- FindStat

Identifier

Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00065: Permutations —permutation poset⟶ Posets
Mp00206: Posets —antichains of maximal size⟶ Lattices
St001630: Lattices ⟶ ℤ

Values

[+,+,+] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 1

[-,+,+] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 1

[+,-,+] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 1

[+,+,-] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 1

[-,-,+] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 1

[-,+,-] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 1

[+,-,-] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 1

[-,-,-] => [1,2,3] => ([(0,2),(2,1)],3) => ([(0,2),(2,1)],3) => 1

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

[-,+,+,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 2

[+,-,+,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 2

[+,+,-,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 2

[+,+,+,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 2

[-,-,+,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 2

[-,+,-,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 2

[-,+,+,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 2

[+,-,-,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 2

[+,-,+,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 2

[+,+,-,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 2

[-,-,-,+] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 2

[-,-,+,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 2

[-,+,-,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 2

[+,-,-,-] => [1,2,3,4] => ([(0,3),(2,1),(3,2)],4) => ([(0,3),(2,1),(3,2)],4) => 2

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

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

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

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

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

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

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

[-,+,+,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[+,-,+,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[+,+,-,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[+,+,+,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[+,+,+,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[-,-,+,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[-,+,-,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[-,+,+,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[-,+,+,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[+,-,-,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[+,-,+,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[+,-,+,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[+,+,-,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[+,+,-,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[+,+,+,-,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[-,-,-,+,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[-,-,+,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[-,-,+,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[-,+,-,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[-,+,-,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[-,+,+,-,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[+,-,-,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[+,-,-,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[+,-,+,-,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[+,+,-,-,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[-,-,-,-,+] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[-,-,-,+,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[-,-,+,-,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[-,+,-,-,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

[+,-,-,-,-] => [1,2,3,4,5] => ([(0,4),(2,3),(3,1),(4,2)],5) => ([(0,4),(2,3),(3,1),(4,2)],5) => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 755 entries. <<<

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

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

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

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

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

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

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

[5,-,+,+,1] => [5,2,3,4,1] => ([(2,3),(3,4)],5) => ([(0,2),(2,1)],3) => 1

[5,+,-,+,1] => [5,2,3,4,1] => ([(2,3),(3,4)],5) => ([(0,2),(2,1)],3) => 1

[5,+,+,-,1] => [5,2,3,4,1] => ([(2,3),(3,4)],5) => ([(0,2),(2,1)],3) => 1

[5,-,-,+,1] => [5,2,3,4,1] => ([(2,3),(3,4)],5) => ([(0,2),(2,1)],3) => 1

[5,-,+,-,1] => [5,2,3,4,1] => ([(2,3),(3,4)],5) => ([(0,2),(2,1)],3) => 1

[5,+,-,-,1] => [5,2,3,4,1] => ([(2,3),(3,4)],5) => ([(0,2),(2,1)],3) => 1

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

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

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

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

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

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

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

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

[-,+,+,+,+,+] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[+,-,+,+,+,+] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[+,+,-,+,+,+] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[+,+,+,-,+,+] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[+,+,+,+,-,+] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[+,+,+,+,+,-] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[-,-,+,+,+,+] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[-,+,-,+,+,+] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[-,+,+,-,+,+] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[-,+,+,+,-,+] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[-,+,+,+,+,-] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[+,-,-,+,+,+] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[+,-,+,-,+,+] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[+,-,+,+,-,+] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[+,-,+,+,+,-] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[+,+,-,-,+,+] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[+,+,-,+,-,+] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[+,+,-,+,+,-] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[+,+,+,-,-,+] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[+,+,+,-,+,-] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[+,+,+,+,-,-] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[-,-,-,+,+,+] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[-,-,+,-,+,+] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[-,-,+,+,-,+] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[-,-,+,+,+,-] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[-,+,-,-,+,+] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[-,+,-,+,-,+] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[-,+,-,+,+,-] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[-,+,+,-,-,+] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[-,+,+,-,+,-] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[-,+,+,+,-,-] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[+,-,-,-,+,+] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[+,-,-,+,-,+] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[+,-,-,+,+,-] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[+,-,+,-,-,+] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[+,-,+,-,+,-] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[+,-,+,+,-,-] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[+,+,-,-,-,+] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[+,+,-,-,+,-] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[+,+,-,+,-,-] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[+,+,+,-,-,-] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[-,-,-,-,+,+] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[-,-,-,+,-,+] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[-,-,-,+,+,-] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[-,-,+,-,-,+] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[-,-,+,-,+,-] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[-,-,+,+,-,-] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[-,+,-,-,-,+] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[-,+,-,-,+,-] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[-,+,-,+,-,-] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[-,+,+,-,-,-] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[+,-,-,-,-,+] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[+,-,-,-,+,-] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[+,-,-,+,-,-] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[+,-,+,-,-,-] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[+,+,-,-,-,-] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[-,-,-,-,-,+] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[-,-,-,-,+,-] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[-,-,-,+,-,-] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[-,-,+,-,-,-] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[-,+,-,-,-,-] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

