Identifier
Mp00024: Dyck paths —to 321-avoiding permutation⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
Mp00318: Graphs —dual on components⟶ Graphs
Images
=>
Cc0005;cc-rep-0Cc0020;cc-rep-2Cc0020;cc-rep-3
[1,0]=>[1]=>([],1)=>([],1) [1,0,1,0]=>[2,1]=>([(0,1)],2)=>([(0,1)],2) [1,1,0,0]=>[1,2]=>([],2)=>([],2) [1,0,1,0,1,0]=>[2,1,3]=>([(1,2)],3)=>([(1,2)],3) [1,0,1,1,0,0]=>[2,3,1]=>([(0,2),(1,2)],3)=>([(0,2),(1,2)],3) [1,1,0,0,1,0]=>[3,1,2]=>([(0,2),(1,2)],3)=>([(0,2),(1,2)],3) [1,1,0,1,0,0]=>[1,3,2]=>([(1,2)],3)=>([(1,2)],3) [1,1,1,0,0,0]=>[1,2,3]=>([],3)=>([],3) [1,0,1,0,1,0,1,0]=>[2,1,4,3]=>([(0,3),(1,2)],4)=>([(0,3),(1,2)],4) [1,0,1,0,1,1,0,0]=>[2,4,1,3]=>([(0,3),(1,2),(2,3)],4)=>([(0,3),(1,2),(2,3)],4) [1,0,1,1,0,0,1,0]=>[2,1,3,4]=>([(2,3)],4)=>([(2,3)],4) [1,0,1,1,0,1,0,0]=>[2,3,1,4]=>([(1,3),(2,3)],4)=>([(1,3),(2,3)],4) [1,0,1,1,1,0,0,0]=>[2,3,4,1]=>([(0,3),(1,3),(2,3)],4)=>([(0,3),(1,3),(2,3)],4) [1,1,0,0,1,0,1,0]=>[3,1,4,2]=>([(0,3),(1,2),(2,3)],4)=>([(0,3),(1,2),(2,3)],4) [1,1,0,0,1,1,0,0]=>[3,4,1,2]=>([(0,2),(0,3),(1,2),(1,3)],4)=>([(0,2),(0,3),(1,2),(1,3)],4) [1,1,0,1,0,0,1,0]=>[3,1,2,4]=>([(1,3),(2,3)],4)=>([(1,3),(2,3)],4) [1,1,0,1,0,1,0,0]=>[1,3,2,4]=>([(2,3)],4)=>([(2,3)],4) [1,1,0,1,1,0,0,0]=>[1,3,4,2]=>([(1,3),(2,3)],4)=>([(1,3),(2,3)],4) [1,1,1,0,0,0,1,0]=>[4,1,2,3]=>([(0,3),(1,3),(2,3)],4)=>([(0,3),(1,3),(2,3)],4) [1,1,1,0,0,1,0,0]=>[1,4,2,3]=>([(1,3),(2,3)],4)=>([(1,3),(2,3)],4) [1,1,1,0,1,0,0,0]=>[1,2,4,3]=>([(2,3)],4)=>([(2,3)],4) [1,1,1,1,0,0,0,0]=>[1,2,3,4]=>([],4)=>([],4) [1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5]=>([(1,4),(2,3)],5)=>([(1,4),(2,3)],5) [1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,5]=>([(1,4),(2,3),(3,4)],5)=>([(1,4),(2,3),(3,4)],5) [1,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,3]=>([(0,1),(2,4),(3,4)],5)=>([(0,1),(2,4),(3,4)],5) [1,0,1,0,1,1,0,1,0,0]=>[2,4,1,5,3]=>([(0,4),(1,3),(2,3),(2,4)],5)=>([(0,4),(1,3),(2,3),(2,4)],5) [1,0,1,0,1,1,1,0,0,0]=>[2,4,5,1,3]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5) [1,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,4]=>([(0,1),(2,4),(3,4)],5)=>([(0,1),(2,4),(3,4)],5) [1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,4]=>([(0,4),(1,4),(2,3),(3,4)],5)=>([(0,4),(1,4),(2,3),(3,4)],5) [1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,4]=>([(1,4),(2,3)],5)=>([(1,4),(2,3)],5) [1,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,4]=>([(0,1),(2,4),(3,4)],5)=>([(0,1),(2,4),(3,4)],5) [1,0,1,1,0,1,1,0,0,0]=>[2,3,5,1,4]=>([(0,4),(1,4),(2,3),(3,4)],5)=>([(0,4),(1,4),(2,3),(3,4)],5) [1,0,1,1,1,0,0,0,1,0]=>[2,1,3,4,5]=>([(3,4)],5)=>([(3,4)],5) [1,0,1,1,1,0,0,1,0,0]=>[2,3,1,4,5]=>([(2,4),(3,4)],5)=>([(2,4),(3,4)],5) [1,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,5]=>([(1,4),(2,4),(3,4)],5)=>([(1,4),(2,4),(3,4)],5) [1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>([(0,4),(1,4),(2,4),(3,4)],5)=>([(0,4),(1,4),(2,4),(3,4)],5) [1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,5]=>([(1,4),(2,3),(3,4)],5)=>([(1,4),(2,3),(3,4)],5) [1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,5]=>([(1,3),(1,4),(2,3),(2,4)],5)=>([(1,3),(1,4),(2,3),(2,4)],5) [1,1,0,0,1,1,0,0,1,0]=>[3,1,4,5,2]=>([(0,4),(1,4),(2,3),(3,4)],5)=>([(0,4),(1,4),(2,3),(3,4)],5) [1,1,0,0,1,1,0,1,0,0]=>[3,4,1,5,2]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5) [1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) [1,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4]=>([(0,4),(1,3),(2,3),(2,4)],5)=>([(0,4),(1,3),(2,3),(2,4)],5) [1,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5) [1,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4]=>([(0,1),(2,4),(3,4)],5)=>([(0,1),(2,4),(3,4)],5) [1,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4]=>([(1,4),(2,3)],5)=>([(1,4),(2,3)],5) [1,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4]=>([(1,4),(2,3),(3,4)],5)=>([(1,4),(2,3),(3,4)],5) [1,1,0,1,1,0,0,0,1,0]=>[3,1,2,4,5]=>([(2,4),(3,4)],5)=>([(2,4),(3,4)],5) [1,1,0,1,1,0,0,1,0,0]=>[1,3,2,4,5]=>([(3,4)],5)=>([(3,4)],5) [1,1,0,1,1,0,1,0,0,0]=>[1,3,4,2,5]=>([(2,4),(3,4)],5)=>([(2,4),(3,4)],5) [1,1,0,1,1,1,0,0,0,0]=>[1,3,4,5,2]=>([(1,4),(2,4),(3,4)],5)=>([(1,4),(2,4),(3,4)],5) [1,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5) [1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) [1,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3]=>([(0,4),(1,4),(2,3),(3,4)],5)=>([(0,4),(1,4),(2,3),(3,4)],5) [1,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,3]=>([(1,4),(2,3),(3,4)],5)=>([(1,4),(2,3),(3,4)],5) [1,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3]=>([(1,3),(1,4),(2,3),(2,4)],5)=>([(1,3),(1,4),(2,3),(2,4)],5) [1,1,1,0,1,0,0,0,1,0]=>[4,1,2,3,5]=>([(1,4),(2,4),(3,4)],5)=>([(1,4),(2,4),(3,4)],5) [1,1,1,0,1,0,0,1,0,0]=>[1,4,2,3,5]=>([(2,4),(3,4)],5)=>([(2,4),(3,4)],5) [1,1,1,0,1,0,1,0,0,0]=>[1,2,4,3,5]=>([(3,4)],5)=>([(3,4)],5) [1,1,1,0,1,1,0,0,0,0]=>[1,2,4,5,3]=>([(2,4),(3,4)],5)=>([(2,4),(3,4)],5) [1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>([(0,4),(1,4),(2,4),(3,4)],5)=>([(0,4),(1,4),(2,4),(3,4)],5) [1,1,1,1,0,0,0,1,0,0]=>[1,5,2,3,4]=>([(1,4),(2,4),(3,4)],5)=>([(1,4),(2,4),(3,4)],5) [1,1,1,1,0,0,1,0,0,0]=>[1,2,5,3,4]=>([(2,4),(3,4)],5)=>([(2,4),(3,4)],5) [1,1,1,1,0,1,0,0,0,0]=>[1,2,3,5,4]=>([(3,4)],5)=>([(3,4)],5) [1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>([],5)=>([],5) [1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5]=>([(0,5),(1,4),(2,3)],6)=>([(0,5),(1,4),(2,3)],6) [1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5]=>([(0,1),(2,5),(3,4),(4,5)],6)=>([(0,1),(2,5),(3,4),(4,5)],6) [1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5]=>([(0,1),(2,5),(3,4),(4,5)],6)=>([(0,1),(2,5),(3,4),(4,5)],6) [1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5]=>([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) [1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>([(2,5),(3,4)],6)=>([(2,5),(3,4)],6) [1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,5,6]=>([(2,5),(3,4),(4,5)],6)=>([(2,5),(3,4),(4,5)],6) [1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>([(1,2),(3,5),(4,5)],6)=>([(1,2),(3,5),(4,5)],6) [1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,5,3,6]=>([(1,5),(2,4),(3,4),(3,5)],6)=>([(1,5),(2,4),(3,4),(3,5)],6) [1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,5,1,3,6]=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6) [1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,5,6,3]=>([(0,1),(2,5),(3,5),(4,5)],6)=>([(0,1),(2,5),(3,5),(4,5)],6) [1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,5,6,3]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,5,1,6,3]=>([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) [1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,5,6,1,3]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) [1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,6,4]=>([(0,1),(2,5),(3,4),(4,5)],6)=>([(0,1),(2,5),(3,4),(4,5)],6) [1,0,1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,5,6,3,4]=>([(0,1),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(2,4),(2,5),(3,4),(3,5)],6) [1,0,1,1,0,0,1,1,0,1,0,0]=>[2,5,1,6,3,4]=>([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) [1,0,1,1,0,0,1,1,1,0,0,0]=>[2,5,6,1,3,4]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) [1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,4,6]=>([(1,2),(3,5),(4,5)],6)=>([(1,2),(3,5),(4,5)],6) [1,0,1,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,4,6]=>([(1,5),(2,5),(3,4),(4,5)],6)=>([(1,5),(2,5),(3,4),(4,5)],6) [1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,6]=>([(2,5),(3,4)],6)=>([(2,5),(3,4)],6) [1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,6]=>([(1,2),(3,5),(4,5)],6)=>([(1,2),(3,5),(4,5)],6) [1,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,6]=>([(1,5),(2,5),(3,4),(4,5)],6)=>([(1,5),(2,5),(3,4),(4,5)],6) [1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,3,5,6,4]=>([(1,2),(3,5),(4,5)],6)=>([(1,2),(3,5),(4,5)],6) [1,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,6,4]=>([(0,5),(1,5),(2,4),(3,4)],6)=>([(0,5),(1,5),(2,4),(3,4)],6) [1,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,5,1,6,4]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,5,6,1,4]=>([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) [1