Identifier
Values
[+] => [1] => [1] => [1,0] => 1
[-] => [1] => [1] => [1,0] => 1
[+,+] => [1,2] => [1,2] => [1,0,1,0] => 1
[-,+] => [2,1] => [2,1] => [1,1,0,0] => 1
[+,-] => [1,2] => [1,2] => [1,0,1,0] => 1
[-,-] => [1,2] => [1,2] => [1,0,1,0] => 1
[2,1] => [2,1] => [2,1] => [1,1,0,0] => 1
[+,+,+] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0] => 2
[-,+,+] => [2,3,1] => [2,3,1] => [1,1,0,1,0,0] => 1
[+,-,+] => [1,3,2] => [3,1,2] => [1,1,1,0,0,0] => 1
[+,+,-] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0] => 2
[-,-,+] => [3,1,2] => [1,3,2] => [1,0,1,1,0,0] => 2
[-,+,-] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0] => 2
[+,-,-] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0] => 2
[-,-,-] => [1,2,3] => [1,2,3] => [1,0,1,0,1,0] => 2
[+,3,2] => [1,3,2] => [3,1,2] => [1,1,1,0,0,0] => 1
[-,3,2] => [3,1,2] => [1,3,2] => [1,0,1,1,0,0] => 2
[2,1,+] => [2,3,1] => [2,3,1] => [1,1,0,1,0,0] => 1
[2,1,-] => [2,1,3] => [2,1,3] => [1,1,0,0,1,0] => 2
[2,3,1] => [3,1,2] => [1,3,2] => [1,0,1,1,0,0] => 2
[3,1,2] => [2,3,1] => [2,3,1] => [1,1,0,1,0,0] => 1
[3,+,1] => [2,3,1] => [2,3,1] => [1,1,0,1,0,0] => 1
[3,-,1] => [3,1,2] => [1,3,2] => [1,0,1,1,0,0] => 2
[+,+,+,+] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 3
[-,+,+,+] => [2,3,4,1] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => 2
[+,-,+,+] => [1,3,4,2] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 2
[+,+,-,+] => [1,2,4,3] => [4,1,2,3] => [1,1,1,1,0,0,0,0] => 1
[+,+,+,-] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 3
[-,-,+,+] => [3,4,1,2] => [1,3,4,2] => [1,0,1,1,0,1,0,0] => 2
[-,+,-,+] => [2,4,1,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 3
[-,+,+,-] => [2,3,1,4] => [2,3,1,4] => [1,1,0,1,0,0,1,0] => 2
[+,-,-,+] => [1,4,2,3] => [1,4,2,3] => [1,0,1,1,1,0,0,0] => 2
[+,-,+,-] => [1,3,2,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 2
[+,+,-,-] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 3
[-,-,-,+] => [4,1,2,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0] => 3
[-,-,+,-] => [3,1,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0] => 3
[-,+,-,-] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 3
[+,-,-,-] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 3
[-,-,-,-] => [1,2,3,4] => [1,2,3,4] => [1,0,1,0,1,0,1,0] => 3
[+,+,4,3] => [1,2,4,3] => [4,1,2,3] => [1,1,1,1,0,0,0,0] => 1
[-,+,4,3] => [2,4,1,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 3
[+,-,4,3] => [1,4,2,3] => [1,4,2,3] => [1,0,1,1,1,0,0,0] => 2
[-,-,4,3] => [4,1,2,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0] => 3
[+,3,2,+] => [1,3,4,2] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 2
[-,3,2,+] => [3,4,1,2] => [1,3,4,2] => [1,0,1,1,0,1,0,0] => 2
[+,3,2,-] => [1,3,2,4] => [3,1,2,4] => [1,1,1,0,0,0,1,0] => 2
[-,3,2,-] => [3,1,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0] => 3
[+,3,4,2] => [1,4,2,3] => [1,4,2,3] => [1,0,1,1,1,0,0,0] => 2
[-,3,4,2] => [4,1,2,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0] => 3
[+,4,2,3] => [1,3,4,2] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 2
[-,4,2,3] => [3,4,1,2] => [1,3,4,2] => [1,0,1,1,0,1,0,0] => 2
[+,4,+,2] => [1,3,4,2] => [3,1,4,2] => [1,1,1,0,0,1,0,0] => 2
[-,4,+,2] => [3,4,1,2] => [1,3,4,2] => [1,0,1,1,0,1,0,0] => 2
[+,4,-,2] => [1,4,2,3] => [1,4,2,3] => [1,0,1,1,1,0,0,0] => 2
[-,4,-,2] => [4,1,2,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0] => 3
[2,1,+,+] => [2,3,4,1] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => 2
[2,1,-,+] => [2,4,1,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 3
[2,1,+,-] => [2,3,1,4] => [2,3,1,4] => [1,1,0,1,0,0,1,0] => 2
[2,1,-,-] => [2,1,3,4] => [2,1,3,4] => [1,1,0,0,1,0,1,0] => 3
[2,1,4,3] => [2,4,1,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 3
[2,3,1,+] => [3,4,1,2] => [1,3,4,2] => [1,0,1,1,0,1,0,0] => 2
[2,3,1,-] => [3,1,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0] => 3
[2,3,4,1] => [4,1,2,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0] => 3
[2,4,1,3] => [3,4,1,2] => [1,3,4,2] => [1,0,1,1,0,1,0,0] => 2
[2,4,+,1] => [3,4,1,2] => [1,3,4,2] => [1,0,1,1,0,1,0,0] => 2
[2,4,-,1] => [4,1,2,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0] => 3
[3,1,2,+] => [2,3,4,1] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => 2
[3,1,2,-] => [2,3,1,4] => [2,3,1,4] => [1,1,0,1,0,0,1,0] => 2
[3,1,4,2] => [2,4,1,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 3
[3,+,1,+] => [2,3,4,1] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => 2
