Identifier
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
Permutations
Mp00064: Permutations —reverse⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00064: Permutations —reverse⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-3
[1,0]=>[1]=>[1]=>[.,.]
[1,0,1,0]=>[1,2]=>[2,1]=>[[.,.],.]
[1,1,0,0]=>[2,1]=>[1,2]=>[.,[.,.]]
[1,0,1,0,1,0]=>[1,2,3]=>[3,2,1]=>[[[.,.],.],.]
[1,0,1,1,0,0]=>[1,3,2]=>[2,3,1]=>[[.,.],[.,.]]
[1,1,0,0,1,0]=>[2,1,3]=>[3,1,2]=>[[.,[.,.]],.]
[1,1,0,1,0,0]=>[2,3,1]=>[1,3,2]=>[.,[[.,.],.]]
[1,1,1,0,0,0]=>[3,2,1]=>[1,2,3]=>[.,[.,[.,.]]]
[1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[3,4,2,1]=>[[[.,.],.],[.,.]]
[1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[2,4,3,1]=>[[.,.],[[.,.],.]]
[1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[2,3,4,1]=>[[.,.],[.,[.,.]]]
[1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[4,3,1,2]=>[[[.,[.,.]],.],.]
[1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[3,4,1,2]=>[[.,[.,.]],[.,.]]
[1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[4,1,3,2]=>[[.,[[.,.],.]],.]
[1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[1,4,3,2]=>[.,[[[.,.],.],.]]
[1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[1,3,4,2]=>[.,[[.,.],[.,.]]]
[1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[4,1,2,3]=>[[.,[.,[.,.]]],.]
[1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[1,4,2,3]=>[.,[[.,[.,.]],.]]
[1,1,1,0,1,0,0,0]=>[3,4,2,1]=>[1,2,4,3]=>[.,[.,[[.,.],.]]]
[1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[4,5,3,2,1]=>[[[[.,.],.],.],[.,.]]
[1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[5,3,4,2,1]=>[[[[.,.],.],[.,.]],.]
[1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[3,5,4,2,1]=>[[[.,.],.],[[.,.],.]]
[1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[3,4,5,2,1]=>[[[.,.],.],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[5,4,2,3,1]=>[[[[.,.],[.,.]],.],.]
[1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[4,5,2,3,1]=>[[[.,.],[.,.]],[.,.]]
[1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[2,5,4,3,1]=>[[.,.],[[[.,.],.],.]]
[1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[2,4,5,3,1]=>[[.,.],[[.,.],[.,.]]]
[1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[2,5,3,4,1]=>[[.,.],[[.,[.,.]],.]]
[1,0,1,1,1,0,1,0,0,0]=>[1,4,5,3,2]=>[2,3,5,4,1]=>[[.,.],[.,[[.,.],.]]]
[1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[2,3,4,5,1]=>[[.,.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[5,4,3,1,2]=>[[[[.,[.,.]],.],.],.]
[1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[5,3,4,1,2]=>[[[.,[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[3,5,4,1,2]=>[[.,[.,.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[3,4,5,1,2]=>[[.,[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[5,4,1,3,2]=>[[[.,[[.,.],.]],.],.]
[1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[4,5,1,3,2]=>[[.,[[.,.],.]],[.,.]]
[1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[5,1,4,3,2]=>[[.,[[[.,.],.],.]],.]
[1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[1,4,5,3,2]=>[.,[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[5,1,3,4,2]=>[[.,[[.,.],[.,.]]],.]
[1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[1,5,3,4,2]=>[.,[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>[1,3,5,4,2]=>[.,[[.,.],[[.,.],.]]]
[1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[1,3,4,5,2]=>[.,[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[5,4,1,2,3]=>[[[.,[.,[.,.]]],.],.]
[1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[4,5,1,2,3]=>[[.,[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[5,1,4,2,3]=>[[.,[[.,[.,.]],.]],.]
[1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[1,5,4,2,3]=>[.,[[[.,[.,.]],.],.]]
[1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[1,4,5,2,3]=>[.,[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,0,1,0]=>[3,4,2,1,5]=>[5,1,2,4,3]=>[[.,[.,[[.,.],.]]],.]
[1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>[1,5,2,4,3]=>[.,[[.,[[.,.],.]],.]]
[1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]]
[1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>[1,2,4,5,3]=>[.,[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[5,1,2,3,4]=>[[.,[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[1,5,2,3,4]=>[.,[[.,[.,[.,.]]],.]]
[1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>[1,2,5,3,4]=>[.,[.,[[.,[.,.]],.]]]