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5]=>([(0,1),(2,5),(3,5),(4,5)],6)=>([(0,1),(2,5),(3,5),(4,5)],6) [1,0,1,1,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6) [1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5]=>([(1,2),(3,5),(4,5)],6)=>([(1,2),(3,5),(4,5)],6) [1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,5]=>([(0,5),(1,5),(2,4),(3,4)],6)=>([(0,5),(1,5),(2,4),(3,4)],6) [1,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6) [1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5]=>([(2,5),(3,4)],6)=>([(2,5),(3,4)],6) [1,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,4,6,5]=>([(1,2),(3,5),(4,5)],6)=>([(1,2),(3,5),(4,5)],6) [1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5]=>([(0,1),(2,5),(3,5),(4,5)],6)=>([(0,1),(2,5),(3,5),(4,5)],6) [1,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,4,6,1,5]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6) [1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,5,6]=>([(4,5)],6)=>([(4,5)],6) [1,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,4,5,6]=>([(3,5),(4,5)],6)=>([(3,5),(4,5)],6) [1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,4,1,5,6]=>([(2,5),(3,5),(4,5)],6)=>([(2,5),(3,5),(4,5)],6) [1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,5,1,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>([(1,5),(2,5),(3,5),(4,5)],6) [1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6) [1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5]=>([(0,1),(2,5),(3,4),(4,5)],6)=>([(0,1),(2,5),(3,4),(4,5)],6) [1,1,0,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5]=>([(0,1),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1),(2,4),(2,5),(3,4),(3,5)],6) [1,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,1,0,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5]=>([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) [1,1,0,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) [1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,5,6]=>([(2,5),(3,4),(4,5)],6)=>([(2,5),(3,4),(4,5)],6) [1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,5,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>([(2,4),(2,5),(3,4),(3,5)],6) [1,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,5,2,6]=>([(1,5),(2,5),(3,4),(4,5)],6)=>([(1,5),(2,5),(3,4),(4,5)],6) [1,1,0,0,1,1,0,1,0,1,0,0]=>[3,4,1,5,2,6]=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6) [1,1,0,0,1,1,0,1,1,0,0,0]=>[3,4,5,1,2,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) [1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,5,6,2]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6) [1,1,0,0,1,1,1,0,0,1,0,0]=>[3,4,1,5,6,2]=>([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) [1,1,0,0,1,1,1,0,1,0,0,0]=>[3,4,5,1,6,2]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) [1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) [1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,6,4]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,6,4]=>([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) [1,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,6,2,4]=>([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) [1,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,6,2,4]=>([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)=>([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) [1,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,6,1,2,4]=>([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) [1,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,6]=>([(1,5),(2,4),(3,4),(3,5)],6)=>([(1,5),(2,4),(3,4),(3,5)],6) [1,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,6]=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6) [1,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,6]=>([(1,2),(3,5),(4,5)],6)=>([(1,2),(3,5),(4,5)],6) [1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,6]=>([(2,5),(3,4)],6)=>([(2,5),(3,4)],6) [1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,6]=>([(2,5),(3,4),(4,5)],6)=>([(2,5),(3,4),(4,5)],6) [1,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,6,4]=>([(0,5),(1,5),(2,4),(3,4)],6)=>([(0,5),(1,5),(2,4),(3,4)],6) [1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,6,4]=>([(1,2),(3,5),(4,5)],6)=>([(1,2),(3,5),(4,5)],6) [1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,6,4]=>([(1,5),(2,4),(3,4),(3,5)],6)=>([(1,5),(2,4),(3,4),(3,5)],6) [1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,6,2,4]=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6) [1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,1,0,1,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,5]=>([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) [1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5]=>([(0,5),(1,5),(2,4),(3,4)],6)=>([(0,5),(1,5),(2,4),(3,4)],6) [1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,5]=>([(1,2),(3,5),(4,5)],6)=>([(1,2),(3,5),(4,5)],6) [1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,5]=>([(1,5),(2,5),(3,4),(4,5)],6)=>([(1,5),(2,5),(3,4),(4,5)],6) [1,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5]=>([(1,2),(3,5),(4,5)],6)=>([(1,2),(3,5),(4,5)],6) [1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5]=>([(2,5),(3,4)],6)=>([(2,5),(3,4)],6) [1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5]=>([(1,2),(3,5),(4,5)],6)=>([(1,2),(3,5),(4,5)],6) [1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5]=>([(1,5),(2,5),(3,4),(4,5)],6)=>([(1,5),(2,5),(3,4),(4,5)],6) [1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,4,5,6]=>([(3,5),(4,5)],6)=>([(3,5),(4,5)],6) [1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,4,5,6]=>([(4,5)],6)=>([(4,5)],6) [1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,4,2,5,6]=>([(3,5),(4,5)],6)=>([(3,5),(4,5)],6) [1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,4,5,2,6]=>([(2,5),(3,5),(4,5)],6)=>([(2,5),(3,5),(4,5)],6) [1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,5,6,2]=>([(1,5),(2,5),(3,5),(4,5)],6)=>([(1,5),(2,5),(3,5),(4,5)],6) [1,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,5,2,6,3]=>([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) [1,1,1,0,0,0,1,0,1,1,0,0]=>[4,5,1,2,6,3]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) [1,1,1,0,0,0,1,1,0,0,1,0]=>[4,1,5,6,2,3]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) [1,1,1,0,0,0,1,1,0,1,0,0]=>[4,5,1,6,2,3]=>([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) [1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) [1,1,1,0,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,6]=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6) [1,1,1,0,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,6]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) [1,1,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,6]=>([(1,5),(2,5),(3,4),(4,5)],6)=>([(1,5),(2,5),(3,4),(4,5)],6) [1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,6]=>([(2,5),(3,4),(4,5)],6)=>([(2,5),(3,4),(4,5)],6) [1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,6]=>([(2,4),(2,5),(3,4),(3,5)],6)=>([(2,4),(2,5),(3,4),(3,5)],6) [1,1,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,5,6,3]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6) [1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,5,6,3]=>([(1,5),(2,5),(3,4),(4,5)],6)=>([(1,5),(2,5),(3,4),(4,5)],6) [1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,5,2,6,3]=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6) [1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,5,6,2,3]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) [1,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5]=>([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) [1,1,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) [1,1,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5]=>([(1,5),(2,4),(3,4),(3,5)],6)=>([(1,5),(2,4),(3,4),(3,5)],6) [1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,5]=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6) [1,1,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5]=>([(0,1),(2,5),(3,5),(4,5)],6)=>([(0,1),(2,5),(3,5),(4,5)],6) [1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5]=>([(1,2),(3,5),(4,5)],6)=>([(1,2),(3,5),(4,5)],6) [1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5]=>([(2,5),(3,4)],6)=>([(2,5),(