Identifier
Mp00025: Dyck paths to 132-avoiding permutationPermutations
Mp00064: Permutations reversePermutations
Mp00160: Permutations graph of inversions Graphs
Images
=>
Cc0005;cc-rep-0Cc0020;cc-rep-3
[1,0]=>[1]=>[1]=>([],1) [1,0,1,0]=>[2,1]=>[1,2]=>([],2) [1,1,0,0]=>[1,2]=>[2,1]=>([(0,1)],2) [1,0,1,0,1,0]=>[3,2,1]=>[1,2,3]=>([],3) [1,0,1,1,0,0]=>[2,3,1]=>[1,3,2]=>([(1,2)],3) [1,1,0,0,1,0]=>[3,1,2]=>[2,1,3]=>([(1,2)],3) [1,1,0,1,0,0]=>[2,1,3]=>[3,1,2]=>([(0,2),(1,2)],3) [1,1,1,0,0,0]=>[1,2,3]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3) [1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[1,2,3,4]=>([],4) [1,0,1,0,1,1,0,0]=>[3,4,2,1]=>[1,2,4,3]=>([(2,3)],4) [1,0,1,1,0,0,1,0]=>[4,2,3,1]=>[1,3,2,4]=>([(2,3)],4) [1,0,1,1,0,1,0,0]=>[3,2,4,1]=>[1,4,2,3]=>([(1,3),(2,3)],4) [1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[1,4,3,2]=>([(1,2),(1,3),(2,3)],4) [1,1,0,0,1,0,1,0]=>[4,3,1,2]=>[2,1,3,4]=>([(2,3)],4) [1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[2,1,4,3]=>([(0,3),(1,2)],4) [1,1,0,1,0,0,1,0]=>[4,2,1,3]=>[3,1,2,4]=>([(1,3),(2,3)],4) [1,1,0,1,0,1,0,0]=>[3,2,1,4]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4) [1,1,0,1,1,0,0,0]=>[2,3,1,4]=>[4,1,3,2]=>([(0,3),(1,2),(1,3),(2,3)],4) [1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4) [1,1,1,0,0,1,0,0]=>[3,1,2,4]=>[4,2,1,3]=>([(0,3),(1,2),(1,3),(2,3)],4) [1,1,1,0,1,0,0,0]=>[2,1,3,4]=>[4,3,1,2]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4) [1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) [1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>[1,2,3,4,5]=>([],5) [1,0,1,0,1,0,1,1,0,0]=>[4,5,3,2,1]=>[1,2,3,5,4]=>([(3,4)],5) [1,0,1,0,1,1,0,0,1,0]=>[5,3,4,2,1]=>[1,2,4,3,5]=>([(3,4)],5) [1,0,1,0,1,1,0,1,0,0]=>[4,3,5,2,1]=>[1,2,5,3,4]=>([(2,4),(3,4)],5) [1,0,1,0,1,1,1,0,0,0]=>[3,4,5,2,1]=>[1,2,5,4,3]=>([(2,3),(2,4),(3,4)],5) [1,0,1,1,0,0,1,0,1,0]=>[5,4,2,3,1]=>[1,3,2,4,5]=>([(3,4)],5) [1,0,1,1,0,0,1,1,0,0]=>[4,5,2,3,1]=>[1,3,2,5,4]=>([(1,4),(2,3)],5) [1,0,1,1,0,1,0,0,1,0]=>[5,3,2,4,1]=>[1,4,2,3,5]=>([(2,4),(3,4)],5) [1,0,1,1,0,1,0,1,0,0]=>[4,3,2,5,1]=>[1,5,2,3,4]=>([(1,4),(2,4),(3,4)],5) [1,0,1,1,0,1,1,0,0,0]=>[3,4,2,5,1]=>[1,5,2,4,3]=>([(1,4),(2,3),(2,4),(3,4)],5) [1,0,1,1,1,0,0,0,1,0]=>[5,2,3,4,1]=>[1,4,3,2,5]=>([(2,3),(2,4),(3,4)],5) [1,0,1,1,1,0,0,1,0,0]=>[4,2,3,5,1]=>[1,5,3,2,4]=>([(1,4),(2,3),(2,4),(3,4)],5) [1,0,1,1,1,0,1,0,0,0]=>[3,2,4,5,1]=>[1,5,4,2,3]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5) [1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[1,5,4,3,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) [1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,2]=>[2,1,3,4,5]=>([(3,4)],5) [1,1,0,0,1,0,1,1,0,0]=>[4,5,3,1,2]=>[2,1,3,5,4]=>([(1,4),(2,3)],5) [1,1,0,0,1,1,0,0,1,0]=>[5,3,4,1,2]=>[2,1,4,3,5]=>([(1,4),(2,3)],5) [1,1,0,0,1,1,0,1,0,0]=>[4,3,5,1,2]=>[2,1,5,3,4]=>([(0,1),(2,4),(3,4)],5) [1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>[2,1,5,4,3]=>([(0,1),(2,3),(2,4),(3,4)],5) [1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,3]=>[3,1,2,4,5]=>([(2,4),(3,4)],5) [1,1,0,1,0,0,1,1,0,0]=>[4,5,2,1,3]=>[3,1,2,5,4]=>([(0,1),(2,4),(3,4)],5) [1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,4]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5) [1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,5]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5) [1,1,0,1,0,1,1,0,0,0]=>[3,4,2,1,5]=>[5,1,2,4,3]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5) [1,1,0,1,1,0,0,0,1,0]=>[5,2,3,1,4]=>[4,1,3,2,5]=>([(1,4),(2,3),(2,4),(3,4)],5) [1,1,0,1,1,0,0,1,0,0]=>[4,2,3,1,5]=>[5,1,3,2,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5) [1,1,0,1,1,0,1,0,0,0]=>[3,2,4,1,5]=>[5,1,4,2,3]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) [1,1,0,1,1,1,0,0,0,0]=>[2,3,4,1,5]=>[5,1,4,3,2]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) [1,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,3]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5) [1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>[3,2,1,5,4]=>([(0,1),(2,3),(2,4),(3,4)],5) [1,1,1,0,0,1,0,0,1,0]=>[5,3,1,2,4]=>[4,2,1,3,5]=>([(1,4),(2,3),(2,4),(3,4)],5) [1,1,1,0,0,1,0,1,0,0]=>[4,3,1,2,5]=>[5,2,1,3,4]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5) [1,1,1,0,0,1,1,0,0,0]=>[3,4,1,2,5]=>[5,2,1,4,3]=>([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) [1,1,1,0,1,0,0,0,1,0]=>[5,2,1,3,4]=>[4,3,1,2,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5) [1,1,1,0,1,0,0,1,0,0]=>[4,2,1,3,5]=>[5,3,1,2,4]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) [1,1,1,0,1,0,1,0,0,0]=>[3,2,1,4,5]=>[5,4,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) [1,1,1,0,1,1,0,0,0,0]=>[2,3,1,4,5]=>[5,4,1,3,2]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) [1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>[4,3,2,1,5]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) [1,1,1,1,0,0,0,1,0,0]=>[4,1,2,3,5]=>[5,3,2,1,4]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) [1,1,1,1,0,0,1,0,0,0]=>[3,1,2,4,5]=>[5,4,2,1,3]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) [1,1,1,1,0,1,0,0,0,0]=>[2,1,3,4,5]=>[5,4,3,1,2]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) [1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) [1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>([],6) [1,0,1,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,2,1]=>[1,2,3,4,6,5]=>([(4,5)],6) [1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,2,1]=>[1,2,3,5,4,6]=>([(4,5)],6) [1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,2,1]=>[1,2,3,6,4,5]=>([(3,5),(4,5)],6) [1,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,2,1]=>[1,2,3,6,5,4]=>([(3,4),(3,5),(4,5)],6) [1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>([(4,5)],6) [1,0,1,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,2,1]=>[1,2,4,3,6,5]=>([(2,5),(3,4)],6) [1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,2,1]=>[1,2,5,3,4,6]=>([(3,5),(4,5)],6) [1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,2,1]=>[