Identifier
Mp00023: Dyck paths to non-crossing permutationPermutations
Mp00089: Permutations Inverse Kreweras complementPermutations
Mp00160: Permutations graph of inversions Graphs
Images
=>
Cc0005;cc-rep-0Cc0020;cc-rep-3
[1,0]=>[1]=>[1]=>([],1) [1,0,1,0]=>[1,2]=>[2,1]=>([(0,1)],2) [1,1,0,0]=>[2,1]=>[1,2]=>([],2) [1,0,1,0,1,0]=>[1,2,3]=>[2,3,1]=>([(0,2),(1,2)],3) [1,0,1,1,0,0]=>[1,3,2]=>[3,2,1]=>([(0,1),(0,2),(1,2)],3) [1,1,0,0,1,0]=>[2,1,3]=>[1,3,2]=>([(1,2)],3) [1,1,0,1,0,0]=>[2,3,1]=>[1,2,3]=>([],3) [1,1,1,0,0,0]=>[3,2,1]=>[2,1,3]=>([(1,2)],3) [1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[2,3,4,1]=>([(0,3),(1,3),(2,3)],4) [1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[2,4,3,1]=>([(0,3),(1,2),(1,3),(2,3)],4) [1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[3,2,4,1]=>([(0,3),(1,2),(1,3),(2,3)],4) [1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[4,2,3,1]=>([(0,2),(0,3),(1,2),(1,3),(2,3)],4) [1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[4,3,2,1]=>([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) [1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[1,3,4,2]=>([(1,3),(2,3)],4) [1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[1,4,3,2]=>([(1,2),(1,3),(2,3)],4) [1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[1,2,4,3]=>([(2,3)],4) [1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[1,2,3,4]=>([],4) [1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[1,3,2,4]=>([(2,3)],4) [1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[2,1,4,3]=>([(0,3),(1,2)],4) [1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[2,1,3,4]=>([(2,3)],4) [1,1,1,0,1,0,0,0]=>[4,2,3,1]=>[2,3,1,4]=>([(1,3),(2,3)],4) [1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[3,2,1,4]=>([(1,2),(1,3),(2,3)],4) [1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[2,3,4,5,1]=>([(0,4),(1,4),(2,4),(3,4)],5) [1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[2,3,5,4,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5) [1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[2,4,3,5,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5) [1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[2,5,3,4,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) [1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[2,5,4,3,1]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) [1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[3,2,4,5,1]=>([(0,4),(1,4),(2,3),(2,4),(3,4)],5) [1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[3,2,5,4,1]=>([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) [1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[4,2,3,5,1]=>([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) [1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[5,2,3,4,1]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) [1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[5,2,4,3,1]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) [1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[4,3,2,5,1]=>([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) [1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[5,3,2,4,1]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) [1,0,1,1,1,0,1,0,0,0]=>[1,5,3,4,2]=>[5,3,4,2,1]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) [1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[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) [1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[1,3,4,5,2]=>([(1,4),(2,4),(3,4)],5) [1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[1,3,5,4,2]=>([(1,4),(2,3),(2,4),(3,4)],5) [1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[1,4,3,5,2]=>([(1,4),(2,3),(2,4),(3,4)],5) [1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[1,5,3,4,2]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5) [1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[1,5,4,3,2]=>([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) [1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[1,2,4,5,3]=>([(2,4),(3,4)],5) [1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[1,2,5,4,3]=>([(2,3),(2,4),(3,4)],5) [1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[1,2,3,5,4]=>([(3,4)],5) [1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[1,2,3,4,5]=>([],5) [1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[1,2,4,3,5]=>([(3,4)],5) [1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[1,3,2,5,4]=>([(1,4),(2,3)],5) [1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[1,3,2,4,5]=>([(3,4)],5) [1,1,0,1,1,0,1,0,0,0]=>[2,5,3,4,1]=>[1,3,4,2,5]=>([(2,4),(3,4)],5) [1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[1,4,3,2,5]=>([(2,3),(2,4),(3,4)],5) [1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[2,1,4,5,3]=>([(0,1),(2,4),(3,4)],5) [1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[2,1,5,4,3]=>([(0,1),(2,3),(2,4),(3,4)],5) [1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[2,1,3,5,4]=>([(1,4),(2,3)],5) [1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[2,1,3,4,5]=>([(3,4)],5) [1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[2,1,4,3,5]=>([(1,4),(2,3)],5) [1,1,1,0,1,0,0,0,1,0]=>[4,2,3,1,5]=>[2,3,1,5,4]=>([(0,1),(2,4),(3,4)],5) [1,1,1,0,1,0,0,1,0,0]=>[4,2,3,5,1]=>[2,3,1,4,5]=>([(2,4),(3,4)],5) [1,1,1,0,1,0,1,0,0,0]=>[5,2,3,4,1]=>[2,3,4,1,5]=>([(1,4),(2,4),(3,4)],5) [1,1,1,0,1,1,0,0,0,0]=>[5,2,4,3,1]=>[2,4,3,1,5]=>([(1,4),(2,3),(2,4),(3,4)],5) [1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[3,2,1,5,4]=>([(0,1),(2,3),(2,4),(3,4)],5) [1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[3,2,1,4,5]=>([(2,3),(2,4),(3,4)],5) [1,1,1,1,0,0,1,0,0,0]=>[5,3,2,4,1]=>[3,2,4,1,5]=>([(1,4),(2,3),(2,4),(3,4)],5) [1,1,1,1,0,1,0,0,0,0]=>[5,3,4,2,1]=>[4,2,3,1,5]=>([(1,3),(1,4),(2,3),(2,4),(3,4)],5) [1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[4,3,2,1,5]=>([(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]=>[1,2,3,4,5,6]=>[2,3,4,5,6,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6) [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[2,3,4,6,5,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[2,3,5,4,6,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[2,3,6,4,5,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[2,3,6,5,4,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[2,4,3,5,6,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[2,4,3,6,5,1]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[2,5,3,4,6,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[2,6,3,4,5,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[2,6,3,5,4,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[2,5,4,3,6,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[2,6,4,3,5,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,6,4,5,3]=>[2,6,4,5,3,1]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[2,6,5,4,3,1]=>([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[3,2,4,5,6,1]=>([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[3,2,4,6,5,1]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[3,2,5,4,6,1]=>([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[3,2,6,4,5,1]=>([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[3,2,6,5,4,1]=>([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[4,2,3,5,6,1]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[4,2,3,6,5,1]=>([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[5,2,3,4,6,1]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[6,2,3,4,5,1]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[6,2,3,5,4,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[5,2,4,3,6,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