Identifier
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
Permutations
Mp00241: Permutations —invert Laguerre heap⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00241: Permutations —invert Laguerre heap⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-3
[1,0]=>[1]=>[1]=>[.,.]
[1,0,1,0]=>[1,2]=>[1,2]=>[.,[.,.]]
[1,1,0,0]=>[2,1]=>[2,1]=>[[.,.],.]
[1,0,1,0,1,0]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[1,0,1,1,0,0]=>[1,3,2]=>[1,3,2]=>[.,[[.,.],.]]
[1,1,0,0,1,0]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[1,1,0,1,0,0]=>[2,3,1]=>[3,1,2]=>[[.,[.,.]],.]
[1,1,1,0,0,0]=>[3,2,1]=>[3,2,1]=>[[[.,.],.],.]
[1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[1,2,4,3]=>[.,[.,[[.,.],.]]]
[1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[1,3,2,4]=>[.,[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[1,4,2,3]=>[.,[[.,[.,.]],.]]
[1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[1,4,3,2]=>[.,[[[.,.],.],.]]
[1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[2,1,4,3]=>[[.,.],[[.,.],.]]
[1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[3,1,2,4]=>[[.,[.,.]],[.,.]]
[1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[4,1,2,3]=>[[.,[.,[.,.]]],.]
[1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[4,3,1,2]=>[[[.,[.,.]],.],.]
[1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[4,1,3,2]=>[[.,[[.,.],.]],.]
[1,1,1,0,1,0,0,0]=>[3,4,2,1]=>[4,2,1,3]=>[[[.,.],[.,.]],.]
[1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[1,2,5,3,4]=>[.,[.,[[.,[.,.]],.]]]
[1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]]
[1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[1,4,2,3,5]=>[.,[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[1,5,2,3,4]=>[.,[[.,[.,[.,.]]],.]]
[1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[1,5,4,2,3]=>[.,[[[.,[.,.]],.],.]]
[1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[1,5,2,4,3]=>[.,[[.,[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,0,0]=>[1,4,5,3,2]=>[1,5,3,2,4]=>[.,[[[.,.],[.,.]],.]]
[1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[2,1,5,3,4]=>[[.,.],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[2,1,5,4,3]=>[[.,.],[[[.,.],.],.]]
[1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[3,1,2,4,5]=>[[.,[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[3,1,2,5,4]=>[[.,[.,.]],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[4,1,2,3,5]=>[[.,[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[5,1,2,3,4]=>[[.,[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[5,4,1,2,3]=>[[[.,[.,[.,.]]],.],.]
[1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[4,3,1,2,5]=>[[[.,[.,.]],.],[.,.]]
[1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[5,1,2,4,3]=>[[.,[.,[[.,.],.]]],.]
[1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>[5,3,1,2,4]=>[[[.,[.,.]],[.,.]],.]
[1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[5,4,3,1,2]=>[[[[.,[.,.]],.],.],.]
[1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]
[1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[4,1,3,2,5]=>[[.,[[.,.],.]],[.,.]]
[1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[5,1,3,2,4]=>[[.,[[.,.],[.,.]]],.]
[1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[5,4,1,3,2]=>[[[.,[[.,.],.]],.],.]
[1,1,1,0,1,0,0,0,1,0]=>[3,4,2,1,5]=>[4,2,1,3,5]=>[[[.,.],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>[5,1,4,2,3]=>[[.,[[.,[.,.]],.]],.]
[1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>[5,2,1,3,4]=>[[[.,.],[.,[.,.]]],.]
[1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>[5,4,2,1,3]=>[[[[.,.],[.,.]],.],.]
[1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[5,1,4,3,2]=>[[.,[[[.,.],.],.]],.]
[1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>[5,2,1,4,3]=>[[[.,.],[[.,.],.]],.]
[1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>[5,3,2,1,4]=>[[[[.,.],.],[.,.]],.]
[1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[.,[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[1,2,3,6,4,5]=>[.,[.,[.,[[.,[.,.]],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[1,2,3,6,5,4]=>[.,[.,[.,[[[.,.],.],.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[.,[.,[[.,.],[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[1,2,5,3,4,6]=>[.,[.,[[.,[.,.]],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[1,2,6,3,4,5]=>[.,[.,[[.,[.,[.,.]]],.]]]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[1,2,6,5,3,4]=>[.,[.,[[[.,[.,.]],.],.]]]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[1,2,5,4,3,6]=>[.,[.,[[[.,.],.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[1,2,6,3,5,4]=>[.,[.,[[.,[[.,.],.]],.]]]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,4,3]=>[1,2,6,4,3,5]=>[.,[.,[[[.,.],[.,.]],.]]]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[1,2,6,5,4,3]=>[.,[.,[[[[.,.],.],.],.]]]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[1,3,2,6,4,5]=>[.,[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[1,3,2,6,5,4]=>[.,[[.,.],[[[.,.],.],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[1,4,2,3,5,6]=>[.,[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[1,4,2,3,6,5]=>[.,[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[1,5,2,3,4,6]=>[.,[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[1,6,2,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[1,6,5,2,3,4]=>[.,[[[.,[.,[.,.]]],.],.]]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[1,5,4,2,3,6]=>[.,[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[1,6,2,3,5,4]=>[.,[[.,[.,[[.,.],.]]],.]]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,4,2]=>[1,6,4,2,3,5]=>[.,[[[.,[.,.]],[.,.]],.]]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[1,6,5,4,2,3]=>[.,[[[[.,[.,.]],.],.],.]]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[1,4,3,2,5,6]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[1,4,3,2,6,5]=>[.,[[[.,.],.],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[1,5,2,4,3,6]=>[.,[[.,[[.,.],.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[1,6,2,4,3,5]=>[.,[[.,[[.,.],[.,.]]],.]]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[1,6,5,2,4,3]=>[.,[[[.,[[.,.],.]],.],.]]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,3,2,6]=>[1,5,3,2,4,6]=>[.,[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,3,6,2]=>[1,6,2,5,3,4]=>[.,[[.,[[.,[.,.]],.]],.]]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,3,2]=>[1,6,3,2,4,5]=>[.,[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,5,3,2]=>[1,6,5,3,2,4]=>[.,[[[[.,.],[.,.]],.],.]]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[1,5,4,3,2,6]=>[.,[[[[.,.],.],.],[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[1,6,2,5,4,3]=>[.,[[.,[[[.,.],.],.]],.]]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,4,6,3,2]=>[1,6,3,2,5,4]=>[.,[[[.,.],[[.,.],.]],.]]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,4,3,2]=>[1,6,4,3,2,5]=>[.,[[[[.,.],.],[.,.]],.]]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[2,1,3,6,4,5]=>[[.,.],[.,[[.,[.,.]],.]]]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[2,1,3,6,5,4]=>[[.,.],[.,[[[.,.],.],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[2,1,5,3,4,6]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[2,1,6,3,4,5]=>[[.,.],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[2,1,6,5,3,4]=>[[.,.],[[[.,[.,.]],.],.]]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[2,1,5,4,3,6]=>[[.,.],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[2,1,6,3,5,4]=>[[.,.],[[.,[[.,.],.]],.]]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,4,3]=>[2,1,6,4,3,5]=>[[.,.],[[[.,.],[.,.]],.]]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[2,1,6,5,4,3]=>[[.,.],[[[[.,.],.],.],.]]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[3,1,2,4,6,5]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[3,1,2,5,4,6]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[3,1,2,6,4,5]=>[[.,[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[3,1,2,6,5,4]=>[[.,[.,.]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[4,1,2,3,6,5]=>[[.,[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[6,5,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],.]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[5,4,1,2,3,6]=>[[[.,[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[6,1,2,3,5,4]=>[[.,[.,[.,[[.,.],.]]]],.]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>[6,4,1,2,3,5]=>[[[.,[.,[.,.]]],[.,.]],.]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[6,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],.]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[4,3,1,2,5,6]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[4,3,1,2,6,5]=>[[[.,[.,.]],.],[[.,.],.]]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[5,1,2,4,3,6]=>[[.,[.,[[.,.],.]]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[6,1,2,4,3,5]=>[[.,[.,[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[6,5,1,2,4,3]=>[[[.,[.,[[.,.],.]]],.],.]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,3,1,6]=>[5,3,1,2,4,6]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>[6,1,2,5,3,4]=>[[.,[.,[[.,[.,.]],.]]],.]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>[6,3,1,2,4,5]=>[[[.,[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>[6,5,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],.]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[5,4,3,1,2,6]=>[[[[.,[.,.]],.],.],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[6,1,2,5,4,3]=>[[.,[.,[[[.,.],.],.]]],.]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>[6,3,1,2,5,4]=>[[[.,[.,.]],[[.,.],.]],.]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>[6,4,3,1,2,5]=>[[[[.,[.,.]],.],[.,.]],.]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[6,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],.]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[3,2,1,4,6,5]=>[[[.,.],.],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[3,2,1,5,4,6]=>[[[.,.],.],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[3,2,1,6,4,5]=>[[[.,.],.],[[.,[.,.]],.]]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[4,1,3,2,5,6]=>[[.,[[.,.],.]