Identifier
Mp00025: to 132-avoiding permutationPermutations
Mp00061: Permutations to increasing treeBinary trees
Mp00011: to graph
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-2Cc0020;cc-rep-3
[1,0]=>[1]=>[.,.]=>([],1) [1,0,1,0]=>[2,1]=>[[.,.],.]=>([(0,1)],2) [1,1,0,0]=>[1,2]=>[.,[.,.]]=>([(0,1)],2) [1,0,1,0,1,0]=>[3,2,1]=>[[[.,.],.],.]=>([(0,2),(1,2)],3) [1,0,1,1,0,0]=>[2,3,1]=>[[.,[.,.]],.]=>([(0,2),(1,2)],3) [1,1,0,0,1,0]=>[3,1,2]=>[[.,.],[.,.]]=>([(0,2),(1,2)],3) [1,1,0,1,0,0]=>[2,1,3]=>[[.,.],[.,.]]=>([(0,2),(1,2)],3) [1,1,1,0,0,0]=>[1,2,3]=>[.,[.,[.,.]]]=>([(0,2),(1,2)],3) [1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[[[[.,.],.],.],.]=>([(0,3),(1,2),(2,3)],4) [1,0,1,0,1,1,0,0]=>[3,4,2,1]=>[[[.,[.,.]],.],.]=>([(0,3),(1,2),(2,3)],4) [1,0,1,1,0,0,1,0]=>[4,2,3,1]=>[[[.,.],[.,.]],.]=>([(0,3),(1,3),(2,3)],4) [1,0,1,1,0,1,0,0]=>[3,2,4,1]=>[[[.,.],[.,.]],.]=>([(0,3),(1,3),(2,3)],4) [1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]=>([(0,3),(1,2),(2,3)],4) [1,1,0,0,1,0,1,0]=>[4,3,1,2]=>[[[.,.],.],[.,.]]=>([(0,3),(1,2),(2,3)],4) [1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[[.,[.,.]],[.,.]]=>([(0,3),(1,2),(2,3)],4) [1,1,0,1,0,0,1,0]=>[4,2,1,3]=>[[[.,.],.],[.,.]]=>([(0,3),(1,2),(2,3)],4) [1,1,0,1,0,1,0,0]=>[3,2,1,4]=>[[[.,.],.],[.,.]]=>([(0,3),(1,2),(2,3)],4) [1,1,0,1,1,0,0,0]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]=>([(0,3),(1,2),(2,3)],4) [1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]=>([(0,3),(1,2),(2,3)],4) [1,1,1,0,0,1,0,0]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]=>([(0,3),(1,2),(2,3)],4) [1,1,1,0,1,0,0,0]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]=>([(0,3),(1,2),(2,3)],4) [1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]=>([(0,3),(1,2),(2,3)],4) [1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]=>([(0,4),(1,3),(2,3),(2,4)],5) [1,0,1,0,1,0,1,1,0,0]=>[4,5,3,2,1]=>[[[[.,[.,.]],.],.],.]=>([(0,4),(1,3),(2,3),(2,4)],5) [1,0,1,0,1,1,0,0,1,0]=>[5,3,4,2,1]=>[[[[.,.],[.,.]],.],.]=>([(0,4),(1,4),(2,3),(3,4)],5) [1,0,1,0,1,1,0,1,0,0]=>[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.]=>([(0,4),(1,4),(2,3),(3,4)],5) [1,0,1,0,1,1,1,0,0,0]=>[3,4,5,2,1]=>[[[.,[.,[.,.]]],.],.]=>([(0,4),(1,3),(2,3),(2,4)],5) [1,0,1,1,0,0,1,0,1,0]=>[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.]=>([(0,4),(1,4),(2,3),(3,4)],5) [1,0,1,1,0,0,1,1,0,0]=>[4,5,2,3,1]=>[[[.,[.,.]],[.,.]],.]=>([(0,4),(1,4),(2,3),(3,4)],5) [1,0,1,1,0,1,0,0,1,0]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]=>([(0,4),(1,4),(2,3),(3,4)],5) [1,0,1,1,0,1,0,1,0,0]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]=>([(0,4),(1,4),(2,3),(3,4)],5) [1,0,1,1,0,1,1,0,0,0]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]=>([(0,4),(1,4),(2,3),(3,4)],5) [1,0,1,1,1,0,0,0,1,0]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]=>([(0,4),(1,4),(2,3),(3,4)],5) [1,0,1,1,1,0,0,1,0,0]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]=>([(0,4),(1,4),(2,3),(3,4)],5) [1,0,1,1,1,0,1,0,0,0]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]=>([(0,4),(1,4),(2,3),(3,4)],5) [1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]=>([(0,4),(1,3),(2,3),(2,4)],5) [1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]]=>([(0,4),(1,3),(2,3),(2,4)],5) [1,1,0,0,1,0,1,1,0,0]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]=>([(0,4),(1,3),(2,3),(2,4)],5) [1,1,0,0,1,1,0,0,1,0]=>[5,3,4,1,2]=>[[[.,.],[.,.]],[.,.]]=>([(0,4),(1,4),(2,3),(3,4)],5) [1,1,0,0,1,1,0,1,0,0]=>[4,3,5,1,2]=>[[[.,.],[.,.]],[.,.]]=>([(0,4),(1,4),(2,3),(3,4)],5) [1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>[[.,[.,[.,.]]],[.,.]]=>([(0,4),(1,3),(2,3),(2,4)],5) [1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,3]=>[[[[.,.],.],.],[.,.]]=>([(0,4),(1,3),(2,3),(2,4)],5) [1,1,0,1,0,0,1,1,0,0]=>[4,5,2,1,3]=>[[[.,[.,.]],.],[.,.]]=>([(0,4),(1,3),(2,3),(2,4)],5) [1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]]=>([(0,4),(1,3),(2,3),(2,4)],5) [1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]=>([(0,4),(1,3),(2,3),(2,4)],5) [1,1,0,1,0,1,1,0,0,0]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]]=>([(0,4),(1,3),(2,3),(2,4)],5) [1,1,0,1,1,0,0,0,1,0]=>[5,2,3,1,4]=>[[[.,.],[.,.]],[.,.]]=>([(0,4),(1,4),(2,3),(3,4)],5) [1,1,0,1,1,0,0,1,0,0]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]=>([(0,4),(1,4),(2,3),(3,4)],5) [1,1,0,1,1,0,1,0,0,0]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]=>([(0,4),(1,4),(2,3),(3,4)],5) [1,1,0,1,1,1,0,0,0,0]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]=>([(0,4),(1,3),(2,3),(2,4)],5) [1,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]=>([(0,4),(1,3),(2,3),(2,4)],5) [1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>[[.,[.,.]],[.,[.,.]]]=>([(0,4),(1,3),(2,3),(2,4)],5) [1,1,1,0,0,1,0,0,1,0]=>[5,3,1,2,4]=>[[[.,.],.],[.,[.,.]]]=>([(0,4),(1,3),(2,3),(2,4)],5) [1,1,1,0,0,1,0,1,0,0]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]=>([(0,4),(1,3),(2,3),(2,4)],5) [1,1,1,0,0,1,1,0,0,0]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]=>([(0,4),(1,3),(2,3),(2,4)],5) [1,1,1,0,1,0,0,0,1,0]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]=>([(0,4),(1,3),(2,3),(2,4)],5) [1,1,1,0,1,0,0,1,0,0]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]=>([(0,4),(1,3),(2,3),(2,4)],5) [1,1,1,0,1,0,1,0,0,0]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]=>([(0,4),(1,3),(2,3),(2,4)],5) [1,1,1,0,1,1,0,0,0,0]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]=>([(0,4),(1,3),(2,3),(2,4)],5) [1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]=>([(0,4),(1,3),(2,3),(2,4)],5) [1,1,1,1,0,0,0,1,0,0]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]=>([(0,4),(1,3),(2,3),(2,4)],5) [1,1,1,1,0,0,1,0,0,0]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]=>([(0,4),(1,3),(2,3),(2,4)],5) [1,1,1,1,0,1,0,0,0,0]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]=>([(0,4),(1,3),(2,3),(2,4)],5) [1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]=>([(0,4),(1,3),(2,3),(2,4)],5) [1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,0,1,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,2,1]=>[[[[[.,[.,.]],.],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,2,1]=>[[[[[.,.],[.,.]],.],.],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,2,1]=>[[[[[.,.],[.,.]],.],.],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,2,1]=>[[[[.,[.,[.,.]]],.],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,0,1,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,2,1]=>[[[[.,[.,.]],[.,.]],.],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,2,1]=>[[[[[.,.],.],[.,.]],.],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,2,1]=>[[[[[.,.],.],[.,.]],.],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,2,1]=>[[[[.,[.,.]],[.,.]],.],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,2,1]=>[[[[.,.],[.,[.,.]]],.],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,2,1]=>[[[[.,.],[.,[.,.]]],.],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[[[[.,.],[.,[.,.]]],.],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,2,1]=>[[[.,[.,[.,[.,.]]]],.],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,3,1]=>[[[[[.,.],.],.],[.,.]