[1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]
[1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[5,6,4,3,2,1]=>[[[[[.,.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[6,4,5,3,2,1]=>[[[[[.,.],.],.],[.,.]],.]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[4,6,5,3,2,1]=>[[[[.,.],.],.],[[.,.],.]]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[4,5,6,3,2,1]=>[[[[.,.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[5,6,3,4,2,1]=>[[[[.,.],.],[.,.]],[.,.]]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[6,3,5,4,2,1]=>[[[[.,.],.],[[.,.],.]],.]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[3,6,5,4,2,1]=>[[[.,.],.],[[[.,.],.],.]]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[3,5,6,4,2,1]=>[[[.,.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[6,3,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],.]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[3,6,4,5,2,1]=>[[[.,.],.],[[.,[.,.]],.]]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,4,3]=>[3,4,6,5,2,1]=>[[[.,.],.],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[3,4,5,6,2,1]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[6,5,4,2,3,1]=>[[[[[.,.],[.,.]],.],.],.]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[5,6,4,2,3,1]=>[[[[.,.],[.,.]],.],[.,.]]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[6,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[4,6,5,2,3,1]=>[[[.,.],[.,.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[4,5,6,2,3,1]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[6,5,2,4,3,1]=>[[[[.,.],[[.,.],.]],.],.]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[5,6,2,4,3,1]=>[[[.,.],[[.,.],.]],[.,.]]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[2,6,5,4,3,1]=>[[.,.],[[[[.,.],.],.],.]]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[2,5,6,4,3,1]=>[[.,.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[6,2,4,5,3,1]=>[[[.,.],[[.,.],[.,.]]],.]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[2,6,4,5,3,1]=>[[.,.],[[[.,.],[.,.]],.]]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,4,2]=>[2,4,6,5,3,1]=>[[.,.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[2,4,5,6,3,1]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[6,5,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],.]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[5,6,2,3,4,1]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[6,2,5,3,4,1]=>[[[.,.],[[.,[.,.]],.]],.]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[2,6,5,3,4,1]=>[[.,.],[[[.,[.,.]],.],.]]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[2,5,6,3,4,1]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,3,2,6]=>[6,2,3,5,4,1]=>[[[.,.],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,3,6,2]=>[2,6,3,5,4,1]=>[[.,.],[[.,[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,3,2]=>[2,3,6,5,4,1]=>[[.,.],[.,[[[.,.],.],.]]]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,5,3,2]=>[2,3,5,6,4,1]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[2,6,3,4,5,1]=>[[.,.],[[.,[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,4,6,3,2]=>[2,3,6,4,5,1]=>[[.,.],[.,[[.,[.,.]],.]]]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,4,3,2]=>[2,3,4,6,5,1]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[2,3,4,5,6,1]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[6,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],.]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[6,4,5,3,1,2]=>[[[[.,[.,.]],.],[.,.]],.]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[4,6,5,3,1,2]=>[[[.,[.,.]],.],[[.,.],.]]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[4,5,6,3,1,2]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[6,5,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],.]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[6,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],.]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[3,6,5,4,1,2]=>[[.,[.,.]],[[[.,.],.],.]]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[3,5,6,4,1,2]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[6,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],.]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[3,6,4,5,1,2]=>[[.,[.,.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,4,3]=>[3,4,6,5,1,2]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[3,4,5,6,1,2]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[6,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],.]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[5,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[6,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],.]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[4,6,5,1,3,2]=>[[.,[[.,.],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[4,5,6,1,3,2]=>[[.,[[.,.],.]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[6,5,1,4,3,2]=>[[[.,[[[.,.],.],.]],.],.]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[5,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[6,1,5,4,3,2]=>[[.,[[[[.,.],.],.],.]],.]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[1,5,6,4,3,2]=>[.,[[[[.,.],.],.],[.,.]]]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[6,1,4,5,3,2]=>[[.,[[[.,.],.],[.,.]]],.]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[1,6,4,5,3,2]=>[.,[[[[.,.],.],[.,.]],.]]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>[1,4,6,5,3,2]=>[.,[[[.,.],.],[[.,.],.]]]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[1,4,5,6,3,2]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[6,5,1,3,4,2]=>[[[.,[[.,.],[.,.]]],.],.]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[5,6,1,3,4,2]=>[[.,[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[6,1,5,3,4,2]=>[[.,[[[.,.],[.,.]],.]],.]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[1,6,5,3,4,2]=>[.,[[[[.,.],[.,.]],.],.]]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[1,5,6,3,4,2]=>[.,[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,3,1,6]=>[6,1,3,5,4,2]=>[[.,[[.,.],[[.,.],.]]],.]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>[1,6,3,5,4,2]=>[.,[[[.,.],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>[1,3,6,5,4,2]=>[.,[[.,.],[[[.,.],.],.]]]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>[1,3,5,6,4,2]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[6,1,3,4,5,2]=>[[.,[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[1,6,3,4,5,2]=>[.,[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>[1,3,6,4,5,2]=>[.,[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>[1,3,4,6,5,2]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[1,3,4,5,6,2]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[6,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],.]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[5,6,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,.]]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[6,4,5,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],.]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[4,6,5,1,2,3]=>[[.,[.,[.,.]]],[[.,.],.]]