1,2,6,3,4,5]=>([(2,5),(3,5),(4,5)],6) [1,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,2,1]=>[1,2,6,3,5,4]=>([(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,2,1]=>[1,2,5,4,3,6]=>([(3,4),(3,5),(4,5)],6) [1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,2,1]=>[1,2,6,4,3,5]=>([(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[1,2,6,5,3,4]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,2,1]=>[1,2,6,5,4,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,3,1]=>[1,3,2,4,5,6]=>([(4,5)],6) [1,0,1,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,3,1]=>[1,3,2,4,6,5]=>([(2,5),(3,4)],6) [1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>([(2,5),(3,4)],6) [1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,3,1]=>[1,3,2,6,4,5]=>([(1,2),(3,5),(4,5)],6) [1,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,3,1]=>[1,3,2,6,5,4]=>([(1,2),(3,4),(3,5),(4,5)],6) [1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,4,1]=>[1,4,2,3,5,6]=>([(3,5),(4,5)],6) [1,0,1,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,4,1]=>[1,4,2,3,6,5]=>([(1,2),(3,5),(4,5)],6) [1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,5,1]=>[1,5,2,3,4,6]=>([(2,5),(3,5),(4,5)],6) [1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,1]=>[1,6,2,3,4,5]=>([(1,5),(2,5),(3,5),(4,5)],6) [1,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,1]=>[1,6,2,3,5,4]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,5,1]=>[1,5,2,4,3,6]=>([(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,6,1]=>[1,6,2,4,3,5]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,6,1]=>[1,6,2,5,3,4]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,6,1]=>[1,6,2,5,4,3]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,4,1]=>[1,4,3,2,5,6]=>([(3,4),(3,5),(4,5)],6) [1,0,1,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,4,1]=>[1,4,3,2,6,5]=>([(1,2),(3,4),(3,5),(4,5)],6) [1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,5,1]=>[1,5,3,2,4,6]=>([(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,6,1]=>[1,6,3,2,4,5]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,6,1]=>[1,6,3,2,5,4]=>([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) [1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1]=>[1,5,4,2,3,6]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[1,6,4,2,3,5]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,6,1]=>[1,6,5,2,3,4]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,6,1]=>[1,6,5,2,4,3]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,6,1]=>[1,6,4,3,2,5]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,6,1]=>[1,6,5,3,2,4]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,6,1]=>[1,6,5,4,2,3]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[1,6,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,2]=>[2,1,3,4,5,6]=>([(4,5)],6) [1,1,0,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,1,2]=>[2,1,3,4,6,5]=>([(2,5),(3,4)],6) [1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,1,2]=>[2,1,3,5,4,6]=>([(2,5),(3,4)],6) [1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,1,2]=>[2,1,3,6,4,5]=>([(1,2),(3,5),(4,5)],6) [1,1,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,1,2]=>[2,1,3,6,5,4]=>([(1,2),(3,4),(3,5),(4,5)],6) [1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>([(2,5),(3,4)],6) [1,1,0,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>([(0,5),(1,4),(2,3)],6) [1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>([(1,2),(3,5),(4,5)],6) [1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,1,2]=>[2,1,6,3,4,5]=>([(0,1),(2,5),(3,5),(4,5)],6) [1,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,1,2]=>[2,1,6,3,5,4]=>([(0,1),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,1,2]=>[2,1,5,4,3,6]=>([(1,2),(3,4),(3,5),(4,5)],6) [1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,1,2]=>[2,1,6,4,3,5]=>([(0,1),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,1,2]=>[2,1,6,5,3,4]=>([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>[2,1,6,5,4,3]=>([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,3]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6) [1,1,0,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,1,3]=>[3,1,2,4,6,5]=>([(1,2),(3,5),(4,5)],6) [1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>([(1,2),(3,5),(4,5)],6) [1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,1,3]=>[3,1,2,6,4,5]=>([(0,5),(1,5),(2,4),(3,4)],6) [1,1,0,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,1,3]=>[3,1,2,6,5,4]=>([(0,5),(1,5),(2,3),(2,4),(3,4)],6) [1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,4]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6) [1,1,0,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,1,4]=>[4,1,2,3,6,5]=>([(0,1),(2,5),(3,5),(4,5)],6) [1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,5]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6) [1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,6]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6) [1,1,0,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,1,6]=>[6,1,2,3,5,4]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,1,5]=>[5,1,2,4,3,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,1,6]=>[6,1,2,4,3,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,1,6]=>[6,1,2,5,3,4]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,1,6]=>[6,1,2,5,4,3]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,1,4]=>[4,1,3,2,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,1,4]=>[4,1,3,2,6,5]=>([(0,1),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,1,5]=>[5,1,3,2,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,1,6]=>[6,1,3,2,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,1,6]=>[6,1,3,2,5,4]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) [1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,1,5]=>[5,1,4,2,3,6]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,1,6]=>[6,1,4,2,3,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,1,6]=>[6,1,5,2,3,4]