Identifier
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00017: Binary trees —to 312-avoiding permutation⟶ Permutations
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-2
[1,0]=>[1]=>[.,.]=>[1]
[1,0,1,0]=>[2,1]=>[[.,.],.]=>[1,2]
[1,1,0,0]=>[1,2]=>[.,[.,.]]=>[2,1]
[1,0,1,0,1,0]=>[3,2,1]=>[[[.,.],.],.]=>[1,2,3]
[1,0,1,1,0,0]=>[2,3,1]=>[[.,.],[.,.]]=>[1,3,2]
[1,1,0,0,1,0]=>[3,1,2]=>[[.,[.,.]],.]=>[2,1,3]
[1,1,0,1,0,0]=>[2,1,3]=>[[.,.],[.,.]]=>[1,3,2]
[1,1,1,0,0,0]=>[1,2,3]=>[.,[.,[.,.]]]=>[3,2,1]
[1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[[[[.,.],.],.],.]=>[1,2,3,4]
[1,0,1,0,1,1,0,0]=>[3,4,2,1]=>[[[.,.],.],[.,.]]=>[1,2,4,3]
[1,0,1,1,0,0,1,0]=>[4,2,3,1]=>[[[.,.],[.,.]],.]=>[1,3,2,4]
[1,0,1,1,0,1,0,0]=>[3,2,4,1]=>[[[.,.],.],[.,.]]=>[1,2,4,3]
[1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[[.,.],[.,[.,.]]]=>[1,4,3,2]
[1,1,0,0,1,0,1,0]=>[4,3,1,2]=>[[[.,[.,.]],.],.]=>[2,1,3,4]
[1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[[.,[.,.]],[.,.]]=>[2,1,4,3]
[1,1,0,1,0,0,1,0]=>[4,2,1,3]=>[[[.,.],[.,.]],.]=>[1,3,2,4]
[1,1,0,1,0,1,0,0]=>[3,2,1,4]=>[[[.,.],.],[.,.]]=>[1,2,4,3]
[1,1,0,1,1,0,0,0]=>[2,3,1,4]=>[[.,.],[.,[.,.]]]=>[1,4,3,2]
[1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[[.,[.,[.,.]]],.]=>[3,2,1,4]
[1,1,1,0,0,1,0,0]=>[3,1,2,4]=>[[.,[.,.]],[.,.]]=>[2,1,4,3]
[1,1,1,0,1,0,0,0]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]=>[1,4,3,2]
[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]=>[4,3,2,1]
[1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]=>[1,2,3,4,5]
[1,0,1,0,1,0,1,1,0,0]=>[4,5,3,2,1]=>[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]
[1,0,1,0,1,1,0,0,1,0]=>[5,3,4,2,1]=>[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]
[1,0,1,0,1,1,0,1,0,0]=>[4,3,5,2,1]=>[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]
[1,0,1,0,1,1,1,0,0,0]=>[3,4,5,2,1]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]
[1,0,1,1,0,0,1,0,1,0]=>[5,4,2,3,1]=>[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]
[1,0,1,1,0,0,1,1,0,0]=>[4,5,2,3,1]=>[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]
[1,0,1,1,0,1,0,0,1,0]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]
[1,0,1,1,0,1,0,1,0,0]=>[4,3,2,5,1]=>[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]
[1,0,1,1,0,1,1,0,0,0]=>[3,4,2,5,1]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]
[1,0,1,1,1,0,0,0,1,0]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]
[1,0,1,1,1,0,0,1,0,0]=>[4,2,3,5,1]=>[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]
[1,0,1,1,1,0,1,0,0,0]=>[3,2,4,5,1]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]
[1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]
[1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,2]=>[[[[.,[.,.]],.],.],.]=>[2,1,3,4,5]
[1,1,0,0,1,0,1,1,0,0]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]
[1,1,0,0,1,1,0,0,1,0]=>[5,3,4,1,2]=>[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]
[1,1,0,0,1,1,0,1,0,0]=>[4,3,5,1,2]=>[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]
[1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]
[1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,3]=>[[[[.,.],[.,.]],.],.]=>[1,3,2,4,5]
[1,1,0,1,0,0,1,1,0,0]=>[4,5,2,1,3]=>[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]
[1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,4]=>[[[[.,.],.],[.,.]],.]=>[1,2,4,3,5]
[1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]=>[1,2,3,5,4]
[1,1,0,1,0,1,1,0,0,0]=>[3,4,2,1,5]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]
[1,1,0,1,1,0,0,0,1,0]=>[5,2,3,1,4]=>[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]
[1,1,0,1,1,0,0,1,0,0]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]
[1,1,0,1,1,0,1,0,0,0]=>[3,2,4,1,5]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]
[1,1,0,1,1,1,0,0,0,0]=>[2,3,4,1,5]=>[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]
[1,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,3]=>[[[.,[.,[.,.]]],.],.]=>[3,2,1,4,5]
[1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]
[1,1,1,0,0,1,0,0,1,0]=>[5,3,1,2,4]=>[[[.,[.,.]],[.,.]],.]=>[2,1,4,3,5]
[1,1,1,0,0,1,0,1,0,0]=>[4,3,1,2,5]=>[[[.,[.,.]],.],[.,.]]=>[2,1,3,5,4]
[1,1,1,0,0,1,1,0,0,0]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]
[1,1,1,0,1,0,0,0,1,0]=>[5,2,1,3,4]=>[[[.,.],[.,[.,.]]],.]=>[1,4,3,2,5]
[1,1,1,0,1,0,0,1,0,0]=>[4,2,1,3,5]=>[[[.,.],[.,.]],[.,.]]=>[1,3,2,5,4]
[1,1,1,0,1,0,1,0,0,0]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]=>[1,2,5,4,3]
[1,1,1,0,1,1,0,0,0,0]=>[2,3,1,4,5]=>[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]
[1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>[[.,[.,[.,[.,.]]]],.]=>[4,3,2,1,5]
[1,1,1,1,0,0,0,1,0,0]=>[4,1,2,3,5]=>[[.,[.,[.,.]]],[.,.]]=>[3,2,1,5,4]
[1,1,1,1,0,0,1,0,0,0]=>[3,1,2,4,5]=>[[.,[.,.]],[.,[.,.]]]=>[2,1,5,4,3]
[1,1,1,1,0,1,0,0,0,0]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]=>[1,5,4,3,2]
[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]=>[1,2,3,4,5,6]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,2,1]=>[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,2,1]=>[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,2,1]=>[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,2,1]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,2,1]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,2,1]=>[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,2,1]=>[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,2,1]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,2,1]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,2,1]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,3,1]=>[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,3,1]=>[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,3,1]=>[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,3,1]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,4,1]=>[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,4,1]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,1]=>[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,1]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,5,1]=>[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,6,1]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,6,1]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,6,1]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,4,1]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,5,1]=>[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,6,1]=>[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,6,1]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,6,1]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,6,1]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,6,1]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,6,1]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,6,1]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],.]=>[2,1,3,4,5,6]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,1,2]=>[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,1,2]=>[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,1,2]=>[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,1,2]=>[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,1,2]=>[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],.]=>[1,3,2,4,5,6]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,1,3]=>[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,1,3]=>[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,1,3]=>[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,1,3]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],.]=>[1,2,4,3,5,6]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,1,4]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,5]=>[[[[[.,.],.],.],[.,.]],.]=>[1,2,3,5,4,6]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]=>[1,2,3,4,6,5]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,1,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,1,5]=>[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,1,6]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,1,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,1,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,1,4]=>[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,1,4]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,1,5]=>[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,1,6]=>[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,1,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,1,5]=>[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,1,6]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,1,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,1,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,1,5]=>[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,1,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,1,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],.]=>[3,2,1,4,5,6]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[5,6,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,5,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,6,1,2,3]=>[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],.]=>[2,1,4,3,5,6]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[5,6,3,1,2,4]=>[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,2,5]=>[[[[.,[.,.]],.],[.,.]],.]=>[2,1,3,5,4,6]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,2,6]=>[[[[.,[.,.]],.],.],[.,.]]=>[2,1,3,4,6,5]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[4,5,3,1,2,6]=>[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,4,1,2,6]=>[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,5,1,2,6]=>[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],.]=>[1,4,3,2,5,6]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[5,6,2,1,3,4]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,3,5]=>[[[[.,.],[.,.]],[.,.]],.]=>[1,3,2,5,4,6]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,3,6]=>[[[[.,.],[.,.]],.],[.,.]]=>[1,3,2,4,6,5]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,5,2,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,4,5]=>[[[[.,.],.],[.,[.,.]]],.]=>[1,2,5,4,3,6]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,4,6]=>[[[[.,.],.],[.,.]],[.,.]]=>[1,2,4,3,6,5]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[1,2,3,6,5,4]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,2,1,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,1,4,5]=>[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,3,1,4,6]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,3,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,4,1,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],.]=>[4,3,2,1,5,6]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>[[[.,[.,[.,.]]],[.,.]],.]=>[3,2,1,5,4,6]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,2,3,6]=>[[[.,[.,[.,.]]],.],[.,.]]=>[3,2,1,4,6,5]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,3,6]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,2,4,5]=>[[[.,[.,.]],[.,[.,.]]],.]=>[2,1,5,4,3,6]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,2,4,6]=>[[[.,[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,2,5,6]=>[[[.,[.,.]],.],[.,[.,.]]]=>[2,1,3,6,5,4]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],.]=>[1,5,4,3,2,6]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,3,4,6]=>[[[.,.],[.,[.,.]]],[.,.]]=>[1,4,3,2,6,5]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,3,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[1,3,2,6,5,4]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[1,2,6,5,4,3]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,1,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],.]=>[5,4,3,2,1,6]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,4,6]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[4,3,2,1,6,5]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,3,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[3,2,1,6,5,4]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,2,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[2,1,6,5,4,3]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[1,6,5,4,3,2]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>[6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,2,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,2,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,2,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,2,1]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,2,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,2,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,2,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,2,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,2,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,2,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,2,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,2,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,2,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,3,1]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,3,1]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,3,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,3,1]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,3,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,3,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,3,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,3,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,3,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,4,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,4,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,4,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,5,1]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,1]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,7,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,7,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,7,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,5,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,5,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,7,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,7,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,7,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,7,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,4,1]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,4,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,4,1]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,5,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,5,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,6,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,7,1]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,7,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,7,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,7,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,7,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,5,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,7,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,7,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,7,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,7,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,5,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,6,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,7,1]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,7,1]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,7,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,7,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,7,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,7,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,7,1]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,7,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],.]=>[2,1,3,4,5,6,7]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,1,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,1,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,1,2]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,1,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,1,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],.]=>[1,3,2,4,5,6,7]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,1,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,1,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,1,3]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,1,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,1,3]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[1,2,4,3,5,6,7]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,1,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[1,2,3,5,4,6,7]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1,6]=>[[[[[[.,.],.],.],.],[.,.]],.]=>[1,2,3,4,6,5,7]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[1,2,3,4,5,7,6]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,1,6]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,1,5]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,1,6]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,1,6]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,1,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,1,4]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,1,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,1,4]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,1,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,1,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,1,5]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,1,6]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,1,7]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,1,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,1,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,1,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,1,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,1,5]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,1,6]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,1,6]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,1,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,1,5]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,1,6]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,1,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,1,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,1,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,1,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,1,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,1,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,1,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,1,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>[3,2,1,4,5,6,7]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,1,2,3]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,1,2,3]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1,2,4]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>[2,1,4,3,5,6,7]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,1,2,4]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1,2,5]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[2,1,3,5,4,6,7]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,1,2,5]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1,2,6]=>[[[[[.,[.,.]],.],.],[.,.]],.]