Identifier
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
Permutations
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00175: Permutations —inverse Foata bijection⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-3
[1,0]=>[1]=>[1]=>[.,.]
[1,0,1,0]=>[1,2]=>[1,2]=>[.,[.,.]]
[1,1,0,0]=>[2,1]=>[2,1]=>[[.,.],.]
[1,0,1,0,1,0]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[1,0,1,1,0,0]=>[1,3,2]=>[3,1,2]=>[[.,.],[.,.]]
[1,1,0,0,1,0]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[1,1,0,1,0,0]=>[2,3,1]=>[2,3,1]=>[[.,[.,.]],.]
[1,1,1,0,0,0]=>[3,2,1]=>[3,2,1]=>[[[.,.],.],.]
[1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[3,4,1,2]=>[[.,[.,.]],[.,.]]
[1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[4,3,1,2]=>[[[.,.],.],[.,.]]
[1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[3,2,4,1]=>[[[.,.],[.,.]],.]
[1,1,1,0,1,0,0,0]=>[3,4,2,1]=>[3,4,2,1]=>[[[.,[.,.]],.],.]
[1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[4,5,1,2,3]=>[[.,[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[3,5,1,2,4]=>[[.,[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[3,4,5,1,2]=>[[.,[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[5,3,4,1,2]=>[[[.,.],[.,.]],[.,.]]
[1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]
[1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[4,3,5,1,2]=>[[[.,.],[.,.]],[.,.]]
[1,0,1,1,1,0,1,0,0,0]=>[1,4,5,3,2]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]
[1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[2,4,5,1,3]=>[[.,[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[5,2,4,1,3]=>[[[.,.],[.,.]],[.,.]]
[1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]
[1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>[4,5,2,3,1]=>[[[.,[.,.]],[.,.]],.]
[1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.]
[1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[3,2,5,1,4]=>[[[.,.],[.,.]],[.,.]]
[1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]
[1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]
[1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[3,5,2,4,1]=>[[[.,[.,.]],[.,.]],.]
[1,1,1,0,1,0,0,0,1,0]=>[3,4,2,1,5]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]]
[1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]
[1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>[3,4,5,2,1]=>[[[.,[.,[.,.]]],.],.]
[1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>[5,3,4,2,1]=>[[[[.,.],[.,.]],.],.]
[1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]
[1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.]
[1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>[4,5,3,2,1]=>[[[[.,[.,.]],.],.],.]
[1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[6,1,2,3,4,5]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[5,1,2,3,4,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[5,6,1,2,3,4]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[6,5,1,2,3,4]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[4,1,2,3,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[4,6,1,2,3,5]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[4,5,1,2,3,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[4,5,6,1,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[6,4,5,1,2,3]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[5,4,1,2,3,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[5,4,6,1,2,3]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,4,3]=>[5,6,4,1,2,3]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[6,5,4,1,2,3]=>[[[[.,.],.],.],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[3,1,2,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[3,6,1,2,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[3,5,1,2,4,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[3,5,6,1,2,4]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[6,3,5,1,2,4]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[3,4,1,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[3,4,6,1,2,5]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[3,4,5,1,2,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[3,4,5,6,1,2]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[6,3,4,5,1,2]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[5,3,4,1,2,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[5,3,4,6,1,2]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,4,2]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[6,5,3,4,1,2]=>[[[[.,.],.],[.,.]],[.,.]]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[4,3,1,2,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[4,3,6,1,2,5]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[4,3,5,1,2,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[4,3,5,6,1,2]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[4,6,3,5,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,3,2,6]=>[4,5,3,1,2,6]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,3,6,2]=>[4,5,3,6,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,3,2]=>[4,5,6,3,1,2]=>[[[.,[.,[.,.]]],.],[.,.]]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,5,3,2]=>[6,4,5,3,1,2]=>[[[[.,.],[.,.]],.],[.,.]]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[5,4,3,1,2,6]=>[[[[.,.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[5,4,3,6,1,2]=>[[[[.,.],.],[.,.]],[.,.]]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,4,6,3,2]=>[5,4,6,3,1,2]=>[[[[.,.],[.,.]],.],[.,.]]