Identifier
-
Mp00114:
Permutations
—connectivity set⟶
Binary words
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000772: Graphs ⟶ ℤ
Values
[1,2] => 1 => [1] => ([],1) => 1
[2,1] => 0 => [1] => ([],1) => 1
[1,3,2] => 10 => [1,1] => ([(0,1)],2) => 1
[2,1,3] => 01 => [1,1] => ([(0,1)],2) => 1
[1,2,4,3] => 110 => [2,1] => ([(0,2),(1,2)],3) => 1
[1,3,2,4] => 101 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 2
[2,1,4,3] => 010 => [1,1,1] => ([(0,1),(0,2),(1,2)],3) => 2
[2,3,1,4] => 001 => [2,1] => ([(0,2),(1,2)],3) => 1
[3,1,2,4] => 001 => [2,1] => ([(0,2),(1,2)],3) => 1
[3,2,1,4] => 001 => [2,1] => ([(0,2),(1,2)],3) => 1
[1,2,3,5,4] => 1110 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[1,2,4,3,5] => 1101 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
[1,3,2,5,4] => 1010 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[1,3,4,2,5] => 1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 1
[1,4,2,3,5] => 1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 1
[1,4,3,2,5] => 1001 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 1
[2,1,3,5,4] => 0110 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4) => 1
[2,1,4,3,5] => 0101 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 3
[2,3,1,5,4] => 0010 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
[2,3,4,1,5] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[2,4,1,3,5] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[2,4,3,1,5] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[3,1,2,5,4] => 0010 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
[3,1,4,2,5] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[3,2,1,5,4] => 0010 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4) => 1
[3,2,4,1,5] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[3,4,1,2,5] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[3,4,2,1,5] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[4,1,2,3,5] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[4,1,3,2,5] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[4,2,1,3,5] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[4,2,3,1,5] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[4,3,1,2,5] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[4,3,2,1,5] => 0001 => [3,1] => ([(0,3),(1,3),(2,3)],4) => 2
[1,2,3,4,6,5] => 11110 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[1,2,3,5,4,6] => 11101 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,2,4,3,6,5] => 11010 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[1,2,4,5,3,6] => 11001 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[1,2,5,3,4,6] => 11001 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[1,2,5,4,3,6] => 11001 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[1,3,2,4,6,5] => 10110 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[1,3,2,5,4,6] => 10101 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[1,3,4,2,6,5] => 10010 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[1,3,4,5,2,6] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,3,5,2,4,6] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,3,5,4,2,6] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,4,2,3,6,5] => 10010 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[1,4,2,5,3,6] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,4,3,2,6,5] => 10010 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[1,4,3,5,2,6] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,4,5,2,3,6] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,4,5,3,2,6] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,5,2,3,4,6] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,5,2,4,3,6] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,5,3,2,4,6] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,5,3,4,2,6] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,5,4,2,3,6] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[1,5,4,3,2,6] => 10001 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[2,1,3,4,6,5] => 01110 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5) => 2
[2,1,3,5,4,6] => 01101 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[2,1,4,3,6,5] => 01010 => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 4
[2,1,4,5,3,6] => 01001 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[2,1,5,3,4,6] => 01001 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[2,1,5,4,3,6] => 01001 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[2,3,1,4,6,5] => 00110 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[2,3,1,5,4,6] => 00101 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[2,3,4,1,6,5] => 00010 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[2,3,4,5,1,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[2,3,5,1,4,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[2,3,5,4,1,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[2,4,1,3,6,5] => 00010 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[2,4,1,5,3,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[2,4,3,1,6,5] => 00010 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[2,4,3,5,1,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[2,4,5,1,3,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[2,4,5,3,1,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[2,5,1,3,4,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[2,5,1,4,3,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[2,5,3,1,4,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[2,5,3,4,1,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[2,5,4,1,3,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[2,5,4,3,1,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[3,1,2,4,6,5] => 00110 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[3,1,2,5,4,6] => 00101 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[3,1,4,2,6,5] => 00010 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[3,1,4,5,2,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[3,1,5,2,4,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[3,1,5,4,2,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[3,2,1,4,6,5] => 00110 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[3,2,1,5,4,6] => 00101 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 1
[3,2,4,1,6,5] => 00010 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[3,2,4,5,1,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[3,2,5,1,4,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[3,2,5,4,1,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[3,4,1,2,6,5] => 00010 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[3,4,1,5,2,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[3,4,2,1,6,5] => 00010 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[3,4,2,5,1,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[3,4,5,1,2,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[3,4,5,2,1,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[3,5,1,2,4,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
>>> Load all 3144 entries. <<<[3,5,1,4,2,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[3,5,2,1,4,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[3,5,2,4,1,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[3,5,4,1,2,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[3,5,4,2,1,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[4,1,2,3,6,5] => 00010 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[4,1,2,5,3,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[4,1,3,2,6,5] => 00010 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[4,1,3,5,2,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[4,1,5,2,3,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[4,1,5,3,2,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[4,2,1,3,6,5] => 00010 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[4,2,1,5,3,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[4,2,3,1,6,5] => 00010 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[4,2,3,5,1,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[4,2,5,1,3,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[4,2,5,3,1,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[4,3,1,2,6,5] => 00010 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[4,3,1,5,2,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[4,3,2,1,6,5] => 00010 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) => 2
[4,3,2,5,1,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[4,3,5,1,2,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[4,3,5,2,1,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[4,5,1,2,3,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[4,5,1,3,2,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[4,5,2,1,3,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[4,5,2,3,1,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[4,5,3,1,2,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[4,5,3,2,1,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[5,1,2,3,4,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[5,1,2,4,3,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[5,1,3,2,4,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[5,1,3,4,2,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[5,1,4,2,3,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[5,1,4,3,2,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[5,2,1,3,4,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[5,2,1,4,3,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[5,2,3,1,4,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[5,2,3,4,1,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[5,2,4,1,3,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[5,2,4,3,1,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[5,3,1,2,4,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[5,3,1,4,2,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[5,3,2,1,4,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[5,3,2,4,1,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[5,3,4,1,2,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[5,3,4,2,1,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[5,4,1,2,3,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[5,4,1,3,2,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[5,4,2,1,3,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[5,4,2,3,1,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[5,4,3,1,2,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[5,4,3,2,1,6] => 00001 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5) => 3
[1,2,3,4,5,7,6] => 111110 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[1,2,3,4,6,5,7] => 111101 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,2,3,5,4,7,6] => 111010 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,2,3,5,6,4,7] => 111001 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,2,3,6,4,5,7] => 111001 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,2,3,6,5,4,7] => 111001 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,2,4,3,5,7,6] => 110110 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,2,4,3,6,5,7] => 110101 => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,2,4,5,3,7,6] => 110010 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,2,4,5,6,3,7] => 110001 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,2,4,6,3,5,7] => 110001 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,2,4,6,5,3,7] => 110001 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,2,5,3,4,7,6] => 110010 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,2,5,3,6,4,7] => 110001 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,2,5,4,3,7,6] => 110010 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,2,5,4,6,3,7] => 110001 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,2,5,6,3,4,7] => 110001 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,2,5,6,4,3,7] => 110001 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,2,6,3,4,5,7] => 110001 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,2,6,3,5,4,7] => 110001 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,2,6,4,3,5,7] => 110001 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,2,6,4,5,3,7] => 110001 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,2,6,5,3,4,7] => 110001 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,2,6,5,4,3,7] => 110001 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,3,2,4,5,7,6] => 101110 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,3,2,4,6,5,7] => 101101 => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,3,2,5,4,7,6] => 101010 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[1,3,2,5,6,4,7] => 101001 => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,3,2,6,4,5,7] => 101001 => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,3,2,6,5,4,7] => 101001 => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,3,4,2,5,7,6] => 100110 => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,3,4,2,6,5,7] => 100101 => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,3,4,5,2,7,6] => 100010 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,3,4,5,6,2,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,3,4,6,2,5,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,3,4,6,5,2,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,3,5,2,4,7,6] => 100010 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,3,5,2,6,4,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,3,5,4,2,7,6] => 100010 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,3,5,4,6,2,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,3,5,6,2,4,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,3,5,6,4,2,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,3,6,2,4,5,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,3,6,2,5,4,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,3,6,4,2,5,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,3,6,4,5,2,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,3,6,5,2,4,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,3,6,5,4,2,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,4,2,3,5,7,6] => 100110 => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,4,2,3,6,5,7] => 100101 => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,4,2,5,3,7,6] => 100010 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,4,2,5,6,3,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,4,2,6,3,5,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,4,2,6,5,3,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,4,3,2,5,7,6] => 100110 => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,4,3,2,6,5,7] => 100101 => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[1,4,3,5,2,7,6] => 100010 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,4,3,5,6,2,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,4,3,6,2,5,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,4,3,6,5,2,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,4,5,2,3,7,6] => 100010 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,4,5,2,6,3,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,4,5,3,2,7,6] => 100010 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,4,5,3,6,2,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,4,5,6,2,3,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,4,5,6,3,2,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,4,6,2,3,5,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,4,6,2,5,3,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,4,6,3,2,5,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,4,6,3,5,2,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,4,6,5,2,3,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,4,6,5,3,2,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,5,2,3,4,7,6] => 100010 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,5,2,3,6,4,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,5,2,4,3,7,6] => 100010 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,5,2,4,6,3,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,5,2,6,3,4,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,5,2,6,4,3,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,5,3,2,4,7,6] => 100010 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,5,3,2,6,4,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,5,3,4,2,7,6] => 100010 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,5,3,4,6,2,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,5,3,6,2,4,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,5,3,6,4,2,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,5,4,2,3,7,6] => 100010 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,5,4,2,6,3,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,5,4,3,2,7,6] => 100010 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[1,5,4,3,6,2,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,5,4,6,2,3,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,5,4,6,3,2,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,5,6,2,3,4,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,5,6,2,4,3,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,5,6,3,2,4,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,5,6,3,4,2,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,5,6,4,2,3,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,5,6,4,3,2,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,6,2,3,4,5,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,6,2,3,5,4,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,6,2,4,3,5,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,6,2,4,5,3,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,6,2,5,3,4,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,6,2,5,4,3,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,6,3,2,4,5,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,6,3,2,5,4,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,6,3,4,2,5,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,6,3,4,5,2,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,6,3,5,2,4,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,6,3,5,4,2,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,6,4,2,3,5,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,6,4,2,5,3,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,6,4,3,2,5,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,6,4,3,5,2,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,6,4,5,2,3,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,6,4,5,3,2,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,6,5,2,3,4,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,6,5,2,4,3,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,6,5,3,2,4,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,6,5,3,4,2,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,6,5,4,2,3,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[1,6,5,4,3,2,7] => 100001 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[2,1,3,4,5,7,6] => 011110 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) => 3
[2,1,3,4,6,5,7] => 011101 => [1,3,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,3,5,4,7,6] => 011010 => [1,2,1,1,1] => ([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[2,1,3,5,6,4,7] => 011001 => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[2,1,3,6,4,5,7] => 011001 => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[2,1,3,6,5,4,7] => 011001 => [1,2,2,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[2,1,4,3,5,7,6] => 010110 => [1,1,1,2,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[2,1,4,3,6,5,7] => 010101 => [1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 5
[2,1,4,5,3,7,6] => 010010 => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[2,1,4,5,6,3,7] => 010001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,4,6,3,5,7] => 010001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,4,6,5,3,7] => 010001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,5,3,4,7,6] => 010010 => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[2,1,5,3,6,4,7] => 010001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,5,4,3,7,6] => 010010 => [1,1,2,1,1] => ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[2,1,5,4,6,3,7] => 010001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,5,6,3,4,7] => 010001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,5,6,4,3,7] => 010001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,6,3,4,5,7] => 010001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,6,3,5,4,7] => 010001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,6,4,3,5,7] => 010001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,6,4,5,3,7] => 010001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,6,5,3,4,7] => 010001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,1,6,5,4,3,7] => 010001 => [1,1,3,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,3,1,4,5,7,6] => 001110 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,3,1,4,6,5,7] => 001101 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[2,3,1,5,4,7,6] => 001010 => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[2,3,1,5,6,4,7] => 001001 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[2,3,1,6,4,5,7] => 001001 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[2,3,1,6,5,4,7] => 001001 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[2,3,4,1,5,7,6] => 000110 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[2,3,4,1,6,5,7] => 000101 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,3,4,5,1,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[2,3,4,5,6,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,4,6,1,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,4,6,5,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,5,1,4,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[2,3,5,1,6,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,5,4,1,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[2,3,5,4,6,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,5,6,1,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,5,6,4,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,6,1,4,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,6,1,5,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,6,4,1,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,6,4,5,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,6,5,1,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,3,6,5,4,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,1,3,5,7,6] => 000110 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[2,4,1,3,6,5,7] => 000101 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,4,1,5,3,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[2,4,1,5,6,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,1,6,3,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,1,6,5,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,3,1,5,7,6] => 000110 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[2,4,3,1,6,5,7] => 000101 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[2,4,3,5,1,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[2,4,3,5,6,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,3,6,1,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,3,6,5,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,5,1,3,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[2,4,5,1,6,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,5,3,1,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[2,4,5,3,6,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,5,6,1,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,5,6,3,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,6,1,3,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,6,1,5,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,6,3,1,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,6,3,5,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,6,5,1,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,4,6,5,3,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,1,3,4,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[2,5,1,3,6,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,1,4,3,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[2,5,1,4,6,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,1,6,3,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,1,6,4,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,3,1,4,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[2,5,3,1,6,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,3,4,1,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[2,5,3,4,6,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,3,6,1,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,3,6,4,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,4,1,3,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[2,5,4,1,6,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,4,3,1,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[2,5,4,3,6,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,4,6,1,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,4,6,3,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,6,1,3,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,6,1,4,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,6,3,1,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,6,3,4,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,6,4,1,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,5,6,4,3,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,1,3,4,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,1,3,5,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,1,4,3,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,1,4,5,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,1,5,3,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,1,5,4,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,3,1,4,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,3,1,5,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,3,4,1,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,3,4,5,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,3,5,1,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,3,5,4,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,4,1,3,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,4,1,5,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,4,3,1,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,4,3,5,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,4,5,1,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,4,5,3,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,5,1,3,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,5,1,4,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,5,3,1,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,5,3,4,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,5,4,1,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[2,6,5,4,3,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,1,2,4,5,7,6] => 