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,0,1,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,3,1]=>[[[[.,[.,.]],.],[.,.]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6) [1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6) [1,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,3,1]=>[[[.,[.,[.,.]]],[.,.]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,4,1]=>[[[[[.,.],.],.],[.,.]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,0,1,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,4,1]=>[[[[.,[.,.]],.],[.,.]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,1]=>[[[[[.,.],.],.],[.,.]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,1]=>[[[[.,[.,.]],.],[.,.]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,5,1]=>[[[[.,.],[.,.]],[.,.]],.]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6) [1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,6,1]=>[[[[.,.],[.,.]],[.,.]],.]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6) [1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,6,1]=>[[[[.,.],[.,.]],[.,.]],.]=>([(0,5),(1,5),(2,4),(3,4),(4,5)],6) [1,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,6,1]=>[[[.,[.,[.,.]]],[.,.]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,4,1]=>[[[[.,.],.],[.,[.,.]]],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,0,1,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,4,1]=>[[[.,[.,.]],[.,[.,.]]],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,5,1]=>[[[[.,.],.],[.,[.,.]]],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,6,1]=>[[[[.,.],.],[.,[.,.]]],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,6,1]=>[[[.,[.,.]],[.,[.,.]]],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[[[[.,.],.],[.,[.,.]]],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,6,1]=>[[[[.,.],.],[.,[.,.]]],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,6,1]=>[[[.,[.,.]],[.,[.,.]]],.]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,6,1]=>[[[.,.],[.,[.,[.,.]]]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,6,1]=>[[[.,.],[.,[.,[.,.]]]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,6,1]=>[[[.,.],[.,[.,[.,.]]]],.]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[[.,[.,[.,[.,[.,.]]]]],.]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,2]=>[[[[[.,.],.],.],.],[.,.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,0,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,1,2]=>[[[[.,.],[.,.]],.],[.,.]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,1,2]=>[[[[.,.],[.,.]],.],[.,.]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,1,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,1,2]=>[[[.,[.,[.,.]]],.],[.,.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,1,2]=>[[[[.,.],.],[.,.]],[.,.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,1,0,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,1,2]=>[[[[.,.],.],[.,.]],[.,.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,1,2]=>[[[[.,.],.],[.,.]],[.,.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,1,2]=>[[[.,.],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,1,2]=>[[[.,.],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,1,2]=>[[[.,.],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>[[.,[.,[.,[.,.]]]],[.,.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,3]=>[[[[[.,.],.],.],.],[.,.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,0,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,1,3]=>[[[[.,[.,.]],.],.],[.,.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,1,3]=>[[[[.,.],[.,.]],.],[.,.]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,1,3]=>[[[[.,.],[.,.]],.],[.,.]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,1,0,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,1,3]=>[[[.,[.,[.,.]]],.],[.,.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,4]=>[[[[[.,.],.],.],.],[.,.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,0,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,1,4]=>[[[[.,[.,.]],.],.],[.,.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,5]=>[[[[[.,.],.],.],.],[.,.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,0,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,1,6]=>[[[[.,[.,.]],.],.],[.,.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,1,5]=>[[[[.,.],[.,.]],.],[.,.]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,1,6]=>[[[[.,.],[.,.]],.],[.,.]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,1,6]=>[[[[.,.],[.,.]],.],[.,.]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,1,6]=>[[[.,[.,[.,.]]],.],[.,.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,1,4]=>[[[[.,.],.],[.,.]],[.,.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,1,0,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,1,4]=>[[[.,[.,.]],[.,.]],[.,.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,1,5]=>[[[[.,.],.],[.,.]],[.,.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,1,6]=>[[[[.,.],.],[.,.]],[.,.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,1,0,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,1,6]=>[[[.,[.,.]],[.,.]],[.,.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,1,5]=>[[[[.,.],.],[.,.]],[.,.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,1,6]=>[[[[.,.],.],[.,.]],[.,.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,1,6]=>[[[[.,.],.],[.,.]],[.,.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,1,6]=>[[[.,[.,.]],[.,.]],[.,.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,1,5]=>[[[.,.],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,5),(4,5)],6) [1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6]=>[[.,[.,[.,[.,.]]]],[.,.]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,2,3]=>[[[[.,.],.],.],[.,[.,.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,0,0,0,1,0,1,1,0,0]=>[5,6,4,1,2,3]=>[[[.,[.,.]],.],[.,[.,.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,5,1,2,3]=>[[[.,.],[.,.]],[.,[.,.]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,6,1,2,3]=>[[[.,.],[.,.]],[.,[.,.]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,2,4]=>[[[[.,.],.],.],[.,[.,.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,0,0,1,0,0,1,1,0,0]=>[5,6,3,1,2,4]=>[[[.,[.,.]],.],[.,[.,.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,2,5]=>[[[[.,.],.],.],[.,[.,.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,2,6]=>[[[[.,.],.],.],[.,[.,.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,0,0,1,0,1,1,0,0,0]=>[4,5,3,1,2,6]=>[[[.,[.,.]],.],[.,[.,.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>[[[.,.],[.,.]],[.,[.,.]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,4,1,2,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,5,1,2,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6]=>[[.,[.,[.,.]]],[.,[.,.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,3,4]=>[[[[.,.],.],.],[.,[.,.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,0,1,0,0,0,1,1,0,0]=>[5,6,2,1,3,4]=>[[[.,[.,.]],.],[.,[.,.