Identifier
-
Mp00127:
Permutations
—left-to-right-maxima to Dyck path⟶
Dyck paths
Mp00102: Dyck paths —rise composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000771: Graphs ⟶ ℤ
Values
=>
Cc0005;cc-rep-1
Cc0020;cc-rep
[1]=>[1,0]=>[1]=>([],1)=>1
[1,2]=>[1,0,1,0]=>[1,1]=>([(0,1)],2)=>1
[1,2,3]=>[1,0,1,0,1,0]=>[1,1,1]=>([(0,1),(0,2),(1,2)],3)=>2
[2,1,3]=>[1,1,0,0,1,0]=>[2,1]=>([(0,2),(1,2)],3)=>1
[2,3,1]=>[1,1,0,1,0,0]=>[2,1]=>([(0,2),(1,2)],3)=>1
[1,2,3,4]=>[1,0,1,0,1,0,1,0]=>[1,1,1,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>3
[1,3,2,4]=>[1,0,1,1,0,0,1,0]=>[1,2,1]=>([(0,3),(1,2),(1,3),(2,3)],4)=>1
[1,3,4,2]=>[1,0,1,1,0,1,0,0]=>[1,2,1]=>([(0,3),(1,2),(1,3),(2,3)],4)=>1
[2,1,3,4]=>[1,1,0,0,1,0,1,0]=>[2,1,1]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>2
[2,3,1,4]=>[1,1,0,1,0,0,1,0]=>[2,1,1]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>2
[2,3,4,1]=>[1,1,0,1,0,1,0,0]=>[2,1,1]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>2
[3,1,2,4]=>[1,1,1,0,0,0,1,0]=>[3,1]=>([(0,3),(1,3),(2,3)],4)=>2
[3,1,4,2]=>[1,1,1,0,0,1,0,0]=>[3,1]=>([(0,3),(1,3),(2,3)],4)=>2
[3,2,1,4]=>[1,1,1,0,0,0,1,0]=>[3,1]=>([(0,3),(1,3),(2,3)],4)=>2
[3,2,4,1]=>[1,1,1,0,0,1,0,0]=>[3,1]=>([(0,3),(1,3),(2,3)],4)=>2
[3,4,1,2]=>[1,1,1,0,1,0,0,0]=>[3,1]=>([(0,3),(1,3),(2,3)],4)=>2
[3,4,2,1]=>[1,1,1,0,1,0,0,0]=>[3,1]=>([(0,3),(1,3),(2,3)],4)=>2
[1,2,3,4,5]=>[1,0,1,0,1,0,1,0,1,0]=>[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)=>4
[1,2,4,3,5]=>[1,0,1,0,1,1,0,0,1,0]=>[1,1,2,1]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>2
[1,2,4,5,3]=>[1,0,1,0,1,1,0,1,0,0]=>[1,1,2,1]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>2
[1,3,2,4,5]=>[1,0,1,1,0,0,1,0,1,0]=>[1,2,1,1]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>2
[1,3,4,2,5]=>[1,0,1,1,0,1,0,0,1,0]=>[1,2,1,1]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>2
[1,3,4,5,2]=>[1,0,1,1,0,1,0,1,0,0]=>[1,2,1,1]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>2
[1,4,2,3,5]=>[1,0,1,1,1,0,0,0,1,0]=>[1,3,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>2
[1,4,2,5,3]=>[1,0,1,1,1,0,0,1,0,0]=>[1,3,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>2
[1,4,3,2,5]=>[1,0,1,1,1,0,0,0,1,0]=>[1,3,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>2
[1,4,3,5,2]=>[1,0,1,1,1,0,0,1,0,0]=>[1,3,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>2
[1,4,5,2,3]=>[1,0,1,1,1,0,1,0,0,0]=>[1,3,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>2
[1,4,5,3,2]=>[1,0,1,1,1,0,1,0,0,0]=>[1,3,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>2
[2,1,3,4,5]=>[1,1,0,0,1,0,1,0,1,0]=>[2,1,1,1]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3
[2,1,4,3,5]=>[1,1,0,0,1,1,0,0,1,0]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1
[2,1,4,5,3]=>[1,1,0,0,1,1,0,1,0,0]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1
[2,3,1,4,5]=>[1,1,0,1,0,0,1,0,1,0]=>[2,1,1,1]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3
[2,3,4,1,5]=>[1,1,0,1,0,1,0,0,1,0]=>[2,1,1,1]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3
[2,3,4,5,1]=>[1,1,0,1,0,1,0,1,0,0]=>[2,1,1,1]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3
[2,4,1,3,5]=>[1,1,0,1,1,0,0,0,1,0]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1
[2,4,1,5,3]=>[1,1,0,1,1,0,0,1,0,0]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1
[2,4,3,1,5]=>[1,1,0,1,1,0,0,0,1,0]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1
[2,4,3,5,1]=>[1,1,0,1,1,0,0,1,0,0]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1
[2,4,5,1,3]=>[1,1,0,1,1,0,1,0,0,0]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1
[2,4,5,3,1]=>[1,1,0,1,1,0,1,0,0,0]=>[2,2,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1
[3,1,2,4,5]=>[1,1,1,0,0,0,1,0,1,0]=>[3,1,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>2
[3,1,4,2,5]=>[1,1,1,0,0,1,0,0,1,0]=>[3,1,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>2
[3,1,4,5,2]=>[1,1,1,0,0,1,0,1,0,0]=>[3,1,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>2
[3,2,1,4,5]=>[1,1,1,0,0,0,1,0,1,0]=>[3,1,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>2
[3,2,4,1,5]=>[1,1,1,0,0,1,0,0,1,0]=>[3,1,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>2
[3,2,4,5,1]=>[1,1,1,0,0,1,0,1,0,0]=>[3,1,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>2
[3,4,1,2,5]=>[1,1,1,0,1,0,0,0,1,0]=>[3,1,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>2
[3,4,1,5,2]=>[1,1,1,0,1,0,0,1,0,0]=>[3,1,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>2
[3,4,2,1,5]=>[1,1,1,0,1,0,0,0,1,0]=>[3,1,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>2
[3,4,2,5,1]=>[1,1,1,0,1,0,0,1,0,0]=>[3,1,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>2
[3,4,5,1,2]=>[1,1,1,0,1,0,1,0,0,0]=>[3,1,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>2
[3,4,5,2,1]=>[1,1,1,0,1,0,1,0,0,0]=>[3,1,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>2
[4,1,2,3,5]=>[1,1,1,1,0,0,0,0,1,0]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[4,1,2,5,3]=>[1,1,1,1,0,0,0,1,0,0]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[4,1,3,2,5]=>[1,1,1,1,0,0,0,0,1,0]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[4,1,3,5,2]=>[1,1,1,1,0,0,0,1,0,0]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[4,1,5,2,3]=>[1,1,1,1,0,0,1,0,0,0]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[4,1,5,3,2]=>[1,1,1,1,0,0,1,0,0,0]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[4,2,1,3,5]=>[1,1,1,1,0,0,0,0,1,0]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[4,2,1,5,3]=>[1,1,1,1,0,0,0,1,0,0]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[4,2,3,1,5]=>[1,1,1,1,0,0,0,0,1,0]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[4,2,3,5,1]=>[1,1,1,1,0,0,0,1,0,0]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[4,2,5,1,3]=>[1,1,1,1,0,0,1,0,0,0]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[4,2,5,3,1]=>[1,1,1,1,0,0,1,0,0,0]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[4,3,1,2,5]=>[1,1,1,1,0,0,0,0,1,0]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[4,3,1,5,2]=>[1,1,1,1,0,0,0,1,0,0]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[4,3,2,1,5]=>[1,1,1,1,0,0,0,0,1,0]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[4,3,2,5,1]=>[1,1,1,1,0,0,0,1,0,0]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[4,3,5,1,2]=>[1,1,1,1,0,0,1,0,0,0]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[4,3,5,2,1]=>[1,1,1,1,0,0,1,0,0,0]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[4,5,1,2,3]=>[1,1,1,1,0,1,0,0,0,0]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[4,5,1,3,2]=>[1,1,1,1,0,1,0,0,0,0]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[4,5,2,1,3]=>[1,1,1,1,0,1,0,0,0,0]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[4,5,2,3,1]=>[1,1,1,1,0,1,0,0,0,0]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[4,5,3,1,2]=>[1,1,1,1,0,1,0,0,0,0]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[4,5,3,2,1]=>[1,1,1,1,0,1,0,0,0,0]=>[4,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>3
[1,2,3,4,5,6]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[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)=>5
[1,2,3,5,4,6]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,2,1]=>([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[1,2,3,5,6,4]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,2,1]=>([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[1,2,4,3,5,6]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,2,1,1]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[1,2,4,5,3,6]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,2,1,1]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[1,2,4,5,6,3]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,2,1,1]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[1,2,5,3,4,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,3,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[1,2,5,3,6,4]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,3,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[1,2,5,4,3,6]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,3,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[1,2,5,4,6,3]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,3,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[1,2,5,6,3,4]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,3,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[1,2,5,6,4,3]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,3,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[1,3,2,4,5,6]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[1,3,2,5,4,6]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
[1,3,2,5,6,4]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
[1,3,4,2,5,6]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[1,3,4,5,2,6]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[1,3,4,5,6,2]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[1,3,5,2,4,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
[1,3,5,2,6,4]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
[1,3,5,4,2,6]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
[1,3,5,4,6,2]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
[1,3,5,6,2,4]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
[1,3,5,6,4,2]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,2,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
[1,4,2,3,5,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[1,4,2,5,3,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[1,4,2,5,6,3]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[1,4,3,2,5,6]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[1,4,3,5,2,6]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[1,4,3,5,6,2]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[1,4,5,2,3,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[1,4,5,2,6,3]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[1,4,5,3,2,6]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[1,4,5,3,6,2]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[1,4,5,6,2,3]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[1,4,5,6,3,2]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[1,5,2,3,4,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>3
[1,5,2,3,6,4]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>3
[1,5,2,4,3,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>3
[1,5,2,4,6,3]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>3
[1,5,2,6,3,4]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>3
[1,5,2,6,4,3]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>3
[1,5,3,2,4,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>3
[1,5,3,2,6,4]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>3
[1,5,3,4,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>3
[1,5,3,4,6,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>3
[1,5,3,6,2,4]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>3
[1,5,3,6,4,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>3
[1,5,4,2,3,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>3
[1,5,4,2,6,3]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>3
[1,5,4,3,2,6]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>3
[1,5,4,3,6,2]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>3
[1,5,4,6,2,3]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>3
[1,5,4,6,3,2]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>3
[1,5,6,2,3,4]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>3
[1,5,6,2,4,3]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>3
[1,5,6,3,2,4]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>3
[1,5,6,3,4,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>3
[1,5,6,4,2,3]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>3
[1,5,6,4,3,2]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,4,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>3
[2,1,3,4,5,6]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[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)=>4
[2,1,3,5,4,6]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,2,1]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,1,3,5,6,4]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,2,1]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,1,4,3,5,6]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,2,1,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,1,4,5,3,6]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,2,1,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,1,4,5,6,3]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,2,1,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,1,5,3,4,6]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,1,5,3,6,4]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,1,5,4,3,6]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,1,5,4,6,3]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,1,5,6,3,4]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,1,5,6,4,3]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,3,1,4,5,6]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[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)=>4
[2,3,1,5,4,6]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,2,1]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,3,1,5,6,4]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,2,1]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,3,4,1,5,6]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[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)=>4
[2,3,4,5,1,6]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[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)=>4
[2,3,4,5,6,1]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[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)=>4
[2,3,5,1,4,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,2,1]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,3,5,1,6,4]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,2,1]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,3,5,4,1,6]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,2,1]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,3,5,4,6,1]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,2,1]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,3,5,6,1,4]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,2,1]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,3,5,6,4,1]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,2,1]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,4,1,3,5,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,2,1,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,4,1,5,3,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,2,1,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,4,1,5,6,3]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,2,1,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,4,3,1,5,6]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,2,1,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,4,3,5,1,6]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,2,1,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,4,3,5,6,1]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,2,1,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,4,5,1,3,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,2,1,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,4,5,1,6,3]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,1,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,4,5,3,1,6]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,2,1,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,4,5,3,6,1]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,2,1,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,4,5,6,1,3]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,2,1,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,4,5,6,3,1]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,2,1,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,5,1,3,4,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,5,1,3,6,4]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,5,1,4,3,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,5,1,4,6,3]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,5,1,6,3,4]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,5,1,6,4,3]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,5,3,1,4,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,5,3,1,6,4]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,5,3,4,1,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,5,3,4,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,5,3,6,1,4]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,5,3,6,4,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,5,4,1,3,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,5,4,1,6,3]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,5,4,3,1,6]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,5,4,3,6,1]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,5,4,6,1,3]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,5,4,6,3,1]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,5,6,1,3,4]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,5,6,1,4,3]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,5,6,3,1,4]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,5,6,3,4,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,5,6,4,1,3]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[2,5,6,4,3,1]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,1,2,4,5,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[3,1,2,5,4,6]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,1,2,5,6,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,1,4,2,5,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[3,1,4,5,2,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[3,1,4,5,6,2]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[3,1,5,2,4,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,1,5,2,6,4]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,1,5,4,2,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,1,5,4,6,2]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,1,5,6,2,4]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,1,5,6,4,2]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,2,1,4,5,6]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,1,1]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[3,2,1,5,4,6]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,2,1,5,6,4]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,2,4,1,5,6]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,1,1]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[3,2,4,5,1,6]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,1,1]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[3,2,4,5,6,1]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,1,1]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[3,2,5,1,4,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,2,5,1,6,4]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,2,5,4,1,6]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,2,5,4,6,1]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,2,5,6,1,4]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,2,5,6,4,1]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,4,1,2,5,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[3,4,1,5,2,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[3,4,1,5,6,2]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[3,4,2,1,5,6]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,1,1]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[3,4,2,5,1,6]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,1,1]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[3,4,2,5,6,1]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,1,1,1]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[3,4,5,1,2,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[3,4,5,1,6,2]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[3,4,5,2,1,6]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,1,1]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[3,4,5,2,6,1]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,1,1,1]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[3,4,5,6,1,2]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[3,4,5,6,2,1]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,1,1,1]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[3,5,1,2,4,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,5,1,2,6,4]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,5,1,4,2,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,5,1,4,6,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,5,1,6,2,4]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,5,1,6,4,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,5,2,1,4,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,5,2,1,6,4]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,5,2,4,1,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,5,2,4,6,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,5,2,6,1,4]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,5,2,6,4,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,5,4,1,2,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,5,4,1,6,2]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,5,4,2,1,6]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,5,4,2,6,1]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,5,4,6,1,2]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,5,4,6,2,1]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,5,6,1,2,4]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,5,6,1,4,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,5,6,2,1,4]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,5,6,2,4,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,5,6,4,1,2]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[3,5,6,4,2,1]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
[4,1,2,3,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,1,2,5,3,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,1,2,5,6,3]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,1,3,2,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,1,3,5,2,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,1,3,5,6,2]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,1,5,2,3,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,1,5,2,6,3]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,1,5,3,2,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,1,5,3,6,2]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,1,5,6,2,3]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,1,5,6,3,2]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,2,1,3,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,2,1,5,3,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,2,1,5,6,3]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,2,3,1,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,2,3,5,1,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,2,3,5,6,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,2,5,1,3,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,2,5,1,6,3]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,2,5,3,1,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,2,5,3,6,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,2,5,6,1,3]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,2,5,6,3,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,3,1,2,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,3,1,5,2,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,3,1,5,6,2]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,3,2,1,5,6]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,3,2,5,1,6]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,3,2,5,6,1]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,3,5,1,2,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,3,5,1,6,2]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,3,5,2,1,6]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,3,5,2,6,1]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,3,5,6,1,2]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,3,5,6,2,1]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,5,1,2,3,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,5,1,2,6,3]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,5,1,3,2,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,5,1,3,6,2]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,5,1,6,2,3]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,5,1,6,3,2]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,5,2,1,3,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,5,2,1,6,3]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,5,2,3,1,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,5,2,3,6,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,5,2,6,1,3]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,5,2,6,3,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,5,3,1,2,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,5,3,1,6,2]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,5,3,2,1,6]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,5,3,2,6,1]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,5,3,6,1,2]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,5,3,6,2,1]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,5,6,1,2,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,5,6,1,3,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,5,6,2,1,3]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,5,6,2,3,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,5,6,3,1,2]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[4,5,6,3,2,1]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,1,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
[5,1,2,3,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,1,2,3,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,1,2,4,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,1,2,4,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,1,2,6,3,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,1,2,6,4,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,1,3,2,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,1,3,2,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,1,3,4,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,1,3,4,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,1,3,6,2,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,1,3,6,4,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,1,4,2,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,1,4,2,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,1,4,3,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,1,4,3,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,1,4,6,2,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,1,4,6,3,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,1,6,2,3,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,1,6,2,4,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,1,6,3,2,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,1,6,3,4,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,1,6,4,2,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,1,6,4,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,2,1,3,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,2,1,3,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,2,1,4,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,2,1,4,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,2,1,6,3,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,2,1,6,4,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,2,3,1,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,2,3,1,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,2,3,4,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,2,3,4,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,2,3,6,1,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,2,3,6,4,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,2,4,1,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,2,4,1,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,2,4,3,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,2,4,3,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,2,4,6,1,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,2,4,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,2,6,1,3,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,2,6,1,4,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,2,6,3,1,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,2,6,3,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,2,6,4,1,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,2,6,4,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,3,1,2,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,3,1,2,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,3,1,4,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,3,1,4,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,3,1,6,2,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,3,1,6,4,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,3,2,1,4,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,3,2,1,6,4]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,3,2,4,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,3,2,4,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,3,2,6,1,4]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,3,2,6,4,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,3,4,1,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,3,4,1,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,3,4,2,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,3,4,2,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,3,4,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,3,4,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,3,6,1,2,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,3,6,1,4,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,3,6,2,1,4]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,3,6,2,4,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,3,6,4,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,3,6,4,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,4,1,2,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,4,1,2,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,4,1,3,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,4,1,3,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,4,1,6,2,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,4,1,6,3,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,4,2,1,3,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,4,2,1,6,3]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,4,2,3,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,4,2,3,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,4,2,6,1,3]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,4,2,6,3,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,4,3,1,2,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,4,3,1,6,2]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,4,3,2,1,6]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,4,3,2,6,1]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,4,3,6,1,2]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,4,3,6,2,1]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,4,6,1,2,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,4,6,1,3,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,4,6,2,1,3]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,4,6,2,3,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,4,6,3,1,2]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,4,6,3,2,1]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,6,1,2,3,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,6,1,2,4,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,6,1,3,2,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,6,1,3,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,6,1,4,2,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,6,1,4,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,6,2,1,3,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,6,2,1,4,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,6,2,3,1,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,6,2,3,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,6,2,4,1,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,6,2,4,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,6,3,1,2,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,6,3,1,4,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,6,3,2,1,4]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,6,3,2,4,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,6,3,4,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,6,3,4,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,6,4,1,2,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,6,4,1,3,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,6,4,2,1,3]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,6,4,2,3,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,6,4,3,1,2]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[5,6,4,3,2,1]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>4