[+,-,-,-,-,-] => [1,2,3,4,5,6] => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6) => 1

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

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

[-,+,4,5,6,3] => [1,2,4,5,6,3] => ([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[+,-,4,5,6,3] => [1,2,4,5,6,3] => ([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => ([(0,2),(2,1)],3) => 1

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

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

[-,+,4,6,3,5] => [1,2,4,6,3,5] => ([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6) => ([(0,2),(2,1)],3) => 1

[+,-,4,6,3,5] => [1,2,4,6,3,5] => ([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6) => ([(0,2),(2,1)],3) => 1

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

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

[-,+,5,3,6,4] => [1,2,5,3,6,4] => ([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6) => ([(0,2),(2,1)],3) => 1

[+,-,5,3,6,4] => [1,2,5,3,6,4] => ([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6) => ([(0,2),(2,1)],3) => 1

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

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

[-,+,5,6,3,4] => [1,2,5,6,3,4] => ([(0,5),(3,2),(4,1),(5,3),(5,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[+,-,5,6,3,4] => [1,2,5,6,3,4] => ([(0,5),(3,2),(4,1),(5,3),(5,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

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

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

[-,+,6,3,4,5] => [1,2,6,3,4,5] => ([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[+,-,6,3,4,5] => [1,2,6,3,4,5] => ([(0,5),(3,4),(4,2),(5,1),(5,3)],6) => ([(0,2),(2,1)],3) => 1

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

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

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

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

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

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

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

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

[-,3,4,5,2,+] => [1,3,4,5,2,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => ([(0,2),(2,1)],3) => 1

[+,3,4,5,2,-] => [1,3,4,5,2,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => ([(0,2),(2,1)],3) => 1

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

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

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

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

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

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

[-,3,5,2,4,+] => [1,3,5,2,4,6] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[+,3,5,2,4,-] => [1,3,5,2,4,6] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1

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

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

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

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

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

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

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

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

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

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

[-,4,2,5,3,+] => [1,4,2,5,3,6] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[+,4,2,5,3,-] => [1,4,2,5,3,6] => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1

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

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

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

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

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

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

[-,4,5,2,3,+] => [1,4,5,2,3,6] => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[+,4,5,2,3,-] => [1,4,5,2,3,6] => ([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

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

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

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

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

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

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

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

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

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

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

[-,4,6,3,+,2] => [1,4,6,3,5,2] => ([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[+,4,6,3,-,2] => [1,4,6,3,5,2] => ([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6) => ([(0,2),(2,1)],3) => 1

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

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

[-,5,2,3,4,+] => [1,5,2,3,4,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => ([(0,2),(2,1)],3) => 1

[+,5,2,3,4,-] => [1,5,2,3,4,6] => ([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) => ([(0,2),(2,1)],3) => 1

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

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

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

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

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

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

[-,5,+,6,4,2] => [1,5,3,6,4,2] => ([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[+,5,-,6,4,2] => [1,5,3,6,4,2] => ([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6) => ([(0,2),(2,1)],3) => 1

