Identifier
Mp00031: Dyck paths to 312-avoiding permutationPermutations
Mp00067: Permutations Foata bijectionPermutations
Mp00065: Permutations permutation poset Posets
Images
=>
Cc0005;cc-rep-0Cc0014;cc-rep-3
[1,0]=>[1]=>[1]=>([],1) [1,0,1,0]=>[1,2]=>[1,2]=>([(0,1)],2) [1,1,0,0]=>[2,1]=>[2,1]=>([],2) [1,0,1,0,1,0]=>[1,2,3]=>[1,2,3]=>([(0,2),(2,1)],3) [1,0,1,1,0,0]=>[1,3,2]=>[3,1,2]=>([(1,2)],3) [1,1,0,0,1,0]=>[2,1,3]=>[2,1,3]=>([(0,2),(1,2)],3) [1,1,0,1,0,0]=>[2,3,1]=>[2,3,1]=>([(1,2)],3) [1,1,1,0,0,0]=>[3,2,1]=>[3,2,1]=>([],3) [1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4) [1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[4,1,2,3]=>([(1,2),(2,3)],4) [1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[3,1,2,4]=>([(0,3),(1,2),(2,3)],4) [1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[3,1,4,2]=>([(0,3),(1,2),(1,3)],4) [1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[4,3,1,2]=>([(2,3)],4) [1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[2,1,3,4]=>([(0,3),(1,3),(3,2)],4) [1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[4,2,1,3]=>([(1,3),(2,3)],4) [1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[2,3,1,4]=>([(0,3),(1,2),(2,3)],4) [1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[2,3,4,1]=>([(1,2),(2,3)],4) [1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[4,2,3,1]=>([(2,3)],4) [1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[3,2,1,4]=>([(0,3),(1,3),(2,3)],4) [1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[3,2,4,1]=>([(1,3),(2,3)],4) [1,1,1,0,1,0,0,0]=>[3,4,2,1]=>[3,4,2,1]=>([(2,3)],4) [1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[4,3,2,1]=>([],4) [1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[5,1,2,3,4]=>([(1,4),(3,2),(4,3)],5) [1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[4,1,2,3,5]=>([(0,4),(1,2),(2,3),(3,4)],5) [1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[4,1,2,5,3]=>([(0,4),(1,2),(2,3),(2,4)],5) [1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[5,4,1,2,3]=>([(2,3),(3,4)],5) [1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[3,1,2,4,5]=>([(0,4),(1,2),(2,4),(4,3)],5) [1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[5,3,1,2,4]=>([(1,4),(2,3),(3,4)],5) [1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[3,1,4,2,5]=>([(0,3),(1,2),(1,3),(2,4),(3,4)],5) [1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[3,1,4,5,2]=>([(0,4),(1,2),(1,4),(4,3)],5) [1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[5,3,1,4,2]=>([(1,4),(2,3),(2,4)],5) [1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[4,3,1,2,5]=>([(0,4),(1,4),(2,3),(3,4)],5) [1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[4,3,1,5,2]=>([(0,4),(1,4),(2,3),(2,4)],5) [1,0,1,1,1,0,1,0,0,0]=>[1,4,5,3,2]=>[4,5,1,3,2]=>([(0,4),(1,2),(1,3)],5) [1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[5,4,3,1,2]=>([(3,4)],5) [1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(0,4),(1,4),(2,3),(4,2)],5) [1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[5,2,1,3,4]=>([(1,4),(2,4),(4,3)],5) [1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[4,2,1,3,5]=>([(0,4),(1,3),(2,3),(3,4)],5) [1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[4,2,1,5,3]=>([(0,4),(1,3),(1,4),(2,3),(2,4)],5) [1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[5,4,2,1,3]=>([(2,4),(3,4)],5) [1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[2,3,1,4,5]=>([(0,4),(1,2),(2,4),(4,3)],5) [1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[5,2,3,1,4]=>([(1,4),(2,3),(3,4)],5) [1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[2,3,4,1,5]=>([(0,4),(1,2),(2,3),(3,4)],5) [1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[2,3,4,5,1]=>([(1,4),(3,2),(4,3)],5) [1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[5,2,3,4,1]=>([(2,3),(3,4)],5) [1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[4,2,3,1,5]=>([(0,4),(1,4),(2,3),(3,4)],5) [1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[4,2,3,5,1]=>([(1,4),(2,3),(3,4)],5) [1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>[4,2,5,3,1]=>([(1,4),(2,3),(2,4)],5) [1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[5,4,2,3,1]=>([(3,4)],5) [1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[3,2,1,4,5]=>([(0,4),(1,4),(2,4),(4,3)],5) [1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[5,3,2,1,4]=>([(1,4),(2,4),(3,4)],5) [1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[3,2,4,1,5]=>([(0,4),(1,3),(2,3),(3,4)],5) [1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[3,2,4,5,1]=>([(1,4),(2,4),(4,3)],5) [1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[5,3,2,4,1]=>([(2,4),(3,4)],5) [1,1,1,0,1,0,0,0,1,0]=>[3,4,2,1,5]=>[3,4,2,1,5]=>([(0,4),(1,4),(2,3),(3,4)],5) [1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>[3,4,2,5,1]=>([(1,4),(2,3),(3,4)],5) [1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>[3,4,5,2,1]=>([(2,3),(3,4)],5) [1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>[5,3,4,2,1]=>([(3,4)],5) [1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[4,3,2,1,5]=>([(0,4),(1,4),(2,4),(3,4)],5) [1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[4,3,2,5,1]=>([(1,4),(2,4),(3,4)],5) [1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>[4,3,5,2,1]=>([(2,4),(3,4)],5) [1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>[4,5,3,2,1]=>([(3,4)],5) [1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[5,4,3,2,1]=>([],5) [1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[6,1,2,3,4,5]=>([(1,5),(3,4),(4,2),(5,3)],6) [1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[5,1,2,3,4,6]=>([(0,5),(1,4),(2,5),(3,2),(4,3)],6) [1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[5,1,2,3,6,4]=>([(0,5),(1,3),(3,4),(4,2),(4,5)],6) [1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[6,5,1,2,3,4]=>([(2,3),(3,5),(5,4)],6) [1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[4,1,2,3,5,6]=>([(0,5),(1,4),(2,5),(4,2),(5,3)],6) [1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[6,4,1,2,3,5]=>([(1,5),(2,3),(3,4),(4,5)],6) [1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[4,1,2,5,3,6]=>([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6) [1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[4,1,2,5,6,3]=>([(0,5),(1,4),(4,2),(4,5),(5,3)],6) [1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[6,4,1,2,5,3]=>([(1,5),(2,3),(3,4),(3,5)],6) [1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[5,4,1,2,3,6]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[5,4,1,2,6,3]=>([(0,5),(1,5),(2,3),(3,4),(3,5)],6) [1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,4,3]=>[5,6,1,2,4,3]=>([(0,4),(1,5),(5,2),(5,3)],6) [1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[6,5,4,1,2,3]=>([(3,4),(4,5)],6) [1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[3,1,2,4,5,6]=>([(0,5),(1,3),(3,5),(4,2),(5,4)],6) [1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[6,3,1,2,4,5]=>([(1,5),(2,3),(3,5),(5,4)],6) [1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[5,3,1,2,4,6]=>([(0,5),(1,4),(2,3),(3,5),(5,4)],6) [1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[5,3,1,2,6,4]=>([(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) [1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[6,5,3,1,2,4]=>([(2,5),(3,4),(4,5)],6) [1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[3,1,4,2,5,6]=>([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) [1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[6,3,1,4,2,5]=>([(1,4),(2,3),(2,4),(3,5),(4,5)],6) [1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[3,1,4,5,2,6]=>([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6) [1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[3,1,4,5,6,2]=>([(0,5),(1,3),(1,5),(4,2),(5,4)],6) [1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[6,3,1,4,5,2]=>([(1,5),(2,3),(2,5),(5,4)],6) [1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[5,3,1,4,2,6]=>([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) [1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[5,3,1,4,6,2]=>([(0,5),(1,4),(2,3),(2,4),(4,5)],6) [1