1] => 10010011 => 4
[5,7,8,2,1,6,4,3] => [4,2,1,1] => 10001011 => 4
[6,7,8,1,3,5,4,2] => [6,1,1] => 10000011 => 3
[6,7,8,1,5,3,4,2] => [5,2,1] => 10000101 => 3
[6,7,8,1,5,4,3,2] => [5,1,1,1] => 10000111 => 4
[6,7,8,1,5,4,2,3] => [5,1,2] => 10000110 => 3
[6,7,8,1,4,5,2,3] => [6,2] => 10000010 => 2
[6,7,8,1,4,5,3,2] => [6,1,1] => 10000011 => 3
[6,7,8,1,4,3,5,2] => [5,2,1] => 10000101 => 3
[6,7,8,1,3,4,5,2] => [7,1] => 10000001 => 2
[5,7,8,2,1,4,6,3] => [4,3,1] => 10001001 => 3
[4,7,2,8,1,5,6,3] => [3,4,1] => 10010001 => 3
[3,2,7,8,1,5,6,4] => [2,5,1] => 10100001 => 3
[3,2,6,8,4,1,7,5] => [2,3,2,1] => 10100101 => 4
[4,6,2,8,3,1,7,5] => [3,2,2,1] => 10010101 => 4
[5,6,8,3,2,1,7,4] => [4,1,2,1] => 10001101 => 4
[5,7,8,3,1,4,6,2] => [4,3,1] => 10001001 => 3
[5,7,8,3,1,6,4,2] => [4,2,1,1] => 10001011 => 4
[5,7,8,3,1,6,2,4] => [4,2,2] => 10001010 => 3
[4,7,3,8,1,6,2,5] => [3,3,2] => 10010010 => 3
[4,7,3,8,1,6,5,2] => [3,3,1,1] => 10010011 => 4
[4,7,3,8,1,5,6,2] => [3,4,1] => 10010001 => 3
[4,6,3,8,2,1,7,5] => [3,2,2,1] => 10010101 => 4
[4,5,3,2,8,1,7,6] => [3,1,3,1] => 10011001 => 4
[4,5,2,3,8,1,7,6] => [4,3,1] => 10001001 => 3
[3,2,5,4,8,1,7,6] => [2,2,3,1] => 10101001 => 4
[4,5,3,2,8,1,6,7] => [3,1,4] => 10011000 => 3
[4,6,3,8,2,1,5,7] => [3,2,3] => 10010100 => 3
[4,7,3,8,1,5,2,6] => [3,3,2] => 10010010 => 3
[4,7,3,8,1,2,6,5] => [3,4,1] => 10010001 => 3
[4,7,3,8,1,2,5,6] => [3,5] => 10010000 => 2
[5,7,8,3,1,2,4,6] => [4,4] => 10001000 => 2
[5,7,8,3,1,2,6,4] => [4,3,1] => 10001001 => 3
[5,7,8,3,1,4,2,6] => [4,2,2] => 10001010 => 3
[5,6,8,3,2,1,4,7] => [4,1,3] => 10001100 => 3
[3,2,7,8,1,5,4,6] => [2,4,2] => 10100010 => 3
[5,7,8,2,1,4,3,6] => [4,2,2] => 10001010 => 3
[6,7,8,1,3,4,2,5] => [6,2] => 10000010 => 2
[6,7,8,1,4,3,2,5] => [5,1,2] => 10000110 => 3
[6,7,8,1,4,2,5,3] => [5,2,1] => 10000101 => 3
[6,7,8,1,4,2,3,5] => [5,3] => 10000100 => 2
[6,7,8,1,2,5,3,4] => [6,2] => 10000010 => 2
[6,7,8,1,2,5,4,3] => [6,1,1] => 10000011 => 3
[6,7,8,1,2,4,5,3] => [7,1] => 10000001 => 2
[6,7,8,1,3,2,5,4] => [5,2,1] => 10000101 => 3
[5,7,8,2,1,3,6,4] => [4,3,1] => 10001001 => 3
[3,2,7,8,1,4,6,5] => [2,5,1] => 10100001 => 3
[6,7,8,1,3,2,4,5] => [5,3] => 10000100 => 2
[6,7,8,1,2,4,3,5] => [6,2] => 10000010 => 2
[6,7,8,1,2,3,5,4] => [7,1] => 10000001 => 2
[7,2,8,5,1,6,4,3] => [2,1,3,1,1] => 10110011 => 5
[1,3,7,5,2,6,4,8] => [1,2,3,2] => 11010010 => 4
[1,3,7,5,4,2,6,8] => [1,2,2,3] => 11010100 => 4
[7,2,8,5,4,1,6,3] => [2,1,2,2,1] => 10110101 => 5
[2,8,5,4,3,1,7,6] => [2,2,1,2,1] => 10101101 => 5
[2,8,4,5,6,1,7,3] => [2,5,1] => 10100001 => 3
[2,8,6,5,7,3,1,4] => [2,1,3,2] => 10110010 => 4
[2,8,4,5,3,7,1,6] => [2,3,3] => 10100100 => 3
[2,8,4,3,5,6,1,7] => [2,4,2] => 10100010 => 3
[7,2,8,4,5,6,1,3] => [2,4,2] => 10100010 => 3
[1,6,3,7,5,2,4,8] => [1,2,2,3] => 11010100 => 4
[6,2,3,8,5,1,7,4] => [3,2,2,1] => 10010101 => 4
[6,3,2,8,5,1,4,7] => [1,2,2,3] => 11010100 => 4
[7,4,8,2,5,6,3,1] => [1,5,1,1] => 11000011 => 4
[7,4,8,5,2,1,3,6] => [1,2,2,3] => 11010100 => 4
[6,4,8,5,1,3,7,2] => [1,2,4,1] => 11010001 => 4
[6,3,7,5,2,1,8,4] => [1,2,2,1,2] => 11010110 => 5
[4,3,7,5,1,2,8,6] => [1,2,3,2] => 11010010 => 4
[4,3,7,1,5,6,8,2] => [1,5,2] => 11000010 => 3
[3,6,1,7,5,2,8,4] => [3,2,1,2] => 10010110 => 4
[3,4,1,2,7,6,8,5] => [4,2,2] => 10001010 => 3
[3,4,2,1,7,5,8,6] => [3,1,2,2] => 10011010 => 4
[3,6,5,7,1,4,8,2] => [2,4,2] => 10100010 => 3
[6,5,2,7,4,1,8,3] => [1,2,2,1,2] => 11010110 => 5
[3,5,2,6,4,8,7,1] => [3,2,2,1] => 10010101 => 4
[5,3,1,8,6,4,7,2] => [1,2,1,3,1] => 11011001 => 5
[5,6,1,8,7,2,4,3] => [3,1,3,1] => 10011001 => 4
[6,3,5,8,2,7,4,1] => [1,4,2,1] => 11000101 => 4
[6,5,8,4,2,3,7,1] => [1,3,3,1] => 11001001 => 4
[6,2,5,8,3,7,1,4] => [2,3,3] => 10100100 => 3
[1,6,5,7,3,4,2,8] => [1,1,4,2] => 11100010 => 4
[1,5,2,7,4,6,3,8] => [1,2,3,2] => 11010010 => 4
[5,2,1,8,7,6,3,4] => [2,1,1,2,2] => 10111010 => 5
[7,1,3,8,4,6,2,5] => [3,3,2] => 10010010 => 3
[2,3,4,8,6,1,7,5] => [4,3,1] => 10001001 => 3
[2,3,4,8,6,5,1,7] => [4,2,2] => 10001010 => 3
[2,7,3,5,8,6,1,4] => [3,3,2] => 10010010 => 3
[3,2,4,7,8,6,1,5] => [2,4,2] => 10100010 => 3
[1,5,4,6,2,7,3,8] => [1,1,3,3] => 11100100 => 4
[5,2,4,7,1,8,3,6] => [2,3,3] => 10100100 => 3
[5,3,6,4,1,8,7,2] => [1,3,1,2,1] => 11001101 => 5
[5,3,6,1,4,8,2,7] => [1,4,3] => 11000100 => 3
[7,3,5,6,8,4,2,1] => [1,5,1,1] => 11000011 => 4
[6,3,5,1,8,2,7,4] => [1,3,3,1] => 11001001 => 4
[2,6,1,5,8,4,7,3] => [3,4,1] => 10010001 => 3
[2,7,6,5,8,3,4,1] => [2,1,4,1] => 10110001 => 4
[5,7,1,6,3,8,4,2] => [3,2,2,1] => 10010101 => 4
[3,2,4,1,7,8,5,6] => [2,2,4] => 10101000 => 3
[3,1,4,2,7,8,6,5] => [2,2,3,1] => 10101001 => 4
[5,1,4,7,2,8,6,3] => [2,3,2,1] => 10100101 => 4
[3,6,4,7,8,2,5,1] => [2,5,1] => 10100001 => 3
[3,1,4,6,8,5,7,2] => [2,5,1] => 10100001 => 3
[6,3,4,5,7,1,8,2] => [1,5,2] => 11000010 => 3
[2,5,4,6,1,7,8,3] => [2,3,3] => 10100100 => 3
[7,2,1,4,3,6,5,8] => [2,2,2,2] => 10101010 => 4
[7,3,4,1,2,6,5,8] => [1,5,2] => 11000010 => 3
[7,4,3,2,1,6,5,8] => [1,2,1,2,2] => 11011010 => 5
[7,6,3,2,5,4,1,8] => [1,2,2,1,2] => 11010110 => 5
[6,7,3,2,5,4,8,1] => [3,2,1,2] => 10010110 => 4
[1,8,3,2,5,4,7,6] => [1,2,2,2,1] => 11010101 => 5
[1,8,4,5,2,3,7,6] => [1,1,5,1] => 11100001 => 4
[7,3,5,1,6,2,4,8] => [1,3,4] => 11001000 => 3
[7,2,1,5,6,3,4,8] => [2,1,5] => 10110000 => 3
[7,2,1,6,5,4,3,8] => [2,1,2,1,2] => 10110110 => 5
[7,3,6,1,5,4,2,8] => [1,4,1,2] => 11000110 => 4
[7,4,6,5,1,3,2,8] => [1,2,3,2] => 11010010 => 4
[1,8,5,4,3,2,7,6] => [1,1,2,1,2,1] => 11101101 => 6
[1,8,6,4,3,7,2,5] => [1,1,2,1,3] => 11101100 => 5
[6,5,7,4,3,1,8,2] => [1,3,1,1,2] => 11001110 => 5
[6,4,7,5,1,3,8,2] => [1,2,3,2] => 11010010 => 4
[6,3,7,1,5,4,8,2] => [1,4,1,2] => 11000110 => 4
[6,2,1,7,5,4,8,3] => [2,1,2,1,2] => 10110110 => 5
[3,2,1,8,5,4,7,6] => [2,1,2,2,1] => 10110101 => 5
[2,3,8,1,5,4,7,6] => [5,2,1] => 10000101 => 3
[2,4,8,5,1,3,7,6] => [3,4,1] => 10010001 => 3
[2,5,8,4,3,1,7,6] => [4,1,2,1] => 10001101 => 4
[2,6,8,4,3,7,1,5] => [4,1,3] => 10001100 => 3
[2,7,8,4,3,6,5,1] => [4,2,1,1] => 10001011 => 4
[1,8,7,4,3,6,5,2] => [1,1,2,2,1,1] => 11101011 => 6
[1,8,7,5,6,3,4,2] => [1,1,1,4,1] => 11110001 => 5
[2,7,8,5,6,3,4,1] => [3,4,1] => 10010001 => 3
[2,6,8,5,7,3,1,4] => [3,3,2] => 10010010 => 3
[2,5,8,6,7,1,3,4] => [3,5] => 10010000 => 2
[2,4,8,6,1,7,3,5] => [3,2,3] => 10010100 => 3
[3,2,1,8,6,7,4,5] => [2,1,1,4] => 10111000 => 4
[5,2,1,7,6,8,4,3] => [2,1,1,3,1] => 10111001 => 5
[5,3,7,1,6,8,4,2] => [1,3,3,1] => 11001001 => 4
[5,4,7,6,1,8,3,2] => [1,2,2,2,1] => 11010101 => 5
[4,5,7,6,8,1,3,2] => [3,4,1] => 10010001 => 3
[4,6,7,5,8,3,1,2] => [3,3,2] => 10010010 => 3
[1,8,6,5,7,3,2,4] => [1,1,1,3,2] => 11110010 => 5
[1,8,5,6,7,2,3,4] => [1,1,6] => 11100000 => 3
[4,7,5,6,8,2,3,1] => [2,5,1] => 10100001 => 3
[4,6,5,7,8,2,1,3] => [2,4,2] => 10100010 => 3
[5,4,6,7,1,8,2,3] => [1,4,3] => 11000100 => 3
[5,3,6,1,7,8,2,4] => [1,3,4] => 11001000 => 3
[5,2,1,6,7,8,3,4] => [2,1,5] => 10110000 => 3
[6,2,1,5,7,3,8,4] => [2,1,3,2] => 10110010 => 4
[6,3,5,1,7,2,8,4] => [1,3,2,2] => 11001010 => 4
[6,4,5,7,1,2,8,3] => [1,5,2] => 11000010 => 3
[6,5,4,7,2,1,8,3] => [1,1,3,1,2] => 11100110 => 5
[5,6,4,7,2,8,1,3] => [2,3,3] => 10100100 => 3
[1,8,4,6,2,7,3,5] => [1,1,3,3] => 11100100 => 4
[1,8,3,2,6,7,4,5] => [1,2,1,4] => 11011000 => 4
[5,7,3,2,6,8,4,1] => [3,1,3,1] => 10011001 => 4
[5,6,3,2,7,8,1,4] => [3,1,4] => 10011000 => 3
[6,5,3,2,7,1,8,4] => [1,2,1,2,2] => 11011010 => 5
[6,4,3,2,1,7,8,5] => [1,2,1,1,3] => 11011100 => 5
[6,2,1,4,3,7,8,5] => [2,2,1,3] => 10101100 => 4
[5,2,1,4,3,8,7,6] => [2,2,1,2,1] => 10101101 => 5
[5,3,4,1,2,8,7,6] => [1,4,2,1] => 11000101 => 4
[4,6,3,2,8,7,1,5] => [3,1,1,3] => 10011100 => 4
[4,7,3,2,8,6,5,1] => [3,1,2,1,1] => 10011011 => 5
[1,8,3,2,7,6,5,4] => [1,2,1,2,1,1] => 11011011 => 6
[1,8,4,7,2,6,5,3] => [1,1,4,1,1] => 11100011 => 5
[3,7,4,8,2,6,5,1] => [2,4,1,1] => 10100011 => 4
[3,6,4,8,2,7,1,5] => [2,3,3] => 10100100 => 3
[3,5,4,8,2,1,7,6] => [2,3,2,1] => 10100101 => 4
[3,4,5,8,1,2,7,6] => [7,1] => 10000001 => 2
[4,3,5,1,8,2,7,6] => [1,3,3,1] => 11001001 => 4
[4,2,1,5,8,3,7,6] => [2,1,4,1] => 10110001 => 4
[4,2,1,6,8,7,3,5] => [2,1,2,3] => 10110100 => 4
[4,3,6,1,8,7,2,5] => [1,3,1,3] => 11001100 => 4
[3,4,6,8,1,7,2,5] => [5,3] => 10000100 => 2
[3,5,6,8,7,1,2,4] => [4,4] => 10001000 => 2
[3,6,5,8,7,2,1,4] => [2,2,2,2] => 10101010 => 4
[3,7,5,8,6,2,4,1] => [2,2,3,1] => 10101001 => 4
[1,8,5,7,6,2,4,3] => [1,1,2,3,1] => 11101001 => 5
[1,8,6,7,5,4,2,3] => [1,1,3,1,2] => 11100110 => 5
[3,6,7,8,5,4,1,2] => [5,1,2] => 10000110 => 3
[3,5,7,8,6,1,4,2] => [4,3,1] => 10001001 => 3
[3,4,7,8,1,6,5,2] => [6,1,1] => 10000011 => 3
[4,2,1,7,8,6,5,3] => [2,1,3,1,1] => 10110011 => 5
[2,3,8,1,7,6,5,4] => [4,2,1,1] => 10001011 => 4
[2,4,8,7,1,6,5,3] => [3,3,1,1] => 10010011 => 4
[2,5,8,7,6,1,4,3] => [3,1,3,1] => 10011001 => 4
[2,6,8,7,5,4,1,3] => [3,2,1,2] => 10010110 => 4
[2,1,4,3,6,5,8,7,10,9,12,11] => [2,2,2,2,2,2] => 101010101010 => 6
[7,4,6,1,8,3,5,2] => [1,3,3,1] => 11001001 => 4
[8,3,5,1,7,4,6,2] => [1,3,3,1] => 11001001 => 4
[8,3,4,1,7,5,6,2] => [1,3,3,1] => 11001001 => 4
[4,8,3,1,7,5,6,2] => [3,1,3,1] => 10011001 => 4
[4,6,2,1,7,5,8,3] => [3,1,2,2] => 10011010 => 4
[1,4,6,2,7,5,8,3] => [1,3,2,2] => 11001010 => 4
[1,7,5,2,6,8,4,3] => [1,1,2,3,1] => 11101001 => 5
[7,5,2,1,6,8,4,3] => [1,2,1,3,1] => 11011001 => 5
[6,8,4,3,1,7,5,2] => [2,2,1,2,1] => 10101101 => 5
[3,6,8,4,1,7,5,2] => [4,1,2,1] => 10001101 => 4
[3,6,7,5,1,8,4,2] => [3,2,2,1] => 10010101 => 4
[7,5,6,1,8,3,4,2] => [1,3,3,1] => 11001001 => 4
[3,4,6,5,7,1,8,2] => [3,3,2] => 10010010 => 3
[4,7,5,6,1,8,3,2] => [2,3,2,1] => 10100101 => 4
[6,7,5,1,8,4,3,2] => [2,2,2,1,1] => 10101011 => 5
[6,8,4,1,7,5,3,2] => [2,2,2,1,1] => 10101011 => 5
[6,7,5,3,1,8,4,2] => [2,2,1,2,1] => 10101101 => 5
[8,4,2,1,6,7,5,3] => [1,2,1,3,1] => 11011001 => 5
[1,8,4,2,6,7,5,3] => [1,1,2,3,1] => 11101001 => 5
[1,5,3,2,7,6,8,4] => [1,2,1,2,2] => 11011010 => 5
[5,3,2,1,7,6,8,4] => [1,2,1,2,2] => 11011010 => 5
[2,5,3,1,7,6,8,4] => [3,1,2,2] => 10011010 => 4
[2,8,4,1,6,7,5,3] => [2,2,3,1] => 10101001 => 4
[2,7,5,1,6,8,4,3] => [2,2,3,1] => 10101001 => 4
[2,4,6,1,7,5,8,3] => [4,2,2] => 10001010 => 3
[4,7,1,6,5,8,2,3] => [3,2,3] => 10010100 => 3
[4,8,2,6,5,7,1,3] => [3,2,3] => 10010100 => 3
[4,6,1,2,7,5,8,3] => [4,2,2] => 10001010 => 3
[7,5,1,2,6,8,4,3] => [1,3,3,1] => 11001001 => 4
[8,4,1,2,6,7,5,3] => [1,3,3,1] => 11001001 => 4
[5,3,1,2,7,6,8,4] => [1,3,2,2] => 11001010 => 4
[1,2,5,3,7,6,8,4] => [2,2,2,2] => 10101010 => 4
[4,3,1,2,7,6,8,5] => [1,3,2,2] => 11001010 => 4
[3,5,1,2,7,6,8,4] => [4,2,2] => 10001010 => 3
[6,7,1,5,8,2,3,4] => [3,5] => 10010000 => 2
[2,7,6,1,5,8,3,4] => [2,3,3] => 10100100 => 3
[2,3,5,1,7,6,8,4] => [4,2,2] => 10001010 => 3
[7,6,1,5,8,3,2,4] => [1,2,3,2] => 11010010 => 4
[3,6,7,1,5,8,2,4] => [5,3] => 10000100 => 2
[7,1,6,5,8,2,4,3] => [2,1,4,1] => 10110001 => 4
[7,5,1,6,8,4,2,3] => [1,2,3,2] => 11010010 => 4
[8,4,1,6,7,5,2,3] => [1,2,3,2] => 11010010 => 4
[5,2,3,1,7,6,8,4] => [3,1,2,2] => 10011010 => 4
[3,5,2,1,7,6,8,4] => [3,1,2,2] => 10011010 => 4
[1,3,5,2,7,6,8,4] => [1,3,2,2] => 11001010 => 4
[1,7,6,2,5,8,3,4] => [1,1,3,3] => 11100100 => 4
[7,6,2,1,5,8,3,4] => [1,2,2,3] => 11010100 => 4
[8,3,1,5,7,6,2,4] => [1,2,3,2] => 11010010 => 4
[6,2,4,1,7,5,8,3] => [2,2,2,2] => 10101010 => 4
[6,2,5,1,7,4,8,3] => [2,2,2,2] => 10101010 => 4
[7,1,6,4,8,2,5,3] => [2,2,3,1] => 10101001 => 4
[8,2,6,4,7,1,5,3] => [2,2,3,1] => 10101001 => 4
[6,1,5,2,7,4,8,3] => [2,2,2,2] => 10101010 => 4
[7,6,2,5,8,3,1,4] => [1,2,3,2] => 11010010 => 4
[8,3,5,7,6,2,1,4] => [1,3,2,2] => 11001010 => 4
[1,8,3,5,7,6,2,4] => [1,2,3,2] => 11010010 => 4
[1,5,2,3,7,6,8,4] => [1,3,2,2] => 11001010 => 4
[5,2,1,3,7,6,8,4] => [2,2,2,2] => 10101010 => 4
[7,5,2,6,8,4,1,3] => [1,2,3,2] => 11010010 => 4
[8,4,2,6,7,5,1,3] => [1,2,3,2] => 11010010 => 4
[6,1,4,2,7,5,8,3] => [2,2,2,2] => 10101010 => 4
[8,2,6,5,7,1,4,3] => [2,1,4,1] => 10110001 => 4
[3,6,8,2,5,7,1,4] => [5,3] => 10000100 => 2
[8,3,2,5,7,6,1,4] => [1,2,3,2] => 11010010 => 4
[5,1,3,2,7,6,8,4] => [3,1,2,2] => 10011010 => 4
[4,1,3,2,7,6,8,5] => [3,1,2,2] => 10011010 => 4
[4,2,1,3,7,6,8,5] => [2,2,2,2] => 10101010 => 4
[1,4,2,3,7,6,8,5] => [1,3,2,2] => 11001010 => 4
[2,4,1,3,7,6,8,5] => [4,2,2] => 10001010 => 3
[2,5,1,3,7,6,8,4] => [4,2,2] => 10001010 => 3
[2,8,3,5,7,6,1,4] => [3,3,2] => 10010010 => 3
[6,8,2,3,5,7,1,4] => [5,3] => 10000100 => 2
[6,7,1,3,5,8,2,4] => [5,3] => 10000100 => 2
[8,3,5,7,6,1,2,4] => [1,3,4] => 11001000 => 3
[5,1,2,3,7,6,8,4] => [4,2,2] => 10001010 => 3
[3,1,2,4,7,6,8,5] => [4,2,2] => 10001010 => 3
[10,8,9,4,5,6,1,2,3,7] => [1,5,4] => 1100001000 => 3
[9,8,10,4,5,6,1,2,3,7] => [1,5,4] => 1100001000 => 3
[8,1,2,4,3,6,5,7] => [4,2,2] => 10001010 => 3
[8,1,3,5,6,2,7,4] => [3,4,1] => 10010001 => 3
[8,1,3,4,2,6,7,5] => [4,3,1] => 10001001 => 3
[8,1,3,2,4,5,7,6] => [3,4,1] => 10010001 => 3
[2,7,8,3,4,5,6,1] => [7,1] => 10000001 => 2
[2,6,3,8,4,5,7,1] => [3,4,1] => 10010001 => 3
[6,3,2,1,4,5,8,7] => [1,2,3,2] => 11010010 => 4
[7,3,1,4,2,6,8,5] => [1,3,2,2] => 11001010 => 4
[7,4,1,5,6,8,2,3] => [1,2,5] => 11010000 => 3
[4,7,8,5,6,1,2,3] => [3,5] => 10010000 => 2
[3,7,8,5,6,2,1,4] => [3,3,2] => 10010010 => 3
[3,7,8,4,2,6,1,5] => [4,2,2] => 10001010 => 3
[3,7,8,2,4,5,1,6] => [6,2] => 10000010 => 2
[3,6,2,8,4,5,1,7] => [3,3,2] => 10010010 => 3
[2,3,6,7,4,5,8,1] => [6,2] => 10000010 => 2
[3,5,2,4,8,6,1,7] => [4,2,2] => 10001010 => 3
[3,5,4,2,8,7,1,6] => [2,2,1,3] => 10101100 => 4
[4,6,5,8,7,1,2,3] => [2,2,4] => 10101000 => 3
[6,4,5,1,7,8,2,3] => [1,3,4] => 11001000 => 3
[7,4,1,2,3,8,5,6] => [1,4,3] => 11000100 => 3
[6,2,4,1,3,7,5,8] => [2,3,3] => 10100100 => 3
[2,6,4,8,3,7,5,1] => [2,3,2,1] => 10100101 => 4
[2,6,5,8,7,3,4,1] => [2,2,3,1] => 10101001 => 4
[6,2,5,1,7,3,4,8] => [2,2,4] => 10101000 => 3
[6,5,2,1,8,3,4,7] => [1,2,1,4] => 11011000 => 4
[2,5,6,7,8,3,4,1] => [7,1] => 10000001 => 2
[2,4,6,7,3,8,5,1] => [5,2,1] => 10000101 => 3
[4,2,6,7,3,1,5,8] => [2,3,3] => 10100100 => 3
[4,7,8,2,3,1,5,6] => [5,3] => 10000100 => 2
[4,7,8,3,2,1,6,5] => [4,1,2,1] => 10001101 => 4
[5,6,4,8,1,7,2,3] => [2,3,3] => 10100100 => 3
[5,6,3,8,1,2,7,4] => [3,4,1] => 10010001 => 3
[4,2,5,3,7,1,6,8] => [2,2,4] => 10101000 => 3
[4,3,6,7,2,1,8,5] => [1,4,1,2] => 11000110 => 4
[3,4,6,7,2,8,1,5] => [5,3] => 10000100 => 2
[3,4,5,2,7,8,1,6] => [4,4] => 10001000 => 2
[3,4,2,5,6,8,1,7] => [3,5] => 10010000 => 2
[5,2,7,8,6,4,1,3] => [2,2,2,2] => 10101010 => 4
[5,1,2,7,8,6,4,3] => [3,3,1,1] => 10010011 => 4
[4,7,1,8,6,5,2,3] => [3,1,2,2] => 10011010 => 4
[4,7,1,2,8,6,5,3] => [4,2,1,1] => 10001011 => 4
[4,6,8,1,2,7,5,3] => [5,2,1] => 10000101 => 3
[6,8,7,1,5,3,2,4] => [2,3,1,2] => 10100110 => 4
[6,8,7,3,5,1,2,4] => [2,3,3] => 10100100 => 3
[7,8,1,6,3,5,2,4] => [3,3,2] => 10010010 => 3
[7,8,1,3,6,5,2,4] => [4,2,2] => 10001010 => 3
[7,8,3,6,5,2,1,4] => [3,2,1,2] => 10010110 => 4
[4,7,2,8,6,1,5,3] => [3,1,3,1] => 10011001 => 4
[1,7,3,4,8,6,5,2] => [1,3,2,1,1] => 11001011 => 5
[4,2,7,1,8,6,5,3] => [2,2,2,1,1] => 10101011 => 5
[7,8,2,3,6,5,1,4] => [4,2,2] => 10001010 => 3
[8,5,7,1,6,2,3,4] => [1,3,4] => 11001000 => 3
[8,5,7,1,2,6,3,4] => [1,5,2] => 11000010 => 3
[6,8,2,7,1,3,5,4] => [3,4,1] => 10010001 => 3
[6,8,7,2,5,3,1,4] => [2,3,1,2] => 10100110 => 4
[6,2,4,8,7,1,5,3] => [2,2,3,1] => 10101001 => 4
[1,6,8,3,7,4,5,2] => [1,3,3,1] => 11001001 => 4
[1,6,8,3,4,7,5,2] => [1,4,2,1] => 11000101 => 4
[6,2,4,8,1,7,5,3] => [2,3,2,1] => 10100101 => 4
[6,8,7,2,3,5,1,4] => [2,4,2] => 10100010 => 3
[6,8,2,1,7,3,5,4] => [3,1,3,1] => 10011001 => 4
[8,5,7,2,1,6,3,4] => [1,3,2,2] => 11001010 => 4
[8,5,7,1,2,3,6,4] => [1,6,1] => 11000001 => 3
[8,7,6,2,1,4,3,5] => [1,1,2,2,2] => 11101010 => 5
[8,5,7,2,3,1,6,4] => [1,4,2,1] => 11000101 => 4
[5,8,4,2,7,1,6,3] => [2,2,3,1] => 10101001 => 4
[1,8,7,5,3,4,6,2] => [1,1,1,4,1] => 11110001 => 5
[1,8,7,3,5,4,6,2] => [1,1,3,2,1] => 11100101 => 5
[8,2,5,4,7,1,6,3] => [2,2,3,1] => 10101001 => 4
[8,5,2,7,3,1,6,4] => [1,2,2,2,1] => 11010101 => 5
[8,7,6,2,4,3,1,5] => [1,1,3,1,2] => 11100110 => 5
[8,7,6,1,2,4,3,5] => [1,1,4,2] => 11100010 => 4
[8,7,6,1,4,2,3,5] => [1,1,3,3] => 11100100 => 4
[8,7,6,4,1,3,2,5] => [1,1,2,2,2] => 11101010 => 5
[5,8,4,7,2,1,6,3] => [2,3,2,1] => 10100101 => 4
[1,8,7,5,4,3,6,2] => [1,1,1,2,2,1] => 11110101 => 6
[1,6,8,4,3,7,5,2] => [1,3,1,2,1] => 11001101 => 5
[6,8,7,3,2,5,1,4] => [2,2,2,2] => 10101010 => 4
[6,8,1,7,3,2,5,4] => [3,2,2,1] => 10010101 => 4
[8,5,7,3,1,6,2,4] => [1,3,2,2] => 11001010 => 4
[8,5,7,1,3,2,6,4] => [1,4,2,1] => 11000101 => 4
[8,5,7,3,1,2,6,4] => [1,3,3,1] => 11001001 => 4
[5,8,4,7,1,2,6,3] => [2,5,1] => 10100001 => 3
[5,8,4,1,7,2,6,3] => [2,2,3,1] => 10101001 => 4
[5,8,4,7,1,6,2,3] => [2,4,2] => 10100010 => 3
[8,1,2,6,5,7,4,3] => [3,2,2,1] => 10010101 => 4
[8,2,5,6,7,4,1,3] => [2,4,2] => 10100010 => 3
[4,8,5,7,1,6,2,3] => [2,4,2] => 10100010 => 3
[4,8,5,7,1,2,6,3] => [2,5,1] => 10100001 => 3
[4,8,5,1,7,2,6,3] => [2,2,3,1] => 10101001 => 4
[8,5,3,1,7,2,6,4] => [1,2,1,3,1] => 11011001 => 5
[8,5,3,7,1,2,6,4] => [1,2,4,1] => 11010001 => 4
[6,8,1,3,7,2,5,4] => [4,3,1] => 10001001 => 3
[4,6,2,8,1,7,5,3] => [3,2,2,1] => 10010101 => 4
[1,6,4,8,3,7,5,2] => [1,1,3,2,1] => 11100101 => 5
[1,8,7,4,5,3,6,2] => [1,1,3,2,1] => 11100101 => 5
[4,8,5,7,2,1,6,3] => [2,3,2,1] => 10100101 => 4
[8,5,3,7,2,1,6,4] => [1,2,2,2,1] => 11010101 => 5
[8,7,6,3,1,4,2,5] => [1,1,2,2,2] => 11101010 => 5
[8,7,6,1,3,2,4,5] => [1,1,3,3] => 11100100 => 4
[8,5,3,2,7,1,6,4] => [1,2,1,3,1] => 11011001 => 5
[4,8,5,2,7,1,6,3] => [2,2,3,1] => 10101001 => 4
[1,8,7,4,3,5,6,2] => [1,1,2,3,1] => 11101001 => 5
[1,8,7,3,4,5,6,2] => [1,1,5,1] => 11100001 => 4
[8,2,4,5,7,1,6,3] => [2,5,1] => 10100001 => 3
[8,5,2,3,7,1,6,4] => [1,3,3,1] => 11001001 => 4
[6,3,1,5,4,2,8,7] => [1,2,2,1,2] => 11010110 => 5
[8,3,1,5,2,7,6,4] => [1,2,2,2,1] => 11010101 => 5
[8,5,4,2,1,7,3,6] => [1,1,2,1,3] => 11101100 => 5
[8,5,4,2,1,7,6,3] => [1,1,2,1,2,1] => 11101101 => 6
[6,5,4,2,1,3,8,7] => [1,1,2,2,2] => 11101010 => 5
[6,5,4,2,3,1,8,7] => [1,1,3,1,2] => 11100110 => 5
[6,3,2,5,1,4,8,7] => [1,2,3,2] => 11010010 => 4
[6,5,4,3,1,2,8,7] => [1,1,2,2,2] => 11101010 => 5
[6,5,4,1,3,2,8,7] => [1,1,3,1,2] => 11100110 => 5
[8,5,4,1,2,7,6,3] => [1,1,3,2,1] => 11100101 => 5
[8,7,4,1,6,3,2,5] => [1,1,2,2,2] => 11101010 => 5
[8,7,4,1,6,3,5,2] => [1,1,2,3,1] => 11101001 => 5
[8,7,4,1,6,5,3,2] => [1,1,2,2,1,1] => 11101011 => 6
[8,5,4,1,3,7,6,2] => [1,1,3,2,1] => 11100101 => 5
[8,5,4,3,1,7,6,2] => [1,1,2,1,2,1] => 11101101 => 6
[8,3,2,5,1,7,6,4] => [1,2,2,2,1] => 11010101 => 5
[2,1,8,5,3,7,6,4] => [2,1,2,2,1] => 10110101 => 5
[8,3,2,5,1,7,4,6] => [1,2,2,3] => 11010100 => 4
[8,5,4,3,1,7,2,6] => [1,1,2,1,3] => 11101100 => 5
[8,5,4,1,3,7,2,6] => [1,1,3,3] => 11100100 => 4
[8,7,4,1,6,5,2,3] => [1,1,2,2,2] => 11101010 => 5
[8,7,4,1,6,2,5,3] => [1,1,2,3,1] => 11101001 => 5
[8,7,6,5,2,1,4,3] => [1,1,1,2,2,1] => 11110101 => 6
[8,7,4,3,6,2,1,5] => [1,1,2,2,2] => 11101010 => 5
[8,3,2,7,6,4,1,5] => [1,2,1,2,2] => 11011010 => 5
[2,1,8,7,6,4,3,5] => [2,1,1,2,2] => 10111010 => 5
[2,1,8,7,6,4,5,3] => [2,1,1,3,1] => 10111001 => 5
[8,3,2,7,6,4,5,1] => [1,2,1,3,1] => 11011001 => 5
[8,7,4,3,6,2,5,1] => [1,1,2,3,1] => 11101001 => 5
[8,7,6,5,2,4,3,1] => [1,1,1,3,1,1] => 11110011 => 6
[8,5,4,2,3,7,6,1] => [1,1,3,2,1] => 11100101 => 5
[8,7,4,2,6,5,3,1] => [1,1,2,2,1,1] => 11101011 => 6
[8,7,4,2,6,3,5,1] => [1,1,2,3,1] => 11101001 => 5
[8,7,4,2,6,3,1,5] => [1,1,2,2,2] => 11101010 => 5
[8,3,1,7,6,4,2,5] => [1,2,1,2,2] => 11011010 => 5
[8,3,1,7,6,4,5,2] => [1,2,1,3,1] => 11011001 => 5
[8,3,1,7,6,5,4,2] => [1,2,1,2,1,1] => 11011011 => 6
[8,3,1,5,4,7,6,2] => [1,2,2,2,1] => 11010101 => 5
[8,3,1,5,4,7,2,6] => [1,2,2,3] => 11010100 => 4
[8,3,1,7,6,5,2,4] => [1,2,1,2,2] => 11011010 => 5
[8,3,1,7,6,2,5,4] => [1,2,1,3,1] => 11011001 => 5
[8,7,4,2,6,1,5,3] => [1,1,2,3,1] => 11101001 => 5
[8,7,4,2,6,5,1,3] => [1,1,2,2,2] => 11101010 => 5
[8,5,4,2,3,7,1,6] => [1,1,3,3] => 11100100 => 4
[8,3,2,5,4,7,1,6] => [1,2,2,3] => 11010100 => 4
[2,1,8,5,4,7,3,6] => [2,1,2,3] => 10110100 => 4
[8,3,2,7,6,5,1,4] => [1,2,1,2,2] => 11011010 => 5
[8,7,4,3,6,5,1,2] => [1,1,2,2,2] => 11101010 => 5
[8,7,6,5,3,1,4,2] => [1,1,1,2,2,1] => 11110101 => 6
[8,7,6,5,1,3,2,4] => [1,1,1,3,2] => 11110010 => 5
[8,7,6,5,1,3,4,2] => [1,1,1,4,1] => 11110001 => 5
[8,7,6,5,1,4,3,2] => [1,1,1,3,1,1] => 11110011 => 6
[8,7,6,5,4,1,3,2] => [1,1,1,2,2,1] => 11110101 => 6
[8,7,4,3,6,1,5,2] => [1,1,2,3,1] => 11101001 => 5
[8,3,2,7,6,1,5,4] => [1,2,1,3,1] => 11011001 => 5
[2,1,8,7,6,3,5,4] => [2,1,1,3,1] => 10111001 => 5
[8,3,2,7,6,1,4,5] => [1,2,1,4] => 11011000 => 4
[8,7,6,5,1,4,2,3] => [1,1,1,3,2] => 11110010 => 5
[8,7,6,5,1,2,4,3] => [1,1,1,4,1] => 11110001 => 5
[7,3,5,1,8,4,6,2] => [1,3,3,1] => 11001001 => 4
[7,3,4,1,8,5,6,2] => [1,3,3,1] => 11001001 => 4
[4,5,6,2,1,8,7,3] => [4,1,2,1] => 10001101 => 4
[1,6,5,2,7,4,3,8] => [1,1,2,2,2] => 11101010 => 5
[7,4,3,1,8,6,5,2] => [1,2,1,2,1,1] => 11011011 => 6
[7,6,5,1,8,4,3,2] => [1,1,2,2,1,1] => 11101011 => 6
[7,6,4,1,8,5,3,2] => [1,1,2,2,1,1] => 11101011 => 6
[6,4,2,1,8,7,5,3] => [1,2,1,1,2,1] => 11011101 => 6
[1,6,4,2,7,5,3,8] => [1,1,2,2,2] => 11101010 => 5
[1,5,3,2,7,6,4,8] => [1,2,1,2,2] => 11011010 => 5
[5,3,2,1,8,7,6,4] => [1,2,1,1,2,1] => 11011101 => 6
[2,5,3,1,7,8,6,4] => [3,1,3,1] => 10011001 => 4
[2,6,4,1,7,8,5,3] => [2,2,3,1] => 10101001 => 4
[2,6,5,1,7,8,4,3] => [2,2,3,1] => 10101001 => 4
[4,5,7,1,6,8,2,3] => [4,4] => 10001000 => 2
[6,5,1,2,8,4,3,7] => [1,3,2,2] => 11001010 => 4
[6,4,1,2,8,5,3,7] => [1,3,2,2] => 11001010 => 4
[5,3,1,2,8,6,4,7] => [1,3,2,2] => 11001010 => 4
[4,3,1,2,8,6,5,7] => [1,3,2,2] => 11001010 => 4
[6,1,2,5,8,3,4,7] => [3,5] => 10010000 => 2
[7,1,3,4,8,2,5,6] => [4,4] => 10001000 => 2
[7,1,5,6,8,2,3,4] => [2,6] => 10100000 => 2
[2,6,1,5,7,8,3,4] => [3,5] => 10010000 => 2
[7,4,1,6,8,5,2,3] => [1,2,3,2] => 11010010 => 4
[5,2,3,1,8,6,7,4] => [3,1,3,1] => 10011001 => 4
[3,5,2,1,6,8,7,4] => [3,1,3,1] => 10011001 => 4
[1,6,2,5,7,3,4,8] => [1,2,5] => 11010000 => 3
[6,2,1,5,8,7,3,4] => [2,1,2,3] => 10110100 => 4
[7,3,1,5,8,6,2,4] => [1,2,3,2] => 11010010 => 4
[6,2,4,1,8,5,7,3] => [2,2,3,1] => 10101001 => 4
[6,2,5,1,8,4,7,3] => [2,2,3,1] => 10101001 => 4
[7,3,1,4,8,6,2,5] => [1,3,2,2] => 11001010 => 4
[6,2,1,4,8,7,3,5] => [2,2,1,3] => 10101100 => 4
[1,6,2,4,7,3,5,8] => [1,3,4] => 11001000 => 3
[5,2,1,3,8,7,4,6] => [2,2,1,3] => 10101100 => 4
[7,4,1,3,8,5,2,6] => [1,3,2,2] => 11001010 => 4
[7,5,1,3,8,4,2,6] => [1,3,2,2] => 11001010 => 4
[3,6,7,1,4,8,2,5] => [5,3] => 10000100 => 2
[7,6,1,4,8,3,2,5] => [1,3,2,2] => 11001010 => 4
[4,2,1,3,8,7,5,6] => [2,2,1,3] => 10101100 => 4
[2,6,1,4,7,8,3,5] => [4,4] => 10001000 => 2
[7,1,4,6,8,2,3,5] => [2,6] => 10100000 => 2
[7,1,3,5,8,2,4,6] => [3,5] => 10010000 => 2
[6,1,2,4,8,3,5,7] => [4,4] => 10001000 => 2
[5,2,3,1,6,4,8,7] => [3,1,2,2] => 10011010 => 4
[7,4,5,2,3,1,8,6] => [1,4,1,2] => 11000110 => 4
[8,6,7,3,5,2,4,1] => [1,4,2,1] => 11000101 => 4
[7,3,5,2,4,1,8,6] => [1,4,1,2] => 11000110 => 4
[6,3,5,2,4,1,8,7] => [1,4,1,2] => 11000110 => 4
[5,2,4,1,6,3,8,7] => [2,2,2,2] => 10101010 => 4
[4,1,6,3,5,2,8,7] => [2,3,1,2] => 10100110 => 4