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[4,5,6,1,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[6,5,1,4,2,3]=>[[[.,[[.,[.,.]],.]],.],.]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[5,6,1,4,2,3]=>[[.,[[.,[.,.]],.]],[.,.]]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[6,1,5,4,2,3]=>[[.,[[[.,[.,.]],.],.]],.]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[1,6,5,4,2,3]=>[.,[[[[.,[.,.]],.],.],.]]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[1,5,6,4,2,3]=>[.,[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[6,1,4,5,2,3]=>[[.,[[.,[.,.]],[.,.]]],.]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[1,6,4,5,2,3]=>[.,[[[.,[.,.]],[.,.]],.]]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>[1,4,6,5,2,3]=>[.,[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[1,4,5,6,2,3]=>[.,[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,2,1,5,6]=>[6,5,1,2,4,3]=>[[[.,[.,[[.,.],.]]],.],.]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2,1,6,5]=>[5,6,1,2,4,3]=>[[.,[.,[[.,.],.]]],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,2,5,1,6]=>[6,1,5,2,4,3]=>[[.,[[.,[[.,.],.]],.]],.]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>[1,6,5,2,4,3]=>[.,[[[.,[[.,.],.]],.],.]]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>[1,5,6,2,4,3]=>[.,[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,2,1,6]=>[6,1,2,5,4,3]=>[[.,[.,[[[.,.],.],.]]],.]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>[1,6,2,5,4,3]=>[.,[[.,[[[.,.],.],.]],.]]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>[1,2,6,5,4,3]=>[.,[.,[[[[.,.],.],.],.]]]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>[1,2,5,6,4,3]=>[.,[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,4,2,1,6]=>[6,1,2,4,5,3]=>[[.,[.,[[.,.],[.,.]]]],.]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>[1,6,2,4,5,3]=>[.,[[.,[[.,.],[.,.]]],.]]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>[1,2,6,4,5,3]=>[.,[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>[1,2,4,6,5,3]=>[.,[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]=>[1,2,4,5,6,3]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[6,5,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],.]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[5,6,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[6,1,5,2,3,4]=>[[.,[[.,[.,[.,.]]],.]],.]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[1,6,5,2,3,4]=>[.,[[[.,[.,[.,.]]],.],.]]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[1,5,6,2,3,4]=>[.,[[.,[.,[.,.]]],[.,.]]]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,3,5,2,1,6]=>[6,1,2,5,3,4]=>[[.,[.,[[.,[.,.]],.]]],.]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>[1,6,2,5,3,4]=>[.,[[.,[[.,[.,.]],.]],.]]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[1,2,6,5,3,4]=>[.,[.,[[[.,[.,.]],.],.]]]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>[1,2,5,6,3,4]=>[.,[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,3,2,1,6]=>[6,1,2,3,5,4]=>[[.,[.,[.,[[.,.],.]]]],.]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>[1,6,2,3,5,4]=>[.,[[.,[.,[[.,.],.]]],.]]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>[1,2,6,3,5,4]=>[.,[.,[[.,[[.,.],.]],.]]]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>[1,2,3,6,5,4]=>[.,[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>[1,2,3,5,6,4]=>[.,[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[6,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[1,6,2,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>[1,2,6,3,4,5]=>[.,[.,[[.,[.,[.,.]]],.]]]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>[1,2,3,6,4,5]=>[.,[.,[.,[[.,[.,.]],.]]]]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[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]=>[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]=>[1,2,3,4,5,7,6]=>[6,7,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[7,5,6,4,3,2,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[5,7,6,4,3,2,1]=>[[[[[.,.],.],.],.],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[5,6,7,4,3,2,1]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[7,6,4,5,3,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[6,7,4,5,3,2,1]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[7,4,6,5,3,2,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[4,7,6,5,3,2,1]=>[[[[.,.],.],.],[[[.,.],.],.]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[4,6,7,5,3,2,1]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[7,4,5,6,3,2,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[4,7,5,6,3,2,1]=>[[[[.,.],.],.],[[.,[.,.]],.]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,5,4]=>[4,5,7,6,3,2,1]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>[4,5,6,7,3,2,1]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[7,6,5,3,4,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[6,7,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[7,5,6,3,4,2,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[5,7,6,3,4,2,1]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[5,6,7,3,4,2,1]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[6,7,3,5,4,2,1]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[7,3,6,5,4,2,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[3,7,6,5,4,2,1]=>[[[.,.],.],[[[[.,.],.],.],.]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[3,6,7,5,4,2,1]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[7,3,5,6,4,2,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>[3,7,5,6,4,2,1]=>[[[.,.],.],[[[.,.],[.,.]],.]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,5,3]=>[3,5,7,6,4,2,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[3,5,6,7,4,2,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[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]=>[1,2,5,4,3,7,6]=>[6,7,3,4,5,2,1]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[7,3,6,4,5,2,1]=>[[[[.,.],.],[[.,[.,.]],.]],.]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[3,7,6,4,5,2,1]=>[[[.,.],.],[[[.,[.,.]],.],.]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[3,6,7,4,5,2,1]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,4,3,7]=>[7,3,4,6,5,2,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,4,7,3]=>[3,7,4,6,5,2,1]=>[[[.,.],.],[[.,[[.,.],.]],.]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,4,3]=>[3,4,7,6,5,2,1]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,6,4,3]=>[3,4,6,7,5,2,1]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[7,3,4,5,6,2,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[3,7,4,5,6,2,1]=>[[[.,.],.],[[.,[.,[.,.]]],.]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,5,7,4,3]=>[3,4,7,5,6,2,1]=>[[[.,.],.],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,5,4,3]=>[3,4,5,7,6,2,1]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[3,4,5,6,7,2,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[7,6,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],.],.]