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,1,6]=>[6,1,5,2,4,3]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,1,5]=>[5,1,4,3,2,6]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,1,6]=>[6,1,4,3,2,5]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,1,6]=>[6,1,5,3,2,4]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,1,6]=>[6,1,5,4,2,3]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6]=>[6,1,5,4,3,2]=>([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,2,3]=>[3,2,1,4,5,6]=>([(3,4),(3,5),(4,5)],6) [1,1,1,0,0,0,1,0,1,1,0,0]=>[5,6,4,1,2,3]=>[3,2,1,4,6,5]=>([(1,2),(3,4),(3,5),(4,5)],6) [1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>([(1,2),(3,4),(3,5),(4,5)],6) [1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,6,1,2,3]=>[3,2,1,6,4,5]=>([(0,5),(1,5),(2,3),(2,4),(3,4)],6) [1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) [1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,0,0,1,0,0,1,1,0,0]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>([(0,1),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,2,6]=>[6,2,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,0,0,1,0,1,1,0,0,0]=>[4,5,3,1,2,6]=>[6,2,1,3,5,4]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) [1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) [1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,4,1,2,6]=>[6,2,1,4,3,5]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) [1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,5,1,2,6]=>[6,2,1,5,3,4]=>([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6]=>[6,2,1,5,4,3]=>([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,3,4]=>[4,3,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,0,1,0,0,0,1,1,0,0]=>[5,6,2,1,3,4]=>[4,3,1,2,6,5]=>([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,3,6]=>[6,3,1,2,4,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,0,1,0,0,1,1,0,0,0]=>[4,5,2,1,3,6]=>[6,3,1,2,5,4]=>([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,4,5]=>[5,4,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,4,6]=>[6,4,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,5,6]=>[6,5,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,2,1,5,6]=>[6,5,1,2,4,3]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,1,4,5]=>[5,4,1,3,2,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,3,1,4,6]=>[6,4,1,3,2,5]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,3,1,5,6]=>[6,5,1,3,2,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,4,1,5,6]=>[6,5,1,4,2,3]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6]=>[6,5,1,4,3,2]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,2,3,4]=>[4,3,2,1,5,6]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>[4,3,2,1,6,5]=>([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,2,3,6]=>[6,3,2,1,4,5]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,3,6]=>[6,3,2,1,5,4]=>([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,2,4,5]=>[5,4,2,1,3,6]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,2,4,6]=>[6,4,2,1,3,5]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,2,5,6]=>[6,5,2,1,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>[6,5,2,1,4,3]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,3,4,5]=>[5,4,3,1,2,6]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,3,4,6]=>[6,4,3,1,2,5]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,3,5,6]=>[6,5,3,1,2,4]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,4,5,6]=>[6,5,4,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,1,4,5,6]=>[6,5,4,1,3,2]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>[5,4,3,2,1,6]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,4,6]=>[6,4,3,2,1,5]=>([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,3,5,6]=>[6,5,3,2,1,4]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,2,4,5,6]=>[6,5,4,2,1,3]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[6,5,4,3,1,2]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>([],7) [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6]=>([(5,6)],7) [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,2,1]=>[1,2,3,4,6,5,7]=>([(5,6)],7) [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,2,1]=>[1,2,3,4,7,5,6]=>([(4,6),(5,6)],7) [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,2,1]=>[1,2,3,4,7,6,5]=>([(4,5),(4,6),(5,6)],7) [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7]=>([(5,6)],7) [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6]=>([(3,6),(4,5)],7) [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,2,1]=>[1,2,3,6,4,5,7]=>([(4,6),(5,6)],7) [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,2,1]=>[1,2,3,7,4,5,6]=>([(3,6),(4,6),(5,6)],7) [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,2,1]=>[1,2,3,7,4,6,5]=>([(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,2,1]=>[1,2,3,6,5,4,7]=>([(4,5),(4,6),(5,6)],7) [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,2,1]=>[1,2,3,7,5,4,6]=>([(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,2,1]=>[1,2,3,7,6,4,5]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,2,1]=>[1,2,4,3,5,6,7]=>([(5,6)],7) [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,2,1]=>[1,2,4,3,5,7,6]=>([(3,6),(4,5)],7) [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7]=>([(3,6),(4,5)],7) [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,2,1]=>[1,2,4,3,7,5,6]=>([(2,3),(4,6),(5,6)],7) [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,2,1]=>[1,2,4,3,7,6,5]=>([(2,3),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,2,1]=>[1,2,5,3,4,6,7]=>([(4,6),(5,6)],7) [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,2,1]=>[1,2,5,3,4,7,6]=>([(2,3),(4,6),(5,6)],7) [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,2,1]=>[1,2,6,3,4,5,7]=>([(3,6),(4,6),(5,6)],7) [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,2,1]=>[1,2,7,3,4,5,6]=>([(2,6),(3,6),(4,6),(5,6)],7) [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,2,1]=>[1,2,7,3,4,6,5]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,2,1]=>[1,2,6,3,5,4,7]=>([(