Identifier
Mp00242: Dyck paths Hessenberg posetPosets
Mp00205: Posets maximal antichains Lattices
Images
=>
Cc0005;cc-rep-0Cc0014;cc-rep-1Cc0029;cc-rep-2
[1,0]=>([],1)=>([],1) [1,0,1,0]=>([(0,1)],2)=>([(0,1)],2) [1,1,0,0]=>([],2)=>([],1) [1,0,1,0,1,0]=>([(0,2),(2,1)],3)=>([(0,2),(2,1)],3) [1,0,1,1,0,0]=>([(0,2),(1,2)],3)=>([(0,1)],2) [1,1,0,0,1,0]=>([(0,1),(0,2)],3)=>([(0,1)],2) [1,1,0,1,0,0]=>([(1,2)],3)=>([(0,1)],2) [1,1,1,0,0,0]=>([],3)=>([],1) [1,0,1,0,1,0,1,0]=>([(0,3),(2,1),(3,2)],4)=>([(0,3),(2,1),(3,2)],4) [1,0,1,0,1,1,0,0]=>([(0,3),(1,3),(3,2)],4)=>([(0,2),(2,1)],3) [1,0,1,1,0,0,1,0]=>([(0,1),(0,2),(1,3),(2,3)],4)=>([(0,2),(2,1)],3) [1,0,1,1,0,1,0,0]=>([(0,3),(1,2),(2,3)],4)=>([(0,2),(2,1)],3) [1,0,1,1,1,0,0,0]=>([(0,3),(1,3),(2,3)],4)=>([(0,1)],2) [1,1,0,0,1,0,1,0]=>([(0,3),(3,1),(3,2)],4)=>([(0,2),(2,1)],3) [1,1,0,0,1,1,0,0]=>([(0,2),(0,3),(1,2),(1,3)],4)=>([(0,1)],2) [1,1,0,1,0,0,1,0]=>([(0,2),(0,3),(3,1)],4)=>([(0,2),(2,1)],3) [1,1,0,1,0,1,0,0]=>([(0,3),(1,2),(1,3)],4)=>([(0,2),(2,1)],3) [1,1,0,1,1,0,0,0]=>([(1,3),(2,3)],4)=>([(0,1)],2) [1,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3)],4)=>([(0,1)],2) [1,1,1,0,0,1,0,0]=>([(1,2),(1,3)],4)=>([(0,1)],2) [1,1,1,0,1,0,0,0]=>([(2,3)],4)=>([(0,1)],2) [1,1,1,1,0,0,0,0]=>([],4)=>([],1) [1,0,1,0,1,0,1,0,1,0]=>([(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]=>([(0,4),(1,4),(2,3),(4,2)],5)=>([(0,3),(2,1),(3,2)],4) [1,0,1,0,1,1,0,0,1,0]=>([(0,2),(0,3),(2,4),(3,4),(4,1)],5)=>([(0,3),(2,1),(3,2)],4) [1,0,1,0,1,1,0,1,0,0]=>([(0,4),(1,2),(2,4),(4,3)],5)=>([(0,3),(2,1),(3,2)],4) [1,0,1,0,1,1,1,0,0,0]=>([(0,4),(1,4),(2,4),(4,3)],5)=>([(0,2),(2,1)],3) [1,0,1,1,0,0,1,0,1,0]=>([(0,3),(1,4),(2,4),(3,1),(3,2)],5)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,0,0,1,1,0,0]=>([(0,3),(0,4),(1,3),(1,4),(3,2),(4,2)],5)=>([(0,2),(2,1)],3) [1,0,1,1,0,1,0,0,1,0]=>([(0,2),(0,3),(1,4),(2,4),(3,1)],5)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,0,1,0,1,0,0]=>([(0,3),(1,2),(1,3),(2,4),(3,4)],5)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,0,1,1,0,0,0]=>([(0,4),(1,3),(2,3),(3,4)],5)=>([(0,2),(2,1)],3) [1,0,1,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,4)],5)=>([(0,2),(2,1)],3) [1,0,1,1,1,0,0,1,0,0]=>([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>([(0,2),(2,1)],3) [1,0,1,1,1,0,1,0,0,0]=>([(0,4),(1,4),(2,3),(3,4)],5)=>([(0,2),(2,1)],3) [1,0,1,1,1,1,0,0,0,0]=>([(0,4),(1,4),(2,4),(3,4)],5)=>([(0,1)],2) [1,1,0,0,1,0,1,0,1,0]=>([(0,3),(3,4),(4,1),(4,2)],5)=>([(0,3),(2,1),(3,2)],4) [1,1,0,0,1,0,1,1,0,0]=>([(0,4),(1,4),(4,2),(4,3)],5)=>([(0,2),(2,1)],3) [1,1,0,0,1,1,0,0,1,0]=>([(0,1),(0,2),(1,3),(1,4),(2,3),(2,4)],5)=>([(0,2),(2,1)],3) [1,1,0,0,1,1,0,1,0,0]=>([(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]=>([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>([(0,1)],2) [1,1,0,1,0,0,1,0,1,0]=>([(0,4),(3,2),(4,1),(4,3)],5)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,0,1,1,0,0]=>([(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]=>([(0,2),(0,3),(2,4),(3,1),(3,4)],5)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,1,0,1,0,0]=>([(0,3),(0,4),(1,2),(1,3),(2,4)],5)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,1,1,0,0,0]=>([(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>([(0,2),(2,1)],3) [1,1,0,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(2,4),(3,4)],5)=>([(0,2),(2,1)],3) [1,1,0,1,1,0,0,1,0,0]=>([(0,4),(1,2),(1,3),(3,4)],5)=>([(0,2),(2,1)],3) [1,1,0,1,1,0,1,0,0,0]=>([(0,4),(1,4),(2,3),(2,4)],5)=>([(0,2),(2,1)],3) [1,1,0,1,1,1,0,0,0,0]=>([(1,4),(2,4),(3,4)],5)=>([(0,1)],2) [1,1,1,0,0,0,1,0,1,0]=>([(0,4),(4,1),(4,2),(4,3)],5)=>([(0,2),(2,1)],3) [1,1,1,0,0,0,1,1,0,0]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4)],5)=>([(0,1)],2) [1,1,1,0,0,1,0,0,1,0]=>([(0,3),(0,4),(4,1),(4,2)],5)=>([(0,2),(2,1)],3) [1,1,1,0,0,1,0,1,0,0]=>([(0,3),(0,4),(1,2),(1,3),(1,4)],5)=>([(0,2),(2,1)],3) [1,1,1,0,0,1,1,0,0,0]=>([(1,3),(1,4),(2,3),(2,4)],5)=>([(0,1)],2) [1,1,1,0,1,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(4,1)],5)=>([(0,2),(2,1)],3) [1,1,1,0,1,0,0,1,0,0]=>([(0,4),(1,2),(1,3),(1,4)],5)=>([(0,2),(2,1)],3) [1,1,1,0,1,0,1,0,0,0]=>([(1,4),(2,3),(2,4)],5)=>([(0,2),(2,1)],3) [1,1,1,0,1,1,0,0,0,0]=>([(2,4),(3,4)],5)=>([(0,1)],2) [1,1,1,1,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4)],5)=>([(0,1)],2) [1,1,1,1,0,0,0,1,0,0]=>([(1,2),(1,3),(1,4)],5)=>([(0,1)],2) [1,1,1,1,0,0,1,0,0,0]=>([(2,3),(2,4)],5)=>([(0,1)],2) [1,1,1,1,0,1,0,0,0,0]=>([(3,4)],5)=>([(0,1)],2) [1,1,1,1,1,0,0,0,0,0]=>([],5)=>([],1) [1,0,1,0,1,0,1,0,1,0,1,0]=>([(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]=>([(0,5),(1,5),(3,2),(4,3),(5,4)],6)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,0,1,0,1,1,0,0,1,0]=>([(0,2),(0,3),(2,5),(3,5),(4,1),(5,4)],6)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,0,1,0,1,1,0,1,0,0]=>([(0,5),(1,3),(3,5),(4,2),(5,4)],6)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,0,1,0,1,1,1,0,0,0]=>([(0,5),(1,5),(2,5),(3,4),(5,3)],6)=>([(0,3),(2,1),(3,2)],4) [1,0,1,0,1,1,0,0,1,0,1,0]=>([(0,4),(1,5),(2,5),(4,1),(4,2),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,0,1,1,0,0,1,1,0,0]=>([(0,4),(0,5),(1,4),(1,5),(3,2),(4,3),(5,3)],6)=>([(0,3),(2,1),(3,2)],4) [1,0,1,0,1,1,0,1,0,0,1,0]=>([(0,3),(0,4),(1,5),(3,5),(4,1),(5,2)],6)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,0,1,1,0,1,0,1,0,0]=>([(0,4),(1,2),(1,4),(2,5),(4,5),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,0,1,1,0,1,1,0,0,0]=>([(0,5),(1,4),(2,4),(4,5),(5,3)],6)=>([(0,3),(2,1),(3,2)],4) [1,0,1,0,1,1,1,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(2,5),(3,5),(4,5),(5,1)],6)=>([(0,3),(2,1),(3,2)],4) [1,0,1,0,1,1,1,0,0,1,0,0]=>([(0,5),(1,2),(1,3),(2,5),(3,5),(5,4)],6)=>([(0,3),(2,1),(3,2)],4) [1,0,1,0,1,1,1,0,1,0,0,0]=>([(0,5),(1,5),(2,3),(3,5),(5,4)],6)=>([(0,3),(2,1),(3,2)],4) [1,0,1,0,1,1,1,1,0,0,0,0]=>([(0,5),(1,5),(2,5),(3,5),(5,4)],6)=>([(0,2),(2,1)],3) [1,0,1,1,0,0,1,0,1,0,1,0]=>([(0,3),(1,5),(2,5),(3,4),(4,1),(4,2)],6)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,0,0,1,0,1,1,0,0]=>([(0,4),(1,4),(2,5),(3,5),(4,2),(4,3)],6)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,0,0,1,1,0,0,1,0]=>([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,0,0,1,1,0,1,0,0]=>([(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,0,0,1,1,1,0,0,0]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)=>([(0,2),(2,1)],3) [1,0,1,1,0,1,0,0,1,0,1,0]=>([(0,4),(1,5),(2,5),(3,2),(4,1),(4,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,0,1,0,0,1,1,0,0]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(4,2),(5,3)],6)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,0,1,0,1,0,0,1,