Identifier
-
Mp00253:
Decorated permutations
—permutation⟶
Permutations
Mp00060: Permutations —Robinson-Schensted tableau shape⟶ Integer partitions
Mp00202: Integer partitions —first row removal⟶ Integer partitions
St001604: Integer partitions ⟶ ℤ
Values
[4,3,2,1] => [4,3,2,1] => [1,1,1,1] => [1,1,1] => 0
[+,5,4,3,2] => [1,5,4,3,2] => [2,1,1,1] => [1,1,1] => 0
[-,5,4,3,2] => [1,5,4,3,2] => [2,1,1,1] => [1,1,1] => 0
[2,1,5,+,3] => [2,1,5,4,3] => [2,2,1] => [2,1] => 0
[2,1,5,-,3] => [2,1,5,4,3] => [2,2,1] => [2,1] => 0
[2,5,1,+,3] => [2,5,1,4,3] => [2,2,1] => [2,1] => 0
[2,5,1,-,3] => [2,5,1,4,3] => [2,2,1] => [2,1] => 0
[2,5,4,1,3] => [2,5,4,1,3] => [2,2,1] => [2,1] => 0
[2,5,4,3,1] => [2,5,4,3,1] => [2,1,1,1] => [1,1,1] => 0
[3,1,5,+,2] => [3,1,5,4,2] => [2,2,1] => [2,1] => 0
[3,1,5,-,2] => [3,1,5,4,2] => [2,2,1] => [2,1] => 0
[3,+,1,5,4] => [3,2,1,5,4] => [2,2,1] => [2,1] => 0
[3,-,1,5,4] => [3,2,1,5,4] => [2,2,1] => [2,1] => 0
[3,+,5,1,4] => [3,2,5,1,4] => [2,2,1] => [2,1] => 0
[3,-,5,1,4] => [3,2,5,1,4] => [2,2,1] => [2,1] => 0
[3,+,5,+,1] => [3,2,5,4,1] => [2,2,1] => [2,1] => 0
[3,-,5,+,1] => [3,2,5,4,1] => [2,2,1] => [2,1] => 0
[3,+,5,-,1] => [3,2,5,4,1] => [2,2,1] => [2,1] => 0
[3,-,5,-,1] => [3,2,5,4,1] => [2,2,1] => [2,1] => 0
[3,5,1,+,2] => [3,5,1,4,2] => [2,2,1] => [2,1] => 0
[3,5,1,-,2] => [3,5,1,4,2] => [2,2,1] => [2,1] => 0
[3,5,2,1,4] => [3,5,2,1,4] => [2,2,1] => [2,1] => 0
[3,5,2,+,1] => [3,5,2,4,1] => [2,2,1] => [2,1] => 0
[3,5,2,-,1] => [3,5,2,4,1] => [2,2,1] => [2,1] => 0
[3,5,4,1,2] => [3,5,4,1,2] => [2,2,1] => [2,1] => 0
[3,5,4,2,1] => [3,5,4,2,1] => [2,1,1,1] => [1,1,1] => 0
[4,1,5,3,2] => [4,1,5,3,2] => [2,2,1] => [2,1] => 0
[4,+,1,5,3] => [4,2,1,5,3] => [2,2,1] => [2,1] => 0
[4,-,1,5,3] => [4,2,1,5,3] => [2,2,1] => [2,1] => 0
[4,+,5,1,3] => [4,2,5,1,3] => [2,2,1] => [2,1] => 0
[4,-,5,1,3] => [4,2,5,1,3] => [2,2,1] => [2,1] => 0
[4,+,5,3,1] => [4,2,5,3,1] => [2,2,1] => [2,1] => 0
[4,-,5,3,1] => [4,2,5,3,1] => [2,2,1] => [2,1] => 0
[4,3,1,5,2] => [4,3,1,5,2] => [2,2,1] => [2,1] => 0
[4,3,2,1,+] => [4,3,2,1,5] => [2,1,1,1] => [1,1,1] => 0
[4,3,2,1,-] => [4,3,2,1,5] => [2,1,1,1] => [1,1,1] => 0
[4,3,2,5,1] => [4,3,2,5,1] => [2,1,1,1] => [1,1,1] => 0
[4,3,5,1,2] => [4,3,5,1,2] => [2,2,1] => [2,1] => 0
[4,3,5,2,1] => [4,3,5,2,1] => [2,1,1,1] => [1,1,1] => 0
[4,5,1,3,2] => [4,5,1,3,2] => [2,2,1] => [2,1] => 0
[4,5,2,1,3] => [4,5,2,1,3] => [2,2,1] => [2,1] => 0
[4,5,2,3,1] => [4,5,2,3,1] => [2,2,1] => [2,1] => 0
[4,5,+,1,2] => [4,5,3,1,2] => [2,2,1] => [2,1] => 0
[4,5,-,1,2] => [4,5,3,1,2] => [2,2,1] => [2,1] => 0
[4,5,+,2,1] => [4,5,3,2,1] => [2,1,1,1] => [1,1,1] => 0
[4,5,-,2,1] => [4,5,3,2,1] => [2,1,1,1] => [1,1,1] => 0
[5,1,4,3,2] => [5,1,4,3,2] => [2,1,1,1] => [1,1,1] => 0
[5,+,1,+,3] => [5,2,1,4,3] => [2,2,1] => [2,1] => 0
[5,-,1,+,3] => [5,2,1,4,3] => [2,2,1] => [2,1] => 0
[5,+,1,-,3] => [5,2,1,4,3] => [2,2,1] => [2,1] => 0
[5,-,1,-,3] => [5,2,1,4,3] => [2,2,1] => [2,1] => 0
[5,+,4,1,3] => [5,2,4,1,3] => [2,2,1] => [2,1] => 0
[5,-,4,1,3] => [5,2,4,1,3] => [2,2,1] => [2,1] => 0
[5,+,4,3,1] => [5,2,4,3,1] => [2,1,1,1] => [1,1,1] => 0
[5,-,4,3,1] => [5,2,4,3,1] => [2,1,1,1] => [1,1,1] => 0
[5,3,1,+,2] => [5,3,1,4,2] => [2,2,1] => [2,1] => 0
[5,3,1,-,2] => [5,3,1,4,2] => [2,2,1] => [2,1] => 0
[5,3,2,1,4] => [5,3,2,1,4] => [2,1,1,1] => [1,1,1] => 0
[5,3,2,+,1] => [5,3,2,4,1] => [2,1,1,1] => [1,1,1] => 0
[5,3,2,-,1] => [5,3,2,4,1] => [2,1,1,1] => [1,1,1] => 0
[5,3,4,1,2] => [5,3,4,1,2] => [2,2,1] => [2,1] => 0
[5,3,4,2,1] => [5,3,4,2,1] => [2,1,1,1] => [1,1,1] => 0
[5,4,1,3,2] => [5,4,1,3,2] => [2,1,1,1] => [1,1,1] => 0
[5,4,2,1,3] => [5,4,2,1,3] => [2,1,1,1] => [1,1,1] => 0
[5,4,2,3,1] => [5,4,2,3,1] => [2,1,1,1] => [1,1,1] => 0
[5,4,+,1,2] => [5,4,3,1,2] => [2,1,1,1] => [1,1,1] => 0
[5,4,-,1,2] => [5,4,3,1,2] => [2,1,1,1] => [1,1,1] => 0
[5,4,+,2,1] => [5,4,3,2,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[5,4,-,2,1] => [5,4,3,2,1] => [1,1,1,1,1] => [1,1,1,1] => 0
[+,+,6,5,4,3] => [1,2,6,5,4,3] => [3,1,1,1] => [1,1,1] => 0
[-,+,6,5,4,3] => [1,2,6,5,4,3] => [3,1,1,1] => [1,1,1] => 0
[+,-,6,5,4,3] => [1,2,6,5,4,3] => [3,1,1,1] => [1,1,1] => 0
[-,-,6,5,4,3] => [1,2,6,5,4,3] => [3,1,1,1] => [1,1,1] => 0
[+,3,2,6,+,4] => [1,3,2,6,5,4] => [3,2,1] => [2,1] => 0
[-,3,2,6,+,4] => [1,3,2,6,5,4] => [3,2,1] => [2,1] => 0
[+,3,2,6,-,4] => [1,3,2,6,5,4] => [3,2,1] => [2,1] => 0
[-,3,2,6,-,4] => [1,3,2,6,5,4] => [3,2,1] => [2,1] => 0
[+,3,6,2,+,4] => [1,3,6,2,5,4] => [3,2,1] => [2,1] => 0
[-,3,6,2,+,4] => [1,3,6,2,5,4] => [3,2,1] => [2,1] => 0
[+,3,6,2,-,4] => [1,3,6,2,5,4] => [3,2,1] => [2,1] => 0
[-,3,6,2,-,4] => [1,3,6,2,5,4] => [3,2,1] => [2,1] => 0
[+,3,6,5,2,4] => [1,3,6,5,2,4] => [3,2,1] => [2,1] => 0
[-,3,6,5,2,4] => [1,3,6,5,2,4] => [3,2,1] => [2,1] => 0
[+,3,6,5,4,2] => [1,3,6,5,4,2] => [3,1,1,1] => [1,1,1] => 0
[-,3,6,5,4,2] => [1,3,6,5,4,2] => [3,1,1,1] => [1,1,1] => 0
[+,4,2,6,+,3] => [1,4,2,6,5,3] => [3,2,1] => [2,1] => 0
[-,4,2,6,+,3] => [1,4,2,6,5,3] => [3,2,1] => [2,1] => 0
[+,4,2,6,-,3] => [1,4,2,6,5,3] => [3,2,1] => [2,1] => 0
[-,4,2,6,-,3] => [1,4,2,6,5,3] => [3,2,1] => [2,1] => 0
[+,4,+,2,6,5] => [1,4,3,2,6,5] => [3,2,1] => [2,1] => 0
[-,4,+,2,6,5] => [1,4,3,2,6,5] => [3,2,1] => [2,1] => 0
[+,4,-,2,6,5] => [1,4,3,2,6,5] => [3,2,1] => [2,1] => 0
[-,4,-,2,6,5] => [1,4,3,2,6,5] => [3,2,1] => [2,1] => 0
[+,4,+,6,2,5] => [1,4,3,6,2,5] => [3,2,1] => [2,1] => 0
[-,4,+,6,2,5] => [1,4,3,6,2,5] => [3,2,1] => [2,1] => 0
[+,4,-,6,2,5] => [1,4,3,6,2,5] => [3,2,1] => [2,1] => 0
[-,4,-,6,2,5] => [1,4,3,6,2,5] => [3,2,1] => [2,1] => 0
[+,4,+,6,+,2] => [1,4,3,6,5,2] => [3,2,1] => [2,1] => 0
[-,4,+,6,+,2] => [1,4,3,6,5,2] => [3,2,1] => [2,1] => 0
[+,4,-,6,+,2] => [1,4,3,6,5,2] => [3,2,1] => [2,1] => 0
[+,4,+,6,-,2] => [1,4,3,6,5,2] => [3,2,1] => [2,1] => 0
>>> Load all 1090 entries. <<<[-,4,-,6,+,2] => [1,4,3,6,5,2] => [3,2,1] => [2,1] => 0
[-,4,+,6,-,2] => [1,4,3,6,5,2] => [3,2,1] => [2,1] => 0
[+,4,-,6,-,2] => [1,4,3,6,5,2] => [3,2,1] => [2,1] => 0
[-,4,-,6,-,2] => [1,4,3,6,5,2] => [3,2,1] => [2,1] => 0
[+,4,6,2,+,3] => [1,4,6,2,5,3] => [3,2,1] => [2,1] => 0
[-,4,6,2,+,3] => [1,4,6,2,5,3] => [3,2,1] => [2,1] => 0
[+,4,6,2,-,3] => [1,4,6,2,5,3] => [3,2,1] => [2,1] => 0
[-,4,6,2,-,3] => [1,4,6,2,5,3] => [3,2,1] => [2,1] => 0
[+,4,6,3,2,5] => [1,4,6,3,2,5] => [3,2,1] => [2,1] => 0
[-,4,6,3,2,5] => [1,4,6,3,2,5] => [3,2,1] => [2,1] => 0
[+,4,6,3,+,2] => [1,4,6,3,5,2] => [3,2,1] => [2,1] => 0
[-,4,6,3,+,2] => [1,4,6,3,5,2] => [3,2,1] => [2,1] => 0
[+,4,6,3,-,2] => [1,4,6,3,5,2] => [3,2,1] => [2,1] => 0
[-,4,6,3,-,2] => [1,4,6,3,5,2] => [3,2,1] => [2,1] => 0
[+,4,6,5,2,3] => [1,4,6,5,2,3] => [3,2,1] => [2,1] => 0
[-,4,6,5,2,3] => [1,4,6,5,2,3] => [3,2,1] => [2,1] => 0
[+,4,6,5,3,2] => [1,4,6,5,3,2] => [3,1,1,1] => [1,1,1] => 0
[-,4,6,5,3,2] => [1,4,6,5,3,2] => [3,1,1,1] => [1,1,1] => 0
[+,5,2,6,4,3] => [1,5,2,6,4,3] => [3,2,1] => [2,1] => 0
[-,5,2,6,4,3] => [1,5,2,6,4,3] => [3,2,1] => [2,1] => 0
[+,5,+,2,6,4] => [1,5,3,2,6,4] => [3,2,1] => [2,1] => 0
[-,5,+,2,6,4] => [1,5,3,2,6,4] => [3,2,1] => [2,1] => 0
[+,5,-,2,6,4] => [1,5,3,2,6,4] => [3,2,1] => [2,1] => 0
[-,5,-,2,6,4] => [1,5,3,2,6,4] => [3,2,1] => [2,1] => 0
[+,5,+,6,2,4] => [1,5,3,6,2,4] => [3,2,1] => [2,1] => 0
[-,5,+,6,2,4] => [1,5,3,6,2,4] => [3,2,1] => [2,1] => 0
[+,5,-,6,2,4] => [1,5,3,6,2,4] => [3,2,1] => [2,1] => 0
[-,5,-,6,2,4] => [1,5,3,6,2,4] => [3,2,1] => [2,1] => 0
[+,5,+,6,4,2] => [1,5,3,6,4,2] => [3,2,1] => [2,1] => 0
[-,5,+,6,4,2] => [1,5,3,6,4,2] => [3,2,1] => [2,1] => 0
[+,5,-,6,4,2] => [1,5,3,6,4,2] => [3,2,1] => [2,1] => 0
[-,5,-,6,4,2] => [1,5,3,6,4,2] => [3,2,1] => [2,1] => 0
[+,5,4,2,6,3] => [1,5,4,2,6,3] => [3,2,1] => [2,1] => 0
[-,5,4,2,6,3] => [1,5,4,2,6,3] => [3,2,1] => [2,1] => 0
[+,5,4,3,2,+] => [1,5,4,3,2,6] => [3,1,1,1] => [1,1,1] => 0
[-,5,4,3,2,+] => [1,5,4,3,2,6] => [3,1,1,1] => [1,1,1] => 0
[+,5,4,3,2,-] => [1,5,4,3,2,6] => [3,1,1,1] => [1,1,1] => 0
[-,5,4,3,2,-] => [1,5,4,3,2,6] => [3,1,1,1] => [1,1,1] => 0
[+,5,4,3,6,2] => [1,5,4,3,6,2] => [3,1,1,1] => [1,1,1] => 0
[-,5,4,3,6,2] => [1,5,4,3,6,2] => [3,1,1,1] => [1,1,1] => 0