[3,-,1,+] => [3,4,1,2] => [1,3,4,2] => [1,0,1,1,0,1,0,0] => 2
[3,+,1,-] => [2,3,1,4] => [2,3,1,4] => [1,1,0,1,0,0,1,0] => 2
[3,-,1,-] => [3,1,2,4] => [1,3,2,4] => [1,0,1,1,0,0,1,0] => 3
[3,+,4,1] => [2,4,1,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 3
[3,-,4,1] => [4,1,2,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0] => 3
[3,4,1,2] => [3,4,1,2] => [1,3,4,2] => [1,0,1,1,0,1,0,0] => 2
[3,4,2,1] => [3,4,1,2] => [1,3,4,2] => [1,0,1,1,0,1,0,0] => 2
[4,1,2,3] => [2,3,4,1] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => 2
[4,1,+,2] => [2,3,4,1] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => 2
[4,1,-,2] => [2,4,1,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 3
[4,+,1,3] => [2,3,4,1] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => 2
[4,-,1,3] => [3,4,1,2] => [1,3,4,2] => [1,0,1,1,0,1,0,0] => 2
[4,+,+,1] => [2,3,4,1] => [2,3,4,1] => [1,1,0,1,0,1,0,0] => 2
[4,-,+,1] => [3,4,1,2] => [1,3,4,2] => [1,0,1,1,0,1,0,0] => 2
[4,+,-,1] => [2,4,1,3] => [2,1,4,3] => [1,1,0,0,1,1,0,0] => 3
[4,-,-,1] => [4,1,2,3] => [1,2,4,3] => [1,0,1,0,1,1,0,0] => 3
[4,3,1,2] => [3,4,1,2] => [1,3,4,2] => [1,0,1,1,0,1,0,0] => 2
[4,3,2,1] => [3,4,1,2] => [1,3,4,2] => [1,0,1,1,0,1,0,0] => 2
[+,+,+,+,+] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => 4
[-,+,+,+,+] => [2,3,4,5,1] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 3
[+,-,+,+,+] => [1,3,4,5,2] => [3,1,4,5,2] => [1,1,1,0,0,1,0,1,0,0] => 3
[+,+,-,+,+] => [1,2,4,5,3] => [4,1,2,5,3] => [1,1,1,1,0,0,0,1,0,0] => 2
[+,+,+,-,+] => [1,2,3,5,4] => [5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0] => 1
[+,+,+,+,-] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => 4
[-,-,+,+,+] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[-,+,-,+,+] => [2,4,5,1,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 3
[-,+,+,-,+] => [2,3,5,1,4] => [2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => 3
[-,+,+,+,-] => [2,3,4,1,5] => [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => 3
[+,-,-,+,+] => [1,4,5,2,3] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => 3
[+,-,+,-,+] => [1,3,5,2,4] => [3,1,2,5,4] => [1,1,1,0,0,0,1,1,0,0] => 3
[+,-,+,+,-] => [1,3,4,2,5] => [3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0] => 3
>>> Load all 414 entries. <<<
[+,+,-,-,+] => [1,2,5,3,4] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[+,+,-,+,-] => [1,2,4,3,5] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => 2
[+,+,+,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => 4
[-,-,-,+,+] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[-,-,+,-,+] => [3,5,1,2,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 4
[-,-,+,+,-] => [3,4,1,2,5] => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => 3
[-,+,-,-,+] => [2,5,1,3,4] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => 4
[-,+,-,+,-] => [2,4,1,3,5] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 4
[-,+,+,-,-] => [2,3,1,4,5] => [2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0] => 3
[+,-,-,-,+] => [1,5,2,3,4] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => 3
[+,-,-,+,-] => [1,4,2,3,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => 3
[+,-,+,-,-] => [1,3,2,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0] => 3
[+,+,-,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => 4
[-,-,-,-,+] => [5,1,2,3,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => 4
[-,-,-,+,-] => [4,1,2,3,5] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => 4
[-,-,+,-,-] => [3,1,2,4,5] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0] => 4
[-,+,-,-,-] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => 4
[+,-,-,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => 4
[-,-,-,-,-] => [1,2,3,4,5] => [1,2,3,4,5] => [1,0,1,0,1,0,1,0,1,0] => 4
[+,+,+,5,4] => [1,2,3,5,4] => [5,1,2,3,4] => [1,1,1,1,1,0,0,0,0,0] => 1
[-,+,+,5,4] => [2,3,5,1,4] => [2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => 3
[+,-,+,5,4] => [1,3,5,2,4] => [3,1,2,5,4] => [1,1,1,0,0,0,1,1,0,0] => 3
[+,+,-,5,4] => [1,2,5,3,4] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[-,-,+,5,4] => [3,5,1,2,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 4
[-,+,-,5,4] => [2,5,1,3,4] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => 4
[+,-,-,5,4] => [1,5,2,3,4] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => 3
[-,-,-,5,4] => [5,1,2,3,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => 4
[+,+,4,3,+] => [1,2,4,5,3] => [4,1,2,5,3] => [1,1,1,1,0,0,0,1,0,0] => 2
[-,+,4,3,+] => [2,4,5,1,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 3