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,3,5]=>[[[[.,.],.],.],[.,[.,.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,3,6]=>[[[[.,.],.],.],[.,[.,.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,0,1,0,0,1,1,0,0,0]=>[4,5,2,1,3,6]=>[[[.,[.,.]],.],[.,[.,.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,4,5]=>[[[[.,.],.],.],[.,[.,.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,4,6]=>[[[[.,.],.],.],[.,[.,.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,2,1,5,6]=>[[[.,[.,.]],.],[.,[.,.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,1,4,5]=>[[[.,.],[.,.]],[.,[.,.]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,3,1,4,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,3,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,4,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>([(0,5),(1,5),(2,3),(3,4),(4,5)],6) [1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,2,3,4]=>[[[.,.],.],[.,[.,[.,.]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>[[.,[.,.]],[.,[.,[.,.]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>[[[.,.],.],[.,[.,[.,.]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,2,3,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,3,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,2,4,5]=>[[[.,.],.],[.,[.,[.,.]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,2,4,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,2,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,3,4,5]=>[[[.,.],.],[.,[.,[.,.]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,3,4,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,3,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,1,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>[[.,.],[.,[.,[.,[.,.]]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,4,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,3,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,2,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>([(0,5),(1,4),(2,3),(2,4),(3,5)],6) [1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,2,1]=>[[[[[[.,[.,.]],.],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,2,1]=>[[[[[[.,.],[.,.]],.],.],.],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,2,1]=>[[[[[[.,.],[.,.]],.],.],.],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,2,1]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,2,1]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,2,1]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,2,1]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,2,1]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,2,1]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,2,1]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,2,1]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,2,1]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,3,1]=>[[[[[[.,.],.],.],.],[.,.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,3,1]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) [1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) [1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,3,1]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,3,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,3,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,3,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,3,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,3,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,3,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,3,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,3,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,3,1]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,4,1]=>[[[[[[.,.],.],.],.],[.,.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,4,1]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,4,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) [1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,4,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) [1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,4,1]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,5,1]=>[[[[[[.,.],.],.],.],[.,.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,5,1]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,1]=>[[[[[[.,.],.],.],.],[.,.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,7,1]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,6,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) [1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,7,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) [1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,7,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7) [1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,7,1]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,5,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,5,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,7,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,7,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,7,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,7,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,6,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,7,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,7,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,7,1]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,4,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,4,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,4,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,4,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,4,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,5,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,5,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,7,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,7,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,7,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,5,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,5,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,7,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,7,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,7,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,7,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,7,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,5,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,5,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,7,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,7,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,7,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1,2]=>[[[[[[.,.],.],.],.],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,1,2]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,1,2]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,1,2]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,1,2]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,1,2]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,1,2]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,