Identifier
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00064: Permutations —reverse⟶ Permutations
Mp00069: Permutations —complement⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-4
[1,0]=>[1]=>[1]=>[1]=>[.,.]
[1,0,1,0]=>[2,1]=>[1,2]=>[2,1]=>[[.,.],.]
[1,1,0,0]=>[1,2]=>[2,1]=>[1,2]=>[.,[.,.]]
[1,0,1,0,1,0]=>[3,2,1]=>[1,2,3]=>[3,2,1]=>[[[.,.],.],.]
[1,0,1,1,0,0]=>[2,3,1]=>[1,3,2]=>[3,1,2]=>[[.,[.,.]],.]
[1,1,0,0,1,0]=>[3,1,2]=>[2,1,3]=>[2,3,1]=>[[.,.],[.,.]]
[1,1,0,1,0,0]=>[2,1,3]=>[3,1,2]=>[1,3,2]=>[.,[[.,.],.]]
[1,1,1,0,0,0]=>[1,2,3]=>[3,2,1]=>[1,2,3]=>[.,[.,[.,.]]]
[1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[1,2,3,4]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[1,0,1,0,1,1,0,0]=>[3,4,2,1]=>[1,2,4,3]=>[4,3,1,2]=>[[[.,[.,.]],.],.]
[1,0,1,1,0,0,1,0]=>[4,2,3,1]=>[1,3,2,4]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[1,0,1,1,0,1,0,0]=>[3,2,4,1]=>[1,4,2,3]=>[4,1,3,2]=>[[.,[[.,.],.]],.]
[1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[1,4,3,2]=>[4,1,2,3]=>[[.,[.,[.,.]]],.]
[1,1,0,0,1,0,1,0]=>[4,3,1,2]=>[2,1,3,4]=>[3,4,2,1]=>[[[.,.],.],[.,.]]
[1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[2,1,4,3]=>[3,4,1,2]=>[[.,[.,.]],[.,.]]
[1,1,0,1,0,0,1,0]=>[4,2,1,3]=>[3,1,2,4]=>[2,4,3,1]=>[[.,.],[[.,.],.]]
[1,1,0,1,0,1,0,0]=>[3,2,1,4]=>[4,1,2,3]=>[1,4,3,2]=>[.,[[[.,.],.],.]]
[1,1,0,1,1,0,0,0]=>[2,3,1,4]=>[4,1,3,2]=>[1,4,2,3]=>[.,[[.,[.,.]],.]]
[1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[3,2,1,4]=>[2,3,4,1]=>[[.,.],[.,[.,.]]]
[1,1,1,0,0,1,0,0]=>[3,1,2,4]=>[4,2,1,3]=>[1,3,4,2]=>[.,[[.,.],[.,.]]]
[1,1,1,0,1,0,0,0]=>[2,1,3,4]=>[4,3,1,2]=>[1,2,4,3]=>[.,[.,[[.,.],.]]]
[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[4,3,2,1]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[1,0,1,0,1,0,1,1,0,0]=>[4,5,3,2,1]=>[1,2,3,5,4]=>[5,4,3,1,2]=>[[[[.,[.,.]],.],.],.]
[1,0,1,0,1,1,0,0,1,0]=>[5,3,4,2,1]=>[1,2,4,3,5]=>[5,4,2,3,1]=>[[[[.,.],[.,.]],.],.]
[1,0,1,0,1,1,0,1,0,0]=>[4,3,5,2,1]=>[1,2,5,3,4]=>[5,4,1,3,2]=>[[[.,[[.,.],.]],.],.]
[1,0,1,0,1,1,1,0,0,0]=>[3,4,5,2,1]=>[1,2,5,4,3]=>[5,4,1,2,3]=>[[[.,[.,[.,.]]],.],.]
[1,0,1,1,0,0,1,0,1,0]=>[5,4,2,3,1]=>[1,3,2,4,5]=>[5,3,4,2,1]=>[[[[.,.],.],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0]=>[4,5,2,3,1]=>[1,3,2,5,4]=>[5,3,4,1,2]=>[[[.,[.,.]],[.,.]],.]
[1,0,1,1,0,1,0,0,1,0]=>[5,3,2,4,1]=>[1,4,2,3,5]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[1,0,1,1,0,1,0,1,0,0]=>[4,3,2,5,1]=>[1,5,2,3,4]=>[5,1,4,3,2]=>[[.,[[[.,.],.],.]],.]
[1,0,1,1,0,1,1,0,0,0]=>[3,4,2,5,1]=>[1,5,2,4,3]=>[5,1,4,2,3]=>[[.,[[.,[.,.]],.]],.]
[1,0,1,1,1,0,0,0,1,0]=>[5,2,3,4,1]=>[1,4,3,2,5]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,0]=>[4,2,3,5,1]=>[1,5,3,2,4]=>[5,1,3,4,2]=>[[.,[[.,.],[.,.]]],.]
[1,0,1,1,1,0,1,0,0,0]=>[3,2,4,5,1]=>[1,5,4,2,3]=>[5,1,2,4,3]=>[[.,[.,[[.,.],.]]],.]
[1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[1,5,4,3,2]=>[5,1,2,3,4]=>[[.,[.,[.,[.,.]]]],.]
[1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,2]=>[2,1,3,4,5]=>[4,5,3,2,1]=>[[[[.,.],.],.],[.,.]]
[1,1,0,0,1,0,1,1,0,0]=>[4,5,3,1,2]=>[2,1,3,5,4]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,0]=>[5,3,4,1,2]=>[2,1,4,3,5]=>[4,5,2,3,1]=>[[[.,.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0]=>[4,3,5,1,2]=>[2,1,5,3,4]=>[4,5,1,3,2]=>[[.,[[.,.],.]],[.,.]]
[1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>[2,1,5,4,3]=>[4,5,1,2,3]=>[[.,[.,[.,.]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,3]=>[3,1,2,4,5]=>[3,5,4,2,1]=>[[[.,.],.],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0]=>[4,5,2,1,3]=>[3,1,2,5,4]=>[3,5,4,1,2]=>[[.,[.,.]],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,4]=>[4,1,2,3,5]=>[2,5,4,3,1]=>[[.,.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,5]=>[5,1,2,3,4]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[1,1,0,1,0,1,1,0,0,0]=>[3,4,2,1,5]=>[5,1,2,4,3]=>[1,5,4,2,3]=>[.,[[[.,[.,.]],.],.]]
[1,1,0,1,1,0,0,0,1,0]=>[5,2,3,1,4]=>[4,1,3,2,5]=>[2,5,3,4,1]=>[[.,.],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0]=>[4,2,3,1,5]=>[5,1,3,2,4]=>[1,5,3,4,2]=>[.,[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,1,0,0,0]=>[3,2,4,1,5]=>[5,1,4,2,3]=>[1,5,2,4,3]=>[.,[[.,[[.,.],.]],.]]
[1,1,0,1,1,1,0,0,0,0]=>[2,3,4,1,5]=>[5,1,4,3,2]=>[1,5,2,3,4]=>[.,[[.,[.,[.,.]]],.]]
[1,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,3]=>[3,2,1,4,5]=>[3,4,5,2,1]=>[[[.,.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>[3,2,1,5,4]=>[3,4,5,1,2]=>[[.,[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,0]=>[5,3,1,2,4]=>[4,2,1,3,5]=>[2,4,5,3,1]=>[[.,.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0]=>[4,3,1,2,5]=>[5,2,1,3,4]=>[1,4,5,3,2]=>[.,[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,1,0,0,0]=>[3,4,1,2,5]=>[5,2,1,4,3]=>[1,4,5,2,3]=>[.,[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,0,1,0]=>[5,2,1,3,4]=>[4,3,1,2,5]=>[2,3,5,4,1]=>[[.,.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0]=>[4,2,1,3,5]=>[5,3,1,2,4]=>[1,3,5,4,2]=>[.,[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,0]=>[3,2,1,4,5]=>[5,4,1,2,3]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]]
[1,1,1,0,1,1,0,0,0,0]=>[2,3,1,4,5]=>[5,4,1,3,2]=>[1,2,5,3,4]=>[.,[.,[[.,[.,.]],.]]]
[1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>[4,3,2,1,5]=>[2,3,4,5,1]=>[[.,.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0]=>[4,1,2,3,5]=>[5,3,2,1,4]=>[1,3,4,5,2]=>[.,[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0]=>[3,1,2,4,5]=>[5,4,2,1,3]=>[1,2,4,5,3]=>[.,[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,0]=>[2,1,3,4,5]=>[5,4,3,1,2]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]
[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,2,1]=>[1,2,3,4,6,5]=>[6,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,2,1]=>[1,2,3,5,4,6]=>[6,5,4,2,3,1]=>[[[[[.,.],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,2,1]=>[1,2,3,6,4,5]=>[6,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],.]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,2,1]=>[1,2,3,6,5,4]=>[6,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],.]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,2,1]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,2,1]=>[1,2,4,3,6,5]=>[6,5,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],.]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,2,1]=>[1,2,5,3,4,6]=>[6,5,2,4,3,1]=>[[[[.,.],[[.,.],.]],.],.]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,2,1]=>[1,2,6,3,4,5]=>[6,5,1,4,3,2]=>[[[.,[[[.,.],.],.]],.],.]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,2,1]=>[1,2,6,3,5,4]=>[6,5,1,4,2,3]=>[[[.,[[.,[.,.]],.]],.],.]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,2,1]=>[1,2,5,4,3,6]=>[6,5,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,2,1]=>[1,2,6,4,3,5]=>[6,5,1,3,4,2]=>[[[.,[[.,.],[.,.]]],.],.]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[1,2,6,5,3,4]=>[6,5,1,2,4,3]=>[[[.,[.,[[.,.],.]]],.],.]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,2,1]=>[1,2,6,5,4,3]=>[6,5,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],.]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,3,1]=>[1,3,2,4,5,6]=>[6,4,5,3,2,1]=>[[[[[.,.],.],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,3,1]=>[1,3,2,4,6,5]=>[6,4,5,3,1,2]=>[[[[.,[.,.]],.],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,3,1]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,3,1]=>[1,3,2,6,4,5]=>[6,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,3,1]=>[1,3,2,6,5,4]=>[6,4,5,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,4,1]=>[1,4,2,3,5,6]=>[6,3,5,4,2,1]=>[[[[.,.],.],[[.,.],.]],.]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,4,1]=>[1,4,2,3,6,5]=>[6,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],.]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,5,1]=>[1,5,2,3,4,6]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,1]=>[1,6,2,3,4,5]=>[6,1,5,4,3,2]=>[[.,[[[[.,.],.],.],.]],.]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,1]=>[1,6,2,3,5,4]=>[6,1,5,4,2,3]=>[[.,[[[.,[.,.]],.],.]],.]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,5,1]=>[1,5,2,4,3,6]=>[6,2,5,3,4,1]=>[[[.,.],[[.,[.,.]],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,6,1]=>[1,6,2,4,3,5]=>[6,1,5,3,4,2]=>[[.,[[[.,.],[.,.]],.]],.]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,6,1]=>[1,6,2,5,3,4]=>[6,1,5,2,4,3]=>[[.,[[.,[[.,.],.]],.]],.]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,6,1]=>[1,6,2,5,4,3]=>[6,1,5,2,3,4]=>[[.,[[.,[.,[.,.]]],.]],.]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,4,1]=>[1,4,3,2,5,6]=>[6,3,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,4,1]=>[1,4,3,2,6,5]=>[6,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,5,1]=>[1,5,3,2,4,6]=>[6,2,4,5,3,1]=>[[[.,.],[[.,.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,6,1]=>[1,6,3,2,4,5]=>[6,1,4,5,3,2]=>[[.,[[[.,.],.],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,6,1]=>[1,6,3,2,5,4]=>[6,1,4,5,2,3]=>[[.,[[.,[.,.]],[.,.]]],.]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1]=>[1,5,4,2,3,6]=>[6,2,3,5,4,1]=>[[[.,.],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[1,6,4,2,3,5]=>[6,1,3,5,4,2]=>[[.,[[.,.],[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,6,1]=>[1,6,5,2,3,4]=>[6,1,2,5,4,3]=>[[.,[.,[[[.,.],.],.]]],.]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,6,1]=>[1,6,5,2,4,3]=>[6,1,2,5,3,4]=>[[.,[.,[[.,[.,.]],.]]],.]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,5,1]=>[1,5,4,3,2,6]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,6,1]=>[1,6,4,3,2,5]=>[6,1,3,4,5,2]=>[[.,[[.,.],[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,6,1]=>[1,6,5,3,2,4]=>[6,1,2,4,5,3]=>[[.,[.,[[.,.],[.,.]]]],.]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,6,1]=>[1,6,5,4,2,3]=>[6,1,2,3,5,4]=>[[.,[.,[.,[[.,.],.]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[1,6,5,4,3,2]=>[6,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,2]=>[2,1,3,4,5,6]=>[5,6,4,3,2,1]=>[[[[[.,.],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,1,2]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,1,2]=>[2,1,3,5,4,6]=>[5,6,4,2,3,1]=>[[[[.,.],[.,.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,1,2]=>[2,1,3,6,4,5]=>[5,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,1,2]=>[2,1,3,6,5,4]=>[5,6,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,1,2]=>[2,1,4,3,5,6]=>[5,6,3,4,2,1]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,1,2]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,1,2]=>[2,1,5,3,4,6]=>[5,6,2,4,3,1]=>[[[.,.],[[.,.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,1,2]=>[2,1,6,3,4,5]=>[5,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,1,2]=>[2,1,6,3,5,4]=>[5,6,1,4,2,3]=>[[.,[[.,[.,.]],.]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,1,2]=>[2,1,5,4,3,6]=>[5,6,2,3,4,1]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,1,2]=>[2,1,6,4,3,5]=>[5,6,1,3,4,2]=>[[.,[[.,.],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,1,2]=>[2,1,6,5,3,4]=>[5,6,1,2,4,3]=>[[.,[.,[[.,.],.]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>[2,1,6,5,4,3]=>[5,6,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,3]=>[3,1,2,4,5,6]=>[4,6,5,3,2,1]=>[[[[.,.],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,1,3]=>[3,1,2,4,6,5]=>[4,6,5,3,1,2]=>[[[.,[.,.]],.],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,1,3]=>[3,1,2,5,4,6]=>[4,6,5,2,3,1]=>[[[.,.],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,1,3]=>[3,1,2,6,4,5]=>[4,6,5,1,3,2]=>[[.,[[.,.],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,1,3]=>[3,1,2,6,5,4]=>[4,6,5,1,2,3]=>[[.,[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,4]=>[4,1,2,3,5,6]=>[3,6,5,4,2,1]=>[[[.,.],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,1,4]=>[4,1,2,3,6,5]=>[3,6,5,4,1,2]=>[[.,[.,.]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,5]=>[5,1,2,3,4,6]=>[2,6,5,4,3,1]=>[[.,.],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,6]=>[6,1,2,3,4,5]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,1,6]=>[6,1,2,3,5,4]=>[1,6,5,4,2,3]=>[.,[[[[.,[.,.]],.],.],.]]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,1,5]=>[5,1,2,4,3,6]=>[2,6,5,3,4,1]=>[[.,.],[[[.,[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,1,6]=>[6,1,2,4,3,5]=>[1,6,5,3,4,2]=>[.,[[[[.,.],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,1,6]=>[6,1,2,5,3,4]=>[1,6,5,2,4,3]=>[.,[[[.,[[.,.],.]],.],.]]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,1,6]=>[6,1,2,5,4,3]=>[1,6,5,2,3,4]=>[.,[[[.,[.,[.,.]]],.],.]]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,1,4]=>[4,1,3,2,5,6]=>[3,6,4,5,2,1]=>[[[.,.],.],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,1,4]=>[4,1,3,2,6,5]=>[3,6,4,5,1,2]=>[[.,[.,.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,1,5]=>[5,1,3,2,4,6]=>[2,6,4,5,3,1]=>[[.,.],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,1,6]=>[6,1,3,2,4,5]=>[1,6,4,5,3,2]=>[.,[[[[.,.],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,1,6]=>[6,1,3,2,5,4]=>[1,6,4,5,2,3]=>[.,[[[.,[.,.]],[.,.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,1,5]=>[5,1,4,2,3,6]=>[2,6,3,5,4,1]=>[[.,.],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,1,6]=>[6,1,4,2,3,5]=>[1,6,3,5,4,2]=>[.,[[[.,.],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,1,6]=>[6,1,5,2,3,4]=>[1,6,2,5,4,3]=>[.,[[.,[[[.,.],.],.]],.]]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,1,6]=>[6,1,5,2,4,3]=>[1,6,2,5,3,4]=>[.,[[.,[[.,[.,.]],.]],.]]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,1,5]=>[5,1,4,3,2,6]=>[2,6,3,4,5,1]=>[[.,.],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,1,6]=>[6,1,4,3,2,5]=>[1,6,3,4,5,2]=>[.,[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,1,6]=>[6,1,5,3,2,4]=>[1,6,2,4,5,3]=>[.,[[.,[[.,.],[.,.]]],.]]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,1,6]=>[6,1,5,4,2,3]=>[1,6,2,3,5,4]=>[.,[[.,[.,[[.,.],.]]],.]]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6]=>[6,1,5,4,3,2]=>[1,6,2,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],.]]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,2,3]=>[3,2,1,4,5,6]=>[4,5,6,3,2,1]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[5,6,4,1,2,3]=>[3,2,1,4,6,5]=>[4,5,6,3,1,2]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,5,1,2,3]=>[3,2,1,5,4,6]=>[4,5,6,2,3,1]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,6,1,2,3]=>[3,2,1,6,4,5]=>[4,5,6,1,3,2]=>[[.,[[.,.],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,2,4]=>[4,2,1,3,5,6]=>[3,5,6,4,2,1]=>[[[.,.],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[5,6,3,1,2,4]=>[4,2,1,3,6,5]=>[3,5,6,4,1,2]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,2,5]=>[5,2,1,3,4,6]=>[2,5,6,4,3,1]=>[[.,.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,2,6]=>[6,2,1,3,4,5]=>[1,5,6,4,3,2]=>[.,[[[[.,.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[4,5,3,1,2,6]=>[6,2,1,3,5,4]=>[1,5,6,4,2,3]=>[.,[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>[5,2,1,4,3,6]=>[2,5,6,3,4,1]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,4,1,2,6]=>[6,2,1,4,3,5]=>[1,5,6,3,4,2]=>[.,[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,5,1,2,6]=>[6,2,1,5,3,4]=>[1,5,6,2,4,3]=>[.,[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6]=>[6,2,1,5,4,3]=>[1,5,6,2,3,4]=>[.,[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,3,4]=>[4,3,1,2,5,6]=>[3,4,6,5,2,1]=>[[[.,.],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[5,6,2,1,3,4]=>[4,3,1,2,6,5]=>[3,4,6,5,1,2]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,3,5]=>[5,3,1,2,4,6]=>[2,4,6,5,3,1]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,3,6]=>[6,3,1,2,4,5]=>[1,4,6,5,3,2]=>[.,[[[.,.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,5,2,1,3,6]=>[6,3,1,2,5,4]=>[1,4,6,5,2,3]=>[.,[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,4,5]=>[5,4,1,2,3,6]=>[2,3,6,5,4,1]=>[[.,.],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,4,6]=>[6,4,1,2,3,5]=>[1,3,6,5,4,2]=>[.,[[.,.],[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,5,6]=>[6,5,1,2,3,4]=>[1,2,6,5,4,3]=>[.,[.,[[[[.,.],.],.],.]]]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,2,1,5,6]=>[6,5,1,2,4,3]=>[1,2,6,5,3,4]=>[.,[.,[[[.,[.,.]],.],.]]]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,1,4,5]=>[5,4,1,3,2,6]=>[2,3,6,4,5,1]=>[[.,.],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,3,1,4,6]=>[6,4,1,3,2,5]=>[1,3,6,4,5,2]=>[.,[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,3,1,5,6]=>[6,5,1,3,2,4]=>[1,2,6,4,5,3]=>[.,[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,4,1,5,6]=>[6,5,1,4,2,3]=>[1,2,6,3,5,4]=>[.,[.,[[.,[[.,.],.]],.]]]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6]=>[6,5,1,4,3,2]=>[1,2,6,3,4,5]=>[.,[.,[[.,[.,[.,.]]],.]]]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,2,3,4]=>[4,3,2,1,5,6]=>[3,4,5,6,2,1]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>[4,3,2,1,6,5]=>[3,4,5,6,1,2]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>[5,3,2,1,4,6]=>[2,4,5,6,3,1]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,2,3,6]=>[6,3,2,1,4,5]=>[1,4,5,6,3,2]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,3,6]=>[6,3,2,1,5,4]=>[1,4,5,6,2,3]=>[.,[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,2,4,5]=>[5,4,2,1,3,6]=>[2,3,5,6,4,1]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,2,4,6]=>[6,4,2,1,3,5]=>[1,3,5,6,4,2]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,2,5,6]=>[6,5,2,1,3,4]=>[1,2,5,6,4,3]=>[.,[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>[6,5,2,1,4,3]=>[1,2,5,6,3,4]=>[.,[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,3,4,5]=>[5,4,3,1,2,6]=>[2,3,4,6,5,1]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,3,4,6]=>[6,4,3,1,2,5]=>[1,3,4,6,5,2]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,3,5,6]=>[6,5,3,1,2,4]=>[1,2,4,6,5,3]=>[.,[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,4,5,6]=>[6,5,4,1,2,3]=>[1,2,3,6,5,4]=>[.,[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,1,4,5,6]=>[6,5,4,1,3,2]=>[1,2,3,6,4,5]=>[.,[.,[.,[[.,[.,.]],.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>[5,4,3,2,1,6]=>[2,3,4,5,6,1]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,4,6]=>[6,4,3,2,1,5]=>[1,3,4,5,6,2]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,3,5,6]=>[6,5,3,2,1,4]=>[1,2,4,5,6,3]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,2,4,5,6]=>[6,5,4,2,1,3]=>[1,2,3,5,6,4]=>[.,[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[6,5,4,3,1,2]=>[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6]=>[7,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,2,1]=>[1,2,3,4,6,5,7]=>[7,6,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,2,1]=>[1,2,3,4,7,5,6]=>[7,6,5,4,1,3,2]=>[[[[[.,[[.,.],.]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,2,1]=>[1,2,3,4,7,6,5]=>[7,6,5,4,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7]=>[7,6,5,3,4,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6]=>[7,6,5,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,2,1]=>[1,2,3,6,4,5,7]=>[7,6,5,2,4,3,1]=>[[[[[.,.],[[.,.],.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,2,1]=>[1,2,3,7,4,5,6]=>[7,6,5,1,4,3,2]=>[[[[.,[[[.,.],.],.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,2,1]=>[1,2,3,7,4,6,5]=>[7,6,5,1,4,2,3]=>[[[[.,[[.,[.,.]],.]],.],.],.]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,2,1]=>[1,2,3,6,5,4,7]=>[7,6,5,2,3,4,1]=>[[[[[.,.],[.,[.,.]]],.],.],.]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,2,1]=>[1,2,3,7,5,4,6]=>[7,6,5,1,3,4,2]=>[[[[.,[[.,.],[.,.]]],.],.],.]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,2,1]=>[1,2,3,7,6,4,5]=>[7,6,5,1,2,4,3]=>[[[[.,[.,[[.,.],.]]],.],.],.]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4]=>[7,6,5,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],.],.],.]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,2,1]=>[1,2,4,3,5,6,7]=>[7,6,4,5,3,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,2,1]=>[1,2,4,3,5,7,6]=>[7,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7]=>[7,6,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,2,1]=>[1,2,4,3,7,5,6]=>[7,6,4,5,1,3,2]=>[[[[.,[[.,.],.]],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,2,1]=>[1,2,4,3,7,6,5]=>[7,6,4,5,1,2,3]=>[[[[.,[.,[.,.]]],[.,.]],.],.]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,2,1]=>[1,2,5,3,4,6,7]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,2,1]=>[1,2,5,3,4,7,6]=>[7,6,3,5,4,1,2]=>[[[[.,[.,.]],[[.,.],.]],.],.]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,2,1]=>[1,2,6,3,4,5,7]=>[7,6,2,5,4,3,1]=>[[[[.,.],[[[.,.],.],.]],.],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,2,1]=>[1,2,7,3,4,5,6]=>[7,6,1,5,4,3,2]=>[[[.,[[[[.,.],.],.],.]],.],.]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,2,1]=>[1,2,7,3,4,6,5]=>[7,6,1,5,4,2,3]=>[[[.,[[[.,[.,.]],.],.]],.],.]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,2,1]=>[1,2,6,3,5,4,7]=>[7,6,2,5,3,4,1]=>[[[[.,.],[[.,[.,.]],.]],.],.]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,2,1]=>[1,2,7,3,5,4,6]=>[7,6,1,5,3,4,2]=>[[[.,[[[.,.],[.,.]],.]],.],.]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[1,2,7,3,6,4,5]=>[7,6,1,5,2,4,3]=>[[[.,[[.,[[.,.],.]],.]],.],.]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,2,1]=>[1,2,7,3,6,5,4]=>[7,6,1,5,2,3,4]=>[[[.,[[.,[.,[.,.]]],.]],.],.]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7]=>[7,6,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,2,1]=>[1,2,5,4,3,7,6]=>[7,6,3,4,5,1,2]=>[[[[.,[.,.]],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,2,1]=>[1,2,6,4,3,5,7]=>[7,6,2,4,5,3,1]=>[[[[.,.],[[.,.],[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,2,1]=>[1,2,7,4,3,5,6]=>[7,6,1,4,5,3,2]=>[[[.,[[[.,.],.],[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,2,1]=>[1,2,7,4,3,6,5]=>[7,6,1,4,5,2,3]=>[[[.,[[.,[.,.]],[.,.]]],.],.]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,2,1]=>[1,2,6,5,3,4,7]=>[7,6,2,3,5,4,1]=>[[[[.,.],[.,[[.,.],.]]],.],.]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,2,1]=>[1,2,7,5,3,4,6]=>[7,6,1,3,5,4,2]=>[[[.,[[.,.],[[.,.],.]]],.],.]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[1,2,7,6,3,4,5]=>[7,6,1,2,5,4,3]=>[[[.,[.,[[[.,.],.],.]]],.],.]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,2,1]=>[1,2,7,6,3,5,4]=>[7,6,1,2,5,3,4]=>[[[.,[.,[[.,[.,.]],.]]],.],.]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,2,1]=>[1,2,6,5,4,3,7]=>[7,6,2,3,4,5,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,2,1]=>[1,2,7,5,4,3,6]=>[7,6,1,3,4,5,2]=>[[[.,[[.,.],[.,[.,.]]]],.],.]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,2,1]=>[1,2,7,6,4,3,5]=>[7,6,1,2,4,5,3]=>[[[.,[.,[[.,.],[.,.]]]],.],.]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,2,1]=>[1,2,7,6,5,3,4]=>[7,6,1,2,3,5,4]=>[[[.,[.,[.,[[.,.],.]]]],.],.]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,2,1]=>[1,2,7,6,5,4,3]=>[7,6,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7]=>[7,5,6,4,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6]=>[7,5,6,4,3,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,3,1]=>[1,3,2,4,7,5,6]=>[7,5,6,4,1,3,2]=>[[[[.,[[.,.],.]],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,3,1]=>[1,3,2,4,7,6,5]=>[7,5,6,4,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7]=>[7,5,6,3,4,2,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6]=>[7,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7]=>[7,5,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6]=>[7,5,6,1,4,3,2]=>[[[.,[[[.,.],.],.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,3,1]=>[1,3,2,7,4,6,5]=>[7,5,6,1,4,2,3]=>[[[.,[[.,[.,.]],.]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7]=>[7,5,6,2,3,4,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,3,1]=>[1,3,2,7,5,4,6]=>[7,5,6,1,3,4,2]=>[[[.,[[.,.],[.,.]]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,3,1]=>[1,3,2,7,6,4,5]=>[7,5,6,1,2,4,3]=>[[[.,[.,[[.,.],.]]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,3,1]=>[1,3,2,7,6,5,4]=>[7,5,6,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7]=>[7,4,6,5,3,2,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6]=>[7,4,6,5,3,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],.]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,4,1]=>[1,4,2,3,6,5,7]=>[7,4,6,5,2,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6]=>[7,4,6,5,1,3,2]=>[[[.,[[.,.],.]],[[.,.],.]],.]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,4,1]=>[1,4,2,3,7,6,5]=>[7,4,6,5,1,2,3]=>[[[.,[.,[.,.]]],[[.,.],.]],.]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7]=>[7,3,6,5,4,2,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6]=>[7,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],.]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6]=>[7,1,6,5,4,3,2]=>[[.,[[[[[.,.],.],.],.],.]],.]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,7,1]=>[1,7,2,3,4,6,5]=>[7,1,6,5,4,2,3]=>[[.,[[[[.,[.,.]],.],.],.]],.]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,6,1]=>[1,6,2,3,5,4,7]=>[7,2,6,5,3,4,1]=>[[[.,.],[[[.,[.,.]],.],.]],.]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,7,1]=>[1,7,2,3,5,4,6]=>[7,1,6,5,3,4,2]=>[[.,[[[[.,.],[.,.]],.],.]],.]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,7,1]=>[1,7,2,3,6,4,5]=>[7,1,6,5,2,4,3]=>[[.,[[[.,[[.,.],.]],.],.]],.]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,7,1]=>[1,7,2,3,6,5,4]=>[7,1,6,5,2,3,4]=>[[.,[[[.,[.,[.,.]]],.],.]],.]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,5,1]=>[1,5,2,4,3,6,7]=>[7,3,6,4,5,2,1]=>[[[[.,.],.],[[.,[.,.]],.]],.]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6]=>[7,3,6,4,5,1,2]=>[[[.,[.,.]],[[.,[.,.]],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,6,1]=>[1,6,2,4,3,5,7]=>[7,2,6,4,5,3,1]=>[[[.,.],[[[.,.],[.,.]],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,7,1]=>[1,7,2,4,3,5,6]=>[7,1,6,4,5,3,2]=>[[.,[[[[.,.],.],[.,.]],.]],.]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,7,1]=>[1,7,2,4,3,6,5]=>[7,1,6,4,5,2,3]=>[[.,[[[.,[.,.]],[.,.]],.]],.]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,6,1]=>[1,6,2,5,3,4,7]=>[7,2,6,3,5,4,1]=>[[[.,.],[[.,[[.,.],.]],.]],.]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>[1,7,2,5,3,4,6]=>[7,1,6,3,5,4,2]=>[[.,[[[.,.],[[.,.],.]],.]],.]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,7,1]=>[1,7,2,6,3,4,5]=>[7,1,6,2,5,4,3]=>[[.,[[.,[[[.,.],.],.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,7,1]=>[1,7,2,6,3,5,4]=>[7,1,6,2,5,3,4]=>[[.,[[.,[[.,[.,.]],.]],.]],.]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,6,1]=>[1,6,2,5,4,3,7]=>[7,2,6,3,4,5,1]=>[[[.,.],[[.,[.,[.,.]]],.]],.]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>[1,7,2,5,4,3,6]=>[7,1,6,3,4,5,2]=>[[.,[[[.,.],[.,[.,.]]],.]],.]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,7,1]=>[1,7,2,6,4,3,5]=>[7,1,6,2,4,5,3]=>[[.,[[.,[[.,.],[.,.]]],.]],.]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,7,1]=>[1,7,2,6,5,3,4]=>[7,1,6,2,3,5,4]=>[[.,[[.,[.,[[.,.],.]]],.]],.]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,7,1]=>[1,7,2,6,5,4,3]=>[7,1,6,2,3,4,5]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,4,1]=>[1,4,3,2,5,6,7]=>[7,4,5,6,3,2,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,4,1]=>[1,4,3,2,5,7,6]=>[7,4,5,6,3,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7]=>[7,4,5,6,2,3,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,4,1]=>[1,4,3,2,7,5,6]=>[7,4,5,6,1,3,2]=>[[[.,[[.,.],.