3,4)],6) [1,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,4,6,3,5]=>([(2,5),(3,4),(4,5)],6)=>([(2,5),(3,4),(4,5)],6) [1,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,5,6]=>([(2,5),(3,5),(4,5)],6)=>([(2,5),(3,5),(4,5)],6) [1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,5,6]=>([(3,5),(4,5)],6)=>([(3,5),(4,5)],6) [1,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,5,6]=>([(4,5)],6)=>([(4,5)],6) [1,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,4,5,3,6]=>([(3,5),(4,5)],6)=>([(3,5),(4,5)],6) [1,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,5,6,3]=>([(2,5),(3,5),(4,5)],6)=>([(2,5),(3,5),(4,5)],6) [1,1,1,1,0,0,0,0,1,0,1,0]=>[5,1,6,2,3,4]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) [1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) [1,1,1,1,0,0,0,1,0,0,1,0]=>[5,1,2,6,3,4]=>([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) [1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,6,3,4]=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6) [1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,6,2,3,4]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) [1,1,1,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,6,4]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6) [1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,6,4]=>([(1,5),(2,5),(3,4),(4,5)],6)=>([(1,5),(2,5),(3,4),(4,5)],6) [1,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,6,4]=>([(2,5),(3,4),(4,5)],6)=>([(2,5),(3,4),(4,5)],6) [1,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,5,6,3,4]=>([(2,4),(2,5),(3,4),(3,5)],6)=>([(2,4),(2,5),(3,4),(3,5)],6) [1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,6]=>([(1,5),(2,5),(3,5),(4,5)],6)=>([(1,5),(2,5),(3,5),(4,5)],6) [1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,6]=>([(2,5),(3,5),(4,5)],6)=>([(2,5),(3,5),(4,5)],6) [1,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,6]=>([(3,5),(4,5)],6)=>([(3,5),(4,5)],6) [1,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,6]=>([(4,5)],6)=>([(4,5)],6) [1,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,6,4]=>([(3,5),(4,5)],6)=>([(3,5),(4,5)],6) [1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6) [1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5]=>([(1,5),(2,5),(3,5),(4,5)],6)=>([(1,5),(2,5),(3,5),(4,5)],6) [1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5]=>([(2,5),(3,5),(4,5)],6)=>([(2,5),(3,5),(4,5)],6) [1,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5]=>([(3,5),(4,5)],6)=>([(3,5),(4,5)],6) [1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5]=>([(4,5)],6)=>([(4,5)],6) [1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>([],6)=>([],6) [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,7]=>([(1,6),(2,5),(3,4)],7)=>([(1,6),(2,5),(3,4)],7) [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5,7]=>([(1,2),(3,6),(4,5),(5,6)],7)=>([(1,2),(3,6),(4,5),(5,6)],7) [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5,7]=>([(1,2),(3,6),(4,5),(5,6)],7)=>([(1,2),(3,6),(4,5),(5,6)],7) [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5,7]=>([(1,6),(2,5),(3,4),(3,5),(4,6)],7)=>([(1,6),(2,5),(3,4),(3,5),(4,6)],7) [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5,7]=>([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,7,5]=>([(0,3),(1,2),(4,6),(5,6)],7)=>([(0,3),(1,2),(4,6),(5,6)],7) [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,7,5]=>([(0,6),(1,5),(2,4),(3,4),(5,6)],7)=>([(0,6),(1,5),(2,4),(3,4),(5,6)],7) [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,6,3,7,5]=>([(0,1),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,1),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,6,1,3,7,5]=>([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7)=>([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,6,7,3,5]=>([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,6,7,3,5]=>([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)=>([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,6,1,7,3,5]=>([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)=>([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,6,7,1,3,5]=>([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7) [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,7,5,6]=>([(0,3),(1,2),(4,6),(5,6)],7)=>([(0,3),(1,2),(4,6),(5,6)],7) [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,3,7,5,6]=>([(0,6),(1,5),(2,4),(3,4),(5,6)],7)=>([(0,6),(1,5),(2,4),(3,4),(5,6)],7) [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,7,3,5,6]=>([(0,1),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,1),(2,6),(3,6),(4,5),(5,6)],7) [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,4,1,7,3,5,6]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,7,1,3,5,6]=>([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7)=>([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7) [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,3,5,7,6]=>([(1,6),(2,5),(3,4)],7)=>([(1,6),(2,5),(3,4)],7) [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,4,1,3,5,7,6]=>([(1,2),(3,6),(4,5),(5,6)],7)=>([(1,2),(3,6),(4,5),(5,6)],7) [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,3,7,6]=>([(0,3),(1,2),(4,6),(5,6)],7)=>([(0,3),(1,2),(4,6),(5,6)],7) [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,7,6]=>([(0,1),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,1),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,5,1,3,7,6]=>([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,5,7,3,6]=>([(0,1),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,1),(2,6),(3,6),(4,5),(5,6)],7) [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,4,1,5,7,3,6]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,4,5,1,7,3,6]=>([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)=>([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,5,7,1,3,6]=>([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>([(3,6),(4,5)],7)=>([(3,6),(4,5)],7) [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,5,6,7]=>([(3,6),(4,5),(5,6)],7)=>([(3,6),(4,5),(5,6)],7) [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,5,3,6,7]=>([(2,3),(4,6),(5,6)],7)=>([(2,3),(4,6),(5,6)],7) [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,4,1,5,3,6,7]=>([(2,6),(3,5),(4,5),(4,6)],7)=>([(2,6),(3,5),(4,5),(4,6)],7) [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,4,5,1,3,6,7]=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7) [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,4,5,6,3,7]=>([(1,2),(3,6),(4,6),(5,6)],7)=>([(1,2),(3,6),(4,6),(5,6)],7) [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,4,1,5,6,3,7]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7) [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,4,5,1,6,3,7]=>([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,4,5,6,1,3,7]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,5,6,7,3]=>([(0,1),(2,6),(3,6),(4,6),(5,6)],7)=>([(0,1),(2,6),(3,6),(4,6),(5,6)],7) [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1,5,6,7,3]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,5,1,6,7,3]=>([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,5,6,1,7,3]=>([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,5,6,7,1,3]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,7]=>([(1,2),(3,6),(4,5),(5,6)],7)=>([(1,2),(3,6),(4,5),(5,6)],7) [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,5,1,3,6,4,7]=>([(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>([(1,6),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,7]=>([(1,2),(3,5),(3,6),(4,5),(4,6)],7)=>([(1,2),(3,5),(3,6),(4,5),(4,6)],7) [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,5,1,6,3,4,7]=>([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)=>([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,6,1,3,4,7]=>([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,6,7,4]=>([(0,1),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,1),(2,6),(3,6),(4,5),(5,6)],7) [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,6,7,4]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,5,6,3,7,4]=>([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,5,1,6,3,7,4]=>([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7)=>([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,5,6,1,3,7,4]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