Identifier
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-2
[1,0]=>[1]=>[.,.]
[1,0,1,0]=>[2,1]=>[[.,.],.]
[1,1,0,0]=>[1,2]=>[.,[.,.]]
[1,0,1,0,1,0]=>[3,2,1]=>[[[.,.],.],.]
[1,0,1,1,0,0]=>[2,3,1]=>[[.,.],[.,.]]
[1,1,0,0,1,0]=>[3,1,2]=>[[.,[.,.]],.]
[1,1,0,1,0,0]=>[2,1,3]=>[[.,.],[.,.]]
[1,1,1,0,0,0]=>[1,2,3]=>[.,[.,[.,.]]]
[1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[1,0,1,0,1,1,0,0]=>[3,4,2,1]=>[[[.,.],.],[.,.]]
[1,0,1,1,0,0,1,0]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[1,0,1,1,0,1,0,0]=>[3,2,4,1]=>[[[.,.],.],[.,.]]
[1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[[.,.],[.,[.,.]]]
[1,1,0,0,1,0,1,0]=>[4,3,1,2]=>[[[.,[.,.]],.],.]
[1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[[.,[.,.]],[.,.]]
[1,1,0,1,0,0,1,0]=>[4,2,1,3]=>[[[.,.],[.,.]],.]
[1,1,0,1,0,1,0,0]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[1,1,0,1,1,0,0,0]=>[2,3,1,4]=>[[.,.],[.,[.,.]]]
[1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[[.,[.,[.,.]]],.]
[1,1,1,0,0,1,0,0]=>[3,1,2,4]=>[[.,[.,.]],[.,.]]
[1,1,1,0,1,0,0,0]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[1,0,1,0,1,0,1,1,0,0]=>[4,5,3,2,1]=>[[[[.,.],.],.],[.,.]]
[1,0,1,0,1,1,0,0,1,0]=>[5,3,4,2,1]=>[[[[.,.],.],[.,.]],.]
[1,0,1,0,1,1,0,1,0,0]=>[4,3,5,2,1]=>[[[[.,.],.],.],[.,.]]
[1,0,1,0,1,1,1,0,0,0]=>[3,4,5,2,1]=>[[[.,.],.],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,0]=>[5,4,2,3,1]=>[[[[.,.],[.,.]],.],.]
[1,0,1,1,0,0,1,1,0,0]=>[4,5,2,3,1]=>[[[.,.],[.,.]],[.,.]]
[1,0,1,1,0,1,0,0,1,0]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[1,0,1,1,0,1,0,1,0,0]=>[4,3,2,5,1]=>[[[[.,.],.],.],[.,.]]
[1,0,1,1,0,1,1,0,0,0]=>[3,4,2,5,1]=>[[[.,.],.],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,0]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,0]=>[4,2,3,5,1]=>[[[.,.],[.,.]],[.,.]]
[1,0,1,1,1,0,1,0,0,0]=>[3,2,4,5,1]=>[[[.,.],.],[.,[.,.]]]
[1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[[.,.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,2]=>[[[[.,[.,.]],.],.],.]
[1,1,0,0,1,0,1,1,0,0]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,0]=>[5,3,4,1,2]=>[[[.,[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,1,0,0]=>[4,3,5,1,2]=>[[[.,[.,.]],.],[.,.]]
[1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>[[.,[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,3]=>[[[[.,.],[.,.]],.],.]
[1,1,0,1,0,0,1,1,0,0]=>[4,5,2,1,3]=>[[[.,.],[.,.]],[.,.]]
[1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,4]=>[[[[.,.],.],[.,.]],.]
[1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[1,1,0,1,0,1,1,0,0,0]=>[3,4,2,1,5]=>[[[.,.],.],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,0]=>[5,2,3,1,4]=>[[[.,.],[.,[.,.]]],.]
[1,1,0,1,1,0,0,1,0,0]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,0,0]=>[3,2,4,1,5]=>[[[.,.],.],[.,[.,.]]]
[1,1,0,1,1,1,0,0,0,0]=>[2,3,4,1,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,3]=>[[[.,[.,[.,.]]],.],.]
[1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>[[.,[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,0,1,0]=>[5,3,1,2,4]=>[[[.,[.,.]],[.,.]],.]
[1,1,1,0,0,1,0,1,0,0]=>[4,3,1,2,5]=>[[[.,[.,.]],.],[.,.]]
[1,1,1,0,0,1,1,0,0,0]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,0]=>[5,2,1,3,4]=>[[[.,.],[.,[.,.]]],.]
