Identifier
Mp00024: Dyck paths to 321-avoiding permutationPermutations
Mp00065: Permutations permutation posetPosets
Mp00125: Posets dual poset Posets
Images
=>
Cc0005;cc-rep-0Cc0014;cc-rep-2Cc0014;cc-rep-3
[1,0]=>[1]=>([],1)=>([],1) [1,0,1,0]=>[2,1]=>([],2)=>([],2) [1,1,0,0]=>[1,2]=>([(0,1)],2)=>([(0,1)],2) [1,0,1,0,1,0]=>[2,1,3]=>([(0,2),(1,2)],3)=>([(0,1),(0,2)],3) [1,0,1,1,0,0]=>[2,3,1]=>([(1,2)],3)=>([(1,2)],3) [1,1,0,0,1,0]=>[3,1,2]=>([(1,2)],3)=>([(1,2)],3) [1,1,0,1,0,0]=>[1,3,2]=>([(0,1),(0,2)],3)=>([(0,2),(1,2)],3) [1,1,1,0,0,0]=>[1,2,3]=>([(0,2),(2,1)],3)=>([(0,2),(2,1)],3) [1,0,1,0,1,0,1,0]=>[2,1,4,3]=>([(0,2),(0,3),(1,2),(1,3)],4)=>([(0,2),(0,3),(1,2),(1,3)],4) [1,0,1,0,1,1,0,0]=>[2,4,1,3]=>([(0,3),(1,2),(1,3)],4)=>([(0,3),(1,2),(1,3)],4) [1,0,1,1,0,0,1,0]=>[2,1,3,4]=>([(0,3),(1,3),(3,2)],4)=>([(0,3),(3,1),(3,2)],4) [1,0,1,1,0,1,0,0]=>[2,3,1,4]=>([(0,3),(1,2),(2,3)],4)=>([(0,2),(0,3),(3,1)],4) [1,0,1,1,1,0,0,0]=>[2,3,4,1]=>([(1,2),(2,3)],4)=>([(1,2),(2,3)],4) [1,1,0,0,1,0,1,0]=>[3,1,4,2]=>([(0,3),(1,2),(1,3)],4)=>([(0,3),(1,2),(1,3)],4) [1,1,0,0,1,1,0,0]=>[3,4,1,2]=>([(0,3),(1,2)],4)=>([(0,3),(1,2)],4) [1,1,0,1,0,0,1,0]=>[3,1,2,4]=>([(0,3),(1,2),(2,3)],4)=>([(0,2),(0,3),(3,1)],4) [1,1,0,1,0,1,0,0]=>[1,3,2,4]=>([(0,1),(0,2),(1,3),(2,3)],4)=>([(0,1),(0,2),(1,3),(2,3)],4) [1,1,0,1,1,0,0,0]=>[1,3,4,2]=>([(0,2),(0,3),(3,1)],4)=>([(0,3),(1,2),(2,3)],4) [1,1,1,0,0,0,1,0]=>[4,1,2,3]=>([(1,2),(2,3)],4)=>([(1,2),(2,3)],4) [1,1,1,0,0,1,0,0]=>[1,4,2,3]=>([(0,2),(0,3),(3,1)],4)=>([(0,3),(1,2),(2,3)],4) [1,1,1,0,1,0,0,0]=>[1,2,4,3]=>([(0,3),(3,1),(3,2)],4)=>([(0,3),(1,3),(3,2)],4) [1,1,1,1,0,0,0,0]=>[1,2,3,4]=>([(0,3),(2,1),(3,2)],4)=>([(0,3),(2,1),(3,2)],4) [1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5]=>([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)=>([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5) [1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,5]=>([(0,3),(1,2),(1,3),(2,4),(3,4)],5)=>([(0,2),(0,3),(2,4),(3,1),(3,4)],5) [1,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,3]=>([(0,3),(0,4),(1,3),(1,4),(4,2)],5)=>([(0,3),(0,4),(1,2),(2,3),(2,4)],5) [1,0,1,0,1,1,0,1,0,0]=>[2,4,1,5,3]=>([(0,3),(0,4),(1,2),(1,3),(2,4)],5)=>([(0,3),(0,4),(1,2),(1,3),(2,4)],5) [1,0,1,0,1,1,1,0,0,0]=>[2,4,5,1,3]=>([(0,4),(1,2),(1,4),(2,3)],5)=>([(0,3),(1,2),(1,4),(3,4)],5) [1,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,4]=>([(0,3),(0,4),(1,3),(1,4),(4,2)],5)=>([(0,3),(0,4),(1,2),(2,3),(2,4)],5) [1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,4]=>([(0,4),(1,2),(1,4),(4,3)],5)=>([(0,4),(1,2),(2,3),(2,4)],5) [1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,4]=>([(0,4),(1,4),(4,2),(4,3)],5)=>([(0,4),(1,4),(4,2),(4,3)],5) [1,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,4]=>([(0,3),(0,4),(1,2),(2,3),(2,4)],5)=>([(0,3),(0,4),(1,3),(1,4),(4,2)],5) [1,0,1,1,0,1,1,0,0,0]=>[2,3,5,1,4]=>([(0,4),(1,2),(2,3),(2,4)],5)=>([(0,4),(1,2),(1,4),(4,3)],5) [1,0,1,1,1,0,0,0,1,0]=>[2,1,3,4,5]=>([(0,4),(1,4),(2,3),(4,2)],5)=>([(0,3),(3,4),(4,1),(4,2)],5) [1,0,1,1,1,0,0,1,0,0]=>[2,3,1,4,5]=>([(0,4),(1,2),(2,4),(4,3)],5)=>([(0,4),(3,2),(4,1),(4,3)],5) [1,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,5]=>([(0,4),(1,2),(2,3),(3,4)],5)=>([(0,2),(0,4),(3,1),(4,3)],5) [1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>([(1,4),(3,2),(4,3)],5)=>([(1,4),(3,2),(4,3)],5) [1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,5]=>([(0,3),(1,2),(1,3),(2,4),(3,4)],5)=>([(0,2),(0,3),(2,4),(3,1),(3,4)],5) [1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,5]=>([(0,3),(1,2),(2,4),(3,4)],5)=>([(0,3),(0,4),(3,2),(4,1)],5) [1,1,0,0,1,1,0,0,1,0]=>[3,1,4,5,2]=>([(0,4),(1,2),(1,4),(4,3)],5)=>([(0,4),(1,2),(2,3),(2,4)],5) [1,1,0,0,1,1,0,1,0,0]=>[3,4,1,5,2]=>([(0,3),(1,2),(1,4),(3,4)],5)=>([(0,4),(1,2),(1,4),(2,3)],5) [1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>([(0,3),(1,4),(4,2)],5)=>([(0,3),(1,4),(4,2)],5) [1,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4]=>([(0,3),(0,4),(1,2),(1,3),(2,4)],5)=>([(0,3),(0,4),(1,2),(1,3),(2,4)],5) [1,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4]=>([(0,3),(1,2),(1,4),(3,4)],5)=>([(0,4),(1,2),(1,4),(2,3)],5) [1,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4]=>([(0,3),(0,4),(1,2),(2,3),(2,4)],5)=>([(0,3),(0,4),(1,3),(1,4),(4,2)],5) [1,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4]=>([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)=>([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5) [1,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4]=>([(0,2),(0,3),(2,4),(3,1),(3,4)],5)=>([(0,3),(1,2),(1,3),(2,4),(3,4)],5) [1,1,0,1,1,0,0,0,1,0]=>[3,1,2,4,5]=>([(0,4),(1,2),(2,4),(4,3)],5)=>([(0,4),(3,2),(4,1),(4,3)],5) [1,1,0,1,1,0,0,1,0,0]=>[1,3,2,4,5]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5) [1,1,0,1,1,0,1,0,0,0]=>[1,3,4,2,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5) [1,1,0,1,1,1,0,0,0,0]=>[1,3,4,5,2]=>([(0,2),(0,4),(3,1),(4,3)],5)=>([(0,4),(1,2),(2,3),(3,4)],5) [1,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3]=>([(0,4),(1,2),(1,4),(2,3)],5)=>([(0,3),(1,2),(1,4),(3,4)],5) [1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>([(0,3),(1,4),(4,2)],5)=>([(0,3),(1,4),(4,2)],5) [1,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3]=>([(0,4),(1,2),(2,3),(2,4)],5)=>([(0,4),(1,2),(1,4),(4,3)],5) [1,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,3]=>([(0,2),(0,3),(2,4),(3,1),(3,4)],5)=>([(0,3),(1,2),(1,3),(2,4),(3,4)],5) [1,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3]=>([(0,3),(0,4),(3,2),(4,1)],5)=>([(0,3),(1,2),(2,4),(3,4)],5) [1,1,1,0,1,0,0,0,1,0]=>[4,1,2,3,5]=>([(0,4),(1,2),(2,3),(3,4)],5)=>([(0,2),(0,4),(3,1),(4,3)],5) [1,1,1,0,1,0,0,1,0,0]=>[1,4,2,3,5]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5) [1,1,1,0,1,0,1,0,0,0]=>[1,2,4,3,5]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5) [1,1,1,0,1,1,0,0,0,0]=>[1,2,4,5,3]=>([(0,4),(3,2),(4,1),(4,3)],5)=>([(0,4),(1,2),(2,4),(4,3)],5) [1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>([(1,4),(3,2),(4,3)],5)=>([(1,4),(3,2),(4,3)],5) [1,1,1,1,0,0,0,1,0,0]=>[1,5,2,3,4]=>([(0,2),(0,4),(3,1),(4,3)],5)=>([(0,4),(1,2),(2,3),(3,4)],5) [1,1,1,1,0,0,1,0,0,0]=>[1,2,5,3,4]=>([(0,4),(3,2),(4,1),(4,3)],5)=>([(0,4),(1,2),(2,4),(4,3)],5) [1,1,1,1,0,1,0,0,0,0]=>[1,2,3,5,4]=>([(0,3),(3,4),(4,1),(4,2)],5)=>([(0,4),(1,4),(2,3),(4,2)],5) [1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>([(0,4),(2,3),(3,1),(4,2)],5)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5]=>([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6)=>([(0,4),(0,5),(1,4),(1,5),(4,2),(4,3),(5,2),(5,3)],6) [1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5]=>([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)=>([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6) [1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5]=>([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)=>([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6) [1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5]=>([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)=>([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6) [1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5]=>([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)=>([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6) [1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6) [1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,5,6]=>([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)=>([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6) [1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6) [1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,5,3,6]=>([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)=>([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6) [1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,5,1,3,6]=>([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6)=>([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6) [1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,5,6,3]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)=>([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6) [1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,5,6,3]=>([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)=>([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6) [1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,5,1,6,3]=>([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6)=>([(0,4),(0,5),(1,2),(1,4),(2,3),(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),(3,2),(4,3)],6)=>([(0,4),(1,3),(1,5),(2,5),(4,2)],6) [1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,6,4]=>([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)=>([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6) [1,0,1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)=>([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6) [1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,5,6,3,4]=>([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6)=>([(0,3),(1,2),(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),(0,5),(1,2),(1,4),(2,5),(4,3)],6)=>([(0,3),(1,2),(1,4),(2,5),(3,4),(3,5)],6) [1,0,1,1,0,0,1,1,1,0,0,0]=>[2,5,6,1,3,4]=>([(0,5),(1,4),(1,5),(4,2),(5,3)],6)=>([(0,3),(1,4),(3,5),(4,2),(4,5)],6) [1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,4,6]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6) [1,0,1,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,4,6]=>([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)=>([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6) [1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,6]=>([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)=>([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6) [1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,6]=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6) [1,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,6]=>([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6)=>([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6) [1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,3,5,6,4]=>([(0,5),(1,5),(4,2),(5,3),(5,4)],6)=>([(0,5),(1,2),(2,5),(5,3),(5,4)],6) [1,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,6,4]=>([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)=>([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6) [1,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,5,1,6,4]=>([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)=>([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6) [1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,5,6,1,4]=>([(0,5),(1,4),(3,2),(4,3),(4,5)],6)=>([(0,4),(1,3),(1,5),(4,5),(5,2)],6) [1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6)=>([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6) [1,0,1,1,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5]=>([(0,5),(1,3),(1,5),(4,2),(5,4)],6)=>([(0,5),(1,3),(3,4),(4,2),(4,5)],6) [1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5]=>([(0,5),(1,5),(4,2),(5,3),(5,4)],6)=>([(0,5),(1,2),(2,5),(5,3),(5,4)],6) [1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,5]=>([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)=>([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6) [1,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5]=>([(0,5),(1,4),(4,2),(4,5),(5,3)],6)=>([(0,5),(1,4),(4,2),(4,5),(5,3)],6) [1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5]=>([(0,5),(1,5),(4,2),(4,3),(5,4)],6)=>([(0,5),(1,5),(4,2),(4,3),(5,4)],6) [1,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,4,6,5]=>([(0,5),(1,2),(2,5),(5,3),(5,4)],6)=>([(0,5),(1,5),(4,2),(5,3),(5,4)],6) [1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5]=>([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6) [1,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,4,6,1,5]=>([(0,5),(1,3),(3,4),(4,2),(4,5)],6)=>([(0,5),(1,3),(1,5),(4,2),(5,4)],6) [1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,5,6]=>([(0,5),(1,5),(3,2),(4,3),(5,4)],6)=>([(0,4),(3,5),(4,3),(5,1),(5,2)],6) [1