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5]=>[7,4,5,6,1,2,3]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7]=>[7,3,5,6,4,2,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,5,1]=>[1,5,3,2,4,7,6]=>[7,3,5,6,4,1,2]=>[[[.,[.,.]],[[.,.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,6,1]=>[1,6,3,2,4,5,7]=>[7,2,5,6,4,3,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,7,1]=>[1,7,3,2,4,5,6]=>[7,1,5,6,4,3,2]=>[[.,[[[[.,.],.],.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,7,1]=>[1,7,3,2,4,6,5]=>[7,1,5,6,4,2,3]=>[[.,[[[.,[.,.]],.],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,6,1]=>[1,6,3,2,5,4,7]=>[7,2,5,6,3,4,1]=>[[[.,.],[[.,[.,.]],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,7,1]=>[1,7,3,2,5,4,6]=>[7,1,5,6,3,4,2]=>[[.,[[[.,.],[.,.]],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,7,1]=>[1,7,3,2,6,4,5]=>[7,1,5,6,2,4,3]=>[[.,[[.,[[.,.],.]],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,7,1]=>[1,7,3,2,6,5,4]=>[7,1,5,6,2,3,4]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,5,1]=>[1,5,4,2,3,6,7]=>[7,3,4,6,5,2,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,5,1]=>[1,5,4,2,3,7,6]=>[7,3,4,6,5,1,2]=>[[[.,[.,.]],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7]=>[7,2,4,6,5,3,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,7,1]=>[1,7,4,2,3,5,6]=>[7,1,4,6,5,3,2]=>[[.,[[[.,.],.],[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,7,1]=>[1,7,4,2,3,6,5]=>[7,1,4,6,5,2,3]=>[[.,[[.,[.,.]],[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,6,1]=>[1,6,5,2,3,4,7]=>[7,2,3,6,5,4,1]=>[[[.,.],[.,[[[.,.],.],.]]],.]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>[1,7,5,2,3,4,6]=>[7,1,3,6,5,4,2]=>[[.,[[.,.],[[[.,.],.],.]]],.]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,7,1]=>[1,7,6,2,3,4,5]=>[7,1,2,6,5,4,3]=>[[.,[.,[[[[.,.],.],.],.]]],.]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,7,1]=>[1,7,6,2,3,5,4]=>[7,1,2,6,5,3,4]=>[[.,[.,[[[.,[.,.]],.],.]]],.]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,6,1]=>[1,6,5,2,4,3,7]=>[7,2,3,6,4,5,1]=>[[[.,.],[.,[[.,[.,.]],.]]],.]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>[1,7,5,2,4,3,6]=>[7,1,3,6,4,5,2]=>[[.,[[.,.],[[.,[.,.]],.]]],.]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,7,1]=>[1,7,6,2,4,3,5]=>[7,1,2,6,4,5,3]=>[[.,[.,[[[.,.],[.,.]],.]]],.]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,7,1]=>[1,7,6,2,5,3,4]=>[7,1,2,6,3,5,4]=>[[.,[.,[[.,[[.,.],.]],.]]],.]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,7,1]=>[1,7,6,2,5,4,3]=>[7,1,2,6,3,4,5]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,5,1]=>[1,5,4,3,2,6,7]=>[7,3,4,5,6,2,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,5,1]=>[1,5,4,3,2,7,6]=>[7,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,6,1]=>[1,6,4,3,2,5,7]=>[7,2,4,5,6,3,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,7,1]=>[1,7,4,3,2,5,6]=>[7,1,4,5,6,3,2]=>[[.,[[[.,.],.],[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,7,1]=>[1,7,4,3,2,6,5]=>[7,1,4,5,6,2,3]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,6,1]=>[1,6,5,3,2,4,7]=>[7,2,3,5,6,4,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,7,1]=>[1,7,5,3,2,4,6]=>[7,1,3,5,6,4,2]=>[[.,[[.,.],[[.,.],[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,7,1]=>[1,7,6,3,2,4,5]=>[7,1,2,5,6,4,3]=>[[.,[.,[[[.,.],.],[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,7,1]=>[1,7,6,3,2,5,4]=>[7,1,2,5,6,3,4]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,6,1]=>[1,6,5,4,2,3,7]=>[7,2,3,4,6,5,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>[1,7,5,4,2,3,6]=>[7,1,3,4,6,5,2]=>[[.,[[.,.],[.,[[.,.],.]]]],.]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,7,1]=>[1,7,6,4,2,3,5]=>[7,1,2,4,6,5,3]=>[[.,[.,[[.,.],[[.,.],.]]]],.]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,7,1]=>[1,7,6,5,2,3,4]=>[7,1,2,3,6,5,4]=>[[.,[.,[.,[[[.,.],.],.]]]],.]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,7,1]=>[1,7,6,5,2,4,3]=>[7,1,2,3,6,4,5]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,6,1]=>[1,6,5,4,3,2,7]=>[7,2,3,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>[1,7,5,4,3,2,6]=>[7,1,3,4,5,6,2]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,7,1]=>[1,7,6,4,3,2,5]=>[7,1,2,4,5,6,3]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,7,1]=>[1,7,6,5,3,2,4]=>[7,1,2,3,5,6,4]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,7,1]=>[1,7,6,5,4,2,3]=>[7,1,2,3,4,6,5]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2]=>[7,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7]=>[6,7,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7]=>[6,7,5,4,2,3,1]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,1,2]=>[2,1,3,4,7,5,6]=>[6,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,1,2]=>[2,1,3,4,7,6,5]=>[6,7,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,.]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7]=>[6,7,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,1,2]=>[2,1,3,5,4,7,6]=>[6,7,5,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7]=>[6,7,5,2,4,3,1]=>[[[[.,.],[[.,.],.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,1,2]=>[2,1,3,7,4,5,6]=>[6,7,5,1,4,3,2]=>[[[.,[[[.,.],.],.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,1,2]=>[2,1,3,7,4,6,5]=>[6,7,5,1,4,2,3]=>[[[.,[[.,[.,.]],.]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7]=>[6,7,5,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,1,2]=>[2,1,3,7,5,4,6]=>[6,7,5,1,3,4,2]=>[[[.,[[.,.],[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,1,2]=>[2,1,3,7,6,4,5]=>[6,7,5,1,2,4,3]=>[[[.,[.,[[.,.],.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,1,2]=>[2,1,3,7,6,5,4]=>[6,7,5,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7]=>[6,7,4,5,3,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,1,2]=>[2,1,4,3,5,7,6]=>[6,7,4,5,3,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7]=>[6,7,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6]=>[6,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5]=>[6,7,4,5,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,1,2]=>[2,1,5,3,4,6,7]=>[6,7,3,5,4,2,1]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,1,2]=>[2,1,5,3,4,7,6]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,1,2]=>[2,1,6,3,4,5,7]=>[6,7,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6]=>[6,7,1,5,4,3,2]=>[[.,[[[[.,.],.],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,1,2]=>[2,1,7,3,4,6,5]=>[6,7,1,5,4,2,3]=>[[.,[[[.,[.,.]],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,1,2]=>[2,1,6,3,5,4,7]=>[6,7,2,5,3,4,1]=>[[[.,.],[[.,[.,.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,1,2]=>[2,1,7,3,5,4,6]=>[6,7,1,5,3,4,2]=>[[.,[[[.,.],[.,.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,1,2]=>[2,1,7,3,6,4,5]=>[6,7,1,5,2,4,3]=>[[.,[[.,[[.,.],.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,1,2]=>[2,1,7,3,6,5,4]=>[6,7,1,5,2,3,4]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,1,2]=>[2,1,5,4,3,6,7]=>[6,7,3,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6]=>[6,7,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,1,2]=>[2,1,6,4,3,5,7]=>[6,7,2,4,5,3,1]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,1,2]=>[2,1,7,4,3,5,6]=>[6,7,1,4,5,3,2]=>[[.,[[[.,.],.],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,1,2]=>[2,1,7,4,3,6,5]=>[6,7,1,4,5,2,3]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7]=>[6,7,2,3,5,4,1]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,1,2]=>[2,1,7,5,3,4,6]=>[6,7,1,3,5,4,2]=>[[.,[[.,.],[[.,.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,1,2]=>[2,1,7,6,3,4,5]=>[6,7,1,2,5,4,3]=>[[.,[.,[[[.,.],.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,1,2]=>[2,1,7,6,3,5,4]=>[6,7,1,2,5,3,4]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7]=>[6,7,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,1,2]=>[2,1,7,5,4,3,6]=>[6,7,1,3,4,5,2]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,1,2]=>[2,1,7,6,4,3,5]=>[6,7,1,2,4,5,3]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,1,2]=>[2,1,7,6,5,3,4]=>[6,7,1,2,3,5,4]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>[2,1,7,6,5,4,3]=>[6,7,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7]=>[5,7,6,4,3,2,1]=>[[[[[.,.],.],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,1,3]=>[3,1,2,4,5,7,6]=>[5,7,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7]=>[5,7,6,4,2,3,1]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,1,3]=>[3,1,2,4,7,5,6]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,1,3]=>[3,1,2,4,7,6,5]=>[5,7,6,4,1,2,3]=>[[[.,[.,[.,.]]],.],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7]=>[5,7,6,3,4,2,1]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,1,3]=>[3,1,2,5,4,7,6]=>[5,7,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7]=>[5,7,6,2,4,3,1]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6]=>[5,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,1,3]=>[3,1,2,7,4,6,5]=>[5,7,6,1,4,2,3]=>[[.,[[.,[.,.]],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7]=>[5,7,6,2,3,4,1]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6]=>[5,7,6,1,3,4,2]=>[[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5]=>[5,7,6,1,2,4,3]=>[[.,[.,[[.,.],.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,1,3]=>[3,1,2,7,6,5,4]=>[5,7,6,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7]=>[4,7,6,5,3,2,1]=>[[[[.,.],.],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6]=>[4,7,6,5,3,1,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7]=>[4,7,6,5,2,3,1]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6]=>[4,7,6,5,1,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5]=>[4,7,6,5,1,2,3]=>[[.,[.,[.,.]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7]=>[3,7,6,5,4,2,1]=>[[[.,.],.],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,1,5]=>[5,1,2,3,4,7,6]=>[3,7,6,5,4,1,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7]=>[2,7,6,5,4,3,1]=>[[.,.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,1,7]=>[7,1,2,3,4,6,5]=>[1,7,6,5,4,2,3]=>[.,[[[[[.,[.,.]],.],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,1,6]=>[6,1,2,3,5,4,7]=>[2,7,6,5,3,4,1]=>[[.,.],[[[[.,[.,.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,1,7]=>[7,1,2,3,5,4,6]=>[1,7,6,5,3,4,2]=>[.,[[[[[.,.],[.,.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,1,7]=>[7,1,2,3,6,4,5]=>[1,7,6,5,2,4,3]=>[.,[[[[.,[[.,.],.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,1,7]=>[7,1,2,3,6,5,4]=>[1,7,6,5,2,3,4]=>[.,[[[[.,[.,[.,.]]],.],.],.]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7]=>[3,7,6,4,5,2,1]=>[[[.,.],.],[[[.,[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,1,5]=>[5,1,2,4,3,7,6]=>[3,7,6,4,5,1,2]=>[[.,[.,.]],[[[.,[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,1,6]=>[6,1,2,4,3,5,7]=>[2,7,6,4,5,3,1]=>[[.,.],[[[[.,.],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,1,7]=>[7,1,2,4,3,5,6]=>[1,7,6,4,5,3,2]=>[.,[[[[[.,.],.],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,1,7]=>[7,1,2,4,3,6,5]=>[1,7,6,4,5,2,3]=>[.,[[[[.,[.,.]],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,1,6]=>[6,1,2,5,3,4,7]=>[2,7,6,3,5,4,1]=>[[.,.],[[[.,[[.,.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,1,7]=>[7,1,2,5,3,4,6]=>[1,7,6,3,5,4,2]=>[.,[[[[.,.],[[.,.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,1,7]=>[7,1,2,6,3,4,5]=>[1,7,6,2,5,4,3]=>[.,[[[.,[[[.,.],.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,1,7]=>[7,1,2,6,3,5,4]=>[1,7,6,2,5,3,4]=>[.,[[[.,[[.,[.,.]],.]],.],.]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,1,6]=>[6,1,2,5,4,3,7]=>[2,7,6,3,4,5,1]=>[[.,.],[[[.,[.,[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,1,7]=>[7,1,2,5,4,3,6]=>[1,7,6,3,4,5,2]=>[.,[[[[.,.],[.,[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,1,7]=>[7,1,2,6,4,3,5]=>[1,7,6,2,4,5,3]=>[.,[[[.,[[.,.],[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,1,7]=>[7,1,2,6,5,3,4]=>[1,7,6,2,3,5,4]=>[.,[[[.,[.,[[.,.],.]]],.],.]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,1,7]=>[7,1,2,6,5,4,3]=>[1,7,6,2,3,4,5]=>[.,[[[.,[.,[.,[.,.]]]],.],.]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7]=>[4,7,5,6,3,2,1]=>[[[[.,.],.],.],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6]=>[4,7,5,6,3,1,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7]=>[4,7,5,6,2,3,1]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6]=>[4,7,5,6,1,3,2]=>[[.,[[.,.],.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5]=>[4,7,5,6,1,2,3]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7]=>[3,7,5,6,4,2,1]=>[[[.,.],.],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,1,5]=>[5,1,3,2,4,7,6]=>[3,7,5,6,4,1,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,1,6]=>[6,1,3,2,4,5,7]=>[2,7,5,6,4,3,1]=>[[.,.],[[[[.,.],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,1,7]=>[7,1,3,2,4,5,6]=>[1,7,5,6,4,3,2]=>[.,[[[[[.,.],.],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,1,7]=>[7,1,3,2,4,6,5]=>[1,7,5,6,4,2,3]=>[.,[[[[.,[.,.]],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,1,6]=>[6,1,3,2,5,4,7]=>[2,7,5,6,3,4,1]=>[[.,.],[[[.,[.,.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,1,7]=>[7,1,3,2,5,4,6]=>[1,7,5,6,3,4,2]=>[.,[[[[.,.],[.,.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,1,7]=>[7,1,3,2,6,4,5]=>[1,7,5,6,2,4,3]=>[.,[[[.,[[.,.],.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,1,7]=>[7,1,3,2,6,5,4]=>[1,7,5,6,2,3,4]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7]=>[3,7,4,6,5,2,1]=>[[[.,.],.],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,1,5]=>[5,1,4,2,3,7,6]=>[3,7,4,6,5,1,2]=>[[.,[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7]=>[2,7,4,6,5,3,1]=>[[.,.],[[[.,.],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,1,7]=>[7,1,4,2,3,5,6]=>[1,7,4,6,5,3,2]=>[.,[[[[.,.],.],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,1,7]=>[7,1,4,2,3,6,5]=>[1,7,4,6,5,2,3]=>[.,[[[.,[.,.]],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,1,6]=>[6,1,5,2,3,4,7]=>[2,7,3,6,5,4,1]=>[[.,.],[[.,[[[.,.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,1,7]=>[7,1,5,2,3,4,6]=>[1,7,3,6,5,4,2]=>[.,[[[.,.],[[[.,.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,1,7]=>[7,1,6,2,3,4,5]=>[1,7,2,6,5,4,3]=>[.,[[.,[[[[.,.],.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,1,7]=>[7,1,6,2,3,5,4]=>[1,7,2,6,5,3,4]=>[.,[[.,[[[.,[.,.]],.],.]],.]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,1,6]=>[6,1,5,2,4,3,7]=>[2,7,3,6,4,5,1]=>[[.,.],[[.,[[.,[.,.]],.]],.]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,1,7]=>[7,1,5,2,4,3,6]=>[1,7,3,6,4,5,2]=>[.,[[[.,.],[[.,[.,.]],.]],.]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,1,7]=>[7,1,6,2,4,3,5]=>[1,7,2,6,4,5,3]=>[.,[[.,[[[.,.],[.,.]],.]],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,1,7]=>[7,1,6,2,5,3,4]=>[1,7,2,6,3,5,4]=>[.,[[.,[[.,[[.,.],.]],.]],.]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,1,7]=>[7,1,6,2,5,4,3]=>[1,7,2,6,3,4,5]=>[.,[[.,[[.,[.,[.,.]]],.]],.]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7]=>[3,7,4,5,6,2,1]=>[[[.,.],.],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,1,5]=>[5,1,4,3,2,7,6]=>[3,7,4,5,6,1,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,1,6]=>[6,1,4,3,2,5,7]=>[2,7,4,5,6,3,1]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,1,7]=>[7,1,4,3,2,5,6]=>[1,7,4,5,6,3,2]=>[.,[[[[.,.],.],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,1,7]=>[7,1,4,3,2,6,5]=>[1,7,4,5,6,2,3]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,1,6]=>[6,1,5,3,2,4,7]=>[2,7,3,5,6,4,1]=>[[.,.],[[.,[[.,.],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,1,7]=>[7,1,5,3,2,4,6]=>[1,7,3,5,6,4,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,1,7]=>[7,1,6,3,2,4,5]=>[1,7,2,5,6,4,3]=>[.,[[.,[[[.,.],.],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,1,7]=>[7,1,6,3,2,5,4]=>[1,7,2,5,6,3,4]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,1,6]=>[6,1,5,4,2,3,7]=>[2,7,3,4,6,5,1]=>[[.,.],[[.,[.,[[.,.],.]]],.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,1,7]=>[7,1,5,4,2,3,6]=>[1,7,3,4,6,5,2]=>[.,[[[.,.],[.,[[.,.],.]]],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,1,7]=>[7,1,6,4,2,3,5]=>[1,7,2,4,6,5,3]=>[.,[[.,[[.,.],[[.,.],.]]],.]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,1,7]=>[7,1,6,5,2,3,4]=>[1,7,2,3,6,5,4]=>[.,[[.,[.,[[[.,.],.],.]]],.]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,1,7]=>[7,1,6,5,2,4,3]=>[1,7,2,3,6,4,5]=>[.,[[.,[.,[[.,[.,.]],.]]],.]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,1,6]=>[6,1,5,4,3,2,7]=>[2,7,3,4,5,6,1]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,1,7]=>[7,1,5,4,3,2,6]=>[1,7,3,4,5,6,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,1,7]=>[7,1,6,4,3,2,5]=>[1,7,2,4,5,6,3]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,1,7]=>[7,1,6,5,3,2,4]=>[1,7,2,3,5,6,4]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,1,7]=>[7,1,6,5,4,2,3]=>[1,7,2,3,4,6,5]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>[7,1,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7]=>[5,6,7,4,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,1,2,3]=>[3,2,1,4,5,7,6]=>[5,6,7,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,1,2,3]=>[3,2,1,4,6,5,7]=>[5,6,7,4,2,3,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,1,2,3]=>[3,2,1,4,7,5,6]=>[5,6,7,4,1,3,2]=>[[[.,[[.,.],.]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5]=>[5,6,7,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,1,2,3]=>[3,2,1,5,4,6,7]=>[5,6,7,3,4,2,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6]=>[5,6,7,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7]=>[5,6,7,2,4,3,1]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6]=>[5,6,7,1,4,3,2]=>[[.,[[[.,.],.],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,1,2,3]=>[3,2,1,7,4,6,5]=>[5,6,7,1,4,2,3]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7]=>[5,6,7,2,3,4,1]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6]=>[5,6,7,1,3,4,2]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5]=>[5,6,7,1,2,4,3]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4]=>[5,6,7,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7]=>[4,6,7,5,3,2,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6]=>[4,6,7,5,3,1,2]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7]=>[4,6,7,5,2,3,1]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,1,2,4]=>[4,2,1,3,7,5,6]=>[4,6,7,5,1,3,2]=>[[.,[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5]=>[4,6,7,5,1,2,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7]=>[3,6,7,5,4,2,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,1,2,5]=>[5,2,1,3,4,7,6]=>[3,6,7,5,4,1,2]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7]=>[2,6,7,5,4,3,1]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6]=>[1,6,7,5,4,3,2]=>[.,[[[[[.,.],.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,1,2,7]=>[7,2,1,3,4,6,5]=>[1,6,7,5,4,2,3]=>[.,[[[[.,[.,.]],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,1,2,6]=>[6,2,1,3,5,4,7]=>[2,6,7,5,3,4,1]=>[[.,.],[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,1,2,7]=>[7,2,1,3,5,4,6]=>[1,6,7,5,3,4,2]=>[.,[[[[.,.],[.,.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,1,2,7]=>[7,2,1,3,6,4,5]=>[1,6,7,5,2,4,3]=>[.,[[[.,[[.,.],.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,1,2,7]=>[7,2,1,3,6,5,4]=>[1,6,7,5,2,3,4]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,1,2,5]=>[5,2,1,4,3,6,7]=>[3,6,7,4,5,2,1]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6]=>[3,6,7,4,5,1,2]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7]=>[2,6,7,4,5,3,1]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,1,2,7]=>[7,2,1,4,3,5,6]=>[1,6,7,4,5,3,2]=>[.,[[[[.,.],.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5]=>[1,6,7,4,5,2,3]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,1,2,6]=>[6,2,1,5,3,4,7]=>[2,6,7,3,5,4,1]=>[[.,.],[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,1,2,7]=>[7,2,1,5,3,4,6]=>[1,6,7,3,5,4,2]=>[.,[[[.,.],[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,1,2,7]=>[7,2,1,6,3,4,5]=>[1,6,7,2,5,4,3]=>[.,[[.,[[[.,.],.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,1,2,7]=>[7,2,1,6,3,5,4]=>[1,6,7,2,5,3,4]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7]=>[2,6,7,3,4,5,1]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6]=>[1,6,7,3,4,5,2]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,1,2,7]=>[7,2,1,6,4,3,5]=>[1,6,7,2,4,5,3]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,1,2,7]=>[7,2,1,6,5,3,4]=>[1,6,7,2,3,5,4]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,1,2,7]=>[7,2,1,6,5,4,3]=>[1,6,7,2,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7]=>[4,5,7,6,3,2,1]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,1,3,4]=>[4,3,1,2,5,7,6]=>[4,5,7,6,3,1,2]=>[[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,1,3,4]=>[4,3,1,2,6,5,7]=>[4,5,7,6,2,3,1]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6]=>[4,5,7,6,1,3,2]=>[[.,[[.,.],.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,1,3,4]=>[4,3,1,2,7,6,5]=>[4,5,7,6,1,2,3]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7]=>[3,5,7,6,4,2,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,1,3,5]=>[5,3,1,2,4,7,6]=>[3,5,7,6,4,1,2]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7]=>[2,5,7,6,4,3,1]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6]=>[1,5,7,6,4,3,2]=>[.,[[[[.,.],.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5]=>[1,5,7,6,4,2,3]=>[.,[[[.,[.,.]],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,1,3,6]=>[6,3,1,2,5,4,7]=>[2,5,7,6,3,4,1]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,1,3,7]=>[7,3,1,2,5,4,6]=>[1,5,7,6,3,4,2]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,1,3,7]=>[7,3,1,2,6,4,5]=>[1,5,7,6,2,4,3]=>[.,[[.,[[.,.],.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,1,3,7]=>[7,3,1,2,6,5,4]=>[1,5,7,6,2,3,4]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7]=>[3,4,7,6,5,2,1]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,1,4,5]=>[5,4,1,2,3,7,6]=>[3,4,7,6,5,1,2]=>[[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7]=>[2,4,7,6,5,3,1]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6]=>[1,4,7,6,5,3,2]=>[.,[[[.,.],.],[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,1,4,7]=>[7,4,1,2,3,6,5]=>[1,4,7,6,5,2,3]=>[.,[[.,[.,.]],[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,5,6]=>[6,5,1,2,3,4,7]=>[2,3,7,6,5,4,1]=>[[.,.],[.,[[[[.,.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6]=>[1,3,7,6,5,4,2]=>[.,[[.,.],[[[[.,.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5]=>[1,2,7,6,5,4,3]=>[.,[.,[[[[[.,.],.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,1,6,7]=>[7,6,1,2,3,5,4]=>[1,2,7,6,5,3,4]=>[.,[.,[[[[.,[.,.]],.],.],.]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,1,5,6]=>[6,5,1,2,4,3,7]=>[2,3,7,6,4,5,1]=>[[.,.],[.,[[[.,[.,.]],.],.]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,1,5,7]=>[7,5,1,2,4,3,6]=>[1,3,7,6,4,5,2]=>[.,[[.,.],[[[.,[.,.]],.],.]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,1,6,7]=>[7,6,1,2,4,3,5]=>[1,2,7,6,4,5,3]=>[.,[.,[[[[.,.],[.,.]],.],.]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,1,6,7]=>[7,6,1,2,5,3,4]=>[1,2,7,6,3,5,4]=>[.,[.,[[[.,[[.,.],.]],.],.]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,1,6,7]=>[7,6,1,2,5,4,3]=>[1,2,7,6,3,4,5]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,1,4,5]=>[5,4,1,3,2,6,7]=>[3,4,7,5,6,2,1]=>[[[.,.],.],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,1,4,5]=>[5,4,1,3,2,7,6]=>[3,4,7,5,6,1,2]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,1,4,6]=>[6,4,1,3,2,5,7]=>[2,4,7,5,6,3,1]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6]=>[1,4,7,5,6,3,2]=>[.,[[[.,.],.],[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5]=>[1,4,7,5,6,2,3]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,1,5,6]=>[6,5,1,3,2,4,7]=>[2,3,7,5,6,4,1]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,1,5,7]=>[7,5,1,3,2,4,6]=>[1,3,7,5,6,4,2]=>[.,[[.,.],[[[.,.],[.,.]],.]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,1,6,7]=>[7,6,1,3,2,4,5]=>[1,2,7,5,6,4,3]=>[.,[.,[[[[.,.],.],[.,.]],.]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,1,6,7]=>[7,6,1,3,2,5,4]=>[1,2,7,5,6,3,4]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,1,5,6]=>[6,5,1,4,2,3,7]=>[2,3,7,4,6,5,1]=>[[.,.],[.,[[.,[[.,.],.]],.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,1,5,7]=>[7,5,1,4,2,3,6]=>[1,3,7,4,6,5,2]=>[.,[[.,.],[[.,[[.,.],.]],.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,1,6,7]=>[7,6,1,4,2,3,5]=>[1,2,7,4,6,5,3]=>[.,[.,[[[.,.],[[.,.],.]],.]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,1,6,7]=>[7,6,1,5,2,3,4]=>[1,2,7,3,6,5,4]=>[.,[.,[[.,[[[.,.],.],.]],.]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,1,6,7]=>[7,6,1,5,2,4,3]=>[1,2,7,3,6,4,5]=>[.,[.,[[.,[[.,[.,.]],.]],.]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,1,5,6]=>[6,5,1,4,3,2,7]=>[2,3,7,4,5,6,1]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,1,5,7]=>[7,5,1,4,3,2,6]=>[1,3,7,4,5,6,2]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,1,6,7]=>[7,6,1,4,3,2,5]=>[1,2,7,4,5,6,3]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,1,6,7]=>[7,6,1,5,3,2,4]=>[1,2,7,3,5,6,4]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,1,6,7]=>[7,6,1,5,4,2,3]=>[1,2,7,3,4,6,5]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7]=>[7,6,1,5,4,3,2]=>[1,2,7,3,4,5,6]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7]=>[4,5,6,7,3,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6]=>[4,5,6,7,3,1,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7]=>[4,5,6,7,2,3,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6]=>[4,5,6,7,1,3,2]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5]=>[4,5,6,7,1,2,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,2,3,5]=>[5,3,2,1,4,6,7]=>[3,5,6,7,4,2,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6]=>[3,5,6,7,4,1,2]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,2,3,6]=>[6,3,2,1,4,5,7]=>[2,5,6,7,4,3,1]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6]=>[1,5,6,7,4,3,2]=>[.,[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5]=>[1,5,6,7,4,2,3]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7]=>[2,5,6,7,3,4,1]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,5,1,2,3,7]=>[7,3,2,1,5,4,6]=>[1,5,6,7,3,4,2]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,6,1,2,3,7]=>[7,3,2,1,6,4,5]=>[1,5,6,7,2,4,3]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>[7,3,2,1,6,5,4]=>[1,5,6,7,2,3,4]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,2,4,5]=>[5,4,2,1,3,6,7]=>[3,4,6,7,5,2,1]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,7,3,1,2,4,5]=>[5,4,2,1,3,7,6]=>[3,4,6,7,5,1,2]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7]=>[2,4,6,7,5,3,1]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,2,4,7]=>[7,4,2,1,3,5,6]=>[1,4,6,7,5,3,2]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5]=>[1,4,6,7,5,2,3]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,2,5,6]=>[6,5,2,1,3,4,7]=>[2,3,6,7,5,4,1]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,2,5,7]=>[7,5,2,1,3,4,6]=>[1,3,6,7,5,4,2]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,2,6,7]=>[7,6,2,1,3,4,5]=>[1,2,6,7,5,4,3]=>[.,[.,[[[[.,.],.],.