Identifier
-
Mp00255:
Decorated permutations
—lower permutation⟶
Permutations
Mp00071: Permutations —descent composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000777: Graphs ⟶ ℤ
Values
=>
Cc0020;cc-rep
[+]=>[1]=>[1]=>([],1)=>1
[-]=>[1]=>[1]=>([],1)=>1
[-,+]=>[2,1]=>[1,1]=>([(0,1)],2)=>2
[-,+,+]=>[2,3,1]=>[2,1]=>([(0,2),(1,2)],3)=>3
[+,-,+]=>[1,3,2]=>[2,1]=>([(0,2),(1,2)],3)=>3
[2,1,+]=>[1,3,2]=>[2,1]=>([(0,2),(1,2)],3)=>3
[3,-,1]=>[1,3,2]=>[2,1]=>([(0,2),(1,2)],3)=>3
[-,+,+,+]=>[2,3,4,1]=>[3,1]=>([(0,3),(1,3),(2,3)],4)=>3
[+,-,+,+]=>[1,3,4,2]=>[3,1]=>([(0,3),(1,3),(2,3)],4)=>3
[+,+,-,+]=>[1,2,4,3]=>[3,1]=>([(0,3),(1,3),(2,3)],4)=>3
[+,3,2,+]=>[1,2,4,3]=>[3,1]=>([(0,3),(1,3),(2,3)],4)=>3
[+,4,-,2]=>[1,2,4,3]=>[3,1]=>([(0,3),(1,3),(2,3)],4)=>3
[-,4,-,2]=>[2,1,4,3]=>[1,2,1]=>([(0,3),(1,2),(1,3),(2,3)],4)=>4
[2,1,+,+]=>[1,3,4,2]=>[3,1]=>([(0,3),(1,3),(2,3)],4)=>3
[2,4,-,1]=>[1,2,4,3]=>[3,1]=>([(0,3),(1,3),(2,3)],4)=>3
[3,1,2,+]=>[1,2,4,3]=>[3,1]=>([(0,3),(1,3),(2,3)],4)=>3
[3,+,1,+]=>[2,1,4,3]=>[1,2,1]=>([(0,3),(1,2),(1,3),(2,3)],4)=>4
[3,-,1,+]=>[1,4,3,2]=>[2,1,1]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>3
[4,1,-,2]=>[1,2,4,3]=>[3,1]=>([(0,3),(1,3),(2,3)],4)=>3
[4,-,1,3]=>[1,3,4,2]=>[3,1]=>([(0,3),(1,3),(2,3)],4)=>3
[4,-,+,1]=>[3,1,4,2]=>[1,2,1]=>([(0,3),(1,2),(1,3),(2,3)],4)=>4
[4,+,-,1]=>[2,1,4,3]=>[1,2,1]=>([(0,3),(1,2),(1,3),(2,3)],4)=>4
[4,3,1,2]=>[1,2,4,3]=>[3,1]=>([(0,3),(1,3),(2,3)],4)=>3
[4,3,2,1]=>[2,1,4,3]=>[1,2,1]=>([(0,3),(1,2),(1,3),(2,3)],4)=>4
[-,+,+,+,+]=>[2,3,4,5,1]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[+,-,+,+,+]=>[1,3,4,5,2]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[+,+,-,+,+]=>[1,2,4,5,3]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[+,+,+,-,+]=>[1,2,3,5,4]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[+,+,4,3,+]=>[1,2,3,5,4]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[+,+,5,-,3]=>[1,2,3,5,4]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[-,+,5,-,3]=>[2,3,1,5,4]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5
[+,-,5,-,3]=>[1,3,2,5,4]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5
[-,-,5,-,3]=>[3,1,2,5,4]=>[1,3,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>4
[+,3,2,+,+]=>[1,2,4,5,3]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[+,3,5,-,2]=>[1,2,3,5,4]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[-,3,5,-,2]=>[2,1,3,5,4]=>[1,3,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>4
[+,4,2,3,+]=>[1,2,3,5,4]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[+,4,+,2,+]=>[1,3,2,5,4]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5
[+,4,-,2,+]=>[1,2,5,4,3]=>[3,1,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3
[-,4,-,2,+]=>[2,5,1,4,3]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5
[+,5,2,-,3]=>[1,2,3,5,4]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[-,5,2,-,3]=>[2,3,1,5,4]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5
[+,5,-,2,4]=>[1,2,4,5,3]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[-,5,-,2,4]=>[2,4,1,5,3]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5
[+,5,-,+,2]=>[1,4,2,5,3]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5
[+,5,+,-,2]=>[1,3,2,5,4]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5
[-,5,-,+,2]=>[4,2,1,5,3]=>[1,1,2,1]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4
[-,5,+,-,2]=>[3,2,1,5,4]=>[1,1,2,1]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4
[+,5,4,2,3]=>[1,2,3,5,4]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[-,5,4,2,3]=>[2,3,1,5,4]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5
[+,5,4,3,2]=>[1,3,2,5,4]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5
[-,5,4,3,2]=>[3,2,1,5,4]=>[1,1,2,1]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4
[2,1,+,+,+]=>[1,3,4,5,2]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[2,1,5,-,3]=>[1,3,2,5,4]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5
[2,3,5,-,1]=>[1,2,3,5,4]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[2,4,-,1,+]=>[1,5,2,4,3]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5
[2,5,1,-,3]=>[1,3,2,5,4]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5
[2,5,-,1,4]=>[1,4,2,5,3]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5
[2,5,-,+,1]=>[4,1,2,5,3]=>[1,3,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>4
[2,5,+,-,1]=>[3,1,2,5,4]=>[1,3,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>4
[2,5,4,1,3]=>[1,3,2,5,4]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5
[2,5,4,3,1]=>[3,1,2,5,4]=>[1,3,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>4
[3,1,2,+,+]=>[1,2,4,5,3]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[3,1,5,-,2]=>[1,2,3,5,4]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[3,+,1,+,+]=>[2,1,4,5,3]=>[1,3,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>4
[3,-,1,+,+]=>[1,4,5,3,2]=>[3,1,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3
[3,+,5,-,1]=>[2,1,3,5,4]=>[1,3,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>4
[3,-,5,-,1]=>[1,3,2,5,4]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5
[3,5,1,-,2]=>[1,2,3,5,4]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[3,5,2,-,1]=>[2,1,3,5,4]=>[1,3,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>4
[3,5,4,1,2]=>[1,2,3,5,4]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[3,5,4,2,1]=>[2,1,3,5,4]=>[1,3,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>4
[4,1,2,3,+]=>[1,2,3,5,4]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[4,1,+,2,+]=>[1,3,2,5,4]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5
[4,1,-,2,+]=>[1,2,5,4,3]=>[3,1,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3
[4,+,1,3,+]=>[2,1,3,5,4]=>[1,3,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>4
[4,-,1,3,+]=>[1,3,5,4,2]=>[3,1,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3
[4,+,+,1,+]=>[2,3,1,5,4]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5
[4,-,+,1,+]=>[3,1,5,4,2]=>[1,2,1,1]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4
[4,+,-,1,+]=>[2,1,5,4,3]=>[1,2,1,1]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4
[4,3,1,2,+]=>[1,2,5,4,3]=>[3,1,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3
[4,3,2,1,+]=>[2,1,5,4,3]=>[1,2,1,1]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4
[4,5,-,1,2]=>[1,2,4,5,3]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[4,5,-,2,1]=>[2,1,4,5,3]=>[1,3,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>4
[5,1,2,-,3]=>[1,2,3,5,4]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[5,1,-,2,4]=>[1,2,4,5,3]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[5,1,-,+,2]=>[1,4,2,5,3]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5
