Identifier
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
Permutations
Mp00073: Permutations —major-index to inversion-number bijection⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00073: Permutations —major-index to inversion-number 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]=>[2,3,1]=>[[.,[.,.]],.]
[1,1,0,0,1,0]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[1,1,0,1,0,0]=>[2,3,1]=>[3,1,2]=>[[.,.],[.,.]]
[1,1,1,0,0,0]=>[3,2,1]=>[3,2,1]=>[[[.,.],.],.]
[1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[3,4,2,1]=>[[[.,[.,.]],.],.]
[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]=>[3,2,4,1]=>[[[.,.],[.,.]],.]
[1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[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]=>[4,2,1,3]=>[[[.,.],.],[.,.]]
[1,1,1,0,1,0,0,0]=>[3,4,2,1]=>[4,3,1,2]=>[[[.,.],.],[.,.]]
[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]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]
[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]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]
[1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[3,5,2,4,1]=>[[[.,[.,.]],[.,.]],.]
[1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]]
[1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[3,5,2,1,4]=>[[[.,[.,.]],.],[.,.]]
[1,0,1,1,1,0,1,0,0,0]=>[1,4,5,3,2]=>[3,5,4,1,2]=>[[.,[[.,.],.]],[.,.]]
[1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[4,5,3,2,1]=>[[[[.,[.,.]],.],.],.]
[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]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]
[1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[3,2,5,1,4]=>[[[.,.],[.,.]],[.,.]]
[1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.]
[1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]
[1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[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]=>[5,2,3,1,4]=>[[[.,.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>[5,2,4,1,3]=>[[[.,.],[.,.]],[.,.]]
[1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[5,3,4,2,1]=>[[[[.,.],[.,.]],.],.]
[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]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]
[1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[1,1,1,0,1,0,0,0,1,0]=>[3,4,2,1,5]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>[5,3,1,2,4]=>[[[.,.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.]
[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]=>[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]]
[1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>[5,4,2,1,3]=>[[[[.,.],.],.],[.,.]]
[1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]]
[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]=>[2,3,4,5,6,1]=>[[.,[.,[.,[.,[.,.]]]]],.]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[2,3,4,5,1,6]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[2,3,4,6,1,5]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[3,4,5,6,2,1]=>[[[.,[.,[.,[.,.]]]],.],.]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[2,3,4,1,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[3,4,5,2,6,1]=>[[[.,[.,[.,.]]],[.,.]],.]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[2,3,5,1,4,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[2,3,6,1,4,5]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[3,4,6,2,5,1]=>[[[.,[.,[.,.]]],[.,.]],.]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[3,4,5,2,1,6]=>[[[.,[.,[.,.]]],.],[.,.]]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[3,4,6,2,1,5]=>[[[.,[.,[.,.]]],.],[.,.]]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,4,3]=>[3,4,6,5,1,2]=>[[.,[.,[[.,.],.]]],[.,.]]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[4,5,6,3,2,1]=>[[[[.,[.,[.,.]]],.],.],.]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[2,3,1,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[3,4,2,5,6,1]=>[[[.,[.,.]],[.,[.,.]]],.]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[3,4,2,5,1,6]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[3,4,2,6,1,5]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[4,5,3,6,2,1]=>[[[[.,[.,.]],[.,.]],.],.]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[2,4,1,3,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[3,5,2,4,6,1]=>[[[.,[.,.]],[.,[.,.]]],.]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[2,5,1,3,4,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[2,6,1,3,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[3,6,2,4,5,1]=>[[[.,[.,.]],[.,[.,.]]],.]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[3,5,2,4,1,6]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[3,6,2,4,1,5]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,4,2]=>[3,6,2,5,1,4]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[4,6,3,5,2,1]=>[[[[.,[.,.]],[.,.]],.],.]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[3,4,2,1,5,6]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[4,5,3,2,6,1]=>[[[[.,[.,.]],.],[.,.]],.]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[3,5,2,1,4,6]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[3,6,2,1,4,5]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[4,6,3,2,5,1]=>[[[[.,[.,.]],.],[.,.]],.]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,3,2,6]=>[3,5,4,1,2,6]=>[[.,[[.,.],.]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,3,6,2]=>[3,6,4,1,2,5]=>[[.,[[.,.],.]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,3,2]=>[3,6,5,1,2,4]=>[[.,[[.,.],.]],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,5,3,2]=>[4,6,5,2,3,1]=>[[[.,[[.,.],.]],[.,.]],.]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[4,5,3,2,1,6]=>[[[[.,[.,.]],.],.],[.,.]]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[4,6,3,2,1,5]=>[[[[.,[.,.]],.],.],[.,.]]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,4,6,3,2]=>[4,6,5,2,1,3]=>[[[.,[[.,.],.]],.],[.,.]]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,4,3,2]=>[4,6,5,3,1,2]=>[[[.,[[.,.],.]],.],[.,.]]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[5,6,4,3,2,1]=>[[[[[.,[.,.]],.],.],.],.]
