Identifier
Mp00025: Dyck paths to 132-avoiding permutationPermutations
Mp00235: Permutations descent views to invisible inversion bottomsPermutations
Mp00065: Permutations permutation poset Posets
Images
=>
Cc0005;cc-rep-0Cc0014;cc-rep-3
[1,0]=>[1]=>[1]=>([],1) [1,0,1,0]=>[2,1]=>[2,1]=>([],2) [1,1,0,0]=>[1,2]=>[1,2]=>([(0,1)],2) [1,0,1,0,1,0]=>[3,2,1]=>[2,3,1]=>([(1,2)],3) [1,0,1,1,0,0]=>[2,3,1]=>[3,2,1]=>([],3) [1,1,0,0,1,0]=>[3,1,2]=>[3,1,2]=>([(1,2)],3) [1,1,0,1,0,0]=>[2,1,3]=>[2,1,3]=>([(0,2),(1,2)],3) [1,1,1,0,0,0]=>[1,2,3]=>[1,2,3]=>([(0,2),(2,1)],3) [1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[2,3,4,1]=>([(1,2),(2,3)],4) [1,0,1,0,1,1,0,0]=>[3,4,2,1]=>[2,4,3,1]=>([(1,2),(1,3)],4) [1,0,1,1,0,0,1,0]=>[4,2,3,1]=>[3,4,2,1]=>([(2,3)],4) [1,0,1,1,0,1,0,0]=>[3,2,4,1]=>[4,3,2,1]=>([],4) [1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[4,2,3,1]=>([(2,3)],4) [1,1,0,0,1,0,1,0]=>[4,3,1,2]=>[3,1,4,2]=>([(0,3),(1,2),(1,3)],4) [1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[4,1,3,2]=>([(1,2),(1,3)],4) [1,1,0,1,0,0,1,0]=>[4,2,1,3]=>[2,4,1,3]=>([(0,3),(1,2),(1,3)],4) [1,1,0,1,0,1,0,0]=>[3,2,1,4]=>[2,3,1,4]=>([(0,3),(1,2),(2,3)],4) [1,1,0,1,1,0,0,0]=>[2,3,1,4]=>[3,2,1,4]=>([(0,3),(1,3),(2,3)],4) [1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[4,1,2,3]=>([(1,2),(2,3)],4) [1,1,1,0,0,1,0,0]=>[3,1,2,4]=>[3,1,2,4]=>([(0,3),(1,2),(2,3)],4) [1,1,1,0,1,0,0,0]=>[2,1,3,4]=>[2,1,3,4]=>([(0,3),(1,3),(3,2)],4) [1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4) [1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>[2,3,4,5,1]=>([(1,4),(3,2),(4,3)],5) [1,0,1,0,1,0,1,1,0,0]=>[4,5,3,2,1]=>[2,3,5,4,1]=>([(1,4),(4,2),(4,3)],5) [1,0,1,0,1,1,0,0,1,0]=>[5,3,4,2,1]=>[2,4,5,3,1]=>([(1,3),(1,4),(4,2)],5) [1,0,1,0,1,1,0,1,0,0]=>[4,3,5,2,1]=>[2,5,4,3,1]=>([(1,2),(1,3),(1,4)],5) [1,0,1,0,1,1,1,0,0,0]=>[3,4,5,2,1]=>[2,5,3,4,1]=>([(1,3),(1,4),(4,2)],5) [1,0,1,1,0,0,1,0,1,0]=>[5,4,2,3,1]=>[3,4,2,5,1]=>([(1,4),(2,3),(3,4)],5) [1,0,1,1,0,0,1,1,0,0]=>[4,5,2,3,1]=>[3,5,2,4,1]=>([(1,4),(2,3),(2,4)],5) [1,0,1,1,0,1,0,0,1,0]=>[5,3,2,4,1]=>[4,3,5,2,1]=>([(2,4),(3,4)],5) [1,0,1,1,0,1,0,1,0,0]=>[4,3,2,5,1]=>[5,3,4,2,1]=>([(3,4)],5) [1,0,1,1,0,1,1,0,0,0]=>[3,4,2,5,1]=>[5,4,3,2,1]=>([],5) [1,0,1,1,1,0,0,0,1,0]=>[5,2,3,4,1]=>[4,5,2,3,1]=>([(1,4),(2,3)],5) [1,0,1,1,1,0,0,1,0,0]=>[4,2,3,5,1]=>[5,4,2,3,1]=>([(3,4)],5) [1,0,1,1,1,0,1,0,0,0]=>[3,2,4,5,1]=>[5,3,2,4,1]=>([(2,4),(3,4)],5) [1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[5,2,3,4,1]=>([(2,3),(3,4)],5) [1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,2]=>[3,1,4,5,2]=>([(0,4),(1,2),(1,4),(4,3)],5) [1,1,0,0,1,0,1,1,0,0]=>[4,5,3,1,2]=>[3,1,5,4,2]=>([(0,3),(0,4),(1,2),(1,3),(1,4)],5) [1,1,0,0,1,1,0,0,1,0]=>[5,3,4,1,2]=>[4,1,5,3,2]=>([(0,4),(1,2),(1,3),(1,4)],5) [1,1,0,0,1,1,0,1,0,0]=>[4,3,5,1,2]=>[5,1,4,3,2]=>([(1,2),(1,3),(1,4)],5) [1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>[5,1,3,4,2]=>([(1,3),(1,4),(4,2)],5) [1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,3]=>[2,4,1,5,3]=>([(0,3),(0,4),(1,2),(1,3),(2,4)],5) [1,1,0,1,0,0,1,1,0,0]=>[4,5,2,1,3]=>[2,5,1,4,3]=>([(0,3),(0,4),(1,2),(1,3),(1,4)],5) [1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,4]=>[2,3,5,1,4]=>([(0,4),(1,2),(2,3),(2,4)],5) [1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,5]=>[2,3,4,1,5]=>([(0,4),(1,2),(2,3),(3,4)],5) [1,1,0,1,0,1,1,0,0,0]=>[3,4,2,1,5]=>[2,4,3,1,5]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5) [1,1,0,1,1,0,0,0,1,0]=>[5,2,3,1,4]=>[3,5,2,1,4]=>([(0,4),(1,4),(2,3),(2,4)],5) [1,1,0,1,1,0,0,1,0,0]=>[4,2,3,1,5]=>[3,4,2,1,5]=>([(0,4),(1,4),(2,3),(3,4)],5) [1,1,0,1,1,0,1,0,0,0]=>[3,2,4,1,5]=>[4,3,2,1,5]=>([(0,4),(1,4),(2,4),(3,4)],5) [1,1,0,1,1,1,0,0,0,0]=>[2,3,4,1,5]=>[4,2,3,1,5]=>([(0,4),(1,4),(2,3),(3,4)],5) [1,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,3]=>[4,1,2,5,3]=>([(0,4),(1,2),(2,3),(2,4)],5) [1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>[5,1,2,4,3]=>([(1,4),(4,2),(4,3)],5) [1,1,1,0,0,1,0,0,1,0]=>[5,3,1,2,4]=>[3,1,5,2,4]=>([(0,3),(0,4),(1,2),(1,3),(2,4)],5) [1,1,1,0,0,1,0,1,0,0]=>[4,3,1,2,5]=>[3,1,4,2,5]=>([(0,3),(1,2),(1,3),(2,4),(3,4)],5) [1,1,1,0,0,1,1,0,0,0]=>[3,4,1,2,5]=>[4,1,3,2,5]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5) [1,1,1,0,1,0,0,0,1,0]=>[5,2,1,3,4]=>[2,5,1,3,4]=>([(0,4),(1,2),(1,4),(4,3)],5) [1,1,1,0,1,0,0,1,0,0]=>[4,2,1,3,5]=>[2,4,1,3,5]=>([(0,3),(1,2),(1,3),(2,4),(3,4)],5) [1,1,1,0,1,0,1,0,0,0]=>[3,2,1,4,5]=>[2,3,1,4,5]=>([(0,4),(1,2),(2,4),(4,3)],5) [1,1,1,0,1,1,0,0,0,0]=>[2,3,1,4,5]=>[3,2,1,4,5]=>([(0,4),(1,4),(2,4),(4,3)],5) [1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>[5,1,2,3,4]=>([(1,4),(3,2),(4,3)],5) [1,1,1,1,0,0,0,1,0,0]=>[4,1,2,3,5]=>[4,1,2,3,5]=>([(0,4),(1,2),(2,3),(3,4)],5) [1,1,1,1,0,0,1,0,0,0]=>[3,1,2,4,5]=>[3,1,2,4,5]=>([(0,4),(1,2),(2,4),(4,3)],5) [1,1,1,1,0,1,0,0,0,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>([(0,4),(1,4),(2,3),(4,2)],5) [1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>([(1,5),(3,4),(4,2),(5,3)],6) [1,0,1,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,2,1]=>[2,3,4,6,5,1]=>([(1,4),(4,5),(5,2),(5,3)],6) [1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,2,1]=>[2,3,5,6,4,1]=>([(1,5),(4,3),(5,2),(5,4)],6) [1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,2,1]=>[2,3,6,5,4,1]=>([(1,5),(5,2),(5,3),(5,4)],6) [1,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,2,1]=>[2,3,6,4,5,1]=>([(1,5),(4,3),(5,2),(5,4)],6) [1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>([(1,3),(1,4),(2,5),(3,5),(4,2)],6) [1,0,1,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,2,1]=>[2,4,6,3,5,1]=>([(1,3),(1,4),(3,5),(4,2),(4,5)],6) [1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,2,1]=>[2,5,4,6,3,1]=>([(1,2),(1,3),(1,4),(3,5),(4,5)],6) [1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,2,1]=>[2,6,4,5,3,1]=>([(1,3),(1,4),(1,5),(5,2)],6) [1,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,2,1]=>[2,6,5,4,3,1]=>([(1,2),(1,3),(1,4),(1,5)],6) [1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,2,1]=>[2,5,6,3,4,1]=>([(1,4),(1,5),(4,3),(5,2)],6) [1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,2,1]=>[2,6,5,3,4,1]=>([(1,3),(1,4),(1,5),(5,2)],6) [1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[2,6,4,3,5,1]=>([(1,2),(1,3),(1,4),(3,5),(4,5)],6) [1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,2,1]=>[2,6,3,4,5,1]=>([(1,3),(1,5),(4,2),(5,4)],6) [1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,3,1]=>[3,4,2,5,6,1]=>([(1,5),(2,3),(3,5),(5,4)],6) [1,0,1,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,3,1]=>[3,4,2,6,5,1]=>([(1,4),(1,5),(2,3),(3,4),(3,5)],6) [1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,3,1]=>[3,5,2,6,4,1]=>([(1,4),(1,5),(2,3),(2,4),(3,5)],6) [1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,3,1]=>[3,6,2,5,4,1]=>([(1,4),(1,5),(2,3),(2,4),(2,5)],6) [1,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,3,1]=>[3,6,2,4,5,1]=>([(1,5),(2,3),(2,5),(5,4)],6) [1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,4,1]=>[4,3,5,2,6,1]=>([(1,5),(2,4),(3,4),(4,5)],6) [1,0,1,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,4,1]=>[4,3,6,2,5,1]=>([(1,5),(2,4),(2,5),(3,4),(3,5)],6) [1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,5,1]=>[5,3,4,6,2,1]=>([(2,5),(3,4),(4,5)],6) [1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,1]=>[6,3,4,5,2,1]=>([(3,4),(4,5)],6) [1,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,1]=>[6,3,5,4,2,1]=>([(3,4),(3,5)],6) [1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,5,1]=>[5,4,6,3,2,1]=>([(3,5),(4,5)],6) [1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,6,1]=>[6,4,5,3,2,1]=>([(4,5)],6) [1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>([],6) [1,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,6,1]=>[6,5,3,4,2,1]=>([(4,5)],6) [1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,4,1]=>[4,5,2,3,6,1]=>([(1,4),(2,3),(3,5),(4,5)],6) [1,0,1,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,4,1]=>[4,6,2,3,5,1]=>([(1,4),(2,3),(2,5),(4,5)],6) [1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,5,1]=>[5,4,2,6,3,1]=>([(1,5),(2,5),(3,4),(3,5)],6) [1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,6,1]=>[6,4,2,5,3,1]=>([(2,5),(3,4),(3,5)],6) [1,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,6,1]=>[6,5,2,4,3,1]=>([(3,4),(3,5)],6) [1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1]=>[5,3,6,2,4,1]=>([(1,5),(2,4),(3,4),(3,5)],6) [1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[6,3,5,2,4,1]=>([(2,5),(3,4),(3,5)],6) [1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,6,1]=>[6,3,4,2,5,1]=>([(2,5),(3,4),(4,5)],6) [1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>([(2,5),(3,5),(4,5)],6) [1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,5,1]=>[5,6,2,3,4,1]=>([(1,3),(2,4),(4,5)],6) [1