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,2,1]=>[1,2,7,3,5,4,6]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[1,2,7,3,6,4,5]=>([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,2,1]=>[1,2,7,3,6,5,4]=>([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7]=>([(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,2,1]=>[1,2,5,4,3,7,6]=>([(2,3),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,2,1]=>[1,2,6,4,3,5,7]=>([(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,2,1]=>[1,2,7,4,3,5,6]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,2,1]=>[1,2,7,4,3,6,5]=>([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,2,1]=>[1,2,6,5,3,4,7]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,2,1]=>[1,2,7,5,3,4,6]=>([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[1,2,7,6,3,4,5]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,2,1]=>[1,2,7,6,3,5,4]=>([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,2,1]=>[1,2,6,5,4,3,7]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,2,1]=>[1,2,7,5,4,3,6]=>([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,2,1]=>[1,2,7,6,4,3,5]=>([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,2,1]=>[1,2,7,6,5,3,4]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,2,1]=>[1,2,7,6,5,4,3]=>([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7]=>([(5,6)],7) [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6]=>([(3,6),(4,5)],7) [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7]=>([(3,6),(4,5)],7) [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,3,1]=>[1,3,2,4,7,5,6]=>([(2,3),(4,6),(5,6)],7) [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,3,1]=>[1,3,2,4,7,6,5]=>([(2,3),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7]=>([(3,6),(4,5)],7) [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6]=>([(1,6),(2,5),(3,4)],7) [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7]=>([(2,3),(4,6),(5,6)],7) [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6]=>([(1,2),(3,6),(4,6),(5,6)],7) [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,3,1]=>[1,3,2,7,4,6,5]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7]=>([(2,3),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,3,1]=>[1,3,2,7,5,4,6]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,3,1]=>[1,3,2,7,6,4,5]=>([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,3,1]=>[1,3,2,7,6,5,4]=>([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7]=>([(4,6),(5,6)],7) [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6]=>([(2,3),(4,6),(5,6)],7) [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7]=>([(2,3),(4,6),(5,6)],7) [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6]=>([(1,6),(2,6),(3,5),(4,5)],7) [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,4,1]=>[1,4,2,3,7,6,5]=>([(1,6),(2,6),(3,4),(3,5),(4,5)],7) [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7]=>([(3,6),(4,6),(5,6)],7) [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6]=>([(1,2),(3,6),(4,6),(5,6)],7) [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7]=>([(2,6),(3,6),(4,6),(5,6)],7) [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7) [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,7,1]=>[1,7,2,3,4,6,5]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,6,1]=>[1,6,2,3,5,4,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,7,1]=>[1,7,2,3,5,4,6]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,7,1]=>[1,7,2,3,6,4,5]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,7,1]=>[1,7,2,3,6,5,4]=>([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,5,1]=>[1,5,2,4,3,6,7]=>([(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,6,1]=>[1,6,2,4,3,5,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,7,1]=>[1,7,2,4,3,5,6]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,7,1]=>[1,7,2,4,3,6,5]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,6,1]=>[1,6,2,5,3,4,7]=>([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>[1,7,2,5,3,4,6]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,7,1]=>[1,7,2,6,3,4,5]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,7,1]=>[1,7,2,6,3,5,4]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,6,1]=>[1,6,2,5,4,3,7]=>([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>[1,7,2,5,4,3,6]=>([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,7,1]=>[1,7,2,6,4,3,5]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,7,1]=>[1,7,2,6,5,3,4]=>([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,7,1]=>[1,7,2,6,5,4,3]=>([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,4,1]=>[1,4,3,2,5,6,7]=>([(4,5),(4,6),(5,6)],7) [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,4,1]=>[1,4,3,2,5,7,6]=>([(2,3),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7]=>([(2,3),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,4,1]=>[1,4,3,2,7,5,6]=>([(1,6),(2,6),(3,4),(3,5),(4,5)],7) [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5]=>([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7]=>([(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,7,1]=>[1,7,3,2,4,5,6]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,7,1]=>[1,7,3,2,4,6,5]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7]=>([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,7,1]=>[1,7,3,2,5,4,6]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,7,1]=>[1,7,3,2,6,4,5]=>([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,7,1]=>[1,7,3,2,6,5,4]=>([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,5,1]=>[1,5,4,2,3,6,7]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,5,1]=>[1,5,4,2,3,7,6]=>([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7]=>([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,7,1]=>[1,7,4,2,3,5,6]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,7,1]=>[1,7,4,2,3,6,5]=>([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,6,1]=>[1,6,5,2,3,4,7]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>[1,7,5,2,3,4,6]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