[5,1,+,-,2]=>[1,3,2,5,4]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5
[5,1,4,2,3]=>[1,2,3,5,4]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[5,1,4,3,2]=>[1,3,2,5,4]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5
[5,-,1,3,4]=>[1,3,4,5,2]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[5,-,1,+,3]=>[1,4,3,5,2]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5
[5,+,1,-,3]=>[2,1,3,5,4]=>[1,3,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>4
[5,-,+,1,4]=>[3,1,4,5,2]=>[1,3,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>4
[5,+,-,1,4]=>[2,1,4,5,3]=>[1,3,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>4
[5,-,+,+,1]=>[3,4,1,5,2]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5
[5,+,-,+,1]=>[2,4,1,5,3]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5
[5,+,+,-,1]=>[2,3,1,5,4]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5
[5,+,4,1,3]=>[2,1,3,5,4]=>[1,3,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>4
[5,+,4,3,1]=>[2,3,1,5,4]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5
[5,3,1,2,4]=>[1,2,4,5,3]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[5,3,1,+,2]=>[1,4,2,5,3]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5
[5,3,2,1,4]=>[2,1,4,5,3]=>[1,3,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>4
[5,3,2,+,1]=>[2,4,1,5,3]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5
[5,4,1,2,3]=>[1,2,3,5,4]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[5,4,1,3,2]=>[1,3,2,5,4]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5
[5,4,2,1,3]=>[2,1,3,5,4]=>[1,3,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>4
[5,4,2,3,1]=>[2,3,1,5,4]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5
[5,4,+,1,2]=>[3,1,2,5,4]=>[1,3,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>4
[5,4,-,1,2]=>[1,2,5,4,3]=>[3,1,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3
[5,4,+,2,1]=>[3,2,1,5,4]=>[1,1,2,1]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4
[5,4,-,2,1]=>[2,1,5,4,3]=>[1,2,1,1]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4
[-,+,+,+,+,+]=>[2,3,4,5,6,1]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[+,-,+,+,+,+]=>[1,3,4,5,6,2]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[+,+,-,+,+,+]=>[1,2,4,5,6,3]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[+,+,+,-,+,+]=>[1,2,3,5,6,4]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[+,+,+,+,-,+]=>[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[+,+,+,5,4,+]=>[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[+,+,+,6,-,4]=>[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[-,+,+,6,-,4]=>[2,3,4,1,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,-,+,6,-,4]=>[1,3,4,2,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,+,-,6,-,4]=>[1,2,4,3,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,-,+,6,-,4]=>[3,4,1,2,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,+,-,6,-,4]=>[2,4,1,3,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,-,-,6,-,4]=>[1,4,2,3,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,-,-,6,-,4]=>[4,1,2,3,6,5]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[+,+,4,3,+,+]=>[1,2,3,5,6,4]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[+,+,4,6,-,3]=>[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[-,+,4,6,-,3]=>[2,3,1,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,-,4,6,-,3]=>[1,3,2,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,-,4,6,-,3]=>[3,1,2,4,6,5]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[+,+,5,3,4,+]=>[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[+,+,5,+,3,+]=>[1,2,4,3,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,+,5,-,3,+]=>[1,2,3,6,5,4]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[-,+,5,-,3,+]=>[2,3,6,1,5,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,-,5,-,3,+]=>[1,3,6,2,5,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,-,5,-,3,+]=>[3,6,1,2,5,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,+,6,3,-,4]=>[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[-,+,6,3,-,4]=>[2,3,4,1,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,-,6,3,-,4]=>[1,3,4,2,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,-,6,3,-,4]=>[3,4,1,2,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,+,6,-,3,5]=>[1,2,3,5,6,4]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[-,+,6,-,3,5]=>[2,3,5,1,6,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,-,6,-,3,5]=>[1,3,5,2,6,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,-,6,-,3,5]=>[3,5,1,2,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,+,6,-,+,3]=>[1,2,5,3,6,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,+,6,+,-,3]=>[1,2,4,3,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,+,6,-,+,3]=>[2,5,3,1,6,4]=>[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)=>5
[-,+,6,+,-,3]=>[2,4,3,1,6,5]=>[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)=>5
[+,-,6,-,+,3]=>[1,5,3,2,6,4]=>[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)=>5
[+,-,6,+,-,3]=>[1,4,3,2,6,5]=>[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)=>5
[-,-,6,-,+,3]=>[5,3,1,2,6,4]=>[1,1,3,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
[-,-,6,+,-,3]=>[4,3,1,2,6,5]=>[1,1,3,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
[+,+,6,5,3,4]=>[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[-,+,6,5,3,4]=>[2,3,4,1,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,-,6,5,3,4]=>[1,3,4,2,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,-,6,5,3,4]=>[3,4,1,2,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,+,6,5,4,3]=>[1,2,4,3,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,+,6,5,4,3]=>[2,4,3,1,6,5]=>[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)=>5
[+,-,6,5,4,3]=>[1,4,3,2,6,5]=>[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)=>5
[-,-,6,5,4,3]=>[4,3,1,2,6,5]=>[1,1,3,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
[+,3,2,+,+,+]=>[1,2,4,5,6,3]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[+,3,2,6,-,4]=>[1,2,4,3,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,3,2,6,-,4]=>[2,4,1,3,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,3,4,6,-,2]=>[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[-,3,4,6,-,2]=>[2,1,3,4,6,5]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[+,3,5,-,2,+]=>[1,2,6,3,5,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,3,5,-,2,+]=>[2,6,1,3,5,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,3,6,2,-,4]=>[1,2,4,3,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,3,6,2,-,4]=>[2,4,1,3,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,3,6,-,2,5]=>[1,2,5,3,6,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,3,6,-,2,5]=>[2,5,1,3,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,3,6,-,+,2]=>[1,5,2,3,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,3,6,+,-,2]=>[1,4,2,3,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,3,6,-,+,2]=>[5,2,1,3,6,4]=>[1,1,3,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