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[6,7,5,4,2,3,1]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[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]=>[1,3,2,4,6,7,5]=>[5,7,6,4,2,3,1]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[5,6,7,4,2,3,1]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[7,6,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[6,7,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[7,4,6,5,2,3,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[4,7,6,5,2,3,1]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[4,6,7,5,2,3,1]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[7,4,5,6,2,3,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[4,7,5,6,2,3,1]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,5,4]=>[4,5,7,6,2,3,1]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[4,5,6,7,2,3,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[7,6,5,2,4,3,1]=>[[[[[.,.],[[.,.],.]],.],.],.]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[6,7,5,2,4,3,1]=>[[[[.,.],[[.,.],.]],.],[.,.]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[7,5,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[5,7,6,2,4,3,1]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[5,6,7,2,4,3,1]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[7,6,2,5,4,3,1]=>[[[[.,.],[[[.,.],.],.]],.],.]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[6,7,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[2,7,6,5,4,3,1]=>[[.,.],[[[[[.,.],.],.],.],.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[2,6,7,5,4,3,1]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[7,2,5,6,4,3,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[2,7,5,6,4,3,1]=>[[.,.],[[[[.,.],.],[.,.]],.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,5,2]=>[2,5,7,6,4,3,1]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[2,5,6,7,4,3,1]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[7,6,2,4,5,3,1]=>[[[[.,.],[[.,.],[.,.]]],.],.]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[6,7,2,4,5,3,1]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>[7,2,6,4,5,3,1]=>[[[.,.],[[[.,.],[.,.]],.]],.]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[2,7,6,4,5,3,1]=>[[.,.],[[[[.,.],[.,.]],.],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[2,6,7,4,5,3,1]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,4,2,7]=>[7,2,4,6,5,3,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,4,7,2]=>[2,7,4,6,5,3,1]=>[[.,.],[[[.,.],[[.,.],.]],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,4,2]=>[2,4,7,6,5,3,1]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,6,4,2]=>[2,4,6,7,5,3,1]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[7,2,4,5,6,3,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[2,7,4,5,6,3,1]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,5,7,4,2]=>[2,4,7,5,6,3,1]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,5,4,2]=>[2,4,5,7,6,3,1]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[2,4,5,6,7,3,1]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[7,6,5,2,3,4,1]=>[[[[[.,.],[.,[.,.]]],.],.],.]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[6,7,5,2,3,4,1]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[7,5,6,2,3,4,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[5,7,6,2,3,4,1]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[5,6,7,2,3,4,1]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[7,6,2,5,3,4,1]=>[[[[.,.],[[.,[.,.]],.]],.],.]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[6,7,2,5,3,4,1]=>[[[.,.],[[.,[.,.]],.]],[.,.]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[7,2,6,5,3,4,1]=>[[[.,.],[[[.,[.,.]],.],.]],.]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[2,7,6,5,3,4,1]=>[[.,.],[[[[.,[.,.]],.],.],.]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[2,6,7,5,3,4,1]=>[[.,.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[7,2,5,6,3,4,1]=>[[[.,.],[[.,[.,.]],[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>[2,7,5,6,3,4,1]=>[[.,.],[[[.,[.,.]],[.,.]],.]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,6,7,5,2]=>[2,5,7,6,3,4,1]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[2,5,6,7,3,4,1]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,3,2,6,7]=>[7,6,2,3,5,4,1]=>[[[[.,.],[.,[[.,.],.]]],.],.]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,3,2,7,6]=>[6,7,2,3,5,4,1]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,3,6,2,7]=>[7,2,6,3,5,4,1]=>[[[.,.],[[.,[[.,.],.]],.]],.]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,3,6,7,2]=>[2,7,6,3,5,4,1]=>[[.,.],[[[.,[[.,.],.]],.],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,3,7,6,2]=>[2,6,7,3,5,4,1]=>[[.,.],[[.,[[.,.],.]],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,3,2,7]=>[7,2,3,6,5,4,1]=>[[[.,.],[.,[[[.,.],.],.]]],.]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,3,7,2]=>[2,7,3,6,5,4,1]=>[[.,.],[[.,[[[.,.],.],.]],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,3,2]=>[2,3,7,6,5,4,1]=>[[.,.],[.,[[[[.,.],.],.],.]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,6,3,2]=>[2,3,6,7,5,4,1]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,5,3,2,7]=>[7,2,3,5,6,4,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,5,3,7,2]=>[2,7,3,5,6,4,1]=>[[.,.],[[.,[[.,.],[.,.]]],.]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,5,7,3,2]=>[2,3,7,5,6,4,1]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,5,3,2]=>[2,3,5,7,6,4,1]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,6,5,3,2]=>[2,3,5,6,7,4,1]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[7,6,2,3,4,5,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[6,7,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[7,2,6,3,4,5,1]=>[[[.,.],[[.,[.,[.,.]]],.]],.]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[2,7,6,3,4,5,1]=>[[.,.],[[[.,[.,[.,.]]],.],.]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[2,6,7,3,4,5,1]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,4,6,3,2,7]=>[7,2,3,6,4,5,1]=>[[[.,.],[.,[[.,[.,.]],.]]],.]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,4,6,3,7,2]=>[2,7,3,6,4,5,1]=>[[.,.],[[.,[[.,[.,.]],.]],.]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,4,6,7,3,2]=>[2,3,7,6,4,5,1]=>[[.,.],[.,[[[.,[.,.]],.],.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,4,7,6,3,2]=>[2,3,6,7,4,5,1]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,4,3,2,7]=>[7,2,3,4,6,5,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,4,3,7,2]=>[2,7,3,4,6,5,1]=>[[.,.],[[.,[.,[[.,.],.]]],.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,4,7,3,2]=>[2,3,7,4,6,5,1]=>[[.,.],[.,[[.,[[.,.],.]],.]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,4,3,2]=>[2,3,4,7,6,5,1]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,6,4,3,2]=>[2,3,4,6,7,5,1]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[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]=>[1,6,5,4,3,7,2]=>[2,7,3,4,5,6,1]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,5,4,7,3,2]=>[2,3,7,4,5,6,1]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,5,7,4,3,2]=>[2,3,4,7,5,6,1]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,5,4,3,2]=>[2,3,4,5,7,6,1]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[2,3,4,5,6,7,1]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[7,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],.]