,7,1]=>[1,7,6,2,3,4,5]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,7,1]=>[1,7,6,2,3,5,4]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,6,1]=>[1,6,5,2,4,3,7]=>([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>[1,7,5,2,4,3,6]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,7,1]=>[1,7,6,2,4,3,5]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,7,1]=>[1,7,6,2,5,3,4]=>([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,7,1]=>[1,7,6,2,5,4,3]=>([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,5,1]=>[1,5,4,3,2,6,7]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,5,1]=>[1,5,4,3,2,7,6]=>([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7]=>([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,7,1]=>[1,7,4,3,2,5,6]=>([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,7,1]=>[1,7,4,3,2,6,5]=>([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,6,1]=>[1,6,5,3,2,4,7]=>([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,7,1]=>[1,7,5,3,2,4,6]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,7,1]=>[1,7,6,3,2,4,5]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,7,1]=>[1,7,6,3,2,5,4]=>([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,6,1]=>[1,6,5,4,2,3,7]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>[1,7,5,4,2,3,6]=>([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,7,1]=>[1,7,6,4,2,3,5]=>([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,7,1]=>[1,7,6,5,2,3,4]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,7,1]=>[1,7,6,5,2,4,3]=>([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,6,1]=>[1,6,5,4,3,2,7]=>([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>[1,7,5,4,3,2,6]=>([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,7,1]=>[1,7,6,4,3,2,5]=>([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,7,1]=>[1,7,6,5,3,2,4]=>([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,7,1]=>[1,7,6,5,4,2,3]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7]=>([(5,6)],7) [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6]=>([(3,6),(4,5)],7) [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7]=>([(3,6),(4,5)],7) [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,1,2]=>[2,1,3,4,7,5,6]=>([(2,3),(4,6),(5,6)],7) [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,1,2]=>[2,1,3,4,7,6,5]=>([(2,3),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7]=>([(3,6),(4,5)],7) [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,1,2]=>[2,1,3,5,4,7,6]=>([(1,6),(2,5),(3,4)],7) [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7]=>([(2,3),(4,6),(5,6)],7) [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,1,2]=>[2,1,3,7,4,5,6]=>([(1,2),(3,6),(4,6),(5,6)],7) [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,1,2]=>[2,1,3,7,4,6,5]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7]=>([(2,3),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,1,2]=>[2,1,3,7,5,4,6]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,1,2]=>[2,1,3,7,6,4,5]=>([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,1,2]=>[2,1,3,7,6,5,4]=>([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>([(3,6),(4,5)],7) [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>([(1,6),(2,5),(3,4)],7) [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>([(1,6),(2,5),(3,4)],7) [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>([(0,3),(1,2),(4,6),(5,6)],7) [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>([(0,3),(1,2),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>([(2,3),(4,6),(5,6)],7) [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>([(0,3),(1,2),(4,6),(5,6)],7) [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>([(1,2),(3,6),(4,6),(5,6)],7) [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6]=>([(0,1),(2,6),(3,6),(4,6),(5,6)],7) [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,1,2]=>[2,1,7,3,4,6,5]=>([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,1,2]=>[2,1,7,3,5,4,6]=>([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,1,2]=>[2,1,7,3,6,4,5]=>([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,1,2]=>[2,1,7,3,6,5,4]=>([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>([(2,3),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>([(0,3),(1,2),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,1,2]=>[2,1,7,4,3,5,6]=>([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,1,2]=>[2,1,7,4,3,6,5]=>([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,1,2]=>[2,1,7,5,3,4,6]=>([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,1,2]=>[2,1,7,6,3,4,5]=>([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,1,2]=>[2,1,7,6,3,5,4]=>([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,1,2]=>[2,1,7,5,4,3,6]=>([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,1,2]=>[2,1,7,6,4,3,5]=>([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,1,2]=>[2,1,7,6,5,3,4]=>([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>[2,1,7,6,5,4,3]=>([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7]=>([(4,6),(5,6)],7) [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6]=>([(2,3),(4,6),(5,6)],7) [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>([(2,3),(4,6),(5,6)],7) [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6]=>([(1,6),(2,6),(3,5),(4,5)],7) [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,1,3]=>[3,1,2,4,7,6,5]=>([(1,6),(2,6),(3,4),(3,5),(4,5)],7) [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>([(2,3),(4,6),(5,6)],7) [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>([(0,3),(1,2),(4,6),(5,6)],7) [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>([(1,6),(2,6),(3,5),(4,5)],7) [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6]=>([(0,6),(1,6),(2,6),(3,5),(4,5)],7) [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,1,3]=>[3,1,2,7,4,6,5]=>([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>([(1,6),(2,6),(3,4),(3,5),(4,5)],7) [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5]=>([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