[+,-,4,3,+] => [1,4,5,2,3] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => 3
[+,+,4,3,-] => [1,2,4,3,5] => [4,1,2,3,5] => [1,1,1,1,0,0,0,0,1,0] => 2
[-,-,4,3,+] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[-,+,4,3,-] => [2,4,1,3,5] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 4
[+,-,4,3,-] => [1,4,2,3,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => 3
[-,-,4,3,-] => [4,1,2,3,5] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => 4
[+,+,4,5,3] => [1,2,5,3,4] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[-,+,4,5,3] => [2,5,1,3,4] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => 4
[+,-,4,5,3] => [1,5,2,3,4] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => 3
[-,-,4,5,3] => [5,1,2,3,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => 4
[+,+,5,3,4] => [1,2,4,5,3] => [4,1,2,5,3] => [1,1,1,1,0,0,0,1,0,0] => 2
[-,+,5,3,4] => [2,4,5,1,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 3
[+,-,5,3,4] => [1,4,5,2,3] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => 3
[-,-,5,3,4] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[+,+,5,+,3] => [1,2,4,5,3] => [4,1,2,5,3] => [1,1,1,1,0,0,0,1,0,0] => 2
[-,+,5,+,3] => [2,4,5,1,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 3
[+,-,5,+,3] => [1,4,5,2,3] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => 3
[+,+,5,-,3] => [1,2,5,3,4] => [1,5,2,3,4] => [1,0,1,1,1,1,0,0,0,0] => 2
[-,-,5,+,3] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[-,+,5,-,3] => [2,5,1,3,4] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => 4
[+,-,5,-,3] => [1,5,2,3,4] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => 3
[-,-,5,-,3] => [5,1,2,3,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => 4
[+,3,2,+,+] => [1,3,4,5,2] => [3,1,4,5,2] => [1,1,1,0,0,1,0,1,0,0] => 3
[-,3,2,+,+] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[+,3,2,-,+] => [1,3,5,2,4] => [3,1,2,5,4] => [1,1,1,0,0,0,1,1,0,0] => 3
[+,3,2,+,-] => [1,3,4,2,5] => [3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0] => 3
[-,3,2,-,+] => [3,5,1,2,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 4
[-,3,2,+,-] => [3,4,1,2,5] => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => 3
[+,3,2,-,-] => [1,3,2,4,5] => [3,1,2,4,5] => [1,1,1,0,0,0,1,0,1,0] => 3
[-,3,2,-,-] => [3,1,2,4,5] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0] => 4
[+,3,2,5,4] => [1,3,5,2,4] => [3,1,2,5,4] => [1,1,1,0,0,0,1,1,0,0] => 3
[-,3,2,5,4] => [3,5,1,2,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 4
[+,3,4,2,+] => [1,4,5,2,3] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => 3
[-,3,4,2,+] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[+,3,4,2,-] => [1,4,2,3,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => 3
[-,3,4,2,-] => [4,1,2,3,5] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => 4
[+,3,4,5,2] => [1,5,2,3,4] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => 3
[-,3,4,5,2] => [5,1,2,3,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => 4
[+,3,5,2,4] => [1,4,5,2,3] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => 3
[-,3,5,2,4] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[+,3,5,+,2] => [1,4,5,2,3] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => 3
[-,3,5,+,2] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[+,3,5,-,2] => [1,5,2,3,4] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => 3
[-,3,5,-,2] => [5,1,2,3,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => 4
[+,4,2,3,+] => [1,3,4,5,2] => [3,1,4,5,2] => [1,1,1,0,0,1,0,1,0,0] => 3
[-,4,2,3,+] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[+,4,2,3,-] => [1,3,4,2,5] => [3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0] => 3
[-,4,2,3,-] => [3,4,1,2,5] => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => 3
[+,4,2,5,3] => [1,3,5,2,4] => [3,1,2,5,4] => [1,1,1,0,0,0,1,1,0,0] => 3
[-,4,2,5,3] => [3,5,1,2,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 4
[+,4,+,2,+] => [1,3,4,5,2] => [3,1,4,5,2] => [1,1,1,0,0,1,0,1,0,0] => 3
[-,4,+,2,+] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[+,4,-,2,+] => [1,4,5,2,3] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => 3
[+,4,+,2,-] => [1,3,4,2,5] => [3,1,4,2,5] => [1,1,1,0,0,1,0,0,1,0] => 3
[-,4,-,2,+] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[-,4,+,2,-] => [3,4,1,2,5] => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => 3
[+,4,-,2,-] => [1,4,2,3,5] => [1,4,2,3,5] => [1,0,1,1,1,0,0,0,1,0] => 3
[-,4,-,2,-] => [4,1,2,3,5] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => 4