[+,5,4,6,2,3] => [1,5,4,6,2,3] => [3,2,1] => [2,1] => 0
[-,5,4,6,2,3] => [1,5,4,6,2,3] => [3,2,1] => [2,1] => 0
[+,5,4,6,3,2] => [1,5,4,6,3,2] => [3,1,1,1] => [1,1,1] => 0
[-,5,4,6,3,2] => [1,5,4,6,3,2] => [3,1,1,1] => [1,1,1] => 0
[+,5,6,2,4,3] => [1,5,6,2,4,3] => [3,2,1] => [2,1] => 0
[-,5,6,2,4,3] => [1,5,6,2,4,3] => [3,2,1] => [2,1] => 0
[+,5,6,3,2,4] => [1,5,6,3,2,4] => [3,2,1] => [2,1] => 0
[-,5,6,3,2,4] => [1,5,6,3,2,4] => [3,2,1] => [2,1] => 0
[+,5,6,3,4,2] => [1,5,6,3,4,2] => [3,2,1] => [2,1] => 0
[-,5,6,3,4,2] => [1,5,6,3,4,2] => [3,2,1] => [2,1] => 0
[+,5,6,+,2,3] => [1,5,6,4,2,3] => [3,2,1] => [2,1] => 0
[-,5,6,+,2,3] => [1,5,6,4,2,3] => [3,2,1] => [2,1] => 0
[+,5,6,-,2,3] => [1,5,6,4,2,3] => [3,2,1] => [2,1] => 0
[-,5,6,-,2,3] => [1,5,6,4,2,3] => [3,2,1] => [2,1] => 0
[+,5,6,+,3,2] => [1,5,6,4,3,2] => [3,1,1,1] => [1,1,1] => 0
[-,5,6,+,3,2] => [1,5,6,4,3,2] => [3,1,1,1] => [1,1,1] => 0
[+,5,6,-,3,2] => [1,5,6,4,3,2] => [3,1,1,1] => [1,1,1] => 0
[-,5,6,-,3,2] => [1,5,6,4,3,2] => [3,1,1,1] => [1,1,1] => 0
[+,6,2,5,4,3] => [1,6,2,5,4,3] => [3,1,1,1] => [1,1,1] => 0
[-,6,2,5,4,3] => [1,6,2,5,4,3] => [3,1,1,1] => [1,1,1] => 0
[+,6,+,2,+,4] => [1,6,3,2,5,4] => [3,2,1] => [2,1] => 0
[-,6,+,2,+,4] => [1,6,3,2,5,4] => [3,2,1] => [2,1] => 0
[+,6,-,2,+,4] => [1,6,3,2,5,4] => [3,2,1] => [2,1] => 0
[+,6,+,2,-,4] => [1,6,3,2,5,4] => [3,2,1] => [2,1] => 0
[-,6,-,2,+,4] => [1,6,3,2,5,4] => [3,2,1] => [2,1] => 0
[-,6,+,2,-,4] => [1,6,3,2,5,4] => [3,2,1] => [2,1] => 0
[+,6,-,2,-,4] => [1,6,3,2,5,4] => [3,2,1] => [2,1] => 0
[-,6,-,2,-,4] => [1,6,3,2,5,4] => [3,2,1] => [2,1] => 0
[+,6,+,5,2,4] => [1,6,3,5,2,4] => [3,2,1] => [2,1] => 0
[-,6,+,5,2,4] => [1,6,3,5,2,4] => [3,2,1] => [2,1] => 0
[+,6,-,5,2,4] => [1,6,3,5,2,4] => [3,2,1] => [2,1] => 0
[-,6,-,5,2,4] => [1,6,3,5,2,4] => [3,2,1] => [2,1] => 0
[+,6,+,5,4,2] => [1,6,3,5,4,2] => [3,1,1,1] => [1,1,1] => 0
[-,6,+,5,4,2] => [1,6,3,5,4,2] => [3,1,1,1] => [1,1,1] => 0
[+,6,-,5,4,2] => [1,6,3,5,4,2] => [3,1,1,1] => [1,1,1] => 0
[-,6,-,5,4,2] => [1,6,3,5,4,2] => [3,1,1,1] => [1,1,1] => 0
[+,6,4,2,+,3] => [1,6,4,2,5,3] => [3,2,1] => [2,1] => 0
[-,6,4,2,+,3] => [1,6,4,2,5,3] => [3,2,1] => [2,1] => 0
[+,6,4,2,-,3] => [1,6,4,2,5,3] => [3,2,1] => [2,1] => 0
[-,6,4,2,-,3] => [1,6,4,2,5,3] => [3,2,1] => [2,1] => 0
[+,6,4,3,2,5] => [1,6,4,3,2,5] => [3,1,1,1] => [1,1,1] => 0
[-,6,4,3,2,5] => [1,6,4,3,2,5] => [3,1,1,1] => [1,1,1] => 0
[+,6,4,3,+,2] => [1,6,4,3,5,2] => [3,1,1,1] => [1,1,1] => 0
[-,6,4,3,+,2] => [1,6,4,3,5,2] => [3,1,1,1] => [1,1,1] => 0
[+,6,4,3,-,2] => [1,6,4,3,5,2] => [3,1,1,1] => [1,1,1] => 0
[-,6,4,3,-,2] => [1,6,4,3,5,2] => [3,1,1,1] => [1,1,1] => 0
[+,6,4,5,2,3] => [1,6,4,5,2,3] => [3,2,1] => [2,1] => 0
[-,6,4,5,2,3] => [1,6,4,5,2,3] => [3,2,1] => [2,1] => 0
[+,6,4,5,3,2] => [1,6,4,5,3,2] => [3,1,1,1] => [1,1,1] => 0
[-,6,4,5,3,2] => [1,6,4,5,3,2] => [3,1,1,1] => [1,1,1] => 0
[+,6,5,2,4,3] => [1,6,5,2,4,3] => [3,1,1,1] => [1,1,1] => 0
[-,6,5,2,4,3] => [1,6,5,2,4,3] => [3,1,1,1] => [1,1,1] => 0
[+,6,5,3,2,4] => [1,6,5,3,2,4] => [3,1,1,1] => [1,1,1] => 0
[-,6,5,3,2,4] => [1,6,5,3,2,4] => [3,1,1,1] => [1,1,1] => 0
[+,6,5,3,4,2] => [1,6,5,3,4,2] => [3,1,1,1] => [1,1,1] => 0
[-,6,5,3,4,2] => [1,6,5,3,4,2] => [3,1,1,1] => [1,1,1] => 0
[+,6,5,+,2,3] => [1,6,5,4,2,3] => [3,1,1,1] => [1,1,1] => 0
[-,6,5,+,2,3] => [1,6,5,4,2,3] => [3,1,1,1] => [1,1,1] => 0
[+,6,5,-,2,3] => [1,6,5,4,2,3] => [3,1,1,1] => [1,1,1] => 0
[-,6,5,-,2,3] => [1,6,5,4,2,3] => [3,1,1,1] => [1,1,1] => 0
[+,6,5,+,3,2] => [1,6,5,4,3,2] => [2,1,1,1,1] => [1,1,1,1] => 0
[-,6,5,+,3,2] => [1,6,5,4,3,2] => [2,1,1,1,1] => [1,1,1,1] => 0
[+,6,5,-,3,2] => [1,6,5,4,3,2] => [2,1,1,1,1] => [1,1,1,1] => 0
[-,6,5,-,3,2] => [1,6,5,4,3,2] => [2,1,1,1,1] => [1,1,1,1] => 0
[2,1,+,6,+,4] => [2,1,3,6,5,4] => [3,2,1] => [2,1] => 0
[2,1,-,6,+,4] => [2,1,3,6,5,4] => [3,2,1] => [2,1] => 0
[2,1,+,6,-,4] => [2,1,3,6,5,4] => [3,2,1] => [2,1] => 0
[2,1,-,6,-,4] => [2,1,3,6,5,4] => [3,2,1] => [2,1] => 0
[2,1,4,3,6,5] => [2,1,4,3,6,5] => [3,3] => [3] => 1
[2,1,4,6,3,5] => [2,1,4,6,3,5] => [3,3] => [3] => 1
[2,1,4,6,+,3] => [2,1,4,6,5,3] => [3,2,1] => [2,1] => 0
[2,1,4,6,-,3] => [2,1,4,6,5,3] => [3,2,1] => [2,1] => 0
[2,1,5,3,6,4] => [2,1,5,3,6,4] => [3,3] => [3] => 1
[2,1,5,+,3,+] => [2,1,5,4,3,6] => [3,2,1] => [2,1] => 0
[2,1,5,-,3,+] => [2,1,5,4,3,6] => [3,2,1] => [2,1] => 0
[2,1,5,+,3,-] => [2,1,5,4,3,6] => [3,2,1] => [2,1] => 0
[2,1,5,-,3,-] => [2,1,5,4,3,6] => [3,2,1] => [2,1] => 0
[2,1,5,+,6,3] => [2,1,5,4,6,3] => [3,2,1] => [2,1] => 0
[2,1,5,-,6,3] => [2,1,5,4,6,3] => [3,2,1] => [2,1] => 0
[2,1,5,6,3,4] => [2,1,5,6,3,4] => [3,3] => [3] => 1
[2,1,5,6,4,3] => [2,1,5,6,4,3] => [3,2,1] => [2,1] => 0
[2,1,6,3,+,4] => [2,1,6,3,5,4] => [3,2,1] => [2,1] => 0
[2,1,6,3,-,4] => [2,1,6,3,5,4] => [3,2,1] => [2,1] => 0
[2,1,6,+,3,5] => [2,1,6,4,3,5] => [3,2,1] => [2,1] => 0
[2,1,6,-,3,5] => [2,1,6,4,3,5] => [3,2,1] => [2,1] => 0
[2,1,6,+,+,3] => [2,1,6,4,5,3] => [3,2,1] => [2,1] => 0
[2,1,6,-,+,3] => [2,1,6,4,5,3] => [3,2,1] => [2,1] => 0
[2,1,6,+,-,3] => [2,1,6,4,5,3] => [3,2,1] => [2,1] => 0
[2,1,6,-,-,3] => [2,1,6,4,5,3] => [3,2,1] => [2,1] => 0
[2,1,6,5,3,4] => [2,1,6,5,3,4] => [3,2,1] => [2,1] => 0
[2,1,6,5,4,3] => [2,1,6,5,4,3] => [2,2,1,1] => [2,1,1] => 0
[2,3,1,6,+,4] => [2,3,1,6,5,4] => [3,2,1] => [2,1] => 0
[2,3,1,6,-,4] => [2,3,1,6,5,4] => [3,2,1] => [2,1] => 0
[2,3,6,1,+,4] => [2,3,6,1,5,4] => [3,2,1] => [2,1] => 0
[2,3,6,1,-,4] => [2,3,6,1,5,4] => [3,2,1] => [2,1] => 0
[2,3,6,5,1,4] => [2,3,6,5,1,4] => [3,2,1] => [2,1] => 0
[2,3,6,5,4,1] => [2,3,6,5,4,1] => [3,1,1,1] => [1,1,1] => 0
[2,4,1,3,6,5] => [2,4,1,3,6,5] => [3,3] => [3] => 1
[2,4,1,6,3,5] => [2,4,1,6,3,5] => [3,3] => [3] => 1
[2,4,1,6,+,3] => [2,4,1,6,5,3] => [3,2,1] => [2,1] => 0
[2,4,1,6,-,3] => [2,4,1,6,5,3] => [3,2,1] => [2,1] => 0
[2,4,+,1,6,5] => [2,4,3,1,6,5] => [3,2,1] => [2,1] => 0
[2,4,-,1,6,5] => [2,4,3,1,6,5] => [3,2,1] => [2,1] => 0
[2,4,+,6,1,5] => [2,4,3,6,1,5] => [3,2,1] => [2,1] => 0
[2,4,-,6,1,5] => [2,4,3,6,1,5] => [3,2,1] => [2,1] => 0
[2,4,+,6,+,1] => [2,4,3,6,5,1] => [3,2,1] => [2,1] => 0
[2,4,-,6,+,1] => [2,4,3,6,5,1] => [3,2,1] => [2,1] => 0
[2,4,+,6,-,1] => [2,4,3,6,5,1] => [3,2,1] => [2,1] => 0
[2,4,-,6,-,1] => [2,4,3,6,5,1] => [3,2,1] => [2,1] => 0
[2,4,6,1,3,5] => [2,4,6,1,3,5] => [3,3] => [3] => 1
[2,4,6,1,+,3] => [2,4,6,1,5,3] => [3,2,1] => [2,1] => 0
[2,4,6,1,-,3] => [2,4,6,1,5,3] => [3,2,1] => [2,1] => 0
[2,4,6,3,1,5] => [2,4,6,3,1,5] => [3,2,1] => [2,1] => 0
[2,4,6,3,+,1] => [2,4,6,3,5,1] => [3,2,1] => [2,1] => 0
[2,4,6,3,-,1] => [2,4,6,3,5,1] => [3,2,1] => [2,1] => 0
[2,4,6,5,1,3] => [2,4,6,5,1,3] => [3,2,1] => [2,1] => 0
[2,4,6,5,3,1] => [2,4,6,5,3,1] => [3,1,1,1] => [1,1,1] => 0
[2,5,1,3,6,4] => [2,5,1,3,6,4] => [3,3] => [3] => 1
[2,5,1,+,3,+] => [2,5,1,4,3,6] => [3,2,1] => [2,1] => 0
[2,5,1,-,3,+] => [2,5,1,4,3,6] => [3,2,1] => [2,1] => 0
[2,5,1,+,3,-] => [2,5,1,4,3,6] => [3,2,1] => [2,1] => 0
[2,5,1,-,3,-] => [2,5,1,4,3,6] => [3,2,1] => [2,1] => 0
[2,5,1,+,6,3] => [2,5,1,4,6,3] => [3,2,1] => [2,1] => 0
[2,5,1,-,6,3] => [2,5,1,4,6,3] => [3,2,1] => [2,1] => 0
[2,5,1,6,3,4] => [2,5,1,6,3,4] => [3,3] => [3] => 1
[2,5,1,6,4,3] => [2,5,1,6,4,3] => [3,2,1] => [2,1] => 0
[2,5,+,1,6,4] => [2,5,3,1,6,4] => [3,2,1] => [2,1] => 0
[2,5,-,1,6,4] => [2,5,3,1,6,4] => [3,2,1] => [2,1] => 0
[2,5,+,6,1,4] => [2,5,3,6,1,4] => [3,2,1] => [2,1] => 0
[2,5,-,6,1,4] => [2,5,3,6,1,4] => [3,2,1] => [2,1] => 0
[2,5,+,6,4,1] => [2,5,3,6,4,1] => [3,2,1] => [2,1] => 0
[2,5,-,6,4,1] => [2,5,3,6,4,1] => [3,2,1] => [2,1] => 0
[2,5,4,1,3,+] => [2,5,4,1,3,6] => [3,2,1] => [2,1] => 0
[2,5,4,1,3,-] => [2,5,4,1,3,6] => [3,2,1] => [2,1] => 0
[2,5,4,1,6,3] => [2,5,4,1,6,3] => [3,2,1] => [2,1] => 0
[2,5,4,3,1,+] => [2,5,4,3,1,6] => [3,1,1,1] => [1,1,1] => 0
[2,5,4,3,1,-] => [2,5,4,3,1,6] => [3,1,1,1] => [1,1,1] => 0
[2,5,4,3,6,1] => [2,5,4,3,6,1] => [3,1,1,1] => [1,1,1] => 0
[2,5,4,6,1,3] => [2,5,4,6,1,3] => [3,2,1] => [2,1] => 0
[2,5,4,6,3,1] => [2,5,4,6,3,1] => [3,1,1,1] => [1,1,1] => 0
[2,5,6,1,3,4] => [2,5,6,1,3,4] => [3,3] => [3] => 1
[2,5,6,1,4,3] => [2,5,6,1,4,3] => [3,2,1] => [2,1] => 0
[2,5,6,3,1,4] => [2,5,6,3,1,4] => [3,2,1] => [2,1] => 0
