Identifier
-
Mp00160:
Permutations
—graph of inversions⟶
Graphs
Mp00154: Graphs —core⟶ Graphs
Mp00037: Graphs —to partition of connected components⟶ Integer partitions
St001603: Integer partitions ⟶ ℤ
Values
=>
Cc0020;cc-rep-1
Cc0020;cc-rep-2
Cc0002;cc-rep
[3,2,1]=>([(0,1),(0,2),(1,2)],3)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,4,3,2]=>([(1,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,4,3,1]=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,2,1,4]=>([(1,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,2,4,1]=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,4,2,1]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,2,3,1]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[1,2,5,4,3]=>([(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,3,5,4,2]=>([(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,4,3,2,5]=>([(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,4,3,5,2]=>([(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,4,5,3,2]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,5,2,4,3]=>([(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,5,3,2,4]=>([(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,5,3,4,2]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,5,4,2,3]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,5,4,3,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[2,1,5,4,3]=>([(0,1),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,3,5,4,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,4,3,1,5]=>([(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,4,3,5,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,4,5,3,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,5,1,4,3]=>([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,5,3,1,4]=>([(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,5,3,4,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,5,4,1,3]=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,5,4,3,1]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[3,1,5,4,2]=>([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,2,1,5,4]=>([(0,1),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,2,4,1,5]=>([(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,2,4,5,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,2,5,1,4]=>([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,2,5,4,1]=>([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,4,2,1,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,4,2,5,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,4,5,2,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,5,1,4,2]=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,5,2,1,4]=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,5,2,4,1]=>([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,5,4,1,2]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,5,4,2,1]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,1,3,5,2]=>([(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,1,5,3,2]=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,2,1,5,3]=>([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,2,3,1,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,2,3,5,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,2,5,1,3]=>([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,2,5,3,1]=>([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,3,1,2,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,3,1,5,2]=>([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,3,2,1,5]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[4,3,2,5,1]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[4,3,5,1,2]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,3,5,2,1]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[4,5,1,3,2]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,5,2,1,3]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,5,2,3,1]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,5,3,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,5,3,2,1]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,1,3,2,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,1,3,4,2]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,1,4,2,3]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,1,4,3,2]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,2,1,4,3]=>([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,2,3,1,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,2,3,4,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,2,4,1,3]=>([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,2,4,3,1]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,3,1,2,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,3,1,4,2]=>([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,3,2,1,4]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,3,2,4,1]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,3,4,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,3,4,2,1]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,4,1,3,2]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,4,2,1,3]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,4,2,3,1]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,4,3,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>1
[1,2,3,6,5,4]=>([(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,2,4,6,5,3]=>([(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,2,5,4,3,6]=>([(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,2,5,4,6,3]=>([(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,2,5,6,4,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,2,6,3,5,4]=>([(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,2,6,4,3,5]=>([(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,2,6,4,5,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,2,6,5,3,4]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,2,6,5,4,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[1,3,2,6,5,4]=>([(1,2),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,3,4,6,5,2]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,3,5,4,2,6]=>([(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,3,5,4,6,2]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,3,5,6,4,2]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,3,6,2,5,4]=>([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,3,6,4,2,5]=>([(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,3,6,4,5,2]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,3,6,5,2,4]=>([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,3,6,5,4,2]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[1,4,2,6,5,3]=>([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,4,3,2,5,6]=>([(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,4,3,2,6,5]=>([(1,2),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,4,3,5,2,6]=>([(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,4,3,5,6,2]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,4,3,6,2,5]=>([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,4,3,6,5,2]=>([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,4,5,3,2,6]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,4,5,3,6,2]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,4,5,6,3,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,4,6,2,5,3]=>([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,4,6,3,2,5]=>([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,4,6,3,5,2]=>([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,4,6,5,2,3]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,4,6,5,3,2]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[1,5,2,4,3,6]=>([(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,5,2,4,6,3]=>([(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,5,2,6,4,3]=>([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,5,3,2,4,6]=>([(