[1,2,3,4,5,6,7]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[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)=>6
[1,2,3,4,6,5,7]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,2,1]=>([(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)=>4
[1,2,3,4,6,7,5]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,2,1]=>([(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)=>4
[1,2,3,5,4,6,7]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,2,1,1]=>([(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)=>3
[1,2,3,5,6,4,7]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,2,1,1]=>([(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)=>3
[1,2,3,5,6,7,4]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,2,1,1]=>([(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)=>3
[1,2,3,6,4,5,7]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,3,1]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,2,3,6,4,7,5]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,3,1]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,2,3,6,5,4,7]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,3,1]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,2,3,6,5,7,4]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,3,1]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,2,3,6,7,4,5]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,3,1]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,2,3,6,7,5,4]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,3,1]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,2,4,3,5,6,7]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,2,1,1,1]=>([(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)=>3
[1,2,4,3,6,5,7]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,2,2,1]=>([(0,6),(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)=>2
[1,2,4,3,6,7,5]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,2,2,1]=>([(0,6),(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)=>2
[1,2,4,5,3,6,7]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,2,1,1,1]=>([(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)=>3
[1,2,4,5,6,3,7]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,2,1,1,1]=>([(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)=>3
[1,2,4,5,6,7,3]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,2,1,1,1]=>([(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)=>3
[1,2,4,6,3,5,7]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,2,2,1]=>([(0,6),(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)=>2
[1,2,4,6,3,7,5]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]=>([(0,6),(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)=>2
[1,2,4,6,5,3,7]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,2,2,1]=>([(0,6),(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)=>2
[1,2,4,6,5,7,3]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,2,2,1]=>([(0,6),(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)=>2
[1,2,4,6,7,3,5]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]=>([(0,6),(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)=>2
[1,2,4,6,7,5,3]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,2,2,1]=>([(0,6),(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)=>2
[1,2,5,3,4,6,7]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,3,1,1]=>([(0,5),(0,6),(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)=>2
[1,2,5,3,6,4,7]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,3,1,1]=>([(0,5),(0,6),(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)=>2
[1,2,5,3,6,7,4]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,3,1,1]=>([(0,5),(0,6),(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)=>2
[1,2,5,4,3,6,7]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,3,1,1]=>([(0,5),(0,6),(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)=>2
[1,2,5,4,6,3,7]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,3,1,1]=>([(0,5),(0,6),(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)=>2
[1,2,5,4,6,7,3]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,3,1,1]=>([(0,5),(0,6),(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)=>2
[1,2,5,6,3,4,7]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,3,1,1]=>([(0,5),(0,6),(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)=>2
[1,2,5,6,3,7,4]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,3,1,1]=>([(0,5),(0,6),(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)=>2
[1,2,5,6,4,3,7]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,3,1,1]=>([(0,5),(0,6),(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)=>2
[1,2,5,6,4,7,3]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,3,1,1]=>([(0,5),(0,6),(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)=>2
[1,2,5,6,7,3,4]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,3,1,1]=>([(0,5),(0,6),(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)=>2
[1,2,5,6,7,4,3]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,3,1,1]=>([(0,5),(0,6),(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)=>2
[1,2,6,3,4,5,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,4,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,2,6,3,4,7,5]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,4,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,2,6,3,5,4,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,4,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,2,6,3,5,7,4]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,4,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,2,6,3,7,4,5]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,4,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,2,6,3,7,5,4]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,4,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,2,6,4,3,5,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,4,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,2,6,4,3,7,5]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,4,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,2,6,4,5,3,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,4,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,2,6,4,5,7,3]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,4,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,2,6,4,7,3,5]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,4,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,2,6,4,7,5,3]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,4,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,2,6,5,3,4,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,4,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,2,6,5,3,7,4]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,4,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,2,6,5,4,3,7]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,4,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,2,6,5,4,7,3]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,4,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,2,6,5,7,3,4]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,4,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,2,6,5,7,4,3]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,4,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,2,6,7,3,4,5]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,4,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,2,6,7,3,5,4]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,4,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,2,6,7,4,3,5]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,4,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,2,6,7,4,5,3]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,4,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,2,6,7,5,3,4]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,4,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,2,6,7,5,4,3]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,4,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,3,2,4,5,6,7]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,1,1,1,1]=>([(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)=>4
[1,3,2,4,6,5,7]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,1,2,1]=>([(0,6),(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)=>2
[1,3,2,4,6,7,5]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,1,2,1]=>([(0,6),(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)=>2
[1,3,2,5,4,6,7]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,2,1,1]=>([(0,5),(0,6),(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)=>2
[1,3,2,5,6,4,7]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,2,1,1]=>([(0,5),(0,6),(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)=>2
[1,3,2,5,6,7,4]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,2,1,1]=>([(0,5),(0,6),(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)=>2
[1,3,2,6,4,5,7]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,3,2,6,4,7,5]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,3,2,6,5,4,7]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,3,2,6,5,7,4]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,3,2,6,7,4,5]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,3,2,6,7,5,4]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,3,4,2,5,6,7]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,2,1,1,1,1]=>([(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)=>4
[1,3,4,2,6,5,7]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,1,2,1]=>([(0,6),(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)=>2
[1,3,4,2,6,7,5]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,1,2,1]=>([(0,6),(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)=>2
[1,3,4,5,2,6,7]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,1,1,1,1]=>([(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)=>4
[1,3,4,5,6,2,7]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,1,1,1,1]=>([(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)=>4
[1,3,4,5,6,7,2]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,1,1,1,1]=>([(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)=>4
[1,3,4,6,2,5,7]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,2,1]=>([(0,6),(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)=>2
[1,3,4,6,2,7,5]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,2,1]=>([(0,6),(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)=>2
[1,3,4,6,5,2,7]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,2,1,2,1]=>([(0,6),(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)=>2
[1,3,4,6,5,7,2]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,2,1,2,1]=>([(0,6),(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)=>2
[1,3,4,6,7,2,5]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]=>([(0,6),(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)=>2
[1,3,4,6,7,5,2]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,2,1,2,1]=>([(0,6),(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)=>2
[1,3,5,2,4,6,7]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,2,1,1]=>([(0,5),(0,6),(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)=>2
[1,3,5,2,6,4,7]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,2,1,1]=>([(0,5),(0,6),(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)=>2
[1,3,5,2,6,7,4]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,2,1,1]=>([(0,5),(0,6),(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)=>2
[1,3,5,4,2,6,7]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,2,1,1]=>([(0,5),(0,6),(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)=>2
[1,3,5,4,6,2,7]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,2,1,1]=>([(0,5),(0,6),(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)=>2
[1,3,5,4,6,7,2]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,2,2,1,1]=>([(0,5),(0,6),(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)=>2
[1,3,5,6,2,4,7]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,2,1,1]=>([(0,5),(0,6),(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)=>2
[1,3,5,6,2,7,4]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,2,1,1]=>([(0,5),(0,6),(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)=>2
[1,3,5,6,4,2,7]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,2,2,1,1]=>([(0,5),(0,6),(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)=>2
[1,3,5,6,4,7,2]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,2,1,1]=>([(0,5),(0,6),(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)=>2
[1,3,5,6,7,2,4]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]=>([(0,5),(0,6),(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)=>2
[1,3,5,6,7,4,2]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,2,1,1]=>([(0,5),(0,6),(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)=>2
[1,3,6,2,4,5,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,3,6,2,4,7,5]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,3,6,2,5,4,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,3,6,2,5,7,4]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,3,6,2,7,4,5]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,3,6,2,7,5,4]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,3,6,4,2,5,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,3,6,4,2,7,5]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,3,6,4,5,2,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,3,6,4,5,7,2]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,3,6,4,7,2,5]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,3,6,4,7,5,2]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,3,6,5,2,4,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,3,6,5,2,7,4]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,3,6,5,4,2,7]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,3,6,5,4,7,2]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,3,6,5,7,2,4]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,3,6,5,7,4,2]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,3,6,7,2,4,5]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,3,6,7,2,5,4]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,3,6,7,4,2,5]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,3,6,7,4,5,2]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,3,6,7,5,2,4]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,3,6,7,5,4,2]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,2,3,5,6,7]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,1,1,1]=>([(0,4),(0,5),(0,6),(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)=>3
[1,4,2,3,6,5,7]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,2,3,6,7,5]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,2,5,3,6,7]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,3,1,1,1]=>([(0,4),(0,5),(0,6),(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)=>3
[1,4,2,5,6,3,7]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,3,1,1,1]=>([(0,4),(0,5),(0,6),(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)=>3
[1,4,2,5,6,7,3]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,1,1,1]=>([(0,4),(0,5),(0,6),(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)=>3
[1,4,2,6,3,5,7]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,2,6,3,7,5]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,2,6,5,3,7]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,2,6,5,7,3]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,2,6,7,3,5]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,2,6,7,5,3]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,3,2,5,6,7]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,1,1,1]=>([(0,4),(0,5),(0,6),(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)=>3
[1,4,3,2,6,5,7]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,3,2,6,7,5]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,3,5,2,6,7]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,3,1,1,1]=>([(0,4),(0,5),(0,6),(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)=>3
[1,4,3,5,6,2,7]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,3,1,1,1]=>([(0,4),(0,5),(0,6),(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)=>3
[1,4,3,5,6,7,2]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,1,1,1]=>([(0,4),(0,5),(0,6),(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)=>3
[1,4,3,6,2,5,7]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,3,6,2,7,5]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,3,6,5,2,7]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,3,6,5,7,2]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,3,6,7,2,5]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,3,6,7,5,2]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,5,2,3,6,7]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,1,1,1]=>([(0,4),(0,5),(0,6),(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)=>3
[1,4,5,2,6,3,7]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,1,1,1]=>([(0,4),(0,5),(0,6),(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)=>3
[1,4,5,2,6,7,3]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,1,1,1]=>([(0,4),(0,5),(0,6),(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)=>3
[1,4,5,3,2,6,7]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,1,1,1]=>([(0,4),(0,5),(0,6),(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)=>3
[1,4,5,3,6,2,7]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,1,1,1]=>([(0,4),(0,5),(0,6),(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)=>3
[1,4,5,3,6,7,2]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,1,1,1]=>([(0,4),(0,5),(0,6),(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)=>3
[1,4,5,6,2,3,7]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,1,1,1]=>([(0,4),(0,5),(0,6),(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)=>3
[1,4,5,6,2,7,3]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,1,1,1]=>([(0,4),(0,5),(0,6),(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)=>3
[1,4,5,6,3,2,7]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,1,1,1]=>([(0,4),(0,5),(0,6),(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)=>3
[1,4,5,6,3,7,2]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,1,1,1]=>([(0,4),(0,5),(0,6),(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)=>3
[1,4,5,6,7,2,3]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1]=>([(0,4),(0,5),(0,6),(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)=>3
[1,4,5,6,7,3,2]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,1,1,1]=>([(0,4),(0,5),(0,6),(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)=>3
[1,4,6,2,3,5,7]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,6,2,3,7,5]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,6,2,5,3,7]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,6,2,5,7,3]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,6,2,7,3,5]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,6,2,7,5,3]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,6,3,2,5,7]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,6,3,2,7,5]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,6,3,5,2,7]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,6,3,5,7,2]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,6,3,7,2,5]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,6,3,7,5,2]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,6,5,2,3,7]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,6,5,2,7,3]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,6,5,3,2,7]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,6,5,3,7,2]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,6,5,7,2,3]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,6,5,7,3,2]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,6,7,2,3,5]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,6,7,2,5,3]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,6,7,3,2,5]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,6,7,3,5,2]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,6,7,5,2,3]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,4,6,7,5,3,2]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[1,5,2,3,4,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,2,3,6,4,7]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,2,3,6,7,4]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,2,4,3,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,2,4,6,3,7]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,2,4,6,7,3]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,2,6,3,4,7]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,2,6,3,7,4]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,2,6,4,3,7]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,2,6,4,7,3]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,2,6,7,3,4]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,2,6,7,4,3]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,3,2,4,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,3,2,6,4,7]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,3,2,6,7,4]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,3,4,2,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,3,4,6,2,7]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,3,4,6,7,2]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,3,6,2,4,7]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,3,6,2,7,4]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,3,6,4,2,7]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,3,6,4,7,2]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,3,6,7,2,4]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,3,6,7,4,2]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,4,2,3,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,4,2,6,3,7]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,4,2,6,7,3]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,4,3,2,6,7]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,4,3,6,2,7]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,4,3,6,7,2]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,4,6,2,3,7]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,4,6,2,7,3]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,4,6,3,2,7]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,4,6,3,7,2]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,4,6,7,2,3]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,4,6,7,3,2]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,6,2,3,4,7]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,6,2,3,7,4]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,6,2,4,3,7]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,6,2,4,7,3]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,6,2,7,3,4]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,6,2,7,4,3]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,6,3,2,4,7]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,6,3,2,7,4]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,6,3,4,2,7]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,6,3,4,7,2]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,6,3,7,2,4]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,6,3,7,4,2]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,6,4,2,3,7]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,6,4,2,7,3]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,6,4,3,2,7]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,6,4,3,7,2]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,6,4,7,2,3]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,6,4,7,3,2]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,6,7,2,3,4]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,6,7,2,4,3]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,6,7,3,2,4]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,6,7,3,4,2]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,6,7,4,2,3]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,5,6,7,4,3,2]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,4,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[1,6,2,3,4,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,2,3,4,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,2,3,5,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,2,3,5,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,2,3,7,4,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,2,3,7,5,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,2,4,3,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,2,4,3,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,2,4,5,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,2,4,5,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,2,4,7,3,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,2,4,7,5,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,2,5,3,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,2,5,3,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,2,5,4,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,2,5,4,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,2,5,7,3,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,2,5,7,4,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,2,7,3,4,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,2,7,3,5,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,2,7,4,3,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,2,7,4,5,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,2,7,5,3,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,2,7,5,4,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,3,2,4,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,3,2,4,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,3,2,5,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,3,2,5,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,3,2,7,4,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,3,2,7,5,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,3,4,2,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,3,4,2,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,3,4,5,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,3,4,5,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,3,4,7,2,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,3,4,7,5,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,3,5,2,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,3,5,2,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,3,5,4,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,3,5,4,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,3,5,7,2,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,3,5,7,4,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,3,7,2,4,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,3,7,2,5,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,3,7,4,2,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,3,7,4,5,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,3,7,5,2,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,3,7,5,4,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,4,2,3,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,4,2,3,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,4,2,5,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,4,2,5,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,4,2,7,3,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,4,2,7,5,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,4,3,2,5,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,4,3,2,7,5]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,4,3,5,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,4,3,5,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,4,3,7,2,5]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,4,3,7,5,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,4,5,2,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,4,5,2,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,4,5,3,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,4,5,3,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,4,5,7,2,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,4,5,7,3,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,4,7,2,3,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,4,7,2,5,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,4,7,3,2,5]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,4,7,3,5,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,4,7,5,2,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,4,7,5,3,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,5,2,3,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,5,2,3,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,5,2,4,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,5,2,4,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,5,2,7,3,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,5,2,7,4,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,5,3,2,4,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,5,3,2,7,4]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,5,3,4,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,5,3,4,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,5,3,7,2,4]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,5,3,7,4,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,5,4,2,3,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,5,4,2,7,3]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,5,4,3,2,7]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,5,4,3,7,2]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,5,4,7,2,3]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,5,4,7,3,2]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,5,7,2,3,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,5,7,2,4,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,5,7,3,2,4]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,5,7,3,4,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,5,7,4,2,3]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,5,7,4,3,2]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,7,2,3,4,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,7,2,3,5,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,7,2,4,3,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,7,2,4,5,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,7,2,5,3,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,7,2,5,4,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,7,3,2,4,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,7,3,2,5,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,7,3,4,2,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,7,3,4,5,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,7,3,5,2,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,7,3,5,4,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,7,4,2,3,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,7,4,2,5,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,7,4,3,2,5]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,7,4,3,5,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,7,4,5,2,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,7,4,5,3,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,7,5,2,3,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,7,5,2,4,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,7,5,3,2,4]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,7,5,3,4,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,7,5,4,2,3]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[1,6,7,5,4,3,2]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,5,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)=>4