[6,3,4,1,5,2,8,7] => [1,4,1,2] => 11000110 => 4
[5,2,6,3,4,1,8,7] => [2,3,1,2] => 10100110 => 4
[5,2,7,3,4,1,8,6] => [2,3,1,2] => 10100110 => 4
[5,2,8,6,7,3,4,1] => [2,1,4,1] => 10110001 => 4
[6,2,8,5,7,3,4,1] => [2,1,4,1] => 10110001 => 4
[6,2,7,3,4,1,8,5] => [2,3,1,2] => 10100110 => 4
[7,3,4,1,5,2,8,6] => [1,4,1,2] => 11000110 => 4
[4,1,7,3,5,2,8,6] => [2,3,1,2] => 10100110 => 4
[3,1,7,4,5,2,8,6] => [2,3,1,2] => 10100110 => 4
[2,1,7,4,5,3,8,6] => [2,3,1,2] => 10100110 => 4
[3,1,8,6,7,4,5,2] => [2,1,4,1] => 10110001 => 4
[4,1,8,6,7,3,5,2] => [2,1,4,1] => 10110001 => 4
[8,6,7,3,4,1,5,2] => [1,4,2,1] => 11000101 => 4
[8,5,7,3,4,1,6,2] => [1,4,2,1] => 11000101 => 4
[8,5,6,2,7,3,4,1] => [1,3,3,1] => 11001001 => 4
[8,4,7,3,5,1,6,2] => [1,4,2,1] => 11000101 => 4
[5,1,8,4,7,3,6,2] => [2,2,3,1] => 10101001 => 4
[4,1,8,5,7,3,6,2] => [2,1,4,1] => 10110001 => 4
[3,1,8,5,7,4,6,2] => [2,1,4,1] => 10110001 => 4
[2,1,8,5,7,4,6,3] => [2,1,4,1] => 10110001 => 4
[2,1,7,4,6,3,8,5] => [2,2,2,2] => 10101010 => 4
[3,1,7,4,6,2,8,5] => [2,2,2,2] => 10101010 => 4
[4,1,7,3,6,2,8,5] => [2,2,2,2] => 10101010 => 4
[5,1,7,3,6,2,8,4] => [2,2,2,2] => 10101010 => 4
[6,2,7,3,5,1,8,4] => [2,3,1,2] => 10100110 => 4
[6,2,8,4,7,3,5,1] => [2,2,3,1] => 10101001 => 4
[8,4,7,3,6,2,5,1] => [1,3,3,1] => 11001001 => 4
[7,3,6,2,5,1,8,4] => [1,4,1,2] => 11000110 => 4
[6,2,5,1,7,3,8,4] => [2,2,2,2] => 10101010 => 4
[5,2,4,1,7,3,8,6] => [2,2,2,2] => 10101010 => 4
[6,2,4,1,7,3,8,5] => [2,2,2,2] => 10101010 => 4
[8,5,7,3,6,2,4,1] => [1,3,3,1] => 11001001 => 4
[8,5,7,4,6,2,3,1] => [1,3,3,1] => 11001001 => 4
[7,4,6,2,3,1,8,5] => [1,4,1,2] => 11000110 => 4
[6,2,3,1,7,4,8,5] => [3,1,2,2] => 10011010 => 4
[5,2,3,1,7,4,8,6] => [3,1,2,2] => 10011010 => 4
[4,2,3,1,7,5,8,6] => [3,1,2,2] => 10011010 => 4
[3,1,4,2,8,6,7,5] => [2,2,3,1] => 10101001 => 4
[6,2,3,1,8,5,7,4] => [3,1,3,1] => 10011001 => 4
[8,5,6,2,3,1,7,4] => [1,4,2,1] => 11000101 => 4
[7,4,8,5,6,2,3,1] => [1,2,4,1] => 11010001 => 4
[7,3,8,5,6,2,4,1] => [1,2,4,1] => 11010001 => 4
[8,5,6,2,4,1,7,3] => [1,4,2,1] => 11000101 => 4
[5,2,4,1,8,6,7,3] => [2,2,3,1] => 10101001 => 4
[4,1,5,2,8,6,7,3] => [2,2,3,1] => 10101001 => 4
[3,1,5,2,8,6,7,4] => [2,2,3,1] => 10101001 => 4
[2,1,6,3,8,5,7,4] => [2,2,3,1] => 10101001 => 4
[3,1,6,2,8,5,7,4] => [2,2,3,1] => 10101001 => 4
[4,1,6,2,8,5,7,3] => [2,2,3,1] => 10101001 => 4
[5,1,6,2,8,4,7,3] => [2,2,3,1] => 10101001 => 4
[8,4,6,2,5,1,7,3] => [1,4,2,1] => 11000101 => 4
[7,3,8,4,6,2,5,1] => [1,3,3,1] => 11001001 => 4
[6,2,7,3,8,4,5,1] => [2,2,3,1] => 10101001 => 4
[8,4,5,1,6,2,7,3] => [1,3,3,1] => 11001001 => 4
[5,1,8,4,6,2,7,3] => [2,2,3,1] => 10101001 => 4
[4,1,8,5,6,2,7,3] => [2,1,4,1] => 10110001 => 4
[3,1,8,5,6,2,7,4] => [2,1,4,1] => 10110001 => 4
[2,1,8,5,6,3,7,4] => [2,1,4,1] => 10110001 => 4
[2,1,7,4,8,5,6,3] => [2,2,3,1] => 10101001 => 4
[3,1,7,4,8,5,6,2] => [2,2,3,1] => 10101001 => 4
[4,1,7,3,8,5,6,2] => [2,2,3,1] => 10101001 => 4
[7,3,8,4,5,1,6,2] => [1,4,2,1] => 11000101 => 4
[8,4,5,1,7,3,6,2] => [1,3,3,1] => 11001001 => 4
[7,3,6,2,8,4,5,1] => [1,3,3,1] => 11001001 => 4
[7,8,5,6,1,3,4,2] => [2,5,1] => 10100001 => 3
[7,8,1,3,6,2,5,4] => [4,3,1] => 10001001 => 3
[1,3,8,4,7,2,5,6] => [1,3,4] => 11001000 => 3
[3,6,1,4,7,2,5,8] => [4,4] => 10001000 => 2
[4,6,1,2,5,7,3,8] => [5,3] => 10000100 => 2
[1,4,8,2,5,7,3,6] => [1,4,3] => 11000100 => 3
[7,8,2,4,5,6,1,3] => [6,2] => 10000010 => 2
[7,8,1,5,4,6,3,2] => [3,3,1,1] => 10010011 => 4
[7,8,2,1,6,3,4,5] => [3,1,4] => 10011000 => 3
[7,8,3,5,6,4,1,2] => [3,3,2] => 10010010 => 3
[7,8,1,4,2,3,6,5] => [4,3,1] => 10001001 => 3
[7,8,5,1,4,2,6,3] => [2,3,2,1] => 10100101 => 4
[7,8,4,5,3,1,6,2] => [2,3,2,1] => 10100101 => 4
[1,5,8,4,3,2,7,6] => [1,3,1,2,1] => 11001101 => 5
[5,6,1,4,3,2,7,8] => [4,1,3] => 10001100 => 3
[2,6,4,8,3,7,1,5] => [2,3,3] => 10100100 => 3
[1,4,6,8,3,7,5,2] => [1,4,2,1] => 11000101 => 4
[2,4,8,5,3,1,6,7] => [3,2,3] => 10010100 => 3
[2,5,8,1,4,7,6,3] => [5,2,1] => 10000101 => 3
[3,5,8,4,7,6,1,2] => [4,2,2] => 10001010 => 3
[1,6,2,4,7,3,8,5] => [1,3,2,2] => 11001010 => 4
[5,6,2,1,4,7,8,3] => [3,2,3] => 10010100 => 3
[4,6,2,5,3,1,8,7] => [3,2,1,2] => 10010110 => 4
[4,7,5,1,3,6,8,2] => [2,4,2] => 10100010 => 3
[7,5,3,6,2,4,1,8] => [1,2,3,2] => 11010010 => 4
[5,7,3,6,1,4,8,2] => [3,3,2] => 10010010 => 3
[5,3,6,7,2,1,8,4] => [1,4,1,2] => 11000110 => 4
[6,1,7,5,2,4,8,3] => [2,1,3,2] => 10110010 => 4
[6,3,1,2,4,5,8,7] => [1,5,2] => 11000010 => 3
[1,4,7,2,5,3,8,6] => [1,4,1,2] => 11000110 => 4
[4,6,7,8,3,5,1,2] => [6,2] => 10000010 => 2
[3,6,1,8,4,2,5,7] => [3,2,3] => 10010100 => 3
[1,6,7,5,8,2,4,3] => [1,2,4,1] => 11010001 => 4
[3,5,6,7,8,1,4,2] => [7,1] => 10000001 => 2
[3,6,5,7,8,2,1,4] => [2,4,2] => 10100010 => 3
[5,2,7,6,1,4,3,8] => [2,1,3,2] => 10110010 => 4
[2,5,7,6,8,1,3,4] => [3,5] => 10010000 => 2
[2,7,5,6,8,4,1,3] => [2,4,2] => 10100010 => 3
[2,1,6,8,4,5,3,7] => [2,4,2] => 10100010 => 3
[2,7,1,8,5,3,4,6] => [3,2,3] => 10010100 => 3
[3,7,6,8,5,4,1,2] => [2,3,1,2] => 10100110 => 4
[4,3,8,5,6,7,1,2] => [1,2,5] => 11010000 => 3
[4,2,8,1,6,3,7,5] => [2,2,3,1] => 10101001 => 4
[3,1,8,5,4,6,7,2] => [2,1,4,1] => 10110001 => 4
[3,2,8,4,5,6,1,7] => [2,4,2] => 10100010 => 3
[3,4,2,8,6,1,7,5] => [3,1,3,1] => 10011001 => 4
[3,4,7,1,5,2,6,8] => [5,3] => 10000100 => 2
[4,3,7,8,1,2,6,5] => [1,6,1] => 11000001 => 3
[1,7,3,8,5,2,6,4] => [1,2,2,2,1] => 11010101 => 5
[4,1,8,3,6,2,5,7] => [2,2,4] => 10101000 => 3
[5,7,8,6,3,2,1,4] => [3,2,1,2] => 10010110 => 4
[5,7,8,6,1,3,4,2] => [3,4,1] => 10010001 => 3
[7,6,5,8,1,3,4,2] => [1,1,5,1] => 11100001 => 4
[1,6,4,3,8,2,5,7] => [1,1,2,4] => 11101000 => 4
[7,1,3,4,8,2,6,5] => [4,3,1] => 10001001 => 3
[3,6,5,4,1,2,7,8] => [2,2,4] => 10101000 => 3
[2,4,5,1,7,8,6,3] => [4,3,1] => 10001001 => 3
[2,6,3,4,5,8,1,7] => [5,3] => 10000100 => 2
[2,6,4,1,8,3,7,5] => [2,2,3,1] => 10101001 => 4
[7,3,6,4,8,5,1,2] => [1,3,2,2] => 11001010 => 4
[7,2,1,4,8,3,5,6] => [2,2,4] => 10101000 => 3
[7,1,6,5,3,8,4,2] => [2,1,2,2,1] => 10110101 => 5
[7,2,5,6,3,8,1,4] => [2,3,3] => 10100100 => 3
[6,5,2,7,1,8,4,3] => [1,2,2,2,1] => 11010101 => 5
[5,6,2,7,3,1,4,8] => [3,2,3] => 10010100 => 3
[5,6,7,4,2,8,1,3] => [4,1,3] => 10001100 => 3
[5,7,6,4,1,8,3,2] => [2,2,1,2,1] => 10101101 => 5
[6,7,1,5,2,8,3,4] => [3,2,3] => 10010100 => 3
[1,7,5,2,4,8,3,6] => [1,1,3,3] => 11100100 => 4
[6,1,5,2,8,3,4,7] => [2,2,4] => 10101000 => 3
[6,7,5,3,8,4,1,2] => [2,2,2,2] => 10101010 => 4
[1,6,5,4,2,3,8,7] => [1,1,2,2,2] => 11101010 => 5
[7,1,5,3,4,2,8,6] => [2,3,1,2] => 10100110 => 4
[7,6,1,5,3,2,8,4] => [1,2,2,1,2] => 11010110 => 5
[7,5,6,4,1,2,8,3] => [1,3,2,2] => 11001010 => 4
[6,7,5,4,3,1,8,2] => [2,2,1,1,2] => 10101110 => 5
[7,5,2,4,3,1,6,8] => [1,3,1,3] => 11001100 => 4
[7,4,6,1,2,5,3,8] => [1,5,2] => 11000010 => 3
[7,1,4,2,5,3,6,8] => [2,3,3] => 10100100 => 3
[6,8,1,4,2,5,7,3] => [4,3,1] => 10001001 => 3
[1,6,4,2,5,7,3,8] => [1,1,3,3] => 11100100 => 4
[1,6,3,7,5,4,2,8] => [1,2,2,1,2] => 11010110 => 5
[6,8,1,3,7,5,4,2] => [4,2,1,1] => 10001011 => 4
[7,1,3,5,6,4,2,8] => [3,3,2] => 10010010 => 3
[7,3,1,6,4,5,2,8] => [1,2,3,2] => 11010010 => 4
[7,4,2,6,5,1,3,8] => [1,2,2,3] => 11010100 => 4
[7,4,6,3,1,5,2,8] => [1,3,2,2] => 11001010 => 4
[7,2,4,1,5,3,6,8] => [2,3,3] => 10100100 => 3
[7,2,3,5,4,1,6,8] => [3,2,3] => 10010100 => 3
[6,8,1,2,3,4,7,5] => [7,1] => 10000001 => 2
[1,5,7,2,3,8,6,4] => [1,4,2,1] => 11000101 => 4
[5,1,8,2,3,6,7,4] => [2,5,1] => 10100001 => 3
[5,8,2,3,7,6,4,1] => [4,2,1,1] => 10001011 => 4
[6,2,8,1,3,7,4,5] => [2,3,3] => 10100100 => 3
[6,8,2,3,5,4,7,1] => [5,2,1] => 10000101 => 3
[6,8,2,4,1,5,7,3] => [4,3,1] => 10001001 => 3
[6,8,3,1,2,4,7,5] => [3,4,1] => 10010001 => 3
[2,6,4,1,5,7,3,8] => [2,3,3] => 10100100 => 3
[2,6,3,5,7,1,4,8] => [3,5] => 10010000 => 2
[2,5,1,7,8,3,6,4] => [3,4,1] => 10010001 => 3
[2,5,3,6,8,4,7,1] => [3,4,1] => 10010001 => 3
[2,1,4,7,8,5,6,3] => [2,5,1] => 10100001 => 3
[2,4,7,6,8,5,1,3] => [3,3,2] => 10010010 => 3
[2,5,3,7,6,1,8,4] => [3,1,2,2] => 10011010 => 4
[2,5,7,8,1,4,6,3] => [7,1] => 10000001 => 2
[3,5,7,4,1,6,2,8] => [4,2,2] => 10001010 => 3
[5,3,4,1,8,6,7,2] => [1,3,3,1] => 11001001 => 4
[5,2,8,4,6,1,7,3] => [2,2,3,1] => 10101001 => 4
[5,2,1,8,6,3,7,4] => [2,1,1,3,1] => 10111001 => 5
[4,2,8,6,5,3,7,1] => [2,1,2,2,1] => 10110101 => 5
[4,2,8,5,7,6,3,1] => [2,1,3,1,1] => 10110011 => 5
[1,4,2,7,5,8,6,3] => [1,2,2,2,1] => 11010101 => 5
[4,1,8,6,7,5,3,2] => [2,1,3,1,1] => 10110011 => 5
[5,3,8,7,6,2,4,1] => [1,2,1,3,1] => 11011001 => 5
[5,8,4,7,6,2,1,3] => [2,2,2,2] => 10101010 => 4
[5,8,7,4,3,6,1,2] => [2,2,2,2] => 10101010 => 4
[6,4,8,3,1,7,2,5] => [1,3,1,3] => 11001100 => 4
[6,4,2,8,7,1,3,5] => [1,2,1,4] => 11011000 => 4
[6,3,8,7,2,5,1,4] => [1,2,3,2] => 11010010 => 4
[5,8,3,7,1,6,4,2] => [3,3,1,1] => 10010011 => 4
[5,1,3,8,6,7,2,4] => [3,1,4] => 10011000 => 3
[1,5,3,7,8,6,2,4] => [1,2,3,2] => 11010010 => 4
[1,5,7,6,4,2,8,3] => [1,2,2,1,2] => 11010110 => 5
[5,8,7,4,1,6,2,3] => [2,2,2,2] => 10101010 => 4
[6,4,8,1,2,7,3,5] => [1,4,3] => 11000100 => 3
[6,8,5,1,2,3,7,4] => [2,5,1] => 10100001 => 3
[6,8,5,2,4,3,7,1] => [2,3,2,1] => 10100101 => 4
[6,8,5,3,1,2,7,4] => [2,2,3,1] => 10101001 => 4
[4,5,1,2,7,6,3,8] => [4,2,2] => 10001010 => 3
[4,5,1,2,6,8,7,3] => [4,3,1] => 10001001 => 3
[3,5,6,1,8,4,7,2] => [4,3,1] => 10001001 => 3
[3,5,7,1,2,8,6,4] => [5,2,1] => 10000101 => 3
[3,6,2,7,5,1,4,8] => [3,2,3] => 10010100 => 3
[4,2,6,1,7,3,5,8] => [2,2,4] => 10101000 => 3
[4,6,3,1,2,7,5,8] => [3,2,3] => 10010100 => 3
[4,5,3,1,7,6,2,8] => [3,1,2,2] => 10011010 => 4
[4,2,5,7,1,6,3,8] => [2,4,2] => 10100010 => 3
[3,5,2,7,8,1,6,4] => [3,4,1] => 10010001 => 3
[3,1,4,7,5,6,2,8] => [2,4,2] => 10100010 => 3
[3,4,6,5,8,7,1,2] => [3,2,3] => 10010100 => 3
[3,1,4,5,8,6,7,2] => [2,5,1] => 10100001 => 3
[3,4,6,8,5,2,7,1] => [5,2,1] => 10000101 => 3
[3,5,6,2,8,4,7,1] => [4,3,1] => 10001001 => 3
[4,2,5,6,1,8,7,3] => [2,3,2,1] => 10100101 => 4
[4,5,3,1,6,8,7,2] => [3,1,3,1] => 10011001 => 4
[2,1,7,5,8,6,4,3] => [2,1,3,1,1] => 10110011 => 5
[1,2,7,5,3,8,6,4] => [2,1,2,2,1] => 10110101 => 5
[4,1,2,7,3,8,6,5] => [3,2,2,1] => 10010101 => 4
[6,4,1,7,5,2,3,8] => [1,2,2,3] => 11010100 => 4
[6,1,3,7,5,2,4,8] => [3,2,3] => 10010100 => 3
[3,1,2,6,8,5,4,7] => [3,3,2] => 10010010 => 3
[3,7,1,2,5,4,8,6] => [5,1,2] => 10000110 => 3
[1,3,7,2,4,8,6,5] => [1,4,2,1] => 11000101 => 4
[2,4,1,7,8,6,5,3] => [3,3,1,1] => 10010011 => 4
[3,4,7,5,1,8,6,2] => [3,2,2,1] => 10010101 => 4
[2,7,4,1,5,8,6,3] => [2,3,2,1] => 10100101 => 4
[2,3,7,1,5,8,6,4] => [5,2,1] => 10000101 => 3
[5,2,8,1,3,7,4,6] => [2,3,3] => 10100100 => 3
[2,1,6,8,3,4,7,5] => [2,5,1] => 10100001 => 3
[2,6,8,3,1,5,7,4] => [4,3,1] => 10001001 => 3
[2,8,6,4,1,5,7,3] => [2,2,3,1] => 10101001 => 4
[3,6,4,8,5,1,7,2] => [2,3,2,1] => 10100101 => 4
[6,3,7,4,5,1,8,2] => [1,4,1,2] => 11000110 => 4
[2,6,3,7,5,8,1,4] => [3,2,3] => 10010100 => 3
[5,2,1,7,8,3,4,6] => [2,1,5] => 10110000 => 3
[4,7,2,3,6,8,1,5] => [4,4] => 10001000 => 2
[5,2,7,3,6,8,1,4] => [2,2,4] => 10101000 => 3
[5,7,4,6,2,8,1,3] => [2,3,3] => 10100100 => 3
[5,7,3,4,6,1,8,2] => [4,2,2] => 10001010 => 3
[5,3,8,4,6,1,7,2] => [1,3,3,1] => 11001001 => 4
[8,5,2,4,1,6,7,3] => [1,3,3,1] => 11001001 => 4
[8,2,3,5,1,6,7,4] => [3,4,1] => 10010001 => 3
[4,2,8,3,6,7,1,5] => [2,2,4] => 10101000 => 3
[2,4,8,1,7,3,5,6] => [4,4] => 10001000 => 2
[8,4,1,3,6,2,5,7] => [1,3,4] => 11001000 => 3
[4,8,3,1,7,2,5,6] => [3,1,4] => 10011000 => 3
[5,2,8,4,7,1,6,3] => [2,2,3,1] => 10101001 => 4
[5,8,4,7,3,1,6,2] => [2,3,2,1] => 10100101 => 4
[4,6,8,3,1,7,5,2] => [4,1,2,1] => 10001101 => 4
[6,3,8,2,7,1,5,4] => [1,3,3,1] => 11001001 => 4
[6,3,1,8,2,4,7,5] => [1,2,4,1] => 11010001 => 4
[5,3,8,1,2,6,4,7] => [1,5,2] => 11000010 => 3
[5,7,4,1,6,2,3,8] => [2,2,4] => 10101000 => 3
[8,5,4,1,2,6,3,7] => [1,1,4,2] => 11100010 => 4
[5,1,8,4,2,7,3,6] => [2,2,1,3] => 10101100 => 4
[1,6,2,8,5,3,7,4] => [1,2,2,2,1] => 11010101 => 5
[6,8,5,3,1,7,4,2] => [2,2,1,2,1] => 10101101 => 5
[8,4,5,1,2,6,3,7] => [1,5,2] => 11000010 => 3
[5,6,3,7,1,2,4,8] => [3,5] => 10010000 => 2
[1,6,3,7,2,8,4,5] => [1,2,2,3] => 11010100 => 4
[6,3,2,7,8,5,1,4] => [1,2,3,2] => 11010010 => 4
[4,5,7,8,3,1,6,2] => [5,2,1] => 10000101 => 3
[4,7,2,5,8,1,6,3] => [3,4,1] => 10010001 => 3
[8,1,3,4,6,2,5,7] => [4,4] => 10001000 => 2
[3,8,2,4,6,7,1,5] => [4,4] => 10001000 => 2
[3,5,6,8,2,7,1,4] => [5,3] => 10000100 => 2
[2,4,5,6,8,1,7,3] => [7,1] => 10000001 => 2
[4,8,3,5,6,1,7,2] => [3,4,1] => 10010001 => 3
[5,6,2,3,7,8,1,4] => [4,4] => 10001000 => 2
[5,8,7,3,4,1,2,6] => [2,3,3] => 10100100 => 3
[6,8,7,3,4,1,2,5] => [2,3,3] => 10100100 => 3
[6,8,4,7,1,5,3,2] => [2,4,1,1] => 10100011 => 4
[6,8,4,7,2,5,3,1] => [2,4,1,1] => 10100011 => 4
[5,4,8,7,2,6,3,1] => [1,2,3,1,1] => 11010011 => 5
[5,4,8,7,1,6,3,2] => [1,2,3,1,1] => 11010011 => 5
[5,3,8,7,6,1,2,4] => [1,2,1,4] => 11011000 => 4
[4,3,8,7,6,1,2,5] => [1,2,1,4] => 11011000 => 4
[4,8,3,7,5,1,2,6] => [3,2,3] => 10010100 => 3
[8,3,4,6,5,1,2,7] => [1,4,3] => 11000100 => 3
[3,8,4,7,5,1,2,6] => [2,3,3] => 10100100 => 3
[3,4,8,7,6,1,2,5] => [3,1,4] => 10011000 => 3
[3,5,8,7,6,1,2,4] => [3,1,4] => 10011000 => 3
[4,5,8,7,6,1,2,3] => [3,1,4] => 10011000 => 3
[4,5,8,7,1,6,3,2] => [3,3,1,1] => 10010011 => 4
[4,5,8,7,2,6,3,1] => [3,3,1,1] => 10010011 => 4
[3,5,8,2,7,6,4,1] => [4,2,1,1] => 10001011 => 4
[3,5,8,1,7,6,4,2] => [4,2,1,1] => 10001011 => 4
[2,5,8,1,7,6,4,3] => [4,2,1,1] => 10001011 => 4
[2,5,8,7,1,6,3,4] => [3,3,2] => 10010010 => 3
[2,4,8,7,1,6,3,5] => [3,3,2] => 10010010 => 3
[2,8,4,7,1,5,3,6] => [2,4,2] => 10100010 => 3
[8,2,4,6,1,5,3,7] => [2,4,2] => 10100010 => 3
[8,1,4,6,2,5,3,7] => [2,4,2] => 10100010 => 3
[1,8,4,7,2,5,3,6] => [1,1,4,2] => 11100010 => 4
[1,4,8,7,2,6,3,5] => [1,2,3,2] => 11010010 => 4
[1,5,8,7,2,6,3,4] => [1,2,3,2] => 11010010 => 4
[1,5,8,2,7,6,4,3] => [1,3,2,1,1] => 11001011 => 5
[2,5,8,3,7,6,4,1] => [4,2,1,1] => 10001011 => 4
[1,4,2,8,7,6,5,3] => [1,2,1,2,1,1] => 11011011 => 6
[1,3,8,2,7,6,4,5] => [1,3,2,2] => 11001010 => 4
[1,8,3,2,7,5,4,6] => [1,2,1,2,2] => 11011010 => 5
[8,1,3,2,6,5,4,7] => [3,1,2,2] => 10011010 => 4
[8,2,3,1,6,5,4,7] => [3,1,2,2] => 10011010 => 4
[2,8,3,1,7,5,4,6] => [3,1,2,2] => 10011010 => 4
[2,3,8,1,7,6,4,5] => [4,2,2] => 10001010 => 3
[3,4,1,8,7,6,5,2] => [3,1,2,1,1] => 10011011 => 5
[4,3,1,8,7,6,5,2] => [1,2,1,2,1,1] => 11011011 => 6
[4,2,1,8,7,6,5,3] => [2,1,1,2,1,1] => 10111011 => 6
[3,8,2,1,7,5,4,6] => [3,1,2,2] => 10011010 => 4
[8,3,2,1,6,5,4,7] => [1,2,1,2,2] => 11011010 => 5
[8,4,2,6,1,5,3,7] => [1,2,3,2] => 11010010 => 4
[4,2,8,7,1,6,3,5] => [2,1,3,2] => 10110010 => 4
[5,2,8,7,1,6,3,4] => [2,1,3,2] => 10110010 => 4
[5,2,8,1,7,6,4,3] => [2,2,2,1,1] => 10101011 => 5
[5,3,8,1,7,6,4,2] => [1,3,2,1,1] => 11001011 => 5
[5,3,8,2,7,6,4,1] => [1,3,2,1,1] => 11001011 => 5
[6,8,3,2,7,5,4,1] => [3,1,2,1,1] => 10011011 => 5
[6,8,3,1,7,5,4,2] => [3,1,2,1,1] => 10011011 => 5
[6,8,2,1,7,5,4,3] => [3,1,2,1,1] => 10011011 => 5
[6,8,2,7,1,5,3,4] => [3,3,2] => 10010010 => 3
[6,8,7,2,1,4,3,5] => [2,2,2,2] => 10101010 => 4
[8,5,6,1,2,4,3,7] => [1,5,2] => 11000010 => 3
[5,8,7,1,2,4,3,6] => [2,4,2] => 10100010 => 3
[6,8,1,2,7,5,4,3] => [4,2,1,1] => 10001011 => 4
[6,8,2,3,7,5,4,1] => [4,2,1,1] => 10001011 => 4
[5,2,8,3,7,6,4,1] => [2,2,2,1,1] => 10101011 => 5
[5,1,8,3,7,6,4,2] => [2,2,2,1,1] => 10101011 => 5
[5,1,8,7,2,6,3,4] => [2,1,3,2] => 10110010 => 4
[4,1,8,7,2,6,3,5] => [2,1,3,2] => 10110010 => 4
[4,8,1,7,2,5,3,6] => [3,3,2] => 10010010 => 3
[8,4,1,6,2,5,3,7] => [1,2,3,2] => 11010010 => 4
[8,3,1,2,6,5,4,7] => [1,3,2,2] => 11001010 => 4
[3,8,1,2,7,5,4,6] => [4,2,2] => 10001010 => 3
[3,1,8,2,7,6,4,5] => [2,2,2,2] => 10101010 => 4
[3,1,2,8,7,6,5,4] => [3,1,2,1,1] => 10011011 => 5
[4,1,3,8,7,6,5,2] => [3,1,2,1,1] => 10011011 => 5
[3,1,4,8,7,6,5,2] => [2,2,2,1,1] => 10101011 => 5
[2,1,8,3,7,6,4,5] => [2,2,2,2] => 10101010 => 4
[2,8,1,3,7,5,4,6] => [4,2,2] => 10001010 => 3
[8,2,1,3,6,5,4,7] => [2,2,2,2] => 10101010 => 4
[8,1,2,3,6,5,4,7] => [4,2,2] => 10001010 => 3
[1,8,2,3,7,5,4,6] => [1,3,2,2] => 11001010 => 4
[1,2,8,3,7,6,4,5] => [2,2,2,2] => 10101010 => 4
[1,4,3,6,8,2,5,7] => [1,2,5] => 11010000 => 3
[3,1,6,2,5,8,4,7] => [2,3,3] => 10100100 => 3
[3,5,1,8,2,4,7,6] => [3,4,1] => 10010001 => 3
[1,4,5,2,8,3,7,6] => [1,3,3,1] => 11001001 => 4
[1,4,2,6,5,8,3,7] => [1,2,2,3] => 11010100 => 4
[1,5,4,2,6,8,3,7] => [1,1,2,4] => 11101000 => 4
[3,1,6,5,8,2,4,7] => [2,1,5] => 10110000 => 3
[1,6,4,2,5,8,3,7] => [1,1,3,3] => 11100100 => 4
[1,5,2,6,4,8,3,7] => [1,2,2,3] => 11010100 => 4
[1,2,6,5,4,8,3,7] => [2,1,2,3] => 10110100 => 4
[1,2,5,4,7,3,8,6] => [2,2,2,2] => 10101010 => 4
[4,1,2,6,3,8,7,5] => [3,2,2,1] => 10010101 => 4
[7,1,5,4,2,8,3,6] => [2,2,1,3] => 10101100 => 4
[1,4,7,5,2,8,3,6] => [1,2,2,3] => 11010100 => 4
[7,1,3,5,2,8,4,6] => [3,2,3] => 10010100 => 3
[7,2,5,1,8,3,4,6] => [2,2,4] => 10101000 => 3
[1,4,5,2,8,7,3,6] => [1,3,1,3] => 11001100 => 4
[1,6,4,2,8,3,7,5] => [1,1,2,3,1] => 11101001 => 5
[1,4,2,8,3,7,6,5] => [1,2,2,2,1] => 11010101 => 5
[1,2,5,3,8,7,6,4] => [2,2,1,2,1] => 10101101 => 5
[1,2,8,6,5,3,7,4] => [2,1,2,2,1] => 10110101 => 5
[1,5,2,8,6,3,7,4] => [1,2,1,3,1] => 11011001 => 5
[1,6,4,2,8,7,3,5] => [1,1,2,1,3] => 11101100 => 5
[6,2,1,8,7,3,4,5] => [2,1,1,4] => 10111000 => 4
[7,6,2,1,8,3,4,5] => [1,2,1,4] => 11011000 => 4
[7,3,1,6,2,8,4,5] => [1,2,2,3] => 11010100 => 4
[1,7,6,4,2,8,3,5] => [1,1,2,1,3] => 11101100 => 5
[1,7,5,2,6,3,8,4] => [1,1,2,2,2] => 11101010 => 5
[1,6,2,7,5,3,8,4] => [1,2,2,1,2] => 11010110 => 5
[1,2,7,6,5,3,8,4] => [2,1,2,1,2] => 10110110 => 5
[1,2,6,5,3,8,7,4] => [2,1,2,2,1] => 10110101 => 5
[1,5,2,6,3,8,7,4] => [1,2,2,2,1] => 11010101 => 5
[1,5,2,7,6,3,8,4] => [1,2,1,2,2] => 11011010 => 5
[1,6,5,2,7,3,8,4] => [1,1,2,2,2] => 11101010 => 5
[1,5,7,4,2,8,3,6] => [1,3,1,3] => 11001100 => 4
[4,1,2,8,6,3,7,5] => [3,1,3,1] => 10011001 => 4
[3,1,8,6,2,4,7,5] => [2,1,4,1] => 10110001 => 4
[4,3,7,1,8,2,5,6] => [1,3,4] => 11001000 => 3
[8,3,1,6,2,4,7,5] => [1,2,4,1] => 11010001 => 4
[7,1,8,3,2,4,6,5] => [2,2,3,1] => 10101001 => 4
[1,8,7,3,2,4,6,5] => [1,1,2,3,1] => 11101001 => 5
[1,4,2,8,7,3,6,5] => [1,2,1,3,1] => 11011001 => 5
[1,7,4,2,8,3,6,5] => [1,1,2,3,1] => 11101001 => 5
[8,1,5,4,2,7,3,6] => [2,2,1,3] => 10101100 => 4
[1,4,8,5,2,7,3,6] => [1,2,2,3] => 11010100 => 4
[8,5,3,1,7,2,4,6] => [1,2,1,4] => 11011000 => 4
[8,6,2,1,7,3,4,5] => [1,2,1,4] => 11011000 => 4
[1,8,6,4,2,7,3,5] => [1,1,2,1,3] => 11101100 => 5
[1,8,5,2,6,3,7,4] => [1,1,2,3,1] => 11101001 => 5
[1,5,2,7,3,8,6,4] => [1,2,2,2,1] => 11010101 => 5
[1,2,8,5,3,7,6,4] => [2,1,2,2,1] => 10110101 => 5
[1,2,6,3,8,7,5,4] => [2,2,1,2,1] => 10101101 => 5
[1,2,7,6,3,8,5,4] => [2,1,2,2,1] => 10110101 => 5
[1,6,2,7,3,8,5,4] => [1,2,2,2,1] => 11010101 => 5
[1,7,2,8,5,3,6,4] => [1,2,2,2,1] => 11010101 => 5
[1,7,4,2,8,6,3,5] => [1,1,2,2,2] => 11101010 => 5
[7,1,8,3,2,6,4,5] => [2,2,2,2] => 10101010 => 4
[7,2,1,8,6,3,4,5] => [2,1,1,4] => 10111000 => 4
[1,8,7,3,2,6,4,5] => [1,1,2,2,2] => 11101010 => 5
[1,4,2,8,7,6,3,5] => [1,2,1,2,2] => 11011010 => 5
[1,2,8,7,5,3,6,4] => [2,1,2,2,1] => 10110101 => 5
[1,2,8,6,3,7,5,4] => [2,1,2,2,1] => 10110101 => 5
[1,2,7,3,8,6,5,4] => [2,2,2,1,1] => 10101011 => 5
[4,1,7,3,6,5,8,2] => [2,2,2,2] => 10101010 => 4
[5,1,8,7,6,2,4,3] => [2,1,1,3,1] => 10111001 => 5
[8,1,7,6,3,4,5,2] => [2,1,4,1] => 10110001 => 4
[5,7,8,6,2,4,1,3] => [3,3,2] => 10010010 => 3
[5,7,1,6,2,4,3,8] => [3,3,2] => 10010010 => 3
[6,4,1,5,2,7,3,8] => [1,2,2,3] => 11010100 => 4
[8,1,4,5,3,7,6,2] => [2,3,2,1] => 10100101 => 4
[6,1,4,5,3,8,7,2] => [2,3,2,1] => 10100101 => 4
[6,1,4,5,3,7,8,2] => [2,3,3] => 10100100 => 3
[5,1,7,8,6,2,4,3] => [2,2,3,1] => 10101001 => 4
[6,1,4,8,3,5,7,2] => [2,5,1] => 10100001 => 3
[7,1,8,6,3,4,5,2] => [2,1,4,1] => 10110001 => 4
[7,1,4,5,3,8,6,2] => [2,3,2,1] => 10100101 => 4
[7,1,4,5,3,6,8,2] => [2,4,2] => 10100010 => 3
[8,1,4,5,3,6,7,2] => [2,5,1] => 10100001 => 3
[7,4,1,5,2,6,3,8] => [1,2,3,2] => 11010010 => 4
[6,3,5,7,2,1,4,8] => [1,4,3] => 11000100 => 3
[6,3,5,8,2,1,7,4] => [1,4,2,1] => 11000101 => 4
[6,3,5,7,2,1,8,4] => [1,4,1,2] => 11000110 => 4
[8,4,5,7,3,6,1,2] => [1,5,2] => 11000010 => 3
[6,4,5,8,3,7,2,1] => [1,4,2,1] => 11000101 => 4
[5,8,7,6,2,4,1,3] => [2,1,3,2] => 10110010 => 4
[5,4,8,6,3,1,7,2] => [1,2,2,2,1] => 11010101 => 5
[5,4,1,8,2,3,7,6] => [1,2,4,1] => 11010001 => 4
[5,8,1,6,2,4,3,7] => [3,3,2] => 10010010 => 3
[8,4,1,5,2,6,3,7] => [1,2,3,2] => 11010010 => 4
[6,3,5,8,2,1,4,7] => [1,4,3] => 11000100 => 3
[2,3,4,1,8,6,5,7] => [4,2,2] => 10001010 => 3
[8,3,5,6,2,1,4,7] => [1,4,3] => 11000100 => 3
[2,3,8,5,1,4,7,6] => [3,4,1] => 10010001 => 3
[2,3,8,6,1,5,7,4] => [3,4,1] => 10010001 => 3
[2,8,6,7,1,3,5,4] => [2,5,1] => 10100001 => 3
[8,3,5,7,2,1,6,4] => [1,4,2,1] => 11000101 => 4
[2,3,8,5,6,1,7,4] => [3,4,1] => 10010001 => 3
[7,4,5,6,3,1,8,2] => [1,4,1,2] => 11000110 => 4
[8,4,5,6,3,1,7,2] => [1,4,2,1] => 11000101 => 4
[7,3,5,6,2,8,1,4] => [1,4,3] => 11000100 => 3
[7,3,5,8,2,1,6,4] => [1,4,2,1] => 11000101 => 4
[7,3,5,6,2,1,4,8] => [1,4,3] => 11000100 => 3
[2,7,6,5,1,3,4,8] => [2,1,5] => 10110000 => 3
[2,7,6,8,1,3,5,4] => [2,5,1] => 10100001 => 3
[2,7,6,5,8,3,1,4] => [2,1,3,2] => 10110010 => 4
[8,7,5,6,1,4,2,3] => [1,1,4,2] => 11100010 => 4
[2,6,4,1,8,5,7,3] => [2,2,3,1] => 10101001 => 4
[2,6,1,3,8,5,7,4] => [4,3,1] => 10001001 => 3
[2,7,1,3,6,5,8,4] => [4,2,2] => 10001010 => 3
[2,7,6,8,4,3,1,5] => [2,3,1,2] => 10100110 => 4
[2,7,6,1,8,3,4,5] => [2,2,4] => 10101000 => 3
[2,7,6,1,4,3,5,8] => [2,3,3] => 10100100 => 3
[7,3,5,1,2,8,4,6] => [1,4,3] => 11000100 => 3
[8,4,1,5,2,3,7,6] => [1,2,4,1] => 11010001 => 4
[7,8,1,6,3,4,2,5] => [3,3,2] => 10010010 => 3
[6,4,1,8,3,2,7,5] => [1,2,2,2,1] => 11010101 => 5
[2,3,8,6,4,1,7,5] => [3,2,2,1] => 10010101 => 4
[2,8,6,7,4,3,1,5] => [2,3,1,2] => 10100110 => 4
[8,3,5,7,2,4,1,6] => [1,5,2] => 11000010 => 3
[2,3,4,1,8,7,5,6] => [4,1,3] => 10001100 => 3
[2,8,6,1,7,3,4,5] => [2,2,4] => 10101000 => 3
[2,3,8,1,6,4,7,5] => [4,3,1] => 10001001 => 3
[2,3,8,1,4,5,7,6] => [7,1] => 10000001 => 2
[2,8,6,1,4,3,5,7] => [2,3,3] => 10100100 => 3
[1,2,3,4,5,6,7,9,8] => [7,2] => 100000010 => 2
[2,1,3,4,5,6,7,8,9] => [9] => 100000000 => 1
[1,2,3,4,5,6,7,8,10,9] => [8,2] => 1000000010 => 2
[2,1,3,4,5,6,7,8,9,10] => [10] => 1000000000 => 1
[1,2,3,4,5,6,7,8,9,11,10] => [9,2] => 10000000010 => 2
[9,1,2,3,4,5,6,7,10,8] => [8,2] => 1000000010 => 2
[7,1,2,3,4,5,6,9,8] => [7,2] => 100000010 => 2
[2,1,9,3,4,5,6,7,8] => [2,7] => 101000000 => 2
[2,8,1,3,4,5,6,7,9] => [9] => 100000000 => 1
[2,10,1,3,4,5,6,7,8,9] => [10] => 1000000000 => 1
[2,1,3,4,5,6,7,8,9,10,11] => [11] => 10000000000 => 1
[8,4,3,6,5,1,7,2] => [1,2,2,2,1] => 11010101 => 5
[8,5,6,3,4,1,7,2] => [1,4,2,1] => 11000101 => 4
[8,6,5,4,3,1,7,2] => [1,1,2,1,2,1] => 11101101 => 6
[1,7,6,5,4,2,3,8] => [1,1,1,2,3] => 11110100 => 5
[1,8,6,5,2,7,3,4] => [1,1,1,2,3] => 11110100 => 5
[8,7,5,4,1,6,3,2] => [1,1,2,2,1,1] => 11101011 => 6
[7,8,5,4,1,3,6,2] => [2,2,3,1] => 10101001 => 4
[6,8,5,4,2,1,7,3] => [2,2,1,2,1] => 10101101 => 5
[5,8,6,2,4,1,7,3] => [2,3,2,1] => 10100101 => 4
[4,8,2,6,5,1,7,3] => [3,2,2,1] => 10010101 => 4
[3,2,8,6,5,1,7,4] => [2,1,2,2,1] => 10110101 => 5
