Identifier
-
Mp00071:
Permutations
—descent composition⟶
Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
Mp00247: Graphs —de-duplicate⟶ Graphs
St000455: Graphs ⟶ ℤ
Values
=>
Cc0020;cc-rep-2
Cc0020;cc-rep
[2,1]=>[1,1]=>([(0,1)],2)=>([(0,1)],2)=>-1
[1,3,2]=>[2,1]=>([(0,2),(1,2)],3)=>([(0,1)],2)=>-1
[2,1,3]=>[1,2]=>([(1,2)],3)=>([(1,2)],3)=>0
[2,3,1]=>[2,1]=>([(0,2),(1,2)],3)=>([(0,1)],2)=>-1
[3,1,2]=>[1,2]=>([(1,2)],3)=>([(1,2)],3)=>0
[3,2,1]=>[1,1,1]=>([(0,1),(0,2),(1,2)],3)=>([(0,1),(0,2),(1,2)],3)=>-1
[1,2,4,3]=>[3,1]=>([(0,3),(1,3),(2,3)],4)=>([(0,1)],2)=>-1
[1,3,2,4]=>[2,2]=>([(1,3),(2,3)],4)=>([(1,2)],3)=>0
[1,3,4,2]=>[3,1]=>([(0,3),(1,3),(2,3)],4)=>([(0,1)],2)=>-1
[1,4,2,3]=>[2,2]=>([(1,3),(2,3)],4)=>([(1,2)],3)=>0
[1,4,3,2]=>[2,1,1]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,2)],3)=>-1
[2,1,3,4]=>[1,3]=>([(2,3)],4)=>([(1,2)],3)=>0
[2,3,1,4]=>[2,2]=>([(1,3),(2,3)],4)=>([(1,2)],3)=>0
[2,3,4,1]=>[3,1]=>([(0,3),(1,3),(2,3)],4)=>([(0,1)],2)=>-1
[2,4,1,3]=>[2,2]=>([(1,3),(2,3)],4)=>([(1,2)],3)=>0
[2,4,3,1]=>[2,1,1]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,2)],3)=>-1
[3,1,2,4]=>[1,3]=>([(2,3)],4)=>([(1,2)],3)=>0
[3,2,1,4]=>[1,1,2]=>([(1,2),(1,3),(2,3)],4)=>([(1,2),(1,3),(2,3)],4)=>0
[3,4,1,2]=>[2,2]=>([(1,3),(2,3)],4)=>([(1,2)],3)=>0
[3,4,2,1]=>[2,1,1]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,2)],3)=>-1
[4,1,2,3]=>[1,3]=>([(2,3)],4)=>([(1,2)],3)=>0
[4,2,1,3]=>[1,1,2]=>([(1,2),(1,3),(2,3)],4)=>([(1,2),(1,3),(2,3)],4)=>0
[4,3,1,2]=>[1,1,2]=>([(1,2),(1,3),(2,3)],4)=>([(1,2),(1,3),(2,3)],4)=>0
[4,3,2,1]=>[1,1,1,1]=>([(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)=>-1
[1,2,3,5,4]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>([(0,1)],2)=>-1
[1,2,4,3,5]=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>([(1,2)],3)=>0
[1,2,4,5,3]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>([(0,1)],2)=>-1
[1,2,5,3,4]=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>([(1,2)],3)=>0
[1,2,5,4,3]=>[3,1,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>-1
[1,3,2,4,5]=>[2,3]=>([(2,4),(3,4)],5)=>([(1,2)],3)=>0
[1,3,4,2,5]=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>([(1,2)],3)=>0
[1,3,4,5,2]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>([(0,1)],2)=>-1
[1,3,5,2,4]=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>([(1,2)],3)=>0
[1,3,5,4,2]=>[3,1,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>-1
[1,4,2,3,5]=>[2,3]=>([(2,4),(3,4)],5)=>([(1,2)],3)=>0
[1,4,3,2,5]=>[2,1,2]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,2),(1,3),(2,3)],4)=>0
[1,4,5,2,3]=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>([(1,2)],3)=>0
[1,4,5,3,2]=>[3,1,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>-1
[1,5,2,3,4]=>[2,3]=>([(2,4),(3,4)],5)=>([(1,2)],3)=>0
[1,5,3,2,4]=>[2,1,2]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,2),(1,3),(2,3)],4)=>0
[1,5,4,2,3]=>[2,1,2]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,2),(1,3),(2,3)],4)=>0
[1,5,4,3,2]=>[2,1,1,1]=>([(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)=>-1
[2,1,3,4,5]=>[1,4]=>([(3,4)],5)=>([(1,2)],3)=>0
[2,3,1,4,5]=>[2,3]=>([(2,4),(3,4)],5)=>([(1,2)],3)=>0
[2,3,4,1,5]=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>([(1,2)],3)=>0
[2,3,4,5,1]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>([(0,1)],2)=>-1
[2,3,5,1,4]=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>([(1,2)],3)=>0
[2,3,5,4,1]=>[3,1,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>-1
[2,4,1,3,5]=>[2,3]=>([(2,4),(3,4)],5)=>([(1,2)],3)=>0
[2,4,3,1,5]=>[2,1,2]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,2),(1,3),(2,3)],4)=>0
[2,4,5,1,3]=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>([(1,2)],3)=>0
[2,4,5,3,1]=>[3,1,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>-1
[2,5,1,3,4]=>[2,3]=>([(2,4),(3,4)],5)=>([(1,2)],3)=>0
[2,5,3,1,4]=>[2,1,2]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,2),(1,3),(2,3)],4)=>0
[2,5,4,1,3]=>[2,1,2]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,2),(1,3),(2,3)],4)=>0
[2,5,4,3,1]=>[2,1,1,1]=>([(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)=>-1
[3,1,2,4,5]=>[1,4]=>([(3,4)],5)=>([(1,2)],3)=>0
[3,2,1,4,5]=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>([(1,2),(1,3),(2,3)],4)=>0
[3,4,1,2,5]=>[2,3]=>([(2,4),(3,4)],5)=>([(1,2)],3)=>0
[3,4,2,1,5]=>[2,1,2]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,2),(1,3),(2,3)],4)=>0
[3,4,5,1,2]=>[3,2]=>([(1,4),(2,4),(3,4)],5)=>([(1,2)],3)=>0
[3,4,5,2,1]=>[3,1,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(0,1),(0,2),(1,2)],3)=>-1
[3,5,1,2,4]=>[2,3]=>([(2,4),(3,4)],5)=>([(1,2)],3)=>0
[3,5,2,1,4]=>[2,1,2]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,2),(1,3),(2,3)],4)=>0
[3,5,4,1,2]=>[2,1,2]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,2),(1,3),(2,3)],4)=>0
[3,5,4,2,1]=>[2,1,1,1]=>([(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)=>-1
[4,1,2,3,5]=>[1,4]=>([(3,4)],5)=>([(1,2)],3)=>0
[4,2,1,3,5]=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>([(1,2),(1,3),(2,3)],4)=>0
[4,3,1,2,5]=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>([(1,2),(1,3),(2,3)],4)=>0
[4,3,2,1,5]=>[1,1,1,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[4,5,1,2,3]=>[2,3]=>([(2,4),(3,4)],5)=>([(1,2)],3)=>0
[4,5,2,1,3]=>[2,1,2]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,2),(1,3),(2,3)],4)=>0
[4,5,3,1,2]=>[2,1,2]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,2),(1,3),(2,3)],4)=>0
[4,5,3,2,1]=>[2,1,1,1]=>([(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)=>-1
[5,1,2,3,4]=>[1,4]=>([(3,4)],5)=>([(1,2)],3)=>0
[5,2,1,3,4]=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>([(1,2),(1,3),(2,3)],4)=>0
[5,3,1,2,4]=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>([(1,2),(1,3),(2,3)],4)=>0
[5,3,2,1,4]=>[1,1,1,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[5,4,1,2,3]=>[1,1,3]=>([(2,3),(2,4),(3,4)],5)=>([(1,2),(1,3),(2,3)],4)=>0
[5,4,2,1,3]=>[1,1,1,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[5,4,3,1,2]=>[1,1,1,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[5,4,3,2,1]=>[1,1,1,1,1]=>([(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)=>-1
[1,2,3,4,6,5]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>([(0,1)],2)=>-1
[1,2,3,5,4,6]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[1,2,3,5,6,4]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>([(0,1)],2)=>-1
[1,2,3,6,4,5]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[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)=>([(0,1),(0,2),(1,2)],3)=>-1
[1,2,4,3,5,6]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[1,2,4,5,3,6]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[1,2,4,5,6,3]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>([(0,1)],2)=>-1
[1,2,4,6,3,5]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[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)=>([(0,1),(0,2),(1,2)],3)=>-1
[1,2,5,3,4,6]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[1,2,5,4,3,6]=>[3,1,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[1,2,5,6,3,4]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[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)=>([(0,1),(0,2),(1,2)],3)=>-1
[1,2,6,3,4,5]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[1,2,6,4,3,5]=>[3,1,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[1,2,6,5,3,4]=>[3,1,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[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)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>-1
[1,3,2,4,5,6]=>[2,4]=>([(3,5),(4,5)],6)=>([(1,2)],3)=>0
[1,3,4,2,5,6]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[1,3,4,5,2,6]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[1,3,4,5,6,2]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>([(0,1)],2)=>-1