001110 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,1,2,4,6,5,7] => 001101 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[3,1,2,5,4,7,6] => 001010 => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[3,1,2,5,6,4,7] => 001001 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[3,1,2,6,4,5,7] => 001001 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[3,1,2,6,5,4,7] => 001001 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[3,1,4,2,5,7,6] => 000110 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[3,1,4,2,6,5,7] => 000101 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,1,4,5,2,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,1,4,5,6,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,1,4,6,2,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,1,4,6,5,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,1,5,2,4,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,1,5,2,6,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,1,5,4,2,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,1,5,4,6,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,1,5,6,2,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,1,5,6,4,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,1,6,2,4,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,1,6,2,5,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,1,6,4,2,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,1,6,4,5,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,1,6,5,2,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,1,6,5,4,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,2,1,4,5,7,6] => 001110 => [2,3,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,1,4,6,5,7] => 001101 => [2,2,1,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[3,2,1,5,4,7,6] => 001010 => [2,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[3,2,1,5,6,4,7] => 001001 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[3,2,1,6,4,5,7] => 001001 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[3,2,1,6,5,4,7] => 001001 => [2,1,2,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[3,2,4,1,5,7,6] => 000110 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[3,2,4,1,6,5,7] => 000101 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,2,4,5,1,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,2,4,5,6,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,2,4,6,1,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,2,4,6,5,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,2,5,1,4,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,2,5,1,6,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,2,5,4,1,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,2,5,4,6,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,2,5,6,1,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,2,5,6,4,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,2,6,1,4,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,2,6,1,5,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,2,6,4,1,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,2,6,4,5,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,2,6,5,1,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,2,6,5,4,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,1,2,5,7,6] => 000110 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[3,4,1,2,6,5,7] => 000101 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,4,1,5,2,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,4,1,5,6,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,1,6,2,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,1,6,5,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,2,1,5,7,6] => 000110 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[3,4,2,1,6,5,7] => 000101 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[3,4,2,5,1,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,4,2,5,6,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,2,6,1,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,2,6,5,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,5,1,2,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,4,5,1,6,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,5,2,1,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,4,5,2,6,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,5,6,1,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,5,6,2,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,6,1,2,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,6,1,5,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,6,2,1,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,6,2,5,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,6,5,1,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,4,6,5,2,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,5,1,2,4,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,5,1,2,6,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,5,1,4,2,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,5,1,4,6,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,5,1,6,2,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,5,1,6,4,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,5,2,1,4,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,5,2,1,6,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,5,2,4,1,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,5,2,4,6,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,5,2,6,1,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,5,2,6,4,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,5,4,1,2,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,5,4,1,6,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,5,4,2,1,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[3,5,4,2,6,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,5,4,6,1,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,5,4,6,2,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,5,6,1,2,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,5,6,1,4,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,5,6,2,1,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,5,6,2,4,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,5,6,4,1,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,5,6,4,2,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,1,2,4,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,1,2,5,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,1,4,2,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,1,4,5,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,1,5,2,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,1,5,4,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,2,1,4,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,2,1,5,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,2,4,1,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,2,4,5,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,2,5,1,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,2,5,4,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,4,1,2,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,4,1,5,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,4,2,1,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,4,2,5,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,4,5,1,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,4,5,2,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,5,1,2,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,5,1,4,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,5,2,1,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,5,2,4,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,5,4,1,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[3,6,5,4,2,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,1,2,3,5,7,6] => 000110 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[4,1,2,3,6,5,7] => 000101 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,1,2,5,3,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,1,2,5,6,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,1,2,6,3,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,1,2,6,5,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,1,3,2,5,7,6] => 000110 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[4,1,3,2,6,5,7] => 000101 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,1,3,5,2,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,1,3,5,6,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,1,3,6,2,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,1,3,6,5,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,1,5,2,3,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,1,5,2,6,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,1,5,3,2,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,1,5,3,6,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,1,5,6,2,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,1,5,6,3,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,1,6,2,3,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,1,6,2,5,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,1,6,3,2,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,1,6,3,5,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,1,6,5,2,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,1,6,5,3,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,2,1,3,5,7,6] => 000110 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[4,2,1,3,6,5,7] => 000101 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,1,5,3,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,2,1,5,6,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,2,1,6,3,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,2,1,6,5,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,2,3,1,5,7,6] => 000110 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[4,2,3,1,6,5,7] => 000101 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,2,3,5,1,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,2,3,5,6,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,2,3,6,1,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,2,3,6,5,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,2,5,1,3,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,2,5,1,6,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,2,5,3,1,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,2,5,3,6,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,2,5,6,1,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,2,5,6,3,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,2,6,1,3,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,2,6,1,5,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,2,6,3,1,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,2,6,3,5,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,2,6,5,1,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,2,6,5,3,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,3,1,2,5,7,6] => 000110 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[4,3,1,2,6,5,7] => 000101 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,3,1,5,2,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,3,1,5,6,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,3,1,6,2,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,3,1,6,5,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,3,2,1,5,7,6] => 000110 => [3,2,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 1
[4,3,2,1,6,5,7] => 000101 => [3,1,1,1] => ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 2
[4,3,2,5,1,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,3,2,5,6,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,3,2,6,1,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,3,2,6,5,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,3,5,1,2,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,3,5,1,6,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,3,5,2,1,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,3,5,2,6,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,3,5,6,1,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,3,5,6,2,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,3,6,1,2,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,3,6,1,5,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,3,6,2,1,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,3,6,2,5,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,3,6,5,1,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,3,6,5,2,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,5,1,2,3,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,5,1,2,6,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,5,1,3,2,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,5,1,3,6,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,5,1,6,2,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,5,1,6,3,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,5,2,1,3,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,5,2,1,6,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,5,2,3,1,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,5,2,3,6,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,5,2,6,1,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,5,2,6,3,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,5,3,1,2,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,5,3,1,6,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,5,3,2,1,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[4,5,3,2,6,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,5,3,6,1,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,5,3,6,2,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,5,6,1,2,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,5,6,1,3,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,5,6,2,1,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,5,6,2,3,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,5,6,3,1,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,5,6,3,2,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,1,2,3,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,1,2,5,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,1,3,2,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,1,3,5,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,1,5,2,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,1,5,3,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,2,1,3,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,2,1,5,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,2,3,1,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,2,3,5,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,2,5,1,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,2,5,3,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,3,1,2,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,3,1,5,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,3,2,1,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,3,2,5,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,3,5,1,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,3,5,2,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,5,1,2,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,5,1,3,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,5,2,1,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,5,2,3,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,5,3,1,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[4,6,5,3,2,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,1,2,3,4,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,1,2,3,6,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,1,2,4,3,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,1,2,4,6,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,1,2,6,3,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,1,2,6,4,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,1,3,2,4,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,1,3,2,6,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,1,3,4,2,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,1,3,4,6,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,1,3,6,2,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,1,3,6,4,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,1,4,2,3,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,1,4,2,6,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,1,4,3,2,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,1,4,3,6,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,1,4,6,2,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,1,4,6,3,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,1,6,2,3,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,1,6,2,4,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,1,6,3,2,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,1,6,3,4,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,1,6,4,2,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,1,6,4,3,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,2,1,3,4,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,2,1,3,6,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,2,1,4,3,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,2,1,4,6,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,2,1,6,3,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,2,1,6,4,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,2,3,1,4,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,2,3,1,6,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,2,3,4,1,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,2,3,4,6,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,2,3,6,1,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,2,3,6,4,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,2,4,1,3,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,2,4,1,6,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,2,4,3,1,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,2,4,3,6,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,2,4,6,1,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,2,4,6,3,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,2,6,1,3,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,2,6,1,4,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,2,6,3,1,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,2,6,3,4,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,2,6,4,1,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,2,6,4,3,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,3,1,2,4,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,3,1,2,6,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,3,1,4,2,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,3,1,4,6,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,3,1,6,2,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,3,1,6,4,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,3,2,1,4,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,3,2,1,6,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,3,2,4,1,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,3,2,4,6,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,3,2,6,1,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,3,2,6,4,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,3,4,1,2,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,3,4,1,6,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,3,4,2,1,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,3,4,2,6,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,3,4,6,1,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,3,4,6,2,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,3,6,1,2,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,3,6,1,4,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,3,6,2,1,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,3,6,2,4,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,3,6,4,1,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,3,6,4,2,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,4,1,2,3,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,4,1,2,6,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,4,1,3,2,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,4,1,3,6,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,4,1,6,2,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,4,1,6,3,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,4,2,1,3,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,4,2,1,6,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,4,2,3,1,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,4,2,3,6,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,4,2,6,1,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,4,2,6,3,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,4,3,1,2,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,4,3,1,6,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,4,3,2,1,7,6] => 000010 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) => 3