[3,2,1,7,6,4,5,8] => [2,1,1,4] => 10111000 => 4
[4,1,3,7,6,2,5,8] => [3,1,4] => 10011000 => 3
[5,1,7,3,6,2,4,8] => [2,2,4] => 10101000 => 3
[6,1,7,5,3,2,4,8] => [2,1,2,3] => 10110100 => 4
[7,1,6,5,2,4,3,8] => [2,1,3,2] => 10110010 => 4
[8,1,6,5,2,3,7,4] => [2,1,4,1] => 10110001 => 4
[1,2,7,6,3,4,5,8] => [2,1,5] => 10110000 => 3
[1,2,8,3,7,4,5,6] => [2,2,4] => 10101000 => 3
[8,1,7,2,6,3,5,4] => [2,2,3,1] => 10101001 => 4
[7,1,8,2,6,4,3,5] => [2,2,2,2] => 10101010 => 4
[6,1,8,2,4,7,3,5] => [2,3,3] => 10100100 => 3
[5,1,8,3,2,7,4,6] => [2,2,1,3] => 10101100 => 4
[4,1,3,8,2,7,5,6] => [3,2,3] => 10010100 => 3
[3,2,1,8,4,7,5,6] => [2,1,2,3] => 10110100 => 4
[3,2,8,7,1,6,5,4] => [2,1,3,1,1] => 10110011 => 5
[4,8,2,7,1,6,5,3] => [3,3,1,1] => 10010011 => 4
[5,8,7,2,1,6,4,3] => [2,2,2,1,1] => 10101011 => 5
[6,8,7,1,3,5,4,2] => [2,4,1,1] => 10100011 => 4
[7,8,6,1,5,3,4,2] => [2,3,2,1] => 10100101 => 4
[8,7,6,1,5,4,3,2] => [1,1,3,1,1,1] => 11100111 => 6
[1,8,7,2,6,5,3,4] => [1,1,2,2,2] => 11101010 => 5
[1,7,8,2,5,6,3,4] => [1,5,2] => 11000010 => 3
[8,6,7,1,4,5,3,2] => [1,5,1,1] => 11000011 => 4
[7,6,8,1,4,3,5,2] => [1,4,2,1] => 11000101 => 4
[6,5,8,3,2,1,7,4] => [1,3,1,2,1] => 11001101 => 5
[7,5,8,3,1,4,6,2] => [1,3,3,1] => 11001001 => 4
[8,5,7,3,1,6,4,2] => [1,3,2,1,1] => 11001011 => 5
[1,6,8,4,2,7,3,5] => [1,3,1,3] => 11001100 => 4
[1,5,4,8,2,7,3,6] => [1,1,3,3] => 11100100 => 4
[8,4,3,7,1,6,5,2] => [1,2,3,1,1] => 11010011 => 5
[7,4,3,8,1,5,6,2] => [1,2,4,1] => 11010001 => 4
[6,4,3,1,5,2,7,8] => [1,2,2,3] => 11010100 => 4
[7,4,3,1,2,6,5,8] => [1,2,3,2] => 11010010 => 4
[8,4,3,1,2,5,7,6] => [1,2,4,1] => 11010001 => 4
[1,5,4,2,3,6,7,8] => [1,1,6] => 11100000 => 3
[8,5,1,4,2,3,7,6] => [1,3,3,1] => 11001001 => 4
[7,5,1,4,2,6,3,8] => [1,3,2,2] => 11001010 => 4
[6,5,1,4,3,2,7,8] => [1,3,1,3] => 11001100 => 4
[5,6,1,3,4,2,7,8] => [5,3] => 10000100 => 2
[4,6,2,1,5,3,7,8] => [3,2,3] => 10010100 => 3
[3,2,6,1,5,4,7,8] => [2,3,3] => 10100100 => 3
[3,2,7,1,4,6,5,8] => [2,4,2] => 10100010 => 3
[4,7,2,1,3,6,5,8] => [3,3,2] => 10010010 => 3
[5,7,1,3,2,6,4,8] => [4,2,2] => 10001010 => 3
[6,7,1,2,4,5,3,8] => [6,2] => 10000010 => 2
[7,6,1,2,5,4,3,8] => [1,4,1,2] => 11000110 => 4
[8,6,1,2,5,3,7,4] => [1,4,2,1] => 11000101 => 4
[1,7,2,3,6,4,5,8] => [1,3,4] => 11001000 => 3
[8,7,1,2,3,6,5,4] => [1,5,1,1] => 11000011 => 4
[7,8,1,2,3,5,6,4] => [7,1] => 10000001 => 2
[6,8,1,2,4,3,7,5] => [5,2,1] => 10000101 => 3
[5,8,1,3,2,4,7,6] => [4,3,1] => 10001001 => 3
[4,8,2,1,3,5,7,6] => [3,4,1] => 10010001 => 3
[3,2,8,1,4,5,7,6] => [2,5,1] => 10100001 => 3
[4,1,3,2,5,6,7,8] => [3,5] => 10010000 => 2
[5,1,2,4,3,6,7,8] => [4,4] => 10001000 => 2
[6,1,2,3,5,4,7,8] => [5,3] => 10000100 => 2
[7,1,2,3,4,6,5,8] => [6,2] => 10000010 => 2
[8,1,2,3,4,5,7,6] => [7,1] => 10000001 => 2
[6,7,3,8,5,1,2,4] => [3,2,3] => 10010100 => 3
[6,7,4,5,1,8,3,2] => [2,3,2,1] => 10100101 => 4
[5,4,7,6,8,1,2,3] => [1,2,5] => 11010000 => 3
[5,3,7,8,6,1,2,4] => [1,3,4] => 11001000 => 3
[3,8,4,5,7,1,2,6] => [2,6] => 10100000 => 2
[3,4,8,6,7,1,2,5] => [3,5] => 10010000 => 2
[4,5,6,7,1,8,3,2] => [5,2,1] => 10000101 => 3
[3,5,6,2,7,4,8,1] => [4,2,2] => 10001010 => 3
[3,5,6,1,7,8,4,2] => [4,3,1] => 10001001 => 3
[2,5,6,1,8,7,4,3] => [4,1,2,1] => 10001101 => 4
[2,5,6,8,1,7,3,4] => [5,3] => 10000100 => 2
[8,2,4,5,1,6,3,7] => [2,4,2] => 10100010 => 3
[1,4,8,6,2,3,7,5] => [1,2,4,1] => 11010001 => 4
[1,5,6,8,2,3,7,4] => [1,6,1] => 11000001 => 3
[1,5,6,2,8,4,7,3] => [1,3,3,1] => 11001001 => 4
[2,5,6,3,4,7,8,1] => [5,3] => 10000100 => 2
[1,4,2,6,8,5,7,3] => [1,2,4,1] => 11010001 => 4
[8,1,3,2,5,4,6,7] => [3,2,3] => 10010100 => 3
[8,2,3,1,5,6,4,7] => [3,3,2] => 10010010 => 3
[2,8,3,1,5,7,4,6] => [3,2,3] => 10010100 => 3
[2,4,1,6,8,7,5,3] => [3,2,2,1] => 10010101 => 4
[3,4,1,6,7,8,5,2] => [3,4,1] => 10010001 => 3
[4,3,1,7,6,8,5,2] => [1,2,1,3,1] => 11011001 => 5
[5,2,7,8,1,6,3,4] => [2,4,2] => 10100010 => 3
[5,3,7,2,6,4,8,1] => [1,3,2,2] => 11001010 => 4
[6,7,3,1,5,8,4,2] => [3,2,2,1] => 10010101 => 4
[6,7,2,1,8,5,4,3] => [3,1,2,1,1] => 10011011 => 5
[6,7,2,8,1,5,3,4] => [3,3,2] => 10010010 => 3
[6,7,8,2,1,4,3,5] => [4,2,2] => 10001010 => 3
[6,7,1,2,8,4,5,3] => [4,3,1] => 10001001 => 3
[6,7,1,3,4,8,5,2] => [5,2,1] => 10000101 => 3
[5,2,7,3,4,6,8,1] => [2,4,2] => 10100010 => 3
[5,1,7,3,4,8,6,2] => [2,3,2,1] => 10100101 => 4
[5,1,7,8,2,3,6,4] => [2,5,1] => 10100001 => 3
[4,1,8,7,2,3,6,5] => [2,1,4,1] => 10110001 => 4
[3,8,1,2,7,4,5,6] => [4,4] => 10001000 => 2
[4,1,3,7,5,8,6,2] => [3,2,2,1] => 10010101 => 4
[3,1,4,5,7,8,6,2] => [2,5,1] => 10100001 => 3
[2,1,8,3,4,7,6,5] => [2,3,2,1] => 10100101 => 4
[8,2,1,3,4,6,5,7] => [2,4,2] => 10100010 => 3
[1,8,2,3,4,5,7,6] => [1,6,1] => 11000001 => 3
[1,2,8,3,4,6,7,5] => [2,5,1] => 10100001 => 3
[4,2,1,6,5,8,7,3] => [2,1,2,2,1] => 10110101 => 5
[5,2,6,1,4,8,7,3] => [2,3,2,1] => 10100101 => 4
[5,2,6,4,1,8,7,3] => [2,2,1,2,1] => 10101101 => 5
[5,2,7,4,8,1,6,3] => [2,2,3,1] => 10101001 => 4
[5,2,7,4,8,6,1,3] => [2,2,2,2] => 10101010 => 4
[5,7,2,3,8,6,1,4] => [4,2,2] => 10001010 => 3
[5,7,2,3,8,1,6,4] => [4,3,1] => 10001001 => 3
[5,6,2,3,1,8,7,4] => [4,1,2,1] => 10001101 => 4
[5,6,2,1,3,8,7,4] => [3,2,2,1] => 10010101 => 4
[5,1,6,4,2,8,7,3] => [2,2,1,2,1] => 10101101 => 5
[5,6,1,3,2,8,7,4] => [4,1,2,1] => 10001101 => 4
[5,6,3,1,2,8,7,4] => [3,2,2,1] => 10010101 => 4
[5,6,3,2,1,8,7,4] => [3,1,1,2,1] => 10011101 => 5
[5,7,3,2,8,1,6,4] => [3,1,3,1] => 10011001 => 4
[5,7,3,2,8,6,1,4] => [3,1,2,2] => 10011010 => 4
[6,7,3,8,2,1,5,4] => [3,2,2,1] => 10010101 => 4
[6,7,3,8,1,2,5,4] => [3,4,1] => 10010001 => 3
[5,7,3,1,8,2,6,4] => [3,1,3,1] => 10011001 => 4
[5,7,1,3,8,2,6,4] => [4,3,1] => 10001001 => 3
[5,1,7,4,8,2,6,3] => [2,2,3,1] => 10101001 => 4
[1,5,7,4,8,3,6,2] => [1,3,3,1] => 11001001 => 4
[1,5,7,4,8,6,3,2] => [1,3,2,1,1] => 11001011 => 5
[5,1,7,4,8,6,2,3] => [2,2,2,2] => 10101010 => 4
[5,7,1,3,8,6,2,4] => [4,2,2] => 10001010 => 3
[5,7,3,1,8,6,2,4] => [3,1,2,2] => 10011010 => 4
[6,7,3,8,1,5,2,4] => [3,3,2] => 10010010 => 3
[6,7,3,8,5,2,1,4] => [3,2,1,2] => 10010110 => 4
[6,7,8,3,1,4,2,5] => [4,2,2] => 10001010 => 3
[6,7,1,8,3,5,2,4] => [3,3,2] => 10010010 => 3
[6,1,7,8,4,5,2,3] => [2,4,2] => 10100010 => 3
[1,6,7,8,4,5,3,2] => [1,5,1,1] => 11000011 => 4
[1,6,7,8,4,3,5,2] => [1,4,2,1] => 11000101 => 4
[6,1,7,8,4,2,5,3] => [2,3,2,1] => 10100101 => 4
[6,7,1,8,3,2,5,4] => [3,2,2,1] => 10010101 => 4
[5,7,2,1,8,3,6,4] => [3,1,3,1] => 10011001 => 4
[6,7,2,8,1,3,5,4] => [3,4,1] => 10010001 => 3
[6,7,2,8,3,1,5,4] => [3,2,2,1] => 10010101 => 4
[6,7,2,8,3,5,1,4] => [3,3,2] => 10010010 => 3
[6,2,7,8,4,5,1,3] => [2,4,2] => 10100010 => 3
[6,2,7,8,4,1,5,3] => [2,3,2,1] => 10100101 => 4
[6,2,7,8,1,4,5,3] => [2,5,1] => 10100001 => 3
[5,2,7,1,8,4,6,3] => [2,2,3,1] => 10101001 => 4
[4,2,1,7,8,5,6,3] => [2,1,4,1] => 10110001 => 4
[4,1,2,7,8,6,5,3] => [3,3,1,1] => 10010011 => 4
[6,2,7,8,1,5,4,3] => [2,4,1,1] => 10100011 => 4
[6,2,7,8,5,1,4,3] => [2,3,2,1] => 10100101 => 4
[6,2,7,8,5,4,1,3] => [2,3,1,2] => 10100110 => 4
[6,7,2,8,5,3,1,4] => [3,2,1,2] => 10010110 => 4
[5,7,2,1,8,6,3,4] => [3,1,2,2] => 10011010 => 4
[5,7,1,2,8,6,3,4] => [4,2,2] => 10001010 => 3
[5,1,7,2,8,6,4,3] => [2,2,2,1,1] => 10101011 => 5
[1,5,7,3,8,6,4,2] => [1,3,2,1,1] => 11001011 => 5
[1,6,7,8,3,5,4,2] => [1,5,1,1] => 11000011 => 4
[6,1,7,8,2,5,4,3] => [2,4,1,1] => 10100011 => 4
[6,7,1,8,2,5,3,4] => [3,3,2] => 10010010 => 3
[6,7,8,2,4,1,3,5] => [5,3] => 10000100 => 2
[6,7,8,2,4,3,1,5] => [5,1,2] => 10000110 => 3
[6,7,1,8,5,2,3,4] => [3,2,3] => 10010100 => 3
[6,1,7,8,5,2,4,3] => [2,3,2,1] => 10100101 => 4
[1,6,7,8,5,3,4,2] => [1,4,2,1] => 11000101 => 4
[6,1,7,8,5,4,2,3] => [2,3,1,2] => 10100110 => 4
[6,7,1,8,5,3,2,4] => [3,2,1,2] => 10010110 => 4
[6,7,8,4,1,3,2,5] => [4,2,2] => 10001010 => 3
[6,3,8,5,2,7,4,1] => [1,2,2,2,1] => 11010101 => 5
[6,5,2,8,4,7,3,1] => [1,2,2,2,1] => 11010101 => 5
[6,3,4,5,8,7,2,1] => [1,4,2,1] => 11000101 => 4
[3,8,4,7,5,2,1,6] => [2,3,1,2] => 10100110 => 4
[5,8,1,4,7,2,3,6] => [4,4] => 10001000 => 2
[5,6,1,4,8,7,3,2] => [4,1,2,1] => 10001101 => 4
[3,6,4,8,5,7,1,2] => [2,3,3] => 10100100 => 3
[5,1,4,8,6,3,7,2] => [2,2,3,1] => 10101001 => 4
[3,4,7,1,8,6,5,2] => [4,2,1,1] => 10001011 => 4
[6,3,8,4,2,7,1,5] => [1,3,1,3] => 11001100 => 4
[3,6,8,7,1,4,2,5] => [3,3,2] => 10010010 => 3
[5,3,7,1,6,8,2,4] => [1,3,4] => 11001000 => 3
[4,3,8,5,6,7,2,1] => [1,2,4,1] => 11010001 => 4
[5,8,1,7,6,2,4,3] => [3,1,3,1] => 10011001 => 4
[4,6,1,2,7,8,5,3] => [4,3,1] => 10001001 => 3
[3,6,4,2,8,7,5,1] => [2,2,1,2,1] => 10101101 => 5
[6,3,7,5,2,8,1,4] => [1,2,2,3] => 11010100 => 4
[6,5,2,7,4,8,1,3] => [1,2,2,3] => 11010100 => 4
[5,7,1,4,8,3,2,6] => [4,2,2] => 10001010 => 3
[7,8,3,5,1,4,6,2] => [3,4,1] => 10010001 => 3
[5,8,1,4,6,7,2,3] => [4,4] => 10001000 => 2
[6,5,8,4,3,7,2,1] => [1,3,1,2,1] => 11001101 => 5
[6,3,7,4,2,8,5,1] => [1,3,1,2,1] => 11001101 => 5
[8,7,1,6,2,4,5,3] => [1,2,4,1] => 11010001 => 4
[3,8,6,7,1,4,5,2] => [2,5,1] => 10100001 => 3
[5,3,8,7,4,1,2,6] => [1,2,2,3] => 11010100 => 4
[4,3,8,7,1,5,6,2] => [1,2,4,1] => 11010001 => 4
[8,3,6,1,2,5,7,4] => [1,6,1] => 11000001 => 3
[5,6,1,8,7,3,2,4] => [3,1,2,2] => 10011010 => 4
[5,4,2,7,3,6,8,1] => [1,2,3,2] => 11010010 => 4
[7,5,3,6,4,2,8,1] => [1,2,2,1,2] => 11010110 => 5
[6,4,1,5,3,8,2,7] => [1,2,2,3] => 11010100 => 4
[8,5,2,6,4,7,3,1] => [1,2,2,2,1] => 11010101 => 5
[8,2,6,3,4,7,5,1] => [2,3,2,1] => 10100101 => 4
[7,2,6,3,5,4,8,1] => [2,3,1,2] => 10100110 => 4
[6,2,7,4,3,5,8,1] => [2,2,2,2] => 10101010 => 4
[5,7,3,6,4,2,8,1] => [3,2,1,2] => 10010110 => 4
[3,7,6,4,5,2,8,1] => [2,3,1,2] => 10100110 => 4
[2,7,6,5,3,4,8,1] => [2,1,3,2] => 10110010 => 4
[6,5,4,3,1,8,2,7] => [1,1,2,1,3] => 11101100 => 5
[8,6,5,4,2,7,3,1] => [1,1,2,1,2,1] => 11101101 => 6
[8,5,4,1,7,2,6,3] => [1,1,2,3,1] => 11101001 => 5
[7,5,4,1,8,3,2,6] => [1,1,2,2,2] => 11101010 => 5
[1,6,5,2,8,3,4,7] => [1,1,2,4] => 11101000 => 4
[5,7,4,2,1,8,3,6] => [2,2,1,3] => 10101100 => 4
[1,6,5,3,4,8,2,7] => [1,1,3,3] => 11100100 => 4
[5,4,6,3,1,8,2,7] => [1,3,1,3] => 11001100 => 4
[6,5,8,4,2,7,3,1] => [1,3,1,2,1] => 11001101 => 5
[5,8,2,6,4,7,3,1] => [3,2,2,1] => 10010101 => 4
[3,8,6,2,5,7,4,1] => [2,3,2,1] => 10100101 => 4
[7,8,5,3,2,6,4,1] => [2,2,2,1,1] => 10101011 => 5
[6,8,3,1,7,2,5,4] => [3,1,3,1] => 10011001 => 4
[1,8,6,3,7,5,2,4] => [1,1,2,2,2] => 11101010 => 5
[8,7,5,2,6,4,3,1] => [1,1,2,2,1,1] => 11101011 => 6
[8,7,1,6,2,5,4,3] => [1,2,3,1,1] => 11010011 => 5
[7,8,1,6,3,2,5,4] => [3,2,2,1] => 10010101 => 4
[2,8,1,7,3,5,6,4] => [3,4,1] => 10010001 => 3
[3,8,6,1,7,4,5,2] => [2,2,3,1] => 10101001 => 4
[4,8,1,3,7,2,6,5] => [4,3,1] => 10001001 => 3
[4,2,8,5,7,3,6,1] => [2,1,4,1] => 10110001 => 4
[5,1,7,6,8,3,2,4] => [2,1,3,2] => 10110010 => 4
[3,7,1,5,8,4,2,6] => [3,3,2] => 10010010 => 3
[6,7,3,1,8,4,2,5] => [3,1,2,2] => 10011010 => 4
[1,7,3,8,4,5,2,6] => [1,2,3,2] => 11010010 => 4
[1,7,2,8,5,3,4,6] => [1,2,2,3] => 11010100 => 4
[7,6,1,8,4,3,2,5] => [1,2,2,1,2] => 11010110 => 5
[8,6,1,7,4,2,5,3] => [1,2,2,2,1] => 11010101 => 5
[8,1,2,7,3,4,6,5] => [3,4,1] => 10010001 => 3
[7,1,2,8,3,5,4,6] => [3,3,2] => 10010010 => 3
[7,2,6,1,8,4,3,5] => [2,2,2,2] => 10101010 => 4
[8,2,6,1,7,3,5,4] => [2,2,3,1] => 10101001 => 4
[8,3,1,4,7,5,6,2] => [1,3,3,1] => 11001001 => 4
[7,3,1,5,8,4,2,6] => [1,2,3,2] => 11010010 => 4
[4,2,1,5,8,3,6,7] => [2,1,5] => 10110000 => 3
[5,4,2,7,1,8,3,6] => [1,2,2,3] => 11010100 => 4
[5,4,3,1,6,8,2,7] => [1,2,1,4] => 11011000 => 4
[4,7,5,6,8,3,2,1] => [2,4,1,1] => 10100011 => 4
[6,5,4,8,2,7,3,1] => [1,1,3,2,1] => 11100101 => 5
[6,5,2,8,7,3,4,1] => [1,2,1,3,1] => 11011001 => 5
[6,5,1,8,7,4,2,3] => [1,2,1,2,2] => 11011010 => 5
[8,6,4,7,5,3,2,1] => [1,1,3,1,1,1] => 11100111 => 6
[5,1,8,3,7,6,2,4] => [2,2,2,2] => 10101010 => 4
[5,4,8,1,7,2,6,3] => [1,3,3,1] => 11001001 => 4
[7,5,8,3,2,6,4,1] => [1,3,2,1,1] => 11001011 => 5
[3,6,8,2,4,7,5,1] => [5,2,1] => 10000101 => 3
[5,7,3,8,2,6,4,1] => [3,3,1,1] => 10010011 => 4
[5,4,6,8,2,7,3,1] => [1,4,2,1] => 11000101 => 4
[5,2,6,8,7,3,4,1] => [2,2,3,1] => 10101001 => 4
[4,7,2,8,6,3,5,1] => [3,1,3,1] => 10011001 => 4
[3,6,8,1,7,2,5,4] => [4,3,1] => 10001001 => 3
[2,3,8,7,4,5,6,1] => [3,4,1] => 10010001 => 3
[7,2,8,6,4,3,5,1] => [2,1,2,2,1] => 10110101 => 5
[2,1,8,7,5,6,3,4] => [2,1,3,2] => 10110010 => 4
[8,2,7,6,3,5,4,1] => [2,1,3,1,1] => 10110011 => 5
[8,1,7,6,5,2,4,3] => [2,1,2,2,1] => 10110101 => 5
[7,1,8,6,5,3,2,4] => [2,1,2,1,2] => 10110110 => 5
[1,2,8,7,6,3,4,5] => [2,1,1,4] => 10111000 => 4
[1,3,8,7,4,6,2,5] => [1,2,3,2] => 11010010 => 4
[1,5,8,3,7,6,2,4] => [1,3,2,2] => 11001010 => 4
[5,1,6,8,7,4,2,3] => [2,2,2,2] => 10101010 => 4
[6,8,4,7,5,3,2,1] => [2,3,1,1,1] => 10100111 => 5
[6,8,7,2,5,4,3,1] => [2,3,1,1,1] => 10100111 => 5
[3,8,7,6,4,5,2,1] => [2,1,3,1,1] => 10110011 => 5
[2,8,7,6,5,3,4,1] => [2,1,2,2,1] => 10110101 => 5
[1,8,7,6,5,4,2,3] => [1,1,1,2,1,2] => 11110110 => 6
[5,8,6,7,3,4,1,2] => [2,4,2] => 10100010 => 3
[4,8,6,7,3,5,1,2] => [2,4,2] => 10100010 => 3
[3,8,6,7,4,5,1,2] => [2,4,2] => 10100010 => 3
[2,8,6,7,4,5,1,3] => [2,4,2] => 10100010 => 3
[1,8,6,7,4,5,2,3] => [1,1,4,2] => 11100010 => 4
[1,8,5,7,4,6,2,3] => [1,1,4,2] => 11100010 => 4
[3,8,5,7,4,6,1,2] => [2,4,2] => 10100010 => 3
[4,8,5,7,3,6,1,2] => [2,4,2] => 10100010 => 3
[7,8,3,6,4,5,1,2] => [3,3,2] => 10010010 => 3
[6,8,3,7,4,5,1,2] => [3,3,2] => 10010010 => 3
[5,8,3,7,4,6,1,2] => [3,3,2] => 10010010 => 3
[3,7,4,8,5,6,1,2] => [2,4,2] => 10100010 => 3
[4,7,3,8,5,6,1,2] => [3,3,2] => 10010010 => 3
[4,7,2,8,5,6,1,3] => [3,3,2] => 10010010 => 3
[4,7,1,8,5,6,2,3] => [3,3,2] => 10010010 => 3
[3,7,1,8,5,6,2,4] => [3,3,2] => 10010010 => 3
[3,7,2,8,5,6,1,4] => [3,3,2] => 10010010 => 3
[2,7,3,8,5,6,1,4] => [3,3,2] => 10010010 => 3
[2,7,4,8,5,6,1,3] => [2,4,2] => 10100010 => 3
[5,8,2,7,4,6,1,3] => [3,3,2] => 10010010 => 3
[6,8,2,7,4,5,1,3] => [3,3,2] => 10010010 => 3
[7,8,2,6,4,5,1,3] => [3,3,2] => 10010010 => 3
[7,8,1,6,4,5,2,3] => [3,3,2] => 10010010 => 3
[6,8,1,7,4,5,2,3] => [3,3,2] => 10010010 => 3
[5,8,1,7,4,6,2,3] => [3,3,2] => 10010010 => 3
[1,7,4,8,5,6,2,3] => [1,1,4,2] => 11100010 => 4
[1,7,3,8,5,6,2,4] => [1,2,3,2] => 11010010 => 4
[2,8,5,6,1,7,3,4] => [2,3,3] => 10100100 => 3
[1,8,5,6,2,7,3,4] => [1,1,3,3] => 11100100 => 4
[1,7,3,8,4,6,2,5] => [1,2,3,2] => 11010010 => 4
[4,8,1,7,3,6,2,5] => [3,3,2] => 10010010 => 3
[5,8,1,7,3,6,2,4] => [3,3,2] => 10010010 => 3
[6,8,1,7,3,5,2,4] => [3,3,2] => 10010010 => 3
[7,8,2,6,3,5,1,4] => [3,3,2] => 10010010 => 3
[6,8,2,7,3,5,1,4] => [3,3,2] => 10010010 => 3
[5,8,2,7,3,6,1,4] => [3,3,2] => 10010010 => 3
[4,8,2,7,3,6,1,5] => [3,3,2] => 10010010 => 3
[2,7,3,8,4,6,1,5] => [3,3,2] => 10010010 => 3
[3,7,2,8,4,6,1,5] => [3,3,2] => 10010010 => 3
[3,7,1,8,4,6,2,5] => [3,3,2] => 10010010 => 3
[1,8,4,7,3,6,2,5] => [1,1,4,2] => 11100010 => 4
[2,8,4,7,3,6,1,5] => [2,4,2] => 10100010 => 3
[3,8,4,7,2,6,1,5] => [2,4,2] => 10100010 => 3
[4,8,5,7,2,6,1,3] => [2,4,2] => 10100010 => 3
[3,8,5,7,2,6,1,4] => [2,4,2] => 10100010 => 3
[2,8,5,7,3,6,1,4] => [2,4,2] => 10100010 => 3
[1,8,5,7,3,6,2,4] => [1,1,4,2] => 11100010 => 4
[1,8,6,7,3,5,2,4] => [1,1,4,2] => 11100010 => 4
[2,8,6,7,3,5,1,4] => [2,4,2] => 10100010 => 3
[3,8,6,7,2,5,1,4] => [2,4,2] => 10100010 => 3
[4,8,6,7,2,5,1,3] => [2,4,2] => 10100010 => 3
[5,8,6,7,2,4,1,3] => [2,4,2] => 10100010 => 3
[6,8,5,7,1,4,2,3] => [2,4,2] => 10100010 => 3
[5,8,6,7,1,4,2,3] => [2,4,2] => 10100010 => 3
[4,8,6,7,1,5,2,3] => [2,4,2] => 10100010 => 3
[3,8,6,7,1,5,2,4] => [2,4,2] => 10100010 => 3
[1,5,2,8,6,7,3,4] => [1,2,1,4] => 11011000 => 4
[2,5,1,8,6,7,3,4] => [3,1,4] => 10011000 => 3
[2,6,1,8,5,7,3,4] => [3,2,3] => 10010100 => 3
[1,6,2,8,5,7,3,4] => [1,2,2,3] => 11010100 => 4
[3,8,5,7,1,6,2,4] => [2,4,2] => 10100010 => 3
[6,8,4,7,1,5,2,3] => [2,4,2] => 10100010 => 3
[7,8,4,6,1,5,2,3] => [2,4,2] => 10100010 => 3
[7,8,3,6,1,5,2,4] => [3,3,2] => 10010010 => 3
[6,8,3,7,1,5,2,4] => [3,3,2] => 10010010 => 3
[4,8,3,7,1,6,2,5] => [3,3,2] => 10010010 => 3
[3,8,4,7,1,6,2,5] => [2,4,2] => 10100010 => 3
[1,6,2,8,4,7,3,5] => [1,2,2,3] => 11010100 => 4
[2,6,1,8,4,7,3,5] => [3,2,3] => 10010100 => 3
[3,7,2,6,1,8,4,5] => [3,2,3] => 10010100 => 3
[3,7,1,6,2,8,4,5] => [3,2,3] => 10010100 => 3
[4,8,1,6,2,7,3,5] => [3,2,3] => 10010100 => 3
[5,8,1,6,2,7,3,4] => [3,2,3] => 10010100 => 3
[7,8,1,5,2,6,3,4] => [3,3,2] => 10010010 => 3
[7,8,2,5,1,6,3,4] => [3,3,2] => 10010010 => 3
[6,8,2,5,1,7,3,4] => [3,2,3] => 10010100 => 3
[5,8,2,6,1,7,3,4] => [3,2,3] => 10010100 => 3
[4,8,2,6,1,7,3,5] => [3,2,3] => 10010100 => 3
[1,7,3,6,2,8,4,5] => [1,2,2,3] => 11010100 => 4
[2,7,3,6,1,8,4,5] => [3,2,3] => 10010100 => 3
[1,2,3,4,5,6,7,8,9] => [9] => 100000000 => 1
[1,2,3,4,5,6,8,9,7] => [6,3] => 100000100 => 2
[1,2,3,4,5,7,8,9,6] => [5,4] => 100001000 => 2
[1,2,3,4,6,7,8,9,5] => [4,5] => 100010000 => 2
[1,2,3,5,6,7,8,9,4] => [3,6] => 100100000 => 2
[1,2,4,5,6,7,8,9,3] => [2,7] => 101000000 => 2
[1,3,4,5,6,7,8,9,2] => [1,8] => 110000000 => 2
[1,2,3,4,5,6,7,8,9,10] => [10] => 1000000000 => 1
[1,2,3,4,5,6,7,9,10,8] => [7,3] => 1000000100 => 2
[1,2,3,4,5,8,7,9,6] => [5,2,2] => 100001010 => 3
[1,2,3,4,7,6,8,9,5] => [4,2,3] => 100010100 => 3
[1,2,5,4,6,7,8,9,3] => [2,2,5] => 101010000 => 3
[1,4,3,5,6,7,8,9,2] => [1,2,6] => 110100000 => 3
[3,2,4,5,6,7,8,9,1] => [2,7] => 101000000 => 2
[6,7,4,8,3,5,1,2] => [2,4,2] => 10100010 => 3
[6,7,4,5,2,8,1,3] => [2,3,3] => 10100100 => 3
[5,7,4,6,2,3,1,8] => [2,4,2] => 10100010 => 3
[5,7,4,6,3,8,1,2] => [2,3,3] => 10100100 => 3
[5,7,4,8,3,6,1,2] => [2,4,2] => 10100010 => 3
[6,8,4,5,3,7,1,2] => [2,3,3] => 10100100 => 3
[5,8,4,6,3,7,1,2] => [2,3,3] => 10100100 => 3
[5,6,4,8,3,7,1,2] => [2,3,3] => 10100100 => 3
[5,6,3,7,2,4,1,8] => [3,3,2] => 10010010 => 3
[5,6,3,7,2,8,1,4] => [3,2,3] => 10010100 => 3
[5,6,3,8,2,7,1,4] => [3,2,3] => 10010100 => 3
[5,6,4,8,2,7,1,3] => [2,3,3] => 10100100 => 3
[5,8,4,6,2,7,1,3] => [2,3,3] => 10100100 => 3
[6,8,4,5,2,7,1,3] => [2,3,3] => 10100100 => 3
[7,8,4,5,2,6,1,3] => [2,4,2] => 10100010 => 3
[6,8,4,5,2,3,1,7] => [2,4,2] => 10100010 => 3
[5,8,4,6,2,3,1,7] => [2,4,2] => 10100010 => 3
[5,6,4,8,2,3,1,7] => [2,4,2] => 10100010 => 3
[5,6,3,8,2,4,1,7] => [3,3,2] => 10010010 => 3
[5,6,3,4,2,8,1,7] => [4,1,3] => 10001100 => 3
[4,6,3,5,2,7,1,8] => [3,2,3] => 10010100 => 3
[4,6,3,5,2,8,1,7] => [3,2,3] => 10010100 => 3
[4,6,3,8,2,5,1,7] => [3,3,2] => 10010010 => 3
[4,8,3,6,2,5,1,7] => [3,3,2] => 10010010 => 3
[5,8,3,6,2,4,1,7] => [3,3,2] => 10010010 => 3
[6,8,3,5,2,4,1,7] => [3,3,2] => 10010010 => 3
[7,8,3,5,2,4,1,6] => [3,3,2] => 10010010 => 3
[7,8,3,5,2,6,1,4] => [3,3,2] => 10010010 => 3
[5,8,3,6,2,7,1,4] => [3,2,3] => 10010100 => 3
[4,8,3,6,2,7,1,5] => [3,2,3] => 10010100 => 3
[4,6,3,8,2,7,1,5] => [3,2,3] => 10010100 => 3
[4,6,3,7,2,8,1,5] => [3,2,3] => 10010100 => 3
[4,7,3,6,2,5,1,8] => [3,3,2] => 10010010 => 3
[4,7,3,6,2,8,1,5] => [3,2,3] => 10010100 => 3
[4,7,3,8,2,6,1,5] => [3,3,2] => 10010010 => 3
[5,7,4,8,2,6,1,3] => [2,4,2] => 10100010 => 3
[5,7,3,6,2,8,1,4] => [3,2,3] => 10010100 => 3
[5,7,3,6,2,4,1,8] => [3,3,2] => 10010010 => 3
[6,7,3,5,2,4,1,8] => [3,3,2] => 10010010 => 3
[6,7,3,5,2,8,1,4] => [3,2,3] => 10010100 => 3
[6,7,4,8,2,5,1,3] => [2,4,2] => 10100010 => 3
[6,7,5,8,2,4,1,3] => [2,4,2] => 10100010 => 3
[6,8,5,7,2,3,1,4] => [2,4,2] => 10100010 => 3
[6,7,4,8,2,3,1,5] => [2,4,2] => 10100010 => 3
[6,7,3,8,2,4,1,5] => [3,3,2] => 10010010 => 3
[6,7,3,4,2,8,1,5] => [4,1,3] => 10001100 => 3
[5,7,3,4,2,6,1,8] => [4,2,2] => 10001010 => 3
[5,7,3,4,2,8,1,6] => [4,1,3] => 10001100 => 3
[5,7,4,8,2,3,1,6] => [2,4,2] => 10100010 => 3
[5,8,4,7,2,3,1,6] => [2,4,2] => 10100010 => 3
[6,8,4,7,2,3,1,5] => [2,4,2] => 10100010 => 3
[7,8,4,6,2,3,1,5] => [2,4,2] => 10100010 => 3
[7,8,3,6,2,4,1,5] => [3,3,2] => 10010010 => 3
[6,8,3,7,2,4,1,5] => [3,3,2] => 10010010 => 3
[5,8,3,7,2,4,1,6] => [3,3,2] => 10010010 => 3
[4,8,3,7,2,5,1,6] => [3,3,2] => 10010010 => 3
[4,7,3,8,2,5,1,6] => [3,3,2] => 10010010 => 3
[4,7,3,5,2,8,1,6] => [3,2,3] => 10010100 => 3
[4,7,3,5,2,6,1,8] => [3,3,2] => 10010010 => 3
[4,5,3,7,2,6,1,8] => [3,3,2] => 10010010 => 3
[4,5,3,7,2,8,1,6] => [3,2,3] => 10010100 => 3
[4,5,3,8,2,7,1,6] => [3,2,3] => 10010100 => 3
[4,8,3,5,2,7,1,6] => [3,2,3] => 10010100 => 3
[5,8,3,4,2,7,1,6] => [4,1,3] => 10001100 => 3
[6,8,3,4,2,7,1,5] => [4,1,3] => 10001100 => 3
[7,8,3,4,2,6,1,5] => [4,2,2] => 10001010 => 3
[6,8,3,4,2,5,1,7] => [4,2,2] => 10001010 => 3
[5,8,3,4,2,6,1,7] => [4,2,2] => 10001010 => 3
[4,8,3,5,2,6,1,7] => [3,3,2] => 10010010 => 3
[4,5,3,8,2,6,1,7] => [3,3,2] => 10010010 => 3
[4,5,3,6,2,8,1,7] => [3,2,3] => 10010100 => 3
[4,7,5,2,1,8,3,6] => [2,2,1,3] => 10101100 => 4
[4,8,5,2,1,7,6,3] => [2,2,1,2,1] => 10101101 => 5
[4,6,5,2,1,3,8,7] => [2,2,2,2] => 10101010 => 4
[5,6,4,2,3,1,8,7] => [2,3,1,2] => 10100110 => 4
[6,4,5,3,1,2,8,7] => [1,3,2,2] => 11001010 => 4
[5,4,6,1,3,2,8,7] => [1,4,1,2] => 11000110 => 4
[4,6,8,1,7,3,2,5] => [4,2,2] => 10001010 => 3
[4,7,8,1,6,3,5,2] => [4,3,1] => 10001001 => 3
[7,4,8,1,6,5,3,2] => [1,3,2,1,1] => 11001011 => 5
[5,4,8,1,3,7,6,2] => [1,4,2,1] => 11000101 => 4
[8,4,5,3,1,7,6,2] => [1,3,1,2,1] => 11001101 => 5
[5,4,7,1,3,8,2,6] => [1,4,3] => 11000100 => 3
[6,4,8,1,7,5,2,3] => [1,3,2,2] => 11001010 => 4
[5,6,8,7,2,1,3,4] => [3,2,3] => 10010100 => 3
[8,5,7,6,4,2,1,3] => [1,2,2,1,2] => 11010110 => 5
[8,4,6,3,7,2,1,5] => [1,3,2,2] => 11001010 => 4
[6,3,2,8,7,4,1,5] => [1,2,1,2,2] => 11011010 => 5
[2,1,6,8,7,4,3,5] => [2,2,2,2] => 10101010 => 4
[2,1,7,8,6,4,5,3] => [2,2,3,1] => 10101001 => 4
[7,3,2,8,6,4,5,1] => [1,2,1,3,1] => 11011001 => 5
[7,6,8,5,2,4,3,1] => [1,2,3,1,1] => 11010011 => 5
[5,7,8,6,2,3,1,4] => [3,3,2] => 10010010 => 3
[5,8,7,6,3,2,1,4] => [2,1,2,1,2] => 10110110 => 5
[6,8,7,5,3,2,4,1] => [2,1,2,2,1] => 10110101 => 5
[5,8,4,2,3,7,6,1] => [2,3,2,1] => 10100101 => 4
[7,8,4,2,6,5,3,1] => [2,2,2,1,1] => 10101011 => 5
[4,8,7,2,6,3,5,1] => [2,2,3,1] => 10101001 => 4
[4,8,6,2,7,3,1,5] => [2,2,2,2] => 10101010 => 4
[3,6,1,8,7,4,2,5] => [3,1,2,2] => 10011010 => 4
[3,7,1,8,6,4,5,2] => [3,1,3,1] => 10011001 => 4
[3,8,1,6,7,5,2,4] => [3,3,2] => 10010010 => 3
[3,7,1,6,8,2,5,4] => [3,4,1] => 10010001 => 3
[4,7,6,2,8,1,3,5] => [2,2,4] => 10101000 => 3
[6,7,4,2,8,1,5,3] => [2,2,3,1] => 10101001 => 4
[6,8,4,2,7,5,1,3] => [2,2,2,2] => 10101010 => 4
[2,1,8,6,7,5,3,4] => [2,1,3,2] => 10110010 => 4
[8,3,2,6,7,5,1,4] => [1,2,3,2] => 11010010 => 4
[8,6,4,3,7,5,1,2] => [1,1,2,2,2] => 11101010 => 5
[5,8,6,7,3,1,2,4] => [2,3,3] => 10100100 => 3
[6,7,5,8,1,3,4,2] => [2,5,1] => 10100001 => 3
[7,6,5,8,1,4,3,2] => [1,1,4,1,1] => 11100011 => 5
[8,6,5,7,4,1,3,2] => [1,1,3,2,1] => 11100101 => 5
[7,6,4,3,8,1,5,2] => [1,1,2,3,1] => 11101001 => 5
[7,3,2,6,8,1,5,4] => [1,2,4,1] => 11010001 => 4
[2,1,7,6,8,3,5,4] => [2,1,4,1] => 10110001 => 4
[7,5,6,8,1,4,2,3] => [1,5,2] => 11000010 => 3
[6,5,7,8,1,2,4,3] => [1,6,1] => 11000001 => 3
[8,1,3,7,4,6,5,2] => [3,3,1,1] => 10010011 => 4
[5,2,8,7,4,6,1,3] => [2,1,3,2] => 10110010 => 4
[1,6,2,5,4,7,3,8] => [1,2,2,3] => 11010100 => 4
[6,2,7,5,4,8,3,1] => [2,1,2,2,1] => 10110101 => 5
[8,1,3,5,4,7,6,2] => [3,2,2,1] => 10010101 => 4
[6,1,5,4,3,8,7,2] => [2,2,1,2,1] => 10101101 => 5