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,1,2,6,7]=>[7,6,2,1,3,5,4]=>[1,2,6,7,5,3,4]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,4,1,2,5,6]=>[6,5,2,1,4,3,7]=>[2,3,6,7,4,5,1]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,4,1,2,5,7]=>[7,5,2,1,4,3,6]=>[1,3,6,7,4,5,2]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,4,1,2,6,7]=>[7,6,2,1,4,3,5]=>[1,2,6,7,4,5,3]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,5,1,2,6,7]=>[7,6,2,1,5,3,4]=>[1,2,6,7,3,5,4]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,4,5,1,2,6,7]=>[7,6,2,1,5,4,3]=>[1,2,6,7,3,4,5]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7]=>[3,4,5,7,6,2,1]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,7,2,1,3,4,5]=>[5,4,3,1,2,7,6]=>[3,4,5,7,6,1,2]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7]=>[2,4,5,7,6,3,1]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,3,4,7]=>[7,4,3,1,2,5,6]=>[1,4,5,7,6,3,2]=>[.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5]=>[1,4,5,7,6,2,3]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,3,5,6]=>[6,5,3,1,2,4,7]=>[2,3,5,7,6,4,1]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6]=>[1,3,5,7,6,4,2]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,3,6,7]=>[7,6,3,1,2,4,5]=>[1,2,5,7,6,4,3]=>[.,[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,2,1,3,6,7]=>[7,6,3,1,2,5,4]=>[1,2,5,7,6,3,4]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,4,5,6]=>[6,5,4,1,2,3,7]=>[2,3,4,7,6,5,1]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,4,5,7]=>[7,5,4,1,2,3,6]=>[1,3,4,7,6,5,2]=>[.,[[.,.],[.,[[[.,.],.],.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,4,6,7]=>[7,6,4,1,2,3,5]=>[1,2,4,7,6,5,3]=>[.,[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4]=>[1,2,3,7,6,5,4]=>[.,[.,[.,[[[[.,.],.],.],.]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,4,2,1,5,6,7]=>[7,6,5,1,2,4,3]=>[1,2,3,7,6,4,5]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,3,1,4,5,6]=>[6,5,4,1,3,2,7]=>[2,3,4,7,5,6,1]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,3,1,4,5,7]=>[7,5,4,1,3,2,6]=>[1,3,4,7,5,6,2]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,3,1,4,6,7]=>[7,6,4,1,3,2,5]=>[1,2,4,7,5,6,3]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,3,1,5,6,7]=>[7,6,5,1,3,2,4]=>[1,2,3,7,5,6,4]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,4,1,5,6,7]=>[7,6,5,1,4,2,3]=>[1,2,3,7,4,6,5]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7]=>[7,6,5,1,4,3,2]=>[1,2,3,7,4,5,6]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7]=>[3,4,5,6,7,2,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6]=>[3,4,5,6,7,1,2]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7]=>[2,4,5,6,7,3,1]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6]=>[1,4,5,6,7,3,2]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5]=>[1,4,5,6,7,2,3]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7]=>[2,3,5,6,7,4,1]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6]=>[1,3,5,6,7,4,2]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5]=>[1,2,5,6,7,4,3]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,5,1,2,3,6,7]=>[7,6,3,2,1,5,4]=>[1,2,5,6,7,3,4]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7]=>[2,3,4,6,7,5,1]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,2,4,5,7]=>[7,5,4,2,1,3,6]=>[1,3,4,6,7,5,2]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5]=>[1,2,4,6,7,5,3]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4]=>[1,2,3,6,7,5,4]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>[7,6,5,2,1,4,3]=>[1,2,3,6,7,4,5]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7]=>[2,3,4,5,7,6,1]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,3,4,5,7]=>[7,5,4,3,1,2,6]=>[1,3,4,5,7,6,2]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,3,4,6,7]=>[7,6,4,3,1,2,5]=>[1,2,4,5,7,6,3]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,3,5,6,7]=>[7,6,5,3,1,2,4]=>[1,2,3,5,7,6,4]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3]=>[1,2,3,4,7,6,5]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>[7,6,5,4,1,3,2]=>[1,2,3,4,7,5,6]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,7,1]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6]=>[1,3,4,5,6,7,2]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5]=>[1,2,4,5,6,7,3]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4]=>[1,2,3,5,6,7,4]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3]=>[1,2,3,4,6,7,5]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2]=>[1,2,3,4,5,7,6]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,2,1]=>[1,2,3,4,5,6,8,7]=>[8,7,6,5,4,3,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6,8]=>[8,7,6,5,4,2,3,1]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,3,2,1]=>[1,2,3,4,5,8,6,7]=>[8,7,6,5,4,1,3,2]=>[[[[[[.,[[.,.],.]],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,3,2,1]=>[1,2,3,4,5,8,7,6]=>[8,7,6,5,4,1,2,3]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,3,2,1]=>[1,2,3,4,6,5,7,8]=>[8,7,6,5,3,4,2,1]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,3,2,1]=>[1,2,3,4,6,5,8,7]=>[8,7,6,5,3,4,1,2]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,3,2,1]=>[1,2,3,4,7,5,6,8]=>[8,7,6,5,2,4,3,1]=>[[[[[[.,.],[[.,.],.]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,3,2,1]=>[1,2,3,4,8,5,6,7]=>[8,7,6,5,1,4,3,2]=>[[[[[.,[[[.,.],.],.]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,3,2,1]=>[1,2,3,4,8,5,7,6]=>[8,7,6,5,1,4,2,3]=>[[[[[.,[[.,[.,.]],.]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,3,2,1]=>[1,2,3,4,7,6,5,8]=>[8,7,6,5,2,3,4,1]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,3,2,1]=>[1,2,3,4,8,6,5,7]=>[8,7,6,5,1,3,4,2]=>[[[[[.,[[.,.],[.,.]]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,3,2,1]=>[1,2,3,4,8,7,5,6]=>[8,7,6,5,1,2,4,3]=>[[[[[.,[.,[[.,.],.]]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,2,1]=>[1,2,3,4,8,7,6,5]=>[8,7,6,5,1,2,3,4]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7,8]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,3,2,1]=>[1,2,3,5,4,6,8,7]=>[8,7,6,4,5,3,1,2]=>[[[[[[.,[.,.]],.],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6,8]=>[8,7,6,4,5,2,3,1]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,3,2,1]=>[1,2,3,5,4,8,6,7]=>[8,7,6,4,5,1,3,2]=>[[[[[.,[[.,.],.]],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,3,2,1]=>[1,2,3,5,4,8,7,6]=>[8,7,6,4,5,1,2,3]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,3,2,1]=>[1,2,3,6,4,5,7,8]=>[8,7,6,3,5,4,2,1]=>[[[[[[.,.],.],[[.,.],.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,6,3,2,1]=>[1,2,3,6,4,5,8,7]=>[8,7,6,3,5,4,1,2]=>[[[[[.,[.,.]],[[.,.],.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,3,2,1]=>[1,2,3,7,4,5,6,8]=>[8,7,6,2,5,4,3,1]=>[[[[[.,.],[[[.,.],.],.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,3,2,1]=>[1,2,3,8,4,5,6,7]=>[8,7,6,1,5,4,3,2]=>[[[[.,[[[[.,.],.],.],.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,3,2,1]=>[1,2,3,8,4,5,7,6]=>[8,7,6,1,5,4,2,3]=>[[[[.,[[[.,[.,.]],.],.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,3,2,1]=>[1,2,3,7,4,6,5,8]=>[8,7,6,2,5,3,4,1]=>[[[[[.,.],[[.,[.,.]],.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,3,2,1]=>[1,2,3,8,4,6,5,7]=>[8,7,6,1,5,3,4,2]=>[[[[.,[[[.,.],[.,.]],.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,3,2,1]=>[1,2,3,8,4,7,5,6]=>[8,7,6,1,5,2,4,3]=>[[[[.,[[.,[[.,.],.]],.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,3,2,1]=>[1,2,3,8,4,7,6,5]=>[8,7,6,1,5,2,3,4]=>[[[[.,[[.,[.,[.,.]]],.]],.],.],.]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,3,2,1]=>[1,2,3,6,5,4,7,8]=>[8,7,6,3,4,5,2,1]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,3,2,1]=>[1,2,3,6,5,4,8,7]=>[8,7,6,3,4,5,1,2]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,3,2,1]=>[1,2,3,8,5,4,6,7]=>[8,7,6,1,4,5,3,2]=>[[[[.,[[[.,.],.],[.,.]]],.],.],.]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,3,2,1]=>[1,2,3,8,5,4,7,6]=>[8,7,6,1,4,5,2,3]=>[[[[.,[[.,[.,.]],[.,.]]],.],.],.]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,3,2,1]=>[1,2,3,8,6,4,5,7]=>[8,7,6,1,3,5,4,2]=>[[[[.,[[.,.],[[.,.],.]]],.],.],.]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,3,2,1]=>[1,2,3,8,7,4,5,6]=>[8,7,6,1,2,5,4,3]=>[[[[.,[.,[[[.,.],.],.]]],.],.],.]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,3,2,1]=>[1,2,3,8,7,4,6,5]=>[8,7,6,1,2,5,3,4]=>[[[[.,[.,[[.,[.,.]],.]]],.],.],.]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4,8]=>[8,7,6,2,3,4,5,1]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,3,2,1]=>[1,2,3,8,6,5,4,7]=>[8,7,6,1,3,4,5,2]=>[[[[.,[[.,.],[.,[.,.]]]],.],.],.]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,3,2,1]=>[1,2,3,8,7,5,4,6]=>[8,7,6,1,2,4,5,3]=>[[[[.,[.,[[.,.],[.,.]]]],.],.],.]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,2,1]=>[1,2,3,8,7,6,4,5]=>[8,7,6,1,2,3,5,4]=>[[[[.,[.,[.,[[.,.],.]]]],.],.],.]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,2,1]=>[1,2,3,8,7,6,5,4]=>[8,7,6,1,2,3,4,5]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,4,2,1]=>[1,2,4,3,5,6,7,8]=>[8,7,5,6,4,3,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,4,2,1]=>[1,2,4,3,5,6,8,7]=>[8,7,5,6,4,3,1,2]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,4,2,1]=>[1,2,4,3,5,7,6,8]=>[8,7,5,6,4,2,3,1]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,4,2,1]=>[1,2,4,3,5,8,6,7]=>[8,7,5,6,4,1,3,2]=>[[[[[.,[[.,.],.]],.],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,2,1]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,2,1]=>[1,2,4,3,6,5,8,7]=>[8,7,5,6,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,4,2,1]=>[1,2,4,3,8,5,6,7]=>[8,7,5,6,1,4,3,2]=>[[[[.,[[[.,.],.],.]],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,4,2,1]=>[1,2,4,3,8,5,7,6]=>[8,7,5,6,1,4,2,3]=>[[[[.,[[.,[.,.]],.]],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,4,2,1]=>[1,2,4,3,7,6,5,8]=>[8,7,5,6,2,3,4,1]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,4,2,1]=>[1,2,4,3,8,6,5,7]=>[8,7,5,6,1,3,4,2]=>[[[[.,[[.,.],[.,.]]],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,4,2,1]=>[1,2,4,3,8,7,5,6]=>[8,7,5,6,1,2,4,3]=>[[[[.,[.,[[.,.],.]]],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,2,1]=>[1,2,4,3,8,7,6,5]=>[8,7,5,6,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,5,2,1]=>[1,2,5,3,4,6,7,8]=>[8,7,4,6,5,3,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,5,2,1]=>[1,2,5,3,4,6,8,7]=>[8,7,4,6,5,3,1,2]=>[[[[[.,[.,.]],.],[[.,.],.]],.],.]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,3,5,2,1]=>[1,2,5,3,4,7,6,8]=>[8,7,4,6,5,2,3,1]=>[[[[[.,.],[.,.]],[[.,.],.]],.],.]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,5,2,1]=>[1,2,5,3,4,8,6,7]=>[8,7,4,6,5,1,3,2]=>[[[[.,[[.,.],.]],[[.,.],.]],.],.]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,6,2,1]=>[1,2,6,3,4,5,7,8]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,8,2,1]=>[1,2,8,3,4,5,6,7]=>[8,7,1,6,5,4,3,2]=>[[[.,[[[[[.,.],.],.],.],.]],.],.]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,8,2,1]=>[1,2,8,3,4,7,5,6]=>[8,7,1,6,5,2,4,3]=>[[[.,[[[.,[[.,.],.]],.],.]],.],.]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,8,2,1]=>[1,2,8,3,4,7,6,5]=>[8,7,1,6,5,2,3,4]=>[[[.,[[[.,[.,[.,.]]],.],.]],.],.]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,3,6,2,1]=>[1,2,6,3,5,4,7,8]=>[8,7,3,6,4,5,2,1]=>[[[[[.,.],.],[[.,[.,.]],.]],.],.]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,3,7,2,1]=>[1,2,7,3,5,4,6,8]=>[8,7,2,6,4,5,3,1]=>[[[[.,.],[[[.,.],[.,.]],.]],.],.]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,8,2,1]=>[1,2,8,3,5,4,6,7]=>[8,7,1,6,4,5,3,2]=>[[[.,[[[[.,.],.],[.,.]],.]],.],.]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,8,2,1]=>[1,2,8,3,5,4,7,6]=>[8,7,1,6,4,5,2,3]=>[[[.,[[[.,[.,.]],[.,.]],.]],.],.]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,7,2,1]=>[1,2,7,3,6,4,5,8]=>[8,7,2,6,3,5,4,1]=>[[[[.,.],[[.,[[.,.],.]],.]],.],.]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,3,8,2,1]=>[1,2,8,3,6,4,5,7]=>[8,7,1,6,3,5,4,2]=>[[[.,[[[.,.],[[.,.],.]],.]],.],.]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,8,2,1]=>[1,2,8,3,7,4,5,6]=>[8,7,1,6,2,5,4,3]=>[[[.,[[.,[[[.,.],.],.]],.]],.],.]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,8,2,1]=>[1,2,8,3,7,4,6,5]=>[8,7,1,6,2,5,3,4]=>[[[.,[[.,[[.,[.,.]],.]],.]],.],.]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,3,8,2,1]=>[1,2,8,3,7,5,4,6]=>[8,7,1,6,2,4,5,3]=>[[[.,[[.,[[.,.],[.,.]]],.]],.],.]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,8,2,1]=>[1,2,8,3,7,6,4,5]=>[8,7,1,6,2,3,5,4]=>[[[.,[[.,[.,[[.,.],.]]],.]],.],.]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,8,2,1]=>[1,2,8,3,7,6,5,4]=>[8,7,1,6,2,3,4,5]=>[[[.,[[.,[.,[.,[.,.]]]],.]],.],.]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,5,2,1]=>[1,2,5,4,3,6,7,8]=>[8,7,4,5,6,3,2,1]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,5,2,1]=>[1,2,5,4,3,7,6,8]=>[8,7,4,5,6,2,3,1]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,5,2,1]=>[1,2,5,4,3,8,6,7]=>[8,7,4,5,6,1,3,2]=>[[[[.,[[.,.],.]],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,5,2,1]=>[1,2,5,4,3,8,7,6]=>[8,7,4,5,6,1,2,3]=>[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,6,2,1]=>[1,2,6,4,3,5,7,8]=>[8,7,3,5,6,4,2,1]=>[[[[[.,.],.],[[.,.],[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,4,7,2,1]=>[1,2,7,4,3,5,6,8]=>[8,7,2,5,6,4,3,1]=>[[[[.,.],[[[.,.],.],[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,8,2,1]=>[1,2,8,4,3,5,6,7]=>[8,7,1,5,6,4,3,2]=>[[[.,[[[[.,.],.],.],[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,8,2,1]=>[1,2,8,4,3,7,5,6]=>[8,7,1,5,6,2,4,3]=>[[[.,[[.,[[.,.],.]],[.,.]]],.],.]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,4,8,2,1]=>[1,2,8,4,3,7,6,5]=>[8,7,1,5,6,2,3,4]=>[[[.,[[.,[.,[.,.]]],[.,.]]],.],.]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,6,2,1]=>[1,2,6,5,3,4,7,8]=>[8,7,3,4,6,5,2,1]=>[[[[[.,.],.],[.,[[.,.],.]]],.],.]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,6,2,1]=>[1,2,6,5,3,4,8,7]=>[8,7,3,4,6,5,1,2]=>[[[[.,[.,.]],[.,[[.,.],.]]],.],.]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,5,7,2,1]=>[1,2,7,5,3,4,6,8]=>[8,7,2,4,6,5,3,1]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,5,8,2,1]=>[1,2,8,5,3,4,6,7]=>[8,7,1,4,6,5,3,2]=>[[[.,[[[.,.],.],[[.,.],.]]],.],.]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,5,8,2,1]=>[1,2,8,5,3,4,7,6]=>[8,7,1,4,6,5,2,3]=>[[[.,[[.,[.,.]],[[.,.],.]]],.],.]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,7,2,1]=>[1,2,7,6,3,4,5,8]=>[8,7,2,3,6,5,4,1]=>[[[[.,.],[.,[[[.,.],.],.]]],.],.]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,8,2,1]=>[1,2,8,6,3,4,5,7]=>[8,7,1,3,6,5,4,2]=>[[[.,[[.,.],[[[.,.],.],.]]],.],.]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,2,1]=>[1,2,8,7,3,4,5,6]=>[8,7,1,2,6,5,4,3]=>[[[.,[.,[[[[.,.],.],.],.]]],.],.]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,7,8,2,1]=>[1,2,8,7,3,4,6,5]=>[8,7,1,2,6,5,3,4]=>[[[.,[.,[[[.,[.,.]],.],.]]],.],.]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,8,2,1]=>[1,2,8,7,3,6,5,4]=>[8,7,1,2,6,3,4,5]=>[[[.,[.,[[.,[.,[.,.]]],.]]],.],.]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,6,2,1]=>[1,2,6,5,4,3,7,8]=>[8,7,3,4,5,6,2,1]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,6,2,1]=>[1,2,6,5,4,3,8,7]=>[8,7,3,4,5,6,1,2]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,5,7,2,1]=>[1,2,7,5,4,3,6,8]=>[8,7,2,4,5,6,3,1]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,8,2,1]=>[1,2,8,5,4,3,6,7]=>[8,7,1,4,5,6,3,2]=>[[[.,[[[.,.],.],[.,[.,.]]]],.],.]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,8,2,1]=>[1,2,8,7,5,3,4,6]=>[8,7,1,2,4,6,5,3]=>[[[.,[.,[[.,.],[[.,.],.]]]],.],.]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,8,2,1]=>[1,2,8,7,6,3,4,5]=>[8,7,1,2,3,6,5,4]=>[[[.,[.,[.,[[[.,.],.],.]]]],.],.]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,8,2,1]=>[1,2,8,7,6,3,5,4]=>[8,7,1,2,3,6,4,5]=>[[[.,[.,[.,[[.,[.,.]],.]]]],.],.]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,7,2,1]=>[1,2,7,6,5,4,3,8]=>[8,7,2,3,4,5,6,1]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,8,2,1]=>[1,2,8,6,5,4,3,7]=>[8,7,1,3,4,5,6,2]=>[[[.,[[.,.],[.,[.,[.,.]]]]],.],.]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,8,2,1]=>[1,2,8,7,5,4,3,6]=>[8,7,1,2,4,5,6,3]=>[[[.,[.,[[.,.],[.,[.,.]]]]],.],.]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,8,2,1]=>[1,2,8,7,6,5,3,4]=>[8,7,1,2,3,4,6,5]=>[[[.,[.,[.,[.,[[.,.],.]]]]],.],.]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,2,1]=>[1,2,8,7,6,5,4,3]=>[8,7,1,2,3,4,5,6]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7,8]=>[8,6,7,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,2,3,1]=>[1,3,2,4,5,6,8,7]=>[8,6,7,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,2,3,1]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,3,1]=>[1,3,2,4,5,8,6,7]=>[8,6,7,5,4,1,3,2]=>[[[[[.,[[.,.],.]],.],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,2,3,1]=>[1,3,2,4,6,5,7,8]=>[8,6,7,5,3,4,2,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,2,3,1]=>[1,3,2,4,7,5,6,8]=>[8,6,7,5,2,4,3,1]=>[[[[[.,.],[[.,.],.]],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,2,3,1]=>[1,3,2,4,8,5,6,7]=>[8,6,7,5,1,4,3,2]=>[[[[.,[[[.,.],.],.]],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,2,3,1]=>[1,3,2,4,8,5,7,6]=>[8,6,7,5,1,4,2,3]=>[[[[.,[[.,[.,.]],.]],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,2,3,1]=>[1,3,2,4,7,6,5,8]=>[8,6,7,5,2,3,4,1]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,2,3,1]=>[1,3,2,4,8,7,6,5]=>[8,6,7,5,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,2,3,1]=>[1,3,2,5,4,6,7,8]=>[8,6,7,4,5,3,2,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,2,3,1]=>[1,3,2,5,4,6,8,7]=>[8,6,7,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,8]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,2,3,1]=>[1,3,2,5,4,8,6,7]=>[8,6,7,4,5,1,3,2]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,2,3,1]=>[1,3,2,5,4,8,7,6]=>[8,6,7,4,5,1,2,3]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,2,3,1]=>[1,3,2,6,4,5,7,8]=>[8,6,7,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,2,3,1]=>[1,3,2,7,4,5,6,8]=>[8,6,7,2,5,4,3,1]=>[[[[.,.],[[[.,.],.],.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,2,3,1]=>[1,3,2,8,4,5,6,7]=>[8,6,7,1,5,4,3,2]=>[[[.,[[[[.,.],.],.],.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,2,3,1]=>[1,3,2,7,4,6,5,8]=>[8,6,7,2,5,3,4,1]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,2,3,1]=>[1,3,2,8,4,6,5,7]=>[8,6,7,1,5,3,4,2]=>[[[.,[[[.,.],[.,.]],.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,2,3,1]=>[1,3,2,8,4,7,5,6]=>[8,6,7,1,5,2,4,3]=>[[[.,[[.,[[.,.],.]],.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,2,3,1]=>[1,3,2,8,4,7,6,5]=>[8,6,7,1,5,2,3,4]=>[[[.,[[.,[.,[.,.]]],.]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,2,3,1]=>[1,3,2,6,5,4,7,8]=>[8,6,7,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,2,3,1]=>[1,3,2,6,5,4,8,7]=>[8,6,7,3,4,5,1,2]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,2,3,1]=>[1,3,2,8,5,4,6,7]=>[8,6,7,1,4,5,3,2]=>[[[.,[[[.,.],.],[.,.]]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,2,3,1]=>[1,3,2,8,5,4,7,6]=>[8,6,7,1,4,5,2,3]=>[[[.,[[.,[.,.]],[.,.]]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,7,2,3,1]=>[1,3,2,7,6,4,5,8]=>[8,6,7,2,3,5,4,1]=>[[[[.,.],[.,[[.,.],.]]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,2,3,1]=>[1,3,2,8,7,4,6,5]=>[8,6,7,1,2,5,3,4]=>[[[.,[.,[[.,[.,.]],.]]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,2,3,1]=>[1,3,2,7,6,5,4,8]=>[8,6,7,2,3,4,5,1]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,2,3,1]=>[1,3,2,8,6,5,4,7]=>[8,6,7,1,3,4,5,2]=>[[[.,[[.,.],[.,[.,.]]]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,2,3,1]=>[1,3,2,8,7,6,5,4]=>[8,6,7,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,4,1]=>[1,4,2,3,5,6,7,8]=>[8,5,7,6,4,3,2,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,2,4,1]=>[1,4,2,3,5,6,8,7]=>[8,5,7,6,4,3,1,2]=>[[[[[.,[.,.]],.],.],[[.,.],.]],.]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,2,4,1]=>[1,4,2,3,5,7,6,8]=>[8,5,7,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,2,4,1]=>[1,4,2,3,5,8,6,7]=>[8,5,7,6,4,1,3,2]=>[[[[.,[[.,.],.]],.],[[.,.],.]],.]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,2,4,1]=>[1,4,2,3,5,8,7,6]=>[8,5,7,6,4,1,2,3]=>[[[[.,[.,[.,.]]],.],[[.,.],.]],.]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,2,4,1]=>[1,4,2,3,6,5,8,7]=>[8,5,7,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[[.,.],.]],.]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,4,1]=>[1,4,2,3,7,5,6,8]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,4,1]=>[1,4,2,3,8,5,6,7]=>[8,5,7,6,1,4,3,2]=>[[[.,[[[.,.],.],.]],[[.,.],.]],.]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,2,4,1]=>[1,4,2,3,8,5,7,6]=>[8,5,7,6,1,4,2,3]=>[[[.,[[.,[.,.]],.]],[[.,.],.]],.]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,2,4,1]=>[1,4,2,3,7,6,5,8]=>[8,5,7,6,2,3,4,1]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,2,4,1]=>[1,4,2,3,8,7,5,6]=>[8,5,7,6,1,2,4,3]=>[[[.,[.,[[.,.],.]]],[[.,.],.]],.]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,2,4,1]=>[1,4,2,3,8,7,6,5]=>[8,5,7,6,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[[.,.],.]],.]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,2,5,1]=>[1,5,2,3,4,6,7,8]=>[8,4,7,6,5,3,2,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,2,5,1]=>[1,5,2,3,4,6,8,7]=>[8,4,7,6,5,3,1,2]=>[[[[.,[.,.]],.],[[[.,.],.],.]],.]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,3,2,5,1]=>[1,5,2,3,4,7,6,8]=>[8,4,7,6,5,2,3,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,2,5,1]=>[1,5,2,3,4,8,6,7]=>[8,4,7,6,5,1,3,2]=>[[[.,[[.,.],.]],[[[.,.],.],.]],.]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,2,5,1]=>[1,5,2,3,4,8,7,6]=>[8,4,7,6,5,1,2,3]=>[[[.,[.,[.,.]]],[[[.,.],.],.]],.]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,2,6,1]=>[1,6,2,3,4,5,7,8]=>[8,3,7,6,5,4,2,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6,8]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,8,1]=>[1,8,2,3,4,5,6,7]=>[8,1,7,6,5,4,3,2]=>[[.,[[[[[[.,.],.],.],.],.],.]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,2,8,1]=>[1,8,2,3,4,5,7,6]=>[8,1,7,6,5,4,2,3]=>[[.,[[[[[.,[.,.]],.],.],.],.]],.]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,3,2,7,1]=>[1,7,2,3,4,6,5,8]=>[8,2,7,6,5,3,4,1]=>[[[.,.],[[[[.,[.,.]],.],.],.]],.]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,2,8,1]=>[1,8,2,3,4,6,5,7]=>[8,1,7,6,5,3,4,2]=>[[.,[[[[[.,.],[.,.]],.],.],.]],.]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,2,8,1]=>[1,8,2,3,4,7,5,6]=>[8,1,7,6,5,2,4,3]=>[[.,[[[[.,[[.,.],.]],.],.],.]],.]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,2,8,1]=>[1,8,2,3,4,7,6,5]=>[8,1,7,6,5,2,3,4]=>[[.,[[[[.,[.,[.,.]]],.],.],.]],.]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,3,2,6,1]=>[1,6,2,3,5,4,8,7]=>[8,3,7,6,4,5,1,2]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,3,2,7,1]=>[1,7,2,3,5,4,6,8]=>[8,2,7,6,4,5,3,1]=>[[[.,.],[[[[.,.],[.,.]],.],.]],.]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,2,8,1]=>[1,8,2,3,5,4,6,7]=>[8,1,7,6,4,5,3,2]=>[[.,[[[[[.,.],.],[.,.]],.],.]],.]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,2,8,1]=>[1,8,2,3,5,4,7,6]=>[8,1,7,6,4,5,2,3]=>[[.,[[[[.,[.,.]],[.,.]],.],.]],.]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,2,7,1]=>[1,7,2,3,6,4,5,8]=>[8,2,7,6,3,5,4,1]=>[[[.,.],[[[.,[[.,.],.]],.],.]],.]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,3,2,8,1]=>[1,8,2,3,6,4,5,7]=>[8,1,7,6,3,5,4,2]=>[[.,[[[[.,.],[[.,.],.]],.],.]],.]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,2,8,1]=>[1,8,2,3,7,4,5,6]=>[8,1,7,6,2,5,4,3]=>[[.,[[[.,[[[.,.],.],.]],.],.]],.]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,3,2,7,1]=>[1,7,2,3,6,5,4,8]=>[8,2,7,6,3,4,5,1]=>[[[.,.],[[[.,[.,[.,.]]],.],.]],.]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,2,8,1]=>[1,8,2,3,6,5,4,7]=>[8,1,7,6,3,4,5,2]=>[[.,[[[[.,.],[.,[.,.]]],.],.]],.]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,3,2,8,1]=>[1,8,2,3,7,5,4,6]=>[8,1,7,6,2,4,5,3]=>[[.,[[[.,[[.,.],[.,.]]],.],.]],.]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,2,8,1]=>[1,8,2,3,7,6,5,4]=>[8,1,7,6,2,3,4,5]=>[[.,[[[.,[.,[.,[.,.]]]],.],.]],.]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,2,5,1]=>[1,5,2,4,3,6,7,8]=>[8,4,7,5,6,3,2,1]=>[[[[[.,.],.],.],[[.,[.,.]],.]],.]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,2,5,1]=>[1,5,2,4,3,7,6,8]=>[8,4,7,5,6,2,3,1]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],.]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,2,5,1]=>[1,5,2,4,3,8,6,7]=>[8,4,7,5,6,1,3,2]=>[[[.,[[.,.],.]],[[.,[.,.]],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,2,6,1]=>[1,6,2,4,3,5,7,8]=>[8,3,7,5,6,4,2,1]=>[[[[.,.],.],[[[.,.],[.,.]],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,4,2,7,1]=>[1,7,2,4,3,5,6,8]=>[8,2,7,5,6,4,3,1]=>[[[.,.],[[[[.,.],.],[.,.]],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,2,8,1]=>[1,8,2,4,3,5,6,7]=>[8,1,7,5,6,4,3,2]=>[[.,[[[[[.,.],.],.],[.,.]],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[6,7,5,3,4,2,8,1]=>[1,8,2,4,3,5,7,6]=>[8,1,7,5,6,4,2,3]=>[[.,[[[[.,[.,.]],.],[.,.]],.]],.]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,2,7,1]=>[1,7,2,4,3,6,5,8]=>[8,2,7,5,6,3,4,1]=>[[[.,.],[[[.,[.,.]],[.,.]],.]],.]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,2,8,1]=>[1,8,2,4,3,6,5,7]=>[8,1,7,5,6,3,4,2]=>[[.,[[[[.,.],[.,.]],[.,.]],.]],.]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,2,8,1]=>[1,8,2,4,3,7,5,6]=>[8,1,7,5,6,2,4,3]=>[[.,[[[.,[[.,.],.]],[.,.]],.]],.]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,4,2,8,1]=>[1,8,2,4,3,7,6,5]=>[8,1,7,5,6,2,3,4]=>[[.,[[[.,[.,[.,.]]],[.,.]],.]],.]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,2,6,1]=>[1,6,2,5,3,4,7,8]=>[8,3,7,4,6,5,2,1]=>[[[[.,.],.],[[.,[[.,.],.]],.]],.]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,2,6,1]=>[1,6,2,5,3,4,8,7]=>[8,3,7,4,6,5,1,2]=>[[[.,[.,.]],[[.,[[.,.],.]],.]],.]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,5,2,7,1]=>[1,7,2,5,3,4,6,8]=>[8,2,7,4,6,5,3,1]=>[[[.,.],[[[.,.],[[.,.],.]],.]],.]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,5,2,8,1]=>[1,8,2,5,3,4,6,7]=>[8,1,7,4,6,5,3,2]=>[[.,[[[[.,.],.],[[.,.],.]],.]],.]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,2,7,1]=>[1,7,2,6,3,4,5,8]=>[8,2,7,3,6,5,4,1]=>[[[.,.],[[.,[[[.,.],.],.]],.]],.]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,2,8,1]=>[1,8,2,6,3,4,5,7]=>[8,1,7,3,6,5,4,2]=>[[.,[[[.,.],[[[.,.],.],.]],.]],.]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,2,8,1]=>[1,8,2,7,3,4,5,6]=>[8,1,7,2,6,5,4,3]=>[[.,[[.,[[[[.,.],.],.],.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,2,7,1]=>[1,7,2,6,3,5,4,8]=>[8,2,7,3,6,4,5,1]=>[[[.,.],[[.,[[.,[.,.]],.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,6,2,8,1]=>[1,8,2,6,3,5,4,7]=>[8,1,7,3,6,4,5,2]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,7,2,8,1]=>[1,8,2,7,3,5,4,6]=>[8,1,7,2,6,4,5,3]=>[[.,[[.,[[[.,.],[.,.]],.