[1,3,4,6,2,5]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[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)=>([(0,1),(0,2),(1,2)],3)=>-1
[1,3,5,2,4,6]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[1,3,5,4,2,6]=>[3,1,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[1,3,5,6,2,4]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[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)=>([(0,1),(0,2),(1,2)],3)=>-1
[1,3,6,2,4,5]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[1,3,6,4,2,5]=>[3,1,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[1,3,6,5,2,4]=>[3,1,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[1,3,6,5,4,2]=>[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)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>-1
[1,4,2,3,5,6]=>[2,4]=>([(3,5),(4,5)],6)=>([(1,2)],3)=>0
[1,4,3,2,5,6]=>[2,1,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[1,4,5,2,3,6]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[1,4,5,3,2,6]=>[3,1,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[1,4,5,6,2,3]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[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)=>([(0,1),(0,2),(1,2)],3)=>-1
[1,4,6,2,3,5]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[1,4,6,3,2,5]=>[3,1,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[1,4,6,5,2,3]=>[3,1,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[1,4,6,5,3,2]=>[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)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>-1
[1,5,2,3,4,6]=>[2,4]=>([(3,5),(4,5)],6)=>([(1,2)],3)=>0
[1,5,3,2,4,6]=>[2,1,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[1,5,4,2,3,6]=>[2,1,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[1,5,4,3,2,6]=>[2,1,1,2]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,5,6,2,3,4]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[1,5,6,3,2,4]=>[3,1,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[1,5,6,4,2,3]=>[3,1,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[1,5,6,4,3,2]=>[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)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>-1
[1,6,2,3,4,5]=>[2,4]=>([(3,5),(4,5)],6)=>([(1,2)],3)=>0
[1,6,3,2,4,5]=>[2,1,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[1,6,4,2,3,5]=>[2,1,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[1,6,4,3,2,5]=>[2,1,1,2]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,6,5,2,3,4]=>[2,1,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[1,6,5,3,2,4]=>[2,1,1,2]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,6,5,4,2,3]=>[2,1,1,2]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,6,5,4,3,2]=>[2,1,1,1,1]=>([(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)=>-1
[2,1,3,4,5,6]=>[1,5]=>([(4,5)],6)=>([(1,2)],3)=>0
[2,3,1,4,5,6]=>[2,4]=>([(3,5),(4,5)],6)=>([(1,2)],3)=>0
[2,3,4,1,5,6]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[2,3,4,5,1,6]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[2,3,4,5,6,1]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>([(0,1)],2)=>-1
[2,3,4,6,1,5]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[2,3,4,6,5,1]=>[4,1,1]=>([(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)=>-1
[2,3,5,1,4,6]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[2,3,5,4,1,6]=>[3,1,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[2,3,5,6,1,4]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[2,3,5,6,4,1]=>[4,1,1]=>([(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)=>-1
[2,3,6,1,4,5]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[2,3,6,4,1,5]=>[3,1,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[2,3,6,5,1,4]=>[3,1,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[2,3,6,5,4,1]=>[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)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>-1
[2,4,1,3,5,6]=>[2,4]=>([(3,5),(4,5)],6)=>([(1,2)],3)=>0
[2,4,3,1,5,6]=>[2,1,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[2,4,5,1,3,6]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[2,4,5,3,1,6]=>[3,1,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[2,4,5,6,1,3]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[2,4,5,6,3,1]=>[4,1,1]=>([(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)=>-1
[2,4,6,1,3,5]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[2,4,6,3,1,5]=>[3,1,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[2,4,6,5,1,3]=>[3,1,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[2,4,6,5,3,1]=>[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)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>-1
[2,5,1,3,4,6]=>[2,4]=>([(3,5),(4,5)],6)=>([(1,2)],3)=>0
[2,5,3,1,4,6]=>[2,1,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[2,5,4,1,3,6]=>[2,1,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[2,5,4,3,1,6]=>[2,1,1,2]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[2,5,6,1,3,4]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[2,5,6,3,1,4]=>[3,1,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[2,5,6,4,1,3]=>[3,1,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[2,5,6,4,3,1]=>[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)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>-1
[2,6,1,3,4,5]=>[2,4]=>([(3,5),(4,5)],6)=>([(1,2)],3)=>0
[2,6,3,1,4,5]=>[2,1,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[2,6,4,1,3,5]=>[2,1,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[2,6,4,3,1,5]=>[2,1,1,2]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[2,6,5,1,3,4]=>[2,1,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[2,6,5,3,1,4]=>[2,1,1,2]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[2,6,5,4,1,3]=>[2,1,1,2]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[2,6,5,4,3,1]=>[2,1,1,1,1]=>([(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)=>-1
[3,1,2,4,5,6]=>[1,5]=>([(4,5)],6)=>([(1,2)],3)=>0
[3,2,1,4,5,6]=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[3,4,1,2,5,6]=>[2,4]=>([(3,5),(4,5)],6)=>([(1,2)],3)=>0
[3,4,2,1,5,6]=>[2,1,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[3,4,5,1,2,6]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[3,4,5,2,1,6]=>[3,1,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[3,4,5,6,1,2]=>[4,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[3,4,5,6,2,1]=>[4,1,1]=>([(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)=>-1
[3,4,6,1,2,5]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[3,4,6,2,1,5]=>[3,1,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[3,4,6,5,1,2]=>[3,1,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[3,4,6,5,2,1]=>[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)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>-1
[3,5,1,2,4,6]=>[2,4]=>([(3,5),(4,5)],6)=>([(1,2)],3)=>0
[3,5,2,1,4,6]=>[2,1,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[3,5,4,1,2,6]=>[2,1,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[3,5,4,2,1,6]=>[2,1,1,2]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[3,5,6,1,2,4]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[3,5,6,2,1,4]=>[3,1,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[3,5,6,4,1,2]=>[3,1,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[3,5,6,4,2,1]=>[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)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>-1
[3,6,1,2,4,5]=>[2,4]=>([(3,5),(4,5)],6)=>([(1,2)],3)=>0
[3,6,2,1,4,5]=>[2,1,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[3,6,4,1,2,5]=>[2,1,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[3,6,4,2,1,5]=>[2,1,1,2]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[3,6,5,1,2,4]=>[2,1,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[3,6,5,2,1,4]=>[2,1,1,2]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[3,6,5,4,1,2]=>[2,1,1,2]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[3,6,5,4,2,1]=>[2,1,1,1,1]=>([(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)=>-1