[2,1,3,4,5,6,7]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[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)=>5
[2,1,3,4,6,5,7]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]=>([(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)=>3
[2,1,3,4,6,7,5]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]=>([(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)=>3
[2,1,3,5,4,6,7]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1]=>([(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)=>2
[2,1,3,5,6,4,7]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]=>([(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)=>2
[2,1,3,5,6,7,4]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]=>([(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)=>2
[2,1,3,6,4,5,7]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,1,3,6,4,7,5]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,1,3,6,5,4,7]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,1,3,6,5,7,4]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,1,3,6,7,4,5]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,1,3,6,7,5,4]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,1,4,3,5,6,7]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,2,1,1,1]=>([(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)=>3
[2,1,4,3,6,5,7]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,1,4,3,6,7,5]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,1,4,5,3,6,7]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,2,1,1,1]=>([(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)=>3
[2,1,4,5,6,3,7]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]=>([(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)=>3
[2,1,4,5,6,7,3]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]=>([(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)=>3
[2,1,4,6,3,5,7]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,1,4,6,3,7,5]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,1,4,6,5,3,7]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,1,4,6,5,7,3]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,1,4,6,7,3,5]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,1,4,6,7,5,3]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,1,5,3,4,6,7]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,1,5,3,6,4,7]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,1,5,3,6,7,4]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,1,5,4,3,6,7]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,1,5,4,6,3,7]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,1,5,4,6,7,3]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,1,5,6,3,4,7]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,1,5,6,3,7,4]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,1,5,6,4,3,7]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,1,5,6,4,7,3]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,1,5,6,7,3,4]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,1,5,6,7,4,3]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,1,6,3,4,5,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,1,6,3,4,7,5]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,1,6,3,5,4,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,1,6,3,5,7,4]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,1,6,3,7,4,5]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,1,6,3,7,5,4]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,1,6,4,3,5,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,1,6,4,3,7,5]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,1,6,4,5,3,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,1,6,4,5,7,3]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,1,6,4,7,3,5]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,1,6,4,7,5,3]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,1,6,5,3,4,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,1,6,5,3,7,4]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,1,6,5,4,3,7]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,1,6,5,4,7,3]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,1,6,5,7,3,4]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,1,6,5,7,4,3]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,1,6,7,3,4,5]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,1,6,7,3,5,4]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,1,6,7,4,3,5]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,1,6,7,4,5,3]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,1,6,7,5,3,4]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,1,6,7,5,4,3]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,3,1,4,5,6,7]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[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)=>5
[2,3,1,4,6,5,7]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,1,2,1]=>([(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)=>3
[2,3,1,4,6,7,5]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,1,2,1]=>([(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)=>3
[2,3,1,5,4,6,7]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,2,1,1]=>([(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)=>2
[2,3,1,5,6,4,7]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,2,1,1]=>([(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)=>2
[2,3,1,5,6,7,4]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,2,1,1]=>([(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)=>2
[2,3,1,6,4,5,7]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,3,1,6,4,7,5]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,3,1,6,5,4,7]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,3,1,6,5,7,4]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,3,1,6,7,4,5]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,3,1,6,7,5,4]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,3,4,1,5,6,7]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[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)=>5
[2,3,4,1,6,5,7]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,1,2,1]=>([(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)=>3
[2,3,4,1,6,7,5]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,1,2,1]=>([(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)=>3
[2,3,4,5,1,6,7]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[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)=>5
[2,3,4,5,6,1,7]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[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)=>5
[2,3,4,5,6,7,1]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[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)=>5
[2,3,4,6,1,5,7]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,1,2,1]=>([(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)=>3
[2,3,4,6,1,7,5]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,1,2,1]=>([(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)=>3
[2,3,4,6,5,1,7]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,1,2,1]=>([(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)=>3
[2,3,4,6,5,7,1]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,1,2,1]=>([(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)=>3
[2,3,4,6,7,1,5]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,2,1]=>([(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)=>3
[2,3,4,6,7,5,1]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,1,2,1]=>([(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)=>3
[2,3,5,1,4,6,7]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,2,1,1]=>([(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)=>2
[2,3,5,1,6,4,7]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,2,1,1]=>([(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)=>2
[2,3,5,1,6,7,4]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,2,1,1]=>([(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)=>2
[2,3,5,4,1,6,7]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,2,1,1]=>([(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)=>2
[2,3,5,4,6,1,7]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,2,1,1]=>([(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)=>2
[2,3,5,4,6,7,1]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,2,1,1]=>([(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)=>2
[2,3,5,6,1,4,7]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,2,1,1]=>([(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)=>2
[2,3,5,6,1,7,4]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,2,1,1]=>([(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)=>2
[2,3,5,6,4,1,7]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,2,1,1]=>([(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)=>2
[2,3,5,6,4,7,1]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,2,1,1]=>([(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)=>2
[2,3,5,6,7,1,4]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,2,1,1]=>([(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)=>2
[2,3,5,6,7,4,1]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,2,1,1]=>([(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)=>2
[2,3,6,1,4,5,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,3,6,1,4,7,5]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,3,6,1,5,4,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,3,6,1,5,7,4]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,3,6,1,7,4,5]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,3,6,1,7,5,4]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,3,6,4,1,5,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,3,6,4,1,7,5]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,3,6,4,5,1,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,3,6,4,5,7,1]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,3,6,4,7,1,5]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,3,6,4,7,5,1]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,3,6,5,1,4,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,3,6,5,1,7,4]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,3,6,5,4,1,7]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,3,6,5,4,7,1]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,3,6,5,7,1,4]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,3,6,5,7,4,1]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,3,6,7,1,4,5]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,3,6,7,1,5,4]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,3,6,7,4,1,5]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,3,6,7,4,5,1]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,3,6,7,5,1,4]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,3,6,7,5,4,1]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,3,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,4,1,3,5,6,7]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,2,1,1,1]=>([(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)=>3
[2,4,1,3,6,5,7]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,1,3,6,7,5]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,1,5,3,6,7]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,2,1,1,1]=>([(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)=>3
[2,4,1,5,6,3,7]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]=>([(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)=>3
[2,4,1,5,6,7,3]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]=>([(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)=>3
[2,4,1,6,3,5,7]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,1,6,3,7,5]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,1,6,5,3,7]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,1,6,5,7,3]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,1,6,7,3,5]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,1,6,7,5,3]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,3,1,5,6,7]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,2,1,1,1]=>([(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)=>3
[2,4,3,1,6,5,7]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,3,1,6,7,5]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,3,5,1,6,7]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,2,1,1,1]=>([(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)=>3
[2,4,3,5,6,1,7]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,2,1,1,1]=>([(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)=>3
[2,4,3,5,6,7,1]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,2,1,1,1]=>([(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)=>3
[2,4,3,6,1,5,7]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,3,6,1,7,5]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,3,6,5,1,7]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,3,6,5,7,1]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,3,6,7,1,5]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,3,6,7,5,1]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,5,1,3,6,7]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,2,1,1,1]=>([(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)=>3
[2,4,5,1,6,3,7]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,2,1,1,1]=>([(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)=>3
[2,4,5,1,6,7,3]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,2,1,1,1]=>([(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)=>3
[2,4,5,3,1,6,7]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,2,1,1,1]=>([(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)=>3
[2,4,5,3,6,1,7]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,2,1,1,1]=>([(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)=>3
[2,4,5,3,6,7,1]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,2,1,1,1]=>([(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)=>3
[2,4,5,6,1,3,7]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,2,1,1,1]=>([(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)=>3
[2,4,5,6,1,7,3]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,2,1,1,1]=>([(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)=>3
[2,4,5,6,3,1,7]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,2,1,1,1]=>([(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)=>3
[2,4,5,6,3,7,1]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,2,1,1,1]=>([(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)=>3
[2,4,5,6,7,1,3]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,2,1,1,1]=>([(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)=>3
[2,4,5,6,7,3,1]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,2,1,1,1]=>([(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)=>3
[2,4,6,1,3,5,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,6,1,3,7,5]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,6,1,5,3,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,6,1,5,7,3]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,6,1,7,3,5]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,6,1,7,5,3]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,6,3,1,5,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,6,3,1,7,5]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,6,3,5,1,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,6,3,5,7,1]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,6,3,7,1,5]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,6,3,7,5,1]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,6,5,1,3,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,6,5,1,7,3]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,6,5,3,1,7]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,6,5,3,7,1]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,6,5,7,1,3]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,6,5,7,3,1]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,6,7,1,3,5]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,6,7,1,5,3]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,6,7,3,1,5]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,6,7,3,5,1]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,6,7,5,1,3]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,4,6,7,5,3,1]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,2,2,1]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>1
[2,5,1,3,4,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,1,3,6,4,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,1,3,6,7,4]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,1,4,3,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,1,4,6,3,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,1,4,6,7,3]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,1,6,3,4,7]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,1,6,3,7,4]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,1,6,4,3,7]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,1,6,4,7,3]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,1,6,7,3,4]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,1,6,7,4,3]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,3,1,4,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,3,1,6,4,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,3,1,6,7,4]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,3,4,1,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,3,4,6,1,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,3,4,6,7,1]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,3,6,1,4,7]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,3,6,1,7,4]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,3,6,4,1,7]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,3,6,4,7,1]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,3,6,7,1,4]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,3,6,7,4,1]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,4,1,3,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,4,1,6,3,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,4,1,6,7,3]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,4,3,1,6,7]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,4,3,6,1,7]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,4,3,6,7,1]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,4,6,1,3,7]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,4,6,1,7,3]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,4,6,3,1,7]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,4,6,3,7,1]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,4,6,7,1,3]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,4,6,7,3,1]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,6,1,3,4,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,6,1,3,7,4]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,6,1,4,3,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,6,1,4,7,3]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,6,1,7,3,4]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,6,1,7,4,3]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,6,3,1,4,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,6,3,1,7,4]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,6,3,4,1,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,6,3,4,7,1]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,6,3,7,1,4]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,6,3,7,4,1]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,6,4,1,3,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,6,4,1,7,3]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,6,4,3,1,7]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,6,4,3,7,1]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,6,4,7,1,3]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,6,4,7,3,1]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,6,7,1,3,4]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,6,7,1,4,3]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,6,7,3,1,4]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,6,7,3,4,1]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,6,7,4,1,3]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,5,6,7,4,3,1]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,1,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[2,6,1,3,4,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,1,3,4,7,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,1,3,5,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,1,3,5,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,1,3,7,4,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,1,3,7,5,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,1,4,3,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,1,4,3,7,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,1,4,5,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,1,4,5,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,1,4,7,3,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,1,4,7,5,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,1,5,3,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,1,5,3,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,1,5,4,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,1,5,4,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,1,5,7,3,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,1,5,7,4,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,1,7,3,4,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,1,7,3,5,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,1,7,4,3,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,1,7,4,5,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,1,7,5,3,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,1,7,5,4,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,3,1,4,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,3,1,4,7,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,3,1,5,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,3,1,5,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,3,1,7,4,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,3,1,7,5,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,3,4,1,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,3,4,1,7,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,3,4,5,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,3,4,5,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,3,4,7,1,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,3,4,7,5,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,3,5,1,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,3,5,1,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,3,5,4,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,3,5,4,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,3,5,7,1,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,3,5,7,4,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,3,7,1,4,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,3,7,1,5,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,3,7,4,1,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,3,7,4,5,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,3,7,5,1,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,3,7,5,4,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,4,1,3,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,4,1,3,7,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,4,1,5,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,4,1,5,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,4,1,7,3,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,4,1,7,5,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,4,3,1,5,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,4,3,1,7,5]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,4,3,5,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,4,3,5,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,4,3,7,1,5]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,4,3,7,5,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,4,5,1,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,4,5,1,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,4,5,3,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,4,5,3,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,4,5,7,1,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,4,5,7,3,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,4,7,1,3,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,4,7,1,5,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,4,7,3,1,5]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,4,7,3,5,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,4,7,5,1,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,4,7,5,3,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,5,1,3,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,5,1,3,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,5,1,4,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,5,1,4,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,5,1,7,3,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,5,1,7,4,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,5,3,1,4,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,5,3,1,7,4]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,5,3,4,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,5,3,4,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,5,3,7,1,4]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,5,3,7,4,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,5,4,1,3,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,5,4,1,7,3]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,5,4,3,1,7]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,5,4,3,7,1]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,5,4,7,1,3]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,5,4,7,3,1]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,5,7,1,3,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,5,7,1,4,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,5,7,3,1,4]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,5,7,3,4,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,5,7,4,1,3]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,5,7,4,3,1]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,7,1,3,4,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,7,1,3,5,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,7,1,4,3,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,7,1,4,5,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,7,1,5,3,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,7,1,5,4,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,7,3,1,4,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,7,3,1,5,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,7,3,4,1,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,7,3,4,5,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,7,3,5,1,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,7,3,5,4,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,7,4,1,3,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,7,4,1,5,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,7,4,3,1,5]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,7,4,3,5,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,7,4,5,1,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,7,4,5,3,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,7,5,1,3,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,7,5,1,4,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,7,5,3,1,4]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,7,5,3,4,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,7,5,4,1,3]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[2,6,7,5,4,3,1]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[3,1,2,4,5,6,7]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[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)=>4