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[4,1,3,2,6,5]=>[[.,[[.,.],.]],[[.,.],.]]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[5,1,3,2,4,6]=>[[.,[[.,.],[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[6,1,3,2,4,5]=>[[.,[[.,.],[.,[.,.]]]],.]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[6,5,1,3,2,4]=>[[[.,[[.,.],[.,.]]],.],.]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[5,4,1,3,2,6]=>[[[.,[[.,.],.]],.],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[6,1,3,2,5,4]=>[[.,[[.,.],[[.,.],.]]],.]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>[6,4,1,3,2,5]=>[[[.,[[.,.],.]],[.,.]],.]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[6,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],.]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,2,1,5,6]=>[4,2,1,3,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2,1,6,5]=>[4,2,1,3,6,5]=>[[[.,.],[.,.]],[[.,.],.]]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,2,5,1,6]=>[5,1,4,2,3,6]=>[[.,[[.,[.,.]],.]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>[6,1,4,2,3,5]=>[[.,[[.,[.,.]],[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>[6,5,1,4,2,3]=>[[[.,[[.,[.,.]],.]],.],.]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,2,1,6]=>[5,2,1,3,4,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>[6,1,5,2,3,4]=>[[.,[[.,[.,[.,.]]],.]],.]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>[6,2,1,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>[6,5,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],.]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,4,2,1,6]=>[5,4,2,1,3,6]=>[[[[.,.],[.,.]],.],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>[6,1,5,4,2,3]=>[[.,[[[.,[.,.]],.],.]],.]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>[6,2,1,3,5,4]=>[[[.,.],[.,[[.,.],.]]],.]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>[6,4,2,1,3,5]=>[[[[.,.],[.,.]],[.,.]],.]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]=>[6,5,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],.]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[4,3,2,1,6,5]=>[[[[.,.],.],.],[[.,.],.]]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[5,1,4,3,2,6]=>[[.,[[[.,.],.],.]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[6,1,4,3,2,5]=>[[.,[[[.,.],.],[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[6,5,1,4,3,2]=>[[[.,[[[.,.],.],.]],.],.]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,3,5,2,1,6]=>[5,2,1,4,3,6]=>[[[.,.],[[.,.],.]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>[6,1,5,2,4,3]=>[[.,[[.,[[.,.],.]],.]],.]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[6,2,1,4,3,5]=>[[[.,.],[[.,.],[.,.]]],.]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>[6,5,2,1,4,3]=>[[[[.,.],[[.,.],.]],.],.]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,3,2,1,6]=>[5,3,2,1,4,6]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>[6,1,5,3,2,4]=>[[.,[[[.,.],[.,.]],.]],.]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>[6,2,1,5,3,4]=>[[[.,.],[[.,[.,.]],.]],.]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>[6,3,2,1,4,5]=>[[[[.,.],.],[.,[.,.]]],.]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>[6,5,3,2,1,4]=>[[[[[.,.],.],[.,.]],.],.]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[6,1,5,4,3,2]=>[[.,[[[[.,.],.],.],.]],.]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>[6,2,1,5,4,3]=>[[[.,.],[[[.,.],.],.]],.]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>[6,3,2,1,5,4]=>[[[[.,.],.],[[.,.],.]],.]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>[6,4,3,2,1,5]=>[[[[[.,.],.],.],[.,.]],.]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,5,6]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[1,2,3,4,7,6,5]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[1,2,3,6,4,5,7]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[1,2,3,7,4,5,6]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[1,2,3,7,6,4,5]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[1,2,3,6,5,4,7]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[1,2,3,7,4,6,5]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,5,4]=>[1,2,3,7,5,4,6]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>[1,2,3,7,6,5,4]=>[.,[.,[.,[[[[.,.],.],.],.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,5,6]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[1,2,4,3,7,6,5]=>[.,[.,[[.,.],[[[.,.],.],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[1,2,5,3,4,6,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[1,2,5,3,4,7,6]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[1,2,6,3,4,5,7]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[1,2,7,3,4,5,6]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[1,2,7,6,3,4,5]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[1,2,6,5,3,4,7]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>[1,2,7,3,4,6,5]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,5,3]=>[1,2,7,5,3,4,6]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[1,2,7,6,5,3,4]=>[.,[.,[[[[.,[.,.]],.],.],.]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[1,2,5,4,3,6,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[1,2,5,4,3,7,6]=>[.,[.,[[[.,.],.],[[.,.],.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[1,2,6,3,5,4,7]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[1,2,7,3,5,4,6]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[1,2,7,6,3,5,4]=>[.,[.,[[[.,[[.,.],.]],.],.]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,4,3,7]=>[1,2,6,4,3,5,7]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,4,7,3]=>[1,2,7,3,6,4,5]=>[.,[.,[[.,[[.,[.,.]],.]],.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,4,3]=>[1,2,7,4,3,5,6]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,6,4,3]=>[1,2,7,6,4,3,5]=>[.,[.,[[[[.,.],[.,.]],.],.]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[1,2,6,5,4,3,7]=>[.,[.,[[[[.,.],.],.],[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[1,2,7,3,6,5,4]=>[.,[.,[[.,[[[.,.],.],.]],.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,5,7,4,3]=>[1,2,7,4,3,6,5]=>[.,[.,[[[.,.],[[.,.],.]],.]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,5,4,3]=>[1,2,7,5,4,3,6]=>[.,[.,[[[[.,.],.],[.,.]],.]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[1,2,7,6,5,4,3]=>[.,[.,[[[[[.,.],.],.],.],.]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,5,6]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[1,3,2,4,7,6,5]=>[.,[[.,.],[.,[[[.,.],.],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[1,3,2,6,4,5,7]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[1,3,2,7,4,5,6]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[1,3,2,7,6,4,5]=>[.,[[.,.],[[[.,[.,.]],.],.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[1,3,2,6,5,4,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[1,3,2,7,4,6,5]=>[.,[[.,.],[[.,[[.,.],.]],.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,5,4]=>[1,3,2,7,5,4,6]=>[.,[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[1,3,2,7,6,5,4]=>[.,[[.,.],[[[[.,.],.],.],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[1,4,2,3,5,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[1,4,2,3,5,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[1,4,2,3,6,5,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[1,4,2,3,7,5,6]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[1,4,2,3,7,6,5]=>[.,[[.,[.,.]],[[[.,.],.],.]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[1,5,2,3,4,6,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[1,5,2,3,4,7,6]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[1,6,2,3,4,5,7]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[1,7,2,3,4,5,6]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[1,7,6,2,3,4,5]=>[.,[[[.,[.,[.,[.,.]]]],.],.]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[1,6,5,2,3,4,7]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[1,7,2,3,4,6,5]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,5,2]=>[1,7,5,2,3,4,6]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[1,7,6,5,2,3,4]=>[.,[[[[.,[.,[.,.]]],.],.],.]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[1,5,4,2,3,6,7]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[1,5,4,2,3,7,6]=>[.,[[[.,[.,.]],.],[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>[1,6,2,3,5,4,7]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[1,7,2,3,5,4,6]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[1,7,6,2,3,5,4]=>[.,[[[.,[.,[[.,.],.]]],.],.]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,4,2,7]=>[1,6,4,2,3,5,7]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,4,7,2]=>[1,7,2,3,6,4,5]=>[.,[[.,[.,[[.,[.,.]],.]]],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,4,2]=>[1,7,4,2,3,5,6]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,6,4,2]=>[1,7,6,4,2,3,5]=>[.,[[[[.,[.,.]],[.,.]],.],.]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[1,6,5,4,2,3,7]=>[.,[[[[.,[.,.]],.],.],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[1,7,2,3,6,5,4]=>[.,[[.,[.,[[[.,.],.],.]]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,5,7,4,2]=>[1,7,4,2,3,6,5]=>[.,[[[.,[.,.]],[[.,.],.]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,5,4,2]=>[1,7,5,4,2,3,6]=>[.,[[[[.,[.,.]],.],[.,.]],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[1,7,6,5,4,2,3]=>[.,[[[[[.,[.,.]],.],.],.],.]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[1,4,3,2,5,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[1,4,3,2,5,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[1,4,3,2,6,5,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[1,4,3,2,7,5,6]=>[.,[[[.,.],.],[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[1,4,3,2,7,6,5]=>[.,[[[.,.],.],[[[.,.],.],.]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[1,5,2,4,3,6,7]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[1,5,2,4,3,7,6]=>[.,[[.,[[.,.],.]],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[1,6,2,4,3,5,7]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[1,7,2,4,3,5,6]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[1,7,6,2,4,3,5]=>[.,[[[.,[[.,.],[.,.]]],.],.]