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

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

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

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

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

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

[-,5,6,+,2,3] => [1,5,6,4,2,3] => ([(0,3),(0,4),(0,5),(4,2),(5,1)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[+,5,6,-,2,3] => [1,5,6,4,2,3] => ([(0,3),(0,4),(0,5),(4,2),(5,1)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

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

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

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

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

[-,6,+,+,+,2] => [1,6,3,4,5,2] => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => ([(0,2),(2,1)],3) => 1

[+,6,-,+,+,2] => [1,6,3,4,5,2] => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => ([(0,2),(2,1)],3) => 1

[+,6,+,-,+,2] => [1,6,3,4,5,2] => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => ([(0,2),(2,1)],3) => 1

[+,6,+,+,-,2] => [1,6,3,4,5,2] => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => ([(0,2),(2,1)],3) => 1

[-,6,-,+,+,2] => [1,6,3,4,5,2] => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => ([(0,2),(2,1)],3) => 1

[-,6,+,-,+,2] => [1,6,3,4,5,2] => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => ([(0,2),(2,1)],3) => 1

[-,6,+,+,-,2] => [1,6,3,4,5,2] => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => ([(0,2),(2,1)],3) => 1

[+,6,-,-,+,2] => [1,6,3,4,5,2] => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => ([(0,2),(2,1)],3) => 1

[+,6,-,+,-,2] => [1,6,3,4,5,2] => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => ([(0,2),(2,1)],3) => 1

[+,6,+,-,-,2] => [1,6,3,4,5,2] => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => ([(0,2),(2,1)],3) => 1

[-,6,-,-,+,2] => [1,6,3,4,5,2] => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => ([(0,2),(2,1)],3) => 1

[-,6,-,+,-,2] => [1,6,3,4,5,2] => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => ([(0,2),(2,1)],3) => 1

[-,6,+,-,-,2] => [1,6,3,4,5,2] => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => ([(0,2),(2,1)],3) => 1

[+,6,-,-,-,2] => [1,6,3,4,5,2] => ([(0,2),(0,3),(0,5),(4,1),(5,4)],6) => ([(0,2),(2,1)],3) => 1

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

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

[-,6,+,5,2,4] => [1,6,3,5,2,4] => ([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[+,6,-,5,2,4] => [1,6,3,5,2,4] => ([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6) => ([(0,2),(2,1)],3) => 1

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

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

[-,6,4,2,+,3] => [1,6,4,2,5,3] => ([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[+,6,4,2,-,3] => [1,6,4,2,5,3] => ([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6) => ([(0,2),(2,1)],3) => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[2,3,4,1,-,+] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[2,3,4,1,+,-] => [2,3,4,1,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,2),(2,1)],3) => 1

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

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

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

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

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

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

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

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

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

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

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

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

[2,4,1,3,-,+] => [2,4,1,3,5,6] => ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[2,4,1,3,+,-] => [2,4,1,3,5,6] => ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => ([(0,2),(2,1)],3) => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[2,6,-,+,+,1] => [2,6,3,4,5,1] => ([(1,3),(1,5),(4,2),(5,4)],6) => ([(0,2),(2,1)],3) => 1

[2,6,+,-,+,1] => [2,6,3,4,5,1] => ([(1,3),(1,5),(4,2),(5,4)],6) => ([(0,2),(2,1)],3) => 1

[2,6,+,+,-,1] => [2,6,3,4,5,1] => ([(1,3),(1,5),(4,2),(5,4)],6) => ([(0,2),(2,1)],3) => 1

[2,6,-,-,+,1] => [2,6,3,4,5,1] => ([(1,3),(1,5),(4,2),(5,4)],6) => ([(0,2),(2,1)],3) => 1

[2,6,-,+,-,1] => [2,6,3,4,5,1] => ([(1,3),(1,5),(4,2),(5,4)],6) => ([(0,2),(2,1)],3) => 1

