Identifier
Mp00025: Dyck paths to 132-avoiding permutationPermutations
Mp00069: Permutations complementPermutations
Mp00065: Permutations permutation posetPosets
Mp00206: Posets antichains of maximal size Lattices
Images
=>
Cc0005;cc-rep-0Cc0014;cc-rep-3Cc0029;cc-rep-4
[1,0]=>[1]=>[1]=>([],1)=>([],1) [1,0,1,0]=>[2,1]=>[1,2]=>([(0,1)],2)=>([(0,1)],2) [1,1,0,0]=>[1,2]=>[2,1]=>([],2)=>([],1) [1,0,1,0,1,0]=>[3,2,1]=>[1,2,3]=>([(0,2),(2,1)],3)=>([(0,2),(2,1)],3) [1,0,1,1,0,0]=>[2,3,1]=>[2,1,3]=>([(0,2),(1,2)],3)=>([],1) [1,1,0,0,1,0]=>[3,1,2]=>[1,3,2]=>([(0,1),(0,2)],3)=>([],1) [1,1,0,1,0,0]=>[2,1,3]=>[2,3,1]=>([(1,2)],3)=>([(0,1)],2) [1,1,1,0,0,0]=>[1,2,3]=>[3,2,1]=>([],3)=>([],1) [1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>([(0,3),(2,1),(3,2)],4) [1,0,1,0,1,1,0,0]=>[3,4,2,1]=>[2,1,3,4]=>([(0,3),(1,3),(3,2)],4)=>([],1) [1,0,1,1,0,0,1,0]=>[4,2,3,1]=>[1,3,2,4]=>([(0,1),(0,2),(1,3),(2,3)],4)=>([],1) [1,0,1,1,0,1,0,0]=>[3,2,4,1]=>[2,3,1,4]=>([(0,3),(1,2),(2,3)],4)=>([(0,1)],2) [1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[3,2,1,4]=>([(0,3),(1,3),(2,3)],4)=>([],1) [1,1,0,0,1,0,1,0]=>[4,3,1,2]=>[1,2,4,3]=>([(0,3),(3,1),(3,2)],4)=>([],1) [1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[2,1,4,3]=>([(0,2),(0,3),(1,2),(1,3)],4)=>([(0,1)],2) [1,1,0,1,0,0,1,0]=>[4,2,1,3]=>[1,3,4,2]=>([(0,2),(0,3),(3,1)],4)=>([(0,1)],2) [1,1,0,1,0,1,0,0]=>[3,2,1,4]=>[2,3,4,1]=>([(1,2),(2,3)],4)=>([(0,2),(2,1)],3) [1,1,0,1,1,0,0,0]=>[2,3,1,4]=>[3,2,4,1]=>([(1,3),(2,3)],4)=>([],1) [1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[1,4,3,2]=>([(0,1),(0,2),(0,3)],4)=>([],1) [1,1,1,0,0,1,0,0]=>[3,1,2,4]=>[2,4,3,1]=>([(1,2),(1,3)],4)=>([],1) [1,1,1,0,1,0,0,0]=>[2,1,3,4]=>[3,4,2,1]=>([(2,3)],4)=>([(0,1)],2) [1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[4,3,2,1]=>([],4)=>([],1) [1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,0,1,0,1,1,0,0]=>[4,5,3,2,1]=>[2,1,3,4,5]=>([(0,4),(1,4),(2,3),(4,2)],5)=>([],1) [1,0,1,0,1,1,0,0,1,0]=>[5,3,4,2,1]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([],1) [1,0,1,0,1,1,0,1,0,0]=>[4,3,5,2,1]=>[2,3,1,4,5]=>([(0,4),(1,2),(2,4),(4,3)],5)=>([(0,1)],2) [1,0,1,0,1,1,1,0,0,0]=>[3,4,5,2,1]=>[3,2,1,4,5]=>([(0,4),(1,4),(2,4),(4,3)],5)=>([],1) [1,0,1,1,0,0,1,0,1,0]=>[5,4,2,3,1]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([],1) [1,0,1,1,0,0,1,1,0,0]=>[4,5,2,3,1]=>[2,1,4,3,5]=>([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)=>([(0,1)],2) [1,0,1,1,0,1,0,0,1,0]=>[5,3,2,4,1]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>([(0,1)],2) [1,0,1,1,0,1,0,1,0,0]=>[4,3,2,5,1]=>[2,3,4,1,5]=>([(0,4),(1,2),(2,3),(3,4)],5)=>([(0,2),(2,1)],3) [1,0,1,1,0,1,1,0,0,0]=>[3,4,2,5,1]=>[3,2,4,1,5]=>([(0,4),(1,3),(2,3),(3,4)],5)=>([],1) [1,0,1,1,1,0,0,0,1,0]=>[5,2,3,4,1]=>[1,4,3,2,5]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>([],1) [1,0,1,1,1,0,0,1,0,0]=>[4,2,3,5,1]=>[2,4,3,1,5]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>([],1) [1,0,1,1,1,0,1,0,0,0]=>[3,2,4,5,1]=>[3,4,2,1,5]=>([(0,4),(1,4),(2,3),(3,4)],5)=>([(0,1)],2) [1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[4,3,2,1,5]=>([(0,4),(1,4),(2,4),(3,4)],5)=>([],1) [1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,2]=>[1,2,3,5,4]=>([(0,3),(3,4),(4,1),(4,2)],5)=>([],1) [1,1,0,0,1,0,1,1,0,0]=>[4,5,3,1,2]=>[2,1,3,5,4]=>([(0,4),(1,4),(4,2),(4,3)],5)=>([(0,1)],2) [1,1,0,0,1,1,0,0,1,0]=>[5,3,4,1,2]=>[1,3,2,5,4]=>([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)=>([(0,1)],2) [1,1,0,0,1,1,0,1,0,0]=>[4,3,5,1,2]=>[2,3,1,5,4]=>([(0,3),(0,4),(1,2),(2,3),(2,4)],5)=>([(0,2),(2,1)],3) [1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>[3,2,1,5,4]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>([],1) [1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,3]=>[1,2,4,5,3]=>([(0,4),(3,2),(4,1),(4,3)],5)=>([(0,1)],2) [1,1,0,1,0,0,1,1,0,0]=>[4,5,2,1,3]=>[2,1,4,5,3]=>([(0,3),(0,4),(1,3),(1,4),(4,2)],5)=>([(0,2),(2,1)],3) [1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,4]=>[1,3,4,5,2]=>([(0,2),(0,4),(3,1),(4,3)],5)=>([(0,2),(2,1)],3) [1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,5]=>[2,3,4,5,1]=>([(1,4),(3,2),(4,3)],5)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,1,1,0,0,0]=>[3,4,2,1,5]=>[3,2,4,5,1]=>([(1,4),(2,4),(4,3)],5)=>([],1) [1,1,0,1,1,0,0,0,1,0]=>[5,2,3,1,4]=>[1,4,3,5,2]=>([(0,1),(0,2),(0,3),(2,4),(3,4)],5)=>([],1) [1,1,0,1,1,0,0,1,0,0]=>[4,2,3,1,5]=>[2,4,3,5,1]=>([(1,2),(1,3),(2,4),(3,4)],5)=>([],1) [1,1,0,1,1,0,1,0,0,0]=>[3,2,4,1,5]=>[3,4,2,5,1]=>([(1,4),(2,3),(3,4)],5)=>([(0,1)],2) [1,1,0,1,1,1,0,0,0,0]=>[2,3,4,1,5]=>[4,3,2,5,1]=>([(1,4),(2,4),(3,4)],5)=>([],1) [1,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,3]=>[1,2,5,4,3]=>([(0,4),(4,1),(4,2),(4,3)],5)=>([],1) [1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>[2,1,5,4,3]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)=>([],1) [1,1,1,0,0,1,0,0,1,0]=>[5,3,1,2,4]=>[1,3,5,4,2]=>([(0,3),(0,4),(4,1),(4,2)],5)=>([],1) [1,1,1,0,0,1,0,1,0,0]=>[4,3,1,2,5]=>[2,3,5,4,1]=>([(1,4),(4,2),(4,3)],5)=>([],1) [1,1,1,0,0,1,1,0,0,0]=>[3,4,1,2,5]=>[3,2,5,4,1]=>([(1,3),(1,4),(2,3),(2,4)],5)=>([(0,1)],2) [1,1,1,0,1,0,0,0,1,0]=>[5,2,1,3,4]=>[1,4,5,3,2]=>([(0,2),(0,3),(0,4),(4,1)],5)=>([(0,1)],2) [1,1,1,0,1,0,0,1,0,0]=>[4,2,1,3,5]=>[2,4,5,3,1]=>([(1,3),(1,4),(4,2)],5)=>([(0,1)],2) [1,1,1,0,1,0,1,0,0,0]=>[3,2,1,4,5]=>[3,4,5,2,1]=>([(2,3),(3,4)],5)=>([(0,2),(2,1)],3) [1,1,1,0,1,1,0,0,0,0]=>[2,3,1,4,5]=>[4,3,5,2,1]=>([(2,4),(3,4)],5)=>([],1) [1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>[1,5,4,3,2]=>([(0,1),(0,2),(0,3),(0,4)],5)=>([],1) [1,1,1,1,0,0,0,1,0,0]=>[4,1,2,3,5]=>[2,5,4,3,1]=>([(1,2),(1,3),(1,4)],5)=>([],1) [1,1,1,1,0,0,1,0,0,0]=>[3,1,2,4,5]=>[3,5,4,2,1]=>([(2,3),(2,4)],5)=>([],1) [1,1,1,1,0,1,0,0,0,0]=>[2,1,3,4,5]=>[4,5,3,2,1]=>([(3,4)],5)=>([(0,1)],2) [1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[5,4,3,2,1]=>([],5)=>([],1) [1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [1,0,1,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,2,1]=>[2,1,3,4,5,6]=>([(0,5),(1,5),(3,2),(4,3),(5,4)],6)=>([],1) [1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,2,1]=>[1,3,2,4,5,6]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>([],1) [1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,2,1]=>[2,3,1,4,5,6]=>([(0,5),(1,3),(3,5),(4,2),(5,4)],6)=>([(0,1)],2) [1,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,2,1]=>[3,2,1,4,5,6]=>([(0,5),(1,5),(2,5),(3,4),(5,3)],6)=>([],1) [1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([],1) [1,0,1,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,2,1]=>[2,1,4,3,5,6]=>([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)=>([(0,1)],2) [1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,2,1]=>[1,3,4,2,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>([(0,1)],2) [1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,2,1]=>[2,3,4,1,5,6]=>([(0,5),(1,4),(2,5),(4,2),(5,3)],6)=>([(0,2),(2,1)],3) [1,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,2,1]=>[3,2,4,1,5,6]=>([(0,5),(1,4),(2,4),(4,5),(5,3)],6)=>([],1) [1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,2,1]=>[1,4,3,2,5,6]=>([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)=>([],1) [1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,2,1]=>[2,4,3,1,5,6]=>([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6)=>([],1) [1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[3,4,2,1,5,6]=>([(0,5),(1,5),(2,3),(3,5),(5,4)],6)=>([(0,1)],2) [1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,2,1]=>[4,3,2,1,5,6]=>([(0,5),(1,5),(2,5),(3,5),(5,4)],6)=>([],1) [1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,3,1]=>[1,2,3,5,4,6]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>([],1) [1,0,1,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,3,1]=>[2,1,3,5,4,6]=>([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)=>([(0,1)],2) [1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>([(0,1)],2) [1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,3,1]=>[2,3,1,5,4,6]=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>([(0,2),(2,1)],3) [1,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,3,1]=>[3,2,1,5,4,6]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>([],1) [1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,4,1]=>[1,2,4,5,3,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>([(0,1)],2) [1,0,1,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,4,1]=>[2,1,4,5,3,6]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)=>([(0,2),(2,1)],3) [1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,5,1]=>[1,3,4,5,2,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>([(0,2),(2,1)],3) [1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,1]=>[2,3,4,5,1,6]=>([(0,5),(1,4),(2,5),(3,2),(4,3)],6)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,1]=>[3,2,4,5,1,6]=>([(0,5),(1,4),(2,4),(3,5),(4,3)],6)=>([],1) [1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,5,1]=>[1,4,3,5,2,6]=>([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)=>([],1) [1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,6,1]=>[2,4,3,5,1,6]=>([(0,4),(1,2),(1,3),(2,5),(3,5),(5,4)],6)=>([],1) [1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,6,1]=>[3,4,2,5,1,6]=>([(0,5),(1,4),(2,3),(3,5),(5,4)],6)=>([(0,1)],2) [1,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,6,1]=>[4,3,2,5,1,6]=>([(0,5),(1,5),(2,5),(3,4),(5,4)],6)=>([],1) [1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,4,1]=>[1,2,5,4,3,6]=>([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)=>([],1) [1,0,1,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,4,1]=>[2,1,5,4,3,6]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>([],1) [1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,5,1]=>[1,3,5,4,2,6]=>([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)=>([],1) [1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,6,1]=>[2,3,5,4,1,6]=>([(0,5),(1,4),(2,5),(3,5),(4,2),(4,3)],6)=>([],1) [1,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,6,1]=>[3,2,5,4,1,6]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1)],2) [1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1]=>[1,4,5,3,2,6]=>([