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[1,6,5,2,4,3,7]=>[.,[[[.,[[.,.],.]],.],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>[1,7,2,4,3,6,5]=>[.,[[.,[[.,.],[[.,.],.]]],.]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,6,7,5,2]=>[1,7,5,2,4,3,6]=>[.,[[[.,[[.,.],.]],[.,.]],.]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[1,7,6,5,2,4,3]=>[.,[[[[.,[[.,.],.]],.],.],.]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,3,2,6,7]=>[1,5,3,2,4,6,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,3,2,7,6]=>[1,5,3,2,4,7,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,3,6,2,7]=>[1,6,2,5,3,4,7]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,3,6,7,2]=>[1,7,2,5,3,4,6]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,3,7,6,2]=>[1,7,6,2,5,3,4]=>[.,[[[.,[[.,[.,.]],.]],.],.]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,3,2,7]=>[1,6,3,2,4,5,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,3,7,2]=>[1,7,2,6,3,4,5]=>[.,[[.,[[.,[.,[.,.]]],.]],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,3,2]=>[1,7,3,2,4,5,6]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,6,3,2]=>[1,7,6,3,2,4,5]=>[.,[[[[.,.],[.,[.,.]]],.],.]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,5,3,2,7]=>[1,6,5,3,2,4,7]=>[.,[[[[.,.],[.,.]],.],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,5,3,7,2]=>[1,7,2,6,5,3,4]=>[.,[[.,[[[.,[.,.]],.],.]],.]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,5,7,3,2]=>[1,7,3,2,4,6,5]=>[.,[[[.,.],[.,[[.,.],.]]],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,5,3,2]=>[1,7,5,3,2,4,6]=>[.,[[[[.,.],[.,.]],[.,.]],.]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,6,5,3,2]=>[1,7,6,5,3,2,4]=>[.,[[[[[.,.],[.,.]],.],.],.]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[1,5,4,3,2,6,7]=>[.,[[[[.,.],.],.],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[1,5,4,3,2,7,6]=>[.,[[[[.,.],.],.],[[.,.],.]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[1,6,2,5,4,3,7]=>[.,[[.,[[[.,.],.],.]],[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[1,7,2,5,4,3,6]=>[.,[[.,[[[.,.],.],[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[1,7,6,2,5,4,3]=>[.,[[[.,[[[.,.],.],.]],.],.]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,4,6,3,2,7]=>[1,6,3,2,5,4,7]=>[.,[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,4,6,3,7,2]=>[1,7,2,6,3,5,4]=>[.,[[.,[[.,[[.,.],.]],.]],.]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,4,6,7,3,2]=>[1,7,3,2,5,4,6]=>[.,[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,4,7,6,3,2]=>[1,7,6,3,2,5,4]=>[.,[[[[.,.],[[.,.],.]],.],.]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,4,3,2,7]=>[1,6,4,3,2,5,7]=>[.,[[[[.,.],.],[.,.]],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,4,3,7,2]=>[1,7,2,6,4,3,5]=>[.,[[.,[[[.,.],[.,.]],.]],.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,4,7,3,2]=>[1,7,3,2,6,4,5]=>[.,[[[.,.],[[.,[.,.]],.]],.]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,4,3,2]=>[1,7,4,3,2,5,6]=>[.,[[[[.,.],.],[.,[.,.]]],.]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,6,4,3,2]=>[1,7,6,4,3,2,5]=>[.,[[[[[.,.],.],[.,.]],.],.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[1,6,5,4,3,2,7]=>[.,[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[1,7,2,6,5,4,3]=>[.,[[.,[[[[.,.],.],.],.]],.]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,5,4,7,3,2]=>[1,7,3,2,6,5,4]=>[.,[[[.,.],[[[.,.],.],.]],.]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,5,7,4,3,2]=>[1,7,4,3,2,6,5]=>[.,[[[[.,.],.],[[.,.],.]],.]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,5,4,3,2]=>[1,7,5,4,3,2,6]=>[.,[[[[[.,.],.],.],[.,.]],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,5,6]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[2,1,3,4,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[2,1,3,6,4,5,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[2,1,3,7,4,5,6]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[2,1,3,7,6,4,5]=>[[.,.],[.,[[[.,[.,.]],.],.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[2,1,3,6,5,4,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[2,1,3,7,4,6,5]=>[[.,.],[.,[[.,[[.,.],.]],.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,5,4]=>[2,1,3,7,5,4,6]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[2,1,3,7,6,5,4]=>[[.,.],[.,[[[[.,.],.],.],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,5,6]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[2,1,4,3,7,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[2,1,5,3,4,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[2,1,5,3,4,7,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[2,1,6,3,4,5,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[2,1,7,3,4,5,6]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[2,1,7,6,3,4,5]=>[[.,.],[[[.,[.,[.,.]]],.],.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[2,1,6,5,3,4,7]=>[[.,.],[[[.,[.,.]],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>[2,1,7,3,4,6,5]=>[[.,.],[[.,[.,[[.,.],.]]],.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,5,3]=>[2,1,7,5,3,4,6]=>[[.,.],[[[.,[.,.]],[.,.]],.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[2,1,7,6,5,3,4]=>[[.,.],[[[[.,[.,.]],.],.],.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[2,1,5,4,3,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[2,1,5,4,3,7,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>[2,1,6,3,5,4,7]=>[[.,.],[[.,[[.,.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[2,1,7,3,5,4,6]=>[[.,.],[[.,[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[2,1,7,6,3,5,4]=>[[.,.],[[[.,[[.,.],.]],.],.]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,4,3,7]=>[2,1,6,4,3,5,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,4,7,3]=>[2,1,7,3,6,4,5]=>[[.,.],[[.,[[.,[.,.]],.]],.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,4,3]=>[2,1,7,4,3,5,6]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,6,4,3]=>[2,1,7,6,4,3,5]=>[[.,.],[[[[.,.],[.,.]],.],.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[2,1,6,5,4,3,7]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[2,1,7,3,6,5,4]=>[[.,.],[[.,[[[.,.],.],.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,5,7,4,3]=>[2,1,7,4,3,6,5]=>[[.,.],[[[.,.],[[.,.],.]],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,5,4,3]=>[2,1,7,5,4,3,6]=>[[.,.],[[[[.,.],.],[.,.]],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[3,1,2,4,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[3,1,2,4,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[3,1,2,4,7,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[3,1,2,4,7,6,5]=>[[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[3,1,2,5,4,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[3,1,2,5,4,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[3,1,2,6,4,5,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[3,1,2,7,4,5,6]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[3,1,2,7,6,4,5]=>[[.,[.,.]],[[[.,[.,.]],.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[3,1,2,6,5,4,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[3,1,2,7,4,6,5]=>[[.,[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,5,4]=>[3,1,2,7,5,4,6]=>[[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[3,1,2,7,6,5,4]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[4,1,2,3,5,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[4,1,2,3,6,5,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[4,1,2,3,7,5,6]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[4,1,2,3,7,6,5]=>[[.,[.,[.,.]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[5,1,2,3,4,7,6]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[7,6,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[6,5,1,2,3,4,7]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[7,1,2,3,4,6,5]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,5,1]=>[7,5,1,2,3,4,6]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[7,6,5,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],.],.],.]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[5,4,1,2,3,6,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[5,4,1,2,3,7,6]=>[[[.,[.,[.,.]]],.],[[.,.],.]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[6,1,2,3,5,4,7]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[7,1,2,3,5,4,6]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[7,6,1,2,3,5,4]=>[[[.,[.,[.,[[.,.],.]]]],.],.]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,4,1,7]=>[6,4,1,2,3,5,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,4,7,1]=>[7,1,2,3,6,4,5]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,4,1]=>[7,4,1,2,3,5,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,6,4,1]=>[7,6,4,1,2,3,5]=>[[[[.,[.,[.,.]]],[.,.]],.],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[6,5,4,1,2,3,7]=>[[[[.,[.,[.,.]]],.],.],[.,.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[7,1,2,3,6,5,4]=>[[.,[.,[.,[[[.,.],.],.]]]],.]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,5,7,4,1]=>[7,4,1,2,3,6,5]=>[[[.,[.,[.,.]]],[[.,.],.]],.]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,5,4,1]=>[7,5,4,1,2,3,6]=>[[[[.,[.,[.,.]]],.],[.,.]],.]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[7,6,5,4,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],.],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>[4,3,1,2,5,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[4,3,1,2,5,7,6]=>[[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[4,3,1,2,6,5,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[4,3,1,2,7,5,6]=>[[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[4,3,1,2,7,6,5]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[5,1,2,4,3,6,7]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[5,1,2,4,3,7,6]=>[[.,[.,[[.,.],.]]],[[.,.],.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[6,1,2,4,3,5,7]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[7,1,2,4,3,5,6]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[7,6,1,2,4,3,5]=>[[[.,[.,[[.,.],[.,.]]]],.],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[6,5,1,2,4,3,7]=>[[[.,[.,[[.,.],.]]],.],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[7,1,2,4,3,6,5]=>[[.,[.,[[.,.],[[.,.],.]]]],.]