[6,2,4,3,5,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,6,4,5,2]=>[6,2,4,5,3,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[6,2,5,4,3,1]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[4,3,2,5,6,1]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[4,3,2,6,5,1]=>([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[5,3,2,4,6,1]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[6,3,2,4,5,1]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[6,3,2,5,4,1]=>([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,5,3,4,2,6]=>[5,3,4,2,6,1]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,5,3,4,6,2]=>[6,3,4,2,5,1]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,6,3,4,5,2]=>[6,3,4,5,2,1]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,6,3,5,4,2]=>[6,3,5,4,2,1]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[5,4,3,2,6,1]=>([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[6,4,3,2,5,1]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,6,4,3,5,2]=>[6,4,3,5,2,1]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,6,4,5,3,2]=>[6,5,3,4,2,1]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[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) [1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[1,3,4,5,6,2]=>([(1,5),(2,5),(3,5),(4,5)],6) [1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[1,3,4,6,5,2]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[1,3,5,4,6,2]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[1,3,6,4,5,2]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[1,3,6,5,4,2]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[1,4,3,5,6,2]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[1,4,3,6,5,2]=>([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) [1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[1,5,3,4,6,2]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[1,6,3,4,5,2]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[1,6,3,5,4,2]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[1,5,4,3,6,2]=>([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[1,6,4,3,5,2]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,6,4,5,3]=>[1,6,4,5,3,2]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[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) [1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[1,2,4,5,6,3]=>([(2,5),(3,5),(4,5)],6) [1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[1,2,4,6,5,3]=>([(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[1,2,5,4,6,3]=>([(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[1,2,6,4,5,3]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[1,2,6,5,4,3]=>([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[1,2,3,5,6,4]=>([(3,5),(4,5)],6) [1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[1,2,3,6,5,4]=>([(3,4),(3,5),(4,5)],6) [1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[1,2,3,4,6,5]=>([(4,5)],6) [1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[1,2,3,4,5,6]=>([],6) [1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[1,2,3,5,4,6]=>([(4,5)],6) [1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[1,2,4,3,6,5]=>([(2,5),(3,4)],6) [1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[1,2,4,3,5,6]=>([(4,5)],6) [1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,6,4,5,1]=>[1,2,4,5,3,6]=>([(3,5),(4,5)],6) [1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[1,2,5,4,3,6]=>([(3,4),(3,5),(4,5)],6) [1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[1,3,2,5,6,4]=>([(1,2),(3,5),(4,5)],6) [1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[1,3,2,6,5,4]=>([(1,2),(3,4),(3,5),(4,5)],6) [1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[1,3,2,4,6,5]=>([(2,5),(3,4)],6) [1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[1,3,2,4,5,6]=>([(4,5)],6) [1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[1,3,2,5,4,6]=>([(2,5),(3,4)],6) [1,1,0,1,1,0,1,0,0,0,1,0]=>[2,5,3,4,1,6]=>[1,3,4,2,6,5]=>([(1,2),(3,5),(4,5)],6) [1,1,0,1,1,0,1,0,0,1,0,0]=>[2,5,3,4,6,1]=>[1,3,4,2,5,6]=>([(3,5),(4,5)],6) [1,1,0,1,1,0,1,0,1,0,0,0]=>[2,6,3,4,5,1]=>[1,3,4,5,2,6]=>([(2,5),(3,5),(4,5)],6) [1,1,0,1,1,0,1,1,0,0,0,0]=>[2,6,3,5,4,1]=>[1,3,5,4,2,6]=>([(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[1,4,3,2,6,5]=>([(1,2),(3,4),(3,5),(4,5)],6) [1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[1,4,3,2,5,6]=>([(3,4),(3,5),(4,5)],6) [1,1,0,1,1,1,0,0,1,0,0,0]=>[2,6,4,3,5,1]=>[1,4,3,5,2,6]=>([(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,1,1,1,0,1,0,0,0,0]=>[2,6,4,5,3,1]=>[1,5,3,4,2,6]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[1,5,4,3,2,6]=>([(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]=>[3,2,1,4,5,6]=>[2,1,4,5,6,3]=>([(0,1),(2,5),(3,5),(4,5)],6) [1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[2,1,4,6,5,3]=>([(0,1),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[2,1,5,4,6,3]=>([(0,1),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[2,1,6,4,5,3]=>([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[2,1,6,5,4,3]=>([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[2,1,3,5,6,4]=>([(1,2),(3,5),(4,5)],6) [1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[2,1,3,6,5,4]=>([(1,2),(3,4),(3,5),(4,5)],6) [1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[2,1,3,4,6,5]=>([(2,5),(3,4)],6) [1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[2,1,3,4,5,6]=>([(4,5)],6) [1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[2,1,3,5,4,6]=>([(2,5),(3,4)],6) [1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[2,1,4,3,6,5]=>([(0,5),(1,4),(2,3)],6) [1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[2,1,4,3,5,6]=>([(2,5),(3,4)],6) [1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,6,4,5,1]=>[2,1,4,5,3,6]=>([(1,2),(3,5),(4,5)],6) [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[2,1,5,4,3,6]=>([(1,2),(3,4),(3,5),(4,5)],6) [1,1,1,0,1,0,0,0,1,0,1,0]=>[4,2,3,1,5,6]=>[2,3,1,5,6,4]=>([(0,5),(1,5),(2,4),(3,4)],6) [1,1,1,0,1,0,0,0,1,1,0,0]=>[4,2,3,1,6,5]=>[2,3,1,6,5,4]=>([(0,5),(1,5),(2,3),(2,4),(3,4)],6) [1,1,1,0,1,0,0,1,0,0,1,0]=>[4,2,3,5,1,6]=>[2,3,1,4,6,5]=>([(1,2),(3,5),(4,5)],6) [1,1,1,0,1,0,0,1,0,1,0,0]=>[4,2,3,5,6,1]=>[2,3,1,4,5,6]=>([(3,5),(4,5)],6) [1,1,1,0,1,0,0,1,1,0,0,0]=>[4,2,3,6,5,1]=>[2,3,1,5,4,6]=>([(1,2),(3,5),(4,5)],6) [1,1,1,0,1,0,1,0,0,0,1,0]=>[5,2,3,4,1,6]=>[2,3,4,1,6,5]=>([(0,1),(2,5),(3,5),(4,5)],6) [1,1,1,0,1,0,1,0,0,1,0,0]=>[5,2,3,4,6,1]=>[2,3,4,1,5,6]=>([(2,5),(3,5),(4,5)],6) [1,1,1,0,1,0,1,0,1,0,0,0]=>[6,2,3,4,5,1]=>[2,3,4,5,1,6]=>([(1,5),(2,5),(3,5),(4,5)],6) [1,1,1,0,1,0,1,1,0,0,0,0]=>[6,2,3,5,4,1]=>[2,3,5,4,1,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,0,1,1,0,0,0,0,1,0]=>[5,2,4,3,1,6]=>[2,4,3,1,6,5]=>([(0,1),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,4,3,6,1]=>[2,4,3,1,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,0,1,1,0,0,1,0,0,0]=>[6,2,4,3,5,1]=>[2,4,3,5,1,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,0,1,1,0,1,0,0,0,0]=>[6,2,4,5,3,1]=>[2,5,3,4,1,6]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,0,1,1,1,0,0,0,0,0]=>[6,2,5,4,3,1]=>[2,5,4,3,1,6]=>([(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]=>[4,3,2,1,5,6]=>[3,2,1,5,6,4]=>([(0,5),(1,5),(2,3),(2,4),(3,4)],6) [1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[3,2,1,6,5,4]=>([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) [1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[3,2,1,4,6,5]=>([(1,2),(3,4),(3,5),(4,5)],6) [1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[3,2,1,4,5,6]=>([(3,4),(3,5),(4,5)],6) [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[3,2,1,5,4,6]=>([(1,2),(3,4),(3,5),(4,5)],6) [1,1,1,1,0,0,1,0,0,0,1,0]=>[5,3,2,4,1,6]=>[3,2,4,1,6,5]=>([(0,1),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[3,2,4,1,5,6]=>([(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,1,0,0,1,0,1,0,0,0]=>[6,3,2,4,5,1]=>[3,2,4,5,1,6]=>([(1,5),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,1,0,0,1,1,0,0,0,0]=>[6,3,2,5,4,1]=>[3,2,5,4,1,6]=>([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) [1,1,1,1,0,1,0,0,0,0,1,0]=>[5,3,4,2,1,6]=>[4,2,3,1,6,5]=>([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,1,0,1,0,0,0,1,0,0]=>[5,3,4,2,6,1]=>[4,2,3,1,5,6]=>([(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,1,0,1,0,0,1,0,0,0]=>[6,3,4,2,5,1]=>[4,2,3,5,1,6]=>([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,1,0,1,0,1,0,0,0,0]=>[6,3,4,5,2,1]=>[5,2,3,4,1,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,1,0,1,1,0,0,0,0,0]=>[6,3,5,4,2,1]=>[5,2,4,3,1,6]=>([(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]=>[5,4,3,2,1,6]=>[4,3,2,1,6,5]=>([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[4,3,2,1,5,6]=>([(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]=>[6,4,3,2,5,1]=>[4,3,2,5,1,6]=>([(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]=>[6,4,3,5,2,1]=>[5,3,2,4,1,6]=>([(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]=>[6,5,3,4,2,1]=>[5,3,4,2,1,6]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[5,4,3,2,1,6]=>([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>[2,3,4,5,6,7,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[2,3,4,5,7,6,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[2,3,4,6,5,7,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[2,3,4,7,5,6,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[2,3,4,7,6,5,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[2,3,5,4,6,7,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[2,3,5,4,7,6,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[2,3,6,4,5,7,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[2,3,7,4,5,6,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[2,3,7,4,6,5,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[2,3,6,5,4,7,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[2,3,7,5,4,6,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,7,5,6,4]=>[2,3,7,5,6,4,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>[2,3,7,6,5,4,1]=>([(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) [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[2,4,3,5,6,7,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[2,4,3,5,7,6,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[2,4,3,6,5,7,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[2,4,3,7,5,6,1]=>([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[2,4,3,7,6,5,1]=>([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[2,5,3,4,6,7,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[2,5,3,4,7,6,1]=>([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[2,6,3,4,5,7,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[2,7,3,4,5,6,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[2,7,3,4,6,5,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[2,6,3,5,4,7,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>[2,7,3,5,4,6,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,7,5,6,3]=>[2,7,3,5,6,4,1]=>([(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) [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[2,7,3,6,5,4,1]=>([(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) [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[2,5,4,3,6,7,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[2,5,4,3,7,6,1]=>([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[2,6,4,3,5,7,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[2,7,4,3,5,6,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[2,7,4,3,6,5,1]=>([(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) [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,6,4,5,3,7]=>[2,6,4,5,3,7,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,6,4,5,7,3]=>[2,7,4,5,3,6,1]=>([(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) [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,7,4,5,6,3]=>[2,7,4,5,6,3,1]=>([(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) [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,7,4,6,5,3]=>[2,7,4,6,5,3,1]=>([(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) [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[2,6,5,4,3,7,1]=>([(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) [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[2,7,5,4,3,6,1]=>([(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) [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,7,5,4,6,3]=>[2,7,5,4,6,3,1]=>([(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) [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,7,5,6,4,3]=>[2,7,6,4,5,3,1]=>([(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) [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[2,7,6,5,4,3,1]=>([(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) [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[3,2,4,5,6,7,1]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[3,2,4,5,7,6,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[3,2,4,6,5,7,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[3,2,4,7,5,6,1]=>([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[3,2,4,7,6,5,1]=>([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[3,2,5,4,6,7,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[3,2,5,4,7,6,1]=>([(0,5),(0,6),(1,4),(1,6),(2,3),(2,6),(3,6),(4,6),(5,6)],7) [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[3,2,6,4,5,7,1]=>([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[3,2,7,4,5,6,1]=>([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[3,2,7,4,6,5,1]=>([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[3,2,6,5,4,7,1]=>([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[3,2,7,5,4,6,1]=>([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,7,5,6,4]=>[3,2,7,5,6,4,1]=>([(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) [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[3,2,7,6,5,4,1]=>([(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) [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[4,2,3,5,6,7,1]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[4,2,3,5,7,6,1]=>([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[4,2,3,6,5,7,1]=>([(0,6),(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[4,2,3,7,5,6,1]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[4,2,3,7,6,5,1]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[5,2,3,4,6,7,1]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[5,2,3,4,7,6,1]=>([(0,1),(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[6,2,3,4,5,7,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[7,2,3,4,5,6,1]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[7,2,3,4,6,5,1]=>([(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) [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[6,2,3,5,4,7,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[7,2,3,5,4,6,1]=>([(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) [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,7,5,6,2]=>[7,2,3,5,6,4,1]=>([(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) [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[7,2,3,6,5,4,1]=>([(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) [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[5,2,4,3,6,7,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[5,2,4,3,7,6,1]=>([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>[6