0]=>([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,0,1,0,1,0,1,0,0]=>([(0,2),(0,5),(1,4),(1,5),(2,4),(4,3),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,0,1,0,1,1,0,0,0]=>([(0,5),(1,3),(1,5),(2,3),(2,5),(3,4),(5,4)],6)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,0,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(1,5),(2,4),(3,4),(4,5)],6)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,0,1,1,0,0,1,0,0]=>([(0,4),(1,2),(1,3),(2,5),(3,4),(4,5)],6)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,0,1,1,0,1,0,0,0]=>([(0,5),(1,5),(2,3),(2,5),(3,4),(5,4)],6)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,0,1,1,1,0,0,0,0]=>([(0,5),(1,5),(2,5),(3,4),(5,4)],6)=>([(0,2),(2,1)],3) [1,0,1,1,1,0,0,0,1,0,1,0]=>([(0,4),(1,5),(2,5),(3,5),(4,1),(4,2),(4,3)],6)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,0,0,0,1,1,0,0]=>([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>([(0,2),(2,1)],3) [1,0,1,1,1,0,0,1,0,0,1,0]=>([(0,3),(0,4),(1,5),(2,5),(3,5),(4,1),(4,2)],6)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,0,0,1,0,1,0,0]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,0,0,1,1,0,0,0]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,2),(2,1)],3) [1,0,1,1,1,0,1,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,1)],6)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,0,1,0,0,1,0,0]=>([(0,4),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,0,1,0,1,0,0,0]=>([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,0,1,1,0,0,0,0]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>([(0,2),(2,1)],3) [1,0,1,1,1,1,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(1,5),(2,5),(3,5),(4,5)],6)=>([(0,2),(2,1)],3) [1,0,1,1,1,1,0,0,0,1,0,0]=>([(0,5),(1,2),(1,3),(1,4),(2,5),(3,5),(4,5)],6)=>([(0,2),(2,1)],3) [1,0,1,1,1,1,0,0,1,0,0,0]=>([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>([(0,2),(2,1)],3) [1,0,1,1,1,1,0,1,0,0,0,0]=>([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>([(0,2),(2,1)],3) [1,0,1,1,1,1,1,0,0,0,0,0]=>([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,0,0,1,0,1,0,1,0,1,0]=>([(0,4),(3,5),(4,3),(5,1),(5,2)],6)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,0,1,0,1,0,1,1,0,0]=>([(0,5),(1,5),(4,2),(4,3),(5,4)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,0,0,1,0,1,1,0,0,1,0]=>([(0,3),(0,4),(3,5),(4,5),(5,1),(5,2)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,0,0,1,0,1,1,0,1,0,0]=>([(0,5),(1,2),(2,5),(5,3),(5,4)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,0,0,1,0,1,1,1,0,0,0]=>([(0,5),(1,5),(2,5),(5,3),(5,4)],6)=>([(0,2),(2,1)],3) [1,1,0,0,1,1,0,0,1,0,1,0]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,0,0,1,1,0,0,1,1,0,0]=>([(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]=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,0,0,1,1,0,1,0,1,0,0]=>([(0,5),(1,2),(1,5),(2,3),(2,4),(5,3),(5,4)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,0,0,1,1,0,1,1,0,0,0]=>([(0,3),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,2),(2,1)],3) [1,1,0,0,1,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,2),(2,1)],3) [1,1,0,0,1,1,1,0,0,1,0,0]=>([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,2),(2,1)],3) [1,1,0,0,1,1,1,0,1,0,0,0]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(3,4),(3,5)],6)=>([(0,2),(2,1)],3) [1,1,0,0,1,1,1,1,0,0,0,0]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2) [1,1,0,1,0,0,1,0,1,0,1,0]=>([(0,4),(3,2),(4,5),(5,1),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,0,0,1,0,1,1,0,0]=>([(0,5),(1,5),(4,2),(5,3),(5,4)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,0,1,1,0,0,1,0]=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(5,1)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,0,1,1,0,1,0,0]=>([(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]=>([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(5,3)],6)=>([(0,2),(2,1)],3) [1,1,0,1,0,1,0,0,1,0,1,0]=>([(0,4),(2,5),(3,1),(3,5),(4,2),(4,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,0,1,0,0,1,1,0,0]=>([(0,4),(0,5),(1,4),(1,5),(4,3),(5,2),(5,3)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,1,0,1,0,0,1,0]=>([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5)],6)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,0,1,0,1,0,1,0,0]=>([(0,2),(0,5),(1,4),(1,5),(2,3),(2,4),(5,3)],6)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,0,1,0,1,1,0,0,0]=>([(0,4),(0,5),(1,3),(1,5),(2,3),(2,5),(3,4)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,1,1,0,0,1,0,0]=>([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4),(3,5)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,1,1,0,1,0,0,0]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,1,1,1,0,0,0,0]=>([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,2),(2,1)],3) [1,1,0,1,1,0,0,0,1,0,1,0]=>([(0,4),(2,5),(3,5),(4,1),(4,2),(4,3)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,0,0,0,1,1,0,0]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(4,2),(5,2)],6)=>([(0,2),(2,1)],3) [1,1,0,1,1,0,0,1,0,0,1,0]=>([(0,3),(0,4),(2,5),(3,5),(4,1),(4,2)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,0,0,1,0,1,0,0]=>([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(5,3)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,0,0,1,1,0,0,0]=>([(0,5),(1,3),(1,4),(2,3),(2,4),(4,5)],6)=>([(0,2),(2,1)],3) [1,1,0,1,1,0,1,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(2,5),(3,5),(4,1),(4,5)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,0,1,0,0,1,0,0]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,5)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,0,1,0,1,0,0,0]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(3,5)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,0,1,1,0,0,0,0]=>([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,2),(2,1)],3) [1,1,0,1,1,1,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(2,5),(3,5),(4,5)],6)=>([(0,2),(2,1)],3) [1,1,0,1,1,1,0,0,0,1,0,0]=>([(0,5),(1,2),(1,3),(1,4),(3,5),(4,5)],6)=>([(0,2),(2,1)],3) [1,1,0,1,1,1,0,0,1,0,0,0]=>([(0,5),(1,5),(2,3),(2,4),(4,5)],6)=>([(0,2),(2,1)],3) [1,1,0,1,1,1,0,1,0,0,0,0]=>([(0,5),(1,5),(2,5),(3,4),(3,5)],6)=>([(0,2),(2,1)],3) [1,1,0,1,1,1,1,0,0,0,0,0]=>([(1,5),(2,5),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,1,0,0,0,1,0,1,0,1,0]=>([(0,4),(4,5),(5,1),(5,2),(5,3)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,0,0,1,0,1,1,0,0]=>([(0,5),(1,5),(5,2),(5,3),(5,4)],6)=>([(0,2),(2,1)],3) [1,1,1,0,0,0,1,1,0,0,1,0]=>([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>([(0,2),(2,1)],3) [1,1,1,0,0,0,1,1,0,1,0,0]=>([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>([(0,2),(2,1)],3) [1,1,1,0,0