,6,7,3,4]=>([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,5,1,6,7,3,4]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7) [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,5,6,1,7,3,4]=>([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,5,6,7,1,3,4]=>([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,6]=>([(0,1),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,1),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,7,4,6]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,5,7,3,4,6]=>([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,5,1,7,3,4,6]=>([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)=>([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,5,7,1,3,4,6]=>([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,4,7,6]=>([(0,3),(1,2),(4,6),(5,6)],7)=>([(0,3),(1,2),(4,6),(5,6)],7) [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,4,7,6]=>([(0,1),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,1),(2,6),(3,6),(4,5),(5,6)],7) [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,7,6]=>([(1,6),(2,5),(3,4)],7)=>([(1,6),(2,5),(3,4)],7) [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,7,6]=>([(0,3),(1,2),(4,6),(5,6)],7)=>([(0,3),(1,2),(4,6),(5,6)],7) [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,7,6]=>([(0,1),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,1),(2,6),(3,6),(4,5),(5,6)],7) [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,3,5,7,4,6]=>([(1,2),(3,6),(4,5),(5,6)],7)=>([(1,2),(3,6),(4,5),(5,6)],7) [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,7,4,6]=>([(0,6),(1,5),(2,4),(3,4),(5,6)],7)=>([(0,6),(1,5),(2,4),(3,4),(5,6)],7) [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,1,7,4,6]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,5,7,1,4,6]=>([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7)=>([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7) [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,7]=>([(2,3),(4,6),(5,6)],7)=>([(2,3),(4,6),(5,6)],7) [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,5,1,3,4,6,7]=>([(2,6),(3,6),(4,5),(5,6)],7)=>([(2,6),(3,6),(4,5),(5,6)],7) [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,3,5,4,6,7]=>([(3,6),(4,5)],7)=>([(3,6),(4,5)],7) [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,1,5,4,6,7]=>([(2,3),(4,6),(5,6)],7)=>([(2,3),(4,6),(5,6)],7) [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,1,4,6,7]=>([(2,6),(3,6),(4,5),(5,6)],7)=>([(2,6),(3,6),(4,5),(5,6)],7) [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,3,5,6,4,7]=>([(2,3),(4,6),(5,6)],7)=>([(2,3),(4,6),(5,6)],7) [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,1,5,6,4,7]=>([(1,6),(2,6),(3,5),(4,5)],7)=>([(1,6),(2,6),(3,5),(4,5)],7) [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,1,6,4,7]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7) [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,6,1,4,7]=>([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,5,6,7,4]=>([(1,2),(3,6),(4,6),(5,6)],7)=>([(1,2),(3,6),(4,6),(5,6)],7) [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1,5,6,7,4]=>([(0,6),(1,6),(2,6),(3,5),(4,5)],7)=>([(0,6),(1,6),(2,6),(3,5),(4,5)],7) [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,5,1,6,7,4]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,5,6,1,7,4]=>([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,5,6,7,1,4]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,6,3,7,4,5]=>([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,6,1,3,7,4,5]=>([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)=>([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7) [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,6,7,3,4,5]=>([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,6,1,7,3,4,5]=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7)=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7) [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,6,7,1,3,4,5]=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,6,3,4,7,5]=>([(0,1),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,1),(2,6),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,6,1,3,4,7,5]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,3,6,4,7,5]=>([(1,2),(3,6),(4,5),(5,6)],7)=>([(1,2),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,7,5]=>([(0,6),(1,5),(2,4),(3,4),(5,6)],7)=>([(0,6),(1,5),(2,4),(3,4),(5,6)],7) [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,6,1,4,7,5]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,3,6,7,4,5]=>([(1,2),(3,5),(3,6),(4,5),(4,6)],7)=>([(1,2),(3,5),(3,6),(4,5),(4,6)],7) [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,1,6,7,4,5]=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,6,1,7,4,5]=>([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7)=>([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7) [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,6,7,1,4,5]=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5,7]=>([(1,2),(3,6),(4,6),(5,6)],7)=>([(1,2),(3,6),(4,6),(5,6)],7) [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5,7]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5,7]=>([(2,3),(4,6),(5,6)],7)=>([(2,3),(4,6),(5,6)],7) [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,5,7]=>([(1,6),(2,6),(3,5),(4,5)],7)=>([(1,6),(2,6),(3,5),(4,5)],7) [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5,7]=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7) [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5,7]=>([(3,6),(4,5)],7)=>([(3,6),(4,5)],7) [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,1,4,6,5,7]=>([(2,3),(4,6),(5,6)],7)=>([(2,3),(4,6),(5,6)],7) [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,7]=>([(1,2),(3,6),(4,6),(5,6)],7)=>([(1,2),(3,6),(4,6),(5,6)],7) [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,4,6,1,5,7]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,7,5]=>([(2,3),(4,6),(5,6)],7)=>([(2,3),(4,6),(5,6)],7) [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,1,4,6,7,5]=>([(1,6),(2,6),(3,5),(4,5)],7)=>([(1,6),(2,6),(3,5),(4,5)],7) [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,4,1,6,7,5]=>([(0,6),(1,6),(2,6),(3,5),(4,5)],7)=>([(0,6),(1,6),(2,6),(3,5),(4,5)],7) [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,4,6,1,7,5]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,6,7,1,5]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,7,3,4,5,6]=>([(0,1),(2,6),(3,6),(4,6),(5,6)],7)=>([(0,1),(2,6),(3,6),(4,6),(5,6)],7) [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,7,1,3,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,6),(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]=>[2,1,3,7,4,5,6]=>([(1,2),(3,6),(4,6),(5,6)],7)=>([(1,2),(3,6),(4,6),(5,6)],7) [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,7,4,5,6]=>([(0,6),(1,6),(2,6),(3,5),(4,5)],7)=>([(0,6),(1,6),(2,6),(3,5),(4,5)],7) [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,7,1,4,5,6]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,3,4,7,5,6]=>([(2,3),(4,6),(5,6)],7)=>([(2,3),(4,6),(5,6)],7) [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,4,7,5,6]=>([(1,6),(2,6),(3,5),(4,5)],7)=>([(1,6),(2,6),(3,5),(4,5)],7) [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,4,1,7,5,6]=>([(0,6),(1,6),(2,6),(3,5),(4,5)],7)=>([(0,6),(1,6),(2,6),(3,5),(4,5)],7) [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,6]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7) [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,3,4,5,7,6]=>([(3,6),(4,5)],7)=>([(3,6),(4,5)],7) [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,5,7,6]=>([(2,3),(4,6),(5,6)],7)=>([(2,3),(4,6),(5,6)],7) [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,4,1,5,7,6]=>([(1,2),(3,6),(4,6),(5,6)],7)=>([(1,2),(3,6),(4,6),(5,6)],7) [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,4,5,1,7,6]=>([(0,1),(2,6),(3,6),(4,6),(5,6)],7)=>([(0,1),(2,6),(3,6),(4,6),(5,6)],7) [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,6]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7]=>([(5,6)],7)=>([(5,6)],7) [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,7]=>([(4,6),(5,6)],7)=>([(4,6),(5,6)],7) [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,4,1,5,6,7]=>([(3,6),(4,6),(5,6)],7)=>([(3,6),(4,6),(5,6)],7) [