[2,6,+,-,-,1] => [2,6,3,4,5,1] => ([(1,3),(1,5),(4,2),(5,4)],6) => ([(0,2),(2,1)],3) => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[3,1,4,2,-,+] => [3,1,4,2,5,6] => ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[3,1,4,2,+,-] => [3,1,4,2,5,6] => ([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) => ([(0,2),(2,1)],3) => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[3,-,6,+,+,1] => [3,2,6,4,5,1] => ([(1,4),(1,5),(2,4),(2,5),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[3,+,6,-,+,1] => [3,2,6,4,5,1] => ([(1,4),(1,5),(2,4),(2,5),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[3,+,6,+,-,1] => [3,2,6,4,5,1] => ([(1,4),(1,5),(2,4),(2,5),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[3,-,6,-,+,1] => [3,2,6,4,5,1] => ([(1,4),(1,5),(2,4),(2,5),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[3,-,6,+,-,1] => [3,2,6,4,5,1] => ([(1,4),(1,5),(2,4),(2,5),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[3,+,6,-,-,1] => [3,2,6,4,5,1] => ([(1,4),(1,5),(2,4),(2,5),(5,3)],6) => ([(0,2),(2,1)],3) => 1

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

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

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

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

[3,4,1,2,-,+] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[3,4,1,2,+,-] => [3,4,1,2,5,6] => ([(0,4),(1,3),(3,5),(4,5),(5,2)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[3,5,2,-,1,+] => [3,5,2,4,1,6] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[3,5,2,+,1,-] => [3,5,2,4,1,6] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(2,1)],3) => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[3,6,2,-,+,1] => [3,6,2,4,5,1] => ([(1,5),(2,3),(2,5),(5,4)],6) => ([(0,3),(2,1),(3,2)],4) => 2

[3,6,2,+,-,1] => [3,6,2,4,5,1] => ([(1,5),(2,3),(2,5),(5,4)],6) => ([(0,3),(2,1),(3,2)],4) => 2

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

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

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

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

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

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

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

[4,1,2,3,-,+] => [4,1,2,3,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[4,1,2,3,+,-] => [4,1,2,3,5,6] => ([(0,5),(1,4),(2,5),(4,2),(5,3)],6) => ([(0,2),(2,1)],3) => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[4,-,+,6,+,1] => [4,2,3,6,5,1] => ([(1,4),(1,5),(2,3),(3,4),(3,5)],6) => ([(0,2),(2,1)],3) => 1

[4,+,-,6,+,1] => [4,2,3,6,5,1] => ([(1,4),(1,5),(2,3),(3,4),(3,5)],6) => ([(0,2),(2,1)],3) => 1

[4,+,+,6,-,1] => [4,2,3,6,5,1] => ([(1,4),(1,5),(2,3),(3,4),(3,5)],6) => ([(0,2),(2,1)],3) => 1

[4,-,-,6,+,1] => [4,2,3,6,5,1] => ([(1,4),(1,5),(2,3),(3,4),(3,5)],6) => ([(0,2),(2,1)],3) => 1

[4,-,+,6,-,1] => [4,2,3,6,5,1] => ([(1,4),(1,5),(2,3),(3,4),(3,5)],6) => ([(0,2),(2,1)],3) => 1

[4,+,-,6,-,1] => [4,2,3,6,5,1] => ([(1,4),(1,5),(2,3),(3,4),(3,5)],6) => ([(0,2),(2,1)],3) => 1

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

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

[4,-,5,3,1,+] => [4,2,5,3,1,6] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[4,+,5,3,1,-] => [4,2,5,3,1,6] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(2,1)],3) => 1

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

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

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

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

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

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

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

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

[4,-,6,3,+,1] => [4,2,6,3,5,1] => ([(1,4),(1,5),(2,3),(2,4),(3,5)],6) => ([(0,3),(2,1),(3,2)],4) => 2

[4,+,6,3,-,1] => [4,2,6,3,5,1] => ([(1,4),(1,5),(2,3),(2,4),(3,5)],6) => ([(0,3),(2,1),(3,2)],4) => 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[4,5,-,1,2,+] => [4,5,3,1,2,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[4,5,+,1,2,-] => [4,5,3,1,2,6] => ([(0,5),(1,4),(2,3),(3,5),(4,5)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[4,6,-,1,+,2] => [4,6,3,1,5,2] => ([(0,5),(1,4),(1,5),(2,3),(2,5)],6) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2