7) [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,1,3]=>[3,1,2,7,6,5,4]=>([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>([(3,6),(4,6),(5,6)],7) [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6]=>([(1,2),(3,6),(4,6),(5,6)],7) [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>([(1,2),(3,6),(4,6),(5,6)],7) [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6]=>([(0,6),(1,6),(2,6),(3,5),(4,5)],7) [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7]=>([(2,6),(3,6),(4,6),(5,6)],7) [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,1,5]=>[5,1,2,3,4,7,6]=>([(0,1),(2,6),(3,6),(4,6),(5,6)],7) [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7) [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,1,7]=>[7,1,2,3,4,6,5]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,1,6]=>[6,1,2,3,5,4,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,1,7]=>[7,1,2,3,5,4,6]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,1,7]=>[7,1,2,3,6,4,5]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,1,7]=>[7,1,2,3,6,5,4]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6]=>([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,1,6]=>[6,1,2,4,3,5,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,1,7]=>[7,1,2,4,3,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,1,7]=>[7,1,2,4,3,6,5]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,1,6]=>[6,1,2,5,3,4,7]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,1,7]=>[7,1,2,5,3,4,6]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,1,7]=>[7,1,2,6,3,4,5]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,1,7]=>[7,1,2,6,3,5,4]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,1,6]=>[6,1,2,5,4,3,7]=>([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,1,7]=>[7,1,2,5,4,3,6]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,1,7]=>[7,1,2,6,4,3,5]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,1,7]=>[7,1,2,6,5,3,4]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,1,7]=>[7,1,2,6,5,4,3]=>([(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) [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7]=>([(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6]=>([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5]=>([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,1,6]=>[6,1,3,2,4,5,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,1,7]=>[7,1,3,2,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,1,7]=>[7,1,3,2,4,6,5]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,1,6]=>[6,1,3,2,5,4,7]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,1,7]=>[7,1,3,2,5,4,6]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,1,7]=>[7,1,3,2,6,4,5]=>([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,1,7]=>[7,1,3,2,6,5,4]=>([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7]=>([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,1,5]=>[5,1,4,2,3,7,6]=>([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,1,7]=>[7,1,4,2,3,5,6]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,1,7]=>[7,1,4,2,3,6,5]=>([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,1,6]=>[6,1,5,2,3,4,7]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,1,7]=>[7,1,5,2,3,4,6]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,1,7]=>[7,1,6,2,3,4,5]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,1,7]=>[7,1,6,2,3,5,4]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,1,6]=>[6,1,5,2,4,3,7]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,1,7]=>[7,1,5,2,4,3,6]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,1,7]=>[7,1,6,2,4,3,5]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,1,7]=>[7,1,6,2,5,3,4]=>([(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) [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,1,7]=>[7,1,6,2,5,4,3]=>([(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) [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7]=>([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,1,5]=>[5,1,4,3,2,7,6]=>([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,1,6]=>[6,1,4,3,2,5,7]=>([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,1,7]=>[7,1,4,3,2,5,6]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,1,7]=>[7,1,4,3,2,6,5]=>([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,1,6]=>[6,1,5,3,2,4,7]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,1,7]=>[7,1,5,3,2,4,6]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,1,7]=>[7,1,6,3,2,4,5]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,1,7]=>[7,1,6,3,2,5,4]=>([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,1,6]=>[6,1,5,4,2,3,7]=>([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,1,7]=>[7,1,5,4,2,3,6]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,1,7]=>[7,1,6,4,2,3,5]=>([(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) [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,1,7]=>[7,1,6,5,2,3,4]=>([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,1,7]=>[7,1,6,5,2,4,3]=>([(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) [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,1,6]=>[6,1,5,4,3,2,7]=>([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,1,7]=>[7,1,5,4,3,2,6]=>([(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) [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,1,7]=>[7,1,6,4,3,2,5]=>([(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) [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,1,7]=>[7,1,6,5,3,2,4]=>([(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) [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,1,7]=>[7,1,6,5,4,2,3]=>([(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) [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>[7,1,6,5,4,3,2]=>([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7]=>([(4,5),(4,6),(5,6)],7) [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6]=>([(2,3),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>([(2,3),