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,6,1]=>[6,5,2,3,4,1]=>([(3,4),(4,5)],6) [1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,6,1]=>[6,4,2,3,5,1]=>([(2,5),(3,4),(4,5)],6) [1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>([(2,5),(3,5),(5,4)],6) [1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>([(2,3),(3,5),(5,4)],6) [1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,2]=>[3,1,4,5,6,2]=>([(0,5),(1,3),(1,5),(4,2),(5,4)],6) [1,1,0,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,1,2]=>[3,1,4,6,5,2]=>([(0,5),(1,2),(1,5),(5,3),(5,4)],6) [1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,1,2]=>[3,1,5,6,4,2]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) [1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,1,2]=>[3,1,6,5,4,2]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) [1,1,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,1,2]=>[3,1,6,4,5,2]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) [1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,1,2]=>[4,1,5,3,6,2]=>([(0,4),(1,2),(1,3),(1,4),(3,5),(4,5)],6) [1,1,0,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6) [1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,1,2]=>[5,1,4,6,3,2]=>([(0,5),(1,2),(1,3),(1,4),(4,5)],6) [1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,1,2]=>[6,1,4,5,3,2]=>([(1,3),(1,4),(1,5),(5,2)],6) [1,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,1,2]=>[6,1,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5)],6) [1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,1,2]=>[5,1,6,3,4,2]=>([(0,5),(1,3),(1,4),(1,5),(4,2)],6) [1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,1,2]=>[6,1,5,3,4,2]=>([(1,3),(1,4),(1,5),(5,2)],6) [1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,1,2]=>[6,1,4,3,5,2]=>([(1,2),(1,3),(1,4),(3,5),(4,5)],6) [1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>[6,1,3,4,5,2]=>([(1,3),(1,5),(4,2),(5,4)],6) [1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,3]=>[2,4,1,5,6,3]=>([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6) [1,1,0,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,1,3]=>[2,4,1,6,5,3]=>([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4)],6) [1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,1,3]=>[2,5,1,6,4,3]=>([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6) [1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,1,3]=>[2,6,1,5,4,3]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6) [1,1,0,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,1,3]=>[2,6,1,4,5,3]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6) [1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,4]=>[2,3,5,1,6,4]=>([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6) [1,1,0,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,1,4]=>[2,3,6,1,5,4]=>([(0,4),(0,5),(1,2),(2,3),(2,4),(2,5)],6) [1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,5]=>[2,3,4,6,1,5]=>([(0,5),(1,3),(3,4),(4,2),(4,5)],6) [1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>([(0,5),(1,4),(2,5),(3,2),(4,3)],6) [1,1,0,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,1,6]=>[2,3,5,4,1,6]=>([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6) [1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,1,5]=>[2,4,6,3,1,5]=>([(0,5),(1,3),(1,4),(3,5),(4,2),(4,5)],6) [1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,1,6]=>[2,4,5,3,1,6]=>([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6) [1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,1,6]=>[2,5,4,3,1,6]=>([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) [1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,1,6]=>[2,5,3,4,1,6]=>([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6) [1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,1,4]=>[3,5,2,1,6,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6) [1,1,0,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,1,4]=>[3,6,2,1,5,4]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6) [1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,1,5]=>[3,4,2,6,1,5]=>([(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6) [1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,1,6]=>[3,4,2,5,1,6]=>([(0,5),(1,4),(2,3),(3,5),(5,4)],6) [1,1,0,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,1,6]=>[3,5,2,4,1,6]=>([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) [1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,1,5]=>[4,3,6,2,1,5]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6) [1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,1,6]=>[4,3,5,2,1,6]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6) [1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,1,6]=>[5,3,4,2,1,6]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6) [1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,1,6]=>[5,4,3,2,1,6]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6) [1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,1,5]=>[4,6,2,3,1,5]=>([(0,5),(1,4),(2,3),(2,5),(4,5)],6) [1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,1,6]=>[4,5,2,3,1,6]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,1,6]=>[5,4,2,3,1,6]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6) [1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,1,6]=>[5,3,2,4,1,6]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6) [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,2,3]=>[4,1,2,5,6,3]=>([(0,5),(1,4),(4,2),(4,5),(5,3)],6) [1,1,1,0,0,0,1,0,1,1,0,0]=>[5,6,4,1,2,3]=>[4,1,2,6,5,3]=>([(0,4),(0,5),(1,2),(2,3),(2,4),(2,5)],6) [1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>([(0,5),(1,4),(4,2),(4,3),(4,5)],6) [1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>([(1,5),(5,2),(5,3),(5,4)],6) [1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>([(1,5),(4,3),(5,2),(5,4)],6) [1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]=>([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6) [1,1,1,0,0,1,0,0,1,1,0,0]=>[5,6,3,1,2,4]=>[3,1,6,2,5,4]=>([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4)],6) [1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,2,5]=>[3,1,4,6,2,5]=>([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6) [1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,2,6]=>[3,1,4,5,2,6]=>([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6) [1,1,1,0,0,1,0,1,1,0,0,0]=>[4,5,3,1,2,6]=>[3,1,5,4,2,6]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) [1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6) [1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,4,1,2,6]=>[4,1,5,3,2,6]=>([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) [1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,5,1,2,6]=>[5,1,4,3,2,6]=>([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6]=>[5,1,3,4,2,6]=>([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6) [1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,3,4]=>[2,5,1,3,6,4]=>([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6) [1,1,1,0,1,0,0,0,1,1,0,0]=>[5,6,2,1,3,4]=>[2,6,1,3,5,4]=>([(0,5),(1,2),(1,5),(5,3),(5,4)],6) [1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,3,5]=>[2,4,1,6,3,5]=>([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6) [1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,3,6]=>[2,4,1,5,3,6]=>([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6) [1,1,1,0,1,0,0,1,1,0,0,0]=>[4,5,2,1,3,6]=>[2,5,1,4,3,6]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6) [1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,4,5]=>[2,3,6,1,4,5]=>([(0,5),(1,4),(4,2),(4,5),(5,3)],6) [1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,4,6]=>[2,3,5,1,4,6]=>([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6) [1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>([(0,5),(1,4),(2,5),(4,2),(5,3)],6) [1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,2,1,5,6]=>[2,4,3,1,5,6]=>([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6) [1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,1,4,5]=>[3,6,2,1,4,5]=>([(0,5),(1,5),(2,3),(2,5),(5,4)],6) [1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,3,1,4,6]=>[3,5,2,1,4,6]=>([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6) [1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,3,1,5,6]=>[3,4,2,1,5,6]=>([(0,5),(1,5),(2,3),(3,5),(5,4)],6) [1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,4,1,5,6]=>[4,3,2,1,5,6]=>([(0,5),(1,5),(2,5),(3,5),(5,4)],6) [1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>([(0,5),(1,5),(2,3),(3,5),(5,4)],6) [1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>([(0,5),(1,3),(3,4),(4,2),(4,5)],6) [1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>([(1,4),(4,5),(5,2),(5,3)],6) [1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6) [1