,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,4,5,6]=>([(0,5),(1,3),(3,5),(4,2),(5,4)],6)=>([(0,4),(3,2),(4,5),(5,1),(5,3)],6) [1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,4,1,5,6]=>([(0,5),(1,4),(2,5),(4,2),(5,3)],6)=>([(0,5),(3,4),(4,2),(5,1),(5,3)],6) [1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,5,1,6]=>([(0,5),(1,4),(2,5),(3,2),(4,3)],6)=>([(0,2),(0,5),(3,4),(4,1),(5,3)],6) [1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>([(1,5),(3,4),(4,2),(5,3)],6)=>([(1,5),(3,4),(4,2),(5,3)],6) [1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5]=>([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)=>([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6) [1,1,0,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5]=>([(0,3),(1,2),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2)],6) [1,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5]=>([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6)=>([(0,4),(1,2),(1,4),(2,5),(4,3),(4,5)],6) [1,1,0,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5]=>([(0,3),(1,2),(1,4),(2,5),(3,4),(3,5)],6)=>([(0,4),(0,5),(1,2),(1,4),(2,5),(4,3)],6) [1,1,0,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5]=>([(0,3),(1,4),(3,5),(4,2),(4,5)],6)=>([(0,5),(1,4),(1,5),(4,2),(5,3)],6) [1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,5,6]=>([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)=>([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6) [1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,5,6]=>([(0,4),(1,3),(3,5),(4,5),(5,2)],6)=>([(0,5),(3,2),(4,1),(5,3),(5,4)],6) [1,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,5,2,6]=>([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6)=>([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6) [1,1,0,0,1,1,0,1,0,1,0,0]=>[3,4,1,5,2,6]=>([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6)=>([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) [1,1,0,0,1,1,0,1,1,0,0,0]=>[3,4,5,1,2,6]=>([(0,3),(1,4),(2,5),(3,5),(4,2)],6)=>([(0,4),(0,5),(3,2),(4,3),(5,1)],6) [1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,5,6,2]=>([(0,5),(1,3),(1,5),(4,2),(5,4)],6)=>([(0,5),(1,3),(3,4),(4,2),(4,5)],6) [1,1,0,0,1,1,1,0,0,1,0,0]=>[3,4,1,5,6,2]=>([(0,4),(1,3),(1,5),(4,5),(5,2)],6)=>([(0,5),(1,4),(3,2),(4,3),(4,5)],6) [1,1,0,0,1,1,1,0,1,0,0,0]=>[3,4,5,1,6,2]=>([(0,4),(1,3),(1,5),(2,5),(4,2)],6)=>([(0,5),(1,4),(1,5),(3,2),(4,3)],6) [1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>([(0,5),(1,3),(4,2),(5,4)],6)=>([(0,5),(1,3),(4,2),(5,4)],6) [1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,6,4]=>([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)=>([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6) [1,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,6,4]=>([(0,3),(1,2),(1,4),(2,5),(3,4),(3,5)],6)=>([(0,4),(0,5),(1,2),(1,4),(2,5),(4,3)],6) [1,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,6,2,4]=>([(0,4),(0,5),(1,2),(1,4),(2,5),(4,3)],6)=>([(0,3),(1,2),(1,4),(2,5),(3,4),(3,5)],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),(1,4),(2,5),(3,4)],6)=>([(0,3),(0,5),(1,2),(1,4),(2,5),(3,4)],6) [1,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,6,1,2,4]=>([(0,3),(1,4),(1,5),(3,5),(4,2)],6)=>([(0,3),(1,4),(1,5),(3,5),(4,2)],6) [1,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,6]=>([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)=>([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6) [1,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,6]=>([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6)=>([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6) [1,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,6]=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6) [1,1,0,1,0,1,0,1,0,1,0,0]=>[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),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) [1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,6]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [1,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,6,4]=>([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)=>([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6) [1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,6,4]=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) [1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,6,4]=>([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)=>([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6) [1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,6,2,4]=>([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)=>([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6) [1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6)=>([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6) [1,1,0,1,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,5]=>([(0,4),(1,3),(1,5),(4,5),(5,2)],6)=>([(0,5),(1,4),(3,2),(4,3),(4,5)],6) [1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5]=>([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6)=>([(0,4),(0,5),(1,3),(3,4),(3,5),(5,2)],6) [1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,5]=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6) [1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,5]=>([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)=>([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6) [1,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5]=>([(0,5),(1,2),(2,5),(5,3),(5,4)],6)=>([(0,5),(1,5),(4,2),(5,3),(5,4)],6) [1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5]=>([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)=>([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6) [1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5]=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6) [1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5]=>([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6)=>([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6) [1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,4,5,6]=>([(0,5),(1,3),(3,5),(4,2),(5,4)],6)=>([(0,4),(3,2),(4,5),(5,1),(5,3)],6) [1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,4,5,6]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6) [1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,4,2,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) [1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,4,5,2,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) [1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,5,6,2]=>([(0,2),(0,5),(3,4),(4,1),(5,3)],6)=>([(0,5),(1,4),(2,5),(3,2),(4,3)],6) [1,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,5,2,6,3]=>([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6)=>([(0,4),(1,2),(1,4),(2,3),(2,5),(4,5)],6) [1,1,1,0,0,0,1,0,1,1,0,0]=>[4,5,1,2,6,3]=>([(0,3),(1,4),(3,5),(4,2),(4,5)],6)=>([(0,5),(1,4),(1,5),(4,2),(5,3)],6) [1,1,1,0,0,0,1,1,0,0,1,0]=>[4,1,5,6,2,3]=>([(0,5),(1,4),(1,5),(4,2),(5,3)],6)=>([(0,3),(1,4),(3,5),(4,2),(4,5)],6) [1,1,1,0,0,0,1,1,0,1,0,0]=>[4,5,1,6,2,3]=>([(0,3),(1,4),(1,5),(3,5),(4,2)],6)=>([(0,3),(1,4),(1,5),(3,5),(4,2)],6) [1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>([(0,5),(1,4),(4,2),(5,3)],6)=>([(0,5),(1,4),(4,2),(5,3)],6) [1,1,1,0,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,6]=>([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6)=>([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6) [1,1,1,0,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,6]=>([(0,3),(1,4),(2,5),(3,5),(4,2)],6)=>([(0,4),(0,5),(3,2),(4,3),(5,1)],6) [1,1,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,6]=>([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6)=>([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6) [1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,6]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6) [1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,6]=>([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6)=>([(0,3),(0,4),(1,5),(2,5),(3,2),(4,1)],6) [1,1,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,5,6,3]=>([(0,5),(1,4),(4,2),(4,5),(5,3)],6)=>([(0,5),(1,4),(4,2),(4,5),(5,3)],6) [1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,5,6,3]=>([(0,3),(0,4),(3,5),(4,1),(4,5),(5,2)],6)=>([(0,5),(1,2),(2,3),(2,5),(3,4),(5,4)],6) [1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,5,2,6,3]=>([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6)=>([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6) [1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,5,6,2,3]=>([(0,4),(0,5),(3,2),(4,3),(5,1)],6)=>([(0,3),(1,4),(2,5),(3,5),(4,2)],6) [1,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5]=>([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6)=>([(0,4),(0,5),(1,2),(1,4),(2,3),(3,5)],6) [1,1,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5]=>([(0,4),(1,3),(1,5),(2,5),(4,2)],6)=>([(0,5),(1,4),(1,5),(3,2),(4,3)],6) [1,1,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5]=>([(0,4),(0,5),(1,2),(2,3),(2,5),(3,4)],6)=>([(0,4),(0,5),(1,2),(1,4),(2,5),(5,3)],6) [1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5]=>([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)=>([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6) [1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,5]=>([(0,3),(0,4),(2,5),(3,2),(4,1),(4,5)],6)=>([(0,4),(1,2),(1,4),(2,3),(3,5),(4,5)],6) [1,1,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5]=>([(0,4),(0,5),(1,2),(2,3),(3,4),(3,5)],6)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(5,2)],6) [1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5]=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6) [1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)=>([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6) [1,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,4,6,3,5]=>([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)=>([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) [1,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,5,6]=>([(0,5),(1,4),(2,5),(4,2),(5,3)],6)=>([(0,5),(3,4),(4,2),(5,1),(5,3)],6) [1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,5,6]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6) [1,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,5,6]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6) [1,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,4,5,3,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) [1,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,5,6,3]=>([(0,5),(3,4),(4,2),(5,1),(5,3)],6)=>([(0,5),(1,4),(2,5),(4,2),(5,3)],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),(3,2),(4,3)],6)=>([(0,4),(1,3),(1,5),(2,5),(4,2)],6) [1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>([(0,5),(1,3),(4,2),(5,4)],6)=>([(0,5),(1,3),(4,2),(5,4)],6) [1,1,1,1,0,0,0,1,0,0,1,0]=>[5,1,2,6,3,4]=>([(0,5),(1,4),(3,2),(4,3),(4,5)],6)=>([(0,4),(1,3),(1,5),(4,5),(5,2)],6) [1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,6,3,4]=>([(0,2),(0,4),(2,5),(3,1),(4,3),(4,5)],6)=>([(0,3),(1,2),(1,4),(2,5),(3,4),(4,5)],6) [1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,6,2,3,4]=>([(0,4),(0,5),(3,2),(4,3),(5,1)],6)=>([(0,3),(1,4),(2,5),(3,5),(4,2)],6) [1,1,1,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,6,4]=>([(0,5),(1,3),(3,4),(4,2),(4,5)],6)=>([(0,5),(1,3),(1,5),(4,2),(5,4)],6) [1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,6,4]=>([(0,2),(0,4),(2,5),(3,1),(3,5),(4,3)],6)=>([(0,4),(1,2),(1,4),(2,5),(3,5),(4,3)],6) [1,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,6,4]=>([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)=>([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6) [1,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,5,6,3,4]=>([(0,5),(3,2),(4,1),(5,3),(5,4)],6)=>([(0,4),(1,3),(3,5),(4,5),(5,2)],6) [1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,6]=>([(0,5),(1,4),(2,5),(3,2),(4,3)],6)=>([(0,2),(0,5),(3,4),(4,1),(5,3)],6) [1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6)=>([(0,2),(0,4),(1,5),(2,5),(3,1),(4,3)],6) [1,