[1,1,1,0,1,0,0,1,0,0]=>[4,2,1,3,5]=>[[[.,.],[.,.]],[.,.]]
[1,1,1,0,1,0,1,0,0,0]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0]=>[2,3,1,4,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>[[.,[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,0,1,0,0]=>[4,1,2,3,5]=>[[.,[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,1,0,0,0]=>[3,1,2,4,5]=>[[.,[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,0]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,2,1]=>[[[[[.,.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,2,1]=>[[[[[.,.],.],.],[.,.]],.]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,2,1]=>[[[[[.,.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,2,1]=>[[[[.,.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,2,1]=>[[[[.,.],.],[.,.]],[.,.]]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,2,1]=>[[[[[.,.],.],.],[.,.]],.]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,2,1]=>[[[[[.,.],.],.],.],[.,.]]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,2,1]=>[[[[.,.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],.]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,2,1]=>[[[[.,.],.],[.,.]],[.,.]]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[[[[.,.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,2,1]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,3,1]=>[[[[[.,.],[.,.]],.],.],.]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,3,1]=>[[[[.,.],[.,.]],.],[.,.]]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,3,1]=>[[[[.,.],[.,.]],.],[.,.]]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,3,1]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,4,1]=>[[[[[.,.],.],[.,.]],.],.]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,4,1]=>[[[[.,.],.],[.,.]],[.,.]]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,1]=>[[[[[.,.],.],.],.],[.,.]]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,1]=>[[[[.,.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,5,1]=>[[[[.,.],.],[.,[.,.]]],.]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,6,1]=>[[[[.,.],.],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,6,1]=>[[[[.,.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,6,1]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],.]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,4,1]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,5,1]=>[[[[.,.],[.,.]],[.,.]],.]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,6,1]=>[[[[.,.],[.,.]],.],[.,.]]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,6,1]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[[[[.,.],.],[.,.]],[.,.]]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,6,1]=>[[[[.,.],.],.],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,6,1]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,6,1]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,6,1]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,6,1]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],.]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,1,2]=>[[[[.,[.,.]],.],[.,.]],.]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,1,2]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],.]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],.]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,1,2]=>[[[[.,[.,.]],.],.],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,1,2]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],.]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,1,2]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],.]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,1,3]=>[[[[.,.],[.,.]],.],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,1,3]=>[[[[.,.],[.,.]],[.,.]],.]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,1,3]=>[[[[.,.],[.,.]],.],[.,.]]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,1,3]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],.]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,1,4]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,5]=>[[[[[.,.],.],.],[.,.]],.]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,1,6]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,1,5]=>[[[[.,.],.],[.,[.,.]]],.]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,1,6]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,1,6]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,1,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,1,4]=>[[[[.,.],[.,[.,.]]],.],.]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,1,4]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,1,5]=>[[[[.,.],[.,.]],[.,.]],.]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,1,6]=>[[[[.,.],[.,.]],.],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,1,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,1,5]=>[[[[.,.],.],[.,[.,.]]],.]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,1,6]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,1,6]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,1,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,1,5]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,1,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,1,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],.]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[5,6,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,.]]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,5,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],.]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,6,1,2,3]=>[[[.,[.,[.,.]]],.],[.,.]]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],.]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[5,6,3,1,2,4]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,2,5]=>[[[[.,[.,.]],.],[.,.]],.]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,2,6]=>[[[[.,[.,.]],.],.],[.,.]]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[4,5,3,1,2,6]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],.]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,4,1,2,6]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,5,1,2,6]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],.]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[5,6,2,1,3,4]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,3,5]=>[[[[.,.],[.,.]],[.,.]],.]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,3,6]=>[[[[.,.],[.,.]],.],[.,.]]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,5,2,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,4,5]=>[[[[.,.],.],[.,[.,.]]],.]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,4,6]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,2,1,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,1,4,5]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,3,1,4,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,3,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,4,1,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],.]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>[[[.,[.,[.,.]]],[.,.]],.]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,2,3,6]=>[[[.,[.,[.,.]]],.],[.,.]]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,3,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,2,4,5]=>[[[.,[.,.]],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,2,4,6]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,2,5,6]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,3,4,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,3,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,1,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,4,6]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,3,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,2,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,2,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,2,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,2,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,2,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,2,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,2,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,2,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,2,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,2,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,2,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,2,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,2,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,2,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],.],.]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,3,1]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,3,1]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,3,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,3,1]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,3,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,3,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,3,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,3,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,3,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],.],.]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,4,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,4,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,4,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,5,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,1]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,7,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,7,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,7,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,5,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,5,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,7,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,7,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,7,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,7,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,4,1]=>[[[[[.,.],[.,[.,.]]],.],.],.]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,4,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,4,1]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,5,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,5,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,6,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,7,1]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,7,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,7,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,7,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,7,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,5,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,7,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,7,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,7,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,7,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,5,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,6,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,7,1]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,7,1]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,7,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,7,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,7,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,7,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,7,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,7,1]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,7,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],.]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],.]