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,2,8,1]=>[1,8,2,7,3,6,4,5]=>[8,1,7,2,6,3,5,4]=>[[.,[[.,[[.,[[.,.],.]],.]],.]],.]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,2,8,1]=>[1,8,2,7,3,6,5,4]=>[8,1,7,2,6,3,4,5]=>[[.,[[.,[[.,[.,[.,.]]],.]],.]],.]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,2,6,1]=>[1,6,2,5,4,3,7,8]=>[8,3,7,4,5,6,2,1]=>[[[[.,.],.],[[.,[.,[.,.]]],.]],.]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,2,6,1]=>[1,6,2,5,4,3,8,7]=>[8,3,7,4,5,6,1,2]=>[[[.,[.,.]],[[.,[.,[.,.]]],.]],.]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,5,2,7,1]=>[1,7,2,5,4,3,6,8]=>[8,2,7,4,5,6,3,1]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],.]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,5,2,8,1]=>[1,8,2,5,4,3,7,6]=>[8,1,7,4,5,6,2,3]=>[[.,[[[.,[.,.]],[.,[.,.]]],.]],.]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,2,8,1]=>[1,8,2,6,4,3,5,7]=>[8,1,7,3,5,6,4,2]=>[[.,[[[.,.],[[.,.],[.,.]]],.]],.]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,7,2,8,1]=>[1,8,2,7,4,3,5,6]=>[8,1,7,2,5,6,4,3]=>[[.,[[.,[[[.,.],.],[.,.]]],.]],.]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,2,8,1]=>[1,8,2,7,4,3,6,5]=>[8,1,7,2,5,6,3,4]=>[[.,[[.,[[.,[.,.]],[.,.]]],.]],.]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,2,7,1]=>[1,7,2,6,5,3,4,8]=>[8,2,7,3,4,6,5,1]=>[[[.,.],[[.,[.,[[.,.],.]]],.]],.]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,2,8,1]=>[1,8,2,7,5,3,4,6]=>[8,1,7,2,4,6,5,3]=>[[.,[[.,[[.,.],[[.,.],.]]],.]],.]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,2,8,1]=>[1,8,2,7,6,3,4,5]=>[8,1,7,2,3,6,5,4]=>[[.,[[.,[.,[[[.,.],.],.]]],.]],.]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,2,8,1]=>[1,8,2,7,6,3,5,4]=>[8,1,7,2,3,6,4,5]=>[[.,[[.,[.,[[.,[.,.]],.]]],.]],.]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,2,7,1]=>[1,7,2,6,5,4,3,8]=>[8,2,7,3,4,5,6,1]=>[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,2,8,1]=>[1,8,2,6,5,4,3,7]=>[8,1,7,3,4,5,6,2]=>[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,2,8,1]=>[1,8,2,7,5,4,3,6]=>[8,1,7,2,4,5,6,3]=>[[.,[[.,[[.,.],[.,[.,.]]]],.]],.]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,7,2,8,1]=>[1,8,2,7,6,4,3,5]=>[8,1,7,2,3,5,6,4]=>[[.,[[.,[.,[[.,.],[.,.]]]],.]],.]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,2,8,1]=>[1,8,2,7,6,5,4,3]=>[8,1,7,2,3,4,5,6]=>[[.,[[.,[.,[.,[.,[.,.]]]]],.]],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,3,4,1]=>[1,4,3,2,5,6,7,8]=>[8,5,6,7,4,3,2,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,2,3,4,1]=>[1,4,3,2,5,7,6,8]=>[8,5,6,7,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,3,4,1]=>[1,4,3,2,5,8,6,7]=>[8,5,6,7,4,1,3,2]=>[[[[.,[[.,.],.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,3,4,1]=>[1,4,3,2,5,8,7,6]=>[8,5,6,7,4,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,3,4,1]=>[1,4,3,2,6,5,7,8]=>[8,5,6,7,3,4,2,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,3,4,1]=>[1,4,3,2,6,5,8,7]=>[8,5,6,7,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,3,4,1]=>[1,4,3,2,7,5,6,8]=>[8,5,6,7,2,4,3,1]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,3,4,1]=>[1,4,3,2,8,5,6,7]=>[8,5,6,7,1,4,3,2]=>[[[.,[[[.,.],.],.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,3,4,1]=>[1,4,3,2,8,5,7,6]=>[8,5,6,7,1,4,2,3]=>[[[.,[[.,[.,.]],.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5,8]=>[8,5,6,7,2,3,4,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,3,4,1]=>[1,4,3,2,8,7,6,5]=>[8,5,6,7,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,3,5,1]=>[1,5,3,2,4,6,7,8]=>[8,4,6,7,5,3,2,1]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,2,3,5,1]=>[1,5,3,2,4,6,8,7]=>[8,4,6,7,5,3,1,2]=>[[[[.,[.,.]],.],[[.,.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,2,3,5,1]=>[1,5,3,2,4,8,6,7]=>[8,4,6,7,5,1,3,2]=>[[[.,[[.,.],.]],[[.,.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,3,5,1]=>[1,5,3,2,4,8,7,6]=>[8,4,6,7,5,1,2,3]=>[[[.,[.,[.,.]]],[[.,.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,3,7,1]=>[1,7,3,2,4,5,6,8]=>[8,2,6,7,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,3,8,1]=>[1,8,3,2,4,5,6,7]=>[8,1,6,7,5,4,3,2]=>[[.,[[[[[.,.],.],.],.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,2,3,8,1]=>[1,8,3,2,4,5,7,6]=>[8,1,6,7,5,4,2,3]=>[[.,[[[[.,[.,.]],.],.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,2,3,8,1]=>[1,8,3,2,4,6,5,7]=>[8,1,6,7,5,3,4,2]=>[[.,[[[[.,.],[.,.]],.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,2,3,8,1]=>[1,8,3,2,4,7,5,6]=>[8,1,6,7,5,2,4,3]=>[[.,[[[.,[[.,.],.]],.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,2,3,8,1]=>[1,8,3,2,4,7,6,5]=>[8,1,6,7,5,2,3,4]=>[[.,[[[.,[.,[.,.]]],.],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,2,3,8,1]=>[1,8,3,2,5,4,6,7]=>[8,1,6,7,4,5,3,2]=>[[.,[[[[.,.],.],[.,.]],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,2,3,8,1]=>[1,8,3,2,5,4,7,6]=>[8,1,6,7,4,5,2,3]=>[[.,[[[.,[.,.]],[.,.]],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,2,3,8,1]=>[1,8,3,2,6,4,5,7]=>[8,1,6,7,3,5,4,2]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,2,3,8,1]=>[1,8,3,2,7,4,5,6]=>[8,1,6,7,2,5,4,3]=>[[.,[[.,[[[.,.],.],.]],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,2,3,8,1]=>[1,8,3,2,7,4,6,5]=>[8,1,6,7,2,5,3,4]=>[[.,[[.,[[.,[.,.]],.]],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,2,3,8,1]=>[1,8,3,2,7,5,4,6]=>[8,1,6,7,2,4,5,3]=>[[.,[[.,[[.,.],[.,.]]],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,2,3,8,1]=>[1,8,3,2,7,6,4,5]=>[8,1,6,7,2,3,5,4]=>[[.,[[.,[.,[[.,.],.]]],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,3,8,1]=>[1,8,3,2,7,6,5,4]=>[8,1,6,7,2,3,4,5]=>[[.,[[.,[.,[.,[.,.]]]],[.,.]]],.]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,4,5,1]=>[1,5,4,2,3,6,7,8]=>[8,4,5,7,6,3,2,1]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,2,4,5,1]=>[1,5,4,2,3,7,6,8]=>[8,4,5,7,6,2,3,1]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,2,4,5,1]=>[1,5,4,2,3,8,6,7]=>[8,4,5,7,6,1,3,2]=>[[[.,[[.,.],.]],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,4,6,1]=>[1,6,4,2,3,5,7,8]=>[8,3,5,7,6,4,2,1]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,2,4,7,1]=>[1,7,4,2,3,5,6,8]=>[8,2,5,7,6,4,3,1]=>[[[.,.],[[[.,.],.],[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,2,4,8,1]=>[1,8,4,2,3,7,5,6]=>[8,1,5,7,6,2,4,3]=>[[.,[[.,[[.,.],.]],[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,2,4,8,1]=>[1,8,4,2,3,7,6,5]=>[8,1,5,7,6,2,3,4]=>[[.,[[.,[.,[.,.]]],[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,5,6,1]=>[1,6,5,2,3,4,7,8]=>[8,3,4,7,6,5,2,1]=>[[[[.,.],.],[.,[[[.,.],.],.]]],.]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,2,5,7,1]=>[1,7,5,2,3,4,6,8]=>[8,2,4,7,6,5,3,1]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,2,5,8,1]=>[1,8,5,2,3,4,6,7]=>[8,1,4,7,6,5,3,2]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,5,8,1]=>[1,8,5,2,3,4,7,6]=>[8,1,4,7,6,5,2,3]=>[[.,[[.,[.,.]],[[[.,.],.],.]]],.]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,2,6,8,1]=>[1,8,6,2,3,4,5,7]=>[8,1,3,7,6,5,4,2]=>[[.,[[.,.],[[[[.,.],.],.],.]]],.]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,7,8,1]=>[1,8,7,2,3,4,5,6]=>[8,1,2,7,6,5,4,3]=>[[.,[.,[[[[[.,.],.],.],.],.]]],.]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,2,6,7,1]=>[1,7,6,2,3,5,4,8]=>[8,2,3,7,6,4,5,1]=>[[[.,.],[.,[[[.,[.,.]],.],.]]],.]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,2,6,8,1]=>[1,8,6,2,3,5,4,7]=>[8,1,3,7,6,4,5,2]=>[[.,[[.,.],[[[.,[.,.]],.],.]]],.]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,2,7,8,1]=>[1,8,7,2,3,5,4,6]=>[8,1,2,7,6,4,5,3]=>[[.,[.,[[[[.,.],[.,.]],.],.]]],.]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,7,8,1]=>[1,8,7,2,3,6,4,5]=>[8,1,2,7,6,3,5,4]=>[[.,[.,[[[.,[[.,.],.]],.],.]]],.]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,2,7,8,1]=>[1,8,7,2,3,6,5,4]=>[8,1,2,7,6,3,4,5]=>[[.,[.,[[[.,[.,[.,.]]],.],.]]],.]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,2,5,7,1]=>[1,7,5,2,4,3,6,8]=>[8,2,4,7,5,6,3,1]=>[[[.,.],[[.,.],[[.,[.,.]],.]]],.]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,2,6,7,1]=>[1,7,6,2,4,3,5,8]=>[8,2,3,7,5,6,4,1]=>[[[.,.],[.,[[[.,.],[.,.]],.]]],.]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,2,6,8,1]=>[1,8,6,2,4,3,5,7]=>[8,1,3,7,5,6,4,2]=>[[.,[[.,.],[[[.,.],[.,.]],.]]],.]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,2,7,8,1]=>[1,8,7,2,4,3,6,5]=>[8,1,2,7,5,6,3,4]=>[[.,[.,[[[.,[.,.]],[.,.]],.]]],.]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,2,6,8,1]=>[1,8,6,2,5,3,4,7]=>[8,1,3,7,4,6,5,2]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],.]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,2,7,8,1]=>[1,8,7,2,5,3,4,6]=>[8,1,2,7,4,6,5,3]=>[[.,[.,[[[.,.],[[.,.],.]],.]]],.]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,7,8,1]=>[1,8,7,2,6,3,4,5]=>[8,1,2,7,3,6,5,4]=>[[.,[.,[[.,[[[.,.],.],.]],.]]],.]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,2,7,8,1]=>[1,8,7,2,6,3,5,4]=>[8,1,2,7,3,6,4,5]=>[[.,[.,[[.,[[.,[.,.]],.]],.]]],.]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,2,6,7,1]=>[1,7,6,2,5,4,3,8]=>[8,2,3,7,4,5,6,1]=>[[[.,.],[.,[[.,[.,[.,.]]],.]]],.]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,2,6,8,1]=>[1,8,6,2,5,4,3,7]=>[8,1,3,7,4,5,6,2]=>[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,2,7,8,1]=>[1,8,7,2,5,4,3,6]=>[8,1,2,7,4,5,6,3]=>[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,2,7,8,1]=>[1,8,7,2,6,4,3,5]=>[8,1,2,7,3,5,6,4]=>[[.,[.,[[.,[[.,.],[.,.]]],.]]],.]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,2,7,8,1]=>[1,8,7,2,6,5,3,4]=>[8,1,2,7,3,4,6,5]=>[[.,[.,[[.,[.,[[.,.],.]]],.]]],.]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,7,8,1]=>[1,8,7,2,6,5,4,3]=>[8,1,2,7,3,4,5,6]=>[[.,[.,[[.,[.,[.,[.,.]]]],.]]],.]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,4,5,1]=>[1,5,4,3,2,6,7,8]=>[8,4,5,6,7,3,2,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,3,4,5,1]=>[1,5,4,3,2,7,6,8]=>[8,4,5,6,7,2,3,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,4,5,1]=>[1,5,4,3,2,8,7,6]=>[8,4,5,6,7,1,2,3]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,2,3,4,6,1]=>[1,6,4,3,2,5,8,7]=>[8,3,5,6,7,4,1,2]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,3,4,7,1]=>[1,7,4,3,2,5,6,8]=>[8,2,5,6,7,4,3,1]=>[[[.,.],[[[.,.],.],[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,4,8,1]=>[1,8,4,3,2,5,6,7]=>[8,1,5,6,7,4,3,2]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,2,3,4,8,1]=>[1,8,4,3,2,5,7,6]=>[8,1,5,6,7,4,2,3]=>[[.,[[[.,[.,.]],.],[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,2,3,4,8,1]=>[1,8,4,3,2,6,5,7]=>[8,1,5,6,7,3,4,2]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,2,3,4,8,1]=>[1,8,4,3,2,7,5,6]=>[8,1,5,6,7,2,4,3]=>[[.,[[.,[[.,.],.]],[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,3,4,8,1]=>[1,8,4,3,2,7,6,5]=>[8,1,5,6,7,2,3,4]=>[[.,[[.,[.,[.,.]]],[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,3,5,6,1]=>[1,6,5,3,2,4,8,7]=>[8,3,4,6,7,5,1,2]=>[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,5,7,1]=>[1,7,5,3,2,4,6,8]=>[8,2,4,6,7,5,3,1]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[6,7,4,2,3,5,8,1]=>[1,8,5,3,2,4,7,6]=>[8,1,4,6,7,5,2,3]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[7,5,4,2,3,6,8,1]=>[1,8,6,3,2,4,5,7]=>[8,1,3,6,7,5,4,2]=>[[.,[[.,.],[[[.,.],.],[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,2,3,7,8,1]=>[1,8,7,3,2,4,5,6]=>[8,1,2,6,7,5,4,3]=>[[.,[.,[[[[.,.],.],.],[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[5,6,4,2,3,7,8,1]=>[1,8,7,3,2,4,6,5]=>[8,1,2,6,7,5,3,4]=>[[.,[.,[[[.,[.,.]],.],[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[8,4,5,2,3,6,7,1]=>[1,7,6,3,2,5,4,8]=>[8,2,3,6,7,4,5,1]=>[[[.,.],[.,[[.,[.,.]],[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,2,3,6,8,1]=>[1,8,6,3,2,5,4,7]=>[8,1,3,6,7,4,5,2]=>[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[6,4,5,2,3,7,8,1]=>[1,8,7,3,2,5,4,6]=>[8,1,2,6,7,4,5,3]=>[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,3,7,8,1]=>[1,8,7,3,2,6,4,5]=>[8,1,2,6,7,3,5,4]=>[[.,[.,[[.,[[.,.],.]],[.,.]]]],.]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[8,7,3,2,4,5,6,1]=>[1,6,5,4,2,3,7,8]=>[8,3,4,5,7,6,2,1]=>[[[[.,.],.],[.,[.,[[.,.],.]]]],.]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,4,5,6,1]=>[1,6,5,4,2,3,8,7]=>[8,3,4,5,7,6,1,2]=>[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,4,5,7,1]=>[1,7,5,4,2,3,6,8]=>[8,2,4,5,7,6,3,1]=>[[[.,.],[[.,.],[.,[[.,.],.]]]],.]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,4,5,8,1]=>[1,8,5,4,2,3,6,7]=>[8,1,4,5,7,6,3,2]=>[[.,[[[.,.],.],[.,[[.,.],.]]]],.]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,4,5,8,1]=>[1,8,5,4,2,3,7,6]=>[8,1,4,5,7,6,2,3]=>[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,2,4,6,7,1]=>[1,7,6,4,2,3,5,8]=>[8,2,3,5,7,6,4,1]=>[[[.,.],[.,[[.,.],[[.,.],.]]]],.]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,4,6,8,1]=>[1,8,6,4,2,3,5,7]=>[8,1,3,5,7,6,4,2]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,5,7,8,1]=>[1,8,7,5,2,3,4,6]=>[8,1,2,4,7,6,5,3]=>[[.,[.,[[.,.],[[[.,.],.],.]]]],.]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,7,8,1]=>[1,8,7,6,2,3,4,5]=>[8,1,2,3,7,6,5,4]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],.]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[6,3,4,2,5,7,8,1]=>[1,8,7,5,2,4,3,6]=>[8,1,2,4,7,5,6,3]=>[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,2,6,7,8,1]=>[1,8,7,6,2,4,3,5]=>[8,1,2,3,7,5,6,4]=>[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,6,7,8,1]=>[1,8,7,6,2,5,4,3]=>[8,1,2,3,7,4,5,6]=>[[.,[.,[.,[[.,[.,[.,.]]],.]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,4,5,6,1]=>[1,6,5,4,3,2,7,8]=>[8,3,4,5,6,7,2,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,4,5,6,1]=>[1,6,5,4,3,2,8,7]=>[8,3,4,5,6,7,1,2]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[8,6,2,3,4,5,7,1]=>[1,7,5,4,3,2,6,8]=>[8,2,4,5,6,7,3,1]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,5,8,1]=>[1,8,5,4,3,2,6,7]=>[8,1,4,5,6,7,3,2]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,4,5,8,1]=>[1,8,5,4,3,2,7,6]=>[8,1,4,5,6,7,2,3]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,3,4,6,7,1]=>[1,7,6,4,3,2,5,8]=>[8,2,3,5,6,7,4,1]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,3,4,6,8,1]=>[1,8,6,4,3,2,5,7]=>[8,1,3,5,6,7,4,2]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,3,4,7,8,1]=>[1,8,7,4,3,2,5,6]=>[8,1,2,5,6,7,4,3]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,6,2,3,4,7,8,1]=>[1,8,7,4,3,2,6,5]=>[8,1,2,5,6,7,3,4]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,3,5,7,8,1]=>[1,8,7,5,3,2,4,6]=>[8,1,2,4,6,7,5,3]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,6,7,8,1]=>[1,8,7,6,3,2,4,5]=>[8,1,2,3,6,7,5,4]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,6,7,8,1]=>[1,8,7,6,3,2,5,4]=>[8,1,2,3,6,7,4,5]=>[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,4,5,6,7,1]=>[1,7,6,5,4,2,3,8]=>[8,2,3,4,5,7,6,1]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,4,5,6,8,1]=>[1,8,6,5,4,2,3,7]=>[8,1,3,4,5,7,6,2]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,6,7,8,1]=>[1,8,7,6,4,2,3,5]=>[8,1,2,3,5,7,6,4]=>[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,6,7,8,1]=>[1,8,7,6,5,2,3,4]=>[8,1,2,3,4,7,6,5]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,6,7,8,1]=>[1,8,7,6,5,2,4,3]=>[8,1,2,3,4,7,5,6]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2,8]=>[8,2,3,4,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,6,8,1]=>[1,8,6,5,4,3,2,7]=>[8,1,3,4,5,6,7,2]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,5,7,8,1]=>[1,8,7,5,4,3,2,6]=>[8,1,2,4,5,6,7,3]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,6,7,8,1]=>[1,8,7,6,4,3,2,5]=>[8,1,2,3,5,6,7,4]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,6,7,8,1]=>[1,8,7,6,5,3,2,4]=>[8,1,2,3,4,6,7,5]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,1]=>[1,8,7,6,5,4,2,3]=>[8,1,2,3,4,5,7,6]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]=>[1,8,7,6,5,4,3,2]=>[8,1,2,3,4,5,6,7]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8]=>[7,8,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,1,2]=>[2,1,3,4,5,6,8,7]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,3,1,2]=>[2,1,3,4,5,7,6,8]=>[7,8,6,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,3,1,2]=>[2,1,3,4,5,8,6,7]=>[7,8,6,5,4,1,3,2]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,3,1,2]=>[2,1,3,4,5,8,7,6]=>[7,8,6,5,4,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,3,1,2]=>[2,1,3,4,6,5,7,8]=>[7,8,6,5,3,4,2,1]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,3,1,2]=>[2,1,3,4,6,5,8,7]=>[7,8,6,5,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,3,1,2]=>[2,1,3,4,7,5,6,8]=>[7,8,6,5,2,4,3,1]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,3,1,2]=>[2,1,3,4,8,5,6,7]=>[7,8,6,5,1,4,3,2]=>[[[[.,[[[.,.],.],.]],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,3,1,2]=>[2,1,3,4,8,5,7,6]=>[7,8,6,5,1,4,2,3]=>[[[[.,[[.,[.,.]],.]],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,3,1,2]=>[2,1,3,4,8,7,5,6]=>[7,8,6,5,1,2,4,3]=>[[[[.,[.,[[.,.],.]]],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,1,2]=>[2,1,3,4,8,7,6,5]=>[7,8,6,5,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,3,1,2]=>[2,1,3,5,4,6,7,8]=>[7,8,6,4,5,3,2,1]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,3,1,2]=>[2,1,3,5,4,6,8,7]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,3,1,2]=>[2,1,3,6,4,5,7,8]=>[7,8,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,3,1,2]=>[2,1,3,8,4,5,6,7]=>[7,8,6,1,5,4,3,2]=>[[[.,[[[[.,.],.],.],.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,3,1,2]=>[2,1,3,8,4,6,5,7]=>[7,8,6,1,5,3,4,2]=>[[[.,[[[.,.],[.,.]],.]],.],[.,.]]
[1,1,0,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,3,1,2]=>[2,1,3,8,4,7,6,5]=>[7,8,6,1,5,2,3,4]=>[[[.,[[.,[.,[.,.]]],.]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,3,1,2]=>[2,1,3,6,5,4,7,8]=>[7,8,6,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,3,1,2]=>[2,1,3,6,5,4,8,7]=>[7,8,6,3,4,5,1,2]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,3,1,2]=>[2,1,3,8,5,4,6,7]=>[7,8,6,1,4,5,3,2]=>[[[.,[[[.,.],.],[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,3,1,2]=>[2,1,3,8,5,4,7,6]=>[7,8,6,1,4,5,2,3]=>[[[.,[[.,[.,.]],[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,7,3,1,2]=>[2,1,3,7,6,4,5,8]=>[7,8,6,2,3,5,4,1]=>[[[[.,.],[.,[[.,.],.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,3,1,2]=>[2,1,3,8,6,4,5,7]=>[7,8,6,1,3,5,4,2]=>[[[.,[[.,.],[[.,.],.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,3,1,2]=>[2,1,3,7,6,5,4,8]=>[7,8,6,2,3,4,5,1]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,3,1,2]=>[2,1,3,8,6,5,4,7]=>[7,8,6,1,3,4,5,2]=>[[[.,[[.,.],[.,[.,.]]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,3,1,2]=>[2,1,3,8,7,5,4,6]=>[7,8,6,1,2,4,5,3]=>[[[.,[.,[[.,.],[.,.]]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,1,2]=>[2,1,3,8,7,6,5,4]=>[7,8,6,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8]=>[7,8,5,6,4,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,4,1,2]=>[2,1,4,3,5,6,8,7]=>[7,8,5,6,4,3,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,4,1,2]=>[2,1,4,3,5,8,6,7]=>[7,8,5,6,4,1,3,2]=>[[[[.,[[.,.],.]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,4,1,2]=>[2,1,4,3,5,8,7,6]=>[7,8,5,6,4,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,1,2]=>[2,1,4,3,6,5,7,8]=>[7,8,5,6,3,4,2,1]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,4,1,2]=>[2,1,4,3,7,5,6,8]=>[7,8,5,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,4,1,2]=>[2,1,4,3,8,5,6,7]=>[7,8,5,6,1,4,3,2]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,4,1,2]=>[2,1,4,3,8,5,7,6]=>[7,8,5,6,1,4,2,3]=>[[[.,[[.,[.,.]],.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,4,1,2]=>[2,1,4,3,7,6,5,8]=>[7,8,5,6,2,3,4,1]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,4,1,2]=>[2,1,4,3,8,6,5,7]=>[7,8,5,6,1,3,4,2]=>[[[.,[[.,.],[.,.]]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,4,1,2]=>[2,1,4,3,8,7,5,6]=>[7,8,5,6,1,2,4,3]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,1,2]=>[2,1,4,3,8,7,6,5]=>[7,8,5,6,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,5,1,2]=>[2,1,5,3,4,6,8,7]=>[7,8,4,6,5,3,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,6,1,2]=>[2,1,6,3,4,5,8,7]=>[7,8,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,7,1,2]=>[2,1,7,3,4,5,6,8]=>[7,8,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,8,1,2]=>[2,1,8,3,4,5,6,7]=>[7,8,1,6,5,4,3,2]=>[[.,[[[[[.,.],.],.],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,8,1,2]=>[2,1,8,3,4,6,5,7]=>[7,8,1,6,5,3,4,2]=>[[.,[[[[.,.],[.,.]],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,8,1,2]=>[2,1,8,3,4,7,5,6]=>[7,8,1,6,5,2,4,3]=>[[.,[[[.,[[.,.],.]],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,8,1,2]=>[2,1,8,3,4,7,6,5]=>[7,8,1,6,5,2,3,4]=>[[.,[[[.,[.,[.,.]]],.],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,3,6,1,2]=>[2,1,6,3,5,4,8,7]=>[7,8,3,6,4,5,1,2]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,3,7,1,2]=>[2,1,7,3,5,4,6,8]=>[7,8,2,6,4,5,3,1]=>[[[.,.],[[[.,.],[.,.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,8,1,2]=>[2,1,8,3,5,4,7,6]=>[7,8,1,6,4,5,2,3]=>[[.,[[[.,[.,.]],[.,.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,7,1,2]=>[2,1,7,3,6,4,5,8]=>[7,8,2,6,3,5,4,1]=>[[[.,.],[[.,[[.,.],.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,3,8,1,2]=>[2,1,8,3,6,4,5,7]=>[7,8,1,6,3,5,4,2]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,8,1,2]=>[2,1,8,3,7,4,5,6]=>[7,8,1,6,2,5,4,3]=>[[.,[[.,[[[.,.],.],.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,8,1,2]=>[2,1,8,3,7,4,6,5]=>[7,8,1,6,2,5,3,4]=>[[.,[[.,[[.,[.,.]],.]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,8,1,2]=>[2,1,8,3,6,5,4,7]=>[7,8,1,6,3,4,5,2]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,3,8,1,2]=>[2,1,8,3,7,5,4,6]=>[7,8,1,6,2,4,5,3]=>[[.,[[.,[[.,.],[.,.]]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,8,1,2]=>[2,1,8,3,7,6,4,5]=>[7,8,1,6,2,3,5,4]=>[[.,[[.,[.,[[.,.],.]]],.]],[.,.]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,8,1,2]=>[2,1,8,3,7,6,5,4]=>[7,8,1,6,2,3,4,5]=>[[.,[[.,[.,[.,[.,.]]]],.]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,5,1,2]=>[2,1,5,4,3,6,8,7]=>[7,8,4,5,6,3,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,5,1,2]=>[2,1,5,4,3,7,6,8]=>[7,8,4,5,6,2,3,1]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,5,1,2]=>[2,1,5,4,3,8,6,7]=>[7,8,4,5,6,1,3,2]=>[[[.,[[.,.],.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,5,1,2]=>[2,1,5,4,3,8,7,6]=>[7,8,4,5,6,1,2,3]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,6,1,2]=>[2,1,6,4,3,5,8,7]=>[7,8,3,5,6,4,1,2]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,8,1,2]=>[2,1,8,4,3,5,6,7]=>[7,8,1,5,6,4,3,2]=>[[.,[[[[.,.],.],.],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[6,7,5,3,4,8,1,2]=>[2,1,8,4,3,5,7,6]=>[7,8,1,5,6,4,2,3]=>[[.,[[[.,[.,.]],.],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,8,1,2]=>[2,1,8,4,3,6,5,7]=>[7,8,1,5,6,3,4,2]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,4,8,1,2]=>[2,1,8,4,3,7,6,5]=>[7,8,1,5,6,2,3,4]=>[[.,[[.,[.,[.,.]]],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,6,1,2]=>[2,1,6,5,3,4,7,8]=>[7,8,3,4,6,5,2,1]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,6,1,2]=>[2,1,6,5,3,4,8,7]=>[7,8,3,4,6,5,1,2]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,5,8,1,2]=>[2,1,8,5,3,4,6,7]=>[7,8,1,4,6,5,3,2]=>[[.,[[[.,.],.],[[.,.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,1,2]=>[2,1,8,7,3,4,5,6]=>[7,8,1,2,6,5,4,3]=>[[.,[.,[[[[.,.],.],.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,7,8,1,2]=>[2,1,8,7,3,4,6,5]=>[7,8,1,2,6,5,3,4]=>[[.,[.,[[[.,[.,.]],.],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,7,1,2]=>[2,1,7,6,3,5,4,8]=>[7,8,2,3,6,4,5,1]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,6,8,1,2]=>[2,1,8,6,3,5,4,7]=>[7,8,1,3,6,4,5,2]=>[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,8,1,2]=>[2,1,8,7,3,6,4,5]=>[7,8,1,2,6,3,5,4]=>[[.,[.,[[.,[[.,.],.]],.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,8,1,2]=>[2,1,8,7,3,6,5,4]=>[7,8,1,2,6,3,4,5]=>[[.,[.,[[.,[.,[.,.]]],.]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,6,1,2]=>[2,1,6,5,4,3,7,8]=>[7,8,3,4,5,6,2,1]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,6,1,2]=>[2,1,6,5,4,3,8,7]=>[7,8,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,8,1,2]=>[2,1,8,5,4,3,6,7]=>[7,8,1,4,5,6,3,2]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,5,8,1,2]=>[2,1,8,5,4,3,7,6]=>[7,8,1,4,5,6,2,3]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,8,1,2]=>[2,1,8,7,4,3,6,5]=>[7,8,1,2,5,6,3,4]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,7,1,2]=>[2,1,7,6,5,3,4,8]=>[7,8,2,3,4,6,5,1]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,8,1,2]=>[2,1,8,7,5,3,4,6]=>[7,8,1,2,4,6,5,3]=>[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,8,1,2]=>[2,1,8,7,6,3,4,5]=>[7,8,1,2,3,6,5,4]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,8,1,2]=>[2,1,8,7,6,3,5,4]=>[7,8,1,2,3,6,4,5]=>[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,7,1,2]=>[2,1,7,6,5,4,3,8]=>[7,8,2,3,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,8,1,2]=>[2,1,8,6,5,4,3,7]=>[7,8,1,3,4,5,6,2]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,8,1,2]=>[2,1,8,7,5,4,3,6]=>[7,8,1,2,4,5,6,3]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,7,8,1,2]=>[2,1,8,7,6,4,3,5]=>[7,8,1,2,3,5,6,4]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,8,1,2]=>[2,1,8,7,6,5,3,4]=>[7,8,1,2,3,4,6,5]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2]=>[2,1,8,7,6,5,4,3]=>[7,8,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8]=>[6,8,7,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,2,1,3]=>[3,1,2,4,5,6,8,7]=>[6,8,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,1,3]=>[3,1,2,4,5,8,6,7]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,2,1,3]=>[3,1,2,4,5,8,7,6]=>[6,8,7,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,2,1,3]=>[3,1,2,4,6,5,7,8]=>[6,8,7,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,2,1,3]=>[3,1,2,4,6,5,8,7]=>[6,8,7,5,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,2,1,3]=>[3,1,2,4,8,5,6,7]=>[6,8,7,5,1,4,3,2]=>[[[.,[[[.,.],.],.]],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,2,1,3]=>[3,1,2,4,8,5,7,6]=>[6,8,7,5,1,4,2,3]=>[[[.,[[.,[.,.]],.]],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,2,1,3]=>[3,1,2,4,8,6,5,7]=>[6,8,7,5,1,3,4,2]=>[[[.,[[.,.],[.,.]]],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,2,1,3]=>[3,1,2,4,8,7,5,6]=>[6,8,7,5,1,2,4,3]=>[[[.,[.,[[.,.],.]]],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,2,1,3]=>[3,1,2,4,8,7,6,5]=>[6,8,7,5,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,2,1,3]=>[3,1,2,5,4,6,7,8]=>[6,8,7,4,5,3,2,1]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,2,1,3]=>[3,1,2,5,4,6,8,7]=>[6,8,7,4,5,3,1,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,2,1,3]=>[3,1,2,5,4,8,6,7]=>[6,8,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,2,1,3]=>[3,1,2,6,4,5,7,8]=>[6,8,7,3,5,4,2,1]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,2,1,3]=>[3,1,2,7,4,5,6,8]=>[6,8,7,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,2,1,3]=>[3,1,2,8,4,5,6,7]=>[6,8,7,1,5,4,3,2]=>[[.,[[[[.,.],.],.],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,2,1,3]=>[3,1,2,8,4,5,7,6]=>[6,8,7,1,5,4,2,3]=>[[.,[[[.,[.,.]],.],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,2,1,3]=>[3,1,2,8,4,7,6,5]=>[6,8,7,1,5,2,3,4]=>[[.,[[.,[.,[.,.]]],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,2,1,3]=>[3,1,2,6,5,4,7,8]=>[6,8,7,3,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,2,1,3]=>[3,1,2,6,5,4,8,7]=>[6,8,7,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,2,1,3]=>[3,1,2,7,5,4,6,8]=>[6,8,7,2,4,5,3,1]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,7,2,1,3]=>[3,1,2,7,6,4,5,8]=>[6,8,7,2,3,5,4,1]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,2,1,3]=>[3,1,2,8,6,4,5,7]=>[6,8,7,1,3,5,4,2]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,2,1,3]=>[3,1,2,7,6,5,4,8]=>[6,8,7,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,2,1,3]=>[3,1,2,8,6,5,4,7]=>[6,8,7,1,3,4,5,2]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,2,1,3]=>[3,1,2,8,7,6,5,4]=>[6,8,7,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8]=>[5,8,7,6,4,3,2,1]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,2,1,4]=>[4,1,2,3,5,6,8,7]=>[5,8,7,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,2,1,4]=>[4,1,2,3,5,7,6,8]=>[5,8,7,6,4,2,3,1]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,2,1,4]=>[4,1,2,3,5,8,6,7]=>[5,8,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,2,1,4]=>[4,1,2,3,5,8,7,6]=>[5,8,7,6,4,1,2,3]=>[[[.,[.,[.,.]]],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,2,1,4]=>[4,1,2,3,6,5,7,8]=>[5,8,7,6,3,4,2,1]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,2,1,4]=>[4,1,2,3,6,5,8,7]=>[5,8,7,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,1,4]=>[4,1,2,3,7,5,6,8]=>[5,8,7,6,2,4,3,1]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,1,4]=>[4,1,2,3,8,5,6,7]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,2,1,4]=>[4,1,2,3,8,5,7,6]=>[5,8,7,6,1,4,2,3]=>[[.,[[.,[.,.]],.]