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,6]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6) [1,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,6]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6) [1,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,6,4]=>([(0,4),(3,2),(4,5),(5,1),(5,3)],6)=>([(0,5),(1,3),(3,5),(4,2),(5,4)],6) [1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>([(1,5),(3,4),(4,2),(5,3)],6)=>([(1,5),(3,4),(4,2),(5,3)],6) [1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5]=>([(0,2),(0,5),(3,4),(4,1),(5,3)],6)=>([(0,5),(1,4),(2,5),(3,2),(4,3)],6) [1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5]=>([(0,5),(3,4),(4,2),(5,1),(5,3)],6)=>([(0,5),(1,4),(2,5),(4,2),(5,3)],6) [1,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5]=>([(0,4),(3,2),(4,5),(5,1),(5,3)],6)=>([(0,5),(1,3),(3,5),(4,2),(5,4)],6) [1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5]=>([(0,4),(3,5),(4,3),(5,1),(5,2)],6)=>([(0,5),(1,5),(3,2),(4,3),(5,4)],6) [1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[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)=>([(0,1),(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5,7]=>([(0,6),(1,2),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7)=>([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7) [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5,7]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(4,3),(5,4),(6,2),(6,4)],7)=>([(0,2),(0,3),(1,5),(1,6),(2,4),(3,1),(3,4),(4,5),(4,6)],7) [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5,7]=>([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4)],7)=>([(0,2),(0,3),(1,4),(1,6),(2,4),(2,5),(3,1),(3,5),(5,6)],7) [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5,7]=>([(0,6),(1,3),(1,6),(2,4),(3,2),(3,5),(5,4),(6,5)],7)=>([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,7,5]=>([(0,5),(0,6),(1,5),(1,6),(4,2),(5,3),(5,4),(6,3),(6,4)],7)=>([(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,7,5]=>([(0,6),(1,3),(1,6),(3,4),(3,5),(5,2),(6,4),(6,5)],7)=>([(0,3),(1,5),(1,6),(3,5),(3,6),(5,4),(6,2),(6,4)],7) [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,6,3,7,5]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(5,2),(5,3),(6,3),(6,4)],7)=>([(0,2),(0,6),(1,5),(1,6),(2,5),(5,3),(5,4),(6,3),(6,4)],7) [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5]=>([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3),(6,4)],7)=>([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3),(6,4)],7) [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,6,1,3,7,5]=>([(0,6),(1,3),(1,6),(2,5),(3,2),(3,4),(6,4),(6,5)],7)=>([(0,3),(0,6),(1,5),(1,6),(3,5),(5,4),(6,2),(6,4)],7) [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,6,7,3,5]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(5,4),(6,2),(6,4)],7)=>([(0,2),(1,3),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7) [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,6,7,3,5]=>([(0,3),(0,6),(1,5),(1,6),(3,4),(3,5),(5,2),(6,4)],7)=>([(0,3),(1,2),(1,6),(2,4),(2,5),(3,4),(3,6),(6,5)],7) [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,6,1,7,3,5]=>([(0,3),(0,6),(1,5),(1,6),(2,5),(3,2),(3,4),(6,4)],7)=>([(0,3),(0,6),(1,2),(1,5),(2,6),(3,4),(3,5),(6,4)],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),(1,6),(3,2),(4,3),(4,5),(6,5)],7)=>([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7) [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,7,5,6]=>([(0,5),(0,6),(1,5),(1,6),(4,2),(5,3),(5,4),(6,3),(6,4)],7)=>([(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7) [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,3,7,5,6]=>([(0,6),(1,3),(1,6),(3,4),(3,5),(5,2),(6,4),(6,5)],7)=>([(0,3),(1,5),(1,6),(3,5),(3,6),(5,4),(6,2),(6,4)],7) [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,7,3,5,6]=>([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2),(6,4)],7)=>([(0,2),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7) [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,4,1,7,3,5,6]=>([(0,3),(0,6),(1,4),(1,6),(3,4),(3,5),(5,2),(6,5)],7)=>([(0,2),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4)],7) [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,7,1,3,5,6]=>([(0,5),(1,4),(1,5),(4,3),(4,6),(5,6),(6,2)],7)=>([(0,6),(1,3),(3,4),(3,6),(4,2),(4,5),(6,5)],7) [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,3,5,7,6]=>([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7)=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7) [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,4,1,3,5,7,6]=>([(0,5),(1,4),(1,5),(4,6),(5,6),(6,2),(6,3)],7)=>([(0,6),(1,6),(3,5),(4,2),(4,5),(6,3),(6,4)],7) [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[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)=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(5,2),(6,3),(6,4)],7) [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,7,6]=>([(0,2),(0,6),(1,5),(1,6),(2,5),(5,3),(5,4),(6,3),(6,4)],7)=>([(0,5),(0,6),(1,5),(1,6),(2,4),(5,2),(5,3),(6,3),(6,4)],7) [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,5,1,3,7,6]=>([(0,6),(1,2),(1,6),(2,3),(3,4),(3,5),(6,4),(6,5)],7)=>([(0,5),(0,6),(1,5),(1,6),(3,4),(5,3),(6,2),(6,4)],7) [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,5,7,3,6]=>([(0,5),(0,6),(1,5),(1,6),(3,2),(3,4),(5,3),(6,4)],7)=>([(0,6),(1,3),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2)],7) [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,4,1,5,7,3,6]=>([(0,3),(0,6),(1,5),(1,6),(3,5),(5,2),(5,4),(6,4)],7)=>([(0,6),(1,3),(1,6),(2,5),(3,4),(3,5),(6,2),(6,4)],7) [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,4,5,1,7,3,6]=>([(0,2),(0,6),(1,5),(1,6),(2,3),(3,4),(3,5),(6,4)],7)=>([(0,3),(0,6),(1,4),(1,6),(2,5),(3,4),(3,5),(6,2)],7) [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,5,7,1,3,6]=>([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)=>([(0,6),(1,4),(1,6),(3,5),(4,2),(4,5),(6,3)],7) [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7)=>([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2)],7) [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,5,6,7]=>([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7)=>([(0,4),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3)],7) [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,5,3,6,7]=>([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7)=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1),(4,3)],7) [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,4,1,5,3,6,7]=>([(0,3),(0,6),(1,5),(1,6),(3,5),(4,2),(5,4),(6,4)],7)=>([(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,2),(4,3)],7) [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,4,5,1,3,6,7]=>([(0,5),(1,4),(1,5),(3,6),(4,3),(5,6),(6,2)],7)=>([(0,5),(2,6),(3,2),(4,1),(4,6),(5,3),(5,4)],7) [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,4,5,6,3,7]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7)=>([(0,2),(0,4),(1,5),(1,6),(2,5),(2,6),(3,1),(4,3)],7) [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,4,1,5,6,3,7]=>([(0,3),(0,6),(1,4),(1,6),(2,5),(3,4),(4,2),(6,5)],7)=>([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,3)],7) [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,4,5,1,6,3,7]=>([(0,2),(0,6),(1,5),(1,6),(2,3),(3,5),(5,4),(6,4)],7)=>([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(4,3),(4,6)],7) [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,4,5,6,1,3,7]=>([(0,6),(1,4),(1,6),(2,5),(3,2),(4,3),(6,5)],7)=>([(0,4),(0,5),(2,6),(3,2),(4,3),(5,1),(5,6)],7) [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,5,6,7,3]=>([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(6,3)],7)=>([(0,5),(0,6),(1,4),(2,5),(2,6),(3,2),(4,3)],7) [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1,5,6,7,3]=>([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(5,4)],7)=>([(0,5),(0,6),(1,3),(2,6),(3,4),(4,2),(4,5)],7) [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,5,1,6,7,3]=>([(0,5),(0,6),(1,4),(1,5),(3,6),(4,3),(6,2)],7)=>([(0,5),(0,6),(1,4),(2,6),(3,2),(4,3),(4,5)],7) [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,5,6,1,7,3]=>([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7)=>([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],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),(3,4),(4,2),(5,3)],7)=>([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7) [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,7]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(4,3),(5,4),(6,2),(6,4)],7)=>([(0,2),(0,3),(1,5),(1,6),(2,4),(3,1),(3,4),(4,5),(4,6)],7) [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,5,1,3,6,4,7]=>([(0,6),(1,3),(1,6),(2,4),(3,5),(5,4),(6,2),(6,5)],7)=>([(0,3),(0,4),(2,5),(3,6),(4,2),(4,6),(6,1),(6,5)],7) [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,7]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(5,3),(6,2)],7)=>([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1)],7) [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,5,1,6,3,4,7]=>([(0,3),(0,5),(1,5),(1,6),(2,4),(3,6),(5,2),(6,4)],7)=>([(0,3),(0,4),(1,5),(2,5),(2,6),(3,2),(4,1),(4,6)],7) [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,6,1,3,4,7]=>([(0,6),(1,4),(1,6),(2,5),(3,5),(4,3),(6,2)],7)=>([(0,4),(0,5),(2,6),(3,1),(3,6),(4,2),(5,3)],7) [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,6,7,4]=>([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2),(6,4)],7)=>([(0,2),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7) [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,6,7,4]=>([(0,6),(1,3),(1,6),(3,5),(5,4),(6,2),(6,5)],7)=>([(0,6),(1,4),(3,5),(4,3),(4,6),(6,2),(6,5)],7) [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,5,6,3,7,4]=>([(0,5),(0,6),(1,5),(1,6),(3,4),(5,3),(6,2),(6,4)],7)=>([(0,6),(1,2),(1,6),(2,3),(3,4),(3,5),(6,4),(6,5)],7) [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,5,1,6,3,7,4]=>([(0,3),(0,6),(1,5),(1,6),(3,5),(5,4),(6,2),(6,4)],7)=>([(0,6),(1,3),(1,6),(2,5),(3,2),(3,4),(6,4),(6,5)],7) [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,5,6,1,3,7,4]=>([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)=>([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7) [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,6,7,3,4]=>([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2)],7)=>([(0,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7) [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,5,1,6,7,3,4]=>([(0,5),(0,6),(1,2),(1,6),(2,5),(5,3),(6,4)],7)=>([(0,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6)],7) [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,5,6,1,7,3,4]=>([(0,5),(0,6),(1,4),(1,6),(3,5),(4,3),(6,2)],7)=>([(0,3),(1,4),(1,6),(2,5),(3,5),(3,6),(4,2)],7) [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,5,6,7,1,3,4]=>([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7)=>([(0,5),(1,4),(3,6),(4,3),(5,2),(5,6)],7) [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,6]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(5,2),(5,3),(6,3),(6,4)],7)=>([(0,2),(0,6),(1,5),(1,6),(2,5),(5,3),(5,4),(6,3),(6,4)],7) [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,7,4,6]=>([(0,6),(1,3),(1,6),(2,5),(3,4),(3,5),(6,2),(6,4)],7)=>([(0,3),(0,6),(1,5),(1,6),(3,5),(5,2),(5,4),(6,4)],7) [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,5,7,3,4,6]=>([(0,5),(0,6),(1,5),(1,6),(3,4),(5,3),(6,2),(6,4)],7)=>([(0,6),(1,2),(1,6),(2,3),(3,4),(3,5),(6,4),(6,5)],7) [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,5,1,7,3,4,6]=>([(0,3),(0,6),(1,4),(1,6),(2,5),(3,4),(3,5),(6,2)],7)=>([(0,2),(0,6),(1,5),(1,6),(2,3),(3,4),(3,5),(6,4)],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),(1,6),(3,5),(4,2),(4,5),(6,3)],7)=>([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7) [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,4,7,6]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(5,2),(6,3),(6,4)],7)=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(5,2),(6,3),(6,4)],7) [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,4,7,6]=>([(0,6),(1,3),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