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[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]=>[2,1,3,4,6,5,7]=>[7,5,6,4,3,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],.]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[5,7,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[5,6,7,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[7,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],.]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[6,7,4,5,3,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[7,4,6,5,3,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],.]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[4,7,6,5,3,1,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[4,6,7,5,3,1,2]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[7,4,5,6,3,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],.]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[4,7,5,6,3,1,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,5,4]=>[4,5,7,6,3,1,2]=>[[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[4,5,6,7,3,1,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[7,6,5,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],.],.],.]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[6,7,5,3,4,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[7,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[5,7,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[5,6,7,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[7,6,3,5,4,1,2]=>[[[[.,[.,.]],[[.,.],.]],.],.]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[6,7,3,5,4,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[7,3,6,5,4,1,2]=>[[[.,[.,.]],[[[.,.],.],.]],.]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[3,7,6,5,4,1,2]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[3,6,7,5,4,1,2]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[7,3,5,6,4,1,2]=>[[[.,[.,.]],[[.,.],[.,.]]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>[3,7,5,6,4,1,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,5,3]=>[3,5,7,6,4,1,2]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[3,5,6,7,4,1,2]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[7,6,3,4,5,1,2]=>[[[[.,[.,.]],[.,[.,.]]],.],.]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[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]=>[2,1,5,4,6,3,7]=>[7,3,6,4,5,1,2]=>[[[.,[.,.]],[[.,[.,.]],.]],.]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[3,7,6,4,5,1,2]=>[[.,[.,.]],[[[.,[.,.]],.],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[3,6,7,4,5,1,2]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,4,3,7]=>[7,3,4,6,5,1,2]=>[[[.,[.,.]],[.,[[.,.],.]]],.]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,4,7,3]=>[3,7,4,6,5,1,2]=>[[.,[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,4,3]=>[3,4,7,6,5,1,2]=>[[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,6,4,3]=>[3,4,6,7,5,1,2]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[7,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[3,7,4,5,6,1,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,5,7,4,3]=>[3,4,7,5,6,1,2]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,5,4,3]=>[3,4,5,7,6,1,2]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[3,4,5,6,7,1,2]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[7,6,5,4,1,3,2]=>[[[[[.,[[.,.],.]],.],.],.],.]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[6,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[.,.]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[7,5,6,4,1,3,2]=>[[[[.,[[.,.],.]],.],[.,.]],.]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[5,7,6,4,1,3,2]=>[[[.,[[.,.],.]],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[5,6,7,4,1,3,2]=>[[[.,[[.,.],.]],.],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[7,6,4,5,1,3,2]=>[[[[.,[[.,.],.]],[.,.]],.],.]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[6,7,4,5,1,3,2]=>[[[.,[[.,.],.]],[.,.]],[.,.]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[7,4,6,5,1,3,2]=>[[[.,[[.,.],.]],[[.,.],.]],.]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[4,7,6,5,1,3,2]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[4,6,7,5,1,3,2]=>[[.,[[.,.],.]],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[7,4,5,6,1,3,2]=>[[[.,[[.,.],.]],[.,[.,.]]],.]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[4,7,5,6,1,3,2]=>[[.,[[.,.],.]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,5,4]=>[4,5,7,6,1,3,2]=>[[.,[[.,.],.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[4,5,6,7,1,3,2]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[7,6,5,1,4,3,2]=>[[[[.,[[[.,.],.],.]],.],.],.]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[6,7,5,1,4,3,2]=>[[[.,[[[.,.],.],.]],.],[.,.]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[7,5,6,1,4,3,2]=>[[[.,[[[.,.],.],.]],[.,.]],.]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[5,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[5,6,7,1,4,3,2]=>[[.,[[[.,.],.],.]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[7,6,1,5,4,3,2]=>[[[.,[[[[.,.],.],.],.]],.],.]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[6,7,1,5,4,3,2]=>[[.,[[[[.,.],.],.],.]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[7,1,6,5,4,3,2]=>[[.,[[[[[.,.],.],.],.],.]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[1,6,7,5,4,3,2]=>[.,[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[7,1,5,6,4,3,2]=>[[.,[[[[.,.],.],.],[.,.]]],.]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[1,7,5,6,4,3,2]=>[.,[[[[[.,.],.],.],[.,.]],.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,5,1]=>[1,5,7,6,4,3,2]=>[.,[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[1,5,6,7,4,3,2]=>[.,[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[7,6,1,4,5,3,2]=>[[[.,[[[.,.],.],[.,.]]],.],.]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[6,7,1,4,5,3,2]=>[[.,[[[.,.],.],[.,.]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[7,1,6,4,5,3,2]=>[[.,[[[[.,.],.],[.,.]],.]],.]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[1,7,6,4,5,3,2]=>[.,[[[[[.,.],.],[.,.]],.],.]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[1,6,7,4,5,3,2]=>[.,[[[[.,.],.],[.,.]],[.,.]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,4,1,7]=>[7,1,4,6,5,3,2]=>[[.,[[[.,.],.],[[.,.],.]]],.]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,4,7,1]=>[1,7,4,6,5,3,2]=>[.,[[[[.,.],.],[[.,.],.]],.]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,4,1]=>[1,4,7,6,5,3,2]=>[.,[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,6,4,1]=>[1,4,6,7,5,3,2]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[7,1,4,5,6,3,2]=>[[.,[[[.,.],.],[.,[.,.]]]],.]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[1,7,4,5,6,3,2]=>[.,[[[[.,.],.],[.,[.,.]]],.]