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],.]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],.]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],.]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,1,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],.],.],.]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],.]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],.]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,1,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,1,2]=>[[[[.,[.,.]],[.,[.,.]]],.],.]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],.]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,1,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,1,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],.]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,1,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,1,3]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,1,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,1,3]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,1,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,1,3]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],.]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,1,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],.]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1,6]=>[[[[[[.,.],.],.],.],[.,.]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,1,6]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,1,5]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,1,6]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,1,6]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,1,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,1,4]=>[[[[[.,.],[.,[.,.]]],.],.],.]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,1,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,1,4]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,1,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,1,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,1,5]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,1,6]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,1,7]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,1,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,1,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,1,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,1,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,1,5]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,1,6]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,1,6]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,1,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,1,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,1,5]=>[[[[.,.],[.,[.,[.,.]]]],.],.]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,1,6]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,1,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,1,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,1,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,1,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,1,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,1,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,1,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,1,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,1,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,1,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],.],.]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,.]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],.]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,.]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,1,2,3]=>[[[[.,[.,[.,.]]],[.,.]],.],.]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],.]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,.]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,1,2,3]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1,2,4]=>[[[[[.,[.,.]],[.,.]],.],.],.]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,1,2,4]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1,2,5]=>[[[[[.,[.,.]],.],[.,.]],.],.]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,1,2,5]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1,2,6]=>[[[[[.,[.,.]],.],.],[.,.]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,2,7]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,1,2,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,1,2,6]=>[[[[.,[.,.]],.],[.,[.,.]]],.]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,1,2,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,1,2,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,1,2,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,1,2,5]=>[[[[.,[.,.]],[.,[.,.]]],.],.]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,1,2,6]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,1,2,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,1,2,6]=>[[[[.,[.,.]],.],[.,[.,.]]],.]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,1,2,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,1,2,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,1,2,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,1,2,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,1,2,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,1,2,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,3,4]=>[[[[[.,.],[.,[.,.]]],.],.],.]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,1,3,4]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1,3,5]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,1,3,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,3,6]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,3,7]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,1,3,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,1,3,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,1,3,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,1,3,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,1,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,4,5]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,1,4,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1,4,6]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,4,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,5,6]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,5,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,1,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,1,5,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,1,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,1,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,1,4,5]=>[[[[.,.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,1,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,1,4,6]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,1,4,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,1,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,1,5,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,1,5,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,1,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,1,5,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,1,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,1,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,1,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,1,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,1,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],.],.],.]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,7,5,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,6,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,7,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,2,3,5]=>[[[[.,[.,[.,.]]],[.,.]],.],.]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,7,4,1,2,3,5]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,2,3,6]=>[[[[.,[.,[.,.]]],.],[.,.]],.]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,2,3,7]=>[[[[.,[.,[.,.]]],.],.],[.,.]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,6,4,1,2,3,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,5,1,2,3,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,5,1,2,3,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,6,1,2,3,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,2,4,5]=>[[[[.,[.,.]],[.,[.,.]]],.],.]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,7,3,1,2,4,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,2,4,6]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,2,4,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,6,3,1,2,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,2,5,6]=>[[[[.,[.,.]],.],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,2,5,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,2,6,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,1,2,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,4,1,2,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,4,1,2,5,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,4,1,2,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,5,1,2,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,4,5,1,2,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,3,4,5]=>[[[[.,.],[.,[.,[.,.]]]],.],.]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,7,2,1,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,3,4,6]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,3,4,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,6,2,1,3,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,3,5,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,3,5,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,3,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,2,1,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,4,5,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,4,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,4,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,4,2,1,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,3,1,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,3,1,4,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,3,1,4,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,3,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,4,1,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,2,3,4,6]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,2,3,4,7]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,4,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,2,3,5,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,2,3,5,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,2,3,6,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,5,1,2,3,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,2,4,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,2,4,5,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,2,4,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,2,5,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,3,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,3,4,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,3,4,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,3,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,5,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,4,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,3,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,3,4,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,2,3,1,4]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
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.
searching the database
Sorry, this map was not found in the database.