- FindStat

Identifier

Mp00109: Permutations —descent word⟶ Binary words
Mp00158: Binary words —alternating inverse⟶ Binary words
Mp00262: Binary words —poset of factors⟶ Posets
St000068: Posets ⟶ ℤ

Values

[1,2] => 0 => 0 => ([(0,1)],2) => 1

[2,1] => 1 => 1 => ([(0,1)],2) => 1

[1,2,3] => 00 => 01 => ([(0,1),(0,2),(1,3),(2,3)],4) => 1

[1,3,2] => 01 => 00 => ([(0,2),(2,1)],3) => 1

[2,1,3] => 10 => 11 => ([(0,2),(2,1)],3) => 1

[2,3,1] => 01 => 00 => ([(0,2),(2,1)],3) => 1

[3,1,2] => 10 => 11 => ([(0,2),(2,1)],3) => 1

[3,2,1] => 11 => 10 => ([(0,1),(0,2),(1,3),(2,3)],4) => 1

[1,2,3,4] => 000 => 010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 1

[1,2,4,3] => 001 => 011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1

[1,3,2,4] => 010 => 000 => ([(0,3),(2,1),(3,2)],4) => 1

[1,3,4,2] => 001 => 011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1

[1,4,2,3] => 010 => 000 => ([(0,3),(2,1),(3,2)],4) => 1

[1,4,3,2] => 011 => 001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1

[2,1,3,4] => 100 => 110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1

[2,1,4,3] => 101 => 111 => ([(0,3),(2,1),(3,2)],4) => 1

[2,3,1,4] => 010 => 000 => ([(0,3),(2,1),(3,2)],4) => 1

[2,3,4,1] => 001 => 011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1

[2,4,1,3] => 010 => 000 => ([(0,3),(2,1),(3,2)],4) => 1

[2,4,3,1] => 011 => 001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1

[3,1,2,4] => 100 => 110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1

[3,1,4,2] => 101 => 111 => ([(0,3),(2,1),(3,2)],4) => 1

[3,2,1,4] => 110 => 100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1

[3,2,4,1] => 101 => 111 => ([(0,3),(2,1),(3,2)],4) => 1

[3,4,1,2] => 010 => 000 => ([(0,3),(2,1),(3,2)],4) => 1

[3,4,2,1] => 011 => 001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1

[4,1,2,3] => 100 => 110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1

[4,1,3,2] => 101 => 111 => ([(0,3),(2,1),(3,2)],4) => 1

[4,2,1,3] => 110 => 100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1

[4,2,3,1] => 101 => 111 => ([(0,3),(2,1),(3,2)],4) => 1

[4,3,1,2] => 110 => 100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => 1

[4,3,2,1] => 111 => 101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) => 1

[1,2,4,3,5] => 0010 => 0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[1,2,5,3,4] => 0010 => 0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[1,3,2,4,5] => 0100 => 0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[1,3,2,5,4] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,3,4,2,5] => 0010 => 0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[1,3,5,2,4] => 0010 => 0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[1,4,2,3,5] => 0100 => 0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[1,4,2,5,3] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,4,3,2,5] => 0110 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 1

[1,4,3,5,2] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,4,5,2,3] => 0010 => 0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[1,5,2,3,4] => 0100 => 0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[1,5,2,4,3] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,5,3,2,4] => 0110 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 1

[1,5,3,4,2] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[1,5,4,2,3] => 0110 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 1

[2,1,3,5,4] => 1001 => 1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 1

[2,1,4,3,5] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[2,1,4,5,3] => 1001 => 1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 1

[2,1,5,3,4] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[2,1,5,4,3] => 1011 => 1110 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[2,3,1,4,5] => 0100 => 0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[2,3,1,5,4] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[2,3,4,1,5] => 0010 => 0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[2,3,5,1,4] => 0010 => 0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[2,4,1,3,5] => 0100 => 0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[2,4,1,5,3] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[2,4,3,1,5] => 0110 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 1

[2,4,3,5,1] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[2,4,5,1,3] => 0010 => 0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[2,5,1,3,4] => 0100 => 0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[2,5,1,4,3] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[2,5,3,1,4] => 0110 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 1

[2,5,3,4,1] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[2,5,4,1,3] => 0110 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 1

[3,1,2,5,4] => 1001 => 1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 1

[3,1,4,2,5] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[3,1,4,5,2] => 1001 => 1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 1

[3,1,5,2,4] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[3,1,5,4,2] => 1011 => 1110 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[3,2,1,5,4] => 1101 => 1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[3,2,4,1,5] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[3,2,4,5,1] => 1001 => 1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 1

[3,2,5,1,4] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[3,2,5,4,1] => 1011 => 1110 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[3,4,1,2,5] => 0100 => 0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[3,4,1,5,2] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[3,4,2,1,5] => 0110 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 1

[3,4,2,5,1] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[3,4,5,1,2] => 0010 => 0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[3,5,1,2,4] => 0100 => 0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[3,5,1,4,2] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[3,5,2,1,4] => 0110 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 1

[3,5,2,4,1] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[3,5,4,1,2] => 0110 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 1

[4,1,2,5,3] => 1001 => 1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 1

[4,1,3,2,5] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[4,1,3,5,2] => 1001 => 1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 1

[4,1,5,2,3] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[4,1,5,3,2] => 1011 => 1110 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[4,2,1,5,3] => 1101 => 1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[4,2,3,1,5] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[4,2,3,5,1] => 1001 => 1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 1

[4,2,5,1,3] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[4,2,5,3,1] => 1011 => 1110 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[4,3,1,5,2] => 1101 => 1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[4,3,2,5,1] => 1101 => 1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[4,3,5,1,2] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[4,3,5,2,1] => 1011 => 1110 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

>>> Load all 3606 entries. <<<

[4,5,1,2,3] => 0100 => 0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[4,5,1,3,2] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[4,5,2,1,3] => 0110 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 1

[4,5,2,3,1] => 0101 => 0000 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[4,5,3,1,2] => 0110 => 0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 1

[5,1,2,4,3] => 1001 => 1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 1

[5,1,3,2,4] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[5,1,3,4,2] => 1001 => 1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 1

[5,1,4,2,3] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[5,1,4,3,2] => 1011 => 1110 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[5,2,1,4,3] => 1101 => 1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[5,2,3,1,4] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[5,2,3,4,1] => 1001 => 1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9) => 1

[5,2,4,1,3] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[5,2,4,3,1] => 1011 => 1110 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[5,3,1,4,2] => 1101 => 1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[5,3,2,4,1] => 1101 => 1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[5,3,4,1,2] => 1010 => 1111 => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[5,3,4,2,1] => 1011 => 1110 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[5,4,1,3,2] => 1101 => 1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[5,4,2,3,1] => 1101 => 1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8) => 1

[1,2,4,3,6,5] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[1,2,5,3,6,4] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[1,2,5,4,6,3] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[1,2,6,3,5,4] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[1,2,6,4,5,3] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[1,3,2,4,6,5] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[1,3,2,5,4,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,3,2,5,6,4] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[1,3,2,6,4,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,3,2,6,5,4] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[1,3,4,2,6,5] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[1,3,5,2,6,4] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[1,3,5,4,6,2] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[1,3,6,2,5,4] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[1,3,6,4,5,2] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[1,4,2,3,6,5] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[1,4,2,5,3,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,4,2,5,6,3] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[1,4,2,6,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,4,2,6,5,3] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[1,4,3,2,6,5] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[1,4,3,5,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,4,3,5,6,2] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[1,4,3,6,2,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,4,3,6,5,2] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[1,4,5,2,6,3] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[1,4,5,3,6,2] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[1,4,6,2,5,3] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[1,4,6,3,5,2] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[1,5,2,3,6,4] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[1,5,2,4,3,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,5,2,4,6,3] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[1,5,2,6,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,5,2,6,4,3] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[1,5,3,2,6,4] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[1,5,3,4,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,5,3,4,6,2] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[1,5,3,6,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,5,3,6,4,2] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[1,5,4,2,6,3] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[1,5,4,3,6,2] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[1,5,4,6,2,3] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,5,4,6,3,2] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[1,5,6,2,4,3] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[1,5,6,3,4,2] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[1,6,2,3,5,4] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[1,6,2,4,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,6,2,4,5,3] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[1,6,2,5,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,6,2,5,4,3] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[1,6,3,2,5,4] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[1,6,3,4,2,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,6,3,4,5,2] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[1,6,3,5,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,6,3,5,4,2] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[1,6,4,2,5,3] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[1,6,4,3,5,2] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[1,6,4,5,2,3] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[1,6,4,5,3,2] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[1,6,5,2,4,3] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[1,6,5,3,4,2] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[2,1,3,5,4,6] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[2,1,3,6,4,5] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[2,1,4,3,5,6] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[2,1,4,3,6,5] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[2,1,4,5,3,6] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[2,1,4,6,3,5] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[2,1,5,3,4,6] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[2,1,5,3,6,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[2,1,5,4,3,6] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[2,1,5,4,6,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[2,1,5,6,3,4] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[2,1,6,3,4,5] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[2,1,6,3,5,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[2,1,6,4,3,5] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[2,1,6,4,5,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[2,1,6,5,3,4] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[2,3,1,4,6,5] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[2,3,1,5,4,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[2,3,1,5,6,4] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[2,3,1,6,4,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[2,3,1,6,5,4] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[2,3,4,1,6,5] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[2,3,5,1,6,4] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[2,3,5,4,6,1] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[2,3,6,1,5,4] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[2,3,6,4,5,1] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[2,4,1,3,6,5] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[2,4,1,5,3,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[2,4,1,5,6,3] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[2,4,1,6,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[2,4,1,6,5,3] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[2,4,3,1,6,5] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[2,4,3,5,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[2,4,3,5,6,1] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[2,4,3,6,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[2,4,3,6,5,1] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[2,4,5,1,6,3] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[2,4,5,3,6,1] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[2,4,6,1,5,3] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[2,4,6,3,5,1] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[2,5,1,3,6,4] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[2,5,1,4,3,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[2,5,1,4,6,3] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[2,5,1,6,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[2,5,1,6,4,3] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[2,5,3,1,6,4] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[2,5,3,4,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[2,5,3,4,6,1] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[2,5,3,6,1,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[2,5,3,6,4,1] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[2,5,4,1,6,3] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[2,5,4,3,6,1] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[2,5,4,6,1,3] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[2,5,4,6,3,1] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[2,5,6,1,4,3] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[2,5,6,3,4,1] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[2,6,1,3,5,4] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[2,6,1,4,3,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[2,6,1,4,5,3] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[2,6,1,5,3,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[2,6,1,5,4,3] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[2,6,3,1,5,4] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[2,6,3,4,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[2,6,3,4,5,1] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[2,6,3,5,1,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[2,6,3,5,4,1] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[2,6,4,1,5,3] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[2,6,4,3,5,1] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[2,6,4,5,1,3] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[2,6,4,5,3,1] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[2,6,5,1,4,3] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[2,6,5,3,4,1] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,1,2,5,4,6] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,1,2,6,4,5] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,1,4,2,5,6] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[3,1,4,2,6,5] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[3,1,4,5,2,6] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,1,4,6,2,5] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,1,5,2,4,6] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[3,1,5,2,6,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[3,1,5,4,2,6] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,1,5,4,6,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[3,1,5,6,2,4] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,1,6,2,4,5] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[3,1,6,2,5,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[3,1,6,4,2,5] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,1,6,4,5,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[3,1,6,5,2,4] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,2,1,5,4,6] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[3,2,1,6,4,5] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[3,2,4,1,5,6] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[3,2,4,1,6,5] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[3,2,4,5,1,6] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,2,4,6,1,5] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,2,5,1,4,6] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[3,2,5,1,6,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[3,2,5,4,1,6] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,2,5,4,6,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[3,2,5,6,1,4] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,2,6,1,4,5] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[3,2,6,1,5,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[3,2,6,4,1,5] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,2,6,4,5,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[3,2,6,5,1,4] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,4,1,2,6,5] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,4,1,5,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[3,4,1,5,6,2] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,4,1,6,2,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[3,4,1,6,5,2] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[3,4,2,1,6,5] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,4,2,5,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[3,4,2,5,6,1] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,4,2,6,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[3,4,2,6,5,1] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[3,4,5,1,6,2] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[3,4,5,2,6,1] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[3,4,6,1,5,2] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[3,4,6,2,5,1] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[3,5,1,2,6,4] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,5,1,4,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[3,5,1,4,6,2] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,5,1,6,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[3,5,1,6,4,2] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[3,5,2,1,6,4] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,5,2,4,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[3,5,2,4,6,1] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,5,2,6,1,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[3,5,2,6,4,1] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[3,5,4,1,6,2] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,5,4,2,6,1] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,5,4,6,1,2] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[3,5,4,6,2,1] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[3,5,6,1,4,2] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[3,5,6,2,4,1] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[3,6,1,2,5,4] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,6,1,4,2,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[3,6,1,4,5,2] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,6,1,5,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[3,6,1,5,4,2] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[3,6,2,1,5,4] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,6,2,4,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[3,6,2,4,5,1] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,6,2,5,1,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[3,6,2,5,4,1] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[3,6,4,1,5,2] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,6,4,2,5,1] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,6,4,5,1,2] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[3,6,4,5,2,1] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[3,6,5,1,4,2] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[3,6,5,2,4,1] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,1,2,5,3,6] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,1,2,6,3,5] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,1,3,2,5,6] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[4,1,3,2,6,5] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[4,1,3,5,2,6] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,1,3,6,2,5] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,1,5,2,3,6] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[4,1,5,2,6,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[4,1,5,3,2,6] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,1,5,3,6,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[4,1,5,6,2,3] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,1,6,2,3,5] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[4,1,6,2,5,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[4,1,6,3,2,5] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,1,6,3,5,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[4,1,6,5,2,3] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,2,1,5,3,6] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[4,2,1,6,3,5] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[4,2,3,1,5,6] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[4,2,3,1,6,5] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[4,2,3,5,1,6] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,2,3,6,1,5] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,2,5,1,3,6] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[4,2,5,1,6,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[4,2,5,3,1,6] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,2,5,3,6,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[4,2,5,6,1,3] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,2,6,1,3,5] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[4,2,6,1,5,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[4,2,6,3,1,5] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,2,6,3,5,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[4,2,6,5,1,3] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,3,1,5,2,6] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[4,3,1,6,2,5] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[4,3,2,5,1,6] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[4,3,2,6,1,5] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[4,3,5,1,2,6] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[4,3,5,1,6,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[4,3,5,2,1,6] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,3,5,2,6,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[4,3,5,6,1,2] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,3,6,1,2,5] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[4,3,6,1,5,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[4,3,6,2,1,5] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,3,6,2,5,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[4,3,6,5,1,2] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,5,1,2,6,3] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,5,1,3,2,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[4,5,1,3,6,2] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,5,1,6,2,3] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[4,5,1,6,3,2] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[4,5,2,1,6,3] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,5,2,3,1,6] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[4,5,2,3,6,1] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,5,2,6,1,3] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[4,5,2,6,3,1] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[4,5,3,1,6,2] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,5,3,2,6,1] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,5,3,6,1,2] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[4,5,3,6,2,1] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[4,5,6,1,3,2] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[4,5,6,2,3,1] => 00101 => 01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[4,6,1,2,5,3] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,6,1,3,2,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[4,6,1,3,5,2] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,6,1,5,2,3] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[4,6,1,5,3,2] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[4,6,2,1,5,3] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,6,2,3,1,5] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[4,6,2,3,5,1] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,6,2,5,1,3] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[4,6,2,5,3,1] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[4,6,3,1,5,2] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,6,3,2,5,1] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,6,3,5,1,2] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[4,6,3,5,2,1] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[4,6,5,1,3,2] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[4,6,5,2,3,1] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[5,1,2,4,3,6] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[5,1,2,6,3,4] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[5,1,3,2,4,6] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[5,1,3,2,6,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[5,1,3,4,2,6] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[5,1,3,6,2,4] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[5,1,4,2,3,6] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[5,1,4,2,6,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[5,1,4,3,2,6] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[5,1,4,3,6,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[5,1,4,6,2,3] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[5,1,6,2,3,4] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[5,1,6,2,4,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[5,1,6,3,2,4] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[5,1,6,3,4,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[5,1,6,4,2,3] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[5,2,1,4,3,6] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[5,2,1,6,3,4] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[5,2,3,1,4,6] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[5,2,3,1,6,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[5,2,3,4,1,6] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[5,2,3,6,1,4] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[5,2,4,1,3,6] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[5,2,4,1,6,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[5,2,4,3,1,6] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[5,2,4,3,6,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[5,2,4,6,1,3] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[5,2,6,1,3,4] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[5,2,6,1,4,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[5,2,6,3,1,4] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[5,2,6,3,4,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[5,2,6,4,1,3] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[5,3,1,4,2,6] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[5,3,1,6,2,4] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[5,3,2,4,1,6] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[5,3,2,6,1,4] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[5,3,4,1,2,6] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[5,3,4,1,6,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[5,3,4,2,1,6] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[5,3,4,2,6,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[5,3,4,6,1,2] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[5,3,6,1,2,4] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[5,3,6,1,4,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[5,3,6,2,1,4] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[5,3,6,2,4,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[5,3,6,4,1,2] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[5,4,1,3,2,6] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[5,4,1,6,2,3] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[5,4,2,3,1,6] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[5,4,2,6,1,3] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[5,4,3,6,1,2] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[5,4,6,1,2,3] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[5,4,6,1,3,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[5,4,6,2,1,3] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[5,4,6,2,3,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[5,4,6,3,1,2] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[5,6,1,2,4,3] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[5,6,1,3,2,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[5,6,1,3,4,2] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[5,6,1,4,2,3] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[5,6,1,4,3,2] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[5,6,2,1,4,3] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[5,6,2,3,1,4] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[5,6,2,3,4,1] => 01001 => 00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[5,6,2,4,1,3] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[5,6,2,4,3,1] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[5,6,3,1,4,2] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[5,6,3,2,4,1] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[5,6,3,4,1,2] => 01010 => 00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[5,6,3,4,2,1] => 01011 => 00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[5,6,4,1,3,2] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[5,6,4,2,3,1] => 01101 => 00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[6,1,2,4,3,5] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[6,1,2,5,3,4] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[6,1,3,2,4,5] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[6,1,3,2,5,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[6,1,3,4,2,5] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[6,1,3,5,2,4] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[6,1,4,2,3,5] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[6,1,4,2,5,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[6,1,4,3,2,5] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[6,1,4,3,5,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[6,1,4,5,2,3] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[6,1,5,2,3,4] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[6,1,5,2,4,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[6,1,5,3,2,4] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[6,1,5,3,4,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[6,1,5,4,2,3] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[6,2,1,4,3,5] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[6,2,1,5,3,4] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[6,2,3,1,4,5] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[6,2,3,1,5,4] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[6,2,3,4,1,5] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[6,2,3,5,1,4] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[6,2,4,1,3,5] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[6,2,4,1,5,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[6,2,4,3,1,5] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[6,2,4,3,5,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[6,2,4,5,1,3] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[6,2,5,1,3,4] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[6,2,5,1,4,3] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[6,2,5,3,1,4] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[6,2,5,3,4,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[6,2,5,4,1,3] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[6,3,1,4,2,5] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[6,3,1,5,2,4] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[6,3,2,4,1,5] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[6,3,2,5,1,4] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[6,3,4,1,2,5] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[6,3,4,1,5,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[6,3,4,2,1,5] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[6,3,4,2,5,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[6,3,4,5,1,2] => 10010 => 11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[6,3,5,1,2,4] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[6,3,5,1,4,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[6,3,5,2,1,4] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[6,3,5,2,4,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[6,3,5,4,1,2] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[6,4,1,3,2,5] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[6,4,1,5,2,3] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[6,4,2,3,1,5] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[6,4,2,5,1,3] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[6,4,3,5,1,2] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[6,4,5,1,2,3] => 10100 => 11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[6,4,5,1,3,2] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[6,4,5,2,1,3] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[6,4,5,2,3,1] => 10101 => 11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[6,4,5,3,1,2] => 10110 => 11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12) => 1