[6,1,8,3,4,5,7,2] => [2,5,1] => 10100001 => 3
[7,1,5,3,4,8,6,2] => [2,3,2,1] => 10100101 => 4
[7,1,4,3,5,6,8,2] => [2,4,2] => 10100010 => 3
[8,1,3,4,5,6,7,2] => [7,1] => 10000001 => 2
[1,7,2,4,5,6,3,8] => [1,5,2] => 11000010 => 3
[6,3,2,7,5,1,8,4] => [1,2,2,1,2] => 11010110 => 5
[8,4,7,2,5,6,1,3] => [1,5,2] => 11000010 => 3
[6,5,8,2,4,7,3,1] => [1,4,2,1] => 11000101 => 4
[8,5,2,1,4,3,7,6] => [1,2,2,2,1] => 11010101 => 5
[6,5,2,8,4,1,3,7] => [1,2,2,3] => 11010100 => 4
[5,6,2,1,4,8,3,7] => [3,2,3] => 10010100 => 3
[3,6,1,8,5,2,4,7] => [3,2,3] => 10010100 => 3
[1,2,6,3,5,4,7,8] => [2,3,3] => 10100100 => 3
[3,4,1,2,8,6,5,7] => [4,2,2] => 10001010 => 3
[4,3,1,2,6,8,5,7] => [1,3,4] => 11001000 => 3
[5,8,1,6,3,2,4,7] => [3,2,3] => 10010100 => 3
[6,3,8,5,2,1,4,7] => [1,2,2,3] => 11010100 => 4
[8,3,1,5,2,4,7,6] => [1,2,4,1] => 11010001 => 4
[3,8,2,6,1,5,7,4] => [3,4,1] => 10010001 => 3
[3,8,6,7,2,1,5,4] => [2,3,2,1] => 10100101 => 4
[8,5,6,4,2,1,7,3] => [1,3,1,2,1] => 11001101 => 5
[7,2,5,8,3,1,6,4] => [2,3,2,1] => 10100101 => 4
[1,7,5,6,3,2,4,8] => [1,1,3,3] => 11100100 => 4
[6,1,2,3,8,5,7,4] => [4,3,1] => 10001001 => 3
[7,1,2,3,6,5,8,4] => [4,2,2] => 10001010 => 3
[7,2,1,3,8,6,4,5] => [2,2,2,2] => 10101010 => 4
[1,5,7,3,2,4,6,8] => [1,3,4] => 11001000 => 3
[5,2,7,3,1,8,4,6] => [2,2,1,3] => 10101100 => 4
[5,8,2,4,1,3,7,6] => [4,3,1] => 10001001 => 3
[8,7,2,6,3,4,1,5] => [1,2,3,2] => 11010010 => 4
[4,8,1,6,3,2,7,5] => [3,2,2,1] => 10010101 => 4
[3,1,8,6,4,2,7,5] => [2,1,2,2,1] => 10110101 => 5
[8,1,6,7,4,3,2,5] => [2,3,1,2] => 10100110 => 4
[3,5,8,7,2,4,1,6] => [3,3,2] => 10010010 => 3
[4,2,1,3,7,8,5,6] => [2,2,4] => 10101000 => 3
[2,4,1,3,8,7,5,6] => [4,1,3] => 10001100 => 3
[2,5,8,3,1,7,4,6] => [4,1,3] => 10001100 => 3
[8,6,1,3,7,2,4,5] => [1,3,4] => 11001000 => 3
[2,8,1,3,6,4,7,5] => [4,3,1] => 10001001 => 3
[6,8,2,3,4,1,5,7] => [5,3] => 10000100 => 2
[5,1,8,3,2,4,6,7] => [2,2,4] => 10101000 => 3
[8,7,6,5,4,3,2,9,1] => [1,1,1,2,1,1,2] => 111101110 => 7
[8,7,6,5,4,3,2,1,9] => [1,1,1,2,1,1,2] => 111101110 => 7
[8,7,6,5,4,2,3,9,1] => [1,1,1,2,2,2] => 111101010 => 6
[1,4,2,7,8,6,3,5] => [1,2,3,2] => 11010010 => 4
[1,6,2,4,8,5,3,7] => [1,3,2,2] => 11001010 => 4
[1,6,2,4,7,5,3,8] => [1,3,2,2] => 11001010 => 4
[1,7,3,8,5,2,4,6] => [1,2,2,3] => 11010100 => 4
[1,7,3,2,8,6,4,5] => [1,2,1,2,2] => 11011010 => 5
[4,2,5,7,8,6,1,3] => [2,4,2] => 10100010 => 3
[7,2,3,1,8,5,6,4] => [3,1,3,1] => 10011001 => 4
[8,2,5,1,7,3,4,6] => [2,2,4] => 10101000 => 3
[6,2,1,8,3,4,7,5] => [2,1,4,1] => 10110001 => 4
[6,2,8,3,5,1,7,4] => [2,3,2,1] => 10100101 => 4
[6,2,4,8,5,7,1,3] => [2,3,3] => 10100100 => 3
[1,3,6,4,8,5,7,2] => [1,3,3,1] => 11001001 => 4
[1,3,6,4,7,5,8,2] => [1,3,2,2] => 11001010 => 4
[6,2,4,7,5,8,1,3] => [2,3,3] => 10100100 => 3
[6,2,1,3,7,8,4,5] => [2,2,4] => 10101000 => 3
[7,8,2,1,4,3,5,6] => [3,2,3] => 10010100 => 3
[7,6,4,2,3,1,8,5] => [1,1,3,1,2] => 11100110 => 5
[5,7,2,3,1,6,8,4] => [4,2,2] => 10001010 => 3
[7,5,4,2,6,8,1,3] => [1,1,2,4] => 11101000 => 4
[1,7,5,3,4,6,8,2] => [1,1,4,2] => 11100010 => 4
[8,2,5,4,6,7,1,3] => [2,2,4] => 10101000 => 3
[5,2,6,3,1,8,7,4] => [2,2,1,2,1] => 10101101 => 5
[8,2,6,4,3,1,7,5] => [2,2,1,2,1] => 10101101 => 5
[8,2,7,4,1,3,5,6] => [2,2,4] => 10101000 => 3
[1,2,8,4,3,5,6,7] => [2,2,4] => 10101000 => 3
[1,7,4,2,3,5,6,8] => [1,1,6] => 11100000 => 3
[6,8,4,1,3,2,5,7] => [2,3,3] => 10100100 => 3
[1,8,7,4,3,2,5,6] => [1,1,2,1,3] => 11101100 => 5
[1,6,3,8,2,4,7,5] => [1,2,4,1] => 11010001 => 4
[5,3,8,1,2,7,4,6] => [1,4,3] => 11000100 => 3
[5,1,8,3,2,6,4,7] => [2,2,2,2] => 10101010 => 4
[5,7,3,1,2,6,4,8] => [3,3,2] => 10010010 => 3
[1,7,5,4,2,6,3,8] => [1,1,2,2,2] => 11101010 => 5
[1,5,8,2,4,6,3,7] => [1,5,2] => 11000010 => 3
[1,5,8,4,2,7,3,6] => [1,3,1,3] => 11001100 => 4
[1,4,6,2,8,3,7,5] => [1,3,3,1] => 11001001 => 4
[5,3,1,6,7,2,4,8] => [1,2,5] => 11010000 => 3
[5,3,6,1,2,8,4,7] => [1,4,3] => 11000100 => 3
[1,6,3,2,7,8,4,5] => [1,2,1,4] => 11011000 => 4
[1,7,4,5,3,8,6,2] => [1,1,3,2,1] => 11100101 => 5
[6,3,4,1,2,5,8,7] => [1,5,2] => 11000010 => 3
[6,3,1,4,2,7,5,8] => [1,3,1,3] => 11001100 => 4
[1,8,3,2,4,5,6,7] => [1,2,5] => 11010000 => 3
[8,6,3,2,4,1,7,5] => [1,2,2,2,1] => 11010101 => 5
[8,5,3,2,6,7,1,4] => [1,2,1,4] => 11011000 => 4
[4,5,2,6,8,1,7,3] => [3,4,1] => 10010001 => 3
[4,2,5,6,7,8,1,3] => [2,6] => 10100000 => 2
[5,2,3,6,7,1,8,4] => [3,3,2] => 10010010 => 3
[6,2,3,4,1,7,8,5] => [4,1,3] => 10001100 => 3
[7,2,3,1,4,5,8,6] => [3,3,2] => 10010010 => 3
[8,6,1,4,3,2,5,7] => [1,3,1,3] => 11001100 => 4
[8,3,1,6,5,2,4,7] => [1,2,2,3] => 11010100 => 4
[3,7,5,1,8,2,4,6] => [2,2,4] => 10101000 => 3
[4,1,5,2,8,7,3,6] => [2,2,1,3] => 10101100 => 4
[8,1,2,4,6,5,3,7] => [4,2,2] => 10001010 => 3
[8,1,2,5,4,6,3,7] => [3,3,2] => 10010010 => 3
[8,2,6,5,1,3,4,7] => [2,1,5] => 10110000 => 3
[8,3,1,6,2,5,4,7] => [1,2,3,2] => 11010010 => 4
[8,1,2,6,4,5,3,7] => [3,3,2] => 10010010 => 3
[8,1,2,5,6,4,3,7] => [3,3,2] => 10010010 => 3
[8,1,2,6,5,4,3,7] => [3,2,1,2] => 10010110 => 4
[1,7,5,4,2,8,3,6] => [1,1,2,1,3] => 11101100 => 5
[5,1,4,8,2,7,3,6] => [2,3,3] => 10100100 => 3
[1,4,6,8,2,7,3,5] => [1,4,3] => 11000100 => 3
[1,4,7,6,2,8,3,5] => [1,2,2,3] => 11010100 => 4
[5,1,4,7,2,8,3,6] => [2,3,3] => 10100100 => 3
[1,7,4,5,2,8,3,6] => [1,1,3,3] => 11100100 => 4
[3,7,5,1,2,8,4,6] => [2,3,3] => 10100100 => 3
[5,7,2,8,1,3,4,6] => [3,5] => 10010000 => 2
[5,2,8,7,1,3,4,6] => [2,1,5] => 10110000 => 3
[4,1,5,8,2,7,3,6] => [2,3,3] => 10100100 => 3
[1,4,6,2,8,7,3,5] => [1,3,1,3] => 11001100 => 4
[1,4,2,8,6,7,3,5] => [1,2,1,4] => 11011000 => 4
[3,1,2,6,4,8,7,5] => [3,2,2,1] => 10010101 => 4
[2,1,7,6,3,4,8,5] => [2,1,3,2] => 10110010 => 4
[3,1,2,7,4,6,8,5] => [3,3,2] => 10010010 => 3
[1,4,7,2,6,8,3,5] => [1,3,4] => 11001000 => 3
[1,2,3,6,8,5,7,4] => [3,4,1] => 10010001 => 3
[5,1,4,2,7,8,3,6] => [2,2,4] => 10101000 => 3
[1,4,2,7,6,8,3,5] => [1,2,1,4] => 11011000 => 4
[1,4,2,6,8,7,3,5] => [1,2,2,3] => 11010100 => 4
[3,1,2,8,4,6,7,5] => [3,4,1] => 10010001 => 3
[3,1,2,7,6,4,8,5] => [3,1,2,2] => 10011010 => 4
[5,3,7,1,8,2,4,6] => [1,3,4] => 11001000 => 3
[1,7,4,3,2,5,8,6] => [1,1,2,2,2] => 11101010 => 5
[4,8,7,2,1,3,5,6] => [2,2,4] => 10101000 => 3
[1,8,7,3,4,2,5,6] => [1,1,3,3] => 11100100 => 4
[3,1,7,8,2,6,4,5] => [2,4,2] => 10100010 => 3
[1,4,2,7,8,3,6,5] => [1,2,4,1] => 11010001 => 4
[5,2,8,1,3,4,7,6] => [2,5,1] => 10100001 => 3
[2,1,8,6,3,4,7,5] => [2,1,4,1] => 10110001 => 4
[1,4,2,6,8,3,7,5] => [1,2,4,1] => 11010001 => 4
[1,2,3,7,8,5,6,4] => [3,4,1] => 10010001 => 3
[1,2,3,7,5,8,6,4] => [3,2,2,1] => 10010101 => 4
[1,4,2,7,3,8,6,5] => [1,2,2,2,1] => 11010101 => 5
[3,1,7,2,8,6,4,5] => [2,2,2,2] => 10101010 => 4
[2,1,7,8,3,4,6,5] => [2,5,1] => 10100001 => 3
[1,2,3,8,7,5,6,4] => [3,1,3,1] => 10011001 => 4
[10,1,2,3,4,5,6,7,8,9] => [10] => 1000000000 => 1
[10,1,2,3,4,5,6,9,7,8] => [7,3] => 1000000100 => 2
[11,1,2,3,4,5,6,7,8,9,10] => [11] => 10000000000 => 1
[10,1,2,3,4,5,6,7,8,11,9] => [9,2] => 10000000010 => 2
[8,1,2,3,4,5,6,9,10,7] => [7,3] => 1000000100 => 2
[2,9,10,1,3,4,5,6,7,8] => [10] => 1000000000 => 1
[4,7,8,5,6,2,1,3] => [3,3,2] => 10010010 => 3
[5,7,8,4,2,6,1,3] => [4,2,2] => 10001010 => 3
[6,7,8,4,2,5,1,3] => [4,2,2] => 10001010 => 3
[8,6,3,7,2,1,5,4] => [1,2,2,2,1] => 11010101 => 5
[7,6,3,8,2,1,5,4] => [1,2,2,2,1] => 11010101 => 5
[6,7,8,3,2,1,5,4] => [4,1,2,1] => 10001101 => 4
[5,7,8,3,2,1,6,4] => [4,1,2,1] => 10001101 => 4
[2,7,8,4,3,5,6,1] => [4,3,1] => 10001001 => 3
[3,7,8,4,2,5,1,6] => [4,2,2] => 10001010 => 3
[4,7,8,3,2,1,5,6] => [4,1,3] => 10001100 => 3
[5,7,8,3,2,1,4,6] => [4,1,3] => 10001100 => 3
[7,6,3,8,2,1,4,5] => [1,2,2,3] => 11010100 => 4
[8,6,3,7,2,1,4,5] => [1,2,2,3] => 11010100 => 4
[5,6,3,8,2,1,4,7] => [3,2,3] => 10010100 => 3
[3,6,4,8,2,5,1,7] => [2,4,2] => 10100010 => 3
[2,6,4,8,3,5,7,1] => [2,5,1] => 10100001 => 3
[2,6,4,7,3,5,8,1] => [2,4,2] => 10100010 => 3
[3,6,4,7,2,5,1,8] => [2,4,2] => 10100010 => 3
[4,6,3,7,2,1,5,8] => [3,2,3] => 10010100 => 3
[5,6,3,7,2,1,4,8] => [3,2,3] => 10010100 => 3
[8,4,3,2,1,6,5,7] => [1,2,1,2,2] => 11011010 => 5
[6,4,3,2,1,7,5,8] => [1,2,1,1,3] => 11011100 => 5
[4,5,3,2,7,1,6,8] => [3,1,4] => 10011000 => 3
[3,5,4,2,8,6,1,7] => [2,2,2,2] => 10101010 => 4
[6,4,3,2,1,8,5,7] => [1,2,1,1,3] => 11011100 => 5
[7,4,3,2,1,8,5,6] => [1,2,1,1,3] => 11011100 => 5
[8,4,3,2,1,7,5,6] => [1,2,1,1,3] => 11011100 => 5
[8,4,3,2,1,7,6,5] => [1,2,1,1,2,1] => 11011101 => 6
[7,4,3,2,1,8,6,5] => [1,2,1,1,2,1] => 11011101 => 6
[6,4,3,2,1,8,7,5] => [1,2,1,1,2,1] => 11011101 => 6
[5,6,3,8,2,1,7,4] => [3,2,2,1] => 10010101 => 4
[7,5,3,2,8,1,6,4] => [1,2,1,3,1] => 11011001 => 5
[8,5,4,2,7,6,1,3] => [1,1,2,2,2] => 11101010 => 5
[7,5,4,2,8,6,1,3] => [1,1,2,2,2] => 11101010 => 5
[6,5,4,2,8,7,1,3] => [1,1,2,1,3] => 11101100 => 5
[4,6,5,8,7,2,1,3] => [2,2,2,2] => 10101010 => 4
[2,6,5,7,8,3,4,1] => [2,5,1] => 10100001 => 3
[6,5,4,2,7,8,1,3] => [1,1,2,4] => 11101000 => 4
[8,5,4,2,6,7,1,3] => [1,1,2,4] => 11101000 => 4
[8,5,3,2,6,1,7,4] => [1,2,1,3,1] => 11011001 => 5
[7,5,3,2,6,1,8,4] => [1,2,1,2,2] => 11011010 => 5
[5,6,3,7,2,1,8,4] => [3,2,1,2] => 10010110 => 4
[4,6,3,7,2,1,8,5] => [3,2,1,2] => 10010110 => 4
[3,6,4,7,2,8,1,5] => [2,3,3] => 10100100 => 3
[2,6,4,7,3,8,5,1] => [2,3,2,1] => 10100101 => 4
[3,5,4,2,7,8,1,6] => [2,2,4] => 10101000 => 3
[4,5,3,2,7,1,8,6] => [3,1,2,2] => 10011010 => 4
[7,4,3,2,1,6,8,5] => [1,2,1,2,2] => 11011010 => 5
[8,4,3,2,1,6,7,5] => [1,2,1,3,1] => 11011001 => 5
[8,4,3,2,1,5,7,6] => [1,2,1,3,1] => 11011001 => 5
[7,4,3,2,1,5,8,6] => [1,2,1,2,2] => 11011010 => 5
[6,4,3,2,1,5,8,7] => [1,2,1,2,2] => 11011010 => 5
[3,5,4,2,6,8,1,7] => [2,2,4] => 10101000 => 3
[5,6,3,4,1,2,8,7] => [4,2,2] => 10001010 => 3
[8,5,3,7,2,6,4,1] => [1,2,3,1,1] => 11010011 => 5
[8,5,7,4,2,6,3,1] => [1,3,2,1,1] => 11001011 => 5
[7,5,8,4,2,6,1,3] => [1,3,2,2] => 11001010 => 4
[2,1,7,8,5,6,3,4] => [2,4,2] => 10100010 => 3
[6,8,3,7,5,1,4,2] => [3,2,2,1] => 10010101 => 4
[5,7,3,8,1,6,2,4] => [3,3,2] => 10010010 => 3
[3,2,6,4,8,5,1,7] => [2,2,2,2] => 10101010 => 4
[3,2,5,8,4,6,1,7] => [2,4,2] => 10100010 => 3
[3,5,2,4,1,7,6,8] => [4,1,3] => 10001100 => 3
[4,2,1,5,7,3,6,8] => [2,1,5] => 10110000 => 3
[4,5,2,3,7,1,6,8] => [4,4] => 10001000 => 2
[4,2,5,3,8,1,6,7] => [2,2,4] => 10101000 => 3
[4,2,5,8,3,1,6,7] => [2,3,3] => 10100100 => 3
[3,1,5,4,2,8,6,7] => [2,2,1,3] => 10101100 => 4
[4,1,5,3,8,2,6,7] => [2,2,4] => 10101000 => 3
[4,1,5,8,3,2,6,7] => [2,3,3] => 10100100 => 3
[4,3,8,5,2,1,6,7] => [1,2,2,3] => 11010100 => 4
[4,7,3,5,2,1,6,8] => [3,2,3] => 10010100 => 3
[4,3,2,7,5,1,6,8] => [1,2,2,3] => 11010100 => 4
[4,3,6,2,5,1,7,8] => [1,4,3] => 11000100 => 3
[4,6,3,2,5,1,7,8] => [3,2,3] => 10010100 => 3
[4,6,7,1,3,2,5,8] => [5,3] => 10000100 => 2
[4,5,1,7,3,2,6,8] => [3,2,3] => 10010100 => 3
[4,5,1,3,7,2,6,8] => [4,4] => 10001000 => 2
[3,5,1,4,2,7,6,8] => [4,1,3] => 10001100 => 3
[2,5,1,4,3,7,8,6] => [4,1,3] => 10001100 => 3
[5,2,1,4,3,7,8,6] => [2,2,1,3] => 10101100 => 4
[5,3,1,4,2,7,6,8] => [1,3,1,3] => 11001100 => 4
[4,3,1,5,7,2,6,8] => [1,2,5] => 11010000 => 3
[4,3,1,7,5,2,6,8] => [1,2,2,3] => 11010100 => 4
[4,3,6,1,5,2,7,8] => [1,4,3] => 11000100 => 3
[4,6,3,1,5,2,7,8] => [3,2,3] => 10010100 => 3
[5,3,6,4,1,2,7,8] => [1,3,4] => 11001000 => 3
[4,3,6,1,7,2,5,8] => [1,3,4] => 11001000 => 3
[6,3,4,1,2,7,5,8] => [1,4,3] => 11000100 => 3
[6,2,4,1,3,7,8,5] => [2,3,3] => 10100100 => 3
[3,6,4,1,2,7,5,8] => [2,3,3] => 10100100 => 3
[4,6,3,1,7,2,5,8] => [3,1,4] => 10011000 => 3
[5,3,6,2,1,4,7,8] => [1,3,4] => 11001000 => 3
[5,6,2,7,1,3,4,8] => [3,5] => 10010000 => 2
[4,5,2,7,3,1,6,8] => [3,2,3] => 10010100 => 3
[4,6,7,2,3,1,5,8] => [5,3] => 10000100 => 2
[4,6,2,1,7,3,5,8] => [3,1,4] => 10011000 => 3
[3,2,6,1,4,7,5,8] => [2,3,3] => 10100100 => 3
[3,6,2,1,4,7,5,8] => [3,2,3] => 10010100 => 3
[3,6,7,2,4,5,1,8] => [6,2] => 10000010 => 2
[3,5,2,7,4,6,1,8] => [3,3,2] => 10010010 => 3
[3,7,2,4,8,5,1,6] => [4,2,2] => 10001010 => 3
[7,2,1,4,6,3,8,5] => [2,2,2,2] => 10101010 => 4
[7,3,1,4,6,8,2,5] => [1,3,4] => 11001000 => 3
[3,2,6,1,5,7,4,8] => [2,3,3] => 10100100 => 3
[3,6,2,1,5,7,4,8] => [3,2,3] => 10010100 => 3
[6,3,2,1,5,7,4,8] => [1,2,2,3] => 11010100 => 4
[6,4,2,1,5,3,7,8] => [1,2,2,3] => 11010100 => 4
[4,2,6,1,5,3,7,8] => [2,3,3] => 10100100 => 3
[4,2,1,7,5,3,6,8] => [2,1,2,3] => 10110100 => 4
[7,4,1,5,6,2,3,8] => [1,2,5] => 11010000 => 3
[7,3,1,5,2,6,4,8] => [1,2,3,2] => 11010010 => 4
[7,2,1,5,3,6,8,4] => [2,1,3,2] => 10110010 => 4
[6,2,5,1,3,7,8,4] => [2,3,3] => 10100100 => 3
[6,3,5,1,2,7,4,8] => [1,4,3] => 11000100 => 3
[6,4,5,1,7,2,3,8] => [1,3,4] => 11001000 => 3
[5,2,6,4,1,3,7,8] => [2,2,4] => 10101000 => 3
[4,6,5,1,7,2,3,8] => [2,2,4] => 10101000 => 3
[3,6,5,1,2,7,4,8] => [2,3,3] => 10100100 => 3
[6,5,2,1,4,7,8,3] => [1,2,2,3] => 11010100 => 4
[6,5,3,1,4,7,2,8] => [1,2,2,3] => 11010100 => 4
[2,3,1,8,5,4,7,6] => [3,2,2,1] => 10010101 => 4
[2,4,1,5,8,3,7,6] => [3,4,1] => 10010001 => 3
[2,4,1,5,3,8,7,6] => [3,2,2,1] => 10010101 => 4
[3,4,5,1,2,8,7,6] => [5,2,1] => 10000101 => 3
[3,4,5,1,8,2,7,6] => [4,3,1] => 10001001 => 3
[1,8,4,5,3,2,7,6] => [1,1,3,2,1] => 11100101 => 5
[2,4,8,5,3,1,7,6] => [3,2,2,1] => 10010101 => 4
[3,4,5,8,2,1,7,6] => [5,2,1] => 10000101 => 3
[3,4,5,2,8,1,7,6] => [4,3,1] => 10001001 => 3
[3,4,6,2,1,7,8,5] => [4,1,3] => 10001100 => 3
[3,4,6,2,1,7,5,8] => [4,1,3] => 10001100 => 3
[3,5,6,2,7,1,4,8] => [4,4] => 10001000 => 2
[3,5,6,2,7,1,8,4] => [4,2,2] => 10001010 => 3
[3,5,6,2,7,8,1,4] => [4,4] => 10001000 => 2
[3,4,6,2,8,7,1,5] => [4,1,3] => 10001100 => 3
[3,4,6,8,2,7,1,5] => [5,3] => 10000100 => 2
[2,4,8,6,3,7,1,5] => [3,2,3] => 10010100 => 3
[1,8,4,6,3,7,2,5] => [1,1,3,3] => 11100100 => 4
[1,8,4,6,3,7,5,2] => [1,1,3,2,1] => 11100101 => 5
[3,4,6,8,2,7,5,1] => [5,2,1] => 10000101 => 3
[3,4,6,2,8,7,5,1] => [4,1,2,1] => 10001101 => 4
[3,5,6,2,7,8,4,1] => [4,3,1] => 10001001 => 3
[3,5,6,2,7,4,1,8] => [4,2,2] => 10001010 => 3
[4,5,6,7,2,8,3,1] => [5,2,1] => 10000101 => 3
[3,5,6,8,7,2,4,1] => [4,3,1] => 10001001 => 3
[2,5,8,6,7,3,4,1] => [3,4,1] => 10010001 => 3
[1,8,5,6,7,3,4,2] => [1,1,5,1] => 11100001 => 4
[1,8,5,6,7,3,2,4] => [1,1,4,2] => 11100010 => 4
[2,5,8,6,7,3,1,4] => [3,3,2] => 10010010 => 3
[3,5,6,8,7,2,1,4] => [4,2,2] => 10001010 => 3
[4,5,6,7,2,1,8,3] => [5,1,2] => 10000110 => 3
[3,4,6,1,8,7,2,5] => [4,1,3] => 10001100 => 3
[2,4,1,6,8,7,3,5] => [3,2,3] => 10010100 => 3
[2,3,1,8,6,7,4,5] => [3,1,4] => 10011000 => 3
[1,8,3,2,6,7,5,4] => [1,2,1,3,1] => 11011001 => 5
[2,5,1,6,7,8,4,3] => [3,4,1] => 10010001 => 3
[2,5,1,6,7,4,8,3] => [3,3,2] => 10010010 => 3
[2,5,1,6,7,4,3,8] => [3,3,2] => 10010010 => 3
[3,5,6,1,7,4,2,8] => [4,2,2] => 10001010 => 3
[3,5,6,1,7,4,8,2] => [4,2,2] => 10001010 => 3
[3,4,6,1,8,7,5,2] => [4,1,2,1] => 10001101 => 4
[3,4,6,8,1,7,5,2] => [5,2,1] => 10000101 => 3
[2,4,8,6,1,7,5,3] => [3,2,2,1] => 10010101 => 4
[1,8,4,6,2,7,5,3] => [1,1,3,2,1] => 11100101 => 5
[1,8,5,6,7,2,4,3] => [1,1,5,1] => 11100001 => 4
[2,5,8,6,7,1,4,3] => [3,4,1] => 10010001 => 3
[3,5,6,8,7,1,4,2] => [4,3,1] => 10001001 => 3
[4,5,6,7,8,1,3,2] => [7,1] => 10000001 => 2
[4,5,6,7,1,3,8,2] => [6,2] => 10000010 => 2
[4,5,6,7,1,3,2,8] => [6,2] => 10000010 => 2
[4,5,6,7,3,1,8,2] => [5,1,2] => 10000110 => 3
[3,5,6,8,7,4,1,2] => [4,2,2] => 10001010 => 3
[2,5,8,6,7,4,1,3] => [3,3,2] => 10010010 => 3
[1,8,5,6,7,4,2,3] => [1,1,4,2] => 11100010 => 4
[1,8,5,6,7,4,3,2] => [1,1,4,1,1] => 11100011 => 5
[2,5,8,6,7,4,3,1] => [3,3,1,1] => 10010011 => 4
[8,2,5,3,7,1,6,4] => [2,2,3,1] => 10101001 => 4
[8,2,4,3,7,1,6,5] => [2,2,3,1] => 10101001 => 4
[5,8,2,4,3,7,1,6] => [4,1,3] => 10001100 => 3
[4,2,5,6,1,8,3,7] => [2,3,3] => 10100100 => 3
[4,2,5,6,1,7,3,8] => [2,3,3] => 10100100 => 3
[6,1,5,7,3,2,4,8] => [2,3,3] => 10100100 => 3
[6,1,5,8,3,2,4,7] => [2,3,3] => 10100100 => 3
[3,8,2,4,7,1,5,6] => [4,4] => 10001000 => 2
[3,6,8,2,4,7,1,5] => [5,3] => 10000100 => 2
[4,3,5,6,7,1,8,2] => [1,5,2] => 11000010 => 3
[3,7,1,5,6,8,2,4] => [3,5] => 10010000 => 2
[3,7,1,5,8,2,4,6] => [3,5] => 10010000 => 2
[8,3,2,4,6,1,5,7] => [1,3,4] => 11001000 => 3
[7,3,2,4,6,1,5,8] => [1,3,4] => 11001000 => 3
[3,2,5,1,7,4,6,8] => [2,2,4] => 10101000 => 3
[3,2,5,1,8,4,6,7] => [2,2,4] => 10101000 => 3
[3,2,5,1,7,8,4,6] => [2,2,4] => 10101000 => 3
[7,8,3,2,4,6,1,5] => [3,3,2] => 10010010 => 3
[6,1,5,7,8,3,2,4] => [2,4,2] => 10100010 => 3
[4,2,5,6,1,7,8,3] => [2,3,3] => 10100100 => 3
[5,7,6,1,8,3,4,2] => [2,2,3,1] => 10101001 => 4
[5,8,6,1,7,3,4,2] => [2,2,3,1] => 10101001 => 4
[6,1,5,8,7,3,2,4] => [2,2,2,2] => 10101010 => 4
[8,7,3,2,4,6,1,5] => [1,2,3,2] => 11010010 => 4
[3,2,5,1,8,7,4,6] => [2,2,1,3] => 10101100 => 4
[3,2,5,1,6,4,7,8] => [2,2,4] => 10101000 => 3
[3,2,4,1,8,7,5,6] => [2,2,1,3] => 10101100 => 4
[3,2,5,1,6,8,7,4] => [2,2,3,1] => 10101001 => 4
[3,8,6,5,1,7,4,2] => [2,1,2,2,1] => 10110101 => 5
[3,7,6,5,1,8,4,2] => [2,1,2,2,1] => 10110101 => 5
[6,5,1,7,8,4,2,3] => [1,2,3,2] => 11010010 => 4
[3,2,5,1,6,7,8,4] => [2,2,4] => 10101000 => 3
[3,2,4,1,8,5,6,7] => [2,2,4] => 10101000 => 3
[3,2,4,1,7,5,6,8] => [2,2,4] => 10101000 => 3
[3,2,4,1,6,8,5,7] => [2,2,4] => 10101000 => 3
[3,2,4,1,8,5,7,6] => [2,2,3,1] => 10101001 => 4
[8,3,2,4,7,6,1,5] => [1,3,2,2] => 11001010 => 4
[3,2,5,1,8,4,7,6] => [2,2,3,1] => 10101001 => 4
[3,2,5,1,6,7,4,8] => [2,2,4] => 10101000 => 3
[6,5,1,7,4,2,3,8] => [1,2,2,3] => 11010100 => 4
[6,5,1,8,4,2,3,7] => [1,2,2,3] => 11010100 => 4
[8,4,2,3,7,5,1,6] => [1,3,2,2] => 11001010 => 4
[4,2,6,1,8,3,7,5] => [2,2,3,1] => 10101001 => 4
[5,2,6,1,8,3,7,4] => [2,2,3,1] => 10101001 => 4
[8,4,6,1,7,3,5,2] => [1,3,3,1] => 11001001 => 4
[5,2,6,1,8,4,7,3] => [2,2,3,1] => 10101001 => 4
[7,4,2,3,8,5,1,6] => [1,3,2,2] => 11001010 => 4
[8,5,1,6,4,2,3,7] => [1,2,2,3] => 11010100 => 4
[7,5,1,6,4,2,3,8] => [1,2,2,3] => 11010100 => 4
[3,2,5,1,7,6,4,8] => [2,2,2,2] => 10101010 => 4
[3,2,5,1,8,6,4,7] => [2,2,2,2] => 10101010 => 4
[7,3,2,4,8,6,1,5] => [1,3,2,2] => 11001010 => 4
[8,6,1,5,7,3,2,4] => [1,2,3,2] => 11010010 => 4
[4,2,6,1,8,5,7,3] => [2,2,3,1] => 10101001 => 4
[8,5,6,1,7,3,4,2] => [1,3,3,1] => 11001001 => 4
[3,6,8,5,1,7,4,2] => [3,2,2,1] => 10010101 => 4
[8,5,1,6,7,4,2,3] => [1,2,3,2] => 11010010 => 4
[3,2,5,1,8,6,7,4] => [2,2,3,1] => 10101001 => 4
[3,2,4,1,8,6,5,7] => [2,2,2,2] => 10101010 => 4
[3,2,4,1,5,8,6,7] => [2,3,3] => 10100100 => 3
[3,2,5,1,7,8,6,4] => [2,2,3,1] => 10101001 => 4
[7,8,5,1,6,4,2,3] => [2,2,2,2] => 10101010 => 4
[3,8,5,1,7,6,4,2] => [2,2,2,1,1] => 10101011 => 5
[3,7,5,1,8,6,4,2] => [2,2,2,1,1] => 10101011 => 5
[8,7,5,1,6,4,2,3] => [1,1,2,2,2] => 11101010 => 5
[3,2,5,1,8,7,6,4] => [2,2,1,2,1] => 10101101 => 5
[6,5,7,3,1,8,4,2] => [1,3,1,2,1] => 11001101 => 5
[4,6,3,7,1,8,5,2] => [3,2,2,1] => 10010101 => 4
[4,6,3,7,5,1,8,2] => [3,2,1,2] => 10010110 => 4
[4,2,6,1,7,5,3,8] => [2,2,2,2] => 10101010 => 4
[2,5,7,4,1,6,3,8] => [4,2,2] => 10001010 => 3
[2,5,7,4,1,6,8,3] => [4,2,2] => 10001010 => 3
[5,4,7,3,6,1,8,2] => [1,3,2,2] => 11001010 => 4
[5,4,7,8,3,1,6,2] => [1,4,2,1] => 11000101 => 4
[4,3,7,5,1,8,6,2] => [1,2,2,2,1] => 11010101 => 5
[6,4,3,8,5,1,7,2] => [1,2,2,2,1] => 11010101 => 5
[5,8,4,3,6,1,7,2] => [2,2,3,1] => 10101001 => 4
[5,4,8,3,6,1,7,2] => [1,3,3,1] => 11001001 => 4
[5,4,3,6,7,1,8,2] => [1,2,3,2] => 11010010 => 4
[2,5,4,6,1,7,3,8] => [2,3,3] => 10100100 => 3
[3,2,5,8,1,6,7,4] => [2,5,1] => 10100001 => 3
[2,5,4,6,8,1,7,3] => [2,5,1] => 10100001 => 3
[5,2,8,4,1,6,7,3] => [2,2,3,1] => 10101001 => 4
[4,6,2,1,8,5,7,3] => [3,1,3,1] => 10011001 => 4
[2,4,1,7,5,8,6,3] => [3,2,2,1] => 10010101 => 4
[2,4,1,7,5,3,8,6] => [3,2,1,2] => 10010110 => 4
[2,6,4,1,8,5,3,7] => [2,2,2,2] => 10101010 => 4
[5,4,8,2,1,6,3,7] => [1,3,2,2] => 11001010 => 4
[2,5,8,4,1,6,3,7] => [4,2,2] => 10001010 => 3
[3,2,5,6,1,8,4,7] => [2,3,3] => 10100100 => 3
[4,8,3,2,6,1,5,7] => [3,1,4] => 10011000 => 3
[3,5,2,8,1,6,4,7] => [3,3,2] => 10010010 => 3
[3,2,1,6,8,5,4,7] => [2,1,3,2] => 10110010 => 4
[3,2,7,1,5,4,8,6] => [2,3,1,2] => 10100110 => 4
[3,2,7,1,5,8,6,4] => [2,3,2,1] => 10100101 => 4
[3,8,2,5,1,6,7,4] => [3,4,1] => 10010001 => 3
[4,8,3,2,6,7,1,5] => [3,1,4] => 10011000 => 3
[4,3,8,2,6,7,1,5] => [1,3,4] => 11001000 => 3
[4,3,2,6,7,8,1,5] => [1,2,5] => 11010000 => 3
[4,3,2,6,7,1,5,8] => [1,2,5] => 11010000 => 3
[4,3,7,2,6,8,1,5] => [1,3,4] => 11001000 => 3
[4,3,7,8,2,6,1,5] => [1,5,2] => 11000010 => 3
[2,5,7,4,8,1,6,3] => [4,3,1] => 10001001 => 3
[3,2,5,7,8,1,6,4] => [2,5,1] => 10100001 => 3
[3,2,5,7,1,6,8,4] => [2,4,2] => 10100010 => 3
[3,2,5,7,1,6,4,8] => [2,4,2] => 10100010 => 3
[6,3,2,7,1,5,4,8] => [1,2,3,2] => 11010010 => 4
[6,3,2,7,1,5,8,4] => [1,2,3,2] => 11010010 => 4
[6,3,2,7,8,1,5,4] => [1,2,4,1] => 11010001 => 4
[4,2,6,1,7,8,5,3] => [2,2,3,1] => 10101001 => 4
[6,5,2,1,7,8,4,3] => [1,2,1,3,1] => 11011001 => 5
[2,1,7,5,3,8,6,4] => [2,1,2,2,1] => 10110101 => 5
[6,2,1,8,5,3,7,4] => [2,1,2,2,1] => 10110101 => 5
[6,3,2,7,1,4,8,5] => [1,2,3,2] => 11010010 => 4
[6,3,2,1,4,7,8,5] => [1,2,2,3] => 11010100 => 4
[6,3,2,1,4,7,5,8] => [1,2,2,3] => 11010100 => 4
[3,5,2,1,7,4,6,8] => [3,1,4] => 10011000 => 3
[3,5,2,1,7,8,4,6] => [3,1,4] => 10011000 => 3
[5,8,4,2,1,7,3,6] => [2,2,1,3] => 10101100 => 4
[4,6,2,1,8,3,7,5] => [3,1,3,1] => 10011001 => 4
[2,4,1,7,3,8,6,5] => [3,2,2,1] => 10010101 => 4
[3,2,7,1,4,8,6,5] => [2,3,2,1] => 10100101 => 4
[3,5,8,2,1,7,4,6] => [4,1,3] => 10001100 => 3
[4,8,3,7,2,1,5,6] => [3,2,3] => 10010100 => 3
[4,3,7,2,8,1,5,6] => [1,3,4] => 11001000 => 3
[4,3,7,2,1,5,6,8] => [1,3,4] => 11001000 => 3
[4,8,3,2,7,1,5,6] => [3,1,4] => 10011000 => 3
[3,5,2,8,1,7,4,6] => [3,2,3] => 10010100 => 3
[6,3,2,8,1,4,7,5] => [1,2,4,1] => 11010001 => 4
[3,2,1,4,7,5,8,6] => [2,2,2,2] => 10101010 => 4
[5,3,2,1,8,4,6,7] => [1,2,1,4] => 11011000 => 4
[4,8,3,2,1,5,6,7] => [3,1,4] => 10011000 => 3
[4,3,8,2,1,5,6,7] => [1,3,4] => 11001000 => 3
[8,7,6,4,5,3,2,1,9] => [1,1,3,1,1,2] => 111001110 => 6
[8,7,5,4,6,3,2,1,9] => [1,1,2,2,1,2] => 111010110 => 6
[8,7,4,6,5,3,2,1,9] => [1,1,3,1,1,2] => 111001110 => 6
[6,2,3,1,5,4,8,7] => [3,2,1,2] => 10010110 => 4
[8,4,5,2,3,1,7,6] => [1,4,2,1] => 11000101 => 4
[8,6,7,2,5,3,4,1] => [1,4,2,1] => 11000101 => 4
[8,2,5,3,4,1,7,6] => [2,3,2,1] => 10100101 => 4
[6,2,5,3,4,1,8,7] => [2,3,1,2] => 10100110 => 4
[6,1,5,2,4,3,8,7] => [2,3,1,2] => 10100110 => 4
[6,4,5,1,3,2,8,7] => [1,4,1,2] => 11000110 => 4
[6,1,5,3,4,2,8,7] => [2,3,1,2] => 10100110 => 4
[6,3,5,1,4,2,8,7] => [1,4,1,2] => 11000110 => 4
[8,3,5,2,4,1,7,6] => [1,4,2,1] => 11000101 => 4
[8,3,7,5,6,2,4,1] => [1,2,4,1] => 11010001 => 4
[8,3,7,2,4,1,6,5] => [1,4,2,1] => 11000101 => 4
[8,3,5,1,4,2,7,6] => [1,4,2,1] => 11000101 => 4
[8,1,5,3,4,2,7,6] => [2,3,2,1] => 10100101 => 4
[8,4,5,1,3,2,7,6] => [1,4,2,1] => 11000101 => 4
[2,1,8,4,5,3,7,6] => [2,3,2,1] => 10100101 => 4
[8,6,7,4,5,1,3,2] => [1,4,2,1] => 11000101 => 4
[8,6,7,1,5,3,4,2] => [1,4,2,1] => 11000101 => 4
[8,6,7,3,5,1,4,2] => [1,4,2,1] => 11000101 => 4
[8,3,7,5,6,1,4,2] => [1,2,4,1] => 11010001 => 4
[8,5,7,3,6,1,4,2] => [1,3,3,1] => 11001001 => 4
[8,3,7,4,6,2,5,1] => [1,3,3,1] => 11001001 => 4
[8,3,7,4,6,1,5,2] => [1,3,3,1] => 11001001 => 4
[8,3,7,1,6,4,5,2] => [1,3,3,1] => 11001001 => 4
[8,1,7,3,6,4,5,2] => [2,2,3,1] => 10101001 => 4