,0,1,1,1,0,0,0]=>([(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]=>([(0,5),(4,2),(4,3),(5,1),(5,4)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,0,1,0,0,1,1,0,0]=>([(0,4),(0,5),(1,4),(1,5),(5,2),(5,3)],6)=>([(0,2),(2,1)],3) [1,1,1,0,0,1,0,1,0,0,1,0]=>([(0,2),(0,3),(2,4),(2,5),(3,1),(3,4),(3,5)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,0,1,0,1,0,1,0,0]=>([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,0,1,0,1,1,0,0,0]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>([(0,2),(2,1)],3) [1,1,1,0,0,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,2),(2,1)],3) [1,1,1,0,0,1,1,0,0,1,0,0]=>([(0,4),(0,5),(1,2),(1,3),(3,4),(3,5)],6)=>([(0,2),(2,1)],3) [1,1,1,0,0,1,1,0,1,0,0,0]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>([(0,2),(2,1)],3) [1,1,1,0,0,1,1,1,0,0,0,0]=>([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2) [1,1,1,0,1,0,0,0,1,0,1,0]=>([(0,5),(4,3),(5,1),(5,2),(5,4)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,0,0,0,1,1,0,0]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(5,2)],6)=>([(0,2),(2,1)],3) [1,1,1,0,1,0,0,1,0,0,1,0]=>([(0,3),(0,4),(3,5),(4,1),(4,2),(4,5)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,0,0,1,0,1,0,0]=>([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,0,0,1,1,0,0,0]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>([(0,2),(2,1)],3) [1,1,1,0,1,0,1,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(3,5),(4,1),(4,5)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,0,1,0,0,1,0,0]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(3,5)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,0,1,0,1,0,0,0]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,0,1,1,0,0,0,0]=>([(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>([(0,2),(2,1)],3) [1,1,1,0,1,1,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(3,5),(4,5)],6)=>([(0,2),(2,1)],3) [1,1,1,0,1,1,0,0,0,1,0,0]=>([(0,5),(1,2),(1,3),(1,4),(4,5)],6)=>([(0,2),(2,1)],3) [1,1,1,0,1,1,0,0,1,0,0,0]=>([(0,5),(1,5),(2,3),(2,4),(2,5)],6)=>([(0,2),(2,1)],3) [1,1,1,0,1,1,0,1,0,0,0,0]=>([(1,5),(2,5),(3,4),(3,5)],6)=>([(0,2),(2,1)],3) [1,1,1,0,1,1,1,0,0,0,0,0]=>([(2,5),(3,5),(4,5)],6)=>([(0,1)],2) [1,1,1,1,0,0,0,0,1,0,1,0]=>([(0,5),(5,1),(5,2),(5,3),(5,4)],6)=>([(0,2),(2,1)],3) [1,1,1,1,0,0,0,0,1,1,0,0]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)=>([(0,1)],2) [1,1,1,1,0,0,0,1,0,0,1,0]=>([(0,4),(0,5),(5,1),(5,2),(5,3)],6)=>([(0,2),(2,1)],3) [1,1,1,1,0,0,0,1,0,1,0,0]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)=>([(0,2),(2,1)],3) [1,1,1,1,0,0,0,1,1,0,0,0]=>([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>([(0,1)],2) [1,1,1,1,0,0,1,0,0,0,1,0]=>([(0,3),(0,4),(0,5),(5,1),(5,2)],6)=>([(0,2),(2,1)],3) [1,1,1,1,0,0,1,0,0,1,0,0]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5)],6)=>([(0,2),(2,1)],3) [1,1,1,1,0,0,1,0,1,0,0,0]=>([(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>([(0,2),(2,1)],3) [1,1,1,1,0,0,1,1,0,0,0,0]=>([(2,4),(2,5),(3,4),(3,5)],6)=>([(0,1)],2) [1,1,1,1,0,1,0,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(0,5),(5,1)],6)=>([(0,2),(2,1)],3) [1,1,1,1,0,1,0,0,0,1,0,0]=>([(0,5),(1,2),(1,3),(1,4),(1,5)],6)=>([(0,2),(2,1)],3) [1,1,1,1,0,1,0,0,1,0,0,0]=>([(1,5),(2,3),(2,4),(2,5)],6)=>([(0,2),(2,1)],3) [1,1,1,1,0,1,0,1,0,0,0,0]=>([(2,5),(3,4),(3,5)],6)=>([(0,2),(2,1)],3) [1,1,1,1,0,1,1,0,0,0,0,0]=>([(3,5),(4,5)],6)=>([(0,1)],2) [1,1,1,1,1,0,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(0,5)],6)=>([(0,1)],2) [1,1,1,1,1,0,0,0,0,1,0,0]=>([(1,2),(1,3),(1,4),(1,5)],6)=>([(0,1)],2) [1,1,1,1,1,0,0,0,1,0,0,0]=>([(2,3),(2,4),(2,5)],6)=>([(0,1)],2) [1,1,1,1,1,0,0,1,0,0,0,0]=>([(3,4),(3,5)],6)=>([(0,1)],2) [1,1,1,1,1,0,1,0,0,0,0,0]=>([(4,5)],6)=>([(0,1)],2) [1,1,1,1,1,1,0,0,0,0,0,0]=>([],6)=>([],1) [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>([(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]=>([(0,6),(1,6),(3,4),(4,2),(5,3),(6,5)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>([(0,2),(0,3),(2,6),(3,6),(4,1),(5,4),(6,5)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>([(0,6),(1,3),(3,6),(4,2),(5,4),(6,5)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>([(0,6),(1,6),(2,6),(3,5),(5,4),(6,3)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>([(0,5),(2,6),(3,6),(4,1),(5,2),(5,3),(6,4)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(4,2),(5,4),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>([(0,3),(0,5),(2,6),(3,6),(4,1),(5,2),(6,4)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>([(0,6),(1,3),(1,6),(3,5),(4,2),(5,4),(6,5)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>([(0,6),(1,5),(2,5),(3,4),(5,6),(6,3)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(2,6),(3,6),(4,6),(5,1),(6,5)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>([(0,6),(1,3),(1,4),(3,6),(4,6),(5,2),(6,5)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>([(0,6),(1,6),(2,3),(3,6),(4,5),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>([(0,4),(1,6),(2,6),(4,5),(5,1),(5,2),(6,3)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>([(0,6),(1,6),(2,5),(3,5),(5,4),(6,2),(6,3)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>([(0,2),(0,3),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6),(6,1)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>([(0,3),(1,5),(1,6),(3,5),(3,6),(4,2),(5,4),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>([(0,5),(1,6),(2,6),(4,2),(5,1),(5,4),(6,3)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>([(0,5),(0,6),(1,5),(1,6),(3,4),(4,2),(5,3),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>([(0,3),(0,4),(2,6),(3,5),(4,2),(4,5),(5,6),(6,1)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>([(0,3),(0,6),(1,5),(1,6),(3,5),(4,2),(5,4),(6,4)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>([(0,6),(1,4),(1,6),(2,4),(2,6),(4,5),(5,3),(6,5)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(2,6),(3,5),(4,5),(5,6),(6,1)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>([(0,5),(1,3),(1,4),(3,6),(4,5),(5,6),(6,2)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>([(0,6),(1,6),(2,3),(2,6),(3,5),(5,4),(6,5)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,5),(5,4),(6,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>([(0,5),(1,6),(2,6),(3,6),(5,1),(5,2),(5,3),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6),(6,2)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>([(0,4),(0,5),(1,6),(2,6),(4,6),(5,1),(5,2),(6,3)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>([(0,4),(0,5),(1,2),(1,4),(1,5),(2,6),(4,6),(5,6),(6,3)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>([(0,6),(1,4),(1,5),(2,4),(2,5),(4,6),(5,6