2)],7)=>([(0,5),(0,6),(1,5),(1,6),(3,2),(3,4),(5,3),(6,4)],7) [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,7,6]=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7)=>([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7) [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[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)=>([(0,5),(0,6),(1,5),(1,6),(4,2),(5,3),(5,4),(6,3),(6,4)],7) [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,7,6]=>([(0,2),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7)=>([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2),(6,4)],7) [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,3,5,7,4,6]=>([(0,6),(1,6),(3,5),(4,2),(4,5),(6,3),(6,4)],7)=>([(0,5),(1,4),(1,5),(4,6),(5,6),(6,2),(6,3)],7) [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,7,4,6]=>([(0,3),(1,5),(1,6),(3,5),(3,6),(5,4),(6,2),(6,4)],7)=>([(0,6),(1,3),(1,6),(3,4),(3,5),(5,2),(6,4),(6,5)],7) [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,1,7,4,6]=>([(0,2),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4)],7)=>([(0,3),(0,6),(1,4),(1,6),(3,4),(3,5),(5,2),(6,5)],7) [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,5,7,1,4,6]=>([(0,6),(1,3),(3,4),(3,6),(4,2),(4,5),(6,5)],7)=>([(0,5),(1,4),(1,5),(4,3),(4,6),(5,6),(6,2)],7) [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,7]=>([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7)=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1),(4,3)],7) [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,5,1,3,4,6,7]=>([(0,6),(1,3),(1,6),(2,5),(3,5),(5,4),(6,2)],7)=>([(0,5),(2,6),(3,4),(4,1),(4,6),(5,2),(5,3)],7) [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,3,5,4,6,7]=>([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7)=>([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7) [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,1,5,4,6,7]=>([(0,3),(1,5),(1,6),(3,5),(3,6),(4,2),(5,4),(6,4)],7)=>([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(6,1)],7) [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,1,4,6,7]=>([(0,5),(1,4),(3,6),(4,3),(4,5),(5,6),(6,2)],7)=>([(0,5),(2,6),(4,1),(4,6),(5,2),(5,4),(6,3)],7) [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,3,5,6,4,7]=>([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7)=>([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7) [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[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),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7) [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,1,6,4,7]=>([(0,3),(1,5),(1,6),(2,6),(3,2),(3,5),(5,4),(6,4)],7)=>([(0,3),(0,4),(2,6),(3,5),(3,6),(4,2),(4,5),(6,1)],7) [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,6,1,4,7]=>([(0,6),(1,4),(2,5),(3,2),(4,3),(4,6),(6,5)],7)=>([(0,4),(0,5),(2,6),(4,2),(5,1),(5,6),(6,3)],7) [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,5,6,7,4]=>([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7)=>([(0,6),(1,5),(2,6),(5,2),(6,3),(6,4)],7) [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1,5,6,7,4]=>([(0,5),(0,6),(1,3),(3,5),(3,6),(4,2),(6,4)],7)=>([(0,5),(0,6),(1,4),(3,5),(3,6),(4,3),(6,2)],7) [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,5,1,6,7,4]=>([(0,5),(0,6),(1,4),(3,6),(4,3),(4,5),(6,2)],7)=>([(0,5),(0,6),(1,4),(3,6),(4,3),(4,5),(6,2)],7) [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,5,6,1,7,4]=>([(0,5),(0,6),(1,4),(2,6),(3,2),(4,3),(4,5)],7)=>([(0,5),(0,6),(1,4),(1,5),(3,6),(4,3),(6,2)],7) [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,5,6,7,1,4]=>([(0,6),(1,5),(3,4),(4,2),(5,3),(5,6)],7)=>([(0,5),(1,4),(1,6),(2,6),(5,2),(6,3)],7) [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,6,3,7,4,5]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(5,4),(6,2),(6,4)],7)=>([(0,2),(1,3),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7) [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,6,1,3,7,4,5]=>([(0,6),(1,3),(1,6),(3,5),(4,2),(6,4),(6,5)],7)=>([(0,3),(1,4),(1,6),(3,6),(4,5),(6,2),(6,5)],7) [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,6,7,3,4,5]=>([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2)],7)=>([(0,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7) [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,6,1,7,3,4,5]=>([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(6,4)],7)=>([(0,3),(0,6),(1,4),(2,5),(2,6),(3,5),(4,2)],7) [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,6,7,1,3,4,5]=>([(0,6),(1,4),(1,6),(4,3),(5,2),(6,5)],7)=>([(0,5),(1,3),(3,6),(4,2),(4,6),(5,4)],7) [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,6,3,4,7,5]=>([(0,5),(0,6),(1,5),(1,6),(3,2),(3,4),(5,3),(6,4)],7)=>([(0,6),(1,3),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2)],7) [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,6,1,3,4,7,5]=>([(0,6),(1,3),(1,6),(3,5),(4,2),(4,5),(6,4)],7)=>([(0,6),(1,3),(1,6),(3,5),(4,2),(4,5),(6,4)],7) [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,3,6,4,7,5]=>([(0,6),(1,6),(3,5),(4,2),(4,5),(6,3),(6,4)],7)=>([(0,5),(1,4),(1,5),(4,6),(5,6),(6,2),(6,3)],7) [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,7,5]=>([(0,3),(1,5),(1,6),(3,5),(3,6),(5,4),(6,2),(6,4)],7)=>([(0,6),(1,3),(1,6),(3,4),(3,5),(5,2),(6,4),(6,5)],7) [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,6,1,4,7,5]=>([(0,6),(1,4),(3,5),(4,3),(4,6),(6,2),(6,5)],7)=>([(0,6),(1,3),(1,6),(3,5),(5,4),(6,2),(6,5)],7) [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,3,6,7,4,5]=>([(0,6),(1,6),(4,3),(5,2),(6,4),(6,5)],7)=>([(0,5),(1,4),(4,6),(5,6),(6,2),(6,3)],7) [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,1,6,7,4,5]=>([(0,5),(0,6),(1,2),(2,5),(2,6),(5,4),(6,3)],7)=>([(0,4),(1,3),(3,5),(3,6),(4,5),(4,6),(6,2)],7) [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,6,1,7,4,5]=>([(0,5),(0,6),(1,4),(3,5),(4,3),(4,6),(6,2)],7)=>([(0,4),(1,3),(1,5),(3,6),(4,5),(4,6),(6,2)],7) [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,6,7,1,4,5]=>([(0,6),(1,5),(4,2),(5,4),(5,6),(6,3)],7)=>([(0,4),(1,5),(4,6),(5,2),(5,6),(6,3)],7) [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5,7]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7)=>([(0,2),(0,4),(1,5),(1,6),(2,5),(2,6),(3,1),(4,3)],7) [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5,7]=>([(0,6),(1,3),(1,6),(2,5),(3,5),(4,2),(6,4)],7)=>([(0,2),(0,5),(2,6),(3,4),(4,1),(4,6),(5,3)],7) [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5,7]=>([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7)=>([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7) [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,5,7]=>([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7)=>([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7) [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5,7]=>([(0,6),(1,4),(2,5),(3,5),(4,3),(4,6),(6,2)],7)=>([(0,3),(0,5),(3,6),(4,1),(4,6),(5,4),(6,2)],7) [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5,7]=>([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7)=>([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7) [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,1,4,6,5,7]=>([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7)=>([(0,3),(0,4),(3,6),(4,6),(5,1),(6,2),(6,5)],7) [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,7]=>([(0,2),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)=>([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(6,4)],7) [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,4,6,1,5,7]=>([(0,6),(1,4),(2,5),(3,2),(3,6),(4,3),(6,5)],7)=>([(0,3),(0,5),(3,6),(4,2),(5,1),(5,6),(6,4)],7) [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,7,5]=>([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7)=>([(0,6),(1,4),(4,6),(5,2),(5,3),(6,5)],7) [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,1,4,6,7,5]=>([(0,6),(1,3),(3,6),(5,2),(6,4),(6,5)],7)=>([(0,6),(1,3),(3,6),(5,2),(6,4),(6,5)],7) [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,4,1,6,7,5]=>([(0,5),(0,6),(1,4),(3,5),(3,6),(4,3),(6,2)],7)=>([(0,5),(0,6),(1,3),(3,5),(3,6),(4,2),(6,4)],7) [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,4,6,1,7,5]=>([(0,5),(0,6),(1,3),(2,6),(3,4),(4,2),(4,5)],7)=>([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(5,4)],7) [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,6,7,1,5]=>([(0,6),(1,4),(3,2),(4,5),(5,3),(5,6)],7)=>([(0,4),(1,3),(1,6),(4,6),(5,2),(6,5)],7) [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,7,3,4,5,6]=>([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(6,3)],7)=>([(0,5),(0,6),(1,4),(2,5),(2,6),(3,2),(4,3)],7) [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,7,1,3,4,5,6]=>([(0,6),(1,3),(1,6),(4,2),(5,4),(6,5)],7)=>([(0,6),(1,4),(3,5),(4,3),(5,2),(5,6)],7) [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,7,4,5,6]=>([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7)=>([(0,6),(1,5),(2,6),(5,2),(6,3),(6,4)],7) [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,7,4,5,6]=>([(0,5),(0,6),(1,3),(3,5),(3,6),(4,2),(6,4)],7)=>([(0,5),(0,6),(1,4),(3,5),(3,6),(4,3),(6,2)],7) [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,7,1,4,5,6]=>([(0,6),(1,4),(4,3),(4,6),(5,2),(6,5)],7)=>([(0,6),(1,4),(4,5),(5,2),(5,6),(6,3)],7) [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,3,4,7,5,6]=>([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7)=>([(0,6),(1,4),(4,6),(5,2),(5,3),(6,5)],7) [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,4,7,5,6]=>([(0,6),(1,3),(3,6),(5,2),(6,4),(6,5)],7)=>([(0,6),(1,3),(3,6),(5,2),(6,4),(6,5)],7) [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,4,1,7,5,6]=>([(0,5),(0,6),(1,4),(3,5),(3,6),(4,3),(6,2)],7)=>([(0,5),(0,6),(1,3),(3,5),(3,6),(4,2),(6,4)],7) [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,6]=>([(0,6),(1,4),(4,5),(5,2),(5,6),(6,3)],7)=>([(0,6),(1,4),(4,3),(4,6),(5,2),(6,5)],7) [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,3,4,5,7,6]=>([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7)=>([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7) [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,5,7,6]=>([(0,6),(1,4),(4,6),(5,2),(5,3),(6,5)],7)=>([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7) [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,4,1,5,7,6]=>([(0,6),(1,5),(2,6),(5,2),(6,3),(6,4)],7)=>([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7) [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,4,5,1,7,6]=>([(0,5),(0,6),(1,4),(2,5),(2,6),(3,2),(4,3)],7)=>([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(6,3)],7) [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,6]=>([(0,6),(1,4),(3,5),(4,3),(5,2),(5,6)],7)=>([(0,6),(1,3),(1,6),(4,2),(5,4),(6,5)],7) [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7]=>([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)=>([(0,5),(3,4),(4,6),(5,3),(6,1),(6,2)],7) [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,7]=>([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)=>([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7) [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,4,1,5,6,7]=>([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)=>([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7) [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,7]=>([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)=>([(0,6),(3,5),(4,3),(5,1),(6,2),(6,4)],7) [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)=>([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>([(1,6),(3,5),(4,3),(5,2),(6,4)],7)=>([(1,6),(3,5),(4,3),(5,2),(6,4)],7) [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,7]=>([(0,6),(1,2),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7)=>([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7) [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,7]=>([(0,3),(1,2),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)=>([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(5,2),(6,1)],7) [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5,7]=>([(0,6),(1,3),(1,6),(2,4),(3,5),