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,2,1,4]=>[4,1,2,3,7,6,5,8]=>[5,8,7,6,2,3,4,1]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,2,1,4]=>[4,1,2,3,8,6,5,7]=>[5,8,7,6,1,3,4,2]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,2,1,4]=>[4,1,2,3,8,7,5,6]=>[5,8,7,6,1,2,4,3]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,2,1,4]=>[4,1,2,3,8,7,6,5]=>[5,8,7,6,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8]=>[4,8,7,6,5,3,2,1]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,2,1,5]=>[5,1,2,3,4,6,8,7]=>[4,8,7,6,5,3,1,2]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,3,2,1,5]=>[5,1,2,3,4,7,6,8]=>[4,8,7,6,5,2,3,1]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,2,1,5]=>[5,1,2,3,4,8,6,7]=>[4,8,7,6,5,1,3,2]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,2,1,5]=>[5,1,2,3,4,8,7,6]=>[4,8,7,6,5,1,2,3]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8]=>[3,8,7,6,5,4,2,1]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,2,1,6]=>[6,1,2,3,4,5,8,7]=>[3,8,7,6,5,4,1,2]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6,8]=>[2,8,7,6,5,4,3,1]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,2,1,8]=>[8,1,2,3,4,5,7,6]=>[1,8,7,6,5,4,2,3]=>[.,[[[[[[.,[.,.]],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,3,2,1,7]=>[7,1,2,3,4,6,5,8]=>[2,8,7,6,5,3,4,1]=>[[.,.],[[[[[.,[.,.]],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,2,1,8]=>[8,1,2,3,4,6,5,7]=>[1,8,7,6,5,3,4,2]=>[.,[[[[[[.,.],[.,.]],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,2,1,8]=>[8,1,2,3,4,7,5,6]=>[1,8,7,6,5,2,4,3]=>[.,[[[[[.,[[.,.],.]],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,2,1,8]=>[8,1,2,3,4,7,6,5]=>[1,8,7,6,5,2,3,4]=>[.,[[[[[.,[.,[.,.]]],.],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,3,2,1,6]=>[6,1,2,3,5,4,7,8]=>[3,8,7,6,4,5,2,1]=>[[[.,.],.],[[[[.,[.,.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,3,2,1,6]=>[6,1,2,3,5,4,8,7]=>[3,8,7,6,4,5,1,2]=>[[.,[.,.]],[[[[.,[.,.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,3,2,1,7]=>[7,1,2,3,5,4,6,8]=>[2,8,7,6,4,5,3,1]=>[[.,.],[[[[[.,.],[.,.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,2,1,8]=>[8,1,2,3,5,4,6,7]=>[1,8,7,6,4,5,3,2]=>[.,[[[[[[.,.],.],[.,.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,2,1,8]=>[8,1,2,3,5,4,7,6]=>[1,8,7,6,4,5,2,3]=>[.,[[[[[.,[.,.]],[.,.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,3,2,1,8]=>[8,1,2,3,6,4,5,7]=>[1,8,7,6,3,5,4,2]=>[.,[[[[[.,.],[[.,.],.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,2,1,8]=>[8,1,2,3,7,4,5,6]=>[1,8,7,6,2,5,4,3]=>[.,[[[[.,[[[.,.],.],.]],.],.],.]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,3,2,1,7]=>[7,1,2,3,6,5,4,8]=>[2,8,7,6,3,4,5,1]=>[[.,.],[[[[.,[.,[.,.]]],.],.],.]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,2,1,8]=>[8,1,2,3,6,5,4,7]=>[1,8,7,6,3,4,5,2]=>[.,[[[[[.,.],[.,[.,.]]],.],.],.]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,3,2,1,8]=>[8,1,2,3,7,5,4,6]=>[1,8,7,6,2,4,5,3]=>[.,[[[[.,[[.,.],[.,.]]],.],.],.]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,2,1,8]=>[8,1,2,3,7,6,5,4]=>[1,8,7,6,2,3,4,5]=>[.,[[[[.,[.,[.,[.,.]]]],.],.],.]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7,8]=>[4,8,7,5,6,3,2,1]=>[[[[.,.],.],.],[[[.,[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,2,1,5]=>[5,1,2,4,3,6,8,7]=>[4,8,7,5,6,3,1,2]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,2,1,5]=>[5,1,2,4,3,8,6,7]=>[4,8,7,5,6,1,3,2]=>[[.,[[.,.],.]],[[[.,[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,2,1,6]=>[6,1,2,4,3,5,7,8]=>[3,8,7,5,6,4,2,1]=>[[[.,.],.],[[[[.,.],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,2,1,6]=>[6,1,2,4,3,5,8,7]=>[3,8,7,5,6,4,1,2]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,4,2,1,7]=>[7,1,2,4,3,5,6,8]=>[2,8,7,5,6,4,3,1]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,2,1,8]=>[8,1,2,4,3,5,6,7]=>[1,8,7,5,6,4,3,2]=>[.,[[[[[[.,.],.],.],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[6,7,5,3,4,2,1,8]=>[8,1,2,4,3,5,7,6]=>[1,8,7,5,6,4,2,3]=>[.,[[[[[.,[.,.]],.],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,2,1,7]=>[7,1,2,4,3,6,5,8]=>[2,8,7,5,6,3,4,1]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,2,1,8]=>[8,1,2,4,3,6,5,7]=>[1,8,7,5,6,3,4,2]=>[.,[[[[[.,.],[.,.]],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,4,2,1,8]=>[8,1,2,4,3,7,6,5]=>[1,8,7,5,6,2,3,4]=>[.,[[[[.,[.,[.,.]]],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,2,1,6]=>[6,1,2,5,3,4,8,7]=>[3,8,7,4,6,5,1,2]=>[[.,[.,.]],[[[.,[[.,.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,5,2,1,7]=>[7,1,2,5,3,4,6,8]=>[2,8,7,4,6,5,3,1]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,5,2,1,8]=>[8,1,2,5,3,4,6,7]=>[1,8,7,4,6,5,3,2]=>[.,[[[[[.,.],.],[[.,.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,2,1,8]=>[8,1,2,6,3,4,5,7]=>[1,8,7,3,6,5,4,2]=>[.,[[[[.,.],[[[.,.],.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,2,1,8]=>[8,1,2,7,3,4,5,6]=>[1,8,7,2,6,5,4,3]=>[.,[[[.,[[[[.,.],.],.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,7,2,1,8]=>[8,1,2,7,3,4,6,5]=>[1,8,7,2,6,5,3,4]=>[.,[[[.,[[[.,[.,.]],.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,7,2,1,8]=>[8,1,2,7,3,5,4,6]=>[1,8,7,2,6,4,5,3]=>[.,[[[.,[[[.,.],[.,.]],.]],.],.]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,2,1,8]=>[8,1,2,7,3,6,4,5]=>[1,8,7,2,6,3,5,4]=>[.,[[[.,[[.,[[.,.],.]],.]],.],.]]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,2,1,8]=>[8,1,2,7,3,6,5,4]=>[1,8,7,2,6,3,4,5]=>[.,[[[.,[[.,[.,[.,.]]],.]],.],.]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,2,1,6]=>[6,1,2,5,4,3,7,8]=>[3,8,7,4,5,6,2,1]=>[[[.,.],.],[[[.,[.,[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,2,1,6]=>[6,1,2,5,4,3,8,7]=>[3,8,7,4,5,6,1,2]=>[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,5,2,1,7]=>[7,1,2,5,4,3,6,8]=>[2,8,7,4,5,6,3,1]=>[[.,.],[[[[.,.],[.,[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,2,1,8]=>[8,1,2,5,4,3,6,7]=>[1,8,7,4,5,6,3,2]=>[.,[[[[[.,.],.],[.,[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,5,2,1,8]=>[8,1,2,5,4,3,7,6]=>[1,8,7,4,5,6,2,3]=>[.,[[[[.,[.,.]],[.,[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,7,2,1,8]=>[8,1,2,7,4,3,5,6]=>[1,8,7,2,5,6,4,3]=>[.,[[[.,[[[.,.],.],[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,2,1,8]=>[8,1,2,7,4,3,6,5]=>[1,8,7,2,5,6,3,4]=>[.,[[[.,[[.,[.,.]],[.,.]]],.],.]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,2,1,7]=>[7,1,2,6,5,3,4,8]=>[2,8,7,3,4,6,5,1]=>[[.,.],[[[.,[.,[[.,.],.]]],.],.]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,6,2,1,8]=>[8,1,2,6,5,3,4,7]=>[1,8,7,3,4,6,5,2]=>[.,[[[[.,.],[.,[[.,.],.]]],.],.]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,2,1,8]=>[8,1,2,7,6,3,4,5]=>[1,8,7,2,3,6,5,4]=>[.,[[[.,[.,[[[.,.],.],.]]],.],.]]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,2,1,8]=>[8,1,2,7,6,3,5,4]=>[1,8,7,2,3,6,4,5]=>[.,[[[.,[.,[[.,[.,.]],.]]],.],.]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,2,1,7]=>[7,1,2,6,5,4,3,8]=>[2,8,7,3,4,5,6,1]=>[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,2,1,8]=>[8,1,2,6,5,4,3,7]=>[1,8,7,3,4,5,6,2]=>[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,2,1,8]=>[8,1,2,7,5,4,3,6]=>[1,8,7,2,4,5,6,3]=>[.,[[[.,[[.,.],[.,[.,.]]]],.],.]]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,7,2,1,8]=>[8,1,2,7,6,4,3,5]=>[1,8,7,2,3,5,6,4]=>[.,[[[.,[.,[[.,.],[.,.]]]],.],.]]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,2,1,8]=>[8,1,2,7,6,5,3,4]=>[1,8,7,2,3,4,6,5]=>[.,[[[.,[.,[.,[[.,.],.]]]],.],.]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,2,1,8]=>[8,1,2,7,6,5,4,3]=>[1,8,7,2,3,4,5,6]=>[.,[[[.,[.,[.,[.,[.,.]]]]],.],.]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7,8]=>[5,8,6,7,4,3,2,1]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,2,3,1,4]=>[4,1,3,2,5,6,8,7]=>[5,8,6,7,4,3,1,2]=>[[[[.,[.,.]],.],.],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,2,3,1,4]=>[4,1,3,2,5,7,6,8]=>[5,8,6,7,4,2,3,1]=>[[[[.,.],[.,.]],.],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,3,1,4]=>[4,1,3,2,5,8,6,7]=>[5,8,6,7,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,3,1,4]=>[4,1,3,2,5,8,7,6]=>[5,8,6,7,4,1,2,3]=>[[[.,[.,[.,.]]],.],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,3,1,4]=>[4,1,3,2,6,5,7,8]=>[5,8,6,7,3,4,2,1]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,3,1,4]=>[4,1,3,2,6,5,8,7]=>[5,8,6,7,3,4,1,2]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,3,1,4]=>[4,1,3,2,7,5,6,8]=>[5,8,6,7,2,4,3,1]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,3,1,4]=>[4,1,3,2,8,5,6,7]=>[5,8,6,7,1,4,3,2]=>[[.,[[[.,.],.],.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,3,1,4]=>[4,1,3,2,8,5,7,6]=>[5,8,6,7,1,4,2,3]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,3,1,4]=>[4,1,3,2,7,6,5,8]=>[5,8,6,7,2,3,4,1]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,2,3,1,4]=>[4,1,3,2,8,6,5,7]=>[5,8,6,7,1,3,4,2]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,3,1,4]=>[4,1,3,2,8,7,5,6]=>[5,8,6,7,1,2,4,3]=>[[.,[.,[[.,.],.]]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,3,1,4]=>[4,1,3,2,8,7,6,5]=>[5,8,6,7,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,3,1,5]=>[5,1,3,2,4,6,7,8]=>[4,8,6,7,5,3,2,1]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,2,3,1,5]=>[5,1,3,2,4,6,8,7]=>[4,8,6,7,5,3,1,2]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,2,3,1,5]=>[5,1,3,2,4,8,6,7]=>[4,8,6,7,5,1,3,2]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,3,1,5]=>[5,1,3,2,4,8,7,6]=>[4,8,6,7,5,1,2,3]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,2,3,1,6]=>[6,1,3,2,4,5,7,8]=>[3,8,6,7,5,4,2,1]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,2,3,1,6]=>[6,1,3,2,4,5,8,7]=>[3,8,6,7,5,4,1,2]=>[[.,[.,.]],[[[[.,.],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,3,1,7]=>[7,1,3,2,4,5,6,8]=>[2,8,6,7,5,4,3,1]=>[[.,.],[[[[[.,.],.],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,3,1,8]=>[8,1,3,2,4,5,6,7]=>[1,8,6,7,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,2,3,1,8]=>[8,1,3,2,4,5,7,6]=>[1,8,6,7,5,4,2,3]=>[.,[[[[[.,[.,.]],.],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,2,3,1,7]=>[7,1,3,2,4,6,5,8]=>[2,8,6,7,5,3,4,1]=>[[.,.],[[[[.,[.,.]],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,2,3,1,8]=>[8,1,3,2,4,6,5,7]=>[1,8,6,7,5,3,4,2]=>[.,[[[[[.,.],[.,.]],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,2,3,1,8]=>[8,1,3,2,4,7,6,5]=>[1,8,6,7,5,2,3,4]=>[.,[[[[.,[.,[.,.]]],.],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,2,3,1,6]=>[6,1,3,2,5,4,8,7]=>[3,8,6,7,4,5,1,2]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,2,3,1,8]=>[8,1,3,2,5,4,6,7]=>[1,8,6,7,4,5,3,2]=>[.,[[[[[.,.],.],[.,.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,2,3,1,8]=>[8,1,3,2,5,4,7,6]=>[1,8,6,7,4,5,2,3]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,2,3,1,8]=>[8,1,3,2,7,4,5,6]=>[1,8,6,7,2,5,4,3]=>[.,[[[.,[[[.,.],.],.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,2,3,1,8]=>[8,1,3,2,7,4,6,5]=>[1,8,6,7,2,5,3,4]=>[.,[[[.,[[.,[.,.]],.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,2,3,1,8]=>[8,1,3,2,6,5,4,7]=>[1,8,6,7,3,4,5,2]=>[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,3,1,8]=>[8,1,3,2,7,6,5,4]=>[1,8,6,7,2,3,4,5]=>[.,[[[.,[.,[.,[.,.]]]],[.,.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,4,1,5]=>[5,1,4,2,3,6,7,8]=>[4,8,5,7,6,3,2,1]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,2,4,1,5]=>[5,1,4,2,3,6,8,7]=>[4,8,5,7,6,3,1,2]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,4,1,6]=>[6,1,4,2,3,5,7,8]=>[3,8,5,7,6,4,2,1]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,2,4,1,7]=>[7,1,4,2,3,5,6,8]=>[2,8,5,7,6,4,3,1]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,2,4,1,8]=>[8,1,4,2,3,5,6,7]=>[1,8,5,7,6,4,3,2]=>[.,[[[[[.,.],.],.],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,2,4,1,7]=>[7,1,4,2,3,6,5,8]=>[2,8,5,7,6,3,4,1]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,2,4,1,8]=>[8,1,4,2,3,7,5,6]=>[1,8,5,7,6,2,4,3]=>[.,[[[.,[[.,.],.]],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,2,4,1,8]=>[8,1,4,2,3,7,6,5]=>[1,8,5,7,6,2,3,4]=>[.,[[[.,[.,[.,.]]],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,5,1,6]=>[6,1,5,2,3,4,7,8]=>[3,8,4,7,6,5,2,1]=>[[[.,.],.],[[.,[[[.,.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,5,1,6]=>[6,1,5,2,3,4,8,7]=>[3,8,4,7,6,5,1,2]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,2,5,1,7]=>[7,1,5,2,3,4,6,8]=>[2,8,4,7,6,5,3,1]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,2,5,1,8]=>[8,1,5,2,3,4,6,7]=>[1,8,4,7,6,5,3,2]=>[.,[[[[.,.],.],[[[.,.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,5,1,8]=>[8,1,5,2,3,4,7,6]=>[1,8,4,7,6,5,2,3]=>[.,[[[.,[.,.]],[[[.,.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2,6,1,7]=>[7,1,6,2,3,4,5,8]=>[2,8,3,7,6,5,4,1]=>[[.,.],[[.,[[[[.,.],.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,2,6,1,8]=>[8,1,6,2,3,4,5,7]=>[1,8,3,7,6,5,4,2]=>[.,[[[.,.],[[[[.,.],.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,7,1,8]=>[8,1,7,2,3,4,5,6]=>[1,8,2,7,6,5,4,3]=>[.,[[.,[[[[[.,.],.],.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,2,6,1,8]=>[8,1,6,2,3,5,4,7]=>[1,8,3,7,6,4,5,2]=>[.,[[[.,.],[[[.,[.,.]],.],.]],.]]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,2,7,1,8]=>[8,1,7,2,3,5,4,6]=>[1,8,2,7,6,4,5,3]=>[.,[[.,[[[[.,.],[.,.]],.],.]],.]]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,7,1,8]=>[8,1,7,2,3,6,4,5]=>[1,8,2,7,6,3,5,4]=>[.,[[.,[[[.,[[.,.],.]],.],.]],.]]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,2,7,1,8]=>[8,1,7,2,3,6,5,4]=>[1,8,2,7,6,3,4,5]=>[.,[[.,[[[.,[.,[.,.]]],.],.]],.]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,2,5,1,6]=>[6,1,5,2,4,3,7,8]=>[3,8,4,7,5,6,2,1]=>[[[.,.],.],[[.,[[.,[.,.]],.]],.]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,5,1,6]=>[6,1,5,2,4,3,8,7]=>[3,8,4,7,5,6,1,2]=>[[.,[.,.]],[[.,[[.,[.,.]],.]],.]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,2,5,1,8]=>[8,1,5,2,4,3,7,6]=>[1,8,4,7,5,6,2,3]=>[.,[[[.,[.,.]],[[.,[.,.]],.]],.]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,2,6,1,7]=>[7,1,6,2,4,3,5,8]=>[2,8,3,7,5,6,4,1]=>[[.,.],[[.,[[[.,.],[.,.]],.]],.]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,2,6,1,8]=>[8,1,6,2,4,3,5,7]=>[1,8,3,7,5,6,4,2]=>[.,[[[.,.],[[[.,.],[.,.]],.]],.]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,2,7,1,8]=>[8,1,7,2,4,3,6,5]=>[1,8,2,7,5,6,3,4]=>[.,[[.,[[[.,[.,.]],[.,.]],.]],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,2,6,1,7]=>[7,1,6,2,5,3,4,8]=>[2,8,3,7,4,6,5,1]=>[[.,.],[[.,[[.,[[.,.],.]],.]],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,2,6,1,8]=>[8,1,6,2,5,3,4,7]=>[1,8,3,7,4,6,5,2]=>[.,[[[.,.],[[.,[[.,.],.]],.]],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,2,7,1,8]=>[8,1,7,2,5,3,4,6]=>[1,8,2,7,4,6,5,3]=>[.,[[.,[[[.,.],[[.,.],.]],.]],.]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,7,1,8]=>[8,1,7,2,6,3,4,5]=>[1,8,2,7,3,6,5,4]=>[.,[[.,[[.,[[[.,.],.],.]],.]],.]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,2,7,1,8]=>[8,1,7,2,6,3,5,4]=>[1,8,2,7,3,6,4,5]=>[.,[[.,[[.,[[.,[.,.]],.]],.]],.]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,2,6,1,7]=>[7,1,6,2,5,4,3,8]=>[2,8,3,7,4,5,6,1]=>[[.,.],[[.,[[.,[.,[.,.]]],.]],.]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,2,6,1,8]=>[8,1,6,2,5,4,3,7]=>[1,8,3,7,4,5,6,2]=>[.,[[[.,.],[[.,[.,[.,.]]],.]],.]]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,2,7,1,8]=>[8,1,7,2,5,4,3,6]=>[1,8,2,7,4,5,6,3]=>[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,2,7,1,8]=>[8,1,7,2,6,4,3,5]=>[1,8,2,7,3,5,6,4]=>[.,[[.,[[.,[[.,.],[.,.]]],.]],.]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,2,7,1,8]=>[8,1,7,2,6,5,3,4]=>[1,8,2,7,3,4,6,5]=>[.,[[.,[[.,[.,[[.,.],.]]],.]],.]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,7,1,8]=>[8,1,7,2,6,5,4,3]=>[1,8,2,7,3,4,5,6]=>[.,[[.,[[.,[.,[.,[.,.]]]],.]],.]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,4,1,5]=>[5,1,4,3,2,6,7,8]=>[4,8,5,6,7,3,2,1]=>[[[[.,.],.],.],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,3,4,1,5]=>[5,1,4,3,2,7,6,8]=>[4,8,5,6,7,2,3,1]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,2,3,4,1,6]=>[6,1,4,3,2,5,8,7]=>[3,8,5,6,7,4,1,2]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,3,4,1,7]=>[7,1,4,3,2,5,6,8]=>[2,8,5,6,7,4,3,1]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,4,1,8]=>[8,1,4,3,2,5,6,7]=>[1,8,5,6,7,4,3,2]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,3,4,1,8]=>[8,1,4,3,2,7,6,5]=>[1,8,5,6,7,2,3,4]=>[.,[[[.,[.,[.,.]]],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,5,1,8]=>[8,1,5,3,2,4,6,7]=>[1,8,4,6,7,5,3,2]=>[.,[[[[.,.],.],[[.,.],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[6,7,4,2,3,5,1,8]=>[8,1,5,3,2,4,7,6]=>[1,8,4,6,7,5,2,3]=>[.,[[[.,[.,.]],[[.,.],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,2,3,6,1,7]=>[7,1,6,3,2,4,5,8]=>[2,8,3,6,7,5,4,1]=>[[.,.],[[.,[[[.,.],.],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[7,5,4,2,3,6,1,8]=>[8,1,6,3,2,4,5,7]=>[1,8,3,6,7,5,4,2]=>[.,[[[.,.],[[[.,.],.],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,2,3,7,1,8]=>[8,1,7,3,2,4,5,6]=>[1,8,2,6,7,5,4,3]=>[.,[[.,[[[[.,.],.],.],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,2,3,6,1,8]=>[8,1,6,3,2,5,4,7]=>[1,8,3,6,7,4,5,2]=>[.,[[[.,.],[[.,[.,.]],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[6,4,5,2,3,7,1,8]=>[8,1,7,3,2,5,4,6]=>[1,8,2,6,7,4,5,3]=>[.,[[.,[[[.,.],[.,.]],[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,5,6,2,3,7,1,8]=>[8,1,7,3,2,6,5,4]=>[1,8,2,6,7,3,4,5]=>[.,[[.,[[.,[.,[.,.]]],[.,.]]],.]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,4,5,1,8]=>[8,1,5,4,2,3,7,6]=>[1,8,4,5,7,6,2,3]=>[.,[[[.,[.,.]],[.,[[.,.],.]]],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,2,4,6,1,7]=>[7,1,6,4,2,3,5,8]=>[2,8,3,5,7,6,4,1]=>[[.,.],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,4,6,1,8]=>[8,1,6,4,2,3,5,7]=>[1,8,3,5,7,6,4,2]=>[.,[[[.,.],[[.,.],[[.,.],.]]],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[6,5,3,2,4,7,1,8]=>[8,1,7,4,2,3,5,6]=>[1,8,2,5,7,6,4,3]=>[.,[[.,[[[.,.],.],[[.,.],.]]],.]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,3,2,4,7,1,8]=>[8,1,7,4,2,3,6,5]=>[1,8,2,5,7,6,3,4]=>[.,[[.,[[.,[.,.]],[[.,.],.]]],.]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,2,5,6,1,8]=>[8,1,6,5,2,3,4,7]=>[1,8,3,4,7,6,5,2]=>[.,[[[.,.],[.,[[[.,.],.],.]]],.]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,5,7,1,8]=>[8,1,7,5,2,3,4,6]=>[1,8,2,4,7,6,5,3]=>[.,[[.,[[.,.],[[[.,.],.],.]]],.]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,7,1,8]=>[8,1,7,6,2,3,4,5]=>[1,8,2,3,7,6,5,4]=>[.,[[.,[.,[[[[.,.],.],.],.]]],.]]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,6,7,1,8]=>[8,1,7,6,2,3,5,4]=>[1,8,2,3,7,6,4,5]=>[.,[[.,[.,[[[.,[.,.]],.],.]]],.]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,2,5,6,1,7]=>[7,1,6,5,2,4,3,8]=>[2,8,3,4,7,5,6,1]=>[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[6,3,4,2,5,7,1,8]=>[8,1,7,5,2,4,3,6]=>[1,8,2,4,7,5,6,3]=>[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,2,6,7,1,8]=>[8,1,7,6,2,4,3,5]=>[1,8,2,3,7,5,6,4]=>[.,[[.,[.,[[[.,.],[.,.]],.]]],.]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,4,5,1,6]=>[6,1,5,4,3,2,7,8]=>[3,8,4,5,6,7,2,1]=>[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[8,6,2,3,4,5,1,7]=>[7,1,5,4,3,2,6,8]=>[2,8,4,5,6,7,3,1]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,5,1,8]=>[8,1,5,4,3,2,6,7]=>[1,8,4,5,6,7,3,2]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,4,5,1,8]=>[8,1,5,4,3,2,7,6]=>[1,8,4,5,6,7,2,3]=>[.,[[[.,[.,.]],[.,[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,3,4,6,1,7]=>[7,1,6,4,3,2,5,8]=>[2,8,3,5,6,7,4,1]=>[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,3,4,6,1,8]=>[8,1,6,4,3,2,5,7]=>[1,8,3,5,6,7,4,2]=>[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,3,4,7,1,8]=>[8,1,7,4,3,2,5,6]=>[1,8,2,5,6,7,4,3]=>[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,6,2,3,4,7,1,8]=>[8,1,7,4,3,2,6,5]=>[1,8,2,5,6,7,3,4]=>[.,[[.,[[.,[.,.]],[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[7,4,2,3,5,6,1,8]=>[8,1,6,5,3,2,4,7]=>[1,8,3,4,6,7,5,2]=>[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,3,5,7,1,8]=>[8,1,7,5,3,2,4,6]=>[1,8,2,4,6,7,5,3]=>[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,6,7,1,8]=>[8,1,7,6,3,2,4,5]=>[1,8,2,3,6,7,5,4]=>[.,[[.,[.,[[[.,.],.],[.,.]]]],.]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,4,5,6,1,7]=>[7,1,6,5,4,2,3,8]=>[2,8,3,4,5,7,6,1]=>[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[6,3,2,4,5,7,1,8]=>[8,1,7,5,4,2,3,6]=>[1,8,2,4,5,7,6,3]=>[.,[[.,[[.,.],[.,[[.,.],.]]]],.]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,6,7,1,8]=>[8,1,7,6,5,2,3,4]=>[1,8,2,3,4,7,6,5]=>[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,6,7,1,8]=>[8,1,7,6,5,2,4,3]=>[1,8,2,3,4,7,5,6]=>[.,[[.,[.,[.,[[.,[.,.]],.]]]],.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,5,6,1,7]=>[7,1,6,5,4,3,2,8]=>[2,8,3,4,5,6,7,1]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,6,1,8]=>[8,1,6,5,4,3,2,7]=>[1,8,3,4,5,6,7,2]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,5,7,1,8]=>[8,1,7,5,4,3,2,6]=>[1,8,2,4,5,6,7,3]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,6,7,1,8]=>[8,1,7,6,4,3,2,5]=>[1,8,2,3,5,6,7,4]=>[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,6,7,1,8]=>[8,1,7,6,5,3,2,4]=>[1,8,2,3,4,6,7,5]=>[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,6,7,1,8]=>[8,1,7,6,5,4,2,3]=>[1,8,2,3,4,5,7,6]=>[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8]=>[8,1,7,6,5,4,3,2]=>[1,8,2,3,4,5,6,7]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8]=>[6,7,8,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,1,2,3]=>[3,2,1,4,5,6,8,7]=>[6,7,8,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,1,2,3]=>[3,2,1,4,5,8,7,6]=>[6,7,8,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,1,2,3]=>[3,2,1,4,6,5,8,7]=>[6,7,8,5,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,1,2,3]=>[3,2,1,4,8,5,6,7]=>[6,7,8,5,1,4,3,2]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,1,2,3]=>[3,2,1,4,8,5,7,6]=>[6,7,8,5,1,4,2,3]=>[[[.,[[.,[.,.]],.]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,1,2,3]=>[3,2,1,4,7,6,5,8]=>[6,7,8,5,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,1,2,3]=>[3,2,1,4,8,7,5,6]=>[6,7,8,5,1,2,4,3]=>[[[.,[.,[[.,.],.]]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,1,2,3]=>[3,2,1,4,8,7,6,5]=>[6,7,8,5,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,1,2,3]=>[3,2,1,5,4,6,8,7]=>[6,7,8,4,5,3,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,1,2,3]=>[3,2,1,5,4,7,6,8]=>[6,7,8,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,1,2,3]=>[3,2,1,5,4,8,7,6]=>[6,7,8,4,5,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,1,2,3]=>[3,2,1,6,4,5,7,8]=>[6,7,8,3,5,4,2,1]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,1,2,3]=>[3,2,1,7,4,5,6,8]=>[6,7,8,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,1,2,3]=>[3,2,1,8,4,5,6,7]=>[6,7,8,1,5,4,3,2]=>[[.,[[[[.,.],.],.],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,1,2,3]=>[3,2,1,8,4,5,7,6]=>[6,7,8,1,5,4,2,3]=>[[.,[[[.,[.,.]],.],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,1,2,3]=>[3,2,1,8,4,6,5,7]=>[6,7,8,1,5,3,4,2]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,1,2,3]=>[3,2,1,8,4,7,5,6]=>[6,7,8,1,5,2,4,3]=>[[.,[[.,[[.,.],.]],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,1,2,3]=>[3,2,1,8,4,7,6,5]=>[6,7,8,1,5,2,3,4]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,1,2,3]=>[3,2,1,6,5,4,7,8]=>[6,7,8,3,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,1,2,3]=>[3,2,1,7,5,4,6,8]=>[6,7,8,2,4,5,3,1]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,1,2,3]=>[3,2,1,8,5,4,6,7]=>[6,7,8,1,4,5,3,2]=>[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,1,2,3]=>[3,2,1,8,5,4,7,6]=>[6,7,8,1,4,5,2,3]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,7,1,2,3]=>[3,2,1,7,6,4,5,8]=>[6,7,8,2,3,5,4,1]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,1,2,3]=>[3,2,1,8,6,4,5,7]=>[6,7,8,1,3,5,4,2]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,1,2,3]=>[3,2,1,8,7,4,5,6]=>[6,7,8,1,2,5,4,3]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,1,2,3]=>[3,2,1,8,7,4,6,5]=>[6,7,8,1,2,5,3,4]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,1,2,3]=>[3,2,1,7,6,5,4,8]=>[6,7,8,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,1,2,3]=>[3,2,1,8,6,5,4,7]=>[6,7,8,1,3,4,5,2]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,1,2,3]=>[3,2,1,8,7,5,4,6]=>[6,7,8,1,2,4,5,3]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,1,2,3]=>[3,2,1,8,7,6,4,5]=>[6,7,8,1,2,3,5,4]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,1,2,3]=>[3,2,1,8,7,6,5,4]=>[6,7,8,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,1,2,4]=>[4,2,1,3,5,6,7,8]=>[5,7,8,6,4,3,2,1]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,1,2,4]=>[4,2,1,3,5,7,6,8]=>[5,7,8,6,4,2,3,1]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,1,2,4]=>[4,2,1,3,5,8,7,6]=>[5,7,8,6,4,1,2,3]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,1,2,4]=>[4,2,1,3,6,5,7,8]=>[5,7,8,6,3,4,2,1]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,1,2,4]=>[4,2,1,3,6,5,8,7]=>[5,7,8,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,1,2,4]=>[4,2,1,3,8,5,6,7]=>[5,7,8,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,1,2,4]=>[4,2,1,3,8,5,7,6]=>[5,7,8,6,1,4,2,3]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,1,2,4]=>[4,2,1,3,7,6,5,8]=>[5,7,8,6,2,3,4,1]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,1,2,4]=>[4,2,1,3,8,6,5,7]=>[5,7,8,6,1,3,4,2]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,1,2,4]=>[4,2,1,3,8,7,5,6]=>[5,7,8,6,1,2,4,3]=>[[.,[.,[[.,.],.]]