[3,1,2,4,6,5,7]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,1]=>([(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)=>2
[3,1,2,4,6,7,5]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,1]=>([(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)=>2
[3,1,2,5,4,6,7]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,1,2,5,6,4,7]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,1,2,5,6,7,4]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]=>([(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)=>2
[3,1,2,6,4,5,7]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,1,2,6,4,7,5]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,1,2,6,5,4,7]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,1,2,6,5,7,4]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,1,2,6,7,4,5]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,1,2,6,7,5,4]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,1,4,2,5,6,7]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[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)=>4
[3,1,4,2,6,5,7]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,2,1]=>([(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)=>2
[3,1,4,2,6,7,5]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,2,1]=>([(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)=>2
[3,1,4,5,2,6,7]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[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)=>4
[3,1,4,5,6,2,7]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[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)=>4
[3,1,4,5,6,7,2]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[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)=>4
[3,1,4,6,2,5,7]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,1]=>([(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)=>2
[3,1,4,6,2,7,5]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,2,1]=>([(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)=>2
[3,1,4,6,5,2,7]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,1]=>([(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)=>2
[3,1,4,6,5,7,2]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,2,1]=>([(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)=>2
[3,1,4,6,7,2,5]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,2,1]=>([(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)=>2
[3,1,4,6,7,5,2]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,2,1]=>([(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)=>2
[3,1,5,2,4,6,7]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,1,5,2,6,4,7]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,1,5,2,6,7,4]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,1,1]=>([(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)=>2
[3,1,5,4,2,6,7]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,1,5,4,6,2,7]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,1,5,4,6,7,2]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,1,1]=>([(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)=>2
[3,1,5,6,2,4,7]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,1,5,6,2,7,4]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,1,1]=>([(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)=>2
[3,1,5,6,4,2,7]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,1,5,6,4,7,2]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,1,1]=>([(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)=>2
[3,1,5,6,7,2,4]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]=>([(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)=>2
[3,1,5,6,7,4,2]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]=>([(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)=>2
[3,1,6,2,4,5,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,1,6,2,4,7,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,1,6,2,5,4,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,1,6,2,5,7,4]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,1,6,2,7,4,5]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,1,6,2,7,5,4]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,1,6,4,2,5,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,1,6,4,2,7,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,1,6,4,5,2,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,1,6,4,5,7,2]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,1,6,4,7,2,5]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,1,6,4,7,5,2]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,1,6,5,2,4,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,1,6,5,2,7,4]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,1,6,5,4,2,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,1,6,5,4,7,2]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,1,6,5,7,2,4]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,1,6,5,7,4,2]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,1,6,7,2,4,5]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,1,6,7,2,5,4]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,1,6,7,4,2,5]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,1,6,7,4,5,2]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,1,6,7,5,2,4]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,1,6,7,5,4,2]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,2,1,4,5,6,7]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[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)=>4
[3,2,1,4,6,5,7]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,1,2,1]=>([(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)=>2
[3,2,1,4,6,7,5]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,1,2,1]=>([(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)=>2
[3,2,1,5,4,6,7]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,2,1,5,6,4,7]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,2,1,5,6,7,4]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,1]=>([(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)=>2
[3,2,1,6,4,5,7]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,2,1,6,4,7,5]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,2,1,6,5,4,7]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,2,1,6,5,7,4]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,2,1,6,7,4,5]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,2,1,6,7,5,4]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,2,4,1,5,6,7]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[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)=>4
[3,2,4,1,6,5,7]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,2,1]=>([(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)=>2
[3,2,4,1,6,7,5]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,2,1]=>([(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)=>2
[3,2,4,5,1,6,7]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[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)=>4
[3,2,4,5,6,1,7]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[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)=>4
[3,2,4,5,6,7,1]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[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)=>4
[3,2,4,6,1,5,7]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,1]=>([(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)=>2
[3,2,4,6,1,7,5]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,2,1]=>([(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)=>2
[3,2,4,6,5,1,7]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,1]=>([(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)=>2
[3,2,4,6,5,7,1]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,2,1]=>([(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)=>2
[3,2,4,6,7,1,5]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,2,1]=>([(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)=>2
[3,2,4,6,7,5,1]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,2,1]=>([(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)=>2
[3,2,5,1,4,6,7]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,2,5,1,6,4,7]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,2,5,1,6,7,4]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,1,1]=>([(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)=>2
[3,2,5,4,1,6,7]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,2,5,4,6,1,7]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,2,5,4,6,7,1]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,1,1]=>([(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)=>2
[3,2,5,6,1,4,7]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,2,5,6,1,7,4]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,1,1]=>([(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)=>2
[3,2,5,6,4,1,7]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,2,5,6,4,7,1]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,1,1]=>([(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)=>2
[3,2,5,6,7,1,4]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]=>([(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)=>2
[3,2,5,6,7,4,1]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,1,1]=>([(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)=>2
[3,2,6,1,4,5,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,2,6,1,4,7,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,2,6,1,5,4,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,2,6,1,5,7,4]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,2,6,1,7,4,5]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,2,6,1,7,5,4]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,2,6,4,1,5,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,2,6,4,1,7,5]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,2,6,4,5,1,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,2,6,4,5,7,1]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,2,6,4,7,1,5]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,2,6,4,7,5,1]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,2,6,5,1,4,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,2,6,5,1,7,4]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,2,6,5,4,1,7]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,2,6,5,4,7,1]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,2,6,5,7,1,4]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,2,6,5,7,4,1]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,2,6,7,1,4,5]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,2,6,7,1,5,4]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,2,6,7,4,1,5]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,2,6,7,4,5,1]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,2,6,7,5,1,4]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,2,6,7,5,4,1]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,4,1,2,5,6,7]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[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)=>4
[3,4,1,2,6,5,7]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,1]=>([(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)=>2
[3,4,1,2,6,7,5]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,1]=>([(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)=>2
[3,4,1,5,2,6,7]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[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)=>4
[3,4,1,5,6,2,7]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[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)=>4
[3,4,1,5,6,7,2]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[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)=>4
[3,4,1,6,2,5,7]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,1]=>([(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)=>2
[3,4,1,6,2,7,5]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,1,2,1]=>([(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)=>2
[3,4,1,6,5,2,7]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,1]=>([(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)=>2
[3,4,1,6,5,7,2]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,1,2,1]=>([(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)=>2
[3,4,1,6,7,2,5]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,2,1]=>([(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)=>2
[3,4,1,6,7,5,2]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,2,1]=>([(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)=>2
[3,4,2,1,5,6,7]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[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)=>4
[3,4,2,1,6,5,7]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,1]=>([(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)=>2
[3,4,2,1,6,7,5]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,1]=>([(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)=>2
[3,4,2,5,1,6,7]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[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)=>4
[3,4,2,5,6,1,7]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[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)=>4
[3,4,2,5,6,7,1]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[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)=>4
[3,4,2,6,1,5,7]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,1]=>([(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)=>2
[3,4,2,6,1,7,5]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,1,2,1]=>([(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)=>2
[3,4,2,6,5,1,7]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,1]=>([(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)=>2
[3,4,2,6,5,7,1]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,1,2,1]=>([(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)=>2
[3,4,2,6,7,1,5]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,2,1]=>([(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)=>2
[3,4,2,6,7,5,1]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,1,2,1]=>([(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)=>2
[3,4,5,1,2,6,7]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[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)=>4
[3,4,5,1,6,2,7]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[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)=>4
[3,4,5,1,6,7,2]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[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)=>4
[3,4,5,2,1,6,7]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[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)=>4
[3,4,5,2,6,1,7]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[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)=>4
[3,4,5,2,6,7,1]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[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)=>4
[3,4,5,6,1,2,7]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[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)=>4
[3,4,5,6,1,7,2]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[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)=>4
[3,4,5,6,2,1,7]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[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)=>4
[3,4,5,6,2,7,1]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[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)=>4
[3,4,5,6,7,1,2]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[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)=>4
[3,4,5,6,7,2,1]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[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)=>4
[3,4,6,1,2,5,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,1]=>([(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)=>2
[3,4,6,1,2,7,5]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,2,1]=>([(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)=>2
[3,4,6,1,5,2,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,1]=>([(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)=>2
[3,4,6,1,5,7,2]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,2,1]=>([(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)=>2
[3,4,6,1,7,2,5]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,1,2,1]=>([(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)=>2
[3,4,6,1,7,5,2]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,1,2,1]=>([(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)=>2
[3,4,6,2,1,5,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,1]=>([(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)=>2
[3,4,6,2,1,7,5]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,2,1]=>([(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)=>2
[3,4,6,2,5,1,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,1]=>([(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)=>2
[3,4,6,2,5,7,1]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,2,1]=>([(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)=>2
[3,4,6,2,7,1,5]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,1,2,1]=>([(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)=>2
[3,4,6,2,7,5,1]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,1,2,1]=>([(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)=>2
[3,4,6,5,1,2,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,1]=>([(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)=>2
[3,4,6,5,1,7,2]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,2,1]=>([(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)=>2
[3,4,6,5,2,1,7]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,1]=>([(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)=>2
[3,4,6,5,2,7,1]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,1,2,1]=>([(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)=>2
[3,4,6,5,7,1,2]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,1,2,1]=>([(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)=>2
[3,4,6,5,7,2,1]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,1,2,1]=>([(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)=>2
[3,4,6,7,1,2,5]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,2,1]=>([(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)=>2
[3,4,6,7,1,5,2]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,2,1]=>([(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)=>2
[3,4,6,7,2,1,5]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,2,1]=>([(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)=>2
[3,4,6,7,2,5,1]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,2,1]=>([(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)=>2
[3,4,6,7,5,1,2]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,2,1]=>([(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)=>2
[3,4,6,7,5,2,1]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,1,2,1]=>([(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)=>2
[3,5,1,2,4,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,5,1,2,6,4,7]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,5,1,2,6,7,4]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,1,4,2,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,5,1,4,6,2,7]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,5,1,4,6,7,2]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,1,6,2,4,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,5,1,6,2,7,4]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,1,6,4,2,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,5,1,6,4,7,2]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,1,6,7,2,4]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,1,6,7,4,2]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,2,1,4,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,5,2,1,6,4,7]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,5,2,1,6,7,4]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,2,4,1,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,5,2,4,6,1,7]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,5,2,4,6,7,1]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,2,6,1,4,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,5,2,6,1,7,4]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,2,6,4,1,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,5,2,6,4,7,1]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,2,6,7,1,4]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,2,6,7,4,1]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,4,1,2,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,5,4,1,6,2,7]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,5,4,1,6,7,2]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,4,2,1,6,7]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,5,4,2,6,1,7]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,5,4,2,6,7,1]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,4,6,1,2,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,5,4,6,1,7,2]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,4,6,2,1,7]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,5,4,6,2,7,1]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,4,6,7,1,2]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,4,6,7,2,1]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,6,1,2,4,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,5,6,1,2,7,4]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,6,1,4,2,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,5,6,1,4,7,2]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,6,1,7,2,4]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,6,1,7,4,2]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,6,2,1,4,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,5,6,2,1,7,4]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,6,2,4,1,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,5,6,2,4,7,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,6,2,7,1,4]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,6,2,7,4,1]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,6,4,1,2,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,5,6,4,1,7,2]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,6,4,2,1,7]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,2,1,1]=>([(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)=>2
[3,5,6,4,2,7,1]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,6,4,7,1,2]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,6,4,7,2,1]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,6,7,1,2,4]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,6,7,1,4,2]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,6,7,2,1,4]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,6,7,2,4,1]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,6,7,4,1,2]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]=>([(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)=>2
[3,5,6,7,4,2,1]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,1]=>([(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)=>2
[3,6,1,2,4,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,1,2,4,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,1,2,5,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,1,2,5,7,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,1,2,7,4,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,1,2,7,5,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,1,4,2,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,1,4,2,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,1,4,5,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,1,4,5,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,1,4,7,2,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,1,4,7,5,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,1,5,2,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,1,5,2,7,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,1,5,4,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,1,5,4,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,1,5,7,2,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,1,5,7,4,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,1,7,2,4,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,1,7,2,5,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,1,7,4,2,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,1,7,4,5,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,1,7,5,2,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,1,7,5,4,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,2,1,4,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,2,1,4,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,2,1,5,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,2,1,5,7,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,2,1,7,4,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,2,1,7,5,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,2,4,1,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,2,4,1,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,2,4,5,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,2,4,5,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,2,4,7,1,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,2,4,7,5,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,2,5,1,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,2,5,1,7,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,2,5,4,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,2,5,4,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,2,5,7,1,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,2,5,7,4,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,2,7,1,4,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,2,7,1,5,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,2,7,4,1,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,2,7,4,5,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,2,7,5,1,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,2,7,5,4,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,4,1,2,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,4,1,2,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,4,1,5,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,4,1,5,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,4,1,7,2,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,4,1,7,5,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,4,2,1,5,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,4,2,1,7,5]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,4,2,5,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,4,2,5,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,4,2,7,1,5]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,4,2,7,5,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,4,5,1,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,4,5,1,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,4,5,2,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,4,5,2,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,4,5,7,1,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,4,5,7,2,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,4,7,1,2,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,4,7,1,5,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,4,7,2,1,5]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,4,7,2,5,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,4,7,5,1,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,4,7,5,2,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,5,1,2,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,5,1,2,7,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,5,1,4,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,5,1,4,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,5,1,7,2,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,5,1,7,4,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,5,2,1,4,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,5,2,1,7,4]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,5,2,4,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,5,2,4,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,5,2,7,1,4]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,5,2,7,4,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,5,4,1,2,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,5,4,1,7,2]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,5,4,2,1,7]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,5,4,2,7,1]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,5,4,7,1,2]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,5,4,7,2,1]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,5,7,1,2,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,5,7,1,4,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,5,7,2,1,4]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,5,7,2,4,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,5,7,4,1,2]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,5,7,4,2,1]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,7,1,2,4,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,7,1,2,5,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,7,1,4,2,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,7,1,4,5,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,7,1,5,2,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,7,1,5,4,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,7,2,1,4,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,7,2,1,5,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,7,2,4,1,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,7,2,4,5,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,7,2,5,1,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,7,2,5,4,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,7,4,1,2,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,7,4,1,5,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,7,4,2,1,5]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,7,4,2,5,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,7,4,5,1,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,7,4,5,2,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,7,5,1,2,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,7,5,1,4,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,7,5,2,1,4]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,7,5,2,4,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,7,5,4,1,2]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[3,6,7,5,4,2,1]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,3,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>2