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,4,2]=>[5,3,1,6,4,2]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) [1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[6,5,3,1,4,2]=>([(2,5),(3,4),(3,5)],6) [1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[4,3,1,2,5,6]=>([(0,5),(1,5),(2,3),(3,5),(5,4)],6) [1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[6,4,3,1,2,5]=>([(1,5),(2,5),(3,4),(4,5)],6) [1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[4,3,1,5,2,6]=>([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6) [1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[4,3,1,5,6,2]=>([(0,5),(1,5),(2,3),(2,5),(5,4)],6) [1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[6,4,3,1,5,2]=>([(1,5),(2,5),(3,4),(3,5)],6) [1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,3,2,6]=>[4,5,1,3,2,6]=>([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) [1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,3,6,2]=>[4,5,1,3,6,2]=>([(0,4),(1,2),(1,3),(3,5),(4,5)],6) [1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,3,2]=>[4,5,1,6,3,2]=>([(0,4),(1,2),(1,3),(1,5),(4,5)],6) [1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,5,3,2]=>[6,4,5,1,3,2]=>([(1,5),(2,3),(2,4)],6) [1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[5,4,3,1,2,6]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6) [1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[5,4,3,1,6,2]=>([(0,5),(1,5),(2,5),(3,4),(3,5)],6) [1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,4,6,3,2]=>[5,4,6,1,3,2]=>([(0,5),(1,5),(2,3),(2,4)],6) [1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,4,3,2]=>[5,6,4,1,3,2]=>([(1,5),(2,3),(2,4)],6) [1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[6,5,4,3,1,2]=>([(4,5)],6) [1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(0,5),(1,5),(3,2),(4,3),(5,4)],6) [1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[6,2,1,3,4,5]=>([(1,5),(2,5),(3,4),(5,3)],6) [1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[5,2,1,3,4,6]=>([(0,5),(1,4),(2,4),(3,5),(4,3)],6) [1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[5,2,1,3,6,4]=>([(0,5),(1,5),(2,4),(5,3),(5,4)],6) [1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[6,5,2,1,3,4]=>([(2,5),(3,5),(5,4)],6) [1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[4,2,1,3,5,6]=>([(0,5),(1,4),(2,4),(4,5),(5,3)],6) [1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[6,4,2,1,3,5]=>([(1,5),(2,4),(3,4),(4,5)],6) [1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[4,2,1,5,3,6]=>([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6) [1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[4,2,1,5,6,3]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6) [1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[6,4,2,1,5,3]=>([(1,5),(2,4),(2,5),(3,4),(3,5)],6) [1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[5,4,2,1,3,6]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6) [1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[5,4,2,1,6,3]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6) [1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,4,3]=>[5,6,2,1,4,3]=>([(0,4),(0,5),(1,4),(1,5),(2,3)],6) [1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[6,5,4,2,1,3]=>([(3,5),(4,5)],6) [1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[2,3,1,4,5,6]=>([(0,5),(1,3),(3,5),(4,2),(5,4)],6) [1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[6,2,3,1,4,5]=>([(1,5),(2,3),(3,5),(5,4)],6) [1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[5,2,3,1,4,6]=>([(0,5),(1,4),(2,3),(3,5),(5,4)],6) [1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[5,2,3,1,6,4]=>([(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) [1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[6,5,2,3,1,4]=>([(2,5),(3,4),(4,5)],6) [1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[2,3,4,1,5,6]=>([(0,5),(1,4),(2,5),(4,2),(5,3)],6) [1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[6,2,3,4,1,5]=>([(1,5),(2,3),(3,4),(4,5)],6) [1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[2,3,4,5,1,6]=>([(0,5),(1,4),(2,5),(3,2),(4,3)],6) [1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[2,3,4,5,6,1]=>([(1,5),(3,4),(4,2),(5,3)],6) [1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[6,2,3,4,5,1]=>([(2,3),(3,5),(5,4)],6) [1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[5,2,3,4,1,6]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[5,2,3,4,6,1]=>([(1,5),(2,3),(3,4),(4,5)],6) [1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>[5,2,3,6,4,1]=>([(1,5),(2,3),(3,4),(3,5)],6) [1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[6,5,2,3,4,1]=>([(3,4),(4,5)],6) [1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[4,2,3,1,5,6]=>([(0,5),(1,5),(2,3),(3,5),(5,4)],6) [1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[6,4,2,3,1,5]=>([(1,5),(2,5),(3,4),(4,5)],6) [1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[4,2,3,5,1,6]=>([(0,5),(1,4),(2,3),(3,5),(5,4)],6) [1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[4,2,3,5,6,1]=>([(1,5),(2,3),(3,5),(5,4)],6) [1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[6,4,2,3,5,1]=>([(2,5),(3,4),(4,5)],6) [1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,3,1,6]=>[4,2,5,3,1,6]=>([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) [1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>[4,2,5,3,6,1]=>([(1,4),(2,3),(2,4),(3,5),(4,5)],6) [1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>[4,2,5,6,3,1]=>([(1,5),(2,3),(2,5),(5,4)],6) [1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>[6,4,2,5,3,1]=>([(2,5),(3,4),(3,5)],6) [1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[5,4,2,3,1,6]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6) [1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[5,4,2,3,6,1]=>([(1,5),(2,5),(3,4),(4,5)],6) [1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>[5,4,2,6,3,1]=>([(1,5),(2,5),(3,4),(3,5)],6) [1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>[5,6,2,4,3,1]=>([(1,5),(2,3),(2,4)],6) [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[6,5,4,2,3,1]=>([(4,5)],6) [1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>([(0,5),(1,5),(2,5),(3,4),(5,3)],6) [1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[6,3,2,1,4,5]=>([(1,5),(2,5),(3,5),(5,4)],6) [1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[5,3,2,1,4,6]=>([(0,5),(1,5),(2,5),(3,4),(5,4)],6) [1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[5,3,2,1,6,4]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) [1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[6,5,3,2,1,4]=>([(2,5),(3,5),(4,5)],6) [1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[3,2,4,1,5,6]=>([(0,5),(1,4),(2,4),(4,5),(5,3)],6) [1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[6,3,2,4,1,5]=>([(1,5),(2,4),(3,4),(4,5)],6) [1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[3,2,4,5,1,6]=>([(0,5),(1,4),(2,4),(3,5),(4,3)],6) [1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[3,2,4,5,6,1]=>([(1,5),(2,5),(3,4),(5,3)],6) [1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[6,3,2,4,5,1]=>([(2,5),(3,5),(5,4)],6) [1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[5,3,2,4,1,6]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6) [1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[5,3,2,4,6,1]=>([(1,5),(2,4),(3,4),(4,5)],6) [1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>[5,3,2,6,4,1]=>([(1,5),(2,4),(2,5),(3,4),(3,5)],6) [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[6,5,3,2,4,1]=>([(3,5),(4,5)],6) [1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,2,1,5,6]=>[3,4,2,1,5,6]=>([(0,5),(1,5),(2,3),(3,5),(5,4)],6) [1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2,1,6,5]=>[6,3,4,2,1,5]=>([(1,5),(2,5),(3,4),(4,5)],6) [1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,2,5,1,6]=>[3,4,2,5,1,6]=>([(0,5),(1,4),(2,3),(3,5),(5,4)],6) [1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>[3,4,2,5,6,1]=>([(1,5),(2,3),(3,5),(5,4)],6) [1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>[6,3,4,2,5,1]=>([(2,5),(3,4),(4,