[2,5,6,3,4,1] => [2,5,6,3,4,1] => [3,2,1] => [2,1] => 0
[2,5,6,+,1,3] => [2,5,6,4,1,3] => [3,2,1] => [2,1] => 0
[2,5,6,-,1,3] => [2,5,6,4,1,3] => [3,2,1] => [2,1] => 0
[2,5,6,+,3,1] => [2,5,6,4,3,1] => [3,1,1,1] => [1,1,1] => 0
[2,5,6,-,3,1] => [2,5,6,4,3,1] => [3,1,1,1] => [1,1,1] => 0
[2,6,1,3,+,4] => [2,6,1,3,5,4] => [3,2,1] => [2,1] => 0
[2,6,1,3,-,4] => [2,6,1,3,5,4] => [3,2,1] => [2,1] => 0
[2,6,1,+,3,5] => [2,6,1,4,3,5] => [3,2,1] => [2,1] => 0
[2,6,1,-,3,5] => [2,6,1,4,3,5] => [3,2,1] => [2,1] => 0
[2,6,1,+,+,3] => [2,6,1,4,5,3] => [3,2,1] => [2,1] => 0
[2,6,1,-,+,3] => [2,6,1,4,5,3] => [3,2,1] => [2,1] => 0
[2,6,1,+,-,3] => [2,6,1,4,5,3] => [3,2,1] => [2,1] => 0
[2,6,1,-,-,3] => [2,6,1,4,5,3] => [3,2,1] => [2,1] => 0
[2,6,1,5,3,4] => [2,6,1,5,3,4] => [3,2,1] => [2,1] => 0
[2,6,1,5,4,3] => [2,6,1,5,4,3] => [2,2,1,1] => [2,1,1] => 0
[2,6,+,1,+,4] => [2,6,3,1,5,4] => [3,2,1] => [2,1] => 0
[2,6,-,1,+,4] => [2,6,3,1,5,4] => [3,2,1] => [2,1] => 0
[2,6,+,1,-,4] => [2,6,3,1,5,4] => [3,2,1] => [2,1] => 0
[2,6,-,1,-,4] => [2,6,3,1,5,4] => [3,2,1] => [2,1] => 0
[2,6,+,5,1,4] => [2,6,3,5,1,4] => [3,2,1] => [2,1] => 0
[2,6,-,5,1,4] => [2,6,3,5,1,4] => [3,2,1] => [2,1] => 0
[2,6,+,5,4,1] => [2,6,3,5,4,1] => [3,1,1,1] => [1,1,1] => 0
[2,6,-,5,4,1] => [2,6,3,5,4,1] => [3,1,1,1] => [1,1,1] => 0
[2,6,4,1,3,5] => [2,6,4,1,3,5] => [3,2,1] => [2,1] => 0
[2,6,4,1,+,3] => [2,6,4,1,5,3] => [3,2,1] => [2,1] => 0
[2,6,4,1,-,3] => [2,6,4,1,5,3] => [3,2,1] => [2,1] => 0
[2,6,4,3,1,5] => [2,6,4,3,1,5] => [3,1,1,1] => [1,1,1] => 0
[2,6,4,3,+,1] => [2,6,4,3,5,1] => [3,1,1,1] => [1,1,1] => 0
[2,6,4,3,-,1] => [2,6,4,3,5,1] => [3,1,1,1] => [1,1,1] => 0
[2,6,4,5,1,3] => [2,6,4,5,1,3] => [3,2,1] => [2,1] => 0
[2,6,4,5,3,1] => [2,6,4,5,3,1] => [3,1,1,1] => [1,1,1] => 0
[2,6,5,1,3,4] => [2,6,5,1,3,4] => [3,2,1] => [2,1] => 0
[2,6,5,1,4,3] => [2,6,5,1,4,3] => [2,2,1,1] => [2,1,1] => 0
[2,6,5,3,1,4] => [2,6,5,3,1,4] => [3,1,1,1] => [1,1,1] => 0
[2,6,5,3,4,1] => [2,6,5,3,4,1] => [3,1,1,1] => [1,1,1] => 0
[2,6,5,+,1,3] => [2,6,5,4,1,3] => [2,2,1,1] => [2,1,1] => 0
[2,6,5,-,1,3] => [2,6,5,4,1,3] => [2,2,1,1] => [2,1,1] => 0
[2,6,5,+,3,1] => [2,6,5,4,3,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[2,6,5,-,3,1] => [2,6,5,4,3,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[3,1,2,6,+,4] => [3,1,2,6,5,4] => [3,2,1] => [2,1] => 0
[3,1,2,6,-,4] => [3,1,2,6,5,4] => [3,2,1] => [2,1] => 0
[3,1,4,2,6,5] => [3,1,4,2,6,5] => [3,3] => [3] => 1
[3,1,4,6,2,5] => [3,1,4,6,2,5] => [3,3] => [3] => 1
[3,1,4,6,+,2] => [3,1,4,6,5,2] => [3,2,1] => [2,1] => 0
[3,1,4,6,-,2] => [3,1,4,6,5,2] => [3,2,1] => [2,1] => 0
[3,1,5,2,6,4] => [3,1,5,2,6,4] => [3,3] => [3] => 1
[3,1,5,+,2,+] => [3,1,5,4,2,6] => [3,2,1] => [2,1] => 0
[3,1,5,-,2,+] => [3,1,5,4,2,6] => [3,2,1] => [2,1] => 0
[3,1,5,+,2,-] => [3,1,5,4,2,6] => [3,2,1] => [2,1] => 0
[3,1,5,-,2,-] => [3,1,5,4,2,6] => [3,2,1] => [2,1] => 0
[3,1,5,+,6,2] => [3,1,5,4,6,2] => [3,2,1] => [2,1] => 0
[3,1,5,-,6,2] => [3,1,5,4,6,2] => [3,2,1] => [2,1] => 0
[3,1,5,6,2,4] => [3,1,5,6,2,4] => [3,3] => [3] => 1
[3,1,5,6,4,2] => [3,1,5,6,4,2] => [3,2,1] => [2,1] => 0
[3,1,6,2,+,4] => [3,1,6,2,5,4] => [3,2,1] => [2,1] => 0
[3,1,6,2,-,4] => [3,1,6,2,5,4] => [3,2,1] => [2,1] => 0
[3,1,6,+,2,5] => [3,1,6,4,2,5] => [3,2,1] => [2,1] => 0
[3,1,6,-,2,5] => [3,1,6,4,2,5] => [3,2,1] => [2,1] => 0
[3,1,6,+,+,2] => [3,1,6,4,5,2] => [3,2,1] => [2,1] => 0
[3,1,6,-,+,2] => [3,1,6,4,5,2] => [3,2,1] => [2,1] => 0
[3,1,6,+,-,2] => [3,1,6,4,5,2] => [3,2,1] => [2,1] => 0
[3,1,6,-,-,2] => [3,1,6,4,5,2] => [3,2,1] => [2,1] => 0
[3,1,6,5,2,4] => [3,1,6,5,2,4] => [3,2,1] => [2,1] => 0
[3,1,6,5,4,2] => [3,1,6,5,4,2] => [2,2,1,1] => [2,1,1] => 0
[3,+,1,+,6,5] => [3,2,1,4,6,5] => [3,2,1] => [2,1] => 0
[3,-,1,+,6,5] => [3,2,1,4,6,5] => [3,2,1] => [2,1] => 0
[3,+,1,-,6,5] => [3,2,1,4,6,5] => [3,2,1] => [2,1] => 0
[3,-,1,-,6,5] => [3,2,1,4,6,5] => [3,2,1] => [2,1] => 0
[3,+,1,5,4,+] => [3,2,1,5,4,6] => [3,2,1] => [2,1] => 0
[3,-,1,5,4,+] => [3,2,1,5,4,6] => [3,2,1] => [2,1] => 0
[3,+,1,5,4,-] => [3,2,1,5,4,6] => [3,2,1] => [2,1] => 0
[3,-,1,5,4,-] => [3,2,1,5,4,6] => [3,2,1] => [2,1] => 0
[3,+,1,5,6,4] => [3,2,1,5,6,4] => [3,2,1] => [2,1] => 0
[3,-,1,5,6,4] => [3,2,1,5,6,4] => [3,2,1] => [2,1] => 0
[3,+,1,6,4,5] => [3,2,1,6,4,5] => [3,2,1] => [2,1] => 0
[3,-,1,6,4,5] => [3,2,1,6,4,5] => [3,2,1] => [2,1] => 0
[3,+,1,6,+,4] => [3,2,1,6,5,4] => [2,2,2] => [2,2] => 1
[3,-,1,6,+,4] => [3,2,1,6,5,4] => [2,2,2] => [2,2] => 1
[3,+,1,6,-,4] => [3,2,1,6,5,4] => [2,2,2] => [2,2] => 1
[3,-,1,6,-,4] => [3,2,1,6,5,4] => [2,2,2] => [2,2] => 1
[3,+,4,1,6,5] => [3,2,4,1,6,5] => [3,2,1] => [2,1] => 0
[3,-,4,1,6,5] => [3,2,4,1,6,5] => [3,2,1] => [2,1] => 0
[3,+,4,6,1,5] => [3,2,4,6,1,5] => [3,2,1] => [2,1] => 0
[3,-,4,6,1,5] => [3,2,4,6,1,5] => [3,2,1] => [2,1] => 0
[3,+,4,6,+,1] => [3,2,4,6,5,1] => [3,2,1] => [2,1] => 0
[3,-,4,6,+,1] => [3,2,4,6,5,1] => [3,2,1] => [2,1] => 0
[3,+,4,6,-,1] => [3,2,4,6,5,1] => [3,2,1] => [2,1] => 0
[3,-,4,6,-,1] => [3,2,4,6,5,1] => [3,2,1] => [2,1] => 0
[3,+,5,1,4,+] => [3,2,5,1,4,6] => [3,2,1] => [2,1] => 0
[3,-,5,1,4,+] => [3,2,5,1,4,6] => [3,2,1] => [2,1] => 0
[3,+,5,1,4,-] => [3,2,5,1,4,6] => [3,2,1] => [2,1] => 0
[3,-,5,1,4,-] => [3,2,5,1,4,6] => [3,2,1] => [2,1] => 0
[3,+,5,1,6,4] => [3,2,5,1,6,4] => [3,2,1] => [2,1] => 0
[3,-,5,1,6,4] => [3,2,5,1,6,4] => [3,2,1] => [2,1] => 0
[3,+,5,+,1,+] => [3,2,5,4,1,6] => [3,2,1] => [2,1] => 0
[3,-,5,+,1,+] => [3,2,5,4,1,6] => [3,2,1] => [2,1] => 0
[3,+,5,-,1,+] => [3,2,5,4,1,6] => [3,2,1] => [2,1] => 0
[3,+,5,+,1,-] => [3,2,5,4,1,6] => [3,2,1] => [2,1] => 0
[3,-,5,-,1,+] => [3,2,5,4,1,6] => [3,2,1] => [2,1] => 0
[3,-,5,+,1,-] => [3,2,5,4,1,6] => [3,2,1] => [2,1] => 0
[3,+,5,-,1,-] => [3,2,5,4,1,6] => [3,2,1] => [2,1] => 0
[3,-,5,-,1,-] => [3,2,5,4,1,6] => [3,2,1] => [2,1] => 0
[3,+,5,+,6,1] => [3,2,5,4,6,1] => [3,2,1] => [2,1] => 0
[3,-,5,+,6,1] => [3,2,5,4,6,1] => [3,2,1] => [2,1] => 0
[3,+,5,-,6,1] => [3,2,5,4,6,1] => [3,2,1] => [2,1] => 0
[3,-,5,-,6,1] => [3,2,5,4,6,1] => [3,2,1] => [2,1] => 0
[3,+,5,6,1,4] => [3,2,5,6,1,4] => [3,2,1] => [2,1] => 0
[3,-,5,6,1,4] => [3,2,5,6,1,4] => [3,2,1] => [2,1] => 0
[3,+,5,6,4,1] => [3,2,5,6,4,1] => [3,2,1] => [2,1] => 0
[3,-,5,6,4,1] => [3,2,5,6,4,1] => [3,2,1] => [2,1] => 0
[3,+,6,1,4,5] => [3,2,6,1,4,5] => [3,2,1] => [2,1] => 0
[3,-,6,1,4,5] => [3,2,6,1,4,5] => [3,2,1] => [2,1] => 0
[3,+,6,1,+,4] => [3,2,6,1,5,4] => [2,2,2] => [2,2] => 1
[3,-,6,1,+,4] => [3,2,6,1,5,4] => [2,2,2] => [2,2] => 1
[3,+,6,1,-,4] => [3,2,6,1,5,4] => [2,2,2] => [2,2] => 1
[3,-,6,1,-,4] => [3,2,6,1,5,4] => [2,2,2] => [2,2] => 1
[3,+,6,+,1,5] => [3,2,6,4,1,5] => [3,2,1] => [2,1] => 0
[3,-,6,+,1,5] => [3,2,6,4,1,5] => [3,2,1] => [2,1] => 0
[3,+,6,-,1,5] => [3,2,6,4,1,5] => [3,2,1] => [2,1] => 0
[3,-,6,-,1,5] => [3,2,6,4,1,5] => [3,2,1] => [2,1] => 0
[3,+,6,+,+,1] => [3,2,6,4,5,1] => [3,2,1] => [2,1] => 0
[3,-,6,+,+,1] => [3,2,6,4,5,1] => [3,2,1] => [2,1] => 0
[3,+,6,-,+,1] => [3,2,6,4,5,1] => [3,2,1] => [2,1] => 0
[3,+,6,+,-,1] => [3,2,6,4,5,1] => [3,2,1] => [2,1] => 0
[3,-,6,-,+,1] => [3,2,6,4,5,1] => [3,2,1] => [2,1] => 0
[3,-,6,+,-,1] => [3,2,6,4,5,1] => [3,2,1] => [2,1] => 0
[3,+,6,-,-,1] => [3,2,6,4,5,1] => [3,2,1] => [2,1] => 0
[3,-,6,-,-,1] => [3,2,6,4,5,1] => [3,2,1] => [2,1] => 0
[3,+,6,5,1,4] => [3,2,6,5,1,4] => [2,2,2] => [2,2] => 1
[3,-,6,5,1,4] => [3,2,6,5,1,4] => [2,2,2] => [2,2] => 1
[3,+,6,5,4,1] => [3,2,6,5,4,1] => [2,2,1,1] => [2,1,1] => 0
[3,-,6,5,4,1] => [3,2,6,5,4,1] => [2,2,1,1] => [2,1,1] => 0
[3,4,1,2,6,5] => [3,4,1,2,6,5] => [3,3] => [3] => 1
[3,4,1,6,2,5] => [3,4,1,6,2,5] => [3,3] => [3] => 1
[3,4,1,6,+,2] => [3,4,1,6,5,2] => [3,2,1] => [2,1] => 0
[3,4,1,6,-,2] => [3,4,1,6,5,2] => [3,2,1] => [2,1] => 0
[3,4,2,1,6,5] => [3,4,2,1,6,5] => [3,2,1] => [2,1] => 0
[3,4,2,6,1,5] => [3,4,2,6,1,5] => [3,2,1] => [2,1] => 0
[3,4,2,6,+,1] => [3,4,2,6,5,1] => [3,2,1] => [2,1] => 0
[3,4,2,6,-,1] => [3,4,2,6,5,1] => [3,2,1] => [2,1] => 0
[3,4,6,1,2,5] => [3,4,6,1,2,5] => [3,3] => [3] => 1
[3,4,6,1,+,2] => [3,4,6,1,5,2] => [3,2,1] => [2,1] => 0
[3,4,6,1,-,2] => [3,4,6,1,5,2] => [3,2,1] => [2,1] => 0