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,5,3,2,6,4]=>([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,5,3,4,2,6]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,5,3,4,6,2]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,5,3,6,2,4]=>([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,5,3,6,4,2]=>([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,5,4,2,3,6]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,5,4,2,6,3]=>([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,5,4,3,2,6]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[1,5,4,3,6,2]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[1,5,4,6,2,3]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,5,4,6,3,2]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[1,5,6,2,4,3]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,5,6,3,2,4]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,5,6,3,4,2]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,5,6,4,2,3]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,5,6,4,3,2]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[1,6,2,3,5,4]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,6,2,4,3,5]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,6,2,4,5,3]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,6,2,5,3,4]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,6,2,5,4,3]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[1,6,3,2,4,5]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,6,3,2,5,4]=>([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,6,3,4,2,5]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,6,3,4,5,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,6,3,5,2,4]=>([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,6,3,5,4,2]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[1,6,4,2,3,5]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,6,4,2,5,3]=>([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,6,4,3,2,5]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[1,6,4,3,5,2]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[1,6,4,5,2,3]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,6,4,5,3,2]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[1,6,5,2,3,4]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[1,6,5,2,4,3]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[1,6,5,3,2,4]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[1,6,5,3,4,2]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[1,6,5,4,2,3]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[1,6,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>1
[2,1,3,6,5,4]=>([(1,2),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,1,4,6,5,3]=>([(0,1),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,1,5,4,3,6]=>([(1,2),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,1,5,4,6,3]=>([(0,1),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,1,5,6,4,3]=>([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,1,6,3,5,4]=>([(0,1),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,1,6,4,3,5]=>([(0,1),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,1,6,4,5,3]=>([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,1,6,5,3,4]=>([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,1,6,5,4,3]=>([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[2,3,1,6,5,4]=>([(0,5),(1,5),(2,3),(2,4),(3,4)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,3,4,6,5,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,3,5,4,1,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,3,5,4,6,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,3,5,6,4,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,3,6,1,5,4]=>([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,3,6,4,1,5]=>([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,3,6,4,5,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,3,6,5,1,4]=>([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,3,6,5,4,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[2,4,1,6,5,3]=>([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,4,3,1,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,4,3,1,6,5]=>([(0,1),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,4,3,5,1,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,4,3,5,6,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,4,3,6,1,5]=>([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,4,3,6,5,1]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,4,5,3,1,6]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,4,5,3,6,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,4,5,6,3,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,4,6,1,5,3]=>([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,4,6,3,1,5]=>([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,4,6,3,5,1]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,4,6,5,1,3]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,4,6,5,3,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[2,5,1,4,3,6]=>([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,5,1,4,6,3]=>([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,5,1,6,4,3]=>([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,5,3,1,4,6]=>([(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,5,3,1,6,4]=>([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,5,3,4,1,6]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,5,3,4,6,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,5,3,6,1,4]=>([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,5,3,6,4,1]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,5,4,1,3,6]=>([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,5,4,1,6,3]=>([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,5,4,3,1,6]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[2,5,4,3,6,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[2,5,4,6,1,3]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,5,4,6,3,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[2,5,6,1,4,3]=>([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,5,6,3,1,4]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,5,6,3,4,1]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,5,6,4,1,3]=>([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,5,6,4,3,1]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[2,6,1,3,5,4]=>([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,6,1,4,3,5]=>([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,6,1,4,5,3]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,6,1,5,3,4]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,6,1,5,4,3]=>([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[2,6,3,1,4,5]=>([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,6,3,1,5,4]=>([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,6,3,4,1,5]=>([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,6,3,4,5,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,6,3,5,1,4]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,6,3,5,4,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[2,6,4,1,3,5]=>([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,6,4,1,5,3]=>([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,6,4,3,1,5]=>([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[2,6,4,3,5,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[2,6,4,5,1,3]=>([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,6,4,5,3,1]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[2,6,5,1,3,4]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[2,6,5,1,4,3]=>([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[2,6,5,3,1,4]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[2,6,5,3,4,1]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[2,6,5,4,1,3]=>([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[2,6,5,4,3,1]=>([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>1