[+,4,+,5,2] => [1,3,5,2,4] => [3,1,2,5,4] => [1,1,1,0,0,0,1,1,0,0] => 3
[-,4,+,5,2] => [3,5,1,2,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 4
[+,4,-,5,2] => [1,5,2,3,4] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => 3
[-,4,-,5,2] => [5,1,2,3,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => 4
[+,4,5,2,3] => [1,4,5,2,3] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => 3
[-,4,5,2,3] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[+,4,5,3,2] => [1,4,5,2,3] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => 3
[-,4,5,3,2] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[+,5,2,3,4] => [1,3,4,5,2] => [3,1,4,5,2] => [1,1,1,0,0,1,0,1,0,0] => 3
[-,5,2,3,4] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[+,5,2,+,3] => [1,3,4,5,2] => [3,1,4,5,2] => [1,1,1,0,0,1,0,1,0,0] => 3
[-,5,2,+,3] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[+,5,2,-,3] => [1,3,5,2,4] => [3,1,2,5,4] => [1,1,1,0,0,0,1,1,0,0] => 3
[-,5,2,-,3] => [3,5,1,2,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 4
[+,5,+,2,4] => [1,3,4,5,2] => [3,1,4,5,2] => [1,1,1,0,0,1,0,1,0,0] => 3
[-,5,+,2,4] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[+,5,-,2,4] => [1,4,5,2,3] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => 3
[-,5,-,2,4] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[+,5,+,+,2] => [1,3,4,5,2] => [3,1,4,5,2] => [1,1,1,0,0,1,0,1,0,0] => 3
[-,5,+,+,2] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[+,5,-,+,2] => [1,4,5,2,3] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => 3
[+,5,+,-,2] => [1,3,5,2,4] => [3,1,2,5,4] => [1,1,1,0,0,0,1,1,0,0] => 3
[-,5,-,+,2] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[-,5,+,-,2] => [3,5,1,2,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 4
[+,5,-,-,2] => [1,5,2,3,4] => [1,2,5,3,4] => [1,0,1,0,1,1,1,0,0,0] => 3
[-,5,-,-,2] => [5,1,2,3,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => 4
[+,5,4,2,3] => [1,4,5,2,3] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => 3
[-,5,4,2,3] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[+,5,4,3,2] => [1,4,5,2,3] => [1,4,2,5,3] => [1,0,1,1,1,0,0,1,0,0] => 3
[-,5,4,3,2] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[2,1,+,+,+] => [2,3,4,5,1] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 3
[2,1,-,+,+] => [2,4,5,1,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 3
[2,1,+,-,+] => [2,3,5,1,4] => [2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => 3
[2,1,+,+,-] => [2,3,4,1,5] => [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => 3
[2,1,-,-,+] => [2,5,1,3,4] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => 4
[2,1,-,+,-] => [2,4,1,3,5] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 4
[2,1,+,-,-] => [2,3,1,4,5] => [2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0] => 3
[2,1,-,-,-] => [2,1,3,4,5] => [2,1,3,4,5] => [1,1,0,0,1,0,1,0,1,0] => 4
[2,1,+,5,4] => [2,3,5,1,4] => [2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => 3
[2,1,-,5,4] => [2,5,1,3,4] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => 4
[2,1,4,3,+] => [2,4,5,1,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 3
[2,1,4,3,-] => [2,4,1,3,5] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 4
[2,1,4,5,3] => [2,5,1,3,4] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => 4
[2,1,5,3,4] => [2,4,5,1,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 3
[2,1,5,+,3] => [2,4,5,1,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 3
[2,1,5,-,3] => [2,5,1,3,4] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => 4
[2,3,1,+,+] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[2,3,1,-,+] => [3,5,1,2,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 4
[2,3,1,+,-] => [3,4,1,2,5] => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => 3
[2,3,1,-,-] => [3,1,2,4,5] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0] => 4
[2,3,1,5,4] => [3,5,1,2,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 4
[2,3,4,1,+] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[2,3,4,1,-] => [4,1,2,3,5] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => 4
[2,3,4,5,1] => [5,1,2,3,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => 4
[2,3,5,1,4] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[2,3,5,+,1] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[2,3,5,-,1] => [5,1,2,3,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => 4
[2,4,1,3,+] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[2,4,1,3,-] => [3,4,1,2,5] => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => 3