[3,4,6,2,1,5] => [3,4,6,2,1,5] => [3,2,1] => [2,1] => 0
[3,4,6,2,+,1] => [3,4,6,2,5,1] => [3,2,1] => [2,1] => 0
[3,4,6,2,-,1] => [3,4,6,2,5,1] => [3,2,1] => [2,1] => 0
[3,4,6,5,1,2] => [3,4,6,5,1,2] => [3,2,1] => [2,1] => 0
[3,4,6,5,2,1] => [3,4,6,5,2,1] => [3,1,1,1] => [1,1,1] => 0
[3,5,1,2,6,4] => [3,5,1,2,6,4] => [3,3] => [3] => 1
[3,5,1,+,2,+] => [3,5,1,4,2,6] => [3,2,1] => [2,1] => 0
[3,5,1,-,2,+] => [3,5,1,4,2,6] => [3,2,1] => [2,1] => 0
[3,5,1,+,2,-] => [3,5,1,4,2,6] => [3,2,1] => [2,1] => 0
[3,5,1,-,2,-] => [3,5,1,4,2,6] => [3,2,1] => [2,1] => 0
[3,5,1,+,6,2] => [3,5,1,4,6,2] => [3,2,1] => [2,1] => 0
[3,5,1,-,6,2] => [3,5,1,4,6,2] => [3,2,1] => [2,1] => 0
[3,5,1,6,2,4] => [3,5,1,6,2,4] => [3,3] => [3] => 1
[3,5,1,6,4,2] => [3,5,1,6,4,2] => [3,2,1] => [2,1] => 0
[3,5,2,1,4,+] => [3,5,2,1,4,6] => [3,2,1] => [2,1] => 0
[3,5,2,1,4,-] => [3,5,2,1,4,6] => [3,2,1] => [2,1] => 0
[3,5,2,1,6,4] => [3,5,2,1,6,4] => [3,2,1] => [2,1] => 0
[3,5,2,+,1,+] => [3,5,2,4,1,6] => [3,2,1] => [2,1] => 0
[3,5,2,-,1,+] => [3,5,2,4,1,6] => [3,2,1] => [2,1] => 0
[3,5,2,+,1,-] => [3,5,2,4,1,6] => [3,2,1] => [2,1] => 0
[3,5,2,-,1,-] => [3,5,2,4,1,6] => [3,2,1] => [2,1] => 0
[3,5,2,+,6,1] => [3,5,2,4,6,1] => [3,2,1] => [2,1] => 0
[3,5,2,-,6,1] => [3,5,2,4,6,1] => [3,2,1] => [2,1] => 0
[3,5,2,6,1,4] => [3,5,2,6,1,4] => [3,2,1] => [2,1] => 0
[3,5,2,6,4,1] => [3,5,2,6,4,1] => [3,2,1] => [2,1] => 0
[3,5,4,1,2,+] => [3,5,4,1,2,6] => [3,2,1] => [2,1] => 0
[3,5,4,1,2,-] => [3,5,4,1,2,6] => [3,2,1] => [2,1] => 0
[3,5,4,1,6,2] => [3,5,4,1,6,2] => [3,2,1] => [2,1] => 0
[3,5,4,2,1,+] => [3,5,4,2,1,6] => [3,1,1,1] => [1,1,1] => 0
[3,5,4,2,1,-] => [3,5,4,2,1,6] => [3,1,1,1] => [1,1,1] => 0
[3,5,4,2,6,1] => [3,5,4,2,6,1] => [3,1,1,1] => [1,1,1] => 0
[3,5,4,6,1,2] => [3,5,4,6,1,2] => [3,2,1] => [2,1] => 0
[3,5,4,6,2,1] => [3,5,4,6,2,1] => [3,1,1,1] => [1,1,1] => 0
[3,5,6,1,2,4] => [3,5,6,1,2,4] => [3,3] => [3] => 1
[3,5,6,1,4,2] => [3,5,6,1,4,2] => [3,2,1] => [2,1] => 0
[3,5,6,2,1,4] => [3,5,6,2,1,4] => [3,2,1] => [2,1] => 0
[3,5,6,2,4,1] => [3,5,6,2,4,1] => [3,2,1] => [2,1] => 0
[3,5,6,+,1,2] => [3,5,6,4,1,2] => [3,2,1] => [2,1] => 0
[3,5,6,-,1,2] => [3,5,6,4,1,2] => [3,2,1] => [2,1] => 0
[3,5,6,+,2,1] => [3,5,6,4,2,1] => [3,1,1,1] => [1,1,1] => 0
[3,5,6,-,2,1] => [3,5,6,4,2,1] => [3,1,1,1] => [1,1,1] => 0
[3,6,1,2,+,4] => [3,6,1,2,5,4] => [3,2,1] => [2,1] => 0
[3,6,1,2,-,4] => [3,6,1,2,5,4] => [3,2,1] => [2,1] => 0
[3,6,1,+,2,5] => [3,6,1,4,2,5] => [3,2,1] => [2,1] => 0
[3,6,1,-,2,5] => [3,6,1,4,2,5] => [3,2,1] => [2,1] => 0
[3,6,1,+,+,2] => [3,6,1,4,5,2] => [3,2,1] => [2,1] => 0
[3,6,1,-,+,2] => [3,6,1,4,5,2] => [3,2,1] => [2,1] => 0
[3,6,1,+,-,2] => [3,6,1,4,5,2] => [3,2,1] => [2,1] => 0
[3,6,1,-,-,2] => [3,6,1,4,5,2] => [3,2,1] => [2,1] => 0
[3,6,1,5,2,4] => [3,6,1,5,2,4] => [3,2,1] => [2,1] => 0
[3,6,1,5,4,2] => [3,6,1,5,4,2] => [2,2,1,1] => [2,1,1] => 0
[3,6,2,1,4,5] => [3,6,2,1,4,5] => [3,2,1] => [2,1] => 0
[3,6,2,1,+,4] => [3,6,2,1,5,4] => [2,2,2] => [2,2] => 1
[3,6,2,1,-,4] => [3,6,2,1,5,4] => [2,2,2] => [2,2] => 1
[3,6,2,+,1,5] => [3,6,2,4,1,5] => [3,2,1] => [2,1] => 0
[3,6,2,-,1,5] => [3,6,2,4,1,5] => [3,2,1] => [2,1] => 0
[3,6,2,+,+,1] => [3,6,2,4,5,1] => [3,2,1] => [2,1] => 0
[3,6,2,-,+,1] => [3,6,2,4,5,1] => [3,2,1] => [2,1] => 0
[3,6,2,+,-,1] => [3,6,2,4,5,1] => [3,2,1] => [2,1] => 0
[3,6,2,-,-,1] => [3,6,2,4,5,1] => [3,2,1] => [2,1] => 0
[3,6,2,5,1,4] => [3,6,2,5,1,4] => [2,2,2] => [2,2] => 1
[3,6,2,5,4,1] => [3,6,2,5,4,1] => [2,2,1,1] => [2,1,1] => 0
[3,6,4,1,2,5] => [3,6,4,1,2,5] => [3,2,1] => [2,1] => 0
[3,6,4,1,+,2] => [3,6,4,1,5,2] => [3,2,1] => [2,1] => 0
[3,6,4,1,-,2] => [3,6,4,1,5,2] => [3,2,1] => [2,1] => 0
[3,6,4,2,1,5] => [3,6,4,2,1,5] => [3,1,1,1] => [1,1,1] => 0
[3,6,4,2,+,1] => [3,6,4,2,5,1] => [3,1,1,1] => [1,1,1] => 0
[3,6,4,2,-,1] => [3,6,4,2,5,1] => [3,1,1,1] => [1,1,1] => 0
[3,6,4,5,1,2] => [3,6,4,5,1,2] => [3,2,1] => [2,1] => 0
[3,6,4,5,2,1] => [3,6,4,5,2,1] => [3,1,1,1] => [1,1,1] => 0
[3,6,5,1,2,4] => [3,6,5,1,2,4] => [3,2,1] => [2,1] => 0
[3,6,5,1,4,2] => [3,6,5,1,4,2] => [2,2,1,1] => [2,1,1] => 0
[3,6,5,2,1,4] => [3,6,5,2,1,4] => [2,2,1,1] => [2,1,1] => 0
[3,6,5,2,4,1] => [3,6,5,2,4,1] => [2,2,1,1] => [2,1,1] => 0
[3,6,5,+,1,2] => [3,6,5,4,1,2] => [2,2,1,1] => [2,1,1] => 0
[3,6,5,-,1,2] => [3,6,5,4,1,2] => [2,2,1,1] => [2,1,1] => 0
[3,6,5,+,2,1] => [3,6,5,4,2,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[3,6,5,-,2,1] => [3,6,5,4,2,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[4,1,2,6,+,3] => [4,1,2,6,5,3] => [3,2,1] => [2,1] => 0
[4,1,2,6,-,3] => [4,1,2,6,5,3] => [3,2,1] => [2,1] => 0
[4,1,+,2,6,5] => [4,1,3,2,6,5] => [3,2,1] => [2,1] => 0
[4,1,-,2,6,5] => [4,1,3,2,6,5] => [3,2,1] => [2,1] => 0
[4,1,+,6,2,5] => [4,1,3,6,2,5] => [3,2,1] => [2,1] => 0
[4,1,-,6,2,5] => [4,1,3,6,2,5] => [3,2,1] => [2,1] => 0
[4,1,+,6,+,2] => [4,1,3,6,5,2] => [3,2,1] => [2,1] => 0
[4,1,-,6,+,2] => [4,1,3,6,5,2] => [3,2,1] => [2,1] => 0
[4,1,+,6,-,2] => [4,1,3,6,5,2] => [3,2,1] => [2,1] => 0
[4,1,-,6,-,2] => [4,1,3,6,5,2] => [3,2,1] => [2,1] => 0
[4,1,5,2,6,3] => [4,1,5,2,6,3] => [3,3] => [3] => 1
[4,1,5,3,2,+] => [4,1,5,3,2,6] => [3,2,1] => [2,1] => 0
[4,1,5,3,2,-] => [4,1,5,3,2,6] => [3,2,1] => [2,1] => 0
[4,1,5,3,6,2] => [4,1,5,3,6,2] => [3,2,1] => [2,1] => 0
[4,1,5,6,2,3] => [4,1,5,6,2,3] => [3,3] => [3] => 1
[4,1,5,6,3,2] => [4,1,5,6,3,2] => [3,2,1] => [2,1] => 0
[4,1,6,2,+,3] => [4,1,6,2,5,3] => [3,2,1] => [2,1] => 0
[4,1,6,2,-,3] => [4,1,6,2,5,3] => [3,2,1] => [2,1] => 0
[4,1,6,3,2,5] => [4,1,6,3,2,5] => [3,2,1] => [2,1] => 0
[4,1,6,3,+,2] => [4,1,6,3,5,2] => [3,2,1] => [2,1] => 0
[4,1,6,3,-,2] => [4,1,6,3,5,2] => [3,2,1] => [2,1] => 0
[4,1,6,5,2,3] => [4,1,6,5,2,3] => [3,2,1] => [2,1] => 0
[4,1,6,5,3,2] => [4,1,6,5,3,2] => [2,2,1,1] => [2,1,1] => 0
[4,+,1,3,6,5] => [4,2,1,3,6,5] => [3,2,1] => [2,1] => 0
[4,-,1,3,6,5] => [4,2,1,3,6,5] => [3,2,1] => [2,1] => 0
[4,+,1,5,3,+] => [4,2,1,5,3,6] => [3,2,1] => [2,1] => 0
[4,-,1,5,3,+] => [4,2,1,5,3,6] => [3,2,1] => [2,1] => 0
[4,+,1,5,3,-] => [4,2,1,5,3,6] => [3,2,1] => [2,1] => 0
[4,-,1,5,3,-] => [4,2,1,5,3,6] => [3,2,1] => [2,1] => 0
[4,+,1,5,6,3] => [4,2,1,5,6,3] => [3,2,1] => [2,1] => 0
[4,-,1,5,6,3] => [4,2,1,5,6,3] => [3,2,1] => [2,1] => 0
[4,+,1,6,3,5] => [4,2,1,6,3,5] => [3,2,1] => [2,1] => 0
[4,-,1,6,3,5] => [4,2,1,6,3,5] => [3,2,1] => [2,1] => 0
[4,+,1,6,+,3] => [4,2,1,6,5,3] => [2,2,2] => [2,2] => 1
[4,-,1,6,+,3] => [4,2,1,6,5,3] => [2,2,2] => [2,2] => 1
[4,+,1,6,-,3] => [4,2,1,6,5,3] => [2,2,2] => [2,2] => 1
[4,-,1,6,-,3] => [4,2,1,6,5,3] => [2,2,2] => [2,2] => 1
[4,+,+,1,6,5] => [4,2,3,1,6,5] => [3,2,1] => [2,1] => 0
[4,-,+,1,6,5] => [4,2,3,1,6,5] => [3,2,1] => [2,1] => 0
[4,+,-,1,6,5] => [4,2,3,1,6,5] => [3,2,1] => [2,1] => 0
[4,-,-,1,6,5] => [4,2,3,1,6,5] => [3,2,1] => [2,1] => 0
[4,+,+,6,1,5] => [4,2,3,6,1,5] => [3,2,1] => [2,1] => 0
[4,-,+,6,1,5] => [4,2,3,6,1,5] => [3,2,1] => [2,1] => 0
[4,+,-,6,1,5] => [4,2,3,6,1,5] => [3,2,1] => [2,1] => 0
[4,-,-,6,1,5] => [4,2,3,6,1,5] => [3,2,1] => [2,1] => 0
[4,+,+,6,+,1] => [4,2,3,6,5,1] => [3,2,1] => [2,1] => 0
[4,-,+,6,+,1] => [4,2,3,6,5,1] => [3,2,1] => [2,1] => 0
[4,+,-,6,+,1] => [4,2,3,6,5,1] => [3,2,1] => [2,1] => 0
[4,+,+,6,-,1] => [4,2,3,6,5,1] => [3,2,1] => [2,1] => 0
[4,-,-,6,+,1] => [4,2,3,6,5,1] => [3,2,1] => [2,1] => 0
[4,-,+,6,-,1] => [4,2,3,6,5,1] => [3,2,1] => [2,1] => 0
[4,+,-,6,-,1] => [4,2,3,6,5,1] => [3,2,1] => [2,1] => 0
[4,-,-,6,-,1] => [4,2,3,6,5,1] => [3,2,1] => [2,1] => 0
[4,+,5,1,3,+] => [4,2,5,1,3,6] => [3,2,1] => [2,1] => 0
[4,-,5,1,3,+] => [4,2,5,1,3,6] => [3,2,1] => [2,1] => 0
[4,+,5,1,3,-] => [4,2,5,1,3,6] => [3,2,1] => [2,1] => 0
[4,-,5,1,3,-] => [4,2,5,1,3,6] => [3,2,1] => [2,1] => 0
[4,+,5,1,6,3] => [4,2,5,1,6,3] => [3,2,1] => [2,1] => 0
[4,-,5,1,6,3] => [4,2,5,1,6,3] => [3,2,1] => [2,1] => 0
[4,+,5,3,1,+] => [4,2,5,3,1,6] => [3,2,1] => [2,1] => 0
[4,-,5,3,1,+] => [4,2,5,3,1,6] => [3,2,1] => [2,1] => 0
[4,+,5,3,1,-] => [4,2,5,3,1,6] => [3,2,1] => [2,1] => 0
[4,-,5,3,1,-] => [4,2,5,3,1,6] => [3,2,1] => [2,1] => 0
[4,+,5,3,6,1] => [4,2,5,3,6,1] => [3,2,1] => [2,1] => 0
[4,-,5,3,6,1] => [4,2,5,3,6,1] => [3,2,1] => [2,1] => 0