5)],6) [1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,2,1,6]=>[3,4,5,2,1,6]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>[3,4,5,2,6,1]=>([(1,5),(2,3),(3,4),(4,5)],6) [1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>[3,4,5,6,2,1]=>([(2,3),(3,5),(5,4)],6) [1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>[6,3,4,5,2,1]=>([(3,4),(4,5)],6) [1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,4,2,1,6]=>[5,3,4,2,1,6]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6) [1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>[5,3,4,2,6,1]=>([(1,5),(2,5),(3,4),(4,5)],6) [1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>[5,3,4,6,2,1]=>([(2,5),(3,4),(4,5)],6) [1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>[5,3,6,4,2,1]=>([(2,5),(3,4),(3,5)],6) [1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]=>[6,5,3,4,2,1]=>([(4,5)],6) [1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>([(0,5),(1,5),(2,5),(3,5),(5,4)],6) [1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[6,4,3,2,1,5]=>([(1,5),(2,5),(3,5),(4,5)],6) [1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[4,3,2,5,1,6]=>([(0,5),(1,5),(2,5),(3,4),(5,4)],6) [1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[4,3,2,5,6,1]=>([(1,5),(2,5),(3,5),(5,4)],6) [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[6,4,3,2,5,1]=>([(2,5),(3,5),(4,5)],6) [1,1,1,1,0,0,1,0,0,0,1,0]=>[4,3,5,2,1,6]=>[4,3,5,2,1,6]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6) [1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>[4,3,5,2,6,1]=>([(1,5),(2,4),(3,4),(4,5)],6) [1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[4,3,5,6,2,1]=>([(2,5),(3,5),(5,4)],6) [1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>[6,4,3,5,2,1]=>([(3,5),(4,5)],6) [1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,3,2,1,6]=>[4,5,3,2,1,6]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6) [1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>[4,5,3,2,6,1]=>([(1,5),(2,5),(3,4),(4,5)],6) [1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>[4,5,3,6,2,1]=>([(2,5),(3,4),(4,5)],6) [1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>[4,5,6,3,2,1]=>([(3,4),(4,5)],6) [1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>[6,4,5,3,2,1]=>([(4,5)],6) [1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6) [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[5,4,3,2,6,1]=>([(1,5),(2,5),(3,5),(4,5)],6) [1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>[5,4,3,6,2,1]=>([(2,5),(3,5),(4,5)],6) [1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>[5,4,6,3,2,1]=>([(3,5),(4,5)],6) [1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>[5,6,4,3,2,1]=>([(4,5)],6) [1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>([],6) [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[7,1,2,3,4,5,6]=>([(1,6),(3,5),(4,3),(5,2),(6,4)],7) [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[6,1,2,3,4,5,7]=>([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[6,1,2,3,4,7,5]=>([(0,6),(1,4),(3,5),(4,3),(5,2),(5,6)],7) [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[7,6,1,2,3,4,5]=>([(2,6),(4,5),(5,3),(6,4)],7) [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[5,1,2,3,4,6,7]=>([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[7,5,1,2,3,4,6]=>([(1,3),(2,6),(3,5),(4,6),(5,4)],7) [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[5,1,2,3,6,4,7]=>([(0,6),(1,4),(2,5),(3,2),(3,6),(4,3),(6,5)],7) [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[5,1,2,3,6,7,4]=>([(0,6),(1,4),(4,5),(5,2),(5,6),(6,3)],7) [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[7,5,1,2,3,6,4]=>([(1,3),(2,6),(3,5),(5,4),(5,6)],7) [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[6,5,1,2,3,4,7]=>([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[6,5,1,2,3,7,4]=>([(0,3),(1,6),(2,6),(3,5),(5,4),(5,6)],7) [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,5,4]=>[6,7,1,2,3,5,4]=>([(0,4),(1,5),(5,6),(6,2),(6,3)],7) [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]=>([(3,4),(4,6),(6,5)],7) [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[4,1,2,3,5,6,7]=>([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[7,4,1,2,3,5,6]=>([(1,6),(2,3),(3,5),(5,6),(6,4)],7) [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[6,4,1,2,3,5,7]=>([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[6,4,1,2,3,7,5]=>([(0,6),(1,5),(1,6),(2,3),(3,4),(4,5),(4,6)],7) [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[7,6,4,1,2,3,5]=>([(2,6),(3,4),(4,5),(5,6)],7) [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[4,1,2,5,3,6,7]=>([(0,5),(1,4),(3,6),(4,3),(4,5),(5,6),(6,2)],7) [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[7,4,1,2,5,3,6]=>([(1,6),(2,3),(3,4),(3,6),(4,5),(6,5)],7) [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[4,1,2,5,6,3,7]=>([(0,6),(1,4),(2,5),(3,5),(4,3),(4,6),(6,2)],7) [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[4,1,2,5,6,7,3]=>([(0,6),(1,4),(4,3),(4,6),(5,2),(6,5)],7) [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[7,4,1,2,5,6,3]=>([(1,6),(2,3),(3,5),(3,6),(6,4)],7) [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[6,4,1,2,5,3,7]=>([(0,6),(1,5),(2,3),(3,4),(3,5),(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]=>[6,4,1,2,5,7,3]=>([(0,6),(1,5),(2,3),(3,4),(3,6),(6,5)],7) [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,5,3]=>[6,4,1,2,7,5,3]=>([(0,6),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7) [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[7,6,4,1,2,5,3]=>([(2,6),(3,4),(4,5),(4,6)],7) [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[5,4,1,2,3,6,7]=>([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[7,5,4,1,2,3,6]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7) [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[5,4,1,2,6,3,7]=>([(0,6),(1,6),(2,3),(3,4),(3,6),(4,5),(6,5)],7) [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[5,4,1,2,6,7,3]=>([(0,6),(1,6),(2,3),(3,5),(3,6),(6,4)],7) [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[7,5,4,1,2,6,3]=>([(1,6),(2,6),(3,4),(4,5),(4,6)],7) [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,4,3,7]=>[5,6,1,2,4,3,7]=>([(0,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7) [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,4,7,3]=>[5,6,1,2,4,7,3]=>([(0,4),(1,5),(3,6),(4,6),(5,2),(5,3)],7) [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,4,3]=>[5,6,1,2,7,4,3]=>([(0,4),(1,5),(4,6),(5,2),(5,3),(5,6)],7) [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,6,4,3]=>[7,5,6,1,2,4,3]=>([(1,5),(2,6),(6,3),(6,4)],7) [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[6,5,4,1,2,3,7]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[6,5,4,1,2,7,3]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(4,6)],7) [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,5,7,4,3]=>[6,5,7,1,2,4,3]=>([(0,3),(1,6),(2,6),(3,4),(3,5)],7) [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,5,4,3]=>[6,7,5,1,2,4,3]=>([(1,5),(2,6),(6,3),(6,4)],7) [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]=>([(4,5),(5,6)],7) [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[7,3,1,2,4,5,6]=>([(1,6),(2,3),(3,6),(4,5),(6,4)],7) [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[6,3,1,2,4,5,7]=>([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[6,3,1,2,4,7,5]=>([(0,6),(1,5),(2,3),(3,6),(6,4),(6,5)],7) [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[7,6,3,1,2,4,5]=>([(2,6),(3,4),(4,6),(6,5)],7) [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[5,3,1,2,4,6,7]=>([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[7,5,3,1,2,4,6]=>([(1,6),(2,5),(3,4),(4,6),(6,5)],7) [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[5,3,1,2,6,4,7]=>([(0,6),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7) [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[5,3,1,2,6,7,4]=>([(0,6),(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7) [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[7,5,3,1,2,6,4]=>([(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[6,5,3,1,2,