- FindStat

Identifier

Mp00256: Decorated permutations —upper permutation⟶ Permutations
Mp00127: Permutations —left-to-right-maxima to Dyck path⟶ Dyck paths
Mp00032: Dyck paths —inverse zeta map⟶ Dyck paths
St001232: Dyck paths ⟶ ℤ

Values

[+] => [1] => [1,0] => [1,0] => 0

[-] => [1] => [1,0] => [1,0] => 0

[+,+] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0

[-,+] => [2,1] => [1,1,0,0] => [1,0,1,0] => 1

[+,-] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0

[-,-] => [1,2] => [1,0,1,0] => [1,1,0,0] => 0

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

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

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

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

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

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

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

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

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

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

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

[3,1,2] => [2,3,1] => [1,1,0,1,0,0] => [1,1,0,0,1,0] => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 743 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[+,+,+,-,+,-] => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 8

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

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

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

[+,-,+,-,+,-] => [1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8

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

[+,+,-,+,-,-] => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 9

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

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

[+,-,+,-,-,-] => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 8

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

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

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

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

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

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

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

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

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

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

[+,+,+,5,4,-] => [1,2,3,5,4,6] => [1,0,1,0,1,0,1,1,0,0,1,0] => [1,1,0,1,1,1,1,0,0,0,0,0] => 8

[+,-,+,5,4,-] => [1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8

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

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

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

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

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

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

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

[+,+,4,3,-,-] => [1,2,4,3,5,6] => [1,0,1,0,1,1,0,0,1,0,1,0] => [1,1,1,0,1,1,1,0,0,0,0,0] => 9

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[+,3,2,-,+,-] => [1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8

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

[+,3,2,-,-,-] => [1,3,2,4,5,6] => [1,0,1,1,0,0,1,0,1,0,1,0] => [1,1,1,1,0,1,1,0,0,0,0,0] => 8

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

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

[+,3,2,5,4,-] => [1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[+,4,2,5,3,-] => [1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8

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

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

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

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

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

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

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

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

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

[+,4,+,5,2,-] => [1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[+,5,2,-,3,-] => [1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8

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

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

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

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

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

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

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

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

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

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

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

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

[+,5,+,-,2,-] => [1,3,5,2,4,6] => [1,0,1,1,0,1,1,0,0,0,1,0] => [1,1,0,1,1,1,0,0,0,1,0,0] => 8

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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$F_{1} = 2$

$F_{2} = 3 + 2\ q$

Description

The number of indecomposable modules with projective dimension 2 for Nakayama algebras with global dimension at most 2.

Map

upper permutation

Description

The upper bound in the Grassmann interval corresponding to the decorated permutation.
Let

$I$ be the anti-exceedance set of a decorated permutation

$w$ . Let

$v$ be the

$k$ -Grassmannian permutation determined by

$v[k] = w^{-1}(I)$ and let

$u$ be the permutation satisfying

$u = wv$ . Then

$[u, v]$ is the Grassmann interval corresponding to

$w$ .
This map returns

$v$ .

Map

left-to-right-maxima to Dyck path

Description

The left-to-right maxima of a permutation as a Dyck path.
Let

$(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are

$c_1, c_1+c_2, \dots, c_1+\dots+c_k$ .
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.

Map

inverse zeta map

Description

The inverse zeta map on Dyck paths.
See its inverse, the zeta map Mp00030zeta map, for the definition and details.