[6,5,1,3,2,4] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[6,5,1,4,2,3] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[6,5,2,3,1,4] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[6,5,2,4,1,3] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[6,5,3,4,1,2] => 11010 => 10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10) => 1

[1,3,2,5,4,7,6] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,3,2,6,4,7,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,3,2,6,5,7,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,3,2,7,4,6,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,3,2,7,5,6,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,4,2,5,3,7,6] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,4,2,6,3,7,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,4,2,6,5,7,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,4,2,7,3,6,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,4,2,7,5,6,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,4,3,5,2,7,6] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,4,3,6,2,7,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,4,3,6,5,7,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,4,3,7,2,6,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,4,3,7,5,6,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,5,2,4,3,7,6] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,5,2,6,3,7,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,5,2,6,4,7,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,5,2,7,3,6,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,5,2,7,4,6,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,5,3,4,2,7,6] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,5,3,6,2,7,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,5,3,6,4,7,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,5,3,7,2,6,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,5,3,7,4,6,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,5,4,6,2,7,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,5,4,6,3,7,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,5,4,7,2,6,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,5,4,7,3,6,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,6,2,4,3,7,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,6,2,5,3,7,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,6,2,5,4,7,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,6,2,7,3,5,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,6,2,7,4,5,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,6,3,4,2,7,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,6,3,5,2,7,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,6,3,5,4,7,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,6,3,7,2,5,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,6,3,7,4,5,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,6,4,5,2,7,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,6,4,5,3,7,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,6,4,7,2,5,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,6,4,7,3,5,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,6,5,7,2,4,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,6,5,7,3,4,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,7,2,4,3,6,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,7,2,5,3,6,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,7,2,5,4,6,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,7,2,6,3,5,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,7,2,6,4,5,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,7,3,4,2,6,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,7,3,5,2,6,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,7,3,5,4,6,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,7,3,6,2,5,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,7,3,6,4,5,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,7,4,5,2,6,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,7,4,5,3,6,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,7,4,6,2,5,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,7,4,6,3,5,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,7,5,6,2,4,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[1,7,5,6,3,4,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,1,4,3,6,5,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,1,4,3,7,5,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,1,5,3,6,4,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,1,5,3,7,4,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,1,5,4,6,3,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,1,5,4,7,3,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,1,6,3,5,4,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,1,6,3,7,4,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,1,6,4,5,3,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,1,6,4,7,3,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,1,6,5,7,3,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,1,7,3,5,4,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,1,7,3,6,4,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,1,7,4,5,3,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,1,7,4,6,3,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,1,7,5,6,3,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,3,1,5,4,7,6] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,3,1,6,4,7,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,3,1,6,5,7,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,3,1,7,4,6,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,3,1,7,5,6,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,4,1,5,3,7,6] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,4,1,6,3,7,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,4,1,6,5,7,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,4,1,7,3,6,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,4,1,7,5,6,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,4,3,5,1,7,6] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,4,3,6,1,7,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,4,3,6,5,7,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,4,3,7,1,6,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,4,3,7,5,6,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,5,1,4,3,7,6] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,5,1,6,3,7,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,5,1,6,4,7,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,5,1,7,3,6,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,5,1,7,4,6,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,5,3,4,1,7,6] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,5,3,6,1,7,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,5,3,6,4,7,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,5,3,7,1,6,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,5,3,7,4,6,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,5,4,6,1,7,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,5,4,6,3,7,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,5,4,7,1,6,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,5,4,7,3,6,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,6,1,4,3,7,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,6,1,5,3,7,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,6,1,5,4,7,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,6,1,7,3,5,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,6,1,7,4,5,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,6,3,4,1,7,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,6,3,5,1,7,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,6,3,5,4,7,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,6,3,7,1,5,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,6,3,7,4,5,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,6,4,5,1,7,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,6,4,5,3,7,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,6,4,7,1,5,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,6,4,7,3,5,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,6,5,7,1,4,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,6,5,7,3,4,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,7,1,4,3,6,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,7,1,5,3,6,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,7,1,5,4,6,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,7,1,6,3,5,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,7,1,6,4,5,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,7,3,4,1,6,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,7,3,5,1,6,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,7,3,5,4,6,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,7,3,6,1,5,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,7,3,6,4,5,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,7,4,5,1,6,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,7,4,5,3,6,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,7,4,6,1,5,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,7,4,6,3,5,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,7,5,6,1,4,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[2,7,5,6,3,4,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,1,4,2,6,5,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,1,4,2,7,5,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,1,5,2,6,4,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,1,5,2,7,4,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,1,5,4,6,2,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,1,5,4,7,2,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,1,6,2,5,4,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,1,6,2,7,4,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,1,6,4,5,2,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,1,6,4,7,2,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,1,6,5,7,2,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,1,7,2,5,4,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,1,7,2,6,4,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,1,7,4,5,2,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,1,7,4,6,2,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,1,7,5,6,2,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,2,4,1,6,5,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,2,4,1,7,5,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,2,5,1,6,4,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,2,5,1,7,4,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,2,5,4,6,1,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,2,5,4,7,1,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,2,6,1,5,4,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,2,6,1,7,4,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,2,6,4,5,1,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,2,6,4,7,1,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,2,6,5,7,1,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,2,7,1,5,4,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,2,7,1,6,4,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,2,7,4,5,1,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,2,7,4,6,1,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,2,7,5,6,1,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,4,1,5,2,7,6] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,4,1,6,2,7,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,4,1,6,5,7,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,4,1,7,2,6,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,4,1,7,5,6,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,4,2,5,1,7,6] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,4,2,6,1,7,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,4,2,6,5,7,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,4,2,7,1,6,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,4,2,7,5,6,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,5,1,4,2,7,6] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,5,1,6,2,7,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,5,1,6,4,7,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,5,1,7,2,6,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,5,1,7,4,6,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,5,2,4,1,7,6] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,5,2,6,1,7,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,5,2,6,4,7,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,5,2,7,1,6,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,5,2,7,4,6,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,5,4,6,1,7,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,5,4,6,2,7,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,5,4,7,1,6,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,5,4,7,2,6,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,6,1,4,2,7,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,6,1,5,2,7,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,6,1,5,4,7,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,6,1,7,2,5,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,6,1,7,4,5,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,6,2,4,1,7,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,6,2,5,1,7,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,6,2,5,4,7,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,6,2,7,1,5,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,6,2,7,4,5,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,6,4,5,1,7,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,6,4,5,2,7,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,6,4,7,1,5,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,6,4,7,2,5,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,6,5,7,1,4,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,6,5,7,2,4,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,7,1,4,2,6,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,7,1,5,2,6,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,7,1,5,4,6,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,7,1,6,2,5,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,7,1,6,4,5,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,7,2,4,1,6,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,7,2,5,1,6,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,7,2,5,4,6,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,7,2,6,1,5,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,7,2,6,4,5,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,7,4,5,1,6,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,7,4,5,2,6,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,7,4,6,1,5,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,7,4,6,2,5,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,7,5,6,1,4,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[3,7,5,6,2,4,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,1,3,2,6,5,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,1,3,2,7,5,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,1,5,2,6,3,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,1,5,2,7,3,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,1,5,3,6,2,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,1,5,3,7,2,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,1,6,2,5,3,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,1,6,2,7,3,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,1,6,3,5,2,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,1,6,3,7,2,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,1,6,5,7,2,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,1,7,2,5,3,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,1,7,2,6,3,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,1,7,3,5,2,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,1,7,3,6,2,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,1,7,5,6,2,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,2,3,1,6,5,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,2,3,1,7,5,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,2,5,1,6,3,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,2,5,1,7,3,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,2,5,3,6,1,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,2,5,3,7,1,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,2,6,1,5,3,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,2,6,1,7,3,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,2,6,3,5,1,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,2,6,3,7,1,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,2,6,5,7,1,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,2,7,1,5,3,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,2,7,1,6,3,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,2,7,3,5,1,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,2,7,3,6,1,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,2,7,5,6,1,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,3,5,1,6,2,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,3,5,1,7,2,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,3,5,2,6,1,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,3,5,2,7,1,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,3,6,1,5,2,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,3,6,1,7,2,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,3,6,2,5,1,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,3,6,2,7,1,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,3,6,5,7,1,2] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,3,7,1,5,2,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,3,7,1,6,2,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,3,7,2,5,1,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,3,7,2,6,1,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,3,7,5,6,1,2] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,5,1,3,2,7,6] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,5,1,6,2,7,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,5,1,6,3,7,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,5,1,7,2,6,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,5,1,7,3,6,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,5,2,3,1,7,6] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,5,2,6,1,7,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,5,2,6,3,7,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,5,2,7,1,6,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,5,2,7,3,6,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,5,3,6,1,7,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,5,3,6,2,7,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,5,3,7,1,6,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,5,3,7,2,6,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,6,1,3,2,7,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,6,1,5,2,7,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,6,1,5,3,7,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,6,1,7,2,5,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,6,1,7,3,5,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,6,2,3,1,7,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,6,2,5,1,7,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,6,2,5,3,7,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,6,2,7,1,5,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,6,2,7,3,5,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,6,3,5,1,7,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,6,3,5,2,7,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,6,3,7,1,5,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,6,3,7,2,5,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,6,5,7,1,3,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,6,5,7,2,3,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,7,1,3,2,6,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,7,1,5,2,6,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,7,1,5,3,6,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,7,1,6,2,5,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,7,1,6,3,5,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,7,2,3,1,6,5] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,7,2,5,1,6,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,7,2,5,3,6,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,7,2,6,1,5,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,7,2,6,3,5,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,7,3,5,1,6,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,7,3,5,2,6,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,7,3,6,1,5,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,7,3,6,2,5,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,7,5,6,1,3,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[4,7,5,6,2,3,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,1,3,2,6,4,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,1,3,2,7,4,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,1,4,2,6,3,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,1,4,2,7,3,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,1,4,3,6,2,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,1,4,3,7,2,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,1,6,2,4,3,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,1,6,2,7,3,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,1,6,3,4,2,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,1,6,3,7,2,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,1,6,4,7,2,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,1,7,2,4,3,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,1,7,2,6,3,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,1,7,3,4,2,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,1,7,3,6,2,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,1,7,4,6,2,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,2,3,1,6,4,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,2,3,1,7,4,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,2,4,1,6,3,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,2,4,1,7,3,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,2,4,3,6,1,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,2,4,3,7,1,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,2,6,1,4,3,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,2,6,1,7,3,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,2,6,3,4,1,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,2,6,3,7,1,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,2,6,4,7,1,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,2,7,1,4,3,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,2,7,1,6,3,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,2,7,3,4,1,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,2,7,3,6,1,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,2,7,4,6,1,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,3,4,1,6,2,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,3,4,1,7,2,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,3,4,2,6,1,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,3,4,2,7,1,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,3,6,1,4,2,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,3,6,1,7,2,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,3,6,2,4,1,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,3,6,2,7,1,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,3,6,4,7,1,2] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,3,7,1,4,2,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,3,7,1,6,2,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,3,7,2,4,1,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,3,7,2,6,1,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,3,7,4,6,1,2] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,4,6,1,3,2,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,4,6,1,7,2,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,4,6,2,3,1,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,4,6,2,7,1,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,4,6,3,7,1,2] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,4,7,1,3,2,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,4,7,1,6,2,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,4,7,2,3,1,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,4,7,2,6,1,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,4,7,3,6,1,2] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,6,1,3,2,7,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,6,1,4,2,7,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,6,1,4,3,7,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,6,1,7,2,4,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,6,1,7,3,4,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,6,2,3,1,7,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,6,2,4,1,7,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,6,2,4,3,7,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,6,2,7,1,4,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,6,2,7,3,4,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,6,3,4,1,7,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,6,3,4,2,7,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,6,3,7,1,4,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,6,3,7,2,4,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,6,4,7,1,3,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,6,4,7,2,3,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,7,1,3,2,6,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,7,1,4,2,6,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,7,1,4,3,6,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,7,1,6,2,4,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,7,1,6,3,4,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,7,2,3,1,6,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,7,2,4,1,6,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,7,2,4,3,6,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,7,2,6,1,4,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,7,2,6,3,4,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,7,3,4,1,6,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,7,3,4,2,6,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,7,3,6,1,4,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,7,3,6,2,4,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,7,4,6,1,3,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[5,7,4,6,2,3,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,1,3,2,5,4,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,1,3,2,7,4,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,1,4,2,5,3,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,1,4,2,7,3,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,1,4,3,5,2,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,1,4,3,7,2,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,1,5,2,4,3,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,1,5,2,7,3,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,1,5,3,4,2,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,1,5,3,7,2,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,1,5,4,7,2,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,1,7,2,4,3,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,1,7,2,5,3,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,1,7,3,4,2,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,1,7,3,5,2,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,1,7,4,5,2,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,2,3,1,5,4,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,2,3,1,7,4,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,2,4,1,5,3,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,2,4,1,7,3,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,2,4,3,5,1,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,2,4,3,7,1,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,2,5,1,4,3,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,2,5,1,7,3,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,2,5,3,4,1,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,2,5,3,7,1,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,2,5,4,7,1,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,2,7,1,4,3,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,2,7,1,5,3,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,2,7,3,4,1,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,2,7,3,5,1,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,2,7,4,5,1,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,3,4,1,5,2,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,3,4,1,7,2,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,3,4,2,5,1,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,3,4,2,7,1,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,3,5,1,4,2,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,3,5,1,7,2,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,3,5,2,4,1,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,3,5,2,7,1,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,3,5,4,7,1,2] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,3,7,1,4,2,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,3,7,1,5,2,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,3,7,2,4,1,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,3,7,2,5,1,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,3,7,4,5,1,2] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,4,5,1,3,2,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,4,5,1,7,2,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,4,5,2,3,1,7] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,4,5,2,7,1,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,4,5,3,7,1,2] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,4,7,1,3,2,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,4,7,1,5,2,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,4,7,2,3,1,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,4,7,2,5,1,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,4,7,3,5,1,2] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,5,7,1,3,2,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,5,7,1,4,2,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,5,7,2,3,1,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,5,7,2,4,1,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,5,7,3,4,1,2] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,7,1,3,2,5,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,7,1,4,2,5,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,7,1,4,3,5,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,7,1,5,2,4,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,7,1,5,3,4,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,7,2,3,1,5,4] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,7,2,4,1,5,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,7,2,4,3,5,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,7,2,5,1,4,3] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,7,2,5,3,4,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,7,3,4,1,5,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,7,3,4,2,5,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,7,3,5,1,4,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,7,3,5,2,4,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,7,4,5,1,3,2] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[6,7,4,5,2,3,1] => 010101 => 000000 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,1,3,2,5,4,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,1,3,2,6,4,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,1,4,2,5,3,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,1,4,2,6,3,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,1,4,3,5,2,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,1,4,3,6,2,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,1,5,2,4,3,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,1,5,2,6,3,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,1,5,3,4,2,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,1,5,3,6,2,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,1,5,4,6,2,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,1,6,2,4,3,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,1,6,2,5,3,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,1,6,3,4,2,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,1,6,3,5,2,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,1,6,4,5,2,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,2,3,1,5,4,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,2,3,1,6,4,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,2,4,1,5,3,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,2,4,1,6,3,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,2,4,3,5,1,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,2,4,3,6,1,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,2,5,1,4,3,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,2,5,1,6,3,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,2,5,3,4,1,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,2,5,3,6,1,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,2,5,4,6,1,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,2,6,1,4,3,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,2,6,1,5,3,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,2,6,3,4,1,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,2,6,3,5,1,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,2,6,4,5,1,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,3,4,1,5,2,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,3,4,1,6,2,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,3,4,2,5,1,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,3,4,2,6,1,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,3,5,1,4,2,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,3,5,1,6,2,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,3,5,2,4,1,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,3,5,2,6,1,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,3,5,4,6,1,2] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,3,6,1,4,2,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,3,6,1,5,2,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,3,6,2,4,1,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,3,6,2,5,1,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,3,6,4,5,1,2] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,4,5,1,3,2,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,4,5,1,6,2,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,4,5,2,3,1,6] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,4,5,2,6,1,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,4,5,3,6,1,2] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,4,6,1,3,2,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,4,6,1,5,2,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,4,6,2,3,1,5] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,4,6,2,5,1,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,4,6,3,5,1,2] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,5,6,1,3,2,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,5,6,1,4,2,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,5,6,2,3,1,4] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,5,6,2,4,1,3] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[7,5,6,3,4,1,2] => 101010 => 111111 => ([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) => 1