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,1,2,4]=>[4,2,1,3,8,7,6,5]=>[5,7,8,6,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,1,2,5]=>[5,2,1,3,4,6,7,8]=>[4,7,8,6,5,3,2,1]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,1,2,5]=>[5,2,1,3,4,8,6,7]=>[4,7,8,6,5,1,3,2]=>[[.,[[.,.],.]],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,1,2,5]=>[5,2,1,3,4,8,7,6]=>[4,7,8,6,5,1,2,3]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,1,2,6]=>[6,2,1,3,4,5,7,8]=>[3,7,8,6,5,4,2,1]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,1,2,7]=>[7,2,1,3,4,5,6,8]=>[2,7,8,6,5,4,3,1]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,1,2,8]=>[8,2,1,3,4,5,6,7]=>[1,7,8,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,1,2,8]=>[8,2,1,3,4,5,7,6]=>[1,7,8,6,5,4,2,3]=>[.,[[[[[.,[.,.]],.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,1,2,8]=>[8,2,1,3,4,6,5,7]=>[1,7,8,6,5,3,4,2]=>[.,[[[[[.,.],[.,.]],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,1,2,8]=>[8,2,1,3,4,7,5,6]=>[1,7,8,6,5,2,4,3]=>[.,[[[[.,[[.,.],.]],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,1,2,8]=>[8,2,1,3,5,4,6,7]=>[1,7,8,6,4,5,3,2]=>[.,[[[[[.,.],.],[.,.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,1,2,7]=>[7,2,1,3,6,4,5,8]=>[2,7,8,6,3,5,4,1]=>[[.,.],[[[.,[[.,.],.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,3,1,2,8]=>[8,2,1,3,6,4,5,7]=>[1,7,8,6,3,5,4,2]=>[.,[[[[.,.],[[.,.],.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,1,2,8]=>[8,2,1,3,7,4,5,6]=>[1,7,8,6,2,5,4,3]=>[.,[[[.,[[[.,.],.],.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,1,2,8]=>[8,2,1,3,6,5,4,7]=>[1,7,8,6,3,4,5,2]=>[.,[[[[.,.],[.,[.,.]]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,1,2,8]=>[8,2,1,3,7,6,4,5]=>[1,7,8,6,2,3,5,4]=>[.,[[[.,[.,[[.,.],.]]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,1,2,8]=>[8,2,1,3,7,6,5,4]=>[1,7,8,6,2,3,4,5]=>[.,[[[.,[.,[.,[.,.]]]],.],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,1,2,5]=>[5,2,1,4,3,7,6,8]=>[4,7,8,5,6,2,3,1]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,1,2,5]=>[5,2,1,4,3,8,6,7]=>[4,7,8,5,6,1,3,2]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,1,2,5]=>[5,2,1,4,3,8,7,6]=>[4,7,8,5,6,1,2,3]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,1,2,6]=>[6,2,1,4,3,5,7,8]=>[3,7,8,5,6,4,2,1]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,1,2,8]=>[8,2,1,4,3,5,6,7]=>[1,7,8,5,6,4,3,2]=>[.,[[[[[.,.],.],.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[6,7,5,3,4,1,2,8]=>[8,2,1,4,3,5,7,6]=>[1,7,8,5,6,4,2,3]=>[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,1,2,7]=>[7,2,1,4,3,6,5,8]=>[2,7,8,5,6,3,4,1]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,1,2,8]=>[8,2,1,4,3,6,5,7]=>[1,7,8,5,6,3,4,2]=>[.,[[[[.,.],[.,.]],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,1,2,8]=>[8,2,1,6,3,4,5,7]=>[1,7,8,3,6,5,4,2]=>[.,[[[.,.],[[[.,.],.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,1,2,7]=>[7,2,1,6,3,5,4,8]=>[2,7,8,3,6,4,5,1]=>[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,6,1,2,8]=>[8,2,1,6,3,5,4,7]=>[1,7,8,3,6,4,5,2]=>[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,7,1,2,8]=>[8,2,1,7,3,5,4,6]=>[1,7,8,2,6,4,5,3]=>[.,[[.,[[[.,.],[.,.]],.]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,1,2,6]=>[6,2,1,5,4,3,7,8]=>[3,7,8,4,5,6,2,1]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,1,2,6]=>[6,2,1,5,4,3,8,7]=>[3,7,8,4,5,6,1,2]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,5,1,2,7]=>[7,2,1,5,4,3,6,8]=>[2,7,8,4,5,6,3,1]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,5,1,2,8]=>[8,2,1,5,4,3,7,6]=>[1,7,8,4,5,6,2,3]=>[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,1,2,8]=>[8,2,1,6,4,3,5,7]=>[1,7,8,3,5,6,4,2]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,1,2,8]=>[8,2,1,7,4,3,6,5]=>[1,7,8,2,5,6,3,4]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,1,2,8]=>[8,2,1,7,6,3,4,5]=>[1,7,8,2,3,6,5,4]=>[.,[[.,[.,[[[.,.],.],.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,1,2,8]=>[8,2,1,7,6,3,5,4]=>[1,7,8,2,3,6,4,5]=>[.,[[.,[.,[[.,[.,.]],.]]],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,1,2,7]=>[7,2,1,6,5,4,3,8]=>[2,7,8,3,4,5,6,1]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,1,2,8]=>[8,2,1,6,5,4,3,7]=>[1,7,8,3,4,5,6,2]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,1,2,8]=>[8,2,1,7,5,4,3,6]=>[1,7,8,2,4,5,6,3]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,7,1,2,8]=>[8,2,1,7,6,4,3,5]=>[1,7,8,2,3,5,6,4]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,1,2,8]=>[8,2,1,7,6,5,4,3]=>[1,7,8,2,3,4,5,6]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7,8]=>[5,6,8,7,4,3,2,1]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,2,1,3,4]=>[4,3,1,2,5,6,8,7]=>[5,6,8,7,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,1,3,4]=>[4,3,1,2,5,8,7,6]=>[5,6,8,7,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,1,3,4]=>[4,3,1,2,6,5,8,7]=>[5,6,8,7,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,1,3,4]=>[4,3,1,2,7,5,6,8]=>[5,6,8,7,2,4,3,1]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,1,3,4]=>[4,3,1,2,8,5,6,7]=>[5,6,8,7,1,4,3,2]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,1,3,4]=>[4,3,1,2,8,5,7,6]=>[5,6,8,7,1,4,2,3]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,2,1,3,4]=>[4,3,1,2,8,6,5,7]=>[5,6,8,7,1,3,4,2]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,1,3,4]=>[4,3,1,2,8,7,5,6]=>[5,6,8,7,1,2,4,3]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,1,3,4]=>[4,3,1,2,8,7,6,5]=>[5,6,8,7,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,1,3,5]=>[5,3,1,2,4,6,7,8]=>[4,6,8,7,5,3,2,1]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,2,1,3,5]=>[5,3,1,2,4,6,8,7]=>[4,6,8,7,5,3,1,2]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,1,3,5]=>[5,3,1,2,4,8,7,6]=>[4,6,8,7,5,1,2,3]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,2,1,3,6]=>[6,3,1,2,4,5,7,8]=>[3,6,8,7,5,4,2,1]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,2,1,3,6]=>[6,3,1,2,4,5,8,7]=>[3,6,8,7,5,4,1,2]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,1,3,7]=>[7,3,1,2,4,5,6,8]=>[2,6,8,7,5,4,3,1]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,1,3,8]=>[8,3,1,2,4,5,6,7]=>[1,6,8,7,5,4,3,2]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,2,1,3,7]=>[7,3,1,2,4,6,5,8]=>[2,6,8,7,5,3,4,1]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,2,1,3,8]=>[8,3,1,2,4,6,5,7]=>[1,6,8,7,5,3,4,2]=>[.,[[[[.,.],[.,.]],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,2,1,3,8]=>[8,3,1,2,4,7,5,6]=>[1,6,8,7,5,2,4,3]=>[.,[[[.,[[.,.],.]],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,2,1,3,8]=>[8,3,1,2,4,7,6,5]=>[1,6,8,7,5,2,3,4]=>[.,[[[.,[.,[.,.]]],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,2,1,3,8]=>[8,3,1,2,5,4,6,7]=>[1,6,8,7,4,5,3,2]=>[.,[[[[.,.],.],[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,2,1,3,8]=>[8,3,1,2,6,4,5,7]=>[1,6,8,7,3,5,4,2]=>[.,[[[.,.],[[.,.],.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,2,1,3,8]=>[8,3,1,2,7,4,5,6]=>[1,6,8,7,2,5,4,3]=>[.,[[.,[[[.,.],.],.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,2,1,3,8]=>[8,3,1,2,7,4,6,5]=>[1,6,8,7,2,5,3,4]=>[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,2,1,3,7]=>[7,3,1,2,6,5,4,8]=>[2,6,8,7,3,4,5,1]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,2,1,3,8]=>[8,3,1,2,6,5,4,7]=>[1,6,8,7,3,4,5,2]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,2,1,3,8]=>[8,3,1,2,7,6,4,5]=>[1,6,8,7,2,3,5,4]=>[.,[[.,[.,[[.,.],.]]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,1,3,8]=>[8,3,1,2,7,6,5,4]=>[1,6,8,7,2,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,1,4,5]=>[5,4,1,2,3,6,7,8]=>[4,5,8,7,6,3,2,1]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,2,1,4,5]=>[5,4,1,2,3,6,8,7]=>[4,5,8,7,6,3,1,2]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,2,1,4,5]=>[5,4,1,2,3,8,6,7]=>[4,5,8,7,6,1,3,2]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,1,4,5]=>[5,4,1,2,3,8,7,6]=>[4,5,8,7,6,1,2,3]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,1,4,6]=>[6,4,1,2,3,5,7,8]=>[3,5,8,7,6,4,2,1]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,2,1,4,6]=>[6,4,1,2,3,5,8,7]=>[3,5,8,7,6,4,1,2]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,2,1,4,7]=>[7,4,1,2,3,5,6,8]=>[2,5,8,7,6,4,3,1]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,2,1,4,8]=>[8,4,1,2,3,5,6,7]=>[1,5,8,7,6,4,3,2]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,2,1,4,8]=>[8,4,1,2,3,6,5,7]=>[1,5,8,7,6,3,4,2]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,2,1,4,8]=>[8,4,1,2,3,7,5,6]=>[1,5,8,7,6,2,4,3]=>[.,[[.,[[.,.],.]],[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,2,1,4,8]=>[8,4,1,2,3,7,6,5]=>[1,5,8,7,6,2,3,4]=>[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,1,5,6]=>[6,5,1,2,3,4,8,7]=>[3,4,8,7,6,5,1,2]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,2,1,5,7]=>[7,5,1,2,3,4,6,8]=>[2,4,8,7,6,5,3,1]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,2,1,5,8]=>[8,5,1,2,3,4,6,7]=>[1,4,8,7,6,5,3,2]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5,8]=>[2,3,8,7,6,5,4,1]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,2,1,6,8]=>[8,6,1,2,3,4,5,7]=>[1,3,8,7,6,5,4,2]=>[.,[[.,.],[[[[[.,.],.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,1,7,8]=>[8,7,1,2,3,4,5,6]=>[1,2,8,7,6,5,4,3]=>[.,[.,[[[[[[.,.],.],.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,2,1,7,8]=>[8,7,1,2,3,4,6,5]=>[1,2,8,7,6,5,3,4]=>[.,[.,[[[[[.,[.,.]],.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,1,7,8]=>[8,7,1,2,3,6,4,5]=>[1,2,8,7,6,3,5,4]=>[.,[.,[[[[.,[[.,.],.]],.],.],.]]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,2,1,7,8]=>[8,7,1,2,3,6,5,4]=>[1,2,8,7,6,3,4,5]=>[.,[.,[[[[.,[.,[.,.]]],.],.],.]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,2,1,5,6]=>[6,5,1,2,4,3,7,8]=>[3,4,8,7,5,6,2,1]=>[[[.,.],.],[.,[[[.,[.,.]],.],.]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,1,5,6]=>[6,5,1,2,4,3,8,7]=>[3,4,8,7,5,6,1,2]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,2,1,5,7]=>[7,5,1,2,4,3,6,8]=>[2,4,8,7,5,6,3,1]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,2,1,6,8]=>[8,6,1,2,4,3,5,7]=>[1,3,8,7,5,6,4,2]=>[.,[[.,.],[[[[.,.],[.,.]],.],.]]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,2,1,7,8]=>[8,7,1,2,4,3,5,6]=>[1,2,8,7,5,6,4,3]=>[.,[.,[[[[[.,.],.],[.,.]],.],.]]]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,2,1,7,8]=>[8,7,1,2,4,3,6,5]=>[1,2,8,7,5,6,3,4]=>[.,[.,[[[[.,[.,.]],[.,.]],.],.]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,2,1,6,8]=>[8,6,1,2,5,3,4,7]=>[1,3,8,7,4,6,5,2]=>[.,[[.,.],[[[.,[[.,.],.]],.],.]]]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,2,1,7,8]=>[8,7,1,2,5,3,4,6]=>[1,2,8,7,4,6,5,3]=>[.,[.,[[[[.,.],[[.,.],.]],.],.]]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,1,7,8]=>[8,7,1,2,6,3,4,5]=>[1,2,8,7,3,6,5,4]=>[.,[.,[[[.,[[[.,.],.],.]],.],.]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,2,1,6,7]=>[7,6,1,2,5,4,3,8]=>[2,3,8,7,4,5,6,1]=>[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,2,1,6,8]=>[8,6,1,2,5,4,3,7]=>[1,3,8,7,4,5,6,2]=>[.,[[.,.],[[[.,[.,[.,.]]],.],.]]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,2,1,7,8]=>[8,7,1,2,5,4,3,6]=>[1,2,8,7,4,5,6,3]=>[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,2,1,7,8]=>[8,7,1,2,6,5,3,4]=>[1,2,8,7,3,4,6,5]=>[.,[.,[[[.,[.,[[.,.],.]]],.],.]]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,1,7,8]=>[8,7,1,2,6,5,4,3]=>[1,2,8,7,3,4,5,6]=>[.,[.,[[[.,[.,[.,[.,.]]]],.],.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,3,1,4,5]=>[5,4,1,3,2,7,6,8]=>[4,5,8,6,7,2,3,1]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,2,3,1,4,5]=>[5,4,1,3,2,8,6,7]=>[4,5,8,6,7,1,3,2]=>[[.,[[.,.],.]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,1,4,5]=>[5,4,1,3,2,8,7,6]=>[4,5,8,6,7,1,2,3]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,3,1,4,7]=>[7,4,1,3,2,5,6,8]=>[2,5,8,6,7,4,3,1]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,2,3,1,4,8]=>[8,4,1,3,2,5,7,6]=>[1,5,8,6,7,4,2,3]=>[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,3,1,4,7]=>[7,4,1,3,2,6,5,8]=>[2,5,8,6,7,3,4,1]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,2,3,1,4,8]=>[8,4,1,3,2,6,5,7]=>[1,5,8,6,7,3,4,2]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,1,5,8]=>[8,5,1,3,2,4,6,7]=>[1,4,8,6,7,5,3,2]=>[.,[[[.,.],.],[[[.,.],[.,.]],.]]]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[6,7,4,2,3,1,5,8]=>[8,5,1,3,2,4,7,6]=>[1,4,8,6,7,5,2,3]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,2,3,1,6,7]=>[7,6,1,3,2,4,5,8]=>[2,3,8,6,7,5,4,1]=>[[.,.],[.,[[[[.,.],.],[.,.]],.]]]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,2,3,1,7,8]=>[8,7,1,3,2,4,5,6]=>[1,2,8,6,7,5,4,3]=>[.,[.,[[[[[.,.],.],.],[.,.]],.]]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[5,6,4,2,3,1,7,8]=>[8,7,1,3,2,4,6,5]=>[1,2,8,6,7,5,3,4]=>[.,[.,[[[[.,[.,.]],.],[.,.]],.]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,2,3,1,6,8]=>[8,6,1,3,2,5,4,7]=>[1,3,8,6,7,4,5,2]=>[.,[[.,.],[[[.,[.,.]],[.,.]],.]]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,3,1,7,8]=>[8,7,1,3,2,6,4,5]=>[1,2,8,6,7,3,5,4]=>[.,[.,[[[.,[[.,.],.]],[.,.]],.]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,4,1,5,6]=>[6,5,1,4,2,3,8,7]=>[3,4,8,5,7,6,1,2]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,4,1,5,7]=>[7,5,1,4,2,3,6,8]=>[2,4,8,5,7,6,3,1]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,4,1,5,8]=>[8,5,1,4,2,3,6,7]=>[1,4,8,5,7,6,3,2]=>[.,[[[.,.],.],[[.,[[.,.],.]],.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,4,1,5,8]=>[8,5,1,4,2,3,7,6]=>[1,4,8,5,7,6,2,3]=>[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,2,4,1,6,7]=>[7,6,1,4,2,3,5,8]=>[2,3,8,5,7,6,4,1]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,4,1,6,8]=>[8,6,1,4,2,3,5,7]=>[1,3,8,5,7,6,4,2]=>[.,[[.,.],[[[.,.],[[.,.],.]],.]]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,5,1,7,8]=>[8,7,1,5,2,3,4,6]=>[1,2,8,4,7,6,5,3]=>[.,[.,[[[.,.],[[[.,.],.],.]],.]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,1,7,8]=>[8,7,1,6,2,3,4,5]=>[1,2,8,3,7,6,5,4]=>[.,[.,[[.,[[[[.,.],.],.],.]],.]]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,6,1,7,8]=>[8,7,1,6,2,3,5,4]=>[1,2,8,3,7,6,4,5]=>[.,[.,[[.,[[[.,[.,.]],.],.]],.]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,2,5,1,6,7]=>[7,6,1,5,2,4,3,8]=>[2,3,8,4,7,5,6,1]=>[[.,.],[.,[[.,[[.,[.,.]],.]],.]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,6,1,7,8]=>[8,7,1,6,2,5,3,4]=>[1,2,8,3,7,4,6,5]=>[.,[.,[[.,[[.,[[.,.],.]],.]],.]]]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,6,1,7,8]=>[8,7,1,6,2,5,4,3]=>[1,2,8,3,7,4,5,6]=>[.,[.,[[.,[[.,[.,[.,.]]],.]],.]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,4,1,5,6]=>[6,5,1,4,3,2,7,8]=>[3,4,8,5,6,7,2,1]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,4,1,5,6]=>[6,5,1,4,3,2,8,7]=>[3,4,8,5,6,7,1,2]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,4,1,5,8]=>[8,5,1,4,3,2,7,6]=>[1,4,8,5,6,7,2,3]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,3,4,1,6,7]=>[7,6,1,4,3,2,5,8]=>[2,3,8,5,6,7,4,1]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,3,4,1,6,8]=>[8,6,1,4,3,2,5,7]=>[1,3,8,5,6,7,4,2]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,3,4,1,7,8]=>[8,7,1,4,3,2,5,6]=>[1,2,8,5,6,7,4,3]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,6,2,3,4,1,7,8]=>[8,7,1,4,3,2,6,5]=>[1,2,8,5,6,7,3,4]=>[.,[.,[[[.,[.,.]],[.,[.,.]]],.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,3,5,1,6,7]=>[7,6,1,5,3,2,4,8]=>[2,3,8,4,6,7,5,1]=>[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[7,4,2,3,5,1,6,8]=>[8,6,1,5,3,2,4,7]=>[1,3,8,4,6,7,5,2]=>[.,[[.,.],[[.,[[.,.],[.,.]]],.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,3,5,1,7,8]=>[8,7,1,5,3,2,4,6]=>[1,2,8,4,6,7,5,3]=>[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,6,1,7,8]=>[8,7,1,6,3,2,5,4]=>[1,2,8,3,6,7,4,5]=>[.,[.,[[.,[[.,[.,.]],[.,.]]],.]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,6,1,7,8]=>[8,7,1,6,4,2,3,5]=>[1,2,8,3,5,7,6,4]=>[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,6,1,7,8]=>[8,7,1,6,5,2,3,4]=>[1,2,8,3,4,7,6,5]=>[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,5,1,6,7]=>[7,6,1,5,4,3,2,8]=>[2,3,8,4,5,6,7,1]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,1,6,8]=>[8,6,1,5,4,3,2,7]=>[1,3,8,4,5,6,7,2]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,5,1,7,8]=>[8,7,1,5,4,3,2,6]=>[1,2,8,4,5,6,7,3]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,6,1,7,8]=>[8,7,1,6,4,3,2,5]=>[1,2,8,3,5,6,7,4]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,6,1,7,8]=>[8,7,1,6,5,3,2,4]=>[1,2,8,3,4,6,7,5]=>[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,6,1,7,8]=>[8,7,1,6,5,4,2,3]=>[1,2,8,3,4,5,7,6]=>[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,1,7,8]=>[8,7,1,6,5,4,3,2]=>[1,2,8,3,4,5,6,7]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8]=>[5,6,7,8,4,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,1,2,3,4]=>[4,3,2,1,5,6,8,7]=>[5,6,7,8,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,1,2,3,4]=>[4,3,2,1,5,7,6,8]=>[5,6,7,8,4,2,3,1]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,1,2,3,4]=>[4,3,2,1,5,8,6,7]=>[5,6,7,8,4,1,3,2]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,1,2,3,4]=>[4,3,2,1,5,8,7,6]=>[5,6,7,8,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,1,2,3,4]=>[4,3,2,1,6,5,7,8]=>[5,6,7,8,3,4,2,1]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7]=>[5,6,7,8,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,1,2,3,4]=>[4,3,2,1,7,5,6,8]=>[5,6,7,8,2,4,3,1]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,1,2,3,4]=>[4,3,2,1,8,5,6,7]=>[5,6,7,8,1,4,3,2]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,1,2,3,4]=>[4,3,2,1,8,5,7,6]=>[5,6,7,8,1,4,2,3]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,1,2,3,4]=>[4,3,2,1,7,6,5,8]=>[5,6,7,8,2,3,4,1]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,1,2,3,4]=>[4,3,2,1,8,6,5,7]=>[5,6,7,8,1,3,4,2]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,1,2,3,4]=>[4,3,2,1,8,7,5,6]=>[5,6,7,8,1,2,4,3]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5]=>[5,6,7,8,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,1,2,3,5]=>[5,3,2,1,4,7,6,8]=>[4,6,7,8,5,2,3,1]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,1,2,3,5]=>[5,3,2,1,4,8,6,7]=>[4,6,7,8,5,1,3,2]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,1,2,3,6]=>[6,3,2,1,4,5,8,7]=>[3,6,7,8,5,4,1,2]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,1,2,3,7]=>[7,3,2,1,4,5,6,8]=>[2,6,7,8,5,4,3,1]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,1,2,3,8]=>[8,3,2,1,4,5,6,7]=>[1,6,7,8,5,4,3,2]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,1,2,3,7]=>[7,3,2,1,4,6,5,8]=>[2,6,7,8,5,3,4,1]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,1,2,3,8]=>[8,3,2,1,4,6,5,7]=>[1,6,7,8,5,3,4,2]=>[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,1,2,3,8]=>[8,3,2,1,4,7,6,5]=>[1,6,7,8,5,2,3,4]=>[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,1,2,3,6]=>[6,3,2,1,5,4,7,8]=>[3,6,7,8,4,5,2,1]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,1,2,3,8]=>[8,3,2,1,5,4,6,7]=>[1,6,7,8,4,5,3,2]=>[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,1,2,3,8]=>[8,3,2,1,6,4,5,7]=>[1,6,7,8,3,5,4,2]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,1,2,3,8]=>[8,3,2,1,7,4,6,5]=>[1,6,7,8,2,5,3,4]=>[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,1,2,3,8]=>[8,3,2,1,6,5,4,7]=>[1,6,7,8,3,4,5,2]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,1,2,3,8]=>[8,3,2,1,7,5,4,6]=>[1,6,7,8,2,4,5,3]=>[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,1,2,3,8]=>[8,3,2,1,7,6,4,5]=>[1,6,7,8,2,3,5,4]=>[.,[[.,[.,[[.,.],.]]],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,1,2,3,8]=>[8,3,2,1,7,6,5,4]=>[1,6,7,8,2,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,1,2,4,5]=>[5,4,2,1,3,6,8,7]=>[4,5,7,8,6,3,1,2]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,1,2,4,6]=>[6,4,2,1,3,5,7,8]=>[3,5,7,8,6,4,2,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[6,7,5,3,1,2,4,8]=>[8,4,2,1,3,5,7,6]=>[1,5,7,8,6,4,2,3]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,1,2,4,7]=>[7,4,2,1,3,6,5,8]=>[2,5,7,8,6,3,4,1]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,1,2,4,8]=>[8,4,2,1,3,6,5,7]=>[1,5,7,8,6,3,4,2]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,1,2,4,8]=>[8,4,2,1,3,7,5,6]=>[1,5,7,8,6,2,4,3]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,1,2,4,8]=>[8,4,2,1,3,7,6,5]=>[1,5,7,8,6,2,3,4]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,1,2,5,7]=>[7,5,2,1,3,4,6,8]=>[2,4,7,8,6,5,3,1]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,1,2,5,8]=>[8,5,2,1,3,4,6,7]=>[1,4,7,8,6,5,3,2]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,1,2,6,8]=>[8,6,2,1,3,4,5,7]=>[1,3,7,8,6,5,4,2]=>[.,[[.,.],[[[[.,.],.],.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,1,2,7,8]=>[8,7,2,1,3,4,5,6]=>[1,2,7,8,6,5,4,3]=>[.,[.,[[[[[.,.],.],.],.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,1,2,7,8]=>[8,7,2,1,3,4,6,5]=>[1,2,7,8,6,5,3,4]=>[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,1,2,7,8]=>[8,7,2,1,3,5,4,6]=>[1,2,7,8,6,4,5,3]=>[.,[.,[[[[.,.],[.,.]],.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,1,2,7,8]=>[8,7,2,1,3,6,4,5]=>[1,2,7,8,6,3,5,4]=>[.,[.,[[[.,[[.,.],.]],.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,1,2,7,8]=>[8,7,2,1,3,6,5,4]=>[1,2,7,8,6,3,4,5]=>[.,[.,[[[.,[.,[.,.]]],.],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,1,2,5,6]=>[6,5,2,1,4,3,8,7]=>[3,4,7,8,5,6,1,2]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,1,2,5,7]=>[7,5,2,1,4,3,6,8]=>[2,4,7,8,5,6,3,1]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,1,2,5,8]=>[8,5,2,1,4,3,6,7]=>[1,4,7,8,5,6,3,2]=>[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,1,2,5,8]=>[8,5,2,1,4,3,7,6]=>[1,4,7,8,5,6,2,3]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,1,2,6,8]=>[8,6,2,1,4,3,5,7]=>[1,3,7,8,5,6,4,2]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,1,2,7,8]=>[8,7,2,1,4,3,5,6]=>[1,2,7,8,5,6,4,3]=>[.,[.,[[[[.,.],.],[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,1,2,7,8]=>[8,7,2,1,4,3,6,5]=>[1,2,7,8,5,6,3,4]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,1,2,6,8]=>[8,6,2,1,5,3,4,7]=>[1,3,7,8,4,6,5,2]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,1,2,7,8]=>[8,7,2,1,6,3,4,5]=>[1,2,7,8,3,6,5,4]=>[.,[.,[[.,[[[.,.],.],.]],[.,.]]]]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,1,2,7,8]=>[8,7,2,1,6,3,5,4]=>[1,2,7,8,3,6,4,5]=>[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,1,2,6,8]=>[8,6,2,1,5,4,3,7]=>[1,3,7,8,4,5,6,2]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,1,2,7,8]=>[8,7,2,1,5,4,3,6]=>[1,2,7,8,4,5,6,3]=>[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,1,2,7,8]=>[8,7,2,1,6,4,3,5]=>[1,2,7,8,3,5,6,4]=>[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,1,2,7,8]=>[8,7,2,1,6,5,3,4]=>[1,2,7,8,3,4,6,5]=>[.,[.,[[.,[.,[[.,.],.]]],[.,.]]]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,1,2,7,8]=>[8,7,2,1,6,5,4,3]=>[1,2,7,8,3,4,5,6]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7,8]=>[4,5,6,8,7,3,2,1]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,2,1,3,4,5]=>[5,4,3,1,2,6,8,7]=>[4,5,6,8,7,3,1,2]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,2,1,3,4,6]=>[6,4,3,1,2,5,7,8]=>[3,5,6,8,7,4,2,1]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,2,1,3,4,6]=>[6,4,3,1,2,5,8,7]=>[3,5,6,8,7,4,1,2]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,2,1,3,4,8]=>[8,4,3,1,2,5,7,6]=>[1,5,6,8,7,4,2,3]=>[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,1,3,4,7]=>[7,4,3,1,2,6,5,8]=>[2,5,6,8,7,3,4,1]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,1,3,4,8]=>[8,4,3,1,2,7,6,5]=>[1,5,6,8,7,2,3,4]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,1,3,5,6]=>[6,5,3,1,2,4,8,7]=>[3,4,6,8,7,5,1,2]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,1,3,5,7]=>[7,5,3,1,2,4,6,8]=>[2,4,6,8,7,5,3,1]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,1,3,5,8]=>[8,5,3,1,2,4,6,7]=>[1,4,6,8,7,5,3,2]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[7,5,4,2,1,3,6,8]=>[8,6,3,1,2,4,5,7]=>[1,3,6,8,7,5,4,2]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[5,6,4,2,1,3,7,8]=>[8,7,3,1,2,4,6,5]=>[1,2,6,8,7,5,3,4]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,2,1,3,6,8]=>[8,6,3,1,2,5,4,7]=>[1,3,6,8,7,4,5,2]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,1,3,7,8]=>[8,7,3,1,2,6,4,5]=>[1,2,6,8,7,3,5,4]=>[.,[.,[[.,[[.,.],.]],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[4,5,6,2,1,3,7,8]=>[8,7,3,1,2,6,5,4]=>[1,2,6,8,7,3,4,5]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,1,4,5,6]=>[6,5,4,1,2,3,8,7]=>[3,4,5,8,7,6,1,2]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,1,4,5,8]=>[8,5,4,1,2,3,6,7]=>[1,4,5,8,7,6,3,2]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,2,1,4,6,7]=>[7,6,4,1,2,3,5,8]=>[2,3,5,8,7,6,4,1]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,1,4,6,8]=>[8,6,4,1,2,3,5,7]=>[1,3,5,8,7,6,4,2]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[6,5,3,2,1,4,7,8]=>[8,7,4,1,2,3,5,6]=>[1,2,5,8,7,6,4,3]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,3,2,1,4,7,8]=>[8,7,4,1,2,3,6,5]=>[1,2,5,8,7,6,3,4]=>[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[8,4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4,8]=>[2,3,4,8,7,6,5,1]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,2,1,5,6,8]=>[8,6,5,1,2,3,4,7]=>[1,3,4,8,7,6,5,2]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,1,5,7,8]=>[8,7,5,1,2,3,4,6]=>[1,2,4,8,7,6,5,3]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,6,7,8]=>[8,7,6,1,2,3,4,5]=>[1,2,3,8,7,6,5,4]=>[.,[.,[.,[[[[[.,.],.],.],.],.]]]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,1,6,7,8]=>[8,7,6,1,2,3,5,4]=>[1,2,3,8,7,6,4,5]=>[.,[.,[.,[[[[.,[.,.]],.],.],.]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,2,1,5,6,7]=>[7,6,5,1,2,4,3,8]=>[2,3,4,8,7,5,6,1]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,2,1,6,7,8]=>[8,7,6,1,2,4,3,5]=>[1,2,3,8,7,5,6,4]=>[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,1,6,7,8]=>[8,7,6,1,2,5,3,4]=>[1,2,3,8,7,4,6,5]=>[.,[.,[.,[[[.,[[.,.],.]],.],.]]]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,1,6,7,8]=>[8,7,6,1,2,5,4,3]=>[1,2,3,8,7,4,5,6]=>[.,[.,[.,[[[.,[.,[.,.]]],.],.]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,1,4,5,6]=>[6,5,4,1,3,2,7,8]=>[3,4,5,8,6,7,2,1]=>[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,1,4,5,6]=>[6,5,4,1,3,2,8,7]=>[3,4,5,8,6,7,1,2]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,1,4,5,8]=>[8,5,4,1,3,2,6,7]=>[1,4,5,8,6,7,3,2]=>[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,3,1,4,6,7]=>[7,6,4,1,3,2,5,8]=>[2,3,5,8,6,7,4,1]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,3,1,4,7,8]=>[8,7,4,1,3,2,5,6]=>[1,2,5,8,6,7,4,3]=>[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[5,6,2,3,1,4,7,8]=>[8,7,4,1,3,2,6,5]=>[1,2,5,8,6,7,3,4]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,3,1,5,6,7]=>[7,6,5,1,3,2,4,8]=>[2,3,4,8,6,7,5,1]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,1,6,7,8]=>[8,7,6,1,3,2,4,5]=>[1,2,3,8,6,7,5,4]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,1,6,7,8]=>[8,7,6,1,3,2,5,4]=>[1,2,3,8,6,7,4,5]=>[.,[.,[.,[[[.,[.,.]],[.,.]],.]