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,7]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(2,6),(3,6),(4,6),(5,6)],7) [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7) [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7) [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,7]=>([(1,2),(3,6),(4,5),(5,6)],7)=>([(1,2),(3,6),(4,5),(5,6)],7) [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,7]=>([(1,2),(3,5),(3,6),(4,5),(4,6)],7)=>([(1,2),(3,5),(3,6),(4,5),(4,6)],7) [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5,7]=>([(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>([(1,6),(2,5),(3,4),(4,6),(5,6)],7) [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5,7]=>([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)=>([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5,7]=>([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,7,5]=>([(0,6),(1,5),(2,4),(3,4),(5,6)],7)=>([(0,6),(1,5),(2,4),(3,4),(5,6)],7) [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,6,7,5]=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,4,6,2,7,5]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,4,1,6,2,7,5]=>([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)=>([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,4,6,1,2,7,5]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7) [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,7,2,5]=>([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)=>([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7) [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,4,1,6,7,2,5]=>([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7)=>([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7) [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,4,6,1,7,2,5]=>([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)=>([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7) [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,6,7,1,2,5]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,6]=>([(0,6),(1,5),(2,4),(3,4),(5,6)],7)=>([(0,6),(1,5),(2,4),(3,4),(5,6)],7) [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,7,5,6]=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,4,7,2,5,6]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,4,1,7,2,5,6]=>([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7)=>([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7) [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,4,7,1,2,5,6]=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,1,4,2,5,7,6]=>([(1,2),(3,6),(4,5),(5,6)],7)=>([(1,2),(3,6),(4,5),(5,6)],7) [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,4,1,2,5,7,6]=>([(1,2),(3,5),(3,6),(4,5),(4,6)],7)=>([(1,2),(3,5),(3,6),(4,5),(4,6)],7) [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,1,4,5,2,7,6]=>([(0,1),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,1),(2,6),(3,6),(4,5),(5,6)],7) [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,4,1,5,2,7,6]=>([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,7,6]=>([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,6),(1,6),(2,5),(3,4),(4,6),(5,6)],7) [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,4,1,5,7,2,6]=>([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)=>([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7) [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,4,5,1,7,2,6]=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7)=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7) [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,7,1,2,6]=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,4),(1,5),(1,6),(2,5),(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]=>[3,1,4,2,5,6,7]=>([(3,6),(4,5),(5,6)],7)=>([(3,6),(4,5),(5,6)],7) [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,5,6,7]=>([(3,5),(3,6),(4,5),(4,6)],7)=>([(3,5),(3,6),(4,5),(4,6)],7) [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,4,5,2,6,7]=>([(2,6),(3,6),(4,5),(5,6)],7)=>([(2,6),(3,6),(4,5),(5,6)],7) [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,4,1,5,2,6,7]=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7) [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,4,5,1,2,6,7]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(2,5),(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]=>[3,1,4,5,6,2,7]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7) [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,4,1,5,6,2,7]=>([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,4,5,1,6,2,7]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,5,6,1,2,7]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,6,7,2]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,4,1,5,6,7,2]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(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]=>[3,4,5,1,6,7,2]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,5,6,1,7,2]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,7]=>([(1,6),(2,5),(3,4),(3,5),(4,6)],7)=>([(1,6),(2,5),(3,4),(3,5),(4,6)],7) [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,5,1,2,6,4,7]=>([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)=>([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,5,6,2,4,7]=>([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)=>([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,5,1,6,2,4,7]=>([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7)=>([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7) [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,5,6,1,2,4,7]=>([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,6,7,4]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,5,1,2,6,7,4]=>([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7)=>([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7) [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,5,6,2,7,4]=>([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)=>([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,5,1,6,2,7,4]=>([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)=>([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,5,6,1,2,7,4]=>([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,6,7,2,4]=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7)=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7) [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,5,1,6,7,2,4]=>([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)=>([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7) [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,5,6,1,7,2,4]=>([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,5,6,7,1,2,4]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,6]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7)=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,7,4,6]=>([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)=>([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,7,2,4,6]=>([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7)=>([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,7,2,4,6]=>([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)=>([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,7,1,2,4,6]=>([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7) [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,7,6]=>([(0,1),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,1),(2,5),(3,4),(4,6),(5,6)],7) [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,7,6]=>([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,7,6]=>([(0,3),(1,2),(4,6),(5,6)],7)=>([(0,3),(1,2),(4,6),(5,6)],7) [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6]=>([(1,6),(2,5),(3,4)],7)=>([(1,6),(2,5),(3,4)],7) [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,7,6]=>([(1,2),(3,6),(4,5),(5,6)],7)=>([(1,2),(3,6),(4,5),(5,6)],7) [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,7,4,6]=>([(0,6),(1,5),(2,4),(3,4),(5,6)],7)=>([(0,6),(1,5),(2,4),(3,4),(5,6)],7) [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,4,6]=>([(1,2),(3,6),(4,5),(5,6)],7)=>([(1,2),(3,6),(4,5),(5,6)],7) [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,7,4,6]=>([(1,6),(2,5),(3,4),(3,5),(4,6)],7)=>([(1,6),(2,5),(3,4),(3,5),(4,6)],7) [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,7,2,4,6]=>([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,