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,4,3,2]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[6,5,4,3,1,2]=>[[[[[.,.],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[2,6,1,3,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[2,5,1,3,4,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[2,5,6,1,3,4]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[6,2,5,1,3,4]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[2,4,1,3,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[2,4,6,1,3,5]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[2,4,5,1,3,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[2,4,5,6,1,3]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[6,2,4,5,1,3]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[5,2,4,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[5,2,4,6,1,3]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,4,3]=>[5,6,2,4,1,3]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[6,5,2,4,1,3]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[2,3,1,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[2,3,6,1,4,5]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[2,3,5,1,4,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[2,3,5,6,1,4]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[6,2,3,5,1,4]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[2,3,4,1,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[2,3,4,6,1,5]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[2,3,4,5,1,6]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[2,3,4,5,6,1]=>[[.,[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[5,2,3,4,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[5,2,3,4,6,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>[5,6,2,3,4,1]=>[[[.,[.,.]],[.,[.,.]]],.]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[6,5,2,3,4,1]=>[[[[.,.],.],[.,[.,.]]],.]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[4,2,3,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[4,2,3,6,1,5]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[4,2,3,5,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[4,2,3,5,6,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[4,6,2,3,5,1]=>[[[.,[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,3,1,6]=>[4,5,2,3,1,6]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>[4,5,2,3,6,1]=>[[[.,[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>[4,5,6,2,3,1]=>[[[.,[.,[.,.]]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>[6,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[5,4,2,3,1,6]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[5,4,2,3,6,1]=>[[[[.,.],.],[.,[.,.]]],.]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>[5,4,6,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>[5,6,4,2,3,1]=>[[[[.,[.,.]],.],[.,.]],.]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[6,5,4,2,3,1]=>[[[[[.,.],.],.],[.,.]],.]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[3,2,6,1,4,5]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[3,2,5,1,4,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[3,2,5,6,1,4]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[3,6,2,5,1,4]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[3,2,4,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[3,2,4,6,1,5]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[3,2,4,5,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[3,2,4,5,6,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[3,6,2,4,5,1]=>[[[.,[.,.]],[.,[.,.]]],.]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[3,5,2,4,1,6]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[3,5,2,4,6,1]=>[[[.,[.,.]],[.,[.,.]]],.]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>[3,5,6,2,4,1]=>[[[.,[.,[.,.]]],[.,.]],.]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[6,3,5,2,4,1]=>[[[[.,.],[.,.]],[.,.]],.]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,2,1,5,6]=>[3,4,2,1,5,6]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2,1,6,5]=>[3,4,2,6,1,5]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,2,5,1,6]=>[3,4,2,5,1,6]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>[3,4,2,5,6,1]=>[[[.,[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>[3,4,6,2,5,1]=>[[[.,[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,2,1,6]=>[3,4,5,2,1,6]=>[[[.,[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>[3,4,5,2,6,1]=>[[[.,[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>[3,4,5,6,2,1]=>[[[.,[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>[6,3,4,5,2,1]=>[[[[.,.],[.,[.,.]]],.],.]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,4,2,1,6]=>[5,3,4,2,1,6]=>[[[[.,.],[.,.]],.],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>[5,3,4,2,6,1]=>[[[[.,.],[.,.]],[.,.]],.]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>[5,3,4,6,2,1]=>[[[[.,.],[.,[.,.]]],.],.]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>[5,6,3,4,2,1]=>[[[[.,[.,.]],[.,.]],.],.]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[4,3,2,6,1,5]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[4,3,2,5,1,6]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[4,3,2,5,6,1]=>[[[[.,.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[4,3,6,2,5,1]=>[[[[.,.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,3,5,2,1,6]=>[4,3,5,2,1,6]=>[[[[.,.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>[4,3,5,2,6,1]=>[[[[.,.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[4,3,5,6,2,1]=>[[[[.,.],[.,[.,.]]],.],.]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>[4,6,3,5,2,1]=>[[[[.,[.,.]],[.,.]],.],.]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,3,2,1,6]=>[4,5,3,2,1,6]=>[[[[.,[.,.]],.],.],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>[4,5,3,2,6,1]=>[[[[.,[.,.]],.],[.,.]],.]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>[4,5,3,6,2,1]=>[[[[.,[.,.]],[.,.]],.],.]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>[4,5,6,3,2,1]=>[[[[.,[.,[.,.]]],.],.],.]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>[6,4,5,3,2,1]=>[[[[[.,.],[.,.]],.],.],.]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[5,4,3,2,6,1]=>[[[[[.,.],.],.],[.,.]],.]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>[5,4,3,6,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>[5,4,6,3,2,1]=>[[[[[.,.],[.,.]],.],.],.]