4,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[6,5,3,1,2,7,4]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,5,4]=>[6,7,3,1,2,5,4]=>([(0,5),(0,6),(1,3),(2,4),(4,5),(4,6)],7) [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[7,6,5,3,1,2,4]=>([(3,6),(4,5),(5,6)],7) [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[3,1,4,2,5,6,7]=>([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7) [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[7,3,1,4,2,5,6]=>([(1,5),(2,3),(2,5),(3,6),(5,6),(6,4)],7) [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[6,3,1,4,2,5,7]=>([(0,4),(1,5),(2,3),(2,4),(3,6),(4,6),(6,5)],7) [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[6,3,1,4,2,7,5]=>([(0,6),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[7,6,3,1,4,2,5]=>([(2,5),(3,4),(3,5),(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]=>[3,1,4,5,2,6,7]=>([(0,6),(1,3),(1,6),(2,5),(3,5),(5,4),(6,2)],7) [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[7,3,1,4,5,2,6]=>([(1,5),(2,3),(2,5),(3,6),(4,6),(5,4)],7) [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[3,1,4,5,6,2,7]=>([(0,6),(1,3),(1,6),(2,5),(3,5),(4,2),(6,4)],7) [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[3,1,4,5,6,7,2]=>([(0,6),(1,3),(1,6),(4,2),(5,4),(6,5)],7) [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[7,3,1,4,5,6,2]=>([(1,6),(2,3),(2,6),(4,5),(6,4)],7) [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[6,3,1,4,5,2,7]=>([(0,6),(1,5),(2,3),(2,5),(3,6),(4,6),(5,4)],7) [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[6,3,1,4,5,7,2]=>([(0,6),(1,5),(2,3),(2,5),(4,6),(5,4)],7) [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,5,2]=>[6,3,1,4,7,5,2]=>([(0,6),(1,5),(2,4),(2,6),(6,3),(6,5)],7) [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[7,6,3,1,4,5,2]=>([(2,6),(3,4),(3,6),(6,5)],7) [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[5,3,1,4,2,6,7]=>([(0,6),(1,5),(2,3),(2,5),(3,6),(5,6),(6,4)],7) [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[7,5,3,1,4,2,6]=>([(1,6),(2,5),(3,4),(3,5),(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]=>[5,3,1,4,6,2,7]=>([(0,5),(1,4),(2,3),(2,4),(3,6),(4,5),(5,6)],7) [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[5,3,1,4,6,7,2]=>([(0,6),(1,5),(2,4),(2,5),(5,6),(6,3)],7) [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[7,5,3,1,4,6,2]=>([(1,6),(2,5),(3,4),(3,5),(5,6)],7) [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,4,2,7]=>[5,3,1,6,4,2,7]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,4,7,2]=>[5,3,1,6,4,7,2]=>([(0,6),(1,4),(1,6),(2,3),(2,4),(2,6),(4,5),(6,5)],7) [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,4,2]=>[5,3,1,6,7,4,2]=>([(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(6,4)],7) [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,6,4,2]=>[7,5,3,1,6,4,2]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[6,5,3,1,4,2,7]=>([(0,6),(1,6),(2,5),(3,4),(3,5),(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]=>[6,5,3,1,4,7,2]=>([(0,6),(1,6),(2,5),(3,4),(3,5),(5,6)],7) [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,5,7,4,2]=>[6,5,3,1,7,4,2]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,5,4,2]=>[6,7,3,1,5,4,2]=>([(0,5),(0,6),(1,3),(2,4),(2,5),(2,6)],7) [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[7,6,5,3,1,4,2]=>([(3,6),(4,5),(4,6)],7) [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[4,3,1,2,5,6,7]=>([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[7,4,3,1,2,5,6]=>([(1,6),(2,6),(3,4),(4,6),(6,5)],7) [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[6,4,3,1,2,5,7]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[6,4,3,1,2,7,5]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[7,6,4,3,1,2,5]=>([(2,6),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[4,3,1,5,2,6,7]=>([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4),(6,5)],7) [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[7,4,3,1,5,2,6]=>([(1,6),(2,6),(3,4),(3,6),(4,5),(6,5)],7) [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[4,3,1,5,6,2,7]=>([(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(6,4)],7) [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[4,3,1,5,6,7,2]=>([(0,6),(1,6),(2,3),(2,6),(4,5),(6,4)],7) [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[7,4,3,1,5,6,2]=>([(1,6),(2,6),(3,4),(3,6),(6,5)],7) [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[6,4,3,1,5,2,7]=>([(0,6),(1,5),(2,5),(3,4),(3,5),(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]=>[6,4,3,1,5,7,2]=>([(0,6),(1,6),(2,5),(3,4),(3,6),(6,5)],7) [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,6,7,5,2]=>[6,4,3,1,7,5,2]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[7,6,4,3,1,5,2]=>([(2,6),(3,6),(4,5),(4,6)],7) [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,3,2,6,7]=>[4,5,1,3,2,6,7]=>([(0,5),(1,2),(1,3),(2,6),(3,6),(5,6),(6,4)],7) [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,3,2,7,6]=>[7,4,5,1,3,2,6]=>([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,3,6,2,7]=>[4,5,1,3,6,2,7]=>([(0,4),(1,2),(1,3),(2,6),(3,5),(4,5),(5,6)],7) [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,3,6,7,2]=>[4,5,1,3,6,7,2]=>([(0,5),(1,2),(1,3),(3,6),(5,6),(6,4)],7) [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,3,7,6,2]=>[7,4,5,1,3,6,2]=>([(1,5),(2,3),(2,4),(4,6),(5,6)],7) [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,3,2,7]=>[4,5,1,6,3,2,7]=>([(0,4),(1,2),(1,3),(1,5),(2,6),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,3,7,2]=>[4,5,1,6,3,7,2]=>([(0,4),(1,2),(1,3),(1,5),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,3,2]=>[4,5,1,6,7,3,2]=>([(0,5),(1,2),(1,3),(1,6),(5,6),(6,4)],7) [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,6,3,2]=>[7,4,5,1,6,3,2]=>([(1,5),(2,3),(2,4),(2,6),(5,6)],7) [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,5,3,2,7]=>[6,4,5,1,3,2,7]=>([(0,6),(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,5,3,7,2]=>[6,4,5,1,3,7,2]=>([(0,6),(1,5),(2,3),(2,4),(4,6),(5,6)],7) [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,5,7,3,2]=>[6,4,5,1,7,3,2]=>([(0,6),(1,5),(2,3),(2,4),(2,6),(5,6)],7) [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,5,3,2]=>[6,4,7,1,5,3,2]=>([(0,5),(1,5),(1,6),(2,3),(2,4),(2,6)],7) [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,6,5,3,2]=>[7,6,4,5,1,3,2]=>([(2,6),(3,4),(3,5)],7) [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[5,4,3,1,2,6,7]=>([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[7,5,4,3,1,2,6]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[5,4,3,1,6,2,7]=>([(0,6),(1,6),(2,6),(3,4),(3,6),(4,5),(6,5)],7) [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[5,4,3,1,6,7,2]=>([(0,6),(1,6),(2,6),(3,4),(3,6),(6,5)],7) [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[7,5,4,3,1,6,2]=>([(1,6),(2,6),(3,6),(4,5),(4,6)],7) [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,4,6,3,2,7]=>[5,4,6,1,3,2,7]=>([(0,5),(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,4,6,3,7,2]=>[5,4,6,1,3,7,2]=>([(0,5),(1,5),(2,3),(2,4),(4,6),(5,6)],7) [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,4,6,7,3,2]=>[5,4,6,1,7,3,2]=>([(0,5),(1,5),(2,3),(2,4),(2,6),(5,6)],7) [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,4,7,6,3,2]=>[7,5,4,6,1,3,2]=>([(1,6),(2,6),(3,4),(3,5)],7) [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,4,3,2,7]=>[5,6,4,1,3,2,7]=>([(0,6),(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,4,3,7,2]=>[5,6,4,1,3,7,2]=>([(0,6),(1,5),(2,3),(2,4),(4,6),(5,6)],7) [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,4,7,3,2]=>[5,6,4,1,7,3,2]=>([(0,6),(1,5),(2,3),(2,4),(2,6),(5,6)],7) [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,4,3,2]=>[5,6,7,1,4,3,2]=>([(0,6),(1,3),(1,4),(1,5),(6,2)],7) [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,6,4,3,2]=>[7,5,6,4,1,3,2]=>([(2,6),(3,4),(3,5)],7) [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[6,5,4,3,1,2,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[6,5,4,3,1,7,2]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6)],7) [