[8,1,7,5,6,3,4,2] => [2,1,4,1] => 10110001 => 4
[8,4,7,5,6,1,3,2] => [1,2,4,1] => 11010001 => 4
[2,1,8,4,7,5,6,3] => [2,2,3,1] => 10101001 => 4
[8,1,7,3,4,2,6,5] => [2,3,2,1] => 10100101 => 4
[8,1,7,3,6,2,5,4] => [2,2,3,1] => 10101001 => 4
[8,3,7,1,6,2,5,4] => [1,3,3,1] => 11001001 => 4
[8,3,7,2,6,4,5,1] => [1,3,3,1] => 11001001 => 4
[8,2,7,3,6,4,5,1] => [2,2,3,1] => 10101001 => 4
[8,2,7,3,6,1,5,4] => [2,2,3,1] => 10101001 => 4
[8,2,7,1,6,3,5,4] => [2,2,3,1] => 10101001 => 4
[8,1,7,2,4,3,6,5] => [2,3,2,1] => 10100101 => 4
[8,1,3,2,7,4,6,5] => [3,1,3,1] => 10011001 => 4
[2,1,8,3,7,4,6,5] => [2,2,3,1] => 10101001 => 4
[8,1,5,2,4,3,7,6] => [2,3,2,1] => 10100101 => 4
[8,2,7,1,4,3,6,5] => [2,3,2,1] => 10100101 => 4
[8,2,7,3,4,1,6,5] => [2,3,2,1] => 10100101 => 4
[8,2,7,5,6,3,4,1] => [2,1,4,1] => 10110001 => 4
[8,4,7,5,6,2,3,1] => [1,2,4,1] => 11010001 => 4
[8,4,7,2,3,1,6,5] => [1,4,2,1] => 11000101 => 4
[8,2,3,1,7,4,6,5] => [3,1,3,1] => 10011001 => 4
[8,2,3,1,5,4,7,6] => [3,2,2,1] => 10010101 => 4
[4,2,3,1,8,5,7,6] => [3,1,3,1] => 10011001 => 4
[4,1,3,2,8,6,7,5] => [3,1,3,1] => 10011001 => 4
[8,6,7,2,3,1,5,4] => [1,4,2,1] => 11000101 => 4
[8,2,3,1,7,5,6,4] => [3,1,3,1] => 10011001 => 4
[8,5,7,2,6,3,4,1] => [1,3,3,1] => 11001001 => 4
[8,5,7,2,6,1,4,3] => [1,3,3,1] => 11001001 => 4
[8,2,7,5,6,1,4,3] => [2,1,4,1] => 10110001 => 4
[8,6,7,2,5,1,4,3] => [1,4,2,1] => 11000101 => 4
[8,6,7,1,5,2,4,3] => [1,4,2,1] => 11000101 => 4
[8,6,7,1,3,2,5,4] => [1,4,2,1] => 11000101 => 4
[2,1,8,6,7,3,5,4] => [2,1,4,1] => 10110001 => 4
[2,1,8,3,7,5,6,4] => [2,2,3,1] => 10101001 => 4
[8,1,3,2,7,5,6,4] => [3,1,3,1] => 10011001 => 4
[8,1,7,5,6,2,4,3] => [2,1,4,1] => 10110001 => 4
[8,1,7,2,6,4,5,3] => [2,2,3,1] => 10101001 => 4
[8,2,7,1,6,4,5,3] => [2,2,3,1] => 10101001 => 4
[8,2,7,4,6,1,5,3] => [2,2,3,1] => 10101001 => 4
[8,2,7,4,6,3,5,1] => [2,2,3,1] => 10101001 => 4
[8,4,7,2,6,3,5,1] => [1,3,3,1] => 11001001 => 4
[8,4,7,2,6,1,5,3] => [1,3,3,1] => 11001001 => 4
[8,4,7,1,6,2,5,3] => [1,3,3,1] => 11001001 => 4
[8,1,7,4,6,2,5,3] => [2,2,3,1] => 10101001 => 4
[8,5,7,1,6,2,4,3] => [1,3,3,1] => 11001001 => 4
[2,1,8,5,7,3,6,4] => [2,1,4,1] => 10110001 => 4
[8,5,7,4,6,1,3,2] => [1,3,3,1] => 11001001 => 4
[8,5,7,1,6,3,4,2] => [1,3,3,1] => 11001001 => 4
[8,1,7,4,6,3,5,2] => [2,2,3,1] => 10101001 => 4
[8,4,7,1,6,3,5,2] => [1,3,3,1] => 11001001 => 4
[8,4,7,3,6,1,5,2] => [1,3,3,1] => 11001001 => 4
[2,4,8,3,6,1,7,5] => [4,3,1] => 10001001 => 3
[6,5,8,1,3,2,7,4] => [1,4,2,1] => 11000101 => 4
[4,5,8,6,3,2,7,1] => [3,2,2,1] => 10010101 => 4
[6,5,8,7,3,1,2,4] => [1,2,2,3] => 11010100 => 4
[1,5,8,7,3,6,2,4] => [1,2,3,2] => 11010010 => 4
[1,7,2,8,4,6,5,3] => [1,2,3,1,1] => 11010011 => 5
[6,7,2,8,4,1,5,3] => [3,2,2,1] => 10010101 => 4
[3,6,2,8,4,5,7,1] => [3,4,1] => 10010001 => 3
[2,6,1,8,4,5,7,3] => [3,4,1] => 10010001 => 3
[2,8,4,6,1,5,7,3] => [2,5,1] => 10100001 => 3
[6,3,1,8,4,5,7,2] => [1,2,4,1] => 11010001 => 4
[3,1,6,8,4,5,7,2] => [2,5,1] => 10100001 => 3
[2,3,6,8,4,5,7,1] => [7,1] => 10000001 => 2
[6,3,7,8,4,1,5,2] => [1,4,2,1] => 11000101 => 4
[1,3,7,8,4,6,5,2] => [1,5,1,1] => 11000011 => 4
[1,5,7,8,2,4,6,3] => [1,6,1] => 11000001 => 3
[5,1,7,8,2,4,6,3] => [2,5,1] => 10100001 => 3
[3,6,7,8,4,2,5,1] => [5,2,1] => 10000101 => 3
[7,6,1,8,4,2,5,3] => [1,2,2,2,1] => 11010101 => 5
[5,6,8,7,3,2,1,4] => [3,2,1,2] => 10010110 => 4
[2,8,3,7,1,6,5,4] => [3,3,1,1] => 10010011 => 4
[5,2,8,7,3,6,1,4] => [2,1,3,2] => 10110010 => 4
[7,2,1,8,4,6,5,3] => [2,1,3,1,1] => 10110011 => 5
[3,2,7,8,4,6,5,1] => [2,4,1,1] => 10100011 => 4
[5,2,7,8,1,4,6,3] => [2,5,1] => 10100001 => 3
[1,2,7,8,5,4,6,3] => [2,3,2,1] => 10100101 => 4
[4,2,1,3,8,5,6,7] => [2,2,4] => 10101000 => 3
[7,2,5,8,3,4,6,1] => [2,5,1] => 10100001 => 3
[6,2,8,5,4,3,1,7] => [2,1,2,1,2] => 10110110 => 5
[2,8,3,5,4,1,6,7] => [3,2,3] => 10010100 => 3
[2,8,4,5,3,1,6,7] => [2,3,3] => 10100100 => 3
[6,4,8,5,2,3,1,7] => [1,2,3,2] => 11010010 => 4
[7,3,5,8,2,4,6,1] => [1,6,1] => 11000001 => 3
[4,3,1,2,8,5,6,7] => [1,3,4] => 11001000 => 3
[3,4,2,1,8,5,6,7] => [3,1,4] => 10011000 => 3
[2,7,6,8,4,3,5,1] => [2,3,2,1] => 10100101 => 4
[5,7,1,8,3,4,6,2] => [3,4,1] => 10010001 => 3
[3,7,5,8,1,4,6,2] => [2,5,1] => 10100001 => 3
[1,7,5,8,3,4,6,2] => [1,1,5,1] => 11100001 => 4
[1,6,8,5,4,3,2,7] => [1,2,2,1,2] => 11010110 => 5
[4,6,8,5,1,3,2,7] => [3,3,2] => 10010010 => 3
[5,6,8,1,4,3,2,7] => [5,1,2] => 10000110 => 3
[7,5,8,6,3,4,2,1] => [1,2,3,1,1] => 11010011 => 5
[2,4,8,3,6,5,1,7] => [4,2,2] => 10001010 => 3
[2,8,4,1,5,6,3,7] => [2,4,2] => 10100010 => 3
[4,1,8,3,5,6,2,7] => [2,4,2] => 10100010 => 3
[5,6,8,4,1,3,2,7] => [4,2,2] => 10001010 => 3
[4,6,8,1,5,3,2,7] => [5,1,2] => 10000110 => 3
[1,6,8,4,5,3,2,7] => [1,4,1,2] => 11000110 => 4
[1,7,3,8,5,4,6,2] => [1,2,2,2,1] => 11010101 => 5
[3,7,1,8,5,4,6,2] => [3,2,2,1] => 10010101 => 4
[2,7,3,8,4,6,5,1] => [3,3,1,1] => 10010011 => 4
[7,1,3,8,4,6,5,2] => [3,3,1,1] => 10010011 => 4
[5,7,8,4,3,6,1,2] => [4,2,2] => 10001010 => 3
[2,8,7,4,1,6,5,3] => [2,2,2,1,1] => 10101011 => 5
[2,8,5,4,3,1,6,7] => [2,2,1,3] => 10101100 => 4
[6,5,8,4,2,3,1,7] => [1,3,2,2] => 11001010 => 4
[4,1,3,2,8,5,6,7] => [3,1,4] => 10011000 => 3
[1,4,3,2,8,5,6,7] => [1,2,1,4] => 11011000 => 4
[7,3,2,8,5,4,6,1] => [1,2,2,2,1] => 11010101 => 5
[6,4,8,2,5,3,1,7] => [1,4,1,2] => 11000110 => 4
[2,8,4,3,5,1,6,7] => [2,3,3] => 10100100 => 3
[2,8,3,4,5,1,6,7] => [5,3] => 10000100 => 2
[6,2,8,4,5,3,1,7] => [2,3,1,2] => 10100110 => 4
[7,2,3,8,5,4,6,1] => [3,2,2,1] => 10010101 => 4
[4,2,3,1,8,5,6,7] => [3,1,4] => 10011000 => 3
[3,2,1,4,8,5,6,7] => [2,2,4] => 10101000 => 3
[5,1,3,2,4,8,6,7] => [3,2,3] => 10010100 => 3
[2,8,1,5,3,4,7,6] => [3,4,1] => 10010001 => 3
[1,2,8,4,5,3,7,6] => [2,3,2,1] => 10100101 => 4
[1,4,2,8,5,3,6,7] => [1,2,2,3] => 11010100 => 4
[1,8,4,2,5,3,6,7] => [1,1,3,3] => 11100100 => 4
[8,1,5,3,2,4,6,7] => [2,2,4] => 10101000 => 3
[3,8,1,5,2,4,6,7] => [3,5] => 10010000 => 2
[3,5,1,4,8,2,6,7] => [4,4] => 10001000 => 2
[1,5,2,8,4,3,6,7] => [1,2,2,3] => 11010100 => 4
[1,2,8,5,4,3,6,7] => [2,1,2,3] => 10110100 => 4
[1,2,5,4,3,8,6,7] => [2,2,1,3] => 10101100 => 4
[1,2,4,8,5,3,7,6] => [2,3,2,1] => 10100101 => 4
[1,2,7,4,8,5,3,6] => [2,2,2,2] => 10101010 => 4
[1,5,2,7,8,4,3,6] => [1,2,3,2] => 11010010 => 4
[5,1,2,7,4,8,3,6] => [3,2,3] => 10010100 => 3
[8,3,5,1,4,7,2,6] => [1,4,3] => 11000100 => 3
[2,8,1,5,4,7,3,6] => [3,2,3] => 10010100 => 3
[1,2,8,5,7,4,3,6] => [2,1,3,2] => 10110010 => 4
[1,2,4,8,7,5,3,6] => [2,2,2,2] => 10101010 => 4
[2,8,1,4,3,7,6,5] => [4,1,2,1] => 10001101 => 4
[6,1,2,8,7,4,3,5] => [3,1,2,2] => 10011010 => 4
[6,4,1,2,8,7,3,5] => [1,3,1,3] => 11001100 => 4
[3,6,4,8,1,7,2,5] => [2,3,3] => 10100100 => 3
[7,6,1,4,2,8,3,5] => [1,3,1,3] => 11001100 => 4
[7,1,6,2,8,4,3,5] => [2,2,2,2] => 10101010 => 4
[1,6,7,2,8,4,3,5] => [1,3,2,2] => 11001010 => 4
[6,7,1,4,2,8,3,5] => [4,1,3] => 10001100 => 3
[6,3,7,1,4,8,2,5] => [1,4,3] => 11000100 => 3
[3,7,8,1,5,2,4,6] => [5,3] => 10000100 => 2
[7,1,2,8,5,3,4,6] => [3,2,3] => 10010100 => 3
[1,7,2,8,4,5,3,6] => [1,2,3,2] => 11010010 => 4
[1,4,2,7,8,5,3,6] => [1,2,3,2] => 11010010 => 4
[6,1,2,8,4,3,7,5] => [3,2,2,1] => 10010101 => 4
[6,4,1,2,8,3,7,5] => [1,3,3,1] => 11001001 => 4
[7,6,1,3,2,4,8,5] => [1,3,2,2] => 11001010 => 4
[6,7,1,3,2,4,8,5] => [4,2,2] => 10001010 => 3
[1,2,7,3,5,8,4,6] => [2,3,3] => 10100100 => 3
[1,2,7,5,8,3,4,6] => [2,1,5] => 10110000 => 3
[5,8,1,3,7,2,4,6] => [4,4] => 10001000 => 2
[1,2,5,8,7,3,4,6] => [2,2,4] => 10101000 => 3
[1,2,5,8,3,7,4,6] => [2,3,3] => 10100100 => 3
[2,8,1,7,3,5,4,6] => [3,3,2] => 10010010 => 3
[8,6,1,3,2,4,7,5] => [1,3,3,1] => 11001001 => 4
[4,2,8,1,7,3,6,5] => [2,2,3,1] => 10101001 => 4
[2,8,1,7,4,3,6,5] => [3,2,2,1] => 10010101 => 4
[7,1,2,8,4,3,6,5] => [3,2,2,1] => 10010101 => 4
[1,2,8,4,7,5,3,6] => [2,2,2,2] => 10101010 => 4
[1,2,8,7,4,5,3,6] => [2,1,3,2] => 10110010 => 4
[2,8,1,7,5,3,4,6] => [3,2,3] => 10010100 => 3
[8,3,7,1,5,2,4,6] => [1,4,3] => 11000100 => 3
[3,8,6,1,4,7,2,5] => [2,3,3] => 10100100 => 3
[8,6,1,4,2,7,3,5] => [1,3,1,3] => 11001100 => 4
[8,1,6,2,7,4,3,5] => [2,2,2,2] => 10101010 => 4
[7,1,2,8,6,4,3,5] => [3,1,2,2] => 10011010 => 4
[7,4,1,2,8,6,3,5] => [1,3,2,2] => 11001010 => 4
[3,7,4,8,1,6,2,5] => [2,4,2] => 10100010 => 3
[3,4,8,7,1,6,2,5] => [3,3,2] => 10010010 => 3
[4,2,8,1,7,6,3,5] => [2,2,2,2] => 10101010 => 4
[2,8,1,7,6,4,3,5] => [3,1,2,2] => 10011010 => 4
[7,8,3,4,1,5,2,6] => [4,2,2] => 10001010 => 3
[7,8,3,4,1,6,2,5] => [4,2,2] => 10001010 => 3
[6,8,3,4,1,7,2,5] => [4,1,3] => 10001100 => 3
[6,7,3,4,1,8,2,5] => [4,1,3] => 10001100 => 3
[5,7,3,4,1,8,2,6] => [4,1,3] => 10001100 => 3
[5,8,3,4,1,7,2,6] => [4,1,3] => 10001100 => 3
[5,8,3,4,1,6,2,7] => [4,2,2] => 10001010 => 3
[6,8,3,4,1,5,2,7] => [4,2,2] => 10001010 => 3
[6,7,3,4,1,5,2,8] => [4,2,2] => 10001010 => 3
[5,7,3,4,1,6,2,8] => [4,2,2] => 10001010 => 3
[5,6,2,8,3,4,1,7] => [3,3,2] => 10010010 => 3
[5,6,2,7,3,4,1,8] => [3,3,2] => 10010010 => 3
[4,6,2,8,3,5,1,7] => [3,3,2] => 10010010 => 3
[4,7,3,5,1,6,2,8] => [3,3,2] => 10010010 => 3
[4,8,3,5,1,6,2,7] => [3,3,2] => 10010010 => 3
[4,8,3,5,1,7,2,6] => [3,2,3] => 10010100 => 3
[4,7,3,5,1,8,2,6] => [3,2,3] => 10010100 => 3
[5,6,2,3,1,7,4,8] => [4,1,3] => 10001100 => 3
[5,6,2,4,1,8,3,7] => [4,1,3] => 10001100 => 3
[5,6,2,4,1,7,3,8] => [4,1,3] => 10001100 => 3
[4,6,2,5,1,7,3,8] => [3,2,3] => 10010100 => 3
[4,6,2,5,1,8,3,7] => [3,2,3] => 10010100 => 3
[4,5,1,8,3,7,2,6] => [3,2,3] => 10010100 => 3
[4,5,1,7,3,8,2,6] => [3,2,3] => 10010100 => 3
[4,6,2,7,3,8,1,5] => [3,2,3] => 10010100 => 3
[5,6,2,7,3,8,1,4] => [3,2,3] => 10010100 => 3
[5,6,2,7,4,8,1,3] => [3,2,3] => 10010100 => 3
[5,6,3,8,4,7,1,2] => [3,2,3] => 10010100 => 3
[5,6,2,8,4,7,1,3] => [3,2,3] => 10010100 => 3
[5,6,2,8,3,7,1,4] => [3,2,3] => 10010100 => 3
[4,6,2,8,3,7,1,5] => [3,2,3] => 10010100 => 3
[4,5,1,7,3,6,2,8] => [3,3,2] => 10010010 => 3
[4,5,1,8,3,6,2,7] => [3,3,2] => 10010010 => 3
[9,2,1,3,4,5,6,7,8] => [2,7] => 101000000 => 2
[9,2,3,1,4,5,6,7,8] => [3,6] => 100100000 => 2
[4,2,3,5,6,7,8,9,1] => [3,6] => 100100000 => 2
[3,4,2,5,6,7,8,9,1] => [3,6] => 100100000 => 2
[2,3,4,5,6,7,8,9,10,11,1] => [11] => 10000000000 => 1
[6,5,3,2,1,4,8,7] => [1,2,1,2,2] => 11011010 => 5
[4,6,3,5,2,1,8,7] => [3,2,1,2] => 10010110 => 4
[8,7,3,5,2,4,1,6] => [1,2,3,2] => 11010010 => 4
[6,8,2,4,5,7,3,1] => [5,2,1] => 10000101 => 3
[8,7,2,4,5,3,1,6] => [1,4,1,2] => 11000110 => 4
[3,6,1,4,5,2,8,7] => [5,1,2] => 10000110 => 3
[8,3,7,4,5,2,1,6] => [1,4,1,2] => 11000110 => 4
[6,3,8,4,5,7,2,1] => [1,4,2,1] => 11000101 => 4
[5,8,7,4,3,6,2,1] => [2,2,2,1,1] => 10101011 => 5
[2,8,7,4,3,6,1,5] => [2,2,2,2] => 10101010 => 4
[8,1,7,4,3,6,2,5] => [2,2,2,2] => 10101010 => 4
[8,7,3,5,1,4,2,6] => [1,2,3,2] => 11010010 => 4
[2,1,6,8,5,7,4,3] => [2,3,2,1] => 10100101 => 4
[6,8,3,5,1,7,4,2] => [3,2,2,1] => 10010101 => 4
[5,1,8,4,7,6,3,2] => [2,2,2,1,1] => 10101011 => 5
[2,5,8,4,7,6,3,1] => [4,2,1,1] => 10001011 => 4
[4,3,8,1,5,6,7,2] => [1,6,1] => 11000001 => 3
[4,8,1,3,5,6,7,2] => [7,1] => 10000001 => 2
[5,8,7,4,1,6,3,2] => [2,2,2,1,1] => 10101011 => 5
[5,8,3,6,1,4,7,2] => [3,4,1] => 10010001 => 3
[4,8,3,6,1,2,7,5] => [3,4,1] => 10010001 => 3
[3,8,7,4,1,6,2,5] => [2,2,2,2] => 10101010 => 4
[3,8,1,2,5,6,7,4] => [7,1] => 10000001 => 2
[8,7,1,4,2,6,3,5] => [1,3,2,2] => 11001010 => 4
[8,6,3,1,2,4,7,5] => [1,2,4,1] => 11010001 => 4
[8,1,7,4,5,2,3,6] => [2,3,3] => 10100100 => 3
[2,8,7,4,5,1,3,6] => [2,3,3] => 10100100 => 3
[8,7,2,4,1,6,3,5] => [1,3,2,2] => 11001010 => 4
[5,8,3,6,2,4,7,1] => [3,4,1] => 10010001 => 3
[8,6,3,2,1,4,7,5] => [1,2,1,3,1] => 11011001 => 5
[8,7,3,5,2,1,4,6] => [1,2,2,3] => 11010100 => 4
[5,8,3,6,2,1,7,4] => [3,2,2,1] => 10010101 => 4
[5,8,7,4,2,6,1,3] => [2,2,2,2] => 10101010 => 4
[2,6,8,4,5,7,1,3] => [5,3] => 10000100 => 2
[6,1,8,4,5,7,2,3] => [2,3,3] => 10100100 => 3
[6,8,3,5,1,7,2,4] => [3,2,3] => 10010100 => 3
[2,1,5,8,3,6,7,4] => [2,5,1] => 10100001 => 3
[5,8,3,6,1,2,7,4] => [3,4,1] => 10010001 => 3
[4,1,8,2,5,6,7,3] => [2,5,1] => 10100001 => 3
[2,4,8,1,5,6,7,3] => [7,1] => 10000001 => 2
[4,8,2,1,5,6,7,3] => [3,4,1] => 10010001 => 3
[3,4,8,2,5,6,7,1] => [7,1] => 10000001 => 2
[5,8,1,4,7,6,2,3] => [4,2,2] => 10001010 => 3
[5,8,3,1,6,2,7,4] => [3,1,3,1] => 10011001 => 4
[4,5,3,8,6,1,7,2] => [3,1,3,1] => 10011001 => 4
[3,4,1,8,5,6,7,2] => [3,4,1] => 10010001 => 3
[2,4,6,8,10,1,3,5,7,9] => [10] => 1000000000 => 1
[2,4,6,9,10,1,3,5,7,8] => [10] => 1000000000 => 1
[2,4,7,8,10,1,3,5,6,9] => [10] => 1000000000 => 1
[2,4,7,9,10,1,3,5,6,8] => [10] => 1000000000 => 1
[2,4,8,9,10,1,3,5,6,7] => [10] => 1000000000 => 1
[2,5,6,8,10,1,3,4,7,9] => [10] => 1000000000 => 1
[2,5,6,9,10,1,3,4,7,8] => [10] => 1000000000 => 1
[2,5,7,8,10,1,3,4,6,9] => [10] => 1000000000 => 1
[2,5,7,9,10,1,3,4,6,8] => [10] => 1000000000 => 1
[2,5,8,9,10,1,3,4,6,7] => [10] => 1000000000 => 1
[2,6,7,8,10,1,3,4,5,9] => [10] => 1000000000 => 1
[2,6,7,9,10,1,3,4,5,8] => [10] => 1000000000 => 1
[2,6,8,9,10,1,3,4,5,7] => [10] => 1000000000 => 1
[2,7,8,9,10,1,3,4,5,6] => [10] => 1000000000 => 1
[3,4,6,8,10,1,2,5,7,9] => [10] => 1000000000 => 1
[3,4,6,9,10,1,2,5,7,8] => [10] => 1000000000 => 1
[3,4,7,8,10,1,2,5,6,9] => [10] => 1000000000 => 1
[3,4,7,9,10,1,2,5,6,8] => [10] => 1000000000 => 1
[3,4,8,9,10,1,2,5,6,7] => [10] => 1000000000 => 1
[3,5,6,8,10,1,2,4,7,9] => [10] => 1000000000 => 1
[3,5,6,9,10,1,2,4,7,8] => [10] => 1000000000 => 1
[3,5,7,8,10,1,2,4,6,9] => [10] => 1000000000 => 1
[3,5,7,9,10,1,2,4,6,8] => [10] => 1000000000 => 1
[3,5,8,9,10,1,2,4,6,7] => [10] => 1000000000 => 1
[3,6,7,8,10,1,2,4,5,9] => [10] => 1000000000 => 1
[3,6,7,9,10,1,2,4,5,8] => [10] => 1000000000 => 1
[3,6,8,9,10,1,2,4,5,7] => [10] => 1000000000 => 1
[3,7,8,9,10,1,2,4,5,6] => [10] => 1000000000 => 1
[4,5,6,8,10,1,2,3,7,9] => [10] => 1000000000 => 1
[4,5,6,9,10,1,2,3,7,8] => [10] => 1000000000 => 1
[4,5,7,8,10,1,2,3,6,9] => [10] => 1000000000 => 1
[4,5,7,9,10,1,2,3,6,8] => [10] => 1000000000 => 1
[4,5,8,9,10,1,2,3,6,7] => [10] => 1000000000 => 1
[4,6,7,8,10,1,2,3,5,9] => [10] => 1000000000 => 1
[4,6,7,9,10,1,2,3,5,8] => [10] => 1000000000 => 1
[4,6,8,9,10,1,2,3,5,7] => [10] => 1000000000 => 1
[4,7,8,9,10,1,2,3,5,6] => [10] => 1000000000 => 1
[5,6,7,8,10,1,2,3,4,9] => [10] => 1000000000 => 1
[5,6,7,9,10,1,2,3,4,8] => [10] => 1000000000 => 1
[5,6,8,9,10,1,2,3,4,7] => [10] => 1000000000 => 1
[5,7,8,9,10,1,2,3,4,6] => [10] => 1000000000 => 1
[4,5,7,6,2,3,8,1] => [3,3,2] => 10010010 => 3
[3,5,7,2,6,4,8,1] => [4,2,2] => 10001010 => 3
[2,5,7,3,6,4,8,1] => [4,2,2] => 10001010 => 3
[1,5,7,3,6,8,4,2] => [1,3,3,1] => 11001001 => 4
[8,4,3,7,6,1,5,2] => [1,2,1,3,1] => 11011001 => 5
[6,7,2,3,5,4,8,1] => [5,1,2] => 10000110 => 3
[5,2,7,3,6,4,8,1] => [2,2,2,2] => 10101010 => 4
[8,3,4,7,6,1,5,2] => [1,3,3,1] => 11001001 => 4
[8,2,4,7,1,6,5,3] => [2,4,1,1] => 10100011 => 4
[3,1,4,7,6,8,5,2] => [2,2,3,1] => 10101001 => 4
[4,1,3,7,6,8,5,2] => [3,1,3,1] => 10011001 => 4
[5,1,7,3,6,8,4,2] => [2,2,3,1] => 10101001 => 4
[6,7,1,3,5,8,4,2] => [5,2,1] => 10000101 => 3
[5,8,7,3,6,1,4,2] => [2,2,3,1] => 10101001 => 4
[4,8,3,7,6,1,5,2] => [3,1,3,1] => 10011001 => 4
[3,8,4,7,6,1,5,2] => [2,2,3,1] => 10101001 => 4
[2,8,4,7,1,6,5,3] => [2,4,1,1] => 10100011 => 4
[8,1,4,7,2,6,5,3] => [2,4,1,1] => 10100011 => 4
[8,1,3,2,7,6,5,4] => [3,1,2,1,1] => 10011011 => 5
[2,8,3,1,7,6,5,4] => [3,1,2,1,1] => 10011011 => 5
[3,8,2,1,7,6,5,4] => [3,1,2,1,1] => 10011011 => 5
[6,7,1,2,8,5,4,3] => [4,2,1,1] => 10001011 => 4
[8,2,3,1,7,6,5,4] => [3,1,2,1,1] => 10011011 => 5
[8,3,2,1,7,6,5,4] => [1,2,1,2,1,1] => 11011011 => 6
[3,4,1,7,6,8,5,2] => [3,1,3,1] => 10011001 => 4
[1,4,2,7,8,6,5,3] => [1,2,3,1,1] => 11010011 => 5
[8,4,2,7,1,6,5,3] => [1,2,3,1,1] => 11010011 => 5
[8,5,7,2,1,6,4,3] => [1,3,2,1,1] => 11001011 => 5
[1,5,7,2,8,6,4,3] => [1,3,2,1,1] => 11001011 => 5
[2,5,7,1,8,6,4,3] => [4,2,1,1] => 10001011 => 4
[3,5,7,1,6,8,4,2] => [4,3,1] => 10001001 => 3
[6,7,4,5,8,1,3,2] => [2,5,1] => 10100001 => 3
[5,4,7,6,8,1,3,2] => [1,2,4,1] => 11010001 => 4
[2,5,7,8,1,6,4,3] => [6,1,1] => 10000011 => 3
[1,5,7,8,2,6,4,3] => [1,5,1,1] => 11000011 => 4
[8,5,7,1,2,6,4,3] => [1,5,1,1] => 11000011 => 4
[8,4,1,7,2,6,5,3] => [1,2,3,1,1] => 11010011 => 5
[1,4,8,7,2,6,5,3] => [1,2,3,1,1] => 11010011 => 5
[3,4,8,7,6,1,5,2] => [3,1,3,1] => 10011001 => 4
[4,3,8,7,6,1,5,2] => [1,2,1,3,1] => 11011001 => 5
[5,3,7,8,6,1,4,2] => [1,3,3,1] => 11001001 => 4
[6,7,2,8,1,5,4,3] => [3,3,1,1] => 10010011 => 4
[5,2,7,8,1,6,4,3] => [2,4,1,1] => 10100011 => 4
[4,2,8,7,1,6,5,3] => [2,1,3,1,1] => 10110011 => 5
[3,2,8,1,7,6,5,4] => [2,2,2,1,1] => 10101011 => 5
[1,3,8,2,7,6,5,4] => [1,3,2,1,1] => 11001011 => 5
[8,3,1,2,7,6,5,4] => [1,3,2,1,1] => 11001011 => 5
[8,2,1,3,7,6,5,4] => [2,2,2,1,1] => 10101011 => 5
[1,2,8,3,7,6,5,4] => [2,2,2,1,1] => 10101011 => 5
[2,1,8,3,7,6,5,4] => [2,2,2,1,1] => 10101011 => 5
[4,1,8,7,2,6,5,3] => [2,1,3,1,1] => 10110011 => 5
[5,1,7,8,2,6,4,3] => [2,4,1,1] => 10100011 => 4
[6,7,1,8,2,5,4,3] => [3,3,1,1] => 10010011 => 4
[5,8,7,1,2,6,4,3] => [2,4,1,1] => 10100011 => 4
[4,8,1,7,2,6,5,3] => [3,3,1,1] => 10010011 => 4
[3,8,1,2,7,6,5,4] => [4,2,1,1] => 10001011 => 4
[2,8,1,3,7,6,5,4] => [4,2,1,1] => 10001011 => 4
[1,8,2,3,7,6,5,4] => [1,3,2,1,1] => 11001011 => 5
[8,1,2,3,7,6,5,4] => [4,2,1,1] => 10001011 => 4
[2,3,4,5,6,7,8,9,11,1,10] => [11] => 10000000000 => 1
[6,7,1,8,4,5,2,3] => [3,3,2] => 10010010 => 3
[3,7,1,5,8,2,6,4] => [3,4,1] => 10010001 => 3
[2,7,1,5,8,3,6,4] => [3,4,1] => 10010001 => 3
[2,6,5,1,8,3,7,4] => [2,2,3,1] => 10101001 => 4
[3,6,5,1,8,2,7,4] => [2,2,3,1] => 10101001 => 4
[4,6,5,1,8,7,2,3] => [2,2,1,3] => 10101100 => 4
[5,6,4,1,8,7,2,3] => [2,2,1,3] => 10101100 => 4
[8,1,4,5,7,6,2,3] => [2,4,2] => 10100010 => 3
[6,4,5,1,8,7,2,3] => [1,3,1,3] => 11001100 => 4
[5,4,6,1,8,7,2,3] => [1,3,1,3] => 11001100 => 4
[4,5,6,1,8,7,2,3] => [4,1,3] => 10001100 => 3
[3,5,6,1,8,2,7,4] => [4,3,1] => 10001001 => 3
[2,5,6,1,8,3,7,4] => [4,3,1] => 10001001 => 3
[2,4,6,1,3,8,7,5] => [5,2,1] => 10000101 => 3
[3,4,6,1,2,8,7,5] => [5,2,1] => 10000101 => 3
[4,3,6,1,2,8,7,5] => [1,4,2,1] => 11000101 => 4
[5,3,6,1,8,2,7,4] => [1,3,3,1] => 11001001 => 4
[7,3,1,5,8,2,6,4] => [1,2,4,1] => 11010001 => 4
[8,1,3,5,7,2,6,4] => [3,4,1] => 10010001 => 3
[8,1,2,5,7,3,6,4] => [3,4,1] => 10010001 => 3
[7,2,1,5,8,3,6,4] => [2,1,4,1] => 10110001 => 4
[6,2,5,1,8,3,7,4] => [2,2,3,1] => 10101001 => 4
[4,2,6,1,3,8,7,5] => [2,3,2,1] => 10100101 => 4
[2,3,6,1,4,8,7,5] => [5,2,1] => 10000101 => 3
[4,2,5,3,1,8,7,6] => [2,2,1,2,1] => 10101101 => 5
[6,2,4,1,3,8,7,5] => [2,3,2,1] => 10100101 => 4
[7,2,1,4,3,8,6,5] => [2,2,1,2,1] => 10101101 => 5
[8,1,2,4,3,7,6,5] => [4,1,2,1] => 10001101 => 4
[8,1,3,4,2,7,6,5] => [4,1,2,1] => 10001101 => 4
[7,3,1,4,2,8,6,5] => [1,3,1,2,1] => 11001101 => 5
[6,3,4,1,2,8,7,5] => [1,4,2,1] => 11000101 => 4
[4,6,3,1,2,8,7,5] => [3,2,2,1] => 10010101 => 4
[3,6,4,1,2,8,7,5] => [2,3,2,1] => 10100101 => 4
[2,6,4,1,3,8,7,5] => [2,3,2,1] => 10100101 => 4
[2,7,1,4,3,8,6,5] => [4,1,2,1] => 10001101 => 4
[3,7,1,4,2,8,6,5] => [4,1,2,1] => 10001101 => 4
[4,7,1,3,2,8,6,5] => [4,1,2,1] => 10001101 => 4
[8,1,6,7,2,3,5,4] => [2,5,1] => 10100001 => 3
[4,7,1,2,3,8,6,5] => [5,2,1] => 10000101 => 3
[3,7,1,2,4,8,6,5] => [5,2,1] => 10000101 => 3
[2,7,1,3,4,8,6,5] => [5,2,1] => 10000101 => 3
[2,6,3,1,4,8,7,5] => [3,2,2,1] => 10010101 => 4
[3,6,2,1,4,8,7,5] => [3,2,2,1] => 10010101 => 4
[5,6,2,1,8,3,7,4] => [3,1,3,1] => 10011001 => 4
[6,5,2,1,8,3,7,4] => [1,2,1,3,1] => 11011001 => 5
[8,1,5,2,7,3,6,4] => [2,2,3,1] => 10101001 => 4
[8,1,4,2,3,7,6,5] => [2,3,2,1] => 10100101 => 4
[7,4,1,2,3,8,6,5] => [1,4,2,1] => 11000101 => 4
[6,4,2,1,3,8,7,5] => [1,2,2,2,1] => 11010101 => 5
[5,4,2,3,1,8,7,6] => [1,3,1,2,1] => 11001101 => 5
[3,5,2,4,1,8,7,6] => [4,1,2,1] => 10001101 => 4
[6,3,2,1,4,8,7,5] => [1,2,2,2,1] => 11010101 => 5
[7,3,1,2,4,8,6,5] => [1,4,2,1] => 11000101 => 4
[8,1,3,2,4,7,6,5] => [3,2,2,1] => 10010101 => 4
[8,1,2,3,4,7,6,5] => [5,2,1] => 10000101 => 3
[7,2,1,3,4,8,6,5] => [2,3,2,1] => 10100101 => 4
[6,2,3,1,4,8,7,5] => [3,2,2,1] => 10010101 => 4
[2,4,3,6,1,5,8,7] => [3,3,2] => 10010010 => 3
[2,4,3,6,5,8,1,7] => [3,2,3] => 10010100 => 3
[2,4,6,3,5,8,7,1] => [5,2,1] => 10000101 => 3
[2,4,6,3,5,8,1,7] => [5,3] => 10000100 => 2
[2,4,6,3,5,1,8,7] => [5,1,2] => 10000110 => 3
[2,4,6,3,1,5,8,7] => [4,2,2] => 10001010 => 3
[2,4,1,6,5,3,8,7] => [3,2,1,2] => 10010110 => 4
[2,4,6,1,5,3,8,7] => [5,1,2] => 10000110 => 3
[4,2,6,5,3,1,8,7] => [2,1,2,1,2] => 10110110 => 5
[4,2,6,5,1,3,8,7] => [2,1,3,2] => 10110010 => 4
[4,2,6,5,1,8,7,3] => [2,1,2,2,1] => 10110101 => 5
[4,2,6,5,8,1,7,3] => [2,1,4,1] => 10110001 => 4
[4,2,6,5,8,1,3,7] => [2,1,5] => 10110000 => 3
[4,2,6,5,8,3,1,7] => [2,1,3,2] => 10110010 => 4
[2,4,6,1,5,8,3,7] => [5,3] => 10000100 => 2
[2,4,1,6,5,8,3,7] => [3,2,3] => 10010100 => 3
[2,1,4,6,5,8,3,7] => [2,3,3] => 10100100 => 3
[2,4,1,6,5,8,7,3] => [3,2,2,1] => 10010101 => 4
[2,4,6,1,5,8,7,3] => [5,2,1] => 10000101 => 3
[4,2,6,5,3,8,7,1] => [2,1,2,2,1] => 10110101 => 5
[4,2,6,5,8,3,7,1] => [2,1,4,1] => 10110001 => 4
[2,6,4,3,8,7,1,5] => [2,2,1,3] => 10101100 => 4
[2,6,4,3,8,7,5,1] => [2,2,1,2,1] => 10101101 => 5
[4,2,6,8,5,3,7,1] => [2,3,2,1] => 10100101 => 4
[2,4,6,8,1,5,7,3] => [7,1] => 10000001 => 2
[2,4,6,1,8,5,7,3] => [4,3,1] => 10001001 => 3
[2,4,1,6,8,5,7,3] => [3,4,1] => 10010001 => 3
[2,1,4,6,8,5,7,3] => [2,5,1] => 10100001 => 3
[2,1,4,6,8,5,3,7] => [2,4,2] => 10100010 => 3
[2,4,1,6,8,5,3,7] => [3,3,2] => 10010010 => 3
[2,4,6,1,8,5,3,7] => [4,2,2] => 10001010 => 3
[2,4,6,8,1,5,3,7] => [6,2] => 10000010 => 2
[4,2,6,8,5,3,1,7] => [2,3,1,2] => 10100110 => 4
[4,2,6,8,5,1,3,7] => [2,3,3] => 10100100 => 3
[4,2,6,8,5,1,7,3] => [2,3,2,1] => 10100101 => 4
[2,4,6,8,3,5,7,1] => [7,1] => 10000001 => 2
[2,4,6,8,3,5,1,7] => [6,2] => 10000010 => 2
[2,4,6,8,3,1,5,7] => [5,3] => 10000100 => 2
[2,4,6,3,1,8,5,7] => [4,1,3] => 10001100 => 3
[2,4,6,3,8,1,5,7] => [4,4] => 10001000 => 2
[2,4,6,3,8,5,1,7] => [4,2,2] => 10001010 => 3
[2,4,6,3,8,5,7,1] => [4,3,1] => 10001001 => 3
[2,4,3,6,8,5,7,1] => [3,4,1] => 10010001 => 3
[2,4,3,6,8,5,1,7] => [3,3,2] => 10010010 => 3
[2,4,3,6,8,1,5,7] => [3,5] => 10010000 => 2
[2,4,3,6,1,8,5,7] => [3,2,3] => 10010100 => 3
[2,4,3,1,6,8,5,7] => [3,1,4] => 10011000 => 3
[2,4,1,3,6,8,7,5] => [4,3,1] => 10001001 => 3
[2,4,3,6,1,8,7,5] => [3,2,2,1] => 10010101 => 4
[2,4,3,6,8,1,7,5] => [3,4,1] => 10010001 => 3
[4,6,5,2,8,7,3,1] => [2,2,1,2,1] => 10101101 => 5
[4,6,5,2,8,7,1,3] => [2,2,1,3] => 10101100 => 4
[4,6,2,5,8,7,1,3] => [3,2,3] => 10010100 => 3
[4,6,2,5,8,7,3,1] => [3,2,2,1] => 10010101 => 4
[2,4,6,3,8,1,7,5] => [4,3,1] => 10001001 => 3
[2,4,6,3,1,8,7,5] => [4,1,2,1] => 10001101 => 4
[2,4,1,6,3,8,7,5] => [3,2,2,1] => 10010101 => 4
[2,1,4,6,3,8,7,5] => [2,3,2,1] => 10100101 => 4
[2,1,4,6,8,3,7,5] => [2,5,1] => 10100001 => 3
[2,4,1,6,8,3,7,5] => [3,4,1] => 10010001 => 3
[2,4,6,1,8,3,7,5] => [4,3,1] => 10001001 => 3
[2,4,6,8,1,3,7,5] => [7,1] => 10000001 => 2
[2,4,6,8,3,1,7,5] => [5,2,1] => 10000101 => 3
[4,6,2,8,5,7,3,1] => [3,2,2,1] => 10010101 => 4
[4,6,2,8,5,7,1,3] => [3,2,3] => 10010100 => 3
[6,2,4,8,7,1,3,5] => [2,2,4] => 10101000 => 3