[4,1,2,3,5,6]=>[1,5]=>([(4,5)],6)=>([(1,2)],3)=>0
[4,2,1,3,5,6]=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[4,3,1,2,5,6]=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[4,3,2,1,5,6]=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[4,5,1,2,3,6]=>[2,4]=>([(3,5),(4,5)],6)=>([(1,2)],3)=>0
[4,5,2,1,3,6]=>[2,1,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[4,5,3,1,2,6]=>[2,1,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[4,5,3,2,1,6]=>[2,1,1,2]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[4,5,6,1,2,3]=>[3,3]=>([(2,5),(3,5),(4,5)],6)=>([(1,2)],3)=>0
[4,5,6,2,1,3]=>[3,1,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[4,5,6,3,1,2]=>[3,1,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[4,5,6,3,2,1]=>[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)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>-1
[4,6,1,2,3,5]=>[2,4]=>([(3,5),(4,5)],6)=>([(1,2)],3)=>0
[4,6,2,1,3,5]=>[2,1,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[4,6,3,1,2,5]=>[2,1,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[4,6,3,2,1,5]=>[2,1,1,2]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[4,6,5,1,2,3]=>[2,1,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[4,6,5,2,1,3]=>[2,1,1,2]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[4,6,5,3,1,2]=>[2,1,1,2]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[4,6,5,3,2,1]=>[2,1,1,1,1]=>([(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)=>-1
[5,1,2,3,4,6]=>[1,5]=>([(4,5)],6)=>([(1,2)],3)=>0
[5,2,1,3,4,6]=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[5,3,1,2,4,6]=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[5,3,2,1,4,6]=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[5,4,1,2,3,6]=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[5,4,2,1,3,6]=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[5,4,3,1,2,6]=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[5,4,3,2,1,6]=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[5,6,1,2,3,4]=>[2,4]=>([(3,5),(4,5)],6)=>([(1,2)],3)=>0
[5,6,2,1,3,4]=>[2,1,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[5,6,3,1,2,4]=>[2,1,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[5,6,3,2,1,4]=>[2,1,1,2]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[5,6,4,1,2,3]=>[2,1,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[5,6,4,2,1,3]=>[2,1,1,2]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[5,6,4,3,1,2]=>[2,1,1,2]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[5,6,4,3,2,1]=>[2,1,1,1,1]=>([(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)=>-1
[6,1,2,3,4,5]=>[1,5]=>([(4,5)],6)=>([(1,2)],3)=>0
[6,2,1,3,4,5]=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[6,3,1,2,4,5]=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[6,3,2,1,4,5]=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[6,4,1,2,3,5]=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[6,4,2,1,3,5]=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[6,4,3,1,2,5]=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[6,4,3,2,1,5]=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[6,5,1,2,3,4]=>[1,1,4]=>([(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(2,3)],4)=>0
[6,5,2,1,3,4]=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[6,5,3,1,2,4]=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[6,5,3,2,1,4]=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[6,5,4,1,2,3]=>[1,1,1,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[6,5,4,2,1,3]=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[6,5,4,3,1,2]=>[1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[6,5,4,3,2,1]=>[1,1,1,1,1,1]=>([(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)=>-1
[1,2,3,4,5,7,6]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(0,1)],2)=>-1
[1,2,3,4,6,5,7]=>[5,2]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,2,3,4,6,7,5]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(0,1)],2)=>-1
[1,2,3,4,7,5,6]=>[5,2]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,2,3,4,7,6,5]=>[5,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(1,2)],3)=>-1
[1,2,3,5,4,6,7]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,2,3,5,6,4,7]=>[5,2]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,2,3,5,6,7,4]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(0,1)],2)=>-1
[1,2,3,5,7,4,6]=>[5,2]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,2,3,5,7,6,4]=>[5,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(1,2)],3)=>-1
[1,2,3,6,4,5,7]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,2,3,6,5,4,7]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,2,3,6,7,4,5]=>[5,2]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,2,3,6,7,5,4]=>[5,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(1,2)],3)=>-1
[1,2,3,7,4,5,6]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,2,3,7,5,4,6]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,2,3,7,6,4,5]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,2,3,7,6,5,4]=>[4,1,1,1]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>-1
[1,2,4,3,5,6,7]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,2,4,5,3,6,7]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,2,4,5,6,3,7]=>[5,2]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,2,4,5,6,7,3]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(0,1)],2)=>-1
[1,2,4,5,7,3,6]=>[5,2]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,2,4,5,7,6,3]=>[5,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(1,2)],3)=>-1
[1,2,4,6,3,5,7]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,2,4,6,5,3,7]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,2,4,6,7,3,5]=>[5,2]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,2,4,6,7,5,3]=>[5,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(1,2)],3)=>-1
[1,2,4,7,3,5,6]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,2,4,7,5,3,6]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,2,4,7,6,3,5]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,2,4,7,6,5,3]=>[4,1,1,1]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>-1
[1,2,5,3,4,6,7]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,2,5,4,3,6,7]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,2,5,6,3,4,7]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,2,5,6,4,3,7]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,2,5,6,7,3,4]=>[5,2]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,2,5,6,7,4,3]=>[5,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(1,2)],3)=>-1
[1,2,5,7,3,4,6]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,2,5,7,4,3,6]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,2,5,7,6,3,4]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,2,5,7,6,4,3]=>[4,1,1,1]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>-1
[1,2,6,3,4,5,7]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,2,6,4,3,5,7]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,2,6,5,3,4,7]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,2,6,5,4,3,7]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,2,6,7,3,4,5]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,2,6,7,4,3,5]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,2,6,7,5,3,4]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,2,6,7,5,4,3]=>[4,1,1,1]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>-1