(5,4),(6,2),(6,5)],7)=>([(0,3),(0,4),(2,5),(3,6),(4,2),(4,6),(6,1),(6,5)],7) [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5,7]=>([(0,3),(1,2),(1,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)=>([(0,3),(0,4),(2,5),(3,5),(3,6),(4,2),(4,6),(6,1)],7) [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5,7]=>([(0,3),(1,4),(2,6),(3,5),(4,2),(4,5),(5,6)],7)=>([(0,3),(0,5),(3,6),(4,1),(5,4),(5,6),(6,2)],7) [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,7,5]=>([(0,6),(1,3),(1,6),(3,4),(3,5),(5,2),(6,4),(6,5)],7)=>([(0,3),(1,5),(1,6),(3,5),(3,6),(5,4),(6,2),(6,4)],7) [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,6,7,5]=>([(0,4),(1,3),(3,5),(3,6),(4,5),(4,6),(6,2)],7)=>([(0,5),(0,6),(1,2),(2,5),(2,6),(5,4),(6,3)],7) [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,4,6,2,7,5]=>([(0,6),(1,3),(1,6),(2,5),(3,4),(3,5),(6,2),(6,4)],7)=>([(0,3),(0,6),(1,5),(1,6),(3,5),(5,2),(5,4),(6,4)],7) [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,4,1,6,2,7,5]=>([(0,3),(1,2),(1,6),(2,4),(2,5),(3,4),(3,6),(6,5)],7)=>([(0,3),(0,6),(1,5),(1,6),(3,4),(3,5),(5,2),(6,4)],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),(2,5),(3,5),(3,6),(4,2),(4,6)],7)=>([(0,5),(0,6),(1,2),(1,6),(2,5),(5,3),(6,4)],7) [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,7,2,5]=>([(0,6),(1,3),(1,6),(3,5),(4,2),(6,4),(6,5)],7)=>([(0,3),(1,4),(1,6),(3,6),(4,5),(6,2),(6,5)],7) [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,4,1,6,7,2,5]=>([(0,4),(1,3),(1,6),(3,5),(4,5),(4,6),(6,2)],7)=>([(0,4),(1,3),(1,6),(3,5),(4,5),(4,6),(6,2)],7) [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,4,6,1,7,2,5]=>([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(4,5)],7)=>([(0,4),(0,6),(1,3),(1,5),(3,6),(4,5),(6,2)],7) [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,6,7,1,2,5]=>([(0,5),(1,3),(3,6),(4,2),(5,4),(5,6)],7)=>([(0,4),(1,5),(1,6),(4,6),(5,2),(6,3)],7) [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,6]=>([(0,6),(1,3),(1,6),(3,4),(3,5),(5,2),(6,4),(6,5)],7)=>([(0,3),(1,5),(1,6),(3,5),(3,6),(5,4),(6,2),(6,4)],7) [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,7,5,6]=>([(0,4),(1,3),(3,5),(3,6),(4,5),(4,6),(6,2)],7)=>([(0,5),(0,6),(1,2),(2,5),(2,6),(5,4),(6,3)],7) [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,4,7,2,5,6]=>([(0,6),(1,3),(1,6),(3,5),(5,4),(6,2),(6,5)],7)=>([(0,6),(1,4),(3,5),(4,3),(4,6),(6,2),(6,5)],7) [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,4,1,7,2,5,6]=>([(0,4),(1,3),(1,5),(3,6),(4,5),(4,6),(6,2)],7)=>([(0,5),(0,6),(1,4),(3,5),(4,3),(4,6),(6,2)],7) [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,4,7,1,2,5,6]=>([(0,4),(1,5),(4,6),(5,2),(5,6),(6,3)],7)=>([(0,6),(1,5),(4,2),(5,4),(5,6),(6,3)],7) [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,1,4,2,5,7,6]=>([(0,5),(1,4),(1,5),(4,6),(5,6),(6,2),(6,3)],7)=>([(0,6),(1,6),(3,5),(4,2),(4,5),(6,3),(6,4)],7) [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,4,1,2,5,7,6]=>([(0,5),(1,4),(4,6),(5,6),(6,2),(6,3)],7)=>([(0,6),(1,6),(4,3),(5,2),(6,4),(6,5)],7) [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,1,4,5,2,7,6]=>([(0,6),(1,3),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2)],7)=>([(0,5),(0,6),(1,5),(1,6),(3,2),(3,4),(5,3),(6,4)],7) [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,4,1,5,2,7,6]=>([(0,2),(1,3),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7)=>([(0,5),(0,6),(1,5),(1,6),(2,3),(5,4),(6,2),(6,4)],7) [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,7,6]=>([(0,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7)=>([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2)],7) [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>([(0,6),(1,3),(1,6),(3,5),(4,2),(4,5),(6,4)],7)=>([(0,6),(1,3),(1,6),(3,5),(4,2),(4,5),(6,4)],7) [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,4,1,5,7,2,6]=>([(0,3),(1,4),(1,6),(3,6),(4,5),(6,2),(6,5)],7)=>([(0,6),(1,3),(1,6),(3,5),(4,2),(6,4),(6,5)],7) [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,4,5,1,7,2,6]=>([(0,3),(0,6),(1,4),(2,5),(2,6),(3,5),(4,2)],7)=>([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(6,4)],7) [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,7,1,2,6]=>([(0,5),(1,3),(3,6),(4,2),(4,6),(5,4)],7)=>([(0,6),(1,4),(1,6),(4,3),(5,2),(6,5)],7) [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,5,6,7]=>([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7)=>([(0,4),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3)],7) [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,5,6,7]=>([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7)=>([(0,5),(3,2),(4,1),(5,6),(6,3),(6,4)],7) [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,4,5,2,6,7]=>([(0,6),(1,3),(1,6),(2,5),(3,5),(5,4),(6,2)],7)=>([(0,5),(2,6),(3,4),(4,1),(4,6),(5,2),(5,3)],7) [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,4,1,5,2,6,7]=>([(0,4),(1,3),(1,5),(3,6),(4,5),(5,6),(6,2)],7)=>([(0,5),(2,6),(3,1),(4,3),(4,6),(5,2),(5,4)],7) [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,4,5,1,2,6,7]=>([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)=>([(0,6),(3,4),(4,1),(5,2),(6,3),(6,5)],7) [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,1,4,5,6,2,7]=>([(0,6),(1,3),(1,6),(2,5),(3,5),(4,2),(6,4)],7)=>([(0,2),(0,5),(2,6),(3,4),(4,1),(4,6),(5,3)],7) [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,4,1,5,6,2,7]=>([(0,3),(1,4),(1,6),(2,5),(3,6),(4,5),(6,2)],7)=>([(0,2),(0,5),(2,6),(3,1),(4,3),(4,6),(5,4)],7) [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,4,5,1,6,2,7]=>([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(6,5)],7)=>([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7) [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,5,6,1,2,7]=>([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)=>([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,6,7,2]=>([(0,6),(1,3),(1,6),(4,2),(5,4),(6,5)],7)=>([(0,6),(1,4),(3,5),(4,3),(5,2),(5,6)],7) [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,4,1,5,6,7,2]=>([(0,4),(1,3),(1,6),(4,6),(5,2),(6,5)],7)=>([(0,6),(1,4),(3,2),(4,5),(5,3),(5,6)],7) [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,5,1,6,7,2]=>([(0,5),(1,4),(1,6),(2,6),(5,2),(6,3)],7)=>([(0,6),(1,5),(3,4),(4,2),(5,3),(5,6)],7) [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,5,6,1,7,2]=>([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7)=>([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7) [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>([(0,6),(1,3),(4,5),(5,2),(6,4)],7)=>([(0,6),(1,3),(4,5),(5,2),(6,4)],7) [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,7]=>([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4)],7)=>([(0,2),(0,3),(1,4),(1,6),(2,4),(2,5),(3,1),(3,5),(5,6)],7) [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,5,1,2,6,4,7]=>([(0,3),(1,2),(1,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)=>([(0,3),(0,4),(2,5),(3,5),(3,6),(4,2),(4,6),(6,1)],7) [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,5,6,2,4,7]=>([(0,3),(0,5),(1,5),(1,6),(2,4),(3,6),(5,2),(6,4)],7)=>([(0,3),(0,4),(1,5),(2,5),(2,6),(3,2),(4,1),(4,6)],7) [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,5,1,6,2,4,7]=>([(0,3),(0,6),(1,2),(1,5),(2,6),(3,5),(5,4),(6,4)],7)=>([(0,3),(0,4),(1,6),(2,5),(3,2),(3,6),(4,1),(4,5)],7) [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,5,6,1,2,4,7]=>([(0,3),(1,4),(1,6),(2,5),(3,6),(4,2),(6,5)],7)=>([(0,4),(0,5),(2,6),(3,1),(4,2),(5,3),(5,6)],7) [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,6,7,4]=>([(0,3),(0,6),(1,4),(1,6),(3,4),(3,5),(5,2),(6,5)],7)=>([(0,2),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4)],7) [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,5,1,2,6,7,4]=>([(0,4),(1,3),(1,5),(3,6),(4,5),(4,6),(6,2)],7)=>([(0,5),(0,6),(1,4),(3,5),(4,3),(4,6),(6,2)],7) [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,5,6,2,7,4]=>([(0,3),(0,6),(1,4),(1,6),(2,5),(3,4),(3,5),(6,2)],7)=>([(0,2),(0,6),(1,5),(1,6),(2,3),(3,4),(3,5),(6,4)],7) [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,5,1,6,2,7,4]=>([(0,3),(0,6),(1,2),(1,5),(2,6),(3,4),(3,5),(6,4)],7)=>([(0,3),(0,6),(1,5),(1,6),(2,5),(3,2),(3,4),(6,4)],7) [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,5,6,1,2,7,4]=>([(0,3),(1,4),(1,6),(2,5),(3,5),(3,6),(4,2)],7)=>([(0,5),(0,6),(1,4),(1,6),(3,5),(4,3),(6,2)],7) [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,6,7,2,4]=>([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(6,4)],7)=>([(0,3),(0,6),(1,4),(2,5),(2,6),(3,5),(4,2)],7) [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,5,1,6,7,2,4]=>([(0,4),(0,6),(1,3),(1,5),(3,6),(4,5),(6,2)],7)=>([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(4,5)],7) [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,5,6,1,7,2,4]=>([(0,3),(0,5),(1,4),(1,6),(2,5),(3,6),(4,2)],7)=>([(0,3),(0,5),(1,4),(1,6),(2,5),(3,6),(4,2)],7) [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,5,6,7,1,2,4]=>([(0,3),(1,5),(1,6),(3,6),(4,2),(5,4)],7)=>([(0,4),(1,5),(1,6),(3,6),(4,3),(5,2)],7) [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,6]=>([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3),(6,4)],7)=>([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3),(6,4)],7) [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,7,4,6]=>([(0,3),(1,2),(1,6),(2,4),(2,5),(3,4),(3,6),(6,5)],7)=>([(0,3),(0,6),(1,5),(1,6),(3,4),(3,5),(5,2),(6,4)],7) [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,7,2,4,6]=>([(0,3),(0,6),(1,5),(1,6),(3,5),(5,4),(6,2),(6,4)],7)=>([(0,6),(1,3),(1,6),(2,5),(3,2),(3,4),(6,4),(6,5)],7) [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,7,2,4,6]=>([(0,3),(0,6),(1,2),(1,5),(2,6),(3,4),(3,5),(6,4)],7)=>([(0,3),(0,6),(1,5),(1,6),(2,5),(3,2),(3,4),(6,4)],7) [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,7,1,2,4,6]=>([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7)=>([(0,6),(1,4),(1,6),(3,2),(4,3),(4,5),(6,5)],7) [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,7,6]=>([(0,2),(0,6),(1,5),(1,6),(2,5),(5,3),(5,4),(6,3),(6,4)],7)=>([(0,5),(0,6),(1,5),(1,6),(2,4),(5,2),(5,3),(6,3),(6,4)],7) [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,7,6]=>([(0,2),(1,3),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7)=>([(0,5),(0,6),(1,5),(1,6),(2,3),(5,4),(6,2),(6,4)],7) [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,7,6]=>([(0,2),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)=>([(0,5),(0,6),(1,5),(1,6),(4,2),(5,3),(5,4),(6,3),(6,4)],7) [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[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)=>([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7) [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,7,6]=>([(0,2),(0,3),(1,5),(1,6),(2,4),(3,1),(3,4),(4,5),(4,6)],7)=>([(0,5),(0,6),(1,5),(1,6),(2,3),(4,3),(5,4),(6,2),(6,4)],7) [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,7,4,6]=>([(0,3),(1,5),(1,6),(3,5),(3,6),(5,4),(6,2),(6,4)],7)=>([(0,6),(1,3),(1,6),(3,4),(3,5),(5,2),(6,4),(6,5)],7) [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,4,6]=>([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7)=>([(0,6),(1,2),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7) [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,7,4,6]=>([(0,2),(0,3),(1,4),(1,6),(2,4),(2,5),(3,1),(3,5),(5,6)],7)=>([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4)],7) [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,7,2,4,6]=>([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7)=>([(0,6),(1,3),(1,6),(2,4),(3,2),(3,5),(5,4),(6,5)],7) [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,4,6,7]=>([(0,3),(0,6),(1,5),(1,6),(3,5),(4,2),(5,4),(6,4)],7)=>([(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,2),(4,3)],7) [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,5,1,2,4,6,7]=>([(0,4),(1,3),(1,5),(3,6),(4,5),(5,6),(6,2)],7)=>([(0,5),(2,6),(3,1),(4,3),(4,6),(5,2),(5,4)],7) [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,5,4,6,7]=>([(0,3),(1,5),(1,6),(3,5),(3,6),(4,2),(5,4),(6,4)],7)=>([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(6,1)],7) [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[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)=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2),(4,6),(5,6)],7) [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,4,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,5,6,4,7]=>([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7)=>([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7) [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[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),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(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]=>([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5),(4,6),(5,6)],7)=>([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5),(4,6),(5,6)],7) [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,6,2,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7) [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,5,6,7,4]=>([(0,5),(0,6),(1,3),(3,5),(3,6),(4,2),(6,4)],7)=>([(0,5),(0,6),(1,4),(3,5),(3,6),(4,3),(6,2)],7) [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,5,6,7,4]=>([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(6,4)],7)=>([(0,2),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7) [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,5,2,6,7,4]=>([(0,3),(0,4),(2,6),(3,5),(3,6),(4,2),(4,5),(6,1)],7)=>([(0,3),(1,5),(1,6),(2,6),(3,2),(3,5),(5,4),(6,4)],7) [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,5,6,2,7,4]=>([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(4,3),(4,6)],7)=>([(0,2),(0,6),(1,5),(1,6),(2,3),(3,5),(5,4),(6,4)],7) [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,5,6,7,2,4]=>([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7)=>([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(6,5)],7) [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,6,2,7,4,5]=>([(0,3),(0,6),(1,5),(1,6),(3,4),(3,5),(5,2),(6,4)],7)=>([(0,3),(1,2),(1,6),(2,4),(2,5),(3,4),(3,6),(6,5)],7) [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,6,1,2,7,4,5]=>([(0,4),(1,3),(1,6),(3,5),(4,5),(4,6),(6,2)],7)=>([(0,4),(1,3),(1,6),(3,5),(4,5),(4,6),(6,2)],7) [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,6,7,2,4,5]=>([(0,5),(0,6),(1,2),(1,6),(2,5),(5,3),(6,4)],7)=>([(0,3),(1,4),(2,5),(3,5),(3,6),(4,2),(4,6)],7) [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,6,1,7,2,4,5]=>([(0,4),(0,6),(1,3),(1,5),(3,6),(4,5),(6,2)],7)=>([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(4,5)],7) [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,6,7,1,2,4,5]=>([(0,4),(1,5),(1,6),(4,6),(5,2),(6,3)],7)=>([(0,5),(1,3),(3,6),(4,2),(5,4),(5,6)],7) [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,6,2,4,7,5]=>([(0,3),(0,6),(1,5),(1,6),(3,5),(5,2),(5,4),(6,4)],7)=>([(0,6),(1,3),(1,6),(2,5),(3,4),(3,5),(6,2),(6,4)],7) [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,6,1,2,4,7,5]=>([(0,3),(1,4),(1,6),(3,6),(4,5),(6,2),(6,5)],7)=>([(0,6),(1,3),(1,6),(3,5),(4,2),(6,4),(6,5)],7) [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,2,6,4,7,5]=>([(0,3),(1,5),(1,6),(3,5),(3,6),(5,4),(6,2),(6,4)],7)=>([(0,6),(1,3),(1,6),(3,4),(3,5),(5,2),(6,4),(6,5)],7) [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,6,4,7,5]=>([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7)=>([(0,6),(1,2),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7) [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,6,2,4,7,5]=>([(0,3),(0,4),(2,5),(3,6),(4,2),(4,6),(6,1),(6,5)],7)=>([(0,6),(1,3),(1,6),(2,4),(3,5),(5,4),(6,2),(6,5)],7) [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,6,7,4,5]=>([(0,5),(0,6),(1,2),(2,5),(2,6),(5,4),(6,3)],7)=>([(0,4),(1,3),(3,5),(3,6),(4,5),(4,6),(6,2)],7) [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,6,7,4,5]=>([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(5,2),(6,1)],7)=>([(0,3),(1,2),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,6,2,7,4,5]=>([(0,3),(0,4),(2,5),(3,5),(3,6),(4,2),(4,6),(6,1)],7)=>([(0,3),(1,2),(1,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,6,7,2,4,5]=>([(0,3),(0,5),(3,6),(4,1),(5,4),(5,6),(6,2)],7)=>([(0,3),(1,4),(2,6),(3,5),(4,2),(4,5),(5,6)],7) [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5,7]=>([(0,3),(0,6),(1,4),(1,6),(2,5),(3,4),(4,2),(6,5)],7)=>([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,3)],7) [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,5,7]=>([(0,3),(1,4),(1,6),(2,5),(3,6),(4,5),(6,2)],7)=>([(0,2),(0,5),(2,6),(3,1),(4,3),(4,6),(5,4)],7) [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5,7]=>([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7)=>([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7) [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,5,7]=>([(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1)],7)=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(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]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5,7]=>([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7)=>([(0,3),(0,4),(3,6),(4,6),(5,1),(6,2),(6,5)],7) [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7) [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[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),(0,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1)],7) [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,7,5]=>([(0,6),(1,3),(3,6),(5,2),(6,4),(6,5)],7)=>([(0,6),(1,3),(3,6),(5,2),(6,4),(6,5)],7) [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,4,6,7,5]=>([(0,3),(0,4),(3,6),(4,6),(5,1),(6,2),(6,5)],7)=>([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7) [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[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),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7) [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,4,6,2,7,5]=>([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,3)],7)=>([(0,3),(0,6),(1,4),(1,6),(2,5),(3,4),(4,2),(6,5)],7) [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,4,6,7,2,5]=>([(0,2),(0,5),(2,6),(3,1),(4,3),(4,6),(5,4)],7)=>([(0,3),(1,4),(1,6),(2,5),(3,6),(4,5),(6,2)],7) [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,7,2,4,5,6]=>([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(5,4)],7)=>([(0,5),(0,6),(1,3),(2,6),(3,4),(4,2),(4,5)],7) [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,7,1,2,4,5,6]=>([(0,4),(1,3),(1,6),(4,6),(5,2),(6,5)],7)=>([(0,6),(1,4),(3,2),(4,5),(5,3),(5,6)],7) [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,7,4,5,6]=>([(0,5),(0,6),(1,3),(3,5),(3,6),(4,2),(6,4)],7)=>([(0,5),(0,6),(1,4),(3,5),(3,6),(4,3),(6,2)],7) [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,7,4,5,6]=>([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(6,4)],7)=>([(0,2),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7) [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,7,2,4,5,6]=>([(0,3),(0,5),(3,6),(4,2),(5,1),(5,6),(6,4)],7)=>([(0,6),(1,4),(2,5),(3,2),(3,6),(4,3),(6,5)],7) [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,6]=>([(0,6),(1,3),(3,6),(5,2),(6,4),(6,5)],7)=>([(0,6),(1,3),(3,6),(5,2),(6,4),(6,5)],7) [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,4,7,5,6]=>([(0,3),(0,4),(3,6),(4,6),(5,1),(6,2),(6,5)],7)=>([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7) [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,4,2,7,5,6]=>([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7)=>([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7) [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,4,7,2,5,6]=>([(0,3),(0,5),(3,6),(4,1),(4,6),(5,4),(6,2)],7)=>([(0,6),(1,4),(2,5),(3,5),(4,3),(4,6),(6,2)],7) [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,4,5,7,6]=>([(0,6),(1,4),(4,6),(5,2),(5,3),(6,5)],7)=>([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7) [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,3,2,4,5,7,6]=>([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7)=>([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7) [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,4,2,5,7,6]=>([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7)=>([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7) [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,4,5,2,7,6]=>([(0,2),(0,4),(1,5),(1,6),(2,5),(2,6),(3,1),(4,3)],7)=>([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7) [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,4,5,7,2,6]=>([(0,2),(0,5),(2,6),(3,4),(4,1),(4,6),(5,3)],7)=>([(0,6),(1,3),(1,6),(2,5),(3,5),(4,2),(6,4)],7) [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7]=>([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)=>([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7) [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7) [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,4,2,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,4,5,2,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7) [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,4,5,6,2,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,4,5,6,7,2]=>([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)=>([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,7]=>([(0,6),(1,3),(1,6),(2,4),(3,2),(3,5),(5,4),(6,5)],7)=>([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7) [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[4,5,1,2,6,3,7]=>([(0,3),(1,4),(2,6),(3,5),(4,2),(4,5),(5,6)],7)=>([(0,3),(0,5),(3,6),(4,1),(5,4),(5,6),(6,2)],7) [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,5,6,2,3,7]=>([(0,6),(1,4),(1,6),(2,5),(3,5),(4,3),(6,2)],7)=>([(0,4),(0,5),(2,6),(3,1),(3,6),(4,2),(5,3)],7) [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[4,5,1,6,2,3,7]=>([(0,3),(1,4),(1,6),(2,5),(3,6),(4,2),(6,5)],7)=>([(0,4),(0,5),(2,6),(3,1),(4,2),(5,3),(5,6)],7) [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,7]=>([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7)=>([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7) [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[4,1,5,2,6,7,3]=>([(0,5),(1,4),(1,5),(4,3),(4,6),(5,6),(6,2)],7)=>([(0,6),(1,3),(3,4),(3,6),(4,2),(4,5),(6,5)],7) [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,5,1,2,6,7,3]=>([(0,4),(1,5),(4,6),(5,2),(5,6),(6,3)],7)=>([(0,6),(1,5),(4,2),(5,4),(5,6),(6,3)],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),(1,6),(3,5),(4,2),(4,5),(6,3)],7)=>([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7) [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,5,1,6,2,7,3]=>([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7)=>([(0,6),(1,4),(1,6),(3,2),(4,3),(4,5),(6,5)],7) [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,5,6,1,2,7,3]=>([(0,5),(1,4),(3,6),(4,3),(5,2),(5,6)],7)=>([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7) [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,5,6,7,2,3]=>([(0,6),(1,4),(1,6),(4,3),(5,2),(6,5)],7)=>([(0,5),(1,3),(3,6),(4,2),(4,6),(5,4)],7) [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,5,1,6,7,2,3]=>([(0,4),(1,5),(1,6),(4,6),(5,2),(6,3)],7)=>([(0,5),(1,3),(3,6),(4,2),(5,4),(5,6)],7) [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,5,6,1,7,2,3]=>([(0,4),(1,5),(1,6),(3,6),(4,3),(5,2)],7)=>([(0,3),(1,5),(1,6),(3,6),(4,2),(5,4)],7) [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>([(0,5),(1,6),(4,3),(5,4),(6,2)],7)=>([(0,5),(1,6),(4,3),(5,4),(6,2)],7) [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,5,2,7,3,6]=>([(0,6),(1,3),(1,6),(2,5),(3,2),(3,4),(6,4),(6,5)],7)=>([(0,3),(0,6),(1,5),(1,6),(3,5),(5,4),(6,2),(6,4)],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),(2,5),(3,5),(3,6),(4,2),(4,6)],7)=>([(0,5),(0,6),(1,2),(1,6),(2,5),(5,3),(6,4)],7) [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,5,7,2,3,6]=>([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7)=>([(0,6),(1,4),(1,6),(3,5),(4,3),(6,2),(6,5)],7) [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,5,1,7,2,3,6]=>([(0,3),(1,4),(1,6),(2,5),(3,5),(3,6),(4,2)],7)=>([(0,5),(0,6),(1,4),(1,6),(3,5),(4,3),(6,2)],7) [