[-,3,6,+,-,2]=>[4,2,1,3,6,5]=>[1,1,3,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
[+,3,6,5,2,4]=>[1,2,4,3,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,3,6,5,2,4]=>[2,4,1,3,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,3,6,5,4,2]=>[1,4,2,3,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,3,6,5,4,2]=>[4,2,1,3,6,5]=>[1,1,3,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
[+,4,2,3,+,+]=>[1,2,3,5,6,4]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[+,4,2,6,-,3]=>[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[-,4,2,6,-,3]=>[2,3,1,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,4,+,2,+,+]=>[1,3,2,5,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,4,-,2,+,+]=>[1,2,5,6,4,3]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[-,4,-,2,+,+]=>[2,5,6,1,4,3]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,4,+,6,-,2]=>[1,3,2,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,4,+,6,-,2]=>[3,2,1,4,6,5]=>[1,1,3,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
[+,4,-,6,-,2]=>[1,2,4,3,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,4,-,6,-,2]=>[2,1,4,3,6,5]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[+,4,6,2,-,3]=>[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[-,4,6,2,-,3]=>[2,3,1,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,4,6,3,-,2]=>[1,3,2,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,4,6,3,-,2]=>[3,2,1,4,6,5]=>[1,1,3,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
[+,4,6,5,2,3]=>[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[-,4,6,5,2,3]=>[2,3,1,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,4,6,5,3,2]=>[1,3,2,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,4,6,5,3,2]=>[3,2,1,4,6,5]=>[1,1,3,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
[+,5,2,3,4,+]=>[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[+,5,2,+,3,+]=>[1,2,4,3,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,5,2,-,3,+]=>[1,2,3,6,5,4]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[-,5,2,-,3,+]=>[2,3,6,1,5,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,5,+,2,4,+]=>[1,3,2,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,5,-,2,4,+]=>[1,2,4,6,5,3]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[-,5,-,2,4,+]=>[2,4,6,1,5,3]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,5,+,+,2,+]=>[1,3,4,2,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,5,-,+,2,+]=>[1,4,2,6,5,3]=>[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)=>5
[+,5,+,-,2,+]=>[1,3,2,6,5,4]=>[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)=>5
[-,5,-,+,2,+]=>[4,2,6,1,5,3]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[-,5,+,-,2,+]=>[3,2,6,1,5,4]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[+,5,4,2,3,+]=>[1,2,3,6,5,4]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[-,5,4,2,3,+]=>[2,3,6,1,5,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,5,4,3,2,+]=>[1,3,2,6,5,4]=>[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)=>5
[-,5,4,3,2,+]=>[3,2,6,1,5,4]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[+,5,6,-,2,3]=>[1,2,3,5,6,4]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[-,5,6,-,2,3]=>[2,3,1,5,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,5,6,-,3,2]=>[1,3,2,5,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,5,6,-,3,2]=>[3,2,1,5,6,4]=>[1,1,3,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
[+,6,2,3,-,4]=>[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[-,6,2,3,-,4]=>[2,3,4,1,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,6,2,-,3,5]=>[1,2,3,5,6,4]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[-,6,2,-,3,5]=>[2,3,5,1,6,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,6,2,-,+,3]=>[1,2,5,3,6,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,6,2,+,-,3]=>[1,2,4,3,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,6,2,-,+,3]=>[2,5,3,1,6,4]=>[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)=>5
[-,6,2,+,-,3]=>[2,4,3,1,6,5]=>[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)=>5
[+,6,2,5,3,4]=>[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[-,6,2,5,3,4]=>[2,3,4,1,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,6,2,5,4,3]=>[1,2,4,3,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,6,2,5,4,3]=>[2,4,3,1,6,5]=>[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)=>5
[+,6,-,2,4,5]=>[1,2,4,5,6,3]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[-,6,-,2,4,5]=>[2,4,5,1,6,3]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,6,-,2,+,4]=>[1,2,5,4,6,3]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,6,+,2,-,4]=>[1,3,2,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,6,-,2,+,4]=>[2,5,4,1,6,3]=>[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)=>5
[-,6,+,2,-,4]=>[3,2,4,1,6,5]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[+,6,-,+,2,5]=>[1,4,2,5,6,3]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,6,+,-,2,5]=>[1,3,2,5,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,6,-,+,2,5]=>[4,2,5,1,6,3]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[-,6,+,-,2,5]=>[3,2,5,1,6,4]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[+,6,-,+,+,2]=>[1,4,5,2,6,3]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,6,+,-,+,2]=>[1,3,5,2,6,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,6,+,+,-,2]=>[1,3,4,2,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,6,-,+,+,2]=>[4,5,2,1,6,3]=>[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)=>5
[-,6,+,-,+,2]=>[3,5,2,1,6,4]=>[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)=>5
[-,6,+,+,-,2]=>[3,4,2,1,6,5]=>[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)=>5
[+,6,+,5,2,4]=>[1,3,2,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,6,+,5,2,4]=>[3,2,4,1,6,5]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[+,6,+,5,4,2]=>[1,3,4,2,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,6,+,5,4,2]=>[3,4,2,1,6,5]=>[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)=>5
[+,6,4,2,3,5]=>[1,2,3,5,6,4]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[-,6,4,2,3,5]=>[2,3,5,1,6,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,6,4,2,+,3]=>[1,2,5,3,6,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,6,4,2,+,3]=>[2,5,3,1,6,4]=>[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)=>5