),(6,3)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>([(0,3),(0,4),(0,5),(1,6),(3,6),(4,6),(5,1),(6,2)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>([(0,5),(1,2),(1,3),(1,5),(2,6),(3,6),(5,6),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>([(0,6),(1,5),(2,3),(2,5),(3,6),(5,6),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>([(0,6),(1,6),(2,5),(3,5),(5,6),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6),(6,1)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>([(0,6),(1,6),(2,3),(2,4),(3,6),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,4),(4,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(6,5)],7)=>([(0,2),(2,1)],3) [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>([(0,4),(1,6),(2,6),(3,5),(4,3),(5,1),(5,2)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>([(0,6),(1,6),(2,5),(3,5),(4,2),(4,3),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>([(0,3),(0,4),(1,5),(2,5),(3,6),(4,6),(6,1),(6,2)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>([(0,6),(1,2),(2,6),(3,5),(4,5),(6,3),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(6,3),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>([(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(3,2),(4,6),(5,6)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>([(0,5),(0,6),(1,5),(1,6),(3,2),(4,2),(5,3),(5,4),(6,3),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,1),(4,6),(5,6)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>([(0,6),(1,2),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>([(0,6),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4),(6,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>([(0,5),(0,6),(1,2),(1,3),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(3,5),(3,6),(5,4),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)=>([(0,2),(2,1)],3) [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>([(0,4),(1,6),(2,6),(3,2),(4,5),(5,1),(5,3)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>([(0,6),(1,6),(2,5),(3,5),(4,3),(6,2),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>([(0,2),(0,3),(1,5),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>([(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(4,2),(6,5)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(5,4),(6,3)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>([(0,4),(1,6),(2,5),(3,1),(3,5),(4,2),(4,3),(5,6)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(4,3),(5,4),(6,2),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>([(0,2),(0,3),(1,4),(2,4),(2,5),(3,1),(3,5),(4,6),(5,6)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(4,3),(5,3),(6,4)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>([(0,3),(0,6),(1,3),(1,6),(2,5),(2,6),(3,5),(5,4),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>([(0,5),(0,6),(1,2),(1,3),(2,6),(3,5),(3,6),(5,4),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,6),(5,4),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(5,4),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>([(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(4,3),(5,6)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(3,2),(4,3),(5,3),(6,2)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>([(0,3),(0,4),(1,6),(2,5),(3,5),(4,1),(4,2),(5,6)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>([(0,5),(0,6),(1,2),(1,5),(1,6),(2,4),(4,3),(5,4),(6,3)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>([(0,4),(1,5),(1,6),(2,5),(2,6),(4,3),(5,4),(6,3)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(1,5),(2,6),(3,6),(4,1),(4,6),(6,5)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>([(0,4),(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(6,5)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>([(0,6),(1,4),(1,6),(2,3),(2,4),(3,6),(4,5),(6,5)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>([(0,6),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,6),(4,5),(6,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>([(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(6,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>([(0,6),(1,6),(2,3),(2,4),(3,6),(4,5),(6,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,4),(3,6),(4,5),(6,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(6,5)],7)=>([(0,2),(2,1)],3) [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>([(0,4),(1,6),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>([(0,5),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3),(5,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>([(0,1),(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>([(0,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>([(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)=>([(0,2),(2,1)],3) [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>([(0,5),(1,6),(2,6),(3,6),(4,2),(4,3),(5,1),(5,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>([(0,4),(0,5),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2),(5,3)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(4,6),(5,6)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,6),(4,6),(5,6)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>([(0,4),(0,5),(1,2),(1,3),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>([(0,6),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>([(0,2),(2,1)],3) [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>([(0,5),(1,6),(2,6),(3,6),(4,3),(5,1),(5,2),(5,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,2)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>([(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,2),(4,5),(5,6)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(3,6),(4,6),(5,6)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,1),(4,5),(5,6)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(3,6),(4,6),(5,6)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>([(0,6),(1,5),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>([(0,5),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>([(0,5),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>([(0,6),(1,5),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(5,6)],7)=>([(0,2),(2,1)],3) [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>([(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>([(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)=>([(0,2),(2,1)],3) [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>([(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>([(0,2),(2,1)],3) [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>([(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1),(5,2)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>([(0,2