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>[5,6,4,3,2,1]=>[[[[[.,[.,.]],.],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[7,1,2,3,4,5,6]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[6,1,2,3,4,5,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[6,7,1,2,3,4,5]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[7,6,1,2,3,4,5]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[5,1,2,3,4,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[5,7,1,2,3,4,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[5,6,1,2,3,4,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[5,6,7,1,2,3,4]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[7,5,6,1,2,3,4]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[6,5,1,2,3,4,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[6,5,7,1,2,3,4]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,5,4]=>[6,7,5,1,2,3,4]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[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]=>[1,2,4,3,5,6,7]=>[4,1,2,3,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[4,7,1,2,3,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[4,6,1,2,3,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[4,6,7,1,2,3,5]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[7,4,6,1,2,3,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[4,5,1,2,3,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[4,5,7,1,2,3,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[4,5,6,1,2,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[4,5,6,7,1,2,3]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[7,4,5,6,1,2,3]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[6,4,5,1,2,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>[6,4,5,7,1,2,3]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,5,3]=>[6,7,4,5,1,2,3]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[7,6,4,5,1,2,3]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[5,4,1,2,3,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[5,4,7,1,2,3,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[5,4,6,1,2,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[5,4,6,7,1,2,3]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[5,7,4,6,1,2,3]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,4,3,7]=>[5,6,4,1,2,3,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,4,7,3]=>[5,6,4,7,1,2,3]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,4,3]=>[5,6,7,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,6,4,3]=>[7,5,6,4,1,2,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[6,5,4,1,2,3,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[6,5,4,7,1,2,3]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,5,7,4,3]=>[6,5,7,4,1,2,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,5,4,3]=>[6,7,5,4,1,2,3]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[7,6,5,4,1,2,3]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[3,7,1,2,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[3,6,1,2,4,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[3,6,7,1,2,4,5]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[7,3,6,1,2,4,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[3,5,1,2,4,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[3,5,7,1,2,4,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[3,5,6,1,2,4,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[3,5,6,7,1,2,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[7,3,5,6,1,2,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[6,3,5,1,2,4,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[6,3,5,7,1,2,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,5,4]=>[6,7,3,5,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[7,6,3,5,1,2,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[3,4,1,2,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[3,4,7,1,2,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[3,4,6,1,2,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[3,4,6,7,1,2,5]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[7,3,4,6,1,2,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[3,4,5,1,2,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[3,4,5,7,1,2,6]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[3,4,5,6,1,2,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[3,4,5,6,7,1,2]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[7,3,4,5,6,1,2]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[6,3,4,5,1,2,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[6,3,4,5,7,1,2]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,5,2]=>[6,7,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[7,6,3,4,5,1,2]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[5,3,4,1,2,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[5,3,4,7,1,2,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>[5,3,4,6,1,2,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[5,3,4,6,7,1,2]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[5,7,3,4,6,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,4,2,7]=>[5,6,3,4,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,4,7,2]=>[5,6,3,4,7,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,4,2]=>[5,6,7,3,4,1,2]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,6,4,2]=>[7,5,6,3,4,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[6,5,3,4,1,2,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[6,5,3,4,7,1,2]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,5,7,4,2]=>[6,5,7,3,4,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,5,4,2]=>[6,7,5,3,4,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[7,6,5,3,4,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[4,3,1,2,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[4,3,7,1,2,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[4,3,6,1,2,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[4,3,6,7,1,2,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[4,7,3,6,1,2,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[4,3,5,1,2,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[4,3,5,7,1,2,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[4,3,5,6,1,2,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[4,3,5,6,7,1,2]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[4,7,3,5,6,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[4,6,3,5,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>[4,6,3,5,7,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,6,7,5,2]=>[4,6,7,3,5,1,2]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[