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,5,4,7,3,2]=>[6,5,4,7,1,3,2]=>([(0,6),(1,6),(2,6),(3,4),(3,5)],7) [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,5,7,4,3,2]=>[6,5,7,4,1,3,2]=>([(1,6),(2,6),(3,4),(3,5)],7) [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,5,4,3,2]=>[6,7,5,4,1,3,2]=>([(2,6),(3,4),(3,5)],7) [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[7,6,5,4,3,1,2]=>([(5,6)],7) [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[7,2,1,3,4,5,6]=>([(1,6),(2,6),(3,5),(5,4),(6,3)],7) [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[6,2,1,3,4,5,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[6,2,1,3,4,7,5]=>([(0,6),(1,5),(2,5),(3,4),(3,6),(5,3)],7) [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[7,6,2,1,3,4,5]=>([(2,6),(3,6),(4,5),(6,4)],7) [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[5,2,1,3,4,6,7]=>([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[7,5,2,1,3,4,6]=>([(1,6),(2,5),(3,5),(4,6),(5,4)],7) [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[5,2,1,3,6,4,7]=>([(0,5),(1,5),(2,4),(3,6),(4,6),(5,3),(5,4)],7) [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[5,2,1,3,6,7,4]=>([(0,6),(1,5),(2,5),(5,3),(5,6),(6,4)],7) [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[7,5,2,1,3,6,4]=>([(1,6),(2,6),(3,5),(6,4),(6,5)],7) [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[6,5,2,1,3,4,7]=>([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[6,5,2,1,3,7,4]=>([(0,6),(1,6),(2,5),(3,5),(5,4),(5,6)],7) [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,5,4]=>[6,7,2,1,3,5,4]=>([(0,6),(1,6),(2,3),(6,4),(6,5)],7) [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[7,6,5,2,1,3,4]=>([(3,6),(4,6),(6,5)],7) [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[4,2,1,3,5,6,7]=>([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[7,4,2,1,3,5,6]=>([(1,6),(2,5),(3,5),(5,6),(6,4)],7) [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[6,4,2,1,3,5,7]=>([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[6,4,2,1,3,7,5]=>([(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7) [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[7,6,4,2,1,3,5]=>([(2,6),(3,5),(4,5),(5,6)],7) [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[4,2,1,5,3,6,7]=>([(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(5,3),(6,5)],7) [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[7,4,2,1,5,3,6]=>([(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[4,2,1,5,6,3,7]=>([(0,6),(1,4),(1,6),(2,4),(2,6),(3,5),(4,5),(6,3)],7) [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[4,2,1,5,6,7,3]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7) [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[7,4,2,1,5,6,3]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[6,4,2,1,5,3,7]=>([(0,6),(1,5),(2,4),(2,5),(3,4),(3,5),(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]=>[6,4,2,1,5,7,3]=>([(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(6,5)],7) [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,5,3]=>[6,4,2,1,7,5,3]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[7,6,4,2,1,5,3]=>([(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[5,4,2,1,3,6,7]=>([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[7,5,4,2,1,3,6]=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7) [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>[5,4,2,1,6,3,7]=>([(0,6),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[5,4,2,1,6,7,3]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[7,5,4,2,1,6,3]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,4,3,7]=>[5,6,2,1,4,3,7]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(3,6),(4,6),(5,6)],7) [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,4,7,3]=>[5,6,2,1,4,7,3]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(3,6),(5,6)],7) [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,4,3]=>[5,6,2,1,7,4,3]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(3,6)],7) [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,6,4,3]=>[7,5,6,2,1,4,3]=>([(1,5),(1,6),(2,5),(2,6),(3,4)],7) [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[6,5,4,2,1,3,7]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[6,5,4,2,1,7,3]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,5,7,4,3]=>[6,5,7,2,1,4,3]=>([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6)],7) [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,5,4,3]=>[6,7,5,2,1,4,3]=>([(1,5),(1,6),(2,5),(2,6),(3,4)],7) [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[7,6,5,4,2,1,3]=>([(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]=>[2,3,1,4,5,6,7]=>([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[7,2,3,1,4,5,6]=>([(1,6),(2,3),(3,6),(4,5),(6,4)],7) [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[6,2,3,1,4,5,7]=>([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[6,2,3,1,4,7,5]=>([(0,6),(1,5),(2,3),(3,6),(6,4),(6,5)],7) [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[7,6,2,3,1,4,5]=>([(2,6),(3,4),(4,6),(6,5)],7) [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[5,2,3,1,4,6,7]=>([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[7,5,2,3,1,4,6]=>([(1,6),(2,5),(3,4),(4,6),(6,5)],7) [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[5,2,3,1,6,4,7]=>([(0,6),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7) [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[5,2,3,1,6,7,4]=>([(0,6),(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7) [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[7,5,2,3,1,6,4]=>([(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[6,5,2,3,1,4,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[6,5,2,3,1,7,4]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,5,4]=>[6,7,2,3,1,5,4]=>([(0,5),(0,6),(1,3),(2,4),(4,5),(4,6)],7) [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[7,6,5,2,3,1,4]=>([(3,6),(4,5),(5,6)],7) [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[2,3,4,1,5,6,7]=>([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[7,2,3,4,1,5,6]=>([(1,6),(2,3),(3,5),(5,6),(6,4)],7) [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[6,2,3,4,1,5,7]=>([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[6,2,3,4,1,7,5]=>([(0,6),(1,5),(1,6),(2,3),(3,4),(4,5),(4,6)],7) [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[7,6,2,3,4,1,5]=>([(2,6),(3,4),(4,5),(5,6)],7) [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[2,3,4,5,1,6,7]=>([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[7,2,3,4,5,1,6]=>([(1,3),(2,6),(3,5),(4,6),(5,4)],7) [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[2,3,4,5,6,1,7]=>([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[2,3,4,5,6,7,1]=>([(1,6),(3,5),(4,3),(5,2),(6,4)],7) [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[7,2,3,4,5,6,1]=>([(2,6),(4,5),(5,3),(6,4)],7) [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[6,2,3,4,5,1,7]=>([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[6,2,3,4,5,7,1]=>([(1,3),(2,6),(3,5),(4,6),(5,4)],7) [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,5,1]=>[6,2,3,4,7,5,1]=>([(1,3),(2,6),(3,5),(5,4),(5,6)],7) [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[7,6,2,3,4,5,1]=>([(3,4),(4,6),(6,5)],7) [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[5,2,3,4,1,6,7]=>([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[7,5,2,3,4,1,6]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7) [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[5,2,3,4,6,1,7]=>([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[5,2,3,4,6,7,1]=>([(1,6),(2,3),(3,5),(5,6),(6,4)],7) [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[7,5,2,3,4,6,1]=>([(2,6),(3,4),(4,5),(5,6)],7) [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,4,1,7]=>[5,2,3,6,4,1,7]=>([(0,6),(1,5),(2,3),(3,4),(3,5),(4,6),(5,6)],7) [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,4,7,1]=>[5,2,3,6,4,7,1]=>([(1,6),(2,3),(3,4),(3,6),(4,5),(6,5)],7) [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,4,1]=>[5,2,3,6,7,4,1]=>([(1,6),(2,3),(3,5),(3,6),(6,4)],7) [