[4,1,2,3,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[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)=>3
[4,1,2,3,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,2,3,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,2,5,3,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[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)=>3
[4,1,2,5,6,3,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[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)=>3
[4,1,2,5,6,7,3]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[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)=>3
[4,1,2,6,3,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,2,6,3,7,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,2,6,5,3,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,2,6,5,7,3]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,2,6,7,3,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,2,6,7,5,3]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,3,2,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[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)=>3
[4,1,3,2,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,3,2,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,3,5,2,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[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)=>3
[4,1,3,5,6,2,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[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)=>3
[4,1,3,5,6,7,2]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[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)=>3
[4,1,3,6,2,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,3,6,2,7,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,3,6,5,2,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,3,6,5,7,2]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,3,6,7,2,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,3,6,7,5,2]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,5,2,3,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[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)=>3
[4,1,5,2,6,3,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[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)=>3
[4,1,5,2,6,7,3]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[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)=>3
[4,1,5,3,2,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[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)=>3
[4,1,5,3,6,2,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[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)=>3
[4,1,5,3,6,7,2]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[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)=>3
[4,1,5,6,2,3,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[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)=>3
[4,1,5,6,2,7,3]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[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)=>3
[4,1,5,6,3,2,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[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)=>3
[4,1,5,6,3,7,2]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[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)=>3
[4,1,5,6,7,2,3]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[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)=>3
[4,1,5,6,7,3,2]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[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)=>3
[4,1,6,2,3,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,6,2,3,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,6,2,5,3,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,6,2,5,7,3]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,6,2,7,3,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,6,2,7,5,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,6,3,2,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,6,3,2,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,6,3,5,2,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,6,3,5,7,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,6,3,7,2,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,6,3,7,5,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,6,5,2,3,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,6,5,2,7,3]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,6,5,3,2,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,6,5,3,7,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,6,5,7,2,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,6,5,7,3,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,6,7,2,3,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,6,7,2,5,3]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,6,7,3,2,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,6,7,3,5,2]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,6,7,5,2,3]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,1,6,7,5,3,2]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,1,3,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[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)=>3
[4,2,1,3,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,1,3,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,1,5,3,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[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)=>3
[4,2,1,5,6,3,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[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)=>3
[4,2,1,5,6,7,3]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[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)=>3
[4,2,1,6,3,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,1,6,3,7,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,1,6,5,3,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,1,6,5,7,3]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,1,6,7,3,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,1,6,7,5,3]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,3,1,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[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)=>3
[4,2,3,1,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,3,1,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,3,5,1,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[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)=>3
[4,2,3,5,6,1,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[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)=>3
[4,2,3,5,6,7,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[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)=>3
[4,2,3,6,1,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,3,6,1,7,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,3,6,5,1,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,3,6,5,7,1]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,3,6,7,1,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,3,6,7,5,1]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,5,1,3,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[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)=>3
[4,2,5,1,6,3,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[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)=>3
[4,2,5,1,6,7,3]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[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)=>3
[4,2,5,3,1,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[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)=>3
[4,2,5,3,6,1,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[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)=>3
[4,2,5,3,6,7,1]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[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)=>3
[4,2,5,6,1,3,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[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)=>3
[4,2,5,6,1,7,3]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[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)=>3
[4,2,5,6,3,1,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[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)=>3
[4,2,5,6,3,7,1]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[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)=>3
[4,2,5,6,7,1,3]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[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)=>3
[4,2,5,6,7,3,1]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[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)=>3
[4,2,6,1,3,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,6,1,3,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,6,1,5,3,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,6,1,5,7,3]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,6,1,7,3,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,6,1,7,5,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,6,3,1,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,6,3,1,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,6,3,5,1,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,6,3,5,7,1]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,6,3,7,1,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,6,3,7,5,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,6,5,1,3,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,6,5,1,7,3]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,6,5,3,1,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,6,5,3,7,1]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,6,5,7,1,3]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,6,5,7,3,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,6,7,1,3,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,6,7,1,5,3]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,6,7,3,1,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,6,7,3,5,1]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,6,7,5,1,3]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,2,6,7,5,3,1]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,1,2,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[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)=>3
[4,3,1,2,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,1,2,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,1,5,2,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[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)=>3
[4,3,1,5,6,2,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[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)=>3
[4,3,1,5,6,7,2]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[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)=>3
[4,3,1,6,2,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,1,6,2,7,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,1,6,5,2,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,1,6,5,7,2]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,1,6,7,2,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,1,6,7,5,2]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,2,1,5,6,7]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[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)=>3
[4,3,2,1,6,5,7]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,2,1,6,7,5]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,2,5,1,6,7]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[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)=>3
[4,3,2,5,6,1,7]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[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)=>3
[4,3,2,5,6,7,1]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[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)=>3
[4,3,2,6,1,5,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,2,6,1,7,5]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,2,6,5,1,7]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,2,6,5,7,1]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,2,6,7,1,5]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,2,6,7,5,1]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,5,1,2,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[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)=>3
[4,3,5,1,6,2,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[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)=>3
[4,3,5,1,6,7,2]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[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)=>3
[4,3,5,2,1,6,7]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[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)=>3
[4,3,5,2,6,1,7]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[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)=>3
[4,3,5,2,6,7,1]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[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)=>3
[4,3,5,6,1,2,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[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)=>3
[4,3,5,6,1,7,2]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[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)=>3
[4,3,5,6,2,1,7]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[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)=>3
[4,3,5,6,2,7,1]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[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)=>3
[4,3,5,6,7,1,2]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[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)=>3
[4,3,5,6,7,2,1]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[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)=>3
[4,3,6,1,2,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,6,1,2,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,6,1,5,2,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,6,1,5,7,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,6,1,7,2,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,6,1,7,5,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,6,2,1,5,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,6,2,1,7,5]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,6,2,5,1,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,6,2,5,7,1]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,6,2,7,1,5]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,6,2,7,5,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,6,5,1,2,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,6,5,1,7,2]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,6,5,2,1,7]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,6,5,2,7,1]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,6,5,7,1,2]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,6,5,7,2,1]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,6,7,1,2,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,6,7,1,5,2]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,6,7,2,1,5]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,6,7,2,5,1]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,6,7,5,1,2]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,3,6,7,5,2,1]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,5,1,2,3,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[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)=>3
[4,5,1,2,6,3,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[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)=>3
[4,5,1,2,6,7,3]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[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)=>3
[4,5,1,3,2,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[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)=>3
[4,5,1,3,6,2,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[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)=>3
[4,5,1,3,6,7,2]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[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)=>3
[4,5,1,6,2,3,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[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)=>3
[4,5,1,6,2,7,3]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[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)=>3
[4,5,1,6,3,2,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[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)=>3
[4,5,1,6,3,7,2]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[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)=>3
[4,5,1,6,7,2,3]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[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)=>3
[4,5,1,6,7,3,2]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[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)=>3
[4,5,2,1,3,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[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)=>3
[4,5,2,1,6,3,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[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)=>3
[4,5,2,1,6,7,3]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[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)=>3
[4,5,2,3,1,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[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)=>3
[4,5,2,3,6,1,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[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)=>3
[4,5,2,3,6,7,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[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)=>3
[4,5,2,6,1,3,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[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)=>3
[4,5,2,6,1,7,3]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[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)=>3
[4,5,2,6,3,1,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[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)=>3
[4,5,2,6,3,7,1]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[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)=>3
[4,5,2,6,7,1,3]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[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)=>3
[4,5,2,6,7,3,1]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[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)=>3
[4,5,3,1,2,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[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)=>3
[4,5,3,1,6,2,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[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)=>3
[4,5,3,1,6,7,2]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[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)=>3
[4,5,3,2,1,6,7]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[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)=>3
[4,5,3,2,6,1,7]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[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)=>3
[4,5,3,2,6,7,1]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[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)=>3
[4,5,3,6,1,2,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[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)=>3
[4,5,3,6,1,7,2]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[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)=>3
[4,5,3,6,2,1,7]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[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)=>3
[4,5,3,6,2,7,1]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[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)=>3
[4,5,3,6,7,1,2]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[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)=>3
[4,5,3,6,7,2,1]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[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)=>3
[4,5,6,1,2,3,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[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)=>3
[4,5,6,1,2,7,3]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[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)=>3
[4,5,6,1,3,2,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[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)=>3
[4,5,6,1,3,7,2]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[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)=>3
[4,5,6,1,7,2,3]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[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)=>3
[4,5,6,1,7,3,2]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[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)=>3
[4,5,6,2,1,3,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[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)=>3
[4,5,6,2,1,7,3]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[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)=>3
[4,5,6,2,3,1,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[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)=>3
[4,5,6,2,3,7,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[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)=>3
[4,5,6,2,7,1,3]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[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)=>3
[4,5,6,2,7,3,1]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[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)=>3
[4,5,6,3,1,2,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[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)=>3
[4,5,6,3,1,7,2]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[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)=>3
[4,5,6,3,2,1,7]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[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)=>3
[4,5,6,3,2,7,1]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[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)=>3
[4,5,6,3,7,1,2]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[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)=>3
[4,5,6,3,7,2,1]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[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)=>3
[4,5,6,7,1,2,3]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[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)=>3
[4,5,6,7,1,3,2]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[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)=>3
[4,5,6,7,2,1,3]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[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)=>3
[4,5,6,7,2,3,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[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)=>3
[4,5,6,7,3,1,2]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[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)=>3
[4,5,6,7,3,2,1]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[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)=>3
[4,6,1,2,3,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,1,2,3,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,1,2,5,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,1,2,5,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,1,2,7,3,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,1,2,7,5,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,1,3,2,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,1,3,2,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,1,3,5,2,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,1,3,5,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,1,3,7,2,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,1,3,7,5,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,1,5,2,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,1,5,2,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,1,5,3,2,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,1,5,3,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,1,5,7,2,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,1,5,7,3,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,1,7,2,3,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,1,7,2,5,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,1,7,3,2,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,1,7,3,5,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,1,7,5,2,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,1,7,5,3,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,2,1,3,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,2,1,3,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,2,1,5,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,2,1,5,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,2,1,7,3,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,2,1,7,5,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,2,3,1,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,2,3,1,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,2,3,5,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,2,3,5,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,2,3,7,1,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,2,3,7,5,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,2,5,1,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,2,5,1,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,2,5,3,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,2,5,3,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,2,5,7,1,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,2,5,7,3,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,2,7,1,3,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,2,7,1,5,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,2,7,3,1,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,2,7,3,5,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,2,7,5,1,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,2,7,5,3,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,3,1,2,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,3,1,2,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,3,1,5,2,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,3,1,5,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,3,1,7,2,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,3,1,7,5,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,3,2,1,5,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,3,2,1,7,5]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,3,2,5,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,3,2,5,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,3,2,7,1,5]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,3,2,7,5,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,3,5,1,2,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,3,5,1,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,3,5,2,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,3,5,2,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,3,5,7,1,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,3,5,7,2,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,3,7,1,2,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,3,7,1,5,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,3,7,2,1,5]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,3,7,2,5,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,3,7,5,1,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,3,7,5,2,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,5,1,2,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,5,1,2,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,5,1,3,2,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,5,1,3,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,5,1,7,2,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,5,1,7,3,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,5,2,1,3,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,5,2,1,7,3]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,5,2,3,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,5,2,3,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,5,2,7,1,3]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,5,2,7,3,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,5,3,1,2,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,5,3,1,7,2]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,5,3,2,1,7]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,5,3,2,7,1]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,5,3,7,1,2]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,5,3,7,2,1]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,5,7,1,2,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,5,7,1,3,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,5,7,2,1,3]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,5,7,2,3,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,5,7,3,1,2]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,5,7,3,2,1]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,7,1,2,3,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,7,1,2,5,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,7,1,3,2,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,7,1,3,5,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,7,1,5,2,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,7,1,5,3,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,7,2,1,3,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,7,2,1,5,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,7,2,3,1,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,7,2,3,5,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,7,2,5,1,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,7,2,5,3,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,7,3,1,2,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,7,3,1,5,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,7,3,2,1,5]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,7,3,2,5,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,7,3,5,1,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,7,3,5,2,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,7,5,1,2,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,7,5,1,3,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,7,5,2,1,3]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,7,5,2,3,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,7,5,3,1,2]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[4,6,7,5,3,2,1]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,2,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)=>3