7,4,6,3,5,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,3,2,6,7]=>[4,5,3,1,2,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,3,2,7,6]=>[4,5,3,7,1,2,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,3,6,2,7]=>[4,5,3,6,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,3,6,7,2]=>[4,5,3,6,7,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,3,7,6,2]=>[4,5,7,3,6,1,2]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,3,2,7]=>[4,5,6,3,1,2,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,3,7,2]=>[4,5,6,3,7,1,2]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,3,2]=>[4,5,6,7,3,1,2]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,6,3,2]=>[7,4,5,6,3,1,2]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,5,3,2,7]=>[6,4,5,3,1,2,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,5,3,7,2]=>[6,4,5,3,7,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,5,7,3,2]=>[6,4,5,7,3,1,2]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,5,3,2]=>[6,7,4,5,3,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,6,5,3,2]=>[7,6,4,5,3,1,2]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[5,4,3,1,2,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[5,4,3,7,1,2,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[5,4,3,6,1,2,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[5,4,3,6,7,1,2]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[5,4,7,3,6,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,4,6,3,2,7]=>[5,4,6,3,1,2,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,4,6,3,7,2]=>[5,4,6,3,7,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,4,6,7,3,2]=>[5,4,6,7,3,1,2]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,4,7,6,3,2]=>[5,7,4,6,3,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,4,3,2,7]=>[5,6,4,3,1,2,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,4,3,7,2]=>[5,6,4,3,7,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,4,7,3,2]=>[5,6,4,7,3,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,4,3,2]=>[5,6,7,4,3,1,2]=>[[[[.,[.,[.,.]]],.],.],[.,.]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,6,4,3,2]=>[7,5,6,4,3,1,2]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[6,5,4,3,1,2,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[6,5,4,3,7,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,5,4,7,3,2]=>[6,5,4,7,3,1,2]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,5,7,4,3,2]=>[6,5,7,4,3,1,2]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,5,4,3,2]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[7,6,5,4,3,1,2]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[2,7,1,3,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[2,6,1,3,4,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[2,6,7,1,3,4,5]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[7,2,6,1,3,4,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[2,5,1,3,4,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[2,5,7,1,3,4,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[2,5,6,1,3,4,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[2,5,6,7,1,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[7,2,5,6,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[6,2,5,1,3,4,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[6,2,5,7,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,5,4]=>[6,7,2,5,1,3,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[7,6,2,5,1,3,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[2,4,1,3,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[2,4,7,1,3,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[2,4,6,1,3,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[2,4,6,7,1,3,5]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[7,2,4,6,1,3,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[2,4,5,1,3,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[2,4,5,7,1,3,6]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[2,4,5,6,1,3,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[2,4,5,6,7,1,3]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[7,2,4,5,6,1,3]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[6,2,4,5,1,3,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>[6,2,4,5,7,1,3]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,5,3]=>[6,7,2,4,5,1,3]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[7,6,2,4,5,1,3]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[5,2,4,1,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[5,2,4,7,1,3,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>[5,2,4,6,1,3,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[5,2,4,6,7,1,3]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[5,7,2,4,6,1,3]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,4,3,7]=>[5,6,2,4,1,3,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,4,7,3]=>[5,6,2,4,7,1,3]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,4,3]=>[5,6,7,2,4,1,3]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,6,4,3]=>[7,5,6,2,4,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[6,5,2,4,1,3,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[6,5,2,4,7,1,3]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,5,7,4,3]=>[6,5,7,2,4,1,3]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,5,4,3]=>[6,7,5,2,4,1,3]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[7,6,5,2,4,1,3]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[2,3,7,1,4,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[2,3,6,1,4,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[2,3,6,7,1,4,5]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[7,2,3,6,1,4,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[2,3,5,1,4,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[2,3,5,7,1,4,6]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[2,3,5,6,1,4,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[2,3,5,6,7,1,4]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[7,2,3,5,6,1,4]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[6,2,3,5,1,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[6,2,3,5,7,1,4]