[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]=>[3,2,4,5,6,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[3,2,4,5,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[3,2,4,6,1,5]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[4,3,5,6,2,1]=>[[[[.,.],[.,[.,.]]],.],.]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[3,2,4,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[4,3,5,2,6,1]=>[[[[.,.],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[3,2,5,1,4,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[3,2,6,1,4,5]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[4,3,6,2,5,1]=>[[[[.,.],[.,.]],[.,.]],.]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[4,3,5,2,1,6]=>[[[[.,.],[.,.]],.],[.,.]]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[4,3,6,2,1,5]=>[[[[.,.],[.,.]],.],[.,.]]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,4,3]=>[4,3,6,5,1,2]=>[[[.,.],[[.,.],.]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[5,4,6,3,2,1]=>[[[[[.,.],[.,.]],.],.],.]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[4,2,3,5,6,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[4,2,3,5,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[4,2,3,6,1,5]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[5,3,4,6,2,1]=>[[[[.,.],[.,[.,.]]],.],.]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[5,2,3,4,6,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[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]=>[6,2,3,4,1,5]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>[6,2,3,5,1,4]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[6,3,4,5,2,1]=>[[[[.,.],[.,[.,.]]],.],.]
[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]=>[5,3,4,2,6,1]=>[[[[.,.],[.,.]],[.,.]],.]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[5,2,3,1,4,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[6,2,3,1,4,5]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[6,3,4,2,5,1]=>[[[[.,.],[.,.]],[.,.]],.]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,3,1,6]=>[5,2,4,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>[6,2,4,1,3,5]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>[6,2,5,1,3,4]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>[6,3,5,2,4,1]=>[[[[.,.],[.,.]],[.,.]],.]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[5,3,4,2,1,6]=>[[[[.,.],[.,.]],.],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[6,3,4,2,1,5]=>[[[[.,.],[.,.]],.],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>[6,3,5,2,1,4]=>[[[[.,.],[.,.]],.],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>[6,3,5,4,1,2]=>[[[.,.],[[.,.],.]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[6,4,5,3,2,1]=>[[[[[.,.],[.,.]],.],.],.]
[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]=>[4,3,2,5,6,1]=>[[[[.,.],.],[.,[.,.]]],.]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[4,3,2,5,1,6]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[4,3,2,6,1,5]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[5,4,3,6,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[4,2,1,3,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[5,3,2,4,6,1]=>[[[[.,.],.],[.,[.,.]]],.]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[5,2,1,3,4,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[6,2,1,3,4,5]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[6,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],.]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[5,3,2,4,1,6]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[6,3,2,4,1,5]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>[6,3,2,5,1,4]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[6,4,3,5,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,2,1,5,6]=>[4,3,1,2,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2,1,6,5]=>[5,4,2,3,6,1]=>[[[[.,.],.],[.,[.,.]]],.]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,2,5,1,6]=>[5,3,1,2,4,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>[6,3,1,2,4,5]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>[6,4,2,3,5,1]=>[[[[.,.],.],[.,[.,.]]],.]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,2,1,6]=>[5,4,1,2,3,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>[6,4,1,2,3,5]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>[6,5,1,2,3,4]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>[6,5,2,3,4,1]=>[[[[.,.],.],[.,[.,.]]],.]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,4,2,1,6]=>[5,4,2,3,1,6]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>[6,4,2,3,1,5]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>[6,5,2,3,1,4]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>[6,5,2,4,1,3]=>[[[[.,.],.],[.,.]],[.,.]]
[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]=>[5,4,3,2,6,1]=>[[[[[.,.],.],.],[.,.]],.]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[5,3,2,1,4,6]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[6,3,2,1,4,5]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,3,5,2,1,6]=>[5,4,2,1,3,6]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[6,5,2,1,3,4]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>[6,5,3,2,4,1]=>[[[[[.,.],.],.],[.,.]],.]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,3,2,1,6]=>[5,4,3,1,2,6]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>[6,5,4,1,2,3]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>[6,5,4,2,3,1]=>[[[[[.,.],.],.],[.,.]],.]
[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]=>[6,4,3,2,1,5]=>[[[[[.,.],.],.],.],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[[[[[.,.],.],.],.],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[[[[[.,.],.],.],.],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>[[[[[.,.],.],.],.],[.,.]]