1,2]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,1,2]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,1,2]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,1,2]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,1,2]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,1,2]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,1,2]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,1,2]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,1,2]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,1,2]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,1,2]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,1,2]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,1,2]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,1,2]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,1,2]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,1,2]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,1,3]=>[[[[[[.,.],.],.],.],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,1,3]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,1,3]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,1,3]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,1,3]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,1,3]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,1,3]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,1,3]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,1,3]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,1,3]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,1,3]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,1,3]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1,4]=>[[[[[[.,.],.],.],.],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,1,4]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,1,4]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,1,4]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,1,4]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1,5]=>[[[[[[.,.],.],.],.],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,1,5]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1,6]=>[[[[[[.,.],.],.],.],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,1,7]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,1,6]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,1,7]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,1,7]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,1,7]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,1,5]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,1,5]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,1,6]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,1,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,1,6]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,1,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,1,6]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,1,7]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,1,4]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,1,4]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,1,4]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,1,4]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,1,4]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,1,5]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,1,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,1,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,1,5]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,1,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,1,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>([(0,6),(1,5),(2,5),(3,4),(4,6),(5,6)],7) [1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,1,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,1,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>([(0,5),(1,4),(2,3),(3,6),(4,6),(5,6)],7) [1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,1,6]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,2,3]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,1,2,3]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,1,2,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,1,2,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,1,2,3]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,1,2,3]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,1,2,3]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,1,2,3]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,1,2,3]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,1,2,3]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,1,2,3]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,1,2,3]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1,2,4]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,1,2,4]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,1,2,4]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,1,2,4]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,1,2,4]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1,2,5]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,1,2,5]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1,2,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,2,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,1,2,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,1,2,6]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,1,2,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,1,2,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,1,2,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,1,2,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,1,2,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,1,2,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,1,2,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,1,2,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,1,2,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,1,2,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,1,2,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,1,2,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,1,2,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,1,2,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,3,4]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,1,3,4]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,1,3,4]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,1,3,4]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,1,3,4]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1,3,5]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,1,3,5]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,3,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,3,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,1,3,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,1,3,6]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,1,3,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,1,3,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,1,3,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,4,5]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,1,4,5]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1,4