[2,4,1,5,3] => [3,5,1,2,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 4
[2,4,+,1,+] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[2,4,-,1,+] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[2,4,+,1,-] => [3,4,1,2,5] => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => 3
[2,4,-,1,-] => [4,1,2,3,5] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => 4
[2,4,+,5,1] => [3,5,1,2,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 4
[2,4,-,5,1] => [5,1,2,3,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => 4
[2,4,5,1,3] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[2,4,5,3,1] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[2,5,1,3,4] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[2,5,1,+,3] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[2,5,1,-,3] => [3,5,1,2,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 4
[2,5,+,1,4] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[2,5,-,1,4] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[2,5,+,+,1] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[2,5,-,+,1] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[2,5,+,-,1] => [3,5,1,2,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 4
[2,5,-,-,1] => [5,1,2,3,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => 4
[2,5,4,1,3] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[2,5,4,3,1] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[3,1,2,+,+] => [2,3,4,5,1] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 3
[3,1,2,-,+] => [2,3,5,1,4] => [2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => 3
[3,1,2,+,-] => [2,3,4,1,5] => [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => 3
[3,1,2,-,-] => [2,3,1,4,5] => [2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0] => 3
[3,1,2,5,4] => [2,3,5,1,4] => [2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => 3
[3,1,4,2,+] => [2,4,5,1,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 3
[3,1,4,2,-] => [2,4,1,3,5] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 4
[3,1,4,5,2] => [2,5,1,3,4] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => 4
[3,1,5,2,4] => [2,4,5,1,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 3
[3,1,5,+,2] => [2,4,5,1,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 3
[3,1,5,-,2] => [2,5,1,3,4] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => 4
[3,+,1,+,+] => [2,3,4,5,1] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 3
[3,-,1,+,+] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[3,+,1,-,+] => [2,3,5,1,4] => [2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => 3
[3,+,1,+,-] => [2,3,4,1,5] => [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => 3
[3,-,1,-,+] => [3,5,1,2,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 4
[3,-,1,+,-] => [3,4,1,2,5] => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => 3
[3,+,1,-,-] => [2,3,1,4,5] => [2,3,1,4,5] => [1,1,0,1,0,0,1,0,1,0] => 3
[3,-,1,-,-] => [3,1,2,4,5] => [1,3,2,4,5] => [1,0,1,1,0,0,1,0,1,0] => 4
[3,+,1,5,4] => [2,3,5,1,4] => [2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => 3
[3,-,1,5,4] => [3,5,1,2,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 4
[3,+,4,1,+] => [2,4,5,1,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 3
[3,-,4,1,+] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[3,+,4,1,-] => [2,4,1,3,5] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 4
[3,-,4,1,-] => [4,1,2,3,5] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => 4
[3,+,4,5,1] => [2,5,1,3,4] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => 4
[3,-,4,5,1] => [5,1,2,3,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => 4
[3,+,5,1,4] => [2,4,5,1,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 3
[3,-,5,1,4] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[3,+,5,+,1] => [2,4,5,1,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 3
[3,-,5,+,1] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[3,+,5,-,1] => [2,5,1,3,4] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => 4
[3,-,5,-,1] => [5,1,2,3,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => 4
[3,4,1,2,+] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[3,4,1,2,-] => [3,4,1,2,5] => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => 3
[3,4,1,5,2] => [3,5,1,2,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 4
[3,4,2,1,+] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[3,4,2,1,-] => [3,4,1,2,5] => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => 3