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,5,7,1,2,3,6]=>([(0,5),(1,4),(3,6),(4,3),(5,2),(5,6)],7)=>([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7) [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,7,6]=>([(0,6),(1,2),(1,6),(2,3),(3,4),(3,5),(6,4),(6,5)],7)=>([(0,5),(0,6),(1,5),(1,6),(3,4),(5,3),(6,2),(6,4)],7) [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,7,6]=>([(0,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,2)],7)=>([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2)],7) [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,7,6]=>([(0,2),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7)=>([(0,5),(0,6),(1,5),(1,6),(4,3),(5,4),(6,2),(6,4)],7) [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,7,6]=>([(0,2),(0,3),(1,5),(1,6),(2,4),(3,1),(3,4),(4,5),(4,6)],7)=>([(0,5),(0,6),(1,5),(1,6),(2,3),(4,3),(5,4),(6,2),(6,4)],7) [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,7,6]=>([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1)],7)=>([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(5,3),(6,2)],7) [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>([(0,6),(1,4),(3,5),(4,3),(4,6),(6,2),(6,5)],7)=>([(0,6),(1,3),(1,6),(3,5),(5,4),(6,2),(6,5)],7) [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,2,5,7,3,6]=>([(0,3),(0,4),(2,5),(3,6),(4,2),(4,6),(6,1),(6,5)],7)=>([(0,6),(1,3),(1,6),(2,4),(3,5),(5,4),(6,2),(6,5)],7) [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,2,7,3,6]=>([(0,3),(0,4),(1,5),(2,5),(2,6),(3,2),(4,1),(4,6)],7)=>([(0,3),(0,5),(1,5),(1,6),(2,4),(3,6),(5,2),(6,4)],7) [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,7,2,3,6]=>([(0,4),(0,5),(2,6),(3,1),(3,6),(4,2),(5,3)],7)=>([(0,6),(1,4),(1,6),(2,5),(3,5),(4,3),(6,2)],7) [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,6,7]=>([(0,5),(1,4),(1,5),(3,6),(4,3),(5,6),(6,2)],7)=>([(0,5),(2,6),(3,2),(4,1),(4,6),(5,3),(5,4)],7) [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3,6,7]=>([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7)=>([(0,6),(3,4),(4,1),(5,2),(6,3),(6,5)],7) [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3,6,7]=>([(0,5),(1,4),(3,6),(4,3),(4,5),(5,6),(6,2)],7)=>([(0,5),(2,6),(4,1),(4,6),(5,2),(5,4),(6,3)],7) [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,3,6,7]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7) [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3,6,7]=>([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7)=>([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7) [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[4,1,2,5,6,3,7]=>([(0,6),(1,4),(2,5),(3,5),(4,3),(4,6),(6,2)],7)=>([(0,3),(0,5),(3,6),(4,1),(4,6),(5,4),(6,2)],7) [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,2,5,6,3,7]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7)=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7) [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,5,2,6,3,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7) [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,5,6,2,3,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7) [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,7,3]=>([(0,6),(1,4),(4,3),(4,6),(5,2),(6,5)],7)=>([(0,6),(1,4),(4,5),(5,2),(5,6),(6,3)],7) [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,5,6,7,3]=>([(0,3),(0,5),(3,6),(4,2),(5,1),(5,6),(6,4)],7)=>([(0,6),(1,4),(2,5),(3,2),(3,6),(4,3),(6,5)],7) [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,5,2,6,7,3]=>([(0,4),(0,5),(2,6),(4,2),(5,1),(5,6),(6,3)],7)=>([(0,6),(1,4),(2,5),(3,2),(4,3),(4,6),(6,5)],7) [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,5,6,2,7,3]=>([(0,4),(0,5),(2,6),(3,2),(4,3),(5,1),(5,6)],7)=>([(0,6),(1,4),(1,6),(2,5),(3,2),(4,3),(6,5)],7) [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,5,6,7,2,3]=>([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)=>([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,5]=>([(0,3),(0,6),(1,5),(1,6),(2,5),(3,2),(3,4),(6,4)],7)=>([(0,3),(0,6),(1,2),(1,5),(2,6),(3,4),(3,5),(6,4)],7) [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,6,1,2,7,3,5]=>([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(4,5)],7)=>([(0,4),(0,6),(1,3),(1,5),(3,6),(4,5),(6,2)],7) [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,6,7,2,3,5]=>([(0,5),(0,6),(1,4),(1,6),(3,5),(4,3),(6,2)],7)=>([(0,3),(1,4),(1,6),(2,5),(3,5),(3,6),(4,2)],7) [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,6,1,7,2,3,5]=>([(0,3),(0,5),(1,4),(1,6),(2,5),(3,6),(4,2)],7)=>([(0,3),(0,5),(1,4),(1,6),(2,5),(3,6),(4,2)],7) [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,6,7,1,2,3,5]=>([(0,4),(1,5),(1,6),(3,6),(4,3),(5,2)],7)=>([(0,3),(1,5),(1,6),(3,6),(4,2),(5,4)],7) [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,6,2,3,7,5]=>([(0,2),(0,6),(1,5),(1,6),(2,3),(3,4),(3,5),(6,4)],7)=>([(0,3),(0,6),(1,4),(1,6),(2,5),(3,4),(3,5),(6,2)],7) [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,6,1,2,3,7,5]=>([(0,3),(0,6),(1,4),(2,5),(2,6),(3,5),(4,2)],7)=>([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(6,4)],7) [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,6,3,7,5]=>([(0,2),(1,5),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4)],7)=>([(0,3),(0,6),(1,4),(1,6),(3,4),(3,5),(5,2),(6,5)],7) [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,7,5]=>([(0,2),(0,3),(1,4),(1,6),(2,4),(2,5),(3,1),(3,5),(5,6)],7)=>([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4)],7) [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,6,2,3,7,5]=>([(0,3),(0,4),(1,5),(2,5),(2,6),(3,2),(4,1),(4,6)],7)=>([(0,3),(0,5),(1,5),(1,6),(2,4),(3,6),(5,2),(6,4)],7) [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,6,7,3,5]=>([(0,5),(0,6),(1,4),(3,5),(4,3),(4,6),(6,2)],7)=>([(0,4),(1,3),(1,5),(3,6),(4,5),(4,6),(6,2)],7) [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,7,3,5]=>([(0,3),(0,4),(2,5),(3,5),(3,6),(4,2),(4,6),(6,1)],7)=>([(0,3),(1,2),(1,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7) [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,4,6,2,7,3,5]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(3,6),(4,1),(4,5)],7)=>([(0,3),(0,6),(1,2),(1,5),(2,6),(3,5),(5,4),(6,4)],7) [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,4,6,7,2,3,5]=>([(0,4),(0,5),(2,6),(3,1),(4,2),(5,3),(5,6)],7)=>([(0,3),(1,4),(1,6),(2,5),(3,6),(4,2),(6,5)],7) [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5,7]=>([(0,2),(0,6),(1,5),(1,6),(2,3),(3,5),(5,4),(6,4)],7)=>([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(4,3),(4,6)],7) [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5,7]=>([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(6,5)],7)=>([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7) [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5,7]=>([(0,3),(1,5),(1,6),(2,6),(3,2),(3,5),(5,4),(6,4)],7)=>([(0,3),(0,4),(2,6),(3,5),(3,6),(4,2),(4,5),(6,1)],7) [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5,7]=>([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5),(4,6),(5,6)],7)=>([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5),(4,6),(5,6)],7) [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,5,7]=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7)=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7) [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,7]=>([(0,2),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)=>([(0,2),(0,3),(2,5),(2,6),(3,5),(3,6),(4,1),(6,4)],7) [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,7]=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(4,6),(5,6)],7)=>([(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1)],7) [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[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)=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7) [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,2,4,6,3,5,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,7,5]=>([(0,5),(0,6),(1,4),(3,5),(3,6),(4,3),(6,2)],7)=>([(0,5),(0,6),(1,3),(3,5),(3,6),(4,2),(6,4)],7) [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,6,7,5]=>([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7)=>([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7) [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,6,7,5]=>([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(6,1)],7)=>([(0,3),(1,5),(1,6),(3,5),(3,6),(4,2),(5,4),(6,4)],7) [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,2,4,6,3,7,5]=>([(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,2),(4,3)],7)=>([(0,3),(0,6),(1,5),(1,6),(3,5),(4,2),(5,4),(6,4)],7) [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,6,7,3,5]=>([(0,5),(2,6),(3,1),(4,3),(4,6),(5,2),(5,4)],7)=>([(0,4),(1,3),(1,5),(3,6),(4,5),(5,6),(6,2)],7) [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,1,7,2,3,5,6]=>([(0,5),(0,6),(1,4),(1,5),(3,6),(4,3),(6,2)],7)=>([(0,5),(0,6),(1,4),(2,6),(3,2),(4,3),(4,5)],7) [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,7,1,2,3,5,6]=>([(0,5),(1,4),(1,6),(2,6),(5,2),(6,3)],7)=>([(0,6),(1,5),(3,4),(4,2),(5,3),(5,6)],7) [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,7,3,5,6]=>([(0,5),(0,6),(1,4),(3,6),(4,3),(4,5),(6,2)],7)=>([(0,5),(0,6),(1,4),(3,6),(4,3),(4,5),(6,2)],7) [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,7,3,5,6]=>([(0,3),(0,4),(2,6),(3,5),(3,6),(4,2),(4,5),(6,1)],7)=>([(0,3),(1,5),(1,6),(2,6),(3,2),(3,5),(5,4),(6,4)],7) [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,4,7,2,3,5,6]=>([(0,4),(0,5),(2,6),(4,2),(5,1),(5,6),(6,3)],7)=>([(0,6),(1,4),(2,5),(3,2),(4,3),(4,6),(6,5)],7) [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,2,3,7,5,6]=>([(0,5),(0,6),(1,4),(3,5),(3,6),(4,3),(6,2)],7)=>([(0,5),(0,6),(1,3),(3,5),(3,6),(4,2),(6,4)],7) [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,4,2,3,7,5,6]=>([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7)=>([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7) [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,2,4,3,7,5,6]=>([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(6,1)],7)=>([(0,3),(1,5),(1,6),(3,5),(3,6),(4,2),(5,4),(6,4)],7) [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,2,4,7,3,5,6]=>([(0,5),(2,6),(4,1),(4,6),(5,2),(5,4),(6,3)],7)=>([(0,5),(1,4),(3,6),(4,3),(4,5),(5,6),(6,2)],7) [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,1,2,3,5,7,6]=>([(0,6),(1,5),(2,6),(5,2),(6,3),(6,4)],7)=>([(0,6),(1,6),(4,2),(5,4),(6,3),(6,5)],7) [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,4,2,3,5,7,6]=>([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7)=>([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7) [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,2,4,3,5,7,6]=>([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7)=>([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7) [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,2,4,5,3,7,6]=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1),(4,3)],7)=>([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7) [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,2,4,5,7,3,6]=>([(0,5),(2,6),(3,4),(4,1),(4,6),(5,2),(5,3)],7)=>([(0,6),(1,3),(1,6),(2,5),(3,5),(5,4),(6,2)],7) [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,7]=>([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7)=>([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7) [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,7]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7) [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,7]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7) [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,2,4,5,3,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,5,6,3,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7) [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,5,6,7,3]=>([(0,6),(3,5),(4,3),(5,1),(6,2),(6,4)],7)=>([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],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),(1,6),(3,2),(4,3),(4,5),(6,5)],7)=>([(0,3),(1,4),(1,6),(3,6),(4,2),(4,5),(6,5)],7) [