[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]=>[2,3,4,5,6,7,1]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[2,3,4,5,6,1,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[2,3,4,5,7,1,6]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[3,4,5,6,7,2,1]=>[[[.,[.,[.,[.,[.,.]]]]],.],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[2,3,4,5,1,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[3,4,5,6,2,7,1]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[2,3,4,6,1,5,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[2,3,4,7,1,5,6]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[3,4,5,7,2,6,1]=>[[[.,[.,[.,[.,.]]]],[.,.]],.]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[3,4,5,6,2,1,7]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[3,4,5,7,2,1,6]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,5,4]=>[3,4,5,7,6,1,2]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]
[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]=>[2,3,4,1,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[3,4,5,2,6,7,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[3,4,5,2,6,1,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[3,4,5,2,7,1,6]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[4,5,6,3,7,2,1]=>[[[[.,[.,[.,.]]],[.,.]],.],.]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[2,3,5,1,4,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[3,4,6,2,5,7,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[2,3,6,1,4,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[2,3,7,1,4,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[3,4,7,2,5,6,1]=>[[[.,[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[3,4,6,2,5,1,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>[3,4,7,2,5,1,6]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,5,3]=>[3,4,7,2,6,1,5]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[4,5,7,3,6,2,1]=>[[[[.,[.,[.,.]]],[.,.]],.],.]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[3,4,5,2,1,6,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[4,5,6,3,2,7,1]=>[[[[.,[.,[.,.]]],.],[.,.]],.]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[3,4,6,2,1,5,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[3,4,7,2,1,5,6]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[4,5,7,3,2,6,1]=>[[[[.,[.,[.,.]]],.],[.,.]],.]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,4,3,7]=>[3,4,6,5,1,2,7]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,4,7,3]=>[3,4,7,5,1,2,6]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,4,3]=>[3,4,7,6,1,2,5]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,6,4,3]=>[4,5,7,6,2,3,1]=>[[[.,[.,[[.,.],.]]],[.,.]],.]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[4,5,6,3,2,1,7]=>[[[[.,[.,[.,.]]],.],.],[.,.]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[4,5,7,3,2,1,6]=>[[[[.,[.,[.,.]]],.],.],[.,.]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,5,7,4,3]=>[4,5,7,6,2,1,3]=>[[[.,[.,[[.,.],.]]],.],[.,.]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,5,4,3]=>[4,5,7,6,3,1,2]=>[[[.,[.,[[.,.],.]]],.],[.,.]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[5,6,7,4,3,2,1]=>[[[[[.,[.,[.,.]]],.],.],.],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[2,3,1,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[3,4,2,5,6,7,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[3,4,2,5,6,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[3,4,2,5,7,1,6]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[4,5,3,6,7,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[3,4,2,5,1,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[4,5,3,6,2,7,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[3,4,2,6,1,5,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[3,4,2,7,1,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[4,5,3,7,2,6,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[4,5,3,6,2,1,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[4,5,3,7,2,1,6]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,5,4]=>[4,5,3,7,6,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[5,6,4,7,3,2,1]=>[[[[[.,[.,.]],[.,.]],.],.],.]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[2,4,1,3,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[3,5,2,4,6,7,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[3,5,2,4,6,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[3,5,2,4,7,1,6]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[4,6,3,5,7,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[2,5,1,3,4,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[3,6,2,4,5,7,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[2,6,1,3,4,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[2,7,1,3,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[3,7,2,4,5,6,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[3,6,2,4,5,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[3,7,2,4,5,1,6]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,5,2]=>[3,7,2,4,6,1,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[4,7,3,5,6,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[3,5,2,4,1,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[4,6,3,5,2,7,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>[3,6,2,4,1,5,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[3,7,2,4,1,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[4,7,3,5,2,6,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,4,2,7]=>[3,6,2,5,1,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,4,7,2]=>[3,7,2,5,1,4,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,4,2]=>[3,7,2,6,1,4,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,6,4,2]=>[4,7,3,6,2,5,1]=>[[[[.,[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[4,6,3,5,2,1,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[4,7,3,5,2,1,6]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,5,7,4,2]=>[4,7,3,6,2,1,5]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,5,4,2]=>[4,7,3,6,5,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[5,7,4,6,3,2,1]=>[[[[[.,[.,.]],[.,.]],.],.],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[3,4,2,1,5,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[4,5,3,2,6,7,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[4,5,3,2,6,1,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[4,5,3,2,7,1,6]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[5,6,4,3,7,2,1]=>[[[[[.,[.,.]],.],[.,.]],.],.]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[3,5,2,1,4,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[4,6,3,2,5,7,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[3,6,2,1,4,5,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[3,7,2,1,4,5,6]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[4,7,3,2,5,6,1]=>[[[[.,[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[4,6,3,2,5,1,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>[4,7,3,2,5,1,6]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,6,7,5,2]=>[4,7,3,2,6,1,5]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[5,7,4,3,6,2,1]=>[[[[[.,[.,.]],.],[.,.]],.],.]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,3,2,6,7]=>[3,5,4,1,2,6,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,3,2,7,6]=>[4,6,5,2,3,7,1]=>[[[.,[[.,.],.]],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,3,6,2,7]=>[3,6,4,1,2,5,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,3,6,7,2]=>[3,7,4,1,2,5,6]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,3,7,6,2]=>[4,7,5,2,3,6,1]=>[[[.,[[.,.],.]],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,3,2,7]=>[3,6,5,1,2,4,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,3,7,2]=>[3,7,5,1,2,4,6]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,3,2]=>[3,7,6,1,2,4,5]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,6,3,2]=>[4,7,6,2,3,5,1]=>[[[.,[[.,.],.]],[.,[.,.]]],.]