[3,4,2,5,1] => [3,5,1,2,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 4
[3,4,5,1,2] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[3,4,5,2,1] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[3,5,1,2,4] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[3,5,1,+,2] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[3,5,1,-,2] => [3,5,1,2,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 4
[3,5,2,1,4] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[3,5,2,+,1] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[3,5,2,-,1] => [3,5,1,2,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 4
[3,5,4,1,2] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[3,5,4,2,1] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[4,1,2,3,+] => [2,3,4,5,1] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 3
[4,1,2,3,-] => [2,3,4,1,5] => [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => 3
[4,1,2,5,3] => [2,3,5,1,4] => [2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => 3
[4,1,+,2,+] => [2,3,4,5,1] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 3
[4,1,-,2,+] => [2,4,5,1,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 3
[4,1,+,2,-] => [2,3,4,1,5] => [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => 3
[4,1,-,2,-] => [2,4,1,3,5] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 4
[4,1,+,5,2] => [2,3,5,1,4] => [2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => 3
[4,1,-,5,2] => [2,5,1,3,4] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => 4
[4,1,5,2,3] => [2,4,5,1,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 3
[4,1,5,3,2] => [2,4,5,1,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 3
[4,+,1,3,+] => [2,3,4,5,1] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 3
[4,-,1,3,+] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[4,+,1,3,-] => [2,3,4,1,5] => [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => 3
[4,-,1,3,-] => [3,4,1,2,5] => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => 3
[4,+,1,5,3] => [2,3,5,1,4] => [2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => 3
[4,-,1,5,3] => [3,5,1,2,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 4
[4,+,+,1,+] => [2,3,4,5,1] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 3
[4,-,+,1,+] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[4,+,-,1,+] => [2,4,5,1,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 3
[4,+,+,1,-] => [2,3,4,1,5] => [2,3,4,1,5] => [1,1,0,1,0,1,0,0,1,0] => 3
[4,-,-,1,+] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[4,-,+,1,-] => [3,4,1,2,5] => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => 3
[4,+,-,1,-] => [2,4,1,3,5] => [2,1,4,3,5] => [1,1,0,0,1,1,0,0,1,0] => 4
[4,-,-,1,-] => [4,1,2,3,5] => [1,2,4,3,5] => [1,0,1,0,1,1,0,0,1,0] => 4
[4,+,+,5,1] => [2,3,5,1,4] => [2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => 3
[4,-,+,5,1] => [3,5,1,2,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 4
[4,+,-,5,1] => [2,5,1,3,4] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => 4
[4,-,-,5,1] => [5,1,2,3,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => 4
[4,+,5,1,3] => [2,4,5,1,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 3
[4,-,5,1,3] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[4,+,5,3,1] => [2,4,5,1,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 3
[4,-,5,3,1] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[4,3,1,2,+] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[4,3,1,2,-] => [3,4,1,2,5] => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => 3
[4,3,1,5,2] => [3,5,1,2,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 4
[4,3,2,1,+] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[4,3,2,1,-] => [3,4,1,2,5] => [1,3,4,2,5] => [1,0,1,1,0,1,0,0,1,0] => 3
[4,3,2,5,1] => [3,5,1,2,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 4
[4,3,5,1,2] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[4,3,5,2,1] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[4,5,1,2,3] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[4,5,1,3,2] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[4,5,2,1,3] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[4,5,2,3,1] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[4,5,+,1,2] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[4,5,-,1,2] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[4,5,+,2,1] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[4,5,-,2,1] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[5,1,2,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 3