[6,4,2,8,7,5,3,1] => [1,2,1,2,1,1] => 11011011 => 6
[2,6,4,8,1,7,5,3] => [2,3,2,1] => 10100101 => 4
[2,6,4,1,8,7,5,3] => [2,2,1,2,1] => 10101101 => 5
[2,6,1,4,8,7,5,3] => [4,1,2,1] => 10001101 => 4
[2,1,6,4,8,7,5,3] => [2,2,1,2,1] => 10101101 => 5
[2,1,6,4,8,7,3,5] => [2,2,1,3] => 10101100 => 4
[2,6,1,4,8,7,3,5] => [4,1,3] => 10001100 => 3
[2,6,4,1,8,7,3,5] => [2,2,1,3] => 10101100 => 4
[2,6,4,8,1,7,3,5] => [2,3,3] => 10100100 => 3
[6,4,2,8,7,5,1,3] => [1,2,1,2,2] => 11011010 => 5
[6,2,4,8,7,3,5,1] => [2,2,3,1] => 10101001 => 4
[6,2,4,8,7,3,1,5] => [2,2,2,2] => 10101010 => 4
[1,6,4,7,3,8,2,5] => [1,1,3,3] => 11100100 => 4
[1,3,7,4,5,8,2,6] => [1,4,3] => 11000100 => 3
[5,2,4,7,3,6,8,1] => [2,4,2] => 10100010 => 3
[1,7,6,3,4,8,2,5] => [1,1,3,3] => 11100100 => 4
[8,1,6,3,7,2,4,5] => [2,2,4] => 10101000 => 3
[7,1,6,3,8,2,4,5] => [2,2,4] => 10101000 => 3
[1,2,7,4,8,3,5,6] => [2,2,4] => 10101000 => 3
[6,1,7,3,4,8,2,5] => [2,3,3] => 10100100 => 3
[2,1,7,4,5,8,3,6] => [2,3,3] => 10100100 => 3
[5,1,4,7,3,8,2,6] => [2,3,3] => 10100100 => 3
[4,3,1,7,5,8,2,6] => [1,2,2,3] => 11010100 => 4
[2,8,6,3,7,1,4,5] => [2,2,4] => 10101000 => 3
[6,8,1,3,7,2,4,5] => [4,4] => 10001000 => 2
[5,8,2,1,7,3,4,6] => [3,1,4] => 10011000 => 3
[5,7,2,1,8,3,4,6] => [3,1,4] => 10011000 => 3
[6,7,1,3,8,2,4,5] => [4,4] => 10001000 => 2
[5,1,2,4,8,3,6,7] => [4,4] => 10001000 => 2
[4,3,6,1,5,8,2,7] => [1,4,3] => 11000100 => 3
[2,6,1,4,5,8,3,7] => [5,3] => 10000100 => 2
[6,5,1,3,4,8,2,7] => [1,4,3] => 11000100 => 3
[1,6,2,4,8,3,5,7] => [1,3,4] => 11001000 => 3
[8,5,1,3,7,2,4,6] => [1,3,4] => 11001000 => 3
[1,5,3,2,8,4,6,7] => [1,2,1,4] => 11011000 => 4
[6,4,2,1,5,8,3,7] => [1,2,2,3] => 11010100 => 4
[2,5,3,4,1,8,6,7] => [4,1,3] => 10001100 => 3
[4,3,5,2,1,8,6,7] => [1,3,1,3] => 11001100 => 4
[2,6,4,8,7,1,3,5] => [2,2,4] => 10101000 => 3
[1,6,4,8,7,2,3,5] => [1,1,2,4] => 11101000 => 4
[2,7,8,3,6,1,4,5] => [4,4] => 10001000 => 2
[4,3,2,8,7,1,5,6] => [1,2,1,4] => 11011000 => 4
[5,2,4,8,7,1,3,6] => [2,2,4] => 10101000 => 3
[6,2,8,3,7,1,4,5] => [2,2,4] => 10101000 => 3
[5,1,4,8,7,2,3,6] => [2,2,4] => 10101000 => 3
[4,8,2,5,1,3,7,6] => [3,4,1] => 10010001 => 3
[4,7,2,5,1,3,8,6] => [3,3,2] => 10010010 => 3
[3,7,2,1,5,4,8,6] => [3,2,1,2] => 10010110 => 4
[3,8,2,1,5,4,7,6] => [3,2,2,1] => 10010101 => 4
[8,3,2,1,5,4,6,7] => [1,2,2,3] => 11010100 => 4
[8,3,2,1,6,4,5,7] => [1,2,1,4] => 11011000 => 4
[8,4,2,5,1,6,3,7] => [1,2,3,2] => 11010010 => 4
[8,3,2,1,5,6,4,7] => [1,2,3,2] => 11010010 => 4
[8,3,2,1,4,6,5,7] => [1,2,3,2] => 11010010 => 4
[3,8,2,1,4,5,7,6] => [3,4,1] => 10010001 => 3
[3,7,2,1,4,5,8,6] => [3,3,2] => 10010010 => 3
[3,2,7,1,4,6,8,5] => [2,4,2] => 10100010 => 3
[3,2,8,1,4,6,7,5] => [2,5,1] => 10100001 => 3
[3,2,8,1,4,7,6,5] => [2,3,2,1] => 10100101 => 4
[3,8,2,1,4,7,5,6] => [3,2,3] => 10010100 => 3
[3,8,2,1,5,7,4,6] => [3,2,3] => 10010100 => 3
[4,8,2,5,1,7,3,6] => [3,2,3] => 10010100 => 3
[4,7,2,5,1,8,3,6] => [3,2,3] => 10010100 => 3
[3,7,2,1,5,8,4,6] => [3,2,3] => 10010100 => 3
[3,7,2,1,4,8,5,6] => [3,2,3] => 10010100 => 3
[3,2,1,7,5,8,6,4] => [2,1,2,2,1] => 10110101 => 5
[3,2,7,1,6,8,4,5] => [2,2,4] => 10101000 => 3
[4,2,7,6,1,8,3,5] => [2,1,2,3] => 10110100 => 4
[4,3,7,6,8,1,2,5] => [1,2,5] => 11010000 => 3
[4,3,8,6,7,1,2,5] => [1,2,5] => 11010000 => 3
[4,2,8,6,1,7,3,5] => [2,1,2,3] => 10110100 => 4
[3,2,8,1,6,7,4,5] => [2,2,4] => 10101000 => 3
[3,2,1,8,7,5,6,4] => [2,1,1,3,1] => 10111001 => 5
[3,8,2,1,7,4,5,6] => [3,1,4] => 10011000 => 3
[3,2,8,1,7,4,6,5] => [2,2,3,1] => 10101001 => 4
[3,2,8,1,6,4,7,5] => [2,2,3,1] => 10101001 => 4
[3,2,7,1,6,4,8,5] => [2,2,2,2] => 10101010 => 4
[4,2,7,6,1,3,8,5] => [2,1,3,2] => 10110010 => 4
[4,2,8,6,1,3,7,5] => [2,1,4,1] => 10110001 => 4
[4,2,8,7,1,3,6,5] => [2,1,4,1] => 10110001 => 4
[5,7,8,3,4,1,2,6] => [5,3] => 10000100 => 2
[4,2,7,8,1,3,6,5] => [2,5,1] => 10100001 => 3
[4,2,6,8,1,3,7,5] => [2,5,1] => 10100001 => 3
[4,2,6,7,1,3,8,5] => [2,4,2] => 10100010 => 3
[3,2,6,1,8,4,7,5] => [2,2,3,1] => 10101001 => 4
[3,7,2,1,8,4,5,6] => [3,1,4] => 10011000 => 3
[3,7,2,1,8,5,4,6] => [3,1,2,2] => 10011010 => 4
[4,7,3,8,5,1,2,6] => [3,2,3] => 10010100 => 3
[4,3,7,8,6,1,2,5] => [1,3,4] => 11001000 => 3
[3,2,7,1,8,6,4,5] => [2,2,2,2] => 10101010 => 4
[3,2,1,6,8,5,7,4] => [2,1,4,1] => 10110001 => 4
[3,2,6,1,8,7,4,5] => [2,2,1,3] => 10101100 => 4
[4,2,6,8,1,7,3,5] => [2,3,3] => 10100100 => 3
[4,3,6,8,7,1,2,5] => [1,3,4] => 11001000 => 3
[4,2,6,7,1,8,3,5] => [2,3,3] => 10100100 => 3
[3,2,6,1,7,8,4,5] => [2,2,4] => 10101000 => 3
[3,4,6,8,7,5,1,2] => [4,2,2] => 10001010 => 3
[5,3,6,4,8,7,1,2] => [1,3,1,3] => 11001100 => 4
[1,4,6,2,7,8,5,3] => [1,3,3,1] => 11001001 => 4
[3,1,8,5,4,2,6,7] => [2,1,2,3] => 10110100 => 4
[1,2,7,5,4,8,6,3] => [2,1,2,2,1] => 10110101 => 5
[6,3,7,5,4,8,1,2] => [1,2,2,3] => 11010100 => 4
[7,3,8,5,4,6,1,2] => [1,2,3,2] => 11010010 => 4
[3,8,7,5,4,6,1,2] => [2,1,3,2] => 10110010 => 4
[4,3,6,7,8,5,1,2] => [1,5,2] => 11000010 => 3
[4,5,6,3,8,7,1,2] => [4,1,3] => 10001100 => 3
[3,6,8,5,4,7,1,2] => [3,2,3] => 10010100 => 3
[6,8,3,5,4,7,1,2] => [3,2,3] => 10010100 => 3
[7,6,3,5,4,8,1,2] => [1,2,2,3] => 11010100 => 4
[1,6,2,5,4,8,7,3] => [1,2,2,2,1] => 11010101 => 5
[7,1,2,5,8,3,6,4] => [3,4,1] => 10010001 => 3
[1,8,2,5,7,3,6,4] => [1,2,4,1] => 11010001 => 4
[6,2,1,5,4,8,7,3] => [2,1,2,2,1] => 10110101 => 5
[4,1,6,2,8,7,5,3] => [2,2,1,2,1] => 10101101 => 5
[7,8,1,2,4,6,5,3] => [6,1,1] => 10000011 => 3
[7,8,3,1,4,2,6,5] => [3,2,2,1] => 10010101 => 4
[4,3,6,1,8,2,7,5] => [1,3,3,1] => 11001001 => 4
[2,3,8,5,4,1,6,7] => [3,2,3] => 10010100 => 3
[4,8,1,5,2,3,7,6] => [3,4,1] => 10010001 => 3
[7,5,1,6,4,3,2,8] => [1,2,2,1,2] => 11010110 => 5
[5,8,1,6,4,3,2,7] => [3,2,1,2] => 10010110 => 4
[6,1,5,7,4,3,2,8] => [2,3,1,2] => 10100110 => 4
[1,5,8,6,4,3,2,7] => [1,2,2,1,2] => 11010110 => 5
[3,4,6,1,5,8,2,7] => [5,3] => 10000100 => 2
[7,8,4,1,5,3,2,6] => [2,3,1,2] => 10100110 => 4
[7,8,5,1,6,3,2,4] => [2,2,2,2] => 10101010 => 4
[2,6,1,5,7,3,8,4] => [3,3,2] => 10010010 => 3
[1,6,8,7,4,3,2,5] => [1,2,2,1,2] => 11010110 => 5
[6,8,1,7,4,3,2,5] => [3,2,1,2] => 10010110 => 4
[5,6,1,7,4,3,2,8] => [3,2,1,2] => 10010110 => 4
[5,1,7,6,4,3,2,8] => [2,1,2,1,2] => 10110110 => 5
[6,1,7,8,4,3,2,5] => [2,3,1,2] => 10100110 => 4
[7,1,8,6,4,3,2,5] => [2,1,2,1,2] => 10110110 => 5
[1,8,7,6,4,3,2,5] => [1,1,1,2,1,2] => 11110110 => 6
[2,1,7,5,6,3,8,4] => [2,1,3,2] => 10110010 => 4
[3,1,6,7,5,8,2,4] => [2,3,3] => 10100100 => 3
[7,8,1,6,5,3,2,4] => [3,2,1,2] => 10010110 => 4
[7,8,2,1,4,5,6,3] => [3,4,1] => 10010001 => 3
[2,8,1,5,4,6,7,3] => [3,4,1] => 10010001 => 3
[7,2,1,5,4,6,8,3] => [2,1,3,2] => 10110010 => 4
[1,2,8,5,6,3,7,4] => [2,1,4,1] => 10110001 => 4
[6,1,2,5,7,3,8,4] => [3,3,2] => 10010010 => 3
[4,2,1,5,6,3,7,8] => [2,1,5] => 10110000 => 3
[4,3,6,1,5,7,2,8] => [1,4,3] => 11000100 => 3
[5,1,6,3,7,8,2,4] => [2,2,4] => 10101000 => 3
[1,3,6,8,5,7,2,4] => [1,4,3] => 11000100 => 3
[2,4,6,3,7,1,8,5] => [4,2,2] => 10001010 => 3
[1,3,6,4,8,7,2,5] => [1,3,1,3] => 11001100 => 4
[4,1,6,7,3,8,2,5] => [2,3,3] => 10100100 => 3
[5,4,6,1,3,7,2,8] => [1,4,3] => 11000100 => 3
[6,4,1,5,2,3,7,8] => [1,2,5] => 11010000 => 3
[4,1,7,5,2,3,8,6] => [2,1,3,2] => 10110010 => 4
[1,2,4,5,8,3,7,6] => [2,5,1] => 10100001 => 3
[7,2,3,5,4,1,8,6] => [3,2,1,2] => 10010110 => 4
[2,8,3,5,4,1,7,6] => [3,2,2,1] => 10010101 => 4
[4,2,6,3,8,1,7,5] => [2,2,3,1] => 10101001 => 4
[7,8,2,3,4,1,6,5] => [5,2,1] => 10000101 => 3
[7,8,1,4,6,3,2,5] => [4,2,2] => 10001010 => 3
[3,1,6,4,7,8,2,5] => [2,2,4] => 10101000 => 3
[1,8,5,7,4,3,2,6] => [1,1,3,1,2] => 11100110 => 5
[7,1,5,8,4,3,2,6] => [2,3,1,2] => 10100110 => 4
[5,1,8,7,4,3,2,6] => [2,1,2,1,2] => 10110110 => 5
[6,5,1,8,4,3,2,7] => [1,2,2,1,2] => 11010110 => 5
[6,5,7,1,4,3,2,8] => [1,4,1,2] => 11000110 => 4
[7,5,8,1,4,3,2,6] => [1,4,1,2] => 11000110 => 4
[5,8,7,1,4,3,2,6] => [2,3,1,2] => 10100110 => 4
[1,5,7,8,4,3,2,6] => [1,4,1,2] => 11000110 => 4
[2,4,7,5,1,3,8,6] => [3,3,2] => 10010010 => 3
[7,8,4,6,1,3,2,5] => [2,4,2] => 10100010 => 3
[7,8,5,4,1,3,2,6] => [2,2,2,2] => 10101010 => 4
[3,5,6,4,1,8,2,7] => [4,1,3] => 10001100 => 3
[2,6,4,5,1,3,8,7] => [2,4,2] => 10100010 => 3
[1,6,5,8,4,3,2,7] => [1,1,3,1,2] => 11100110 => 5
[6,8,5,1,4,3,2,7] => [2,3,1,2] => 10100110 => 4
[7,6,5,1,4,3,2,8] => [1,1,3,1,2] => 11100110 => 5
[1,2,3,4,5,6,9,7,8] => [6,3] => 100000100 => 2
[1,2,3,4,5,8,6,9,7] => [5,2,2] => 100001010 => 3
[1,2,3,4,7,5,8,9,6] => [4,2,3] => 100010100 => 3
[1,2,5,3,6,7,8,9,4] => [2,2,5] => 101010000 => 3
[1,4,2,5,6,7,8,9,3] => [1,2,6] => 110100000 => 3
[9,8,1,2,3,4,5,6,7] => [1,8] => 110000000 => 2
[7,8,9,1,2,3,4,5,6] => [9] => 100000000 => 1
[9,8,7,1,2,3,4,5,6] => [1,1,7] => 111000000 => 3
[6,7,8,9,1,2,3,4,5] => [9] => 100000000 => 1
[9,6,7,8,1,2,3,4,5] => [1,8] => 110000000 => 2
[8,9,6,7,1,2,3,4,5] => [2,7] => 101000000 => 2
[9,8,6,7,1,2,3,4,5] => [1,1,7] => 111000000 => 3
[9,8,7,6,1,2,3,4,5] => [1,1,1,6] => 111100000 => 4
[9,5,6,7,8,1,2,3,4] => [1,8] => 110000000 => 2
[8,9,5,6,7,1,2,3,4] => [2,7] => 101000000 => 2
[9,8,5,6,7,1,2,3,4] => [1,1,7] => 111000000 => 3
[9,7,8,5,6,1,2,3,4] => [1,2,6] => 110100000 => 3
[9,8,7,5,6,1,2,3,4] => [1,1,1,6] => 111100000 => 4
[9,8,7,6,5,1,2,3,4] => [1,1,1,2,4] => 111101000 => 5
[7,8,9,4,5,6,1,2,3] => [6,3] => 100000100 => 2
[8,9,6,7,4,5,1,2,3] => [2,4,3] => 101000100 => 3
[9,8,7,6,4,5,1,2,3] => [1,1,1,3,3] => 111100100 => 5
[9,8,7,6,5,3,4,1,2] => [1,1,1,2,2,2] => 111101010 => 6
[9,8,7,6,5,4,3,1,2] => [1,1,1,2,1,1,2] => 111101110 => 7
[9,10,1,2,3,4,5,6,7,8] => [10] => 1000000000 => 1
[8,9,10,1,2,3,4,5,6,7] => [10] => 1000000000 => 1
[7,8,9,10,1,2,3,4,5,6] => [10] => 1000000000 => 1
[10,9,8,7,6,1,2,3,4,5] => [1,1,1,1,6] => 1111100000 => 5
[10,9,8,7,5,6,1,2,3,4] => [1,1,1,3,4] => 1111001000 => 5
[10,9,8,7,4,5,6,1,2,3] => [1,1,1,4,3] => 1111000100 => 5
[10,9,8,6,7,4,5,1,2,3] => [1,1,1,4,3] => 1111000100 => 5
[10,9,7,8,5,6,3,4,1,2] => [1,1,4,2,2] => 1110001010 => 5
[3,4,6,2,7,1,5,8] => [4,4] => 10001000 => 2
[3,6,2,5,4,1,7,8] => [3,2,3] => 10010100 => 3
[3,2,7,5,4,1,6,8] => [2,1,2,3] => 10110100 => 4
[4,3,6,2,8,1,5,7] => [1,3,4] => 11001000 => 3
[6,1,2,5,4,7,8,3] => [3,2,3] => 10010100 => 3
[6,2,4,5,1,3,7,8] => [2,6] => 10100000 => 2
[4,2,8,5,1,3,7,6] => [2,1,4,1] => 10110001 => 4
[4,3,6,8,1,7,2,5] => [1,4,3] => 11000100 => 3
[5,3,6,4,1,7,2,8] => [1,3,1,3] => 11001100 => 4
[6,2,1,5,8,3,7,4] => [2,1,4,1] => 10110001 => 4
[1,6,7,4,8,3,5,2] => [1,3,3,1] => 11001001 => 4
[1,4,6,3,7,5,8,2] => [1,3,2,2] => 11001010 => 4
[4,6,7,2,5,8,1,3] => [5,3] => 10000100 => 2
[2,4,6,1,7,5,3,8] => [4,2,2] => 10001010 => 3
[2,7,5,4,1,6,3,8] => [2,2,2,2] => 10101010 => 4
[7,5,4,6,2,8,1,3] => [1,1,3,3] => 11100100 => 4
[1,7,5,4,3,8,6,2] => [1,1,2,1,2,1] => 11101101 => 6
[1,4,6,3,5,8,7,2] => [1,4,2,1] => 11000101 => 4
[1,5,8,4,3,6,7,2] => [1,3,3,1] => 11001001 => 4
[5,4,6,2,7,8,1,3] => [1,3,4] => 11001000 => 3
[2,5,4,1,6,7,3,8] => [2,2,4] => 10101000 => 3
[5,6,3,2,7,1,4,8] => [3,1,4] => 10011000 => 3
[5,6,3,2,7,1,8,4] => [3,1,2,2] => 10011010 => 4
[8,5,6,3,2,7,1,4] => [1,3,1,3] => 11001100 => 4
[5,4,6,2,8,1,7,3] => [1,3,3,1] => 11001001 => 4
[2,4,1,7,8,5,3,6] => [3,3,2] => 10010010 => 3
[2,5,4,1,6,3,8,7] => [2,2,2,2] => 10101010 => 4
[5,6,3,2,1,8,4,7] => [3,1,1,3] => 10011100 => 4
[3,5,2,1,6,4,7,8] => [3,1,4] => 10011000 => 3
[6,8,4,3,2,1,5,7] => [2,2,1,3] => 10101100 => 4
[5,3,8,2,1,6,4,7] => [1,3,2,2] => 11001010 => 4
[3,7,5,8,2,1,4,6] => [2,3,3] => 10100100 => 3
[7,3,2,8,5,1,6,4] => [1,2,2,2,1] => 11010101 => 5
[8,4,6,3,2,1,7,5] => [1,3,1,2,1] => 11001101 => 5
[8,6,4,3,2,1,7,5] => [1,1,2,1,2,1] => 11101101 => 6
[7,6,4,3,2,1,8,5] => [1,1,2,1,1,2] => 11101110 => 6
[7,8,4,3,2,1,6,5] => [2,2,1,2,1] => 10101101 => 5
[5,4,7,2,1,8,6,3] => [1,3,1,2,1] => 11001101 => 5
[7,5,8,3,2,6,1,4] => [1,3,2,2] => 11001010 => 4
[5,7,3,2,1,6,8,4] => [3,1,2,2] => 10011010 => 4
[5,7,3,2,1,6,4,8] => [3,1,2,2] => 10011010 => 4
[6,3,7,2,5,1,8,4] => [1,4,1,2] => 11000110 => 4
[6,7,8,3,5,2,1,4] => [5,1,2] => 10000110 => 3
[6,2,5,7,8,4,1,3] => [2,4,2] => 10100010 => 3
[2,1,5,7,8,6,3,4] => [2,4,2] => 10100010 => 3
[3,6,7,2,8,1,4,5] => [4,4] => 10001000 => 2
[6,3,7,2,8,1,4,5] => [1,3,4] => 11001000 => 3
[3,2,6,1,7,4,5,8] => [2,2,4] => 10101000 => 3
[3,5,2,1,4,7,6,8] => [3,2,3] => 10010100 => 3
[7,3,5,2,1,8,4,6] => [1,3,1,3] => 11001100 => 4
[2,5,4,1,3,7,8,6] => [2,3,3] => 10100100 => 3
[2,5,8,4,1,3,7,6] => [4,3,1] => 10001001 => 3
[2,4,1,7,8,3,6,5] => [3,4,1] => 10010001 => 3
[3,7,2,8,6,1,4,5] => [3,1,4] => 10011000 => 3
[3,6,8,2,1,7,4,5] => [4,1,3] => 10001100 => 3
[5,3,8,2,1,4,7,6] => [1,3,3,1] => 11001001 => 4
[4,8,7,3,2,1,5,6] => [2,2,1,3] => 10101100 => 4
[4,7,3,2,1,5,6,8] => [3,1,4] => 10011000 => 3
[8,4,7,3,2,1,5,6] => [1,3,1,3] => 11001100 => 4
[8,3,5,2,1,4,7,6] => [1,3,3,1] => 11001001 => 4
[7,3,2,8,6,1,4,5] => [1,2,1,4] => 11011000 => 4
[3,5,2,1,4,6,8,7] => [3,3,2] => 10010010 => 3
[7,8,6,5,4,3,2,1,9] => [2,1,2,1,1,2] => 101101110 => 6
[6,8,7,5,4,3,2,1,9] => [2,1,2,1,1,2] => 101101110 => 6
[7,8,3,5,4,6,1,2] => [3,3,2] => 10010010 => 3
[8,6,3,7,5,2,4,1] => [1,2,2,2,1] => 11010101 => 5
[5,4,1,6,3,2,8,7] => [1,2,2,1,2] => 11010110 => 5
[5,4,1,6,2,3,8,7] => [1,2,3,2] => 11010010 => 4
[5,7,1,6,2,8,3,4] => [3,2,3] => 10010100 => 3
[5,7,1,6,2,8,4,3] => [3,2,2,1] => 10010101 => 4
[2,7,6,5,1,8,3,4] => [2,1,2,3] => 10110100 => 4
[2,7,6,5,1,8,4,3] => [2,1,2,2,1] => 10110101 => 5
[2,3,6,5,1,4,8,7] => [3,3,2] => 10010010 => 3
[2,3,6,4,1,5,8,7] => [4,2,2] => 10001010 => 3
[2,3,6,1,5,4,8,7] => [5,1,2] => 10000110 => 3
[2,7,6,1,4,8,5,3] => [2,3,2,1] => 10100101 => 4
[2,7,6,1,4,8,3,5] => [2,3,3] => 10100100 => 3
[7,3,5,1,8,4,2,6] => [1,3,2,2] => 11001010 => 4
[7,3,5,1,8,6,4,2] => [1,3,2,1,1] => 11001011 => 5
[2,7,6,1,5,8,4,3] => [2,3,2,1] => 10100101 => 4
[2,7,6,4,1,8,5,3] => [2,2,1,2,1] => 10101101 => 5
[2,1,7,6,3,8,5,4] => [2,1,2,2,1] => 10110101 => 5
[2,1,7,6,3,8,4,5] => [2,1,2,3] => 10110100 => 4
[5,7,3,6,2,8,4,1] => [3,2,2,1] => 10010101 => 4
[2,7,6,4,1,8,3,5] => [2,2,1,3] => 10101100 => 4
[7,3,5,1,8,6,2,4] => [1,3,2,2] => 11001010 => 4
[6,3,5,1,8,2,4,7] => [1,3,4] => 11001000 => 3
[2,3,4,8,7,6,1,5] => [4,2,2] => 10001010 => 3
[2,3,4,8,5,7,1,6] => [5,3] => 10000100 => 2
[7,3,5,4,8,1,2,6] => [1,3,4] => 11001000 => 3
[6,4,3,5,8,7,2,1] => [1,2,2,2,1] => 11010101 => 5
[2,1,4,5,8,7,3,6] => [2,3,3] => 10100100 => 3
[6,4,3,5,8,7,1,2] => [1,2,2,3] => 11010100 => 4
[7,3,5,4,8,1,6,2] => [1,3,3,1] => 11001001 => 4
[2,3,4,8,7,5,6,1] => [4,3,1] => 10001001 => 3
[2,3,4,8,7,5,1,6] => [4,2,2] => 10001010 => 3
[2,7,6,5,4,8,1,3] => [2,1,2,3] => 10110100 => 4
[7,3,5,6,8,4,1,2] => [1,5,2] => 11000010 => 3
[7,3,5,6,8,1,4,2] => [1,6,1] => 11000001 => 3
[7,3,5,6,8,1,2,4] => [1,7] => 11000000 => 2
[6,4,1,5,8,7,2,3] => [1,2,2,3] => 11010100 => 4
[6,4,1,5,8,7,3,2] => [1,2,2,2,1] => 11010101 => 5
[6,4,1,5,8,3,7,2] => [1,2,4,1] => 11010001 => 4
[5,7,1,6,3,8,2,4] => [3,2,3] => 10010100 => 3
[6,4,1,5,8,3,2,7] => [1,2,3,2] => 11010010 => 4
[7,4,1,5,8,2,3,6] => [1,2,5] => 11010000 => 3
[7,4,1,5,8,2,6,3] => [1,2,4,1] => 11010001 => 4
[6,3,5,7,8,2,1,4] => [1,5,2] => 11000010 => 3
[6,3,5,7,8,2,4,1] => [1,6,1] => 11000001 => 3
[2,7,6,4,5,8,3,1] => [2,3,2,1] => 10100101 => 4
[5,7,3,6,1,8,4,2] => [3,2,2,1] => 10010101 => 4
[2,1,4,5,8,6,3,7] => [2,4,2] => 10100010 => 3
[7,3,5,4,8,6,2,1] => [1,3,2,1,1] => 11001011 => 5
[2,3,4,8,5,6,1,7] => [6,2] => 10000010 => 2
[2,3,4,8,7,1,6,5] => [4,3,1] => 10001001 => 3
[2,3,4,8,1,7,6,5] => [5,2,1] => 10000101 => 3
[2,3,4,8,1,6,7,5] => [7,1] => 10000001 => 2
[2,3,4,8,5,1,7,6] => [5,2,1] => 10000101 => 3
[6,3,5,4,8,2,7,1] => [1,3,3,1] => 11001001 => 4
[7,4,3,5,8,2,1,6] => [1,2,3,2] => 11010010 => 4
[2,1,4,5,8,3,7,6] => [2,5,1] => 10100001 => 3
[7,4,3,5,8,2,6,1] => [1,2,4,1] => 11010001 => 4
[6,3,5,4,8,2,1,7] => [1,3,2,2] => 11001010 => 4
[2,3,4,8,5,1,6,7] => [5,3] => 10000100 => 2
[2,3,4,8,1,6,5,7] => [6,2] => 10000010 => 2
[2,3,4,8,1,5,7,6] => [7,1] => 10000001 => 2
[7,8,2,6,1,5,3,4] => [3,3,2] => 10010010 => 3
[7,8,1,6,2,5,3,4] => [3,3,2] => 10010010 => 3
[1,8,6,7,2,5,3,4] => [1,1,4,2] => 11100010 => 4
[1,8,5,7,2,6,3,4] => [1,1,4,2] => 11100010 => 4
[5,8,1,7,2,6,3,4] => [3,3,2] => 10010010 => 3
[5,8,2,7,1,6,3,4] => [3,3,2] => 10010010 => 3
[2,8,6,7,1,5,3,4] => [2,4,2] => 10100010 => 3
[2,8,5,7,1,6,3,4] => [2,4,2] => 10100010 => 3
[2,8,1,7,5,6,3,4] => [3,3,2] => 10010010 => 3
[1,8,2,7,5,6,3,4] => [1,2,3,2] => 11010010 => 4
[1,8,2,7,4,6,3,5] => [1,2,3,2] => 11010010 => 4
[2,8,1,7,4,6,3,5] => [3,3,2] => 10010010 => 3
[2,8,4,7,1,6,3,5] => [2,4,2] => 10100010 => 3
[4,8,2,7,1,6,3,5] => [3,3,2] => 10010010 => 3
[4,8,1,7,2,6,3,5] => [3,3,2] => 10010010 => 3
[1,8,4,7,2,6,3,5] => [1,1,4,2] => 11100010 => 4
[4,8,1,7,5,6,2,3] => [3,3,2] => 10010010 => 3
[1,8,4,7,5,6,2,3] => [1,1,4,2] => 11100010 => 4
[1,8,3,7,5,6,2,4] => [1,2,3,2] => 11010010 => 4
[3,8,1,7,5,6,2,4] => [3,3,2] => 10010010 => 3
[3,8,1,7,4,6,2,5] => [3,3,2] => 10010010 => 3
[1,8,3,7,4,6,2,5] => [1,2,3,2] => 11010010 => 4
[1,8,3,7,2,6,4,5] => [1,2,3,2] => 11010010 => 4
[3,8,1,7,2,6,4,5] => [3,3,2] => 10010010 => 3
[3,8,2,7,1,6,4,5] => [3,3,2] => 10010010 => 3
[3,8,2,7,4,6,1,5] => [3,3,2] => 10010010 => 3
[3,8,2,7,5,6,1,4] => [3,3,2] => 10010010 => 3
[4,8,2,7,5,6,1,3] => [3,3,2] => 10010010 => 3
[4,8,3,7,5,6,1,2] => [3,3,2] => 10010010 => 3
[3,8,4,7,5,6,1,2] => [2,4,2] => 10100010 => 3
[2,8,4,7,5,6,1,3] => [2,4,2] => 10100010 => 3
[2,8,3,7,5,6,1,4] => [3,3,2] => 10010010 => 3
[2,8,3,7,4,6,1,5] => [3,3,2] => 10010010 => 3
[2,8,3,7,1,6,4,5] => [3,3,2] => 10010010 => 3
[2,8,1,7,3,6,4,5] => [3,3,2] => 10010010 => 3
[7,5,2,8,6,4,1,3] => [1,2,1,2,2] => 11011010 => 5
[7,5,1,8,6,2,3,4] => [1,2,1,4] => 11011000 => 4
[7,4,8,6,1,5,2,3] => [1,2,3,2] => 11010010 => 4
[7,1,8,4,5,2,6,3] => [2,3,2,1] => 10100101 => 4
[6,8,1,7,4,2,5,3] => [3,2,2,1] => 10010101 => 4
[1,6,7,4,2,8,5,3] => [1,3,1,2,1] => 11001101 => 5
[1,6,7,3,8,5,2,4] => [1,3,2,2] => 11001010 => 4
[7,1,8,3,5,6,2,4] => [2,4,2] => 10100010 => 3
[7,3,8,6,2,5,1,4] => [1,2,3,2] => 11010010 => 4
[7,4,2,8,6,1,3,5] => [1,2,1,4] => 11011000 => 4
[7,3,1,8,4,2,5,6] => [1,2,2,3] => 11010100 => 4
[7,2,8,4,1,5,3,6] => [2,2,2,2] => 10101010 => 4
[7,2,8,3,5,1,6,4] => [2,3,2,1] => 10100101 => 4
[7,2,8,3,4,6,1,5] => [2,4,2] => 10100010 => 3
[1,5,7,8,2,6,3,4] => [1,5,2] => 11000010 => 3
[6,2,3,8,5,7,4,1] => [3,2,2,1] => 10010101 => 4
[6,2,4,8,5,3,1,7] => [2,3,1,2] => 10100110 => 4
[6,3,1,4,8,5,2,7] => [1,3,2,2] => 11001010 => 4
[2,6,3,7,8,5,4,1] => [3,3,1,1] => 10010011 => 4
[2,6,3,7,8,4,5,1] => [3,4,1] => 10010001 => 3
[2,4,7,3,5,6,8,1] => [6,2] => 10000010 => 2
[2,4,7,3,6,8,5,1] => [4,3,1] => 10001001 => 3
[2,5,3,7,8,1,6,4] => [3,4,1] => 10010001 => 3
[3,1,5,4,7,8,2,6] => [2,2,4] => 10101000 => 3
[5,3,1,4,8,2,6,7] => [1,3,4] => 11001000 => 3
[5,2,4,8,6,1,3,7] => [2,2,4] => 10101000 => 3
[5,2,3,8,4,6,7,1] => [3,4,1] => 10010001 => 3
[4,8,2,3,6,1,7,5] => [4,3,1] => 10001001 => 3
[4,8,2,3,5,7,1,6] => [5,3] => 10000100 => 2
[1,4,7,8,3,6,2,5] => [1,5,2] => 11000010 => 3
[4,8,1,3,6,7,2,5] => [4,4] => 10001000 => 2
[5,3,8,2,4,7,1,6] => [1,4,3] => 11000100 => 3
[5,4,3,8,1,2,7,6] => [1,2,4,1] => 11010001 => 4
[6,4,2,8,1,3,7,5] => [1,2,4,1] => 11010001 => 4
[6,3,8,2,5,1,7,4] => [1,4,2,1] => 11000101 => 4
[6,3,8,1,4,7,2,5] => [1,4,3] => 11000100 => 3
[5,8,1,3,6,2,7,4] => [4,3,1] => 10001001 => 3
[1,5,7,4,2,6,8,3] => [1,3,2,2] => 11001010 => 4
[5,8,1,4,2,6,3,7] => [4,2,2] => 10001010 => 3
[5,8,4,1,2,7,6,3] => [2,3,2,1] => 10100101 => 4
[6,5,1,2,8,7,3,4] => [1,3,1,3] => 11001100 => 4
[6,5,3,1,4,2,8,7] => [1,2,2,1,2] => 11010110 => 5
[5,3,1,6,4,2,7,8] => [1,2,2,3] => 11010100 => 4
[5,2,6,4,1,7,3,8] => [2,2,1,3] => 10101100 => 4
[4,6,1,7,5,2,8,3] => [3,2,1,2] => 10010110 => 4
[4,5,1,7,2,6,3,8] => [3,3,2] => 10010010 => 3
[3,5,6,1,2,8,7,4] => [5,2,1] => 10000101 => 3
[3,5,7,1,8,6,2,4] => [4,2,2] => 10001010 => 3
[3,6,2,7,5,1,8,4] => [3,2,1,2] => 10010110 => 4
[4,2,5,7,1,8,6,3] => [2,3,2,1] => 10100101 => 4
[3,4,7,2,8,6,1,5] => [4,2,2] => 10001010 => 3
[3,4,5,8,2,7,1,6] => [5,3] => 10000100 => 2
[3,4,6,2,8,1,5,7] => [4,4] => 10001000 => 2
[3,5,2,6,8,1,7,4] => [3,4,1] => 10010001 => 3
[4,2,5,6,1,3,8,7] => [2,4,2] => 10100010 => 3
[4,3,1,2,5,6,8,7] => [1,5,2] => 11000010 => 3
[5,3,6,8,4,7,2,1] => [1,4,2,1] => 11000101 => 4
[3,7,2,5,4,8,6,1] => [3,2,2,1] => 10010101 => 4
[8,4,2,5,7,3,6,1] => [1,2,4,1] => 11010001 => 4
[4,7,2,5,8,3,6,1] => [3,4,1] => 10010001 => 3
[5,2,6,8,4,3,7,1] => [2,3,2,1] => 10100101 => 4
[3,1,6,5,4,8,2,7] => [2,1,2,3] => 10110100 => 4
[4,1,6,5,8,3,2,7] => [2,1,3,2] => 10110010 => 4
[5,1,6,8,4,3,2,7] => [2,3,1,2] => 10100110 => 4
[8,5,4,7,6,3,2,1] => [1,1,2,2,1,1] => 11101011 => 6
[5,7,1,8,4,3,2,6] => [3,2,1,2] => 10010110 => 4
[2,7,1,5,4,3,8,6] => [3,2,1,2] => 10010110 => 4
[8,2,1,5,4,3,7,6] => [2,1,2,2,1] => 10110101 => 5
[8,4,1,5,7,3,2,6] => [1,2,3,2] => 11010010 => 4
[8,5,6,7,1,3,2,4] => [1,5,2] => 11000010 => 3
[8,4,6,1,7,3,2,5] => [1,3,2,2] => 11001010 => 4
[8,3,6,1,4,7,2,5] => [1,4,3] => 11000100 => 3
[2,7,6,1,4,3,8,5] => [2,3,1,2] => 10100110 => 4
[6,7,8,5,1,3,2,4] => [3,3,2] => 10010010 => 3
[5,7,6,8,2,3,4,1] => [2,5,1] => 10100001 => 3
[5,7,2,8,4,3,6,1] => [3,2,2,1] => 10010101 => 4
[6,7,8,2,4,3,5,1] => [5,2,1] => 10000101 => 3
[4,7,6,2,8,3,5,1] => [2,2,3,1] => 10101001 => 4
[8,3,6,2,4,7,5,1] => [1,4,2,1] => 11000101 => 4
[3,7,6,2,4,8,5,1] => [2,3,2,1] => 10100101 => 4
[5,7,3,8,4,6,2,1] => [3,3,1,1] => 10010011 => 4
[4,7,3,5,8,6,2,1] => [3,3,1,1] => 10010011 => 4
[8,7,2,1,4,3,6,5] => [1,2,2,2,1] => 11010101 => 5
[8,7,3,1,4,6,2,5] => [1,2,3,2] => 11010010 => 4
[8,7,6,3,2,5,4,1] => [1,1,2,2,1,1] => 11101011 => 6
[8,7,3,5,1,6,2,4] => [1,2,3,2] => 11010010 => 4
[8,7,2,5,1,3,6,4] => [1,2,4,1] => 11010001 => 4
[8,2,6,5,1,3,7,4] => [2,1,4,1] => 10110001 => 4
[8,4,6,5,7,1,2,3] => [1,2,5] => 11010000 => 3
[5,7,6,8,4,1,2,3] => [2,3,3] => 10100100 => 3
[4,7,6,5,8,1,2,3] => [2,1,5] => 10110000 => 3
[3,7,6,5,1,8,2,4] => [2,1,2,3] => 10110100 => 4
[8,1,2,3,4,5,6,7,9] => [9] => 100000000 => 1
[1,9,2,3,4,5,6,7,8] => [1,8] => 110000000 => 2
[9,1,2,3,4,5,6,7,8,10] => [10] => 1000000000 => 1
[7,8,1,2,3,4,5,6,9] => [9] => 100000000 => 1
[1,8,9,2,3,4,5,6,7] => [1,8] => 110000000 => 2
[10,1,2,3,4,5,6,7,8,9,11] => [11] => 10000000000 => 1
[8,9,1,2,3,4,5,6,7,10] => [10] => 1000000000 => 1
[7,1,8,2,3,4,5,6,9] => [2,7] => 101000000 => 2
[6,8,1,2,3,4,5,7,9] => [9] => 100000000 => 1
[1,8,2,9,3,4,5,6,7] => [1,2,6] => 110100000 => 3
[1,7,9,2,3,4,5,6,8] => [1,8] => 110000000 => 2
[3,6,4,8,7,5,1,2] => [2,2,2,2] => 10101010 => 4
[5,6,4,3,8,7,1,2] => [2,2,1,3] => 10101100 => 4
[1,6,2,4,7,8,5,3] => [1,3,3,1] => 11001001 => 4
[3,6,2,4,8,1,5,7] => [4,4] => 10001000 => 2
[3,4,7,2,8,1,6,5] => [4,3,1] => 10001001 => 3
[1,4,7,2,5,8,6,3] => [1,4,2,1] => 11000101 => 4
[7,3,8,4,5,6,1,2] => [1,5,2] => 11000010 => 3
[3,5,6,4,8,7,1,2] => [4,1,3] => 10001100 => 3
[4,6,8,5,3,7,1,2] => [3,2,3] => 10010100 => 3
[6,8,5,3,4,7,1,2] => [2,3,3] => 10100100 => 3
[1,6,5,4,2,8,7,3] => [1,1,2,1,2,1] => 11101101 => 6
[1,8,5,2,7,3,6,4] => [1,1,2,3,1] => 11101001 => 5
[4,2,7,5,1,8,6,3] => [2,1,2,2,1] => 10110101 => 5
[7,8,1,4,2,6,5,3] => [4,2,1,1] => 10001011 => 4