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)=>([(0,1)],2) [1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[2,4,5,3,1,6]=>([(0,5),(1,3),(1,4),(2,5),(3,5),(4,2)],6)=>([(0,1)],2) [1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,6,1]=>[3,4,5,2,1,6]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>([(0,2),(2,1)],3) [1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,6,1]=>[4,3,5,2,1,6]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>([],1) [1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)=>([],1) [1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,6,1]=>[2,5,4,3,1,6]=>([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>([],1) [1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,6,1]=>[3,5,4,2,1,6]=>([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([],1) [1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,6,1]=>[4,5,3,2,1,6]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>([(0,1)],2) [1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[5,4,3,2,1,6]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>([],1) [1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,2]=>[1,2,3,4,6,5]=>([(0,4),(3,5),(4,3),(5,1),(5,2)],6)=>([],1) [1,1,0,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,1,2]=>[2,1,3,4,6,5]=>([(0,5),(1,5),(4,2),(4,3),(5,4)],6)=>([(0,1)],2) [1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,1,2]=>[1,3,2,4,6,5]=>([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)=>([(0,1)],2) [1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,1,2]=>[2,3,1,4,6,5]=>([(0,5),(1,2),(2,5),(5,3),(5,4)],6)=>([(0,2),(2,1)],3) [1,1,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,1,2]=>[3,2,1,4,6,5]=>([(0,5),(1,5),(2,5),(5,3),(5,4)],6)=>([],1) [1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,1,2]=>[1,2,4,3,6,5]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)=>([(0,1)],2) [1,1,0,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)=>([(0,2),(2,1)],3) [1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,1,2]=>[1,3,4,2,6,5]=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)=>([(0,2),(2,1)],3) [1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,1,2]=>[2,3,4,1,6,5]=>([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,1,2]=>[3,2,4,1,6,5]=>([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>([],1) [1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,1,2]=>[1,4,3,2,6,5]=>([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([],1) [1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,1,2]=>[2,4,3,1,6,5]=>([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>([],1) [1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,1,2]=>[3,4,2,1,6,5]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6)=>([(0,1)],2) [1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>[4,3,2,1,6,5]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([],1) [1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,3]=>[1,2,3,5,6,4]=>([(0,4),(3,2),(4,5),(5,1),(5,3)],6)=>([(0,1)],2) [1,1,0,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,1,3]=>[2,1,3,5,6,4]=>([(0,5),(1,5),(4,2),(5,3),(5,4)],6)=>([(0,2),(2,1)],3) [1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,1,3]=>[1,3,2,5,6,4]=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)=>([(0,2),(2,1)],3) [1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,1,3]=>[2,3,1,5,6,4]=>([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,1,3]=>[3,2,1,5,6,4]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)=>([],1) [1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,4]=>[1,2,4,5,6,3]=>([(0,5),(3,4),(4,2),(5,1),(5,3)],6)=>([(0,2),(2,1)],3) [1,1,0,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,1,4]=>[2,1,4,5,6,3]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,5]=>[1,3,4,5,6,2]=>([(0,2),(0,5),(3,4),(4,1),(5,3)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,6]=>[2,3,4,5,6,1]=>([(1,5),(3,4),(4,2),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,1,6]=>[3,2,4,5,6,1]=>([(1,5),(2,5),(3,4),(5,3)],6)=>([],1) [1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,1,5]=>[1,4,3,5,6,2]=>([(0,2),(0,3),(0,4),(3,5),(4,5),(5,1)],6)=>([],1) [1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,1,6]=>[2,4,3,5,6,1]=>([(1,2),(1,3),(2,5),(3,5),(5,4)],6)=>([],1) [1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,1,6]=>[3,4,2,5,6,1]=>([(1,5),(2,3),(3,5),(5,4)],6)=>([(0,1)],2) [1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,1,6]=>[4,3,2,5,6,1]=>([(1,5),(2,5),(3,5),(5,4)],6)=>([],1) [1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,1,4]=>[1,2,5,4,6,3]=>([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6)=>([],1) [1,1,0,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,1,4]=>[2,1,5,4,6,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6)=>([],1) [1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,1,5]=>[1,3,5,4,6,2]=>([(0,3),(0,4),(1,5),(2,5),(4,1),(4,2)],6)=>([],1) [1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,1,6]=>[2,3,5,4,6,1]=>([(1,4),(2,5),(3,5),(4,2),(4,3)],6)=>([],1) [1,1,0,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,1,6]=>[3,2,5,4,6,1]=>([(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,1,5]=>[1,4,5,3,6,2]=>([(0,2),(0,3),(0,4),(1,5),(3,5),(4,1)],6)=>([(0,1)],2) [1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,1,6]=>[2,4,5,3,6,1]=>([(1,3),(1,4),(2,5),(3,5),(4,2)],6)=>([(0,1)],2) [1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,1,6]=>[3,4,5,2,6,1]=>([(1,5),(2,3),(3,4),(4,5)],6)=>([(0,2),(2,1)],3) [1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,1,6]=>[4,3,5,2,6,1]=>([(1,5),(2,4),(3,4),(4,5)],6)=>([],1) [1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,1,5]=>[1,5,4,3,6,2]=>([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)=>([],1) [1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,1,6]=>[2,5,4,3,6,1]=>([(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>([],1) [1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,1,6]=>[3,5,4,2,6,1]=>([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([],1) [1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,1,6]=>[4,5,3,2,6,1]=>([(1,5),(2,5),(3,4),(4,5)],6)=>([(0,1)],2) [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6]=>[5,4,3,2,6,1]=>([(1,5),(2,5),(3,5),(4,5)],6)=>([],1) [1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,2,3]=>[1,2,3,6,5,4]=>([(0,4),(4,5),(5,1),(5,2),(5,3)],6)=>([],1) [1,1,1,0,0,0,1,0,1,1,0,0]=>[5,6,4,1,2,3]=>[2,1,3,6,5,4]=>([(0,5),(1,5),(5,2),(5,3),(5,4)],6)=>([],1) [1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,5,1,2,3]=>[1,3,2,6,5,4]=>([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>([],1) [1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,6,1,2,3]=>[2,3,1,6,5,4]=>([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>([],1) [1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>([(0,1)],2) [1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,2,4]=>[1,2,4,6,5,3]=>([(0,5),(4,2),(4,3),(5,1),(5,4)],6)=>([],1) [1,1,1,0,0,1,0,0,1,1,0,0]=>[5,6,3,1,2,4]=>[2,1,4,6,5,3]=>([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6)=>([],1) [1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,2,5]=>[1,3,4,6,5,2]=>([(0,3),(0,4),(4,5),(5,1),(5,2)],6)=>([],1) [1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,2,6]=>[2,3,4,6,5,1]=>([(1,4),(4,5),(5,2),(5,3)],6)=>([],1) [1,1,1,0,0,1,0,1,1,0,0,0]=>[4,5,3,1,2,6]=>[3,2,4,6,5,1]=>([(1,5),(2,5),(5,3),(5,4)],6)=>([(0,1)],2) [1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>[1,4,3,6,5,2]=>([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2) [1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,4,1,2,6]=>[2,4,3,6,5,1]=>([(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2) [1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,5,1,2,6]=>[3,4,2,6,5,1]=>([(1,4),(1,5),(2,3),(3,4),(3,5)],6)=>([(0,2),(2,1)],3) [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6]=>[4,3,2,6,5,1]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([],1) [1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,3,4]=>[1,2,5,6,4,3]=>([(0,5),(4,3),(5,1),(5,2),(5,4)],6)=>([(0,1)],2) [1,1,1,0,1,0,0,0,1,1,0,0]=>[5,6,2,1,3,4]=>[2,1,5,6,4,3]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)=>([(0,1)],2) [1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,3,5]=>[1,3,5,6,4,2]=>([(0,3),(0,5),(4,2),(5,1),(5,4)],6)=>([(0,1)],2) [1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,3,6]=>[2,3,5,6,4,1]=>([(1,5),(4,3),(5,2),(5,4)],6)=>([(0,1)],2) [1,1,1,0,1,0,0,1,1,0,0,0]=>[4,5,2,1,3,6]=>[3,2,5,6,4,1]=>([(1,4),(1,5),(2,4),(2,5),(5,3)],6)=>([(0,2),(2,1)],3) [1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,4,5]=>[1,4,5,6,3,2]=>([(0,2),(0,3),(0,5),(4,1),(5,4)],6)=>([(0,2),(2,1)],3) [1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,4,6]=>[2,4,5,6,3,1]=>([(1,3),(1,5),(4,2),(5,4)],6)=>([(0,2),(2,1)],3) [1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,5,6]=>[3,4,5,6,2,1]=>([(2,3),(3,5),(5,4)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,2,1,5,6]=>[4,3,5,6,2,1]=>([(2,5),(3,5),(5,4)],6)=>([],1) [1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,1,4,5]=>[1,5,4,6,3,2]=>([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)=>([],1) [1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,3,1,4,6]=>[2,5,4,6,3,1]=>([(1,2),(1,3),(1,4),(3,5),(4,5)],6)=>([],1) [1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,3,1,5,6]=>[3,5,4,6,2,1]=>([(2,3),(2,4),(3,5),(4,5)],6)=>([],1) [1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,4,1,5,6]=>[4,5,3,6,2,1]=>([(2,5),(3,4),(4,5)],6)=>([(0,1)],2) [1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6]=>[5,4,3,6,2,1]=>([(2,5),(3,5),(4,5)],6)=>([],1) [1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,2,3,4]=>[1,2,6,5,4,3]=>([(0,5),(5,1),(5,2),(5,3),(5,4)],6)=>([],1) [1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>[2,1,6,5,4,3]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)=>([],1) [1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>[1,3,6,5,4,2]=>([(0,4),(0,5),(5,1),(5,2),(5,3)],6)=>([],1) [1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,2,3,6]=>[2,3,6,5,4,1]=>([(1,5),(5,2),(5,3),(5,4)],6)=>([],1) [