4,6,7]=>([(2,6),(3,5),(4,5),(4,6)],7)=>([(2,6),(3,5),(4,5),(4,6)],7) [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,5,1,2,4,6,7]=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7) [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,5,4,6,7]=>([(2,3),(4,6),(5,6)],7)=>([(2,3),(4,6),(5,6)],7) [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,5,4,6,7]=>([(3,6),(4,5)],7)=>([(3,6),(4,5)],7) [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,4,6,7]=>([(3,6),(4,5),(5,6)],7)=>([(3,6),(4,5),(5,6)],7) [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,5,6,4,7]=>([(1,6),(2,6),(3,5),(4,5)],7)=>([(1,6),(2,6),(3,5),(4,5)],7) [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,5,6,4,7]=>([(2,3),(4,6),(5,6)],7)=>([(2,3),(4,6),(5,6)],7) [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,2,6,4,7]=>([(2,6),(3,5),(4,5),(4,6)],7)=>([(2,6),(3,5),(4,5),(4,6)],7) [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,6,2,4,7]=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7) [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,5,6,7,4]=>([(0,6),(1,6),(2,6),(3,5),(4,5)],7)=>([(0,6),(1,6),(2,6),(3,5),(4,5)],7) [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,5,6,7,4]=>([(1,2),(3,6),(4,6),(5,6)],7)=>([(1,2),(3,6),(4,6),(5,6)],7) [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,5,2,6,7,4]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7) [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,5,6,2,7,4]=>([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,5,6,7,2,4]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,6,2,7,4,5]=>([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7)=>([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(4,6)],7) [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,6,1,2,7,4,5]=>([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7)=>([(0,4),(0,5),(1,2),(1,3),(2,6),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,6,7,2,4,5]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,6,1,7,2,4,5]=>([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)=>([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,6,7,1,2,4,5]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,6,2,4,7,5]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7)=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,6,1,2,4,7,5]=>([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7)=>([(0,5),(1,6),(2,3),(2,4),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,2,6,4,7,5]=>([(0,6),(1,5),(2,4),(3,4),(5,6)],7)=>([(0,6),(1,5),(2,4),(3,4),(5,6)],7) [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,6,4,7,5]=>([(1,2),(3,6),(4,5),(5,6)],7)=>([(1,2),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,6,2,4,7,5]=>([(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>([(1,6),(2,5),(3,4),(4,6),(5,6)],7) [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,6,7,4,5]=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7)=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5)],7) [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,6,7,4,5]=>([(1,2),(3,5),(3,6),(4,5),(4,6)],7)=>([(1,2),(3,5),(3,6),(4,5),(4,6)],7) [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,6,2,7,4,5]=>([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)=>([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,6,7,2,4,5]=>([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5,7]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7) [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,5,7]=>([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5,7]=>([(1,6),(2,6),(3,5),(4,5)],7)=>([(1,6),(2,6),(3,5),(4,5)],7) [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,5,7]=>([(2,3),(4,6),(5,6)],7)=>([(2,3),(4,6),(5,6)],7) [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,5,7]=>([(2,6),(3,6),(4,5),(5,6)],7)=>([(2,6),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5,7]=>([(2,3),(4,6),(5,6)],7)=>([(2,3),(4,6),(5,6)],7) [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5,7]=>([(3,6),(4,5)],7)=>([(3,6),(4,5)],7) [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5,7]=>([(2,3),(4,6),(5,6)],7)=>([(2,3),(4,6),(5,6)],7) [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5,7]=>([(2,6),(3,6),(4,5),(5,6)],7)=>([(2,6),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,7,5]=>([(1,6),(2,6),(3,5),(4,5)],7)=>([(1,6),(2,6),(3,5),(4,5)],7) [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,4,6,7,5]=>([(2,3),(4,6),(5,6)],7)=>([(2,3),(4,6),(5,6)],7) [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,4,2,6,7,5]=>([(1,6),(2,6),(3,5),(4,5)],7)=>([(1,6),(2,6),(3,5),(4,5)],7) [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,4,6,2,7,5]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7) [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,4,6,7,2,5]=>([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,7,2,4,5,6]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,7,1,2,4,5,6]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,7,4,5,6]=>([(0,6),(1,6),(2,6),(3,5),(4,5)],7)=>([(0,6),(1,6),(2,6),(3,5),(4,5)],7) [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,7,4,5,6]=>([(1,2),(3,6),(4,6),(5,6)],7)=>([(1,2),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,7,2,4,5,6]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,6]=>([(1,6),(2,6),(3,5),(4,5)],7)=>([(1,6),(2,6),(3,5),(4,5)],7) [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,4,7,5,6]=>([(2,3),(4,6),(5,6)],7)=>([(2,3),(4,6),(5,6)],7) [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,4,2,7,5,6]=>([(1,6),(2,6),(3,5),(4,5)],7)=>([(1,6),(2,6),(3,5),(4,5)],7) [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,4,7,2,5,6]=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7) [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,4,5,7,6]=>([(2,3),(4,6),(5,6)],7)=>([(2,3),(4,6),(5,6)],7) [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,3,2,4,5,7,6]=>([(3,6),(4,5)],7)=>([(3,6),(4,5)],7) [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,4,2,5,7,6]=>([(2,3),(4,6),(5,6)],7)=>([(2,3),(4,6),(5,6)],7) [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,4,5,2,7,6]=>([(1,2),(3,6),(4,6),(5,6)],7)=>([(1,2),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,4,5,7,2,6]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7]=>([(4,6),(5,6)],7)=>([(4,6),(5,6)],7) [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7]=>([(5,6)],7)=>([(5,6)],7) [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,4,2,5,6,7]=>([(4,6),(5,6)],7)=>([(4,6),(5,6)],7) [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,4,5,2,6,7]=>([(3,6),(4,6),(5,6)],7)=>([(3,6),(4,6),(5,6)],7) [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,4,5,6,2,7]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(2,6),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,4,5,6,7,2]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7) [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,7]=>([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[4,5,1,2,6,3,7]=>([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,5,6,2,3,7]=>([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[4,5,1,6,2,3,7]=>([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,7]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[4,1,5,2,6,7,3]=>([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7)=>([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7) [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,5,1,2,6,7,3]=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[4,1,5,6,2,7,3]=>([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,5,1,6,2,7,3]=>([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7) [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,5,6,1,2,7,3]=>([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,5,6,7,2,3]=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,5,1,6,7,2,3]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,5,6,1,7,2,3]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,5,2,7,3,6]=>([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7)=>([(0,6),(1,4),(2,3),(2,6),(3,5),(4,5),(5,6)],7) [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[4,5,1,2,7,3,6]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,6)],7) [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,5,7,2,3,6]