[5,1,2,3,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[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)=>4
[5,1,2,3,6,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[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)=>4
[5,1,2,3,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[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)=>4
[5,1,2,4,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[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)=>4
[5,1,2,4,6,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[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)=>4
[5,1,2,4,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[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)=>4
[5,1,2,6,3,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[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)=>4
[5,1,2,6,3,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[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)=>4
[5,1,2,6,4,3,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[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)=>4
[5,1,2,6,4,7,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[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)=>4
[5,1,2,6,7,3,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[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)=>4
[5,1,2,6,7,4,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[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)=>4
[5,1,3,2,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[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)=>4
[5,1,3,2,6,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[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)=>4
[5,1,3,2,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[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)=>4
[5,1,3,4,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[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)=>4
[5,1,3,4,6,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[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)=>4
[5,1,3,4,6,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[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)=>4
[5,1,3,6,2,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[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)=>4
[5,1,3,6,2,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[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)=>4
[5,1,3,6,4,2,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[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)=>4
[5,1,3,6,4,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[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)=>4
[5,1,3,6,7,2,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[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)=>4
[5,1,3,6,7,4,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[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)=>4
[5,1,4,2,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[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)=>4
[5,1,4,2,6,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[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)=>4
[5,1,4,2,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[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)=>4
[5,1,4,3,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[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)=>4
[5,1,4,3,6,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[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)=>4
[5,1,4,3,6,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[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)=>4
[5,1,4,6,2,3,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[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)=>4
[5,1,4,6,2,7,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[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)=>4
[5,1,4,6,3,2,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[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)=>4
[5,1,4,6,3,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[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)=>4
[5,1,4,6,7,2,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[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)=>4
[5,1,4,6,7,3,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[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)=>4
[5,1,6,2,3,4,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[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)=>4
[5,1,6,2,3,7,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[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)=>4
[5,1,6,2,4,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[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)=>4
[5,1,6,2,4,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[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)=>4
[5,1,6,2,7,3,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[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)=>4
[5,1,6,2,7,4,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[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)=>4
[5,1,6,3,2,4,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[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)=>4
[5,1,6,3,2,7,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[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)=>4
[5,1,6,3,4,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[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)=>4
[5,1,6,3,4,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[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)=>4
[5,1,6,3,7,2,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[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)=>4
[5,1,6,3,7,4,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[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)=>4
[5,1,6,4,2,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[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)=>4
[5,1,6,4,2,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[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)=>4
[5,1,6,4,3,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[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)=>4
[5,1,6,4,3,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[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)=>4
[5,1,6,4,7,2,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[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)=>4
[5,1,6,4,7,3,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[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)=>4
[5,1,6,7,2,3,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[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)=>4
[5,1,6,7,2,4,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[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)=>4
[5,1,6,7,3,2,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[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)=>4
[5,1,6,7,3,4,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[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)=>4
[5,1,6,7,4,2,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[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)=>4
[5,1,6,7,4,3,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[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)=>4
[5,2,1,3,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[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)=>4
[5,2,1,3,6,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[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)=>4
[5,2,1,3,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[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)=>4
[5,2,1,4,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[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)=>4
[5,2,1,4,6,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[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)=>4
[5,2,1,4,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[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)=>4
[5,2,1,6,3,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[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)=>4
[5,2,1,6,3,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[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)=>4
[5,2,1,6,4,3,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[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)=>4
[5,2,1,6,4,7,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[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)=>4
[5,2,1,6,7,3,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[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)=>4
[5,2,1,6,7,4,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[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)=>4
[5,2,3,1,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[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)=>4
[5,2,3,1,6,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[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)=>4
[5,2,3,1,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[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)=>4
[5,2,3,4,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[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)=>4
[5,2,3,4,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[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)=>4
[5,2,3,4,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[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)=>4
[5,2,3,6,1,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[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)=>4
[5,2,3,6,1,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[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)=>4
[5,2,3,6,4,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[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)=>4
[5,2,3,6,4,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[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)=>4
[5,2,3,6,7,1,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[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)=>4
[5,2,3,6,7,4,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[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)=>4
[5,2,4,1,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[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)=>4
[5,2,4,1,6,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[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)=>4
[5,2,4,1,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[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)=>4
[5,2,4,3,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[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)=>4
[5,2,4,3,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[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)=>4
[5,2,4,3,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[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)=>4
[5,2,4,6,1,3,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[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)=>4
[5,2,4,6,1,7,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[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)=>4
[5,2,4,6,3,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[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)=>4
[5,2,4,6,3,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[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)=>4
[5,2,4,6,7,1,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[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)=>4
[5,2,4,6,7,3,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[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)=>4
[5,2,6,1,3,4,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[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)=>4
[5,2,6,1,3,7,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[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)=>4
[5,2,6,1,4,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[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)=>4
[5,2,6,1,4,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[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)=>4
[5,2,6,1,7,3,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[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)=>4
[5,2,6,1,7,4,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[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)=>4
[5,2,6,3,1,4,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[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)=>4
[5,2,6,3,1,7,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[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)=>4
[5,2,6,3,4,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[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)=>4
[5,2,6,3,4,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[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)=>4
[5,2,6,3,7,1,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[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)=>4
[5,2,6,3,7,4,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[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)=>4
[5,2,6,4,1,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[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)=>4
[5,2,6,4,1,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[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)=>4
[5,2,6,4,3,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[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)=>4
[5,2,6,4,3,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[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)=>4
[5,2,6,4,7,1,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[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)=>4
[5,2,6,4,7,3,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[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)=>4
[5,2,6,7,1,3,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[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)=>4
[5,2,6,7,1,4,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[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)=>4
[5,2,6,7,3,1,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[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)=>4
[5,2,6,7,3,4,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[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)=>4
[5,2,6,7,4,1,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[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)=>4
[5,2,6,7,4,3,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[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)=>4
[5,3,1,2,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[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)=>4
[5,3,1,2,6,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[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)=>4
[5,3,1,2,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[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)=>4
[5,3,1,4,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[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)=>4
[5,3,1,4,6,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[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)=>4
[5,3,1,4,6,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[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)=>4
[5,3,1,6,2,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[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)=>4
[5,3,1,6,2,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[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)=>4
[5,3,1,6,4,2,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[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)=>4
[5,3,1,6,4,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[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)=>4
[5,3,1,6,7,2,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[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)=>4
[5,3,1,6,7,4,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[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)=>4
[5,3,2,1,4,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[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)=>4
[5,3,2,1,6,4,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[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)=>4
[5,3,2,1,6,7,4]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[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)=>4
[5,3,2,4,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[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)=>4
[5,3,2,4,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[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)=>4
[5,3,2,4,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[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)=>4
[5,3,2,6,1,4,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[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)=>4
[5,3,2,6,1,7,4]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[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)=>4
[5,3,2,6,4,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[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)=>4
[5,3,2,6,4,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[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)=>4
[5,3,2,6,7,1,4]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[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)=>4
[5,3,2,6,7,4,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[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)=>4
[5,3,4,1,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[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)=>4
[5,3,4,1,6,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[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)=>4
[5,3,4,1,6,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[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)=>4
[5,3,4,2,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[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)=>4
[5,3,4,2,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[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)=>4
[5,3,4,2,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[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)=>4
[5,3,4,6,1,2,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[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)=>4
[5,3,4,6,1,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[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)=>4
[5,3,4,6,2,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[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)=>4
[5,3,4,6,2,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[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)=>4
[5,3,4,6,7,1,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[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)=>4
[5,3,4,6,7,2,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[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)=>4
[5,3,6,1,2,4,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[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)=>4
[5,3,6,1,2,7,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[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)=>4
[5,3,6,1,4,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[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)=>4
[5,3,6,1,4,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[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)=>4
[5,3,6,1,7,2,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[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)=>4
[5,3,6,1,7,4,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[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)=>4
[5,3,6,2,1,4,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[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)=>4
[5,3,6,2,1,7,4]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[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)=>4
[5,3,6,2,4,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[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)=>4
[5,3,6,2,4,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[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)=>4
[5,3,6,2,7,1,4]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[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)=>4
[5,3,6,2,7,4,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[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)=>4
[5,3,6,4,1,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[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)=>4
[5,3,6,4,1,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[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)=>4
[5,3,6,4,2,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[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)=>4
[5,3,6,4,2,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[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)=>4
[5,3,6,4,7,1,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[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)=>4
[5,3,6,4,7,2,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[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)=>4
[5,3,6,7,1,2,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[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)=>4
[5,3,6,7,1,4,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[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)=>4
[5,3,6,7,2,1,4]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[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)=>4
[5,3,6,7,2,4,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[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)=>4
[5,3,6,7,4,1,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[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)=>4
[5,3,6,7,4,2,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[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)=>4
[5,4,1,2,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[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)=>4
[5,4,1,2,6,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[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)=>4
[5,4,1,2,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[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)=>4
[5,4,1,3,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[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)=>4
[5,4,1,3,6,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[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)=>4
[5,4,1,3,6,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[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)=>4
[5,4,1,6,2,3,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[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)=>4
[5,4,1,6,2,7,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[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)=>4
[5,4,1,6,3,2,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[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)=>4
[5,4,1,6,3,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[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)=>4
[5,4,1,6,7,2,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[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)=>4
[5,4,1,6,7,3,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[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)=>4
[5,4,2,1,3,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[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)=>4
[5,4,2,1,6,3,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[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)=>4
[5,4,2,1,6,7,3]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[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)=>4
[5,4,2,3,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[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)=>4
[5,4,2,3,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[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)=>4
[5,4,2,3,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[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)=>4
[5,4,2,6,1,3,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[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)=>4
[5,4,2,6,1,7,3]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[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)=>4
[5,4,2,6,3,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[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)=>4
[5,4,2,6,3,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[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)=>4
[5,4,2,6,7,1,3]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[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)=>4
[5,4,2,6,7,3,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[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)=>4
[5,4,3,1,2,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[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)=>4
[5,4,3,1,6,2,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[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)=>4
[5,4,3,1,6,7,2]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[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)=>4
[5,4,3,2,1,6,7]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[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)=>4
[5,4,3,2,6,1,7]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[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)=>4
[5,4,3,2,6,7,1]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[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)=>4
[5,4,3,6,1,2,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[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)=>4
[5,4,3,6,1,7,2]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[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)=>4
[5,4,3,6,2,1,7]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[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)=>4
[5,4,3,6,2,7,1]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[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)=>4
[5,4,3,6,7,1,2]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[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)=>4
[5,4,3,6,7,2,1]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[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)=>4
[5,4,6,1,2,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[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)=>4
[5,4,6,1,2,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[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)=>4
[5,4,6,1,3,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[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)=>4
[5,4,6,1,3,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[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)=>4
[5,4,6,1,7,2,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[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)=>4
[5,4,6,1,7,3,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[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)=>4
[5,4,6,2,1,3,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[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)=>4
[5,4,6,2,1,7,3]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[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)=>4
[5,4,6,2,3,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[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)=>4
[5,4,6,2,3,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[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)=>4
[5,4,6,2,7,1,3]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[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)=>4
[5,4,6,2,7,3,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[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)=>4
[5,4,6,3,1,2,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[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)=>4
[5,4,6,3,1,7,2]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[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)=>4
[5,4,6,3,2,1,7]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[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)=>4
[5,4,6,3,2,7,1]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[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)=>4
[5,4,6,3,7,1,2]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[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)=>4
[5,4,6,3,7,2,1]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[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)=>4
[5,4,6,7,1,2,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[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)=>4
[5,4,6,7,1,3,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[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)=>4
[5,4,6,7,2,1,3]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[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)=>4
[5,4,6,7,2,3,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[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)=>4
[5,4,6,7,3,1,2]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[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)=>4