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6) [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6) [1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6) [1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6) [1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) [1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6) [1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>([(0,5),(1,3),(1,5),(4,2),(5,4)],6) [1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6) [1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) [1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>([(0,5),(1,3),(3,5),(4,2),(5,4)],6) [1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>([(0,5),(1,5),(2,5),(3,4),(5,3)],6) [1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>([(1,5),(3,4),(4,2),(5,3)],6) [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>([(0,5),(1,4),(2,5),(3,2),(4,3)],6) [1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>([(0,5),(1,4),(2,5),(4,2),(5,3)],6) [1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>([(0,5),(1,3),(3,5),(4,2),(5,4)],6) [1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>([(0,5),(1,5),(3,2),(4,3),(5,4)],6) [1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>([(1,6),(3,5),(4,3),(5,2),(6,4)],7) [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,2,1]=>[2,3,4,5,7,6,1]=>([(1,5),(4,6),(5,4),(6,2),(6,3)],7) [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,2,1]=>[2,3,4,6,7,5,1]=>([(1,5),(4,3),(5,6),(6,2),(6,4)],7) [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,2,1]=>[2,3,4,7,6,5,1]=>([(1,5),(5,6),(6,2),(6,3),(6,4)],7) [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,2,1]=>[2,3,4,7,5,6,1]=>([(1,5),(4,3),(5,6),(6,2),(6,4)],7) [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,2,1]=>[2,3,5,6,4,7,1]=>([(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7) [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,2,1]=>[2,3,5,7,4,6,1]=>([(1,5),(3,6),(4,2),(4,6),(5,3),(5,4)],7) [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,2,1]=>[2,3,6,5,7,4,1]=>([(1,5),(3,6),(4,6),(5,2),(5,3),(5,4)],7) [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,2,1]=>[2,3,7,5,6,4,1]=>([(1,6),(5,4),(6,2),(6,3),(6,5)],7) [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,2,1]=>[2,3,7,6,5,4,1]=>([(1,6),(6,2),(6,3),(6,4),(6,5)],7) [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,2,1]=>[2,3,6,7,4,5,1]=>([(1,6),(4,3),(5,2),(6,4),(6,5)],7) [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,2,1]=>[2,3,7,6,4,5,1]=>([(1,6),(5,4),(6,2),(6,3),(6,5)],7) [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,2,1]=>[2,3,7,5,4,6,1]=>([(1,5),(3,6),(4,6),(5,2),(5,3),(5,4)],7) [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[2,3,7,4,5,6,1]=>([(1,6),(4,5),(5,3),(6,2),(6,4)],7) [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,2,1]=>[2,4,5,3,6,7,1]=>([(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7) [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,2,1]=>[2,4,5,3,7,6,1]=>([(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7) [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,2,1]=>[2,4,6,3,7,5,1]=>([(1,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6)],7) [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,2,1]=>[2,4,7,3,6,5,1]=>([(1,3),(1,4),(3,5),(3,6),(4,2),(4,5),(4,6)],7) [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,2,1]=>[2,4,7,3,5,6,1]=>([(1,3),(1,5),(3,6),(5,2),(5,6),(6,4)],7) [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7) [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,2,1]=>[2,5,4,7,3,6,1]=>([(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,2,1]=>[2,6,4,5,7,3,1]=>([(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7) [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,2,1]=>[2,7,4,5,6,3,1]=>([(1,3),(1,4),(1,6),(5,2),(6,5)],7) [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,2,1]=>[2,7,4,6,5,3,1]=>([(1,4),(1,5),(1,6),(6,2),(6,3)],7) [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,2,1]=>[2,6,5,7,4,3,1]=>([(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7) [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,2,1]=>[2,7,5,6,4,3,1]=>([(1,3),(1,4),(1,5),(1,6),(6,2)],7) [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[2,7,6,5,4,3,1]=>([(1,2),(1,3),(1,4),(1,5),(1,6)],7) [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,2,1]=>[2,7,6,4,5,3,1]=>([(1,3),(1,4),(1,5),(1,6),(6,2)],7) [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,2,1]=>[2,5,6,3,4,7,1]=>([(1,4),(1,5),(2,6),(3,6),(4,3),(5,2)],7) [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,2,1]=>[2,5,7,3,4,6,1]=>([(1,4),(1,5),(3,6),(4,3),(5,2),(5,6)],7) [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,2,1]=>[2,6,5,3,7,4,1]=>([(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7) [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,2,1]=>[2,7,5,3,6,4,1]=>([(1,3),(1,4),(1,5),(4,6),(5,2),(5,6)],7) [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,2,1]=>[2,7,6,3,5,4,1]=>([(1,4),(1,5),(1,6),(6,2),(6,3)],7) [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,2,1]=>[2,6,4,7,3,5,1]=>([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(4,6)],7) [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,2,1]=>[2,7,4,6,3,5,1]=>([(1,3),(1,4),(1,5),(4,6),(5,2),(5,6)],7) [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[2,7,4,5,3,6,1]=>([(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7) [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,2,1]=>[2,7,5,4,3,6,1]=>([(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7) [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,2,1]=>[2,6,7,3,4,5,1]=>([(1,5),(1,6),(4,3),(5,4),(6,2)],7) [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,2,1]=>[2,7,6,3,4,5,1]=>([(1,3),(1,4),(1,6),(5,2),(6,5)],7) [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,2,1]=>[2,7,5,3,4,6,1]=>([(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7) [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,2,1]=>[2,7,4,3,5,6,1]=>([(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7) [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,2,1]=>[2,7,3,4,5,6,1]=>([(1,3),(1,6),(4,5),(5,2),(6,4)],7) [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,3,1]=>[3,4,2,5,6,7,1]=>([(1,6),(2,3),(3,6),(4,5),(6,4)],7) [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,3,1]=>[3,4,2,5,7,6,1]=>([(1,6),(2,3),(3,6),(6,4),(6,5)],7) [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,3,1]=>[3,4,2,6,7,5,1]=>([(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7) [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,3,1]=>[3,4,2,7,6,5,1]=>([(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7) [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,3,1]=>[3,4,2,7,5,6,1]=>([(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7) [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,3,1]=>[3,5,2,6,4,7,1]=>([(1,4),(1,6),(2,3),(2,4),(3,6),(4,5),(6,5)],7) [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,3,1]=>[3,5,2,7,4,6,1]=>([(1,4),(1,5),(2,3),(2,4),(3,5),(3,6),(4,6)],7) [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,3,1]=>[3,6,2,5,7,4,1]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(5,6)],7) [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,3,1]=>[3,7,2,5,6,4,1]=>([(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7) [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,3,1]=>[3,7,2,6,5,4,1]=>([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,3,1]=>[3,6,2,7,4,5,1]=>([(1,5),(1,6),(2,3),(2,5),(3,6),(5,4)],7) [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,3,1]=>[3,7,2,6,4,5,1]=>([(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7) [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,3,1]=>[3,7,2,5,4,6,1]=>([(1,4),(1,5),(2,3),(2,4),(2,5),(4,6),(5,6)],7) [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,3,1]=>[3,7,2,4,5,6,1]=>([(1,6),(2,3),(2,6),(4,5),(6,4)],7) [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,4,1]=>[4,3,5,2,6,7,1]=>([(1,6),(2,5),(3,5),(5,6),(6,4)],7) [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,4,1]=>[4,3,5,2,7,6,1]=>([(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7) [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,4,1]=>[4,3,6,2,7,5,1]=>([(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,4,1]=>[4,3,7,2,6,5,1]=>([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,4,1]=>[4,3,7,2,5,6,1]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,5,1]=>[5,3,4,6,2,7,1]=>([(1,6),(2,5),(3,4),(4,6),(6,5)],7) [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,5,1]=>[5,3,4,7,2,6,1]=>([(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>([(2,6),(3,4),(4,5),(5,6)],7) [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,1]=>[7,3,4,5,6,2,1]=>([(3,4),(4,6),(6,5)],7) [