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,5,3,2,7]=>[4,6,5,2,3,1,7]=>[[[.,[[.,.],.]],[.,.]],[.,.]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,5,3,7,2]=>[4,7,5,2,3,1,6]=>[[[.,[[.,.],.]],[.,.]],[.,.]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,5,7,3,2]=>[4,7,6,2,3,1,5]=>[[[.,[[.,.],.]],[.,.]],[.,.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,5,3,2]=>[4,7,6,2,5,1,3]=>[[[.,[[.,.],.]],[.,.]],[.,.]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,6,5,3,2]=>[5,7,6,3,4,2,1]=>[[[[.,[[.,.],.]],[.,.]],.],.]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[4,5,3,2,1,6,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[5,6,4,3,2,7,1]=>[[[[[.,[.,.]],.],.],[.,.]],.]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[4,6,3,2,1,5,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[4,7,3,2,1,5,6]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[5,7,4,3,2,6,1]=>[[[[[.,[.,.]],.],.],[.,.]],.]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,4,6,3,2,7]=>[4,6,5,2,1,3,7]=>[[[.,[[.,.],.]],.],[.,[.,.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,4,6,3,7,2]=>[4,7,5,2,1,3,6]=>[[[.,[[.,.],.]],.],[.,[.,.]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,4,6,7,3,2]=>[4,7,6,2,1,3,5]=>[[[.,[[.,.],.]],.],[.,[.,.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,4,7,6,3,2]=>[5,7,6,3,2,4,1]=>[[[[.,[[.,.],.]],.],[.,.]],.]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,4,3,2,7]=>[4,6,5,3,1,2,7]=>[[[.,[[.,.],.]],.],[.,[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,4,3,7,2]=>[4,7,5,3,1,2,6]=>[[[.,[[.,.],.]],.],[.,[.,.]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,4,7,3,2]=>[4,7,6,3,1,2,5]=>[[[.,[[.,.],.]],.],[.,[.,.]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,4,3,2]=>[4,7,6,5,1,2,3]=>[[.,[[[.,.],.],.]],[.,[.,.]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,6,4,3,2]=>[5,7,6,4,2,3,1]=>[[[[.,[[.,.],.]],.],[.,.]],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[5,6,4,3,2,1,7]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[5,7,4,3,2,1,6]=>[[[[[.,[.,.]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,5,4,7,3,2]=>[5,7,6,3,2,1,4]=>[[[[.,[[.,.],.]],.],.],[.,.]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,5,7,4,3,2]=>[5,7,6,4,2,1,3]=>[[[[.,[[.,.],.]],.],.],[.,.]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,5,4,3,2]=>[5,7,6,4,3,1,2]=>[[[[.,[[.,.],.]],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[6,7,5,4,3,2,1]=>[[[[[[.,[.,.]],.],.],.],.],.]
[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]=>[3,2,4,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[3,2,4,5,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[3,2,4,5,7,1,6]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[4,3,5,6,7,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[3,2,4,5,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[4,3,5,6,2,7,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[3,2,4,6,1,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[3,2,4,7,1,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[4,3,5,7,2,6,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[4,3,5,6,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[4,3,5,7,2,1,6]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,5,4]=>[4,3,5,7,6,1,2]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[5,4,6,7,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[3,2,4,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[4,3,5,2,6,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[4,3,5,2,6,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[4,3,5,2,7,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[5,4,6,3,7,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[3,2,5,1,4,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[4,3,6,2,5,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[3,2,6,1,4,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[3,2,7,1,4,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[4,3,7,2,5,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[4,3,6,2,5,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>[4,3,7,2,5,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,5,3]=>[4,3,7,2,6,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[5,4,7,3,6,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[4,3,5,2,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[5,4,6,3,2,7,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>[4,3,6,2,1,5,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[4,3,7,2,1,5,6]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[5,4,7,3,2,6,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,4,3,7]=>[4,3,6,5,1,2,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,4,7,3]=>[4,3,7,5,1,2,6]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,4,3]=>[4,3,7,6,1,2,5]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,6,4,3]=>[5,4,7,6,2,3,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[5,4,6,3,2,1,7]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[5,4,7,3,2,1,6]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,5,7,4,3]=>[5,4,7,6,2,1,3]=>[[[[.,.],[[.,.],.]],.],[.,.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,5,4,3]=>[5,4,7,6,3,1,2]=>[[[[.,.],[[.,.],.]],.],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[6,5,7,4,3,2,1]=>[[[[[[.,.],[.,.]],.],.],.],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[4,2,3,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[4,2,3,5,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[4,2,3,5,7,1,6]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[5,3,4,6,7,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[4,2,3,5,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[5,3,4,6,2,7,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[4,2,3,6,1,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[4,2,3,7,1,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[5,3,4,7,2,6,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[5,3,4,6,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[5,3,4,7,2,1,6]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,5,4]=>[5,3,4,7,6,1,2]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[6,4,5,7,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[5,2,3,4,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[5,2,3,4,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[5,2,3,4,7,1,6]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[6,3,4,5,7,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[6,2,3,4,5,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[7,2,3,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[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]=>[7,2,3,4,5,1,6]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,5,1]=>[7,2,3,4,6,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[7,3,4,5,6,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.]
[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]=>[6,3,4,5,2,7,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[6,2,3,4,1,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[7,2,3,4,1,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[7,3,4,5,2,6,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,4,1,7]=>[6,2,3,5,1,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,4,7,1]=>[7,2,3,5,1,4,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,4,1]=>[7,2,3,6,1,4,5]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,6,4,1]=>[7,3,4,6,2,5,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[6,3,4,5,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[7,3,4,5,2,1,6]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,5,7,4,1]=>[7,3,4,6,2,1,5]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,5,4,1]=>[7,3,4,6,5,1,2]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[7,4,5,6,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.]