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,6,7,5,1]=>[7,5,1,2,4,3,6]=>[[[.,[.,[[.,.],.]]],[.,.]],.]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[7,6,5,1,2,4,3]=>[[[[.,[.,[[.,.],.]]],.],.],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,3,1,6,7]=>[5,3,1,2,4,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,3,1,7,6]=>[5,3,1,2,4,7,6]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,3,6,1,7]=>[6,1,2,5,3,4,7]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,3,6,7,1]=>[7,1,2,5,3,4,6]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,3,7,6,1]=>[7,6,1,2,5,3,4]=>[[[.,[.,[[.,[.,.]],.]]],.],.]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,3,1,7]=>[6,3,1,2,4,5,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,3,7,1]=>[7,1,2,6,3,4,5]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,3,1]=>[7,3,1,2,4,5,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,6,3,1]=>[7,6,3,1,2,4,5]=>[[[[.,[.,.]],[.,[.,.]]],.],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,5,3,1,7]=>[6,5,3,1,2,4,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,5,3,7,1]=>[7,1,2,6,5,3,4]=>[[.,[.,[[[.,[.,.]],.],.]]],.]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,5,7,3,1]=>[7,3,1,2,4,6,5]=>[[[.,[.,.]],[.,[[.,.],.]]],.]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,5,3,1]=>[7,5,3,1,2,4,6]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,6,5,3,1]=>[7,6,5,3,1,2,4]=>[[[[[.,[.,.]],[.,.]],.],.],.]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[5,4,3,1,2,6,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[5,4,3,1,2,7,6]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[6,1,2,5,4,3,7]=>[[.,[.,[[[.,.],.],.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[7,1,2,5,4,3,6]=>[[.,[.,[[[.,.],.],[.,.]]]],.]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[7,6,1,2,5,4,3]=>[[[.,[.,[[[.,.],.],.]]],.],.]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,4,6,3,1,7]=>[6,3,1,2,5,4,7]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,4,6,3,7,1]=>[7,1,2,6,3,5,4]=>[[.,[.,[[.,[[.,.],.]],.]]],.]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,4,6,7,3,1]=>[7,3,1,2,5,4,6]=>[[[.,[.,.]],[[.,.],[.,.]]],.]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,4,7,6,3,1]=>[7,6,3,1,2,5,4]=>[[[[.,[.,.]],[[.,.],.]],.],.]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,4,3,1,7]=>[6,4,3,1,2,5,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,4,3,7,1]=>[7,1,2,6,4,3,5]=>[[.,[.,[[[.,.],[.,.]],.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,4,7,3,1]=>[7,3,1,2,6,4,5]=>[[[.,[.,.]],[[.,[.,.]],.]],.]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,4,3,1]=>[7,4,3,1,2,5,6]=>[[[[.,[.,.]],.],[.,[.,.]]],.]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,6,4,3,1]=>[7,6,4,3,1,2,5]=>[[[[[.,[.,.]],.],[.,.]],.],.]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[6,5,4,3,1,2,7]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[7,1,2,6,5,4,3]=>[[.,[.,[[[[.,.],.],.],.]]],.]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,5,4,7,3,1]=>[7,3,1,2,6,5,4]=>[[[.,[.,.]],[[[.,.],.],.]],.]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,5,7,4,3,1]=>[7,4,3,1,2,6,5]=>[[[[.,[.,.]],.],[[.,.],.]],.]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,5,4,3,1]=>[7,5,4,3,1,2,6]=>[[[[[.,[.,.]],.],.],[.,.]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[7,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[3,2,1,4,7,5,6]=>[[[.,.],.],[.,[[.,[.,.]],.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[3,2,1,4,7,6,5]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[3,2,1,6,4,5,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[3,2,1,7,4,5,6]=>[[[.,.],.],[[.,[.,[.,.]]],.]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[3,2,1,7,6,4,5]=>[[[.,.],.],[[[.,[.,.]],.],.]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[3,2,1,6,5,4,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[3,2,1,7,4,6,5]=>[[[.,.],.],[[.,[[.,.],.]],.]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,6,7,5,4]=>[3,2,1,7,5,4,6]=>[[[.,.],.],[[[.,.],[.,.]],.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>[4,1,3,2,5,6,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[4,1,3,2,5,7,6]=>[[.,[[.,.],.]],[.,[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>[4,1,3,2,6,5,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>[4,1,3,2,7,5,6]=>[[.,[[.,.],.]],[[.,[.,.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[4,1,3,2,7,6,5]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[5,1,3,2,4,6,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[5,1,3,2,4,7,6]=>[[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[6,1,3,2,4,5,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[7,1,3,2,4,5,6]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[7,6,1,3,2,4,5]=>[[[.,[[.,.],[.,[.,.]]]],.],.]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[6,5,1,3,2,4,7]=>[[[.,[[.,.],[.,.]]],.],[.,.]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[7,1,3,2,4,6,5]=>[[.,[[.,.],[.,[[.,.],.]]]],.]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,6,7,5,1]=>[7,5,1,3,2,4,6]=>[[[.,[[.,.],[.,.]]],[.,.]],.]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[7,6,5,1,3,2,4]=>[[[[.,[[.,.],[.,.]]],.],.],.]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[5,4,1,3,2,6,7]=>[[[.,[[.,.],.]],.],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[5,4,1,3,2,7,6]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[6,1,3,2,5,4,7]=>[[.,[[.,.],[[.,.],.]]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[7,1,3,2,5,4,6]=>[[.,[[.,.],[[.,.],[.,.]]]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[7,6,1,3,2,5,4]=>[[[.,[[.,.],[[.,.],.]]],.],.]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,5,6,4,1,7]=>[6,4,1,3,2,5,7]=>[[[.,[[.,.],.]],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,5,6,4,7,1]=>[7,1,3,2,6,4,5]=>[[.,[[.,.],[[.,[.,.]],.]]],.]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,4,1]=>[7,4,1,3,2,5,6]=>[[[.,[[.,.],.]],[.,[.,.]]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,5,7,6,4,1]=>[7,6,4,1,3,2,5]=>[[[[.,[[.,.],.]],[.,.]],.],.]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[6,5,4,1,3,2,7]=>[[[[.,[[.,.],.]],.],.],[.,.]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[7,1,3,2,6,5,4]=>[[.,[[.,.],[[[.,.],.],.]]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,6,5,7,4,1]=>[7,4,1,3,2,6,5]=>[[[.,[[.,.],.]],[[.,.],.]],.]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,6,7,5,4,1]=>[7,5,4,1,3,2,6]=>[[[[.,[[.,.],.]],.],[.,.]],.]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[7,6,5,4,1,3,2]=>[[[[[.,[[.,.],.]],.],.],.],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7]=>[4,2,1,3,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,2,1,5,7,6]=>[4,2,1,3,5,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,2,1,6,5,7]=>[4,2,1,3,6,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,2,1,6,7,5]=>[4,2,1,3,7,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,2,1,7,6,5]=>[4,2,1,3,7,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,2,5,1,6,7]=>[5,1,4,2,3,6,7]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,2,5,1,7,6]=>[5,1,4,2,3,7,6]=>[[.,[[.,[.,.]],.]],[[.,.],.]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,1,7]=>[6,1,4,2,3,5,7]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,1]=>[7,1,4,2,3,5,6]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,2,5,7,6,1]=>[7,6,1,4,2,3,5]=>[[[.,[[.,[.,.]],[.,.]]],.],.]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,2,6,5,1,7]=>[6,5,1,4,2,3,7]=>[[[.,[[.,[.,.]],.]],.],[.,.]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,2,6,5,7,1]=>[7,1,4,2,3,6,5]=>[[.,[[.,[.,.]],[[.,.],.]]],.]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,2,6,7,5,1]=>[7,5,1,4,2,3,6]=>[[[.,[[.,[.,.]],.]],[.,.]],.]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,2,7,6,5,1]=>[7,6,5,1,4,2,3]=>[[[[.,[[.,[.,.]],.]],.],.],.]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,2,1,6,7]=>[5,2,1,3,4,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,2,1,7,6]=>[5,2,1,3,4,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,2,6,1,7]=>[6,1,5,2,3,4,7]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,2,6,7,1]=>[7,1,5,2,3,4,6]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,2,7,6,1]=>[7,6,1,5,2,3,4]=>[[[.,[[.,[.,[.,.]]],.]],.],.]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,2,1,7]=>[6,2,1,3,4,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,2,7,1]=>[7,1,6,2,3,4,5]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,2,1]=>[7,2,1,3,4,5,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,6,2,1]=>[7,6,2,1,3,4,5]=>[[[[.,.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,5,2,1,7]=>[6,5,2,1,3,4,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,5,2,7,1]=>[7,1,6,5,2,3,4]=>[[.,[[[.,[.,[.,.]]],.],.]],.]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,5,7,2,1]=>[7,2,1,3,4,6,5]=>[[[.,.],[.,[.,[[.,.],.]]]],.]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,5,2,1]=>[7,5,2,1,3,4,6]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,6,5,2,1]=>[7,6,5,2,1,3,4]=>[[[[[.,.],[.,[.,.]]],.],.],.]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,4,2,1,6,7]=>[5,4,2,1,3,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,4,2,1,7,6]=>[5,4,2,1,3,7,6]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,4,2,6,1,7]=>[6,1,5,4,2,3,7]=>[[.,[[[.,[.,.]],.],.]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,4,2,6,7,1]=>[7,1,5,4,2,3,6]=>[[.,[[[.,[.,.]],.],[.,.]]],.]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,4,2,7,6,1]=>[7,6,1,5,4,2,3]=>[[[.,[[[.,[.,.]],.],.]],.],.]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,4,6,2,1,7]=>[6,2,1,3,5,4,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,4,6,2,7,1]=>[7,1,6,2,3,5,4]=>[[.,[[.,[.,[[.,.],.]]],.]],.]