[5,4,3,2,6,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,4,3,6,1,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,4,3,6,2,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,4,6,1,2,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,4,6,1,3,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,4,6,2,1,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,4,6,2,3,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,4,6,3,1,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,4,6,3,2,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,1,2,3,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,1,2,4,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,1,3,2,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,1,3,4,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,1,4,2,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,1,4,3,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,2,1,3,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,2,1,4,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,2,3,1,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,2,3,4,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,2,4,1,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,2,4,3,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,3,1,2,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,3,1,4,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,3,2,1,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,3,2,4,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,3,4,1,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,3,4,2,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,4,1,2,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,4,1,3,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,4,2,1,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,4,2,3,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,4,3,1,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[5,6,4,3,2,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,1,2,3,4,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,1,2,3,5,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,1,2,4,3,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,1,2,4,5,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,1,2,5,3,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,1,2,5,4,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,1,3,2,4,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,1,3,2,5,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,1,3,4,2,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,1,3,4,5,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,1,3,5,2,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,1,3,5,4,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,1,4,2,3,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,1,4,2,5,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,1,4,3,2,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,1,4,3,5,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,1,4,5,2,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,1,4,5,3,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,1,5,2,3,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,1,5,2,4,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,1,5,3,2,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,1,5,3,4,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,1,5,4,2,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,1,5,4,3,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,2,1,3,4,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,2,1,3,5,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,2,1,4,3,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,2,1,4,5,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,2,1,5,3,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,2,1,5,4,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,2,3,1,4,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,2,3,1,5,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,2,3,4,1,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,2,3,4,5,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,2,3,5,1,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,2,3,5,4,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,2,4,1,3,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,2,4,1,5,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,2,4,3,1,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,2,4,3,5,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,2,4,5,1,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,2,4,5,3,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,2,5,1,3,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,2,5,1,4,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,2,5,3,1,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,2,5,3,4,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,2,5,4,1,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,2,5,4,3,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,3,1,2,4,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,3,1,2,5,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,3,1,4,2,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,3,1,4,5,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,3,1,5,2,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,3,1,5,4,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,3,2,1,4,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,3,2,1,5,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,3,2,4,1,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,3,2,4,5,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,3,2,5,1,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,3,2,5,4,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,3,4,1,2,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,3,4,1,5,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,3,4,2,1,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,3,4,2,5,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,3,4,5,1,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,3,4,5,2,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,3,5,1,2,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,3,5,1,4,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,3,5,2,1,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,3,5,2,4,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,3,5,4,1,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,3,5,4,2,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,4,1,2,3,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,4,1,2,5,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,4,1,3,2,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,4,1,3,5,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,4,1,5,2,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,4,1,5,3,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,4,2,1,3,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,4,2,1,5,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,4,2,3,1,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,4,2,3,5,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,4,2,5,1,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,4,2,5,3,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,4,3,1,2,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,4,3,1,5,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,4,3,2,1,5,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,4,3,2,5,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,4,3,5,1,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,4,3,5,2,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,4,5,1,2,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,4,5,1,3,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,4,5,2,1,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,4,5,2,3,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,4,5,3,1,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,4,5,3,2,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,1,2,3,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,1,2,4,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,1,3,2,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,1,3,4,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,1,4,2,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,1,4,3,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,2,1,3,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,2,1,4,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,2,3,1,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,2,3,4,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,2,4,1,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,2,4,3,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,3,1,2,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,3,1,4,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,3,2,1,4,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,3,2,4,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,3,4,1,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,3,4,2,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,4,1,2,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,4,1,3,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,4,2,1,3,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,4,2,3,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,4,3,1,2,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[6,5,4,3,2,1,7] => 000001 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6) => 4
[7,6,5,4,3,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,5,4,3,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,6,4,3,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,7,4,3,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,7,4,3,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,4,5,3,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,4,5,3,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,4,6,3,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,5,6,3,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,4,7,3,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,4,7,3,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,6,7,3,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,6,7,3,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,5,3,4,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,5,3,4,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,6,3,4,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,7,3,4,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,4,3,5,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,4,3,5,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,3,4,5,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,4,3,6,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,4,5,6,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,4,3,7,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,4,3,7,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,6,3,7,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,3,6,7,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,4,5,6,7,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,5,4,2,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,5,4,2,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,6,4,2,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,7,4,2,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,4,5,2,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,4,5,2,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,4,6,2,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,4,7,2,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,4,7,2,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,6,7,2,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,6,7,2,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,5,3,2,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,7,3,2,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,7,3,2,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,5,2,3,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,5,2,3,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,6,2,3,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,7,2,3,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,7,2,3,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,4,3,2,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,4,3,2,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,3,4,2,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,4,2,3,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,4,2,3,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,3,2,4,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,3,2,4,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,2,3,4,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,2,3,4,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,4,3,2,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,5,3,2,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,3,4,2,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,3,5,2,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,5,2,3,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,3,2,4,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,3,4,5,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,4,3,2,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,4,3,2,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,6,3,2,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,3,4,2,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,4,5,2,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,3,6,2,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,3,6,2,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,4,5,6,2,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,2,4,5,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,3,4,5,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,3,2,6,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,2,3,6,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,3,4,6,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,2,5,6,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,4,2,5,6,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,3,5,6,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,4,5,6,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,3,4,5,6,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,5,4,3,1,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,5,4,3,1,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,6,4,3,1,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,4,5,3,1,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,6,7,3,1,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,6,7,3,1,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,5,3,4,1,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,7,3,4,1,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,3,4,5,1,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,4,3,7,1,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,5,3,7,1,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,3,4,7,1,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,5,6,7,1,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,4,5,6,7,1,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,5,4,2,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,7,4,2,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,4,5,2,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,6,7,2,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,5,4,1,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,7,4,1,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,5,6,1,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,4,7,1,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,6,7,1,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,5,3,2,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,5,2,3,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,7,3,1,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,5,2,1,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,5,2,1,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,7,2,1,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,5,1,2,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,5,1,2,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,6,1,2,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,7,1,2,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,7,1,2,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,4,3,2,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,4,3,2,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,3,4,2,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,3,4,2,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,4,2,3,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,3,2,4,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,3,2,4,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,2,3,4,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,2,3,4,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,4,3,1,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,3,4,1,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,4,2,1,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,3,2,1,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,3,2,1,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,2,3,1,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,3,1,2,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,1,2,3,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,1,2,3,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,4,3,2,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,5,3,2,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,3,5,2,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,4,5,2,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,4,2,3,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,3,2,4,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,2,3,4,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,3,4,5,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,4,3,1,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,5,2,1,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,5,1,2,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,3,2,1,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,2,3,1,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,3,1,2,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,1,2,3,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,3,2,1,5,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,3,4,1,5,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,3,1,2,5,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,1,2,3,5,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,2,1,4,5,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,3,1,4,5,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,1,2,4,5,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,1,3,4,5,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,2,3,4,5,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,4,3,2,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,6,4,3,2,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,6,5,3,2,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,6,3,2,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,5,6,3,2,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,6,5,4,2,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,3,6,5,2,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,4,5,6,2,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,6,5,4,3,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,3,2,6,5,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,3,2,6,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,5,3,2,6,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,5,4,2,6,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,2,5,4,6,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,3,2,5,6,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,4,3,5,6,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,3,4,5,6,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,5,4,3,2,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,5,6,4,3,2,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,5,4,6,3,2,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,3,6,5,4,2,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,3,4,5,6,2,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[2,1,6,5,4,3,8,7] => 0100010 => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[2,1,5,6,4,3,8,7] => 0100010 => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[2,1,5,4,6,3,8,7] => 0100010 => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[2,1,4,5,6,3,8,7] => 0100010 => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,2,4,5,6,3,8,7] => 1100010 => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[3,2,1,6,5,4,8,7] => 0010010 => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[2,3,1,6,5,4,8,7] => 0010010 => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,3,2,6,5,4,8,7] => 1010010 => [1,1,1,2,1,1] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,3,2,5,6,4,8,7] => 1010010 => [1,1,1,2,1,1] => ([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[2,1,3,6,5,4,8,7] => 0110010 => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[2,1,3,5,6,4,8,7] => 0110010 => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,2,3,6,5,4,8,7] => 1110010 => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,2,3,5,6,4,8,7] => 1110010 => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[4,3,2,1,6,5,8,7] => 0001010 => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[3,4,2,1,6,5,8,7] => 0001010 => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[3,2,4,1,6,5,8,7] => 0001010 => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[2,3,4,1,6,5,8,7] => 0001010 => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,3,4,2,6,5,8,7] => 1001010 => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[2,1,4,3,6,5,8,7] => 0101010 => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[1,2,4,3,6,5,8,7] => 1101010 => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[2,3,1,4,6,5,8,7] => 0011010 => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,3,2,4,6,5,8,7] => 1011010 => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[2,1,3,4,6,5,8,7] => 0111010 => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,2,3,4,6,5,8,7] => 1111010 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,4,3,2,1,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[4,5,3,2,1,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[3,5,4,2,1,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[4,3,5,2,1,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[3,4,5,2,1,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[2,5,4,3,1,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[2,4,5,3,1,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[3,2,5,4,1,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[2,3,5,4,1,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[2,4,3,5,1,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[2,3,4,5,1,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,4,5,3,2,6,8,7] => 1000110 => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,3,5,4,2,6,8,7] => 1000110 => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[2,1,5,4,3,6,8,7] => 0100110 => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,2,5,4,3,6,8,7] => 1100110 => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[2,1,3,5,4,6,8,7] => 0110110 => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,2,3,5,4,6,8,7] => 1110110 => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[4,3,2,1,5,6,8,7] => 0001110 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[2,3,4,1,5,6,8,7] => 0001110 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,4,3,2,5,6,8,7] => 1001110 => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,3,4,2,5,6,8,7] => 1001110 => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[2,1,4,3,5,6,8,7] => 0101110 => [1,1,1,3,1] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,2,4,3,5,6,8,7] => 1101110 => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[3,2,1,4,5,6,8,7] => 0011110 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[2,3,1,4,5,6,8,7] => 0011110 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,3,2,4,5,6,8,7] => 1011110 => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[2,1,3,4,5,6,8,7] => 0111110 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,2,3,4,5,6,8,7] => 1111110 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,6,4,3,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,6,5,3,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,7,5,3,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,7,6,3,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,7,6,3,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,5,7,3,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,7,6,4,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,6,7,4,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,7,6,5,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,4,7,6,5,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,3,7,6,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,4,7,6,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,5,7,6,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,5,4,7,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,6,5,7,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,7,6,5,4,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,7,5,4,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,5,7,6,4,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,5,6,7,4,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,4,6,7,5,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,5,6,4,7,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,7,6,5,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,6,7,5,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,5,7,6,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,6,5,7,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,5,6,7,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,3,7,6,5,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,3,6,7,5,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,3,5,7,6,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,3,6,5,7,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,3,5,6,7,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,4,6,7,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,3,4,7,6,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,3,2,7,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,3,2,7,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,4,2,7,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,5,2,7,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,4,5,2,7,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,5,4,7,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,3,4,5,7,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,4,6,5,2,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,4,6,2,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,5,4,6,3,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,6,5,4,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,2,6,5,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,4,2,6,5,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,4,3,6,5,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,3,4,6,5,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,4,2,6,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,5,4,3,6,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,7,6,5,4,3,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,7,5,4,3,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,5,7,4,3,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,5,6,7,4,3,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,5,6,4,7,3,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,4,6,5,7,3,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,3,6,7,5,4,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,3,5,7,6,4,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,3,5,6,7,4,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,3,4,6,7,5,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,3,5,4,7,6,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,4,3,5,7,6,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,5,4,6,3,7,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,3,6,5,4,7,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,3,5,6,4,7,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,4,3,6,5,7,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,4,5,3,6,7,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,3,4,5,6,7,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,1,7,6,5,4,3,8] => 0100001 => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[2,1,6,7,5,4,3,8] => 0100001 => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[2,1,5,6,7,4,3,8] => 0100001 => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[2,1,5,4,6,7,3,8] => 0100001 => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[2,1,4,5,6,7,3,8] => 0100001 => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,7,6,5,4,3,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,6,7,5,4,3,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,5,7,6,4,3,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,5,6,7,4,3,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,4,6,7,5,3,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,5,6,4,7,3,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,5,4,6,7,3,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,4,5,6,7,3,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[3,2,1,7,6,5,4,8] => 0010001 => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[3,2,1,5,7,6,4,8] => 0010001 => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[3,2,1,6,5,7,4,8] => 0010001 => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[2,3,1,6,5,7,4,8] => 0010001 => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[2,3,1,5,6,7,4,8] => 0010001 => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,3,2,5,7,6,4,8] => 1010001 => [1,1,1,3,1] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,3,2,6,5,7,4,8] => 1010001 => [1,1,1,3,1] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[2,1,3,6,7,5,4,8] => 0110001 => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,2,3,7,6,5,4,8] => 1110001 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,2,3,6,7,5,4,8] => 1110001 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,2,3,5,7,6,4,8] => 1110001 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,2,3,6,5,7,4,8] => 1110001 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,2,3,5,6,7,4,8] => 1110001 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[4,3,2,1,7,6,5,8] => 0001001 => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[4,3,2,1,6,7,5,8] => 0001001 => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[2,3,4,1,7,6,5,8] => 0001001 => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[2,3,4,1,6,7,5,8] => 0001001 => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,4,3,2,7,6,5,8] => 1001001 => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,4,3,2,6,7,5,8] => 1001001 => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,3,4,2,6,7,5,8] => 1001001 => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[2,1,4,3,6,7,5,8] => 0101001 => [1,1,1,1,2,1] => ([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,2,4,3,6,7,5,8] => 1101001 => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[3,2,1,4,7,6,5,8] => 0011001 => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,3,2,4,7,6,5,8] => 1011001 => [1,1,2,2,1] => ([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,2,3,4,7,6,5,8] => 1111001 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,2,3,4,6,7,5,8] => 1111001 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[5,4,3,2,1,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[3,5,4,2,1,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[3,4,5,2,1,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[2,4,5,3,1,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[3,2,5,4,1,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[2,3,5,4,1,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[3,4,2,5,1,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[2,4,3,5,1,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[2,3,4,5,1,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,3,5,4,2,7,6,8] => 1000101 => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,4,3,5,2,7,6,8] => 1000101 => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,3,4,5,2,7,6,8] => 1000101 => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[2,1,5,4,3,7,6,8] => 0100101 => [1,1,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,2,4,5,3,7,6,8] => 1100101 => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[3,2,1,5,4,7,6,8] => 0010101 => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[2,3,1,5,4,7,6,8] => 0010101 => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,3,2,5,4,7,6,8] => 1010101 => [1,1,1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 6
[1,2,3,5,4,7,6,8] => 1110101 => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[4,3,2,1,5,7,6,8] => 0001101 => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,4,3,2,5,7,6,8] => 1001101 => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,2,4,3,5,7,6,8] => 1101101 => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[3,2,1,4,5,7,6,8] => 0011101 => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[2,3,1,4,5,7,6,8] => 0011101 => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,3,2,4,5,7,6,8] => 1011101 => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[2,1,3,4,5,7,6,8] => 0111101 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,3,4,5,7,6,8] => 1111101 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,2,3,7,5,6,4,8] => 1110001 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,2,7,5,4,6,3,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,3,6,4,5,2,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,3,6,4,5,7,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,5,3,4,6,2,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,5,3,4,6,7,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,3,4,5,6,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,3,5,4,6,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,3,6,5,4,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,4,5,3,2,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,7,4,6,5,3,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,5,4,3,6,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,6,4,5,3,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,1,6,4,5,3,8,7] => 0100010 => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[2,3,7,5,6,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,5,3,4,6,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,3,5,4,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,7,3,6,5,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,7,4,6,5,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,1,7,5,6,4,8] => 0010001 => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[3,2,7,4,5,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,7,4,6,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,7,5,4,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,7,5,6,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,3,1,5,7,6,8] => 0001101 => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[4,2,3,1,7,6,5,8] => 0001001 => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[4,2,3,5,1,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[4,2,3,5,6,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,2,3,7,5,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,3,4,6,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,2,3,4,7,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,3,4,6,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,3,5,4,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,2,3,5,4,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,3,5,4,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,3,5,6,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,3,6,5,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,4,3,1,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[5,2,4,3,1,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,4,3,6,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,2,4,3,6,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,4,3,7,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,4,3,6,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,4,5,3,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,4,6,5,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,5,4,3,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,2,5,4,3,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,6,4,5,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,2,4,1,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[5,3,2,4,1,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,2,4,6,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,2,4,7,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,2,5,4,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,2,5,4,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,2,5,4,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,4,2,1,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[5,3,4,2,7,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,4,2,6,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,4,5,2,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,4,6,5,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,5,4,2,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,5,4,2,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,5,4,2,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,5,4,6,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,6,4,5,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,6,5,4,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,3,2,5,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,3,5,2,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,3,6,5,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,3,4,2,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,6,3,5,4,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,4,1,3,6,5,8,7] => 0001010 => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[2,4,1,6,3,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,4,6,1,3,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,1,4,6,3,7,5,8] => 0100001 => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[2,4,1,6,3,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,4,6,1,3,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,4,1,5,3,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[2,4,5,1,3,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[2,4,1,5,3,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[2,4,1,5,6,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,4,5,1,6,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,4,1,5,6,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,4,5,6,1,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,4,5,6,7,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,1,5,3,6,4,8,7] => 0100010 => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[2,5,1,3,6,4,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,1,5,6,3,4,8,7] => 0100010 => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[2,5,1,6,3,4,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,1,5,3,6,7,4,8] => 0100001 => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[2,1,5,6,3,7,4,8] => 0100001 => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[2,5,1,6,3,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,5,6,1,3,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,1,5,6,7,3,4,8] => 0100001 => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[2,5,6,1,7,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,5,1,3,7,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,1,5,7,3,4,6,8] => 0100001 => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[2,3,5,1,4,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[2,3,5,7,1,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,1,6,3,7,4,5,8] => 0100001 => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[2,6,1,7,3,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,7,1,3,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,1,3,4,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,3,1,6,4,7,5,8] => 0010001 => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[2,3,6,1,4,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,1,6,3,4,5,8,7] => 0100010 => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[2,1,3,6,4,5,8,7] => 0110010 => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[2,3,6,1,4,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,3,4,6,1,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,3,4,6,7,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,1,7,3,4,5,6,8] => 0100001 => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[2,7,1,3,4,5,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,1,3,4,7,5,6,8] => 0111001 => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[2,3,1,4,7,5,6,8] => 0011001 => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[2,3,4,1,7,5,6,8] => 0001001 => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[2,3,4,7,1,5,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,3,4,5,7,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,1,4,2,6,5,8,7] => 0001010 => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[3,4,1,2,6,5,8,7] => 0001010 => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[3,1,4,6,2,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,4,1,6,2,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,4,6,1,2,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,1,4,2,6,7,5,8] => 0001001 => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[3,4,1,2,6,7,5,8] => 0001001 => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[3,4,1,6,2,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,4,1,6,7,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,4,6,7,1,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,1,4,2,7,5,6,8] => 0001001 => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[3,4,1,5,2,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[3,4,1,5,7,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,4,5,7,1,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,4,1,2,5,6,8,7] => 0001110 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[3,4,5,1,2,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[3,4,5,1,6,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,4,5,6,1,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,1,4,5,6,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,4,1,5,6,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,4,5,6,1,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,1,5,2,6,4,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,5,1,2,6,4,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,1,5,6,2,4,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,5,1,6,2,4,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,5,1,2,6,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,1,6,2,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,6,1,2,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,1,6,7,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,1,5,2,7,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,1,2,7,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,1,5,7,2,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,1,7,2,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,7,1,2,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,1,5,2,4,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[3,5,1,2,4,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[3,1,2,5,4,7,6,8] => 0010101 => [2,1,1,1,1,1] => ([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,3,5,2,4,7,6,8] => 1000101 => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[3,1,2,5,7,4,6,8] => 0010001 => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,3,2,5,7,4,6,8] => 1010001 => [1,1,1,3,1] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,3,5,2,7,4,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,3,5,7,2,4,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,5,1,2,4,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[3,1,2,5,4,6,8,7] => 0010110 => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,3,5,2,4,6,8,7] => 1000110 => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,3,5,2,6,4,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,3,5,6,2,4,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[3,1,2,5,6,7,4,8] => 0010001 => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,3,5,2,6,7,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,3,5,6,2,7,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,3,5,6,7,2,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,1,6,2,7,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,1,6,7,2,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,7,1,2,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,1,6,2,4,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,1,2,4,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,1,2,6,4,7,5,8] => 0010001 => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,3,2,6,4,7,5,8] => 1010001 => [1,1,1,3,1] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,3,6,2,4,7,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,3,6,2,7,4,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,1,6,2,4,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,1,2,6,4,5,8,7] => 0010010 => [2,1,2,1,1] => ([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,3,6,2,4,5,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[3,1,2,4,6,5,8,7] => 0011010 => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,3,4,6,2,5,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[3,1,2,4,6,7,5,8] => 0011001 => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,3,4,6,2,7,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,1,7,2,4,5,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,1,2,4,5,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,3,2,7,4,5,6,8] => 1010001 => [1,1,1,3,1] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,3,7,2,4,5,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,1,2,4,7,5,6,8] => 0011001 => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,3,4,7,2,5,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,1,2,4,5,7,6,8] => 0011101 => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,3,4,5,7,2,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,1,2,4,5,6,8,7] => 0011110 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,5,2,6,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,5,1,2,6,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,1,5,6,2,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,5,1,6,2,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,5,6,1,2,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,5,1,2,6,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,1,6,2,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,6,1,2,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,5,6,7,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,1,6,7,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,6,1,7,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,5,2,7,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,1,2,7,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,5,2,3,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,1,2,3,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,2,5,3,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,4,2,5,3,7,6,8] => 1000101 => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[4,1,2,5,7,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,4,2,5,7,3,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,4,5,2,7,3,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,4,5,7,2,3,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,4,2,5,3,6,8,7] => 1000110 => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[4,1,2,5,6,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,4,5,2,6,3,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,2,5,6,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,4,2,5,6,7,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,4,5,6,7,2,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,1,6,2,7,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,1,2,7,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,6,7,2,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,1,7,2,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,1,2,3,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,2,6,3,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,4,2,6,3,7,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,1,2,6,7,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,4,2,6,7,3,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,4,6,2,7,3,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,4,6,7,2,3,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,1,6,2,3,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,6,1,2,3,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,4,2,6,3,5,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,4,6,2,3,5,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,2,3,6,5,8,7] => 0001010 => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,4,2,3,6,5,8,7] => 1001010 => [1,2,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,2,4,6,3,5,8,7] => 1100010 => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,4,2,3,6,7,5,8] => 1001001 => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[4,1,7,2,3,5,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,2,7,3,5,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,4,2,7,3,5,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,4,7,2,3,5,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,1,2,3,7,5,6,8] => 0001001 => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,4,2,3,7,5,6,8] => 1001001 => [1,2,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,2,4,3,7,5,6,8] => 1101001 => [2,1,1,2,1] => ([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,2,4,7,3,5,6,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,1,2,3,5,7,6,8] => 0001101 => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,4,2,3,5,7,6,8] => 1001101 => [1,2,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,2,4,5,7,3,6,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,4,2,3,5,6,8,7] => 1001110 => [1,2,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[5,1,6,2,7,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,1,6,2,3,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,1,2,6,3,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,5,2,6,3,7,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,1,2,6,7,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,5,2,6,7,3,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,5,6,7,2,3,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,5,2,6,3,4,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,5,6,2,3,4,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,5,2,3,6,4,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,5,3,6,4,8,7] => 1100010 => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,2,5,6,3,4,8,7] => 1100010 => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,5,2,3,6,7,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,2,5,3,6,7,4,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,5,6,3,7,4,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,7,2,3,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,1,2,3,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,5,2,7,3,4,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,5,2,3,7,4,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,2,5,3,7,4,6,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,5,7,3,4,6,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,5,2,3,4,7,6,8] => 1000101 => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,2,5,3,4,7,6,8] => 1100101 => [2,2,1,1,1] => ([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,2,3,5,7,4,6,8] => 1110001 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[5,1,2,3,4,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,5,2,3,4,6,8,7] => 1000110 => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,2,5,3,4,6,8,7] => 1100110 => [2,2,2,1] => ([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[6,1,7,2,3,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,1,2,7,3,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,6,2,7,3,4,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,7,2,3,4,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,2,3,7,4,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,2,6,3,7,4,5,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,6,7,3,4,5,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,2,3,4,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,6,2,3,4,7,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,2,6,3,4,7,5,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,3,6,4,7,5,8] => 1110001 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,2,3,6,7,4,5,8] => 1110001 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[6,1,2,3,4,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,2,3,4,5,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,6,3,4,5,8,7] => 1100010 => [2,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,2,3,6,4,5,8,7] => 1110010 => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,7,2,3,4,5,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,2,7,3,4,5,6,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,3,7,4,5,6,8] => 1110001 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,2,3,4,7,5,6,8] => 1111001 