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,3,6]=>[3,2,6,5,4,1]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>([],1) [1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,2,4,5]=>[1,4,6,5,3,2]=>([(0,3),(0,4),(0,5),(5,1),(5,2)],6)=>([],1) [1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,2,4,6]=>[2,4,6,5,3,1]=>([(1,4),(1,5),(5,2),(5,3)],6)=>([],1) [1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,2,5,6]=>[3,4,6,5,2,1]=>([(2,3),(3,4),(3,5)],6)=>([],1) [1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>[4,3,6,5,2,1]=>([(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2) [1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,3,4,5]=>[1,5,6,4,3,2]=>([(0,2),(0,3),(0,4),(0,5),(5,1)],6)=>([(0,1)],2) [1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,3,4,6]=>[2,5,6,4,3,1]=>([(1,3),(1,4),(1,5),(5,2)],6)=>([(0,1)],2) [1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,3,5,6]=>[3,5,6,4,2,1]=>([(2,3),(2,4),(4,5)],6)=>([(0,1)],2) [1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,4,5,6]=>[4,5,6,3,2,1]=>([(3,4),(4,5)],6)=>([(0,2),(2,1)],3) [1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,1,4,5,6]=>[5,4,6,3,2,1]=>([(3,5),(4,5)],6)=>([],1) [1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>[1,6,5,4,3,2]=>([(0,1),(0,2),(0,3),(0,4),(0,5)],6)=>([],1) [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,4,6]=>[2,6,5,4,3,1]=>([(1,2),(1,3),(1,4),(1,5)],6)=>([],1) [1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,3,5,6]=>[3,6,5,4,2,1]=>([(2,3),(2,4),(2,5)],6)=>([],1) [1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>([(3,4),(3,5)],6)=>([],1) [1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>([(4,5)],6)=>([(0,1)],2) [1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>([],6)=>([],1) [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7) [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,2,1]=>[2,1,3,4,5,6,7]=>([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)=>([],1) [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,2,1]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>([],1) [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,2,1]=>[2,3,1,4,5,6,7]=>([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)=>([(0,1)],2) [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,2,1]=>[3,2,1,4,5,6,7]=>([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7)=>([],1) [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,2,1]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>([],1) [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,2,1]=>[2,1,4,3,5,6,7]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7)=>([(0,1)],2) [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,2,1]=>[1,3,4,2,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>([(0,1)],2) [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,2,1]=>[2,3,4,1,5,6,7]=>([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)=>([(0,2),(2,1)],3) [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,2,1]=>[3,2,4,1,5,6,7]=>([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)=>([],1) [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,2,1]=>[1,4,3,2,5,6,7]=>([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)=>([],1) [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,2,1]=>[2,4,3,1,5,6,7]=>([(0,6),(1,3),(1,4),(3,6),(4,6),(5,2),(6,5)],7)=>([],1) [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,2,1]=>[3,4,2,1,5,6,7]=>([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7)=>([(0,1)],2) [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[4,3,2,1,5,6,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7)=>([],1) [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,2,1]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>([],1) [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,2,1]=>[2,1,3,5,4,6,7]=>([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7)=>([(0,1)],2) [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,2,1]=>[1,3,2,5,4,6,7]=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7)=>([(0,1)],2) [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,2,1]=>[2,3,1,5,4,6,7]=>([(0,3),(1,5),(1,6),(3,5),(3,6),(4,2),(5,4),(6,4)],7)=>([(0,2),(2,1)],3) [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,2,1]=>[3,2,1,5,4,6,7]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7)=>([],1) [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,2,1]=>[1,2,4,5,3,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>([(0,1)],2) [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,2,1]=>[2,1,4,5,3,6,7]=>([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7)=>([(0,2),(2,1)],3) [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,2,1]=>[1,3,4,5,2,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>([(0,2),(2,1)],3) [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,2,1]=>[2,3,4,5,1,6,7]=>([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,2,1]=>[3,2,4,5,1,6,7]=>([(0,6),(1,5),(2,5),(4,6),(5,4),(6,3)],7)=>([],1) [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,2,1]=>[1,4,3,5,2,6,7]=>([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)=>([],1) [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,2,1]=>[2,4,3,5,1,6,7]=>([(0,6),(1,3),(1,4),(3,5),(4,5),(5,6),(6,2)],7)=>([],1) [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[3,4,2,5,1,6,7]=>([(0,6),(1,5),(2,3),(3,6),(5,4),(6,5)],7)=>([(0,1)],2) [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,2,1]=>[4,3,2,5,1,6,7]=>([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7)=>([],1) [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7]=>([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)=>([],1) [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,2,1]=>[2,1,5,4,3,6,7]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6),(6,2)],7)=>([],1) [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,2,1]=>[1,3,5,4,2,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>([],1) [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,2,1]=>[2,3,5,4,1,6,7]=>([(0,6),(1,5),(2,6),(3,6),(5,2),(5,3),(6,4)],7)=>([],1) [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,2,1]=>[3,2,5,4,1,6,7]=>([(0,6),(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7)=>([(0,1)],2) [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,2,1]=>[1,4,5,3,2,6,7]=>([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)=>([(0,1)],2) [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,2,1]=>[2,4,5,3,1,6,7]=>([(0,6),(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7)=>([(0,1)],2) [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[3,4,5,2,1,6,7]=>([(0,6),(1,6),(2,3),(3,5),(5,6),(6,4)],7)=>([(0,2),(2,1)],3) [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,2,1]=>[4,3,5,2,1,6,7]=>([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7)=>([],1) [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,2,1]=>[1,5,4,3,2,6,7]=>([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)=>([],1) [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,2,1]=>[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) [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,2,1]=>[3,5,4,2,1,6,7]=>([(0,6),(1,6),(2,3),(2,4),(3,6),(4,6),(6,5)],7)=>([],1) [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,2,1]=>[4,5,3,2,1,6,7]=>([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7)=>([(0,1)],2) [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,2,1]=>[5,4,3,2,1,6,7]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7)=>([],1) [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,3,1]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>([],1) [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,3,1]=>[2,1,3,4,6,5,7]=>([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7)=>([(0,1)],2) [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>([(0,1)],2) [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,3,1]=>[2,3,1,4,6,5,7]=>([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7)=>([(0,2),(2,1)],3) [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,3,1]=>[3,2,1,4,6,5,7]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(6,3),(6,4)],7)=>([],1) [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,3,1]=>[1,2,4,3,6,5,7]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2),(4,6),(5,6)],7)=>([(0,1)],2) [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,3,1]=>[2,1,4,3,6,5,7]=>([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7)=>([(0,2),(2,1)],3) [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,3,1]=>[1,3,4,2,6,5,7]=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(4,6),(5,6)],7)=>([(0,2),(2,1)],3) [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,3,1]=>[2,3,4,1,6,5,7]=>([(0,2),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,3,1]=>[3,2,4,1,6,5,7]=>([(0,6),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7)=>([],1) [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,3,1]=>[1,4,3,2,6,5,7]=>([(0,1),(0,2),(0,3),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)=>([],1) [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,3,1]=>[2,4,3,1,6,5,7]=>([(0,5),(0,6),(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)=>([],1) [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,3,1]=>[3,4,2,1,6,5,7]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)=>([(0,1)],2) [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,3,1]=>[4,3,2,1,6,5,7]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)=>([],1) [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,4,1]=>[1,2,3,5,6,4,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>([(0,1)],2) [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,4,1]=>[2,1,3,5,6,4,7]=>([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7)=>([(0,2),(2,1)],3) [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,4,1]=>[1,3,2,5,6,4,7]=>([(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1)],7)=>([(0,2),(2,1)],3) [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,4,1]=>[2,3,1,5,6,4,7]=>([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,4,1]=>[3,2,1,5,6,4,7]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,4),(6,3)],7)=>([],1) [