=>[2,1,3,4,6,5,7]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,2,7]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[2,1,3,4,5,7,6]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,1,2,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,1,2,6]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,1,2,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,1,2,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,1,2,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,1,2,5]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,1,2,6]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,1,2,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,1,2,6]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,1,2,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,1,2,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,1,2,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,1,2,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,1,2,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,1,2,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,3,4]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[1,4,3,2,5,6,7]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,1,3,4]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1,3,5]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[1,3,2,5,4,6,7]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,1,3,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,3,6]=>[[[[[.,.],[.,.]],.],[.,.]],.]=>[1,3,2,4,6,5,7]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,3,7]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[1,3,2,4,5,7,6]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,1,3,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,1,3,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,1,3,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,1,3,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,1,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,4,5]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[1,2,5,4,3,6,7]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,1,4,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1,4,6]=>[[[[[.,.],.],[.,.]],[.,.]],.]=>[1,2,4,3,6,5,7]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,4,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[1,2,4,3,5,7,6]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,5,6]=>[[[[[.,.],.],.],[.,[.,.]]],.]=>[1,2,3,6,5,4,7]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,5,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[1,2,3,5,4,7,6]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[1,2,3,4,7,6,5]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,1,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,1,5,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,1,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,1,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,1,4,5]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,1,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,1,4,6]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,1,4,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,1,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,1,5,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,1,5,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,1,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,1,5,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,1,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,1,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,1,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,1,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,1,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>[4,3,2,1,5,6,7]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,7,5,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,6,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,7,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,2,3,5]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[3,2,1,5,4,6,7]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,7,4,1,2,3,5]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,2,3,6]=>[[[[.,[.,[.,.]]],.],[.,.]],.]=>[3,2,1,4,6,5,7]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,2,3,7]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[3,2,1,4,5,7,6]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,6,4,1,2,3,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,5,1,2,3,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,5,1,2,3,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,6,1,2,3,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,2,4,5]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[2,1,5,4,3,6,7]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,7,3,1,2,4,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,2,4,6]=>[[[[.,[.,.]],[.,.]],[.,.]],.]=>[2,1,4,3,6,5,7]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,2,4,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[2,1,4,3,5,7,6]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,6,3,1,2,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,2,5,6]=>[[[[.,[.,.]],.],[.,[.,.]]],.]=>[2,1,3,6,5,4,7]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,2,5,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[2,1,3,5,4,7,6]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,2,6,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[2,1,3,4,7,6,5]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,1,2,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,4,1,2,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,4,1,2,5,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,4,1,2,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,5,1,2,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,4,5,1,2,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,3,4,5]=>[[[[.,.],[.,[.,[.,.]]]],.],.]=>[1,5,4,3,2,6,7]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,7,2,1,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,3,4,6]=>[[[[.,.],[.,[.,.]]],[.,.]],.]=>[1,4,3,2,6,5,7]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,3,4,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[1,4,3,2,5,7,6]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,6,2,1,3,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,3,5,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.]=>[1,3,2,6,5,4,7]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,3,5,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[1,3,2,5,4,7,6]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,3,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[1,3,2,4,7,6,5]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,2,1,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,4,5,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[1,2,6,5,4,3,7]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,4,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[1,2,5,4,3,7,6]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,4,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[1,2,4,3,7,6,5]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[1,2,3,7,6,5,4]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,4,2,1,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,3,1,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,3,1,4,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,3,1,4,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,3,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,4,1,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]=>[5,4,3,2,1,6,7]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,2,3,4,6]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]=>[4,3,2,1,6,5,7]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,2,3,4,7]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[4,3,2,1,5,7,6]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,4,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,2,3,5,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]=>[3,2,1,6,5,4,7]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,2,3,5,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[3,2,1,5,4,7,6]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,2,3,6,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[3,2,1,4,7,6,5]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,5,1,2,3,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,2,4,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]=>[2,1,6,5,4,3,7]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,2,4,5,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[2,1,5,4,3,7,6]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,2,4,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[2,1,4,3,7,6,5]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,2,5,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[2,1,3,7,6,5,4]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,3,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]=>[1,6,5,4,3,2,7]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,3,4,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[1,5,4,3,2,7,6]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,3,4,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[1,4,3,2,7,6,5]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,3,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[1,3,2,7,6,5,4]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[1,2,7,6,5,4,3]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[6,5,4,3,2,1,7]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,5,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[5,4,3,2,1,7,6]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,4,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[4,3,2,1,7,6,5]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,3,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[3,2,1,7,6,5,4]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[2,1,7,6,5,4,3]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[1,7,6,5,4,3,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]=>[7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,3,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,2,3,4,6,5,7,8]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,3,2,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,3,2,1]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,2,3,5,4,6,8,7]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,3,2,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,3,2,1]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,2,3,5,4,6,8,7]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,3,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,2,3,4,6,5,7,8]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,3,2,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,3,2,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,3,2,1]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[1,2,3,6,5,4,7,8]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,3,2,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,3,2,1]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,2,3,5,4,6,8,7]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,3,2,1]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,3,2,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,3,2,1]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,3,2,1]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,2,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,4,2,1]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,2,4,3,5,6,7,8]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,4,2,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,4,2,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,2,4,3,5,7,6,8]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,4,2,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,2,1]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,4,2,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,2,4,3,5,8,7,6]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,4,2,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,2,4,3,7,6,5,8]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,2,4,3,5,8,7,6]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,2,1]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,5,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,2,3,5,4,6,8,7]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,2,3,5,4,6,8,7]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,5,2,1]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,2,3,4,6,5,7,8]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,6,2,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,7,2,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,8,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,8,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,8,2,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,8,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,8,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,3,6,2,1]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[1,2,3,6,5,4,7,8]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,8,2,1]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,2,3,5,4,6,8,7]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,8,2,1]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,7,2,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,3,8,2,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,8,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,8,2,1]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,3,8,2,1]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,8,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,8,2,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,5,2,1]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,2,5,4,3,6,7,8]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,2,5,4,3,7,6,8]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,6,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,6,2,1]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,8,2,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,6,2,1]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[1,2,3,6,5,4,7,8]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,5,7,2,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,5,8,2,1]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,2,3,5,4,6,8,7]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,7,2,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,8,2,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,6,2,1]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,2,6,5,4,3,7,8]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,6,2,1]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,2,6,5,4,3,8,7]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,8,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,6,7,2,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,2,4,3,7,6,5,8]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,8,2,1]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,7,8,2,1]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,2,4,3,5,8,7,6]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,7,2,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,8,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,7,2,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,2,7,6,5,4,3,8]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,8,2,1]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,2,6,5,4,3,8,7]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,8,2,1]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,7,8,2,1]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,8,2,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,2,1]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,3,1]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,3,2,4,5,6,8,7]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,3,2,4,5,6,8,7]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,2,3,1]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,3,2,4,6,5,7,8]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,3,2,4,5,6,8,7]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,2,3,1]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,3,2,4,5,8,7,6]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,3,2,4,7,6,5,8]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,3,2,4,6,5,8,7]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,2,3,1]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,2,3,1]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,3,2,5,4,6,8,7]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,2,3,1]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,3,2,4,6,5,7,8]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,2,3,1]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,3,2,4,5,6,8,7]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,2,3,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,3,2,4,7,6,5,8]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,3,2,4,6,5,8,7]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,2,3,1]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,3,2,4,5,8,7,6]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,2,3,1]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[1,3,2,6,5,4,7,8]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,2,3,1]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,3,2,6,5,4,8,7]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,3,2,5,4,6,8,7]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,2,3,1]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,2,3,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,3,2,7,6,5,4,8]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,2,3,1]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,4,1]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,2,4,3,5,6,7,8]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,2,4,3,5,7,6,8]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,2,4,1]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,2,4,3,5,8,7,6]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,2,4,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,2,4,3,5,7,6,8]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,2,4,1]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,2,4,3,5,8,7,6]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,2,4,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,2,4,3,7,6,5,8]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,2,4,1]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,2,5,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,2,5,1]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,2,3,5,4,6,8,7]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,3,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,2,5,1]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,2,3,5,4,6,8,7]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,2,6,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,2,3,4,6,5,7,8]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,8,1]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,2,8,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,3,2,7,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,2,8,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,2,8,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,2,8,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,3,2,7,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,2,8,1]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,2,3,5,4,6,8,7]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,2,8,1]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,2,7,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,2,8,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,2,8,1]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,3,2,8,1]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,2,8,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,2,5,1]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,2,5,4,3,6,7,8]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,2,5,1]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,2,5,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,2,5,4,3,7,6,8]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,2,5,1]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,2,5,1]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,2,6,