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,6,4,1]=>[7,5,2,3,6,4,1]=>([(2,6),(3,4),(4,5),(4,6)],7) [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[6,5,2,3,4,1,7]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[6,5,2,3,4,7,1]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7) [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,5,7,4,1]=>[6,5,2,3,7,4,1]=>([(1,6),(2,6),(3,4),(4,5),(4,6)],7) [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,5,4,1]=>[6,7,2,3,5,4,1]=>([(1,5),(2,6),(6,3),(6,4)],7) [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[7,6,5,2,3,4,1]=>([(4,5),(5,6)],7) [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>[4,2,3,1,5,6,7]=>([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[7,4,2,3,1,5,6]=>([(1,6),(2,6),(3,4),(4,6),(6,5)],7) [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[6,4,2,3,1,5,7]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[6,4,2,3,1,7,5]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[7,6,4,2,3,1,5]=>([(2,6),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[4,2,3,5,1,6,7]=>([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[7,4,2,3,5,1,6]=>([(1,6),(2,5),(3,4),(4,6),(6,5)],7) [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[4,2,3,5,6,1,7]=>([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[4,2,3,5,6,7,1]=>([(1,6),(2,3),(3,6),(4,5),(6,4)],7) [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[7,4,2,3,5,6,1]=>([(2,6),(3,4),(4,6),(6,5)],7) [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[6,4,2,3,5,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[6,4,2,3,5,7,1]=>([(1,6),(2,5),(3,4),(4,6),(6,5)],7) [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,6,7,5,1]=>[6,4,2,3,7,5,1]=>([(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[7,6,4,2,3,5,1]=>([(3,6),(4,5),(5,6)],7) [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,3,1,6,7]=>[4,2,5,3,1,6,7]=>([(0,6),(1,5),(2,3),(2,5),(3,6),(5,6),(6,4)],7) [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,3,1,7,6]=>[7,4,2,5,3,1,6]=>([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,3,6,1,7]=>[4,2,5,3,6,1,7]=>([(0,4),(1,5),(2,3),(2,4),(3,6),(4,6),(6,5)],7) [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,3,6,7,1]=>[4,2,5,3,6,7,1]=>([(1,5),(2,3),(2,5),(3,6),(5,6),(6,4)],7) [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,3,7,6,1]=>[7,4,2,5,3,6,1]=>([(2,5),(3,4),(3,5),(4,6),(5,6)],7) [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,3,1,7]=>[4,2,5,6,3,1,7]=>([(0,6),(1,5),(2,3),(2,5),(3,6),(4,6),(5,4)],7) [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,3,7,1]=>[4,2,5,6,3,7,1]=>([(1,5),(2,3),(2,5),(3,6),(4,6),(5,4)],7) [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,3,1]=>[4,2,5,6,7,3,1]=>([(1,6),(2,3),(2,6),(4,5),(6,4)],7) [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,6,3,1]=>[7,4,2,5,6,3,1]=>([(2,6),(3,4),(3,6),(6,5)],7) [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,5,3,1,7]=>[6,4,2,5,3,1,7]=>([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,5,3,7,1]=>[6,4,2,5,3,7,1]=>([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,5,7,3,1]=>[6,4,2,5,7,3,1]=>([(1,6),(2,5),(3,4),(3,5),(5,6)],7) [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,5,3,1]=>[6,4,2,7,5,3,1]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7) [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,6,5,3,1]=>[7,6,4,2,5,3,1]=>([(3,6),(4,5),(4,6)],7) [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[5,4,2,3,1,6,7]=>([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[7,5,4,2,3,1,6]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[5,4,2,3,6,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[5,4,2,3,6,7,1]=>([(1,6),(2,6),(3,4),(4,6),(6,5)],7) [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[7,5,4,2,3,6,1]=>([(2,6),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,4,6,3,1,7]=>[5,4,2,6,3,1,7]=>([(0,6),(1,5),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,4,6,3,7,1]=>[5,4,2,6,3,7,1]=>([(1,6),(2,6),(3,4),(3,6),(4,5),(6,5)],7) [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,4,6,7,3,1]=>[5,4,2,6,7,3,1]=>([(1,6),(2,6),(3,4),(3,6),(6,5)],7) [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,4,7,6,3,1]=>[7,5,4,2,6,3,1]=>([(2,6),(3,6),(4,5),(4,6)],7) [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,4,3,1,7]=>[5,6,2,4,3,1,7]=>([(0,6),(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,4,3,7,1]=>[5,6,2,4,3,7,1]=>([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,4,7,3,1]=>[5,6,2,4,7,3,1]=>([(1,5),(2,3),(2,4),(4,6),(5,6)],7) [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,4,3,1]=>[5,6,2,7,4,3,1]=>([(1,5),(2,3),(2,4),(2,6),(5,6)],7) [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,6,4,3,1]=>[7,5,6,2,4,3,1]=>([(2,6),(3,4),(3,5)],7) [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[6,5,4,2,3,1,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[6,5,4,2,3,7,1]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,5,4,7,3,1]=>[6,5,4,2,7,3,1]=>([(1,6),(2,6),(3,6),(4,5),(4,6)],7) [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,5,7,4,3,1]=>[6,5,7,2,4,3,1]=>([(1,6),(2,6),(3,4),(3,5)],7) [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,5,4,3,1]=>[6,7,5,2,4,3,1]=>([(2,6),(3,4),(3,5)],7) [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[7,6,5,4,2,3,1]=>([(5,6)],7) [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7) [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[7,3,2,1,4,5,6]=>([(1,6),(2,6),(3,6),(4,5),(6,4)],7) [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[6,3,2,1,4,5,7]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7) [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[6,3,2,1,4,7,5]=>([(0,6),(1,6),(2,6),(3,5),(6,4),(6,5)],7) [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[7,6,3,2,1,4,5]=>([(2,6),(3,6),(4,6),(6,5)],7) [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[5,3,2,1,4,6,7]=>([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[7,5,3,2,1,4,6]=>([(1,6),(2,6),(3,6),(4,5),(6,5)],7) [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[5,3,2,1,6,4,7]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[5,3,2,1,6,7,4]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[7,5,3,2,1,6,4]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[6,5,3,2,1,4,7]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[6,5,3,2,1,7,4]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,6,7,5,4]=>[6,7,3,2,1,5,4]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4)],7) [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[7,6,5,3,2,1,4]=>([(3,6),(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]=>[3,2,4,1,5,6,7]=>([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7) [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[7,3,2,4,1,5,6]=>([(1,6),(2,5),(3,5),(5,6),(6,4)],7) [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>[6,3,2,4,1,5,7]=>([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>[6,3,2,4,1,7,5]=>([(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7) [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[7,6,3,2,4,1,5]=>([(2,6),(3,5),(4,5),(5,6)],7) [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[3,2,4,5,1,6,7]=>([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7) [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[7,3,2,4,5,1,6]=>([(1,6),(2,5),(3,5),(4,6),(5,4)],7) [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[3,2,4,5,6,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7) [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[3,2,4,5,6,7,1]=>([(1,6),(2,6),(3,5),(5,4),(6,3)],7) [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[7,3,2,4,5,6,1]=>([(2,6),(3,6),(4,5),(6,4)],7) [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[6,3,2,4,5,1,7]=>([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[6,3,2,4,5,7,1]=>([(1,6),(2,5),(3,5),(4,6),(5,4)],7) [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,6,7,5,1]=>[6,3,2,4,7,5,1]=>([(1,6),(2,6),(3,5),(6,4),(6,5)],7) [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[7,6,3,2,4,5,1]=>([(3,6),(4,6),(6,5)],7) [