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,4,1,5,6,7]=>[7,6,5,1,4,2,3,8]=>[2,3,4,8,5,7,6,1]=>[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,1,6,7,8]=>[8,7,6,1,4,2,3,5]=>[1,2,3,8,5,7,6,4]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,1,6,7,8]=>[8,7,6,1,5,2,3,4]=>[1,2,3,8,4,7,6,5]=>[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,1,6,7,8]=>[8,7,6,1,5,2,4,3]=>[1,2,3,8,4,7,5,6]=>[.,[.,[.,[[.,[[.,[.,.]],.]],.]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,1,5,6,7]=>[7,6,5,1,4,3,2,8]=>[2,3,4,8,5,6,7,1]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,1,5,6,8]=>[8,6,5,1,4,3,2,7]=>[1,3,4,8,5,6,7,2]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,1,5,7,8]=>[8,7,5,1,4,3,2,6]=>[1,2,4,8,5,6,7,3]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,1,6,7,8]=>[8,7,6,1,4,3,2,5]=>[1,2,3,8,5,6,7,4]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,1,6,7,8]=>[8,7,6,1,5,3,2,4]=>[1,2,3,8,4,6,7,5]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,1,6,7,8]=>[8,7,6,1,5,4,2,3]=>[1,2,3,8,4,5,7,6]=>[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>[8,7,6,1,5,4,3,2]=>[1,2,3,8,4,5,6,7]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8]=>[4,5,6,7,8,3,2,1]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,1,2,3,4,5]=>[5,4,3,2,1,6,8,7]=>[4,5,6,7,8,3,1,2]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,1,2,3,4,5]=>[5,4,3,2,1,7,6,8]=>[4,5,6,7,8,2,3,1]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,1,2,3,4,5]=>[5,4,3,2,1,8,6,7]=>[4,5,6,7,8,1,3,2]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,1,2,3,4,5]=>[5,4,3,2,1,8,7,6]=>[4,5,6,7,8,1,2,3]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,1,2,3,4,6]=>[6,4,3,2,1,5,7,8]=>[3,5,6,7,8,4,2,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,1,2,3,4,6]=>[6,4,3,2,1,5,8,7]=>[3,5,6,7,8,4,1,2]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,1,2,3,4,7]=>[7,4,3,2,1,5,6,8]=>[2,5,6,7,8,4,3,1]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,1,2,3,4,8]=>[8,4,3,2,1,5,6,7]=>[1,5,6,7,8,4,3,2]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,1,2,3,4,8]=>[8,4,3,2,1,5,7,6]=>[1,5,6,7,8,4,2,3]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,1,2,3,4,7]=>[7,4,3,2,1,6,5,8]=>[2,5,6,7,8,3,4,1]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,1,2,3,4,8]=>[8,4,3,2,1,6,5,7]=>[1,5,6,7,8,3,4,2]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,1,2,3,4,8]=>[8,4,3,2,1,7,5,6]=>[1,5,6,7,8,2,4,3]=>[.,[[.,[[.,.],.]],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,1,2,3,4,8]=>[8,4,3,2,1,7,6,5]=>[1,5,6,7,8,2,3,4]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[8,7,4,1,2,3,5,6]=>[6,5,3,2,1,4,7,8]=>[3,4,6,7,8,5,2,1]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,1,2,3,5,6]=>[6,5,3,2,1,4,8,7]=>[3,4,6,7,8,5,1,2]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,1,2,3,5,7]=>[7,5,3,2,1,4,6,8]=>[2,4,6,7,8,5,3,1]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,1,2,3,5,8]=>[8,5,3,2,1,4,6,7]=>[1,4,6,7,8,5,3,2]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,1,2,3,6,7]=>[7,6,3,2,1,4,5,8]=>[2,3,6,7,8,5,4,1]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[7,5,4,1,2,3,6,8]=>[8,6,3,2,1,4,5,7]=>[1,3,6,7,8,5,4,2]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,1,2,3,7,8]=>[8,7,3,2,1,4,5,6]=>[1,2,6,7,8,5,4,3]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[5,6,4,1,2,3,7,8]=>[8,7,3,2,1,4,6,5]=>[1,2,6,7,8,5,3,4]=>[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[6,4,5,1,2,3,7,8]=>[8,7,3,2,1,5,4,6]=>[1,2,6,7,8,4,5,3]=>[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,1,2,3,7,8]=>[8,7,3,2,1,6,4,5]=>[1,2,6,7,8,3,5,4]=>[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[4,5,6,1,2,3,7,8]=>[8,7,3,2,1,6,5,4]=>[1,2,6,7,8,3,4,5]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[8,7,3,1,2,4,5,6]=>[6,5,4,2,1,3,7,8]=>[3,4,5,7,8,6,2,1]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,1,2,4,5,6]=>[6,5,4,2,1,3,8,7]=>[3,4,5,7,8,6,1,2]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,1,2,4,5,7]=>[7,5,4,2,1,3,6,8]=>[2,4,5,7,8,6,3,1]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,1,2,4,6,7]=>[7,6,4,2,1,3,5,8]=>[2,3,5,7,8,6,4,1]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,1,2,4,6,8]=>[8,6,4,2,1,3,5,7]=>[1,3,5,7,8,6,4,2]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[5,6,3,1,2,4,7,8]=>[8,7,4,2,1,3,6,5]=>[1,2,5,7,8,6,3,4]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[8,4,3,1,2,5,6,7]=>[7,6,5,2,1,3,4,8]=>[2,3,4,7,8,6,5,1]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,1,2,5,7,8]=>[8,7,5,2,1,3,4,6]=>[1,2,4,7,8,6,5,3]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,1,2,6,7,8]=>[8,7,6,2,1,3,4,5]=>[1,2,3,7,8,6,5,4]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,1,2,6,7,8]=>[8,7,6,2,1,3,5,4]=>[1,2,3,7,8,6,4,5]=>[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,1,2,5,6,7]=>[7,6,5,2,1,4,3,8]=>[2,3,4,7,8,5,6,1]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[6,3,4,1,2,5,7,8]=>[8,7,5,2,1,4,3,6]=>[1,2,4,7,8,5,6,3]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,1,2,6,7,8]=>[8,7,6,2,1,4,3,5]=>[1,2,3,7,8,5,6,4]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,1,2,6,7,8]=>[8,7,6,2,1,5,3,4]=>[1,2,3,7,8,4,6,5]=>[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,1,2,6,7,8]=>[8,7,6,2,1,5,4,3]=>[1,2,3,7,8,4,5,6]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7,8]=>[3,4,5,6,8,7,2,1]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,1,3,4,5,6]=>[6,5,4,3,1,2,8,7]=>[3,4,5,6,8,7,1,2]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,1,3,4,5,8]=>[8,5,4,3,1,2,7,6]=>[1,4,5,6,8,7,2,3]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,1,3,4,6,7]=>[7,6,4,3,1,2,5,8]=>[2,3,5,6,8,7,4,1]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,1,3,4,6,8]=>[8,6,4,3,1,2,5,7]=>[1,3,5,6,8,7,4,2]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,1,3,4,7,8]=>[8,7,4,3,1,2,5,6]=>[1,2,5,6,8,7,4,3]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[5,6,2,1,3,4,7,8]=>[8,7,4,3,1,2,6,5]=>[1,2,5,6,8,7,3,4]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,1,3,5,6,7]=>[7,6,5,3,1,2,4,8]=>[2,3,4,6,8,7,5,1]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,1,3,5,7,8]=>[8,7,5,3,1,2,4,6]=>[1,2,4,6,8,7,5,3]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,1,3,6,7,8]=>[8,7,6,3,1,2,4,5]=>[1,2,3,6,8,7,5,4]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,1,3,6,7,8]=>[8,7,6,3,1,2,5,4]=>[1,2,3,6,8,7,4,5]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3,8]=>[2,3,4,5,8,7,6,1]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,1,4,5,6,8]=>[8,6,5,4,1,2,3,7]=>[1,3,4,5,8,7,6,2]=>[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[6,3,2,1,4,5,7,8]=>[8,7,5,4,1,2,3,6]=>[1,2,4,5,8,7,6,3]=>[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,1,4,6,7,8]=>[8,7,6,4,1,2,3,5]=>[1,2,3,5,8,7,6,4]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1,5,6,7,8]=>[8,7,6,5,1,2,3,4]=>[1,2,3,4,8,7,6,5]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,1,5,6,7,8]=>[8,7,6,5,1,2,4,3]=>[1,2,3,4,8,7,5,6]=>[.,[.,[.,[.,[[[.,[.,.]],.],.]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,1,4,5,6,7]=>[7,6,5,4,1,3,2,8]=>[2,3,4,5,8,6,7,1]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,1,4,5,6,8]=>[8,6,5,4,1,3,2,7]=>[1,3,4,5,8,6,7,2]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,1,4,5,7,8]=>[8,7,5,4,1,3,2,6]=>[1,2,4,5,8,6,7,3]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,1,4,6,7,8]=>[8,7,6,4,1,3,2,5]=>[1,2,3,5,8,6,7,4]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,1,5,6,7,8]=>[8,7,6,5,1,3,2,4]=>[1,2,3,4,8,6,7,5]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,1,5,6,7,8]=>[8,7,6,5,1,4,2,3]=>[1,2,3,4,8,5,7,6]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8]=>[8,7,6,5,1,4,3,2]=>[1,2,3,4,8,5,6,7]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8]=>[3,4,5,6,7,8,2,1]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7]=>[3,4,5,6,7,8,1,2]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8]=>[2,4,5,6,7,8,3,1]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[7,6,1,2,3,4,5,8]=>[8,5,4,3,2,1,6,7]=>[1,4,5,6,7,8,3,2]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,7,1,2,3,4,5,8]=>[8,5,4,3,2,1,7,6]=>[1,4,5,6,7,8,2,3]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[8,5,1,2,3,4,6,7]=>[7,6,4,3,2,1,5,8]=>[2,3,5,6,7,8,4,1]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[7,5,1,2,3,4,6,8]=>[8,6,4,3,2,1,5,7]=>[1,3,5,6,7,8,4,2]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,5,1,2,3,4,7,8]=>[8,7,4,3,2,1,5,6]=>[1,2,5,6,7,8,4,3]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[5,6,1,2,3,4,7,8]=>[8,7,4,3,2,1,6,5]=>[1,2,5,6,7,8,3,4]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[8,4,1,2,3,5,6,7]=>[7,6,5,3,2,1,4,8]=>[2,3,4,6,7,8,5,1]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[7,4,1,2,3,5,6,8]=>[8,6,5,3,2,1,4,7]=>[1,3,4,6,7,8,5,2]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[6,4,1,2,3,5,7,8]=>[8,7,5,3,2,1,4,6]=>[1,2,4,6,7,8,5,3]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[5,4,1,2,3,6,7,8]=>[8,7,6,3,2,1,4,5]=>[1,2,3,6,7,8,5,4]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[4,5,1,2,3,6,7,8]=>[8,7,6,3,2,1,5,4]=>[1,2,3,6,7,8,4,5]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[8,3,1,2,4,5,6,7]=>[7,6,5,4,2,1,3,8]=>[2,3,4,5,7,8,6,1]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[7,3,1,2,4,5,6,8]=>[8,6,5,4,2,1,3,7]=>[1,3,4,5,7,8,6,2]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[6,3,1,2,4,5,7,8]=>[8,7,5,4,2,1,3,6]=>[1,2,4,5,7,8,6,3]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[5,3,1,2,4,6,7,8]=>[8,7,6,4,2,1,3,5]=>[1,2,3,5,7,8,6,4]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[4,3,1,2,5,6,7,8]=>[8,7,6,5,2,1,3,4]=>[1,2,3,4,7,8,6,5]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8]=>[8,7,6,5,2,1,4,3]=>[1,2,3,4,7,8,5,6]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[8,2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2,8]=>[2,3,4,5,6,8,7,1]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[7,2,1,3,4,5,6,8]=>[8,6,5,4,3,1,2,7]=>[1,3,4,5,6,8,7,2]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[6,2,1,3,4,5,7,8]=>[8,7,5,4,3,1,2,6]=>[1,2,4,5,6,8,7,3]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[5,2,1,3,4,6,7,8]=>[8,7,6,4,3,1,2,5]=>[1,2,3,5,6,8,7,4]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[4,2,1,3,5,6,7,8]=>[8,7,6,5,3,1,2,4]=>[1,2,3,4,6,8,7,5]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8]=>[8,7,6,5,4,1,2,3]=>[1,2,3,4,5,8,7,6]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8]=>[8,7,6,5,4,1,3,2]=>[1,2,3,4,5,8,6,7]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,8,1]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,2,3,4,5,6,8]=>[8,6,5,4,3,2,1,7]=>[1,3,4,5,6,7,8,2]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,2,3,4,5,7,8]=>[8,7,5,4,3,2,1,6]=>[1,2,4,5,6,7,8,3]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,2,3,4,6,7,8]=>[8,7,6,4,3,2,1,5]=>[1,2,3,5,6,7,8,4]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,2,3,5,6,7,8]=>[8,7,6,5,3,2,1,4]=>[1,2,3,4,6,7,8,5]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8]=>[8,7,6,5,4,2,1,3]=>[1,2,3,4,5,7,8,6]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]=>[8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,8,7]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1,9]=>[2,3,4,5,6,7,8,9,1]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1]=>[1,9,8,7,6,5,4,3,2]=>[9,1,2,3,4,5,6,7,8]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[10,1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1,10]=>[2,3,4,5,6,7,8,9,10,1]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[9,2,1,3,4,5,6,7,8]=>[8,7,6,5,4,3,1,2,9]=>[2,3,4,5,6,7,9,8,1]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,9,1]=>[1,9,8,7,6,5,4,2,3]=>[9,1,2,3,4,5,6,8,7]=>[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,1]=>[1,10,9,8,7,6,5,4,3,2]=>[10,1,2,3,4,5,6,7,8,9]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[11,1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1,11]=>[2,3,4,5,6,7,8,9,10,11,1]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,1,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,1,2,10]=>[2,3,4,5,6,7,8,10,9,1]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[9,3,1,2,4,5,6,7,8]=>[8,7,6,5,4,2,1,3,9]=>[2,3,4,5,6,8,9,7,1]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,1,4,5,6,7,8]=>[8,7,6,5,4,1,3,2,9]=>[2,3,4,5,6,9,7,8,1]=>[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[4,2,3,5,6,7,8,9,1]=>[1,9,8,7,6,5,3,2,4]=>[9,1,2,3,4,5,7,8,6]=>[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[3,4,2,5,6,7,8,9,1]=>[1,9,8,7,6,5,2,4,3]=>[9,1,2,3,4,5,8,6,7]=>[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,9,10,1]=>[1,10,9,8,7,6,5,4,2,3]=>[10,1,2,3,4,5,6,7,9,8]=>[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>[1,11,10,9,8,7,6,5,4,3,2]=>[11,1,2,3,4,5,6,7,8,9,10]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]=>[12,1,2,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[2,3,4,5,6,7,8,9,10,11,12,1]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]=>[11,2,1,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,1,2,11]=>[2,3,4,5,6,7,8,9,11,10,1]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,1,4,5,6,7,8,9]=>[9,8,7,6,5,4,1,3,2,10]=>[2,3,4,5,6,7,10,8,9,1]=>[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[9,4,1,2,3,5,6,7,8]=>[8,7,6,5,3,2,1,4,9]=>[2,3,4,5,7,8,9,6,1]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[9,3,2,1,4,5,6,7,8]=>[8,7,6,5,4,1,2,3,9]=>[2,3,4,5,6,9,8,7,1]=>[[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,4,1,5,6,7,8]=>[8,7,6,5,1,4,3,2,9]=>[2,3,4,5,9,6,7,8,1]=>[[.,.],[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,5,6,7,8,9,1]=>[1,9,8,7,6,5,2,3,4]=>[9,1,2,3,4,5,8,7,6]=>[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,2,6,7,8,9,1]=>[1,9,8,7,6,2,5,4,3]=>[9,1,2,3,4,8,5,6,7]=>[[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]],.]
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[3,4,2,5,6,7,8,9,10,1]=>[1,10,9,8,7,6,5,2,4,3]=>[10,1,2,3,4,5,6,9,7,8]=>[[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]],.]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[10,3,2,1,4,5,6,7,8,9]=>[9,8,7,6,5,4,1,2,3,10]=>[2,3,4,5,6,7,10,9,8,1]=>[[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,4,5,1,6,7,8]=>[8,7,6,1,5,4,3,2,9]=>[2,3,4,9,5,6,7,8,1]=>[[.,.],[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[4,5,2,3,6,7,8,9,1]=>[1,9,8,7,6,3,2,5,4]=>[9,1,2,3,4,7,8,5,6]=>[[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]],.]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[4,3,2,5,6,7,8,9,10,1]=>[1,10,9,8,7,6,5,2,3,4]=>[10,1,2,3,4,5,6,9,8,7]=>[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.]
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,2,6,7,8,9,10,1]=>[1,10,9,8,7,6,2,5,4,3]=>[10,1,2,3,4,5,9,6,7,8]=>[[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]],.]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,4,5,1,6,7,8,9]=>[9,8,7,6,1,5,4,3,2,10]=>[2,3,4,5,10,6,7,8,9,1]=>[[.,.],[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]=>[9,4,3,1,2,5,6,7,8]=>[8,7,6,5,2,1,3,4,9]=>[2,3,4,5,8,9,7,6,1]=>[[.,.],[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,4,5,6,1,7,8]=>[8,7,1,6,5,4,3,2,9]=>[2,3,9,4,5,6,7,8,1]=>[[.,.],[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[6,2,3,4,5,7,8,9,10,1]=>[1,10,9,8,7,5,4,3,2,6]=>[10,1,2,3,4,6,7,8,9,5]=>[[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]],.]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[5,4,2,3,6,7,8,9,1]=>[1,9,8,7,6,3,2,4,5]=>[9,1,2,3,4,7,8,6,5]=>[[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]],.]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,2,8,9,1]=>[1,9,8,2,7,6,5,4,3]=>[9,1,2,8,3,4,5,6,7]=>[[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]],.]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,4,5,6,1,7,8,9]=>[9,8,7,1,6,5,4,3,2,10]=>[2,3,4,10,5,6,7,8,9,1]=>[[.,.],[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[9,7,1,2,3,4,5,6,8]=>[8,6,5,4,3,2,1,7,9]=>[2,4,5,6,7,8,9,3,1]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,4,5,6,7,1,8]=>[8,1,7,6,5,4,3,2,9]=>[2,9,3,4,5,6,7,8,1]=>[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[8,9,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,9,8]=>[3,4,5,6,7,8,9,1,2]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[8,2,3,4,5,6,7,9,1]=>[1,9,7,6,5,4,3,2,8]=>[9,1,3,4,5,6,7,8,2]=>[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,1,2]=>[2,1,9,8,7,6,5,4,3]=>[8,9,1,2,3,4,5,6,7]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,2,9,1]=>[1,9,2,8,7,6,5,4,3]=>[9,1,8,2,3,4,5,6,7]=>[[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]],.]
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,2,8,9,10,1]=>[1,10,9,8,2,7,6,5,4,3]=>[10,1,2,3,9,4,5,6,7,8]=>[[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[9,8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8,9]=>[3,4,5,6,7,8,9,2,1]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,4,5,6,7,8,1]=>[1,8,7,6,5,4,3,2,9]=>[9,2,3,4,5,6,7,8,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,2,1]=>[1,2,9,8,7,6,5,4,3]=>[9,8,1,2,3,4,5,6,7]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,2,9,10,1]=>[1,10,9,2,8,7,6,5,4,3]=>[10,1,2,9,3,4,5,6,7,8]=>[[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]=>[10,8,1,2,3,4,5,6,7,9]=>[9,7,6,5,4,3,2,1,8,10]=>[2,4,5,6,7,8,9,10,3,1]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,4,5,6,7,8,1,9]=>[9,1,8,7,6,5,4,3,2,10]=>[2,10,3,4,5,6,7,8,9,1]=>[[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[9,10,1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1,10,9]=>[3,4,5,6,7,8,9,10,1,2]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[9,2,3,4,5,6,7,8,10,1]=>[1,10,8,7,6,5,4,3,2,9]=>[10,1,3,4,5,6,7,8,9,2]=>[[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,1,2]=>[2,1,10,9,8,7,6,5,4,3]=>[9,10,1,2,3,4,5,6,7,8]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[10,9,1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1,9,10]=>[3,4,5,6,7,8,9,10,2,1]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,4,5,6,7,8,9,1]=>[1,9,8,7,6,5,4,3,2,10]=>[10,2,3,4,5,6,7,8,9,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,2,1]=>[1,2,10,9,8,7,6,5,4,3]=>[10,9,1,2,3,4,5,6,7,8]=>[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]
[]=>[]=>[]=>[]=>.
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,1,9]=>[9,1,2,3,4,5,6,7,8]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[7,8,6,5,4,3,2,1,9]=>[9,1,2,3,4,5,6,8,7]=>[1,9,8,7,6,5,4,2,3]=>[.,[[[[[[[.,[.,.]],.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[7,6,8,5,4,3,2,1,9]=>[9,1,2,3,4,5,8,6,7]=>[1,9,8,7,6,5,2,4,3]=>[.,[[[[[[.,[[.,.],.]],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[6,7,8,5,4,3,2,1,9]=>[9,1,2,3,4,5,8,7,6]=>[1,9,8,7,6,5,2,3,4]=>[.,[[[[[[.,[.,[.,.]]],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[7,6,5,8,4,3,2,1,9]=>[9,1,2,3,4,8,5,6,7]=>[1,9,8,7,6,2,5,4,3]=>[.,[[[[[.,[[[.,.],.],.]],.],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[8,7,6,4,5,3,2,1,9]=>[9,1,2,3,5,4,6,7,8]=>[1,9,8,7,5,6,4,3,2]=>[.,[[[[[[[.,.],.],.],[.,.]],.],.],.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[8,7,6,4,3,5,2,1,9]=>[9,1,2,5,3,4,6,7,8]=>[1,9,8,5,7,6,4,3,2]=>[.,[[[[[[.,.],.],.],[[.,.],.]],.],.]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,8,2,1,9]=>[9,1,2,8,3,4,5,6,7]=>[1,9,8,2,7,6,5,4,3]=>[.,[[[.,[[[[[.,.],.],.],.],.]],.],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,2,8,1,9]=>[9,1,8,2,3,4,5,6,7]=>[1,9,2,8,7,6,5,4,3]=>[.,[[.,[[[[[[.,.],.],.],.],.],.]],.]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[8,2,3,4,5,6,7,1,9]=>[9,1,7,6,5,4,3,2,8]=>[1,9,3,4,5,6,7,8,2]=>[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,1,9]=>[9,1,8,7,6,5,4,2,3]=>[1,9,2,3,4,5,6,8,7]=>[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1,9]=>[9,1,8,7,6,5,4,3,2]=>[1,9,2,3,4,5,6,7,8]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,1,2,9]=>[9,2,1,3,4,5,6,7,8]=>[1,8,9,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[7,8,5,6,3,4,1,2,9]=>[9,2,1,4,3,6,5,8,7]=>[1,8,9,6,7,4,5,2,3]=>[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2,9]=>[9,2,1,8,7,6,5,4,3]=>[1,8,9,2,3,4,5,6,7]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,2,1,3,9]=>[9,3,1,2,4,5,6,7,8]=>[1,7,9,8,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[8,6,5,4,3,2,1,7,9]=>[9,7,1,2,3,4,5,6,8]=>[1,3,9,8,7,6,5,4,2]=>[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,2,1,8,9]=>[9,8,1,2,3,4,5,6,7]=>[1,2,9,8,7,6,5,4,3]=>[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[8,2,3,4,5,6,1,7,9]=>[9,7,1,6,5,4,3,2,8]=>[1,3,9,4,5,6,7,8,2]=>[.,[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[7,2,3,4,5,6,1,8,9]=>[9,8,1,6,5,4,3,2,7]=>[1,2,9,4,5,6,7,8,3]=>[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8,9]=>[9,8,1,7,6,5,4,3,2]=>[1,2,9,3,4,5,6,7,8]=>[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,1,2,3,9]=>[9,3,2,1,4,5,6,7,8]=>[1,7,8,9,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,1,2,3,9]=>[9,3,2,1,8,7,6,5,4]=>[1,7,8,9,2,3,4,5,6]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[8,6,4,3,2,1,5,7,9]=>[9,7,5,1,2,3,4,6,8]=>[1,3,5,9,8,7,6,4,2]=>[.,[[.,.],[[.,.],[[[[.,.],.],.],.]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[7,5,4,3,2,1,6,8,9]=>[9,8,6,1,2,3,4,5,7]=>[1,2,4,9,8,7,6,5,3]=>[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,1,7,8,9]=>[9,8,7,1,2,3,4,5,6]=>[1,2,3,9,8,7,6,5,4]=>[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[6,2,3,4,5,1,7,8,9]=>[9,8,7,1,5,4,3,2,6]=>[1,2,3,9,5,6,7,8,4]=>[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,1,7,8,9]=>[9,8,7,1,6,5,4,3,2]=>[1,2,3,9,4,5,6,7,8]=>[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,1,2,3,4,9]=>[9,4,3,2,1,5,6,7,8]=>[1,6,7,8,9,5,4,3,2]=>[.,[[[[[.,.],.],.],.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,1,2,3,4,9]=>[9,4,3,2,1,8,7,6,5]=>[1,6,7,8,9,2,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0,0]=>[5,6,3,4,1,2,7,8,9]=>[9,8,7,2,1,4,3,6,5]=>[1,2,3,8,9,6,7,4,5]=>[.,[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[8,6,4,2,1,3,5,7,9]=>[9,7,5,3,1,2,4,6,8]=>[1,3,5,7,9,8,6,4,2]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[6,4,3,2,1,5,7,8,9]=>[9,8,7,5,1,2,3,4,6]=>[1,2,3,5,9,8,7,6,4]=>[.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,1,6,7,8,9]=>[9,8,7,6,1,2,3,4,5]=>[1,2,3,4,9,8,7,6,5]=>[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[5,2,3,4,1,6,7,8,9]=>[9,8,7,6,1,4,3,2,5]=>[1,2,3,4,9,6,7,8,5]=>[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,4,5,1,6,7,8,9]=>[9,8,7,6,1,5,4,2,3]=>[1,2,3,4,9,5,6,8,7]=>[.,[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9]=>[9,8,7,6,1,5,4,3,2]=>[1,2,3,4,9,5,6,7,8]=>[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[8,7,6,1,2,3,4,5,9]=>[9,5,4,3,2,1,6,7,8]=>[1,5,6,7,8,9,4,3,2]=>[.,[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,0]=>[6,7,8,1,2,3,4,5,9]=>[9,5,4,3,2,1,8,7,6]=>[1,5,6,7,8,9,2,3,4]=>[.,[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[4,5,6,1,2,3,7,8,9]=>[9,8,7,3,2,1,6,5,4]=>[1,2,3,7,8,9,4,5,6]=>[.,[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[7,5,3,1,2,4,6,8,9]=>[9,8,6,4,2,1,3,5,7]=>[1,2,4,6,8,9,7,5,3]=>[.,[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,1,2,6,7,8,9]=>[9,8,7,6,2,1,5,4,3]=>[1,2,3,4,8,9,5,6,7]=>[.,[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[5,3,2,1,4,6,7,8,9]=>[9,8,7,6,4,1,2,3,5]=>[1,2,3,4,6,9,8,7,5]=>[.,[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1,5,6,7,8,9]=>[9,8,7,6,5,1,2,3,4]=>[1,2,3,4,5,9,8,7,6]=>[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[4,2,3,1,5,6,7,8,9]=>[9,8,7,6,5,1,3,2,4]=>[1,2,3,4,5,9,7,8,6]=>[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,4,1,5,6,7,8,9]=>[9,8,7,6,5,1,4,2,3]=>[1,2,3,4,5,9,6,8,7]=>[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9]=>[9,8,7,6,5,1,4,3,2]=>[1,2,3,4,5,9,6,7,8]=>[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[8,7,1,2,3,4,5,6,9]=>[9,6,5,4,3,2,1,7,8]=>[1,4,5,6,7,8,9,3,2]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[7,8,1,2,3,4,5,6,9]=>[9,6,5,4,3,2,1,8,7]=>[1,4,5,6,7,8,9,2,3]=>[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[4,3,1,2,5,6,7,8,9]=>[9,8,7,6,5,2,1,3,4]=>[1,2,3,4,5,8,9,7,6]=>[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8,9]=>[9,8,7,6,5,2,1,4,3]=>[1,2,3,4,5,8,9,6,7]=>[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[8,2,1,3,4,5,6,7,9]=>[9,7,6,5,4,3,1,2,8]=>[1,3,4,5,6,7,9,8,2]=>[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[4,2,1,3,5,6,7,8,9]=>[9,8,7,6,5,3,1,2,4]=>[1,2,3,4,5,7,9,8,6]=>[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8,9]=>[9,8,7,6,5,4,1,2,3]=>[1,2,3,4,5,6,9,8,7]=>[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9]=>[9,8,7,6,5,4,1,3,2]=>[1,2,3,4,5,6,9,7,8]=>[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1,2,3,4,5,6,7,9]=>[9,7,6,5,4,3,2,1,8]=>[1,3,4,5,6,7,8,9,2]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[7,1,2,3,4,5,6,8,9]=>[9,8,6,5,4,3,2,1,7]=>[1,2,4,5,6,7,8,9,3]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[6,1,2,3,4,5,7,8,9]=>[9,8,7,5,4,3,2,1,6]=>[1,2,3,5,6,7,8,9,4]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[5,1,2,3,4,6,7,8,9]=>[9,8,7,6,4,3,2,1,5]=>[1,2,3,4,6,7,8,9,5]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8,9]=>[9,8,7,6,5,3,2,1,4]=>[1,2,3,4,5,7,8,9,6]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9]=>[9,8,7,6,5,4,2,1,3]=>[1,2,3,4,5,6,8,9,7]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,9,8]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,9,8]=>[9,8,7,6,5,4,3,1,2]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,7,9,6,5,4,3,2,1]=>[1,2,3,4,5,6,9,7,8]=>[9,8,7,6,5,4,1,3,2]=>[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,9,2,1]=>[1,2,9,3,4,5,6,7,8]=>[9,8,1,7,6,5,4,3,2]=>[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,9,1]=>[1,9,2,3,4,5,6,7,8]=>[9,1,8,7,6,5,4,3,2]=>[[.,[[[[[[[.,.],.],.],.],.],.],.]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,10,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,10,9]=>[10,9,8,7,6,5,4,3,1,2]=>[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[7,8,9,6,5,4,3,2,1]=>[1,2,3,4,5,6,9,8,7]=>[9,8,7,6,5,4,1,2,3]=>[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[8,7,6,4,5,9,3,2,1]=>[1,2,3,9,5,4,6,7,8]=>[9,8,7,1,5,6,4,3,2]=>[[[[.,[[[[.,.],.],.],[.,.]]],.],.],.]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,2,3,9,1]=>[1,9,3,2,4,5,6,7,8]=>[9,1,7,8,6,5,4,3,2]=>[[.,[[[[[[.,.],.],.],.],.],[.,.]]