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,4,6,7,2,1]=>[7,2,1,3,5,4,6]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,4,7,6,2,1]=>[7,6,2,1,3,5,4]=>[[[[.,.],[.,[[.,.],.]]],.],.]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,4,2,1,7]=>[6,4,2,1,3,5,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,4,2,7,1]=>[7,1,6,4,2,3,5]=>[[.,[[[.,[.,.]],[.,.]],.]],.]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,4,7,2,1]=>[7,2,1,3,6,4,5]=>[[[.,.],[.,[[.,[.,.]],.]]],.]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,4,2,1]=>[7,4,2,1,3,5,6]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,6,4,2,1]=>[7,6,4,2,1,3,5]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,5,4,2,1,7]=>[6,5,4,2,1,3,7]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,5,4,2,7,1]=>[7,1,6,5,4,2,3]=>[[.,[[[[.,[.,.]],.],.],.]],.]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,5,4,7,2,1]=>[7,2,1,3,6,5,4]=>[[[.,.],[.,[[[.,.],.],.]]],.]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,5,7,4,2,1]=>[7,4,2,1,3,6,5]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,5,4,2,1]=>[7,5,4,2,1,3,6]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,6,5,4,2,1]=>[7,6,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[4,3,2,1,5,7,6]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[4,3,2,1,6,5,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[4,3,2,1,7,5,6]=>[[[[.,.],.],.],[[.,[.,.]],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>[5,1,4,3,2,6,7]=>[[.,[[[.,.],.],.]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[5,1,4,3,2,7,6]=>[[.,[[[.,.],.],.]],[[.,.],.]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[6,1,4,3,2,5,7]=>[[.,[[[.,.],.],[.,.]]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[7,1,4,3,2,5,6]=>[[.,[[[.,.],.],[.,[.,.]]]],.]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[7,6,1,4,3,2,5]=>[[[.,[[[.,.],.],[.,.]]],.],.]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[6,5,1,4,3,2,7]=>[[[.,[[[.,.],.],.]],.],[.,.]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[7,1,4,3,2,6,5]=>[[.,[[[.,.],.],[[.,.],.]]],.]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,6,7,5,1]=>[7,5,1,4,3,2,6]=>[[[.,[[[.,.],.],.]],[.,.]],.]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[7,6,5,1,4,3,2]=>[[[[.,[[[.,.],.],.]],.],.],.]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,3,5,2,1,6,7]=>[5,2,1,4,3,6,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,3,5,2,1,7,6]=>[5,2,1,4,3,7,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,3,5,2,6,1,7]=>[6,1,5,2,4,3,7]=>[[.,[[.,[[.,.],.]],.]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,3,5,2,6,7,1]=>[7,1,5,2,4,3,6]=>[[.,[[.,[[.,.],.]],[.,.]]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,3,5,2,7,6,1]=>[7,6,1,5,2,4,3]=>[[[.,[[.,[[.,.],.]],.]],.],.]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,3,5,6,2,1,7]=>[6,2,1,4,3,5,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,2,7,1]=>[7,1,6,2,4,3,5]=>[[.,[[.,[[.,.],[.,.]]],.]],.]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,2,1]=>[7,2,1,4,3,5,6]=>[[[.,.],[[.,.],[.,[.,.]]]],.]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,3,5,7,6,2,1]=>[7,6,2,1,4,3,5]=>[[[[.,.],[[.,.],[.,.]]],.],.]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,3,6,5,2,1,7]=>[6,5,2,1,4,3,7]=>[[[[.,.],[[.,.],.]],.],[.,.]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,3,6,5,2,7,1]=>[7,1,6,5,2,4,3]=>[[.,[[[.,[[.,.],.]],.],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,3,6,5,7,2,1]=>[7,2,1,4,3,6,5]=>[[[.,.],[[.,.],[[.,.],.]]],.]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,6,7,5,2,1]=>[7,5,2,1,4,3,6]=>[[[[.,.],[[.,.],.]],[.,.]],.]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3,7,6,5,2,1]=>[7,6,5,2,1,4,3]=>[[[[[.,.],[[.,.],.]],.],.],.]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,3,2,1,6,7]=>[5,3,2,1,4,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,3,2,1,7,6]=>[5,3,2,1,4,7,6]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,3,2,6,1,7]=>[6,1,5,3,2,4,7]=>[[.,[[[.,.],[.,.]],.]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,3,2,6,7,1]=>[7,1,5,3,2,4,6]=>[[.,[[[.,.],[.,.]],[.,.]]],.]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,3,2,7,6,1]=>[7,6,1,5,3,2,4]=>[[[.,[[[.,.],[.,.]],.]],.],.]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,3,6,2,1,7]=>[6,2,1,5,3,4,7]=>[[[.,.],[[.,[.,.]],.]],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1]=>[7,1,6,2,5,3,4]=>[[.,[[.,[[.,[.,.]],.]],.]],.]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,3,6,7,2,1]=>[7,2,1,5,3,4,6]=>[[[.,.],[[.,[.,.]],[.,.]]],.]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,3,7,6,2,1]=>[7,6,2,1,5,3,4]=>[[[[.,.],[[.,[.,.]],.]],.],.]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,3,2,1,7]=>[6,3,2,1,4,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,3,2,7,1]=>[7,1,6,3,2,4,5]=>[[.,[[[.,.],[.,[.,.]]],.]],.]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,3,7,2,1]=>[7,2,1,6,3,4,5]=>[[[.,.],[[.,[.,[.,.]]],.]],.]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[7,3,2,1,4,5,6]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,6,3,2,1]=>[7,6,3,2,1,4,5]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,5,3,2,1,7]=>[6,5,3,2,1,4,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,5,3,2,7,1]=>[7,1,6,5,3,2,4]=>[[.,[[[[.,.],[.,.]],.],.]],.]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,5,3,7,2,1]=>[7,2,1,6,5,3,4]=>[[[.,.],[[[.,[.,.]],.],.]],.]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,5,7,3,2,1]=>[7,3,2,1,4,6,5]=>[[[[.,.],.],[.,[[.,.],.]]],.]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,5,3,2,1]=>[7,5,3,2,1,4,6]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,6,5,3,2,1]=>[7,6,5,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[6,1,5,4,3,2,7]=>[[.,[[[[.,.],.],.],.]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[7,1,5,4,3,2,6]=>[[.,[[[[.,.],.],.],[.,.]]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[7,6,1,5,4,3,2]=>[[[.,[[[[.,.],.],.],.]],.],.]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,4,3,6,2,1,7]=>[6,2,1,5,4,3,7]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,4,3,6,2,7,1]=>[7,1,6,2,5,4,3]=>[[.,[[.,[[[.,.],.],.]],.]],.]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[7,2,1,5,4,3,6]=>[[[.,.],[[[.,.],.],[.,.]]],.]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,4,3,7,6,2,1]=>[7,6,2,1,5,4,3]=>[[[[.,.],[[[.,.],.],.]],.],.]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,4,6,3,2,1,7]=>[6,3,2,1,5,4,7]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,4,6,3,2,7,1]=>[7,1,6,3,2,5,4]=>[[.,[[[.,.],[[.,.],.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[7,2,1,6,3,5,4]=>[[[.,.],[[.,[[.,.],.]],.]],.]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1]=>[7,3,2,1,5,4,6]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,3,2,1]=>[7,6,3,2,1,5,4]=>[[[[[.,.],.],[[.,.],.]],.],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,4,3,2,1,7]=>[6,4,3,2,1,5,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,4,3,2,7,1]=>[7,1,6,4,3,2,5]=>[[.,[[[[.,.],.],[.,.]],.]],.]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,4,3,7,2,1]=>[7,2,1,6,4,3,5]=>[[[.,.],[[[.,.],[.,.]],.]],.]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,4,7,3,2,1]=>[7,3,2,1,6,4,5]=>[[[[.,.],.],[[.,[.,.]],.]],.]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,4,3,2,1]=>[7,4,3,2,1,5,6]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,6,4,3,2,1]=>[7,6,4,3,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[7,1,6,5,4,3,2]=>[[.,[[[[[.,.],.],.],.],.]],.]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,5,4,3,7,2,1]=>[7,2,1,6,5,4,3]=>[[[.,.],[[[[.,.],.],.],.]],.]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,5,4,7,3,2,1]=>[7,3,2,1,6,5,4]=>[[[[.,.],.],[[[.,.],.],.]],.]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,5,7,4,3,2,1]=>[7,4,3,2,1,6,5]=>[[[[[.,.],.],.],[[.,.],.]],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,5,4,3,2,1]=>[7,5,4,3,2,1,6]=>[[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,6,7]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,8,7,6]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,5,6,7]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,4,7,6,8,5]=>[1,2,3,4,8,5,7,6]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,4,7,8,6,5]=>[1,2,3,4,8,6,5,7]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,8,7,6,5]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,4,5,6,7]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,3,5,6,8,7,4]=>[1,2,3,8,7,4,5,6]=>[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,3,5,7,6,8,4]=>[1,2,3,8,4,5,7,6]=>[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,3,5,7,8,6,4]=>[1,2,3,8,6,4,5,7]=>[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3,5,8,7,6,4]=>[1,2,3,8,7,6,4,5]=>[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,6,5,7,8,4]=>[1,2,3,8,4,6,5,7]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,6,5,8,7,4]=>[1,2,3,8,7,4,6,5]=>[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,6,7,5,8,4]=>[1,2,3,8,4,7,5,6]=>[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,6,7,8,5,4]=>[1,2,3,8,5,4,6,7]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,6,8,7,5,4]=>[1,2,3,8,7,5,4,6]=>[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,3,7,6,5,8,4]=>[1,2,3,8,4,7,6,5]=>[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,3,7,6,8,5,4]=>[1,2,3,8,5,4,7,6]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,3,7,8,6,5,4]=>[1,2,3,8,6,5,4,7]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,8,7,6,5,4]=>[1,2,3,8,7,6,5,4]=>[.,[.,[.,[[[[[.,.],.],.],.],.]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,5,6,7]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,4,3,7,6,8,5]=>[1,2,4,3,8,5,7,6]=>[.,[.,[[.,.],[[.,[[.,.],.]],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,8,7,6,5]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,8,3]=>[1,2,8,3,4,5,6,7]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,2,4,6,5,3,7,8]=>[1,2,6,5,3,4,7,8]=>[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,4,6,7,8,5,3]=>[1,2,8,5,3,4,6,7]=>[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4,8,7,6,5,3]=>[1,2,8,7,6,5,3,4]=>[.,[.,[[[[[.,[.,.]],.],.],.],.]