[1,2,7,3,4,5,6]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,2,7,4,3,5,6]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,2,7,5,3,4,6]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,2,7,5,4,3,6]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,2,7,6,3,4,5]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,2,7,6,4,3,5]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,2,7,6,5,3,4]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,2,7,6,5,4,3]=>[3,1,1,1,1]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[1,3,2,4,5,6,7]=>[2,5]=>([(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,3,4,2,5,6,7]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,3,4,5,2,6,7]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,3,4,5,6,2,7]=>[5,2]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,3,4,5,6,7,2]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(0,1)],2)=>-1
[1,3,4,5,7,2,6]=>[5,2]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,3,4,5,7,6,2]=>[5,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(1,2)],3)=>-1
[1,3,4,6,2,5,7]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,3,4,6,5,2,7]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,3,4,6,7,2,5]=>[5,2]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,3,4,6,7,5,2]=>[5,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(1,2)],3)=>-1
[1,3,4,7,2,5,6]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,3,4,7,5,2,6]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,3,4,7,6,2,5]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,3,4,7,6,5,2]=>[4,1,1,1]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>-1
[1,3,5,2,4,6,7]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,3,5,4,2,6,7]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,3,5,6,2,4,7]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,3,5,6,4,2,7]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,3,5,6,7,2,4]=>[5,2]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,3,5,6,7,4,2]=>[5,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(1,2)],3)=>-1
[1,3,5,7,2,4,6]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,3,5,7,4,2,6]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,3,5,7,6,2,4]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,3,5,7,6,4,2]=>[4,1,1,1]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>-1
[1,3,6,2,4,5,7]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,3,6,4,2,5,7]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,3,6,5,2,4,7]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,3,6,5,4,2,7]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,3,6,7,2,4,5]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,3,6,7,4,2,5]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,3,6,7,5,2,4]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,3,6,7,5,4,2]=>[4,1,1,1]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>-1
[1,3,7,2,4,5,6]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,3,7,4,2,5,6]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,3,7,5,2,4,6]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,3,7,5,4,2,6]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,3,7,6,2,4,5]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,3,7,6,4,2,5]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,3,7,6,5,2,4]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,3,7,6,5,4,2]=>[3,1,1,1,1]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[1,4,2,3,5,6,7]=>[2,5]=>([(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,4,3,2,5,6,7]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,4,5,2,3,6,7]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,4,5,3,2,6,7]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,4,5,6,2,3,7]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,4,5,6,3,2,7]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,4,5,6,7,2,3]=>[5,2]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,4,5,6,7,3,2]=>[5,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(1,2)],3)=>-1
[1,4,5,7,2,3,6]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,4,5,7,3,2,6]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,4,5,7,6,2,3]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,4,5,7,6,3,2]=>[4,1,1,1]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>-1
[1,4,6,2,3,5,7]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,4,6,3,2,5,7]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,4,6,5,2,3,7]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,4,6,5,3,2,7]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,4,6,7,2,3,5]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,4,6,7,3,2,5]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,4,6,7,5,2,3]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,4,6,7,5,3,2]=>[4,1,1,1]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>-1
[1,4,7,2,3,5,6]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,4,7,3,2,5,6]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,4,7,5,2,3,6]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,4,7,5,3,2,6]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,4,7,6,2,3,5]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,4,7,6,3,2,5]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,4,7,6,5,2,3]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,4,7,6,5,3,2]=>[3,1,1,1,1]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[1,5,2,3,4,6,7]=>[2,5]=>([(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,5,3,2,4,6,7]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,5,4,2,3,6,7]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,5,4,3,2,6,7]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,5,6,2,3,4,7]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,5,6,3,2,4,7]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,5,6,4,2,3,7]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,5,6,4,3,2,7]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,5,6,7,2,3,4]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,5,6,7,3,2,4]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,5,6,7,4,2,3]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,5,6,7,4,3,2]=>[4,1,1,1]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>-1
[1,5,7,2,3,4,6]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,5,7,3,2,4,6]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,5,7,4,2,3,6]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,5,7,4,3,2,6]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,5,7,6,2,3,4]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,5,7,6,3,2,4]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,5,7,6,4,2,3]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,5,7,6,4,3,2]=>[3,1,1,1,1]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[1,6,2,3,4,5,7]=>[2,5]=>([(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,6,3,2,4,5,7]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,6,4,2,3,5,7]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,6,4,3,2,5,7]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,6,5,2,3,4,7]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,6,5,3,2,4,7]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,6,5,4,2,3,7]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,6,5,4,3,2,7]=>[2,1,1,1,2]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[1,6,7,2,3,4,5]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,6,7,3,2,4,5]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,6,7,4,2,3,5]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,6,7,4,3,2,5]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,6,7,5,2,3,4]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,6,7,5,3,2,4]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,6,7,5,4,2,3]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,6,7,5,4,3,2]=>[3,1,1,1,1]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[1,7,2,3,4,5,6]=>[2,5]=>([(4,6),(5,6)],7)=>([(1,2)],3)=>0