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,2,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,4,2,7,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,2,4,3,5,7,6,8]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,2,8,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,2,7,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,2,4,3,7,6,5,8]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,2,8,1]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,2,8,1]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,2,4,3,5,8,7,6]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,2,6,1]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[1,2,3,6,5,4,7,8]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,2,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,5,2,7,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,5,2,8,1]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,2,3,5,4,6,8,7]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,2,7,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,2,8,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,2,8,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,2,7,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,6,2,8,1]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,7,2,8,1]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,2,8,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,2,8,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,5,2,7,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,2,5,4,3,7,6,8]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,2,8,1]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,2,8,1]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,7,2,8,1]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,2,4,3,5,8,7,6]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,2,8,1]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,2,7,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,2,8,1]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,2,8,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,2,8,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,2,7,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,2,7,6,5,4,3,8]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,2,8,1]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,2,6,5,4,3,8,7]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,2,8,1]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,2,8,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,2,8,1]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,3,4,1]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,4,3,2,5,6,7,8]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,2,3,4,1]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,3,4,1]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,4,3,2,5,6,8,7]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,3,4,1]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[1,4,3,2,6,5,7,8]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,3,4,1]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,4,3,2,6,5,8,7]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,3,4,1]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,3,4,1]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,4,3,2,5,6,8,7]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,3,4,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,3,4,1]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,2,3,5,1]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,3,2,5,4,6,8,7]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,3,5,1]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,2,3,6,1]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,3,2,4,6,5,7,8]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,3,7,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,3,8,1]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,3,2,4,5,6,8,7]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,2,3,8,1]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,3,2,4,5,8,7,6]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,2,3,8,1]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,3,2,4,6,5,8,7]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,2,3,8,1]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,3,2,4,5,8,7,6]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,2,3,8,1]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,2,3,8,1]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,3,2,5,4,6,8,7]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,2,3,8,1]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,2,3,8,1]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,3,2,4,6,5,8,7]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,2,3,8,1]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,3,2,4,5,8,7,6]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,2,3,8,1]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,2,3,8,1]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,3,2,6,5,4,8,7]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,2,3,8,1]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,3,8,1]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,4,5,1]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,2,5,4,3,6,7,8]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,2,4,5,1]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,2,4,5,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,2,5,4,3,7,6,8]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,4,6,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,2,4,7,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,2,4,3,5,7,6,8]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,2,4,8,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[6,7,5,3,2,4,8,1]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,2,4,3,5,8,7,6]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,2,4,8,1]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,2,4,3,5,8,7,6]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,5,6,1]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[1,2,3,6,5,4,7,8]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,5,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,2,5,7,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,5,8,1]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2,6,7,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,2,6,8,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,7,8,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,2,6,7,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,7,8,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,2,7,8,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,2,6,5,4,3,8,7]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,2,6,7,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,2,4,3,7,6,5,8]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,2,7,8,1]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,2,4,3,5,8,7,6]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,2,6,8,1]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,7,8,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,2,6,7,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,2,7,6,5,4,3,8]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,2,7,8,1]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,2,7,8,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,7,8,1]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,4,5,1]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,5,4,3,2,6,7,8]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,2,3,4,5,1]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,5,4,3,2,6,8,7]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,3,4,5,1]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,5,4,3,2,7,6,8]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,2,3,4,5,1]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,5,4,3,2,6,8,7]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,5,4,3,2,8,7,6]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,4,8,1]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,4,3,2,5,6,8,7]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,2,3,4,8,1]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,4,3,2,6,5,8,7]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,3,4,8,1]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,3,5,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,3,2,6,5,4,8,7]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,5,7,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,5,8,1]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,3,2,5,4,6,8,7]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,2,3,6,7,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,3,2,4,7,6,5,8]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[7,5,4,2,3,6,8,1]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,3,2,4,6,5,8,7]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,2,3,7,8,1]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,3,2,4,5,8,7,6]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[8,4,5,2,3,6,7,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,3,2,7,6,5,4,8]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,2,3,6,8,1]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,3,2,6,5,4,8,7]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[6,4,5,2,3,7,8,1]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,5,6,2,3,7,8,1]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,4,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,2,6,5,4,3,8,7]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,4,5,8,1]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,4,5,8,1]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,4,6,8,1]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[6,5,3,2,4,7,8,1]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,2,4,3,5,8,7,6]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[8,4,3,2,5,6,7,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,7,8,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,6,7,8,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,2,5,6,7,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,2,7,6,5,4,3,8]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,2,6,7,8,1]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,6,7,8,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,6,7,8,1]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,4,5,6,1]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[1,6,5,4,3,2,7,8]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,6,5,4,3,2,8,7]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[8,6,2,3,4,5,7,1]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,5,4,3,2,7,6,8]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,5,8,1]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,5,4,3,2,6,8,7]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,4,5,8,1]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,5,4,3,2,8,7,6]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,3,4,6,8,1]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,4,3,2,6,5,8,7]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,3,4,7,8,1]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,3,5,6,7,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,3,2,7,6,5,4,8]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,6,7,8,1]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,6,7,8,1]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,4,5,6,7,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,2,7,6,5,4,3,8]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,4,5,6,8,1]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,2,6,5,4,3,8,7]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,6,7,8,1]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,6,7,8,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,6,7,8,1]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,7,6,5,4,3,2,8]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,6,8,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,6,5,4,3,2,8,7]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,5,7,8,1]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,5,4,3,2,8,7,6]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,6,7,8,1]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,6,7,8,1]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,1]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[2,1,3,4,5,7,6,8]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[2,1,3,4,5,8,7,6]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,3,1,2]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[2,1,3,4,6,5,7,8]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,3,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[2,1,3,4,6,5,8,7]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[2,1,3,4,5,7,6,8]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[2,1,3,4,5,8,7,6]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,3,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[2,1,3,4,6,5,8,7]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[2,1,3,4,5,8,7,6]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,3,1,2]=>[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[2,1,3,5,4,6,7,8]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[2,1,3,5,4,6,8,7]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[2,1,3,5,4,7,6,8]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,3,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[2,1,3,5,4,8,7,6]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,3,1,2]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[2,1,3,4,6,5,7,8]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,3,1,2]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[2,1,3,4,7,6,5,8]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,3,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[2,1,3,4,6,5,8,7]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[2,1,3,4,5,8,7,6]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,3,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[2,1,3,6,5,4,8,7]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[2,1,3,5,4,7,6,8]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[2,1,3,5,4,6,8,7]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,3,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[2,1,3,5,4,8,7,6]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,7,3,1,2]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[2,1,3,4,7,6,5,8]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[2,1,3,4,5,8,7,6]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,3,1,2]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,1,2]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,1,2]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,4,1,2]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[2,1,4,3,5,6,7,8]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[2,1,4,3,5,6,8,7]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[2,1,4,3,5,6,8,7]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[2,1,4,3,5,8,7,6]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[2,1,4,3,6,5,7,8]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[2,1,4,3,5,7,6,8]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[2,1,4,3,5,6,8,7]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[2,1,4,3,5,8,7,6]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[2,1,4,3,7,6,5,8]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[2,1,4,3,5,8,7,6]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[2,1,3,5,4,8,7,6]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[2,1,3,4,6,5,8,7]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,7,1,2]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[2,1,3,4,5,7,6,8]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,8,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,8,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[2,1,3,4,6,5,8,7]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,8,1,2]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,3,6,1,2]=>[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[2,1,3,6,5,4,7,8]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,3,6,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[2,1,3,6,5,4,8,7]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,8,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[2,1,3,5,4,8,7,6]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,7,1,2]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[2,1,3,4,7,6,5,8]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,3,8,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[2,1,3,4,6,5,8,7]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,8,1,2]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[2,1,3,4,5,8,7,6]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,8,1,2]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,3,8,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[2,1,3,5,4,8,7,6]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,8,1,2]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,5,1,2]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[2,1,5,4,3,6,7,8]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,5,1,2]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[2,1,5,4,3,6,8,7]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,5,1,2]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[2,1,5,4,3,7,6,8]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,6,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,8,1,2]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[2,1,4,3,5,6,8,7]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,6,1,2]=>[[[[[.,[.,.]],.],[.,[.,.]]],.],.]