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,2,5,4,6,7,8,3]=>[1,2,8,3,5,4,6,7]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,2,5,6,4,7,8,3]=>[1,2,8,3,6,4,5,7]=>[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,8,4,3]=>[1,2,8,4,3,5,6,7]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,6,5,4,7,8,3]=>[1,2,8,3,6,5,4,7]=>[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,6,7,8,5,4,3]=>[1,2,8,5,4,3,6,7]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,2,4,6,7,8,5]=>[1,3,2,4,8,5,6,7]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,2,4,7,6,8,5]=>[1,3,2,4,8,5,7,6]=>[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,8,7,6,5]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,8,7,6,5,4]=>[1,3,2,8,7,6,5,4]=>[.,[[.,.],[[[[[.,.],.],.],.],.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,6,7,5,8]=>[1,4,2,3,7,5,6,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,4,2,6,7,8,5]=>[1,4,2,3,8,5,6,7]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,4,2,7,6,8,5]=>[1,4,2,3,8,5,7,6]=>[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,8,7,6,5]=>[1,4,2,3,8,7,6,5]=>[.,[[.,[.,.]],[[[[.,.],.],.],.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,2]=>[1,8,2,3,4,5,6,7]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,6,8,7,2]=>[1,8,7,2,3,4,5,6]=>[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,5,7,6,2,8]=>[1,7,6,2,3,4,5,8]=>[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,5,7,8,6,2]=>[1,8,6,2,3,4,5,7]=>[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,4,6,7,5,2,8]=>[1,7,5,2,3,4,6,8]=>[.,[[[.,[.,[.,.]]],[.,.]],[.,.]]]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,4,7,6,8,5,2]=>[1,8,5,2,3,4,7,6]=>[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,8,7,6,5,2]=>[1,8,7,6,5,2,3,4]=>[.,[[[[[.,[.,[.,.]]],.],.],.],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,8,4,2]=>[1,8,4,2,3,5,6,7]=>[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,5,7,8,6,4,2]=>[1,8,6,4,2,3,5,7]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,6,5,7,8,4,2]=>[1,8,4,2,3,6,5,7]=>[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,4,3,2,6,7,8,5]=>[1,4,3,2,8,5,6,7]=>[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,7,6,5,8]=>[1,4,3,2,7,6,5,8]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,3,2,8,7,6,5]=>[1,4,3,2,8,7,6,5]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,8,2]=>[1,8,2,4,3,5,6,7]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,3,8,7,6,5,2]=>[1,8,7,6,5,2,4,3]=>[.,[[[[[.,[[.,.],.]],.],.],.],.]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,5,3,6,7,8,2]=>[1,8,2,5,3,4,6,7]=>[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,4,7,8,6,5,3,2]=>[1,8,6,5,3,2,4,7]=>[.,[[[[[.,.],[.,.]],.],[.,.]],.]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,4,8,7,6,5,3,2]=>[1,8,7,6,5,3,2,4]=>[.,[[[[[[.,.],[.,.]],.],.],.],.]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,8,4,3,2]=>[1,8,4,3,2,5,6,7]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,5,8,7,6,4,3,2]=>[1,8,7,6,4,3,2,5]=>[.,[[[[[[.,.],.],[.,.]],.],.],.]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,5,4,3,8,7,2]=>[1,8,7,2,6,5,4,3]=>[.,[[[.,[[[[.,.],.],.],.]],.],.]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,6,7,8,5,4,3,2]=>[1,8,5,4,3,2,6,7]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,6,8,7,5,4,3,2]=>[1,8,7,5,4,3,2,6]=>[.,[[[[[[.,.],.],.],[.,.]],.],.]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,7,6,5,8,4,3,2]=>[1,8,4,3,2,7,6,5]=>[.,[[[[.,.],.],[[[.,.],.],.]],.]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,7,6,8,5,4,3,2]=>[1,8,5,4,3,2,7,6]=>[.,[[[[[.,.],.],.],[[.,.],.]],.]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,7,8,6,5,4,3,2]=>[1,8,6,5,4,3,2,7]=>[.,[[[[[[.,.],.],.],.],[.,.]],.]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8,7,6,5,4,3,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,4,6,7,8,5]=>[2,1,3,4,8,5,6,7]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,4,7,6,8,5]=>[2,1,3,4,8,5,7,6]=>[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,4,7,8,6,5]=>[2,1,3,4,8,6,5,7]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,8,7,6,5]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,8,7,6,5,4]=>[2,1,3,8,7,6,5,4]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,5,6,7]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,3,6,8,7,5]=>[2,1,4,3,8,7,5,6]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,6,8,5]=>[2,1,4,3,8,5,7,6]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,4,3,7,8,6,5]=>[2,1,4,3,8,6,5,7]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,8,7,6,5]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,6,3,8,7]=>[2,1,6,3,4,5,8,7]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,8,3]=>[2,1,8,3,4,5,6,7]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,4,5,8,7,6,3]=>[2,1,8,7,6,3,4,5]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,4,6,5,3,8,7]=>[2,1,6,5,3,4,8,7]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,4,6,5,8,7,3]=>[2,1,8,7,3,4,6,5]=>[[.,.],[[[.,[.,[[.,.],.]]],.],.]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4,8,7,6,5,3]=>[2,1,8,7,6,5,3,4]=>[[.,.],[[[[[.,[.,.]],.],.],.],.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,5,4,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,4,6,3,8,7]=>[2,1,6,3,5,4,8,7]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,4,7,6,8,3]=>[2,1,8,3,5,4,7,6]=>[[.,.],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,1,5,6,4,3,8,7]=>[2,1,6,4,3,5,8,7]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>[2,1,6,5,4,3,8,7]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,5,7,4,8,3]=>[2,1,8,3,7,4,6,5]=>[[.,.],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,6,5,7,8,4,3]=>[2,1,8,4,3,6,5,7]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,6,5,8,7,4,3]=>[2,1,8,7,4,3,6,5]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,6,7,5,8,4,3]=>[2,1,8,4,3,7,5,6]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,6,7,8,5,4,3]=>[2,1,8,5,4,3,6,7]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,7,6,5,8,4,3]=>[2,1,8,4,3,7,6,5]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>[3,1,2,4,5,8,6,7]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,1,4,6,7,8,5]=>[3,1,2,4,8,5,6,7]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,1,4,7,6,8,5]=>[3,1,2,4,8,5,7,6]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,8,7,6,5]=>[3,1,2,4,8,7,6,5]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,8]=>[3,1,2,5,4,7,6,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,1,5,6,7,4,8]=>[3,1,2,7,4,5,6,8]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,8,7,6,5,4]=>[3,1,2,8,7,6,5,4]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,4,1,5,6,8,7]=>[4,1,2,3,5,6,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,5,7,6,8]=>[4,1,2,3,5,7,6,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,4,1,5,7,8,6]=>[4,1,2,3,5,8,6,7]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,8,7,6]=>[4,1,2,3,5,8,7,6]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,4,1,6,5,7,8]=>[4,1,2,3,6,5,7,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,8,7]=>[4,1,2,3,6,5,8,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,4,1,6,7,5,8]=>[4,1,2,3,7,5,6,8]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>[4,1,2,3,8,5,6,7]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,4,1,6,8,7,5]=>[4,1,2,3,8,7,5,6]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,4,1,7,6,5,8]=>[4,1,2,3,7,6,5,8]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,4,1,7,6,8,5]=>[4,1,2,3,8,5,7,6]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,7,8,6,5]=>[4,1,2,3,8,6,5,7]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,8,7,6,5]=>[4,1,2,3,8,7,6,5]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,1,8,7,6]=>[5,1,2,3,4,8,7,6]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,1,8,7]=>[6,1,2,3,4,5,8,7]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,8,7,1]=>[8,7,1,2,3,4,5,6]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,5,7,6,1,8]=>[7,6,1,2,3,4,5,8]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,4,7,6,5,8,1]=>[8,1,2,3,4,7,6,5]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,8,7,6,5,1]=>[8,7,6,5,1,2,3,4]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,4,1,8,7,6]=>[5,4,1,2,3,8,7,6]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,5,4,7,6,8,1]=>[8,1,2,3,5,4,7,6]=>[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,8,4,1]=>[8,4,1,2,3,5,6,7]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,5,6,8,7,4,1]=>[8,7,4,1,2,3,5,6]=>[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,6,5,4,1,8,7]=>[6,5,4,1,2,3,8,7]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,4,3,1,6,5,8,7]=>[4,3,1,2,6,5,8,7]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,4,3,1,6,7,8,5]=>[4,3,1,2,8,5,6,7]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,4,3,1,6,8,7,5]=>[4,3,1,2,8,7,5,6]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,4,3,1,7,6,8,5]=>[4,3,1,2,8,5,7,6]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,4,3,1,7,8,6,5]=>[4,3,1,2,8,6,5,7]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,4,3,1,8,7,6,5]=>[4,3,1,2,8,7,6,5]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,4,3,5,6,8,7,1]=>[8,7,1,2,4,3,5,6]=>[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,6,5,1,8,7]=>[6,5,1,2,4,3,8,7]=>[[[.,[.,[[.,.],.]]],.],[[.,.],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,6,5,7,8,1]=>[8,1,2,4,3,6,5,7]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,8,7,1]=>[8,7,1,2,4,3,6,5]=>[[[.,[.,[[.,.],[[.,.],.]]]],.],.]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,4,3,7,6,5,8,1]=>[8,1,2,4,3,7,6,5]=>[[.,[.,[[.,.],[[[.,.],.],.]]]],.]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,4,3,8,7,6,5,1]=>[8,7,6,5,1,2,4,3]=>[[[[[.,[.,[[.,.],.]]],.],.],.],.]