),(2,1)],3) [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,1)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>([(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>([(0,6),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>([(0,6),(1,6),(2,5),(3,4),(3,5),(4,6),(5,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)=>([(0,2),(2,1)],3) [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(0,2),(2,1)],3) [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>([(0,6),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6),(5,6)],7)=>([(0,2),(2,1)],3) [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6),(5,6)],7)=>([(0,2),(2,1)],3) [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)=>([(0,2),(2,1)],3) [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)=>([(0,2),(2,1)],3) [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(0,1)],2) [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>([(0,5),(3,4),(4,6),(5,3),(6,1),(6,2)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>([(0,6),(1,6),(4,5),(5,2),(5,3),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>([(0,3),(0,4),(3,6),(4,6),(5,1),(5,2),(6,5)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>([(0,6),(1,4),(4,6),(5,2),(5,3),(6,5)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(6,3)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>([(0,5),(1,6),(2,6),(5,1),(5,2),(6,3),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>([(0,5),(0,6),(1,5),(1,6),(4,2),(4,3),(5,4),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>([(0,4),(0,5),(1,6),(4,6),(5,1),(6,2),(6,3)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>([(0,5),(1,4),(1,5),(4,6),(5,6),(6,2),(6,3)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>([(0,6),(1,5),(2,5),(5,6),(6,3),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>([(0,3),(0,4),(0,5),(3,6),(4,6),(5,6),(6,1),(6,2)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>([(0,6),(1,2),(1,3),(2,6),(3,6),(6,4),(6,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>([(0,6),(1,6),(2,3),(3,6),(6,4),(6,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,6),(6,4),(6,5)],7)=>([(0,2),(2,1)],3) [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>([(0,3),(1,5),(1,6),(2,5),(2,6),(3,4),(4,1),(4,2)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(6,2),(6,3)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>([(0,1),(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) [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>([(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]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,3),(5,4),(6,3),(6,4)],7)=>([(0,2),(2,1)],3) [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,2),(4,1),(4,3)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>([(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]=>([(0,2),(0,3),(1,5),(1,6),(2,4),(3,1),(3,4),(4,5),(4,6)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>([(0,2),(0,6),(1,5),(1,6),(2,5),(5,3),(5,4),(6,3),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>([(0,6),(1,3),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(1,4),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>([(0,2),(0,3),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>([(0,6),(1,6),(2,3),(2,6),(3,4),(3,5),(6,4),(6,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(6,4),(6,5)],7)=>([(0,2),(2,1)],3) [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>([(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>([(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)=>([(0,2),(2,1)],3) [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>([(0,3),(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,2),(2,1)],3) [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>([(0,4),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>([(0,5),(0,6),(1,4),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(3,4),(4,5),(4,6)],7)=>([(0,2),(2,1)],3) [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>([(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)=>([(0,2),(2,1)],3) [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,2),(2,1)],3) [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,2),(2,1)],3) [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(4,5),(4,6)],7)=>([(0,2),(2,1)],3) [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,1)],2) [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>([(0,5),(3,6),(4,1),(5,3),(6,2),(6,4)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>([(0,6),(1,6),(4,3),(5,2),(5,4),(6,5)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>([(0,3),(0,4),(3,6),(4,6),(5,1),(6,2),(6,5)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>([(0,6),(1,3),(3,6),(5,2),(6,4),(6,5)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>([(0,6),(1,6),(2,6),(4,5),(6,3),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>([(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(4,3),(6,1)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>([(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]=>([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,2),(6,1)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>([(0,6),(1,3),(1,6),(3,4),(3,5),(5,2),(6,4),(6,5)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>([(0,5),(0,6),(1,4),(2,4),(4,5),(4,6),(6,3)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(6,1)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>([(0,5),(0,6),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6),(6,2)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(4,5),(4,6),(6,3)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(6,4)],7)=>([(0,2),(2,1)],3) [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>([(0,4),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>([(0,6),(1,6),(3,5),(4,2),(4,5),(6,3),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>([(0,2),(0,3),(2,4),(2,6),(3,4),(3,6),(4,5),(6,1),(6,5)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>([(0,3),(1,5),(1,6),(3,5),(3,6),(5,4),(6,2),(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]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(5,4),(6,3),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>([(0,4),(1,5),(2,5),(2,6),(3,1),(3,6),(4,2),(4,3)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(5,2),(5,3),(6,3),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>([(0,2),(0,3),(1,4),(1,6),(2,4),(2,5),(3,1),(3,5),(5,6)],7)=>([(0,5),(2,4),(3,2),(4,1),(5,3)],6) [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>([(0,2),(0,6),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3),(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]=>([(0,3),(0,6),