[4,+,5,6,1,3] => [4,2,5,6,1,3] => [3,2,1] => [2,1] => 0
[4,-,5,6,1,3] => [4,2,5,6,1,3] => [3,2,1] => [2,1] => 0
[4,+,5,6,3,1] => [4,2,5,6,3,1] => [3,2,1] => [2,1] => 0
[4,-,5,6,3,1] => [4,2,5,6,3,1] => [3,2,1] => [2,1] => 0
[4,+,6,1,3,5] => [4,2,6,1,3,5] => [3,2,1] => [2,1] => 0
[4,-,6,1,3,5] => [4,2,6,1,3,5] => [3,2,1] => [2,1] => 0
[4,+,6,1,+,3] => [4,2,6,1,5,3] => [2,2,2] => [2,2] => 1
[4,-,6,1,+,3] => [4,2,6,1,5,3] => [2,2,2] => [2,2] => 1
[4,+,6,1,-,3] => [4,2,6,1,5,3] => [2,2,2] => [2,2] => 1
[4,-,6,1,-,3] => [4,2,6,1,5,3] => [2,2,2] => [2,2] => 1
[4,+,6,3,1,5] => [4,2,6,3,1,5] => [3,2,1] => [2,1] => 0
[4,-,6,3,1,5] => [4,2,6,3,1,5] => [3,2,1] => [2,1] => 0
[4,+,6,3,+,1] => [4,2,6,3,5,1] => [3,2,1] => [2,1] => 0
[4,-,6,3,+,1] => [4,2,6,3,5,1] => [3,2,1] => [2,1] => 0
[4,+,6,3,-,1] => [4,2,6,3,5,1] => [3,2,1] => [2,1] => 0
[4,-,6,3,-,1] => [4,2,6,3,5,1] => [3,2,1] => [2,1] => 0
[4,+,6,5,1,3] => [4,2,6,5,1,3] => [2,2,2] => [2,2] => 1
[4,-,6,5,1,3] => [4,2,6,5,1,3] => [2,2,2] => [2,2] => 1
[4,+,6,5,3,1] => [4,2,6,5,3,1] => [2,2,1,1] => [2,1,1] => 0
[4,-,6,5,3,1] => [4,2,6,5,3,1] => [2,2,1,1] => [2,1,1] => 0
[4,3,1,2,6,5] => [4,3,1,2,6,5] => [3,2,1] => [2,1] => 0
[4,3,1,5,2,+] => [4,3,1,5,2,6] => [3,2,1] => [2,1] => 0
[4,3,1,5,2,-] => [4,3,1,5,2,6] => [3,2,1] => [2,1] => 0
[4,3,1,5,6,2] => [4,3,1,5,6,2] => [3,2,1] => [2,1] => 0
[4,3,1,6,2,5] => [4,3,1,6,2,5] => [3,2,1] => [2,1] => 0
[4,3,1,6,+,2] => [4,3,1,6,5,2] => [2,2,2] => [2,2] => 1
[4,3,1,6,-,2] => [4,3,1,6,5,2] => [2,2,2] => [2,2] => 1
[4,3,2,1,+,+] => [4,3,2,1,5,6] => [3,1,1,1] => [1,1,1] => 0
[4,3,2,1,-,+] => [4,3,2,1,5,6] => [3,1,1,1] => [1,1,1] => 0
[4,3,2,1,+,-] => [4,3,2,1,5,6] => [3,1,1,1] => [1,1,1] => 0
[4,3,2,1,-,-] => [4,3,2,1,5,6] => [3,1,1,1] => [1,1,1] => 0
[4,3,2,1,6,5] => [4,3,2,1,6,5] => [2,2,1,1] => [2,1,1] => 0
[4,3,2,5,1,+] => [4,3,2,5,1,6] => [3,1,1,1] => [1,1,1] => 0
[4,3,2,5,1,-] => [4,3,2,5,1,6] => [3,1,1,1] => [1,1,1] => 0
[4,3,2,5,6,1] => [4,3,2,5,6,1] => [3,1,1,1] => [1,1,1] => 0
[4,3,2,6,1,5] => [4,3,2,6,1,5] => [2,2,1,1] => [2,1,1] => 0
[4,3,2,6,+,1] => [4,3,2,6,5,1] => [2,2,1,1] => [2,1,1] => 0
[4,3,2,6,-,1] => [4,3,2,6,5,1] => [2,2,1,1] => [2,1,1] => 0
[4,3,5,1,2,+] => [4,3,5,1,2,6] => [3,2,1] => [2,1] => 0
[4,3,5,1,2,-] => [4,3,5,1,2,6] => [3,2,1] => [2,1] => 0
[4,3,5,1,6,2] => [4,3,5,1,6,2] => [3,2,1] => [2,1] => 0
[4,3,5,2,1,+] => [4,3,5,2,1,6] => [3,1,1,1] => [1,1,1] => 0
[4,3,5,2,1,-] => [4,3,5,2,1,6] => [3,1,1,1] => [1,1,1] => 0
[4,3,5,2,6,1] => [4,3,5,2,6,1] => [3,1,1,1] => [1,1,1] => 0
[4,3,5,6,1,2] => [4,3,5,6,1,2] => [3,2,1] => [2,1] => 0
[4,3,5,6,2,1] => [4,3,5,6,2,1] => [3,1,1,1] => [1,1,1] => 0
[4,3,6,1,2,5] => [4,3,6,1,2,5] => [3,2,1] => [2,1] => 0
[4,3,6,1,+,2] => [4,3,6,1,5,2] => [2,2,2] => [2,2] => 1
[4,3,6,1,-,2] => [4,3,6,1,5,2] => [2,2,2] => [2,2] => 1
[4,3,6,2,1,5] => [4,3,6,2,1,5] => [2,2,1,1] => [2,1,1] => 0
[4,3,6,2,+,1] => [4,3,6,2,5,1] => [2,2,1,1] => [2,1,1] => 0
[4,3,6,2,-,1] => [4,3,6,2,5,1] => [2,2,1,1] => [2,1,1] => 0
[4,3,6,5,1,2] => [4,3,6,5,1,2] => [2,2,2] => [2,2] => 1
[4,3,6,5,2,1] => [4,3,6,5,2,1] => [2,2,1,1] => [2,1,1] => 0
[4,5,1,2,6,3] => [4,5,1,2,6,3] => [3,3] => [3] => 1
[4,5,1,3,2,+] => [4,5,1,3,2,6] => [3,2,1] => [2,1] => 0
[4,5,1,3,2,-] => [4,5,1,3,2,6] => [3,2,1] => [2,1] => 0
[4,5,1,3,6,2] => [4,5,1,3,6,2] => [3,2,1] => [2,1] => 0
[4,5,1,6,2,3] => [4,5,1,6,2,3] => [3,3] => [3] => 1
[4,5,1,6,3,2] => [4,5,1,6,3,2] => [3,2,1] => [2,1] => 0
[4,5,2,1,3,+] => [4,5,2,1,3,6] => [3,2,1] => [2,1] => 0
[4,5,2,1,3,-] => [4,5,2,1,3,6] => [3,2,1] => [2,1] => 0
[4,5,2,1,6,3] => [4,5,2,1,6,3] => [3,2,1] => [2,1] => 0
[4,5,2,3,1,+] => [4,5,2,3,1,6] => [3,2,1] => [2,1] => 0
[4,5,2,3,1,-] => [4,5,2,3,1,6] => [3,2,1] => [2,1] => 0
[4,5,2,3,6,1] => [4,5,2,3,6,1] => [3,2,1] => [2,1] => 0
[4,5,2,6,1,3] => [4,5,2,6,1,3] => [3,2,1] => [2,1] => 0
[4,5,2,6,3,1] => [4,5,2,6,3,1] => [3,2,1] => [2,1] => 0
[4,5,+,1,2,+] => [4,5,3,1,2,6] => [3,2,1] => [2,1] => 0
[4,5,-,1,2,+] => [4,5,3,1,2,6] => [3,2,1] => [2,1] => 0
[4,5,+,1,2,-] => [4,5,3,1,2,6] => [3,2,1] => [2,1] => 0
[4,5,-,1,2,-] => [4,5,3,1,2,6] => [3,2,1] => [2,1] => 0
[4,5,+,1,6,2] => [4,5,3,1,6,2] => [3,2,1] => [2,1] => 0
[4,5,-,1,6,2] => [4,5,3,1,6,2] => [3,2,1] => [2,1] => 0
[4,5,+,2,1,+] => [4,5,3,2,1,6] => [3,1,1,1] => [1,1,1] => 0
[4,5,-,2,1,+] => [4,5,3,2,1,6] => [3,1,1,1] => [1,1,1] => 0
[4,5,+,2,1,-] => [4,5,3,2,1,6] => [3,1,1,1] => [1,1,1] => 0
[4,5,-,2,1,-] => [4,5,3,2,1,6] => [3,1,1,1] => [1,1,1] => 0
[4,5,+,2,6,1] => [4,5,3,2,6,1] => [3,1,1,1] => [1,1,1] => 0
[4,5,-,2,6,1] => [4,5,3,2,6,1] => [3,1,1,1] => [1,1,1] => 0
[4,5,+,6,1,2] => [4,5,3,6,1,2] => [3,2,1] => [2,1] => 0
[4,5,-,6,1,2] => [4,5,3,6,1,2] => [3,2,1] => [2,1] => 0
[4,5,+,6,2,1] => [4,5,3,6,2,1] => [3,1,1,1] => [1,1,1] => 0
[4,5,-,6,2,1] => [4,5,3,6,2,1] => [3,1,1,1] => [1,1,1] => 0
[4,5,6,1,2,3] => [4,5,6,1,2,3] => [3,3] => [3] => 1
[4,5,6,1,3,2] => [4,5,6,1,3,2] => [3,2,1] => [2,1] => 0
[4,5,6,2,1,3] => [4,5,6,2,1,3] => [3,2,1] => [2,1] => 0
[4,5,6,2,3,1] => [4,5,6,2,3,1] => [3,2,1] => [2,1] => 0
[4,5,6,3,1,2] => [4,5,6,3,1,2] => [3,2,1] => [2,1] => 0
[4,5,6,3,2,1] => [4,5,6,3,2,1] => [3,1,1,1] => [1,1,1] => 0
[4,6,1,2,+,3] => [4,6,1,2,5,3] => [3,2,1] => [2,1] => 0
[4,6,1,2,-,3] => [4,6,1,2,5,3] => [3,2,1] => [2,1] => 0
[4,6,1,3,2,5] => [4,6,1,3,2,5] => [3,2,1] => [2,1] => 0
[4,6,1,3,+,2] => [4,6,1,3,5,2] => [3,2,1] => [2,1] => 0
[4,6,1,3,-,2] => [4,6,1,3,5,2] => [3,2,1] => [2,1] => 0
[4,6,1,5,2,3] => [4,6,1,5,2,3] => [3,2,1] => [2,1] => 0
[4,6,1,5,3,2] => [4,6,1,5,3,2] => [2,2,1,1] => [2,1,1] => 0
[4,6,2,1,3,5] => [4,6,2,1,3,5] => [3,2,1] => [2,1] => 0
[4,6,2,1,+,3] => [4,6,2,1,5,3] => [2,2,2] => [2,2] => 1
[4,6,2,1,-,3] => [4,6,2,1,5,3] => [2,2,2] => [2,2] => 1
[4,6,2,3,1,5] => [4,6,2,3,1,5] => [3,2,1] => [2,1] => 0
[4,6,2,3,+,1] => [4,6,2,3,5,1] => [3,2,1] => [2,1] => 0
[4,6,2,3,-,1] => [4,6,2,3,5,1] => [3,2,1] => [2,1] => 0
[4,6,2,5,1,3] => [4,6,2,5,1,3] => [2,2,2] => [2,2] => 1
[4,6,2,5,3,1] => [4,6,2,5,3,1] => [2,2,1,1] => [2,1,1] => 0
[4,6,+,1,2,5] => [4,6,3,1,2,5] => [3,2,1] => [2,1] => 0
[4,6,-,1,2,5] => [4,6,3,1,2,5] => [3,2,1] => [2,1] => 0
[4,6,+,1,+,2] => [4,6,3,1,5,2] => [2,2,2] => [2,2] => 1
[4,6,-,1,+,2] => [4,6,3,1,5,2] => [2,2,2] => [2,2] => 1
[4,6,+,1,-,2] => [4,6,3,1,5,2] => [2,2,2] => [2,2] => 1
[4,6,-,1,-,2] => [4,6,3,1,5,2] => [2,2,2] => [2,2] => 1
[4,6,+,2,1,5] => [4,6,3,2,1,5] => [2,2,1,1] => [2,1,1] => 0
[4,6,-,2,1,5] => [4,6,3,2,1,5] => [2,2,1,1] => [2,1,1] => 0
[4,6,+,2,+,1] => [4,6,3,2,5,1] => [2,2,1,1] => [2,1,1] => 0
[4,6,-,2,+,1] => [4,6,3,2,5,1] => [2,2,1,1] => [2,1,1] => 0
[4,6,+,2,-,1] => [4,6,3,2,5,1] => [2,2,1,1] => [2,1,1] => 0
[4,6,-,2,-,1] => [4,6,3,2,5,1] => [2,2,1,1] => [2,1,1] => 0
[4,6,+,5,1,2] => [4,6,3,5,1,2] => [2,2,2] => [2,2] => 1
[4,6,-,5,1,2] => [4,6,3,5,1,2] => [2,2,2] => [2,2] => 1
[4,6,+,5,2,1] => [4,6,3,5,2,1] => [2,2,1,1] => [2,1,1] => 0
[4,6,-,5,2,1] => [4,6,3,5,2,1] => [2,2,1,1] => [2,1,1] => 0
[4,6,5,1,2,3] => [4,6,5,1,2,3] => [3,2,1] => [2,1] => 0
[4,6,5,1,3,2] => [4,6,5,1,3,2] => [2,2,1,1] => [2,1,1] => 0
[4,6,5,2,1,3] => [4,6,5,2,1,3] => [2,2,1,1] => [2,1,1] => 0
[4,6,5,2,3,1] => [4,6,5,2,3,1] => [2,2,1,1] => [2,1,1] => 0
[4,6,5,3,1,2] => [4,6,5,3,1,2] => [2,2,1,1] => [2,1,1] => 0
[4,6,5,3,2,1] => [4,6,5,3,2,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[5,1,2,6,4,3] => [5,1,2,6,4,3] => [3,2,1] => [2,1] => 0
[5,1,+,2,6,4] => [5,1,3,2,6,4] => [3,2,1] => [2,1] => 0
[5,1,-,2,6,4] => [5,1,3,2,6,4] => [3,2,1] => [2,1] => 0
[5,1,+,6,2,4] => [5,1,3,6,2,4] => [3,2,1] => [2,1] => 0
[5,1,-,6,2,4] => [5,1,3,6,2,4] => [3,2,1] => [2,1] => 0
[5,1,+,6,4,2] => [5,1,3,6,4,2] => [3,2,1] => [2,1] => 0
[5,1,-,6,4,2] => [5,1,3,6,4,2] => [3,2,1] => [2,1] => 0
[5,1,4,2,6,3] => [5,1,4,2,6,3] => [3,2,1] => [2,1] => 0
[5,1,4,3,2,+] => [5,1,4,3,2,6] => [3,1,1,1] => [1,1,1] => 0
[5,1,4,3,2,-] => [5,1,4,3,2,6] => [3,1,1,1] => [1,1,1] => 0
[5,1,4,3,6,2] => [5,1,4,3,6,2] => [3,1,1,1] => [1,1,1] => 0
[5,1,4,6,2,3] => [5,1,4,6,2,3] => [3,2,1] => [2,1] => 0
[5,1,4,6,3,2] => [5,1,4,6,3,2] => [3,1,1,1] => [1,1,1] => 0
[5,1,6,2,4,3] => [5,1,6,2,4,3] => [3,2,1] => [2,1] => 0