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,5,1]=>[1,2,4,5,6,3,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>([(0,2),(2,1)],3) [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,5,1]=>[2,1,4,5,6,3,7]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,6,1]=>[1,3,4,5,6,2,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,1]=>[2,3,4,5,6,1,7]=>([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,7,1]=>[3,2,4,5,6,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(6,3)],7)=>([],1) [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,6,1]=>[1,4,3,5,6,2,7]=>([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,5),(6,1)],7)=>([],1) [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,7,1]=>[2,4,3,5,6,1,7]=>([(0,5),(1,2),(1,3),(2,6),(3,6),(4,5),(6,4)],7)=>([],1) [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,7,1]=>[3,4,2,5,6,1,7]=>([(0,6),(1,5),(2,3),(3,6),(4,5),(6,4)],7)=>([(0,1)],2) [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,7,1]=>[4,3,2,5,6,1,7]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(6,4)],7)=>([],1) [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,5,1]=>[1,2,5,4,6,3,7]=>([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7)=>([],1) [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,5,1]=>[2,1,5,4,6,3,7]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(3,2),(4,3),(5,3),(6,2)],7)=>([],1) [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,6,1]=>[1,3,5,4,6,2,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,1),(4,2),(5,6)],7)=>([],1) [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,7,1]=>[2,3,5,4,6,1,7]=>([(0,6),(1,4),(2,5),(3,5),(4,2),(4,3),(5,6)],7)=>([],1) [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,7,1]=>[3,2,5,4,6,1,7]=>([(0,3),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7)=>([(0,1)],2) [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,6,1]=>[1,4,5,3,6,2,7]=>([(0,2),(0,3),(0,4),(1,5),(2,6),(3,5),(4,1),(5,6)],7)=>([(0,1)],2) [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>[2,4,5,3,6,1,7]=>([(0,6),(1,3),(1,4),(2,5),(3,5),(4,2),(5,6)],7)=>([(0,1)],2) [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,7,1]=>[3,4,5,2,6,1,7]=>([(0,6),(1,5),(2,3),(3,4),(4,5),(5,6)],7)=>([(0,2),(2,1)],3) [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,7,1]=>[4,3,5,2,6,1,7]=>([(0,4),(1,4),(2,5),(3,6),(4,6),(6,5)],7)=>([],1) [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,6,1]=>[1,5,4,3,6,2,7]=>([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)=>([],1) [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>[2,5,4,3,6,1,7]=>([(0,5),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)=>([],1) [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,7,1]=>[3,5,4,2,6,1,7]=>([(0,6),(1,5),(2,3),(2,4),(3,6),(4,6),(6,5)],7)=>([],1) [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,7,1]=>[4,5,3,2,6,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,6),(6,5)],7)=>([(0,1)],2) [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,7,1]=>[5,4,3,2,6,1,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7)=>([],1) [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,4,1]=>[1,2,3,6,5,4,7]=>([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)=>([],1) [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,4,1]=>[2,1,3,6,5,4,7]=>([(0,5),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7)=>([],1) [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,4,1]=>[1,3,2,6,5,4,7]=>([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>([],1) [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,4,1]=>[2,3,1,6,5,4,7]=>([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>([],1) [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,4,1]=>[3,2,1,6,5,4,7]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(4,3),(5,3),(6,3)],7)=>([(0,1)],2) [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,5,1]=>[1,2,4,6,5,3,7]=>([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>([],1) [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,5,1]=>[2,1,4,6,5,3,7]=>([(0,4),(0,5),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7)=>([],1) [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,6,1]=>[1,3,4,6,5,2,7]=>([(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2)],7)=>([],1) [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,7,1]=>[2,3,4,6,5,1,7]=>([(0,6),(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7)=>([],1) [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,7,1]=>[3,2,4,6,5,1,7]=>([(0,6),(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7)=>([(0,1)],2) [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,6,1]=>[1,4,3,6,5,2,7]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>([(0,1)],2) [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,7,1]=>[2,4,3,6,5,1,7]=>([(0,6),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>([(0,1)],2) [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,7,1]=>[3,4,2,6,5,1,7]=>([(0,6),(1,4),(1,5),(2,3),(3,4),(3,5),(4,6),(5,6)],7)=>([(0,2),(2,1)],3) [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,7,1]=>[4,3,2,6,5,1,7]=>([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>([],1) [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,5,1]=>[1,2,5,6,4,3,7]=>([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)=>([(0,1)],2) [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,5,1]=>[2,1,5,6,4,3,7]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)=>([(0,1)],2) [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,6,1]=>[1,3,5,6,4,2,7]=>([(0,3),(0,5),(1,6),(2,6),(3,6),(4,2),(5,1),(5,4)],7)=>([(0,1)],2) [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,7,1]=>[2,3,5,6,4,1,7]=>([(0,6),(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7)=>([(0,1)],2) [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,7,1]=>[3,2,5,6,4,1,7]=>([(0,6),(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,3)],7)=>([(0,2),(2,1)],3) [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,6,1]=>[1,4,5,6,3,2,7]=>([(0,2),(0,3),(0,5),(1,6),(2,6),(3,6),(4,1),(5,4)],7)=>([(0,2),(2,1)],3) [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>[2,4,5,6,3,1,7]=>([(0,6),(1,3),(1,5),(2,6),(3,6),(4,2),(5,4)],7)=>([(0,2),(2,1)],3) [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,7,1]=>[3,4,5,6,2,1,7]=>([(0,3),(1,6),(2,6),(3,5),(4,6),(5,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,7,1]=>[4,3,5,6,2,1,7]=>([(0,6),(1,6),(2,5),(3,5),(4,6),(5,4)],7)=>([],1) [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,6,1]=>[1,5,4,6,3,2,7]=>([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>([],1) [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>[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) [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,7,1]=>[3,5,4,6,2,1,7]=>([(0,6),(1,6),(2,3),(2,4),(3,5),(4,5),(5,6)],7)=>([],1) [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,7,1]=>[4,5,3,6,2,1,7]=>([(0,6),(1,6),(2,5),(3,4),(4,5),(5,6)],7)=>([(0,1)],2) [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,7,1]=>[5,4,3,6,2,1,7]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7)=>([],1) [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,5,1]=>[1,2,6,5,4,3,7]=>([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)=>([],1) [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,5,1]=>[2,1,6,5,4,3,7]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)=>([],1) [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,6,1]=>[1,3,6,5,4,2,7]=>([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)=>([],1) [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,7,1]=>[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) [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,7,1]=>[3,2,6,5,4,1,7]=>([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>([],1) [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,6,1]=>[1,4,6,5,3,2,7]=>([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)=>([],1) [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,7,1]=>[2,4,6,5,3,1,7]=>([(0,6),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7)=>([],1) [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,7,1]=>[3,4,6,5,2,1,7]=>([(0,3),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>([],1) [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,7,1]=>[4,3,6,5,2,1,7]=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>([(0,1)],2) [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,6,1]=>[1,5,6,4,3,2,7]=>([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)=>([(0,1)],2) [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>[2,5,6,4,3,1,7]=>([(0,6),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)=>([(0,1)],2) [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,7,1]=>[3,5,6,4,2,1,7]=>([(0,6),(1,6),(2,3),(2,4),(3,5),(4,6),(5,6)],7)=>([(0,1)],2) [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,7,1]=>[4,5,6,3,2,1,7]=>([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>([(0,2),(2,1)],3) [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,7,1]=>[5,4,6,3,2,1,7]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>([],1) [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,6,1]=>[1,6,5,4,3,2,7]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([],1) [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>[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) [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,7,1]=>[3,6,5,4,2,1,7]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>([],1) [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,7,1]=>[4,6,5,3,2,1,7]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>([],1) [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,7,1]=>[5,6,4,3,2,1,7]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,1)],2) [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[6,5,4,3,2,1,7]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([],1) [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1,2]=>[1,2,3,4,5,7,6]=>([(0,5),(3,4),(4,6),(5,3),(6,1),(6,2)],7)=>([],1) [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6]=>([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7)=>([(0,1)],2) [