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,7,1]=>[7,3,4,6,5,2,1]=>([(3,4),(4,5),(4,6)],7) [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,6,1]=>[6,3,5,7,4,2,1]=>([(2,6),(3,4),(3,5),(5,6)],7) [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,7,1]=>[7,3,5,6,4,2,1]=>([(3,4),(3,5),(5,6)],7) [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,7,1]=>[7,3,6,5,4,2,1]=>([(3,4),(3,5),(3,6)],7) [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,7,1]=>[7,3,6,4,5,2,1]=>([(3,4),(3,5),(5,6)],7) [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,5,1]=>[5,4,6,3,2,7,1]=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7) [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,5,1]=>[5,4,7,3,2,6,1]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,6,1]=>[6,4,5,3,7,2,1]=>([(2,6),(3,6),(4,5),(5,6)],7) [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,7,1]=>[7,4,5,3,6,2,1]=>([(3,6),(4,5),(5,6)],7) [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,7,1]=>[7,4,6,3,5,2,1]=>([(3,6),(4,5),(4,6)],7) [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,6,1]=>[6,5,4,7,3,2,1]=>([(3,6),(4,6),(5,6)],7) [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>[7,5,4,6,3,2,1]=>([(4,6),(5,6)],7) [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,7,1]=>[7,6,4,5,3,2,1]=>([(5,6)],7) [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,7,1]=>[7,6,5,4,3,2,1]=>([],7) [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,6,1]=>[6,5,7,3,4,2,1]=>([(2,6),(3,6),(4,5)],7) [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>[7,5,6,3,4,2,1]=>([(3,6),(4,5)],7) [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,7,1]=>[7,6,5,3,4,2,1]=>([(5,6)],7) [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,7,1]=>[7,6,4,3,5,2,1]=>([(4,6),(5,6)],7) [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,7,1]=>[7,6,3,4,5,2,1]=>([(4,5),(5,6)],7) [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,4,1]=>[4,5,2,3,6,7,1]=>([(1,4),(2,3),(3,6),(4,6),(6,5)],7) [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,4,1]=>[4,5,2,3,7,6,1]=>([(1,4),(2,3),(3,5),(3,6),(4,5),(4,6)],7) [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,4,1]=>[4,6,2,3,7,5,1]=>([(1,4),(2,3),(2,5),(3,6),(4,5),(4,6)],7) [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,4,1]=>[4,7,2,3,6,5,1]=>([(1,4),(2,3),(2,5),(2,6),(4,5),(4,6)],7) [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,4,1]=>[4,7,2,3,5,6,1]=>([(1,4),(2,3),(2,6),(4,6),(6,5)],7) [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,5,1]=>[5,4,2,6,3,7,1]=>([(1,6),(2,6),(3,4),(3,6),(4,5),(6,5)],7) [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,5,1]=>[5,4,2,7,3,6,1]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,6,1]=>[6,4,2,5,7,3,1]=>([(1,6),(2,5),(3,4),(3,5),(5,6)],7) [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,7,1]=>[7,4,2,5,6,3,1]=>([(2,6),(3,4),(3,6),(6,5)],7) [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,7,1]=>[7,4,2,6,5,3,1]=>([(2,5),(2,6),(3,4),(3,5),(3,6)],7) [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,6,1]=>[6,5,2,7,4,3,1]=>([(1,6),(2,6),(3,4),(3,5),(3,6)],7) [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,7,1]=>[7,5,2,6,4,3,1]=>([(2,6),(3,4),(3,5),(3,6)],7) [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,7,1]=>[7,6,2,5,4,3,1]=>([(3,4),(3,5),(3,6)],7) [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,7,1]=>[7,6,2,4,5,3,1]=>([(3,4),(3,5),(5,6)],7) [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,5,1]=>[5,3,6,2,4,7,1]=>([(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,5,1]=>[5,3,7,2,4,6,1]=>([(1,5),(2,4),(2,6),(3,4),(3,5),(5,6)],7) [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,6,1]=>[6,3,5,2,7,4,1]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,7,1]=>[7,3,5,2,6,4,1]=>([(2,5),(2,6),(3,4),(3,5),(4,6)],7) [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,7,1]=>[7,3,6,2,5,4,1]=>([(2,5),(2,6),(3,4),(3,5),(3,6)],7) [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,6,1]=>[6,3,4,7,2,5,1]=>([(1,6),(2,5),(3,4),(4,5),(4,6)],7) [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>[7,3,4,6,2,5,1]=>([(2,6),(3,4),(4,5),(4,6)],7) [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,7,1]=>[7,3,4,5,2,6,1]=>([(2,6),(3,4),(4,5),(5,6)],7) [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,7,1]=>[7,3,5,4,2,6,1]=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7) [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,6,1]=>[6,4,7,3,2,5,1]=>([(1,6),(2,6),(3,5),(4,5),(4,6)],7) [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>[7,4,6,3,2,5,1]=>([(2,6),(3,6),(4,5),(4,6)],7) [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,7,1]=>[7,4,5,3,2,6,1]=>([(2,6),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,7,1]=>[7,5,4,3,2,6,1]=>([(2,6),(3,6),(4,6),(5,6)],7) [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,7,1]=>[7,5,3,4,2,6,1]=>([(2,6),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,5,1]=>[5,6,2,3,4,7,1]=>([(1,3),(2,4),(3,5),(4,6),(5,6)],7) [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,5,1]=>[5,7,2,3,4,6,1]=>([(1,4),(2,3),(2,6),(4,5),(5,6)],7) [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,6,1]=>[6,5,2,3,7,4,1]=>([(1,6),(2,6),(3,4),(4,5),(4,6)],7) [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,7,1]=>[7,5,2,3,6,4,1]=>([(2,6),(3,4),(4,5),(4,6)],7) [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,7,1]=>[7,6,2,3,5,4,1]=>([(3,4),(4,5),(4,6)],7) [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,6,1]=>[6,4,2,7,3,5,1]=>([(1,6),(2,5),(2,6),(3,4),(3,6),(4,5)],7) [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,7,1]=>[7,4,2,6,3,5,1]=>([(2,5),(2,6),(3,4),(3,5),(4,6)],7) [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,7,1]=>[7,4,2,5,3,6,1]=>([(2,5),(3,4),(3,5),(4,6),(5,6)],7) [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,7,1]=>[7,5,2,4,3,6,1]=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7) [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,6,1]=>[6,3,7,2,4,5,1]=>([(1,6),(2,5),(3,5),(3,6),(6,4)],7) [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>[7,3,6,2,4,5,1]=>([(2,6),(3,4),(3,6),(6,5)],7) [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,7,1]=>[7,3,5,2,4,6,1]=>([(2,5),(3,4),(3,5),(4,6),(5,6)],7) [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,7,1]=>[7,3,4,2,5,6,1]=>([(2,6),(3,4),(4,6),(6,5)],7) [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,7,1]=>[7,4,3,2,5,6,1]=>([(2,6),(3,6),(4,6),(6,5)],7) [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,6,1]=>[6,7,2,3,4,5,1]=>([(1,6),(2,4),(5,3),(6,5)],7) [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>[7,6,2,3,4,5,1]=>([(3,4),(4,6),(6,5)],7) [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,7,1]=>[7,5,2,3,4,6,1]=>([(2,6),(3,4),(4,5),(5,6)],7) [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,7,1]=>[7,4,2,3,5,6,1]=>([(2,6),(3,4),(4,6),(6,5)],7) [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,7,1]=>[7,3,2,4,5,6,1]=>([(2,6),(3,6),(4,5),(6,4)],7) [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>([(2,6),(4,5),(5,3),(6,4)],7) [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1,2]=>[3,1,4,5,6,7,2]=>([(0,6),(1,3),(1,6),(4,2),(5,4),(6,5)],7) [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,1,2]=>[3,1,4,5,7,6,2]=>([(0,6),(1,4),(1,6),(5,2),(5,3),(6,5)],7) [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,1,2]=>[3,1,4,6,7,5,2]=>([(0,6),(1,3),(1,6),(5,2),(6,4),(6,5)],7) [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,1,2]=>[3,1,4,7,6,5,2]=>([(0,6),(1,2),(1,6),(6,3),(6,4),(6,5)],7) [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,1,2]=>[3,1,4,7,5,6,2]=>([(0,6),(1,3),(1,6),(5,2),(6,4),(6,5)],7) [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,1,2]=>[3,1,5,6,4,7,2]=>([(0,5),(0,6),(1,2),(1,5),(1,6),(3,4),(5,3),(6,4)],7) [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,1,2]=>[3,1,5,7,4,6,2]=>([(0,5),(0,6),(1,3),(1,5),(1,6),(5,4),(6,2),(6,4)],7) [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,1,2]=>[3,1,6,5,7,4,2]=>([(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(5,3),(6,3)],7) [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,1,2]=>[3,1,7,5,6,4,2]=>([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(6,2)],7) [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,1,2]=>[3,1,7,6,5,4,2]=>([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7) [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,1,2]=>[3,1,6,7,4,5,2]=>([(0,5),(0,6),(1,2),(1,5),(1,6),(5,4),(6,3)],7) [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,1,2]=>[3,1,7,6,4,5,2]=>([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(6,2)],7) [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,1,2]=>[3,1,7,5,4,6,2]=>([(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(5,3),(6,3)],7) [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