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,1,2,3]=>[3,2,1,4,7,5,6]=>([(1,6),(2,6),(3,4),(3,5),(4,5)],7) [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>([(2,3),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>([(0,3),(1,2),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>([(1,6),(2,6),(3,4),(3,5),(4,5)],7) [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5]=>([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5]=>([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4]=>([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>([(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,1,2,7]=>[7,2,1,3,4,6,5]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,1,2,7]=>[7,2,1,3,5,4,6]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,1,2,7]=>[7,2,1,3,6,4,5]=>([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,1,2,7]=>[7,2,1,3,6,5,4]=>([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5]=>([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7) [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,1,2,7]=>[7,2,1,5,3,4,6]=>([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,1,2,7]=>[7,2,1,6,3,4,5]=>([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,1,2,7]=>[7,2,1,6,3,5,4]=>([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6]=>([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,1,2,7]=>[7,2,1,6,4,3,5]=>([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,1,2,7]=>[7,2,1,6,5,3,4]=>([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,1,2,7]=>[7,2,1,6,5,4,3]=>([(0,1),(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) [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6]=>([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6]=>([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7) [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,1,3,4]=>[4,3,1,2,7,6,5]=>([(0,1),(0,2),(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5]=>([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6]=>([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,1,3,7]=>[7,3,1,2,6,4,5]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,1,3,7]=>[7,3,1,2,6,5,4]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,1,4,5]=>[5,4,1,2,3,7,6]=>([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,1,4,7]=>[7,4,1,2,3,6,5]=>([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,5,6]=>[6,5,1,2,3,4,7]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,1,6,7]=>[7,6,1,2,3,5,4]=>([(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) [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,1,5,6]=>[6,5,1,2,4,3,7]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,1,5,7]=>[7,5,1,2,4,3,6]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,1,6,7]=>[7,6,1,2,4,3,5]=>([(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) [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,1,6,7]=>[7,6,1,2,5,3,4]=>([(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) [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,1,6,7]=>[7,6,1,2,5,4,3]=>([(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) [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7]=>([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,1,4,5]=>[5,4,1,3,2,7,6]=>([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5]=>([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,1,5,6]=>[6,5,1,3,2,4,7]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,1,5,7]=>[7,5,1,3,2,4,6]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,1,6,7]=>[7,6,1,3,2,4,5]=>([(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) [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,1,6,7]=>[7,6,1,3,2,5,4]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,1,5,6]=>[6,5,1,4,2,3,7]=>([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,1,5,7]=>[7,5,1,4,2,3,6]=>([(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) [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,1,6,7]=>[7,6,1,4,2,3,5]=>([(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) [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,1,6,7]=>[7,6,1,5,2,3,4]=>([(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) [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,1,6,7]=>[7,6,1,5,2,4,3]=>([(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) [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,1,5,6]=>[6,5,1,4,3,2,7]=>([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,1,5,7]=>[7,5,1,4,3,2,6]=>([(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) [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,1,6,7]=>[7,6,1,4,3,2,5]=>([(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) [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,1,6,7]=>[7,6,1,5,3,2,4]=>([(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) [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,1,6,7]=>[7,6,1,5,4,2,3]=>([(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) [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7]=>[7,6,1,5,4,3,2]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6]=>([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>([(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>([(0,1),(0,2),(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5]=>([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>[7,3,2,1,6,5,4]=>([(0,4),(0,5),(0,6),(1,2),(1,3),(1,6),(2,3),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5]=>([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,2,5,7]=>[7,5,2,1,3,4,6]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,2,6,7]=>[7,6,2,1,3,4,5]=>([(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) [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,1,2,6,7]=>[7,6,2,1,3,5,4]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,4,1,2,5,7]=>[7,5,2,1,4,3,6]=>([(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,4,1,2,6,7]=>[7,6,2,1,4,3,5]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,5,1,2,6,7]=>[7,6,2,1,5,3,4]=>([(0,1),(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