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,5,4]=>[6,7,2,3,5,1,4]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[7,6,2,3,5,1,4]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[2,3,4,1,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[2,3,4,7,1,5,6]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[2,3,4,6,1,5,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[2,3,4,6,7,1,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[7,2,3,4,6,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[2,3,4,5,1,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[2,3,4,5,7,1,6]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[2,3,4,5,6,1,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[2,3,4,5,6,7,1]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[7,2,3,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[6,2,3,4,5,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[6,2,3,4,5,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,5,1]=>[6,7,2,3,4,5,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[7,6,2,3,4,5,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[5,2,3,4,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[5,2,3,4,7,1,6]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[5,2,3,4,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[5,2,3,4,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[5,7,2,3,4,6,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,4,1,7]=>[5,6,2,3,4,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,4,7,1]=>[5,6,2,3,4,7,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,4,1]=>[5,6,7,2,3,4,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,6,4,1]=>[7,5,6,2,3,4,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[6,5,2,3,4,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[6,5,2,3,4,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,5,7,4,1]=>[6,5,7,2,3,4,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,5,4,1]=>[6,7,5,2,3,4,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[7,6,5,2,3,4,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>[4,2,3,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[4,2,3,7,1,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[4,2,3,6,1,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[4,2,3,6,7,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[4,7,2,3,6,1,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[4,2,3,5,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[4,2,3,5,7,1,6]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[4,2,3,5,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[4,2,3,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[4,7,2,3,5,6,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[4,6,2,3,5,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[4,6,2,3,5,7,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,6,7,5,1]=>[4,6,7,2,3,5,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[7,4,6,2,3,5,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,3,1,6,7]=>[4,5,2,3,1,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,3,1,7,6]=>[4,5,2,3,7,1,6]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,3,6,1,7]=>[4,5,2,3,6,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,3,6,7,1]=>[4,5,2,3,6,7,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,3,7,6,1]=>[4,5,7,2,3,6,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,3,1,7]=>[4,5,6,2,3,1,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,3,7,1]=>[4,5,6,2,3,7,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,3,1]=>[4,5,6,7,2,3,1]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,6,3,1]=>[7,4,5,6,2,3,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,5,3,1,7]=>[6,4,5,2,3,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,5,3,7,1]=>[6,4,5,2,3,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,5,7,3,1]=>[6,4,5,7,2,3,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,5,3,1]=>[6,7,4,5,2,3,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,6,5,3,1]=>[7,6,4,5,2,3,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[5,4,2,3,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[5,4,2,3,7,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[5,4,2,3,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[5,4,2,3,6,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[5,4,7,2,3,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,4,6,3,1,7]=>[5,4,6,2,3,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,4,6,3,7,1]=>[5,4,6,2,3,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,4,6,7,3,1]=>[5,4,6,7,2,3,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,4,7,6,3,1]=>[5,7,4,6,2,3,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,4,3,1,7]=>[5,6,4,2,3,1,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,4,3,7,1]=>[5,6,4,2,3,7,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,4,7,3,1]=>[5,6,4,7,2,3,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,4,3,1]=>[5,6,7,4,2,3,1]=>[[[[.,[.,[.,.]]],.],[.,.]],.]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,6,4,3,1]=>[7,5,6,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[6,5,4,2,3,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[6,5,4,2,3,7,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,5,4,7,3,1]=>[6,5,4,7,2,3,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,5,7,4,3,1]=>[6,5,7,4,2,3,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,5,4,3,1]=>[6,7,5,4,2,3,1]=>[[[[[.,[.,.]],.],.],[.,.]