[3,1,2,6,5,4]=>([(0,5),(1,5),(2,3),(2,4),(3,4)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,1,4,6,5,2]=>([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,1,5,4,2,6]=>([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,1,5,4,6,2]=>([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,1,5,6,4,2]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,1,6,2,5,4]=>([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,1,6,4,2,5]=>([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,1,6,4,5,2]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,1,6,5,2,4]=>([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,1,6,5,4,2]=>([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[3,2,1,4,5,6]=>([(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,2,1,4,6,5]=>([(1,2),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,2,1,5,4,6]=>([(1,2),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,2,1,5,6,4]=>([(0,5),(1,5),(2,3),(2,4),(3,4)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,2,1,6,4,5]=>([(0,5),(1,5),(2,3),(2,4),(3,4)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,2,1,6,5,4]=>([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,2,4,1,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,2,4,1,6,5]=>([(0,1),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,2,4,5,1,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,2,4,5,6,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,2,4,6,1,5]=>([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,2,4,6,5,1]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,2,5,1,4,6]=>([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,2,5,1,6,4]=>([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,2,5,4,1,6]=>([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,2,5,4,6,1]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,2,5,6,1,4]=>([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,2,5,6,4,1]=>([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,2,6,1,4,5]=>([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,2,6,1,5,4]=>([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,2,6,4,1,5]=>([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,2,6,4,5,1]=>([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,2,6,5,1,4]=>([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,2,6,5,4,1]=>([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[3,4,1,6,5,2]=>([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,4,2,1,5,6]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,4,2,1,6,5]=>([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,4,2,5,1,6]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,4,2,5,6,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,4,2,6,1,5]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,4,2,6,5,1]=>([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,4,5,2,1,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,4,5,2,6,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,4,5,6,2,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,4,6,1,5,2]=>([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,4,6,2,1,5]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,4,6,2,5,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,4,6,5,1,2]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,4,6,5,2,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[3,5,1,4,2,6]=>([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,5,1,4,6,2]=>([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,5,1,6,4,2]=>([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,5,2,1,4,6]=>([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,5,2,1,6,4]=>([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,5,2,4,1,6]=>([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,5,2,4,6,1]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,5,2,6,1,4]=>([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,5,2,6,4,1]=>([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,5,4,1,2,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,5,4,1,6,2]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,5,4,2,1,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[3,5,4,2,6,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[3,5,4,6,1,2]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,5,4,6,2,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[3,5,6,1,4,2]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,5,6,2,1,4]=>([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,5,6,2,4,1]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,5,6,4,1,2]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,5,6,4,2,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[3,6,1,2,5,4]=>([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,6,1,4,2,5]=>([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,6,1,4,5,2]=>([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,6,1,5,2,4]=>([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,6,1,5,4,2]=>([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[3,6,2,1,4,5]=>([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,6,2,1,5,4]=>([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,6,2,4,1,5]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,6,2,4,5,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,6,2,5,1,4]=>([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,6,2,5,4,1]=>([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[3,6,4,1,2,5]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,6,4,1,5,2]=>([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,6,4,2,1,5]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[3,6,4,2,5,1]=>([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[3,6,4,5,1,2]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,6,4,5,2,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[3,6,5,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[3,6,5,1,4,2]=>([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[3,6,5,2,1,4]=>([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[3,6,5,2,4,1]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[3,6,5,4,1,2]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[3,6,5,4,2,1]=>([(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)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>1
[4,1,2,6,5,3]=>([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,1,3,2,6,5]=>([(0,1),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,1,3,5,2,6]=>([(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,1,3,5,6,2]=>([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,1,3,6,2,5]=>([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,1,3,6,5,2]=>([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,1,5,3,2,6]=>([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,1,5,3,6,2]=>([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,1,5,6,3,2]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,1,6,2,5,3]=>([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,1,6,3,2,5]=>([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,1,6,3,5,2]=>([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,1,6,5,2,3]=>([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,1,6,5,3,2]=>([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[4,2,1,3,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,2,1,3,6,5]=>([(0,1),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,2,1,5,3,6]=>([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,2,1,5,6,3]=>([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,2,1,6,3,5]=>([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,2,1,6,5,3]=>([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,2,3,1,5,6]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,2,3,1,6,5]=>([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