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,1,2]=>[1,3,2,4,5,7,6]=>([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7)=>([(0,1)],2) [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,1,2]=>[2,3,1,4,5,7,6]=>([(0,6),(1,4),(4,6),(5,2),(5,3),(6,5)],7)=>([(0,2),(2,1)],3) [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,1,2]=>[3,2,1,4,5,7,6]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(6,3)],7)=>([],1) [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,1,2]=>[1,2,4,3,5,7,6]=>([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7)=>([(0,1)],2) [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,1,2]=>[2,1,4,3,5,7,6]=>([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7)=>([(0,2),(2,1)],3) [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,1,2]=>[1,3,4,2,5,7,6]=>([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7)=>([(0,2),(2,1)],3) [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,1,2]=>[2,3,4,1,5,7,6]=>([(0,6),(1,5),(2,6),(5,2),(6,3),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,1,2]=>[3,2,4,1,5,7,6]=>([(0,6),(1,5),(2,5),(5,6),(6,3),(6,4)],7)=>([],1) [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,1,2]=>[1,4,3,2,5,7,6]=>([(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1),(6,2)],7)=>([],1) [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,1,2]=>[2,4,3,1,5,7,6]=>([(0,6),(1,2),(1,3),(2,6),(3,6),(6,4),(6,5)],7)=>([],1) [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,1,2]=>[3,4,2,1,5,7,6]=>([(0,6),(1,6),(2,3),(3,6),(6,4),(6,5)],7)=>([(0,1)],2) [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,1,2]=>[4,3,2,1,5,7,6]=>([(0,6),(1,6),(2,6),(3,6),(6,4),(6,5)],7)=>([],1) [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,1,2]=>[1,2,3,5,4,7,6]=>([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2)],7)=>([(0,1)],2) [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,1,2]=>[2,1,3,5,4,7,6]=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7)=>([(0,2),(2,1)],3) [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,1,2]=>[1,3,2,5,4,7,6]=>([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)=>([(0,2),(2,1)],3) [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,1,2]=>[2,3,1,5,4,7,6]=>([(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,1,2]=>[3,2,1,5,4,7,6]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)=>([],1) [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,1,2]=>[1,2,4,5,3,7,6]=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1),(4,3)],7)=>([(0,2),(2,1)],3) [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,1,2]=>[2,1,4,5,3,7,6]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(5,2),(6,3),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,1,2]=>[1,3,4,5,2,7,6]=>([(0,2),(0,4),(1,5),(1,6),(2,5),(2,6),(3,1),(4,3)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,1,2]=>[2,3,4,5,1,7,6]=>([(0,5),(0,6),(1,4),(2,5),(2,6),(3,2),(4,3)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,1,2]=>[3,2,4,5,1,7,6]=>([(0,4),(1,4),(2,5),(2,6),(3,5),(3,6),(4,3)],7)=>([],1) [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,1,2]=>[1,4,3,5,2,7,6]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>([],1) [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,1,2]=>[2,4,3,5,1,7,6]=>([(0,2),(0,3),(1,4),(1,5),(2,6),(3,6),(6,4),(6,5)],7)=>([],1) [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,1,2]=>[3,4,2,5,1,7,6]=>([(0,6),(1,4),(1,5),(2,3),(3,6),(6,4),(6,5)],7)=>([(0,1)],2) [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,1,2]=>[4,3,2,5,1,7,6]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7)=>([],1) [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,1,2]=>[1,2,5,4,3,7,6]=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7)=>([],1) [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([],1) [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,1,2]=>[1,3,5,4,2,7,6]=>([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2)],7)=>([],1) [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,1,2]=>[2,3,5,4,1,7,6]=>([(0,5),(0,6),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3)],7)=>([],1) [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,1,2]=>[3,2,5,4,1,7,6]=>([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,1)],2) [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,1,2]=>[1,4,5,3,2,7,6]=>([(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1)],7)=>([(0,1)],2) [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,1,2]=>[2,4,5,3,1,7,6]=>([(0,5),(0,6),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7)=>([(0,1)],2) [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,1,2]=>[3,4,5,2,1,7,6]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(4,5),(4,6)],7)=>([(0,2),(2,1)],3) [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,1,2]=>[4,3,5,2,1,7,6]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7)=>([],1) [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,1,2]=>[1,5,4,3,2,7,6]=>([(0,1),(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([],1) [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,1,2]=>[2,5,4,3,1,7,6]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([],1) [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,1,2]=>[3,5,4,2,1,7,6]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>([],1) [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,1,2]=>[4,5,3,2,1,7,6]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)=>([(0,1)],2) [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>[5,4,3,2,1,7,6]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([],1) [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,1,3]=>[1,2,3,4,6,7,5]=>([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7)=>([(0,1)],2) [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,1,3]=>[2,1,3,4,6,7,5]=>([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7)=>([(0,2),(2,1)],3) [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,1,3]=>[1,3,2,4,6,7,5]=>([(0,3),(0,4),(3,6),(4,6),(5,1),(6,2),(6,5)],7)=>([(0,2),(2,1)],3) [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,1,3]=>[2,3,1,4,6,7,5]=>([(0,6),(1,3),(3,6),(5,2),(6,4),(6,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,1,3]=>[3,2,1,4,6,7,5]=>([(0,6),(1,6),(2,6),(4,5),(6,3),(6,4)],7)=>([],1) [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,1,3]=>[1,2,4,3,6,7,5]=>([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(6,1)],7)=>([(0,2),(2,1)],3) [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,1,3]=>[2,1,4,3,6,7,5]=>([(0,5),(0,6),(1,5),(1,6),(4,2),(5,3),(5,4),(6,3),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,1,3]=>[1,3,4,2,6,7,5]=>([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,1,3]=>[2,3,4,1,6,7,5]=>([(0,5),(0,6),(1,4),(3,5),(3,6),(4,3),(6,2)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,1,3]=>[3,2,4,1,6,7,5]=>([(0,5),(0,6),(1,4),(2,4),(4,5),(4,6),(6,3)],7)=>([],1) [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,1,3]=>[1,4,3,2,6,7,5]=>([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7)=>([],1) [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,1,3]=>[2,4,3,1,6,7,5]=>([(0,5),(0,6),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(6,2)],7)=>([],1) [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,1,3]=>[3,4,2,1,6,7,5]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7)=>([(0,1)],2) [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,1,3]=>[4,3,2,1,6,7,5]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7)=>([],1) [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1,4]=>[1,2,3,5,6,7,4]=>([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7)=>([(0,2),(2,1)],3) [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,1,4]=>[2,1,3,5,6,7,4]=>([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,1,4]=>[1,3,2,5,6,7,4]=>([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,1,4]=>[2,3,1,5,6,7,4]=>([(0,5),(0,6),(1,3),(3,5),(3,6),(4,2),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,1,4]=>[3,2,1,5,6,7,4]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7)=>([],1) [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1,5]=>[1,2,4,5,6,7,3]=>([(0,6),(3,5),(4,3),(5,1),(6,2),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,1,5]=>[2,1,4,5,6,7,3]=>([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(6,3)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1,6]=>[1,3,4,5,6,7,2]=>([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,7,1]=>([(1,6),(3,5),(4,3),(5,2),(6,4)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,1,7]=>[3,2,4,5,6,7,1]=>([(1,6),(2,6),(3,5),(5,4),(6,3)],7)=>([],1) [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,1,6]=>[1,4,3,5,6,7,2]=>([(0,2),(0,3),(0,4),(3,6),(4,6),(5,1),(6,5)],7)=>([],1) [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,1,7]=>[2,4,3,5,6,7,1]=>([(1,3),(1,4),(3,6),(4,6),(5,2),(6,5)],7)=>([],1) [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,1,7]=>[3,4,2,5,6,7,1]=>([(1,6),(2,3),(3,6),(4,5),(6,4)],7)=>([(0,1)],2) [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,1,7]=>[4,3,2,5,6,7,1]=>([(1,6),(2,6),(3,6),(4,5),(6,4)],7)=>([],1) [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,1,5]=>[1,2,5,4,6,7,3]=>([(0,5),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)=>([],1) [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,1,5]=>[2,1,5,4,6,7,3]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(3,2),(5,3),(6,3)],7)=>([],1) [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,1,6]=>[1,3,5,4,6,7,2]=>([(0,4),(0,5),(1,6),(2,6),(5,1),(5,2),(6,3)],7)=>([],1) [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,1,7]=>[2,3,5,4,6,7,1]=>([(1,5),(2,6),(3,6),(5,2),(5,3),(6,4)],7)=>([],1) [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,1,7]=>[3,2,5,4,6,7,1]=>([(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7)=>([(0,1)],2) [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,1,6]=>[1,4,5,3,6,7,2]=>([(0,3),(0,4),(0,5),(1,6),(4,6),(5,1),(6,2)],7)=>([(0,1)],2) [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,1,7]=>[2,4,5,3,6,7,1]=>([(1,3),(1,5),(2,6),(3,6),(5,2),(6,4)],7)=>([(0,1)],2) [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,1,7]=>[3,4,5,2,6,7,1]=>([(1,6),(2,3),(3,5