[8,6,7,4,5,2,3,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,6,8,4,5,2,3,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,5,6,4,7,2,3,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,5,6,4,8,2,3,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,5,7,4,8,2,3,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,6,7,3,4,2,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,6,8,3,4,2,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,5,6,3,4,2,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,5,3,6,2,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,5,6,3,4,2,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,5,7,3,4,2,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,4,5,3,6,2,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,5,3,7,2,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,6,3,7,2,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,5,6,3,4,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,5,8,3,4,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,4,5,3,6,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,4,5,3,8,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,4,7,3,8,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,5,6,2,3,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,5,8,2,3,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,4,5,2,3,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,3,4,2,5,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,4,5,2,3,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,4,7,2,3,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,3,4,2,5,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,3,4,2,7,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,3,6,2,7,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,6,5,7,2,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,6,5,7,4,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,5,2,7,6,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,5,4,7,6,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,6,5,7,4,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,5,4,7,6,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,4,1,7,6,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,4,3,7,6,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,5,2,6,1,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,5,4,6,1,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,5,4,6,3,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,4,1,6,5,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,4,3,6,5,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,4,6,2,7,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,5,4,6,3,7,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,4,2,6,5,7,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,4,3,6,5,7,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,4,6,3,7,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,4,3,6,5,7,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,3,1,6,5,7,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,3,2,6,5,7,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,4,2,5,1,7,6,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,4,3,5,1,7,6,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,4,3,5,2,7,6,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,3,1,5,4,7,6,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,3,2,5,4,7,6,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,3,5,4,6,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,4,3,8,6,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,5,4,8,6,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,6,4,5,3,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,7,4,6,5,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,8,4,6,5,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,7,5,6,4,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,8,5,6,4,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,3,1,7,5,6,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,4,1,8,6,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,5,4,8,6,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,6,4,5,1,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,7,4,6,5,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,8,4,6,5,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,7,5,6,4,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,8,5,6,4,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,3,1,6,5,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,3,1,7,6,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,3,1,8,6,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,4,3,6,1,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,4,3,7,6,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,4,3,5,1,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,4,3,6,5,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,4,3,6,5,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,5,4,6,3,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,6,4,5,3,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,6,4,5,3,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,4,2,6,1,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,4,2,7,6,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,4,2,8,6,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,4,2,5,1,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,4,2,6,5,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,4,2,6,5,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,5,4,6,2,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,6,4,5,2,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,6,4,5,2,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,4,1,6,3,8,5,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,4,1,6,3,7,5,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,4,3,7,5,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,4,1,7,3,8,5,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,4,1,5,3,7,6,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,4,1,5,3,8,6,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,5,3,6,4,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,5,1,6,3,8,4,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,5,1,6,3,7,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,5,3,7,4,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,6,3,7,4,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,1,7,3,8,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,3,1,6,4,7,5,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,3,1,6,4,8,5,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,3,1,7,4,8,5,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,4,2,6,5,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,4,1,6,2,8,5,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,4,1,6,2,7,5,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,4,2,7,5,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,4,1,5,2,7,6,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,4,1,5,2,8,6,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,5,2,6,4,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,1,6,2,7,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,5,2,7,4,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,1,7,2,8,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,3,2,5,4,8,6,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,6,2,7,4,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,1,7,2,8,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,3,2,6,4,7,5,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,3,2,6,4,8,5,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,3,2,7,4,8,5,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,5,2,6,3,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,1,6,2,8,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,1,6,2,7,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,5,2,7,3,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,1,7,2,8,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,4,2,5,3,7,6,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,4,2,5,3,8,6,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,6,2,7,3,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,1,7,2,8,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,4,2,6,3,7,5,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,4,2,6,3,8,5,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,4,2,7,3,8,5,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,6,2,7,3,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,2,6,3,7,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,2,6,3,8,4,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,2,7,3,8,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,2,7,3,8,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,5,2,3,1,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,1,5,4,8,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,8,6,7,4,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,6,8,1,3,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,6,2,7,3,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,8,2,7,1,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,4,3,6,5,8,7,10,9] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[10,8,9,6,7,4,5,2,3,1] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[3,5,1,7,2,9,4,10,6,8] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[4,8,3,7,2,6,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,3,7,2,6,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,4,7,2,6,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,4,7,3,6,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,3,7,2,5,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,4,7,2,5,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,4,7,3,5,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,5,7,2,4,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,5,7,3,4,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,3,6,2,5,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,4,6,2,5,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,4,6,3,5,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,5,6,2,4,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,7,2,6,4,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,4,2,7,3,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,4,2,6,3,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,5,2,6,3,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,7,5,6,2,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,4,1,8,3,7,5,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,1,5,3,8,4,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,1,5,3,7,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,4,1,8,6,7,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,1,5,2,7,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,4,1,7,2,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,4,1,6,2,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,5,1,6,2,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,4,5,1,8,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,4,5,1,7,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,4,6,1,7,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,5,2,7,4,9,6,8] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[2,4,1,6,3,8,5,9,7] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[5,3,4,1,9,7,8,2,6] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[9,3,7,5,6,1,8,2,4] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[3,5,2,7,4,8,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,1,7,4,8,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,2,7,1,8,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,4,7,6,8,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,8,4,5,1,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,1,3,2,5,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,3,7,2,6,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,1,5,2,8,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,1,5,2,7,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,1,8,2,7,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,7,2,5,1,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,8,2,5,1,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,7,2,8,1,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,8,4,7,2,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,8,4,7,1,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,8,1,7,2,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,3,2,6,5,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,3,2,6,4,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,3,2,5,4,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,3,2,5,4,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,3,2,5,4,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,4,2,5,3,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,4,2,5,3,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,4,2,5,3,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,4,2,6,3,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,6,3,5,4,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,6,2,5,4,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,6,2,5,3,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,5,1,4,3,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,6,1,4,3,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,7,1,4,3,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,8,1,4,3,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,8,1,4,3,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,7,1,4,3,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,6,1,4,3,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,5,1,4,3,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,7,2,5,3,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,7,2,5,4,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,7,3,5,4,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,8,3,5,4,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,8,2,5,4,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,8,2,5,3,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,5,1,4,3,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,6,1,4,3,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,4,3,8,2,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,4,3,7,2,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,5,3,7,2,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,5,3,8,2,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,6,1,5,3,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,8,2,6,3,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,8,2,6,3,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,8,2,6,4,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,8,3,6,4,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,7,3,6,4,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,7,2,6,3,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,7,2,6,3,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,6,1,5,3,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,7,1,5,3,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,8,1,5,3,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,5,2,6,3,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,5,2,7,3,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,4,2,7,3,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,4,2,6,3,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,3,2,6,4,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,3,2,6,4,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,3,2,7,4,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,3,2,7,4,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,3,2,7,5,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,4,3,8,5,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,4,2,8,5,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,3,2,8,5,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,3,2,8,4,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,3,2,8,4,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,7,1,3,2,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,4,8,1,3,2,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,8,1,4,2,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,7,1,4,2,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,4,2,8,3,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,4,2,8,3,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,5,2,8,3,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,5,2,8,4,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,5,3,8,4,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,6,3,8,4,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,6,2,8,4,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,6,2,8,3,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,6,2,8,3,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,5,2,8,3,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,7,1,5,2,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,8,1,5,2,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,7,3,8,1,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,8,3,7,1,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,7,2,6,1,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,8,3,7,2,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,8,3,7,2,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,8,4,7,2,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,8,4,7,3,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,7,4,8,3,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,7,4,8,2,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,7,3,8,2,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,7,3,8,2,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,8,2,6,1,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,6,3,7,1,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,6,3,8,1,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,3,8,2,4,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,2,6,3,8,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,1,6,3,8,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,4,5,3,8,2,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,7,1,8,3,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,2,8,4,5,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,1,5,2,8,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,3,8,2,6,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,7,1,8,2,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,3,7,1,8,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,5,3,7,2,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,2,7,4,8,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,2,7,3,5,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,5,4,8,2,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,7,2,8,4,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,2,7,1,5,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,7,1,8,4,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,1,7,2,5,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,5,2,8,4,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,5,2,7,4,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,7,2,8,4,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,8,2,7,4,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,8,2,7,4,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,5,1,6,4,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,5,4,7,1,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,5,3,7,6,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,5,3,7,1,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,5,3,6,1,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,5,1,6,3,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,5,4,6,2,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,5,3,6,2,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,5,1,6,2,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,5,2,7,1,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,6,2,7,5,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,6,2,7,1,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,6,1,7,2,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,5,1,7,2,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,5,4,7,2,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,5,4,7,3,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,5,4,7,6,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,5,3,7,6,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,5,1,7,6,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,6,1,7,5,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,6,5,7,1,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,6,4,7,2,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,6,4,7,1,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,6,1,7,4,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,6,3,7,4,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,6,3,7,5,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,6,4,7,5,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,6,4,7,5,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,6,4,7,3,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,6,4,7,2,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,6,3,7,2,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,6,3,7,2,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,6,1,7,2,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,6,2,7,1,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,6,2,7,4,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,6,3,7,4,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,6,3,7,1,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,6,1,7,3,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,5,1,7,3,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,6,1,7,3,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,6,3,7,1,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,6,3,7,5,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,6,4,7,5,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,6,4,7,1,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,6,1,7,4,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,5,1,7,4,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,4,1,7,5,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,4,2,7,6,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,5,1,7,6,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,6,1,7,5,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,6,5,7,1,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,6,5,7,3,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,6,5,7,1,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,6,1,7,5,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,5,1,7,6,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,5,2,7,6,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,5,2,7,6,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,5,3,7,6,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,6,3,7,5,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,6,2,7,5,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,6,2,7,5,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,6,2,7,4,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,6,1,7,4,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,6,4,7,1,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,6,4,7,3,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,6,2,7,3,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,6,2,7,1,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,6,1,7,2,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,6,4,7,2,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,6,5,7,2,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,6,5,7,2,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,6,5,7,3,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,6,5,7,4,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,6,5,7,3,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,6,4,7,3,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,6,1,7,3,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,6,3,7,1,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,6,8,1,4,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,1,6,4,8,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,2,6,4,8,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,6,4,5,2,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,3,8,1,7,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,2,4,3,6,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,3,8,1,4,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,3,6,1,8,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,5,3,8,6,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,2,5,4,8,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,1,5,3,8,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,5,7,4,6,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,6,2,4,1,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,6,2,7,1,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,8,2,7,1,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,3,7,1,6,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,2,6,3,5,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,2,3,1,8,6,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,6,3,8,5,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,6,7,2,4,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,6,1,4,2,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,5,6,1,4,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,3,6,1,7,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,5,4,6,1,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,7,3,8,4,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,3,7,4,8,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,2,8,1,5,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,8,2,5,1,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,2,4,3,5,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,5,8,2,4,1,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,5,8,2,4,3,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,8,3,6,5,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,8,3,6,2,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,2,6,3,7,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,2,7,3,8,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,6,5,8,3,4,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,7,1,6,4,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,5,8,3,6,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,6,3,4,2,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,4,1,8,3,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,4,2,7,6,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,2,4,1,6,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,7,1,6,3,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,1,6,4,5,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,2,6,3,7,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,2,8,1,6,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,2,3,1,8,4,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,3,5,2,7,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,2,7,1,8,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,3,8,2,5,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,5,8,3,6,2,4,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,5,3,6,2,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,6,8,1,3,2,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,2,7,3,5,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,2,8,3,5,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,2,8,3,5,4,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,2,8,3,6,4,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,4,2,8,3,6,5,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,3,2,8,4,6,5,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,3,2,7,4,6,5,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,4,2,7,3,6,5,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,2,7,3,6,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,2,7,3,5,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,2,6,3,5,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,2,6,3,5,4,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,2,5,3,6,4,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,2,5,3,6,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,2,5,3,7,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,2,4,3,7,6,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,2,4,3,7,5,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,2,4,3,6,5,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,2,4,3,6,5,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,2,4,3,7,5,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,2,4,3,8,5,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,2,4,3,8,5,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,2,4,3,8,6,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,2,5,3,8,4,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,2,5,3,8,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,2,5,3,7,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,2,6,3,7,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,2,6,3,8,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,3,2,8,4,7,5,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,4,2,8,3,7,5,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,2,8,3,7,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,2,8,3,7,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,2,8,3,6,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,2,7,3,6,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,3,7,2,5,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,2,8,1,6,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,3,8,1,6,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,5,4,8,1,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,3,8,1,5,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,4,5,3,7,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,5,7,3,4,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,2,7,4,6,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,4,6,2,7,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,5,1,8,2,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,7,1,5,4,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,5,1,7,2,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,4,7,2,8,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,4,6,2,7,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,4,8,2,7,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,5,1,8,2,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,4,6,1,8,3,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,5,1,7,4,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,4,1,7,5,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,5,6,1,8,3,4,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,1,6,5,8,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,2,6,5,7,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,6,5,8,2,4,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,3,1,7,6,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,4,1,7,5,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,5,1,7,4,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,6,4,8,2,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,6,4,7,1,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,5,2,7,4,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,4,2,7,5,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,6,5,7,1,4,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,3,2,7,6,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,3,2,7,6,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,2,8,4,5,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,4,8,1,7,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,1,6,3,5,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,5,7,2,3,1,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,5,4,7,1,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,5,7,1,3,2,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,4,7,1,6,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,5,7,1,