[+,6,4,3,2,5]=>[1,3,2,5,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,6,4,3,2,5]=>[3,2,5,1,6,4]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[+,6,4,3,+,2]=>[1,3,5,2,6,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,6,4,3,+,2]=>[3,5,2,1,6,4]=>[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)=>5
[+,6,5,2,3,4]=>[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[-,6,5,2,3,4]=>[2,3,4,1,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[+,6,5,2,4,3]=>[1,2,4,3,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,6,5,2,4,3]=>[2,4,3,1,6,5]=>[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)=>5
[+,6,5,3,2,4]=>[1,3,2,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,6,5,3,2,4]=>[3,2,4,1,6,5]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[+,6,5,3,4,2]=>[1,3,4,2,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,6,5,3,4,2]=>[3,4,2,1,6,5]=>[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)=>5
[+,6,5,+,2,3]=>[1,4,2,3,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[-,6,5,+,2,3]=>[4,2,3,1,6,5]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[+,6,5,-,2,3]=>[1,2,3,6,5,4]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[-,6,5,-,2,3]=>[2,3,1,6,5,4]=>[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)=>5
[+,6,5,+,3,2]=>[1,4,3,2,6,5]=>[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)=>5
[-,6,5,+,3,2]=>[4,3,2,1,6,5]=>[1,1,1,2,1]=>([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
[+,6,5,-,3,2]=>[1,3,2,6,5,4]=>[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)=>5
[-,6,5,-,3,2]=>[3,2,1,6,5,4]=>[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)=>4
[2,1,+,+,+,+]=>[1,3,4,5,6,2]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[2,1,+,6,-,4]=>[1,3,4,2,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,1,-,6,-,4]=>[1,4,2,3,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,1,4,6,-,3]=>[1,3,2,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,1,5,-,3,+]=>[1,3,6,2,5,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,1,6,3,-,4]=>[1,3,4,2,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,1,6,-,3,5]=>[1,3,5,2,6,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,1,6,-,+,3]=>[1,5,3,2,6,4]=>[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)=>5
[2,1,6,+,-,3]=>[1,4,3,2,6,5]=>[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)=>5
[2,1,6,5,3,4]=>[1,3,4,2,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,1,6,5,4,3]=>[1,4,3,2,6,5]=>[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)=>5
[2,3,1,6,-,4]=>[1,4,2,3,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,3,4,6,-,1]=>[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[2,3,5,-,1,+]=>[1,6,2,3,5,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,3,6,1,-,4]=>[1,4,2,3,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,3,6,-,1,5]=>[1,5,2,3,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,3,6,-,+,1]=>[5,1,2,3,6,4]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[2,3,6,+,-,1]=>[4,1,2,3,6,5]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[2,3,6,5,1,4]=>[1,4,2,3,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,3,6,5,4,1]=>[4,1,2,3,6,5]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[2,4,1,6,-,3]=>[1,3,2,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,4,-,1,+,+]=>[1,5,6,2,4,3]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,4,+,6,-,1]=>[3,1,2,4,6,5]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[2,4,-,6,-,1]=>[1,2,4,3,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,4,6,1,-,3]=>[1,3,2,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,4,6,3,-,1]=>[3,1,2,4,6,5]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[2,4,6,5,1,3]=>[1,3,2,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,4,6,5,3,1]=>[3,1,2,4,6,5]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[2,5,1,-,3,+]=>[1,3,6,2,5,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,5,-,1,4,+]=>[1,4,6,2,5,3]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,5,-,+,1,+]=>[4,1,6,2,5,3]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[2,5,+,-,1,+]=>[3,1,6,2,5,4]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[2,5,4,1,3,+]=>[1,3,6,2,5,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,5,4,3,1,+]=>[3,1,6,2,5,4]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[2,5,6,-,1,3]=>[1,3,2,5,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,5,6,-,3,1]=>[3,1,2,5,6,4]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[2,6,1,3,-,4]=>[1,3,4,2,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,6,1,-,3,5]=>[1,3,5,2,6,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,6,1,-,+,3]=>[1,5,3,2,6,4]=>[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)=>5
[2,6,1,+,-,3]=>[1,4,3,2,6,5]=>[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)=>5
[2,6,1,5,3,4]=>[1,3,4,2,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,6,1,5,4,3]=>[1,4,3,2,6,5]=>[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)=>5
[2,6,-,1,4,5]=>[1,4,5,2,6,3]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,6,-,1,+,4]=>[1,5,4,2,6,3]=>[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)=>5
[2,6,+,1,-,4]=>[3,1,4,2,6,5]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[2,6,-,+,1,5]=>[4,1,5,2,6,3]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[2,6,+,-,1,5]=>[3,1,5,2,6,4]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[2,6,-,+,+,1]=>[4,5,1,2,6,3]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,6,+,-,+,1]=>[3,5,1,2,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,6,+,+,-,1]=>[3,4,1,2,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,6,+,5,1,4]=>[3,1,4,2,6,5]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[2,6,+,5,4,1]=>[3,4,1,2,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,6,4,1,3,5]=>[1,3,5,2,6,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,6,4,1,+,3]=>[1,5,3,2,6,4]=>[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)=>5
[2,6,4,3,1,5]=>[3,1,5,2,6,4]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[2,6,4,3,+,1]=>[3,5,1,2,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,6,5,1,3,4]=>[1,3,4,2,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,6,5,1,4,3]=>[1,4,3,2,6,5]=>[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)=>5
[2,6,5,3,1,4]=>[3,1,4,2,6,5]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[2,6,5,3,4,1]=>[3,4,1,2,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[2,6,5,+,1,3]=>[4,1,3,2,6,5]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[2,6,5,-,1,3]=>[1,3,2,6,5,4]=>[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)=>5
[2,6,5,+,3,1]=>[4,3,1,2,6,5]=>[1,1,3,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
[2,6,5,-,3,1]=>[3,1,2,6,5,4]=>[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)=>4