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[5,3,2,6,1,4,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,5,2,3,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,6,2,1,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,6,1,5,4,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,6,5,1,3,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,6,4,3,1,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,7,1,2,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,7,1,2,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,7,1,3,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,7,1,2,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,7,1,2,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,5,1,2,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,6,1,2,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,6,1,2,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,5,7,1,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,5,7,1,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,4,7,1,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,6,7,1,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,6,7,1,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,6,7,1,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,5,7,1,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,5,7,1,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,2,5,1,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,3,5,1,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,2,4,1,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,2,6,1,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,3,6,1,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,2,6,1,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,2,5,1,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,2,7,1,5,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,2,7,1,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,3,7,1,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,2,7,1,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,2,7,1,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,3,7,1,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,2,7,1,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,3,7,1,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,2,5,1,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,2,5,1,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,2,6,1,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,2,6,1,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,3,6,1,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,2,6,1,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,3,6,1,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,3,5,1,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,7,2,6,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,7,2,6,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,7,2,6,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,7,2,5,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,7,2,5,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,7,3,5,1,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,6,2,5,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,3,2,7,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,3,2,7,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,3,2,7,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,4,2,7,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,3,2,6,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,4,2,6,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,2,6,1,4,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,5,2,6,4,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,5,6,2,3,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,5,6,2,1,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,5,1,6,4,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,5,6,1,3,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,5,6,3,1,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,7,4,5,2,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,5,4,7,6,2,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,5,3,7,2,6,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,7,3,2,5,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,1,5,2,4,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,5,1,2,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,6,1,2,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,6,5,1,2,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,6,4,1,2,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,5,4,1,2,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,2,7,6,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,2,6,7,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,2,6,1,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,2,7,1,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,7,2,1,5,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,7,2,1,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,2,1,7,5,6,8] => 0001001 => [3,1,2,1] => ([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[4,1,3,2,6,5,8,7] => 0001010 => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[5,1,4,2,6,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,1,6,3,5,4,8,7] => 0100010 => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[3,1,6,2,5,4,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,1,6,2,5,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,5,2,3,7,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,3,7,2,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,2,7,3,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,6,7,4,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,2,6,5,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,6,2,4,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,1,2,7,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,1,7,2,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,1,6,2,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,1,7,6,2,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,1,6,2,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,6,1,2,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,5,3,6,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,2,5,1,6,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,1,5,4,6,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,1,5,3,6,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,3,5,1,6,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,5,3,1,2,4,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,6,3,5,1,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,3,6,1,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,1,6,4,5,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,2,3,7,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,2,7,3,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,2,6,3,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,7,6,4,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,2,6,3,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,6,2,3,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,5,6,1,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,1,4,6,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,1,6,5,4,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,5,7,2,4,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,7,2,4,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,2,6,3,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,1,2,5,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,1,4,7,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,1,7,5,4,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,6,2,7,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,2,1,5,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,4,7,1,5,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,1,4,7,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,7,5,2,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,1,6,3,4,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,7,2,4,1,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,7,2,6,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,1,6,4,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,1,7,6,5,3,4,8] => 0100001 => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,5,1,3,6,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,1,3,2,6,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,1,3,2,5,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,3,1,2,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,3,1,2,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,3,1,7,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,3,7,2,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,7,2,4,3,5,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,2,5,3,4,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,2,6,3,4,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,2,3,7,4,6,5,8] => 1110001 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,3,2,7,4,6,5,8] => 1010001 => [1,1,1,3,1] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,4,2,7,3,6,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,5,2,7,3,6,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,2,7,3,5,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,2,6,3,5,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,2,5,3,6,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,2,5,3,7,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,5,2,4,3,7,6,8] => 1000101 => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,6,2,4,3,7,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,2,4,3,6,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,2,3,4,6,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,6,3,7,2,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,3,7,5,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,2,7,5,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,7,2,4,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,3,7,5,2,6,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,3,7,5,4,2,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,3,7,5,2,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,5,2,7,4,6,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,5,4,6,2,7,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,2,1,4,3,6,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,4,1,2,6,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,3,2,1,6,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,3,2,5,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,5,1,6,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,1,5,6,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,1,6,5,4,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,6,5,1,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,2,1,4,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,2,4,1,3,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,5,1,7,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,6,7,3,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,5,3,7,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,6,5,2,7,4,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,5,3,2,7,6,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,2,5,7,3,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,5,2,4,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,6,1,4,7,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,1,2,5,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,2,5,3,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,5,3,6,2,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,1,2,4,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,2,7,6,1,4,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,4,7,1,5,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,2,7,3,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,6,5,4,2,3,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,5,2,4,3,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,6,1,2,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,4,2,5,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,6,4,2,5,7,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,3,7,5,4,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,1,3,5,6,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,1,6,4,5,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,2,6,5,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,6,3,1,5,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,4,1,5,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,3,5,4,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,4,1,5,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,3,5,7,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,7,4,1,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,1,2,7,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,2,7,5,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,6,1,7,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,3,1,2,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,3,1,7,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,5,7,1,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,1,4,7,5,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,1,7,5,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,1,3,7,5,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,4,1,6,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,3,7,1,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,1,6,2,4,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,5,7,2,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,7,6,5,4,2,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,2,1,7,6,4,5,8] => 0010001 => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[4,1,3,7,6,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,1,7,3,6,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,1,7,5,3,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,6,5,2,4,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,2,7,6,3,4,5,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,4,3,1,2,6,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,1,4,2,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,7,1,4,6,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,2,1,3,6,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,1,3,2,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,1,2,4,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,1,2,5,4,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,7,2,3,6,4,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,1,2,3,4,6,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,4,6,2,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,3,7,2,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,3,5,2,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,3,6,2,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,3,6,2,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,3,5,2,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,3,4,2,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,3,5,2,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,3,7,2,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,5,2,1,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,5,7,3,2,4,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,2,4,7,5,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,4,2,3,5,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,7,3,1,2,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,7,5,4,2,6,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,1,6,7,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,4,1,2,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,1,4,2,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,4,7,2,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,3,7,2,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,3,7,2,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,3,2,1,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,3,2,7,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,3,2,1,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,5,2,4,1,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,1,5,7,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,2,3,7,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,3,5,2,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,2,7,5,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,7,1,3,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,1,7,3,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,1,3,7,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,1,4,2,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,1,4,2,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,1,5,7,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,1,7,5,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,6,1,7,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,4,1,2,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,4,1,2,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,3,1,7,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,2,7,1,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,2,7,3,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,7,2,3,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,2,1,7,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,6,1,4,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,2,1,4,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,7,2,4,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,2,7,4,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,6,1,5,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,2,1,5,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,2,1,5,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,1,7,5,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,1,5,6,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,1,5,2,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,5,1,2,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,5,1,7,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,5,1,7,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,5,1,2,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,3,1,4,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,6,2,7,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,6,2,7,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,6,7,1,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,1,5,7,3,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,2,4,6,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,5,1,7,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,5,1,6,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,1,6,4,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,5,1,7,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,6,1,7,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,5,7,4,1,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,5,4,6,1,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,2,6,7,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,5,7,1,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,2,7,1,5,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,2,1,4,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,2,1,7,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,7,2,1,5,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,5,3,4,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,1,5,2,4,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,7,3,4,1,5,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,3,4,1,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,2,7,3,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,3,5,1,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,2,3,1,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,2,4,1,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,2,5,1,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,1,7,3,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,1,6,4,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,1,5,7,4,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,1,7,4,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,1,7,6,4,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,6,1,5,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,6,1,3,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,7,1,4,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,4,5,1,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,6,5,1,4,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,4,6,2,7,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,7,5,4,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,6,4,1,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,4,6,1,7,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,7,5,4,1,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,5,4,1,6,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,3,2,7,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,5,4,1,6,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,7,3,2,1,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,6,1,7,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,2,1,4,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,3,2,1,5,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,2,1,4,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[5,4,1,6,2,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,3,6,1,5,4,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,5,3,1,4,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,2,6,4,1,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,1,7,2,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,5,6,1,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,3,1,2,5,6,8,7] => 0001110 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[4,1,7,5,3,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,1,3,4,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,4,7,2,5,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,2,4,7,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,7,6,5,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,6,2,5,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,1,6,2,5,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,1,6,4,7,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,7,1,4,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,7,4,1,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,4,7,1,6,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,1,3,6,5,8,7] => 0001010 => [3,1,1,1,1] => ([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[7,2,1,5,4,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,1,5,7,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,1,6,3,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,2,1,4,3,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,2,4,1,3,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,1,6,4,3,5,8,7] => 0100010 => [1,1,3,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[6,4,2,1,3,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,2,6,1,5,4,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,3,6,1,5,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,5,3,6,1,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,5,2,6,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,1,5,6,4,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,4,3,7,2,5,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,4,3,7,2,6,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,1,6,4,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,1,2,7,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,1,5,4,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,6,2,4,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,7,6,5,3,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,6,5,2,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,2,1,5,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,6,5,2,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,6,5,1,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,7,6,5,1,4,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,5,1,2,4,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,5,1,2,4,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,6,1,5,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,4,2,6,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,3,6,5,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,1,6,5,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,1,4,6,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,3,6,5,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,2,3,6,5,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,3,1,2,4,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,6,2,4,3,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,6,1,2,4,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,7,4,1,3,6,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,4,2,6,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,7,3,2,6,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,3,2,5,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,3,2,1,5,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,1,7,5,6,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,7,5,6,1,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,7,6,1,5,4,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,6,5,1,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,6,5,3,1,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,1,7,2,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,1,4,2,7,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,4,2,7,6,3,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,1,7,2,6,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,3,1,4,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,3,6,1,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,5,7,3,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,3,7,2,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,6,2,7,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,3,1,5,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,7,3,6,5,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,7,6,4,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,3,2,7,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,6,3,7,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,3,5,2,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,6,2,5,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,2,6,4,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,7,5,4,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,3,2,7,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,6,3,5,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,5,7,2,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,6,7,3,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,2,4,7,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,5,6,4,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,6,4,2,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,6,4,5,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,6,5,4,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,5,1,7,4,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,4,1,7,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,4,1,5,7,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,3,4,1,6,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,5,2,1,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,6,4,7,2,5,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,5,6,2,4,7,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,5,7,2,4,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,5,2,3,7,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,4,2,3,7,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,2,6,5,3,7,4,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,6,4,3,7,5,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[3,6,5,2,4,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,5,3,7,1,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,1,5,3,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,3,1,2,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,3,1,5,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,3,1,5,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,1,5,3,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,5,6,2,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,4,5,2,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,4,7,3,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,7,3,6,4,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,7,5,6,3,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,2,5,3,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,4,2,7,5,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,2,5,4,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,2,7,3,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,5,7,2,3,6,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,6,1,5,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,5,4,7,3,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,4,6,3,7,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,7,3,6,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,6,3,1,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,5,3,1,6,4,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,5,3,7,6,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,5,3,7,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,7,6,3,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,7,5,3,6,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,3,7,5,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,4,7,1,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,5,7,1,4,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,7,6,1,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,7,6,2,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,5,7,6,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,6,7,5,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,1,7,4,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,2,6,7,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,1,5,7,6,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,4,1,7,5,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,6,7,5,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,1,6,7,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,2,4,5,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,4,1,7,5,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,6,7,2,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,6,7,1,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,5,2,7,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,2,3,1,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[7,3,1,4,5,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,4,1,7,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,1,4,2,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,7,5,6,3,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,1,4,3,6,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,1,3,7,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,1,3,4,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,1,7,4,2,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,7,3,2,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,3,7,2,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,7,6,2,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,2,7,5,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,2,7,5,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,2,6,7,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,7,6,5,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,4,2,1,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,7,2,1,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,2,7,1,4,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,2,7,1,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,2,6,1,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,2,7,6,1,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,7,6,1,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,2,1,5,4,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,2,1,6,4,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,2,7,1,5,4,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,7,1,6,4,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,7,1,5,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,7,1,5,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,1,6,7,4,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,1,6,5,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,7,2,3,5,4,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,2,6,5,4,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,1,5,2,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,6,1,4,3,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,5,4,1,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,2,4,6,1,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,3,5,7,2,6,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,7,5,3,2,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,3,6,5,2,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,5,7,4,2,6,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,5,1,4,3,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[2,6,1,4,3,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,1,5,3,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,1,3,2,6,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,1,4,2,6,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,1,5,2,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,2,6,1,5,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,3,7,1,5,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,7,4,1,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,4,2,3,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,2,5,1,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,7,2,4,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,4,7,2,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,6,2,5,3,4,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,7,3,5,4,6,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,6,2,7,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,3,4,7,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,2,3,7,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,1,7,3,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,6,2,3,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,7,6,1,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,7,6,1,3,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,7,6,2,3,4,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,6,2,5,7,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,5,2,1,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,7,4,1,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,4,7,2,6,3,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,5,1,7,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,1,2,5,7,6,4,8] => 0010001 => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[7,1,6,3,4,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,1,4,2,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,6,4,5,7,2,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,2,4,6,1,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,2,6,5,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,2,5,4,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,5,2,6,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,6,4,7,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,3,7,5,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,4,6,5,1,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,2,6,4,7,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,3,4,7,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,4,2,7,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,1,7,2,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,2,6,4,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,6,2,5,4,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,1,7,4,2,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,2,7,3,4,6,5,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[2,6,1,7,3,5,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,7,5,3,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,7,6,3,5,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,7,6,5,2,4,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,6,5,7,4,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,7,4,2,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,1,5,7,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,4,7,1,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,7,2,6,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,1,7,4,3,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,7,3,2,5,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,6,3,2,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,2,1,6,7,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,1,5,2,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,4,3,1,6,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,1,5,2,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[2,6,7,1,3,5,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,1,2,7,3,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,5,7,6,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,7,2,5,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,7,2,1,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,7,3,1,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,7,1,5,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,7,1,5,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,7,3,1,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,1,4,6,7,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,5,4,6,7,2,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,7,3,2,4,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,2,4,6,7,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,5,4,6,7,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,7,4,5,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,7,4,5,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,5,6,7,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,2,6,7,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,1,7,3,2,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,1,7,4,5,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,1,6,7,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,2,5,4,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,5,2,4,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,5,2,1,4,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,2,5,1,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,1,7,3,5,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,7,3,1,5,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,1,5,7,4,6,8] => 0010001 => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[2,1,7,3,6,4,5,8] => 0100001 => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[2,7,3,1,5,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,4,7,5,1,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,1,6,7,4,5,8] => 0010001 => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[3,2,1,7,4,5,6,8] => 0010001 => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,2,5,3,7,6,4,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,6,4,2,7,3,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,6,3,2,4,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,2,7,5,3,6,4,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,2,6,3,7,5,4,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,4,2,1,6,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,1,3,5,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,6,7,5,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,3,6,4,7,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,7,3,6,1,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,2,5,6,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,5,2,6,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,6,2,7,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,6,3,7,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,6,4,1,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,6,5,1,4,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,5,1,2,4,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,5,1,3,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,5,1,3,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,4,3,1,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,6,4,2,1,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,4,5,1,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,5,6,4,1,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,4,2,5,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,2,5,6,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,7,5,6,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,4,7,5,6,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,3,5,6,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,2,5,6,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,6,1,4,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,6,2,1,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,6,2,1,5,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,2,6,3,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,6,1,5,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,3,7,4,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,7,6,5,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,2,4,6,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,1,4,3,5,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,3,1,5,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,4,1,5,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,1,4,6,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,1,4,7,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,1,3,6,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,2,5,1,4,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[7,1,3,5,4,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,3,2,5,7,6,8] => 0001101 => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[4,6,7,3,1,5,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,1,4,2,3,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,6,4,2,7,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,2,1,7,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,1,4,5,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,1,5,4,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,7,6,2,4,3,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,2,5,4,3,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,6,1,7,3,5,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,1,7,3,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,1,6,4,2,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,1,6,7,4,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,5,3,7,1,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,3,7,5,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,4,3,7,1,6,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,4,7,6,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,1,3,6,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,7,1,5,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,3,1,5,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,2,1,5,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,7,4,1,6,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,4,1,7,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,3,1,5,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,6,1,5,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,1,5,6,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,6,7,1,4,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,7,6,1,4,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,7,2,1,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,4,5,1,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,4,5,1,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,7,4,2,6,3,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,7,4,1,6,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,3,5,6,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,4,3,6,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,4,1,6,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,1,5,6,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,7,1,5,6,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,7,1,4,3,6,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,3,1,4,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,7,3,2,5,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,2,4,7,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,1,6,3,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,1,7,3,6,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,5,2,1,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,5,6,4,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,7,1,4,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,1,5,6,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,5,1,6,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,2,7,3,6,4,5,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,4,2,3,5,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,1,2,3,4,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,7,4,1,2,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,4,6,3,5,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,4,6,3,7,2,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,1,4,3,7,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,1,3,5,7,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,1,4,7,5,3,6,8] => 0100001 => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,1,3,6,2,5,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,3,1,4,6,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,1,3,2,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,7,1,2,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,4,1,2,6,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,1,4,2,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,7,1,3,5,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,2,5,7,6,3,4,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,5,7,6,2,3,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,5,7,4,3,6,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,6,2,7,1,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,2,4,7,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,3,7,1,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,6,3,5,2,4,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,7,4,2,5,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,2,7,3,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,7,4,5,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,1,3,7,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,1,2,4,6,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,1,6,5,2,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,4,2,1,5,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,2,6,5,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,6,7,5,1,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,7,3,6,5,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,7,3,6,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,6,7,5,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,6,1,4,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,1,7,5,6,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,7,5,6,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,1,6,3,5,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,7,1,6,3,5,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,7,1,5,4,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,1,5,4,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,1,4,5,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,7,1,4,5,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,1,4,5,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,1,5,4,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,1,6,2,5,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,1,6,2,5,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,1,4,5,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,5,1,3,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,5,1,3,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,2,1,3,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,1,2,4,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,1,2,5,4,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,2,1,3,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,6,1,3,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,1,3,5,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,1,5,3,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,1,4,2,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,3,1,2,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,6,1,2,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,2,5,3,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,4,3,1,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,6,1,2,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,6,1,5,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,6,1,2,5,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,7,1,3,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,6,2,1,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,7,4,5,2,3,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,3,5,2,4,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,3,4,2,5,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,3,4,2,6,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,3,5,2,6,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,3,6,2,5,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,3,6,2,4,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,4,6,2,3,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,7,6,1,2,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,6,1,2,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,4,3,2,5,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,4,6,5,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,4,6,5,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,4,1,7,5,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,2,7,5,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,4,7,2,6,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,4,7,1,6,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,3,7,5,1,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,4,3,1,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,4,7,3,6,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,7,3,6,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,4,2,6,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,7,2,4,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,3,4,2,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,6,4,2,1,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,3,7,5,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,7,2,5,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,2,7,5,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,2,3,1,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[5,6,1,3,4,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,6,2,1,5,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,4,7,6,3,2,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,3,6,4,7,2,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,1,7,5,4,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,1,5,2,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,6,3,7,5,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,1,7,4,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,3,5,4,7,2,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,2,7,4,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,7,3,5,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,1,6,3,7,5,4,8] => 0100001 => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,4,1,2,6,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,1,2,7,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,7,1,3,6,5,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,3,2,5,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,1,4,2,7,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,4,2,1,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,3,1,4,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,7,1,4,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,6,2,4,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,5,2,6,4,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,6,3,4,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,7,6,3,1,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,7,6,4,5,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,2,6,4,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,4,2,7,1,5,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,7,3,1,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,4,5,7,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,6,2,7,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,7,6,2,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,1,7,6,4,5,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,1,3,4,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,1,4,2,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,3,4,1,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,4,3,7,1,5,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,2,6,1,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,2,5,6,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,5,6,4,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,3,1,5,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,5,2,6,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,7,1,2,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,6,1,3,4,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,7,1,3,2,5,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,1,4,3,5,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,4,2,6,5,7,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,6,1,4,2,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,2,4,1,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,2,4,3,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,2,3,1,5,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,4,1,6,5,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,5,2,6,4,7,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,5,1,6,4,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,2,4,3,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,2,6,1,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,1,6,3,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,3,6,1,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,3,4,1,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,1,4,3,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,1,3,2,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,4,7,1,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,4,5,1,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,1,3,2,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,5,7,1,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,1,3,2,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,4,3,6,2,7,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,4,1,6,5,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,2,3,1,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,5,7,2,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,4,6,1,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,1,6,4,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,5,3,6,4,7,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,5,3,6,2,7,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,5,2,6,1,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,2,6,4,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,4,2,6,1,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,2,3,1,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,4,3,6,1,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,5,3,6,4,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,5,3,6,1,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,6,2,1,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,3,2,1,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,3,1,7,5,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,6,1,7,5,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,2,6,1,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,1,6,2,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,1,6,3,2,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,1,4,7,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,1,7,4,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,1,7,5,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,1,6,3,7,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,1,6,3,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,6,3,1,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,2,1,7,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,2,7,4,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,4,7,1,3,6,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,1,3,7,5,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,1,7,5,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,1,6,2,7,4,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,1,6,2,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,1,6,4,2,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,2,1,5,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,2,1,5,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,2,6,7,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,7,2,5,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,2,3,1,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,2,4,3,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,2,7,1,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,1,6,2,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,1,5,3,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,3,5,1,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,3,5,1,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,3,7,1,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,1,6,3,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,6,7,2,3,5,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,4,5,7,6,2,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,2,5,7,3,6,4,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,2,1,6,5,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,1,5,7,3,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,1,7,3,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,2,4,3,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,3,1,4,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,4,1,5,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,5,1,7,4,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,3,7,5,6,2,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,7,4,3,5,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,6,5,7,3,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,5,7,4,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,5,4,2,6,7,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,5,4,2,6,3,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,2,7,4,1,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,3,1,5,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,3,7,1,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,3,7,5,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,6,2,1,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,1,6,7,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,6,1,7,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,6,5,2,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,5,2,1,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,7,5,3,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,2,7,5,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,4,1,5,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,7,5,2,1,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,1,7,3,2,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,2,1,7,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,2,1,7,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,1,6,2,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,2,1,6,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,2,7,3,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,2,7,3,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,3,6,2,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,5,3,4,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,7,4,3,1,5,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,5,2,4,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,7,3,1,5,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,2,4,7,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,6,2,3,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,2,5,7,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,5,7,6,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,1,4,3,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,7,1,6,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,5,2,7,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,5,1,3,7,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,2,1,7,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,6,1,5,4,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,7,2,1,6,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,5,7,3,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,6,1,5,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,1,2,5,4,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,6,3,4,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,4,2,1,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,4,1,2,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,6,2,4,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,6,1,7,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,2,3,7,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,3,7,1,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,1,7,5,2,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,1,3,4,7,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,1,2,7,5,4,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,1,5,7,4,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,3,7,4,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,4,1,2,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,1,3,4,6,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,4,5,3,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,1,2,5,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,4,2,6,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,2,6,3,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,5,2,4,7,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,4,7,2,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,4,7,6,1,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,7,4,6,1,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,7,4,6,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,5,7,4,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,2,7,6,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,7,2,6,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,7,6,2,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,7,6,1,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,7,6,4,1,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,7,2,6,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,2,7,6,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,2,7,1,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,7,2,1,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,7,1,6,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,7,1,4,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,7,1,4,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,7,2,1,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,2,7,1,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,5,7,4,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,2,7,4,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,7,4,2,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,7,4,1,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,4,7,1,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,4,7,2,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,4,2,7,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,5,4,7,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,5,2,4,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,7,2,4,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,5,2,4,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,3,2,4,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,5,3,2,4,7,6,8] => 1000101 => [1,3,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,5,3,2,7,4,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,7,3,2,1,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,3,2,4,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,2,5,4,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,1,3,2,4,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,3,2,7,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,3,2,5,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,7,3,2,5,4,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,1,3,5,2,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,1,3,7,2,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,7,5,1,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,5,1,2,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,3,1,2,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,5,3,7,2,4,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,2,7,4,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,2,4,7,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,2,1,4,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,2,1,7,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,3,2,7,5,4,6,8] => 1010001 => [1,1,1,3,1] => ([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,3,7,2,5,4,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,3,1,2,5,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,1,2,7,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,1,2,4,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[3,2,5,1,4,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,1,5,2,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,3,7,5,2,4,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,5,1,3,2,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,1,3,2,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,1,5,2,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,1,2,5,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,2,1,5,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,1,7,5,4,6,8] => 0010001 => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[3,1,2,7,5,4,6,8] => 0010001 => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[3,1,7,2,5,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,1,7,5,2,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,5,3,2,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,7,5,3,2,4,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,2,5,6,3,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,1,5,6,3,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,3,6,1,2,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,1,7,4,5,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,6,1,3,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,2,1,3,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,1,4,7,6,5,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,2,7,1,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,1,7,5,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,5,3,7,1,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,1,3,6,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,2,6,5,1,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,5,7,2,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,2,4,6,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,3,6,4,2,5,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,6,2,7,3,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,3,1,4,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,1,4,7,5,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,4,7,3,5,2,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,7,4,2,6,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,6,3,5,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,1,3,7,4,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,3,1,7,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,7,2,5,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,7,6,2,4,5,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,7,6,3,2,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,7,2,4,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,2,1,7,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,2,6,3,5,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,1,7,5,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,2,7,4,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,1,4,5,7,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,7,3,2,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,1,6,4,7,5,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,5,1,2,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,2,1,6,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,5,6,3,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,2,7,5,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,2,6,5,4,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,7,4,1,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,7,5,1,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,2,3,7,6,4,5,8] => 1110001 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[5,7,3,2,6,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,7,5,2,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,6,1,3,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,4,5,1,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,4,5,1,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,4,1,6,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,7,4,2,6,5,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,6,1,4,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,1,7,6,5,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,1,6,5,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,1,7,6,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,1,6,5,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,6,1,4,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,6,1,4,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,5,1,4,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,3,4,7,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,6,7,4,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,5,7,1,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,5,4,6,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,4,3,7,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,4,3,1,5,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,4,6,1,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,2,7,5,3,4,6,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,4,7,1,5,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,7,2,1,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,6,5,2,3,4,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,3,2,5,1,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,5,2,7,4,3,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,3,6,5,2,7,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,7,2,5,3,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,7,1,2,5,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,4,6,1,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,5,3,7,4,6,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,7,5,2,3,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,6,5,3,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,2,6,4,7,5,3,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,7,2,3,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,7,3,4,1,5,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,1,7,4,5,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,3,7,2,4,6,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,3,2,4,6,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,2,1,7,4,6,5,8] => 0010001 => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[5,4,2,1,7,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,5,7,3,2,6,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,1,3,7,2,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,1,5,2,4,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,6,3,5,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,6,2,7,4,5,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,2,6,4,3,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,2,5,4,6,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,1,2,6,4,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,3,6,5,1,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,4,5,1,7,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,1,5,6,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,3,1,4,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,4,6,2,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,4,6,1,5,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,7,3,1,5,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,3,7,4,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,2,5,3,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,2,7,4,3,5,6,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,6,3,1,2,5,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,1,3,7,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,2,5,3,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,5,3,6,1,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,5,3,1,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,5,7,1,6,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,4,7,2,5,6,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,6,3,1,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,2,1,4,6,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,4,2,1,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,4,1,3,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,3,2,7,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,7,2,6,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,2,5,3,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,2,4,5,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,2,4,3,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,2,3,5,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,7,1,5,6,4,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,6,4,1,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,5,6,1,7,4,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,4,2,1,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,1,4,7,6,3,5,8] => 0100001 => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,5,7,3,1,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,5,3,7,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,4,3,7,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,3,6,4,7,5,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,2,5,3,6,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,5,3,7,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,6,3,7,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,7,3,6,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,6,2,5,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,1,4,6,5,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,4,7,3,6,5,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,2,5,3,1,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,4,3,1,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,4,3,1,6,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,5,2,4,7,6,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,2,5,3,1,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,5,3,1,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,6,3,1,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,6,4,1,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,7,4,1,6,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,7,3,1,6,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,7,3,1,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,7,3,1,5,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,6,3,1,5,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,1,5,3,7,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,1,6,4,7,5,8] => 0010001 => [2,1,3,1] => ([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[7,1,3,2,5,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,3,7,6,2,4,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,6,1,5,4,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,5,1,3,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,6,1,7,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,5,3,4,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,4,2,5,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,1,6,3,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,2,6,3,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,1,4,6,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,6,5,4,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,7,6,5,3,2,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,7,6,5,4,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,5,7,2,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,3,2,5,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,6,2,7,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,1,2,4,3,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[5,4,3,7,2,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,3,5,6,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,7,1,4,6,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,3,1,5,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,4,6,7,3,5,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,3,2,4,5,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,2,3,7,5,4,6,8] => 1110001 => [3,3,1] => ([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 2