6,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,5,1,8,4,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,4,1,8,5,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,3,1,8,6,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,4,1,8,5,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,5,1,8,4,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,3,1,6,4,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,4,5,2,3,1,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,6,7,3,5,2,4,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,5,2,4,1,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,5,2,4,1,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,4,1,6,3,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,6,3,5,2,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,4,1,5,2,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,6,3,4,1,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,7,3,4,1,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,8,6,7,3,4,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,8,5,7,3,4,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,7,3,4,1,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,4,1,5,2,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,7,3,5,2,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,7,4,5,2,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,7,4,5,3,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,8,6,7,4,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,8,6,7,3,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,6,7,3,4,1,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,5,7,3,4,1,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,5,6,2,7,3,4,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,7,3,5,1,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,8,4,7,3,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,8,5,7,3,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,8,5,7,4,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,8,5,7,4,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,7,4,6,3,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,7,4,6,2,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,7,3,6,2,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,7,3,6,2,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,7,3,5,1,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,8,4,7,3,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,7,3,6,2,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,6,2,5,1,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,5,1,7,3,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,4,1,7,3,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,4,1,7,3,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,5,7,3,6,2,4,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,5,7,4,6,2,3,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,4,6,2,3,1,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,3,1,7,4,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,3,1,7,4,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,3,1,7,5,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,4,2,8,6,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,3,1,8,5,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,5,6,2,3,1,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,4,8,5,6,2,3,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,8,5,6,2,4,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,5,6,2,4,1,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,4,1,8,6,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,5,2,8,6,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,5,2,8,6,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,6,3,8,5,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,6,2,8,5,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,6,2,8,5,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,6,2,8,4,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,6,2,5,1,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,8,4,6,2,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,7,3,8,4,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,5,1,6,2,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,8,4,6,2,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,8,5,6,2,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,8,5,6,2,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,8,5,6,3,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,7,4,8,5,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,7,4,8,5,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,7,3,8,5,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,8,4,5,1,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,5,1,7,3,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,6,2,8,4,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,4,8,3,7,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,8,1,6,3,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,1,5,2,8,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,5,3,4,2,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,4,1,8,6,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,8,4,6,1,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,7,4,5,1,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,3,7,5,8,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,4,6,2,8,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,8,4,6,1,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,8,4,7,1,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,8,2,7,1,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,3,7,2,8,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,4,7,1,5,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,4,7,2,5,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,2,7,1,5,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,1,7,2,5,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,4,2,6,5,8,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,2,6,4,8,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,7,3,6,5,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,1,6,2,4,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,1,6,2,4,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,1,6,3,4,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,5,6,3,4,1,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,7,2,6,3,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,6,8,1,4,3,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,4,8,2,7,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,1,3,2,6,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,7,2,6,4,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,2,8,1,5,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,7,4,8,1,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,7,4,8,2,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,3,8,1,5,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,1,8,3,5,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,2,8,3,5,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,7,1,8,4,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,1,8,2,5,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,4,8,5,7,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,6,3,5,4,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,8,5,7,3,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,3,8,4,5,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,6,1,7,3,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,8,1,7,2,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,6,7,3,4,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,6,7,3,5,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,6,7,4,5,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,6,7,4,5,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,6,7,4,5,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,5,7,4,6,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,5,7,4,6,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,5,7,3,6,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,3,6,4,5,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,3,7,4,5,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,3,7,4,6,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,4,8,5,6,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,3,8,5,6,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,2,8,5,6,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,1,8,5,6,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,1,8,5,6,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,2,8,5,6,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,3,8,5,6,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,4,8,5,6,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,2,7,4,6,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,2,7,4,5,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,2,6,4,5,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,1,6,4,5,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,1,7,4,5,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,1,7,4,6,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,4,8,5,6,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,3,8,5,6,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,5,6,1,7,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,5,6,2,7,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,3,8,4,6,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,1,7,3,6,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,1,7,3,6,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,1,7,3,5,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,2,6,3,5,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,2,7,3,5,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,2,7,3,6,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,2,7,3,6,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,3,8,4,6,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,2,8,4,6,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,1,8,4,6,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,4,7,3,6,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,4,7,3,6,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,4,7,2,6,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,5,7,2,6,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,5,7,2,6,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,5,7,3,6,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,5,7,3,6,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,6,7,3,5,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,6,7,3,5,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,6,7,2,5,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,6,7,2,5,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,6,7,2,4,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,5,7,1,4,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,6,7,1,4,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,6,7,1,5,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,6,7,1,5,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,2,8,6,7,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,5,1,8,6,7,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,1,8,5,7,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,2,8,5,7,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,5,7,1,6,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,4,7,1,5,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,4,6,1,5,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,3,6,1,5,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,3,7,1,5,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,3,7,1,6,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,4,7,1,6,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,2,8,4,7,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,1,8,4,7,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,2,6,1,8,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,1,6,2,8,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,1,6,2,7,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,1,6,2,7,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,1,5,2,6,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,2,5,1,6,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,2,5,1,7,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,2,6,1,7,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,2,6,1,7,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,3,6,2,8,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,3,6,1,8,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,4,8,3,5,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,4,5,2,8,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,4,6,2,3,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,4,6,3,8,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,4,8,3,6,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,4,5,3,7,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,4,6,3,7,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,4,8,3,7,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,3,7,2,4,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,3,7,2,8,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,3,8,2,7,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,4,8,2,7,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,4,6,2,7,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,4,5,2,7,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,4,5,2,6,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,4,5,2,3,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,4,6,2,3,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,4,8,2,3,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,3,8,2,4,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,3,4,2,8,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,3,5,2,7,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,3,5,2,8,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,3,8,2,5,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,3,6,2,5,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,3,6,2,4,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,3,5,2,4,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,3,5,2,4,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,3,5,2,6,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,3,6,2,7,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,3,6,2,7,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,3,8,2,7,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,3,7,2,8,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,3,6,2,5,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,3,6,2,8,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,3,8,2,6,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,4,8,2,6,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,3,6,2,8,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,3,6,2,4,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,3,5,2,4,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,3,5,2,8,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,4,8,2,5,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,5,8,2,4,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,5,7,2,3,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,4,8,2,3,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,3,8,2,4,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,3,4,2,8,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,3,4,2,6,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,3,4,2,8,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,4,8,2,3,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,4,7,2,3,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,4,7,2,3,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,4,6,2,3,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,3,6,2,4,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,3,7,2,4,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,3,7,2,4,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,3,7,2,5,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,3,8,2,5,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,3,5,2,8,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,3,5,2,6,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,3,7,2,6,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,3,7,2,8,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,3,8,2,7,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,3,5,2,7,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,3,4,2,7,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,3,4,2,7,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,3,4,2,6,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,3,4,2,5,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,3,4,2,6,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,3,5,2,6,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,3,8,2,6,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,3,6,2,8,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,6,1,3,2,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,7,6,8,3,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,2,5,4,7,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,3,1,8,5,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,8,3,5,1,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,4,5,2,8,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,4,2,8,6,7,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,4,2,7,6,8,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,4,8,2,5,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,4,7,2,5,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,4,7,2,8,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,3,8,1,6,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,2,4,1,7,6,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,2,7,4,6,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,4,6,3,7,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,3,1,8,6,7,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,5,3,7,1,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,4,3,7,1,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,2,4,3,7,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,4,1,8,5,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,5,1,8,4,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,6,1,8,3,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,6,1,8,3,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,6,1,7,3,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,6,1,8,4,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,6,1,8,5,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,5,6,1,7,3,4,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,5,1,8,6,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,7,3,6,1,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,8,3,6,1,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,5,4,6,1,7,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,2,8,1,6,4,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,7,1,5,4,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,2,8,1,7,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,3,1,5,4,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,5,2,3,1,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,6,7,2,5,3,4,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,5,3,4,1,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,5,3,4,1,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,5,2,4,3,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,5,1,3,2,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,5,3,4,2,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,5,1,4,2,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,5,2,4,1,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,7,5,6,2,4,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,7,2,4,1,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,5,1,4,2,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,5,3,4,2,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,5,1,3,2,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,8,4,5,3,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,6,7,4,5,1,3,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,6,7,1,5,3,4,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,6,7,3,5,1,4,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,7,5,6,1,4,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,5,7,3,6,1,4,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,7,4,6,2,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,7,4,6,1,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,7,1,6,4,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,7,3,6,4,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,7,5,6,3,4,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,7,5,6,1,3,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,8,4,7,5,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,7,3,4,2,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,7,3,6,2,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,7,1,6,2,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,7,2,6,4,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,7,3,6,4,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,7,3,6,1,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,7,1,6,3,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,7,2,4,3,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,3,2,7,4,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,8,3,7,4,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,5,2,4,3,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,7,1,4,3,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,7,3,4,1,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,7,5,6,3,4,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,7,5,6,2,3,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,7,2,3,1,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,3,1,7,4,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,3,1,5,4,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,3,1,8,5,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,3,2,8,6,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,6,7,2,3,1,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,3,1,7,5,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,5,7,2,6,3,4,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,5,7,2,6,1,4,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,7,5,6,1,4,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,6,7,2,5,1,4,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,6,7,1,5,2,4,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,6,7,1,3,2,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,8,6,7,3,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,8,3,7,5,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,3,2,7,5,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,7,5,6,2,4,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,7,2,6,4,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,7,1,6,4,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,7,4,6,1,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,7,4,6,3,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,7,2,6,3,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,7,2,6,1,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,7,1,6,2,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,7,4,6,2,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,5,7,1,6,2,4,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,8,5,7,3,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,5,7,4,6,1,3,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,5,7,1,6,3,4,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,7,4,6,3,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,7,1,6,3,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,7,3,6,1,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,5,8,1,3,2,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,1,5,4,7,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,4,8,1,7,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,1,4,2,8,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,2,8,4,5,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,1,7,3,5,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,8,1,7,3,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,4,8,1,6,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,3,4,1,5,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,3,4,1,6,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,3,4,1,7,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,3,4,1,8,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,3,4,1,8,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,3,4,1,7,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,3,4,1,6,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,3,4,1,5,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,3,4,1,5,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,3,4,1,6,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,2,8,3,4,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,2,7,3,4,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,2,8,3,5,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,3,5,1,6,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,3,5,1,6,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,3,5,1,7,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,3,5,1,8,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,2,3,1,7,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,2,4,1,8,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,2,4,1,7,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,2,5,1,7,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,2,5,1,8,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,1,8,3,7,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,1,7,3,8,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,2,7,3,8,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,2,7,3,8,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,2,7,4,8,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,3,8,4,7,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,2,8,4,7,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,2,8,3,7,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,2,8,3,7,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,1,7,3,6,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,1,8,3,6,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,3,5,1,7,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,7,3,6,4,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,7,6,8,1,3,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,1,8,4,5,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,6,1,8,2,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,5,1,8,3,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,5,2,7,3,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,4,3,6,5,8,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,6,5,8,1,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,4,1,6,5,8,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,6,5,8,3,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,4,3,6,1,8,5,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,2,8,5,7,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,4,8,1,7,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,4,7,3,8,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,5,3,4,1,8,6,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,2,5,1,7,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,2,5,1,8,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,8,1,7,4,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,8,1,6,4,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,7,1,6,4,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,6,1,8,4,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,3,5,4,7,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,6,1,8,2,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,7,5,6,3,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,6,3,8,1,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,4,6,1,3,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[9,7,8,5,6,3,4,1,2] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[9,10,7,8,5,6,3,4,1,2] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[5,4,6,2,8,1,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,7,2,5,1,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,3,5,4,6,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,1,6,2,8,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,5,4,8,1,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,1,6,3,8,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,5,4,8,2,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,2,6,1,5,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,1,6,2,5,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,6,7,2,5,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,5,7,2,6,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,1,7,2,6,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,2,7,1,6,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,6,7,1,5,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,5,7,1,6,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,1,7,5,6,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,2,7,5,6,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,2,7,4,6,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,1,7,4,6,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,4,7,1,6,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,2,7,1,6,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,1,7,2,6,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,4,7,2,6,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,1,7,5,6,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,4,7,5,6,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,3,7,5,6,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,1,7,5,6,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,1,7,4,6,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,3,7,4,6,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,3,7,2,6,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,1,7,2,6,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,2,7,1,6,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,2,7,4,6,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,2,7,5,6,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,2,7,5,6,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,3,7,5,6,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,4,7,5,6,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,4,7,5,6,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,3,7,5,6,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,3,7,4,6,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,3,7,1,6,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,1,7,3,6,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,8,4,5,2,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,8,3,5,1,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,8,2,5,1,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,1,4,2,6,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,1,7,2,6,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,3,6,1,4,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,3,2,7,5,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,3,8,5,7,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,6,3,8,2,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,4,5,3,8,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,4,2,8,5,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,5,6,2,4,1,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,1,6,3,7,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,5,6,3,7,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,4,2,6,5,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,3,6,5,7,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,1,6,5,7,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,4,6,2,5,1,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,6,4,5,1,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,2,6,1,5,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,6,2,5,1,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