,1,2]=>[3,1,7,4,5,6,2]=>([(0,5),(0,6),(1,3),(1,5),(1,6),(4,2),(6,4)],7) [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,1,2]=>[4,1,5,3,6,7,2]=>([(0,5),(1,3),(1,4),(1,5),(4,6),(5,6),(6,2)],7) [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,1,2]=>[4,1,5,3,7,6,2]=>([(0,6),(1,2),(1,3),(1,6),(3,4),(3,5),(6,4),(6,5)],7) [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,1,2]=>[4,1,6,3,7,5,2]=>([(0,2),(0,3),(0,6),(1,5),(1,6),(3,4),(3,5),(6,4)],7) [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,1,2]=>[4,1,7,3,6,5,2]=>([(0,2),(0,3),(0,6),(1,4),(1,5),(1,6),(3,4),(3,5)],7) [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,1,2]=>[4,1,7,3,5,6,2]=>([(0,5),(0,6),(1,3),(1,4),(1,5),(4,6),(6,2)],7) [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,1,2]=>[5,1,4,6,3,7,2]=>([(0,6),(1,2),(1,3),(1,4),(3,6),(4,5),(6,5)],7) [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,1,2]=>[5,1,4,7,3,6,2]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(3,6),(4,5),(4,6)],7) [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,1,2]=>[6,1,4,5,7,3,2]=>([(0,6),(1,2),(1,3),(1,5),(4,6),(5,4)],7) [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,1,2]=>[7,1,4,5,6,3,2]=>([(1,3),(1,4),(1,6),(5,2),(6,5)],7) [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,1,2]=>[7,1,4,6,5,3,2]=>([(1,4),(1,5),(1,6),(6,2),(6,3)],7) [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,1,2]=>[6,1,5,7,4,3,2]=>([(0,6),(1,2),(1,3),(1,4),(1,5),(5,6)],7) [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,1,2]=>[7,1,5,6,4,3,2]=>([(1,3),(1,4),(1,5),(1,6),(6,2)],7) [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,1,2]=>[7,1,6,5,4,3,2]=>([(1,2),(1,3),(1,4),(1,5),(1,6)],7) [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,1,2]=>[7,1,6,4,5,3,2]=>([(1,3),(1,4),(1,5),(1,6),(6,2)],7) [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,1,2]=>[5,1,6,3,4,7,2]=>([(0,6),(1,2),(1,4),(1,6),(3,5),(4,3),(6,5)],7) [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,1,2]=>[5,1,7,3,4,6,2]=>([(0,5),(0,6),(1,2),(1,4),(1,6),(3,5),(4,3)],7) [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,1,2]=>[6,1,5,3,7,4,2]=>([(0,6),(1,3),(1,4),(1,5),(4,6),(5,2),(5,6)],7) [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,1,2]=>[7,1,5,3,6,4,2]=>([(1,3),(1,4),(1,5),(4,6),(5,2),(5,6)],7) [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,1,2]=>[7,1,6,3,5,4,2]=>([(1,4),(1,5),(1,6),(6,2),(6,3)],7) [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,1,2]=>[6,1,4,7,3,5,2]=>([(0,6),(1,2),(1,3),(1,4),(3,5),(4,5),(4,6)],7) [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,1,2]=>[7,1,4,6,3,5,2]=>([(1,3),(1,4),(1,5),(4,6),(5,2),(5,6)],7) [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,1,2]=>[7,1,4,5,3,6,2]=>([(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7) [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,1,2]=>[7,1,5,4,3,6,2]=>([(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7) [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,1,2]=>[6,1,7,3,4,5,2]=>([(0,6),(1,3),(1,5),(1,6),(4,2),(5,4)],7) [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,1,2]=>[7,1,6,3,4,5,2]=>([(1,3),(1,4),(1,6),(5,2),(6,5)],7) [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,1,2]=>[7,1,5,3,4,6,2]=>([(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7) [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,1,2]=>[7,1,4,3,5,6,2]=>([(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7) [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>[7,1,3,4,5,6,2]=>([(1,3),(1,6),(4,5),(5,2),(6,4)],7) [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]=>([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(5,4)],7) [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,1,3]=>[2,4,1,5,7,6,3]=>([(0,5),(0,6),(1,4),(1,5),(4,6),(6,2),(6,3)],7) [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,1,3]=>[2,4,1,6,7,5,3]=>([(0,3),(0,6),(1,4),(1,5),(1,6),(3,4),(3,5),(5,2)],7) [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,1,3]=>[2,4,1,7,6,5,3]=>([(0,2),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5)],7) [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,1,3]=>[2,4,1,7,5,6,3]=>([(0,3),(0,6),(1,4),(1,5),(1,6),(3,4),(3,5),(5,2)],7) [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,1,3]=>[2,5,1,6,4,7,3]=>([(0,2),(0,4),(0,6),(1,4),(1,5),(1,6),(2,5),(5,3),(6,3)],7) [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,1,3]=>[2,5,1,7,4,6,3]=>([(0,2),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(6,3)],7) [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,1,3]=>[2,6,1,5,7,4,3]=>([(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(6,3)],7) [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,1,3]=>[2,7,1,5,6,4,3]=>([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(6,2)],7) [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,1,3]=>[2,7,1,6,5,4,3]=>([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7) [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,1,3]=>[2,6,1,7,4,5,3]=>([(0,3),(0,5),(0,6),(1,4),(1,5),(1,6),(3,4),(6,2)],7) [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,1,3]=>[2,7,1,6,4,5,3]=>([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(6,2)],7) [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,1,3]=>[2,7,1,5,4,6,3]=>([(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(5,3),(6,3)],7) [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,1,3]=>[2,7,1,4,5,6,3]=>([(0,5),(0,6),(1,3),(1,5),(1,6),(4,2),(6,4)],7) [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]=>([(0,5),(0,6),(1,4),(3,6),(4,3),(4,5),(6,2)],7) [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,1,4]=>[2,3,5,1,7,6,4]=>([(0,2),(1,4),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5)],7) [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,1,4]=>[2,3,6,1,7,5,4]=>([(0,3),(1,4),(1,5),(1,6),(2,6),(3,2),(3,4),(3,5)],7) [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,1,4]=>[2,3,7,1,6,5,4]=>([(0,3),(1,4),(1,5),(1,6),(3,2),(3,4),(3,5),(3,6)],7) [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,1,4]=>[2,3,7,1,5,6,4]=>([(0,5),(0,6),(1,4),(4,3),(4,5),(4,6),(6,2)],7) [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1,5]=>[2,3,4,6,1,7,5]=>([(0,5),(0,6),(1,3),(2,6),(3,4),(4,2),(4,5)],7) [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,1,5]=>[2,3,4,7,1,6,5]=>([(0,5),(0,6),(1,3),(3,4),(4,2),(4,5),(4,6)],7) [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1,6]=>[2,3,4,5,7,1,6]=>([(0,6),(1,4),(3,5),(4,3),(5,2),(5,6)],7) [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,1,7]=>[2,3,4,6,5,1,7]=>([(0,6),(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7) [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,1,6]=>[2,3,5,7,4,1,6]=>([(0,6),(1,5),(3,6),(4,2),(4,6),(5,3),(5,4)],7) [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,1,7]=>[2,3,5,6,4,1,7]=>([(0,6),(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7) [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,1,7]=>[2,3,6,5,4,1,7]=>([(0,6),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7) [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,1,7]=>[2,3,6,4,5,1,7]=>([(0,6),(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7) [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,1,5]=>[2,4,6,3,1,7,5]=>([(0,5),(0,6),(1,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6)],7) [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,1,5]=>[2,4,7,3,1,6,5]=>([(0,5),(0,6),(1,3),(1,4),(3,5),(3,6),(4,2),(4,5),(4,6)],7) [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,1,6]=>[2,4,5,3,7,1,6]=>([(0,6),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7) [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,1,7]=>[2,4,5,3,6,1,7]=>([(0,6),(1,3),(1,4),(2,5),(3,5),(4,2),(5,6)],7) [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,1,7]=>[2,4,6,3,5,1,7]=>([(0,6),(1,3),(1,4),(2,6),(3,5),(4,2),(4,5),(5,6)],7) [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,1,6]=>[2,5,4,7,3,1,6]=>([(0,6),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,1,7]=>[2,5,4,6,3,1,7]=>([(0,6),(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7) [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,1,7]=>[2,6,4,5,3,1,7]=>([(0,6),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7) [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,1,7]=>[2,6,5,4,3,1,7]=>([(0,6),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,1,6]=>[2,5,7,3,4,1,6]=>([(0,6),(1,4),(1,5),(3,6),(4,3),(5,2),(5,6)],7) [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,1,7]=>[2,5,6,3,4,1,7]=>([(0,6),(1,4),(1,5),(2,6),(3,6),(4,3),(5,2)],7) [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,1,7]=>[2,6,5,3,4,1,7]=>([(0,6),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7) [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