[4,6,+,1,-,2] => [4,6,3,1,5,2] => ([(0,5),(1,4),(1,5),(2,3),(2,5)],6) => ([(0,2),(0,3),(2,4),(3,4),(4,1)],5) => 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[5,-,+,+,1,+] => [5,2,3,4,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[5,+,-,+,1,+] => [5,2,3,4,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[5,+,+,-,1,+] => [5,2,3,4,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[5,+,+,+,1,-] => [5,2,3,4,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[5,-,-,+,1,+] => [5,2,3,4,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[5,-,+,-,1,+] => [5,2,3,4,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[5,-,+,+,1,-] => [5,2,3,4,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[5,+,-,-,1,+] => [5,2,3,4,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[5,+,-,+,1,-] => [5,2,3,4,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[5,+,+,-,1,-] => [5,2,3,4,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[5,-,-,-,1,+] => [5,2,3,4,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[5,-,-,+,1,-] => [5,2,3,4,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[5,-,+,-,1,-] => [5,2,3,4,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[5,+,-,-,1,-] => [5,2,3,4,1,6] => ([(0,5),(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1

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

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

[5,-,+,+,6,1] => [5,2,3,4,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[5,+,-,+,6,1] => [5,2,3,4,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[5,+,+,-,6,1] => [5,2,3,4,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[5,-,-,+,6,1] => [5,2,3,4,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[5,-,+,-,6,1] => [5,2,3,4,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[5,+,-,-,6,1] => [5,2,3,4,6,1] => ([(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1

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

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

[5,-,+,6,4,1] => [5,2,3,6,4,1] => ([(1,5),(2,3),(3,4),(3,5)],6) => ([(0,3),(2,1),(3,2)],4) => 2

[5,+,-,6,4,1] => [5,2,3,6,4,1] => ([(1,5),(2,3),(3,4),(3,5)],6) => ([(0,3),(2,1),(3,2)],4) => 2

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

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

[5,-,4,1,3,+] => [5,2,4,1,3,6] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[5,+,4,1,3,-] => [5,2,4,1,3,6] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(2,1)],3) => 1

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

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

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

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

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

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

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

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

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

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

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

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

[5,-,6,+,1,3] => [5,2,6,4,1,3] => ([(0,5),(1,4),(2,3),(2,4),(2,5)],6) => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 2

[5,+,6,-,1,3] => [5,2,6,4,1,3] => ([(0,5),(1,4),(2,3),(2,4),(2,5)],6) => ([(0,3),(1,4),(2,4),(3,1),(3,2)],5) => 2

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

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

[5,3,1,-,2,+] => [5,3,1,4,2,6] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[5,3,1,+,2,-] => [5,3,1,4,2,6] => ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) => ([(0,2),(2,1)],3) => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[5,6,-,+,2,1] => [5,6,3,4,2,1] => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[5,6,+,-,2,1] => [5,6,3,4,2,1] => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

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

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

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

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

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

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

[6,1,-,+,+,2] => [6,1,3,4,5,2] => ([(1,3),(1,5),(4,2),(5,4)],6) => ([(0,2),(2,1)],3) => 1

[6,1,+,-,+,2] => [6,1,3,4,5,2] => ([(1,3),(1,5),(4,2),(5,4)],6) => ([(0,2),(2,1)],3) => 1

[6,1,+,+,-,2] => [6,1,3,4,5,2] => ([(1,3),(1,5),(4,2),(5,4)],6) => ([(0,2),(2,1)],3) => 1

[6,1,-,-,+,2] => [6,1,3,4,5,2] => ([(1,3),(1,5),(4,2),(5,4)],6) => ([(0,2),(2,1)],3) => 1

[6,1,-,+,-,2] => [6,1,3,4,5,2] => ([(1,3),(1,5),(4,2),(5,4)],6) => ([(0,2),(2,1)],3) => 1