[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]=>[5,3,4,2,6,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[5,3,4,2,6,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[5,3,4,2,7,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[6,4,5,3,7,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[5,2,3,1,4,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[6,3,4,2,5,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[6,2,3,1,4,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[7,2,3,1,4,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[7,3,4,2,5,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[6,3,4,2,5,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[7,3,4,2,5,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,6,7,5,1]=>[7,3,4,2,6,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[7,4,5,3,6,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,3,1,6,7]=>[5,2,4,1,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,3,1,7,6]=>[6,3,5,2,4,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,3,6,1,7]=>[6,2,4,1,3,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,3,6,7,1]=>[7,2,4,1,3,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,3,7,6,1]=>[7,3,5,2,4,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,3,1,7]=>[6,2,5,1,3,4,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,3,7,1]=>[7,2,5,1,3,4,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,3,1]=>[7,2,6,1,3,4,5]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,6,3,1]=>[7,3,6,2,4,5,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,5,3,1,7]=>[6,3,5,2,4,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,5,3,7,1]=>[7,3,5,2,4,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,5,7,3,1]=>[7,3,6,2,4,1,5]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,5,3,1]=>[7,3,6,2,5,1,4]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,6,5,3,1]=>[7,4,6,3,5,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[5,3,4,2,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[6,4,5,3,2,7,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[6,3,4,2,1,5,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[7,3,4,2,1,5,6]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[7,4,5,3,2,6,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,4,6,3,1,7]=>[6,3,5,2,1,4,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,4,6,3,7,1]=>[7,3,5,2,1,4,6]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,4,6,7,3,1]=>[7,3,6,2,1,4,5]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,4,7,6,3,1]=>[7,4,6,3,2,5,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,4,3,1,7]=>[6,3,5,4,1,2,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,4,3,7,1]=>[7,3,5,4,1,2,6]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,4,7,3,1]=>[7,3,6,4,1,2,5]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,4,3,1]=>[7,3,6,5,1,2,4]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,6,4,3,1]=>[7,4,6,5,2,3,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[6,4,5,3,2,1,7]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[7,4,5,3,2,1,6]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,5,4,7,3,1]=>[7,4,6,3,2,1,5]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,5,7,4,3,1]=>[7,4,6,5,2,1,3]=>[[[[.,.],[[.,.],.]],.],[.,.]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,5,4,3,1]=>[7,4,6,5,3,1,2]=>[[[[.,.],[[.,.],.]],.],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[7,5,6,4,3,2,1]=>[[[[[[.,.],[.,.]],.],.],.],.]
[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]=>[4,3,2,5,6,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[4,3,2,5,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[4,3,2,5,7,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[5,4,3,6,7,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[4,3,2,5,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[5,4,3,6,2,7,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[4,3,2,6,1,5,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[4,3,2,7,1,5,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[5,4,3,7,2,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[5,4,3,6,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[5,4,3,7,2,1,6]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,6,7,5,4]=>[5,4,3,7,6,1,2]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[6,5,4,7,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>[4,2,1,3,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[5,3,2,4,6,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>[5,3,2,4,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>[5,3,2,4,7,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[6,4,3,5,7,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[5,2,1,3,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[6,3,2,4,5,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[6,2,1,3,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[7,2,1,3,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[7,3,2,4,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[6,3,2,4,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[7,3,2,4,5,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,6,7,5,1]=>[7,3,2,4,6,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[7,4,3,5,6,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[5,3,2,4,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[6,4,3,5,2,7,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[6,3,2,4,1,5,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[7,3,2,4,1,5,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[7,4,3,5,2,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,5,6,4,1,7]=>[6,3,2,5,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,5,6,4,7,1]=>[7,3,2,5,1,4,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,4,1]=>[7,3,2,6,1,4,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,5,7,6,4,1]=>[7,4,3,6,2,5,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[6,4,3,5,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[7,4,3,5,2,1,6]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,6,5,7,4,1]=>[7,4,3,6,2,1,5]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,6,7,5,4,1]=>[7,4,3,6,5,1,2]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[7,5,4,6,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7]=>[4,3,1,2,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,2,1,5,7,6]=>[5,4,2,3,6,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,2,1,6,5,7]=>[5,4,2,3,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,2,1,6,7,5]=>[5,4,2,3,7,