,1,7]=>[2,6,4,3,5,1,7]=>([(0,6),(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7) [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,1,7]=>[2,6,3,4,5,1,7]=>([(0,6),(1,3),(1,5),(2,6),(3,6),(4,2),(5,4)],7) [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,1,4]=>[3,5,2,1,6,7,4]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(6,4)],7) [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,1,4]=>[3,5,2,1,7,6,4]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6)],7) [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,1,4]=>[3,6,2,1,7,5,4]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6)],7) [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,1,4]=>[3,7,2,1,6,5,4]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7) [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,1,4]=>[3,7,2,1,5,6,4]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7) [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,1,5]=>[3,4,2,6,1,7,5]=>([(0,5),(0,6),(1,4),(1,6),(2,3),(3,5),(3,6),(5,4)],7) [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,1,5]=>[3,4,2,7,1,6,5]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7) [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,1,6]=>[3,4,2,5,7,1,6]=>([(0,6),(1,5),(2,3),(3,6),(6,4),(6,5)],7) [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,1,7]=>[3,4,2,5,6,1,7]=>([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7) [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,1,7]=>[3,4,2,6,5,1,7]=>([(0,6),(1,4),(1,5),(2,3),(3,4),(3,5),(4,6),(5,6)],7) [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,1,6]=>[3,5,2,7,4,1,6]=>([(0,6),(1,4),(1,5),(2,3),(2,4),(3,5),(3,6),(4,6)],7) [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,1,7]=>[3,5,2,6,4,1,7]=>([(0,6),(1,4),(1,5),(2,3),(2,4),(3,5),(4,6),(5,6)],7) [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,1,7]=>[3,6,2,5,4,1,7]=>([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,1,7]=>[3,6,2,4,5,1,7]=>([(0,6),(1,5),(2,3),(2,5),(3,6),(4,6),(5,4)],7) [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,1,5]=>[4,3,6,2,1,7,5]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7) [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,1,5]=>[4,3,7,2,1,6,5]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,1,6]=>[4,3,5,2,7,1,6]=>([(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7) [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,1,7]=>[4,3,5,2,6,1,7]=>([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7) [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,1,7]=>[4,3,6,2,5,1,7]=>([(0,6),(1,5),(2,4),(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]=>[7,4,3,2,5,1,6]=>[5,3,4,7,2,1,6]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7) [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,1,7]=>[5,3,4,6,2,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,1,7]=>[6,3,4,5,2,1,7]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,1,7]=>[6,3,5,4,2,1,7]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,1,6]=>[5,4,7,3,2,1,6]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,1,7]=>[5,4,6,3,2,1,7]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,1,7]=>[6,4,5,3,2,1,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,1,7]=>[6,5,4,3,2,1,7]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,1,7]=>[6,5,3,4,2,1,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,1,5]=>[4,6,2,3,1,7,5]=>([(0,5),(0,6),(1,4),(2,3),(2,5),(3,6),(4,5),(4,6)],7) [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,1,5]=>[4,7,2,3,1,6,5]=>([(0,5),(0,6),(1,4),(2,3),(2,5),(2,6),(4,5),(4,6)],7) [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,1,6]=>[4,5,2,3,7,1,6]=>([(0,6),(1,4),(2,3),(3,5),(3,6),(4,5),(4,6)],7) [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,1,7]=>[4,5,2,3,6,1,7]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(6,5)],7) [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,1,7]=>[4,6,2,3,5,1,7]=>([(0,6),(1,4),(2,3),(2,5),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,1,6]=>[5,4,2,7,3,1,6]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7) [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,1,7]=>[5,4,2,6,3,1,7]=>([(0,6),(1,5),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,1,7]=>[6,4,2,5,3,1,7]=>([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,1,7]=>[6,5,2,4,3,1,7]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,1,6]=>[5,3,7,2,4,1,6]=>([(0,6),(1,5),(2,4),(2,6),(3,4),(3,5),(5,6)],7) [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,1,7]=>[5,3,6,2,4,1,7]=>([(0,6),(1,5),(2,4),(3,4),(3,5),(4,6),(5,6)],7) [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,1,7]=>[6,3,5,2,4,1,7]=>([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,1,7]=>[6,3,4,2,5,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,1,7]=>[6,4,3,2,5,1,7]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7) [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,1,6]=>[5,7,2,3,4,1,6]=>([(0,6),(1,4),(2,3),(2,6),(4,5),(5,6)],7) [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,1,7]=>[5,6,2,3,4,1,7]=>([(0,6),(1,3),(2,4),(3,5),(4,6),(5,6)],7) [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,1,7]=>[6,5,2,3,4,1,7]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,1,7]=>[6,4,2,3,5,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7) [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,1,7]=>[6,3,2,4,5,1,7]=>([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7) [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7) [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,2,3]=>[4,1,2,5,6,7,3]=>([(0,6),(1,4),(4,3),(4,6),(5,2),(6,5)],7) [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,1,2,3]=>[4,1,2,5,7,6,3]=>([(0,6),(1,5),(5,2),(5,6),(6,3),(6,4)],7) [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,1,2,3]=>[4,1,2,6,7,5,3]=>([(0,5),(0,6),(1,4),(4,3),(4,5),(4,6),(6,2)],7) [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,1,2,3]=>[4,1,2,7,6,5,3]=>([(0,3),(1,4),(1,5),(1,6),(3,2),(3,4),(3,5),(3,6)],7) [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,1,2,3]=>[4,1,2,7,5,6,3]=>([(0,5),(0,6),(1,4),(4,3),(4,5),(4,6),(6,2)],7) [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,1,2,3]=>[5,1,2,6,4,7,3]=>([(0,6),(1,4),(3,5),(4,2),(4,3),(4,6),(6,5)],7) [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,1,2,3]=>[5,1,2,7,4,6,3]=>([(0,5),(0,6),(1,4),(3,5),(4,2),(4,3),(4,6)],7) [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,1,2,3]=>[6,1,2,5,7,4,3]=>([(0,6),(1,5),(4,6),(5,2),(5,3),(5,4)],7) [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,1,2,3]=>[7,1,2,5,6,4,3]=>([(1,6),(5,4),(6,2),(6,3),(6,5)],7) [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,1,2,3]=>[7,1,2,6,5,4,3]=>([(1,6),(6,2),(6,3),(6,4),(6,5)],7) [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,1,2,3]=>[6,1,2,7,4,5,3]=>([(0,6),(1,5),(4,3),(5,2),(5,4),(5,6)],7) [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,1,2,3]=>[7,1,2,6,4,5,3]=>([(1,6),(5,4),(6,2),(6,3),(6,5)],7) [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,1,2,3]=>[7,1,2,5,4,6,3]=>([(1,5),(3,6),(4,6),(5,2),(5,3),(5,4)],7) [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[7,1,2,4,5,6,3]=>([(1,6),(4,5),(5,3),(6,2),(6,4)],7) [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]=>([(0,3),(0,6),(1,4),(1,6),(3,4),(3,5),(5,2),(6,5)],7) [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,1,2,4]=>[3,1,5,2,7,6,4]=>([(0,2),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4)],7) [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,1,2,4]=>[3,1,6,2,7,5,4]=>([(0,2),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(6,3)],7) [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,1,2,4]=>[3,1,7,2,6,5,4]=>([(0,2),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5)],7) [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,1,2,4]=>[3,1,7,2,5,6,4]=>([(0,3),(0,6),(1,4),(1,5),(1,6),(3,4),(3,5),(5,2)],7) [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]=>([(0,6),(1,3),(1,6),(2,5),(3,4),(3,5),(6,2),(6,4)],7) [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,1,2,5]=>[3,1,4,7,2,6,5]=>([(0,6),(1,3),(1,6),(3,4),(3,5),(6,2),(6,4),(6,5)],7) [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1,2,6]=>[3,1,4,5,7,2,6]=>([(0,6),(1,3),(1,6),(3,5),(4,2),(4,5),(6,4)],7) [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,2,7]=>[3,1,4,5,6,2,7]=>([(0,6),(1,3),(1,6),(2,5),(3,5),(4,2),(6,4)],7) [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,1,2,7]=>[3,1,4,6,5,2,7]=>([(0,5),(1,2),(1,5),(2,6),(3,6),(4,6),(5,3),(5,4)],7) [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,1,2,6]=>[3,1,5,7,4,2,6]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7) [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,1,2,7]=>[3,1,5,6,4,2,7]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