[6,1,+,-,-,2] => [6,1,3,4,5,2] => ([(1,3),(1,5),(4,2),(5,4)],6) => ([(0,2),(2,1)],3) => 1

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

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

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

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

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

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

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

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

[6,-,1,+,+,3] => [6,2,1,4,5,3] => ([(1,4),(1,5),(2,4),(2,5),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[6,+,1,-,+,3] => [6,2,1,4,5,3] => ([(1,4),(1,5),(2,4),(2,5),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[6,+,1,+,-,3] => [6,2,1,4,5,3] => ([(1,4),(1,5),(2,4),(2,5),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[6,-,1,-,+,3] => [6,2,1,4,5,3] => ([(1,4),(1,5),(2,4),(2,5),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[6,-,1,+,-,3] => [6,2,1,4,5,3] => ([(1,4),(1,5),(2,4),(2,5),(5,3)],6) => ([(0,2),(2,1)],3) => 1

[6,+,1,-,-,3] => [6,2,1,4,5,3] => ([(1,4),(1,5),(2,4),(2,5),(5,3)],6) => ([(0,2),(2,1)],3) => 1

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

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

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

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

[6,-,+,1,+,4] => [6,2,3,1,5,4] => ([(1,4),(1,5),(2,3),(3,4),(3,5)],6) => ([(0,2),(2,1)],3) => 1

[6,+,-,1,+,4] => [6,2,3,1,5,4] => ([(1,4),(1,5),(2,3),(3,4),(3,5)],6) => ([(0,2),(2,1)],3) => 1

[6,+,+,1,-,4] => [6,2,3,1,5,4] => ([(1,4),(1,5),(2,3),(3,4),(3,5)],6) => ([(0,2),(2,1)],3) => 1

[6,-,-,1,+,4] => [6,2,3,1,5,4] => ([(1,4),(1,5),(2,3),(3,4),(3,5)],6) => ([(0,2),(2,1)],3) => 1

[6,-,+,1,-,4] => [6,2,3,1,5,4] => ([(1,4),(1,5),(2,3),(3,4),(3,5)],6) => ([(0,2),(2,1)],3) => 1

[6,+,-,1,-,4] => [6,2,3,1,5,4] => ([(1,4),(1,5),(2,3),(3,4),(3,5)],6) => ([(0,2),(2,1)],3) => 1

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

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

[6,-,+,+,1,5] => [6,2,3,4,1,5] => ([(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[6,+,-,+,1,5] => [6,2,3,4,1,5] => ([(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[6,+,+,-,1,5] => [6,2,3,4,1,5] => ([(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[6,-,-,+,1,5] => [6,2,3,4,1,5] => ([(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[6,-,+,-,1,5] => [6,2,3,4,1,5] => ([(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1

[6,+,-,-,1,5] => [6,2,3,4,1,5] => ([(1,5),(2,3),(3,4),(4,5)],6) => ([(0,2),(2,1)],3) => 1

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

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

[6,-,+,+,+,1] => [6,2,3,4,5,1] => ([(2,3),(3,5),(5,4)],6) => ([(0,3),(2,1),(3,2)],4) => 2

[6,+,-,+,+,1] => [6,2,3,4,5,1] => ([(2,3),(3,5),(5,4)],6) => ([(0,3),(2,1),(3,2)],4) => 2

[6,+,+,-,+,1] => [6,2,3,4,5,1] => ([(2,3),(3,5),(5,4)],6) => ([(0,3),(2,1),(3,2)],4) => 2

[6,+,+,+,-,1] => [6,2,3,4,5,1] => ([(2,3),(3,5),(5,4)],6) => ([(0,3),(2,1),(3,2)],4) => 2

[6,-,-,+,+,1] => [6,2,3,4,5,1] => ([(2,3),(3,5),(5,4)],6) => ([(0,3),(2,1),(3,2)],4) => 2

[6,-,+,-,+,1] => [6,2,3,4,5,1] => ([(2,3),(3,5),(5,4)],6) => ([(0,3),(2,1),(3,2)],4) => 2