(1,3),(1,6),(2,4),(2,6),(3,4),(3,5),(6,5)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>([(0,4),(0,6),(1,2),(1,3),(2,5),(2,6),(3,4),(3,6),(4,5)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(3,4),(3,6),(5,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,6),(5,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>([(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(3,6),(4,2),(4,6),(5,2),(5,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>([(0,3),(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>([(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,6),(4,6),(5,3),(5,6)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>([(0,5),(0,6),(1,3),(1,4),(2,3),(2,4),(3,6),(4,5),(4,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(1,5),(2,5),(2,6),(3,5),(3,6),(4,1),(4,6)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6),(4,6)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>([(0,5),(0,6),(1,4),(1,5),(2,3),(2,4),(3,5),(3,6),(4,6)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,6),(3,4),(3,6),(4,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(3,6),(4,5),(4,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,2),(2,1)],3) [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>([(0,4),(2,6),(3,6),(4,5),(5,1),(5,2),(5,3)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>([(0,6),(1,6),(3,5),(4,5),(6,2),(6,3),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>([(0,1),(0,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>([(0,2),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(5,3),(6,3)],7)=>([(0,2),(2,1)],3) [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>([(0,5),(2,6),(3,6),(4,1),(4,3),(5,2),(5,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>([(0,5),(0,6),(1,5),(1,6),(3,4),(5,2),(5,3),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>([(0,2),(0,3),(1,6),(2,4),(2,5),(3,1),(3,4),(3,5),(5,6)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>([(0,2),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(5,3),(6,3)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>([(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>([(0,2),(0,3),(1,4),(1,6),(2,5),(3,4),(3,6),(6,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(6,4)],7)=>([(0,2),(2,1)],3) [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>([(0,5),(2,6),(3,6),(4,1),(4,6),(5,2),(5,3),(5,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(3,6),(4,6),(5,2),(5,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>([(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,1),(4,2),(4,5)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>([(0,2),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,6),(4,6),(5,6)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>([(0,5),(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,1),(4,5)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6),(4,6)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>([(0,5),(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(4,6)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(3,4),(3,5),(4,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(2,6),(3,6),(4,5),(4,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,2),(2,1)],3) [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>([(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7)=>([(0,2),(2,1)],3) [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>([(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,2),(5,3)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(4,6),(5,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>([(0,6),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(4,6),(5,6)],7)=>([(0,2),(2,1)],3) [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>([(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,2)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(5,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>([(0,6),(1,4),(1,5),(2,3),(2,4),(2,5),(3,6),(5,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>([(0,6),(1,6),(2,4),(2,5),(3,4),(3,5),(5,6)],7)=>([(0,2),(2,1)],3) [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,1),(5,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6),(4,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6),(4,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(4,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,2),(2,1)],3) [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(2,6),(3,6),(4,6),(5,6)],7)=>([(0,2),(2,1)],3) [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>([(0,6),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6),(5,6)],7)=>([(0,2),(2,1)],3) [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(4,6),(5,6)],7)=>([(0,2),(2,1)],3) [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(5,6)],7)=>([(0,2),(2,1)],3) [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6)],7)=>([(0,2),(2,1)],3) [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>([(1,6),(2,6),(3,6),(4,6),(5,6)],7)=>([(0,1)],2) [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>([(0,5),(4,6),(5,4),(6,1),(6,2),(6,3)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>([(0,6),(1,6),(5,2),(5,3),(5,4),(6,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>([(0,4),(0,5),(4,6),(5,6),(6,1),(6,2),(6,3)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>([(0,6),(1,2),(2,6),(6,3),(6,4),(6,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>([(0,6),(1,6),(2,6),(6,3),(6,4),(6,5)],7)=>([(0,2),(2,1)],3) [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,1),(3,2)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>([(0,5),(0,6),(1,5),(1,6),(5,2),(5,3),(5,4),(6,2),(6,3),(6,4)],7)=>([(0,2),(2,1)],3) [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>([(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,1)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>([(0,6),(1,2),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4),(6,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4),(6,5)],7)=>([(0,2),(2,1)],3) [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>([(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)=>([(0,2),(2,1)],3) [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>([(0,2),(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,2),(2,1)],3) [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>([(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]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,1)],2) [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>([(0,4),(4,6),(5,2),(5,3),(6,1),(6,5)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>([(0,6),(1,6),(5,2),(5,3),(6,4),(6,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