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,5,7,4,1]=>[1,4,7,5,6,3,2]=>[.,[[[.,.],.],[[.,[.,.]],.]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,5,4,1]=>[1,4,5,7,6,3,2]=>[.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[1,4,5,6,7,3,2]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>[7,6,5,1,3,4,2]=>[[[[.,[[.,.],[.,.]]],.],.],.]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[6,7,5,1,3,4,2]=>[[[.,[[.,.],[.,.]]],.],[.,.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[7,5,6,1,3,4,2]=>[[[.,[[.,.],[.,.]]],[.,.]],.]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[5,7,6,1,3,4,2]=>[[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[5,6,7,1,3,4,2]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[7,6,1,5,3,4,2]=>[[[.,[[[.,.],[.,.]],.]],.],.]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[6,7,1,5,3,4,2]=>[[.,[[[.,.],[.,.]],.]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[7,1,6,5,3,4,2]=>[[.,[[[[.,.],[.,.]],.],.]],.]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[1,7,6,5,3,4,2]=>[.,[[[[[.,.],[.,.]],.],.],.]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[1,6,7,5,3,4,2]=>[.,[[[[.,.],[.,.]],.],[.,.]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[7,1,5,6,3,4,2]=>[[.,[[[.,.],[.,.]],[.,.]]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[1,7,5,6,3,4,2]=>[.,[[[[.,.],[.,.]],[.,.]],.]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,6,7,5,1]=>[1,5,7,6,3,4,2]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[1,5,6,7,3,4,2]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,3,1,6,7]=>[7,6,1,3,5,4,2]=>[[[.,[[.,.],[[.,.],.]]],.],.]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,3,1,7,6]=>[6,7,1,3,5,4,2]=>[[.,[[.,.],[[.,.],.]]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,3,6,1,7]=>[7,1,6,3,5,4,2]=>[[.,[[[.,.],[[.,.],.]],.]],.]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,3,6,7,1]=>[1,7,6,3,5,4,2]=>[.,[[[[.,.],[[.,.],.]],.],.]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,3,7,6,1]=>[1,6,7,3,5,4,2]=>[.,[[[.,.],[[.,.],.]],[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,3,1,7]=>[7,1,3,6,5,4,2]=>[[.,[[.,.],[[[.,.],.],.]]],.]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,3,7,1]=>[1,7,3,6,5,4,2]=>[.,[[[.,.],[[[.,.],.],.]],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,3,1]=>[1,3,7,6,5,4,2]=>[.,[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,6,3,1]=>[1,3,6,7,5,4,2]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,5,3,1,7]=>[7,1,3,5,6,4,2]=>[[.,[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,5,3,7,1]=>[1,7,3,5,6,4,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,5,7,3,1]=>[1,3,7,5,6,4,2]=>[.,[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,5,3,1]=>[1,3,5,7,6,4,2]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,6,5,3,1]=>[1,3,5,6,7,4,2]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[7,6,1,3,4,5,2]=>[[[.,[[.,.],[.,[.,.]]]],.],.]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[6,7,1,3,4,5,2]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[7,1,6,3,4,5,2]=>[[.,[[[.,.],[.,[.,.]]],.]],.]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[1,7,6,3,4,5,2]=>[.,[[[[.,.],[.,[.,.]]],.],.]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[1,6,7,3,4,5,2]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,4,6,3,1,7]=>[7,1,3,6,4,5,2]=>[[.,[[.,.],[[.,[.,.]],.]]],.]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,4,6,3,7,1]=>[1,7,3,6,4,5,2]=>[.,[[[.,.],[[.,[.,.]],.]],.]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,4,6,7,3,1]=>[1,3,7,6,4,5,2]=>[.,[[.,.],[[[.,[.,.]],.],.]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,4,7,6,3,1]=>[1,3,6,7,4,5,2]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,4,3,1,7]=>[7,1,3,4,6,5,2]=>[[.,[[.,.],[.,[[.,.],.]]]],.]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,4,3,7,1]=>[1,7,3,4,6,5,2]=>[.,[[[.,.],[.,[[.,.],.]]],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,4,7,3,1]=>[1,3,7,4,6,5,2]=>[.,[[.,.],[[.,[[.,.],.]],.]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,4,3,1]=>[1,3,4,7,6,5,2]=>[.,[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,6,4,3,1]=>[1,3,4,6,7,5,2]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[7,1,3,4,5,6,2]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[1,7,3,4,5,6,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,5,4,7,3,1]=>[1,3,7,4,5,6,2]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,5,7,4,3,1]=>[1,3,4,7,5,6,2]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,5,4,3,1]=>[1,3,4,5,7,6,2]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[1,3,4,5,6,7,2]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[7,6,5,4,1,2,3]=>[[[[[.,[.,[.,.]]],.],.],.],.]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[6,7,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,.]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[7,5,6,4,1,2,3]=>[[[[.,[.,[.,.]]],.],[.,.]],.]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[5,7,6,4,1,2,3]=>[[[.,[.,[.,.]]],.],[[.,.],.]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[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]=>[3,2,1,5,4,6,7]=>[7,6,4,5,1,2,3]=>[[[[.,[.,[.,.]]],[.,.]],.],.]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[6,7,4,5,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[7,4,6,5,1,2,3]=>[[[.,[.,[.,.]]],[[.,.],.]],.]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[4,7,6,5,1,2,3]=>[[.,[.,[.,.]]],[[[.,.],.],.]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[4,6,7,5,1,2,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[7,4,5,6,1,2,3]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[4,7,5,6,1,2,3]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,6,7,5,4]=>[4,5,7,6,1,2,3]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[4,5,6,7,1,2,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>[7,6,5,1,4,2,3]=>[[[[.,[[.,[.,.]],.]],.],.],.]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[6,7,5,1,4,2,3]=>[[[.,[[.,[.,.]],.]],.],[.,.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>[7,5,6,1,4,2,3]=>[[[.,[[.,[.,.]],.]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>[5,7,6,1,4,2,3]=>[[.,[[.,[.,.]],.]],[[.,.],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[5,6,7,1,4,2,3]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[7,6,1,5,4,2,3]=>[[[.,[[[.,[.,.]],.],.]],.],.]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[6,7,1,5,4,2,3]=>[[.,[[[.,[.,.]],.],.]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[7,1,6,5,4,2,3]=>[[.,[[[[.,[.,.]],.],.],.]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[1,7,6,5,4,2,3]=>[.,[[[[[.,[.,.]],.],.],.],.]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[1,6,7,5,4,2,3]=>[.,[[[[.,[.,.]],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[7,1,5,6,4,2,3]=>[[.,[[[.,[.,.]],.],[.,.]]],.]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[1,7,5,6,4,2,3]=>[.,[[[[.,[.,.]],.],[.,.]],.]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,6,7,5,1]=>[1,5,7,6,4,2,3]=>[.,[[[.,[.,.]],.