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,6),(1,5),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,5,1,7,2,3,6]=>([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,5,7,1,2,3,6]=>([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,7,6]=>([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,1),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,7,6]=>([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,1),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,7,6]=>([(0,1),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,1),(2,6),(3,6),(4,5),(5,6)],7) [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,7,6]=>([(1,2),(3,6),(4,5),(5,6)],7)=>([(1,2),(3,6),(4,5),(5,6)],7) [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,7,6]=>([(1,2),(3,5),(3,6),(4,5),(4,6)],7)=>([(1,2),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7)=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,2,5,7,3,6]=>([(1,6),(2,5),(3,4),(4,6),(5,6)],7)=>([(1,6),(2,5),(3,4),(4,6),(5,6)],7) [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,2,7,3,6]=>([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)=>([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,7,2,3,6]=>([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,6,7]=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7) [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3,6,7]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3,6,7]=>([(2,6),(3,6),(4,5),(5,6)],7)=>([(2,6),(3,6),(4,5),(5,6)],7) [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,3,6,7]=>([(3,6),(4,5),(5,6)],7)=>([(3,6),(4,5),(5,6)],7) [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3,6,7]=>([(3,5),(3,6),(4,5),(4,6)],7)=>([(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[4,1,2,5,6,3,7]=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7) [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,2,5,6,3,7]=>([(2,6),(3,6),(4,5),(5,6)],7)=>([(2,6),(3,6),(4,5),(5,6)],7) [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,5,2,6,3,7]=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7) [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,5,6,2,3,7]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(2,5),(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]=>[4,1,2,5,6,7,3]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],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]=>[1,4,2,5,6,7,3]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7) [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,5,2,6,7,3]=>([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,5,6,2,7,3]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,5,6,7,2,3]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,5]=>([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7)=>([(0,6),(1,2),(1,4),(2,5),(3,4),(3,6),(4,5),(5,6)],7) [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,6,1,2,7,3,5]=>([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7)=>([(0,1),(0,6),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(5,6)],7) [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,6,7,2,3,5]=>([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,6),(1,4),(1,5),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,6,1,7,2,3,5]=>([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,5),(0,6),(1,4),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,6,7,1,2,3,5]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,6,2,3,7,5]=>([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7)=>([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5)],7) [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,6,1,2,3,7,5]=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7)=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,6)],7) [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,6,3,7,5]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7)=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,7,5]=>([(1,6),(2,5),(3,4),(3,5),(4,6)],7)=>([(1,6),(2,5),(3,4),(3,5),(4,6)],7) [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,6,2,3,7,5]=>([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)=>([(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]=>[4,1,2,6,7,3,5]=>([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7)=>([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7) [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,7,3,5]=>([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)=>([(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7) [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,4,6,2,7,3,5]=>([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7)=>([(1,4),(1,6),(2,3),(2,6),(3,5),(4,5),(5,6)],7) [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,4,6,7,2,3,5]=>([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5,7]=>([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5,7]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5,7]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7) [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5,7]=>([(2,6),(3,5),(4,5),(4,6)],7)=>([(2,6),(3,5),(4,5),(4,6)],7) [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,5,7]=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7) [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,7]=>([(1,2),(3,6),(4,6),(5,6)],7)=>([(1,2),(3,6),(4,6),(5,6)],7) [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,7]=>([(2,3),(4,6),(5,6)],7)=>([(2,3),(4,6),(5,6)],7) [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,7]=>([(3,6),(4,5)],7)=>([(3,6),(4,5)],7) [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,2,4,6,3,5,7]=>([(3,6),(4,5),(5,6)],7)=>([(3,6),(4,5),(5,6)],7) [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,7,5]=>([(0,6),(1,6),(2,6),(3,5),(4,5)],7)=>([(0,6),(1,6),(2,6),(3,5),(4,5)],7) [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,6,7,5]=>([(1,6),(2,6),(3,5),(4,5)],7)=>([(1,6),(2,6),(3,5),(4,5)],7) [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,6,7,5]=>([(2,3),(4,6),(5,6)],7)=>([(2,3),(4,6),(5,6)],7) [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,2,4,6,3,7,5]=>([(2,6),(3,5),(4,5),(4,6)],7)=>([(2,6),(3,5),(4,5),(4,6)],7) [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,6,7,3,5]=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7) [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,1,7,2,3,5,6]=>([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,7,1,2,3,5,6]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,7,3,5,6]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,7,3,5,6]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7) [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,4,7,2,3,5,6]=>([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,2,3,7,5,6]=>([(0,6),(1,6),(2,6),(3,5),(4,5)],7)=>([(0,6),(1,6),(2,6),(3,5),(4,5)],7) [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,4,2,3,7,5,6]=>([(1,6),(2,6),(3,5),(4,5)],7)=>([(1,6),(2,6),(3,5),(4,5)],7) [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,2,4,3,7,5,6]=>([(2,3),(4,6),(5,6)],7)=>([(2,3),(4,6),(5,6)],7) [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,2,4,7,3,5,6]=>([(2,6),(3,6),(4,5),(5,6)],7)=>([(2,6),(3,6),(4,5),(5,6)],7) [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,1,2,3,5,7,6]=>([(1,2),(3,6),(4,6),(5,6)],7)=>([(1,2),(3,6),(4,6),(5,6)],7) [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,4,2,3,5,7,6]=>([(2,3),(4,6),(5,6)],7)=>([(2,3),(4,6),(5,6)],7) [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,2,4,3,5,7,6]=>([(3,6),(4,5)],7)=>([(3,6),(4,5)],7) [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,2,4,5,3,7,6]=>([(2,3),(4,6),(5,6)],7)=>([(2,3),(4,6),(5,6)],7) [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,2,4,5,7,3,6]=>([(2,6),(3,6),(4,5),(5,6)],7)=>([(2,6),(3,6),(4,5),(5,6)],7) [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,7]=>([(3,6),(4,6),(5,6)],7)=>([(3,6),(4,6),(5,6)],7) [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,7]=>([(4,6),(5,6)],7)=>([(4,6),(5,6)],7) [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,7]=>([(5,6)],7)=>([(5,6)],7) [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,2,4,5,3,6,7]=>([(4,6),(5,6)],7)=>([(4,6),(5,6)],7) [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,5,6,3,7]=>([(3,6),(4,6),(5,6)],7)=>([(3,6),(4,6),