=>[2,1,3,6,5,4,7,8]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,6,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[2,1,3,6,5,4,8,7]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,5,8,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[2,1,3,5,4,6,8,7]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,7,1,2]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[2,1,3,4,7,6,5,8]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,8,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[2,1,3,4,6,5,8,7]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,1,2]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[2,1,3,4,5,8,7,6]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,7,8,1,2]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,6,8,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[2,1,3,6,5,4,8,7]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,8,1,2]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,8,1,2]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,6,1,2]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[2,1,6,5,4,3,7,8]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,8,1,2]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[2,1,5,4,3,6,8,7]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,6,7,1,2]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[2,1,4,3,7,6,5,8]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,8,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,8,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,7,1,2]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[2,1,3,7,6,5,4,8]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,8,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[2,1,3,5,4,8,7,6]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,8,1,2]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,8,1,2]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,7,1,2]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[2,1,7,6,5,4,3,8]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,8,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,8,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,7,8,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,8,1,2]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,1,3]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]=>[1,3,2,4,5,6,7,8]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,3,2,4,5,6,8,7]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,3,2,4,5,6,8,7]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,3,2,4,5,8,7,6]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,2,1,3]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]=>[1,3,2,4,6,5,7,8]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,2,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,3,2,4,6,5,8,7]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,3,2,4,5,6,8,7]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,3,2,4,5,8,7,6]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,2,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,3,2,4,6,5,8,7]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,3,2,4,5,8,7,6]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,2,1,3]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,2,1,3]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,3,2,4,5,6,8,7]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,3,2,4,5,8,7,6]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,3,2,4,5,8,7,6]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,2,1,3]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,3,2,5,4,6,8,7]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,2,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,3,2,4,6,5,8,7]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,2,1,3]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,3,2,7,6,5,4,8]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,2,1,3]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,3,2,6,5,4,8,7]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,2,1,3]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,2,1,3]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,1,4]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]=>[1,2,4,3,5,6,7,8]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,2,4,3,5,7,6,8]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,2,4,3,5,8,7,6]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,2,1,4]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,2,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,2,4,3,5,7,6,8]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,2,4,3,5,8,7,6]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,2,1,4]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,2,4,3,7,6,5,8]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,2,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,2,4,3,5,8,7,6]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,2,1,4]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,2,1,5]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]=>[1,2,3,5,4,6,7,8]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,2,3,5,4,6,8,7]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,3,2,1,5]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,2,3,5,4,6,8,7]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,2,1,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,2,1,6]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]=>[1,2,3,4,6,5,7,8]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,2,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,1,7]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,7,6,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,8,7]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,2,1,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,3,2,1,7]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,2,1,8]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,2,1,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,2,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,3,2,1,6]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[1,2,3,6,5,4,7,8]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,3,2,1,6]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,3,2,1,7]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,2,1,8]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,2,3,5,4,6,8,7]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,2,1,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,3,2,1,8]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,2,1,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,2,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,3,2,1,7]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,2,1,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,2,1,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,2,1,5]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,2,5,4,3,6,7,8]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,2,1,5]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,2,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,2,1,6]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,4,2,1,7]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,2,4,3,5,7,6,8]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,2,1,8]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[6,7,5,3,4,2,1,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,2,4,3,5,8,7,6]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,2,1,7]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,2,4,3,7,6,5,8]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,2,1,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,2,1,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,2,4,3,5,8,7,6]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,4,2,1,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,5,2,1,8]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,2,3,5,4,6,8,7]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,5,2,1,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,2,1,8]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,2,1,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,7,2,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,2,1,7]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,2,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,2,1,6]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,2,6,5,4,3,7,8]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,2,1,6]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,2,6,5,4,3,8,7]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,2,1,8]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,2,1,7]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,2,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,2,1,7]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,2,7,6,5,4,3,8]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,2,1,8]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,2,6,5,4,3,8,7]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,2,1,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,3,1,4]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,4,3,2,5,6,7,8]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,2,3,1,4]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,4,3,2,5,6,8,7]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,2,3,1,4]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,3,1,4]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,4,3,2,5,6,8,7]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,3,1,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,3,1,4]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[1,4,3,2,6,5,7,8]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,3,1,4]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,4,3,2,6,5,8,7]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,3,1,4]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,3,1,4]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,4,3,2,5,6,8,7]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,3,1,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,3,1,4]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,2,3,1,4]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,4,3,2,6,5,8,7]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,3,1,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,3,1,4]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,3,1,5]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,2,3,1,5]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,3,2,5,4,6,8,7]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,3,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,3,1,7]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,3,1,8]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,3,2,4,5,6,8,7]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,2,3,1,8]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,3,2,4,5,8,7,6]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,2,3,1,7]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,3,2,4,7,6,5,8]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,2,3,1,8]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,3,2,4,6,5,8,7]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,2,3,1,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,2,3,1,6]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[1,3,2,6,5,4,7,8]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,2,3,1,6]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,3,2,6,5,4,8,7]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,2,3,1,8]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,3,2,5,4,6,8,7]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,2,3,1,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,2,3,1,8]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,3,2,4,6,5,8,7]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,2,3,1,8]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,3,2,4,5,8,7,6]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,2,3,1,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,2,3,1,7]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,3,2,7,6,5,4,8]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,2,3,1,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,3,1,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,4,1,5]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,2,5,4,3,6,7,8]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,2,4,1,5]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,2,5,4,3,7,6,8]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,4,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,4,1,6]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,2,4,1,7]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,2,4,3,5,7,6,8]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,2,4,1,8]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,2,4,1,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,2,4,3,5,8,7,6]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,2,4,1,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,5,1,6]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[1,2,3,6,5,4,7,8]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,5,1,6]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,2,5,1,8]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,2,3,5,4,6,8,7]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,5,1,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2,6,1,7]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,2,6,1,8]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,7,1,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,2,7,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,2,6,1,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,7,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,2,5,1,6]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,2,6,5,4,3,7,8]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,5,1,6]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,2,6,5,4,3,8,7]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,2,5,1,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,2,6,1,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,2,7,1,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,2,6,1,7]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,2,6,1,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,7,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,2,7,1,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,2,7,1,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,2,7,1,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,2,7,1,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,7,1,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,4,1,5]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,5,4,3,2,6,7,8]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,3,4,1,5]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,5,4,3,2,7,6,8]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,2,3,4,1,5]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,5,4,3,2,6,8,7]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,4,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,5,4,3,2,8,7,6]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,2,3,4,1,6]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,4,3,2,6,5,8,7]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,3,4,1,7]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,4,1,8]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,4,3,2,5,6,8,7]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,2,3,4,1,8]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,3,4,1,7]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,2,3,4,1,8]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,4,3,2,6,5,8,7]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,2,3,4,1,8]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,3,4,1,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,5,1,7]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,5,1,8]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,3,2,5,4,6,8,7]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[6,7,4,2,3,5,1,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,2,3,6,1,7]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,3,2,4,7,6,5,8]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[8,4,5,2,3,6,1,7]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,3,2,7,6,5,4,8]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,2,3,6,1,8]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,3,2,6,5,4,8,7]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,3,7,1,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,4,5,1,7]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,2,5,4,3,7,6,8]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,4,5,1,8]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,4,5,1,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,2,4,6,1,7]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,2,4,3,7,6,5,8]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,4,6,1,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[6,5,3,2,4,7,1,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,2,4,3,5,8,7,6]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,7,1,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,2,5,6,1,7]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,2,7,6,5,4,3,8]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,6,7,1,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,4,5,1,6]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[1,6,5,4,3,2,7,8]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,4,5,1,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,6,5,4,3,2,8,7]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,5,1,8]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,5,4,3,2,6,8,7]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,4,5,1,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,5,4,3,2,8,7,6]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,3,4,6,1,7]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[7,4,2,3,5,6,1,8]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,3,2,6,5,4,8,7]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,3,5,7,1,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,6,7,1,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,6,7,1,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,4,5,6,1,7]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,2,7,6,5,4,3,8]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[6,3,2,4,5,7,1,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,6,7,1,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,6,7,1,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,5,6,1,7]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,7,6,5,4,3,2,8]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,6,1,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,6,5,4,3,2,8,7]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,5,7,1,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,5,4,3,2,8,7,6]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,6,7,1,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,6,7,1,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,6,7,1,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,1,2,3]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]=>[3,2,1,4,5,6,7,8]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[3,2,1,4,5,6,8,7]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[3,2,1,4,5,6,8,7]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[3,2,1,4,6,5,8,7]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[3,2,1,4,5,7,6,8]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[3,2,1,4,5,6,8,7]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[3,2,1,4,7,6,5,8]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[3,2,1,4,6,5,8,7]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,1,2,3]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[3,2,1,5,4,6,7,8]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,1,2,3]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[3,2,1,5,4,7,6,8]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[3,2,1,5,4,8,7,6]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,1,2,3]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[3,2,1,4,6,5,7,8]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,6,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[3,2,1,4,6,5,8,7]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[3,2,1,4,5,7,6,8]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[3,2,1,4,5,6,8,7]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[3,2,1,4,7,6,5,8]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[3,2,1,4,6,5,8,7]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,1,2,3]=>[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[3,2,1,6,5,4,7,8]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,1,2,3]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[3,2,1,6,5,4,8,7]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,1,2,3]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[3,2,1,5,4,7,6,8]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,1,2,3]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[3,2,1,5,4,6,8,7]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[3,2,1,5,4,8,7,6]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,7,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[3,2,1,4,7,6,5,8]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[3,2,1,4,6,5,8,7]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,1,2,3]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[3,2,1,7,6,5,4,8]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,1,2,3]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[3,2,1,6,5,4,8,7]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[3,2,1,5,4,8,7,6]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,1,2,3]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,1,2,4]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]=>[2,1,4,3,5,6,7,8]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,1,2,4]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[2,1,4,3,5,6,8,7]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,1,2,4]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[2,1,4,3,5,7,6,8]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,1,2,4]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[2,1,4,3,5,6,8,7]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,1,2,4]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[2,1,4,3,6,5,7,8]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,1,2,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,1,2,4]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[2,1,4,3,5,7,6,8]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,1,2,4]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[2,1,4,3,5,6,8,7]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[2,1,4,3,5,8,7,6]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,1,2,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[2,1,4,3,5,8,7,6]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,1,2,5]=>[[[[[[.,[.,.]],.],[.,.]],.],.],.]