),(5,6),(6,4)],7)=>([(0,2),(2,1)],3) [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,1,7]=>[4,3,5,2,6,7,1]=>([(1,6),(2,5),(3,5),(5,6),(6,4)],7)=>([],1) [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,1,6]=>[1,5,4,3,6,7,2]=>([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1)],7)=>([],1) [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,1,7]=>[2,5,4,3,6,7,1]=>([(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)=>([],1) [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,1,7]=>[3,5,4,2,6,7,1]=>([(1,6),(2,3),(2,4),(3,6),(4,6),(6,5)],7)=>([],1) [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,1,7]=>[4,5,3,2,6,7,1]=>([(1,6),(2,6),(3,4),(4,6),(6,5)],7)=>([(0,1)],2) [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,1,7]=>[5,4,3,2,6,7,1]=>([(1,6),(2,6),(3,6),(4,6),(6,5)],7)=>([],1) [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,1,4]=>[1,2,3,6,5,7,4]=>([(0,4),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)=>([],1) [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,1,4]=>[2,1,3,6,5,7,4]=>([(0,6),(1,6),(3,5),(4,5),(6,2),(6,3),(6,4)],7)=>([],1) [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,1,4]=>[1,3,2,6,5,7,4]=>([(0,1),(0,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)=>([],1) [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,1,4]=>[2,3,1,6,5,7,4]=>([(0,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)=>([],1) [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,1,4]=>[3,2,1,6,5,7,4]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)=>([(0,1)],2) [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,1,5]=>[1,2,4,6,5,7,3]=>([(0,5),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>([],1) [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,1,5]=>[2,1,4,6,5,7,3]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(6,2),(6,3)],7)=>([],1) [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,1,6]=>[1,3,4,6,5,7,2]=>([(0,3),(0,4),(1,6),(2,6),(4,5),(5,1),(5,2)],7)=>([],1) [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,1,7]=>[2,3,4,6,5,7,1]=>([(1,4),(2,6),(3,6),(4,5),(5,2),(5,3)],7)=>([],1) [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,1,7]=>[3,2,4,6,5,7,1]=>([(1,5),(2,5),(3,6),(4,6),(5,3),(5,4)],7)=>([(0,1)],2) [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,1,6]=>[1,4,3,6,5,7,2]=>([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>([(0,1)],2) [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,1,7]=>[2,4,3,6,5,7,1]=>([(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)=>([(0,1)],2) [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,1,7]=>[3,4,2,6,5,7,1]=>([(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)=>([(0,2),(2,1)],3) [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,1,7]=>[4,3,2,6,5,7,1]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)=>([],1) [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,1,5]=>[1,2,5,6,4,7,3]=>([(0,5),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)=>([(0,1)],2) [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,1,5]=>[2,1,5,6,4,7,3]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(5,2),(6,3)],7)=>([(0,1)],2) [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,1,6]=>[1,3,5,6,4,7,2]=>([(0,3),(0,5),(1,6),(2,6),(4,2),(5,1),(5,4)],7)=>([(0,1)],2) [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,1,7]=>[2,3,5,6,4,7,1]=>([(1,5),(2,6),(3,6),(4,3),(5,2),(5,4)],7)=>([(0,1)],2) [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,1,7]=>[3,2,5,6,4,7,1]=>([(1,4),(1,5),(2,4),(2,5),(3,6),(4,6),(5,3)],7)=>([(0,2),(2,1)],3) [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,1,6]=>[1,4,5,6,3,7,2]=>([(0,2),(0,3),(0,5),(1,6),(3,6),(4,1),(5,4)],7)=>([(0,2),(2,1)],3) [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,1,7]=>[2,4,5,6,3,7,1]=>([(1,3),(1,5),(2,6),(3,6),(4,2),(5,4)],7)=>([(0,2),(2,1)],3) [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,1,7]=>[3,4,5,6,2,7,1]=>([(1,3),(2,6),(3,5),(4,6),(5,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,1,7]=>[4,3,5,6,2,7,1]=>([(1,6),(2,5),(3,5),(4,6),(5,4)],7)=>([],1) [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,1,6]=>[1,5,4,6,3,7,2]=>([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6)],7)=>([],1) [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,1,7]=>[2,5,4,6,3,7,1]=>([(1,2),(1,3),(1,4),(2,6),(3,5),(4,5),(5,6)],7)=>([],1) [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,1,7]=>[3,5,4,6,2,7,1]=>([(1,5),(2,3),(2,4),(3,6),(4,6),(6,5)],7)=>([],1) [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,1,7]=>[4,5,3,6,2,7,1]=>([(1,6),(2,5),(3,4),(4,6),(6,5)],7)=>([(0,1)],2) [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,1,7]=>[5,4,3,6,2,7,1]=>([(1,6),(2,6),(3,6),(4,5),(6,5)],7)=>([],1) [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,1,5]=>[1,2,6,5,4,7,3]=>([(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)=>([],1) [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,1,5]=>[2,1,6,5,4,7,3]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7)=>([],1) [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,1,6]=>[1,3,6,5,4,7,2]=>([(0,4),(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3)],7)=>([],1) [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,1,7]=>[2,3,6,5,4,7,1]=>([(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7)=>([],1) [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,1,7]=>[3,2,6,5,4,7,1]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>([],1) [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,1,6]=>[1,4,6,5,3,7,2]=>([(0,3),(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2)],7)=>([],1) [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,1,7]=>[2,4,6,5,3,7,1]=>([(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7)=>([],1) [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,1,7]=>[3,4,6,5,2,7,1]=>([(1,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>([],1) [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,1,7]=>[4,3,6,5,2,7,1]=>([(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>([(0,1)],2) [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,1,6]=>[1,5,6,4,3,7,2]=>([(0,2),(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1)],7)=>([(0,1)],2) [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,1,7]=>[2,5,6,4,3,7,1]=>([(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)=>([(0,1)],2) [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,1,7]=>[3,5,6,4,2,7,1]=>([(1,6),(2,3),(2,4),(3,5),(4,6),(5,6)],7)=>([(0,1)],2) [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,1,7]=>[4,5,6,3,2,7,1]=>([(1,6),(2,6),(3,4),(4,5),(5,6)],7)=>([(0,2),(2,1)],3) [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,1,7]=>[5,4,6,3,2,7,1]=>([(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>([],1) [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,1,6]=>[1,6,5,4,3,7,2]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6)],7)=>([],1) [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,1,7]=>[2,6,5,4,3,7,1]=>([(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)=>([],1) [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,1,7]=>[3,6,5,4,2,7,1]=>([(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>([],1) [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,1,7]=>[4,6,5,3,2,7,1]=>([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>([],1) [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,1,7]=>[5,6,4,3,2,7,1]=>([(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,1)],2) [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>[6,5,4,3,2,7,1]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([],1) [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,2,3]=>[1,2,3,4,7,6,5]=>([(0,5),(4,6),(5,4),(6,1),(6,2),(6,3)],7)=>([],1) [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,1,2,3]=>[2,1,3,4,7,6,5]=>([(0,6),(1,6),(5,2),(5,3),(5,4),(6,5)],7)=>([],1) [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,1,2,3]=>[1,3,2,4,7,6,5]=>([(0,4),(0,5),(4,6),(5,6),(6,1),(6,2),(6,3)],7)=>([],1) [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,1,2,3]=>[2,3,1,4,7,6,5]=>([(0,6),(1,2),(2,6),(6,3),(6,4),(6,5)],7)=>([],1) [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>([(0,6),(1,6),(2,6),(6,3),(6,4),(6,5)],7)=>([(0,1)],2) [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,1,2,3]=>[1,2,4,3,7,6,5]=>([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,1),(3,2)],7)=>([],1) [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,1,2,3]=>[2,1,4,3,7,6,5]=>([(0,5),(0,6),(1,5),(1,6),(5,2),(5,3),(5,4),(6,2),(6,3),(6,4)],7)=>([],1) [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,1,2,3]=>[1,3,4,2,7,6,5]=>([(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,1)],7)=>([],1) [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,1,2,3]=>[2,3,4,1,7,6,5]=>([(0,2),(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7)=>([],1) [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,1,2,3]=>[3,2,4,1,7,6,5]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4),(6,5)],7)=>([(0,1)],2) [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,1,2,3]=>[1,4,3,2,7,6,5]=>([(0,1),(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,1)],2) [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,1,2,3]=>[2,4,3,1,7,6,5]=>([(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,1)],2) [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,1,2,3]=>[3,4,2,1,7,6,5]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7)=>([(0,2),(2,1)],3) [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[4,3,2,1,7,6,5]=>([(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) [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1,2,4]=>[1,2,3,5,7,6,4]=>([(0,4),(4,6),(5,2),(5,3),(6,1),(6,5)],7)=>([],1) [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,1,2,4]=>[2,1,3,5,7,6,4]=>([(0,6),(1,6),(5,2),(5,3),(6,4),(6,5)],7)=>([],1) [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,1,2,4]=>[1,3,2,5,7,6,4]=>([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1),(6,2)],7)=>([],1) [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,1,2,4]=>[2,3,1,5,7,6,4]=>([(0,5),(0,6),(1,4),(4,5),(4,6),(6,2),(6,3)],7)=>([],1) [