[1,7,3,2,4,5,6]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,7,4,2,3,5,6]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,7,4,3,2,5,6]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,7,5,2,3,4,6]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,7,5,3,2,4,6]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,7,5,4,2,3,6]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,7,5,4,3,2,6]=>[2,1,1,1,2]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[1,7,6,2,3,4,5]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[1,7,6,3,2,4,5]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,7,6,4,2,3,5]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,7,6,4,3,2,5]=>[2,1,1,1,2]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[1,7,6,5,2,3,4]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[1,7,6,5,3,2,4]=>[2,1,1,1,2]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[1,7,6,5,4,2,3]=>[2,1,1,1,2]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[1,7,6,5,4,3,2]=>[2,1,1,1,1,1]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(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)=>-1
[2,1,3,4,5,6,7]=>[1,6]=>([(5,6)],7)=>([(1,2)],3)=>0
[2,3,1,4,5,6,7]=>[2,5]=>([(4,6),(5,6)],7)=>([(1,2)],3)=>0
[2,3,4,1,5,6,7]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[2,3,4,5,1,6,7]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[2,3,4,5,6,1,7]=>[5,2]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[2,3,4,5,6,7,1]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(0,1)],2)=>-1
[2,3,4,5,7,1,6]=>[5,2]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[2,3,4,5,7,6,1]=>[5,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(1,2)],3)=>-1
[2,3,4,6,1,5,7]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[2,3,4,6,5,1,7]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,3,4,6,7,1,5]=>[5,2]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[2,3,4,6,7,5,1]=>[5,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(1,2)],3)=>-1
[2,3,4,7,1,5,6]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[2,3,4,7,5,1,6]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,3,4,7,6,1,5]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,3,4,7,6,5,1]=>[4,1,1,1]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>-1
[2,3,5,1,4,6,7]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[2,3,5,4,1,6,7]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,3,5,6,1,4,7]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[2,3,5,6,4,1,7]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,3,5,6,7,1,4]=>[5,2]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[2,3,5,6,7,4,1]=>[5,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(1,2)],3)=>-1
[2,3,5,7,1,4,6]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[2,3,5,7,4,1,6]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,3,5,7,6,1,4]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,3,5,7,6,4,1]=>[4,1,1,1]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>-1
[2,3,6,1,4,5,7]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[2,3,6,4,1,5,7]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,3,6,5,1,4,7]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,3,6,5,4,1,7]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[2,3,6,7,1,4,5]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[2,3,6,7,4,1,5]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,3,6,7,5,1,4]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,3,6,7,5,4,1]=>[4,1,1,1]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>-1
[2,3,7,1,4,5,6]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[2,3,7,4,1,5,6]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,3,7,5,1,4,6]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,3,7,5,4,1,6]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[2,3,7,6,1,4,5]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,3,7,6,4,1,5]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[2,3,7,6,5,1,4]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[2,3,7,6,5,4,1]=>[3,1,1,1,1]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[2,4,1,3,5,6,7]=>[2,5]=>([(4,6),(5,6)],7)=>([(1,2)],3)=>0
[2,4,3,1,5,6,7]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,4,5,1,3,6,7]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[2,4,5,3,1,6,7]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,4,5,6,1,3,7]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[2,4,5,6,3,1,7]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,4,5,6,7,1,3]=>[5,2]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[2,4,5,6,7,3,1]=>[5,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(1,2)],3)=>-1
[2,4,5,7,1,3,6]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[2,4,5,7,3,1,6]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,4,5,7,6,1,3]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,4,5,7,6,3,1]=>[4,1,1,1]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>-1
[2,4,6,1,3,5,7]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[2,4,6,3,1,5,7]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,4,6,5,1,3,7]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,4,6,5,3,1,7]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[2,4,6,7,1,3,5]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[2,4,6,7,3,1,5]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,4,6,7,5,1,3]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,4,6,7,5,3,1]=>[4,1,1,1]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>-1
[2,4,7,1,3,5,6]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[2,4,7,3,1,5,6]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,4,7,5,1,3,6]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,4,7,5,3,1,6]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[2,4,7,6,1,3,5]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,4,7,6,3,1,5]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[2,4,7,6,5,1,3]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[2,4,7,6,5,3,1]=>[3,1,1,1,1]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[2,5,1,3,4,6,7]=>[2,5]=>([(4,6),(5,6)],7)=>([(1,2)],3)=>0
[2,5,3,1,4,6,7]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,5,4,1,3,6,7]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,5,4,3,1,6,7]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[2,5,6,1,3,4,7]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[2,5,6,3,1,4,7]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,5,6,4,1,3,7]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,5,6,4,3,1,7]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[2,5,6,7,1,3,4]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[2,5,6,7,3,1,4]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,5,6,7,4,1,3]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,5,6,7,4,3,1]=>[4,1,1,1]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>-1
[2,5,7,1,3,4,6]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[2,5,7,3,1,4,6]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,5,7,4,1,3,6]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,5,7,4,3,1,6]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[2,5,7,6,1,3,4]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,5,7,6,3,1,4]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[2,5,7,6,4,1,3]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[2,5,7,6,4,3,1]=>[3,1,1,1,1]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[2,6,1,3,4,5,7]=>[2,5]=>([(4,6),(5,6)],7)=>([(1,2)],3)=>0