,2,3,5,1,6]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,2,3,5,6,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,2,3,6,1,5]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,2,3,6,5,1]=>([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,2,5,1,3,6]=>([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,2,5,1,6,3]=>([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,2,5,3,1,6]=>([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,2,5,3,6,1]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,2,5,6,1,3]=>([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,2,5,6,3,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,2,6,1,3,5]=>([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,2,6,1,5,3]=>([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,2,6,3,1,5]=>([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,2,6,3,5,1]=>([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,2,6,5,1,3]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,2,6,5,3,1]=>([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[4,3,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,3,1,2,6,5]=>([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,3,1,5,2,6]=>([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,3,1,5,6,2]=>([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,3,1,6,2,5]=>([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,3,1,6,5,2]=>([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,3,2,1,5,6]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[4,3,2,1,6,5]=>([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[4,3,2,5,1,6]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[4,3,2,5,6,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[4,3,2,6,1,5]=>([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[4,3,2,6,5,1]=>([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[4,3,5,1,2,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,3,5,1,6,2]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,3,5,2,1,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[4,3,5,2,6,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[4,3,5,6,1,2]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,3,5,6,2,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[4,3,6,1,2,5]=>([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,3,6,1,5,2]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,3,6,2,1,5]=>([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[4,3,6,2,5,1]=>([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[4,3,6,5,1,2]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,3,6,5,2,1]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[4,5,1,3,2,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,5,1,3,6,2]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,5,1,6,3,2]=>([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,5,2,1,3,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,5,2,1,6,3]=>([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,5,2,3,1,6]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,5,2,3,6,1]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,5,2,6,1,3]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,5,2,6,3,1]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,5,3,1,2,6]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,5,3,1,6,2]=>([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,5,3,2,1,6]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[4,5,3,2,6,1]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[4,5,3,6,1,2]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,5,3,6,2,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[4,5,6,1,3,2]=>([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,5,6,2,1,3]=>([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,5,6,2,3,1]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,5,6,3,1,2]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,5,6,3,2,1]=>([(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)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[4,6,1,2,5,3]=>([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,6,1,3,2,5]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,6,1,3,5,2]=>([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,6,1,5,2,3]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,6,1,5,3,2]=>([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[4,6,2,1,3,5]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,6,2,1,5,3]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,6,2,3,1,5]=>([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,6,2,3,5,1]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,6,2,5,1,3]=>([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,6,2,5,3,1]=>([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[4,6,3,1,2,5]=>([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,6,3,1,5,2]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,6,3,2,1,5]=>([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[4,6,3,2,5,1]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[4,6,3,5,1,2]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,6,3,5,2,1]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[4,6,5,1,2,3]=>([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[4,6,5,1,3,2]=>([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[4,6,5,2,1,3]=>([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[4,6,5,2,3,1]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[4,6,5,3,1,2]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[4,6,5,3,2,1]=>([(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)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>1
[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,1,2,4,6,3]=>([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,1,2,6,4,3]=>([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,1,3,2,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,1,3,2,6,4]=>([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,1,3,4,2,6]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,1,3,4,6,2]=>([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,1,3,6,2,4]=>([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,1,3,6,4,2]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,1,4,2,3,6]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,1,4,2,6,3]=>([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,1,4,3,2,6]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,1,4,3,6,2]=>([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,1,4,6,2,3]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,1,4,6,3,2]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,1,6,2,4,3]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,1,6,3,2,4]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,1,6,3,4,2]=>([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,1,6,4,2,3]=>([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,1,6,4,3,2]=>([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,2,1,3,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,2,1,3,6,4]=>([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,2,1,4,3,6]=>([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,2,1,4,6,3]=>([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,2,1,6,3,4]=>([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,2,1,6,4,3]=>([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,2,3,1,4,6]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,2,3,1,6,4]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,2,3,4,1,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,2,3,4,6,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,2,3,6,1,4]=>([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,2,3,6,4,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,2,4,1,3,6]=>([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