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[5,3,2,4,1,6,7]=>([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[7,5,3,2,4,1,6]=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7) [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[5,3,2,4,6,1,7]=>([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[5,3,2,4,6,7,1]=>([(1,6),(2,5),(3,5),(5,6),(6,4)],7) [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[7,5,3,2,4,6,1]=>([(2,6),(3,5),(4,5),(5,6)],7) [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,5,6,4,1,7]=>[5,3,2,6,4,1,7]=>([(0,6),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,5,6,4,7,1]=>[5,3,2,6,4,7,1]=>([(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,4,1]=>[5,3,2,6,7,4,1]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,5,7,6,4,1]=>[7,5,3,2,6,4,1]=>([(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[6,5,3,2,4,1,7]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[6,5,3,2,4,7,1]=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7) [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,6,5,7,4,1]=>[6,5,3,2,7,4,1]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,6,7,5,4,1]=>[6,7,3,2,5,4,1]=>([(1,5),(1,6),(2,5),(2,6),(3,4)],7) [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[7,6,5,3,2,4,1]=>([(4,6),(5,6)],7) [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7]=>[3,4,2,1,5,6,7]=>([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,2,1,5,7,6]=>[7,3,4,2,1,5,6]=>([(1,6),(2,6),(3,4),(4,6),(6,5)],7) [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,2,1,6,5,7]=>[6,3,4,2,1,5,7]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,2,1,6,7,5]=>[6,3,4,2,1,7,5]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,2,1,7,6,5]=>[7,6,3,4,2,1,5]=>([(2,6),(3,6),(4,5),(5,6)],7) [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,2,5,1,6,7]=>[3,4,2,5,1,6,7]=>([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,2,5,1,7,6]=>[7,3,4,2,5,1,6]=>([(1,6),(2,5),(3,4),(4,6),(6,5)],7) [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,1,7]=>[3,4,2,5,6,1,7]=>([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,1]=>[3,4,2,5,6,7,1]=>([(1,6),(2,3),(3,6),(4,5),(6,4)],7) [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,2,5,7,6,1]=>[7,3,4,2,5,6,1]=>([(2,6),(3,4),(4,6),(6,5)],7) [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,2,6,5,1,7]=>[6,3,4,2,5,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,2,6,5,7,1]=>[6,3,4,2,5,7,1]=>([(1,6),(2,5),(3,4),(4,6),(6,5)],7) [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,2,6,7,5,1]=>[6,3,4,2,7,5,1]=>([(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,2,7,6,5,1]=>[7,6,3,4,2,5,1]=>([(3,6),(4,5),(5,6)],7) [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,2,1,6,7]=>[3,4,5,2,1,6,7]=>([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,2,1,7,6]=>[7,3,4,5,2,1,6]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7) [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,2,6,1,7]=>[3,4,5,2,6,1,7]=>([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7) [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,2,6,7,1]=>[3,4,5,2,6,7,1]=>([(1,6),(2,3),(3,5),(5,6),(6,4)],7) [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,2,7,6,1]=>[7,3,4,5,2,6,1]=>([(2,6),(3,4),(4,5),(5,6)],7) [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,2,1,7]=>[3,4,5,6,2,1,7]=>([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,2,7,1]=>[3,4,5,6,2,7,1]=>([(1,3),(2,6),(3,5),(4,6),(5,4)],7) [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,2,1]=>[3,4,5,6,7,2,1]=>([(2,6),(4,5),(5,3),(6,4)],7) [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,6,2,1]=>[7,3,4,5,6,2,1]=>([(3,4),(4,6),(6,5)],7) [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,5,2,1,7]=>[6,3,4,5,2,1,7]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,5,2,7,1]=>[6,3,4,5,2,7,1]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7) [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,5,7,2,1]=>[6,3,4,5,7,2,1]=>([(2,6),(3,4),(4,5),(5,6)],7) [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,5,2,1]=>[6,3,4,7,5,2,1]=>([(2,6),(3,4),(4,5),(4,6)],7) [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,6,5,2,1]=>[7,6,3,4,5,2,1]=>([(4,5),(5,6)],7) [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,4,2,1,6,7]=>[5,3,4,2,1,6,7]=>([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,4,2,1,7,6]=>[7,5,3,4,2,1,6]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7) [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,4,2,6,1,7]=>[5,3,4,2,6,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,4,2,6,7,1]=>[5,3,4,2,6,7,1]=>([(1,6),(2,6),(3,4),(4,6),(6,5)],7) [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,4,2,7,6,1]=>[7,5,3,4,2,6,1]=>([(2,6),(3,6),(4,5),(5,6)],7) [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,4,6,2,1,7]=>[5,3,4,6,2,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,4,6,2,7,1]=>[5,3,4,6,2,7,1]=>([(1,6),(2,5),(3,4),(4,6),(6,5)],7) [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,4,6,7,2,1]=>[5,3,4,6,7,2,1]=>([(2,6),(3,4),(4,6),(6,5)],7) [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,4,7,6,2,1]=>[7,5,3,4,6,2,1]=>([(3,6),(4,5),(5,6)],7) [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,4,2,1,7]=>[5,3,6,4,2,1,7]=>([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,4,2,7,1]=>[5,3,6,4,2,7,1]=>([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,4,7,2,1]=>[5,3,6,4,7,2,1]=>([(2,5),(3,4),(3,5),(4,6),(5,6)],7) [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,4,2,1]=>[5,3,6,7,4,2,1]=>([(2,6),(3,4),(3,6),(6,5)],7) [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,6,4,2,1]=>[7,5,3,6,4,2,1]=>([(3,6),(4,5),(4,6)],7) [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,5,4,2,1,7]=>[6,5,3,4,2,1,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,5,4,2,7,1]=>[6,5,3,4,2,7,1]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7) [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,5,4,7,2,1]=>[6,5,3,4,7,2,1]=>([(2,6),(3,6),(4,5),(5,6)],7) [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,5,7,4,2,1]=>[6,5,3,7,4,2,1]=>([(2,6),(3,6),(4,5),(4,6)],7) [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,5,4,2,1]=>[6,7,3,5,4,2,1]=>([(2,6),(3,4),(3,5)],7) [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,6,5,4,2,1]=>[7,6,5,3,4,2,1]=>([(5,6)],7) [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7) [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[7,4,3,2,1,5,6]=>([(1,6),(2,6),(3,6),(4,6),(6,5)],7) [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[6,4,3,2,1,5,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[6,4,3,2,1,7,5]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[7,6,4,3,2,1,5]=>([(2,6),(3,6),(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]=>[4,3,2,5,1,6,7]=>([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7) [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[7,4,3,2,5,1,6]=>([(1,6),(2,6),(3,6),(4,5),(6,5)],7) [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[4,3,2,5,6,1,7]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7) [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[4,3,2,5,6,7,1]=>([(1,6),(2,6),(3,6),(4,5),(6,4)],7) [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[7,4,3,2,5,6,1]=>([(2,6),(3,6),(4,6),(6,5)],7) [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[6,4,3,2,5,1,7]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[6,4,3,2,5,7,1]=>([(1,6),(2,6),(3,6),(4,5),(6,5)],7) [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,6,7,5,1]=>[6,4,3,2,7,5,1]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[7,6,4,3,2,5,1]=>([(3,6),(4,6),(5,6)],7) [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,3,5,2,1,6,7]=>[4,3,5,2,1,6,7]=>([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,3,5,2,1,7,6]=>[7,4,3,5,2,1,6]=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7) [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,3,5,2,6,1,7]=>[4,3,5,2,6,1,7]=>([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,3,5,2,6,7,1]=>[4,3,5,2,6,7,1]=>([(1,6),(2,5),(3,5),(5,6),(6,4)],7) [