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,1,2,4]=>[3,2,1,5,7,6,4]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7)=>([(0,1)],2) [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1,2,5]=>[1,2,4,5,7,6,3]=>([(0,6),(4,5),(5,2),(5,3),(6,1),(6,4)],7)=>([],1) [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,1,2,5]=>[2,1,4,5,7,6,3]=>([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(6,4)],7)=>([],1) [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1,2,6]=>[1,3,4,5,7,6,2]=>([(0,3),(0,5),(4,6),(5,4),(6,1),(6,2)],7)=>([],1) [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,2,7]=>[2,3,4,5,7,6,1]=>([(1,5),(4,6),(5,4),(6,2),(6,3)],7)=>([],1) [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,1,2,7]=>[3,2,4,5,7,6,1]=>([(1,6),(2,6),(3,4),(3,5),(6,3)],7)=>([(0,1)],2) [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,1,2,6]=>[1,4,3,5,7,6,2]=>([(0,3),(0,4),(0,5),(4,6),(5,6),(6,1),(6,2)],7)=>([(0,1)],2) [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,1,2,7]=>[2,4,3,5,7,6,1]=>([(1,2),(1,3),(2,6),(3,6),(6,4),(6,5)],7)=>([(0,1)],2) [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,1,2,7]=>[3,4,2,5,7,6,1]=>([(1,6),(2,3),(3,6),(6,4),(6,5)],7)=>([(0,2),(2,1)],3) [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,1,2,7]=>[4,3,2,5,7,6,1]=>([(1,6),(2,6),(3,6),(6,4),(6,5)],7)=>([],1) [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,1,2,5]=>[1,2,5,4,7,6,3]=>([(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7)=>([(0,1)],2) [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,1,2,5]=>[2,1,5,4,7,6,3]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(5,2),(5,3),(6,2),(6,3)],7)=>([(0,1)],2) [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,1,2,6]=>[1,3,5,4,7,6,2]=>([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(4,1),(4,2)],7)=>([(0,1)],2) [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,1,2,7]=>[2,3,5,4,7,6,1]=>([(1,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3)],7)=>([(0,1)],2) [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,1,2,7]=>[3,2,5,4,7,6,1]=>([(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)=>([(0,2),(2,1)],3) [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,1,2,6]=>[1,4,5,3,7,6,2]=>([(0,2),(0,3),(0,4),(1,5),(1,6),(3,5),(3,6),(4,1)],7)=>([(0,2),(2,1)],3) [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,1,2,7]=>[2,4,5,3,7,6,1]=>([(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7)=>([(0,2),(2,1)],3) [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,1,2,7]=>[3,4,5,2,7,6,1]=>([(1,5),(1,6),(2,3),(3,4),(4,5),(4,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,1,2,7]=>[4,3,5,2,7,6,1]=>([(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>([],1) [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>[1,5,4,3,7,6,2]=>([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([],1) [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,1,2,7]=>[2,5,4,3,7,6,1]=>([(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([],1) [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,1,2,7]=>[3,5,4,2,7,6,1]=>([(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>([],1) [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,1,2,7]=>[4,5,3,2,7,6,1]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)=>([(0,1)],2) [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,1,2,7]=>[5,4,3,2,7,6,1]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([],1) [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,3,4]=>[1,2,3,6,7,5,4]=>([(0,5),(4,3),(5,6),(6,1),(6,2),(6,4)],7)=>([(0,1)],2) [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,1,3,4]=>[2,1,3,6,7,5,4]=>([(0,6),(1,6),(5,2),(6,3),(6,4),(6,5)],7)=>([(0,1)],2) [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,1,3,4]=>[1,3,2,6,7,5,4]=>([(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(6,1)],7)=>([(0,1)],2) [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,1,3,4]=>[2,3,1,6,7,5,4]=>([(0,3),(1,4),(1,5),(1,6),(3,4),(3,5),(3,6),(6,2)],7)=>([(0,1)],2) [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,1,3,4]=>[3,2,1,6,7,5,4]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7)=>([(0,2),(2,1)],3) [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1,3,5]=>[1,2,4,6,7,5,3]=>([(0,6),(4,3),(5,2),(5,4),(6,1),(6,5)],7)=>([(0,1)],2) [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,1,3,5]=>[2,1,4,6,7,5,3]=>([(0,5),(0,6),(1,5),(1,6),(4,3),(6,2),(6,4)],7)=>([(0,1)],2) [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,3,6]=>[1,3,4,6,7,5,2]=>([(0,3),(0,5),(4,2),(5,6),(6,1),(6,4)],7)=>([(0,1)],2) [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,3,7]=>[2,3,4,6,7,5,1]=>([(1,5),(4,3),(5,6),(6,2),(6,4)],7)=>([(0,1)],2) [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,1,3,7]=>[3,2,4,6,7,5,1]=>([(1,6),(2,6),(4,5),(6,3),(6,4)],7)=>([(0,2),(2,1)],3) [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,1,3,6]=>[1,4,3,6,7,5,2]=>([(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1)],7)=>([(0,2),(2,1)],3) [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,1,3,7]=>[2,4,3,6,7,5,1]=>([(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(6,2)],7)=>([(0,2),(2,1)],3) [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,1,3,7]=>[3,4,2,6,7,5,1]=>([(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,1,3,7]=>[4,3,2,6,7,5,1]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7)=>([],1) [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,4,5]=>[1,2,5,6,7,4,3]=>([(0,6),(4,5),(5,3),(6,1),(6,2),(6,4)],7)=>([(0,2),(2,1)],3) [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,1,4,5]=>[2,1,5,6,7,4,3]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(6,2)],7)=>([(0,2),(2,1)],3) [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1,4,6]=>[1,3,5,6,7,4,2]=>([(0,3),(0,6),(4,5),(5,2),(6,1),(6,4)],7)=>([(0,2),(2,1)],3) [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,4,7]=>[2,3,5,6,7,4,1]=>([(1,6),(4,5),(5,3),(6,2),(6,4)],7)=>([(0,2),(2,1)],3) [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,1,4,7]=>[3,2,5,6,7,4,1]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(6,3)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,5,6]=>[1,4,5,6,7,3,2]=>([(0,2),(0,3),(0,6),(4,5),(5,1),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,5,7]=>[2,4,5,6,7,3,1]=>([(1,3),(1,6),(4,5),(5,2),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,6,7]=>[3,4,5,6,7,2,1]=>([(2,6),(4,5),(5,3),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,1,6,7]=>[4,3,5,6,7,2,1]=>([(2,6),(3,6),(4,5),(6,4)],7)=>([],1) [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,1,5,6]=>[1,5,4,6,7,3,2]=>([(0,2),(0,3),(0,4),(0,5),(4,6),(5,6),(6,1)],7)=>([],1) [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,1,5,7]=>[2,5,4,6,7,3,1]=>([(1,2),(1,3),(1,4),(3,6),(4,6),(6,5)],7)=>([],1) [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,1,6,7]=>[3,5,4,6,7,2,1]=>([(2,3),(2,4),(3,6),(4,6),(6,5)],7)=>([],1) [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,1,6,7]=>[4,5,3,6,7,2,1]=>([(2,6),(3,4),(4,6),(6,5)],7)=>([(0,1)],2) [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,1,6,7]=>[5,4,3,6,7,2,1]=>([(2,6),(3,6),(4,6),(6,5)],7)=>([],1) [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,1,4,5]=>[1,2,6,5,7,4,3]=>([(0,5),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)=>([],1) [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,1,4,5]=>[2,1,6,5,7,4,3]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(5,2),(6,2)],7)=>([],1) [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,1,4,6]=>[1,3,6,5,7,4,2]=>([(0,4),(0,5),(2,6),(3,6),(5,1),(5,2),(5,3)],7)=>([],1) [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,1,4,7]=>[2,3,6,5,7,4,1]=>([(1,5),(3,6),(4,6),(5,2),(5,3),(5,4)],7)=>([],1) [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,1,4,7]=>[3,2,6,5,7,4,1]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)=>([],1) [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,1,5,6]=>[1,4,6,5,7,3,2]=>([(0,3),(0,4),(0,5),(1,6),(2,6),(5,1),(5,2)],7)=>([],1) [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,1,5,7]=>[2,4,6,5,7,3,1]=>([(1,2),(1,5),(3,6),(4,6),(5,3),(5,4)],7)=>([],1) [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,1,6,7]=>[3,4,6,5,7,2,1]=>([(2,3),(3,4),(3,5),(4,6),(5,6)],7)=>([],1) [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,1,6,7]=>[4,3,6,5,7,2,1]=>([(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>([(0,1)],2) [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,1,5,6]=>[1,5,6,4,7,3,2]=>([(0,2),(0,3),(0,4),(0,5),(1,6),(4,6),(5,1)],7)=>([(0,1)],2) [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,1,5,7]=>[2,5,6,4,7,3,1]=>([(1,2),(1,4),(1,5),(3,6),(4,6),(5,3)],7)=>([(0,1)],2) [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,1,6,7]=>[3,5,6,4,7,2,1]=>([(2,3),(2,4),(3,5),(4,6),(5,6)],7)=>([(0,1)],2) [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,1,6,7]=>[4,5,6,3,7,2,1]=>([(2,6),(3,4),(4,5),(5,6)],7)=>([(0,2),(2,1)],3) [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,1,6,7]=>[5,4,6,3,7,2,1]=>([(2,6),(3,5),(4,5),(5,6)],7)=>([],1) [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,1,5,6]=>[1,6,5,4,7,3,2]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6)],7)=>([],1) [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,1,5,7]=>[2,6,5,4,7,3,1]=>([(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7)=>([],1) [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,1,6,7]=>[3,6,5,4,7,2,1]=>([(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>([],1) [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,1,6,7]=>[4,6,5,3,7,2,1]=>([(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>([],1) [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,1,6,7]=>[5,6,4,3,7,2,1]=>([(2,6),(3,6),(4,5),(5,6)],7)=>([(0,1)],2) [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7]=>[6,5,4,3,7,2,1]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([],1) [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,2,3,4]=>[1,2,3,7,6,5,4]=>([(0,5),(5,6),(6,1),(6,2),(6,3),(6,4)],7)=>([],1) [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,7,5,1,2,3,4]=>[2,1,3,7,6,5,4]=>([(0,6),(1,6),(6,2),(6,3),(6,4),(6,5)],7)=>([],1) [