,2,4,3,5,7,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[7,2,4,3,5,6,1]=>([(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) [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[7,2,4,3,6,5,1]=>([(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) [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,6,4,5,2,7]=>[6,2,4,5,3,7,1]=>([(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) [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,6,4,5,7,2]=>[7,2,4,5,3,6,1]=>([(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) [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,7,4,5,6,2]=>[7,2,4,5,6,3,1]=>([(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) [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,7,4,6,5,2]=>[7,2,4,6,5,3,1]=>([(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) [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[6,2,5,4,3,7,1]=>([(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) [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[7,2,5,4,3,6,1]=>([(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) [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,7,5,4,6,2]=>[7,2,5,4,6,3,1]=>([(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) [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,7,5,6,4,2]=>[7,2,6,4,5,3,1]=>([(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) [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[7,2,6,5,4,3,1]=>([(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) [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[4,3,2,5,6,7,1]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[4,3,2,5,7,6,1]=>([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[4,3,2,6,5,7,1]=>([(0,6),(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[4,3,2,7,5,6,1]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[4,3,2,7,6,5,1]=>([(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) [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[5,3,2,4,6,7,1]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[5,3,2,4,7,6,1]=>([(0,1),(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[6,3,2,4,5,7,1]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[7,3,2,4,5,6,1]=>([(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) [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[7,3,2,4,6,5,1]=>([(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) [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[6,3,2,5,4,7,1]=>([(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) [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>[7,3,2,5,4,6,1]=>([(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) [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,7,5,6,2]=>[7,3,2,5,6,4,1]=>([(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) [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[7,3,2,6,5,4,1]=>([(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) [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,5,3,4,2,6,7]=>[5,3,4,2,6,7,1]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,5,3,4,2,7,6]=>[5,3,4,2,7,6,1]=>([(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) [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,5,3,4,6,2,7]=>[6,3,4,2,5,7,1]=>([(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) [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,5,3,4,6,7,2]=>[7,3,4,2,5,6,1]=>([(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) [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,5,3,4,7,6,2]=>[7,3,4,2,6,5,1]=>([(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) [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,6,3,4,5,2,7]=>[6,3,4,5,2,7,1]=>([(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) [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,6,3,4,5,7,2]=>[7,3,4,5,2,6,1]=>([(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) [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,7,3,4,5,6,2]=>[7,3,4,5,6,2,1]=>([(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) [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,7,3,4,6,5,2]=>[7,3,4,6,5,2,1]=>([(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) [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,6,3,5,4,2,7]=>[6,3,5,4,2,7,1]=>([(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) [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,6,3,5,4,7,2]=>[7,3,5,4,2,6,1]=>([(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) [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,7,3,5,4,6,2]=>[7,3,5,4,6,2,1]=>([(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) [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,7,3,5,6,4,2]=>[7,3,6,4,5,2,1]=>([(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) [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,7,3,6,5,4,2]=>[7,3,6,5,4,2,1]=>([(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) [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[5,4,3,2,6,7,1]=>([(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) [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[5,4,3,2,7,6,1]=>([(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) [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[6,4,3,2,5,7,1]=>([(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) [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[7,4,3,2,5,6,1]=>([(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) [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[7,4,3,2,6,5,1]=>([(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) [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,6,4,3,5,2,7]=>[6,4,3,5,2,7,1]=>([(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) [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,6,4,3,5,7,2]=>[7,4,3,5,2,6,1]=>([(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) [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,7,4,3,5,6,2]=>[7,4,3,5,6,2,1]=>([(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) [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,7,4,3,6,5,2]=>[7,4,3,6,5,2,1]=>([(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) [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,6,4,5,3,2,7]=>[6,5,3,4,2,7,1]=>([(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) [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,6,4,5,3,7,2]=>[7,5,3,4,2,6,1]=>([(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) [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,7,4,5,3,6,2]=>[7,5,3,4,6,2,1]=>([(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) [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,7,4,5,6,3,2]=>[7,6,3,4,5,2,1]=>([(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) [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,7,4,6,5,3,2]=>[7,6,3,5,4,2,1]=>([(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) [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[6,5,4,3,2,7,1]=>([(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) [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[7,5,4,3,2,6,1]=>([(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) [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,7,5,4,3,6,2]=>[7,5,4,3,6,2,1]=>([(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) [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,7,5,4,6,3,2]=>[7,6,4,3,5,2,1]=>([(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) [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,7,6,4,5,3,2]=>[7,6,4,5,3,2,1]=>([(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) [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[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) [