[2,6,3,1,4,5,7]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,6,4,1,3,5,7]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,6,4,3,1,5,7]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[2,6,5,1,3,4,7]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,6,5,3,1,4,7]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[2,6,5,4,1,3,7]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[2,6,5,4,3,1,7]=>[2,1,1,1,2]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[2,6,7,1,3,4,5]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[2,6,7,3,1,4,5]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,6,7,4,1,3,5]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,6,7,4,3,1,5]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[2,6,7,5,1,3,4]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,6,7,5,3,1,4]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[2,6,7,5,4,1,3]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[2,6,7,5,4,3,1]=>[3,1,1,1,1]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[2,7,1,3,4,5,6]=>[2,5]=>([(4,6),(5,6)],7)=>([(1,2)],3)=>0
[2,7,3,1,4,5,6]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,7,4,1,3,5,6]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,7,4,3,1,5,6]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[2,7,5,1,3,4,6]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,7,5,3,1,4,6]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[2,7,5,4,1,3,6]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[2,7,5,4,3,1,6]=>[2,1,1,1,2]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[2,7,6,1,3,4,5]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[2,7,6,3,1,4,5]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[2,7,6,4,1,3,5]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[2,7,6,4,3,1,5]=>[2,1,1,1,2]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[2,7,6,5,1,3,4]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[2,7,6,5,3,1,4]=>[2,1,1,1,2]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[2,7,6,5,4,1,3]=>[2,1,1,1,2]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[2,7,6,5,4,3,1]=>[2,1,1,1,1,1]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(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)=>-1
[3,1,2,4,5,6,7]=>[1,6]=>([(5,6)],7)=>([(1,2)],3)=>0
[3,2,1,4,5,6,7]=>[1,1,5]=>([(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,4,1,2,5,6,7]=>[2,5]=>([(4,6),(5,6)],7)=>([(1,2)],3)=>0
[3,4,2,1,5,6,7]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,4,5,1,2,6,7]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[3,4,5,2,1,6,7]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,4,5,6,1,2,7]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[3,4,5,6,2,1,7]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,4,5,6,7,1,2]=>[5,2]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[3,4,5,6,7,2,1]=>[5,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(1,2)],3)=>-1
[3,4,5,7,1,2,6]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[3,4,5,7,2,1,6]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,4,5,7,6,1,2]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,4,5,7,6,2,1]=>[4,1,1,1]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>-1
[3,4,6,1,2,5,7]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[3,4,6,2,1,5,7]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,4,6,5,1,2,7]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,4,6,5,2,1,7]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[3,4,6,7,1,2,5]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[3,4,6,7,2,1,5]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,4,6,7,5,1,2]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,4,6,7,5,2,1]=>[4,1,1,1]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>-1
[3,4,7,1,2,5,6]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[3,4,7,2,1,5,6]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,4,7,5,1,2,6]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,4,7,5,2,1,6]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[3,4,7,6,1,2,5]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,4,7,6,2,1,5]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[3,4,7,6,5,1,2]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[3,4,7,6,5,2,1]=>[3,1,1,1,1]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[3,5,1,2,4,6,7]=>[2,5]=>([(4,6),(5,6)],7)=>([(1,2)],3)=>0
[3,5,2,1,4,6,7]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,5,4,1,2,6,7]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,5,4,2,1,6,7]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[3,5,6,1,2,4,7]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[3,5,6,2,1,4,7]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,5,6,4,1,2,7]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,5,6,4,2,1,7]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[3,5,6,7,1,2,4]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[3,5,6,7,2,1,4]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,5,6,7,4,1,2]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,5,6,7,4,2,1]=>[4,1,1,1]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>-1
[3,5,7,1,2,4,6]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[3,5,7,2,1,4,6]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,5,7,4,1,2,6]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,5,7,4,2,1,6]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[3,5,7,6,1,2,4]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,5,7,6,2,1,4]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[3,5,7,6,4,1,2]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[3,5,7,6,4,2,1]=>[3,1,1,1,1]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[3,6,1,2,4,5,7]=>[2,5]=>([(4,6),(5,6)],7)=>([(1,2)],3)=>0
[3,6,2,1,4,5,7]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,6,4,1,2,5,7]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,6,4,2,1,5,7]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[3,6,5,1,2,4,7]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,6,5,2,1,4,7]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[3,6,5,4,1,2,7]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[3,6,5,4,2,1,7]=>[2,1,1,1,2]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[3,6,7,1,2,4,5]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[3,6,7,2,1,4,5]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,6,7,4,1,2,5]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,6,7,4,2,1,5]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[3,6,7,5,1,2,4]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,6,7,5,2,1,4]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[3,6,7,5,4,1,2]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[3,6,7,5,4,2,1]=>[3,1,1,1,1]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[3,7,1,2,4,5,6]=>[2,5]=>([(4,6),(5,6)],7)=>([(1,2)],3)=>0
[3,7,2,1,4,5,6]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,7,4,1,2,5,6]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,7,4,2,1,5,6]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[3,7,5,1,2,4,6]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,7,5,2,1,4,6]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[3,7,5,4,1,2,6]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[3,7,5,4,2,1,6]=>[2,1,1,1,2]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[3,7,6,1,2,4,5]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[3,7,6,2,1,4,5]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[3,7,6,4,1,2,5]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[3,7,6,4,2,1,5]=>[2,1,1,1,2]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[3,7,6,5,1,2,4]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[3,7,6,5,2,1,4]=>[2,1,1,1,2]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[3,7,6,5,4,1,2]=>[2,1,1,1,2]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[3,7,6,5,4,2,1]=>[2,1,1,1,1,1]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(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)=>-1
[4,1,2,3,5,6,7]=>[1,6]=>([(5,6)],7)=>([(1,2)],3)=>0
[4,2,1,3,5,6,7]=>[1,1,5]=>([(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[4,3,1,2,5,6,7]=>[1,1,5]=>([(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[4,3,2,1,5,6,7]=>[1,1,1,4]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[4,5,1,2,3,6,7]=>[2,5]=>([(4,6),(5,6)],7)=>([(1,2)],3)=>0