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,6,1,2,3,4]=>[1,3,2,7,6,5,4]=>([(0,1),(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)=>([],1) [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,7,1,2,3,4]=>[2,3,1,7,6,5,4]=>([(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)=>([],1) [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>[3,2,1,7,6,5,4]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)=>([],1) [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,2,3,5]=>[1,2,4,7,6,5,3]=>([(0,5),(5,4),(5,6),(6,1),(6,2),(6,3)],7)=>([],1) [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,7,4,1,2,3,5]=>[2,1,4,7,6,5,3]=>([(0,5),(0,6),(1,5),(1,6),(6,2),(6,3),(6,4)],7)=>([],1) [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,2,3,6]=>[1,3,4,7,6,5,2]=>([(0,4),(0,5),(5,6),(6,1),(6,2),(6,3)],7)=>([],1) [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,2,3,7]=>[2,3,4,7,6,5,1]=>([(1,5),(5,6),(6,2),(6,3),(6,4)],7)=>([],1) [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,6,4,1,2,3,7]=>[3,2,4,7,6,5,1]=>([(1,6),(2,6),(6,3),(6,4),(6,5)],7)=>([],1) [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,5,1,2,3,6]=>[1,4,3,7,6,5,2]=>([(0,1),(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([],1) [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,5,1,2,3,7]=>[2,4,3,7,6,5,1]=>([(1,2),(1,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([],1) [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,6,1,2,3,7]=>[3,4,2,7,6,5,1]=>([(1,4),(1,5),(1,6),(2,3),(3,4),(3,5),(3,6)],7)=>([],1) [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>[4,3,2,7,6,5,1]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,1)],2) [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,2,4,5]=>[1,2,5,7,6,4,3]=>([(0,6),(5,3),(5,4),(6,1),(6,2),(6,5)],7)=>([],1) [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,7,3,1,2,4,5]=>[2,1,5,7,6,4,3]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(6,2),(6,3)],7)=>([],1) [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,2,4,6]=>[1,3,5,7,6,4,2]=>([(0,4),(0,6),(5,2),(5,3),(6,1),(6,5)],7)=>([],1) [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,2,4,7]=>[2,3,5,7,6,4,1]=>([(1,6),(5,3),(5,4),(6,2),(6,5)],7)=>([],1) [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,6,3,1,2,4,7]=>[3,2,5,7,6,4,1]=>([(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7)=>([],1) [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,2,5,6]=>[1,4,5,7,6,3,2]=>([(0,3),(0,4),(0,5),(5,6),(6,1),(6,2)],7)=>([],1) [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,2,5,7]=>[2,4,5,7,6,3,1]=>([(1,4),(1,5),(5,6),(6,2),(6,3)],7)=>([],1) [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,2,6,7]=>[3,4,5,7,6,2,1]=>([(2,5),(5,6),(6,3),(6,4)],7)=>([],1) [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,1,2,6,7]=>[4,3,5,7,6,2,1]=>([(2,6),(3,6),(6,4),(6,5)],7)=>([(0,1)],2) [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,4,1,2,5,6]=>[1,5,4,7,6,3,2]=>([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,1)],2) [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,4,1,2,5,7]=>[2,5,4,7,6,3,1]=>([(1,2),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,1)],2) [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,4,1,2,6,7]=>[3,5,4,7,6,2,1]=>([(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,1)],2) [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,5,1,2,6,7]=>[4,5,3,7,6,2,1]=>([(2,5),(2,6),(3,4),(4,5),(4,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,4,5,1,2,6,7]=>[5,4,3,7,6,2,1]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([],1) [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,3,4,5]=>[1,2,6,7,5,4,3]=>([(0,6),(5,4),(6,1),(6,2),(6,3),(6,5)],7)=>([(0,1)],2) [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,7,2,1,3,4,5]=>[2,1,6,7,5,4,3]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(6,2)],7)=>([(0,1)],2) [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,3,4,6]=>[1,3,6,7,5,4,2]=>([(0,4),(0,6),(5,3),(6,1),(6,2),(6,5)],7)=>([(0,1)],2) [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,3,4,7]=>[2,3,6,7,5,4,1]=>([(1,6),(5,4),(6,2),(6,3),(6,5)],7)=>([(0,1)],2) [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,6,2,1,3,4,7]=>[3,2,6,7,5,4,1]=>([(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7)=>([(0,1)],2) [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,3,5,6]=>[1,4,6,7,5,3,2]=>([(0,3),(0,4),(0,6),(5,2),(6,1),(6,5)],7)=>([(0,1)],2) [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,3,5,7]=>[2,4,6,7,5,3,1]=>([(1,4),(1,6),(5,3),(6,2),(6,5)],7)=>([(0,1)],2) [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,3,6,7]=>[3,4,6,7,5,2,1]=>([(2,6),(5,4),(6,3),(6,5)],7)=>([(0,1)],2) [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,2,1,3,6,7]=>[4,3,6,7,5,2,1]=>([(2,5),(2,6),(3,5),(3,6),(6,4)],7)=>([(0,2),(2,1)],3) [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,4,5,6]=>[1,5,6,7,4,3,2]=>([(0,2),(0,3),(0,4),(0,6),(5,1),(6,5)],7)=>([(0,2),(2,1)],3) [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,4,5,7]=>[2,5,6,7,4,3,1]=>([(1,3),(1,4),(1,6),(5,2),(6,5)],7)=>([(0,2),(2,1)],3) [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,4,6,7]=>[3,5,6,7,4,2,1]=>([(2,4),(2,6),(5,3),(6,5)],7)=>([(0,2),(2,1)],3) [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,5,6,7]=>[4,5,6,7,3,2,1]=>([(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,4,2,1,5,6,7]=>[5,4,6,7,3,2,1]=>([(3,6),(4,6),(6,5)],7)=>([],1) [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,3,1,4,5,6]=>[1,6,5,7,4,3,2]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(4,6),(5,6)],7)=>([],1) [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,3,1,4,5,7]=>[2,6,5,7,4,3,1]=>([(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7)=>([],1) [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,3,1,4,6,7]=>[3,6,5,7,4,2,1]=>([(2,3),(2,4),(2,5),(4,6),(5,6)],7)=>([],1) [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,3,1,5,6,7]=>[4,6,5,7,3,2,1]=>([(3,4),(3,5),(4,6),(5,6)],7)=>([],1) [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,4,1,5,6,7]=>[5,6,4,7,3,2,1]=>([(3,6),(4,5),(5,6)],7)=>([(0,1)],2) [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7]=>[6,5,4,7,3,2,1]=>([(3,6),(4,6),(5,6)],7)=>([],1) [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,2,3,4,5]=>[1,2,7,6,5,4,3]=>([(0,6),(6,1),(6,2),(6,3),(6,4),(6,5)],7)=>([],1) [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>[2,1,7,6,5,4,3]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7)=>([],1) [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,2,3,4,6]=>[1,3,7,6,5,4,2]=>([(0,5),(0,6),(6,1),(6,2),(6,3),(6,4)],7)=>([],1) [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,2,3,4,7]=>[2,3,7,6,5,4,1]=>([(1,6),(6,2),(6,3),(6,4),(6,5)],7)=>([],1) [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,4,7]=>[3,2,7,6,5,4,1]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)=>([],1) [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,2,3,5,6]=>[1,4,7,6,5,3,2]=>([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7)=>([],1) [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,2,3,5,7]=>[2,4,7,6,5,3,1]=>([(1,5),(1,6),(6,2),(6,3),(6,4)],7)=>([],1) [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,2,3,6,7]=>[3,4,7,6,5,2,1]=>([(2,6),(6,3),(6,4),(6,5)],7)=>([],1) [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,5,1,2,3,6,7]=>[4,3,7,6,5,2,1]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([],1) [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,2,4,5,6]=>[1,5,7,6,4,3,2]=>([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7)=>([],1) [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,2,4,5,7]=>[2,5,7,6,4,3,1]=>([(1,4),(1,5),(1,6),(6,2),(6,3)],7)=>([],1) [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,2,4,6,7]=>[3,5,7,6,4,2,1]=>([(2,5),(2,6),(6,3),(6,4)],7)=>([],1) [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,2,5,6,7]=>[4,5,7,6,3,2,1]=>([(3,4),(4,5),(4,6)],7)=>([],1) [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>[5,4,7,6,3,2,1]=>([(3,5),(3,6),(4,5),(4,6)],7)=>([(0,1)],2) [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,3,4,5,6]=>[1,6,7,5,4,3,2]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7)=>([(0,1)],2) [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,3,4,5,7]=>[2,6,7,5,4,3,1]=>([(1,3),(1,4),(1,5),(1,6),(6,2)],7)=>([(0,1)],2) [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,3,4,6,7]=>[3,6,7,5,4,2,1]=>([(2,4),(2,5),(2,6),(6,3)],7)=>([(0,1)],2) [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,3,5,6,7]=>[4,6,7,5,3,2,1]=>([(3,4),(3,5),(5,6)],7)=>([(0,1)],2) [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,4,5,6,7]=>[5,6,7,4,3,2,1]=>([(4,5),(5,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>[6,5,7,4,3,2,1]=>([(4,6),(5,6)],7)=>([],1) [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>[1,7,6,5,4,3,2]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7)=>([],1) [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,5,7]=>[2,7,6,5,4,3,1]=>([(1,2),(1,3),(1,4),(1,5),(1,6)],7)=>([],1) [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,4,6,7]=>[3,7,6,5,4,2,1]=>([(2,3),(2,4),(2,5),(2,6)],7)=>([],1) [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,3,5,6,7]=>[4,7,6,5,3,2,1]=>([(3,4),(3,5),(3,6)],7)=>([],1) [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>[5,7,6,4,3,2,1]=>([(4,5),(4,6)],7)=>([],1) [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>[6,7,5,4,3,2,1]=>([(5,6)],7)=>([(0,1)],2) [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>([],7)=>([],1)
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
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
$$\{ (2, 1) \prec (5, 2),\ (2, 1) \prec (4, 4),\ (2, 1) \prec (3, 5),\ (1, 3) \prec (4, 4),\ (1, 3) \prec (3, 5) \}.$$
Map
antichains of maximal size
Description
The lattice of antichains of maximal size in a poset.
The set of antichains of maximal size can be ordered by setting $A \leq B \leftrightarrow \mathop{\downarrow} A \subseteq \mathop{\downarrow} B$, where $\mathop{\downarrow} A$ is the order ideal generated by $A$.
This is a sublattice of the lattice of all antichains with respect to the same order relation. In particular, it is distributive.