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,2,1,7,6,5]=>[6,5,3,4,7,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,2,5,1,6,7]=>[5,3,1,2,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,2,5,1,7,6]=>[6,4,2,3,5,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,1,7]=>[6,3,1,2,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,1]=>[7,3,1,2,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,2,5,7,6,1]=>[7,4,2,3,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,2,6,5,1,7]=>[6,4,2,3,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,2,6,5,7,1]=>[7,4,2,3,5,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,2,6,7,5,1]=>[7,4,2,3,6,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,2,7,6,5,1]=>[7,5,3,4,6,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,2,1,6,7]=>[5,4,1,2,3,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,2,1,7,6]=>[6,5,2,3,4,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,2,6,1,7]=>[6,4,1,2,3,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,2,6,7,1]=>[7,4,1,2,3,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,2,7,6,1]=>[7,5,2,3,4,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,2,1,7]=>[6,5,1,2,3,4,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,2,7,1]=>[7,5,1,2,3,4,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,2,1]=>[7,6,1,2,3,4,5]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,6,2,1]=>[7,6,2,3,4,5,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,5,2,1,7]=>[6,5,2,3,4,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,5,2,7,1]=>[7,5,2,3,4,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,5,7,2,1]=>[7,6,2,3,4,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,5,2,1]=>[7,6,2,3,5,1,4]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[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]=>[5,4,2,3,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,4,2,1,7,6]=>[6,5,3,4,2,7,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,4,2,6,1,7]=>[6,4,2,3,1,5,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,4,2,6,7,1]=>[7,4,2,3,1,5,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,4,2,7,6,1]=>[7,5,3,4,2,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,4,6,2,1,7]=>[6,5,2,3,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,4,6,2,7,1]=>[7,5,2,3,1,4,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,4,6,7,2,1]=>[7,6,2,3,1,4,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,4,7,6,2,1]=>[7,6,3,4,2,5,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,4,2,1,7]=>[6,5,2,4,1,3,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,4,2,7,1]=>[7,5,2,4,1,3,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,4,7,2,1]=>[7,6,2,4,1,3,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,4,2,1]=>[7,6,2,5,1,3,4]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,6,4,2,1]=>[7,6,3,5,2,4,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[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]=>[7,5,3,4,2,1,6]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,5,4,7,2,1]=>[7,6,3,4,2,1,5]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,5,7,4,2,1]=>[7,6,3,5,2,1,4]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,5,4,2,1]=>[7,6,3,5,4,1,2]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,6,5,4,2,1]=>[7,6,4,5,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]
[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]=>[5,4,3,2,6,7,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[5,4,3,2,6,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[5,4,3,2,7,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[6,5,4,3,7,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>[5,3,2,1,4,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[6,4,3,2,5,7,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[6,3,2,1,4,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[7,3,2,1,4,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[7,4,3,2,5,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[6,4,3,2,5,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[7,4,3,2,5,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,6,7,5,1]=>[7,4,3,2,6,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[7,5,4,3,6,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,3,5,2,1,6,7]=>[5,4,2,1,3,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,3,5,2,1,7,6]=>[6,5,3,2,4,7,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,3,5,2,6,1,7]=>[6,4,2,1,3,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,3,5,2,6,7,1]=>[7,4,2,1,3,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,3,5,2,7,6,1]=>[7,5,3,2,4,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,3,5,6,2,1,7]=>[6,5,2,1,3,4,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,2,7,1]=>[7,5,2,1,3,4,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,2,1]=>[7,6,2,1,3,4,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,3,5,7,6,2,1]=>[7,6,3,2,4,5,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,3,6,5,2,1,7]=>[6,5,3,2,4,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,3,6,5,2,7,1]=>[7,5,3,2,4,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,3,6,5,7,2,1]=>[7,6,3,2,4,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,6,7,5,2,1]=>[7,6,3,2,5,1,4]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3,7,6,5,2,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,3,2,1,6,7]=>[5,4,3,1,2,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,3,2,1,7,6]=>[6,5,4,2,3,7,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,3,2,6,1,7]=>[6,4,3,1,2,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,3,2,6,7,1]=>[7,4,3,1,2,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,3,2,7,6,1]=>[7,5,4,2,3,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,3,6,2,1,7]=>[6,5,3,1,2,4,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,3,6,7,2,1]=>[7,6,3,1,2,4,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,3,7,6,2,1]=>[7,6,4,2,3,5,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,3,2,1,7]=>[6,5,4,1,2,3,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,3,2,7,1]=>[7,5,4,1,2,3,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,3,7,2,1]=>[7,6,4,1,2,3,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[7,6,5,1,2,3,4]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,6,3,2,1]=>[7,6,5,2,3,4,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,5,3,2,1,7]=>[6,5,4,2,3,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,5,3,2,7,1]=>[7,5,4,2,3,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,5,3,7,2,1]=>[7,6,