=>[2,1,3,5,4,6,7,8]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,1,2,5]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[2,1,3,5,4,8,7,6]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,1,2,6]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]=>[2,1,3,4,6,5,7,8]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,1,2,6]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[2,1,3,4,6,5,8,7]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,1,2,7]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[2,1,3,4,5,7,6,8]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,1,2,8]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,8,7]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,1,2,8]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[2,1,3,4,5,8,7,6]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,1,2,8]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[2,1,3,4,6,5,8,7]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,3,1,2,7]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[2,1,3,5,4,7,6,8]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,1,2,8]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[2,1,3,5,4,6,8,7]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,1,2,8]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,1,2,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,1,2,5]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[2,1,5,4,3,6,7,8]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,1,2,5]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[2,1,5,4,3,6,8,7]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,1,2,5]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[2,1,5,4,3,7,6,8]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,1,2,6]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[2,1,4,3,6,5,7,8]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,4,1,2,7]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[2,1,4,3,5,7,6,8]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,1,2,8]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[2,1,4,3,5,6,8,7]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,1,2,7]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[2,1,4,3,7,6,5,8]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,1,2,8]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[2,1,4,3,5,8,7,6]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,1,2,7]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[2,1,3,4,7,6,5,8]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,1,2,8]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[2,1,3,4,5,8,7,6]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,1,2,7]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[2,1,3,7,6,5,4,8]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,7,1,2,8]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[2,1,3,5,4,8,7,6]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,1,2,6]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[2,1,6,5,4,3,7,8]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,1,2,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,5,1,2,7]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[2,1,5,4,3,7,6,8]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,5,1,2,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,6,1,2,7]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[2,1,4,3,7,6,5,8]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,1,2,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,1,2,7]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[2,1,3,7,6,5,4,8]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,1,2,7]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[2,1,7,6,5,4,3,8]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,1,2,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,1,2,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,1,2,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,1,3,4]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]=>[1,4,3,2,5,6,7,8]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,2,1,3,4]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,4,3,2,5,6,8,7]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,1,3,4]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,4,3,2,5,6,8,7]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,1,3,4]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[1,4,3,2,6,5,7,8]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,1,3,4]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,4,3,2,6,5,8,7]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,1,3,4]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,1,3,4]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,4,3,2,5,6,8,7]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,1,3,4]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,2,1,3,4]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,4,3,2,6,5,8,7]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,1,3,5]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]=>[1,3,2,5,4,6,7,8]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,2,1,3,5]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,3,2,5,4,6,8,7]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,2,1,3,5]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,1,3,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,2,1,3,6]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,3,2,4,6,5,8,7]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,1,3,7]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[1,3,2,4,5,7,6,8]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,1,3,8]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[1,3,2,4,5,6,8,7]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,2,1,3,7]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,3,2,4,7,6,5,8]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,2,1,3,8]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,3,2,4,5,8,7,6]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,2,1,3,8]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,3,2,5,4,6,8,7]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,2,1,3,8]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,3,2,4,6,5,8,7]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,2,1,3,7]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,3,2,7,6,5,4,8]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,2,1,3,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,1,3,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,1,4,5]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]=>[1,2,5,4,3,6,7,8]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,2,1,4,5]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,2,1,4,5]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,2,5,4,3,7,6,8]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,2,1,4,5]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,1,4,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,1,4,6]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]=>[1,2,4,3,6,5,7,8]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,2,1,4,6]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,2,1,4,7]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[1,2,4,3,5,7,6,8]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,2,1,4,8]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[1,2,4,3,5,6,8,7]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,2,1,4,7]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,2,4,3,7,6,5,8]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,1,5,6]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]=>[1,2,3,6,5,4,7,8]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,1,5,6]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,2,1,5,7]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[1,2,3,5,4,7,6,8]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,2,1,5,8]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[1,2,3,5,4,6,8,7]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,1,5,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2,1,6,7]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,7,6,5,8]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,2,1,6,8]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,6,5,8,7]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,1,7,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,8,7,6]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,2,1,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,2,1,6,7]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,2,1,6,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,1,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,2,1,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,2,1,5,6]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,2,6,5,4,3,7,8]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,1,5,6]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,2,6,5,4,3,8,7]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,2,1,5,7]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,2,5,4,3,7,6,8]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,2,1,5,8]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,2,1,5,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,2,1,7,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,2,4,3,5,8,7,6]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,2,1,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,2,1,6,7]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,2,1,6,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,1,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,2,1,6,7]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,2,7,6,5,4,3,8]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,2,1,6,8]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,2,6,5,4,3,8,7]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,2,1,7,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,1,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,1,4,5]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,5,4,3,2,6,7,8]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,2,3,1,4,5]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,5,4,3,2,6,8,7]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,3,1,4,5]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,5,4,3,2,7,6,8]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,2,3,1,4,5]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,5,4,3,2,6,8,7]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,1,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,5,4,3,2,8,7,6]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,3,1,4,7]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,1,4,8]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,4,3,2,5,6,8,7]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,2,3,1,4,8]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,3,1,4,7]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,2,3,1,4,8]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,4,3,2,6,5,8,7]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,2,3,1,4,8]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,3,1,4,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,3,1,5,6]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,3,2,6,5,4,8,7]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,1,5,7]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,1,5,8]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,3,2,5,4,6,8,7]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[6,7,4,2,3,1,5,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[7,5,4,2,3,1,6,8]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[1,3,2,4,6,5,8,7]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[8,4,5,2,3,1,6,7]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,3,2,7,6,5,4,8]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,3,1,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[8,7,3,2,4,1,5,6]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,2,6,5,4,3,7,8]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,4,1,5,6]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,2,6,5,4,3,8,7]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,4,1,5,7]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,2,5,4,3,7,6,8]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,4,1,5,8]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,4,1,5,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,4,1,6,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,3,2,4,1,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,5,1,7,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,1,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,6,1,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,6,1,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,6,1,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,4,1,5,6]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[1,6,5,4,3,2,7,8]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,4,1,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,6,5,4,3,2,8,7]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[8,6,2,3,4,1,5,7]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,5,4,3,2,7,6,8]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,1,5,8]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,5,4,3,2,6,8,7]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,4,1,5,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,5,4,3,2,8,7,6]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,3,4,1,6,7]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,3,4,1,6,8]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,4,3,2,6,5,8,7]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,3,4,1,7,8]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,6,2,3,4,1,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,3,5,1,6,7]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,3,2,7,6,5,4,8]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[7,4,2,3,5,1,6,8]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,3,2,6,5,4,8,7]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,6,1,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,6,1,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,6,1,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,5,1,6,7]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,7,6,5,4,3,2,8]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,1,6,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,6,5,4,3,2,8,7]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,5,1,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,5,4,3,2,8,7,6]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,6,1,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,6,1,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,6,1,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,1,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,1,2,3,4]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]=>[4,3,2,1,5,6,7,8]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,1,2,3,5]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],.]=>[3,2,1,5,4,6,7,8]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,1,2,3,5]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[3,2,1,5,4,6,8,7]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,1,2,3,5]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[3,2,1,5,4,6,8,7]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,1,2,3,5]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[3,2,1,5,4,8,7,6]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,1,2,3,6]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],.]