[3,1,2,+,+,+]=>[1,2,4,5,6,3]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[3,1,2,6,-,4]=>[1,2,4,3,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[3,1,4,6,-,2]=>[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[3,1,5,-,2,+]=>[1,2,6,3,5,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[3,1,6,2,-,4]=>[1,2,4,3,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[3,1,6,-,2,5]=>[1,2,5,3,6,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[3,1,6,-,+,2]=>[1,5,2,3,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[3,1,6,+,-,2]=>[1,4,2,3,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[3,1,6,5,2,4]=>[1,2,4,3,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[3,1,6,5,4,2]=>[1,4,2,3,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[3,+,1,+,+,+]=>[2,1,4,5,6,3]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[3,-,1,+,+,+]=>[1,4,5,6,3,2]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[3,+,1,6,-,4]=>[2,1,4,3,6,5]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[3,-,1,6,-,4]=>[1,4,3,2,6,5]=>[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)=>5
[3,+,4,6,-,1]=>[2,1,3,4,6,5]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[3,-,4,6,-,1]=>[1,3,2,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[3,+,5,-,1,+]=>[2,1,6,3,5,4]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[3,-,5,-,1,+]=>[1,6,3,2,5,4]=>[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)=>5
[3,+,6,1,-,4]=>[2,1,4,3,6,5]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[3,-,6,1,-,4]=>[1,4,3,2,6,5]=>[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)=>5
[3,+,6,-,1,5]=>[2,1,5,3,6,4]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[3,-,6,-,1,5]=>[1,5,3,2,6,4]=>[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)=>5
[3,+,6,-,+,1]=>[2,5,1,3,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[3,+,6,+,-,1]=>[2,4,1,3,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[3,-,6,-,+,1]=>[5,1,3,2,6,4]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[3,-,6,+,-,1]=>[4,1,3,2,6,5]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[3,+,6,5,1,4]=>[2,1,4,3,6,5]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[3,-,6,5,1,4]=>[1,4,3,2,6,5]=>[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)=>5
[3,+,6,5,4,1]=>[2,4,1,3,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[3,-,6,5,4,1]=>[4,1,3,2,6,5]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[3,4,1,6,-,2]=>[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[3,4,2,6,-,1]=>[2,1,3,4,6,5]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[3,4,6,1,-,2]=>[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[3,4,6,2,-,1]=>[2,1,3,4,6,5]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[3,4,6,5,1,2]=>[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[3,4,6,5,2,1]=>[2,1,3,4,6,5]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[3,5,1,-,2,+]=>[1,2,6,3,5,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[3,5,2,-,1,+]=>[2,1,6,3,5,4]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[3,5,4,1,2,+]=>[1,2,6,3,5,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[3,5,4,2,1,+]=>[2,1,6,3,5,4]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[3,5,6,-,1,2]=>[1,2,3,5,6,4]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[3,5,6,-,2,1]=>[2,1,3,5,6,4]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[3,6,1,2,-,4]=>[1,2,4,3,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[3,6,1,-,2,5]=>[1,2,5,3,6,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[3,6,1,-,+,2]=>[1,5,2,3,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[3,6,1,+,-,2]=>[1,4,2,3,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[3,6,1,5,2,4]=>[1,2,4,3,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[3,6,1,5,4,2]=>[1,4,2,3,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[3,6,2,1,-,4]=>[2,1,4,3,6,5]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[3,6,2,-,1,5]=>[2,1,5,3,6,4]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[3,6,2,-,+,1]=>[2,5,1,3,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[3,6,2,+,-,1]=>[2,4,1,3,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[3,6,2,5,1,4]=>[2,1,4,3,6,5]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[3,6,2,5,4,1]=>[2,4,1,3,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[3,6,4,1,2,5]=>[1,2,5,3,6,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[3,6,4,1,+,2]=>[1,5,2,3,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[3,6,4,2,1,5]=>[2,1,5,3,6,4]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[3,6,4,2,+,1]=>[2,5,1,3,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[3,6,5,1,2,4]=>[1,2,4,3,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[3,6,5,1,4,2]=>[1,4,2,3,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[3,6,5,2,1,4]=>[2,1,4,3,6,5]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[3,6,5,2,4,1]=>[2,4,1,3,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[3,6,5,+,1,2]=>[4,1,2,3,6,5]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[3,6,5,-,1,2]=>[1,2,3,6,5,4]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[3,6,5,+,2,1]=>[4,2,1,3,6,5]=>[1,1,3,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
[3,6,5,-,2,1]=>[2,1,3,6,5,4]=>[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)=>4
[4,1,2,3,+,+]=>[1,2,3,5,6,4]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[4,1,2,6,-,3]=>[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[4,1,+,2,+,+]=>[1,3,2,5,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[4,1,-,2,+,+]=>[1,2,5,6,4,3]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,1,+,6,-,2]=>[1,3,2,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[4,1,-,6,-,2]=>[1,2,4,3,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[4,1,6,2,-,3]=>[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[4,1,6,3,-,2]=>[1,3,2,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[4,1,6,5,2,3]=>[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[4,1,6,5,3,2]=>[1,3,2,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[4,+,1,3,+,+]=>[2,1,3,5,6,4]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[4,-,1,3,+,+]=>[1,3,5,6,4,2]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,+,1,6,-,3]=>[2,1,3,4,6,5]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[4,-,1,6,-,3]=>[1,3,4,2,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[4,+,+,1,+,+]=>[2,3,1,5,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[4,-,+,1,+,+]=>[3,1,5,6,4,2]=>[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)=>4
[4,+,-,1,+,+]=>[2,1,5,6,4,3]=>[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)=>4