4,2,3,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,5,7,3,2,1]=>[7,6,5,2,3,1,4]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,5,3,2,1]=>[7,6,5,2,4,1,3]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,6,5,3,2,1]=>[7,6,5,3,4,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[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]=>[6,5,4,3,2,7,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[6,4,3,2,1,5,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[7,4,3,2,1,5,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,4,3,6,2,1,7]=>[6,5,3,2,1,4,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[7,6,3,2,1,4,5]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,4,3,7,6,2,1]=>[7,6,4,3,2,5,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,4,6,3,2,1,7]=>[6,5,4,2,1,3,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1]=>[7,6,5,2,1,3,4]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,3,2,1]=>[7,6,5,3,2,4,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,4,3,2,1,7]=>[6,5,4,3,1,2,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,4,3,2,1]=>[7,6,5,4,1,2,3]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,6,4,3,2,1]=>[7,6,5,4,2,3,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[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]=>[7,5,4,3,2,1,6]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,8,7]=>[2,3,4,5,6,7,8,1]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,8]=>[2,3,4,5,6,7,1,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,7,8,6]=>[2,3,4,5,6,8,1,7]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,8,7,6]=>[3,4,5,6,7,8,2,1]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,6,5,7,8]=>[2,3,4,5,6,1,7,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,6,5,8,7]=>[3,4,5,6,7,2,8,1]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,4,6,7,5,8]=>[2,3,4,5,7,1,6,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,5]=>[2,3,4,5,8,1,6,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,4,6,8,7,5]=>[3,4,5,6,8,2,7,1]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,4,7,6,5,8]=>[3,4,5,6,7,2,1,8]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,4,7,8,6,5]=>[3,4,5,6,8,7,1,2]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,8,7,6,5]=>[4,5,6,7,8,3,2,1]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8]=>[2,3,4,5,1,6,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,3,5,4,6,8,7]=>[3,4,5,6,2,7,8,1]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,8]=>[3,4,5,6,2,7,1,8]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,3,5,4,7,8,6]=>[3,4,5,6,2,8,1,7]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,8,7,6]=>[4,5,6,7,3,8,2,1]=>[[[[.,[.,[.,[.,.]]]],[.,.]],.],.]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,3,5,6,4,7,8]=>[2,3,4,6,1,5,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,3,5,6,4,8,7]=>[3,4,5,7,2,6,8,1]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,3,5,6,7,4,8]=>[2,3,4,7,1,5,6,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,4]=>[2,3,4,8,1,5,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,3,5,6,8,7,4]=>[3,4,5,8,2,6,7,1]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,3,5,7,8,6,4]=>[3,4,5,8,2,7,1,6]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,3,6,5,4,7,8]=>[3,4,5,6,2,1,7,8]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,6,5,4,8,7]=>[4,5,6,7,3,2,8,1]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,3,6,5,7,4,8]=>[3,4,5,7,2,1,6,8]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,6,5,7,8,4]=>[3,4,5,8,2,1,6,7]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,6,5,8,7,4]=>[4,5,6,8,3,2,7,1]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,6,7,8,5,4]=>[3,4,5,8,7,1,2,6]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,3,7,6,5,4,8]=>[4,5,6,7,3,2,1,8]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,3,7,6,5,8,4]=>[4,5,6,8,3,2,1,7]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,3,7,6,8,5,4]=>[4,5,6,8,7,2,1,3]=>[[[.,[.,[.,[[.,.],.]]]],.],[.,.]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,8,7,6,5,4]=>[5,6,7,8,4,3,2,1]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],.]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,4,3,5,6,8,7]=>[3,4,5,2,6,7,8,1]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>[3,4,5,2,6,1,7,8]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7]=>[4,5,6,3,7,2,8,1]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,2,4,3,6,7,5,8]=>[3,4,5,2,7,1,6,8]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,4,3,6,8,7,5]=>[4,5,6,3,8,2,7,1]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,4,3,7,6,8,5]=>[4,5,6,3,8,2,1,7]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,2,4,3,7,8,6,5]=>[4,5,6,3,8,7,1,2]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,8,7,6,5]=>[5,6,7,4,8,3,2,1]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],.]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,2,4,5,3,6,7,8]=>[2,3,5,1,4,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,2,4,5,3,7,6,8]=>[3,4,6,2,5,7,1,8]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,4,5,3,8,7,6]=>[4,5,7,3,6,8,2,1]=>[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,6,3,7,8]=>[2,3,6,1,4,5,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,7,3,8]=>[2,3,7,1,4,5,6,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,8,3]=>[2,3,8,1,4,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,6,8,7,3]=>[3,4,8,2,5,6,7,1]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,4,5,8,7,6,3]=>[4,5,8,3,6,7,2,1]=>[[[[.,[.,[.,.]]],[.,[.,.]]],.],.]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,2,4,6,5,7,3,8]=>[3,4,7,2,5,1,6,8]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,2,4,6,7,8,5,3]=>[3,4,8,2,7,1,5,6]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,4,6,8,7,5,3]=>[4,5,8,3,7,2,6,1]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,4,7,6,8,5,3]=>[4,5,8,3,7,2,1,6]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,4,7,8,6,5,3]=>[4,5,8,3,7,6,1,2]=>[[[.,[.,[.,.]]],[[.,.],.]],[.,.]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4,8,7,6,5,3]=>[5,6,8,4,7,3,2,1]=>[[[[[.,[.,[.,.]]],[.,.]],.],.],.]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,5,4,3,6,7,8]=>[3,4,5,2,1,6,7,8]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,5,4,3,6,8,7]=>[4,5,6,3,2,7,8,1]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,5,4,3,7,8,6]=>[4,5,6,3,2,8,1,7]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,5,4,3,8,7,6]=>[5,6,7,4,3,8,2,1]=>[[[[[.,[.,[.,.]]],.],[.,.]],.],.]