=>[3,2,1,4,6,5,7,8]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,1,2,3,6]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[3,2,1,4,6,5,8,7]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,1,2,3,7]=>[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[3,2,1,4,5,7,6,8]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,1,2,3,8]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[3,2,1,4,5,6,8,7]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,1,2,3,7]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[3,2,1,4,7,6,5,8]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,1,2,3,8]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,1,2,3,6]=>[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[3,2,1,6,5,4,7,8]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,1,2,3,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[3,2,1,6,5,4,8,7]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,1,2,3,7]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[3,2,1,5,4,7,6,8]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,1,2,3,8]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,1,2,3,7]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[3,2,1,7,6,5,4,8]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,1,2,3,8]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[3,2,1,6,5,4,8,7]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,1,2,3,8]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,1,2,3,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,1,2,4,5]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]=>[2,1,5,4,3,6,7,8]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,1,2,4,5]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[2,1,5,4,3,6,8,7]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,1,2,4,5]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[2,1,5,4,3,7,6,8]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,1,2,4,5]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[2,1,5,4,3,6,8,7]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,1,2,4,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,1,2,4,6]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]=>[2,1,4,3,6,5,7,8]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,1,2,4,6]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,1,2,4,7]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[2,1,4,3,7,6,5,8]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,1,2,4,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,1,2,5,6]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[2,1,3,6,5,4,8,7]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,1,2,5,7]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[2,1,3,5,4,7,6,8]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,1,2,5,8]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[2,1,3,5,4,6,8,7]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,1,2,6,8]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[2,1,3,4,6,5,8,7]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,1,2,7,8]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[2,1,3,4,5,8,7,6]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,1,2,7,8]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,1,2,7,8]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[2,1,3,5,4,8,7,6]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,1,2,7,8]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,1,2,5,6]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[2,1,6,5,4,3,7,8]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,1,2,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,1,2,5,7]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[2,1,5,4,3,7,6,8]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,1,2,5,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,1,2,6,7]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[2,1,4,3,7,6,5,8]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,1,2,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,1,2,7,8]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[2,1,3,5,4,8,7,6]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,1,2,7,8]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,1,2,6,7]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[2,1,7,6,5,4,3,8]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,1,2,7,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,1,2,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,1,3,4,5]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]=>[1,5,4,3,2,6,7,8]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,2,1,3,4,5]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,5,4,3,2,6,8,7]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,1,3,4,5]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[1,5,4,3,2,7,6,8]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,1,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,5,4,3,2,8,7,6]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,2,1,3,4,6]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]=>[1,4,3,2,6,5,7,8]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,2,1,3,4,6]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,4,3,2,6,5,8,7]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,1,3,4,7]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[1,4,3,2,5,7,6,8]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,1,3,4,8]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[1,4,3,2,5,6,8,7]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,2,1,3,4,8]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[1,4,3,2,5,8,7,6]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,1,3,4,7]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,2,1,3,4,8]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,4,3,2,6,5,8,7]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,1,3,4,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[8,7,4,2,1,3,5,6]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]=>[1,3,2,6,5,4,7,8]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,1,3,5,6]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,3,2,6,5,4,8,7]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,1,3,5,7]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[1,3,2,5,4,7,6,8]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,1,3,5,8]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[1,3,2,5,4,6,8,7]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,2,1,3,6,7]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[1,3,2,4,7,6,5,8]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,2,1,3,7,8]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[1,3,2,4,5,8,7,6]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[5,6,4,2,1,3,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,2,1,3,6,8]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[1,3,2,6,5,4,8,7]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[6,4,5,2,1,3,7,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,1,3,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[4,5,6,2,1,3,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[8,7,3,2,1,4,5,6]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[1,2,6,5,4,3,7,8]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,1,4,5,6]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,2,6,5,4,3,8,7]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,1,4,5,7]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[1,2,5,4,3,7,6,8]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,1,4,5,8]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[1,2,5,4,3,6,8,7]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,1,4,5,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,2,1,4,6,7]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[1,2,4,3,7,6,5,8]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,1,4,6,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[1,2,4,3,6,5,8,7]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[6,5,3,2,1,4,7,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[1,2,4,3,5,8,7,6]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,3,2,1,4,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[8,4,3,2,1,5,6,7]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,7,6,5,4,8]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,2,1,5,6,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[1,2,3,6,5,4,8,7]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,1,5,7,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,5,4,8,7,6]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,6,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,8,7,6,5]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,1,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,2,1,5,6,7]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,2,7,6,5,4,3,8]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[6,3,4,2,1,5,7,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[1,2,5,4,3,8,7,6]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,2,1,6,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,1,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,1,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,1,4,5,6]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[1,6,5,4,3,2,7,8]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,1,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,6,5,4,3,2,8,7]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,1,4,5,8]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[1,5,4,3,2,6,8,7]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,1,4,5,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,5,4,3,2,8,7,6]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,3,1,4,6,8]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[1,4,3,2,6,5,8,7]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,3,1,5,6,7]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,3,2,7,6,5,4,8]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,1,6,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,1,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,1,6,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,1,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,1,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,1,5,6,7]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,7,6,5,4,3,2,8]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,1,5,6,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,6,5,4,3,2,8,7]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,1,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,1,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,1,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,1,2,3,4,5]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]=>[5,4,3,2,1,6,7,8]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[5,4,3,2,1,6,8,7]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[5,4,3,2,1,7,6,8]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[5,4,3,2,1,6,8,7]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,1,2,3,4,6]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]=>[4,3,2,1,6,5,7,8]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,1,2,3,4,6]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,1,2,3,4,7]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[4,3,2,1,5,7,6,8]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,1,2,3,4,8]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[4,3,2,1,5,6,8,7]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,1,2,3,4,8]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,1,2,3,4,7]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,1,2,3,4,8]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,1,2,3,4,8]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[4,3,2,1,5,8,7,6]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,1,2,3,4,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[8,7,4,1,2,3,5,6]=>[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]=>[3,2,1,6,5,4,7,8]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,1,2,3,5,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[3,2,1,6,5,4,8,7]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,1,2,3,5,7]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[3,2,1,5,4,7,6,8]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,1,2,3,6,7]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[3,2,1,4,7,6,5,8]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,1,2,3,7,8]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[3,2,1,4,5,8,7,6]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[8,4,5,1,2,3,6,7]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[3,2,1,7,6,5,4,8]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,1,2,3,6,8]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[3,2,1,6,5,4,8,7]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[4,5,6,1,2,3,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,1,2,4,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,1,2,4,5,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,1,2,4,6,7]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[2,1,4,3,7,6,5,8]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,1,2,4,6,8]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,1,2,5,6,8]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[2,1,3,6,5,4,8,7]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,1,2,5,7,8]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[2,1,3,5,4,8,7,6]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,1,2,6,7,8]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[2,1,3,4,8,7,6,5]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,1,2,5,6,7]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[2,1,7,6,5,4,3,8]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[7,3,4,1,2,5,6,8]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,1,2,6,7,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,1,2,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,1,3,4,5,6]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[1,6,5,4,3,2,7,8]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,1,3,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,6,5,4,3,2,8,7]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,1,3,4,6,7]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[1,4,3,2,7,6,5,8]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[5,6,2,1,3,4,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,1,3,5,6,7]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[1,3,2,7,6,5,4,8]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,1,3,5,7,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[1,3,2,5,4,8,7,6]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,1,3,6,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[1,3,2,4,8,7,6,5]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,1,3,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,1,4,5,6,7]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[1,2,7,6,5,4,3,8]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,1,4,5,6,8]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[1,2,6,5,4,3,8,7]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,1,4,6,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,4,3,8,7,6,5]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1,5,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,8,7,6,5,4]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,1,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,1,4,5,6,7]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,7,6,5,4,3,2,8]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,1,4,5,6,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,6,5,4,3,2,8,7]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,1,4,5,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[1,5,4,3,2,8,7,6]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,1,4,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,1,5,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,1,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[8,7,1,2,3,4,5,6]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[6,5,4,3,2,1,7,8]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[8,6,1,2,3,4,5,7]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[5,4,3,2,1,7,6,8]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[7,6,1,2,3,4,5,8]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[5,4,3,2,1,6,8,7]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,7,1,2,3,4,5,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[8,5,1,2,3,4,6,7]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[4,3,2,1,7,6,5,8]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[7,5,1,2,3,4,6,8]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[4,3,2,1,6,5,8,7]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[8,4,1,2,3,5,6,7]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[3,2,1,7,6,5,4,8]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[7,4,1,2,3,5,6,8]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[3,2,1,6,5,4,8,7]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[6,4,1,2,3,5,7,8]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[3,2,1,5,4,8,7,6]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[5,4,1,2,3,6,7,8]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[3,2,1,4,8,7,6,5]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[4,5,1,2,3,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[8,3,1,2,4,5,6,7]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[2,1,7,6,5,4,3,8]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[7,3,1,2,4,5,6,8]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[2,1,6,5,4,3,8,7]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[6,3,1,2,4,5,7,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[2,1,5,4,3,8,7,6]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[5,3,1,2,4,6,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[2,1,4,3,8,7,6,5]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[4,3,1,2,5,6,7,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[2,1,3,8,7,6,5,4]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[8,2,1,3,4,5,6,7]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,7,6,5,4,3,2,8]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[7,2,1,3,4,5,6,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[1,6,5,4,3,2,8,7]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[5,2,1,3,4,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[1,4,3,2,8,7,6,5]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[4,2,1,3,5,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,3,2,8,7,6,5,4]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,8,7,6,5,4,3]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[7,6,5,4,3,2,1,8]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,2,3,4,5,6,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[6,5,4,3,2,1,8,7]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,2,3,4,5,7,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[5,4,3,2,1,8,7,6]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,2,3,4,6,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[4,3,2,1,8,7,6,5]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,2,3,5,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[3,2,1,8,7,6,5,4]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,8,7,6,5,4,3]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[8,7,6,5,4,3,2,1]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,8]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[8,7,6,5,4,3,2,1,9]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[10,1,2,3,4,5,6,7,8,9]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[9,8,7,6,5,4,3,2,1,10]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[9,2,1,3,4,5,6,7,8]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[1,8,7,6,5,4,3,2,9]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,9,1]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,9,8,7,6,5,4,3]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,1]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[11,1,2,3,4,5,6,7,8,9,10]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[10,9,8,7,6,5,4,3,2,1,11]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,1,3,4,5,6,7,8,9]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[1,9,8,7,6,5,4,3,2,10]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[9,3,1,2,4,5,6,7,8]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]=>[2,1,8,7,6,5,4,3,9]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,1,4,5,6,7,8]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[1,8,7,6,5,4,3,2,9]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[4,2,3,5,6,7,8,9,1]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,3,2,9,8,7,6,5,4]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[3,4,2,5,6,7,8,9,1]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,9,8,7,6,5,4,3]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,9,10,1]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,2,10,9,8,7,6,5,4,3]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[1,11,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,1,4,5,6,7,8,9]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[1,9,8,7,6,5,4,3,2,10]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,4,1,5,6,7,8]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[1,8,7,6,5,4,3,2,9]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,5,6,7,8,9,1]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,9,8,7,6,5,4]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,4,1,5,6,7,8,9]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[1,9,8,7,6,5,4,3,2,10]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,1,2,5,6,7,8]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]=>[2,1,8,7,6,5,4,3,9]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,4,5,1,6,7,8]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[1,8,7,6,5,4,3,2,9]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[4,5,2,3,6,7,8,9,1]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,3,2,9,8,7,6,5,4]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[4,3,2,5,6,7,8,9,10,1]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,3,10,9,8,7,6,5,4]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,4,5,1,6,7,8,9]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[1,9,8,7,6,5,4,3,2,10]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[9,6,1,2,3,4,5,7,8]=>[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.]=>[5,4,3,2,1,8,7,6,9]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,4,5,6,1,7,8]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[1,8,7,6,5,4,3,2,9]