>([(0,3),(0,4),(3,5),(3,6),(4,5),(4,6),(6,1),(6,2)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>([(0,5),(0,6),(1,4),(4,5),(4,6),(6,2),(6,3)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7)=>([(0,2),(2,1)],3) [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>([(0,4),(2,5),(2,6),(3,1),(3,5),(3,6),(4,2),(4,3)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>([(0,5),(0,6),(1,5),(1,6),(5,3),(5,4),(6,2),(6,3),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>([(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(2,6),(3,1),(3,6)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>([(0,2),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(6,3),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>([(0,3),(0,6),(1,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>([(0,4),(0,5),(0,6),(1,2),(1,3),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,2),(2,1)],3) [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>([(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2),(4,3)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(5,2),(5,3),(6,2),(6,3)],7)=>([(0,2),(2,1)],3) [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>([(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,2)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>([(0,5),(0,6),(1,2),(1,5),(1,6),(2,3),(2,4),(6,3),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>([(0,3),(0,4),(1,5),(1,6),(2,5),(2,6),(6,3),(6,4)],7)=>([(0,2),(2,1)],3) [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(2,5),(2,6),(3,5),(3,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(3,5),(3,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,2),(2,1)],3) [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,2),(2,1)],3) [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,2),(2,1)],3) [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(4,5),(4,6)],7)=>([(0,2),(2,1)],3) [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,2),(2,1)],3) [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,1)],2) [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>([(0,5),(4,3),(5,6),(6,1),(6,2),(6,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>([(0,6),(1,6),(5,2),(6,3),(6,4),(6,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>([(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6),(6,1)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>([(0,3),(1,4),(1,5),(1,6),(3,4),(3,5),(3,6),(6,2)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>([(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]=>([(0,5),(3,6),(4,1),(4,2),(4,6),(5,3),(5,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>([(0,5),(0,6),(1,5),(1,6),(5,4),(6,2),(6,3),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>([(0,2),(0,3),(1,4),(2,4),(2,5),(2,6),(3,1),(3,5),(3,6)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>([(0,2),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(6,3)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>([(0,4),(0,5),(0,6),(1,3),(1,5),(1,6),(2,3),(2,5),(2,6),(3,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>([(0,4),(0,5),(0,6),(1,2),(1,3),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>([(0,6),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,2),(2,1)],3) [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>([(0,5),(3,6),(4,2),(4,6),(5,1),(5,3),(5,4)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(5,3),(6,2),(6,3)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>([(0,3),(0,4),(2,5),(3,5),(3,6),(4,1),(4,2),(4,6)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>([(0,2),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(6,3)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>([(0,5),(0,6),(1,3),(1,4),(1,6),(2,3),(2,4),(2,6),(4,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,1),(4,5),(4,6)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(2,6),(3,5),(3,6)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6)],7)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>([(0,6),(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(3,6),(4,5),(4,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(4,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>([(0,6),(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,2),(2,1)],3) [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>([(0,5),(3,6),(4,6),(5,1),(5,2),(5,3),(5,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(5,2),(6,2)],7)=>([(0,2),(2,1)],3) [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>([(0,4),(0,5),(3,6),(4,6),(5,1),(5,2),(5,3)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>([(0,4),(0,5),(0,6),(1,2),(1,4),(1,5),(1,6),(2,3),(6,3)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>([(0,3),(1,4),(1,5),(1,6),(2,4),(2,5),(2,6),(6,3)],7)=>([(0,2),(2,1)],3) [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>([(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,2),(5,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(2,6),(3,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(3,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>([(0,6),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,2),(2,1)],3) [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,1),(5,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(3,6),(4,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(4,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>([(0,6),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,2),(2,1)],3) [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(3,6),(4,6),(5,6)],7)=>([(0,2),(2,1)],3) [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>([(0,6),(1,2),(1,3),(1,4),(1,5),(4,6),(5,6)],7)=>([(0,2),(2,1)],3) [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(5,6)],7)=>([(0,2),(2,1)],3) [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>([(0,6),(1,6),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,2),(2,1)],3) [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>([(1,6),(2,6),(3,6),(4,5),(4,6)],7)=>([(0,2),(2,1)],3) [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>([(2,6),(3,6),(4,6),(5,6)],7)=>([(0,1)],2) [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>([(0,5),(5,6),(6,1),(6,2),(6,3),(6,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>([(0,6),(1,6),(6,2),(6,3),(6,4),(6,5)],7)=>([(0,2),(2,1)],3) [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>([(0,1),(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>([(0,2),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>([(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)=>([(0,1)],2) [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>([(0,5),(5,4),(5,6),(6,1),(