) [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,4,5,1,2,6,7]=>[7,6,2,1,5,4,3]=>([(0,1),(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) [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6]=>([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5]=>([(0,1),(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6]=>([(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) [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,3,6,7]=>[7,6,3,1,2,4,5]=>([(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) [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,2,1,3,6,7]=>[7,6,3,1,2,5,4]=>([(0,1),(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) [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,4,5,7]=>[7,5,4,1,2,3,6]=>([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,4,6,7]=>[7,6,4,1,2,3,5]=>([(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) [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4]=>([(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) [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,4,2,1,5,6,7]=>[7,6,5,1,2,4,3]=>([(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) [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,3,1,4,5,6]=>[6,5,4,1,3,2,7]=>([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,3,1,4,5,7]=>[7,5,4,1,3,2,6]=>([(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) [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,3,1,4,6,7]=>[7,6,4,1,3,2,5]=>([(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) [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,3,1,5,6,7]=>[7,6,5,1,3,2,4]=>([(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) [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,4,1,5,6,7]=>[7,6,5,1,4,2,3]=>([(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) [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7]=>[7,6,5,1,4,3,2]=>([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7]=>([(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>([(0,1),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6]=>([(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) [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5]=>([(0,1),(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) [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6]=>([(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) [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5]=>([(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) [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,5,1,2,3,6,7]=>[7,6,3,2,1,5,4]=>([(0,1),(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) [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7]=>([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,2,4,5,7]=>[7,5,4,2,1,3,6]=>([(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) [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5]=>([(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) [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4]=>([(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) [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>[7,6,5,2,1,4,3]=>([(0,3),(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,3,4,5,7]=>[7,5,4,3,1,2,6]=>([(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) [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,3,4,6,7]=>[7,6,4,3,1,2,5]=>([(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) [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,3,5,6,7]=>[7,6,5,3,1,2,4]=>([(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) [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3]=>([(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) [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>[7,6,5,4,1,3,2]=>([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7]=>([(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6]=>([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4]=>([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3]=>([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>([(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) [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>([],8) [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7,8]=>([(4,7),(5,6)],8) [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6,8]=>([(4,7),(5,6)],8) [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6,8]=>([(2,7),(3,7),(4,6),(5,6)],8) [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5,8]=>([(2,6),(2,7),(3,4),(3,5),(4,5),(6,7)],8) [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,1,2]=>[2,1,3,4,5,6,8,7]=>([(4,7),(5,6)],8) [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>([(0,7),(1,6),(2,5),(3,4)],8) [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2]=>[2,1,8,7,6,5,4,3]=>([(0,1),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,1,3]=>[3,1,2,4,5,8,6,7]=>([(2,7),(3,7),(4,6),(5,6)],8) [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,1,4]=>[4,1,2,3,8,5,6,7]=>([(0,7),(1,7),(2,7),(3,6),(4,6),(5,6)],8) [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,2,3,1,4]=>[4,1,3,2,8,6,5,7]=>([(0,7),(1,6),(2,3),(2,6),(3,6),(4,5),(4,7),(5,7)],8) [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,1,2,3]=>[3,2,1,4,5,8,7,6]=>([(2,6),(2,7),(3,4),(3,5),(4,5),(6,7)],8) [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,1,2,4]=>[4,2,1,3,8,5,7,6]=>([(0,7),(1,6),(2,3),(2,6),(3,6),(4,5),(4,7),(5,7)],8) [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,1,3,4]=>[4,3,1,2,8,7,5,6]=>([(0,6),(0,7),(1,4),(1,5),(2,4),(2,5),(3,6),(3,7),(4,5),(6,7)],8) [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7]=>([(0,3),(1,2),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>([(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4),(5,6),(5,7),(6,7)],8) [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7]=>([(0,1),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(2,3),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
Map
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.