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,4,5,3,1,8,7,6]=>[5,3,1,2,4,8,7,6]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,4,5,3,7,8,6,1]=>[8,6,1,2,5,3,4,7]=>[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,4,6,8,7,5,3,1]=>[8,7,5,3,1,2,4,6]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,4,8,7,6,5,3,1]=>[8,7,6,5,3,1,2,4]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,5,4,3,1,8,7,6]=>[5,4,3,1,2,8,7,6]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,5,4,3,6,7,8,1]=>[8,1,2,5,4,3,6,7]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,5,4,3,6,8,7,1]=>[8,7,1,2,5,4,3,6]=>[[[.,[.,[[[.,.],.],[.,.]]]],.],.]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[2,5,4,3,7,8,6,1]=>[8,6,1,2,5,4,3,7]=>[[[.,[.,[[[.,.],.],.]]],[.,.]],.]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,5,4,3,8,7,6,1]=>[8,7,6,1,2,5,4,3]=>[[[[.,[.,[[[.,.],.],.]]],.],.],.]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,5,4,6,7,3,8,1]=>[8,1,2,7,3,5,4,6]=>[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,5,4,7,6,3,8,1]=>[8,1,2,7,6,3,5,4]=>[[.,[.,[[[.,[[.,.],.]],.],.]]],.]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,6,8,7,5,4,3,1]=>[8,7,5,4,3,1,2,6]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,7,6,5,4,8,3,1]=>[8,3,1,2,7,6,5,4]=>[[[.,[.,.]],[[[[.,.],.],.],.]],.]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,7,8,6,5,4,3,1]=>[8,6,5,4,3,1,2,7]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,5,8,7,6]=>[3,2,1,4,5,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,2,1,4,6,7,8,5]=>[3,2,1,4,8,5,6,7]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,2,1,4,7,6,5,8]=>[3,2,1,4,7,6,5,8]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,2,1,4,7,6,8,5]=>[3,2,1,4,8,5,7,6]=>[[[.,.],.],[.,[[.,[[.,.],.]],.]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,2,1,4,8,7,6,5]=>[3,2,1,4,8,7,6,5]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,8,4]=>[3,2,1,8,4,5,6,7]=>[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,2,1,5,6,8,7,4]=>[3,2,1,8,7,4,5,6]=>[[[.,.],.],[[[.,[.,[.,.]]],.],.]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,2,1,5,7,6,8,4]=>[3,2,1,8,4,5,7,6]=>[[[.,.],.],[[.,[.,[[.,.],.]]],.]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,1,5,7,8,6,4]=>[3,2,1,8,6,4,5,7]=>[[[.,.],.],[[[.,[.,.]],[.,.]],.]]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,1,5,8,7,6,4]=>[3,2,1,8,7,6,4,5]=>[[[.,.],.],[[[[.,[.,.]],.],.],.]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,2,1,6,5,7,8,4]=>[3,2,1,8,4,6,5,7]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,2,1,6,5,8,7,4]=>[3,2,1,8,7,4,6,5]=>[[[.,.],.],[[[.,[[.,.],.]],.],.]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,2,1,6,7,5,8,4]=>[3,2,1,8,4,7,5,6]=>[[[.,.],.],[[.,[[.,[.,.]],.]],.]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,2,1,6,7,8,5,4]=>[3,2,1,8,5,4,6,7]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,2,1,6,8,7,5,4]=>[3,2,1,8,7,5,4,6]=>[[[.,.],.],[[[[.,.],[.,.]],.],.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,2,1,7,6,5,8,4]=>[3,2,1,8,4,7,6,5]=>[[[.,.],.],[[.,[[[.,.],.],.]],.]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,2,1,7,6,8,5,4]=>[3,2,1,8,5,4,7,6]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,1,7,8,6,5,4]=>[3,2,1,8,6,5,4,7]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,2,1,8,7,6,5,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,2,4,1,5,7,6,8]=>[4,1,3,2,5,7,6,8]=>[[.,[[.,.],.]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,4,1,6,5,8,7]=>[4,1,3,2,6,5,8,7]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,2,4,1,6,7,8,5]=>[4,1,3,2,8,5,6,7]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,4,1,7,6,8,5]=>[4,1,3,2,8,5,7,6]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,2,4,1,7,8,6,5]=>[4,1,3,2,8,6,5,7]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,2,4,1,8,7,6,5]=>[4,1,3,2,8,7,6,5]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,7,1,8]=>[7,1,3,2,4,5,6,8]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,1]=>[8,1,3,2,4,5,6,7]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,5,7,6,8,1]=>[8,1,3,2,4,5,7,6]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,2,4,7,6,5,8,1]=>[8,1,3,2,4,7,6,5]=>[[.,[[.,.],[.,[[[.,.],.],.]]]],.]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,2,4,8,7,6,5,1]=>[8,7,6,5,1,3,2,4]=>[[[[[.,[[.,.],[.,.]]],.],.],.],.]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,5,4,1,8,7,6]=>[5,4,1,3,2,8,7,6]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,5,4,6,1,8,7]=>[6,1,3,2,5,4,8,7]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,7,6,8,1]=>[8,1,3,2,5,4,7,6]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,6,5,7,4,8,1]=>[8,1,3,2,7,4,6,5]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],.]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,2,6,7,5,4,1,8]=>[7,5,4,1,3,2,6,8]=>[[[[.,[[.,.],.]],.],[.,.]],[.,.]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,2,7,6,5,4,1,8]=>[7,6,5,4,1,3,2,8]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,4,2,1,6,5,8,7]=>[4,2,1,3,6,5,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,4,2,1,6,7,8,5]=>[4,2,1,3,8,5,6,7]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,4,2,1,6,8,7,5]=>[4,2,1,3,8,7,5,6]=>[[[.,.],[.,.]],[[[.,[.,.]],.],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,4,2,1,7,6,8,5]=>[4,2,1,3,8,5,7,6]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,4,2,1,7,8,6,5]=>[4,2,1,3,8,6,5,7]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4,2,1,8,7,6,5]=>[4,2,1,3,8,7,6,5]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,4,2,5,1,8,7,6]=>[5,1,4,2,3,8,7,6]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,8,1]=>[8,1,4,2,3,5,6,7]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,4,2,5,7,8,6,1]=>[8,6,1,4,2,3,5,7]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,4,2,6,7,5,8,1]=>[8,1,4,2,3,7,5,6]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,4,2,7,6,5,8,1]=>[8,1,4,2,3,7,6,5]=>[[.,[[.,[.,.]],[[[.,.],.],.]]],.]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,2,8,7,6,5,1]=>[8,7,6,5,1,4,2,3]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,5,2,1,8,7,6]=>[5,2,1,3,4,8,7,6]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,5,2,6,7,8,1]=>[8,1,5,2,3,4,6,7]=>[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,8,7,6,2,1]=>[8,7,6,2,1,3,4,5]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,4,7,6,5,2,1,8]=>[7,6,5,2,1,3,4,8]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,8,7,6,5,2,1]=>[8,7,6,5,2,1,3,4]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,5,4,2,6,7,1,8]=>[7,1,5,4,2,3,6,8]=>[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,8,4,2,1]=>[8,4,2,1,3,5,6,7]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,5,6,8,7,4,2,1]=>[8,7,4,2,1,3,5,6]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,5,8,7,6,4,2,1]=>[8,7,6,4,2,1,3,5]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,6,5,4,2,1,8,7]=>[6,5,4,2,1,3,8,7]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,7,6,8,5,4,2,1]=>[8,5,4,2,1,3,7,6]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,3,2,1,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,3,2,1,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,3,2,1,5,7,8,6]=>[4,3,2,1,5,8,6,7]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,3,2,1,5,8,7,6]=>[4,3,2,1,5,8,7,6]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,3,2,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,3,2,1,6,7,5,8]=>[4,3,2,1,7,5,6,8]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,3,2,1,6,7,8,5]=>[4,3,2,1,8,5,6,7]=>[[[[.,.],.],.],[[.,[.,[.,.]]],.]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,3,2,1,6,8,7,5]=>[4,3,2,1,8,7,5,6]=>[[[[.,.],.],.],[[[.,[.,.]],.],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,2,1,7,6,5,8]=>[4,3,2,1,7,6,5,8]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,3,2,1,7,6,8,5]=>[4,3,2,1,8,5,7,6]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,2,1,7,8,6,5]=>[4,3,2,1,8,6,5,7]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,3,2,5,1,8,7,6]=>[5,1,4,3,2,8,7,6]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,8,1]=>[8,1,4,3,2,5,6,7]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[4,3,2,7,6,5,8,1]=>[8,1,4,3,2,7,6,5]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,3,2,8,7,6,5,1]=>[8,7,6,5,1,4,3,2]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[4,3,5,2,1,8,7,6]=>[5,2,1,4,3,8,7,6]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,3,5,2,6,1,8,7]=>[6,1,5,2,4,3,8,7]=>[[.,[[.,[[.,.],.]],.]],[[.,.],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,3,5,2,7,6,8,1]=>[8,1,5,2,4,3,7,6]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],.]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[4,3,5,6,2,1,8,7]=>[6,2,1,4,3,5,8,7]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[4,3,6,5,2,1,8,7]=>[6,5,2,1,4,3,8,7]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[4,3,6,5,2,8,7,1]=>[8,7,1,6,5,2,4,3]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,3,6,5,7,2,8,1]=>[8,1,7,2,4,3,6,5]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,8,7,2,1]=>[8,7,2,1,4,3,6,5]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[4,5,3,2,1,8,7,6]=>[5,3,2,1,4,8,7,6]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[4,5,3,6,2,1,8,7]=>[6,2,1,5,3,4,8,7]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[4,5,3,6,2,7,1,8]=>[7,1,6,2,5,3,4,8]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,6,3,2,1,8,7]=>[6,3,2,1,4,5,8,7]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,7,3,2,1,8]=>[7,3,2,1,4,5,6,8]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,7,3,2,8,1]=>[8,1,7,3,2,4,5,6]=>[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,7,3,8,2,1]=>[8,2,1,7,3,4,5,6]=>[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,3,2,1]=>[8,3,2,1,4,5,6,7]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[4,7,6,5,3,2,1,8]=>[7,6,5,3,2,1,4,8]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,7,6,5,8,3,2,1]=>[8,3,2,1,4,7,6,5]=>[[[[.,.],.],[.,[[[.,.],.],.]]],.]