[4,+,+,6,-,1]=>[2,3,1,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[4,-,+,6,-,1]=>[3,1,4,2,6,5]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[4,+,-,6,-,1]=>[2,1,4,3,6,5]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[4,-,-,6,-,1]=>[1,4,2,3,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[4,+,6,1,-,3]=>[2,1,3,4,6,5]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[4,-,6,1,-,3]=>[1,3,4,2,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[4,+,6,3,-,1]=>[2,3,1,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[4,-,6,3,-,1]=>[3,1,4,2,6,5]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[4,+,6,5,1,3]=>[2,1,3,4,6,5]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[4,-,6,5,1,3]=>[1,3,4,2,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[4,+,6,5,3,1]=>[2,3,1,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[4,-,6,5,3,1]=>[3,1,4,2,6,5]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[4,3,1,2,+,+]=>[1,2,5,6,4,3]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,3,1,6,-,2]=>[1,2,4,3,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[4,3,2,1,+,+]=>[2,1,5,6,4,3]=>[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)=>4
[4,3,2,6,-,1]=>[2,1,4,3,6,5]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[4,3,6,1,-,2]=>[1,2,4,3,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[4,3,6,2,-,1]=>[2,1,4,3,6,5]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[4,3,6,5,1,2]=>[1,2,4,3,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[4,3,6,5,2,1]=>[2,1,4,3,6,5]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[4,5,-,1,2,+]=>[1,2,6,4,5,3]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[4,5,-,2,1,+]=>[2,1,6,4,5,3]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[4,6,1,2,-,3]=>[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[4,6,1,3,-,2]=>[1,3,2,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[4,6,1,5,2,3]=>[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[4,6,1,5,3,2]=>[1,3,2,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[4,6,2,1,-,3]=>[2,1,3,4,6,5]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[4,6,2,3,-,1]=>[2,3,1,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[4,6,2,5,1,3]=>[2,1,3,4,6,5]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[4,6,2,5,3,1]=>[2,3,1,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[4,6,-,1,2,5]=>[1,2,5,4,6,3]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[4,6,-,1,+,2]=>[1,5,2,4,6,3]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[4,6,+,1,-,2]=>[3,1,2,4,6,5]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[4,6,-,2,1,5]=>[2,1,5,4,6,3]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[4,6,-,2,+,1]=>[2,5,1,4,6,3]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[4,6,+,2,-,1]=>[3,2,1,4,6,5]=>[1,1,3,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
[4,6,+,5,1,2]=>[3,1,2,4,6,5]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[4,6,+,5,2,1]=>[3,2,1,4,6,5]=>[1,1,3,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
[4,6,5,1,2,3]=>[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[4,6,5,1,3,2]=>[1,3,2,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[4,6,5,2,1,3]=>[2,1,3,4,6,5]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[4,6,5,2,3,1]=>[2,3,1,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[4,6,5,3,1,2]=>[3,1,2,4,6,5]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[4,6,5,3,2,1]=>[3,2,1,4,6,5]=>[1,1,3,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
[5,1,2,3,4,+]=>[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[5,1,2,+,3,+]=>[1,2,4,3,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[5,1,2,-,3,+]=>[1,2,3,6,5,4]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[5,1,+,2,4,+]=>[1,3,2,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[5,1,-,2,4,+]=>[1,2,4,6,5,3]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[5,1,+,+,2,+]=>[1,3,4,2,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[5,1,-,+,2,+]=>[1,4,2,6,5,3]=>[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)=>5
[5,1,+,-,2,+]=>[1,3,2,6,5,4]=>[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)=>5
[5,1,4,2,3,+]=>[1,2,3,6,5,4]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[5,1,4,3,2,+]=>[1,3,2,6,5,4]=>[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)=>5
[5,1,6,-,2,3]=>[1,2,3,5,6,4]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[5,1,6,-,3,2]=>[1,3,2,5,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[5,+,1,3,4,+]=>[2,1,3,4,6,5]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[5,-,1,3,4,+]=>[1,3,4,6,5,2]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[5,+,1,+,3,+]=>[2,1,4,3,6,5]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[5,-,1,+,3,+]=>[1,4,3,6,5,2]=>[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)=>5
[5,+,1,-,3,+]=>[2,1,3,6,5,4]=>[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)=>4
[5,+,+,1,4,+]=>[2,3,1,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[5,-,+,1,4,+]=>[3,1,4,6,5,2]=>[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)=>4
[5,+,-,1,4,+]=>[2,1,4,6,5,3]=>[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)=>4
[5,+,+,+,1,+]=>[2,3,4,1,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[5,-,+,+,1,+]=>[3,4,1,6,5,2]=>[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)=>5
[5,+,-,+,1,+]=>[2,4,1,6,5,3]=>[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)=>5
[5,+,+,-,1,+]=>[2,3,1,6,5,4]=>[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)=>5
[5,+,4,1,3,+]=>[2,1,3,6,5,4]=>[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)=>4
[5,+,4,3,1,+]=>[2,3,1,6,5,4]=>[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)=>5
[5,+,6,-,1,3]=>[2,1,3,5,6,4]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[5,-,6,-,1,3]=>[1,3,5,2,6,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[5,+,6,-,3,1]=>[2,3,1,5,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[5,-,6,-,3,1]=>[3,1,5,2,6,4]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[5,3,1,2,4,+]=>[1,2,4,6,5,3]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[5,3,1,+,2,+]=>[1,4,2,6,5,3]=>[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)=>5
[5,3,2,1,4,+]=>[2,1,4,6,5,3]=>[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)=>4
[5,3,2,+,1,+]=>[2,4,1,6,5,3]=>[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)=>5
[5,3,6,-,1,2]=>[1,2,5,3,6,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[5,3,6,-,2,1]=>[2,1,5,3,6,4]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[5,4,1,2,3,+]=>[1,2,3,6,5,4]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[5,4,1,3,2,+]=>[1,3,2,6,5,4]=>[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)=>5