[5,4,6,7,3,2,1]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[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)=>4
[5,6,1,2,3,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[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)=>4
[5,6,1,2,3,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[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)=>4
[5,6,1,2,4,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[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)=>4
[5,6,1,2,4,7,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[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)=>4
[5,6,1,2,7,3,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[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)=>4
[5,6,1,2,7,4,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[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)=>4
[5,6,1,3,2,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[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)=>4
[5,6,1,3,2,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[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)=>4
[5,6,1,3,4,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[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)=>4
[5,6,1,3,4,7,2]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[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)=>4
[5,6,1,3,7,2,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[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)=>4
[5,6,1,3,7,4,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[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)=>4
[5,6,1,4,2,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[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)=>4
[5,6,1,4,2,7,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[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)=>4
[5,6,1,4,3,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[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)=>4
[5,6,1,4,3,7,2]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[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)=>4
[5,6,1,4,7,2,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[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)=>4
[5,6,1,4,7,3,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[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)=>4
[5,6,1,7,2,3,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[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)=>4
[5,6,1,7,2,4,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[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)=>4
[5,6,1,7,3,2,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[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)=>4
[5,6,1,7,3,4,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[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)=>4
[5,6,1,7,4,2,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[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)=>4
[5,6,1,7,4,3,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[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)=>4
[5,6,2,1,3,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[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)=>4
[5,6,2,1,3,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[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)=>4
[5,6,2,1,4,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[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)=>4
[5,6,2,1,4,7,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[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)=>4
[5,6,2,1,7,3,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[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)=>4
[5,6,2,1,7,4,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[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)=>4
[5,6,2,3,1,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[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)=>4
[5,6,2,3,1,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[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)=>4
[5,6,2,3,4,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[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)=>4
[5,6,2,3,4,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[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)=>4
[5,6,2,3,7,1,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[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)=>4
[5,6,2,3,7,4,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[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)=>4
[5,6,2,4,1,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[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)=>4
[5,6,2,4,1,7,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[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)=>4
[5,6,2,4,3,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[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)=>4
[5,6,2,4,3,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[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)=>4
[5,6,2,4,7,1,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[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)=>4
[5,6,2,4,7,3,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[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)=>4
[5,6,2,7,1,3,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[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)=>4
[5,6,2,7,1,4,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[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)=>4
[5,6,2,7,3,1,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[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)=>4
[5,6,2,7,3,4,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[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)=>4
[5,6,2,7,4,1,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[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)=>4
[5,6,2,7,4,3,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[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)=>4
[5,6,3,1,2,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[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)=>4
[5,6,3,1,2,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[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)=>4
[5,6,3,1,4,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[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)=>4
[5,6,3,1,4,7,2]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[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)=>4
[5,6,3,1,7,2,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[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)=>4
[5,6,3,1,7,4,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[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)=>4
[5,6,3,2,1,4,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[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)=>4
[5,6,3,2,1,7,4]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[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)=>4
[5,6,3,2,4,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[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)=>4
[5,6,3,2,4,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[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)=>4
[5,6,3,2,7,1,4]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[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)=>4
[5,6,3,2,7,4,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[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)=>4
[5,6,3,4,1,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[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)=>4
[5,6,3,4,1,7,2]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[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)=>4
[5,6,3,4,2,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[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)=>4
[5,6,3,4,2,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[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)=>4
[5,6,3,4,7,1,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[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)=>4
[5,6,3,4,7,2,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[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)=>4
[5,6,3,7,1,2,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[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)=>4
[5,6,3,7,1,4,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[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)=>4
[5,6,3,7,2,1,4]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[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)=>4
[5,6,3,7,2,4,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[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)=>4
[5,6,3,7,4,1,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[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)=>4
[5,6,3,7,4,2,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[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)=>4
[5,6,4,1,2,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[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)=>4
[5,6,4,1,2,7,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[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)=>4
[5,6,4,1,3,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[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)=>4
[5,6,4,1,3,7,2]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[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)=>4
[5,6,4,1,7,2,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[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)=>4
[5,6,4,1,7,3,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[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)=>4
[5,6,4,2,1,3,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[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)=>4
[5,6,4,2,1,7,3]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[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)=>4
[5,6,4,2,3,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[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)=>4
[5,6,4,2,3,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[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)=>4
[5,6,4,2,7,1,3]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[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)=>4
[5,6,4,2,7,3,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[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)=>4
[5,6,4,3,1,2,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[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)=>4
[5,6,4,3,1,7,2]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[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)=>4
[5,6,4,3,2,1,7]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[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)=>4
[5,6,4,3,2,7,1]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[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)=>4
[5,6,4,3,7,1,2]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[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)=>4
[5,6,4,3,7,2,1]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[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)=>4
[5,6,4,7,1,2,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[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)=>4
[5,6,4,7,1,3,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[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)=>4
[5,6,4,7,2,1,3]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[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)=>4
[5,6,4,7,2,3,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[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)=>4
[5,6,4,7,3,1,2]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[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)=>4
[5,6,4,7,3,2,1]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[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)=>4
[5,6,7,1,2,3,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[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)=>4
[5,6,7,1,2,4,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[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)=>4
[5,6,7,1,3,2,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[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)=>4
[5,6,7,1,3,4,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[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)=>4
[5,6,7,1,4,2,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[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)=>4
[5,6,7,1,4,3,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[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)=>4
[5,6,7,2,1,3,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[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)=>4
[5,6,7,2,1,4,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[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)=>4
[5,6,7,2,3,1,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[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)=>4
[5,6,7,2,3,4,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[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)=>4
[5,6,7,2,4,1,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[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)=>4
[5,6,7,2,4,3,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[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)=>4
[5,6,7,3,1,2,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[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)=>4
[5,6,7,3,1,4,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[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)=>4
[5,6,7,3,2,1,4]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[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)=>4
[5,6,7,3,2,4,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[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)=>4
[5,6,7,3,4,1,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[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)=>4
[5,6,7,3,4,2,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[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)=>4
[5,6,7,4,1,2,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[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)=>4
[5,6,7,4,1,3,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[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)=>4
[5,6,7,4,2,1,3]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[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)=>4
[5,6,7,4,2,3,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[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)=>4
[5,6,7,4,3,1,2]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[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)=>4
[5,6,7,4,3,2,1]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[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)=>4
[6,1,2,3,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,2,3,4,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,2,3,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,2,3,5,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,2,3,7,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,2,3,7,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,2,4,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,2,4,3,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,2,4,5,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,2,4,5,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,2,4,7,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,2,4,7,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,2,5,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,2,5,3,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,2,5,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,2,5,4,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,2,5,7,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,2,5,7,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,2,7,3,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,2,7,3,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,2,7,4,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,2,7,4,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,2,7,5,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,2,7,5,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,3,2,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,3,2,4,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,3,2,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,3,2,5,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,3,2,7,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,3,2,7,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,3,4,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,3,4,2,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,3,4,5,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,3,4,5,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,3,4,7,2,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,3,4,7,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,3,5,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,3,5,2,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,3,5,4,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,3,5,4,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,3,5,7,2,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,3,5,7,4,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,3,7,2,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,3,7,2,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,3,7,4,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,3,7,4,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,3,7,5,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,3,7,5,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,4,2,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,4,2,3,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,4,2,5,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,4,2,5,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,4,2,7,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,4,2,7,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,4,3,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,4,3,2,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,4,3,5,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,4,3,5,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,4,3,7,2,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,4,3,7,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,4,5,2,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,4,5,2,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,4,5,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,4,5,3,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,4,5,7,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,4,5,7,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,4,7,2,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,4,7,2,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,4,7,3,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,4,7,3,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,4,7,5,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,4,7,5,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,5,2,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,5,2,3,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,5,2,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,5,2,4,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,5,2,7,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,5,2,7,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,5,3,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,5,3,2,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,5,3,4,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,5,3,4,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,5,3,7,2,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,5,3,7,4,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,5,4,2,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,5,4,2,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,5,4,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,5,4,3,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,5,4,7,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,5,4,7,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,5,7,2,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,5,7,2,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,5,7,3,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,5,7,3,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,5,7,4,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,5,7,4,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,7,2,3,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,7,2,3,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,7,2,4,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,7,2,4,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,7,2,5,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,7,2,5,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,7,3,2,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,7,3,2,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,7,3,4,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,7,3,4,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,7,3,5,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,7,3,5,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,7,4,2,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,7,4,2,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,7,4,3,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,7,4,3,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,7,4,5,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,7,4,5,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,7,5,2,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,7,5,2,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,7,5,3,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,7,5,3,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,7,5,4,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,1,7,5,4,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,1,3,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,1,3,4,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,1,3,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,1,3,5,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,1,3,7,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,1,3,7,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,1,4,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,1,4,3,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,1,4,5,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,1,4,5,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,1,4,7,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,1,4,7,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,1,5,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,1,5,3,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,1,5,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,1,5,4,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,1,5,7,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,1,5,7,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,1,7,3,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,1,7,3,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,1,7,4,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,1,7,4,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,1,7,5,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,1,7,5,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,3,1,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,3,1,4,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,3,1,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,3,1,5,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,3,1,7,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,3,1,7,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,3,4,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,3,4,1,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,3,4,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,3,4,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,3,4,7,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,3,4,7,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,3,5,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,3,5,1,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,3,5,4,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,3,5,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,3,5,7,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,3,5,7,4,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,3,7,1,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,3,7,1,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,3,7,4,1,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,3,7,4,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,3,7,5,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,3,7,5,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,4,1,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,4,1,3,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,4,1,5,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,4,1,5,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,4,1,7,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,4,1,7,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,4,3,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,4,3,1,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,4,3,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,4,3,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,4,3,7,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,4,3,7,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,4,5,1,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,4,5,1,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,4,5,3,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,4,5,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,4,5,7,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,4,5,7,3,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,4,7,1,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,4,7,1,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,4,7,3,1,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,4,7,3,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,4,7,5,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,4,7,5,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,5,1,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,5,1,3,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,5,1,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,5,1,4,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,5,1,7,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,5,1,7,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,5,3,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,5,3,1,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,5,3,4,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,5,3,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,5,3,7,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,5,3,7,4,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,5,4,1,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,5,4,1,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,5,4,3,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,5,4,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,5,4,7,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,5,4,7,3,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,5,7,1,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,5,7,1,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,5,7,3,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,5,7,3,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,5,7,4,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,5,7,4,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,7,1,3,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,7,1,3,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,7,1,4,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,7,1,4,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,7,1,5,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,7,1,5,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,7,3,1,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,7,3,1,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,7,3,4,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,7,3,4,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,7,3,5,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,7,3,5,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,7,4,1,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,7,4,1,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,7,4,3,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,7,4,3,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,7,4,5,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,7,4,5,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,7,5,1,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,7,5,1,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,7,5,3,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,7,5,3,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,7,5,4,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,2,7,5,4,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,1,2,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,1,2,4,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,1,2,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,1,2,5,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,1,2,7,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,1,2,7,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,1,4,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,1,4,2,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,1,4,5,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,1,4,5,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,1,4,7,2,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,1,4,7,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,1,5,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