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,2,7,8,9,10,1]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,2,10,9,8,7,6,5,4,3]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,4,5,6,1,7,8,9]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[1,9,8,7,6,5,4,3,2,10]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[9,7,1,2,3,4,5,6,8]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]=>[6,5,4,3,2,1,8,7,9]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,4,5,6,7,1,8]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[1,8,7,6,5,4,3,2,9]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[8,9,1,2,3,4,5,6,7]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[7,6,5,4,3,2,1,9,8]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[8,2,3,4,5,6,7,9,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[1,7,6,5,4,3,2,9,8]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,6,7,8,9,1]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,9,8,7,6,5]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,1,2]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[2,1,9,8,7,6,5,4,3]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,2,9,1]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,9,8,7,6,5,4,3]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,4,5,6,7,1,8,9]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[1,9,8,7,6,5,4,3,2,10]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[9,8,1,2,3,4,5,6,7]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[7,6,5,4,3,2,1,8,9]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,4,5,6,7,8,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[1,8,7,6,5,4,3,2,9]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[8,9,2,1,3,4,5,6,7]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[1,7,6,5,4,3,2,9,8]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[5,4,3,2,6,7,8,9,10,1]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,4,10,9,8,7,6,5]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[4,3,5,6,7,8,9,1,2]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,3,9,8,7,6,5,4]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,2,1]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,9,8,7,6,5,4,3]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,4,5,6,7,8,1,9]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[1,9,8,7,6,5,4,3,2,10]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[9,10,1,2,3,4,5,6,7,8]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[8,7,6,5,4,3,2,1,10,9]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[9,3,2,4,5,6,7,8,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,2,8,7,6,5,4,3,9]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[9,2,3,4,5,6,7,8,10,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[1,8,7,6,5,4,3,2,10,9]
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[4,5,3,6,7,8,9,1,2]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,3,9,8,7,6,5,4]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,1,2]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,1,10,9,8,7,6,5,4,3]
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,2,10,1]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,2,10,9,8,7,6,5,4,3]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[10,9,1,2,3,4,5,6,7,8]=>[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[8,7,6,5,4,3,2,1,9,10]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,4,5,6,7,8,9,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[1,9,8,7,6,5,4,3,2,10]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,2,5,6,7,8,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,2,8,7,6,5,4,3,9]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,2,1]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,2,10,9,8,7,6,5,4,3]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,9,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[7,8,6,5,4,3,2,1,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[8,6,7,5,4,3,2,1,9]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,7,6,9,8]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[7,6,8,5,4,3,2,1,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[6,7,8,5,4,3,2,1,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,9,8,7,6]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[8,6,5,7,4,3,2,1,9]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,7,6,9,8]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[7,6,5,8,4,3,2,1,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]
[1,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[6,7,5,8,4,3,2,1,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,9,8,7,6]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[6,5,7,8,4,3,2,1,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,9,8,7,6]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[6,5,4,7,8,3,2,1,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,9,8,7,6]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,8,2,1,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,7,8,2,1,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,9,8,7,6]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,2,1,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,9,8,7,6,5,4,3]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,2,3,1,9]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[1,3,2,4,5,6,7,9,8]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,2,8,1,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[5,4,6,3,7,2,8,1,9]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,9,8,7,6,5]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,7,8,1,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,9,8,7,6]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[8,2,3,4,5,6,7,1,9]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[1,7,6,5,4,3,2,9,8]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[4,2,3,5,6,7,8,1,9]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,3,2,9,8,7,6,5,4]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,1,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,9,8,7,6,5,4,3]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,9,8,7,6,5,4,3,2]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,1,2,9]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,7,9,8]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[2,1,9,8,7,6,5,4,3]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,2,1,3,9]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[1,3,2,4,5,6,7,9,8]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[8,6,5,4,3,2,1,7,9]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,7,6,9,8]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,2,1,8,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[6,7,5,4,3,2,1,8,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,9,8,7,6]
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,2,1,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,9,8,7,6,5,4,3]
[1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,7,1,8,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,9,8,7,6]
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,4,3,2,7,1,8,9]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,9,8,7,6,5]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,9,8,7,6,5,4,3,2]
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,1,2,3,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[3,2,1,9,8,7,6,5,4]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,1,2,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[2,1,9,8,7,6,5,4,3]
[1,1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[6,7,4,3,2,1,5,8,9]=>[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,3,5,4,9,8,7,6]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,1,7,8,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,9,8,7,6]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,4,3,2,1,7,8,9]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,9,8,7,6,5]
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,2,1,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,9,8,7,6,5,4,3]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,6,1,7,8,9]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,9,8,7,6,5]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[4,3,5,2,6,1,7,8,9]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,9,8,7,6,5,4]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,1,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,1,2,3,4,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[4,3,2,1,9,8,7,6,5]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,1,6,7,8,9]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,9,8,7,6,5]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[4,5,3,2,1,6,7,8,9]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,9,8,7,6,5,4]
[1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,2,1,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,9,8,7,6,5,4,3]
[1,1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,5,1,6,7,8,9]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,9,8,7,6,5,4]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[3,4,2,5,1,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,9,8,7,6,5,4,3]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[6,7,8,1,2,3,4,5,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[5,4,3,2,1,9,8,7,6]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[4,5,6,1,2,3,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[3,2,1,9,8,7,6,5,4]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[4,3,5,1,2,6,7,8,9]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,3,9,8,7,6,5,4]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,1,2,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[2,1,9,8,7,6,5,4,3]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[4,5,2,1,3,6,7,8,9]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,3,2,9,8,7,6,5,4]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1,5,6,7,8,9]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,9,8,7,6,5,4]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[3,4,2,1,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,9,8,7,6,5,4,3]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[8,2,3,1,4,5,6,7,9]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[1,7,6,5,4,3,2,9,8]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[4,2,3,1,5,6,7,8,9]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,3,2,9,8,7,6,5,4]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,4,1,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,9,8,7,6,5,4,3]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[7,8,1,2,3,4,5,6,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[6,5,4,3,2,1,9,8,7]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[4,3,1,2,5,6,7,8,9]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,3,9,8,7,6,5,4]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[2,1,9,8,7,6,5,4,3]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[8,2,1,3,4,5,6,7,9]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[1,7,6,5,4,3,2,9,8]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,9,8,7,6,5,4,3]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1,2,3,4,5,6,7,9]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[7,6,5,4,3,2,1,9,8]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[7,1,2,3,4,5,6,8,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[6,5,4,3,2,1,9,8,7]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[6,1,2,3,4,5,7,8,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[5,4,3,2,1,9,8,7,6]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[5,1,2,3,4,6,7,8,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[4,3,2,1,9,8,7,6,5]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[3,2,1,9,8,7,6,5,4]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[2,1,9,8,7,6,5,4,3]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[9,8,7,6,5,4,3,2,1]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,9,8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,7,9,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,9,8]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[8,7,6,9,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,9,8]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,9,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,9,8]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,9,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,9,8]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,9,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,9,8]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,9,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,9,8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,10,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[7,8,9,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[9,8,10,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[8,6,7,9,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,7,6,9,8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[9,8,7,10,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,10,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,10,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,10,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,2,3,9,1]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[1,3,2,4,5,6,7,9,8]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,10,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,2,10,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,10,9]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]=>[1,2,3,4,5,6,7,8,9,10,11]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[10,11,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,9,11,10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[8,9,10,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,7,10,9,8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[10,9,11,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,9,11,10]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[7,6,8,9,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,9,8,7,6]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,1,2,10]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,7,8,10,9]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,9,8,7,6,5,4,3,2,11,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,9,11,10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,9,8,7,6,5,4,3,2,1,11]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[1,2,3,4,5,6,7,8,9,11,10]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[8,7,9,10,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,7,10,9,8]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,6,10,9,8,7]
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[6,5,7,8,9,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,9,8,7,6]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,2,1,3,10]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]]=>[1,3,2,4,5,6,7,8,10,9]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,4,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,9,8,7,6,5]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,5,10,9,8,7,6]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[8,6,5,4,3,2,7,9,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,7,6,9,8]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,2,8,9,1]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[5,4,6,7,8,9,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,9,8,7,6,5]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,3,2,1]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,9,8,7,6,5,4]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,7,8,9,1]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,9,8,7,6]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[6,5,7,8,9,10,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,5,10,9,8,7,6]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,10,4,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,4,10,9,8,7,6,5]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,6,5,4,3,2,9,10,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,7,10,9,8]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[9,7,6,5,4,3,2,1,8,10]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,6,8,7,10,9]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[7,6,5,4,3,2,8,9,10,1]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,6,10,9,8,7]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[9,7,8,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,8,7,9]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[8,9,6,7,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,7,6,9,8]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[9,6,7,8,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,5,8,7,6,9]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,6,4,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]=>[1,2,3,4,6,5,7,8,9]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,5,3,2,1]=>[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]=>[1,2,3,5,4,6,7,8,9]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,4,2,1]=>[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]=>[1,2,4,3,5,6,7,8,9]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,5,6,7,8,2,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,2,8,7,6,5,4,3,9]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,2,3,1]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]=>[1,3,2,4,5,6,7,8,9]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,2,3,1]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[1,3,2,4,5,6,7,9,8]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,5,2,3,1]=>[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.]=>[1,3,2,5,4,6,7,8,9]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,2,3,1]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,3,2,9,8,7,6,5,4]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,2,3,4,1]=>[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]=>[1,4,3,2,5,6,7,8,9]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[9,8,2,3,4,5,6,7,1]=>[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]=>[1,7,6,5,4,3,2,8,9]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[8,9,2,3,4,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[1,7,6,5,4,3,2,9,8]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,3,1,2]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,3,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,7,9,8]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[9,7,8,6,5,4,3,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]=>[2,1,3,4,5,6,8,7,9]