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[7,6,5,4,2,3,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[3,2,7,1,4,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[3,2,6,1,4,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[3,2,6,7,1,4,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[3,7,2,6,1,4,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[3,2,5,1,4,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[3,2,5,7,1,4,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[3,2,5,6,1,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[3,2,5,6,7,1,4]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[3,7,2,5,6,1,4]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[3,6,2,5,1,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[3,6,2,5,7,1,4]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,6,7,5,4]=>[3,6,7,2,5,1,4]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[7,3,6,2,5,1,4]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>[3,2,4,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[3,2,4,7,1,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>[3,2,4,6,1,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>[3,2,4,6,7,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[3,7,2,4,6,1,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[3,2,4,5,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[3,2,4,5,7,1,6]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[3,2,4,5,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[3,2,4,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[3,7,2,4,5,6,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[3,6,2,4,5,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[3,6,2,4,5,7,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,6,7,5,1]=>[3,6,7,2,4,5,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[7,3,6,2,4,5,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[3,5,2,4,1,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[3,5,2,4,7,1,6]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[3,5,2,4,6,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[3,5,2,4,6,7,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[3,5,7,2,4,6,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,5,6,4,1,7]=>[3,5,6,2,4,1,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,5,6,4,7,1]=>[3,5,6,2,4,7,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,4,1]=>[3,5,6,7,2,4,1]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,5,7,6,4,1]=>[7,3,5,6,2,4,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[6,3,5,2,4,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[6,3,5,2,4,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,6,5,7,4,1]=>[6,3,5,7,2,4,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,6,7,5,4,1]=>[6,7,3,5,2,4,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[7,6,3,5,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7]=>[3,4,2,1,5,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,2,1,5,7,6]=>[3,4,2,7,1,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,2,1,6,5,7]=>[3,4,2,6,1,5,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,2,1,6,7,5]=>[3,4,2,6,7,1,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,2,1,7,6,5]=>[3,4,7,2,6,1,5]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,2,5,1,6,7]=>[3,4,2,5,1,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,2,5,1,7,6]=>[3,4,2,5,7,1,6]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,1,7]=>[3,4,2,5,6,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,1]=>[3,4,2,5,6,7,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,2,5,7,6,1]=>[3,4,7,2,5,6,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,2,6,5,1,7]=>[3,4,6,2,5,1,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,2,6,5,7,1]=>[3,4,6,2,5,7,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,2,6,7,5,1]=>[3,4,6,7,2,5,1]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,2,7,6,5,1]=>[7,3,4,6,2,5,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,2,1,6,7]=>[3,4,5,2,1,6,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,2,1,7,6]=>[3,4,5,2,7,1,6]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,2,6,1,7]=>[3,4,5,2,6,1,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,2,6,7,1]=>[3,4,5,2,6,7,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,2,7,6,1]=>[3,4,5,7,2,6,1]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,2,1,7]=>[3,4,5,6,2,1,7]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,2,7,1]=>[3,4,5,6,2,7,1]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,2,1]=>[3,4,5,6,7,2,1]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,6,2,1]=>[7,3,4,5,6,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,5,2,1,7]=>[6,3,4,5,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,5,2,7,1]=>[6,3,4,5,2,7,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,5,7,2,1]=>[6,3,4,5,7,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,5,2,1]=>[6,7,3,4,5,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,6,5,2,1]=>[7,6,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,4,2,1,6,7]=>[5,3,4,2,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,4,2,1,7,6]=>[5,3,4,2,7,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,4,2,6,1,7]=>[5,3,4,2,6,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,4,2,6,7,1]=>[5,3,4,2,6,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,4,2,7,6,1]=>[5,3,4,7,2,6,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,4,6,2,1,7]=>[5,3,4,6,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,4,6,2,7,1]=>[5,3,4,6,2,7,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,4,6,7,2,1]=>[5,3,4,6,7,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,4,7,6,2,1]=>[5,7,3,4,6,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,4,2,1,7]=>[5,6,3,4,2,1,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,4,2,7,1]=>[5,6,3,4,2,7,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,4,7,2,1]=>[5,6,3,4,7,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,4,2,1]=>[5,6,7,3,4,2,1]=>[[[[.,[.,[.,.]]],[.,.]],.],.]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,6,4,2,1]=>[7,5,6,3,4,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,5,4,2,1,7]=>[6,5,3,4,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,5,4,2,7,1]=>[6,5,3,4,2,7,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,5,4,7,2,1]=>[6,5,3,4,7,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,5,7,4,2,1]=>[6,5,7,3,4,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,5,4,2,1]=>[6,7,5,3,4,2,1]=>[[[[[.,[.,.]],.],[.,.]],.],.]