6,2),(6,3)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>([(0,5),(0,6),(1,5),(1,6),(6,2),(6,3),(6,4)],7)=>([(0,2),(2,1)],3) [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>([(0,2),(0,3),(2,4),(2,5),(2,6),(3,1),(3,4),(3,5),(3,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>([(0,2),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>([(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>([(0,2),(0,3),(1,4),(1,5),(1,6),(3,4),(3,5),(3,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>([(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]=>([(0,6),(5,3),(5,4),(6,1),(6,2),(6,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>([(0,4),(0,5),(0,6),(1,4),(1,5),(1,6),(6,2),(6,3)],7)=>([(0,2),(2,1)],3) [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>([(0,3),(0,4),(3,5),(3,6),(4,1),(4,2),(4,5),(4,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>([(0,2),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>([(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(3,5),(3,6),(4,1),(4,5),(4,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>([(0,2),(0,3),(0,6),(1,4),(1,5),(1,6),(3,4),(3,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>([(0,5),(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>([(1,5),(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(4,5),(4,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>([(0,5),(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>([(1,5),(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,1)],2) [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>([(0,6),(5,4),(6,1),(6,2),(6,3),(6,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>([(0,3),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(6,2)],7)=>([(0,2),(2,1)],3) [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>([(0,4),(0,5),(4,6),(5,1),(5,2),(5,3),(5,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>([(0,2),(0,4),(0,5),(0,6),(1,3),(1,4),(1,5),(1,6),(2,3)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>([(0,6),(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>([(0,3),(0,4),(0,5),(4,6),(5,1),(5,2),(5,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>([(0,2),(0,3),(0,5),(0,6),(1,4),(1,5),(1,6),(3,4)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>([(0,6),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>([(1,6),(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>([(0,2),(0,3),(0,4),(0,5),(4,6),(5,1),(5,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(1,6),(4,5)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>([(0,6),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>([(1,6),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,3),(2,1),(3,2)],4) [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>([(2,6),(3,5),(3,6),(4,5),(4,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(4,6),(5,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>([(0,6),(1,2),(1,3),(1,4),(1,5),(5,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>([(0,6),(1,6),(2,3),(2,4),(2,5),(2,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>([(1,6),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>([(2,6),(3,6),(4,5),(4,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>([(3,6),(4,6),(5,6)],7)=>([(0,1)],2) [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>([(0,6),(6,1),(6,2),(6,3),(6,4),(6,5)],7)=>([(0,2),(2,1)],3) [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7)=>([(0,1)],2) [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>([(0,5),(0,6),(6,1),(6,2),(6,3),(6,4)],7)=>([(0,2),(2,1)],3) [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>([(0,3),(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>([(1,3),(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)=>([(0,1)],2) [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>([(0,4),(0,5),(0,6),(6,1),(6,2),(6,3)],7)=>([(0,2),(2,1)],3) [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>([(0,4),(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>([(1,4),(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>([(2,4),(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,1)],2) [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>([(0,3),(0,4),(0,5),(0,6),(6,1),(6,2)],7)=>([(0,2),(2,1)],3) [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>([(0,5),(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>([(1,5),(1,6),(2,3),(2,4),(2,5),(2,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>([(2,5),(2,6),(3,4),(3,5),(3,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>([(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]=>([(0,2),(0,3),(0,4),(0,5),(0,6),(6,1)],7)=>([(0,2),(2,1)],3) [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>([(0,6),(1,2),(1,3),(1,4),(1,5),(1,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>([(1,6),(2,3),(2,4),(2,5),(2,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>([(2,6),(3,4),(3,5),(3,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>([(3,6),(4,5),(4,6)],7)=>([(0,2),(2,1)],3) [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>([(4,6),(5,6)],7)=>([(0,1)],2) [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>([(0,1),(0,2),(0,3),(0,4),(0,5),(0,6)],7)=>([(0,1)],2) [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>([(1,2),(1,3),(1,4),(1,5),(1,6)],7)=>([(0,1)],2) [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>([(2,3),(2,4),(2,5),(2,6)],7)=>([(0,1)],2) [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>([(3,4),(3,5),(3,6)],7)=>([(0,1)],2) [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>([(4,5),(4,6)],7)=>([(0,1)],2) [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>([(5,6)],7)=>([(0,1)],2) [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>([],7)=>([],1) [1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)=>([(0,4),(2,3),(3,1),(4,2)],5) [1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>([(0,4),(1,7),(2,6),(3,1),(3,6),(4,5),(5,2),(5,3),(6,7)],8)=>([(0,6),(2,3),(3,5),(4,2),(5,1),(6,4)],7)
Map
Hessenberg poset
Description
The Hessenberg poset of a Dyck path.
Let $D$ be a Dyck path of semilength $n$, regarded as a subdiagonal path from $(0,0)$ to $(n,n)$, and let $\boldsymbol{m}_i$ be the $x$-coordinate of the $i$-th up step.
Then the Hessenberg poset (or natural unit interval order) corresponding to $D$ has elements $\{1,\dots,n\}$ with $i < j$ if $j < \boldsymbol{m}_i$.
Map
maximal antichains
Description
The lattice of maximal antichains in a poset.
An antichain $A$ in a poset is maximal if there is no antichain of larger cardinality which contains all elements of $A$.
The set of maximal antichains 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 $A$.