,2,4,1,6,3]=>([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,2,4,3,1,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,2,4,3,6,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,2,4,6,1,3]=>([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,2,4,6,3,1]=>([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,2,6,1,3,4]=>([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,2,6,1,4,3]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,2,6,3,1,4]=>([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,2,6,3,4,1]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,2,6,4,1,3]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,2,6,4,3,1]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,3,1,2,4,6]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,3,1,2,6,4]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,3,1,4,2,6]=>([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,3,1,4,6,2]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,3,1,6,2,4]=>([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,3,1,6,4,2]=>([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,3,2,1,4,6]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,3,2,1,6,4]=>([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,3,2,4,1,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,3,2,4,6,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,3,2,6,1,4]=>([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,3,2,6,4,1]=>([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,3,4,1,2,6]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,3,4,1,6,2]=>([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,3,4,2,1,6]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,3,4,2,6,1]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,3,4,6,1,2]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,3,4,6,2,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,3,6,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,3,6,1,4,2]=>([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,3,6,2,1,4]=>([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,3,6,2,4,1]=>([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,3,6,4,1,2]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,3,6,4,2,1]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,4,1,2,6,3]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,4,1,3,2,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,4,1,3,6,2]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,4,1,6,2,3]=>([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,4,1,6,3,2]=>([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,4,2,1,3,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,4,2,1,6,3]=>([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,4,2,3,1,6]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,4,2,3,6,1]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,4,2,6,1,3]=>([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,4,2,6,3,1]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,4,3,1,2,6]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,4,3,1,6,2]=>([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,4,3,2,1,6]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>1
[5,4,3,2,6,1]=>([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>1
[5,4,3,6,1,2]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,4,3,6,2,1]=>([(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)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>1
[5,4,6,1,2,3]=>([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,4,6,1,3,2]=>([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,4,6,2,1,3]=>([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,4,6,2,3,1]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,4,6,3,1,2]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,4,6,3,2,1]=>([(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)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>1
[5,6,1,2,4,3]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,6,1,3,2,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,6,1,3,4,2]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,6,1,4,2,3]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,6,1,4,3,2]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,6,2,1,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,6,2,1,4,3]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,6,2,3,1,4]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,6,2,3,4,1]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,6,2,4,1,3]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,6,2,4,3,1]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,6,3,1,2,4]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,6,3,1,4,2]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,6,3,2,1,4]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,6,3,2,4,1]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,6,3,4,1,2]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,6,3,4,2,1]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,6,4,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[5,6,4,1,3,2]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,6,4,2,1,3]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,6,4,2,3,1]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,6,4,3,1,2]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[5,6,4,3,2,1]=>([(0,2),(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)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>1
[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,1,2,4,3,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,1,2,4,5,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,1,2,5,3,4]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,1,2,5,4,3]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,1,3,2,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,1,3,2,5,4]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,1,3,4,2,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,1,3,4,5,2]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,1,3,5,2,4]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,1,3,5,4,2]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,1,4,2,3,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,1,4,2,5,3]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,1,4,3,2,5]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,1,4,3,5,2]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,1,4,5,2,3]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,1,4,5,3,2]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,1,5,2,3,4]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,1,5,2,4,3]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,1,5,3,2,4]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,1,5,3,4,2]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,1,5,4,2,3]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,1,5,4,3,2]=>([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>1
[6,2,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,2,1,3,5,4]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,2,1,4,3,5]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,2,1,4,5,3]=>([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,2,1,5,3,4]=>([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,2,1,5,4,3]=>([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,2,3,1,4,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,2,3,1,5,4]=>([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,2,3,4,1,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,2,3,4,5,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,2,3,5,1,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,2,3,5,4,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,2,4,1,3,5]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,2,4,1,5,3]=>([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,2,4,3,1,5]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,2,4,3,5,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,2,4,5,1,3]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,2,4,5,3,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,2,5,1,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,2,5,1,4,3]=>([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,2,5,3,1,4]=>([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,2,5,3,4,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,2,5,4,1,3]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,2,5,4,3,1]=>([(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)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>1