,1,7,4,8,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,7,5,6,4,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,4,7,5,8,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,6,5,7,2,4,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,1,8,4,5,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,8,5,7,4,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,1,4,3,8,5,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,1,4,3,6,5,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,4,1,8,3,6,5,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,6,1,5,4,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,4,3,8,1,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,4,1,5,3,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,6,1,5,2,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,5,2,8,1,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,7,2,6,5,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,8,2,6,1,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,8,1,7,2,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,8,1,5,2,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,8,3,4,2,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,8,1,3,2,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,5,4,8,3,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,7,6,8,3,4,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,7,6,8,1,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,7,1,8,5,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,6,5,8,1,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,5,4,7,2,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,5,4,8,1,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,6,3,8,4,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,4,6,5,8,1,3,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,8,4,6,3,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,6,1,3,2,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,6,3,4,2,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,6,3,7,2,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,5,1,7,2,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,5,2,6,1,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,5,2,6,4,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,6,3,5,1,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,7,1,5,3,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,4,1,5,3,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,4,1,7,3,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,4,3,6,1,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,8,4,6,1,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,8,1,5,4,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,7,6,8,1,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,7,1,8,5,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,6,5,8,1,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,5,7,2,4,3,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,5,8,2,4,1,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,4,1,8,5,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,6,8,2,4,1,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,6,8,1,5,2,4,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,7,3,8,5,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,3,2,8,5,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,8,5,6,2,4,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,8,2,6,4,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,8,1,5,4,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,7,4,5,3,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,7,2,6,3,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,8,2,6,1,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,5,8,1,7,2,4,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,6,5,8,3,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,5,7,4,8,1,3,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,5,7,1,8,3,4,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,7,4,8,3,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,7,1,8,3,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,6,3,8,1,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,5,3,7,4,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,8,1,7,3,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,6,3,4,1,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,1,8,3,5,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,6,2,7,4,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,4,6,3,7,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,3,5,1,8,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,5,2,7,4,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,5,1,7,4,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,5,2,7,1,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,4,3,6,5,8,7,9] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[2,4,1,6,3,7,5,9,8] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[2,4,1,5,3,7,6,9,8] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[2,3,1,5,4,7,6,9,8] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[1,3,2,5,4,7,6,9,8] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[2,4,1,6,3,8,5,10,7,9] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[2,4,1,6,3,8,5,9,7,10] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[2,4,1,5,3,8,6,9,7] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[2,4,1,6,3,7,5,9,8,10] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[2,3,1,6,4,7,5,9,8] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[2,4,1,5,3,7,6,9,8,10] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[1,4,2,5,3,7,6,9,8] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[2,3,1,5,4,7,6,9,8,10] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[1,3,2,5,4,7,6,9,8,10] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[1,4,3,7,6,8,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,4,3,7,5,8,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,4,3,7,2,6,5,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,3,7,4,8,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,3,2,6,5,8,4,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,4,8,2,6,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,4,8,3,7,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,8,3,6,2,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,8,3,6,1,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,5,3,8,1,7,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,5,4,8,2,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,2,5,4,6,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,7,1,8,3,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,6,8,3,5,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,3,6,4,8,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,8,5,6,1,4,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,5,8,1,4,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,8,1,7,3,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,6,9,4,7,2,5,1,3] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[3,7,5,8,2,4,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,5,7,2,4,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,1,8,3,6,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,1,4,3,7,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,1,4,3,8,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,2,6,3,4,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,2,7,3,4,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,2,8,3,4,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,3,7,1,4,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,8,1,7,3,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,8,4,7,2,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,4,1,8,2,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,5,7,2,8,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,3,2,8,6,7,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,7,4,5,2,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,5,8,3,4,1,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,5,6,3,4,1,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,5,8,3,6,1,4,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,5,6,3,8,1,4,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,5,7,2,4,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,2,4,1,8,5,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,2,7,1,5,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,5,4,6,2,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,7,2,5,3,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,5,3,7,2,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,4,7,2,5,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,4,8,2,5,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,5,8,2,4,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,5,7,2,4,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,5,6,2,8,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,4,6,2,8,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,3,5,2,8,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,3,4,2,8,5,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,1,4,2,8,5,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,5,6,3,8,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,2,6,3,8,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,8,3,7,2,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,4,3,8,5,6,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,6,8,3,4,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,6,8,4,5,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,4,7,6,8,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,4,6,5,8,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,4,6,5,8,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,4,8,6,7,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,4,6,5,7,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,4,7,5,8,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,2,7,5,8,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,4,8,5,7,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,4,6,5,7,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,4,8,6,7,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,1,5,4,6,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,1,5,2,4,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,2,6,5,7,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,2,8,5,6,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,2,6,5,8,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,2,7,6,8,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,6,8,2,5,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,6,8,4,5,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,6,8,1,4,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,5,6,1,3,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,6,7,1,3,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,3,2,7,6,8,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,6,8,2,4,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,1,3,2,6,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,1,6,2,4,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,6,7,2,4,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,1,4,2,6,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,1,4,2,5,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,2,4,3,7,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,7,6,8,2,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,7,1,8,5,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,7,2,8,5,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,4,3,7,1,8,5,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,1,4,3,8,5,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,5,8,4,6,1,3,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,6,4,7,3,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,7,2,5,4,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,3,8,4,5,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,4,5,1,8,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,5,6,2,3,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,5,6,1,8,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,5,6,3,8,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,5,8,4,6,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,3,8,6,7,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,3,6,5,7,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,4,7,1,8,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,1,7,3,8,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,1,8,2,7,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,1,8,4,7,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,1,6,5,7,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,1,8,6,7,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,4,5,1,6,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,2,3,1,6,5,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,2,8,1,4,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,3,4,1,8,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,4,5,2,7,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,4,5,1,8,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,4,8,1,5,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,3,6,1,5,4,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,3,4,1,6,5,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,2,5,3,4,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,1,5,3,6,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,3,8,6,7,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,3,6,2,7,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,4,8,2,7,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,4,7,3,5,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,3,6,4,5,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,3,6,4,8,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,2,8,4,6,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,5,8,4,6,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,5,8,2,6,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,5,6,3,8,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,5,6,3,4,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,2,5,3,4,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,1,5,3,8,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,5,8,1,4,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,6,7,2,3,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,2,3,1,8,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,2,8,1,4,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,4,2,7,5,6,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,4,1,7,5,8,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,5,8,1,4,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,3,1,7,5,8,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,3,1,8,4,7,5,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,2,3,1,6,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,2,6,1,4,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,6,7,1,4,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,1,4,3,7,5,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,2,5,4,6,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,2,7,3,6,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,1,8,2,7,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,4,1,8,2,7,5,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,4,1,8,6,7,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,4,2,5,1,8,6,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,4,2,8,1,6,5,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,2,5,1,6,4,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,2,8,1,6,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,3,6,1,8,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,6,7,1,4,2,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,7,1,5,2,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,6,5,8,4,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,8,1,5,2,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,4,6,1,8,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,4,6,1,7,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,4,8,1,6,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,5,4,7,3,6,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,5,3,8,1,6,4,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,4,7,1,5,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,5,7,1,4,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,4,3,8,1,6,5,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,8,5,6,1,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,4,2,8,5,6,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,6,7,1,3,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,5,7,1,4,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,4,7,1,5,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,2,8,4,6,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,1,7,4,6,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,4,7,2,5,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,4,1,7,5,6,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,6,7,2,3,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,7,4,5,2,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,2,6,3,4,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,5,2,8,4,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,1,8,5,7,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,7,6,8,2,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,4,2,8,5,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,8,2,5,4,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,8,4,6,1,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,8,1,6,4,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,6,8,2,3,1,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,5,1,8,2,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,3,8,1,4,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,6,3,8,1,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,8,3,4,1,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,4,3,6,2,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,4,3,7,2,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,4,3,8,2,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,8,2,7,5,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,4,3,8,2,6,5,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,8,3,7,5,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,8,1,5,4,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,4,1,8,2,6,5,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,8,2,6,4,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,5,8,2,4,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,4,8,1,3,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,4,8,1,6,2,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,7,2,5,1,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,2,6,1,4,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,4,2,8,3,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,8,2,5,3,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,6,3,8,4,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,2,5,3,8,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,7,2,6,5,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,3,7,5,8,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,7,4,5,1,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,5,1,8,2,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,7,2,8,4,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,4,2,7,3,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,6,2,8,1,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,6,4,8,1,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,7,1,6,2,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,3,2,8,6,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,1,7,6,8,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,5,6,3,4,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,4,1,5,2,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,6,4,5,1,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,2,6,5,8,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,1,4,2,7,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,4,1,7,6,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,3,2,7,5,8,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,3,2,8,5,7,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,3,5,2,7,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,1,7,5,8,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,1,7,4,8,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,1,5,4,8,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,4,2,8,6,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,1,3,2,5,4,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,1,4,2,5,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,3,6,1,4,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,2,5,3,6,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,2,5,1,4,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,1,4,3,6,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,1,4,3,7,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,2,5,1,4,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,2,5,3,7,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,2,5,4,7,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,5,4,7,6,8,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,5,3,7,6,8,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,5,1,4,3,7,6,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,1,4,3,7,5,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,5,8,1,4,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,1,5,3,7,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,3,7,4,8,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,4,7,5,8,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,3,6,4,7,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,2,6,4,7,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,2,6,3,7,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,1,5,3,7,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,1,5,2,6,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,3,7,1,5,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,3,7,1,4,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,1,3,2,6,4,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,4,7,1,3,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,4,7,1,3,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,5,7,1,3,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,6,8,2,4,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,6,8,1,3,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,5,8,1,3,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,1,3,2,6,5,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,1,4,2,6,5,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,5,8,1,4,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,6,8,1,4,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,6,8,2,5,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,6,8,2,5,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,5,8,3,6,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,5,8,2,6,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,5,8,2,6,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,4,8,2,6,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,4,8,1,5,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,1,5,2,6,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,2,6,1,5,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,2,6,5,8,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,3,6,5,8,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,5,8,4,7,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,5,8,4,7,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,5,8,3,7,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,3,7,1,5,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,6,8,3,5,2,4,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,8,2,4,1,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,5,3,7,1,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,3,7,1,8,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,6,4,7,2,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,7,3,5,4,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,4,3,7,5,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,7,2,4,3,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,8,3,6,2,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,1,7,5,8,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,3,1,8,4,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,7,1,8,4,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,3,7,5,8,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,1,4,2,7,5,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,4,6,1,8,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,5,3,8,2,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,3,5,4,8,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,5,3,8,2,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,8,4,5,2,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,1,7,3,5,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,8,1,5,4,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,4,7,1,6,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,9,3,8,2,7,1,6] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[5,10,4,9,3,8,2,7,1,6] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[2,1,7,3,8,4,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,8,2,7,3,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,7,2,8,3,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,3,2,8,4,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,8,2,4,3,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,7,2,5,3,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,5,2,8,3,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,7,2,8,3,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,8,2,7,3,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,8,2,4,3,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,6,2,4,3,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,8,2,4,3,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,8,2,5,3,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,6,2,5,3,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,6,2,7,3,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,8,2,7,3,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,7,2,8,3,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,7,2,5,3,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,7,2,4,3,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,6,2,4,3,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,5,2,4,3,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,6,2,4,3,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,6,2,5,3,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,6,2,8,3,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,8,2,6,3,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,4,6,1,8,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,4,6,5,8,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,4,8,3,6,1,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,10,7,9,5,6,3,4,1,2] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[9,10,6,8,5,7,3,4,1,2] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[8,10,6,9,5,7,3,4,1,2] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[7,10,6,9,5,8,3,4,1,2] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[9,10,7,8,4,6,3,5,1,2] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[8,10,7,9,4,6,3,5,1,2] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[9,10,6,8,4,7,3,5,1,2] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[8,10,6,9,4,7,3,5,1,2] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[7,10,6,9,4,8,3,5,1,2] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[9,10,5,8,4,7,3,6,1,2] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[8,10,5,9,4,7,3,6,1,2] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[7,10,5,9,4,8,3,6,1,2] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[6,10,5,9,4,8,3,7,1,2] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[9,10,7,8,5,6,2,4,1,3] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[8,10,7,9,5,6,2,4,1,3] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[9,10,6,8,5,7,2,4,1,3] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[8,10,6,9,5,7,2,4,1,3] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[7,10,6,9,5,8,2,4,1,3] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[9,10,7,8,4,6,2,5,1,3] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[8,10,7,9,4,6,2,5,1,3] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[9,10,6,8,4,7,2,5,1,3] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[8,10,6,9,4,7,2,5,1,3] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[7,10,6,9,4,8,2,5,1,3] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[9,10,5,8,4,7,2,6,1,3] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[8,10,5,9,4,7,2,6,1,3] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[7,10,5,9,4,8,2,6,1,3] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[6,10,5,9,4,8,2,7,1,3] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[9,10,7,8,3,6,2,5,1,4] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[8,10,7,9,3,6,2,5,1,4] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[9,10,6,8,3,7,2,5,1,4] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[8,10,6,9,3,7,2,5,1,4] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[7,10,6,9,3,8,2,5,1,4] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[9,10,5,8,3,7,2,6,1,4] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[8,10,5,9,3,7,2,6,1,4] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[7,10,5,9,3,8,2,6,1,4] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[6,10,5,9,3,8,2,7,1,4] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[9,10,4,8,3,7,2,6,1,5] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[8,10,4,9,3,7,2,6,1,5] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[7,10,4,9,3,8,2,6,1,5] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[6,10,4,9,3,8,2,7,1,5] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[4,3,7,5,6,1,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,4,1,7,5,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,6,2,8,4,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,8,2,7,4,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,2,8,1,5,4,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,5,4,8,3,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,6,3,7,2,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,7,3,8,1,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,7,3,8,1,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,7,2,8,1,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,7,1,5,3,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,7,3,5,1,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,1,7,5,8,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,2,8,1,5,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,2,7,4,8,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,1,8,5,6,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,8,3,7,1,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,8,3,6,1,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,4,5,1,7,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,6,4,7,3,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,6,8,1,5,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,9,5,8,3,6,1,4,2] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[7,6,8,3,5,1,4,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,9,5,7,3,6,1,4,2] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[8,9,6,7,3,5,1,4,2] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[8,9,6,7,4,5,1,3,2] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[8,9,6,7,4,5,2,3,1] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[9,7,10,5,8,3,6,1,4,2] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[10,7,9,5,8,3,6,1,4,2] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[7,9,6,8,3,5,1,4,2] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[10,8,9,5,7,3,6,1,4,2] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[6,5,