,1,5,2,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,1,5,4,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,1,5,4,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,1,5,7,2,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,1,5,7,4,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,1,7,2,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,1,7,2,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,1,7,4,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,1,7,4,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,1,7,5,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,1,7,5,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,2,1,4,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,2,1,4,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,2,1,5,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,2,1,5,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,2,1,7,4,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,2,1,7,5,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,2,4,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,2,4,1,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,2,4,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,2,4,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,2,4,7,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,2,4,7,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,2,5,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,2,5,1,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,2,5,4,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,2,5,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,2,5,7,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,2,5,7,4,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,2,7,1,4,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,2,7,1,5,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,2,7,4,1,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,2,7,4,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,2,7,5,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,2,7,5,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,4,1,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,4,1,2,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,4,1,5,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,4,1,5,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,4,1,7,2,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,4,1,7,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,4,2,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,4,2,1,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,4,2,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,4,2,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,4,2,7,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,4,2,7,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,4,5,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,4,5,1,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,4,5,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,4,5,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,4,5,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,4,5,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,4,7,1,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,4,7,1,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,4,7,2,1,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,4,7,2,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,4,7,5,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,4,7,5,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,5,1,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,5,1,2,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,5,1,4,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,5,1,4,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,5,1,7,2,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,5,1,7,4,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,5,2,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,5,2,1,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,5,2,4,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,5,2,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,5,2,7,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,5,2,7,4,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,5,4,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,5,4,1,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,5,4,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,5,4,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,5,4,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,5,4,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,5,7,1,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,5,7,1,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,5,7,2,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,5,7,2,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,5,7,4,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,5,7,4,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,7,1,2,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,7,1,2,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,7,1,4,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,7,1,4,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,7,1,5,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,7,1,5,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,7,2,1,4,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,7,2,1,5,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,7,2,4,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,7,2,4,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,7,2,5,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,7,2,5,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,7,4,1,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,7,4,1,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,7,4,2,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,7,4,2,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,7,4,5,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,7,4,5,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,7,5,1,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,7,5,1,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,7,5,2,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,7,5,2,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,7,5,4,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,3,7,5,4,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,1,2,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,1,2,3,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,1,2,5,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,1,2,5,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,1,2,7,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,1,2,7,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,1,3,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,1,3,2,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,1,3,5,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,1,3,5,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,1,3,7,2,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,1,3,7,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,1,5,2,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,1,5,2,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,1,5,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,1,5,3,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,1,5,7,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,1,5,7,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,1,7,2,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,1,7,2,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,1,7,3,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,1,7,3,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,1,7,5,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,1,7,5,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,2,1,3,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,2,1,3,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,2,1,5,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,2,1,5,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,2,1,7,3,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,2,1,7,5,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,2,3,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,2,3,1,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,2,3,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,2,3,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,2,3,7,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,2,3,7,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,2,5,1,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,2,5,1,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,2,5,3,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,2,5,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,2,5,7,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,2,5,7,3,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,2,7,1,3,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,2,7,1,5,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,2,7,3,1,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,2,7,3,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,2,7,5,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,2,7,5,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,3,1,2,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,3,1,2,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,3,1,5,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,3,1,5,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,3,1,7,2,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,3,1,7,5,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,3,2,1,5,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,3,2,1,7,5]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,3,2,5,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,3,2,5,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,3,2,7,1,5]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,3,2,7,5,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,3,5,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,3,5,1,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,3,5,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,3,5,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,3,5,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,3,5,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,3,7,1,2,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,3,7,1,5,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,3,7,2,1,5]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,3,7,2,5,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,3,7,5,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,3,7,5,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,5,1,2,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,5,1,2,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,5,1,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,5,1,3,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,5,1,7,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,5,1,7,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,5,2,1,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,5,2,1,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,5,2,3,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,5,2,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,5,2,7,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,5,2,7,3,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,5,3,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,5,3,1,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,5,3,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,5,3,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,5,3,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,5,3,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,5,7,1,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,5,7,1,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,5,7,2,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,5,7,2,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,5,7,3,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,5,7,3,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,7,1,2,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,7,1,2,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,7,1,3,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,7,1,3,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,7,1,5,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,7,1,5,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,7,2,1,3,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,7,2,1,5,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,7,2,3,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,7,2,3,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,7,2,5,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,7,2,5,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,7,3,1,2,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,7,3,1,5,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,7,3,2,1,5]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,7,3,2,5,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,7,3,5,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,7,3,5,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,7,5,1,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,7,5,1,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,7,5,2,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,7,5,2,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,7,5,3,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,4,7,5,3,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,1,2,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,1,2,3,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,1,2,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,1,2,4,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,1,2,7,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,1,2,7,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,1,3,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,1,3,2,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,1,3,4,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,1,3,4,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,1,3,7,2,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,1,3,7,4,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,1,4,2,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,1,4,2,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,1,4,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,1,4,3,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,1,4,7,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,1,4,7,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,1,7,2,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,1,7,2,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,1,7,3,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,1,7,3,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,1,7,4,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,1,7,4,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,2,1,3,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,2,1,3,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,2,1,4,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,2,1,4,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,2,1,7,3,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,2,1,7,4,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,2,3,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,2,3,1,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,2,3,4,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,2,3,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,2,3,7,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,2,3,7,4,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,2,4,1,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,2,4,1,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,2,4,3,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,2,4,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,2,4,7,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,2,4,7,3,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,2,7,1,3,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,2,7,1,4,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,2,7,3,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,2,7,3,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,2,7,4,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,2,7,4,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,3,1,2,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,3,1,2,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,3,1,4,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,3,1,4,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,3,1,7,2,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,3,1,7,4,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,3,2,1,4,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,3,2,1,7,4]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,3,2,4,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,3,2,4,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,3,2,7,1,4]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,3,2,7,4,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,3,4,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,3,4,1,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,3,4,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,3,4,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,3,4,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,3,4,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,3,7,1,2,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,3,7,1,4,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,3,7,2,1,4]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,3,7,2,4,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,3,7,4,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,3,7,4,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,4,1,2,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,4,1,2,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,4,1,3,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,4,1,3,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,4,1,7,2,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,4,1,7,3,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,4,2,1,3,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,4,2,1,7,3]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,4,2,3,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,4,2,3,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,4,2,7,1,3]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,4,2,7,3,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,4,3,1,2,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,4,3,1,7,2]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,4,3,2,1,7]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,4,3,2,7,1]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,4,3,7,1,2]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,4,3,7,2,1]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,4,7,1,2,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,4,7,1,3,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,4,7,2,1,3]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,4,7,2,3,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,4,7,3,1,2]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,4,7,3,2,1]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,7,1,2,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,7,1,2,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,7,1,3,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,7,1,3,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,7,1,4,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,7,1,4,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,7,2,1,3,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,7,2,1,4,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,7,2,3,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,7,2,3,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,7,2,4,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,7,2,4,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,7,3,1,2,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,7,3,1,4,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,7,3,2,1,4]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,7,3,2,4,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,7,3,4,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,7,3,4,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,7,4,1,2,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,7,4,1,3,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,7,4,2,1,3]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,7,4,2,3,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,7,4,3,1,2]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,5,7,4,3,2,1]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,1,2,3,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,1,2,3,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,1,2,4,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,1,2,4,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,1,2,5,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,1,2,5,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,1,3,2,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,1,3,2,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,1,3,4,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,1,3,4,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,1,3,5,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,1,3,5,4,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,1,4,2,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,1,4,2,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,1,4,3,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,1,4,3,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,1,4,5,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,1,4,5,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,1,5,2,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,1,5,2,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,1,5,3,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,1,5,3,4,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,1,5,4,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,1,5,4,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,2,1,3,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,2,1,3,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,2,1,4,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,2,1,4,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,2,1,5,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,2,1,5,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,2,3,1,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,2,3,1,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,2,3,4,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,2,3,4,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,2,3,5,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,2,3,5,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,2,4,1,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,2,4,1,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,2,4,3,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,2,4,3,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,2,4,5,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,2,4,5,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,2,5,1,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,2,5,1,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,2,5,3,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,2,5,3,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,2,5,4,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,2,5,4,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,3,1,2,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,3,1,2,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,3,1,4,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,3,1,4,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,3,1,5,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,3,1,5,4,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,3,2,1,4,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,3,2,1,5,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,3,2,4,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,3,2,4,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,3,2,5,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,3,2,5,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,3,4,1,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,3,4,1,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,3,4,2,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,3,4,2,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,3,4,5,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,3,4,5,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,3,5,1,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,3,5,1,4,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,3,5,2,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,3,5,2,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,3,5,4,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,3,5,4,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,4,1,2,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,4,1,2,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,4,1,3,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,4,1,3,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,4,1,5,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,4,1,5,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,4,2,1,3,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,4,2,1,5,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,4,2,3,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,4,2,3,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,4,2,5,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,4,2,5,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,4,3,1,2,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,4,3,1,5,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,4,3,2,1,5]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,4,3,2,5,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,4,3,5,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,4,3,5,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,4,5,1,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,4,5,1,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,4,5,2,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,4,5,2,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,4,5,3,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,4,5,3,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,5,1,2,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,5,1,2,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,5,1,3,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,5,1,3,4,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,5,1,4,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,5,1,4,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,5,2,1,3,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,5,2,1,4,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,5,2,3,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,5,2,3,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,5,2,4,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,5,2,4,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,5,3,1,2,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,5,3,1,4,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,5,3,2,1,4]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,5,3,2,4,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,5,3,4,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,5,3,4,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,5,4,1,2,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,5,4,1,3,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,5,4,2,1,3]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,5,4,2,3,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,5,4,3,1,2]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
[6,7,5,4,3,2,1]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>5
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Description
The largest multiplicity of a distance Laplacian eigenvalue in a connected graph.
The distance Laplacian of a graph is the (symmetric) matrix with row and column sums $0$, which has the negative distances between two vertices as its off-diagonal entries. This statistic is the largest multiplicity of an eigenvalue.
For example, the cycle on four vertices has distance Laplacian
$$ \left(\begin{array}{rrrr} 4 & -1 & -2 & -1 \\ -1 & 4 & -1 & -2 \\ -2 & -1 & 4 & -1 \\ -1 & -2 & -1 & 4 \end{array}\right). $$
Its eigenvalues are $0,4,4,6$, so the statistic is $2$.
The path on four vertices has eigenvalues $0, 4.7\dots, 6, 9.2\dots$ and therefore statistic $1$.
The distance Laplacian of a graph is the (symmetric) matrix with row and column sums $0$, which has the negative distances between two vertices as its off-diagonal entries. This statistic is the largest multiplicity of an eigenvalue.
For example, the cycle on four vertices has distance Laplacian
$$ \left(\begin{array}{rrrr} 4 & -1 & -2 & -1 \\ -1 & 4 & -1 & -2 \\ -2 & -1 & 4 & -1 \\ -1 & -2 & -1 & 4 \end{array}\right). $$
Its eigenvalues are $0,4,4,6$, so the statistic is $2$.
The path on four vertices has eigenvalues $0, 4.7\dots, 6, 9.2\dots$ and therefore statistic $1$.
Map
left-to-right-maxima to Dyck path
Description
The left-to-right maxima of a permutation as a Dyck path.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Let $(c_1, \dots, c_k)$ be the rise composition Mp00102rise composition of the path. Then the corresponding left-to-right maxima are $c_1, c_1+c_2, \dots, c_1+\dots+c_k$.
Restricted to 321-avoiding permutations, this is the inverse of Mp00119to 321-avoiding permutation (Krattenthaler), restricted to 312-avoiding permutations, this is the inverse of Mp00031to 312-avoiding permutation.
Map
rise composition
Description
Send a Dyck path to the composition of sizes of its rises.
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.
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