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[1,3,4,5,6,7,2]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7) [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[1,3,4,5,7,6,2]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[1,3,4,6,5,7,2]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[1,3,4,7,5,6,2]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[1,3,4,7,6,5,2]=>([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[1,3,5,4,6,7,2]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[1,3,5,4,7,6,2]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[1,3,6,4,5,7,2]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[1,3,7,4,5,6,2]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[1,3,7,4,6,5,2]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[1,3,6,5,4,7,2]=>([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[1,3,7,5,4,6,2]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,7,5,6,4]=>[1,3,7,5,6,4,2]=>([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[1,3,7,6,5,4,2]=>([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[1,4,3,5,6,7,2]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[1,4,3,5,7,6,2]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[1,4,3,6,5,7,2]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[1,4,3,7,5,6,2]=>([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[1,4,3,7,6,5,2]=>([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[1,5,3,4,6,7,2]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[1,5,3,4,7,6,2]=>([(1,2),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[1,6,3,4,5,7,2]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[1,7,3,4,5,6,2]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[1,7,3,4,6,5,2]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[1,6,3,5,4,7,2]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>[1,7,3,5,4,6,2]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,7,5,6,3]=>[1,7,3,5,6,4,2]=>([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[1,7,3,6,5,4,2]=>([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[1,5,4,3,6,7,2]=>([(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[1,5,4,3,7,6,2]=>([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>[1,6,4,3,5,7,2]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[1,7,4,3,5,6,2]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[1,7,4,3,6,5,2]=>([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,6,4,5,3,7]=>[1,6,4,5,3,7,2]=>([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,6,4,5,7,3]=>[1,7,4,5,3,6,2]=>([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,7,4,5,6,3]=>[1,7,4,5,6,3,2]=>([(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) [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,7,4,6,5,3]=>[1,7,4,6,5,3,2]=>([(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) [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[1,6,5,4,3,7,2]=>([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[1,7,5,4,3,6,2]=>([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,7,5,4,6,3]=>[1,7,5,4,6,3,2]=>([(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) [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,7,5,6,4,3]=>[1,7,6,4,5,3,2]=>([(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) [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[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) [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[1,2,4,5,6,7,3]=>([(2,6),(3,6),(4,6),(5,6)],7) [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[1,2,4,5,7,6,3]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[1,2,4,6,5,7,3]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[1,2,4,7,5,6,3]=>([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[1,2,4,7,6,5,3]=>([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[1,2,5,4,6,7,3]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[1,2,5,4,7,6,3]=>([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[1,2,6,4,5,7,3]=>([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[1,2,7,4,5,6,3]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[1,2,7,4,6,5,3]=>([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[1,2,6,5,4,7,3]=>([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[1,2,7,5,4,6,3]=>([(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,7,5,6,4]=>[1,2,7,5,6,4,3]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[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) [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[1,2,3,5,6,7,4]=>([(3,6),(4,6),(5,6)],7) [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[1,2,3,5,7,6,4]=>([(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[1,2,3,6,5,7,4]=>([(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[1,2,3,7,5,6,4]=>([(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[1,2,3,7,6,5,4]=>([(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[1,2,3,4,6,7,5]=>([(4,6),(5,6)],7) [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[1,2,3,4,7,6,5]=>([(4,5),(4,6),(5,6)],7) [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[1,2,3,4,5,7,6]=>([(5,6)],7) [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[1,2,3,4,5,6,7]=>([],7) [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[1,2,3,4,6,5,7]=>([(5,6)],7) [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[1,2,3,5,4,7,6]=>([(3,6),(4,5)],7) [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[1,2,3,5,4,6,7]=>([(5,6)],7) [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,7,5,6,1]=>[1,2,3,5,6,4,7]=>([(4,6),(5,6)],7) [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[1,2,3,6,5,4,7]=>([(4,5),(4,6),(5,6)],7) [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[1,2,4,3,6,7,5]=>([(2,3),(4,6),(5,6)],7) [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[1,2,4,3,7,6,5]=>([(2,3),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[1,2,4,3,5,7,6]=>([(3,6),(4,5)],7) [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[1,2,4,3,5,6,7]=>([(5,6)],7) [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[1,2,4,3,6,5,7]=>([(3,6),(4,5)],7) [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,6,4,5,1,7]=>[1,2,4,5,3,7,6]=>([(2,3),(4,6),(5,6)],7) [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,6,4,5,7,1]=>[1,2,4,5,3,6,7]=>([(4,6),(5,6)],7) [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,7,4,5,6,1]=>[1,2,4,5,6,3,7]=>([(3,6),(4,6),(5,6)],7) [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,7,4,6,5,1]=>[1,2,4,6,5,3,7]=>([(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[1,2,5,4,3,7,6]=>([(2,3),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[1,2,5,4,3,6,7]=>([(4,5),(4,6),(5,6)],7) [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,7,5,4,6,1]=>[1,2,5,4,6,3,7]=>([(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,7,5,6,4,1]=>[1,2,6,4,5,3,7]=>([(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]=>[2,3,7,6,5,4,1]=>[1,2,6,5,4,3,7]=>([(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]=>[2,4,3,1,5,6,7]=>[1,3,2,5,6,7,4]=>([(1,2),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[1,3,2,5,7,6,4]=>([(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]=>[2,4,3,1,6,5,7]=>[1,3,2,6,5,7,4]=>([(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]=>[2,4,3,1,6,7,5]=>[1,3,2,7,5,6,4]=>([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[1,3,2,7,6,5,4]=>([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[1,3,2,4,6,7,5]=>([(2,3),(4,6),(5,6)],7) [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[1,3,2,4,7,6,5]=>([(2,3),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[1,3,2,4,5,7,6]=>([(3,6),(4,5)],7) [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