[5,4,2,1,3,+]=>[2,1,3,6,5,4]=>[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)=>4
[5,4,2,3,1,+]=>[2,3,1,6,5,4]=>[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)=>5
[5,4,+,1,2,+]=>[3,1,2,6,5,4]=>[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)=>4
[5,4,-,1,2,+]=>[1,2,6,5,4,3]=>[3,1,1,1]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[5,4,+,2,1,+]=>[3,2,1,6,5,4]=>[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)=>4
[5,4,-,2,1,+]=>[2,1,6,5,4,3]=>[1,2,1,1,1]=>([(0,3),(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)=>4
[5,6,1,-,2,3]=>[1,2,3,5,6,4]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[5,6,1,-,3,2]=>[1,3,2,5,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[5,6,2,-,1,3]=>[2,1,3,5,6,4]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[5,6,2,-,3,1]=>[2,3,1,5,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[5,6,-,1,2,4]=>[1,2,4,5,6,3]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[5,6,-,1,4,2]=>[1,4,2,5,6,3]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[5,6,-,2,1,4]=>[2,1,4,5,6,3]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[5,6,-,2,4,1]=>[2,4,1,5,6,3]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[5,6,-,+,1,2]=>[4,1,2,5,6,3]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[5,6,+,-,1,2]=>[3,1,2,5,6,4]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[5,6,-,+,2,1]=>[4,2,1,5,6,3]=>[1,1,3,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
[5,6,+,-,2,1]=>[3,2,1,5,6,4]=>[1,1,3,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
[5,6,4,1,2,3]=>[1,2,3,5,6,4]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[5,6,4,1,3,2]=>[1,3,2,5,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[5,6,4,2,1,3]=>[2,1,3,5,6,4]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[5,6,4,2,3,1]=>[2,3,1,5,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[5,6,4,3,1,2]=>[3,1,2,5,6,4]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[5,6,4,3,2,1]=>[3,2,1,5,6,4]=>[1,1,3,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
[6,1,2,3,-,4]=>[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[6,1,2,-,3,5]=>[1,2,3,5,6,4]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[6,1,2,-,+,3]=>[1,2,5,3,6,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,1,2,+,-,3]=>[1,2,4,3,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,1,2,5,3,4]=>[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[6,1,2,5,4,3]=>[1,2,4,3,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,1,-,2,4,5]=>[1,2,4,5,6,3]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[6,1,-,2,+,4]=>[1,2,5,4,6,3]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,1,+,2,-,4]=>[1,3,2,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,1,-,+,2,5]=>[1,4,2,5,6,3]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,1,+,-,2,5]=>[1,3,2,5,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,1,-,+,+,2]=>[1,4,5,2,6,3]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,1,+,-,+,2]=>[1,3,5,2,6,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,1,+,+,-,2]=>[1,3,4,2,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,1,+,5,2,4]=>[1,3,2,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,1,+,5,4,2]=>[1,3,4,2,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,1,4,2,3,5]=>[1,2,3,5,6,4]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[6,1,4,2,+,3]=>[1,2,5,3,6,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,1,4,3,2,5]=>[1,3,2,5,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,1,4,3,+,2]=>[1,3,5,2,6,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,1,5,2,3,4]=>[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[6,1,5,2,4,3]=>[1,2,4,3,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,1,5,3,2,4]=>[1,3,2,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,1,5,3,4,2]=>[1,3,4,2,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,1,5,+,2,3]=>[1,4,2,3,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,1,5,-,2,3]=>[1,2,3,6,5,4]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[6,1,5,+,3,2]=>[1,4,3,2,6,5]=>[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)=>5
[6,1,5,-,3,2]=>[1,3,2,6,5,4]=>[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)=>5
[6,-,1,3,4,5]=>[1,3,4,5,6,2]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[6,-,1,3,+,4]=>[1,3,5,4,6,2]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,+,1,3,-,4]=>[2,1,3,4,6,5]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[6,-,1,+,3,5]=>[1,4,3,5,6,2]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,+,1,-,3,5]=>[2,1,3,5,6,4]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[6,-,1,+,+,3]=>[1,4,5,3,6,2]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,+,1,-,+,3]=>[2,1,5,3,6,4]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[6,+,1,+,-,3]=>[2,1,4,3,6,5]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[6,+,1,5,3,4]=>[2,1,3,4,6,5]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[6,+,1,5,4,3]=>[2,1,4,3,6,5]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[6,-,+,1,4,5]=>[3,1,4,5,6,2]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[6,+,-,1,4,5]=>[2,1,4,5,6,3]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[6,-,+,1,+,4]=>[3,1,5,4,6,2]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[6,+,-,1,+,4]=>[2,1,5,4,6,3]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[6,+,+,1,-,4]=>[2,3,1,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,-,+,+,1,5]=>[3,4,1,5,6,2]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,+,-,+,1,5]=>[2,4,1,5,6,3]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,+,+,-,1,5]=>[2,3,1,5,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,-,+,+,+,1]=>[3,4,5,1,6,2]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,+,-,+,+,1]=>[2,4,5,1,6,3]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,+,+,-,+,1]=>[2,3,5,1,6,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,+,+,+,-,1]=>[2,3,4,1,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,+,+,5,1,4]=>[2,3,1,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,+,+,5,4,1]=>[2,3,4,1,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,+,4,1,3,5]=>[2,1,3,5,6,4]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[6,+,4,1,+,3]=>[2,1,5,3,6,4]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[6,+,4,3,1,5]=>[2,3,1,5,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,+,4,3,+,1]=>[2,3,5,1,6,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,+,5,1,3,4]=>[2,1,3,4,6,5]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[6,+,5,1,4,3]=>[2,1,4,3,6,5]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[6,+,5,3,1,4]=>[2,3,1,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,+,5,3,4,1]=>[2,3,4,1,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,+,5,+,1,3]=>[2,4,1,3,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,+,5,-,1,3]=>[2,1,3,6,5,4]=>[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)=>4