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,6,1,2,7,3,4]=>([(0,5),(1,3),(3,6),(4,2),(5,4),(5,6)],7)=>([(0,4),(1,5),(1,6),(4,6),(5,2),(6,3)],7) [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[5,1,6,7,2,3,4]=>([(0,6),(1,5),(1,6),(4,2),(5,4),(6,3)],7)=>([(0,5),(1,4),(3,6),(4,3),(5,2),(5,6)],7) [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[5,6,1,7,2,3,4]=>([(0,3),(1,5),(1,6),(3,6),(4,2),(5,4)],7)=>([(0,4),(1,5),(1,6),(3,6),(4,3),(5,2)],7) [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>([(0,5),(1,6),(4,3),(5,4),(6,2)],7)=>([(0,5),(1,6),(4,3),(5,4),(6,2)],7) [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[5,1,6,2,3,7,4]=>([(0,6),(1,3),(1,6),(3,4),(4,2),(4,5),(6,5)],7)=>([(0,6),(1,4),(1,6),(3,5),(4,2),(4,5),(6,3)],7) [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,6,1,2,3,7,4]=>([(0,5),(1,3),(3,6),(4,2),(4,6),(5,4)],7)=>([(0,6),(1,4),(1,6),(4,3),(5,2),(6,5)],7) [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[5,1,2,6,3,7,4]=>([(0,6),(1,3),(3,4),(3,6),(4,2),(4,5),(6,5)],7)=>([(0,5),(1,4),(1,5),(4,3),(4,6),(5,6),(6,2)],7) [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,2,6,3,7,4]=>([(0,2),(0,4),(2,5),(3,1),(3,6),(4,3),(4,5),(5,6)],7)=>([(0,6),(1,3),(1,6),(2,4),(3,2),(3,5),(5,4),(6,5)],7) [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,6,2,3,7,4]=>([(0,4),(0,5),(2,6),(3,1),(3,6),(4,2),(5,3)],7)=>([(0,6),(1,4),(1,6),(2,5),(3,5),(4,3),(6,2)],7) [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[5,1,2,6,7,3,4]=>([(0,6),(1,5),(4,2),(5,4),(5,6),(6,3)],7)=>([(0,4),(1,5),(4,6),(5,2),(5,6),(6,3)],7) [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,5,2,6,7,3,4]=>([(0,3),(0,5),(3,6),(4,1),(5,4),(5,6),(6,2)],7)=>([(0,3),(1,4),(2,6),(3,5),(4,2),(4,5),(5,6)],7) [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,5,6,2,7,3,4]=>([(0,4),(0,5),(2,6),(3,1),(4,2),(5,3),(5,6)],7)=>([(0,3),(1,4),(1,6),(2,5),(3,6),(4,2),(6,5)],7) [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,5,6,7,2,3,4]=>([(0,5),(0,6),(3,2),(4,1),(5,3),(6,4)],7)=>([(0,5),(1,4),(2,6),(3,6),(4,2),(5,3)],7) [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[5,1,6,2,3,4,7]=>([(0,6),(1,4),(1,6),(2,5),(3,2),(4,3),(6,5)],7)=>([(0,4),(0,5),(2,6),(3,2),(4,3),(5,1),(5,6)],7) [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,6,1,2,3,4,7]=>([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7)=>([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7) [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,2,6,3,4,7]=>([(0,6),(1,4),(2,5),(3,2),(4,3),(4,6),(6,5)],7)=>([(0,4),(0,5),(2,6),(4,2),(5,1),(5,6),(6,3)],7) [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,3,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(4,3),(4,5),(5,6)],7)=>([(0,3),(0,4),(1,6),(2,5),(3,2),(4,1),(4,5),(5,6)],7) [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,6,2,3,4,7]=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7)=>([(0,4),(0,5),(1,6),(2,6),(3,2),(4,3),(5,1)],7) [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[5,1,2,3,6,4,7]=>([(0,6),(1,4),(2,5),(3,2),(3,6),(4,3),(6,5)],7)=>([(0,3),(0,5),(3,6),(4,2),(5,1),(5,6),(6,4)],7) [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,2,3,6,4,7]=>([(0,2),(0,4),(1,6),(2,5),(3,1),(3,5),(4,3),(5,6)],7)=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,2),(4,6),(6,1)],7) [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,2,5,3,6,4,7]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7) [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,2,5,6,3,4,7]=>([(0,5),(1,6),(2,6),(3,2),(4,1),(5,3),(5,4)],7)=>([(0,4),(0,5),(1,6),(2,6),(4,2),(5,1),(6,3)],7) [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[5,1,2,3,6,7,4]=>([(0,6),(1,4),(4,5),(5,2),(5,6),(6,3)],7)=>([(0,6),(1,4),(4,3),(4,6),(5,2),(6,5)],7) [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,6,7,4]=>([(0,3),(0,5),(3,6),(4,1),(4,6),(5,4),(6,2)],7)=>([(0,6),(1,4),(2,5),(3,5),(4,3),(4,6),(6,2)],7) [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,2,5,3,6,7,4]=>([(0,5),(2,6),(4,1),(4,6),(5,2),(5,4),(6,3)],7)=>([(0,5),(1,4),(3,6),(4,3),(4,5),(5,6),(6,2)],7) [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,2,5,6,3,7,4]=>([(0,5),(2,6),(3,2),(4,1),(4,6),(5,3),(5,4)],7)=>([(0,5),(1,4),(1,5),(3,6),(4,3),(5,6),(6,2)],7) [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,2,5,6,7,3,4]=>([(0,6),(3,4),(4,1),(5,2),(6,3),(6,5)],7)=>([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,1,7,2,3,4,6]=>([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7)=>([(0,5),(0,6),(1,4),(1,6),(2,5),(3,2),(4,3)],7) [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,7,1,2,3,4,6]=>([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7)=>([(0,6),(1,5),(1,6),(3,4),(4,2),(5,3)],7) [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,6]=>([(0,5),(0,6),(1,4),(2,6),(3,2),(4,3),(4,5)],7)=>([(0,5),(0,6),(1,4),(1,5),(3,6),(4,3),(6,2)],7) [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,5,2,7,3,4,6]=>([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(4,3),(4,6)],7)=>([(0,2),(0,6),(1,5),(1,6),(2,3),(3,5),(5,4),(6,4)],7) [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,5,7,2,3,4,6]=>([(0,4),(0,5),(2,6),(3,2),(4,3),(5,1),(5,6)],7)=>([(0,6),(1,4),(1,6),(2,5),(3,2),(4,3),(6,5)],7) [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,7,4,6]=>([(0,5),(0,6),(1,3),(2,6),(3,4),(4,2),(4,5)],7)=>([(0,5),(0,6),(1,3),(1,6),(3,5),(4,2),(5,4)],7) [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,7,4,6]=>([(0,2),(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,3)],7)=>([(0,3),(0,6),(1,4),(1,6),(2,5),(3,4),(4,2),(6,5)],7) [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,7,4,6]=>([(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,2),(4,3)],7)=>([(0,3),(0,6),(1,5),(1,6),(3,5),(4,2),(5,4),(6,4)],7) [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6]=>([(0,5),(2,6),(3,2),(4,1),(4,6),(5,3),(5,4)],7)=>([(0,5),(1,4),(1,5),(3,6),(4,3),(5,6),(6,2)],7) [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,7,6]=>([(0,5),(0,6),(1,4),(2,5),(2,6),(3,2),(4,3)],7)=>([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(6,3)],7) [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,7,6]=>([(0,2),(0,4),(1,5),(1,6),(2,5),(2,6),(3,1),(4,3)],7)=>([(0,5),(0,6),(1,5),(1,6),(2,3),(3,4),(5,2),(6,4)],7) [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,7,6]=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1),(4,3)],7)=>([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7) [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,7,6]=>([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2)],7)=>([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7) [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,7,4,6]=>([(0,4),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3)],7)=>([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7) [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,7]=>([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7)=>([(0,6),(3,5),(4,3),(5,1),(6,2),(6,4)],7) [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,6,7]=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7)=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7) [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,5,3,4,6,7]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7) [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,7]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7) [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,3,5,6,4,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,6,7,4]=>([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7)=>([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],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),(3,4),(4,2),(5,3)],7)=>([(0,5),(1,3),(1,6),(2,6),(4,2),(5,4)],7) [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>([(0,6),(1,3),(4,5),(5,2),(6,4)],7)=>([(0,6),(1,3),(4,5),(5,2),(6,4)],7) [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,1,2,7,3,4,5]=>([(0,6),(1,5),(3,4),(4,2),(5,3),(5,6)],7)=>([(0,5),(1,4),(1,6),(2,6),(5,2),(6,3)],7) [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,6,2,7,3,4,5]=>([(0,2),(0,5),(2,6),(3,4),(4,1),(5,3),(5,6)],7)=>([(0,3),(0,6),(1,4),(2,6),(3,5),(4,2),(6,5)],7) [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,7,2,3,4,5]=>([(0,5),(0,6),(3,4),(4,2),(5,3),(6,1)],7)=>([(0,5),(1,3),(2,6),(3,6),(4,2),(5,4)],7) [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,1,2,3,7,4,5]=>([(0,6),(1,4),(3,2),(4,5),(5,3),(5,6)],7)=>([(0,4),(1,3),(1,6),(4,6),(5,2),(6,5)],7) [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,6,2,3,7,4,5]=>([(0,2),(0,5),(2,6),(3,1),(4,3),(4,6),(5,4)],7)=>([(0,3),(1,4),(1,6),(2,5),(3,6),(4,5),(6,2)],7) [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,6,3,7,4,5]=>([(0,5),(2,6),(3,1),(4,3),(4,6),(5,2),(5,4)],7)=>([(0,4),(1,3),(1,5),(3,6),(4,5),(5,6),(6,2)],7) [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,6,7,3,4,5]=>([(0,6),(3,4),(4,1),(5,2),(6,3),(6,5)],7)=>([(0,4),(1,5),(2,6),(4,6),(5,2),(6,3)],7) [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,1,2,3,4,7,5]=>([(0,6),(1,4),(3,5),(4,3),(5,2),(5,6)],7)=>([(0,6),(1,3),(1,6),(4,2),(5,4),(6,5)],7) [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,3,4,7,5]=>([(0,2),(0,5),(2,6),(3,4),(4,1),(4,6),(5,3)],7)=>([(0,6),(1,3),(1,6),(2,5),(3,5),(4,2),(6,4)],7) [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,6,3,4,7,5]=>([(0,5),(2,6),(3,4),(4,1),(4,6),(5,2),(5,3)],7)=>([(0,6),(1,3),(1,6),(2,5),(3,5),(5,4),(6,2)],7) [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,2,3,6,4,7,5]=>([(0,4),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3)],7)=>([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7) [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,2,3,6,7,4,5]=>([(0,5),(3,2),(4,1),(5,6),(6,3),(6,4)],7)=>([(0,4),(1,3),(3,6),(4,6),(5,2),(6,5)],7) [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7]=>([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7)=>([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7) [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5,7]=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7)=>([(0,2),(0,5),(1,6),(2,6),(3,4),(4,1),(5,3)],7) [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5,7]=>([(0,5),(1,6),(2,6),(3,4),(4,2),(5,1),(5,3)],7)=>([(0,3),(0,5),(1,6),(3,6),(4,1),(5,4),(6,2)],7) [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5,7]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7) [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,7]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7) [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,6,7,5]=>([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7)=>([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>([(1,6),(3,5),(4,3),(5,2),(6,4)],7)=>([(1,6),(3,5),(4,3),(5,2),(6,4)],7) [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,7,2,3,4,5,6]=>([(0,2),(0,6),(3,5),(4,3),(5,1),(6,4)],7)=>([(0,6),(1,5),(2,6),(3,4),(4,2),(5,3)],7) [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,7,3,4,5,6]=>([(0,6),(3,5),(4,3),(5,1),(6,2),(6,4)],7)=>([(0,6),(1,5),(2,6),(4,2),(5,4),(6,3)],7) [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,3,7,4,5,6]=>([(0,5),(3,4),(4,1),(5,6),(6,2),(6,3)],7)=>([(0,6),(1,4),(3,6),(4,3),(5,2),(6,5)],7) [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,6]=>([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7)=>([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7) [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,7,6]=>([(0,5),(3,4),(4,6),(5,3),(6,1),(6,2)],7)=>([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7) [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>([(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) [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)=>([(0,7),(2,4),(3,2),(4,6),(5,3),(6,1),(7,5)],8)
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
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
dual poset
Description
The dual of a poset.
The dual (or opposite) of a poset $(\mathcal P,\leq)$ is the poset $(\mathcal P^d,\leq_d)$ with $x \leq_d y$ if $y \leq x$.