8,4,7,1,3,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,9,5,7,4,6,1,3,2] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[10,8,9,6,7,3,5,1,4,2] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[8,9,6,7,3,5,2,4,1] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[10,8,9,6,7,4,5,1,3,2] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[7,4,8,5,6,1,3,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,4,3,7,1,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,4,3,5,2,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,1,6,4,8,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,1,7,4,8,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,8,2,7,3,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,8,1,6,5,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,4,2,6,5,8,7,9] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[3,1,5,2,6,4,8,7,9] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[3,1,5,2,7,4,8,6,9] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[3,1,4,2,6,5,8,7,10,9] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[4,1,5,2,6,3,8,7,9] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[3,1,5,2,6,4,8,7,10,9] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[3,1,6,2,7,4,8,5,9] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[3,1,5,2,7,4,8,6,10,9] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[3,1,5,2,8,4,9,6,7] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[3,1,5,2,7,4,9,6,10,8] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[3,4,1,6,5,8,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,5,3,6,2,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,7,2,8,3,9,4,10,5] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[6,1,4,3,8,5,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,4,3,6,5,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,8,3,6,5,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,1,5,4,6,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,7,2,8,3,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,1,5,4,6,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,1,5,4,8,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,1,5,4,7,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,1,5,4,7,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,3,5,1,7,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,3,4,1,7,5,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,4,6,3,5,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,4,5,2,7,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,5,4,7,1,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,4,5,2,6,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,8,4,6,3,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,5,8,3,4,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,3,6,4,7,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,1,7,3,5,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,1,7,3,4,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,7,3,4,2,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,4,8,1,5,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,5,3,7,1,6,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,5,8,1,6,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,4,3,7,1,6,5,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,6,8,1,5,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,1,4,3,6,5,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,6,2,3,1,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,1,8,4,5,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,4,6,2,5,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,1,8,2,6,4,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,8,5,7,1,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,7,1,5,4,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,3,6,5,8,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,3,8,2,6,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,3,7,2,5,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,1,5,2,7,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,3,4,2,7,5,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,1,4,2,5,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,3,8,2,6,4,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,5,7,3,8,2,4,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,3,8,4,6,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,7,1,8,4,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,1,3,2,8,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,7,1,8,2,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,4,5,3,6,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,5,4,8,3,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,3,7,1,6,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[9,4,8,3,7,2,6,1,5] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[4,8,1,6,3,5,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,4,3,5,1,8,6,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,1,8,4,7,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,2,8,4,7,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,5,1,8,3,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,5,3,8,1,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,5,8,2,6,3,4,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,8,4,7,2,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,6,3,7,1,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,8,3,7,2,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,2,6,3,8,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,5,6,3,7,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,1,4,2,6,5,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,7,3,6,1,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,7,3,6,5,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,5,6,2,4,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,7,5,6,3,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,7,5,6,1,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,1,5,2,6,4,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,7,2,5,1,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,8,3,4,2,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,1,6,3,5,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,1,6,2,5,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,1,4,2,6,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,5,6,2,7,1,4,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,8,3,5,2,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,3,8,1,6,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,6,3,5,2,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,6,7,3,4,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,5,7,3,4,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,3,4,2,6,5,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,2,8,4,7,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,4,2,8,5,7,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,3,5,2,6,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,4,7,3,5,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,3,6,2,5,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,5,6,2,4,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,3,2,8,5,6,4,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,4,2,8,5,6,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,2,8,4,6,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,2,8,4,5,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,4,1,7,5,8,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,1,6,3,4,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,7,3,6,2,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,7,2,6,1,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,5,3,8,2,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,4,6,3,8,2,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,5,6,3,8,2,4,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,5,6,3,7,2,4,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,4,6,3,5,2,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,6,3,5,2,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,7,3,5,2,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,5,7,3,4,2,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,5,8,3,4,2,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,5,8,3,4,2,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,5,8,4,6,2,3,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,4,8,3,6,2,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,4,8,3,5,2,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,8,3,5,2,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,7,3,5,2,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,8,3,7,2,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,5,8,3,7,2,4,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,5,8,4,7,2,3,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,7,3,8,2,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,7,3,8,2,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,6,3,8,2,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,7,1,8,3,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,7,3,4,2,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,5,8,2,3,1,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,8,2,7,1,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,7,4,8,1,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,4,6,2,8,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,6,4,8,2,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,5,3,7,4,8,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,6,8,2,3,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,6,8,2,3,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,4,8,2,5,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,5,8,1,7,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,6,5,8,3,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,8,3,7,1,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,3,8,5,7,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,6,1,8,5,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,1,4,3,5,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,2,4,1,8,6,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,7,2,6,1,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,8,1,6,3,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,7,3,6,5,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,7,2,6,5,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,7,1,6,5,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,5,2,6,1,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,4,2,6,1,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,4,2,6,1,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,2,5,1,8,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,5,2,7,3,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,4,5,2,6,1,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,8,5,6,1,4,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,8,5,6,3,4,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,5,8,1,6,3,4,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,7,1,4,2,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,4,3,5,2,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,6,5,7,1,4,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,7,3,8,1,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,6,2,8,1,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,4,1,8,5,7,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,1,8,2,6,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,7,4,5,1,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,8,6,7,1,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,5,8,1,3,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,1,5,3,8,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,8,2,5,4,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,7,6,8,2,4,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,8,6,7,2,4,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,1,8,2,6,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,4,5,1,3,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,1,3,2,5,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,1,4,3,5,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,2,3,1,5,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,2,4,3,5,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,2,4,1,5,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,4,2,6,5,7,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,1,4,2,7,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,2,4,1,5,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,2,4,3,5,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,2,3,1,5,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,3,5,4,8,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,4,1,6,5,7,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,2,6,4,7,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,5,1,6,4,7,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,5,7,4,8,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,2,4,3,7,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,2,6,1,7,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,1,6,3,7,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,3,6,1,7,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,3,4,1,7,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,1,4,3,7,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,1,3,2,7,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,4,7,1,3,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,4,5,1,3,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,5,8,1,3,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,1,3,2,7,6,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,5,7,1,3,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,1,3,2,7,5,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,4,3,6,2,7,5,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,4,1,6,5,7,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,2,3,1,7,6,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,3,7,6,8,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,5,7,3,8,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,5,7,2,3,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,4,6,1,7,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,1,6,4,7,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,3,6,4,7,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,3,6,2,7,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,2,6,1,7,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,2,6,4,7,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,4,2,6,1,7,5,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,2,3,1,7,5,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,4,3,6,1,7,5,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,5,3,6,4,7,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,5,3,6,1,7,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,1,7,3,8,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,2,7,1,8,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,1,6,3,5,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,1,8,3,4,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,8,3,5,1,4,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,2,7,1,8,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,2,4,3,8,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,4,3,8,6,7,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,2,7,4,5,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,5,4,8,3,6,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,3,1,8,5,6,4,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,5,6,4,7,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,3,6,4,8,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,2,3,1,6,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,2,4,3,6,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,2,7,1,5,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,1,6,2,5,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,1,5,3,6,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,3,5,1,7,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,3,5,1,4,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,3,7,1,4,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,1,6,3,4,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,5,6,3,4,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,5,6,4,7,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,1,6,4,8,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,5,8,1,7,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,1,4,2,8,5,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,1,4,2,8,6,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,5,8,3,7,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,5,8,2,3,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,4,2,6,5,8,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,4,6,2,8,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,3,5,4,7,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,4,2,7,1,8,5,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,2,3,1,8,5,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,4,3,8,1,7,5,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,5,3,8,4,7,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,3,8,1,7,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,1,8,3,6,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,8,4,7,3,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,1,8,4,5,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,6,3,5,1,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,6,4,8,5,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,4,3,8,5,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,4,8,3,5,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,1,8,3,5,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,1,7,3,5,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,1,5,3,7,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,8,3,5,1,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,1,8,4,5,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,4,3,5,1,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,7,5,8,2,3,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,5,8,3,4,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,5,7,3,4,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,5,7,3,8,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,5,3,8,4,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,6,3,8,2,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,2,5,4,8,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,1,5,4,8,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,2,5,4,8,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,3,5,4,8,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,3,5,4,8,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,4,5,1,7,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,8,1,6,2,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,8,3,7,4,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,6,5,7,3,4,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,4,6,1,3,2,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,4,5,3,8,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,8,1,3,2,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,4,6,1,3,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,5,1,8,4,7,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,7,2,8,5,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,7,4,8,3,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,7,1,8,3,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,1,3,2,7,5,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,5,4,6,1,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,7,3,8,2,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,1,8,4,6,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,6,5,7,1,3,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,7,5,8,3,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,8,3,5,4,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,2,5,4,7,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,8,3,7,1,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,1,8,2,5,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,7,5,8,2,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,7,1,8,4,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,7,5,6,2,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,4,8,1,3,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,4,3,6,5,8,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,5,1,7,2,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,8,6,7,3,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,2,8,3,6,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,3,8,1,7,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,6,8,1,5,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,7,2,3,1,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,4,6,1,5,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,6,1,8,4,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,4,1,7,2,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,4,3,5,1,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,4,1,6,3,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,6,3,4,2,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,8,4,5,2,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,6,4,5,2,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,5,1,4,3,8,6,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,6,4,8,1,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,5,6,1,4,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,5,8,1,4,2,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,1,5,2,4,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,7,5,8,3,4,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,8,3,7,5,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,8,6,7,4,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,7,3,6,4,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,8,1,5,3,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,4,3,7,5,8,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,4,3,6,2,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,5,7,3,4,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,8,3,4,2,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,7,1,8,2,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,5,3,8,4,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,6,9,4,7,3,5,1,2] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[8,6,9,5,7,3,4,1,2] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[8,7,9,5,6,3,4,1,2] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[9,7,10,5,8,3,6,2,4,1] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[8,6,9,5,7,2,4,1,3] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[9,7,10,5,8,4,6,2,3,1] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[7,6,8,2,5,1,4,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,7,9,4,6,3,5,1,2] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[9,7,10,6,8,4,5,2,3,1] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[9,6,8,5,7,3,4,1,2] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[9,8,10,6,7,4,5,2,3,1] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[3,5,4,7,2,6,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,2,7,1,6,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,2,5,1,8,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,7,5,8,4,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,2,4,1,6,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,8,6,7,1,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,8,1,5,3,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,4,1,8,3,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,5,7,1,8,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,7,6,8,2,3,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,1,7,4,5,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,8,2,5,3,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,5,3,7,1,8,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,1,4,3,6,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,5,3,8,1,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,8,3,6,4,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,5,6,1,7,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,6,1,5,4,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,7,2,8,1,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,5,8,3,4,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,5,4,7,2,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,6,5,8,4,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,7,1,6,5,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,6,4,8,3,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,7,5,8,2,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,7,4,8,2,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,7,4,8,1,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,8,1,6,2,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,7,1,5,2,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,8,2,6,3,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,8,1,6,3,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,2,8,3,5,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,4,1,6,5,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,7,3,8,5,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,4,3,8,5,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[10,1,3,2,5,4,7,6,9,8] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[7,4,5,1,6,2,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,4,1,8,5,6,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,7,3,5,2,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,1,3,2,7,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,5,8,1,7,3,4,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,5,8,3,4,1,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,4,6,2,8,3,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,6,1,5,3,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,3,6,1,7,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,6,3,5,4,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,5,4,8,1,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,4,3,8,1,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,7,2,5,4,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,4,5,1,6,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,4,8,2,5,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,4,8,3,5,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,2,5,3,7,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,5,1,4,2,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,7,1,3,2,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,6,8,2,5,3,4,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,3,8,1,7,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,7,4,5,3,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,8,6,7,2,3,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,6,4,8,2,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,7,4,6,2,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,6,3,7,4,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,6,5,7,3,4,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,6,2,8,3,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,6,1,7,2,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,2,4,1,6,5,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,7,2,8,5,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,1,3,2,6,5,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,3,8,1,5,4,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,2,8,4,6,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,2,6,4,8,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,8,2,4,1,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,5,8,2,4,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,7,2,5,1,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,2,8,1,5,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,8,1,4,3,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,7,1,3,2,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,6,2,8,1,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,2,8,4,5,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,1,8,4,6,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,4,5,1,6,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,7,2,8,3,9,4,5] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[5,1,6,2,7,3,8,4,9] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[5,1,6,2,7,3,9,4,8] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[5,1,6,2,7,3,8,4,10,9] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[4,1,5,2,7,3,8,6,9] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[4,1,5,2,6,3,8,7,10,9] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[1,8,5,7,2,4,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,3,8,2,7,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,8,5,6,3,4,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,5,6,2,7,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,7,5,6,2,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,4,6,1,7,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,2,5,4,8,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,7,5,8,3,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,1,8,4,6,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,5,8,1,6,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,4,2,7,5,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,5,2,7,4,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,7,5,8,2,4,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,3,5,1,6,4,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,5,3,7,1,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,5,1,8,3,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,8,1,7,5,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,6,4,8,3,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,1,8,2,5,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,1,7,4,5,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,2,5,4,7,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,5,8,1,7,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,8,3,6,4,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,7,4,5,1,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,8,2,7,5,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,6,3,8,5,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,2,8,1,7,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,8,4,7,1,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,6,1,4,2,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,7,5,8,3,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,8,2,3,1,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,7,2,8,4,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,5,6,2,8,3,4,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,3,8,2,7,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,3,7,4,6,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,4,7,3,6,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,1,7,6,8,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,5,2,6,1,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,8,4,5,1,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,8,2,5,4,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,4,8,2,6,3,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,2,7,4,5,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,2,5,4,6,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,5,7,2,8,3,4,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,7,5,8,1,4,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,5,7,3,8,1,4,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,7,4,8,2,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,7,4,8,1,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,6,8,3,5,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,2,6,5,7,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,4,1,7,6,8,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,4,1,6,5,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,4,6,1,5,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,4,8,2,6,1,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,2,5,3,6,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,3,7,2,8,