[1,3,2,4,5,6,7]=>([(5,6)],7) [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[1,3,2,4,6,5,7]=>([(3,6),(4,5)],7) [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[1,3,2,5,4,7,6]=>([(1,6),(2,5),(3,4)],7) [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[1,3,2,5,4,6,7]=>([(3,6),(4,5)],7) [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,7,5,6,1]=>[1,3,2,5,6,4,7]=>([(2,3),(4,6),(5,6)],7) [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[1,3,2,6,5,4,7]=>([(2,3),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,5,3,4,1,6,7]=>[1,3,4,2,6,7,5]=>([(1,6),(2,6),(3,5),(4,5)],7) [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,5,3,4,1,7,6]=>[1,3,4,2,7,6,5]=>([(1,6),(2,6),(3,4),(3,5),(4,5)],7) [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,5,3,4,6,1,7]=>[1,3,4,2,5,7,6]=>([(2,3),(4,6),(5,6)],7) [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,5,3,4,6,7,1]=>[1,3,4,2,5,6,7]=>([(4,6),(5,6)],7) [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,5,3,4,7,6,1]=>[1,3,4,2,6,5,7]=>([(2,3),(4,6),(5,6)],7) [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,6,3,4,5,1,7]=>[1,3,4,5,2,7,6]=>([(1,2),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,6,3,4,5,7,1]=>[1,3,4,5,2,6,7]=>([(3,6),(4,6),(5,6)],7) [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,7,3,4,5,6,1]=>[1,3,4,5,6,2,7]=>([(2,6),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,7,3,4,6,5,1]=>[1,3,4,6,5,2,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,6,3,5,4,1,7]=>[1,3,5,4,2,7,6]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,6,3,5,4,7,1]=>[1,3,5,4,2,6,7]=>([(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,7,3,5,4,6,1]=>[1,3,5,4,6,2,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,7,3,5,6,4,1]=>[1,3,6,4,5,2,7]=>([(2,6),(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]=>[2,7,3,6,5,4,1]=>[1,3,6,5,4,2,7]=>([(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[1,4,3,2,6,7,5]=>([(1,6),(2,6),(3,4),(3,5),(4,5)],7) [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[1,4,3,2,7,6,5]=>([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[1,4,3,2,5,7,6]=>([(2,3),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[1,4,3,2,5,6,7]=>([(4,5),(4,6),(5,6)],7) [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[1,4,3,2,6,5,7]=>([(2,3),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,6,4,3,5,1,7]=>[1,4,3,5,2,7,6]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,6,4,3,5,7,1]=>[1,4,3,5,2,6,7]=>([(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,7,4,3,5,6,1]=>[1,4,3,5,6,2,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,7,4,3,6,5,1]=>[1,4,3,6,5,2,7]=>([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,6,4,5,3,1,7]=>[1,5,3,4,2,7,6]=>([(1,2),(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]=>[2,6,4,5,3,7,1]=>[1,5,3,4,2,6,7]=>([(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]=>[2,7,4,5,3,6,1]=>[1,5,3,4,6,2,7]=>([(2,6),(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]=>[2,7,4,5,6,3,1]=>[1,6,3,4,5,2,7]=>([(2,5),(2,6),(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]=>[2,7,4,6,5,3,1]=>[1,6,3,5,4,2,7]=>([(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]=>[2,6,5,4,3,1,7]=>[1,5,4,3,2,7,6]=>([(1,2),(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]=>[2,6,5,4,3,7,1]=>[1,5,4,3,2,6,7]=>([(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]=>[2,7,5,4,3,6,1]=>[1,5,4,3,6,2,7]=>([(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]=>[2,7,5,4,6,3,1]=>[1,6,4,3,5,2,7]=>([(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]=>[2,7,6,4,5,3,1]=>[1,6,4,5,3,2,7]=>([(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]=>[2,7,6,5,4,3,1]=>[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) [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[2,1,4,5,6,7,3]=>([(0,1),(2,6),(3,6),(4,6),(5,6)],7) [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[2,1,4,5,7,6,3]=>([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[2,1,4,6,5,7,3]=>([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[2,1,4,7,5,6,3]=>([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[2,1,4,7,6,5,3]=>([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[2,1,5,4,6,7,3]=>([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[2,1,5,4,7,6,3]=>([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[2,1,6,4,5,7,3]=>([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[2,1,7,4,5,6,3]=>([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[2,1,7,4,6,5,3]=>([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[2,1,6,5,4,7,3]=>([(0,1),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[2,1,7,5,4,6,3]=>([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,7,5,6,4]=>[2,1,7,5,6,4,3]=>([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[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) [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>[2,1,3,5,6,7,4]=>([(1,2),(3,6),(4,6),(5,6)],7) [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[2,1,3,5,7,6,4]=>([(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]=>[3,2,4,1,6,5,7]=>[2,1,3,6,5,7,4]=>([(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]=>[3,2,4,1,6,7,5]=>[2,1,3,7,5,6,4]=>([(1,2),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[2,1,3,7,6,5,4]=>([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[2,1,3,4,6,7,5]=>([(2,3),(4,6),(5,6)],7) [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[2,1,3,4,7,6,5]=>([(2,3),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[2,1,3,4,5,7,6]=>([(3,6),(4,5)],7) [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[2,1,3,4,5,6,7]=>([(5,6)],7) [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[2,1,3,4,6,5,7]=>([(3,6),(4,5)],7) [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[2,1,3,5,4,7,6]=>([(1,6),(2,5),(3,4)],7) [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[2,1,3,5,4,6,7]=>([(3,6),(4,5)],7) [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,7,5,6,1]=>[2,1,3,5,6,4,7]=>([(2,3),(4,6),(5,6)],7) [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[2,1,3,6,5,4,7]=>([(2,3),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[2,1,4,3,6,7,5]=>([(0,3),(1,2),(4,6),(5,6)],7) [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[2,1,4,3,7,6,5]=>([(0,3),(1,2),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[2,1,4,3,5,7,6]=>([(1,6),(2,5),(3,4)],7) [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[2,1,4,3,5,6,7]=>([(3,6),(4,5)],7) [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[2,1,4,3,6,5,7]=>([(1,6),(2,5),(3,4)],7) [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,6,4,5,1,7]=>[2,1,4,5,3,7,6]=>([(0,3),(1,2),(4,6),(5,6)],7) [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,6,4,5,7,1]=>[2,1,4,5,3,6,7]=>([(2,3),(4,6),(5,6)],7) [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,7,4,5,6,1]=>[2,1,4,5,6,3,7]=>([(1,2),(3,6),(4,6),(5,6)],7) [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,7,4,6,5,1]=>[2,1,4,6,5,3,7]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[2,1,5,4,3,7,6]=>([(0,3),(1,2),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[2,1,5,4,3,6,7]=>([(2,3),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,7,5,4,6,1]=>[2,1,5,4,6,3,7]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,7,5,6,4,1]=>[2,1,6,4,5,3,7]=>([(1,2),(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]=>[3,2,7,6,5,4,1]=>[2,1,6,5,4,3,7]=>([(1,2),(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]=>[4,2,3,1,5,6,7]=>[2,3,1,5,6,7,4]=>([(0,6),(1,6),(2,6),(3,5),(4,5)],7) [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,2,3,1,5,7,6]=>[2,3,1,5,7,6,4]=>([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