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,3,1,2]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,3,9,8,7,6,5,4]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,4,1,2]=>[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.]=>[2,1,4,3,5,6,7,8,9]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,5,6,7,8,1,2]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]=>[2,1,8,7,6,5,4,3,9]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,1,2,3]=>[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,5,1,2,3]=>[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.]=>[3,2,1,5,4,6,7,8,9]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,1,2,3]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[3,2,1,9,8,7,6,5,4]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,1,2,3,4]=>[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[4,3,2,1,9,8,7,6,5]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,1,2,3,4,5]=>[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[5,4,3,2,1,6,7,8,9]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[7,8,9,6,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,[.,.]]]=>[5,4,3,2,1,6,9,8,7]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[9,6,7,8,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.]=>[5,4,3,2,1,8,7,6,9]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[5,4,3,2,1,9,8,7,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[9,8,7,1,2,3,4,5,6]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[6,5,4,3,2,1,7,8,9]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[9,7,8,1,2,3,4,5,6]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]=>[6,5,4,3,2,1,8,7,9]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,8,9,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[6,5,4,3,2,1,9,8,7]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[10,8,9,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,7,9,8,10]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[10,9,8,6,7,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]=>[1,2,3,4,5,7,6,8,9,10]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[1,2,3,4,6,5,7,8,9,10]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,7,8,9,10,3,2,1]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,3,10,9,8,7,6,5,4]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,2,3,1]=>[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[1,3,2,4,5,6,7,8,9,10]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,3,1,2]=>[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,10,8,7,6,5,4,3,1,2]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,7,8,10,9]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,5,6,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,1,2,3]=>[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[3,2,1,4,5,6,7,8,9,10]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,7,8,9,10,1,2,3]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[3,2,1,10,9,8,7,6,5,4]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,1,2,3,4]=>[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[4,3,2,1,5,6,7,8,9,10]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,10,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[4,3,2,1,10,9,8,7,6,5]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,1,2,3,4,5]=>[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[5,4,3,2,1,6,7,8,9,10]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,1,2,3,4,5,6]=>[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[6,5,4,3,2,1,7,8,9,10]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[6,5,4,3,2,1,10,9,8,7]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[10,9,8,1,2,3,4,5,6,7]=>[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[7,6,5,4,3,2,1,8,9,10]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[10,8,9,1,2,3,4,5,6,7]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.]=>[7,6,5,4,3,2,1,9,8,10]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[8,9,10,1,2,3,4,5,6,7]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]=>[7,6,5,4,3,2,1,10,9,8]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[10,9,8,7,6,5,4,3,2,1]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,2,1,3]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]=>[1,3,2,4,5,6,7,8,9]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,2,1,4]=>[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]=>[1,2,4,3,5,6,7,8,9]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,3,2,1,5]=>[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]=>[1,2,3,5,4,6,7,8,9]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,4,3,2,1,6]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]=>[1,2,3,4,6,5,7,8,9]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[9,8,6,5,4,3,2,1,7]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[1,2,3,4,5,7,6,8,9]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,2,1,8]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,8,7,9]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,2,1,3]=>[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[1,3,2,4,5,6,7,8,9,10]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,2,3,1,4]=>[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]=>[1,4,3,2,5,6,7,8,9]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,3,2,1,4]=>[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]=>[1,2,4,3,5,6,7,8,9,10]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,4,3,2,1,5]=>[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[1,2,3,5,4,6,7,8,9,10]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,5,4,3,2,1,6]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[1,2,3,4,6,5,7,8,9,10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[10,9,8,6,5,4,3,2,1,7]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]=>[1,2,3,4,5,7,6,8,9,10]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[9,6,7,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,5,8,7,6,9]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[10,9,7,6,5,4,3,2,1,8]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[1,2,3,4,5,6,8,7,9,10]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,5,4,3,2,1,9]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,7,9,8,10]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,6,4,3,2,1,7,8,9,10]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,4,10,9,8,7,6,5]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[6,7,5,4,3,2,1,8,9,10]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,5,10,9,8,7,6]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,10,9,8,7,6,5,4,3,1,2]=>[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[2,1,3,4,5,6,7,8,9,10,11]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,7,9,6,5,4,3,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,7,9,8]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[8,9,7,6,5,4,3,2,1,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,7,10,9,8]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,1,10,9,8,7,6,5,4,3]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9,10,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[1,11,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[3,4,2,1,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,2,10,9,8,7,6,5,4,3]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[9,8,10,7,6,5,4,3,1,2]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,7,8,10,9]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,7,9,6,5,4,2,1,3]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[1,3,2,4,5,6,7,9,8]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,7,9,6,5,4,2,3,1]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[1,3,2,4,5,6,7,9,8]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,2,1,3]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[1,3,2,4,5,6,7,9,8]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[9,6,5,4,3,2,1,7,8]=>[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,5,8,7,6,9]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,2,1,3,4]=>[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]=>[1,4,3,2,5,6,7,8,9]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,1,2,3,4,5,6,7,8,10]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[8,7,6,5,4,3,2,1,10,9]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[9,2,1,3,4,5,6,7,8,10]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[1,8,7,6,5,4,3,2,10,9]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,1,2,3,5]=>[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.]=>[3,2,1,5,4,6,7,8,9]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,1,2,4]=>[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.]=>[2,1,4,3,5,6,7,8,9]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,1,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[1,10,9,8,7,6,5,4,3,2]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[9,6,5,4,3,2,7,1,8]=>[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]=>[1,2,3,4,5,8,7,6,9]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,6,5,4,3,2,9,1,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,7,10,9,8]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[1,11,10,9,8,7,6,5,4,3,2]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,2,1,3]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[1,3,2,9,8,7,6,5,4]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,3,2,5,1]=>[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]=>[1,2,3,5,4,6,7,8,9]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,3,5,2,1]=>[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]=>[1,2,3,5,4,6,7,8,9]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[10,9,7,6,8,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[1,2,3,4,5,6,8,7,9,10]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,9,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,7,9,8,10]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,4,3,2,7,8,9,10,1]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,5,10,9,8,7,6]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,1,2,8]=>[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]=>[2,1,3,4,5,6,8,7,9]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[7,8,6,5,4,3,2,9,1]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[8,9,6,5,4,3,2,1,7]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,7,6,9,8]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,9,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[2,1,3,4,5,6,7,9,8]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[7,8,9,5,4,3,2,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]=>[1,2,3,4,6,5,9,8,7]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[7,8,9,6,5,4,3,2,1,10]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,6,10,9,8,7]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,4,3,2,1,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]]=>[1,2,3,5,4,9,8,7,6]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[7,6,8,9,5,4,3,2,1,10]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,6,10,9,8,7]
[1,1,0,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[7,6,5,8,9,4,3,2,1,10]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,6,10,9,8,7]
[1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[7,6,5,4,8,9,3,2,1,10]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,6,10,9,8,7]
[1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[7,6,5,4,3,8,9,2,1,10]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,6,10,9,8,7]
[1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[7,6,5,4,3,2,8,9,1,10]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,6,10,9,8,7]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[7,6,5,4,3,2,1,8,9,10]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[1,2,3,4,5,6,10,9,8,7]
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,3,9,1,2]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]=>[2,1,3,9,8,7,6,5,4]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[8,9,2,3,4,5,1,6,7]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[1,7,6,5,4,3,2,9,8]
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[5,6,7,4,8,9,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,[.,[.,.]]]]]=>[3,2,1,4,9,8,7,6,5]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[6,5,7,8,9,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,[.,.]]]]=>[4,3,2,1,5,9,8,7,6]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[8,7,9,1,2,3,4,5,6]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]]=>[6,5,4,3,2,1,7,9,8]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[8,1,2,3,4,5,6,7,9,10]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]=>[7,6,5,4,3,2,1,10,9,8]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[7,6,8,9,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,[.,.]]]=>[5,4,3,2,1,6,9,8,7]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[7,1,2,3,4,5,6,8,9,10]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[6,5,4,3,2,1,10,9,8,7]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[6,1,2,3,4,5,7,8,9,10]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[5,4,6,7,8,9,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,[.,[.,.]]]]]=>[3,2,1,4,9,8,7,6,5]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[5,1,2,3,4,6,7,8,9,10]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[4,3,2,1,10,9,8,7,6,5]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8,9,10]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[3,2,1,10,9,8,7,6,5,4]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[8,7,9,6,5,4,3,2,1,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,7,10,9,8]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[8,7,6,9,5,4,3,2,1,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,7,10,9,8]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,6,5,4,9,3,2,1,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,7,10,9,8]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,6,5,4,3,9,2,1,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,7,10,9,8]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,6,5,4,3,2,1,9,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,7,10,9,8]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,1,10,9,8,7,6,5,4,3]
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,1,2,3,7,8,9,10]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[3,2,1,10,9,8,7,6,5,4]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,1,2,3,4,9,10]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[4,3,2,1,10,9,8,7,6,5]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,1,2,3,4,5,10]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[5,4,3,2,1,10,9,8,7,6]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[6,5,7,4,8,3,9,2,10,1]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,5,10,9,8,7,6]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[9,5,4,3,2,1,6,7,8]=>[[[[[[.,.],.],.],.],[.,[.,[.,.]]]],.]=>[1,2,3,4,8,7,6,5,9]
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[3,2,4,1,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,2,10,9,8,7,6,5,4,3]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,1,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[1,11,10,9,8,7,6,5,4,3,2]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,4,3,2,1,7,8,9,10]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,5,10,9,8,7,6]
[1,0,1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[5,4,6,7,8,9,10,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,4,10,9,8,7,6,5]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,2,4,1]=>[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]=>[1,2,4,3,5,6,7,8,9]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,2,10,9,8,7,6,5,4,3]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[11,9,10,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,7,8,10,9,11]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,5,4,3,9,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,7,9,8,10]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[5,4,3,2,1,6,7,8,9,10]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,4,10,9,8,7,6,5]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[4,3,2,1,5,6,7,8,9,10]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[1,2,3,10,9,8,7,6,5,4]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[11,9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,7,8,10,9,11]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,8,7,9]
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,3,2,1,4]=>[[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]]=>[1,2,4,3,9,8,7,6,5]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[8,9,1,2,3,4,5,6,7,10]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]=>[7,6,5,4,3,2,1,10,9,8]
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,1,2,3,4,10]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[4,3,2,1,10,9,8,7,6,5]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,1,2,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,1,10,9,8,7,6,5,4,3]
[1,0,1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[5,4,6,7,8,3,9,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,9,8,7,6,5]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[7,6,8,5,9,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[9,10,7,6,5,4,3,2,1,8]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]=>[1,2,3,4,5,6,8,7,10,9]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0]=>[9,8,4,1,2,3,5,6,7]=>[[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.],.]=>[3,2,1,7,6,5,4,8,9]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]=>[1,2,3,4,6,5,7,8,9]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[10,9,8,6,5,7,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]=>[1,2,3,4,5,7,6,8,9,10]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,7,9,8,10]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[7,6,8,5,4,3,2,9,1]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,9,8,7]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[9,8,6,5,4,3,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[1,2,3,4,5,7,6,8,9]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[10,9,7,6,5,4,8,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[1,2,3,4,5,6,8,7,9,10]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[9,8,6,5,4,7,3,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[1,2,3,4,5,7,6,8,9]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[10,9,7,6,5,4,3,8,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[1,2,3,4,5,6,8,7,9,10]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,5,4,3,1,2,9]=>[[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]],.]=>[2,1,3,4,5,6,7,9,8,10]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,8,2,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[1,2,3,4,5,6,8,7,9]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,5,6,7,2,1,8]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]=>[1,2,8,7,6,5,4,3,9]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,5,6,7,1,2,8]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]=>[2,1,8,7,6,5,4,3,9]
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[2,1,10,9,8,7,6,5,4,3]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[8,9,7,6,5,4,3,2,10,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[1,2,3,4,5,6,7,10,9,8]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[5,6,4,7,3,8,2,9,1]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[1,2,3,4,9,8,7,6,5]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,4,6,3,7,2,8,1,9,10]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,4,10,9,8,7,6,5]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[9,4,3,5,6,7,8,2,1]=>[[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],.]=>[1,2,3,8,7,6,5,4,9]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[9,2,3,4,5,6,7,8,1,10]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[1,8,7,6,5,4,3,2,10,9]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[9,7,5,3,1,2,4,6,8,10]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[2,1,4,3,6,5,8,7,10,9,12,11]
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[3,4,2,5,1,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,2,10,9,8,7,6,5,4,3]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[5,6,4,7,3,8,2,9,1,10]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[1,2,3,4,10,9,8,7,6,5]
[1,1,1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,2,1,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[1,2,10,9,8,7,6,5,4,3]
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
Map
to 312-avoiding permutation
Description
Return a 312-avoiding permutation corresponding to a binary tree.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
The linear extensions of a binary tree form an interval of the weak order called the Sylvester class of the tree. This permutation is the minimal element of this Sylvester class.
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