[1,3,6,4,8,2,5,7] => [1,3,4] => 11001000 => 3
[4,1,7,5,3,2,6,8] => [2,1,2,3] => 10110100 => 4
[6,5,1,3,4,2,8,7] => [1,4,1,2] => 11000110 => 4
[4,8,5,3,1,7,2,6] => [2,2,1,3] => 10101100 => 4
[7,4,5,3,2,8,1,6] => [1,3,1,3] => 11001100 => 4
[5,8,3,6,1,4,2,7] => [3,3,2] => 10010010 => 3
[2,5,8,6,4,1,3,7] => [3,2,3] => 10010100 => 3
[1,4,6,2,5,8,3,7] => [1,4,3] => 11000100 => 3
[3,6,2,5,8,1,7,4] => [3,4,1] => 10010001 => 3
[1,6,8,7,4,2,3,5] => [1,2,2,3] => 11010100 => 4
[6,1,7,8,2,4,3,5] => [2,4,2] => 10100010 => 3
[7,1,8,6,3,4,2,5] => [2,1,3,2] => 10110010 => 4
[7,2,1,4,5,6,8,3] => [2,4,2] => 10100010 => 3
[1,2,8,3,6,5,7,4] => [2,2,3,1] => 10101001 => 4
[6,1,3,2,7,5,8,4] => [3,1,2,2] => 10011010 => 4
[1,6,3,8,5,7,2,4] => [1,2,2,3] => 11010100 => 4
[2,6,4,1,7,5,8,3] => [2,2,2,2] => 10101010 => 4
[7,6,5,8,1,4,2,3] => [1,1,4,2] => 11100010 => 4
[5,8,6,7,3,2,1,4] => [2,3,1,2] => 10100110 => 4
[1,6,4,3,7,2,8,5] => [1,1,2,2,2] => 11101010 => 5
[2,6,3,4,8,7,1,5] => [4,1,3] => 10001100 => 3
[7,1,3,4,5,2,8,6] => [5,1,2] => 10000110 => 3
[1,8,3,5,4,2,7,6] => [1,2,2,2,1] => 11010101 => 5
[4,1,6,3,8,2,7,5] => [2,2,3,1] => 10101001 => 4
[7,8,2,4,6,3,1,5] => [4,2,2] => 10001010 => 3
[3,2,6,4,7,8,1,5] => [2,2,4] => 10101000 => 3
[2,8,5,7,4,3,1,6] => [2,3,1,2] => 10100110 => 4
[7,2,5,8,3,4,1,6] => [2,4,2] => 10100010 => 3
[5,3,8,7,1,2,6,4] => [1,2,4,1] => 11010001 => 4
[6,5,3,8,2,1,7,4] => [1,2,2,2,1] => 11010101 => 5
[7,5,8,4,1,2,3,6] => [1,3,4] => 11001000 => 3
[5,8,7,4,1,3,2,6] => [2,2,2,2] => 10101010 => 4
[3,5,7,8,4,1,2,6] => [5,3] => 10000100 => 2
[1,4,7,5,3,8,2,6] => [1,2,2,3] => 11010100 => 4
[2,4,6,7,3,1,8,5] => [5,1,2] => 10000110 => 3
[7,8,4,6,3,1,2,5] => [2,3,3] => 10100100 => 3
[2,6,4,5,3,8,1,7] => [2,3,3] => 10100100 => 3
[3,6,5,8,4,2,1,7] => [2,3,1,2] => 10100110 => 4
[5,6,8,4,2,3,1,7] => [4,2,2] => 10001010 => 3
[6,8,5,4,3,1,2,7] => [2,2,1,3] => 10101100 => 4
[6,1,4,2,8,5,7,3] => [2,2,3,1] => 10101001 => 4
[4,8,6,5,3,2,7,1] => [2,1,2,2,1] => 10110101 => 5
[8,6,5,1,2,4,7,3] => [1,1,5,1] => 11100001 => 4
[6,7,5,8,2,1,4,3] => [2,3,2,1] => 10100101 => 4
[1,7,5,8,2,6,4,3] => [1,1,4,1,1] => 11100011 => 5
[1,3,8,5,7,6,2,4] => [1,2,3,2] => 11010010 => 4
[6,3,8,5,7,1,2,4] => [1,2,5] => 11010000 => 3
[8,3,1,5,6,2,7,4] => [1,2,4,1] => 11010001 => 4
[6,8,5,2,1,4,7,3] => [2,2,3,1] => 10101001 => 4
[3,8,2,5,6,1,7,4] => [3,4,1] => 10010001 => 3
[2,8,1,5,6,3,7,4] => [3,4,1] => 10010001 => 3
[8,1,2,5,6,3,7,4] => [3,4,1] => 10010001 => 3
[1,8,2,5,7,6,3,4] => [1,2,3,2] => 11010010 => 4
[5,1,8,6,2,7,3,4] => [2,1,2,3] => 10110100 => 4
[2,5,8,6,1,7,3,4] => [3,2,3] => 10010100 => 3
[8,6,1,5,7,2,3,4] => [1,2,5] => 11010000 => 3
[3,8,6,5,7,1,2,4] => [2,1,5] => 10110000 => 3
[7,6,5,8,1,2,4,3] => [1,1,5,1] => 11100001 => 4
[5,1,7,6,8,4,2,3] => [2,1,3,2] => 10110010 => 4
[5,1,3,7,8,6,2,4] => [3,3,2] => 10010010 => 3
[7,2,5,8,1,6,4,3] => [2,4,1,1] => 10100011 => 4
[3,2,8,5,7,6,1,4] => [2,1,3,2] => 10110010 => 4
[8,2,1,5,7,6,3,4] => [2,1,3,2] => 10110010 => 4
[5,2,8,6,1,7,3,4] => [2,1,2,3] => 10110100 => 4
[1,2,8,6,5,7,3,4] => [2,1,2,3] => 10110100 => 4
[4,2,1,3,6,7,8,5] => [2,2,4] => 10101000 => 3
[8,2,5,6,3,7,1,4] => [2,3,3] => 10100100 => 3
[7,2,6,5,4,1,8,3] => [2,1,2,1,2] => 10110110 => 5
[6,1,3,5,4,7,8,2] => [3,2,3] => 10010100 => 3
[6,1,5,3,4,7,8,2] => [2,3,3] => 10100100 => 3
[7,5,6,2,4,1,8,3] => [1,4,1,2] => 11000110 => 4
[8,5,2,6,3,7,1,4] => [1,2,2,3] => 11010100 => 4
[4,3,1,2,6,7,8,5] => [1,3,4] => 11001000 => 3
[8,1,6,5,7,3,2,4] => [2,1,3,2] => 10110010 => 4
[3,5,8,6,2,7,1,4] => [3,2,3] => 10010100 => 3
[5,8,1,6,3,7,2,4] => [3,2,3] => 10010100 => 3
[1,8,5,6,3,7,2,4] => [1,1,3,3] => 11100100 => 4
[1,7,6,5,4,2,8,3] => [1,1,1,2,1,2] => 11110110 => 6
[5,7,6,1,4,2,8,3] => [2,3,1,2] => 10100110 => 4
[7,1,4,2,6,5,8,3] => [2,2,2,2] => 10101010 => 4
[4,1,7,3,5,6,8,2] => [2,4,2] => 10100010 => 3
[2,7,4,1,5,6,8,3] => [2,4,2] => 10100010 => 3
[5,7,6,4,1,2,8,3] => [2,2,2,2] => 10101010 => 4
[4,7,6,1,5,2,8,3] => [2,3,1,2] => 10100110 => 4
[1,7,6,4,5,2,8,3] => [1,1,3,1,2] => 11100110 => 5
[1,8,3,6,5,7,2,4] => [1,2,2,3] => 11010100 => 4
[3,8,1,6,5,7,2,4] => [3,2,3] => 10010100 => 3
[8,1,3,5,7,6,2,4] => [3,3,2] => 10010010 => 3
[7,8,5,4,1,6,2,3] => [2,2,2,2] => 10101010 => 4
[6,1,5,4,3,7,8,2] => [2,2,1,3] => 10101100 => 4
[7,5,6,4,2,1,8,3] => [1,3,1,1,2] => 11001110 => 5
[8,3,2,6,5,7,1,4] => [1,2,2,3] => 11010100 => 4
[7,4,6,2,5,1,8,3] => [1,4,1,2] => 11000110 => 4
[6,1,4,3,5,7,8,2] => [2,3,3] => 10100100 => 3
[6,1,3,4,5,7,8,2] => [5,3] => 10000100 => 2
[7,2,6,4,5,1,8,3] => [2,3,1,2] => 10100110 => 4
[8,2,3,6,5,7,1,4] => [3,2,3] => 10010100 => 3
[5,4,7,3,6,8,1,2] => [1,3,4] => 11001000 => 3
[3,4,7,8,5,6,1,2] => [6,2] => 10000010 => 2
[3,4,7,2,5,1,6,8] => [5,3] => 10000100 => 2
[1,4,7,2,5,8,3,6] => [1,4,3] => 11000100 => 3
[3,6,2,4,7,1,5,8] => [4,4] => 10001000 => 2
[6,8,3,4,5,7,1,2] => [5,3] => 10000100 => 2
[4,3,6,7,5,8,1,2] => [1,4,3] => 11000100 => 3
[6,3,7,5,8,4,1,2] => [1,2,3,2] => 11010010 => 4
[7,3,8,6,4,5,1,2] => [1,2,3,2] => 11010010 => 4
[3,2,7,6,5,1,4,8] => [2,1,2,3] => 10110100 => 4
[1,2,7,6,5,8,3,4] => [2,1,2,3] => 10110100 => 4
[4,8,2,6,1,5,3,7] => [3,3,2] => 10010010 => 3
[2,3,8,6,4,1,5,7] => [3,2,3] => 10010100 => 3
[4,3,6,2,5,1,8,7] => [1,4,1,2] => 11000110 => 4
[7,8,3,2,5,1,4,6] => [3,2,3] => 10010100 => 3
[7,8,1,2,5,6,3,4] => [6,2] => 10000010 => 2
[4,1,6,2,5,7,3,8] => [2,3,3] => 10100100 => 3
[6,1,2,5,8,7,3,4] => [3,2,3] => 10010100 => 3
[2,1,8,6,4,7,3,5] => [2,1,2,3] => 10110100 => 4
[7,1,3,6,8,4,2,5] => [3,3,2] => 10010010 => 3
[1,8,3,6,7,4,5,2] => [1,2,4,1] => 11010001 => 4
[7,1,5,8,3,6,2,4] => [2,4,2] => 10100010 => 3
[5,1,8,7,2,3,6,4] => [2,1,4,1] => 10110001 => 4
[6,1,5,7,4,2,8,3] => [2,3,1,2] => 10100110 => 4
[3,1,6,4,7,2,5,8] => [2,2,4] => 10101000 => 3
[2,4,7,5,1,8,3,6] => [3,2,3] => 10010100 => 3
[6,5,7,1,4,2,3,8] => [1,4,3] => 11000100 => 3
[5,6,8,1,3,2,4,7] => [5,3] => 10000100 => 2
[6,8,5,1,3,4,2,7] => [2,4,2] => 10100010 => 3
[2,8,3,4,5,1,7,6] => [5,2,1] => 10000101 => 3
[6,2,4,3,1,5,7,8] => [2,2,4] => 10101000 => 3
[4,2,8,3,1,7,5,6] => [2,2,1,3] => 10101100 => 4
[1,3,7,4,8,2,5,6] => [1,3,4] => 11001000 => 3
[5,3,7,4,1,6,2,8] => [1,3,2,2] => 11001010 => 4
[2,4,7,3,6,1,8,5] => [4,2,2] => 10001010 => 3
[5,8,7,6,3,1,2,4] => [2,1,2,3] => 10110100 => 4
[7,5,6,8,1,4,3,2] => [1,5,1,1] => 11000011 => 4
[2,4,7,1,6,5,3,8] => [4,2,2] => 10001010 => 3
[1,2,7,8,5,4,3,6] => [2,3,1,2] => 10100110 => 4
[6,3,1,2,8,4,5,7] => [1,3,4] => 11001000 => 3
[4,2,1,3,6,5,8,7] => [2,2,2,2] => 10101010 => 4
[2,8,1,4,5,6,3,7] => [6,2] => 10000010 => 2
[7,2,1,5,4,6,3,8] => [2,1,3,2] => 10110010 => 4
[4,2,6,1,8,5,3,7] => [2,2,2,2] => 10101010 => 4
[7,8,2,1,4,5,3,6] => [3,3,2] => 10010010 => 3
[7,8,4,1,5,3,6,2] => [2,3,2,1] => 10100101 => 4
[3,4,6,1,5,8,7,2] => [5,2,1] => 10000101 => 3
[7,5,1,6,4,3,8,2] => [1,2,2,1,2] => 11010110 => 5
[5,8,1,6,3,4,7,2] => [3,4,1] => 10010001 => 3
[6,5,1,8,2,7,4,3] => [1,2,2,2,1] => 11010101 => 5
[6,8,1,7,5,2,3,4] => [3,2,3] => 10010100 => 3
[7,6,1,8,5,3,2,4] => [1,2,2,1,2] => 11010110 => 5
[5,6,1,7,4,8,2,3] => [3,2,3] => 10010100 => 3
[3,6,1,5,7,4,2,8] => [3,3,2] => 10010010 => 3
[2,5,6,1,7,4,8,3] => [4,2,2] => 10001010 => 3
[3,1,7,5,6,4,8,2] => [2,1,3,2] => 10110010 => 4
[5,1,7,6,4,8,3,2] => [2,1,2,2,1] => 10110101 => 5
[6,1,7,8,5,3,4,2] => [2,3,2,1] => 10100101 => 4
[7,1,8,6,5,4,2,3] => [2,1,2,1,2] => 10110110 => 5
[2,6,5,7,3,4,8,1] => [2,4,2] => 10100010 => 3
[1,6,4,7,5,8,2,3] => [1,1,3,3] => 11100100 => 4
[8,5,3,6,2,7,4,1] => [1,2,2,2,1] => 11010101 => 5
[1,3,7,4,6,8,2,5] => [1,3,4] => 11001000 => 3
[4,7,5,6,3,2,8,1] => [2,3,1,2] => 10100110 => 4
[1,7,6,5,4,8,2,3] => [1,1,1,2,3] => 11110100 => 5
[8,1,6,5,7,2,4,3] => [2,1,4,1] => 10110001 => 4
[1,2,7,6,8,3,4,5] => [2,1,5] => 10110000 => 3
[6,1,7,5,3,8,2,4] => [2,1,2,3] => 10110100 => 4
[2,1,7,5,6,8,3,4] => [2,1,5] => 10110000 => 3
[5,4,1,7,6,8,2,3] => [1,2,1,4] => 11011000 => 4
[4,8,5,6,2,7,3,1] => [2,3,2,1] => 10100101 => 4
[3,8,6,4,2,7,5,1] => [2,2,1,2,1] => 10101101 => 5
[7,8,5,2,4,6,3,1] => [2,4,1,1] => 10100011 => 4
[2,8,6,3,7,4,5,1] => [2,2,3,1] => 10101001 => 4
[7,8,1,6,2,4,5,3] => [3,4,1] => 10010001 => 3
[6,8,1,4,7,2,5,3] => [4,3,1] => 10001001 => 3
[3,8,4,1,7,2,6,5] => [2,2,3,1] => 10101001 => 4
[5,4,7,1,8,3,2,6] => [1,3,2,2] => 11001010 => 4
[3,7,4,1,8,5,2,6] => [2,2,2,2] => 10101010 => 4
[6,7,1,4,8,3,2,5] => [4,2,2] => 10001010 => 3
[2,7,1,8,4,5,3,6] => [3,3,2] => 10010010 => 3
[6,1,2,8,4,3,5,7] => [3,2,3] => 10010100 => 3
[6,5,1,4,3,8,2,7] => [1,3,1,3] => 11001100 => 4
[1,6,2,5,8,3,4,7] => [1,2,5] => 11010000 => 3
[8,5,1,3,7,2,6,4] => [1,3,3,1] => 11001001 => 4
[8,4,2,1,7,3,6,5] => [1,2,1,3,1] => 11011001 => 5
[7,4,2,1,8,5,3,6] => [1,2,1,2,2] => 11011010 => 5
[1,5,4,2,8,3,6,7] => [1,1,2,4] => 11101000 => 4
[6,4,3,1,5,8,2,7] => [1,2,2,3] => 11010100 => 4
[3,7,6,8,4,5,2,1] => [2,4,1,1] => 10100011 => 4
[2,7,6,8,5,3,4,1] => [2,3,2,1] => 10100101 => 4
[1,7,6,8,5,4,2,3] => [1,1,3,1,2] => 11100110 => 5
[1,4,8,6,7,5,2,3] => [1,2,3,2] => 11010010 => 4
[2,4,8,6,7,3,5,1] => [3,4,1] => 10010001 => 3
[7,3,8,5,4,6,2,1] => [1,2,3,1,1] => 11010011 => 5
[3,4,8,5,6,7,2,1] => [3,4,1] => 10010001 => 3
[6,3,5,8,4,7,2,1] => [1,4,2,1] => 11000101 => 4
[5,4,3,8,6,7,2,1] => [1,2,1,3,1] => 11011001 => 5
[5,4,2,8,7,3,6,1] => [1,2,1,3,1] => 11011001 => 5
[6,2,5,8,7,3,4,1] => [2,2,3,1] => 10101001 => 4
[3,2,8,5,7,4,6,1] => [2,1,4,1] => 10110001 => 4
[1,3,8,7,5,6,2,4] => [1,2,3,2] => 11010010 => 4
[2,1,8,7,4,6,3,5] => [2,1,3,2] => 10110010 => 4
[3,1,8,5,7,6,2,4] => [2,1,3,2] => 10110010 => 4
[6,1,5,8,7,4,2,3] => [2,2,2,2] => 10101010 => 4
[5,4,1,8,7,6,2,3] => [1,2,1,2,2] => 11011010 => 5
[5,8,6,7,4,3,2,1] => [2,3,1,1,1] => 10100111 => 5
[4,8,7,5,6,3,2,1] => [2,1,3,1,1] => 10110011 => 5
[4,2,1,6,3,5,8,7] => [2,1,3,2] => 10110010 => 4
[6,2,1,4,3,5,8,7] => [2,2,2,2] => 10101010 => 4
[6,2,1,4,3,8,5,7] => [2,2,1,3] => 10101100 => 4
[8,2,1,4,3,6,5,7] => [2,2,2,2] => 10101010 => 4
[8,2,4,1,3,6,5,7] => [2,4,2] => 10100010 => 3
[6,2,4,1,3,8,5,7] => [2,3,3] => 10100100 => 3
[6,2,4,1,3,5,8,7] => [2,4,2] => 10100010 => 3
[4,2,6,1,3,5,8,7] => [2,4,2] => 10100010 => 3
[2,1,6,4,3,5,8,7] => [2,2,2,2] => 10101010 => 4
[2,6,1,4,3,5,8,7] => [4,2,2] => 10001010 => 3
[2,6,4,1,3,5,8,7] => [2,4,2] => 10100010 => 3
[4,6,2,1,3,5,8,7] => [3,3,2] => 10010010 => 3
[6,4,2,1,3,5,8,7] => [1,2,3,2] => 11010010 => 4
[8,4,2,1,3,6,5,7] => [1,2,3,2] => 11010010 => 4
[8,4,2,1,6,3,5,7] => [1,2,1,4] => 11011000 => 4
[6,4,2,1,8,3,5,7] => [1,2,1,4] => 11011000 => 4
[4,6,2,1,8,3,5,7] => [3,1,4] => 10011000 => 3
[2,6,1,4,3,8,5,7] => [4,1,3] => 10001100 => 3
[2,1,6,4,3,8,5,7] => [2,2,1,3] => 10101100 => 4
[2,1,8,4,3,6,5,7] => [2,2,2,2] => 10101010 => 4
[2,8,1,4,3,6,5,7] => [4,2,2] => 10001010 => 3
[2,8,4,1,3,6,5,7] => [2,4,2] => 10100010 => 3
[4,8,2,1,3,6,5,7] => [3,3,2] => 10010010 => 3
[4,8,2,1,6,3,5,7] => [3,1,4] => 10011000 => 3
[6,8,2,1,4,3,5,7] => [3,2,3] => 10010100 => 3
[8,6,2,1,4,3,5,7] => [1,2,2,3] => 11010100 => 4
[2,8,1,4,6,3,5,7] => [4,4] => 10001000 => 2
[2,1,8,4,6,3,5,7] => [2,2,4] => 10101000 => 3
[2,1,6,4,8,3,5,7] => [2,2,4] => 10101000 => 3
[2,6,1,4,8,3,5,7] => [4,4] => 10001000 => 2
[2,6,4,1,8,3,5,7] => [2,2,4] => 10101000 => 3
[2,6,4,8,1,3,5,7] => [2,6] => 10100000 => 2
[4,6,2,8,1,3,5,7] => [3,5] => 10010000 => 2
[4,2,6,1,3,8,5,7] => [2,3,3] => 10100100 => 3
[4,2,6,1,8,3,5,7] => [2,2,4] => 10101000 => 3
[6,2,4,1,8,3,5,7] => [2,2,4] => 10101000 => 3
[8,2,4,1,6,3,5,7] => [2,2,4] => 10101000 => 3
[8,2,1,4,6,3,5,7] => [2,2,4] => 10101000 => 3
[6,2,1,4,8,3,5,7] => [2,2,4] => 10101000 => 3
[4,2,1,6,8,3,5,7] => [2,1,5] => 10110000 => 3
[4,2,1,6,3,8,5,7] => [2,1,2,3] => 10110100 => 4
[4,2,1,3,6,8,5,7] => [2,2,4] => 10101000 => 3
[2,1,4,3,8,6,5,7] => [2,2,2,2] => 10101010 => 4
[2,4,1,3,8,6,5,7] => [4,2,2] => 10001010 => 3
[4,2,1,3,8,6,5,7] => [2,2,2,2] => 10101010 => 4
[4,2,1,8,3,6,5,7] => [2,1,3,2] => 10110010 => 4
[4,2,1,8,6,3,5,7] => [2,1,1,4] => 10111000 => 4
[6,2,1,8,4,3,5,7] => [2,1,2,3] => 10110100 => 4
[8,2,1,6,4,3,5,7] => [2,1,2,3] => 10110100 => 4
[8,2,6,1,4,3,5,7] => [2,3,3] => 10100100 => 3
[6,2,8,1,4,3,5,7] => [2,3,3] => 10100100 => 3
[4,2,8,1,6,3,5,7] => [2,2,4] => 10101000 => 3
[4,2,8,1,3,6,5,7] => [2,4,2] => 10100010 => 3
[2,4,8,1,3,6,5,7] => [6,2] => 10000010 => 2
[2,4,1,8,3,6,5,7] => [3,3,2] => 10010010 => 3
[2,1,4,8,3,6,5,7] => [2,4,2] => 10100010 => 3
[2,1,4,8,6,3,5,7] => [2,2,4] => 10101000 => 3
[2,4,8,1,6,3,5,7] => [4,4] => 10001000 => 2
[2,4,8,6,1,3,5,7] => [3,5] => 10010000 => 2
[4,2,8,6,1,3,5,7] => [2,1,5] => 10110000 => 3
[6,2,8,4,1,3,5,7] => [2,2,4] => 10101000 => 3
[8,2,6,4,1,3,5,7] => [2,2,4] => 10101000 => 3
[8,4,6,2,1,3,5,7] => [1,3,4] => 11001000 => 3
[6,4,8,2,1,3,5,7] => [1,3,4] => 11001000 => 3
[4,6,8,2,1,3,5,7] => [4,4] => 10001000 => 2
[2,6,8,4,1,3,5,7] => [4,4] => 10001000 => 2
[2,6,8,1,4,3,5,7] => [5,3] => 10000100 => 2
[2,6,1,8,4,3,5,7] => [3,2,3] => 10010100 => 3
[2,1,6,8,4,3,5,7] => [2,3,3] => 10100100 => 3
[2,1,8,6,4,3,5,7] => [2,1,2,3] => 10110100 => 4
[2,8,1,6,4,3,5,7] => [3,2,3] => 10010100 => 3
[2,8,6,4,1,3,5,7] => [2,2,4] => 10101000 => 3
[4,8,6,2,1,3,5,7] => [2,2,4] => 10101000 => 3
[6,8,4,2,1,3,5,7] => [2,2,4] => 10101000 => 3
[3,2,6,1,5,4,8,7] => [2,3,1,2] => 10100110 => 4
[5,2,4,3,8,1,7,6] => [2,2,3,1] => 10101001 => 4
[6,2,4,1,5,3,8,7] => [2,3,1,2] => 10100110 => 4
[4,3,6,1,5,2,8,7] => [1,4,1,2] => 11000110 => 4
[4,3,5,2,8,1,7,6] => [1,3,3,1] => 11001001 => 4
[4,3,7,2,6,5,8,1] => [1,3,2,2] => 11001010 => 4
[4,3,8,2,6,1,7,5] => [1,3,3,1] => 11001001 => 4
[4,3,8,1,7,2,6,5] => [1,3,3,1] => 11001001 => 4
[4,3,8,1,5,2,7,6] => [1,4,2,1] => 11000101 => 4
[5,1,8,3,4,2,7,6] => [2,3,2,1] => 10100101 => 4
[5,4,8,1,3,2,7,6] => [1,4,2,1] => 11000101 => 4
[2,1,5,4,8,3,7,6] => [2,2,3,1] => 10101001 => 4
[5,1,7,6,8,3,4,2] => [2,1,4,1] => 10110001 => 4
[4,3,7,6,8,1,5,2] => [1,2,4,1] => 11010001 => 4
[4,3,7,1,8,5,6,2] => [1,3,3,1] => 11001001 => 4
[4,3,6,5,8,1,7,2] => [1,2,4,1] => 11010001 => 4
[6,3,5,4,7,2,8,1] => [1,3,2,2] => 11001010 => 4
[6,3,5,4,8,1,7,2] => [1,3,3,1] => 11001001 => 4
[7,1,6,3,8,4,5,2] => [2,2,3,1] => 10101001 => 4
[7,4,6,5,8,1,3,2] => [1,2,4,1] => 11010001 => 4
[2,1,8,4,6,3,7,5] => [2,2,3,1] => 10101001 => 4
[8,4,6,1,3,2,7,5] => [1,4,2,1] => 11000101 => 4
[8,1,6,3,4,2,7,5] => [2,3,2,1] => 10100101 => 4
[8,1,6,3,7,2,5,4] => [2,2,3,1] => 10101001 => 4
[8,3,5,1,7,2,6,4] => [1,3,3,1] => 11001001 => 4
[8,3,5,2,6,1,7,4] => [1,3,3,1] => 11001001 => 4
[7,3,5,2,6,4,8,1] => [1,3,2,2] => 11001010 => 4
[8,2,6,3,5,1,7,4] => [2,3,2,1] => 10100101 => 4
[8,2,7,1,5,3,6,4] => [2,3,2,1] => 10100101 => 4
[8,2,4,1,5,3,7,6] => [2,3,2,1] => 10100101 => 4
[8,2,4,1,7,3,6,5] => [2,2,3,1] => 10101001 => 4
[8,2,4,3,6,1,7,5] => [2,2,3,1] => 10101001 => 4
[3,2,8,4,6,1,7,5] => [2,2,3,1] => 10101001 => 4
[3,2,8,1,5,4,7,6] => [2,3,2,1] => 10100101 => 4
[3,2,7,6,8,1,5,4] => [2,1,4,1] => 10110001 => 4
[3,2,7,1,8,5,6,4] => [2,2,3,1] => 10101001 => 4
[3,2,6,5,8,1,7,4] => [2,1,4,1] => 10110001 => 4
[6,5,7,2,4,3,8,1] => [1,4,1,2] => 11000110 => 4
[6,5,8,2,4,1,7,3] => [1,4,2,1] => 11000101 => 4
[7,2,4,1,8,5,6,3] => [2,2,3,1] => 10101001 => 4
[7,6,8,2,4,1,5,3] => [1,4,2,1] => 11000101 => 4
[7,6,8,1,5,2,4,3] => [1,4,2,1] => 11000101 => 4
[2,1,7,3,8,5,6,4] => [2,2,3,1] => 10101001 => 4
[7,1,3,2,8,5,6,4] => [3,1,3,1] => 10011001 => 4
[7,1,8,5,6,2,4,3] => [2,1,4,1] => 10110001 => 4
[7,1,8,2,6,4,5,3] => [2,2,3,1] => 10101001 => 4
[7,2,8,1,5,4,6,3] => [2,3,2,1] => 10100101 => 4
[6,2,7,4,5,3,8,1] => [2,3,1,2] => 10100110 => 4
[5,4,7,2,6,3,8,1] => [1,3,2,2] => 11001010 => 4
[5,4,8,2,6,1,7,3] => [1,3,3,1] => 11001001 => 4
[6,5,8,1,7,2,4,3] => [1,3,3,1] => 11001001 => 4
[2,1,6,5,8,3,7,4] => [2,1,4,1] => 10110001 => 4
[6,5,7,4,8,1,3,2] => [1,3,3,1] => 11001001 => 4
[6,5,7,1,8,3,4,2] => [1,3,3,1] => 11001001 => 4
[6,1,7,4,8,3,5,2] => [2,2,3,1] => 10101001 => 4
[5,4,7,1,8,3,6,2] => [1,3,3,1] => 11001001 => 4
[5,4,6,3,8,1,7,2] => [1,3,3,1] => 11001001 => 4
[2,1,4,3,6,5,8,7,11,12,10,9] => [2,2,2,2,3,1] => 101010101001 => 6
[2,1,4,3,6,5,9,11,8,12,10,7] => [2,2,2,3,2,1] => 101010100101 => 6
[2,1,4,3,7,9,6,11,8,12,10,5] => [2,2,3,2,2,1] => 101010010101 => 6
[2,1,5,7,4,9,6,11,8,12,10,3] => [2,3,2,2,2,1] => 101001010101 => 6
[3,5,2,7,4,9,6,11,8,12,10,1] => [3,2,2,2,2,1] => 100101010101 => 6
[2,8,3,1,5,4,6,7] => [3,2,3] => 10010100 => 3
[2,5,3,4,7,1,8,6] => [4,2,2] => 10001010 => 3
[2,4,8,3,5,7,6,1] => [5,2,1] => 10000101 => 3
[4,2,5,3,1,8,6,7] => [2,2,1,3] => 10101100 => 4
[4,2,1,8,5,3,6,7] => [2,1,2,3] => 10110100 => 4
[5,4,1,3,8,2,6,7] => [1,3,4] => 11001000 => 3
[5,1,4,8,3,2,6,7] => [2,3,3] => 10100100 => 3
[1,5,8,4,3,2,6,7] => [1,3,1,3] => 11001100 => 4
[1,8,5,4,3,2,6,7] => [1,1,2,1,3] => 11101100 => 5
[1,7,4,3,8,5,2,6] => [1,1,2,2,2] => 11101010 => 5
[1,5,7,3,8,4,2,6] => [1,3,2,2] => 11001010 => 4
[5,1,4,7,8,3,2,6] => [2,4,2] => 10100010 => 3
[4,8,1,5,7,3,6,2] => [3,4,1] => 10010001 => 3
[8,1,5,3,7,4,6,2] => [2,2,3,1] => 10101001 => 4
[3,8,4,7,6,5,2,1] => [2,2,2,1,1] => 10101011 => 5
[1,6,8,5,3,7,4,2] => [1,2,2,2,1] => 11010101 => 5
[6,8,1,7,4,3,5,2] => [3,2,2,1] => 10010101 => 4
[6,4,8,1,7,3,5,2] => [1,3,3,1] => 11001001 => 4
[6,4,8,7,1,5,2,3] => [1,2,3,2] => 11010010 => 4
[7,6,4,1,3,8,2,5] => [1,1,3,3] => 11100100 => 4
[1,7,5,6,3,2,8,4] => [1,1,3,1,2] => 11100110 => 5
[4,2,1,7,8,5,3,6] => [2,1,3,2] => 10110010 => 4
[2,7,4,6,3,1,8,5] => [2,3,1,2] => 10100110 => 4
[2,6,8,4,3,7,5,1] => [4,1,2,1] => 10001101 => 4
[6,2,4,8,3,7,5,1] => [2,3,2,1] => 10100101 => 4
[7,2,6,3,4,1,8,5] => [2,3,1,2] => 10100110 => 4
[2,6,7,3,1,4,8,5] => [4,2,2] => 10001010 => 3
[2,7,1,8,3,5,4,6] => [3,3,2] => 10010010 => 3
[2,1,7,3,5,8,4,6] => [2,3,3] => 10100100 => 3
[8,7,1,3,6,2,4,5] => [1,3,4] => 11001000 => 3
[8,2,1,7,3,5,6,4] => [2,1,4,1] => 10110001 => 4
[7,8,2,6,3,1,5,4] => [3,2,2,1] => 10010101 => 4
[8,7,2,6,3,5,4,1] => [1,2,3,1,1] => 11010011 => 5
[1,2,8,7,4,5,6,3] => [2,1,4,1] => 10110001 => 4
[8,3,7,1,5,6,2,4] => [1,5,2] => 11000010 => 3
[8,6,1,2,7,5,3,4] => [1,3,2,2] => 11001010 => 4
[8,1,6,2,7,4,5,3] => [2,2,3,1] => 10101001 => 4
[1,8,5,2,6,7,4,3] => [1,1,2,3,1] => 11101001 => 5
[5,2,1,8,6,7,4,3] => [2,1,1,3,1] => 10111001 => 5
[2,8,5,7,6,4,3,1] => [2,2,2,1,1] => 10101011 => 5
[1,7,8,5,2,6,4,3] => [1,2,3,1,1] => 11010011 => 5
[7,8,1,6,4,2,5,3] => [3,2,2,1] => 10010101 => 4
[7,8,6,1,5,3,2,4] => [2,3,1,2] => 10100110 => 4
[7,3,8,6,1,5,2,4] => [1,2,3,2] => 11010010 => 4
[8,7,6,1,5,3,4,2] => [1,1,3,2,1] => 11100101 => 5
[8,7,1,6,4,5,3,2] => [1,2,3,1,1] => 11010011 => 5
[8,1,7,5,6,4,3,2] => [2,1,3,1,1] => 10110011 => 5
[1,8,6,7,5,4,3,2] => [1,1,3,1,1,1] => 11100111 => 6
[6,3,5,2,1,4,8,7] => [1,3,2,2] => 11001010 => 4
[6,3,5,7,2,8,4,1] => [1,4,2,1] => 11000101 => 4
[8,5,2,7,4,3,1,6] => [1,2,2,1,2] => 11010110 => 5
[4,5,3,6,1,2,8,7] => [3,3,2] => 10010010 => 3
[3,5,1,4,6,2,8,7] => [4,2,2] => 10001010 => 3
[8,3,4,5,7,2,1,6] => [1,5,2] => 11000010 => 3
[5,7,4,6,3,8,2,1] => [2,3,2,1] => 10100101 => 4
[2,8,4,6,3,7,1,5] => [2,3,3] => 10100100 => 3
[8,1,4,7,3,6,2,5] => [2,4,2] => 10100010 => 3
[8,3,4,7,5,1,2,6] => [1,4,3] => 11000100 => 3
[8,5,1,4,7,3,2,6] => [1,3,2,2] => 11001010 => 4
[8,5,3,7,1,4,2,6] => [1,2,3,2] => 11010010 => 4
[2,1,8,5,7,4,3,6] => [2,1,3,2] => 10110010 => 4
[6,5,3,7,1,8,4,2] => [1,2,2,2,1] => 11010101 => 5
[6,5,1,4,7,8,3,2] => [1,3,3,1] => 11001001 => 4
[6,3,4,7,5,8,1,2] => [1,4,3] => 11000100 => 3
[5,1,4,6,8,3,7,2] => [2,5,1] => 10100001 => 3
[4,7,1,3,5,8,6,2] => [5,2,1] => 10000101 => 3
[4,8,3,7,1,2,6,5] => [3,4,1] => 10010001 => 3
[3,8,6,4,1,7,2,5] => [2,2,1,3] => 10101100 => 4
[3,8,1,2,5,7,6,4] => [5,2,1] => 10000101 => 3
[2,8,7,5,4,1,3,6] => [2,1,2,3] => 10110100 => 4
[8,7,2,6,4,1,3,5] => [1,2,2,3] => 11010100 => 4
[3,8,6,7,4,2,1,5] => [2,3,1,2] => 10100110 => 4
[5,7,6,8,4,2,3,1] => [2,3,2,1] => 10100101 => 4
[5,3,7,8,2,4,6,1] => [1,6,1] => 11000001 => 3
[8,3,6,2,1,4,7,5] => [1,3,3,1] => 11001001 => 4
[5,3,7,6,2,1,8,4] => [1,2,2,1,2] => 11010110 => 5
[5,3,6,2,8,7,1,4] => [1,3,1,3] => 11001100 => 4
[5,7,8,6,4,2,1,3] => [3,2,1,2] => 10010110 => 4
[2,6,7,5,4,8,1,3] => [3,2,3] => 10010100 => 3
[6,1,7,4,5,8,2,3] => [2,3,3] => 10100100 => 3
[6,7,3,5,1,8,2,4] => [3,2,3] => 10010100 => 3
[2,1,6,7,5,8,3,4] => [2,3,3] => 10100100 => 3
[2,1,5,7,3,6,8,4] => [2,4,2] => 10100010 => 3
[5,7,3,6,1,2,8,4] => [3,3,2] => 10010010 => 3
[4,1,7,2,5,6,8,3] => [2,4,2] => 10100010 => 3
[2,4,7,1,6,5,8,3] => [4,2,2] => 10001010 => 3
[4,6,2,1,8,7,5,3] => [3,1,1,2,1] => 10011101 => 5
[3,4,6,2,7,8,5,1] => [4,3,1] => 10001001 => 3
[4,6,1,2,5,8,7,3] => [5,2,1] => 10000101 => 3
[5,6,1,4,8,2,7,3] => [4,3,1] => 10001001 => 3
[5,6,3,1,8,7,2,4] => [3,1,1,3] => 10011100 => 4
[3,5,6,4,7,1,8,2] => [4,2,2] => 10001010 => 3
[3,4,6,1,5,7,8,2] => [5,3] => 10000100 => 2
[3,4,1,5,7,6,8,2] => [3,3,2] => 10010010 => 3
[3,8,2,7,1,6,5,4] => [3,3,1,1] => 10010011 => 4
[3,8,2,7,6,1,5,4] => [3,1,3,1] => 10011001 => 4
[3,8,2,7,6,5,1,4] => [3,1,2,2] => 10011010 => 4
[3,8,2,7,6,5,4,1] => [3,1,2,1,1] => 10011011 => 5
[4,8,7,2,6,5,3,1] => [2,2,2,1,1] => 10101011 => 5
[4,8,7,2,6,5,1,3] => [2,2,2,2] => 10101010 => 4
[4,8,7,2,6,1,5,3] => [2,2,3,1] => 10101001 => 4
[4,8,7,2,1,6,5,3] => [2,2,2,1,1] => 10101011 => 5
[4,8,7,3,1,6,5,2] => [2,2,2,1,1] => 10101011 => 5
[4,8,7,3,2,1,6,5] => [2,2,1,2,1] => 10101101 => 5
[4,8,7,3,2,6,1,5] => [2,2,2,2] => 10101010 => 4
[4,8,7,3,2,6,5,1] => [2,2,2,1,1] => 10101011 => 5
[4,8,7,3,6,2,5,1] => [2,2,3,1] => 10101001 => 4
[4,8,7,3,6,2,1,5] => [2,2,2,2] => 10101010 => 4
[4,8,7,3,6,1,5,2] => [2,2,3,1] => 10101001 => 4
[4,8,7,3,6,5,1,2] => [2,2,2,2] => 10101010 => 4
[4,8,7,3,6,5,2,1] => [2,2,2,1,1] => 10101011 => 5
[5,8,7,6,3,4,2,1] => [2,1,3,1,1] => 10110011 => 5
[5,8,7,6,3,1,4,2] => [2,1,2,2,1] => 10110101 => 5
[5,8,7,6,3,2,4,1] => [2,1,2,2,1] => 10110101 => 5
[5,8,7,6,2,4,3,1] => [2,1,3,1,1] => 10110011 => 5
[5,8,7,6,2,1,4,3] => [2,1,2,2,1] => 10110101 => 5
[5,8,7,6,4,2,3,1] => [2,1,2,2,1] => 10110101 => 5
[5,8,7,6,4,2,1,3] => [2,1,2,1,2] => 10110110 => 5
[5,8,7,6,4,1,3,2] => [2,1,2,2,1] => 10110101 => 5
[5,8,7,6,4,3,1,2] => [2,1,2,1,2] => 10110110 => 5
[7,3,4,2,1,6,5,8] => [1,3,2,2] => 11001010 => 4
[7,3,5,2,6,1,4,8] => [1,3,4] => 11001000 => 3
[7,3,5,2,6,4,1,8] => [1,3,2,2] => 11001010 => 4
[6,3,5,2,7,4,8,1] => [1,3,2,2] => 11001010 => 4
[7,2,1,5,6,4,3,8] => [2,1,3,2] => 10110010 => 4
[7,3,5,1,6,4,2,8] => [1,3,2,2] => 11001010 => 4
[7,4,5,6,1,3,2,8] => [1,5,2] => 11000010 => 3
[1,4,5,7,3,2,8,6] => [1,4,1,2] => 11000110 => 4
[1,4,6,7,3,8,2,5] => [1,4,3] => 11000100 => 3
[6,4,5,7,3,1,8,2] => [1,4,1,2] => 11000110 => 4
[6,4,5,7,1,3,8,2] => [1,5,2] => 11000010 => 3
[6,3,5,1,7,4,8,2] => [1,3,2,2] => 11001010 => 4
[6,2,1,5,7,4,8,3] => [2,1,3,2] => 10110010 => 4
[3,2,1,5,7,4,8,6] => [2,1,3,2] => 10110010 => 4
[2,4,6,7,3,8,1,5] => [5,3] => 10000100 => 2
[1,4,6,7,3,8,5,2] => [1,4,2,1] => 11000101 => 4
[1,5,6,7,8,3,4,2] => [1,6,1] => 11000001 => 3
[2,5,6,7,8,3,1,4] => [6,2] => 10000010 => 2
[3,2,1,6,7,8,4,5] => [2,1,5] => 10110000 => 3
[5,2,1,6,7,8,4,3] => [2,1,4,1] => 10110001 => 4
[5,3,6,1,7,8,4,2] => [1,3,3,1] => 11001001 => 4
[5,4,6,7,1,8,3,2] => [1,4,2,1] => 11000101 => 4