[5,1,2,+,3] => [2,3,4,5,1] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 3
[5,1,2,-,3] => [2,3,5,1,4] => [2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => 3
[5,1,+,2,4] => [2,3,4,5,1] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 3
[5,1,-,2,4] => [2,4,5,1,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 3
[5,1,+,+,2] => [2,3,4,5,1] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 3
[5,1,-,+,2] => [2,4,5,1,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 3
[5,1,+,-,2] => [2,3,5,1,4] => [2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => 3
[5,1,-,-,2] => [2,5,1,3,4] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => 4
[5,1,4,2,3] => [2,4,5,1,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 3
[5,1,4,3,2] => [2,4,5,1,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 3
[5,+,1,3,4] => [2,3,4,5,1] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 3
[5,-,1,3,4] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[5,+,1,+,3] => [2,3,4,5,1] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 3
[5,-,1,+,3] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[5,+,1,-,3] => [2,3,5,1,4] => [2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => 3
[5,-,1,-,3] => [3,5,1,2,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 4
[5,+,+,1,4] => [2,3,4,5,1] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 3
[5,-,+,1,4] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[5,+,-,1,4] => [2,4,5,1,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 3
[5,-,-,1,4] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[5,+,+,+,1] => [2,3,4,5,1] => [2,3,4,5,1] => [1,1,0,1,0,1,0,1,0,0] => 3
[5,-,+,+,1] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[5,+,-,+,1] => [2,4,5,1,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 3
[5,+,+,-,1] => [2,3,5,1,4] => [2,3,1,5,4] => [1,1,0,1,0,0,1,1,0,0] => 3
[5,-,-,+,1] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[5,-,+,-,1] => [3,5,1,2,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 4
[5,+,-,-,1] => [2,5,1,3,4] => [2,1,3,5,4] => [1,1,0,0,1,0,1,1,0,0] => 4
[5,-,-,-,1] => [5,1,2,3,4] => [1,2,3,5,4] => [1,0,1,0,1,0,1,1,0,0] => 4
[5,+,4,1,3] => [2,4,5,1,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 3
[5,-,4,1,3] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[5,+,4,3,1] => [2,4,5,1,3] => [2,1,4,5,3] => [1,1,0,0,1,1,0,1,0,0] => 3
[5,-,4,3,1] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[5,3,1,2,4] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[5,3,1,+,2] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[5,3,1,-,2] => [3,5,1,2,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 4
[5,3,2,1,4] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[5,3,2,+,1] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[5,3,2,-,1] => [3,5,1,2,4] => [1,3,2,5,4] => [1,0,1,1,0,0,1,1,0,0] => 4
[5,3,4,1,2] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[5,3,4,2,1] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[5,4,1,2,3] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[5,4,1,3,2] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[5,4,2,1,3] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[5,4,2,3,1] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[5,4,+,1,2] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[5,4,-,1,2] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
[5,4,+,2,1] => [3,4,5,1,2] => [1,3,4,5,2] => [1,0,1,1,0,1,0,1,0,0] => 3
[5,4,-,2,1] => [4,5,1,2,3] => [1,2,4,5,3] => [1,0,1,0,1,1,0,1,0,0] => 3
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Description
The dimension of the top of the Auslander-Reiten translate of the regular modules as a bimodule.
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
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
Foata bijection
Description
Sends a permutation to its image under the Foata bijection.
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
  • If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
  • If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
In either case, place a vertical line at the start of the word as well. Now, within each block between vertical lines, cyclically shift the entries one place to the right.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
  • $1$
  • $|1|4 \to 14$
  • $|14|2 \to 412$
  • $|4|1|2|5 \to 4125$
  • $|4|125|3 \to 45123.$
In total, this gives $\phi([1,4,2,5,3]) = [4,5,1,2,3]$.
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).