[1,5,4,2,3,6,8,7] => 1000110 => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[6,1,5,2,3,4,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,2,4,5,3,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,4,5,3,2,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,4,7,3,5,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,4,7,5,2,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,5,2,6,7,4,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,6,4,2,3,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,5,7,2,4,3,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,2,4,6,5,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,4,7,2,6,5,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,5,2,4,3,6,8,7] => 1000110 => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[7,5,1,4,2,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,6,2,5,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,1,7,2,6,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,4,7,3,5,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,3,7,5,4,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,4,6,2,1,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,4,7,2,1,6,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,5,7,1,4,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,4,7,1,6,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,3,7,1,6,5,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,5,7,1,4,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,5,7,3,1,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,3,7,1,5,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,5,7,3,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,7,5,2,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,6,7,4,3,2,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,4,5,7,3,2,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,5,1,4,7,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,7,1,5,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,3,1,7,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,7,4,3,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,4,1,7,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,2,7,4,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,2,5,7,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,6,5,7,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,7,3,2,5,6,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,3,2,5,7,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,4,6,5,2,7,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,6,1,5,2,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,6,5,3,7,2,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,4,5,7,3,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,4,3,2,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,4,2,1,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,1,4,7,3,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,6,3,5,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,1,3,4,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,5,4,6,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,2,4,5,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,2,1,5,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,2,1,7,5,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,7,3,1,5,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,1,6,4,7,5,3,8] => 0100001 => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,6,1,4,5,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,5,6,4,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,6,3,7,2,5,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,2,4,6,3,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,4,2,5,7,6,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,5,3,2,4,6,8,7] => 1000110 => [1,3,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,5,7,6,3,2,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,3,2,4,7,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,2,7,6,4,3,5,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,7,5,2,4,6,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,4,2,5,3,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,5,2,3,6,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,5,2,6,3,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,3,7,4,2,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,3,2,7,5,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,4,7,5,2,6,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,3,7,6,4,2,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,4,6,3,2,7,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,5,7,6,4,2,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,3,5,2,7,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,4,1,6,2,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,1,4,2,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,7,4,5,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,5,6,4,7,2,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,4,3,7,5,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,5,4,7,2,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,3,2,7,4,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,5,7,6,2,4,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,7,1,3,6,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,1,3,5,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,6,1,2,3,5,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,5,1,4,6,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,1,3,4,2,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[4,7,1,2,5,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,1,6,7,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,5,4,6,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,1,3,6,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,3,1,7,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,7,3,5,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,6,4,5,2,7,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,2,1,5,7,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,5,7,1,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,2,7,1,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,2,5,6,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,2,6,7,4,3,5,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,3,6,4,7,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,6,5,7,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,6,2,7,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,6,2,4,1,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,5,3,7,1,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,4,6,5,7,2,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,2,4,1,6,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,2,6,4,7,3,5,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,6,4,3,7,2,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,1,5,7,6,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,1,7,6,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,5,3,7,4,2,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,2,3,7,1,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,1,3,4,2,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,6,2,4,3,5,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,5,4,1,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,1,5,4,7,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,6,3,7,2,4,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,1,6,4,2,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,3,7,5,2,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,1,7,3,4,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,4,1,3,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,6,5,2,4,7,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,5,4,2,7,3,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,5,3,2,6,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,7,1,4,2,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,5,1,4,7,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,1,6,5,7,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,1,5,7,4,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,5,1,7,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,3,6,1,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,2,7,6,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,1,6,3,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,5,7,1,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,5,1,4,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,6,5,7,1,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,5,7,6,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,4,7,6,1,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,6,5,2,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,5,7,2,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,7,6,2,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,2,6,3,7,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,5,2,7,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,5,2,1,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,2,1,5,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,7,4,2,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,7,4,3,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,3,7,4,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,1,3,7,4,5,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,3,2,4,5,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,2,1,4,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,7,6,4,2,5,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,5,1,4,2,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,7,5,4,3,2,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,7,3,1,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,5,6,2,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,6,2,1,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,1,6,7,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,5,1,4,6,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,1,6,5,4,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,7,1,3,5,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,1,2,4,7,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,1,6,4,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,5,4,7,2,6,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,6,3,5,4,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,2,5,1,3,4,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,6,5,1,3,4,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,6,5,1,2,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,4,1,2,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,5,1,2,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,1,4,3,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,4,1,3,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,2,7,6,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,2,1,7,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,1,3,5,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,6,4,2,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,7,4,1,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,5,4,7,6,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,3,7,6,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,3,7,6,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,7,3,5,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,2,3,4,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,7,3,5,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,6,3,5,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,6,3,4,2,7,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,2,1,5,3,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,3,4,2,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,1,3,4,2,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,7,5,1,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,6,3,5,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,1,3,4,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,2,4,1,7,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,7,1,4,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,2,6,1,5,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,1,2,6,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,2,7,4,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,7,3,1,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,2,1,6,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,1,7,4,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,3,6,4,1,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,5,4,6,1,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,1,2,4,3,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,1,2,3,6,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,1,3,6,5,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,1,2,6,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,3,6,4,2,7,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,4,6,7,2,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,4,6,3,7,5,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,3,1,2,4,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[1,5,7,4,2,3,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,1,3,6,7,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,1,6,7,3,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,2,6,7,4,5,3,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[2,1,7,6,3,4,5,8] => 0100001 => [1,1,4,1] => ([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,3,2,4,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[5,7,1,6,2,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,2,3,5,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,5,1,6,4,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,7,1,4,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,2,7,6,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,6,5,3,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,6,5,3,2,4,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,3,7,2,5,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,1,4,3,2,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[7,2,1,3,5,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,3,6,2,5,4,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[6,2,4,7,5,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,4,1,2,7,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,4,7,6,2,3,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,7,5,6,4,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,4,2,6,5,3,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[3,7,6,2,5,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,7,1,5,3,4,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,6,2,7,5,3,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,3,7,2,6,4,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,2,6,7,5,3,4,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,2,1,4,5,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,5,7,3,6,4,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,4,7,1,5,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,6,4,1,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[2,5,6,4,1,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,6,1,3,5,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,5,6,3,7,2,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,5,6,7,4,2,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,1,6,7,3,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,1,5,6,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,1,5,7,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,7,6,5,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,3,6,7,5,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,1,4,5,7,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,2,5,3,6,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,1,6,7,5,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,7,5,2,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,6,4,1,2,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,1,6,7,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,1,5,7,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,2,1,3,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,3,2,1,6,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,7,1,3,5,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,1,4,3,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,3,7,1,5,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,3,4,5,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,5,1,3,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,5,3,6,4,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,4,7,2,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,7,1,6,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,1,7,3,6,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,7,5,6,1,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,2,7,1,6,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,1,7,5,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,4,7,2,5,3,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,5,3,1,2,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[4,1,5,3,2,7,6,8] => 0000101 => [4,1,1,1] => ([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[7,3,5,1,4,2,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,4,3,6,7,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,5,2,1,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,1,5,3,7,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,6,5,4,1,7,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,5,6,2,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,1,7,2,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,6,4,2,3,5,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[4,7,3,2,6,5,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,3,5,7,1,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,4,3,6,2,5,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[3,7,1,4,5,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,2,1,5,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,7,4,6,3,5,2,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,3,6,5,7,2,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,2,5,6,4,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,4,3,7,6,1,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,1,3,7,6,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,4,2,6,7,5,3,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,1,3,6,2,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[7,1,4,6,3,2,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,7,2,5,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,6,7,4,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,6,4,7,5,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,4,7,5,2,3,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,4,7,2,3,6,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[1,7,2,5,6,3,4,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,1,5,7,2,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,2,1,3,6,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,5,6,7,2,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,7,5,2,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,2,6,4,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,1,2,6,5,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,3,1,6,5,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,5,7,1,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,4,1,6,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,1,6,5,2,4,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,5,2,1,6,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,5,2,1,6,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[2,5,1,6,4,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,1,2,5,7,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,4,5,3,1,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,1,2,6,3,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,2,7,5,6,3,4,8] => 1100001 => [2,4,1] => ([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[5,1,4,7,2,3,6,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,1,3,2,6,8,7] => 0000110 => [4,2,1] => ([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[6,4,7,5,1,3,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,2,1,6,4,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,2,5,4,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,7,6,1,5,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,5,7,1,4,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,5,3,4,7,2,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[3,2,6,4,7,1,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,4,7,6,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,4,2,1,7,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,7,1,2,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,3,2,5,7,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,4,2,1,7,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,2,6,4,1,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,3,5,6,1,4,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,2,7,1,4,3,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,1,6,5,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,6,5,2,3,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,3,1,6,2,5,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[4,7,1,2,5,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[7,4,1,2,5,6,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,3,1,2,5,7,6,8] => 0001101 => [3,2,1,1] => ([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 1
[3,5,4,6,1,2,8,7] => 0000010 => [5,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 4
[5,7,4,3,6,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,1,3,6,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,5,4,1,7,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,6,3,4,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,1,3,7,6,5,2,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,3,6,4,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,5,7,6,2,1,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,7,1,6,4,2,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[3,7,6,2,1,4,5,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[4,6,7,5,2,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[6,7,2,4,5,3,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,2,7,6,4,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,3,7,4,6,2,1,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,7,3,5,4,2,6,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
[6,1,2,4,7,5,3,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[5,6,7,1,3,2,4,8] => 0000001 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) => 5
[1,6,3,4,2,5,8,7] => 1000010 => [1,4,1,1] => ([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) => 3
[1,4,3,7,6,2,5,8] => 1000001 => [1,5,1] => ([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) => 4
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same generating function
Generating function
$F_{2} = 2\ q$
Description
The multiplicity of the largest distance Laplacian eigenvalue in a connected graph.
The distance Laplacian of a graph is the (symmetric) matrix with row and column sums $0$, which has the negative distances between two vertices as its off-diagonal entries. This statistic is the largest multiplicity of an eigenvalue.
For example, the cycle on four vertices has distance Laplacian
$$ \left(\begin{array}{rrrr} 4 & -1 & -2 & -1 \\ -1 & 4 & -1 & -2 \\ -2 & -1 & 4 & -1 \\ -1 & -2 & -1 & 4 \end{array}\right). $$
Its eigenvalues are $0,4,4,6$, so the statistic is $1$.
The path on four vertices has eigenvalues $0, 4.7\dots, 6, 9.2\dots$ and therefore also statistic $1$.
The graphs with statistic $n-1$, $n-2$ and $n-3$ have been characterised, see [1].
The distance Laplacian of a graph is the (symmetric) matrix with row and column sums $0$, which has the negative distances between two vertices as its off-diagonal entries. This statistic is the largest multiplicity of an eigenvalue.
For example, the cycle on four vertices has distance Laplacian
$$ \left(\begin{array}{rrrr} 4 & -1 & -2 & -1 \\ -1 & 4 & -1 & -2 \\ -2 & -1 & 4 & -1 \\ -1 & -2 & -1 & 4 \end{array}\right). $$
Its eigenvalues are $0,4,4,6$, so the statistic is $1$.
The path on four vertices has eigenvalues $0, 4.7\dots, 6, 9.2\dots$ and therefore also statistic $1$.
The graphs with statistic $n-1$, $n-2$ and $n-3$ have been characterised, see [1].
Map
connectivity set
Description
The connectivity set of a permutation as a binary word.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.
According to [2], also known as the global ascent set.
The connectivity set is
$$C(\pi)=\{i\in [n-1] | \forall 1 \leq j \leq i < k \leq n : \pi(j) < \pi(k)\}.$$
For $n > 1$ it can also be described as the set of occurrences of the mesh pattern
$$([1,2], \{(0,2),(1,0),(1,1),(2,0),(2,1) \})$$
or equivalently
$$([1,2], \{(0,1),(0,2),(1,1),(1,2),(2,0) \}),$$
see [3].
The permutation is connected, when the connectivity set is empty.
Map
to threshold graph
Description
The threshold graph corresponding to the composition.
A threshold graph is a graph that can be obtained from the empty graph by adding successively isolated and dominating vertices.
A threshold graph is uniquely determined by its degree sequence.
The Laplacian spectrum of a threshold graph is integral. Interpreting it as an integer partition, it is the conjugate of the partition given by its degree sequence.
A threshold graph is a graph that can be obtained from the empty graph by adding successively isolated and dominating vertices.
A threshold graph is uniquely determined by its degree sequence.
The Laplacian spectrum of a threshold graph is integral. Interpreting it as an integer partition, it is the conjugate of the partition given by its degree sequence.
Map
delta morphism
Description
Applies the delta morphism to a binary word.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.
The delta morphism of a finite word $w$ is the integer compositions composed of the lengths of consecutive runs of the same letter in $w$.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!