[5,1,6,3,2,4] => [5,1,6,3,2,4] => [3,2,1] => [2,1] => 0
[5,1,6,3,4,2] => [5,1,6,3,4,2] => [3,2,1] => [2,1] => 0
[5,1,6,+,2,3] => [5,1,6,4,2,3] => [3,2,1] => [2,1] => 0
[5,1,6,-,2,3] => [5,1,6,4,2,3] => [3,2,1] => [2,1] => 0
[5,1,6,+,3,2] => [5,1,6,4,3,2] => [2,2,1,1] => [2,1,1] => 0
[5,1,6,-,3,2] => [5,1,6,4,3,2] => [2,2,1,1] => [2,1,1] => 0
[5,+,1,3,6,4] => [5,2,1,3,6,4] => [3,2,1] => [2,1] => 0
[5,-,1,3,6,4] => [5,2,1,3,6,4] => [3,2,1] => [2,1] => 0
[5,+,1,+,3,+] => [5,2,1,4,3,6] => [3,2,1] => [2,1] => 0
[5,-,1,+,3,+] => [5,2,1,4,3,6] => [3,2,1] => [2,1] => 0
[5,+,1,-,3,+] => [5,2,1,4,3,6] => [3,2,1] => [2,1] => 0
[5,+,1,+,3,-] => [5,2,1,4,3,6] => [3,2,1] => [2,1] => 0
[5,-,1,-,3,+] => [5,2,1,4,3,6] => [3,2,1] => [2,1] => 0
[5,-,1,+,3,-] => [5,2,1,4,3,6] => [3,2,1] => [2,1] => 0
[5,+,1,-,3,-] => [5,2,1,4,3,6] => [3,2,1] => [2,1] => 0
[5,-,1,-,3,-] => [5,2,1,4,3,6] => [3,2,1] => [2,1] => 0
[5,+,1,+,6,3] => [5,2,1,4,6,3] => [3,2,1] => [2,1] => 0
[5,-,1,+,6,3] => [5,2,1,4,6,3] => [3,2,1] => [2,1] => 0
[5,+,1,-,6,3] => [5,2,1,4,6,3] => [3,2,1] => [2,1] => 0
[5,-,1,-,6,3] => [5,2,1,4,6,3] => [3,2,1] => [2,1] => 0
[5,+,1,6,3,4] => [5,2,1,6,3,4] => [3,2,1] => [2,1] => 0
[5,-,1,6,3,4] => [5,2,1,6,3,4] => [3,2,1] => [2,1] => 0
[5,+,1,6,4,3] => [5,2,1,6,4,3] => [2,2,2] => [2,2] => 1
[5,-,1,6,4,3] => [5,2,1,6,4,3] => [2,2,2] => [2,2] => 1
[5,+,+,1,6,4] => [5,2,3,1,6,4] => [3,2,1] => [2,1] => 0
[5,-,+,1,6,4] => [5,2,3,1,6,4] => [3,2,1] => [2,1] => 0
[5,+,-,1,6,4] => [5,2,3,1,6,4] => [3,2,1] => [2,1] => 0
[5,-,-,1,6,4] => [5,2,3,1,6,4] => [3,2,1] => [2,1] => 0
[5,+,+,6,1,4] => [5,2,3,6,1,4] => [3,2,1] => [2,1] => 0
[5,-,+,6,1,4] => [5,2,3,6,1,4] => [3,2,1] => [2,1] => 0
[5,+,-,6,1,4] => [5,2,3,6,1,4] => [3,2,1] => [2,1] => 0
[5,-,-,6,1,4] => [5,2,3,6,1,4] => [3,2,1] => [2,1] => 0
[5,+,+,6,4,1] => [5,2,3,6,4,1] => [3,2,1] => [2,1] => 0
[5,-,+,6,4,1] => [5,2,3,6,4,1] => [3,2,1] => [2,1] => 0
[5,+,-,6,4,1] => [5,2,3,6,4,1] => [3,2,1] => [2,1] => 0
[5,-,-,6,4,1] => [5,2,3,6,4,1] => [3,2,1] => [2,1] => 0
[5,+,4,1,3,+] => [5,2,4,1,3,6] => [3,2,1] => [2,1] => 0
[5,-,4,1,3,+] => [5,2,4,1,3,6] => [3,2,1] => [2,1] => 0
[5,+,4,1,3,-] => [5,2,4,1,3,6] => [3,2,1] => [2,1] => 0
[5,-,4,1,3,-] => [5,2,4,1,3,6] => [3,2,1] => [2,1] => 0
[5,+,4,1,6,3] => [5,2,4,1,6,3] => [3,2,1] => [2,1] => 0
[5,-,4,1,6,3] => [5,2,4,1,6,3] => [3,2,1] => [2,1] => 0
[5,+,4,3,1,+] => [5,2,4,3,1,6] => [3,1,1,1] => [1,1,1] => 0
[5,-,4,3,1,+] => [5,2,4,3,1,6] => [3,1,1,1] => [1,1,1] => 0
[5,+,4,3,1,-] => [5,2,4,3,1,6] => [3,1,1,1] => [1,1,1] => 0
[5,-,4,3,1,-] => [5,2,4,3,1,6] => [3,1,1,1] => [1,1,1] => 0
[5,+,4,3,6,1] => [5,2,4,3,6,1] => [3,1,1,1] => [1,1,1] => 0
[5,-,4,3,6,1] => [5,2,4,3,6,1] => [3,1,1,1] => [1,1,1] => 0
[5,+,4,6,1,3] => [5,2,4,6,1,3] => [3,2,1] => [2,1] => 0
[5,-,4,6,1,3] => [5,2,4,6,1,3] => [3,2,1] => [2,1] => 0
[5,+,4,6,3,1] => [5,2,4,6,3,1] => [3,1,1,1] => [1,1,1] => 0
[5,-,4,6,3,1] => [5,2,4,6,3,1] => [3,1,1,1] => [1,1,1] => 0
[5,+,6,1,3,4] => [5,2,6,1,3,4] => [3,2,1] => [2,1] => 0
[5,-,6,1,3,4] => [5,2,6,1,3,4] => [3,2,1] => [2,1] => 0
[5,+,6,1,4,3] => [5,2,6,1,4,3] => [2,2,2] => [2,2] => 1
[5,-,6,1,4,3] => [5,2,6,1,4,3] => [2,2,2] => [2,2] => 1
[5,+,6,3,1,4] => [5,2,6,3,1,4] => [3,2,1] => [2,1] => 0
[5,-,6,3,1,4] => [5,2,6,3,1,4] => [3,2,1] => [2,1] => 0
[5,+,6,3,4,1] => [5,2,6,3,4,1] => [3,2,1] => [2,1] => 0
[5,-,6,3,4,1] => [5,2,6,3,4,1] => [3,2,1] => [2,1] => 0
[5,+,6,+,1,3] => [5,2,6,4,1,3] => [2,2,2] => [2,2] => 1
[5,-,6,+,1,3] => [5,2,6,4,1,3] => [2,2,2] => [2,2] => 1
[5,+,6,-,1,3] => [5,2,6,4,1,3] => [2,2,2] => [2,2] => 1
[5,-,6,-,1,3] => [5,2,6,4,1,3] => [2,2,2] => [2,2] => 1
[5,+,6,+,3,1] => [5,2,6,4,3,1] => [2,2,1,1] => [2,1,1] => 0
[5,-,6,+,3,1] => [5,2,6,4,3,1] => [2,2,1,1] => [2,1,1] => 0
[5,+,6,-,3,1] => [5,2,6,4,3,1] => [2,2,1,1] => [2,1,1] => 0
[5,-,6,-,3,1] => [5,2,6,4,3,1] => [2,2,1,1] => [2,1,1] => 0
[5,3,1,2,6,4] => [5,3,1,2,6,4] => [3,2,1] => [2,1] => 0
[5,3,1,+,2,+] => [5,3,1,4,2,6] => [3,2,1] => [2,1] => 0
[5,3,1,-,2,+] => [5,3,1,4,2,6] => [3,2,1] => [2,1] => 0
[5,3,1,+,2,-] => [5,3,1,4,2,6] => [3,2,1] => [2,1] => 0
[5,3,1,-,2,-] => [5,3,1,4,2,6] => [3,2,1] => [2,1] => 0
[5,3,1,+,6,2] => [5,3,1,4,6,2] => [3,2,1] => [2,1] => 0
[5,3,1,-,6,2] => [5,3,1,4,6,2] => [3,2,1] => [2,1] => 0
[5,3,1,6,2,4] => [5,3,1,6,2,4] => [3,2,1] => [2,1] => 0
[5,3,1,6,4,2] => [5,3,1,6,4,2] => [2,2,2] => [2,2] => 1
[5,3,2,1,4,+] => [5,3,2,1,4,6] => [3,1,1,1] => [1,1,1] => 0
[5,3,2,1,4,-] => [5,3,2,1,4,6] => [3,1,1,1] => [1,1,1] => 0
[5,3,2,1,6,4] => [5,3,2,1,6,4] => [2,2,1,1] => [2,1,1] => 0
[5,3,2,+,1,+] => [5,3,2,4,1,6] => [3,1,1,1] => [1,1,1] => 0
[5,3,2,-,1,+] => [5,3,2,4,1,6] => [3,1,1,1] => [1,1,1] => 0
[5,3,2,+,1,-] => [5,3,2,4,1,6] => [3,1,1,1] => [1,1,1] => 0
[5,3,2,-,1,-] => [5,3,2,4,1,6] => [3,1,1,1] => [1,1,1] => 0
[5,3,2,+,6,1] => [5,3,2,4,6,1] => [3,1,1,1] => [1,1,1] => 0
[5,3,2,-,6,1] => [5,3,2,4,6,1] => [3,1,1,1] => [1,1,1] => 0
[5,3,2,6,1,4] => [5,3,2,6,1,4] => [2,2,1,1] => [2,1,1] => 0
[5,3,2,6,4,1] => [5,3,2,6,4,1] => [2,2,1,1] => [2,1,1] => 0
[5,3,4,1,2,+] => [5,3,4,1,2,6] => [3,2,1] => [2,1] => 0
[5,3,4,1,2,-] => [5,3,4,1,2,6] => [3,2,1] => [2,1] => 0
[5,3,4,1,6,2] => [5,3,4,1,6,2] => [3,2,1] => [2,1] => 0
[5,3,4,2,1,+] => [5,3,4,2,1,6] => [3,1,1,1] => [1,1,1] => 0
[5,3,4,2,1,-] => [5,3,4,2,1,6] => [3,1,1,1] => [1,1,1] => 0
[5,3,4,2,6,1] => [5,3,4,2,6,1] => [3,1,1,1] => [1,1,1] => 0
[5,3,4,6,1,2] => [5,3,4,6,1,2] => [3,2,1] => [2,1] => 0
[5,3,4,6,2,1] => [5,3,4,6,2,1] => [3,1,1,1] => [1,1,1] => 0
[5,3,6,1,2,4] => [5,3,6,1,2,4] => [3,2,1] => [2,1] => 0
[5,3,6,1,4,2] => [5,3,6,1,4,2] => [2,2,2] => [2,2] => 1
[5,3,6,2,1,4] => [5,3,6,2,1,4] => [2,2,1,1] => [2,1,1] => 0
[5,3,6,2,4,1] => [5,3,6,2,4,1] => [2,2,1,1] => [2,1,1] => 0
[5,3,6,+,1,2] => [5,3,6,4,1,2] => [2,2,2] => [2,2] => 1
[5,3,6,-,1,2] => [5,3,6,4,1,2] => [2,2,2] => [2,2] => 1
[5,3,6,+,2,1] => [5,3,6,4,2,1] => [2,2,1,1] => [2,1,1] => 0
[5,3,6,-,2,1] => [5,3,6,4,2,1] => [2,2,1,1] => [2,1,1] => 0
[5,4,1,2,6,3] => [5,4,1,2,6,3] => [3,2,1] => [2,1] => 0
[5,4,1,3,2,+] => [5,4,1,3,2,6] => [3,1,1,1] => [1,1,1] => 0
[5,4,1,3,2,-] => [5,4,1,3,2,6] => [3,1,1,1] => [1,1,1] => 0
[5,4,1,3,6,2] => [5,4,1,3,6,2] => [3,1,1,1] => [1,1,1] => 0
[5,4,1,6,2,3] => [5,4,1,6,2,3] => [3,2,1] => [2,1] => 0
[5,4,1,6,3,2] => [5,4,1,6,3,2] => [2,2,1,1] => [2,1,1] => 0
[5,4,2,1,3,+] => [5,4,2,1,3,6] => [3,1,1,1] => [1,1,1] => 0
[5,4,2,1,3,-] => [5,4,2,1,3,6] => [3,1,1,1] => [1,1,1] => 0
[5,4,2,1,6,3] => [5,4,2,1,6,3] => [2,2,1,1] => [2,1,1] => 0
[5,4,2,3,1,+] => [5,4,2,3,1,6] => [3,1,1,1] => [1,1,1] => 0
[5,4,2,3,1,-] => [5,4,2,3,1,6] => [3,1,1,1] => [1,1,1] => 0
[5,4,2,3,6,1] => [5,4,2,3,6,1] => [3,1,1,1] => [1,1,1] => 0
[5,4,2,6,1,3] => [5,4,2,6,1,3] => [2,2,1,1] => [2,1,1] => 0
[5,4,2,6,3,1] => [5,4,2,6,3,1] => [2,2,1,1] => [2,1,1] => 0
[5,4,+,1,2,+] => [5,4,3,1,2,6] => [3,1,1,1] => [1,1,1] => 0
[5,4,-,1,2,+] => [5,4,3,1,2,6] => [3,1,1,1] => [1,1,1] => 0
[5,4,+,1,2,-] => [5,4,3,1,2,6] => [3,1,1,1] => [1,1,1] => 0
[5,4,-,1,2,-] => [5,4,3,1,2,6] => [3,1,1,1] => [1,1,1] => 0
[5,4,+,1,6,2] => [5,4,3,1,6,2] => [2,2,1,1] => [2,1,1] => 0
[5,4,-,1,6,2] => [5,4,3,1,6,2] => [2,2,1,1] => [2,1,1] => 0
[5,4,+,2,1,+] => [5,4,3,2,1,6] => [2,1,1,1,1] => [1,1,1,1] => 0
[5,4,-,2,1,+] => [5,4,3,2,1,6] => [2,1,1,1,1] => [1,1,1,1] => 0
[5,4,+,2,1,-] => [5,4,3,2,1,6] => [2,1,1,1,1] => [1,1,1,1] => 0
[5,4,-,2,1,-] => [5,4,3,2,1,6] => [2,1,1,1,1] => [1,1,1,1] => 0
[5,4,+,2,6,1] => [5,4,3,2,6,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[5,4,-,2,6,1] => [5,4,3,2,6,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[5,4,+,6,1,2] => [5,4,3,6,1,2] => [2,2,1,1] => [2,1,1] => 0
[5,4,-,6,1,2] => [5,4,3,6,1,2] => [2,2,1,1] => [2,1,1] => 0
[5,4,+,6,2,1] => [5,4,3,6,2,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[5,4,-,6,2,1] => [5,4,3,6,2,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[5,4,6,1,2,3] => [5,4,6,1,2,3] => [3,2,1] => [2,1] => 0
[5,4,6,1,3,2] => [5,4,6,1,3,2] => [2,2,1,1] => [2,1,1] => 0
[5,4,6,2,1,3] => [5,4,6,2,1,3] => [2,2,1,1] => [2,1,1] => 0
[5,4,6,2,3,1] => [5,4,6,2,3,1] => [2,2,1,1] => [2,1,1] => 0