(5,6)],7) [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,5,6,7,3]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(2,6),(3,6),(4,6),(5,6)],7) [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,4]=>([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>([(0,6),(1,4),(1,5),(2,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7) [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,6,1,2,7,3,4]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[5,1,6,7,2,3,4]=>([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7) [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[5,6,1,7,2,3,4]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,5),(0,6),(1,2),(1,3),(1,4),(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]=>[5,6,7,1,2,3,4]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[5,1,6,2,3,7,4]=>([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,6,1,2,3,7,4]=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[5,1,2,6,3,7,4]=>([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7)=>([(0,6),(1,6),(2,5),(3,4),(3,6),(4,5),(5,6)],7) [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,2,6,3,7,4]=>([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>([(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,6,2,3,7,4]=>([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[5,1,2,6,7,3,4]=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,5,2,6,7,3,4]=>([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7) [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,5,6,2,7,3,4]=>([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,5,6,7,2,3,4]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7) [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[5,1,6,2,3,4,7]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,6,1,2,3,4,7]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,2,6,3,4,7]=>([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,3,4,7]=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7) [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,6,2,3,4,7]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[5,1,2,3,6,4,7]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7) [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,2,3,6,4,7]=>([(2,6),(3,6),(4,5),(5,6)],7)=>([(2,6),(3,6),(4,5),(5,6)],7) [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,2,5,3,6,4,7]=>([(3,6),(4,5),(5,6)],7)=>([(3,6),(4,5),(5,6)],7) [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,2,5,6,3,4,7]=>([(3,5),(3,6),(4,5),(4,6)],7)=>([(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[5,1,2,3,6,7,4]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],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]=>[1,5,2,3,6,7,4]=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>([(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]=>[1,2,5,3,6,7,4]=>([(2,6),(3,6),(4,5),(5,6)],7)=>([(2,6),(3,6),(4,5),(5,6)],7) [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,2,5,6,3,7,4]=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7) [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,2,5,6,7,3,4]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,1,7,2,3,4,6]=>([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,6),(1,5),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,7,1,2,3,4,6]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,6]=>([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,5,2,7,3,4,6]=>([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)=>([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,5,7,2,3,4,6]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,7,4,6]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7) [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,7,4,6]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7) [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,7,4,6]=>([(2,6),(3,5),(4,5),(4,6)],7)=>([(2,6),(3,5),(4,5),(4,6)],7) [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6]=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7) [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,7,6]=>([(0,1),(2,6),(3,6),(4,6),(5,6)],7)=>([(0,1),(2,6),(3,6),(4,6),(5,6)],7) [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,7,6]=>([(1,2),(3,6),(4,6),(5,6)],7)=>([(1,2),(3,6),(4,6),(5,6)],7) [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,7,6]=>([(2,3),(4,6),(5,6)],7)=>([(2,3),(4,6),(5,6)],7) [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,7,6]=>([(3,6),(4,5)],7)=>([(3,6),(4,5)],7) [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,7,4,6]=>([(3,6),(4,5),(5,6)],7)=>([(3,6),(4,5),(5,6)],7) [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,7]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(2,6),(3,6),(4,6),(5,6)],7) [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,6,7]=>([(3,6),(4,6),(5,6)],7)=>([(3,6),(4,6),(5,6)],7) [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,5,3,4,6,7]=>([(4,6),(5,6)],7)=>([(4,6),(5,6)],7) [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,7]=>([(5,6)],7)=>([(5,6)],7) [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,3,5,6,4,7]=>([(4,6),(5,6)],7)=>([(4,6),(5,6)],7) [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,6,7,4]=>([(3,6),(4,6),(5,6)],7)=>([(3,6),(4,6),(5,6)],7) [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,1,7,2,3,4,5]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,1,2,7,3,4,5]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,6,2,7,3,4,5]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,7,2,3,4,5]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,1,2,3,7,4,5]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,6,2,3,7,4,5]=>([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7) [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,6,3,7,4,5]=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7) [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,6,7,3,4,5]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,1,2,3,4,7,5]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7) [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,3,4,7,5]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7) [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,6,3,4,7,5]=>([(2,6),(3,6),(4,5),(5,6)],7)=>([(2,6),(3,6),(4,5),(5,6)],7) [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,2,3,6,4,7,5]=>([(3,6),(4,5),(5,6)],7)=>([(3,6),(4,5),(5,6)],7) [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,2,3,6,7,4,5]=>([(3,5),(3,6),(4,5),(4,6)],7)=>([(3,5),(3,6),(4,5),(4,6)],7) [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7) [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5,7]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(2,6),(3,6),(4,6),(5,6)],7) [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5,7]=>([(3,6),(4,6),(5,6)],7)=>([(3,6),(4,6),(5,6)],7) [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5,7]=>([(4,6),(5,6)],7)=>([(4,6),(5,6)],7) [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,7]=>([(5,6)],7)=>([(5,6)],7) [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,6,7,5]=>([(4,6),(5,6)],7)=>([(4,6),(5,6)],7) [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],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]=>[1,7,2,3,4,5,6]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(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]=>[1,2,7,3,4,5,6]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(2,6),(3,6),(4,6),(5,6)],7) [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,3,7,4,5,6]=>([(3,6),(4,6),(5,6)],7)=>([(3,6),(4,6),(5,6)],7) [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,6]=>([(4,6),(5,6)],7)=>([(4,6),(5,6)],7) [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,7,6]=>([(5,6)],7)=>([(5,6)],7) [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>([],7)=>([],7)
Map
to 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
Map
graph of inversions
Description
The graph of inversions of a permutation.
For a permutation of $\{1,\dots,n\}$, this is the graph with vertices $\{1,\dots,n\}$, where $(i,j)$ is an edge if and only if it is an inversion of the permutation.
Map
dual on components
Description
The dual of the 3-connected planar components of a graph.
Replace each connected component which is 3-connected and planar with its planar dual.