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,3,5,2,7,6,1]=>[7,4,3,5,2,6,1]=>([(2,6),(3,5),(4,5),(5,6)],7) [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,3,5,6,2,1,7]=>[4,3,5,6,2,1,7]=>([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,2,7,1]=>[4,3,5,6,2,7,1]=>([(1,6),(2,5),(3,5),(4,6),(5,4)],7) [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,2,1]=>[4,3,5,6,7,2,1]=>([(2,6),(3,6),(4,5),(6,4)],7) [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,3,5,7,6,2,1]=>[7,4,3,5,6,2,1]=>([(3,6),(4,6),(6,5)],7) [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,3,6,5,2,1,7]=>[6,4,3,5,2,1,7]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,3,6,5,2,7,1]=>[6,4,3,5,2,7,1]=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7) [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,3,6,5,7,2,1]=>[6,4,3,5,7,2,1]=>([(2,6),(3,5),(4,5),(5,6)],7) [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,6,7,5,2,1]=>[6,4,3,7,5,2,1]=>([(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3,7,6,5,2,1]=>[7,6,4,3,5,2,1]=>([(4,6),(5,6)],7) [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,3,2,1,6,7]=>[4,5,3,2,1,6,7]=>([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,3,2,1,7,6]=>[7,4,5,3,2,1,6]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7) [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,3,2,6,1,7]=>[4,5,3,2,6,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7) [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,3,2,6,7,1]=>[4,5,3,2,6,7,1]=>([(1,6),(2,6),(3,4),(4,6),(6,5)],7) [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,3,2,7,6,1]=>[7,4,5,3,2,6,1]=>([(2,6),(3,6),(4,5),(5,6)],7) [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,3,6,2,1,7]=>[4,5,3,6,2,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1]=>[4,5,3,6,2,7,1]=>([(1,6),(2,5),(3,4),(4,6),(6,5)],7) [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,3,6,7,2,1]=>[4,5,3,6,7,2,1]=>([(2,6),(3,4),(4,6),(6,5)],7) [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,3,7,6,2,1]=>[7,4,5,3,6,2,1]=>([(3,6),(4,5),(5,6)],7) [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,3,2,1,7]=>[4,5,6,3,2,1,7]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,3,2,7,1]=>[4,5,6,3,2,7,1]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7) [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,3,7,2,1]=>[4,5,6,3,7,2,1]=>([(2,6),(3,4),(4,5),(5,6)],7) [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[4,5,6,7,3,2,1]=>([(3,4),(4,6),(6,5)],7) [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,6,3,2,1]=>[7,4,5,6,3,2,1]=>([(4,5),(5,6)],7) [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,5,3,2,1,7]=>[6,4,5,3,2,1,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,5,3,2,7,1]=>[6,4,5,3,2,7,1]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7) [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,5,3,7,2,1]=>[6,4,5,3,7,2,1]=>([(2,6),(3,6),(4,5),(5,6)],7) [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,5,7,3,2,1]=>[6,4,5,7,3,2,1]=>([(3,6),(4,5),(5,6)],7) [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,5,3,2,1]=>[6,4,7,5,3,2,1]=>([(3,6),(4,5),(4,6)],7) [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,6,5,3,2,1]=>[7,6,4,5,3,2,1]=>([(5,6)],7) [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7) [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[7,5,4,3,2,1,6]=>([(1,6),(2,6),(3,6),(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]=>[5,4,3,2,6,1,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7) [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[5,4,3,2,6,7,1]=>([(1,6),(2,6),(3,6),(4,6),(6,5)],7) [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[7,5,4,3,2,6,1]=>([(2,6),(3,6),(4,6),(5,6)],7) [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,4,3,6,2,1,7]=>[5,4,3,6,2,1,7]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,4,3,6,2,7,1]=>[5,4,3,6,2,7,1]=>([(1,6),(2,6),(3,6),(4,5),(6,5)],7) [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[5,4,3,6,7,2,1]=>([(2,6),(3,6),(4,6),(6,5)],7) [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,4,3,7,6,2,1]=>[7,5,4,3,6,2,1]=>([(3,6),(4,6),(5,6)],7) [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,4,6,3,2,1,7]=>[5,4,6,3,2,1,7]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,4,6,3,2,7,1]=>[5,4,6,3,2,7,1]=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7) [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[5,4,6,3,7,2,1]=>([(2,6),(3,5),(4,5),(5,6)],7) [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1]=>[5,4,6,7,3,2,1]=>([(3,6),(4,6),(6,5)],7) [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,3,2,1]=>[7,5,4,6,3,2,1]=>([(4,6),(5,6)],7) [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,4,3,2,1,7]=>[5,6,4,3,2,1,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,4,3,2,7,1]=>[5,6,4,3,2,7,1]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7) [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,4,3,7,2,1]=>[5,6,4,3,7,2,1]=>([(2,6),(3,6),(4,5),(5,6)],7) [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,4,7,3,2,1]=>[5,6,4,7,3,2,1]=>([(3,6),(4,5),(5,6)],7) [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,4,3,2,1]=>[5,6,7,4,3,2,1]=>([(4,5),(5,6)],7) [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,6,4,3,2,1]=>[7,5,6,4,3,2,1]=>([(5,6)],7) [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>([(0,6),(1,6),(2,6),(3,6),(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]=>[6,5,4,3,2,7,1]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7) [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,5,4,3,7,2,1]=>[6,5,4,3,7,2,1]=>([(2,6),(3,6),(4,6),(5,6)],7) [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,5,4,7,3,2,1]=>[6,5,4,7,3,2,1]=>([(3,6),(4,6),(5,6)],7) [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,5,7,4,3,2,1]=>[6,5,7,4,3,2,1]=>([(4,6),(5,6)],7) [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,5,4,3,2,1]=>[6,7,5,4,3,2,1]=>([(5,6)],7) [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>([],7) [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8) [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>([],8)
Map
to 312-avoiding permutation
Description
Sends a Dyck path to the 312-avoiding permutation according to Bandlow-Killpatrick.
This map is defined in [1] and sends the area (St000012The area of a Dyck path.) to the inversion number (St000018The number of inversions of a permutation.).
Map
Foata bijection
Description
Sends a permutation to its image under the Foata bijection.
The Foata bijection $\phi$ is a bijection on the set of words with no two equal letters. It can be defined by induction on the size of the word:
Given a word $w_1 w_2 ... w_n$, compute the image inductively by starting with $\phi(w_1) = w_1$.
At the $i$-th step, if $\phi(w_1 w_2 ... w_i) = v_1 v_2 ... v_i$, define $\phi(w_1 w_2 ... w_i w_{i+1})$ by placing $w_{i+1}$ on the end of the word $v_1 v_2 ... v_i$ and breaking the word up into blocks as follows.
  • If $w_{i+1} \geq v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} \geq v_k$.
  • If $w_{i+1} < v_i$, place a vertical line to the right of each $v_k$ for which $w_{i+1} < v_k$.
In either case, place a vertical line at the start of the word as well. Now, within each block between vertical lines, cyclically shift the entries one place to the right.
To compute $\phi([1,4,2,5,3])$, the sequence of words is
  • $1$
  • $|1|4 \to 14$
  • $|14|2 \to 412$
  • $|4|1|2|5 \to 4125$
  • $|4|125|3 \to 45123.$
In total, this gives $\phi([1,4,2,5,3]) = [4,5,1,2,3]$.
This bijection sends the major index (St000004The major index of a permutation.) to the number of inversions (St000018The number of inversions of a permutation.).
Map
permutation poset
Description
Sends a permutation to its permutation poset.
For a permutation $\pi$ of length $n$, this poset has vertices
$$\{ (i,\pi(i))\ :\ 1 \leq i \leq n \}$$
and the cover relation is given by $(w, x) \leq (y, z)$ if $w \leq y$ and $x \leq z$.
For example, the permutation $[3,1,5,4,2]$ is mapped to the poset with cover relations
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$