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,2,10,1]=>[1,10,2,3,4,5,6,7,8,9]=>[10,1,9,8,7,6,5,4,3,2]=>[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,2,1,10]=>[10,1,2,3,4,5,6,7,8,9]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[10,11,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,11,10]=>[11,10,9,8,7,6,5,4,3,1,2]=>[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[8,9,10,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,10,9,8]=>[10,9,8,7,6,5,4,1,2,3]=>[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,5,4,3,2,1]=>[1,2,3,4,5,9,8,7,6]=>[9,8,7,6,5,1,2,3,4]=>[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,1,2,10]=>[10,2,1,3,4,5,6,7,8,9]=>[1,9,10,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,9,8,7,6,5,4,3,2,11,1]=>[1,11,2,3,4,5,6,7,8,9,10]=>[11,1,10,9,8,7,6,5,4,3,2]=>[[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,9,8,7,6,5,4,3,2,1,11]=>[11,1,2,3,4,5,6,7,8,9,10]=>[1,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,6,5,4,3,2,1]=>[1,2,3,4,5,6,10,9,8,7]=>[10,9,8,7,6,5,1,2,3,4]=>[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,1,2,3,10]=>[10,3,2,1,4,5,6,7,8,9]=>[1,8,9,10,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,4,3,2,1]=>[1,2,3,4,9,8,7,6,5]=>[9,8,7,6,1,2,3,4,5]=>[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,5,4,3,2,1]=>[1,2,3,4,5,10,9,8,7,6]=>[10,9,8,7,6,1,2,3,4,5]=>[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,1,2,3,4,10]=>[10,4,3,2,1,5,6,7,8,9]=>[1,7,8,9,10,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,3,2,1]=>[1,2,3,9,8,7,6,5,4]=>[9,8,7,1,2,3,4,5,6]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,10,4,3,2,1]=>[1,2,3,4,10,9,8,7,6,5]=>[10,9,8,7,1,2,3,4,5,6]=>[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,1,2,3,4,5,10]=>[10,5,4,3,2,1,6,7,8,9]=>[1,6,7,8,9,10,5,4,3,2]=>[.,[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[9,7,6,5,4,3,2,1,8,10]=>[10,8,1,2,3,4,5,6,7,9]=>[1,3,10,9,8,7,6,5,4,2]=>[.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[9,7,8,6,5,4,3,2,1]=>[1,2,3,4,5,6,8,7,9]=>[9,8,7,6,5,4,2,3,1]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[9,8,6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6,8,9]=>[9,8,7,6,5,3,4,2,1]=>[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[8,9,6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6,9,8]=>[9,8,7,6,5,3,4,1,2]=>[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[9,6,7,8,5,4,3,2,1]=>[1,2,3,4,5,8,7,6,9]=>[9,8,7,6,5,2,3,4,1]=>[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,6,4,3,2,1]=>[1,2,3,4,6,5,7,8,9]=>[9,8,7,6,4,5,3,2,1]=>[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[9,7,8,5,6,4,3,2,1]=>[1,2,3,4,6,5,8,7,9]=>[9,8,7,6,4,5,2,3,1]=>[[[[[[[.,.],[.,.]],[.,.]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[7,8,9,5,6,4,3,2,1]=>[1,2,3,4,6,5,9,8,7]=>[9,8,7,6,4,5,1,2,3]=>[[[[[[.,[.,[.,.]]],[.,.]],.],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7,8,9]=>[9,8,7,5,6,4,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[8,9,6,7,4,5,3,2,1]=>[1,2,3,5,4,7,6,9,8]=>[9,8,7,5,6,3,4,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,4,5,3,2,1]=>[1,2,3,5,4,9,8,7,6]=>[9,8,7,5,6,1,2,3,4]=>[[[[[.,[.,[.,[.,.]]]],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[9,8,7,4,5,6,3,2,1]=>[1,2,3,6,5,4,7,8,9]=>[9,8,7,4,5,6,3,2,1]=>[[[[[[[.,.],.],.],[.,[.,.]]],.],.],.]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,3,4,2,1]=>[1,2,4,3,9,8,7,6,5]=>[9,8,6,7,1,2,3,4,5]=>[[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.],.]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[7,8,9,3,4,5,6,2,1]=>[1,2,6,5,4,3,9,8,7]=>[9,8,4,5,6,7,1,2,3]=>[[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.],.]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[8,9,3,4,5,6,7,2,1]=>[1,2,7,6,5,4,3,9,8]=>[9,8,3,4,5,6,7,1,2]=>[[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.],.]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,5,6,7,8,2,1]=>[1,2,8,7,6,5,4,3,9]=>[9,8,2,3,4,5,6,7,1]=>[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7,8,9]=>[9,7,8,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7,9,8]=>[9,7,8,6,5,4,3,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[8,9,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,9,8]=>[9,7,8,5,6,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,2,3,1]=>[1,3,2,9,8,7,6,5,4]=>[9,7,8,1,2,3,4,5,6]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,2,3,4,1]=>[1,4,3,2,5,6,7,8,9]=>[9,6,7,8,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,2,3,4,1]=>[1,4,3,2,9,8,7,6,5]=>[9,6,7,8,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]],.]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,2,3,4,5,1]=>[1,5,4,3,2,9,8,7,6]=>[9,5,6,7,8,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[9,8,2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2,8,9]=>[9,3,4,5,6,7,8,2,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[8,9,2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2,9,8]=>[9,3,4,5,6,7,8,1,2]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8,9]=>[8,9,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,9,8]=>[8,9,7,6,5,4,3,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[9,7,8,6,5,4,3,1,2]=>[2,1,3,4,5,6,8,7,9]=>[8,9,7,6,5,4,2,3,1]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,4,1,2]=>[2,1,4,3,5,6,7,8,9]=>[8,9,6,7,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[9,7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7,9]=>[8,9,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[7,8,9,5,6,3,4,1,2]=>[2,1,4,3,6,5,9,8,7]=>[8,9,6,7,4,5,1,2,3]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,5,6,7,8,1,2]=>[2,1,8,7,6,5,4,3,9]=>[8,9,2,3,4,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8,9]=>[7,8,9,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[7,8,9,4,5,6,1,2,3]=>[3,2,1,6,5,4,9,8,7]=>[7,8,9,4,5,6,1,2,3]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,1,2,3]=>[3,2,1,9,8,7,6,5,4]=>[7,8,9,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8,9]=>[6,7,8,9,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[9,5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5,9]=>[6,7,8,9,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,1,2,3,4]=>[4,3,2,1,9,8,7,6,5]=>[6,7,8,9,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8,9]=>[5,6,7,8,9,4,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,1,2,3,4,5]=>[5,4,3,2,1,9,8,7,6]=>[5,6,7,8,9,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[9,8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8,9]=>[4,5,6,7,8,9,3,2,1]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[9,7,8,1,2,3,4,5,6]=>[6,5,4,3,2,1,8,7,9]=>[4,5,6,7,8,9,2,3,1]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,8,9,1,2,3,4,5,6]=>[6,5,4,3,2,1,9,8,7]=>[4,5,6,7,8,9,1,2,3]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[10,8,9,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,9,8,10]=>[10,9,8,7,6,5,4,2,3,1]=>[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,6,5,4,3,2,1]=>[1,2,3,4,5,6,8,7,10,9]=>[10,9,8,7,6,5,3,4,1,2]=>[[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,5,6,4,3,2,1]=>[1,2,3,4,6,5,7,8,9,10]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,5,6,4,3,2,1]=>[1,2,3,4,6,5,8,7,10,9]=>[10,9,8,7,5,6,3,4,1,2]=>[[[[[[[.,[.,.]],[.,.]],[.,.]],.],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,4,5,3,2,1]=>[1,2,3,5,4,6,7,8,9,10]=>[10,9,8,6,7,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,7,8,9,10,3,2,1]=>[1,2,3,10,9,8,7,6,5,4]=>[10,9,8,1,2,3,4,5,6,7]=>[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,5,6,3,4,2,1]=>[1,2,4,3,6,5,8,7,10,9]=>[10,9,7,8,5,6,3,4,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.],.]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[9,10,3,4,5,6,7,8,2,1]=>[1,2,8,7,6,5,4,3,10,9]=>[10,9,3,4,5,6,7,8,1,2]=>[[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[10,3,4,5,6,7,8,9,2,1]=>[1,2,9,8,7,6,5,4,3,10]=>[10,9,2,3,4,5,6,7,8,1]=>[[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7,8,9,10]=>[10,8,9,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[10,8,9,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,9,8,10]=>[10,8,9,6,7,4,5,2,3,1]=>[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[8,9,10,5,6,7,2,3,4,1]=>[1,4,3,2,7,6,5,10,9,8]=>[10,7,8,9,4,5,6,1,2,3]=>[[[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,10,2,3,4,1]=>[1,4,3,2,10,9,8,7,6,5]=>[10,7,8,9,1,2,3,4,5,6]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]],.]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,2,3,4,5,1]=>[1,5,4,3,2,10,9,8,7,6]=>[10,6,7,8,9,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[10,9,2,3,4,5,6,7,8,1]=>[1,8,7,6,5,4,3,2,9,10]=>[10,3,4,5,6,7,8,9,2,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[9,10,2,3,4,5,6,7,8,1]=>[1,8,7,6,5,4,3,2,10,9]=>[10,3,4,5,6,7,8,9,1,2]=>[[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8,9,10]=>[9,10,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,10,8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8,10,9]=>[9,10,8,7,6,5,4,3,1,2]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7,10,9]=>[9,10,7,8,5,6,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,5,6,3,4,1,2]=>[2,1,4,3,6,5,10,9,8,7]=>[9,10,7,8,5,6,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,3,4,5,6,1,2]=>[2,1,6,5,4,3,10,9,8,7]=>[9,10,5,6,7,8,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[9,10,3,4,5,6,7,8,1,2]=>[2,1,8,7,6,5,4,3,10,9]=>[9,10,3,4,5,6,7,8,1,2]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,1,2,3]=>[3,2,1,4,5,6,7,8,9,10]=>[8,9,10,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,7,8,9,10,1,2,3]=>[3,2,1,10,9,8,7,6,5,4]=>[8,9,10,1,2,3,4,5,6,7]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,1,2,3,4]=>[4,3,2,1,5,6,7,8,9,10]=>[7,8,9,10,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,5,6,1,2,3,4]=>[4,3,2,1,6,5,8,7,10,9]=>[7,8,9,10,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,5,6,1,2,3,4]=>[4,3,2,1,6,5,10,9,8,7]=>[7,8,9,10,5,6,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[9,10,5,6,7,8,1,2,3,4]=>[4,3,2,1,8,7,6,5,10,9]=>[7,8,9,10,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,10,1,2,3,4]=>[4,3,2,1,10,9,8,7,6,5]=>[7,8,9,10,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,1,2,3,4,5]=>[5,4,3,2,1,6,7,8,9,10]=>[6,7,8,9,10,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,1,2,3,4,5]=>[5,4,3,2,1,10,9,8,7,6]=>[6,7,8,9,10,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,1,2,3,4,5,6]=>[6,5,4,3,2,1,7,8,9,10]=>[5,6,7,8,9,10,4,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,1,2,3,4,5,6]=>[6,5,4,3,2,1,10,9,8,7]=>[5,6,7,8,9,10,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[10,9,8,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,8,9,10]=>[4,5,6,7,8,9,10,3,2,1]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[10,8,9,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,9,8,10]=>[4,5,6,7,8,9,10,2,3,1]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[8,9,10,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,10,9,8]=>[4,5,6,7,8,9,10,1,2,3]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8,9]=>[7,9,8,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8,9]=>[6,9,8,7,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8,9]=>[5,9,8,7,6,4,3,2,1]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8,9]=>[4,9,8,7,6,5,3,2,1]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[9,8,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6,8,9]=>[3,9,8,7,6,5,4,2,1]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7,9]=>[2,9,8,7,6,5,4,3,1]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8,9,10]=>[8,10,9,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,2,3,1,4]=>[4,1,3,2,5,6,7,8,9]=>[6,9,7,8,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,3,2,1,4]=>[4,1,2,3,5,6,7,8,9,10]=>[7,10,9,8,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,3,4,2,1,5]=>[5,1,2,4,3,6,7,8,9]=>[5,9,8,6,7,4,3,2,1]=>[[[[[.,.],.],.],.],[[[.,[.,.]],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8,9,10]=>[6,10,9,8,7,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[9,8,7,4,5,3,2,1,6]=>[6,1,2,3,5,4,7,8,9]=>[4,9,8,7,5,6,3,2,1]=>[[[[.,.],.],.],[[[[.,[.,.]],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,5,4,3,2,1,6]=>[6,1,2,3,4,5,7,8,9,10]=>[5,10,9,8,7,6,4,3,2,1]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[9,8,5,6,4,3,2,1,7]=>[7,1,2,3,4,6,5,8,9]=>[3,9,8,7,6,4,5,2,1]=>[[[.,.],.],[[[[[.,[.,.]],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[10,9,8,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6,8,9,10]=>[4,10,9,8,7,6,5,3,2,1]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[9,6,7,5,4,3,2,1,8]=>[8,1,2,3,4,5,7,6,9]=>[2,9,8,7,6,5,3,4,1]=>[[.,.],[[[[[[.,[.,.]],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[10,9,7,6,5,4,3,2,1,8]=>[8,1,2,3,4,5,6,7,9,10]=>[3,10,9,8,7,6,5,4,2,1]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,5,4,3,2,1,9]=>[9,1,2,3,4,5,6,7,8,10]=>[2,10,9,8,7,6,5,4,3,1]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,10,9,8,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,8,9,10,11]=>[10,11,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,7,9,6,5,4,3,1,2]=>[2,1,3,4,5,6,9,7,8]=>[8,9,7,6,5,4,1,3,2]=>[[[[[[.,[[.,.],.]],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[8,9,7,6,5,4,3,2,1,10]=>[10,1,2,3,4,5,6,7,9,8]=>[1,10,9,8,7,6,5,4,2,3]=>[.,[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,1,3,2]=>[1,2,3,4,5,6,7,10,8,9]=>[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,2,1,3]=>[1,2,3,4,5,6,7,9,10,8]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,1,3,2]=>[1,2,3,4,5,6,7,8,11,9,10]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,2,1,3]=>[1,2,3,4,5,6,7,8,10,11,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[9,8,10,7,6,5,4,3,1,2]=>[2,1,3,4,5,6,7,10,8,9]=>[9,10,8,7,6,5,4,1,3,2]=>[[[[[[[.,[[.,.],.]],.],.],.],.],.],[.,.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,7,9,6,5,4,2,3,1]=>[1,3,2,4,5,6,9,7,8]=>[9,7,8,6,5,4,1,3,2]=>[[[[[[.,[[.,.],.]],.],.],.],[.,.]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[9,6,5,4,3,2,1,7,8]=>[8,7,1,2,3,4,5,6,9]=>[2,3,9,8,7,6,5,4,1]=>[[.,.],[.,[[[[[[.,.],.],.],.],.],.]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7,8,9]=>[6,7,9,8,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,[[.,.],.]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1,10]=>[10,1,9,8,7,6,5,4,3,2]=>[1,10,2,3,4,5,6,7,8,9]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,1,2,3,4,5,6,7,8,10]=>[10,8,7,6,5,4,3,2,1,9]=>[1,3,4,5,6,7,8,9,10,2]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[10,1,2,3,4,5,6,7,8,9,11]=>[11,9,8,7,6,5,4,3,2,1,10]=>[1,3,4,5,6,7,8,9,10,11,2]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[9,2,1,3,4,5,6,7,8,10]=>[10,8,7,6,5,4,3,1,2,9]=>[1,3,4,5,6,7,8,10,9,2]=>[.,[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[9,8,6,1,2,3,4,5,7]=>[7,5,4,3,2,1,6,8,9]=>[3,5,6,7,8,9,4,2,1]=>[[[.,.],.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,8,10,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9,10]=>[10,9,8,7,6,5,1,4,3,2]=>[1,2,3,4,5,6,10,7,8,9]=>[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9,10]=>[10,9,8,7,6,1,5,4,3,2]=>[1,2,3,4,5,10,6,7,8,9]=>[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,1,7,8,9,10]=>[10,9,8,7,1,6,5,4,3,2]=>[1,2,3,4,10,5,6,7,8,9]=>[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8,9,10]=>[10,9,8,1,7,6,5,4,3,2]=>[1,2,3,10,4,5,6,7,8,9]=>[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1,9,10]=>[10,9,1,8,7,6,5,4,3,2]=>[1,2,10,3,4,5,6,7,8,9]=>[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,1,2]=>[1,2,3,4,5,6,7,8,9,11,10]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,9,8]=>[5,9,8,7,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,4,5,3,2,1,10]=>[10,1,2,3,5,4,6,7,8,9]=>[1,10,9,8,6,7,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,1,2,8]=>[8,2,1,3,4,5,6,7,9]=>[2,8,9,7,6,5,4,3,1]=>[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[8,9,6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6,9,8]=>[3,9,8,7,6,5,4,1,2]=>[[.,[.,.]],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,9,1,2]=>[2,1,9,3,4,5,6,7,8]=>[8,9,1,7,6,5,4,3,2]=>[[.,[[[[[[.,.],.],.],.],.],.]],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[7,6,5,4,3,2,1,8,9,10]=>[10,9,8,1,2,3,4,5,6,7]=>[1,2,3,10,9,8,7,6,5,4]=>[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[8,7,9,1,2,3,4,5,6]=>[6,5,4,3,2,1,9,7,8]=>[4,5,6,7,8,9,1,3,2]=>[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[8,1,2,3,4,5,6,7,9,10]=>[10,9,7,6,5,4,3,2,1,8]=>[1,2,4,5,6,7,8,9,10,3]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[7,1,2,3,4,5,6,8,9,10]=>[10,9,8,6,5,4,3,2,1,7]=>[1,2,3,5,6,7,8,9,10,4]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[6,1,2,3,4,5,7,8,9,10]=>[10,9,8,7,5,4,3,2,1,6]=>[1,2,3,4,6,7,8,9,10,5]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[5,1,2,3,4,6,7,8,9,10]=>[10,9,8,7,6,4,3,2,1,5]=>[1,2,3,4,5,7,8,9,10,6]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8,9,10]=>[10,9,8,7,6,5,3,2,1,4]=>[1,2,3,4,5,6,8,9,10,7]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[8,7,9,6,5,4,3,2,1,10]=>[10,1,2,3,4,5,6,9,7,8]=>[1,10,9,8,7,6,5,2,4,3]=>[.,[[[[[[[.,[[.,.],.]],.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[8,7,6,9,5,4,3,2,1,10]=>[10,1,2,3,4,5,9,6,7,8]=>[1,10,9,8,7,6,2,5,4,3]=>[.,[[[[[[.,[[[.,.],.],.]],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,6,5,4,9,3,2,1,10]=>[10,1,2,3,9,4,5,6,7,8]=>[1,10,9,8,2,7,6,5,4,3]=>[.,[[[[.,[[[[[.,.],.],.],.],.]],.],.],.]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,6,5,4,3,9,2,1,10]=>[10,1,2,9,3,4,5,6,7,8]=>[1,10,9,2,8,7,6,5,4,3]=>[.,[[[.,[[[[[[.,.],.],.],.],.],.]],.],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,6,5,4,3,2,1,9,10]=>[10,9,1,2,3,4,5,6,7,8]=>[1,2,10,9,8,7,6,5,4,3]=>[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[9,8,10,7,6,5,4,3,2,1,11]=>[11,1,2,3,4,5,6,7,10,8,9]=>[1,11,10,9,8,7,6,5,2,4,3]=>[.,[[[[[[[[.,[[.,.],.]],.],.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[9,8,7,10,6,5,4,3,2,1,11]=>[11,1,2,3,4,5,6,10,7,8,9]=>[1,11,10,9,8,7,6,2,5,4,3]=>[.,[[[[[[[.,[[[.,.],.],.]],.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[9,8,7,6,5,10,4,3,2,1,11]=>[11,1,2,3,4,10,5,6,7,8,9]=>[1,11,10,9,8,2,7,6,5,4,3]=>[.,[[[[[.,[[[[[.,.],.],.],.],.]],.],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[9,8,7,6,5,4,10,3,2,1,11]=>[11,1,2,3,10,4,5,6,7,8,9]=>[1,11,10,9,2,8,7,6,5,4,3]=>[.,[[[[.,[[[[[[.,.],.],.],.],.],.]],.],.],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[9,8,7,6,5,4,3,2,10,1,11]=>[11,1,10,2,3,4,5,6,7,8,9]=>[1,11,2,10,9,8,7,6,5,4,3]=>[.,[[.,[[[[[[[[.,.],.],.],.],.],.],.],.]],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[9,8,7,6,5,4,3,2,1,10,11]=>[11,10,1,2,3,4,5,6,7,8,9]=>[1,2,11,10,9,8,7,6,5,4,3]=>[.,[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8,9,10]=>[10,9,8,7,6,5,2,1,4,3]=>[1,2,3,4,5,6,9,10,7,8]=>[.,[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,1,2,3,7,8,9,10]=>[10,9,8,7,3,2,1,6,5,4]=>[1,2,3,4,8,9,10,5,6,7]=>[.,[.,[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,1,2,3,4,9,10]=>[10,9,4,3,2,1,8,7,6,5]=>[1,2,7,8,9,10,3,4,5,6]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,1,2,3,4,5,10]=>[10,5,4,3,2,1,9,8,7,6]=>[1,6,7,8,9,10,2,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[6,5,7,4,8,3,9,2,10,1]=>[1,10,2,9,3,8,4,7,5,6]=>[10,1,9,2,8,3,7,4,6,5]=>[[.,[[.,[[.,[[.,[[.,.],.]],.]],.]],.]],.]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10,11]=>[11,10,9,8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8,9,10,11]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,11,1,2]=>[2,1,11,10,9,8,7,6,5,4,3]=>[10,11,1,2,3,4,5,6,7,8,9]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,9,1,10]=>[10,1,9,8,7,6,5,4,2,3]=>[1,10,2,3,4,5,6,7,9,8]=>[.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,1,11]=>[11,1,10,9,8,7,6,5,4,3,2]=>[1,11,2,3,4,5,6,7,8,9,10]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]=>[11,1,2,3,4,5,6,7,8,9,10,12]=>[12,10,9,8,7,6,5,4,3,2,1,11]=>[1,3,4,5,6,7,8,9,10,11,12,2]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,10,9,8,7,6,5,4,2,1,3]=>[3,1,2,4,5,6,7,8,9,10,11]=>[9,11,10,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,9,1,2,3]=>[3,2,1,9,4,5,6,7,8]=>[7,8,9,1,6,5,4,3,2]=>[[.,[[[[[.,.],.],.],.],.]],[.,[.,.]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,11,1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1,11,10]=>[3,4,5,6,7,8,9,10,11,1,2]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,4,3,2,1,7,8,9,10]=>[10,9,8,7,1,2,3,4,5,6]=>[1,2,3,4,10,9,8,7,6,5]=>[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[4,2,1,3,5,6,7,8,9,10]=>[10,9,8,7,6,5,3,1,2,4]=>[1,2,3,4,5,6,8,10,9,7]=>[.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]=>[9,8,7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7,8,9]=>[4,5,6,7,9,8,3,2,1]=>[[[[.,.],.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,2,1,3,4,5]=>[5,4,3,1,2,6,7,8,9]=>[5,6,7,9,8,4,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0]=>[7,8,9,1,2,3,4,5,6,10]=>[10,6,5,4,3,2,1,9,8,7]=>[1,5,6,7,8,9,10,2,3,4]=>[.,[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,10,1,2]=>[2,1,10,3,4,5,6,7,8,9]=>[9,10,1,8,7,6,5,4,3,2]=>[[.,[[[[[[[.,.],.],.],.],.],.],.]],[.,.]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,1,2,3]=>[1,2,3,4,5,6,7,10,9,8]=>[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[9,7,6,8,5,4,3,2,1]=>[1,2,3,4,5,8,6,7,9]=>[9,8,7,6,5,2,4,3,1]=>[[[[[[[.,.],[[.,.],.]],.],.],.],.],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[10,9,7,6,5,4,3,2,8,1]=>[1,8,2,3,4,5,6,7,9,10]=>[10,3,9,8,7,6,5,4,2,1]=>[[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[9,10,8,7,6,4,3,2,1,5]=>[5,1,2,3,4,6,7,8,10,9]=>[6,10,9,8,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[[[[.,.],.],.],.]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[5,4,3,2,1,6,7,8,9,10]=>[10,9,8,7,6,1,2,3,4,5]=>[1,2,3,4,5,10,9,8,7,6]=>[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[4,3,2,1,5,6,7,8,9,10]=>[10,9,8,7,6,5,1,2,3,4]=>[1,2,3,4,5,6,10,9,8,7]=>[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[10,2,3,4,5,6,7,8,9,11,1]=>[1,11,9,8,7,6,5,4,3,2,10]=>[11,1,3,4,5,6,7,8,9,10,2]=>[[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[11,9,8,7,6,5,4,3,2,1,10]=>[10,1,2,3,4,5,6,7,8,9,11]=>[2,11,10,9,8,7,6,5,4,3,1]=>[[.,.],[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,2,8,1]=>[1,8,2,3,4,5,6,7,9]=>[9,2,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,10,9,8,7,6,5,4,2,3,1]=>[1,3,2,4,5,6,7,8,9,10,11]=>[11,9,10,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[8,9,1,2,3,4,5,6,7,10]=>[10,7,6,5,4,3,2,1,9,8]=>[1,4,5,6,7,8,9,10,2,3]=>[.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,1,2,3,4,10]=>[10,4,3,2,1,9,8,7,6,5]=>[1,7,8,9,10,2,3,4,5,6]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,7,8,9,1,2,3,10]=>[10,3,2,1,9,8,7,6,5,4]=>[1,8,9,10,2,3,4,5,6,7]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,1,2,10]=>[10,2,1,9,8,7,6,5,4,3]=>[1,9,10,2,3,4,5,6,7,8]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[6,4,3,2,1,5,7,8,9,10]=>[10,9,8,7,5,1,2,3,4,6]=>[1,2,3,4,6,10,9,8,7,5]=>[.,[.,[.,[.,[[.,.],[[[[.,.],.],.],.]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]=>[5,3,1,2,4,6,7,8,9,10]=>[10,9,8,7,6,4,2,1,3,5]=>[1,2,3,4,5,7,9,10,8,6]=>[.,[.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,2,1,3,4]=>[4,3,1,2,5,6,7,8,9,10]=>[7,8,10,9,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],[.,[[.,.],.]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,2,1,3,4,5,6]=>[6,5,4,3,1,2,7,8,9,10]=>[5,6,7,8,10,9,4,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[10,9,8,2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2,8,9,10]=>[4,5,6,7,8,10,9,3,2,1]=>[[[[.,.],.],.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[8,7,9,5,6,3,4,1,2]=>[2,1,4,3,6,5,9,7,8]=>[8,9,6,7,4,5,1,3,2]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[7,5,4,3,2,1,6,8,9,10]=>[10,9,8,6,1,2,3,4,5,7]=>[1,2,3,5,10,9,8,7,6,4]=>[.,[.,[.,[[.,.],[[[[[.,.],.],.],.],.]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]=>[11,10,1,2,3,4,5,6,7,8,9]=>[9,8,7,6,5,4,3,2,1,10,11]=>[3,4,5,6,7,8,9,10,11,2,1]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,4,6,3,2,1]=>[1,2,3,6,4,5,7,8,9]=>[9,8,7,4,6,5,3,2,1]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,5,4,6,3,2,1]=>[1,2,3,6,4,5,7,8,9,10]=>[10,9,8,5,7,6,4,3,2,1]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,5,4,3,2,9,1]=>[1,9,2,3,4,5,6,7,8,10]=>[10,2,9,8,7,6,5,4,3,1]=>[[[.,.],[[[[[[[.,.],.],.],.],.],.],.]],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[9,8,6,5,4,3,7,2,1]=>[1,2,7,3,4,5,6,8,9]=>[9,8,3,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[10,9,7,6,5,4,3,8,2,1]=>[1,2,8,3,4,5,6,7,9,10]=>[10,9,3,8,7,6,5,4,2,1]=>[[[[[.,.],.],[[[[[.,.],.],.],.],.]],.],.]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[11,2,3,4,5,6,7,8,9,10,1]=>[1,10,9,8,7,6,5,4,3,2,11]=>[11,2,3,4,5,6,7,8,9,10,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[9,8,1,2,3,4,5,6,7,10]=>[10,7,6,5,4,3,2,1,8,9]=>[1,4,5,6,7,8,9,10,3,2]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,0]=>[9,8,7,1,2,3,4,5,6,10]=>[10,6,5,4,3,2,1,7,8,9]=>[1,5,6,7,8,9,10,4,3,2]=>[.,[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[9,8,10,6,7,4,5,2,3,1]=>[1,3,2,5,4,7,6,10,8,9]=>[10,8,9,6,7,4,5,1,3,2]=>[[[[[.,[[.,.],.]],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[5,6,4,7,3,8,2,9,1]=>[1,9,2,8,3,7,4,6,5]=>[9,1,8,2,7,3,6,4,5]=>[[.,[[.,[[.,[[.,[.,.]],.]],.]],.]],.]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[8,6,4,2,1,3,5,7,9,10]=>[10,9,7,5,3,1,2,4,6,8]=>[1,2,4,6,8,10,9,7,5,3]=>[.,[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[8,9,6,7,4,5,2,3,10,1]=>[1,10,3,2,5,4,7,6,9,8]=>[10,1,8,9,6,7,4,5,2,3]=>[[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]],.]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[9,2,3,4,5,6,7,8,1,10]=>[10,1,8,7,6,5,4,3,2,9]=>[1,10,3,4,5,6,7,8,9,2]=>[.,[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[9,7,5,3,1,2,4,6,8,10]=>[10,8,6,4,2,1,3,5,7,9]=>[1,3,5,7,9,10,8,6,4,2]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[7,8,5,6,3,4,1,2,9,10]=>[10,9,2,1,4,3,6,5,8,7]=>[1,2,9,10,7,8,5,6,3,4]=>[.,[.,[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[11,12,1,2,3,4,5,6,7,8,9,10]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[3,4,5,6,7,8,9,10,11,12,1,2]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,11,2,1]=>[1,2,11,10,9,8,7,6,5,4,3]=>[11,10,1,2,3,4,5,6,7,8,9]=>[[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[9,7,5,4,3,2,1,6,8,10]=>[10,8,6,1,2,3,4,5,7,9]=>[1,3,5,10,9,8,7,6,4,2]=>[.,[[.,.],[[.,.],[[[[[.,.],.],.],.],.]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[8,6,5,4,3,2,1,7,9,10]=>[10,9,7,1,2,3,4,5,6,8]=>[1,2,4,10,9,8,7,6,5,3]=>[.,[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0]=>[9,8,10,1,2,3,4,5,6,7]=>[7,6,5,4,3,2,1,10,8,9]=>[4,5,6,7,8,9,10,1,3,2]=>[[.,[[.,.],.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[6,7,8,9,10,1,2,3,4,5,11]=>[11,5,4,3,2,1,10,9,8,7,6]=>[1,7,8,9,10,11,2,3,4,5,6]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[7,8,9,4,5,6,1,2,3,10]=>[10,3,2,1,6,5,4,9,8,7]=>[1,8,9,10,5,6,7,2,3,4]=>[.,[[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,11,2,3,4,5,6,7,8,9,1]=>[1,9,8,7,6,5,4,3,2,11,10]=>[11,3,4,5,6,7,8,9,10,1,2]=>[[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
Map
reverse
Description
Sends a permutation to its reverse.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
The reverse of a permutation $\sigma$ of length $n$ is given by $\tau$ with $\tau(i) = \sigma(n+1-i)$.
Map
complement
Description
Sents a permutation to its complement.
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
The complement of a permutation $\sigma$ of length $n$ is the permutation $\tau$ with $\tau(i) = n+1-\sigma(i)$
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.