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,6,5,4,2,1]=>[7,6,5,3,4,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[4,3,2,7,1,5,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[4,3,2,6,1,5,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[4,3,2,6,7,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[4,3,7,2,6,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>[4,3,2,5,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[4,3,2,5,7,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[4,3,2,5,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[4,3,2,5,6,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[4,3,7,2,5,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[4,3,6,2,5,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[4,3,6,2,5,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,6,7,5,1]=>[4,3,6,7,2,5,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[4,7,3,6,2,5,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,3,5,2,1,6,7]=>[4,3,5,2,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,3,5,2,1,7,6]=>[4,3,5,2,7,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,3,5,2,6,1,7]=>[4,3,5,2,6,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,3,5,2,6,7,1]=>[4,3,5,2,6,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,3,5,2,7,6,1]=>[4,3,5,7,2,6,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,3,5,6,2,1,7]=>[4,3,5,6,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,2,7,1]=>[4,3,5,6,2,7,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,2,1]=>[4,3,5,6,7,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,3,5,7,6,2,1]=>[4,7,3,5,6,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,3,6,5,2,1,7]=>[4,6,3,5,2,1,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,3,6,5,2,7,1]=>[4,6,3,5,2,7,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,3,6,5,7,2,1]=>[4,6,3,5,7,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,6,7,5,2,1]=>[4,6,7,3,5,2,1]=>[[[[.,[.,[.,.]]],[.,.]],.],.]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3,7,6,5,2,1]=>[7,4,6,3,5,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,3,2,1,6,7]=>[4,5,3,2,1,6,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,3,2,1,7,6]=>[4,5,3,2,7,1,6]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,3,2,6,1,7]=>[4,5,3,2,6,1,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,3,2,6,7,1]=>[4,5,3,2,6,7,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,3,2,7,6,1]=>[4,5,3,7,2,6,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,3,6,2,1,7]=>[4,5,3,6,2,1,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1]=>[4,5,3,6,2,7,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,3,6,7,2,1]=>[4,5,3,6,7,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,3,7,6,2,1]=>[4,5,7,3,6,2,1]=>[[[[.,[.,[.,.]]],[.,.]],.],.]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,3,2,1,7]=>[4,5,6,3,2,1,7]=>[[[[.,[.,[.,.]]],.],.],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,3,2,7,1]=>[4,5,6,3,2,7,1]=>[[[[.,[.,[.,.]]],.],[.,.]],.]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,3,7,2,1]=>[4,5,6,3,7,2,1]=>[[[[.,[.,[.,.]]],[.,.]],.],.]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[4,5,6,7,3,2,1]=>[[[[.,[.,[.,[.,.]]]],.],.],.]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,6,3,2,1]=>[7,4,5,6,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,5,3,2,1,7]=>[6,4,5,3,2,1,7]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,5,3,2,7,1]=>[6,4,5,3,2,7,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,5,3,7,2,1]=>[6,4,5,3,7,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,5,7,3,2,1]=>[6,4,5,7,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,5,3,2,1]=>[6,7,4,5,3,2,1]=>[[[[[.,[.,.]],[.,.]],.],.],.]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,6,5,3,2,1]=>[7,6,4,5,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[5,4,3,2,7,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[5,4,3,2,6,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[5,4,3,2,6,7,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[5,4,3,7,2,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,4,3,6,2,1,7]=>[5,4,3,6,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,4,3,6,2,7,1]=>[5,4,3,6,2,7,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[5,4,3,6,7,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,4,3,7,6,2,1]=>[5,4,7,3,6,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,4,6,3,2,1,7]=>[5,4,6,3,2,1,7]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,4,6,3,2,7,1]=>[5,4,6,3,2,7,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[5,4,6,3,7,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1]=>[5,4,6,7,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,3,2,1]=>[5,7,4,6,3,2,1]=>[[[[[.,[.,.]],[.,.]],.],.],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,4,3,2,1,7]=>[5,6,4,3,2,1,7]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,4,3,2,7,1]=>[5,6,4,3,2,7,1]=>[[[[[.,[.,.]],.],.],[.,.]],.]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,4,3,7,2,1]=>[5,6,4,3,7,2,1]=>[[[[[.,[.,.]],.],[.,.]],.],.]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,4,7,3,2,1]=>[5,6,4,7,3,2,1]=>[[[[[.,[.,.]],[.,.]],.],.],.]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,4,3,2,1]=>[5,6,7,4,3,2,1]=>[[[[[.,[.,[.,.]]],.],.],.],.]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,6,4,3,2,1]=>[7,5,6,4,3,2,1]=>[[[[[[.,.],[.,.]],.],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[6,5,4,3,2,7,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,5,4,3,7,2,1]=>[6,5,4,3,7,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,5,4,7,3,2,1]=>[6,5,4,7,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,5,7,4,3,2,1]=>[6,5,7,4,3,2,1]=>[[[[[[.,.],[.,.]],.],.],.],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,5,4,3,2,1]=>[6,7,5,4,3,2,1]=>[[[[[[.,[.,.]],.],.],.],.],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,7,8,6]=>[7,8,1,2,3,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,2]=>[3,4,5,6,7,8,1,2]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
Map
to 312-avoiding permutation
Description
Map
inverse Foata bijection
Description
The inverse of Foata's bijection.
See Mp00067Foata bijection.
See Mp00067Foata bijection.
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
searching the database
Sorry, this map was not found in the database.