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,8,5,6,3,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,8,4,6,1,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,4,6,2,8,1,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,5,6,1,7,2,4,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,6,4,8,3,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,3,6,4,7,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,3,7,4,5,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,8,5,7,2,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,6,3,8,5,7,2,9] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[5,7,1,9,2,8,4,6,3] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[5,7,1,9,2,8,4,6,3,10] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[4,1,6,3,8,5,10,7,9,2] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[2,7,4,8,3,6,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,8,3,5,2,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,8,3,5,1,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,5,2,8,6,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,8,3,5,4,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,4,6,3,8,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,8,1,7,3,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,6,2,4,1,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,5,7,2,4,1,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,8,2,6,1,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,7,2,8,1,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,5,8,3,4,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,5,4,6,3,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,2,7,3,4,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,8,2,6,4,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,8,4,6,2,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,5,2,8,4,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,5,1,6,4,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,4,6,1,5,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,6,2,8,4,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,6,3,7,4,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,8,2,7,1,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,5,2,7,1,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,2,8,1,4,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,4,3,8,5,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,1,5,4,7,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,8,4,5,3,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,3,8,4,6,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,8,1,4,2,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,8,3,7,4,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,7,1,5,4,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,7,1,5,3,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,5,3,8,4,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,2,7,5,8,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,5,4,6,2,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,5,4,7,2,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,8,1,7,4,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,3,2,6,5,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,4,2,6,3,8,5,10,7,9] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[2,5,3,6,1,8,4,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,4,7,3,5,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,5,6,1,4,3,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,4,5,3,6,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,8,2,4,1,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,4,3,7,5,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,6,3,4,1,7,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,5,7,1,3,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,2,6,4,8,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,3,6,1,7,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,2,8,1,6,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,5,6,4,8,1,2] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,4,7,3,8,2,9,1] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[5,6,4,7,3,9,2,8,1] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[5,4,6,3,7,2,8,1,9] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[6,5,7,4,8,3,9,2,10,1] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[6,5,7,4,8,3,10,2,9,1] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[5,6,4,7,3,8,2,9,1,10] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[4,6,3,7,1,5,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,1,5,2,7,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,5,6,2,4,3,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,5,1,8,6,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,5,1,6,4,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,6,2,5,3,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,8,4,6,5,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,2,5,1,7,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,2,8,4,7,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,4,8,1,3,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,3,7,2,5,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,3,5,2,7,4,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,7,1,5,3,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,8,2,6,4,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,8,2,6,5,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,5,7,1,4,3,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,1,5,2,6,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,5,2,8,1,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,4,6,3,8,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,2,5,3,4,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,5,2,8,1,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,8,3,6,4,5,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,5,3,6,4,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,7,3,5,4,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,6,1,7,4,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,4,8,1,5,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[10,1,9,2,8,3,7,4,6,5] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[2,6,3,8,4,7,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,8,4,5,3,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,5,3,6,4,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,4,5,2,8,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,5,4,7,3,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,2,7,1,4,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,5,4,8,1,7,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,6,5,8,3,4,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,2,7,4,5,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,4,5,2,7,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,4,8,3,5,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,2,6,3,5,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,2,7,1,6,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,8,4,5,1,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,8,4,5,2,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,8,5,7,2,4,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,5,2,6,3,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,3,1,9,5,6,4,8] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[3,8,1,4,2,9,6,7,5] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[2,8,4,5,1,6,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,6,2,3,1,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,7,6,8,4,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,4,7,2,8,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,8,5,7,1,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,8,4,7,1,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,6,8,2,4,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,5,3,8,4,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,6,2,4,1,8,7] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,3,2,6,5,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,7,5,6,1,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,5,6,1,3,2,8,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,4,5,1,6,3,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,5,6,1,4,3,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,4,3,5,2,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[10,5,9,4,8,3,7,2,6,1] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[3,4,1,5,2,7,6,9,8] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[1,4,2,5,3,7,6,9,8,10] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[3,4,2,8,6,7,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,1,7,2,8,3,9,4] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[3,2,4,1,6,5,8,7,10,9] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[3,2,5,4,7,6,9,8,10,1] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[3,5,4,8,1,7,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,8,4,6,2,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,4,8,1,5,2,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,5,1,8,6,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,8,1,7,5,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,1,7,3,4,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,3,1,8,4,6,5,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,3,1,7,6,8,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,6,5,7,2,3,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,5,7,2,4,3,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,7,2,6,4,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,8,5,6,2,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,8,6,7,2,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,6,8,1,5,3,4,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,4,6,1,5,3,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,8,1,7,2,5,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,5,4,8,2,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,5,4,7,1,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,4,5,1,8,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,1,6,4,8,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,5,6,2,4,3,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,4,5,1,3,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,7,6,8,4,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,5,7,1,4,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,2,4,3,6,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,6,4,5,1,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,1,6,4,5,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,3,2,8,5,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,5,6,2,4,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,4,1,6,5,8,7,9] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[4,2,5,1,6,3,8,7,9] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[4,2,6,1,7,3,8,5,9] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[4,2,6,1,8,3,9,5,7] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[3,2,5,4,6,1,8,7,9] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[4,2,5,1,6,3,8,7,10,9] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[4,2,5,1,7,6,8,3,9] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[4,2,6,1,7,3,8,5,10,9] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[4,2,6,1,8,3,9,5,10,7] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[5,3,4,2,7,1,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,4,8,3,6,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,5,1,8,3,7,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,4,2,6,5,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,8,4,5,3,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,4,2,6,3,7,5,9,8] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[1,3,2,6,4,7,5,9,8] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[2,1,6,3,7,4,8,5,9] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[7,9,6,8,4,5,2,3,1] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[7,9,5,8,4,6,2,3,1] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[7,9,5,8,3,6,2,4,1] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[6,9,5,8,4,7,2,3,1] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[7,9,4,8,3,6,2,5,1] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[7,9,5,8,2,6,1,4,3] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[3,6,2,5,4,7,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,7,1,6,4,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,8,1,6,5,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,2,5,1,8,3,9,6] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[4,7,2,5,1,8,3,9,6,10] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[1,5,4,7,2,6,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,8,1,6,5,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,3,1,8,4,6,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,1,8,3,5,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,3,6,1,5,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,4,6,3,8,1,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,2,4,1,7,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,3,4,2,7,5,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,2,3,1,5,4,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,2,3,1,6,4,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,5,3,7,4,6,1,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,3,7,2,9,4,6,1] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[5,6,4,8,2,9,3,7,1] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[5,7,4,6,3,9,2,8,1] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[10,5,8,3,6,1,9,4,7,2] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[9,4,7,2,10,5,8,3,6,1] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[10,5,7,2,8,3,9,4,6,1] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[8,3,10,5,7,2,9,4,6,1] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[8,3,9,4,7,2,10,5,6,1] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[6,5,9,3,8,2,10,4,7,1] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[6,4,7,5,10,3,9,2,8,1] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[6,4,7,5,9,2,10,3,8,1] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[7,5,6,4,9,2,10,3,8,1] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[6,5,7,4,9,2,10,3,8,1] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[6,5,8,4,7,3,10,2,9,1] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[1,6,5,7,2,8,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,4,6,2,8,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,5,8,2,7,3,4,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,5,8,2,7,1,4,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,1,3,2,8,5,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,5,4,7,3,8,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,5,7,4,8,3,9,2] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[5,4,6,3,8,2,7,1,9] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[4,8,1,6,3,7,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,4,6,3,5,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,1,5,4,7,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,7,2,5,4,8,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,7,4,8,5,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,2,8,3,7,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,4,3,7,5,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,4,3,8,5,7,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,8,1,6,2,5,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,4,3,6,5,9,7,10,8] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[2,1,4,3,7,5,8,6,10,9] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[2,1,4,3,7,5,9,6,10,8] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[2,1,4,3,8,5,9,6,10,7] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[2,1,5,3,6,4,8,7,10,9] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[2,1,5,3,6,4,9,7,10,8] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[2,1,5,3,7,4,8,6,10,9] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[2,1,5,3,7,4,9,6,10,8] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[2,1,5,3,8,4,9,6,10,7] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[2,1,6,3,7,4,8,5,10,9] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[2,1,6,3,7,4,9,5,10,8] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[2,1,6,3,8,4,9,5,10,7] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[2,1,7,3,8,4,9,5,10,6] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[3,1,4,2,6,5,9,7,10,8] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[3,1,4,2,7,5,8,6,10,9] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[3,1,4,2,7,5,9,6,10,8] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[3,1,4,2,8,5,9,6,10,7] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[3,1,5,2,6,4,9,7,10,8] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[3,1,5,2,8,4,9,6,10,7] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[3,1,6,2,7,4,8,5,10,9] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[3,1,6,2,7,4,9,5,10,8] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[3,1,6,2,8,4,9,5,10,7] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[3,1,7,2,8,4,9,5,10,6] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[4,1,5,2,6,3,9,7,10,8] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[4,1,5,2,7,3,8,6,10,9] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[4,1,5,2,7,3,9,6,10,8] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[4,1,5,2,8,3,9,6,10,7] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[4,1,6,2,7,3,8,5,10,9] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[4,1,6,2,7,3,9,5,10,8] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[4,1,6,2,8,3,9,5,10,7] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[4,1,7,2,8,3,9,5,10,6] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[5,1,6,2,7,3,9,4,10,8] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[5,1,6,2,8,3,9,4,10,7] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[5,1,7,2,8,3,9,4,10,6] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[6,5,8,1,4,3,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,4,2,7,5,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,2,8,3,9,4,10,5,6] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[5,8,1,4,2,7,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,1,8,3,7,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,5,1,7,6,8,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,8,6,7,1,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,5,8,2,6,1,4,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,7,4,6,1,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[9,6,7,3,10,2,5,4,8,1] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[4,6,2,5,3,8,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,8,4,7,2,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,4,5,2,8,1,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,5,4,8,3,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,4,5,2,8,3,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,5,2,8,3,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,8,2,3,1,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,5,8,2,3,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,3,6,5,8,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,7,2,4,1,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,8,2,6,5,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,1,7,4,5,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,6,2,5,4,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,8,5,7,1,4,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,4,3,8,5,7,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,1,6,5,8,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,8,1,4,2,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,3,8,4,7,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,8,1,7,4,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,2,7,4,5,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,8,1,7,5,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,5,2,8,4,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,3,5,2,8,4,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,5,1,8,4,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,4,3,5,2,8,6,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,4,8,2,6,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,5,4,8,1,6,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,4,1,6,5,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,4,3,7,5,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,7,4,6,1,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,7,6,8,3,4,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,5,2,7,3,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,7,4,5,2,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,4,2,8,5,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,3,6,5,8,2,7,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,7,4,5,3,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,8,4,5,3,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,8,2,7,4,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,8,4,7,5,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,6,2,7,4,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,8,1,7,2,4,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,5,7,3,8,2,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,4,1,7,5,6,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[9,10,6,7,4,5,2,3,1,8] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[5,6,2,8,1,7,3,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,5,3,7,4,8,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,4,6,5,8,2,3,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,6,5,8,2,4,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,6,4,8,2,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,5,4,8,2,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,2,7,5,8,1,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,2,8,6,7,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,5,1,6,4,8,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,1,3,2,8,6,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,5,7,1,4,2,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,5,4,7,3,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,5,6,2,8,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,4,8,1,6,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,5,6,4,8,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,5,7,1,4,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,6,1,4,2,7,5,9] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[4,5,2,6,1,8,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,1,8,6,7,3,4,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,9,6,10,5,7,2,4,1,3] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[6,7,4,8,3,5,2,10,1,9] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[1,4,3,7,5,8,2,9,6,10] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[2,1,5,3,8,6,9,4,10,7] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[2,4,1,7,5,8,3,9,6,10] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[5,7,1,4,3,6,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,8,1,5,4,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,2,4,1,7,6,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,4,7,3,9,1,8,2] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[5,6,4,9,1,8,2,7,3] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[5,9,1,8,2,7,3,6,4] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[9,1,8,2,7,3,6,4,5] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[5,4,9,1,8,2,7,3,6] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[5,4,6,3,9,1,8,2,7] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[5,4,6,3,7,2,9,1,8] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[6,5,7,4,8,3,10,1,9,2] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[5,6,4,8,2,9,1,7,3] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[6,5,7,4,10,1,9,2,8,3] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[5,7,3,9,1,8,2,6,4] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[6,5,10,1,9,2,8,3,7,4] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[6,4,9,1,8,2,7,3,5] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[5,10,1,9,2,8,3,7,4,6] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[6,4,5,3,9,1,8,2,7] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[5,6,4,10,1,9,2,8,3,7] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[5,4,7,3,6,2,9,1,8] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[5,6,4,7,3,10,1,9,2,8] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[5,6,4,7,3,8,2,10,1,9] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[4,8,2,5,1,6,3,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,6,2,7,3,8,4,9,5] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[4,7,2,6,1,8,3,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,1,4,3,6,5,10,7,9,8] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[2,1,4,3,8,5,7,6,10,9] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[2,1,6,3,5,4,8,7,10,9] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[2,1,6,3,5,4,10,7,9,8] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[4,1,3,2,6,5,8,7,10,9] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[4,1,3,2,6,5,10,7,9,8] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[4,1,3,2,8,5,7,6,10,9] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[7,3,8,2,5,1,6,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,6,8,3,4,2,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,8,2,6,5,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,6,3,8,5,9,7,10,2] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[1,7,4,6,3,5,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,7,5,6,1,4,2,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,7,1,3,2,8,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,5,3,6,1,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,3,7,4,6,1,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,7,1,5,2,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,6,2,8,3,9,5,7] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[4,1,6,2,7,3,8,5,9] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[8,2,5,1,6,3,9,4,10,7] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[1,8,3,5,2,6,4,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,5,6,4,8,1,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,8,3,6,5,7,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,4,6,3,8,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,2,5,3,8,1,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,8,5,7,1,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,6,2,8,5,7,1,4] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,5,1,8,3,6,4,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,4,1,7,5,8,3,9,6] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[7,1,4,3,6,5,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,2,4,3,6,1,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,3,7,1,4,2,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,3,5,1,8,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,6,3,5,4,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,6,3,8,1,7,2,9] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[1,6,5,7,4,9,2,8,3] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[5,6,4,7,3,9,1,8,2,10] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[5,4,8,1,7,2,6,3,9] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[5,4,8,1,6,3,7,2,9] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[1,6,5,9,2,8,3,7,4] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[1,6,5,9,2,7,4,8,3] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[7,2,4,1,5,3,8,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,5,2,6,4,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,8,5,7,2,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,8,2,7,5,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,6,8,2,4,3,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,4,5,3,8,1,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,3,6,1,4,2,8,5] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,4,8,3,5,1,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,6,7,1,4,3,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,6,1,7,2,4,3,8] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[5,4,7,1,6,2,8,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,9,3,10,5,7,1,8,2,6] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[5,7,1,8,2,4,3,9,6,10] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[5,8,1,6,4,7,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,1,7,6,8,2,5,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,7,3,8,2,5,4,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,4,7,1,5,2,6,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,5,7,1,4,3,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,1,5,4,7,3,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,8,2,3,1,7,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,1,6,2,5,4,7,3] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,5,1,7,6,8,2,9,3] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[7,8,2,9,3,10,4,5,1,6] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[3,8,2,6,1,7,4,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,5,6,1,3,2,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,7,1,3,2,8,5,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,3,8,4,7,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,2,3,1,6,5,7,4] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,8,2,6,4,7,1,5] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,6,1,7,4,5,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,4,8,1,5,3,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[9,6,7,4,5,2,3,1,8] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[9,7,8,5,6,2,4,1,3] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[9,7,8,4,6,2,5,1,3] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[9,6,8,4,7,2,5,1,3] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[9,7,8,3,6,2,5,1,4] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[9,5,8,4,7,2,6,1,3] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[7,6,9,4,8,2,5,1,3] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[7,5,8,2,4,3,6,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[8,3,5,4,7,1,6,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[3,1,8,4,5,2,7,6] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,6,1,7,3,8,4,9,5] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[3,2,6,1,7,4,8,5,9] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[3,4,2,7,1,8,5,9,6] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[5,3,6,4,7,1,8,2,9] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[4,3,5,2,7,1,8,6,9] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[4,6,2,7,5,8,1,9,3] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[4,5,3,6,2,8,1,9,7] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[2,6,1,7,3,8,4,9,5,10] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[3,2,7,1,8,4,9,5,10,6] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[3,4,2,7,1,8,5,9,6,10] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[5,3,6,4,8,1,9,2,10,7] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[4,3,5,2,8,1,9,6,10,7] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[4,6,2,7,5,8,1,9,3,10] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[4,5,3,6,2,8,1,9,7,10] => 010101010 => 000000000 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[5,3,7,2,8,6,9,1,10,4] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[5,4,6,3,7,2,9,1,10,8] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[8,4,6,3,5,1,7,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[7,1,5,4,6,3,8,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[2,7,3,4,1,8,5,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,2,6,3,8,5,7,1,9] => 10101010 => 11111111 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[4,2,6,3,8,5,10,7,9,1] => 101010101 => 111111111 => ([(0,9),(2,4),(3,2),(4,6),(5,3),(6,8),(7,5),(8,1),(9,7)],10) => 1