[4,5,2,1,3,6,7]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[4,5,3,1,2,6,7]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[4,5,3,2,1,6,7]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[4,5,6,1,2,3,7]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[4,5,6,2,1,3,7]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[4,5,6,3,1,2,7]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[4,5,6,3,2,1,7]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[4,5,6,7,1,2,3]=>[4,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[4,5,6,7,2,1,3]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[4,5,6,7,3,1,2]=>[4,1,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[4,5,6,7,3,2,1]=>[4,1,1,1]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>-1
[4,5,7,1,2,3,6]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[4,5,7,2,1,3,6]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[4,5,7,3,1,2,6]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[4,5,7,3,2,1,6]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[4,5,7,6,1,2,3]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[4,5,7,6,2,1,3]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[4,5,7,6,3,1,2]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[4,5,7,6,3,2,1]=>[3,1,1,1,1]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[4,6,1,2,3,5,7]=>[2,5]=>([(4,6),(5,6)],7)=>([(1,2)],3)=>0
[4,6,2,1,3,5,7]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[4,6,3,1,2,5,7]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[4,6,3,2,1,5,7]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[4,6,5,1,2,3,7]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[4,6,5,2,1,3,7]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[4,6,5,3,1,2,7]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[4,6,5,3,2,1,7]=>[2,1,1,1,2]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[4,6,7,1,2,3,5]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[4,6,7,2,1,3,5]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[4,6,7,3,1,2,5]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[4,6,7,3,2,1,5]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[4,6,7,5,1,2,3]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[4,6,7,5,2,1,3]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[4,6,7,5,3,1,2]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[4,6,7,5,3,2,1]=>[3,1,1,1,1]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[4,7,1,2,3,5,6]=>[2,5]=>([(4,6),(5,6)],7)=>([(1,2)],3)=>0
[4,7,2,1,3,5,6]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[4,7,3,1,2,5,6]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[4,7,3,2,1,5,6]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[4,7,5,1,2,3,6]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[4,7,5,2,1,3,6]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[4,7,5,3,1,2,6]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[4,7,5,3,2,1,6]=>[2,1,1,1,2]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[4,7,6,1,2,3,5]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[4,7,6,2,1,3,5]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[4,7,6,3,1,2,5]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[4,7,6,3,2,1,5]=>[2,1,1,1,2]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[4,7,6,5,1,2,3]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[4,7,6,5,2,1,3]=>[2,1,1,1,2]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[4,7,6,5,3,1,2]=>[2,1,1,1,2]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[4,7,6,5,3,2,1]=>[2,1,1,1,1,1]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(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)=>-1
[5,1,2,3,4,6,7]=>[1,6]=>([(5,6)],7)=>([(1,2)],3)=>0
[5,2,1,3,4,6,7]=>[1,1,5]=>([(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[5,3,1,2,4,6,7]=>[1,1,5]=>([(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[5,3,2,1,4,6,7]=>[1,1,1,4]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[5,4,1,2,3,6,7]=>[1,1,5]=>([(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[5,4,2,1,3,6,7]=>[1,1,1,4]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[5,4,3,1,2,6,7]=>[1,1,1,4]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[5,4,3,2,1,6,7]=>[1,1,1,1,3]=>([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[5,6,1,2,3,4,7]=>[2,5]=>([(4,6),(5,6)],7)=>([(1,2)],3)=>0
[5,6,2,1,3,4,7]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[5,6,3,1,2,4,7]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[5,6,3,2,1,4,7]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[5,6,4,1,2,3,7]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[5,6,4,2,1,3,7]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[5,6,4,3,1,2,7]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[5,6,4,3,2,1,7]=>[2,1,1,1,2]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[5,6,7,1,2,3,4]=>[3,4]=>([(3,6),(4,6),(5,6)],7)=>([(1,2)],3)=>0
[5,6,7,2,1,3,4]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[5,6,7,3,1,2,4]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[5,6,7,3,2,1,4]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[5,6,7,4,1,2,3]=>[3,1,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[5,6,7,4,2,1,3]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[5,6,7,4,3,1,2]=>[3,1,1,2]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[5,6,7,4,3,2,1]=>[3,1,1,1,1]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[5,7,1,2,3,4,6]=>[2,5]=>([(4,6),(5,6)],7)=>([(1,2)],3)=>0
[5,7,2,1,3,4,6]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[5,7,3,1,2,4,6]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[5,7,3,2,1,4,6]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[5,7,4,1,2,3,6]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[5,7,4,2,1,3,6]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[5,7,4,3,1,2,6]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[5,7,4,3,2,1,6]=>[2,1,1,1,2]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[5,7,6,1,2,3,4]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[5,7,6,2,1,3,4]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[5,7,6,3,1,2,4]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[5,7,6,3,2,1,4]=>[2,1,1,1,2]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[5,7,6,4,1,2,3]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[5,7,6,4,2,1,3]=>[2,1,1,1,2]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[5,7,6,4,3,1,2]=>[2,1,1,1,2]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[5,7,6,4,3,2,1]=>[2,1,1,1,1,1]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(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)=>-1
[6,1,2,3,4,5,7]=>[1,6]=>([(5,6)],7)=>([(1,2)],3)=>0
[6,2,1,3,4,5,7]=>[1,1,5]=>([(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[6,3,1,2,4,5,7]=>[1,1,5]=>([(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[6,3,2,1,4,5,7]=>[1,1,1,4]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[6,4,1,2,3,5,7]=>[1,1,5]=>([(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[6,4,2,1,3,5,7]=>[1,1,1,4]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[6,4,3,1,2,5,7]=>[1,1,1,4]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[6,4,3,2,1,5,7]=>[1,1,1,1,3]=>([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[6,5,1,2,3,4,7]=>[1,1,5]=>([(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[6,5,2,1,3,4,7]=>[1,1,1,4]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[6,5,3,1,2,4,7]=>[1,1,1,4]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[6,5,3,2,1,4,7]=>[1,1,1,1,3]=>([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[6,5,4,1,2,3,7]=>[1,1,1,4]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[6,5,4,2,1,3,7]=>[1,1,1,1,3]=>([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[6,5,4,3,1,2,7]=>[1,1,1,1,3]=>([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[6,5,4,3,2,1,7]=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