,2,3,1,6,5,7]=>[2,3,1,6,5,7,4]=>([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,2,3,1,6,7,5]=>[2,3,1,7,5,6,4]=>([(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]=>[4,2,3,1,7,6,5]=>[2,3,1,7,6,5,4]=>([(0,2),(1,2),(3,4),(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]=>[4,2,3,5,1,6,7]=>[2,3,1,4,6,7,5]=>([(1,6),(2,6),(3,5),(4,5)],7) [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,2,3,5,1,7,6]=>[2,3,1,4,7,6,5]=>([(1,6),(2,6),(3,4),(3,5),(4,5)],7) [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,2,3,5,6,1,7]=>[2,3,1,4,5,7,6]=>([(2,3),(4,6),(5,6)],7) [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,2,3,5,6,7,1]=>[2,3,1,4,5,6,7]=>([(4,6),(5,6)],7) [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,2,3,5,7,6,1]=>[2,3,1,4,6,5,7]=>([(2,3),(4,6),(5,6)],7) [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,2,3,6,5,1,7]=>[2,3,1,5,4,7,6]=>([(0,3),(1,2),(4,6),(5,6)],7) [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[4,2,3,6,5,7,1]=>[2,3,1,5,4,6,7]=>([(2,3),(4,6),(5,6)],7) [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,2,3,7,5,6,1]=>[2,3,1,5,6,4,7]=>([(1,6),(2,6),(3,5),(4,5)],7) [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,2,3,7,6,5,1]=>[2,3,1,6,5,4,7]=>([(1,6),(2,6),(3,4),(3,5),(4,5)],7) [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[5,2,3,4,1,6,7]=>[2,3,4,1,6,7,5]=>([(0,6),(1,6),(2,6),(3,5),(4,5)],7) [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[5,2,3,4,1,7,6]=>[2,3,4,1,7,6,5]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[5,2,3,4,6,1,7]=>[2,3,4,1,5,7,6]=>([(1,2),(3,6),(4,6),(5,6)],7) [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[5,2,3,4,6,7,1]=>[2,3,4,1,5,6,7]=>([(3,6),(4,6),(5,6)],7) [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,2,3,4,7,6,1]=>[2,3,4,1,6,5,7]=>([(1,2),(3,6),(4,6),(5,6)],7) [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[6,2,3,4,5,1,7]=>[2,3,4,5,1,7,6]=>([(0,1),(2,6),(3,6),(4,6),(5,6)],7) [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>[2,3,4,5,1,6,7]=>([(2,6),(3,6),(4,6),(5,6)],7) [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,2,3,4,5,6,1]=>[2,3,4,5,6,1,7]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7) [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[7,2,3,4,6,5,1]=>[2,3,4,6,5,1,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,5,4,1,7]=>[2,3,5,4,1,7,6]=>([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,2,3,5,4,7,1]=>[2,3,5,4,1,6,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[7,2,3,5,4,6,1]=>[2,3,5,4,6,1,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[7,2,3,5,6,4,1]=>[2,3,6,4,5,1,7]=>([(1,6),(2,6),(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]=>[7,2,3,6,5,4,1]=>[2,3,6,5,4,1,7]=>([(1,6),(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]=>[5,2,4,3,1,6,7]=>[2,4,3,1,6,7,5]=>([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[5,2,4,3,1,7,6]=>[2,4,3,1,7,6,5]=>([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[5,2,4,3,6,1,7]=>[2,4,3,1,5,7,6]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[5,2,4,3,6,7,1]=>[2,4,3,1,5,6,7]=>([(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,2,4,3,7,6,1]=>[2,4,3,1,6,5,7]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[6,2,4,3,5,1,7]=>[2,4,3,5,1,7,6]=>([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,2,4,3,5,7,1]=>[2,4,3,5,1,6,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[7,2,4,3,5,6,1]=>[2,4,3,5,6,1,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[7,2,4,3,6,5,1]=>[2,4,3,6,5,1,7]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[6,2,4,5,3,1,7]=>[2,5,3,4,1,7,6]=>([(0,1),(2,6),(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]=>[6,2,4,5,3,7,1]=>[2,5,3,4,1,6,7]=>([(2,6),(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]=>[7,2,4,5,3,6,1]=>[2,5,3,4,6,1,7]=>([(1,6),(2,6),(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]=>[7,2,4,5,6,3,1]=>[2,6,3,4,5,1,7]=>([(1,6),(2,5),(2,6),(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]=>[7,2,4,6,5,3,1]=>[2,6,3,5,4,1,7]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[6,2,5,4,3,1,7]=>[2,5,4,3,1,7,6]=>([(0,1),(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]=>[6,2,5,4,3,7,1]=>[2,5,4,3,1,6,7]=>([(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]=>[7,2,5,4,3,6,1]=>[2,5,4,3,6,1,7]=>([(1,6),(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]=>[7,2,5,4,6,3,1]=>[2,6,4,3,5,1,7]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[7,2,6,4,5,3,1]=>[2,6,4,5,3,1,7]=>([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[7,2,6,5,4,3,1]=>[2,6,5,4,3,1,7]=>([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[3,2,1,5,6,7,4]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(4,5)],7) [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[3,2,1,5,7,6,4]=>([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[3,2,1,6,5,7,4]=>([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[3,2,1,7,5,6,4]=>([(0,1),(0,2),(1,2),(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]=>[4,3,2,1,7,6,5]=>[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) [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>[3,2,1,4,6,7,5]=>([(1,6),(2,6),(3,4),(3,5),(4,5)],7) [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[3,2,1,4,7,6,5]=>([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[3,2,1,4,5,7,6]=>([(2,3),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[3,2,1,4,5,6,7]=>([(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[3,2,1,4,6,5,7]=>([(2,3),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[3,2,1,5,4,7,6]=>([(0,3),(1,2),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[3,2,1,5,4,6,7]=>([(2,3),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,7,5,6,1]=>[3,2,1,5,6,4,7]=>([(1,6),(2,6),(3,4),(3,5),(4,5)],7) [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[3,2,1,6,5,4,7]=>([(1,5),(1,6),(2,3),(2,4),(3,4),(5,6)],7) [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[5,3,2,4,1,6,7]=>[3,2,4,1,6,7,5]=>([(0,6),(1,3),(2,3),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,3,2,4,1,7,6]=>[3,2,4,1,7,6,5]=>([(0,6),(1,2),(1,3),(2,3),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[5,3,2,4,6,1,7]=>[3,2,4,1,5,7,6]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[5,3,2,4,6,7,1]=>[3,2,4,1,5,6,7]=>([(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,3,2,4,7,6,1]=>[3,2,4,1,6,5,7]=>([(1,2),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1,7]=>[3,2,4,5,1,7,6]=>([(0,1),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>[3,2,4,5,1,6,7]=>([(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[7,3,2,4,5,6,1]=>[3,2,4,5,6,1,7]=>([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[7,3,2,4,6,5,1]=>[3,2,4,6,5,1,7]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[6,3,2,5,4,1,7]=>[3,2,5,4,1,7,6]=>([(0,1),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,2,5,4,7,1]=>[3,2,5,4,1,6,7]=>([(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[7,3,2,5,4,6,1]=>[3,2,5,4,6,1,7]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,6),(5,6)],7) [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[7,3,2,5,6,4,1]=>[3,2,6,4,5,1,7]=>([(1,2),(1,6),(2,6),(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]=>[7,3,2,6,5,4,1]=>[3,2,6,5,4,1,7]=>([(1,2),(1,6),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,3,4,2,1,6,7]=>[4,2,3,1,6,7,5]=>([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(5,6)],7) [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,3,4,2,1,7,6]=>[4,2,3,1,7,6,5]=>([(0,1),(0,2),(1,2),(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]=>[5,3,4,2,6,1,7]=>[4,2,3,1,5,7,6]=>([(1,2),(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