[6,5,8,3,7,1,4,2] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,4,3,6,5,8,7,9,2] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[1,4,2,6,5,8,7,9,3] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[1,5,2,6,4,8,7,9,3] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[1,5,2,7,4,8,6,9,3] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[1,5,2,7,4,9,6,8,3] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[1,5,2,6,3,8,7,9,4] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[1,6,2,7,4,8,5,9,3] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[1,5,2,8,4,9,6,7,3] => 01010101 => 00000000 => ([(0,8),(2,3),(3,5),(4,2),(5,7),(6,4),(7,1),(8,6)],9) => 1

[2,5,4,7,1,8,3,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,5,4,7,3,8,2,6] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[6,2,8,3,7,4,5,1] => 1010101 => 1111111 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[1,4,3,8,5,6,2,7] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

[4,6,5,7,1,8,2,3] => 0101010 => 0000000 => ([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) => 1

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Description

The number of minimal elements in a poset.

Map

descent word

Description

The descent positions of a permutation as a binary word.
For a permutation $\pi$ of $n$ letters and each $1\leq i\leq n-1$ such that $\pi(i) > \pi(i+1)$ we set $w_i=1$, otherwise $w_i=0$.
Thus, the length of the word is one less the size of the permutation. In particular, the descent word is undefined for the empty permutation.

Map

alternating inverse

Description

Sends a binary word $w_1\cdots w_m$ to the binary word $v_1 \cdots v_m$ with $v_i = w_i$ if $i$ is odd and $v_i = 1 - w_i$ if $i$ is even.
This map is used in [1], see Definitions 3.2 and 5.1.

Map

poset of factors

Description

The poset of factors of a binary word.
This is the partial order on the set of distinct factors of a binary word, such that $u < v$ if and only if $u$ is a factor of $v$.