[6,-,5,-,1,3]=>[1,3,6,2,5,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,+,5,+,3,1]=>[2,4,3,1,6,5]=>[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)=>5
[6,+,5,-,3,1]=>[2,3,1,6,5,4]=>[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)=>5
[6,-,5,-,3,1]=>[3,1,6,2,5,4]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[6,3,1,2,4,5]=>[1,2,4,5,6,3]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[6,3,1,2,+,4]=>[1,2,5,4,6,3]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,3,1,+,2,5]=>[1,4,2,5,6,3]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,3,1,+,+,2]=>[1,4,5,2,6,3]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,3,2,1,4,5]=>[2,1,4,5,6,3]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[6,3,2,1,+,4]=>[2,1,5,4,6,3]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[6,3,2,+,1,5]=>[2,4,1,5,6,3]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,3,2,+,+,1]=>[2,4,5,1,6,3]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,3,5,-,1,2]=>[1,2,6,3,5,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,3,5,-,2,1]=>[2,1,6,3,5,4]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[6,4,1,2,3,5]=>[1,2,3,5,6,4]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[6,4,1,2,+,3]=>[1,2,5,3,6,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,4,1,3,2,5]=>[1,3,2,5,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,4,1,3,+,2]=>[1,3,5,2,6,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,4,2,1,3,5]=>[2,1,3,5,6,4]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[6,4,2,1,+,3]=>[2,1,5,3,6,4]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[6,4,2,3,1,5]=>[2,3,1,5,6,4]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,4,2,3,+,1]=>[2,3,5,1,6,4]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,4,+,1,2,5]=>[3,1,2,5,6,4]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[6,4,-,1,2,5]=>[1,2,5,6,4,3]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[6,4,+,1,+,2]=>[3,1,5,2,6,4]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[6,4,-,1,+,2]=>[1,5,2,6,4,3]=>[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)=>5
[6,4,+,2,1,5]=>[3,2,1,5,6,4]=>[1,1,3,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
[6,4,-,2,1,5]=>[2,1,5,6,4,3]=>[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)=>4
[6,4,+,2,+,1]=>[3,2,5,1,6,4]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[6,4,-,2,+,1]=>[2,5,1,6,4,3]=>[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)=>5
[6,5,1,2,3,4]=>[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>3
[6,5,1,2,4,3]=>[1,2,4,3,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,5,1,3,2,4]=>[1,3,2,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,5,1,3,4,2]=>[1,3,4,2,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,5,1,+,2,3]=>[1,4,2,3,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,5,1,-,2,3]=>[1,2,3,6,5,4]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[6,5,1,+,3,2]=>[1,4,3,2,6,5]=>[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)=>5
[6,5,1,-,3,2]=>[1,3,2,6,5,4]=>[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)=>5
[6,5,2,1,3,4]=>[2,1,3,4,6,5]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[6,5,2,1,4,3]=>[2,1,4,3,6,5]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[6,5,2,3,1,4]=>[2,3,1,4,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,5,2,3,4,1]=>[2,3,4,1,6,5]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,5,2,+,1,3]=>[2,4,1,3,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,5,2,-,1,3]=>[2,1,3,6,5,4]=>[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)=>4
[6,5,2,+,3,1]=>[2,4,3,1,6,5]=>[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)=>5
[6,5,2,-,3,1]=>[2,3,1,6,5,4]=>[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)=>5
[6,5,+,1,2,4]=>[3,1,2,4,6,5]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4
[6,5,-,1,2,4]=>[1,2,4,6,5,3]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[6,5,+,1,4,2]=>[3,1,4,2,6,5]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[6,5,-,1,4,2]=>[1,4,2,6,5,3]=>[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)=>5
[6,5,+,2,1,4]=>[3,2,1,4,6,5]=>[1,1,3,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
[6,5,-,2,1,4]=>[2,1,4,6,5,3]=>[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)=>4
[6,5,+,2,4,1]=>[3,2,4,1,6,5]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
[6,5,-,2,4,1]=>[2,4,1,6,5,3]=>[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)=>5
[6,5,+,+,1,2]=>[3,4,1,2,6,5]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
[6,5,-,+,1,2]=>[4,1,2,6,5,3]=>[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)=>4
[6,5,+,-,1,2]=>[3,1,2,6,5,4]=>[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)=>4
[6,5,+,+,2,1]=>[3,4,2,1,6,5]=>[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)=>5
[6,5,-,+,2,1]=>[4,2,1,6,5,3]=>[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)=>4
[6,5,+,-,2,1]=>[3,2,1,6,5,4]=>[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)=>4
[6,5,4,1,2,3]=>[1,2,3,6,5,4]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[6,5,4,1,3,2]=>[1,3,2,6,5,4]=>[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)=>5
[6,5,4,2,1,3]=>[2,1,3,6,5,4]=>[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)=>4
[6,5,4,2,3,1]=>[2,3,1,6,5,4]=>[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)=>5
[6,5,4,3,1,2]=>[3,1,2,6,5,4]=>[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)=>4
[6,5,4,3,2,1]=>[3,2,1,6,5,4]=>[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)=>4
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Description
The number of distinct eigenvalues of the distance Laplacian of a connected graph.
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.
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.
Map
lower permutation
Description
The lower 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 $u$.
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 $u$.
Map
descent composition
Description
The descent composition of a permutation.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
The descent composition of a permutation $\pi$ of length $n$ is the integer composition of $n$ whose descent set equals the descent set of $\pi$. The descent set of a permutation $\pi$ is $\{i \mid 1 \leq i < n, \pi(i) > \pi(i+1)\}$. The descent set of a composition $c = (i_1, i_2, \ldots, i_k)$ is the set $\{ i_1, i_1 + i_2, i_1 + i_2 + i_3, \ldots, i_1 + i_2 + \cdots + i_{k-1} \}$.
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