- FindStat

Identifier

Mp00253: Decorated permutations —permutation⟶ Permutations
Mp00248: Permutations —DEX composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000772: Graphs ⟶ ℤ

Values

[+] => [1] => [1] => ([],1) => 1

[-] => [1] => [1] => ([],1) => 1

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

>>> Load all 728 entries. <<<

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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Description

The multiplicity of the largest distance Laplacian eigenvalue in a connected graph.
The distance Laplacian of a graph is the (symmetric) matrix with row and column sums $0$, which has the negative distances between two vertices as its off-diagonal entries. This statistic is the largest multiplicity of an eigenvalue.
For example, the cycle on four vertices has distance Laplacian
$$ \left(\begin{array}{rrrr} 4 & -1 & -2 & -1 \\ -1 & 4 & -1 & -2 \\ -2 & -1 & 4 & -1 \\ -1 & -2 & -1 & 4 \end{array}\right). $$
Its eigenvalues are $0,4,4,6$, so the statistic is $1$.
The path on four vertices has eigenvalues $0, 4.7\dots, 6, 9.2\dots$ and therefore also statistic $1$.
The graphs with statistic $n-1$, $n-2$ and $n-3$ have been characterised, see [1].

Map

DEX composition

Description

The DEX composition of a permutation.
Let $\pi$ be a permutation in $\mathfrak S_n$. Let $\bar\pi$ be the word in the ordered set $\bar 1 < \dots < \bar n < 1 \dots < n$ obtained from $\pi$ by replacing every excedance $\pi(i) > i$ by $\overline{\pi(i)}$. Then the DEX set of $\pi$ is the set of indices $1 \leq i < n$ such that $\bar\pi(i) > \bar\pi(i+1)$. Finally, the DEX composition $c_1, \dots, c_k$ of $n$ corresponds to the DEX subset $\{c_1, c_1 + c_2, \dots, c_1 + \dots + c_{k-1}\}$.
The (quasi)symmetric function
$$ \sum_{\pi\in\mathfrak S_{\lambda, j}} F_{DEX(\pi)}, $$
where the sum is over the set of permutations of cycle type $\lambda$ with $j$ excedances, is the Eulerian quasisymmetric function.

Map

permutation

Description

The underlying permutation of the decorated permutation.

Map

to threshold graph

Description

The threshold graph corresponding to the composition.
A threshold graph is a graph that can be obtained from the empty graph by adding successively isolated and dominating vertices.
A threshold graph is uniquely determined by its degree sequence.
The Laplacian spectrum of a threshold graph is integral. Interpreting it as an integer partition, it is the conjugate of the partition given by its degree sequence.