[6,3,1,2,4,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,3,1,2,5,4]=>([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,3,1,4,2,5]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,3,1,4,5,2]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,3,1,5,2,4]=>([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,3,1,5,4,2]=>([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,3,2,1,4,5]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,3,2,1,5,4]=>([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,3,2,4,1,5]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,3,2,4,5,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,3,2,5,1,4]=>([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,3,2,5,4,1]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,3,4,1,2,5]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,3,4,1,5,2]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,3,4,2,1,5]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,3,4,2,5,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,3,4,5,1,2]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,3,4,5,2,1]=>([(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)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,3,5,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,3,5,1,4,2]=>([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,3,5,2,1,4]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,3,5,2,4,1]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,3,5,4,1,2]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,3,5,4,2,1]=>([(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)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>1
[6,4,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,4,1,2,5,3]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,4,1,3,2,5]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,4,1,3,5,2]=>([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,4,1,5,2,3]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,4,1,5,3,2]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,4,2,1,3,5]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,4,2,1,5,3]=>([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,4,2,3,1,5]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,4,2,3,5,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,4,2,5,1,3]=>([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,4,2,5,3,1]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,4,3,1,2,5]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,4,3,1,5,2]=>([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,4,3,2,1,5]=>([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>1
[6,4,3,2,5,1]=>([(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)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>1
[6,4,3,5,1,2]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,4,3,5,2,1]=>([(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)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>1
[6,4,5,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,4,5,1,3,2]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,4,5,2,1,3]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,4,5,2,3,1]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,4,5,3,1,2]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,4,5,3,2,1]=>([(0,2),(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)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>1
[6,5,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(1,2)],3)=>[3]=>1
[6,5,1,2,4,3]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,5,1,3,2,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,5,1,3,4,2]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,5,1,4,2,3]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,5,1,4,3,2]=>([(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)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>1
[6,5,2,1,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,5,2,1,4,3]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,5,2,3,1,4]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,5,2,3,4,1]=>([(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)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,5,2,4,1,3]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,5,2,4,3,1]=>([(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)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>1
[6,5,3,1,2,4]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,5,3,1,4,2]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,5,3,2,1,4]=>([(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)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>1
[6,5,3,2,4,1]=>([(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)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>1
[6,5,3,4,1,2]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,5,3,4,2,1]=>([(0,2),(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)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>1
[6,5,4,1,2,3]=>([(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)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>[4]=>1
[6,5,4,1,3,2]=>([(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)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>1
[6,5,4,2,1,3]=>([(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)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>1
[6,5,4,2,3,1]=>([(0,2),(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)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>1
[6,5,4,3,1,2]=>([(0,2),(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)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>[5]=>1
[6,5,4,3,2,1]=>([(0,1),(0,2),(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)=>([(0,1),(0,2),(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)=>[6]=>1
search for individual values
searching the database for the individual values of this statistic
Description
The number of colourings of a polygon such that the multiplicities of a colour are given by a partition.
Two colourings are considered equal, if they are obtained by an action of the dihedral group.
This statistic is only defined for partitions of size at least 3, to avoid ambiguity.
Two colourings are considered equal, if they are obtained by an action of the dihedral group.
This statistic is only defined for partitions of size at least 3, to avoid ambiguity.
Map
core
Description
The core of a graph.
The core of a graph $G$ is the smallest graph $C$ such that there is a homomorphism from $G$ to $C$ and a homomorphism from $C$ to $G$.
Note that the core of a graph is not necessarily connected, see [2].
The core of a graph $G$ is the smallest graph $C$ such that there is a homomorphism from $G$ to $C$ and a homomorphism from $C$ to $G$.
Note that the core of a graph is not necessarily connected, see [2].
Map
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
Map
to partition of connected components
Description
Return the partition of the sizes of the connected components of the graph.
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!