]=>[5,3,4,2,6,7,1]=>[4,2,3,1,5,6,7]=>([(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]=>[5,3,4,2,7,6,1]=>[4,2,3,1,6,5,7]=>([(1,2),(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]=>[6,3,4,2,5,1,7]=>[4,2,3,5,1,7,6]=>([(0,1),(2,6),(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]=>[6,3,4,2,5,7,1]=>[4,2,3,5,1,6,7]=>([(2,6),(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]=>[7,3,4,2,5,6,1]=>[4,2,3,5,6,1,7]=>([(1,6),(2,6),(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]=>[7,3,4,2,6,5,1]=>[4,2,3,6,5,1,7]=>([(1,2),(1,6),(2,6),(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]=>[6,3,4,5,2,1,7]=>[5,2,3,4,1,7,6]=>([(0,1),(2,5),(2,6),(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]=>[6,3,4,5,2,7,1]=>[5,2,3,4,1,6,7]=>([(2,5),(2,6),(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]=>[7,3,4,5,2,6,1]=>[5,2,3,4,6,1,7]=>([(1,6),(2,5),(2,6),(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]=>[7,3,4,5,6,2,1]=>[6,2,3,4,5,1,7]=>([(1,5),(1,6),(2,5),(2,6),(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]=>[7,3,4,6,5,2,1]=>[6,2,3,5,4,1,7]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[6,3,5,4,2,1,7]=>[5,2,4,3,1,7,6]=>([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,3,5,4,2,7,1]=>[5,2,4,3,1,6,7]=>([(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]=>[7,3,5,4,2,6,1]=>[5,2,4,3,6,1,7]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[7,3,5,4,6,2,1]=>[6,2,4,3,5,1,7]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[7,3,6,4,5,2,1]=>[6,2,4,5,3,1,7]=>([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[7,3,6,5,4,2,1]=>[6,2,5,4,3,1,7]=>([(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) [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[4,3,2,1,6,7,5]=>([(0,2),(1,2),(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]=>[5,4,3,2,1,7,6]=>[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) [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[4,3,2,1,5,7,6]=>([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[4,3,2,1,5,6,7]=>([(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]=>[5,4,3,2,7,6,1]=>[4,3,2,1,6,5,7]=>([(1,2),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,4,3,2,5,1,7]=>[4,3,2,5,1,7,6]=>([(0,1),(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]=>[6,4,3,2,5,7,1]=>[4,3,2,5,1,6,7]=>([(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]=>[7,4,3,2,5,6,1]=>[4,3,2,5,6,1,7]=>([(1,6),(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]=>[7,4,3,2,6,5,1]=>[4,3,2,6,5,1,7]=>([(1,2),(1,6),(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]=>[6,4,3,5,2,1,7]=>[5,3,2,4,1,7,6]=>([(0,1),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>[5,3,2,4,1,6,7]=>([(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]=>[7,4,3,5,2,6,1]=>[5,3,2,4,6,1,7]=>([(1,6),(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]=>[7,4,3,5,6,2,1]=>[6,3,2,4,5,1,7]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[7,4,3,6,5,2,1]=>[6,3,2,5,4,1,7]=>([(1,4),(1,5),(1,6),(2,3),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,5,3,4,2,1,7]=>[5,3,4,2,1,7,6]=>([(0,1),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,5,3,4,2,7,1]=>[5,3,4,2,1,6,7]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[7,5,3,4,2,6,1]=>[5,3,4,2,6,1,7]=>([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[7,5,3,4,6,2,1]=>[6,3,4,2,5,1,7]=>([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[7,6,3,4,5,2,1]=>[6,3,4,5,2,1,7]=>([(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) [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[7,6,3,5,4,2,1]=>[6,3,5,4,2,1,7]=>([(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) [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[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) [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[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) [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[7,5,4,3,2,6,1]=>[5,4,3,2,6,1,7]=>([(1,6),(2,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(4,5),(4,6),(5,6)],7) [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[7,5,4,3,6,2,1]=>[6,4,3,2,5,1,7]=>([(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) [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[7,6,4,3,5,2,1]=>[6,4,3,5,2,1,7]=>([(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) [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[7,6,4,5,3,2,1]=>[6,5,3,4,2,1,7]=>([(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) [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[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) [1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,8,7,2]=>[8,3,2,5,4,7,6,1]=>([(0,5),(0,6),(0,7),(1,4),(1,6),(1,7),(2,3),(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) [1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,3,8,7,6,5,2]=>[8,3,2,7,6,5,4,1]=>([(0,1),(0,6),(0,7),(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) [1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,5,4,3,8,7,2]=>[8,5,4,3,2,7,6,1]=>([(0,1),(0,6),(0,7),(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) [1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,8,5,4,7,6,3,2]=>[8,7,4,3,6,5,2,1]=>([(0,3),(0,4),(0,5),(0,6),(0,7),(1,2),(1,4),(1,5),(1,6),(1,7),(2,4),(2,5),(2,6),(2,7),(3,4),(3,5),(3,6),(3,7),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8,7,6,5,4,3,2]=>[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) [1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,1]=>[1,2,3,4,5,6,7,8]=>([],8) [1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,2,1,6,5,8,7,4]=>[2,1,8,5,4,7,6,3]=>([(0,1),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) [1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,2,1,8,7,6,5,4]=>[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) [1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,5,4,1,8,7,6]=>[2,1,4,3,8,7,6,5]=>([(0,3),(1,2),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) [1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,7,6,1,8]=>[2,1,4,3,6,5,8,7]=>([(0,7),(1,6),(2,5),(3,4)],8) [1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,2,7,6,5,4,1,8]=>[2,1,6,5,4,3,8,7]=>([(0,3),(1,2),(4,5),(4,6),(4,7),(5,6),(5,7),(6,7)],8) [1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,4,3,2,1,8,7,6]=>[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) [1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[5,4,3,2,7,6,1,8]=>[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) [1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[7,4,3,6,5,2,1,8]=>[6,3,2,5,4,1,8,7]=>([(0,1),(2,5),(2,6),(2,7),(3,4),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8) [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,6,5,4,3,2,1,8]=>[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)
Map
to non-crossing permutation
Description
Sends a Dyck path $D$ with valley at positions $\{(i_1,j_1),\ldots,(i_k,j_k)\}$ to the unique non-crossing permutation $\pi$ having descents $\{i_1,\ldots,i_k\}$ and whose inverse has descents $\{j_1,\ldots,j_k\}$.
It sends the area St000012The area of a Dyck path. to the number of inversions St000018The number of inversions of a permutation. and the major index St000027The major index of a Dyck path. to $n(n-1)$ minus the sum of the major index St000004The major index of a permutation. and the inverse major index St000305The inverse major index of a permutation..
Map
Inverse Kreweras complement
Description
Sends the permutation $\pi \in \mathfrak{S}_n$ to the permutation $c\pi^{-1}$ where $c = (1,\ldots,n)$ is the long cycle.
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.