[1,5,6,7,8,3,2,4] => [1,5,2] => 11000010 => 3
[6,4,5,7,2,1,8,3] => [1,4,1,2] => 11000110 => 4
[5,4,6,7,2,8,3,1] => [1,4,2,1] => 11000101 => 4
[5,3,6,2,7,8,4,1] => [1,3,3,1] => 11001001 => 4
[5,3,6,2,7,8,1,4] => [1,3,4] => 11001000 => 3
[6,3,5,2,7,1,8,4] => [1,3,2,2] => 11001010 => 4
[6,3,4,2,1,7,8,5] => [1,3,1,3] => 11001100 => 4
[5,3,4,1,2,7,8,6] => [1,4,3] => 11000100 => 3
[4,3,6,2,7,8,1,5] => [1,3,4] => 11001000 => 3
[4,3,6,2,7,8,5,1] => [1,3,3,1] => 11001001 => 4
[1,3,6,2,7,8,5,4] => [1,3,3,1] => 11001001 => 4
[1,4,6,7,2,8,5,3] => [1,4,2,1] => 11000101 => 4
[3,4,6,7,2,8,5,1] => [5,2,1] => 10000101 => 3
[3,4,5,7,2,1,8,6] => [5,1,2] => 10000110 => 3
[4,2,1,5,7,3,8,6] => [2,1,3,2] => 10110010 => 4
[4,2,1,6,7,8,3,5] => [2,1,5] => 10110000 => 3
[4,3,6,1,7,8,2,5] => [1,3,4] => 11001000 => 3
[1,5,6,7,8,2,4,3] => [1,6,1] => 11000001 => 3
[1,5,6,7,8,4,2,3] => [1,5,2] => 11000010 => 3
[3,4,6,7,1,8,5,2] => [5,2,1] => 10000101 => 3
[4,3,6,1,7,8,5,2] => [1,3,3,1] => 11001001 => 4
[4,2,1,6,7,8,5,3] => [2,1,4,1] => 10110001 => 4
[2,3,6,1,7,8,5,4] => [4,3,1] => 10001001 => 3
[2,4,6,7,1,8,5,3] => [5,2,1] => 10000101 => 3
[2,5,6,7,8,1,4,3] => [7,1] => 10000001 => 2
[2,1,4,3,6,5,8,7,9] => [2,2,2,3] => 101010100 => 4
[2,4,1,3,6,5,8,7,9] => [4,2,3] => 100010100 => 3
[2,4,1,6,3,5,8,7,9] => [3,3,3] => 100100100 => 3
[2,4,1,6,3,7,5,9,8] => [3,2,2,2] => 100101010 => 4
[2,4,1,5,3,7,6,9,8] => [3,2,2,2] => 100101010 => 4
[2,3,1,5,4,7,6,9,8] => [3,2,2,2] => 100101010 => 4
[1,3,2,5,4,7,6,9,8] => [1,2,2,2,2] => 110101010 => 5
[2,4,6,1,3,5,8,7,9] => [6,3] => 100000100 => 2
[2,4,1,6,8,3,5,7,9] => [3,6] => 100100000 => 2
[2,4,1,5,3,8,6,9,7] => [3,2,2,2] => 100101010 => 4
[2,3,1,6,4,7,5,9,8] => [3,2,2,2] => 100101010 => 4
[1,4,2,5,3,7,6,9,8] => [1,2,2,2,2] => 110101010 => 5
[1,3,2,5,4,7,6,9,8,10] => [1,2,2,2,3] => 1101010100 => 5
[7,1,2,3,4,5,6,8,9] => [9] => 100000000 => 1
[1,4,3,6,2,5,7,8] => [1,2,5] => 11010000 => 3
[1,4,3,7,2,5,6,8] => [1,2,5] => 11010000 => 3
[1,4,3,7,6,8,2,5] => [1,2,1,4] => 11011000 => 4
[1,4,3,7,5,8,2,6] => [1,2,2,3] => 11010100 => 4
[1,4,3,7,2,6,5,8] => [1,2,3,2] => 11010010 => 4
[1,5,3,7,4,8,2,6] => [1,2,2,3] => 11010100 => 4
[1,3,2,6,5,8,4,7] => [1,2,2,3] => 11010100 => 4
[1,5,4,8,2,6,3,7] => [1,1,4,2] => 11100010 => 4
[1,5,4,8,3,7,2,6] => [1,1,3,3] => 11100100 => 4
[1,2,3,6,5,8,4,7] => [3,2,3] => 10010100 => 3
[6,8,2,4,5,7,1,3] => [5,3] => 10000100 => 2
[3,7,8,4,5,2,6,1] => [5,2,1] => 10000101 => 3
[7,8,1,4,5,3,6,2] => [5,2,1] => 10000101 => 3
[3,8,7,4,1,6,5,2] => [2,2,2,1,1] => 10101011 => 5
[4,8,3,6,1,5,7,2] => [3,4,1] => 10010001 => 3
[5,8,3,1,6,4,7,2] => [3,1,3,1] => 10011001 => 4
[5,8,1,4,7,6,3,2] => [4,2,1,1] => 10001011 => 4
[7,5,1,8,6,2,4,3] => [1,2,1,3,1] => 11011001 => 5
[7,4,1,8,2,6,3,5] => [1,2,3,2] => 11010010 => 4
[7,1,8,4,2,6,3,5] => [2,2,2,2] => 10101010 => 4
[1,6,3,8,5,2,4,7] => [1,2,2,3] => 11010100 => 4
[6,1,3,8,5,2,4,7] => [3,2,3] => 10010100 => 3
[7,1,8,3,6,2,5,4] => [2,2,3,1] => 10101001 => 4
[7,3,1,8,4,2,6,5] => [1,2,2,2,1] => 11010101 => 5
[7,2,8,4,1,6,5,3] => [2,2,2,1,1] => 10101011 => 5
[7,2,8,3,6,5,1,4] => [2,2,2,2] => 10101010 => 4
[7,2,8,3,6,1,5,4] => [2,2,3,1] => 10101001 => 4
[7,1,8,2,3,6,5,4] => [2,4,1,1] => 10100011 => 4
[6,1,2,8,3,5,4,7] => [3,3,2] => 10010010 => 3
[1,5,2,3,8,4,7,6] => [1,3,3,1] => 11001001 => 4
[5,1,2,3,8,4,7,6] => [4,3,1] => 10001001 => 3
[5,2,3,8,1,4,7,6] => [3,4,1] => 10010001 => 3
[6,2,8,1,3,5,4,7] => [2,4,2] => 10100010 => 3
[6,2,4,1,8,7,3,5] => [2,2,1,3] => 10101100 => 4
[6,3,1,4,2,8,5,7] => [1,3,1,3] => 11001100 => 4
[3,1,6,4,2,8,5,7] => [2,2,1,3] => 10101100 => 4
[2,6,3,8,7,1,5,4] => [3,1,3,1] => 10011001 => 4
[2,6,3,8,5,1,4,7] => [3,2,3] => 10010100 => 3
[2,5,1,8,3,4,7,6] => [3,4,1] => 10010001 => 3
[2,5,1,3,8,4,7,6] => [4,3,1] => 10001001 => 3
[1,2,5,3,8,4,7,6] => [2,2,3,1] => 10101001 => 4
[1,2,4,8,3,7,6,5] => [2,3,2,1] => 10100101 => 4
[2,4,8,1,3,7,6,5] => [5,2,1] => 10000101 => 3
[2,4,8,3,7,1,6,5] => [4,3,1] => 10001001 => 3
[2,4,8,3,7,6,1,5] => [4,2,2] => 10001010 => 3
[2,5,3,8,1,7,4,6] => [3,2,3] => 10010100 => 3
[2,5,4,1,3,8,7,6] => [2,3,2,1] => 10100101 => 4
[3,1,5,4,8,2,7,6] => [2,2,3,1] => 10101001 => 4
[5,3,1,4,8,2,7,6] => [1,3,3,1] => 11001001 => 4
[5,2,3,8,4,7,1,6] => [3,2,3] => 10010100 => 3
[4,8,2,3,7,6,1,5] => [4,2,2] => 10001010 => 3
[4,8,2,3,7,1,6,5] => [4,3,1] => 10001001 => 3
[4,8,1,2,3,7,6,5] => [5,2,1] => 10000101 => 3
[1,4,8,2,3,7,6,5] => [1,4,2,1] => 11000101 => 4
[1,4,8,3,7,2,6,5] => [1,3,3,1] => 11001001 => 4
[6,3,8,1,5,2,4,7] => [1,4,3] => 11000100 => 3
[5,3,8,1,2,4,7,6] => [1,6,1] => 11000001 => 3
[5,1,3,8,2,4,7,6] => [3,4,1] => 10010001 => 3
[1,5,3,8,2,4,7,6] => [1,2,4,1] => 11010001 => 4
[1,5,4,8,2,7,6,3] => [1,1,3,2,1] => 11100101 => 5
[5,1,4,8,2,7,6,3] => [2,3,2,1] => 10100101 => 4
[5,4,8,1,2,7,6,3] => [1,4,2,1] => 11000101 => 4
[6,5,1,2,8,7,4,3] => [1,3,1,2,1] => 11001101 => 5
[5,3,1,6,4,2,8,7] => [1,2,2,1,2] => 11010110 => 5
[5,1,6,2,8,7,4,3] => [2,2,1,2,1] => 10101101 => 5
[4,1,5,8,2,7,6,3] => [2,3,2,1] => 10100101 => 4
[4,1,2,5,8,7,6,3] => [3,2,2,1] => 10010101 => 4
[1,4,2,5,8,7,6,3] => [1,2,2,2,1] => 11010101 => 5
[1,3,5,2,8,7,4,6] => [1,3,1,3] => 11001100 => 4
[3,5,1,2,8,7,4,6] => [4,1,3] => 10001100 => 3
[3,6,2,8,7,5,1,4] => [3,1,2,2] => 10011010 => 4
[4,2,6,1,8,7,3,5] => [2,2,1,3] => 10101100 => 4
[4,3,1,5,8,2,7,6] => [1,2,4,1] => 11010001 => 4
[3,5,2,8,7,1,4,6] => [3,1,4] => 10011000 => 3
[3,4,8,7,2,6,1,5] => [3,3,2] => 10010010 => 3
[3,4,8,7,1,2,6,5] => [3,4,1] => 10010001 => 3
[3,4,8,1,7,2,6,5] => [4,3,1] => 10001001 => 3
[1,3,4,8,7,2,6,5] => [1,3,3,1] => 11001001 => 4
[1,3,4,8,2,7,6,5] => [1,4,2,1] => 11000101 => 4
[3,4,8,1,2,7,6,5] => [5,2,1] => 10000101 => 3
[3,4,8,2,7,1,6,5] => [4,3,1] => 10001001 => 3
[3,4,8,2,7,6,1,5] => [4,2,2] => 10001010 => 3
[4,2,5,8,1,7,6,3] => [2,3,2,1] => 10100101 => 4
[4,3,1,2,5,8,7,6] => [1,4,2,1] => 11000101 => 4
[3,1,4,2,5,8,7,6] => [2,3,2,1] => 10100101 => 4
[2,3,5,1,8,7,6,4] => [4,1,2,1] => 10001101 => 4
[7,8,2,1,5,3,6,4] => [3,2,2,1] => 10010101 => 4
[6,4,1,2,7,3,5,8] => [1,3,4] => 11001000 => 3
[2,3,7,5,4,1,8,6] => [3,2,1,2] => 10010110 => 4
[6,3,1,5,4,2,7,8] => [1,2,2,3] => 11010100 => 4
[7,8,1,5,4,2,6,3] => [3,2,2,1] => 10010101 => 4
[7,8,3,5,4,1,6,2] => [3,2,2,1] => 10010101 => 4
[7,8,2,5,4,1,3,6] => [3,2,3] => 10010100 => 3
[7,8,2,5,4,6,1,3] => [3,3,2] => 10010010 => 3
[6,2,1,5,4,7,3,8] => [2,1,2,3] => 10110100 => 4
[5,3,6,1,4,7,8,2] => [1,4,3] => 11000100 => 3
[5,3,6,2,4,7,1,8] => [1,4,3] => 11000100 => 3
[6,4,2,1,7,3,8,5] => [1,2,1,2,2] => 11011010 => 5
[4,3,7,5,8,6,1,2] => [1,2,3,2] => 11010010 => 4
[4,2,7,1,8,3,6,5] => [2,2,3,1] => 10101001 => 4
[3,2,6,7,4,8,1,5] => [2,3,3] => 10100100 => 3
[3,1,6,7,4,8,5,2] => [2,3,2,1] => 10100101 => 4
[1,7,6,5,3,8,4,2] => [1,1,1,2,2,1] => 11110101 => 6
[2,7,6,5,3,8,1,4] => [2,1,2,3] => 10110100 => 4
[1,7,6,5,2,4,8,3] => [1,1,1,3,2] => 11110010 => 5
[2,7,6,5,3,1,4,8] => [2,1,2,3] => 10110100 => 4
[2,7,1,4,8,3,5,6] => [4,4] => 10001000 => 2
[3,7,6,4,8,5,1,2] => [2,2,2,2] => 10101010 => 4
[5,7,6,3,8,4,1,2] => [2,2,2,2] => 10101010 => 4
[5,1,6,2,4,8,3,7] => [2,3,3] => 10100100 => 3
[4,7,6,5,2,1,3,8] => [2,1,2,3] => 10110100 => 4
[4,7,6,5,2,8,1,3] => [2,1,2,3] => 10110100 => 4
[4,7,6,5,1,8,3,2] => [2,1,2,2,1] => 10110101 => 5
[1,7,6,5,2,8,3,4] => [1,1,1,2,3] => 11110100 => 5
[1,7,6,5,3,2,8,4] => [1,1,1,2,1,2] => 11110110 => 6
[4,7,6,5,1,2,8,3] => [2,1,3,2] => 10110010 => 4
[4,7,6,5,3,1,8,2] => [2,1,2,1,2] => 10110110 => 5
[6,1,3,5,4,8,7,2] => [3,2,2,1] => 10010101 => 4
[5,2,6,3,4,1,7,8] => [2,3,3] => 10100100 => 3
[5,1,6,2,4,7,8,3] => [2,3,3] => 10100100 => 3
[1,2,6,3,4,8,7,5] => [2,3,2,1] => 10100101 => 4
[1,7,2,4,8,3,6,5] => [1,3,3,1] => 11001001 => 4
[6,1,4,2,8,3,5,7] => [2,2,4] => 10101000 => 3
[4,1,8,2,6,3,5,7] => [2,2,4] => 10101000 => 3
[4,7,2,1,5,3,6,8] => [3,2,3] => 10010100 => 3
[4,7,1,6,2,3,8,5] => [3,3,2] => 10010010 => 3
[1,7,2,6,8,3,5,4] => [1,2,4,1] => 11010001 => 4
[1,2,6,7,4,8,5,3] => [2,3,2,1] => 10100101 => 4
[3,1,6,7,4,2,8,5] => [2,3,1,2] => 10100110 => 4
[3,2,8,5,4,6,1,7] => [2,1,3,2] => 10110010 => 4
[4,7,6,3,5,8,1,2] => [2,3,3] => 10100100 => 3
[4,7,1,2,5,3,8,6] => [5,1,2] => 10000110 => 3
[3,7,6,5,2,4,1,8] => [2,1,3,2] => 10110010 => 4
[3,7,6,5,1,4,8,2] => [2,1,3,2] => 10110010 => 4
[3,7,6,5,2,1,8,4] => [2,1,2,1,2] => 10110110 => 5
[1,7,6,5,8,2,4,3] => [1,1,1,4,1] => 11110001 => 5
[3,7,6,5,8,1,4,2] => [2,1,4,1] => 10110001 => 4
[3,7,6,5,1,2,4,8] => [2,1,5] => 10110000 => 3
[3,1,6,8,4,2,5,7] => [2,3,3] => 10100100 => 3
[4,7,6,8,3,5,1,2] => [2,4,2] => 10100010 => 3
[2,7,6,5,1,4,3,8] => [2,1,3,2] => 10110010 => 4
[2,7,6,5,8,1,3,4] => [2,1,5] => 10110000 => 3
[2,7,6,5,8,4,1,3] => [2,1,3,2] => 10110010 => 4
[6,3,2,1,7,4,8,5] => [1,2,1,2,2] => 11011010 => 5
[4,2,1,7,3,5,8,6] => [2,1,3,2] => 10110010 => 4
[7,3,1,5,4,2,8,6] => [1,2,2,1,2] => 11010110 => 5
[8,4,1,5,2,7,6,3] => [1,2,2,2,1] => 11010101 => 5
[8,2,5,1,3,7,6,4] => [2,3,2,1] => 10100101 => 4
[4,3,7,2,1,5,8,6] => [1,3,2,2] => 11001010 => 4
[6,3,7,4,2,1,8,5] => [1,3,1,1,2] => 11001110 => 5
[4,7,2,5,3,1,8,6] => [3,2,1,2] => 10010110 => 4
[2,7,5,4,1,3,8,6] => [2,2,2,2] => 10101010 => 4
[7,5,4,3,2,1,8,6] => [1,1,2,1,1,2] => 11101110 => 6
[8,5,3,2,1,7,6,4] => [1,2,1,1,2,1] => 11011101 => 6
[6,5,2,1,8,4,3,7] => [1,2,1,2,2] => 11011010 => 5
[4,6,3,2,8,1,5,7] => [3,1,4] => 10011000 => 3
[5,7,4,3,2,8,1,6] => [2,2,1,3] => 10101100 => 4
[1,7,6,2,4,8,3,5] => [1,1,3,3] => 11100100 => 4
[2,7,3,6,4,8,1,5] => [3,2,3] => 10010100 => 3
[6,2,7,5,3,8,1,4] => [2,1,2,3] => 10110100 => 4
[7,1,8,5,3,6,4,2] => [2,1,3,1,1] => 10110011 => 5
[5,8,1,6,2,7,4,3] => [3,2,2,1] => 10010101 => 4
[1,8,6,2,3,7,5,4] => [1,1,3,2,1] => 11100101 => 5
[1,8,6,3,2,7,5,4] => [1,1,2,1,2,1] => 11101101 => 6
[5,8,3,2,7,1,6,4] => [3,1,3,1] => 10011001 => 4
[8,7,3,1,6,5,4,2] => [1,2,1,2,1,1] => 11011011 => 6
[8,7,2,6,1,5,4,3] => [1,2,3,1,1] => 11010011 => 5
[1,8,5,7,4,3,6,2] => [1,1,3,2,1] => 11100101 => 5
[1,8,5,7,2,4,6,3] => [1,1,5,1] => 11100001 => 4
[3,8,6,1,7,2,5,4] => [2,2,3,1] => 10101001 => 4
[5,8,4,6,7,1,3,2] => [2,5,1] => 10100001 => 3
[7,2,8,5,6,1,4,3] => [2,1,4,1] => 10110001 => 4
[6,3,7,5,8,2,1,4] => [1,2,3,2] => 11010010 => 4
[3,7,2,6,8,4,1,5] => [3,3,2] => 10010010 => 3
[3,6,5,8,1,4,2,7] => [2,4,2] => 10100010 => 3
[2,6,5,8,4,1,3,7] => [2,3,3] => 10100100 => 3
[6,5,4,8,3,2,1,7] => [1,1,3,1,2] => 11100110 => 5
[8,4,3,7,2,1,6,5] => [1,2,2,2,1] => 11010101 => 5
[8,2,4,7,1,3,6,5] => [2,5,1] => 10100001 => 3
[6,2,5,8,1,4,3,7] => [2,4,2] => 10100010 => 3
[4,3,6,8,2,1,5,7] => [1,4,3] => 11000100 => 3
[6,3,5,1,8,4,2,7] => [1,3,2,2] => 11001010 => 4
[8,4,1,5,7,3,6,2] => [1,2,4,1] => 11010001 => 4
[6,4,2,5,8,3,1,7] => [1,2,3,2] => 11010010 => 4
[5,4,1,6,8,2,3,7] => [1,2,5] => 11010000 => 3
[6,5,2,1,7,8,3,4] => [1,2,1,4] => 11011000 => 4
[6,3,7,4,8,5,2,1] => [1,3,2,1,1] => 11001011 => 5
[4,7,2,5,8,6,3,1] => [3,3,1,1] => 10010011 => 4
[6,3,1,8,4,7,5,2] => [1,2,2,2,1] => 11010101 => 5
[6,4,2,8,7,3,5,1] => [1,2,1,3,1] => 11011001 => 5
[6,5,3,8,7,4,1,2] => [1,2,1,2,2] => 11011010 => 5
[8,5,3,7,6,4,2,1] => [1,2,1,2,1,1] => 11011011 => 6
[5,4,8,1,7,6,2,3] => [1,3,2,2] => 11001010 => 4
[5,2,8,1,7,3,6,4] => [2,2,3,1] => 10101001 => 4
[6,4,8,2,1,7,5,3] => [1,3,1,2,1] => 11001101 => 5
[3,6,8,1,4,7,5,2] => [5,2,1] => 10000101 => 3
[5,7,3,8,1,6,4,2] => [3,3,1,1] => 10010011 => 4
[6,4,7,8,1,5,3,2] => [1,5,1,1] => 11000011 => 4
[6,3,7,8,5,2,4,1] => [1,4,2,1] => 11000101 => 4
[2,5,8,7,1,3,6,4] => [3,4,1] => 10010001 => 3
[5,3,8,7,2,1,6,4] => [1,2,2,2,1] => 11010101 => 5
[8,3,7,6,1,5,4,2] => [1,2,3,1,1] => 11010011 => 5
[8,2,7,6,5,1,4,3] => [2,1,2,2,1] => 10110101 => 5
[4,3,8,7,6,2,1,5] => [1,2,1,2,2] => 11011010 => 5
[2,4,8,7,6,1,3,5] => [3,1,4] => 10011000 => 3
[3,5,8,7,2,6,1,4] => [3,3,2] => 10010010 => 3
[4,7,3,8,6,5,1,2] => [3,1,2,2] => 10011010 => 4
[7,5,8,6,4,3,2,1] => [1,2,2,1,1,1] => 11010111 => 6
[5,8,7,3,6,4,2,1] => [2,2,2,1,1] => 10101011 => 5
[4,8,7,6,2,5,3,1] => [2,1,3,1,1] => 10110011 => 5
[3,8,7,6,5,1,4,2] => [2,1,2,2,1] => 10110101 => 5
[2,8,7,6,5,4,1,3] => [2,1,2,1,2] => 10110110 => 5
[3,4,1,2,5,6,7,8,9] => [9] => 100000000 => 1
[3,2,1,4,5,6,7,8,9] => [2,7] => 101000000 => 2
[4,5,6,1,2,3,7,8,9] => [9] => 100000000 => 1
[4,2,5,1,3,6,7,8,9] => [2,7] => 101000000 => 2
[4,3,2,1,5,6,7,8,9] => [1,2,6] => 110100000 => 3
[5,6,7,8,1,2,3,4,9] => [9] => 100000000 => 1
[5,2,6,7,1,3,4,8,9] => [2,7] => 101000000 => 2
[5,6,3,4,1,2,7,8,9] => [4,5] => 100010000 => 2
[5,3,2,6,1,4,7,8,9] => [1,2,6] => 110100000 => 3
[6,2,7,8,9,1,3,4,5] => [2,7] => 101000000 => 2
[6,7,3,4,8,1,2,5,9] => [4,5] => 100010000 => 2
[6,3,2,7,8,1,4,5,9] => [1,2,6] => 110100000 => 3
[6,4,7,2,5,1,3,8,9] => [1,4,4] => 110001000 => 3
[7,4,8,2,5,9,1,3,6] => [1,4,4] => 110001000 => 3
[7,8,5,6,3,4,1,2,9] => [2,4,3] => 101000100 => 3
[7,5,3,8,2,6,1,4,9] => [1,2,3,3] => 110100100 => 4
[8,6,9,4,7,2,5,1,3] => [1,3,3,2] => 110010010 => 4
[3,4,1,2,5,6,7,8,9,10] => [10] => 1000000000 => 1
[4,5,6,1,2,3,7,8,9,10] => [10] => 1000000000 => 1
[5,6,7,8,1,2,3,4,9,10] => [10] => 1000000000 => 1
[6,5,4,3,2,1,7,8,9,10] => [1,1,2,1,5] => 1110110000 => 5
[7,5,4,3,2,8,1,6,9,10] => [1,1,2,1,5] => 1110110000 => 5
[8,6,4,3,9,2,7,1,5,10] => [1,1,2,3,3] => 1110100100 => 5
[3,6,5,1,2,4,8,7] => [2,4,2] => 10100010 => 3
[3,7,5,8,2,4,1,6] => [2,4,2] => 10100010 => 3
[3,8,5,7,2,4,1,6] => [2,4,2] => 10100010 => 3
[5,1,7,8,4,3,2,6] => [2,3,1,2] => 10100110 => 4
[5,1,2,6,4,3,8,7] => [3,2,1,2] => 10010110 => 4
[6,1,2,5,4,3,8,7] => [3,2,1,2] => 10010110 => 4
[5,1,2,4,6,3,8,7] => [4,2,2] => 10001010 => 3
[4,1,2,6,5,3,8,7] => [3,2,1,2] => 10010110 => 4
[4,1,5,7,8,3,2,6] => [2,4,2] => 10100010 => 3
[4,1,5,8,7,3,2,6] => [2,2,2,2] => 10101010 => 4
[4,7,1,8,3,6,2,5] => [3,3,2] => 10010010 => 3
[4,1,7,8,5,2,3,6] => [2,3,3] => 10100100 => 3
[5,1,7,4,8,2,3,6] => [2,2,4] => 10101000 => 3
[7,5,3,8,1,4,2,6] => [1,2,3,2] => 11010010 => 4
[2,1,5,8,7,3,4,6] => [2,2,4] => 10101000 => 3
[5,1,8,4,7,2,3,6] => [2,2,4] => 10101000 => 3
[4,1,8,7,5,2,3,6] => [2,1,2,3] => 10110100 => 4
[4,7,1,6,3,2,8,5] => [3,2,1,2] => 10010110 => 4
[6,1,2,3,7,5,8,4] => [4,2,2] => 10001010 => 3
[7,1,2,3,8,6,5,4] => [4,2,1,1] => 10001011 => 4
[7,1,2,3,5,8,6,4] => [5,2,1] => 10000101 => 3
[6,8,1,4,3,7,2,5] => [4,1,3] => 10001100 => 3
[8,7,3,2,4,1,6,5] => [1,2,2,2,1] => 11010101 => 5
[2,1,7,3,4,8,6,5] => [2,3,2,1] => 10100101 => 4
[7,8,3,2,4,1,6,5] => [3,2,2,1] => 10010101 => 4
[6,7,1,4,3,8,2,5] => [4,1,3] => 10001100 => 3
[8,1,2,3,5,7,6,4] => [5,2,1] => 10000101 => 3
[8,1,2,3,6,7,5,4] => [4,3,1] => 10001001 => 3
[7,1,2,3,6,8,5,4] => [4,3,1] => 10001001 => 3
[7,1,2,3,8,5,6,4] => [4,3,1] => 10001001 => 3
[8,1,2,3,7,5,6,4] => [4,3,1] => 10001001 => 3
[8,1,2,3,6,5,7,4] => [4,3,1] => 10001001 => 3
[7,1,8,5,4,3,2,6] => [2,1,2,1,2] => 10110110 => 5
[7,8,2,6,3,4,1,5] => [3,3,2] => 10010010 => 3
[6,8,2,7,3,4,1,5] => [3,3,2] => 10010010 => 3
[6,7,2,8,3,4,1,5] => [3,3,2] => 10010010 => 3
[3,8,7,1,4,2,6,5] => [2,3,2,1] => 10100101 => 4
[3,7,8,1,4,2,6,5] => [5,2,1] => 10000101 => 3
[3,6,8,1,4,2,7,5] => [5,2,1] => 10000101 => 3
[3,5,7,8,2,4,1,6] => [6,2] => 10000010 => 2
[3,6,7,1,4,2,8,5] => [5,1,2] => 10000110 => 3
[7,6,2,8,3,1,4,5] => [1,2,2,3] => 11010100 => 4
[8,6,2,7,3,1,4,5] => [1,2,2,3] => 11010100 => 4
[8,1,7,5,4,3,2,6] => [2,1,2,1,2] => 10110110 => 5
[8,1,7,4,5,3,2,6] => [2,3,1,2] => 10100110 => 4
[5,8,3,7,1,4,2,6] => [3,3,2] => 10010010 => 3
[2,1,7,3,4,6,8,5] => [2,4,2] => 10100010 => 3
[6,7,3,2,4,1,8,5] => [3,2,1,2] => 10010110 => 4
[8,7,2,4,3,6,1,5] => [1,3,2,2] => 11001010 => 4
[7,1,2,3,5,6,8,4] => [6,2] => 10000010 => 2
[6,1,2,3,8,7,4,5] => [4,1,3] => 10001100 => 3
[5,1,2,3,7,8,6,4] => [4,3,1] => 10001001 => 3
[5,1,2,3,8,7,6,4] => [4,1,2,1] => 10001101 => 4
[5,1,2,3,8,6,7,4] => [4,3,1] => 10001001 => 3
[6,1,2,3,5,8,7,4] => [5,2,1] => 10000101 => 3
[8,6,2,4,3,1,7,5] => [1,3,1,2,1] => 11001101 => 5
[7,6,3,2,4,8,1,5] => [1,2,2,3] => 11010100 => 4
[2,1,6,3,4,8,7,5] => [2,3,2,1] => 10100101 => 4
[8,6,3,2,4,7,1,5] => [1,2,2,3] => 11010100 => 4
[7,6,2,4,3,1,8,5] => [1,3,1,1,2] => 11001110 => 5
[6,1,2,3,5,7,8,4] => [5,3] => 10000100 => 2
[5,1,2,3,6,8,7,4] => [4,3,1] => 10001001 => 3
[7,8,1,2,6,3,5,4] => [4,3,1] => 10001001 => 3
[1,4,8,2,7,3,5,6] => [1,3,4] => 11001000 => 3
[1,2,8,5,4,7,3,6] => [2,1,2,3] => 10110100 => 4
[1,3,8,5,4,2,7,6] => [1,2,2,2,1] => 11010101 => 5
[2,3,6,8,4,7,1,5] => [5,3] => 10000100 => 2
[1,3,6,8,4,7,5,2] => [1,4,2,1] => 11000101 => 4
[2,4,8,1,7,3,6,5] => [4,3,1] => 10001001 => 3
[3,4,8,5,7,6,1,2] => [3,3,2] => 10010010 => 3
[1,2,6,8,4,5,7,3] => [2,5,1] => 10100001 => 3
[7,5,1,2,4,3,6,8] => [1,4,3] => 11000100 => 3
[7,4,6,1,5,2,3,8] => [1,4,3] => 11000100 => 3
[7,1,4,2,6,3,5,8] => [2,2,4] => 10101000 => 3
[6,8,1,4,7,2,3,5] => [4,4] => 10001000 => 2
[1,6,4,2,8,3,5,7] => [1,1,2,4] => 11101000 => 4
[1,6,3,8,5,4,2,7] => [1,2,2,1,2] => 11010110 => 5
[6,8,1,7,3,5,4,2] => [3,3,1,1] => 10010011 => 4
[7,1,3,6,5,4,2,8] => [3,2,1,2] => 10010110 => 4
[7,3,1,6,5,4,2,8] => [1,2,2,1,2] => 11010110 => 5
[7,2,1,4,6,3,5,8] => [2,2,4] => 10101000 => 3
[7,2,3,6,5,1,4,8] => [3,2,3] => 10010100 => 3
[7,1,2,3,6,5,4,8] => [4,2,2] => 10001010 => 3
[6,8,1,2,7,3,5,4] => [4,3,1] => 10001001 => 3
[1,6,2,3,8,5,4,7] => [1,3,2,2] => 11001010 => 4
[1,5,8,2,7,6,3,4] => [1,3,2,2] => 11001010 => 4
[5,1,8,2,7,6,3,4] => [2,2,2,2] => 10101010 => 4
[5,8,2,7,6,3,4,1] => [3,1,3,1] => 10011001 => 4
[6,2,8,1,7,3,5,4] => [2,2,3,1] => 10101001 => 4
[6,8,2,1,7,4,3,5] => [3,1,2,2] => 10011010 => 4
[3,6,4,1,2,8,5,7] => [2,3,3] => 10100100 => 3
[2,1,6,3,8,5,4,7] => [2,2,2,2] => 10101010 => 4
[2,5,1,8,7,6,3,4] => [3,1,2,2] => 10011010 => 4
[2,5,3,8,7,4,6,1] => [3,1,3,1] => 10011001 => 4
[1,2,5,3,8,7,4,6] => [2,2,1,3] => 10101100 => 4
[2,4,8,7,6,5,1,3] => [3,1,2,2] => 10011010 => 4
[2,5,3,8,7,1,6,4] => [3,1,3,1] => 10011001 => 4
[2,5,8,4,1,7,6,3] => [4,1,2,1] => 10001101 => 4
[3,5,8,7,1,4,2,6] => [3,3,2] => 10010010 => 3
[5,3,8,4,1,7,6,2] => [1,3,1,2,1] => 11001101 => 5
[4,2,8,7,6,3,5,1] => [2,1,1,3,1] => 10111001 => 5
[4,2,8,7,6,5,3,1] => [2,1,1,2,1,1] => 10111011 => 6
[4,1,8,7,6,5,3,2] => [2,1,1,2,1,1] => 10111011 => 6
[4,3,8,7,6,5,1,2] => [1,2,1,2,2] => 11011010 => 5
[6,3,1,8,7,2,5,4] => [1,2,1,3,1] => 11011001 => 5
[5,8,3,7,6,1,4,2] => [3,1,3,1] => 10011001 => 4
[5,1,3,8,7,6,2,4] => [3,1,2,2] => 10011010 => 4
[1,5,3,8,7,6,2,4] => [1,2,1,2,2] => 11011010 => 5
[1,5,8,4,7,2,6,3] => [1,3,3,1] => 11001001 => 4
[5,1,8,4,7,2,6,3] => [2,2,3,1] => 10101001 => 4
[5,8,7,4,6,1,2,3] => [2,2,4] => 10101000 => 3
[6,8,5,1,2,4,7,3] => [2,5,1] => 10100001 => 3
[5,6,3,1,2,4,8,7] => [3,3,2] => 10010010 => 3
[5,6,2,4,3,1,8,7] => [4,1,1,2] => 10001110 => 4
[5,6,1,2,4,3,8,7] => [5,1,2] => 10000110 => 3
[4,5,8,1,7,2,3,6] => [4,4] => 10001000 => 2
[4,5,8,1,7,2,6,3] => [4,3,1] => 10001001 => 3
[1,3,2,5,8,7,4,6] => [1,2,2,3] => 11010100 => 4
[3,5,1,8,7,4,6,2] => [3,1,3,1] => 10011001 => 4
[3,5,1,8,7,2,6,4] => [3,1,3,1] => 10011001 => 4
[4,3,6,1,2,8,5,7] => [1,4,3] => 11000100 => 3
[4,5,8,3,1,7,2,6] => [4,1,3] => 10001100 => 3
[4,5,2,8,7,1,3,6] => [3,1,4] => 10011000 => 3
[3,2,5,8,7,1,6,4] => [2,2,3,1] => 10101001 => 4
[3,4,8,7,6,2,1,5] => [3,1,2,2] => 10011010 => 4
[3,1,4,8,7,6,2,5] => [2,2,2,2] => 10101010 => 4
[3,4,8,7,6,5,1,2] => [3,1,2,2] => 10011010 => 4
[1,3,4,8,7,6,2,5] => [1,3,2,2] => 11001010 => 4
[3,4,8,7,6,2,5,1] => [3,1,3,1] => 10011001 => 4
[3,2,5,8,7,4,6,1] => [2,2,3,1] => 10101001 => 4
[4,5,8,3,1,7,6,2] => [4,1,2,1] => 10001101 => 4
[2,1,3,5,8,7,4,6] => [3,2,3] => 10010100 => 3
[1,2,7,5,8,6,4,3] => [2,1,3,1,1] => 10110011 => 5
[7,1,4,8,2,6,5,3] => [2,4,1,1] => 10100011 => 4
[6,8,1,3,7,5,2,4] => [4,2,2] => 10001010 => 3
[3,7,8,1,2,6,5,4] => [6,1,1] => 10000011 => 3
[1,3,7,8,2,6,5,4] => [1,5,1,1] => 11000011 => 4
[2,3,7,8,1,6,5,4] => [6,1,1] => 10000011 => 3
[2,7,8,1,3,6,5,4] => [6,1,1] => 10000011 => 3
[8,1,2,6,7,3,5,4] => [3,4,1] => 10010001 => 3
[8,1,2,6,7,5,3,4] => [3,3,2] => 10010010 => 3
[8,2,5,7,1,3,6,4] => [2,5,1] => 10100001 => 3
[2,8,1,6,7,3,5,4] => [3,4,1] => 10010001 => 3
[2,6,8,3,7,1,5,4] => [4,3,1] => 10001001 => 3
[2,8,6,4,7,1,5,3] => [2,2,3,1] => 10101001 => 4
[6,8,3,4,1,7,5,2] => [4,1,2,1] => 10001101 => 4
[6,8,3,7,4,1,5,2] => [3,2,2,1] => 10010101 => 4
[2,6,8,3,7,5,1,4] => [4,2,2] => 10001010 => 3
[2,8,1,6,7,5,3,4] => [3,3,2] => 10010010 => 3
[8,2,5,7,1,6,3,4] => [2,4,2] => 10100010 => 3
[8,4,7,2,3,6,1,5] => [1,5,2] => 11000010 => 3
[8,5,7,4,2,6,1,3] => [1,3,2,2] => 11001010 => 4
[8,3,5,7,4,1,6,2] => [1,4,2,1] => 11000101 => 4
[8,5,2,4,7,1,6,3] => [1,3,3,1] => 11001001 => 4
[8,2,3,5,7,1,6,4] => [3,4,1] => 10010001 => 3
[8,2,4,7,3,6,1,5] => [2,4,2] => 10100010 => 3
[8,2,7,1,4,6,3,5] => [2,4,2] => 10100010 => 3
[8,7,1,2,4,6,3,5] => [1,5,2] => 11000010 => 3
[8,7,1,4,6,2,3,5] => [1,3,4] => 11001000 => 3
[8,4,7,1,3,6,2,5] => [1,5,2] => 11000010 => 3
[1,6,8,3,7,2,5,4] => [1,3,3,1] => 11001001 => 4
[8,3,5,7,1,2,6,4] => [1,6,1] => 11000001 => 3
[5,8,7,1,3,6,2,4] => [2,4,2] => 10100010 => 3
[8,5,4,7,1,6,2,3] => [1,1,4,2] => 11100010 => 4
[8,5,4,7,1,2,6,3] => [1,1,5,1] => 11100001 => 4
[8,5,1,4,7,2,6,3] => [1,3,3,1] => 11001001 => 4
[1,4,6,8,2,7,5,3] => [1,4,2,1] => 11000101 => 4
[1,6,5,8,2,7,4,3] => [1,1,3,2,1] => 11100101 => 5
[8,5,6,3,1,7,4,2] => [1,3,1,2,1] => 11001101 => 5
[5,6,2,8,1,7,4,3] => [3,2,2,1] => 10010101 => 4
[1,8,4,5,7,2,6,3] => [1,1,5,1] => 11100001 => 4
[5,8,7,3,6,1,2,4] => [2,2,4] => 10101000 => 3
[8,3,5,7,1,6,2,4] => [1,5,2] => 11000010 => 3
[1,6,8,3,7,5,2,4] => [1,3,2,2] => 11001010 => 4
[6,3,8,2,7,5,1,4] => [1,3,2,2] => 11001010 => 4
[6,8,4,2,7,1,5,3] => [2,2,3,1] => 10101001 => 4
[8,6,4,7,3,1,5,2] => [1,1,3,2,1] => 11100101 => 5
[8,4,5,7,3,1,6,2] => [1,4,2,1] => 11000101 => 4
[8,4,2,5,7,1,6,3] => [1,2,4,1] => 11010001 => 4
[8,3,4,7,2,6,1,5] => [1,5,2] => 11000010 => 3
[8,7,1,3,4,6,2,5] => [1,5,2] => 11000010 => 3
[8,3,7,2,4,6,1,5] => [1,5,2] => 11000010 => 3
[2,8,4,5,7,1,6,3] => [2,5,1] => 10100001 => 3
[8,7,3,4,5,1,6,2] => [1,4,2,1] => 11000101 => 4
[8,7,4,5,2,6,1,3] => [1,1,4,2] => 11100010 => 4
[5,8,7,2,3,6,1,4] => [2,4,2] => 10100010 => 3
[8,7,2,3,4,6,1,5] => [1,5,2] => 11000010 => 3
[8,7,2,3,6,1,4,5] => [1,3,4] => 11001000 => 3
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Description
The number of ones in a binary word.
This is also known as the Hamming weight of the word.
Map
DEX composition
Description
The DEX composition of a permutation.
Let $\pi$ be a permutation in $\mathfrak S_n$. Let $\bar\pi$ be the word in the ordered set $\bar 1 < \dots < \bar n < 1 \dots < n$ obtained from $\pi$ by replacing every excedance $\pi(i) > i$ by $\overline{\pi(i)}$. Then the DEX set of $\pi$ is the set of indices $1 \leq i < n$ such that $\bar\pi(i) > \bar\pi(i+1)$. Finally, the DEX composition $c_1, \dots, c_k$ of $n$ corresponds to the DEX subset $\{c_1, c_1 + c_2, \dots, c_1 + \dots + c_{k-1}\}$.
The (quasi)symmetric function
$$ \sum_{\pi\in\mathfrak S_{\lambda, j}} F_{DEX(\pi)}, $$
where the sum is over the set of permutations of cycle type $\lambda$ with $j$ excedances, is the Eulerian quasisymmetric function.
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 $0$.