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[1,5,6,7,4,2,3]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[7,6,1,4,5,2,3]=>[[[.,[[.,[.,.]],[.,.]]],.],.]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[6,7,1,4,5,2,3]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[7,1,6,4,5,2,3]=>[[.,[[[.,[.,.]],[.,.]],.]],.]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[1,7,6,4,5,2,3]=>[.,[[[[.,[.,.]],[.,.]],.],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[1,6,7,4,5,2,3]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,5,6,4,1,7]=>[7,1,4,6,5,2,3]=>[[.,[[.,[.,.]],[[.,.],.]]],.]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,5,6,4,7,1]=>[1,7,4,6,5,2,3]=>[.,[[[.,[.,.]],[[.,.],.]],.]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,4,1]=>[1,4,7,6,5,2,3]=>[.,[[.,[.,.]],[[[.,.],.],.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,5,7,6,4,1]=>[1,4,6,7,5,2,3]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[7,1,4,5,6,2,3]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[1,7,4,5,6,2,3]=>[.,[[[.,[.,.]],[.,[.,.]]],.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,6,5,7,4,1]=>[1,4,7,5,6,2,3]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,6,7,5,4,1]=>[1,4,5,7,6,2,3]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[1,4,5,6,7,2,3]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7]=>[7,6,5,1,2,4,3]=>[[[[.,[.,[[.,.],.]]],.],.],.]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,2,1,5,7,6]=>[6,7,5,1,2,4,3]=>[[[.,[.,[[.,.],.]]],.],[.,.]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,2,1,6,5,7]=>[7,5,6,1,2,4,3]=>[[[.,[.,[[.,.],.]]],[.,.]],.]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,2,1,6,7,5]=>[5,7,6,1,2,4,3]=>[[.,[.,[[.,.],.]]],[[.,.],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,2,1,7,6,5]=>[5,6,7,1,2,4,3]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,2,5,1,6,7]=>[7,6,1,5,2,4,3]=>[[[.,[[.,[[.,.],.]],.]],.],.]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,2,5,1,7,6]=>[6,7,1,5,2,4,3]=>[[.,[[.,[[.,.],.]],.]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,1,7]=>[7,1,6,5,2,4,3]=>[[.,[[[.,[[.,.],.]],.],.]],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,1]=>[1,7,6,5,2,4,3]=>[.,[[[[.,[[.,.],.]],.],.],.]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,2,5,7,6,1]=>[1,6,7,5,2,4,3]=>[.,[[[.,[[.,.],.]],.],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,2,6,5,1,7]=>[7,1,5,6,2,4,3]=>[[.,[[.,[[.,.],.]],[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,2,6,5,7,1]=>[1,7,5,6,2,4,3]=>[.,[[[.,[[.,.],.]],[.,.]],.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,2,6,7,5,1]=>[1,5,7,6,2,4,3]=>[.,[[.,[[.,.],.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,2,7,6,5,1]=>[1,5,6,7,2,4,3]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,2,1,6,7]=>[7,6,1,2,5,4,3]=>[[[.,[.,[[[.,.],.],.]]],.],.]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,2,1,7,6]=>[6,7,1,2,5,4,3]=>[[.,[.,[[[.,.],.],.]]],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,2,6,1,7]=>[7,1,6,2,5,4,3]=>[[.,[[.,[[[.,.],.],.]],.]],.]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,2,6,7,1]=>[1,7,6,2,5,4,3]=>[.,[[[.,[[[.,.],.],.]],.],.]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,2,7,6,1]=>[1,6,7,2,5,4,3]=>[.,[[.,[[[.,.],.],.]],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,2,1,7]=>[7,1,2,6,5,4,3]=>[[.,[.,[[[[.,.],.],.],.]]],.]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,2,7,1]=>[1,7,2,6,5,4,3]=>[.,[[.,[[[[.,.],.],.],.]],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,2,1]=>[1,2,7,6,5,4,3]=>[.,[.,[[[[[.,.],.],.],.],.]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,6,2,1]=>[1,2,6,7,5,4,3]=>[.,[.,[[[[.,.],.],.],[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,5,2,1,7]=>[7,1,2,5,6,4,3]=>[[.,[.,[[[.,.],.],[.,.]]]],.]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,5,2,7,1]=>[1,7,2,5,6,4,3]=>[.,[[.,[[[.,.],.],[.,.]]],.]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,5,7,2,1]=>[1,2,7,5,6,4,3]=>[.,[.,[[[[.,.],.],[.,.]],.]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,5,2,1]=>[1,2,5,7,6,4,3]=>[.,[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,6,5,2,1]=>[1,2,5,6,7,4,3]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,4,2,1,6,7]=>[7,6,1,2,4,5,3]=>[[[.,[.,[[.,.],[.,.]]]],.],.]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,4,2,1,7,6]=>[6,7,1,2,4,5,3]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,4,2,6,1,7]=>[7,1,6,2,4,5,3]=>[[.,[[.,[[.,.],[.,.]]],.]],.]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,4,2,6,7,1]=>[1,7,6,2,4,5,3]=>[.,[[[.,[[.,.],[.,.]]],.],.]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,4,2,7,6,1]=>[1,6,7,2,4,5,3]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,4,6,2,1,7]=>[7,1,2,6,4,5,3]=>[[.,[.,[[[.,.],[.,.]],.]]],.]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,4,6,2,7,1]=>[1,7,2,6,4,5,3]=>[.,[[.,[[[.,.],[.,.]],.]],.]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,4,6,7,2,1]=>[1,2,7,6,4,5,3]=>[.,[.,[[[[.,.],[.,.]],.],.]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,4,7,6,2,1]=>[1,2,6,7,4,5,3]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,4,2,1,7]=>[7,1,2,4,6,5,3]=>[[.,[.,[[.,.],[[.,.],.]]]],.]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,4,2,7,1]=>[1,7,2,4,6,5,3]=>[.,[[.,[[.,.],[[.,.],.]]],.]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,4,7,2,1]=>[1,2,7,4,6,5,3]=>[.,[.,[[[.,.],[[.,.],.]],.]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,4,2,1]=>[1,2,4,7,6,5,3]=>[.,[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,6,4,2,1]=>[1,2,4,6,7,5,3]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,5,4,2,1,7]=>[7,1,2,4,5,6,3]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,5,4,2,7,1]=>[1,7,2,4,5,6,3]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,5,4,7,2,1]=>[1,2,7,4,5,6,3]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,5,7,4,2,1]=>[1,2,4,7,5,6,3]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,5,4,2,1]=>[1,2,4,5,7,6,3]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,6,5,4,2,1]=>[1,2,4,5,6,7,3]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[7,6,5,1,2,3,4]=>[[[[.,[.,[.,[.,.]]]],.],.],.]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[6,7,5,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[7,5,6,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[5,7,6,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[5,6,7,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>[7,6,1,5,2,3,4]=>[[[.,[[.,[.,[.,.]]],.]],.],.]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[6,7,1,5,2,3,4]=>[[.,[[.,[.,[.,.]]],.]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[7,1,6,5,2,3,4]=>[[.,[[[.,[.,[.,.]]],.],.]],.]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[1,7,6,5,2,3,4]=>[.,[[[[.,[.,[.,.]]],.],.],.]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[1,6,7,5,2,3,4]=>[.,[[[.,[.,[.,.]]],.],[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[7,1,5,6,2,3,4]=>[[.,[[.,[.,[.,.]]],[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[1,7,5,6,2,3,4]=>[.,[[[.,[.,[.,.]]],[.,.]],.]