7) [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,1,2,7]=>[3,1,6,5,4,2,7]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,1,2,7]=>[3,1,6,4,5,2,7]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7) [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,1,2,5]=>[4,1,6,3,2,7,5]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6)],7) [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,1,2,5]=>[4,1,7,3,2,6,5]=>([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6)],7) [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,1,2,6]=>[4,1,5,3,7,2,6]=>([(0,4),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,1,2,7]=>[4,1,5,3,6,2,7]=>([(0,6),(1,2),(1,3),(1,6),(2,5),(3,4),(5,4),(6,5)],7) [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,1,2,7]=>[4,1,6,3,5,2,7]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,6),(4,6),(5,6)],7) [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,1,2,6]=>[5,1,4,7,3,2,6]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(4,6)],7) [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,1,2,7]=>[5,1,4,6,3,2,7]=>([(0,5),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(5,6)],7) [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,1,2,7]=>[6,1,4,5,3,2,7]=>([(0,6),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7) [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,1,2,7]=>[6,1,5,4,3,2,7]=>([(0,6),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>[5,1,7,3,4,2,6]=>([(0,5),(0,6),(1,3),(1,4),(1,5),(2,6),(3,6),(4,2)],7) [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,1,2,7]=>[5,1,6,3,4,2,7]=>([(0,5),(1,3),(1,4),(1,5),(2,6),(3,6),(4,2),(5,6)],7) [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,1,2,7]=>[6,1,5,3,4,2,7]=>([(0,6),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7) [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,1,2,7]=>[6,1,4,3,5,2,7]=>([(0,6),(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7) [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,1,2,7]=>[6,1,3,4,5,2,7]=>([(0,6),(1,3),(1,5),(2,6),(3,6),(4,2),(5,4)],7) [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,3,4]=>[2,5,1,3,6,7,4]=>([(0,6),(1,3),(1,6),(3,5),(5,4),(6,2),(6,5)],7) [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,1,3,4]=>[2,5,1,3,7,6,4]=>([(0,6),(1,3),(1,6),(3,4),(3,5),(6,2),(6,4),(6,5)],7) [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,1,3,4]=>[2,6,1,3,7,5,4]=>([(0,6),(1,4),(1,6),(4,5),(6,2),(6,3),(6,5)],7) [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,1,3,4]=>[2,7,1,3,6,5,4]=>([(0,6),(1,2),(1,6),(6,3),(6,4),(6,5)],7) [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,1,3,4]=>[2,7,1,3,5,6,4]=>([(0,6),(1,3),(1,6),(5,2),(6,4),(6,5)],7) [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]=>([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3),(6,4)],7) [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,1,3,5]=>[2,4,1,7,3,6,5]=>([(0,2),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4)],7) [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,3,6]=>[2,4,1,5,7,3,6]=>([(0,3),(0,6),(1,5),(1,6),(3,5),(5,2),(5,4),(6,4)],7) [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,3,7]=>[2,4,1,5,6,3,7]=>([(0,3),(0,6),(1,4),(1,6),(2,5),(3,4),(4,2),(6,5)],7) [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,1,3,7]=>[2,4,1,6,5,3,7]=>([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,1,3,6]=>[2,5,1,7,4,3,6]=>([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,6),(4,6),(5,6)],7) [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,1,3,7]=>[2,5,1,6,4,3,7]=>([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(3,6),(4,6),(5,6)],7) [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,1,3,7]=>[2,6,1,5,4,3,7]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7) [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,1,3,7]=>[2,6,1,4,5,3,7]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7) [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,4,5]=>[2,3,6,1,4,7,5]=>([(0,6),(1,4),(3,5),(4,3),(4,6),(6,2),(6,5)],7) [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,1,4,5]=>[2,3,7,1,4,6,5]=>([(0,6),(1,5),(5,2),(5,6),(6,3),(6,4)],7) [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1,4,6]=>[2,3,5,1,7,4,6]=>([(0,2),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4)],7) [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,4,7]=>[2,3,5,1,6,4,7]=>([(0,3),(1,5),(1,6),(2,6),(3,2),(3,5),(5,4),(6,4)],7) [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,1,4,7]=>[2,3,6,1,5,4,7]=>([(0,4),(0,5),(1,2),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,5,6]=>[2,3,4,7,1,5,6]=>([(0,6),(1,4),(4,5),(5,2),(5,6),(6,3)],7) [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,5,7]=>[2,3,4,6,1,5,7]=>([(0,6),(1,4),(2,5),(3,2),(3,6),(4,3),(6,5)],7) [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,1,6,7]=>[2,3,5,4,1,6,7]=>([(0,6),(1,5),(2,6),(3,6),(5,2),(5,3),(6,4)],7) [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,1,5,6]=>[2,4,7,3,1,5,6]=>([(0,6),(1,3),(1,5),(3,6),(5,2),(5,6),(6,4)],7) [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,1,5,7]=>[2,4,6,3,1,5,7]=>([(0,6),(1,2),(1,4),(2,6),(3,5),(4,3),(4,6),(6,5)],7) [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,1,6,7]=>[2,4,5,3,1,6,7]=>([(0,6),(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7) [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,1,6,7]=>[2,5,4,3,1,6,7]=>([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7) [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,1,6,7]=>[2,5,3,4,1,6,7]=>([(0,6),(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7) [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,1,4,5]=>[3,6,2,1,4,7,5]=>([(0,6),(1,6),(2,4),(2,6),(4,5),(6,3),(6,5)],7) [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,1,4,5]=>[3,7,2,1,4,6,5]=>([(0,6),(1,6),(2,3),(2,6),(6,4),(6,5)],7) [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,1,4,6]=>[3,5,2,1,7,4,6]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(5,4)],7) [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,1,4,7]=>[3,5,2,1,6,4,7]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(5,4),(6,4)],7) [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,1,4,7]=>[3,6,2,1,5,4,7]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,1,5,6]=>[3,4,2,7,1,5,6]=>([(0,6),(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7) [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,1,5,7]=>[3,4,2,6,1,5,7]=>([(0,6),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7) [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,1,6,7]=>[3,4,2,5,1,6,7]=>([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7) [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,1,6,7]=>[3,5,2,4,1,6,7]=>([(0,6),(1,5),(2,3),(2,5),(3,6),(5,6),(6,4)],7) [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,1,5,6]=>[4,3,7,2,1,5,6]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7) [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,1,5,7]=>[4,3,6,2,1,5,7]=>([(0,6),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7) [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,1,6,7]=>[4,3,5,2,1,6,7]=>([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,1,6,7]=>[5,3,4,2,1,6,7]=>([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,1,6,7]=>[5,4,3,2,1,6,7]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7) [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,1,5,6]=>[4,7,2,3,1,5,6]=>([(0,6),(1,4),(2,3),(2,6),(4,6),(6,5)],7) [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,1,5,7]=>[4,6,2,3,1,5,7]=>([(0,6),(1,3),(2,4),(2,6),(3,6),(4,5),(6,5)],7) [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,1,6,7]=>[4,5,2,3,1,6,7]=>([(0,6),(1,4),(2,3),(3,6),(4,6),(6,5)],7) [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,1,6,7]=>[5,4,2,3,1,6,7]=>([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7) [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,1,6,7]=>[5,3,2,4,1,6,7]=>([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7) [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7) [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,2,3,4]=>[5,1,2,3,6,7,4]=>([(0,6),(1,4),(4,5),(5,2),(5,6),(6,3)],7) [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,7,5,1,2,3,4]=>[5,1,2,3,7,6,4]=>([(0,5),(0,6),(1,3),(3,4),(4,2),(4,5),(4,6)],7) [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,6,1,2,3,4]=>[6,1,2,3,7,5,4]=>([(0,6),(1,4),(4,5),(5,2),(5,3),(5,6)],7) [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,7,1,2,3,4]=>[7,1,2,3,6,5,4]=>([(1,5),(5,6),(6,2),(6,3),(6,4)],7) [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>([(1,5),(4,3),(5,6),(6,2),(6,4)],7) [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,2,3,5]=>[4,1,2,6,3,7,5]=>([(0,2),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4)],7) [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,7,4,1,2,3,5]=>[4,1,2,7,3,6,5]=>([(0,2),(1,4),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5)],7) [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,2,3,6]=>[4,1,2,5,7,3,6]=>([(0,6),(1,4),(3,5),(4,3),(4,6),(6,2),(6,5)],7) [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,2,3,7]=>[4,1,2,5,6,3,7]=>([(0,6),(1,4),(2,5),(3,5),(4,3),(4,6),(6,2)],7) [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,6,4,1,2,3,7]=>[4,1,2,6,5,3,7]=>([(0,4),(0,5),(1,2),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,5,1,2,3,6]=>[5,1,2,7,4,3,6]=>([(0,5),(0,6),(1,4),(2,6),(3,6),(4,2),(4,3),(4,5)],7) [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,5,1,2,3,7]=>[5,1,2,6,4,3,7]=>([(0,5),(1,4),(2,6),(3,6),(4,2),(4,3),(4,5),(5,6)],7) [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,6,1,2,3,7]=>[6,1,2,5,4,3,7]=>([(0,6),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7) [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>([(0,6),(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7) [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,2,4,5]=>[3,1,6,2,4,7,5]=>([(0,3),(0,6),(1,5),(1,6),(3,5),(5,2),(5,4),(6,4)],7) [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,7,3,1,2,4,5]=>[3,1,7,2,4,6,5]=>([(0,5),(0,6),(1,4),(1,5),(4,6),(6,2),(6,3)],7) [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,2,4,6]=>[3,1,5,2,7,4,6]=>([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3),(6,4)],7) [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,2,4,7]=>[3,1,5,2,6,4,7]=>([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4)],7) [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,6,3,1,2,4,7]=>[3,1,6,2,5,4,7]=>([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,2,5,6]=>[3,1,4,7,2,5,6]=>([(0,6),(1,3),(1,6),(3,5),(5,4),(6,2),(6,5)],7) [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,2,5,7]=>[3,1,4,6,2,5,7]=>([(0,6),(1,3),(1,6),(2,4),(3,5),(5,4),(6,2),(6,5)],7) [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,2,6,7]=>[3,1,4,5,2,6,7]=>([(0,6),(1,3),(1,6),(2,5),(3,5),(5,4),(6,2)],7) [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,1,2,6,7]=>[3,1,5,4,2,6,7]=>([(0,4),(0,5),(1,2),(1,4),(1,5),(2,6),(4,6),(5,6),(6,3)],7) [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,4,1,2,5,6]=>[4,1,7,3,2,5,6]=>([(0,5),(0,6),(1,2),(1,3),(1,5),(2,6),(3,6),(6,4)],7) [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,4,1,2,5,7]=>[4,1,6,3,2,5,7]=>([(0,4),(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(6,5)],7) [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,4,1,2,6,7]=>[4,1,5,3,2,6,7]=>([(0,5),(1,2),(1,3),(1,5),(2,6),(3,6),(5,6),(6,4)],7) [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,5,1,2,6,7]=>[5,1,4,3,2,6,7]=>([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7) [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,4,5,1,2,6,7]=>[5,1,3,4,2,6,7]=>([(0,6),(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7) [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,3,4,5]=>[2,6,1,3,4,7,5]=>([(0,6),(1,3),(1,6),(3,5),(4,2),(4,5),(6,4)],7) [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,7,2,1,3,4,5]=>[2,7,1,3,4,6,5]=>([(0,6),(1,4),(1,6),(5,2),(5,3),(6,5)],7) [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,3,4,6]=>[2,5,1,3,7,4,6]=>([(0,6),(1,3),(1,6),(2,5),(3,4),(3,5),(6,2),(6,4)],7) [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,3,4,7]=>[2,5,1,3,6,4,7]=>([(0,6),(1,3),(1,6),(2,4),(3,5),(5,4),(6,2),(6,5)],7) [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,6,2,1,3,4,7]=>[2,6,1,3,5,4,7]=>([(0,5),(1,2),(1,5),(2,6),(3,6),(4,6),(5,3),(5,4)],7) [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,3,5,6]=>[2,4,1,7,3,5,6]=>([(0,3),(0,6),(1,4),(1,6),(3,4),(3,5),(5,2),(6,5)],7) [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,3,5,7]=>[2,4,1,6,3,5,7]=>([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4)],7) [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,3,6,7]=>[2,4,1,5,3,6,7]=>([(0,3),(0,6),(1,5),(1,6),(3,5),(4,2),(5,4),(6,4)],7) [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,2,1,3,6,7]=>[2,5,1,4,3,6,7]=>([(0,4),(0,5),(1,2),(1,4),(1,5),(2,6),(4,6),(5,6),(6,3)],7) [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,4,5,6]=>[2,3,7,1,4,5,6]=>([(0,6),(1,4),(4,3),(4,6),(5,2),(6,5)],7) [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,4,5,7]=>[2,3,6,1,4,5,7]=>([(0,6),(1,4),(2,5),(3,5),(4,3),(4,6),(6,2)],7) [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,4,6,7]=>[2,3,5,1,4,6,7]=>([(0,5),(1,4),(3,6),(4,3),(4,5),(5,6),(6,2)],7) [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]=>([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,4,2,1,5,6,7]=>[2,4,3,1,5,6,7]=>([(0,6),(1,3),(1,4),(3,6),(4,6),(5,2),(6,5)],7) [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,3,1,4,5,6]=>[3,7,2,1,4,5,6]=>([(0,6),(1,6),(2,3),(2,6),(4,5),(6,4)],7) [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,3,1,4,5,7]=>[3,6,2,1,4,5,7]=>([(0,6),(1,6),(2,3),(2,6),(3,5),(4,5),(6,4)],7) [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,3,1,4,6,7]=>[3,5,2,1,4,6,7]=>([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4),(6,5)],7) [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,3,1,5,6,7]=>[3,4,2,1,5,6,7]=>([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,4,1,5,6,7]=>[4,3,2,1,5,6,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7) [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7) [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,2,3,4,5]=>[6,1,2,3,4,7,5]=>([(0,6),(1,4),(3,5),(4,3),(5,2),(5,6)],7) [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]=>([(1,5),(4,6),(5,4),(6,2),(6,3)],7) [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,2,3,4,6]=>[5,1,2,3,7,4,6]=>([(0,5),(0,6),(1,3),(2,6),(3,4),(4,2),(4,5)],7) [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,2,3,4,7]=>[5,1,2,3,6,4,7]=>([(0,6),(1,4),(2,5),(3,2),(3,6),(4,3),(6,5)],7) [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]=>([(0,6),(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7) [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,2,3,5,6]=>[4,1,2,7,3,5,6]=>([(0,5),(0,6),(1,4),(3,6),(4,3),(4,5),(6,2)],7) [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,2,3,5,7]=>[4,1,2,6,3,5,7]=>([(0,3),(1,5),(1,6),(2,6),(3,2),(3,5),(5,4),(6,4)],7) [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,2,3,6,7]=>[4,1,2,5,3,6,7]=>([(0,5),(1,4),(3,6),(4,3),(4,5),(5,6),(6,2)],7) [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]=>([(0,6),(1,5),(2,6),(3,6),(5,2),(5,3),(6,4)],7) [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,2,4,5,6]=>[3,1,7,2,4,5,6]=>([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(5,4)],7) [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,2,4,5,7]=>[3,1,6,2,4,5,7]=>([(0,3),(0,6),(1,4),(1,6),(2,5),(3,4),(4,2),(6,5)],7) [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,2,4,6,7]=>[3,1,5,2,4,6,7]=>([(0,3),(0,6),(1,5),(1,6),(3,5),(4,2),(5,4),(6,4)],7) [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,2,5,6,7]=>[3,1,4,2,5,6,7]=>([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7) [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>([(0,6),(1,3),(1,4),(3,6),(4,6),(5,2),(6,5)],7) [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,3,4,5,6]=>[2,7,1,3,4,5,6]=>([(0,6),(1,3),(1,6),(4,2),(5,4),(6,5)],7) [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,3,4,5,7]=>[2,6,1,3,4,5,7]=>([(0,6),(1,3),(1,6),(2,5),(3,5),(4,2),(6,4)],7) [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,3,4,6,7]=>[2,5,1,3,4,6,7]=>([(0,6),(1,3),(1,6),(2,5),(3,5),(5,4),(6,2)],7) [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,3,5,6,7]=>[2,4,1,3,5,6,7]=>([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7) [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7) [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>([(1,6),(3,5),(4,3),(5,2),(6,4)],7) [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[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) [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[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) [1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,2,8,1]=>[8,7,6,5,4,3,2,1]=>([],8) [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
  • the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
  • the set of left-to-right maximima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
  • the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
  • the set of maximal elements in the decreasing runs of $\pi$ is the set of deficiency positions of $\chi(\pi)$, and
  • the set of minimal elements in the decreasing runs of $\pi$ is the set of deficiency values of $\chi(\pi)$.
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
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$