[6,7,1,2,3,4,5]=>[2,5]=>([(4,6),(5,6)],7)=>([(1,2)],3)=>0
[6,7,2,1,3,4,5]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[6,7,3,1,2,4,5]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[6,7,3,2,1,4,5]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[6,7,4,1,2,3,5]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[6,7,4,2,1,3,5]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[6,7,4,3,1,2,5]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[6,7,4,3,2,1,5]=>[2,1,1,1,2]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[6,7,5,1,2,3,4]=>[2,1,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[6,7,5,2,1,3,4]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[6,7,5,3,1,2,4]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[6,7,5,3,2,1,4]=>[2,1,1,1,2]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[6,7,5,4,1,2,3]=>[2,1,1,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[6,7,5,4,2,1,3]=>[2,1,1,1,2]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[6,7,5,4,3,1,2]=>[2,1,1,1,2]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[6,7,5,4,3,2,1]=>[2,1,1,1,1,1]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(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)=>-1
[7,1,2,3,4,5,6]=>[1,6]=>([(5,6)],7)=>([(1,2)],3)=>0
[7,2,1,3,4,5,6]=>[1,1,5]=>([(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[7,3,1,2,4,5,6]=>[1,1,5]=>([(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[7,3,2,1,4,5,6]=>[1,1,1,4]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[7,4,1,2,3,5,6]=>[1,1,5]=>([(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[7,4,2,1,3,5,6]=>[1,1,1,4]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[7,4,3,1,2,5,6]=>[1,1,1,4]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[7,4,3,2,1,5,6]=>[1,1,1,1,3]=>([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[7,5,1,2,3,4,6]=>[1,1,5]=>([(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[7,5,2,1,3,4,6]=>[1,1,1,4]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[7,5,3,1,2,4,6]=>[1,1,1,4]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[7,5,3,2,1,4,6]=>[1,1,1,1,3]=>([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[7,5,4,1,2,3,6]=>[1,1,1,4]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[7,5,4,2,1,3,6]=>[1,1,1,1,3]=>([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[7,5,4,3,1,2,6]=>[1,1,1,1,3]=>([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[7,5,4,3,2,1,6]=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
[7,6,1,2,3,4,5]=>[1,1,5]=>([(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(2,3)],4)=>0
[7,6,2,1,3,4,5]=>[1,1,1,4]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[7,6,3,1,2,4,5]=>[1,1,1,4]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[7,6,3,2,1,4,5]=>[1,1,1,1,3]=>([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[7,6,4,1,2,3,5]=>[1,1,1,4]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[7,6,4,2,1,3,5]=>[1,1,1,1,3]=>([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[7,6,4,3,1,2,5]=>[1,1,1,1,3]=>([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[7,6,4,3,2,1,5]=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
[7,6,5,1,2,3,4]=>[1,1,1,4]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
[7,6,5,2,1,3,4]=>[1,1,1,1,3]=>([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[7,6,5,3,1,2,4]=>[1,1,1,1,3]=>([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[7,6,5,3,2,1,4]=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
[7,6,5,4,1,2,3]=>[1,1,1,1,3]=>([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
[7,6,5,4,2,1,3]=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
[7,6,5,4,3,1,2]=>[1,1,1,1,1,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>0
[7,6,5,4,3,2,1]=>[1,1,1,1,1,1,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>-1
[5,6,7,8,4,3,2,1]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[4,6,7,8,5,3,2,1]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[4,5,7,8,6,3,2,1]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[4,5,6,8,7,3,2,1]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[3,6,7,8,5,4,2,1]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[3,5,7,8,6,4,2,1]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[3,5,6,8,7,4,2,1]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[3,4,7,8,6,5,2,1]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[3,4,6,8,7,5,2,1]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[3,4,5,8,7,6,2,1]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[2,6,7,8,5,4,3,1]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[2,5,7,8,6,4,3,1]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[2,5,6,8,7,4,3,1]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[2,4,7,8,6,5,3,1]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[2,4,6,8,7,5,3,1]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[2,3,7,8,6,5,4,1]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[2,3,6,8,7,5,4,1]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[2,3,4,8,7,6,5,1]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[1,6,7,8,5,4,3,2]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[1,5,7,8,6,4,3,2]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[1,5,6,8,7,4,3,2]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[1,4,7,8,6,5,3,2]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[1,4,6,8,7,5,3,2]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[1,4,5,8,7,6,3,2]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[1,3,7,8,6,5,4,2]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[1,3,6,8,7,5,4,2]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[1,3,5,8,7,6,4,2]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[1,3,4,8,7,6,5,2]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[1,2,7,8,6,5,4,3]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[1,2,6,8,7,5,4,3]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[1,2,5,8,7,6,4,3]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[1,2,4,8,7,6,5,3]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
[1,2,3,8,7,6,5,4]=>[4,1,1,1,1]=>([(0,4),(0,5),(0,6),(0,7),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>-1
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Description
The second largest eigenvalue of a graph if it is integral.
This statistic is undefined if the second largest eigenvalue of the graph is not integral.
Chapter 4 of [1] provides lots of context.
This statistic is undefined if the second largest eigenvalue of the graph is not integral.
Chapter 4 of [1] provides lots of context.
Map
de-duplicate
Description
The de-duplicate of a graph.
Let $G = (V, E)$ be a graph. This map yields the graph whose vertex set is the set of (distinct) neighbourhoods $\{N_v | v \in V\}$ of $G$, and has an edge $(N_a, N_b)$ between two vertices if and only if $(a, b)$ is an edge of $G$. This is well-defined, because if $N_a = N_c$ and $N_b = N_d$, then $(a, b)\in E$ if and only if $(c, d)\in E$.
The image of this map is the set of so-called 'mating graphs' or 'point-determining graphs'.
This map preserves the chromatic number.
Let $G = (V, E)$ be a graph. This map yields the graph whose vertex set is the set of (distinct) neighbourhoods $\{N_v | v \in V\}$ of $G$, and has an edge $(N_a, N_b)$ between two vertices if and only if $(a, b)$ is an edge of $G$. This is well-defined, because if $N_a = N_c$ and $N_b = N_d$, then $(a, b)\in E$ if and only if $(c, d)\in E$.
The image of this map is the set of so-called 'mating graphs' or 'point-determining graphs'.
This map preserves the chromatic number.
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
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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