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,6,7,5,1]=>[1,5,7,6,2,3,4]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[1,5,6,7,2,3,4]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,3,5,2,1,6,7]=>[7,6,1,2,5,3,4]=>[[[.,[.,[[.,[.,.]],.]]],.],.]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,3,5,2,1,7,6]=>[6,7,1,2,5,3,4]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,3,5,2,6,1,7]=>[7,1,6,2,5,3,4]=>[[.,[[.,[[.,[.,.]],.]],.]],.]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,3,5,2,6,7,1]=>[1,7,6,2,5,3,4]=>[.,[[[.,[[.,[.,.]],.]],.],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,3,5,2,7,6,1]=>[1,6,7,2,5,3,4]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,3,5,6,2,1,7]=>[7,1,2,6,5,3,4]=>[[.,[.,[[[.,[.,.]],.],.]]],.]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,2,7,1]=>[1,7,2,6,5,3,4]=>[.,[[.,[[[.,[.,.]],.],.]],.]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,2,1]=>[1,2,7,6,5,3,4]=>[.,[.,[[[[.,[.,.]],.],.],.]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,3,5,7,6,2,1]=>[1,2,6,7,5,3,4]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,3,6,5,2,1,7]=>[7,1,2,5,6,3,4]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,3,6,5,2,7,1]=>[1,7,2,5,6,3,4]=>[.,[[.,[[.,[.,.]],[.,.]]],.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,3,6,5,7,2,1]=>[1,2,7,5,6,3,4]=>[.,[.,[[[.,[.,.]],[.,.]],.]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,6,7,5,2,1]=>[1,2,5,7,6,3,4]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3,7,6,5,2,1]=>[1,2,5,6,7,3,4]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,3,2,1,6,7]=>[7,6,1,2,3,5,4]=>[[[.,[.,[.,[[.,.],.]]]],.],.]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,3,2,1,7,6]=>[6,7,1,2,3,5,4]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,3,2,6,1,7]=>[7,1,6,2,3,5,4]=>[[.,[[.,[.,[[.,.],.]]],.]],.]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,3,2,6,7,1]=>[1,7,6,2,3,5,4]=>[.,[[[.,[.,[[.,.],.]]],.],.]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,3,2,7,6,1]=>[1,6,7,2,3,5,4]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,3,6,2,1,7]=>[7,1,2,6,3,5,4]=>[[.,[.,[[.,[[.,.],.]],.]]],.]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1]=>[1,7,2,6,3,5,4]=>[.,[[.,[[.,[[.,.],.]],.]],.]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,3,6,7,2,1]=>[1,2,7,6,3,5,4]=>[.,[.,[[[.,[[.,.],.]],.],.]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,3,7,6,2,1]=>[1,2,6,7,3,5,4]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,3,2,1,7]=>[7,1,2,3,6,5,4]=>[[.,[.,[.,[[[.,.],.],.]]]],.]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,3,2,7,1]=>[1,7,2,3,6,5,4]=>[.,[[.,[.,[[[.,.],.],.]]],.]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,3,7,2,1]=>[1,2,7,3,6,5,4]=>[.,[.,[[.,[[[.,.],.],.]],.]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[1,2,3,7,6,5,4]=>[.,[.,[.,[[[[.,.],.],.],.]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,6,3,2,1]=>[1,2,3,6,7,5,4]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,5,3,2,1,7]=>[7,1,2,3,5,6,4]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,5,3,2,7,1]=>[1,7,2,3,5,6,4]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,5,3,7,2,1]=>[1,2,7,3,5,6,4]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,5,7,3,2,1]=>[1,2,3,7,5,6,4]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,5,3,2,1]=>[1,2,3,5,7,6,4]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,6,5,3,2,1]=>[1,2,3,5,6,7,4]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[7,6,1,2,3,4,5]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[6,7,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[7,1,6,2,3,4,5]=>[[.,[[.,[.,[.,[.,.]]]],.]],.]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[1,7,6,2,3,4,5]=>[.,[[[.,[.,[.,[.,.]]]],.],.]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[1,6,7,2,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,4,3,6,2,1,7]=>[7,1,2,6,3,4,5]=>[[.,[.,[[.,[.,[.,.]]],.]]],.]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,4,3,6,2,7,1]=>[1,7,2,6,3,4,5]=>[.,[[.,[[.,[.,[.,.]]],.]],.]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[1,2,7,6,3,4,5]=>[.,[.,[[[.,[.,[.,.]]],.],.]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,4,3,7,6,2,1]=>[1,2,6,7,3,4,5]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,4,6,3,2,1,7]=>[7,1,2,3,6,4,5]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,4,6,3,2,7,1]=>[1,7,2,3,6,4,5]=>[.,[[.,[.,[[.,[.,.]],.]]],.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[1,2,7,3,6,4,5]=>[.,[.,[[.,[[.,[.,.]],.]],.]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1]=>[1,2,3,7,6,4,5]=>[.,[.,[.,[[[.,[.,.]],.],.]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,3,2,1]=>[1,2,3,6,7,4,5]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,4,3,2,1,7]=>[7,1,2,3,4,6,5]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,4,3,2,7,1]=>[1,7,2,3,4,6,5]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,4,3,7,2,1]=>[1,2,7,3,4,6,5]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,4,7,3,2,1]=>[1,2,3,7,4,6,5]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,4,3,2,1]=>[1,2,3,4,7,6,5]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,6,4,3,2,1]=>[1,2,3,4,6,7,5]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[7,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[1,7,2,3,4,5,6]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,5,4,3,7,2,1]=>[1,2,7,3,4,5,6]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,5,4,7,3,2,1]=>[1,2,3,7,4,5,6]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,5,7,4,3,2,1]=>[1,2,3,4,7,5,6]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,5,4,3,2,1]=>[1,2,3,4,5,7,6]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>[8,7,5,6,3,4,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,6,7,5,8]=>[8,5,7,6,2,4,3,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,7,6,5,8]=>[8,5,6,7,2,3,4,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,8,7]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>[5,6,7,8,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>[7,8,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>[3,4,5,6,7,8,1,2]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>[6,8,7,5,4,1,3,2]=>[[[[.,[[.,.],.]],.],.],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>[5,8,7,6,1,4,3,2]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,4,3,1,7,6,8,5]=>[5,8,6,7,1,3,4,2]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,5,8,7,6]=>[6,7,8,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,2,4,1,6,8,7,5]=>[5,7,8,6,1,4,2,3]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,4,2,1,7,8,6,5]=>[5,6,8,7,1,2,4,3]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7]=>[7,8,5,6,1,2,3,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>[5,6,7,8,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,5,4,3,2,1,8,7]=>[7,8,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
Map
to 312-avoiding permutation
Description
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
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.