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,8,7,6,5,3,2,1]=>[8,7,6,5,3,2,1,4]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,4,3,2,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,4,3,2,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,4,3,2,1,7,8,6]=>[5,4,3,2,1,8,6,7]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,4,3,2,1,8,7,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[5,4,3,2,6,1,8,7]=>[6,1,5,4,3,2,8,7]=>[[.,[[[[.,.],.],.],.]],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,7,8,1]=>[8,1,5,4,3,2,6,7]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[5,4,3,2,7,6,8,1]=>[8,1,5,4,3,2,7,6]=>[[.,[[[[.,.],.],.],[[.,.],.]]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,3,2,7,8,6,1]=>[8,6,1,5,4,3,2,7]=>[[[.,[[[[.,.],.],.],.]],[.,.]],.]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,4,3,2,8,7,6,1]=>[8,7,6,1,5,4,3,2]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[5,4,3,6,2,1,8,7]=>[6,2,1,5,4,3,8,7]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,4,6,3,7,2,8,1]=>[8,1,7,2,6,3,5,4]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,4,6,7,3,8,2,1]=>[8,2,1,7,3,5,4,6]=>[[[.,.],[[.,[[.,.],[.,.]]],.]],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[5,6,4,3,2,1,8,7]=>[6,4,3,2,1,5,8,7]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,6,7,4,3,2,1,8]=>[7,4,3,2,1,5,6,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,4,3,2,1]=>[8,4,3,2,1,5,6,7]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[5,7,6,4,3,2,1,8]=>[7,6,4,3,2,1,5,8]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[5,7,6,4,3,8,2,1]=>[8,2,1,7,6,4,3,5]=>[[[.,.],[[[[.,.],[.,.]],.],.]],.]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,8,7,6,4,3,2,1]=>[8,7,6,4,3,2,1,5]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,5,4,3,2,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,5,4,3,7,2,8,1]=>[8,1,7,2,6,5,4,3]=>[[.,[[.,[[[[.,.],.],.],.]],.]],.]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[6,5,7,4,3,2,1,8]=>[7,4,3,2,1,6,5,8]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,5,7,4,3,2,8,1]=>[8,1,7,4,3,2,6,5]=>[[.,[[[[.,.],.],[[.,.],.]],.]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[6,5,7,4,8,3,2,1]=>[8,3,2,1,7,4,6,5]=>[[[[.,.],.],[[.,[[.,.],.]],.]],.]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[6,5,7,8,4,3,2,1]=>[8,4,3,2,1,6,5,7]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[6,5,8,7,4,3,2,1]=>[8,7,4,3,2,1,6,5]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[6,7,5,4,3,2,1,8]=>[7,5,4,3,2,1,6,8]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,7,5,4,3,2,8,1]=>[8,1,7,5,4,3,2,6]=>[[.,[[[[[.,.],.],.],[.,.]],.]],.]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,5,4,3,2,1]=>[8,5,4,3,2,1,6,7]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,6,5,4,3,2,8,1]=>[8,1,7,6,5,4,3,2]=>[[.,[[[[[[.,.],.],.],.],.],.]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[7,6,5,4,3,8,2,1]=>[8,2,1,7,6,5,4,3]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[7,6,5,4,8,3,2,1]=>[8,3,2,1,7,6,5,4]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[7,6,5,8,4,3,2,1]=>[8,4,3,2,1,7,6,5]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[7,6,8,5,4,3,2,1]=>[8,5,4,3,2,1,7,6]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[7,8,6,5,4,3,2,1]=>[8,6,5,4,3,2,1,7]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>[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]=>[8,7,6,5,4,3,2,1,9]=>[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]=>[1,9,8,7,6,5,4,3,2]=>[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]=>[9,8,7,6,5,4,3,2,1,10]=>[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]=>[7,8,6,5,4,3,2,1,9]=>[8,6,5,4,3,2,1,7,9]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,8,9,7,6,5,4,3,2]=>[1,9,7,6,5,4,3,2,8]=>[.,[[[[[[[.,.],.],.],.],.],[.,.]],.]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,10,9,8,7,6,5,4,3,2]=>[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]=>[10,9,8,7,6,5,4,3,2,1,11]=>[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]=>[8,9,7,6,5,4,3,2,1,10]=>[9,7,6,5,4,3,2,1,8,10]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[6,8,7,5,4,3,2,1,9]=>[8,7,5,4,3,2,1,6,9]=>[[[[[[[.,.],.],.],.],[.,.]],.],[.,.]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,8,7,9,6,5,4,3,2]=>[1,9,6,5,4,3,2,8,7]=>[.,[[[[[[.,.],.],.],.],[[.,.],.]],.]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,7,9,8,6,5,4,3,2]=>[1,9,8,6,5,4,3,2,7]=>[.,[[[[[[[.,.],.],.],.],[.,.]],.],.]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,9,10,8,7,6,5,4,3,2]=>[1,10,8,7,6,5,4,3,2,9]=>[.,[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,11,10,9,8,7,6,5,4,3,2]=>[1,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,8,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,7,6,5,4,3,2,1,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,1,10,9,8,7,6,5,4,3]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[8,7,6,5,4,3,2,1,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,9,1]=>[9,1,3,2,4,5,6,7,8]=>[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[7,8,9,6,5,4,3,2,1]=>[9,6,5,4,3,2,1,7,8]=>[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,7,6,5,4,3,2,9,1]=>[9,1,8,7,6,5,4,3,2]=>[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[8,7,6,5,4,3,9,2,1]=>[9,2,1,8,7,6,5,4,3]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[8,7,6,5,9,4,3,2,1]=>[9,4,3,2,1,8,7,6,5]=>[[[[[.,.],.],.],[[[[.,.],.],.],.]],.]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[8,7,9,6,5,4,3,2,1]=>[9,6,5,4,3,2,1,8,7]=>[[[[[[[.,.],.],.],.],.],[[.,.],.]],.]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[8,9,7,6,5,4,3,2,1]=>[9,7,6,5,4,3,2,1,8]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[9,8,7,6,5,4,3,2,1]=>[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]=>[1,2,3,4,5,6,7,8,9]=>[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]=>[1,2,3,4,5,6,7,9,8]=>[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]=>[1,2,3,4,5,6,8,9,7]=>[1,2,3,4,5,6,9,7,8]=>[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,5,7,8,9,6]=>[1,2,3,4,5,9,6,7,8]=>[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,9,5]=>[1,2,3,4,9,5,6,7,8]=>[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,9,4]=>[1,2,3,9,4,5,6,7,8]=>[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,8,9,3]=>[1,2,9,3,4,5,6,7,8]=>[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,9,2]=>[1,9,2,3,4,5,6,7,8]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8,9,10]=>[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]=>[1,2,3,4,5,6,7,8,10,9]=>[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]=>[1,2,3,4,5,6,9,8,7]=>[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]=>[1,2,3,4,5,6,7,9,10,8]=>[1,2,3,4,5,6,7,10,8,9]=>[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,4,5,8,7,9,6]=>[1,2,3,4,5,9,6,8,7]=>[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,5,6,8,9,10,7]=>[1,2,3,4,5,6,10,7,8,9]=>[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,4,5,7,8,9,10,6]=>[1,2,3,4,5,10,6,7,8,9]=>[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,9,10,5]=>[1,2,3,4,10,5,6,7,8,9]=>[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,9,10,4]=>[1,2,3,10,4,5,6,7,8,9]=>[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,8,9,10,3]=>[1,2,10,3,4,5,6,7,8,9]=>[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,2,3,4,5,6,7,8,9]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,8,9,11,10]=>[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]=>[2,3,4,5,6,7,8,9,10,11,1]=>[11,1,2,3,4,5,6,7,8,9,10]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3,10,9,8,7]=>[2,1,6,5,4,3,10,9,8,7]=>[[.,.],[[[[.,.],.],.],[[[[.,.],.],.],.]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7,10,9]=>[4,3,2,1,6,5,8,7,10,9]=>[[[[.,.],.],.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,8,7,6,5,10,9]=>[4,3,2,1,8,7,6,5,10,9]=>[[[[.,.],.],.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,3,2,1,10,9,8,7,6,5]=>[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]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1,7,8,9,10]=>[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]=>[6,5,4,3,2,1,10,9,8,7]=>[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]=>[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,6,7,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[9,8,10,7,6,5,4,3,2,1]=>[10,7,6,5,4,3,2,1,9,8]=>[[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,8,7,6,5,4,3,2,10,1]=>[10,1,9,8,7,6,5,4,3,2]=>[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[9,10,8,7,6,5,4,3,2,1]=>[10,8,7,6,5,4,3,2,1,9]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[9,8,7,6,5,4,3,10,2,1]=>[10,2,1,9,8,7,6,5,4,3]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,9,8]=>[3,1,2,5,4,7,6,9,8]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,9,8,10]=>[3,1,2,5,4,7,6,9,8,10]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
Map
to 312-avoiding permutation
Description
Map
invert Laguerre heap
Description
The permutation obtained by inverting the corresponding Laguerre heap, according to Viennot.
Let $\pi$ be a permutation. Following Viennot [1], we associate to $\pi$ a heap of pieces, by considering each decreasing run $(\pi_i, \pi_{i+1}, \dots, \pi_j)$ of $\pi$ as one piece, beginning with the left most run. Two pieces commute if and only if the minimal element of one piece is larger than the maximal element of the other piece.
This map yields the permutation corresponding to the heap obtained by reversing the reading direction of the heap.
Equivalently, this is the permutation obtained by flipping the noncrossing arc diagram of Reading [2] vertically.
By definition, this map preserves the set of decreasing runs.
Let $\pi$ be a permutation. Following Viennot [1], we associate to $\pi$ a heap of pieces, by considering each decreasing run $(\pi_i, \pi_{i+1}, \dots, \pi_j)$ of $\pi$ as one piece, beginning with the left most run. Two pieces commute if and only if the minimal element of one piece is larger than the maximal element of the other piece.
This map yields the permutation corresponding to the heap obtained by reversing the reading direction of the heap.
Equivalently, this is the permutation obtained by flipping the noncrossing arc diagram of Reading [2] vertically.
By definition, this map preserves the set of decreasing runs.
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.