[5,4,6,3,1,2] => [5,4,6,3,1,2] => [2,2,1,1] => [2,1,1] => 0
[5,4,6,3,2,1] => [5,4,6,3,2,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[5,6,1,2,4,3] => [5,6,1,2,4,3] => [3,2,1] => [2,1] => 0
[5,6,1,3,2,4] => [5,6,1,3,2,4] => [3,2,1] => [2,1] => 0
[5,6,1,3,4,2] => [5,6,1,3,4,2] => [3,2,1] => [2,1] => 0
[5,6,1,+,2,3] => [5,6,1,4,2,3] => [3,2,1] => [2,1] => 0
[5,6,1,-,2,3] => [5,6,1,4,2,3] => [3,2,1] => [2,1] => 0
[5,6,1,+,3,2] => [5,6,1,4,3,2] => [2,2,1,1] => [2,1,1] => 0
[5,6,1,-,3,2] => [5,6,1,4,3,2] => [2,2,1,1] => [2,1,1] => 0
[5,6,2,1,3,4] => [5,6,2,1,3,4] => [3,2,1] => [2,1] => 0
[5,6,2,1,4,3] => [5,6,2,1,4,3] => [2,2,2] => [2,2] => 1
[5,6,2,3,1,4] => [5,6,2,3,1,4] => [3,2,1] => [2,1] => 0
[5,6,2,3,4,1] => [5,6,2,3,4,1] => [3,2,1] => [2,1] => 0
[5,6,2,+,1,3] => [5,6,2,4,1,3] => [2,2,2] => [2,2] => 1
[5,6,2,-,1,3] => [5,6,2,4,1,3] => [2,2,2] => [2,2] => 1
[5,6,2,+,3,1] => [5,6,2,4,3,1] => [2,2,1,1] => [2,1,1] => 0
[5,6,2,-,3,1] => [5,6,2,4,3,1] => [2,2,1,1] => [2,1,1] => 0
[5,6,+,1,2,4] => [5,6,3,1,2,4] => [3,2,1] => [2,1] => 0
[5,6,-,1,2,4] => [5,6,3,1,2,4] => [3,2,1] => [2,1] => 0
[5,6,+,1,4,2] => [5,6,3,1,4,2] => [2,2,2] => [2,2] => 1
[5,6,-,1,4,2] => [5,6,3,1,4,2] => [2,2,2] => [2,2] => 1
[5,6,+,2,1,4] => [5,6,3,2,1,4] => [2,2,1,1] => [2,1,1] => 0
[5,6,-,2,1,4] => [5,6,3,2,1,4] => [2,2,1,1] => [2,1,1] => 0
[5,6,+,2,4,1] => [5,6,3,2,4,1] => [2,2,1,1] => [2,1,1] => 0
[5,6,-,2,4,1] => [5,6,3,2,4,1] => [2,2,1,1] => [2,1,1] => 0
[5,6,+,+,1,2] => [5,6,3,4,1,2] => [2,2,2] => [2,2] => 1
[5,6,-,+,1,2] => [5,6,3,4,1,2] => [2,2,2] => [2,2] => 1
[5,6,+,-,1,2] => [5,6,3,4,1,2] => [2,2,2] => [2,2] => 1
[5,6,-,-,1,2] => [5,6,3,4,1,2] => [2,2,2] => [2,2] => 1
[5,6,+,+,2,1] => [5,6,3,4,2,1] => [2,2,1,1] => [2,1,1] => 0
[5,6,-,+,2,1] => [5,6,3,4,2,1] => [2,2,1,1] => [2,1,1] => 0
[5,6,+,-,2,1] => [5,6,3,4,2,1] => [2,2,1,1] => [2,1,1] => 0
[5,6,-,-,2,1] => [5,6,3,4,2,1] => [2,2,1,1] => [2,1,1] => 0
[5,6,4,1,2,3] => [5,6,4,1,2,3] => [3,2,1] => [2,1] => 0
[5,6,4,1,3,2] => [5,6,4,1,3,2] => [2,2,1,1] => [2,1,1] => 0
[5,6,4,2,1,3] => [5,6,4,2,1,3] => [2,2,1,1] => [2,1,1] => 0
[5,6,4,2,3,1] => [5,6,4,2,3,1] => [2,2,1,1] => [2,1,1] => 0
[5,6,4,3,1,2] => [5,6,4,3,1,2] => [2,2,1,1] => [2,1,1] => 0
[5,6,4,3,2,1] => [5,6,4,3,2,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,1,2,5,4,3] => [6,1,2,5,4,3] => [3,1,1,1] => [1,1,1] => 0
[6,1,+,2,+,4] => [6,1,3,2,5,4] => [3,2,1] => [2,1] => 0
[6,1,-,2,+,4] => [6,1,3,2,5,4] => [3,2,1] => [2,1] => 0
[6,1,+,2,-,4] => [6,1,3,2,5,4] => [3,2,1] => [2,1] => 0
[6,1,-,2,-,4] => [6,1,3,2,5,4] => [3,2,1] => [2,1] => 0
[6,1,+,5,2,4] => [6,1,3,5,2,4] => [3,2,1] => [2,1] => 0
[6,1,-,5,2,4] => [6,1,3,5,2,4] => [3,2,1] => [2,1] => 0
[6,1,+,5,4,2] => [6,1,3,5,4,2] => [3,1,1,1] => [1,1,1] => 0
[6,1,-,5,4,2] => [6,1,3,5,4,2] => [3,1,1,1] => [1,1,1] => 0
[6,1,4,2,+,3] => [6,1,4,2,5,3] => [3,2,1] => [2,1] => 0
[6,1,4,2,-,3] => [6,1,4,2,5,3] => [3,2,1] => [2,1] => 0
[6,1,4,3,2,5] => [6,1,4,3,2,5] => [3,1,1,1] => [1,1,1] => 0
[6,1,4,3,+,2] => [6,1,4,3,5,2] => [3,1,1,1] => [1,1,1] => 0
[6,1,4,3,-,2] => [6,1,4,3,5,2] => [3,1,1,1] => [1,1,1] => 0
[6,1,4,5,2,3] => [6,1,4,5,2,3] => [3,2,1] => [2,1] => 0
[6,1,4,5,3,2] => [6,1,4,5,3,2] => [3,1,1,1] => [1,1,1] => 0
[6,1,5,2,4,3] => [6,1,5,2,4,3] => [3,1,1,1] => [1,1,1] => 0
[6,1,5,3,2,4] => [6,1,5,3,2,4] => [3,1,1,1] => [1,1,1] => 0
[6,1,5,3,4,2] => [6,1,5,3,4,2] => [3,1,1,1] => [1,1,1] => 0
[6,1,5,+,2,3] => [6,1,5,4,2,3] => [3,1,1,1] => [1,1,1] => 0
[6,1,5,-,2,3] => [6,1,5,4,2,3] => [3,1,1,1] => [1,1,1] => 0
[6,1,5,+,3,2] => [6,1,5,4,3,2] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,1,5,-,3,2] => [6,1,5,4,3,2] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,+,1,3,+,4] => [6,2,1,3,5,4] => [3,2,1] => [2,1] => 0
[6,-,1,3,+,4] => [6,2,1,3,5,4] => [3,2,1] => [2,1] => 0
[6,+,1,3,-,4] => [6,2,1,3,5,4] => [3,2,1] => [2,1] => 0
[6,-,1,3,-,4] => [6,2,1,3,5,4] => [3,2,1] => [2,1] => 0
[6,+,1,+,3,5] => [6,2,1,4,3,5] => [3,2,1] => [2,1] => 0
[6,-,1,+,3,5] => [6,2,1,4,3,5] => [3,2,1] => [2,1] => 0
[6,+,1,-,3,5] => [6,2,1,4,3,5] => [3,2,1] => [2,1] => 0
[6,-,1,-,3,5] => [6,2,1,4,3,5] => [3,2,1] => [2,1] => 0
[6,+,1,+,+,3] => [6,2,1,4,5,3] => [3,2,1] => [2,1] => 0
[6,-,1,+,+,3] => [6,2,1,4,5,3] => [3,2,1] => [2,1] => 0
[6,+,1,-,+,3] => [6,2,1,4,5,3] => [3,2,1] => [2,1] => 0
[6,+,1,+,-,3] => [6,2,1,4,5,3] => [3,2,1] => [2,1] => 0
[6,-,1,-,+,3] => [6,2,1,4,5,3] => [3,2,1] => [2,1] => 0
[6,-,1,+,-,3] => [6,2,1,4,5,3] => [3,2,1] => [2,1] => 0
[6,+,1,-,-,3] => [6,2,1,4,5,3] => [3,2,1] => [2,1] => 0
[6,-,1,-,-,3] => [6,2,1,4,5,3] => [3,2,1] => [2,1] => 0
[6,+,1,5,3,4] => [6,2,1,5,3,4] => [3,2,1] => [2,1] => 0
[6,-,1,5,3,4] => [6,2,1,5,3,4] => [3,2,1] => [2,1] => 0
[6,+,1,5,4,3] => [6,2,1,5,4,3] => [2,2,1,1] => [2,1,1] => 0
[6,-,1,5,4,3] => [6,2,1,5,4,3] => [2,2,1,1] => [2,1,1] => 0
[6,+,+,1,+,4] => [6,2,3,1,5,4] => [3,2,1] => [2,1] => 0
[6,-,+,1,+,4] => [6,2,3,1,5,4] => [3,2,1] => [2,1] => 0
[6,+,-,1,+,4] => [6,2,3,1,5,4] => [3,2,1] => [2,1] => 0
[6,+,+,1,-,4] => [6,2,3,1,5,4] => [3,2,1] => [2,1] => 0
[6,-,-,1,+,4] => [6,2,3,1,5,4] => [3,2,1] => [2,1] => 0
[6,-,+,1,-,4] => [6,2,3,1,5,4] => [3,2,1] => [2,1] => 0
[6,+,-,1,-,4] => [6,2,3,1,5,4] => [3,2,1] => [2,1] => 0
[6,-,-,1,-,4] => [6,2,3,1,5,4] => [3,2,1] => [2,1] => 0
[6,+,+,5,1,4] => [6,2,3,5,1,4] => [3,2,1] => [2,1] => 0
[6,-,+,5,1,4] => [6,2,3,5,1,4] => [3,2,1] => [2,1] => 0
[6,+,-,5,1,4] => [6,2,3,5,1,4] => [3,2,1] => [2,1] => 0
[6,-,-,5,1,4] => [6,2,3,5,1,4] => [3,2,1] => [2,1] => 0
[6,+,+,5,4,1] => [6,2,3,5,4,1] => [3,1,1,1] => [1,1,1] => 0
[6,-,+,5,4,1] => [6,2,3,5,4,1] => [3,1,1,1] => [1,1,1] => 0
[6,+,-,5,4,1] => [6,2,3,5,4,1] => [3,1,1,1] => [1,1,1] => 0
[6,-,-,5,4,1] => [6,2,3,5,4,1] => [3,1,1,1] => [1,1,1] => 0
[6,+,4,1,3,5] => [6,2,4,1,3,5] => [3,2,1] => [2,1] => 0
[6,-,4,1,3,5] => [6,2,4,1,3,5] => [3,2,1] => [2,1] => 0
[6,+,4,1,+,3] => [6,2,4,1,5,3] => [3,2,1] => [2,1] => 0
[6,-,4,1,+,3] => [6,2,4,1,5,3] => [3,2,1] => [2,1] => 0
[6,+,4,1,-,3] => [6,2,4,1,5,3] => [3,2,1] => [2,1] => 0
[6,-,4,1,-,3] => [6,2,4,1,5,3] => [3,2,1] => [2,1] => 0
[6,+,4,3,1,5] => [6,2,4,3,1,5] => [3,1,1,1] => [1,1,1] => 0
[6,-,4,3,1,5] => [6,2,4,3,1,5] => [3,1,1,1] => [1,1,1] => 0
[6,+,4,3,+,1] => [6,2,4,3,5,1] => [3,1,1,1] => [1,1,1] => 0
[6,-,4,3,+,1] => [6,2,4,3,5,1] => [3,1,1,1] => [1,1,1] => 0
[6,+,4,3,-,1] => [6,2,4,3,5,1] => [3,1,1,1] => [1,1,1] => 0
[6,-,4,3,-,1] => [6,2,4,3,5,1] => [3,1,1,1] => [1,1,1] => 0
[6,+,4,5,1,3] => [6,2,4,5,1,3] => [3,2,1] => [2,1] => 0
[6,-,4,5,1,3] => [6,2,4,5,1,3] => [3,2,1] => [2,1] => 0
[6,+,4,5,3,1] => [6,2,4,5,3,1] => [3,1,1,1] => [1,1,1] => 0
[6,-,4,5,3,1] => [6,2,4,5,3,1] => [3,1,1,1] => [1,1,1] => 0
[6,+,5,1,3,4] => [6,2,5,1,3,4] => [3,2,1] => [2,1] => 0
[6,-,5,1,3,4] => [6,2,5,1,3,4] => [3,2,1] => [2,1] => 0
[6,+,5,1,4,3] => [6,2,5,1,4,3] => [2,2,1,1] => [2,1,1] => 0
[6,-,5,1,4,3] => [6,2,5,1,4,3] => [2,2,1,1] => [2,1,1] => 0
[6,+,5,3,1,4] => [6,2,5,3,1,4] => [3,1,1,1] => [1,1,1] => 0
[6,-,5,3,1,4] => [6,2,5,3,1,4] => [3,1,1,1] => [1,1,1] => 0
[6,+,5,3,4,1] => [6,2,5,3,4,1] => [3,1,1,1] => [1,1,1] => 0
[6,-,5,3,4,1] => [6,2,5,3,4,1] => [3,1,1,1] => [1,1,1] => 0
[6,+,5,+,1,3] => [6,2,5,4,1,3] => [2,2,1,1] => [2,1,1] => 0
[6,-,5,+,1,3] => [6,2,5,4,1,3] => [2,2,1,1] => [2,1,1] => 0
[6,+,5,-,1,3] => [6,2,5,4,1,3] => [2,2,1,1] => [2,1,1] => 0
[6,-,5,-,1,3] => [6,2,5,4,1,3] => [2,2,1,1] => [2,1,1] => 0
[6,+,5,+,3,1] => [6,2,5,4,3,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,-,5,+,3,1] => [6,2,5,4,3,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,+,5,-,3,1] => [6,2,5,4,3,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,-,5,-,3,1] => [6,2,5,4,3,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,3,1,2,+,4] => [6,3,1,2,5,4] => [3,2,1] => [2,1] => 0
[6,3,1,2,-,4] => [6,3,1,2,5,4] => [3,2,1] => [2,1] => 0
[6,3,1,+,2,5] => [6,3,1,4,2,5] => [3,2,1] => [2,1] => 0
[6,3,1,-,2,5] => [6,3,1,4,2,5] => [3,2,1] => [2,1] => 0
[6,3,1,+,+,2] => [6,3,1,4,5,2] => [3,2,1] => [2,1] => 0
[6,3,1,-,+,2] => [6,3,1,4,5,2] => [3,2,1] => [2,1] => 0
[6,3,1,+,-,2] => [6,3,1,4,5,2] => [3,2,1] => [2,1] => 0
[6,3,1,-,-,2] => [6,3,1,4,5,2] => [3,2,1] => [2,1] => 0