[6,-,+,+,-,1] => [6,2,3,4,5,1] => ([(2,3),(3,5),(5,4)],6) => ([(0,3),(2,1),(3,2)],4) => 2

[6,+,-,-,+,1] => [6,2,3,4,5,1] => ([(2,3),(3,5),(5,4)],6) => ([(0,3),(2,1),(3,2)],4) => 2

[6,+,-,+,-,1] => [6,2,3,4,5,1] => ([(2,3),(3,5),(5,4)],6) => ([(0,3),(2,1),(3,2)],4) => 2

[6,+,+,-,-,1] => [6,2,3,4,5,1] => ([(2,3),(3,5),(5,4)],6) => ([(0,3),(2,1),(3,2)],4) => 2

[6,-,-,-,+,1] => [6,2,3,4,5,1] => ([(2,3),(3,5),(5,4)],6) => ([(0,3),(2,1),(3,2)],4) => 2

[6,-,-,+,-,1] => [6,2,3,4,5,1] => ([(2,3),(3,5),(5,4)],6) => ([(0,3),(2,1),(3,2)],4) => 2

[6,-,+,-,-,1] => [6,2,3,4,5,1] => ([(2,3),(3,5),(5,4)],6) => ([(0,3),(2,1),(3,2)],4) => 2

[6,+,-,-,-,1] => [6,2,3,4,5,1] => ([(2,3),(3,5),(5,4)],6) => ([(0,3),(2,1),(3,2)],4) => 2

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

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

[6,-,+,5,1,4] => [6,2,3,5,1,4] => ([(1,5),(2,3),(3,4),(3,5)],6) => ([(0,3),(2,1),(3,2)],4) => 2

[6,+,-,5,1,4] => [6,2,3,5,1,4] => ([(1,5),(2,3),(3,4),(3,5)],6) => ([(0,3),(2,1),(3,2)],4) => 2

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

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

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

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

[6,-,4,1,+,3] => [6,2,4,1,5,3] => ([(1,4),(1,5),(2,3),(2,4),(3,5)],6) => ([(0,3),(2,1),(3,2)],4) => 2

[6,+,4,1,-,3] => [6,2,4,1,5,3] => ([(1,4),(1,5),(2,3),(2,4),(3,5)],6) => ([(0,3),(2,1),(3,2)],4) => 2

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

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

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

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

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

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

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

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

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

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

[6,3,1,-,+,2] => [6,3,1,4,5,2] => ([(1,5),(2,3),(2,5),(5,4)],6) => ([(0,3),(2,1),(3,2)],4) => 2

[6,3,1,+,-,2] => [6,3,1,4,5,2] => ([(1,5),(2,3),(2,5),(5,4)],6) => ([(0,3),(2,1),(3,2)],4) => 2

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[6,5,-,+,1,2] => [6,5,3,4,1,2] => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

[6,5,+,-,1,2] => [6,5,3,4,1,2] => ([(2,5),(3,4)],6) => ([(0,1),(0,2),(1,3),(2,3)],4) => 2

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

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

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searching the database for the individual values of this statistic

Description

The global dimension of the incidence algebra of the lattice over the rational numbers.

Map

antichains of maximal size

Description

The lattice of antichains of maximal size in a poset.
The set of antichains of maximal size can be ordered by setting

$A \leq B \leftrightarrow \mathop{\downarrow} A \subseteq \mathop{\downarrow} B$ , where

$\mathop{\downarrow} A$ is the order ideal generated by

$A$ .
This is a sublattice of the lattice of all antichains with respect to the same order relation. In particular, it is distributive.

Map

permutation

Description

The underlying permutation of the decorated permutation.

Map

permutation poset

Description

Sends a permutation to its permutation poset.
For a permutation

$\pi$ of length

$n$ , this poset has vertices

$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$
and the cover relation is given by

$(w, x) \leq (y, z)$ if

$w \leq y$ and

$x \leq z$ .
For example, the permutation

$[3,1,5,4,2]$ is mapped to the poset with cover relations

$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$