,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,4,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,1,4,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,5,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,5,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,1,6,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,1,5,6]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,1,5,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,1,6,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,1,4,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,1,4,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,1,4,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,1,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,1,5,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,1,5,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,1,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,1,5,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,1,5,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,1,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,1,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,1,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>([(0,6),(1,4),(2,3),(3,6),(4,5),(5,6)],7) [1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,2,3,4]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,7,5,1,2,3,4]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,6,1,2,3,4]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,7,1,2,3,4]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,2,3,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,7,4,1,2,3,5]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,2,3,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,2,3,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,6,4,1,2,3,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,5,1,2,3,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,5,1,2,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,6,1,2,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,2,4,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,7,3,1,2,4,5]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,2,4,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,2,4,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,6,3,1,2,4,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,2,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,2,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,2,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,1,2,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,4,1,2,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,4,1,2,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,4,1,2,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,5,1,2,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,4,5,1,2,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,3,4,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,7,2,1,3,4,5]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,3,4,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,3,4,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,6,2,1,3,4,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,3,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,3,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,3,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,2,1,3,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,4,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,4,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,4,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,4,2,1,5,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,3,1,4,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,3,1,4,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,3,1,4,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,3,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,4,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>([(0,6),(1,6),(2,3),(3,5),(4,5),(4,6)],7) [1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,2,3,4,5]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,2,3,4,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,2,3,4,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,4,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,2,3,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,2,3,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,2,3,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,5,1,2,3,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,2,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,2,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,2,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,2,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,3,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,3,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,3,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,3,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,5,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,4,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,3,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>([(0,6),(1,5),(2,3),(2,4),(3,5),(4,6)],7) [1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) [1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) [1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>([(0,6),(1,6),(2,7),(3,7),(4,5),(4,7),(5,6)],8) [1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>([(0,7),(1,6),(2,6),(3,4),(4,7),(5,6),(5,7)],8) [1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,3,4,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) [1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) [1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) [1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,1,2]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) [1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>([(0,6),(1,5),(2,4),(3,4),(3,7),(5,7),(6,7)],8) [1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) [1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>([(0,6),(1,7),(2,7),(3,4),(3,5),(4,6),(5,7)],8) [1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) [1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,2,3,1,4]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>([(0,7),(1,6),(2,4),(3,5),(4,6),(5,7),(6,7)],8) [1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) [1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) [1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) [1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,1,2,3,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>([(0,6),(1,5),(2,7),(3,4),(3,5),(4,7),(6,7)],8) [1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) [1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8) [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>([(0,7),(1,6),(2,3),(2,4),(3,5),(4,6),(5,7)],8)
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
Map
to graph
Description
Return the undirected graph obtained from the tree nodes and edges, with leaves being ignored.