[6,3,1,5,2,4] => [6,3,1,5,2,4] => [3,2,1] => [2,1] => 0
[6,3,1,5,4,2] => [6,3,1,5,4,2] => [2,2,1,1] => [2,1,1] => 0
[6,3,2,1,4,5] => [6,3,2,1,4,5] => [3,1,1,1] => [1,1,1] => 0
[6,3,2,1,+,4] => [6,3,2,1,5,4] => [2,2,1,1] => [2,1,1] => 0
[6,3,2,1,-,4] => [6,3,2,1,5,4] => [2,2,1,1] => [2,1,1] => 0
[6,3,2,+,1,5] => [6,3,2,4,1,5] => [3,1,1,1] => [1,1,1] => 0
[6,3,2,-,1,5] => [6,3,2,4,1,5] => [3,1,1,1] => [1,1,1] => 0
[6,3,2,+,+,1] => [6,3,2,4,5,1] => [3,1,1,1] => [1,1,1] => 0
[6,3,2,-,+,1] => [6,3,2,4,5,1] => [3,1,1,1] => [1,1,1] => 0
[6,3,2,+,-,1] => [6,3,2,4,5,1] => [3,1,1,1] => [1,1,1] => 0
[6,3,2,-,-,1] => [6,3,2,4,5,1] => [3,1,1,1] => [1,1,1] => 0
[6,3,2,5,1,4] => [6,3,2,5,1,4] => [2,2,1,1] => [2,1,1] => 0
[6,3,2,5,4,1] => [6,3,2,5,4,1] => [2,2,1,1] => [2,1,1] => 0
[6,3,4,1,2,5] => [6,3,4,1,2,5] => [3,2,1] => [2,1] => 0
[6,3,4,1,+,2] => [6,3,4,1,5,2] => [3,2,1] => [2,1] => 0
[6,3,4,1,-,2] => [6,3,4,1,5,2] => [3,2,1] => [2,1] => 0
[6,3,4,2,1,5] => [6,3,4,2,1,5] => [3,1,1,1] => [1,1,1] => 0
[6,3,4,2,+,1] => [6,3,4,2,5,1] => [3,1,1,1] => [1,1,1] => 0
[6,3,4,2,-,1] => [6,3,4,2,5,1] => [3,1,1,1] => [1,1,1] => 0
[6,3,4,5,1,2] => [6,3,4,5,1,2] => [3,2,1] => [2,1] => 0
[6,3,4,5,2,1] => [6,3,4,5,2,1] => [3,1,1,1] => [1,1,1] => 0
[6,3,5,1,2,4] => [6,3,5,1,2,4] => [3,2,1] => [2,1] => 0
[6,3,5,1,4,2] => [6,3,5,1,4,2] => [2,2,1,1] => [2,1,1] => 0
[6,3,5,2,1,4] => [6,3,5,2,1,4] => [2,2,1,1] => [2,1,1] => 0
[6,3,5,2,4,1] => [6,3,5,2,4,1] => [2,2,1,1] => [2,1,1] => 0
[6,3,5,+,1,2] => [6,3,5,4,1,2] => [2,2,1,1] => [2,1,1] => 0
[6,3,5,-,1,2] => [6,3,5,4,1,2] => [2,2,1,1] => [2,1,1] => 0
[6,3,5,+,2,1] => [6,3,5,4,2,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,3,5,-,2,1] => [6,3,5,4,2,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,4,1,2,+,3] => [6,4,1,2,5,3] => [3,2,1] => [2,1] => 0
[6,4,1,2,-,3] => [6,4,1,2,5,3] => [3,2,1] => [2,1] => 0
[6,4,1,3,2,5] => [6,4,1,3,2,5] => [3,1,1,1] => [1,1,1] => 0
[6,4,1,3,+,2] => [6,4,1,3,5,2] => [3,1,1,1] => [1,1,1] => 0
[6,4,1,3,-,2] => [6,4,1,3,5,2] => [3,1,1,1] => [1,1,1] => 0
[6,4,1,5,2,3] => [6,4,1,5,2,3] => [3,2,1] => [2,1] => 0
[6,4,1,5,3,2] => [6,4,1,5,3,2] => [2,2,1,1] => [2,1,1] => 0
[6,4,2,1,3,5] => [6,4,2,1,3,5] => [3,1,1,1] => [1,1,1] => 0
[6,4,2,1,+,3] => [6,4,2,1,5,3] => [2,2,1,1] => [2,1,1] => 0
[6,4,2,1,-,3] => [6,4,2,1,5,3] => [2,2,1,1] => [2,1,1] => 0
[6,4,2,3,1,5] => [6,4,2,3,1,5] => [3,1,1,1] => [1,1,1] => 0
[6,4,2,3,+,1] => [6,4,2,3,5,1] => [3,1,1,1] => [1,1,1] => 0
[6,4,2,3,-,1] => [6,4,2,3,5,1] => [3,1,1,1] => [1,1,1] => 0
[6,4,2,5,1,3] => [6,4,2,5,1,3] => [2,2,1,1] => [2,1,1] => 0
[6,4,2,5,3,1] => [6,4,2,5,3,1] => [2,2,1,1] => [2,1,1] => 0
[6,4,+,1,2,5] => [6,4,3,1,2,5] => [3,1,1,1] => [1,1,1] => 0
[6,4,-,1,2,5] => [6,4,3,1,2,5] => [3,1,1,1] => [1,1,1] => 0
[6,4,+,1,+,2] => [6,4,3,1,5,2] => [2,2,1,1] => [2,1,1] => 0
[6,4,-,1,+,2] => [6,4,3,1,5,2] => [2,2,1,1] => [2,1,1] => 0
[6,4,+,1,-,2] => [6,4,3,1,5,2] => [2,2,1,1] => [2,1,1] => 0
[6,4,-,1,-,2] => [6,4,3,1,5,2] => [2,2,1,1] => [2,1,1] => 0
[6,4,+,2,1,5] => [6,4,3,2,1,5] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,4,-,2,1,5] => [6,4,3,2,1,5] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,4,+,2,+,1] => [6,4,3,2,5,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,4,-,2,+,1] => [6,4,3,2,5,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,4,+,2,-,1] => [6,4,3,2,5,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,4,-,2,-,1] => [6,4,3,2,5,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,4,+,5,1,2] => [6,4,3,5,1,2] => [2,2,1,1] => [2,1,1] => 0
[6,4,-,5,1,2] => [6,4,3,5,1,2] => [2,2,1,1] => [2,1,1] => 0
[6,4,+,5,2,1] => [6,4,3,5,2,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,4,-,5,2,1] => [6,4,3,5,2,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,4,5,1,2,3] => [6,4,5,1,2,3] => [3,2,1] => [2,1] => 0
[6,4,5,1,3,2] => [6,4,5,1,3,2] => [2,2,1,1] => [2,1,1] => 0
[6,4,5,2,1,3] => [6,4,5,2,1,3] => [2,2,1,1] => [2,1,1] => 0
[6,4,5,2,3,1] => [6,4,5,2,3,1] => [2,2,1,1] => [2,1,1] => 0
[6,4,5,3,1,2] => [6,4,5,3,1,2] => [2,2,1,1] => [2,1,1] => 0
[6,4,5,3,2,1] => [6,4,5,3,2,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,5,1,2,4,3] => [6,5,1,2,4,3] => [3,1,1,1] => [1,1,1] => 0
[6,5,1,3,2,4] => [6,5,1,3,2,4] => [3,1,1,1] => [1,1,1] => 0
[6,5,1,3,4,2] => [6,5,1,3,4,2] => [3,1,1,1] => [1,1,1] => 0
[6,5,1,+,2,3] => [6,5,1,4,2,3] => [3,1,1,1] => [1,1,1] => 0
[6,5,1,-,2,3] => [6,5,1,4,2,3] => [3,1,1,1] => [1,1,1] => 0
[6,5,1,+,3,2] => [6,5,1,4,3,2] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,5,1,-,3,2] => [6,5,1,4,3,2] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,5,2,1,3,4] => [6,5,2,1,3,4] => [3,1,1,1] => [1,1,1] => 0
[6,5,2,1,4,3] => [6,5,2,1,4,3] => [2,2,1,1] => [2,1,1] => 0
[6,5,2,3,1,4] => [6,5,2,3,1,4] => [3,1,1,1] => [1,1,1] => 0
[6,5,2,3,4,1] => [6,5,2,3,4,1] => [3,1,1,1] => [1,1,1] => 0
[6,5,2,+,1,3] => [6,5,2,4,1,3] => [2,2,1,1] => [2,1,1] => 0
[6,5,2,-,1,3] => [6,5,2,4,1,3] => [2,2,1,1] => [2,1,1] => 0
[6,5,2,+,3,1] => [6,5,2,4,3,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,5,2,-,3,1] => [6,5,2,4,3,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,5,+,1,2,4] => [6,5,3,1,2,4] => [3,1,1,1] => [1,1,1] => 0
[6,5,-,1,2,4] => [6,5,3,1,2,4] => [3,1,1,1] => [1,1,1] => 0
[6,5,+,1,4,2] => [6,5,3,1,4,2] => [2,2,1,1] => [2,1,1] => 0
[6,5,-,1,4,2] => [6,5,3,1,4,2] => [2,2,1,1] => [2,1,1] => 0
[6,5,+,2,1,4] => [6,5,3,2,1,4] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,5,-,2,1,4] => [6,5,3,2,1,4] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,5,+,2,4,1] => [6,5,3,2,4,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,5,-,2,4,1] => [6,5,3,2,4,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,5,+,+,1,2] => [6,5,3,4,1,2] => [2,2,1,1] => [2,1,1] => 0
[6,5,-,+,1,2] => [6,5,3,4,1,2] => [2,2,1,1] => [2,1,1] => 0
[6,5,+,-,1,2] => [6,5,3,4,1,2] => [2,2,1,1] => [2,1,1] => 0
[6,5,-,-,1,2] => [6,5,3,4,1,2] => [2,2,1,1] => [2,1,1] => 0
[6,5,+,+,2,1] => [6,5,3,4,2,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,5,-,+,2,1] => [6,5,3,4,2,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,5,+,-,2,1] => [6,5,3,4,2,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,5,-,-,2,1] => [6,5,3,4,2,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,5,4,1,2,3] => [6,5,4,1,2,3] => [3,1,1,1] => [1,1,1] => 0
[6,5,4,1,3,2] => [6,5,4,1,3,2] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,5,4,2,1,3] => [6,5,4,2,1,3] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,5,4,2,3,1] => [6,5,4,2,3,1] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,5,4,3,1,2] => [6,5,4,3,1,2] => [2,1,1,1,1] => [1,1,1,1] => 0
[6,5,4,3,2,1] => [6,5,4,3,2,1] => [1,1,1,1,1,1] => [1,1,1,1,1] => 1
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Description
The multiplicity of the irreducible representation corresponding to a partition in the relabelling action on polygons.
Equivalently, this is the multiplicity of the irreducible representation corresponding to a partition in the cycle index of the dihedral group.
This statistic is only defined for partitions of size at least 3, to avoid ambiguity.
Equivalently, this is the multiplicity of the irreducible representation corresponding to a partition in the cycle index of the dihedral group.
This statistic is only defined for partitions of size at least 3, to avoid ambiguity.
Map
Robinson-Schensted tableau shape
Description
Sends a permutation to its Robinson-Schensted tableau shape.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to the shape of its corresponding insertion and recording tableau.
The Robinson-Schensted corrspondence is a bijection between permutations of length $n$ and pairs of standard Young tableaux of the same shape and of size $n$, see [1]. These two tableaux are the insertion tableau and the recording tableau.
This map sends a permutation to the shape of its corresponding insertion and recording tableau.
Map
permutation
Description
The underlying permutation of the decorated permutation.
Map
first row removal
Description
Removes the first entry of an integer partition
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