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,2,5,4,6,7,8,3]=>[3,4,8,2,1,5,6,7]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,2,5,4,7,6,8,3]=>[4,5,8,3,2,6,1,7]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,2,5,4,7,8,6,3]=>[4,5,8,3,2,7,1,6]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,2,5,6,4,3,7,8]=>[3,4,6,5,1,2,7,8]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,2,5,6,7,4,8,3]=>[3,4,8,6,1,2,5,7]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,8,4,3]=>[3,4,8,7,1,2,5,6]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,5,6,8,7,4,3]=>[4,5,8,7,2,3,6,1]=>[[[.,[.,[[.,.],.]]],[.,[.,.]]],.]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,5,7,6,8,4,3]=>[4,5,8,7,2,3,1,6]=>[[[.,[.,[[.,.],.]]],[.,.]],[.,.]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,6,5,4,3,7,8]=>[4,5,6,3,2,1,7,8]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,6,5,4,7,8,3]=>[4,5,8,3,2,1,6,7]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,6,5,4,8,7,3]=>[5,6,8,4,3,2,7,1]=>[[[[[.,[.,[.,.]]],.],.],[.,.]],.]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,6,7,8,5,4,3]=>[4,5,8,7,6,1,2,3]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,7,6,5,4,3,8]=>[5,6,7,4,3,2,1,8]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,7,6,5,4,8,3]=>[5,6,8,4,3,2,1,7]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,7,6,5,8,4,3]=>[5,6,8,7,3,2,1,4]=>[[[[.,[.,[[.,.],.]]],.],.],[.,.]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,7,6,8,5,4,3]=>[5,6,8,7,4,2,1,3]=>[[[[.,[.,[[.,.],.]]],.],.],[.,.]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,7,8,6,5,4,3]=>[5,6,8,7,4,3,1,2]=>[[[[.,[.,[[.,.],.]]],.],.],[.,.]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,8,7,6,5,4,3]=>[6,7,8,5,4,3,2,1]=>[[[[[[.,[.,[.,.]]],.],.],.],.],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,6,8,7]=>[3,4,2,5,6,7,8,1]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>[3,4,2,5,6,7,1,8]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,5,7,8,6]=>[3,4,2,5,6,8,1,7]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,6,5,7,8]=>[3,4,2,5,6,1,7,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,2,4,6,5,8,7]=>[4,5,3,6,7,2,8,1]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,2,4,6,8,7,5]=>[4,5,3,6,8,2,7,1]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,8,7,6,5]=>[5,6,4,7,8,3,2,1]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,7,8]=>[3,4,2,5,1,6,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,8]=>[4,5,3,6,2,7,1,8]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,4,7,8,6]=>[4,5,3,6,2,8,1,7]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,2,5,6,7,4,8]=>[3,4,2,7,1,5,6,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,8,4]=>[3,4,2,8,1,5,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,2,5,7,6,4,8]=>[4,5,3,7,2,6,1,8]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,6,8,4]=>[4,5,3,8,2,6,1,7]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,2,5,7,8,6,4]=>[4,5,3,8,2,7,1,6]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,2,5,8,7,6,4]=>[5,6,4,8,3,7,2,1]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,5,7,8,4]=>[4,5,3,8,2,1,6,7]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,2,6,7,5,8,4]=>[4,5,3,8,6,1,2,7]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,7,6,5,4,8]=>[5,6,4,7,3,2,1,8]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,3,2,7,6,5,8,4]=>[5,6,4,8,3,2,1,7]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,3,2,7,6,8,5,4]=>[5,6,4,8,7,2,1,3]=>[[[[.,[.,.]],[[.,.],.]],.],[.,.]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,8,7,6,5,4]=>[6,7,5,8,4,3,2,1]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7,8]=>[2,4,1,3,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,4,2,5,6,8,7]=>[3,5,2,4,6,7,8,1]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,4,2,5,7,8,6]=>[3,5,2,4,6,8,1,7]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,4,2,5,8,7,6]=>[4,6,3,5,7,8,2,1]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,4,2,6,5,8,7]=>[4,6,3,5,7,2,8,1]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,6,7,5,8]=>[3,5,2,4,7,1,6,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,4,2,6,8,7,5]=>[4,6,3,5,8,2,7,1]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,4,2,7,6,8,5]=>[4,6,3,5,8,2,1,7]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,4,2,7,8,6,5]=>[4,6,3,5,8,7,1,2]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,8,7,6,5]=>[5,7,4,6,8,3,2,1]=>[[[[[.,[.,.]],[.,[.,.]]],.],.],.]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,5,2,6,7,8]=>[2,5,1,3,4,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,6,2,7,8]=>[2,6,1,3,4,5,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,7,2,8]=>[2,7,1,3,4,5,6,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,2]=>[2,8,1,3,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,6,8,7,2]=>[3,8,2,4,5,6,7,1]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,4,6,5,7,2,8]=>[3,7,2,4,5,1,6,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,4,6,7,8,5,2]=>[3,8,2,4,7,1,5,6]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,5,4,2,6,7,8]=>[3,5,2,4,1,6,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,5,4,2,6,8,7]=>[4,6,3,5,2,7,8,1]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,5,4,2,7,6,8]=>[4,6,3,5,2,7,1,8]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,5,4,2,7,8,6]=>[4,6,3,5,2,8,1,7]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,3,5,4,7,6,2,8]=>[4,7,3,5,2,6,1,8]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,5,4,7,6,8,2]=>[4,8,3,5,2,6,1,7]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,5,4,7,8,6,2]=>[4,8,3,5,2,7,1,6]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,5,6,4,2,7,8]=>[3,6,2,5,1,4,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,5,6,4,7,2,8]=>[3,7,2,5,1,4,6,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,5,6,7,4,2,8]=>[3,7,2,6,1,4,5,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,8,4,2]=>[3,8,2,7,1,4,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,5,7,6,4,2,8]=>[4,7,3,6,2,5,1,8]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,5,7,6,4,8,2]=>[4,8,3,6,2,5,1,7]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,5,7,6,8,4,2]=>[4,8,3,7,2,5,1,6]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,5,7,8,6,4,2]=>[4,8,3,7,2,6,1,5]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,5,8,7,6,4,2]=>[5,8,4,7,3,6,2,1]=>[[[[[.,[.,.]],[.,.]],[.,.]],.],.]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,3,6,5,4,7,2,8]=>[4,7,3,5,2,1,6,8]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,6,5,4,8,7,2]=>[5,8,4,6,3,2,7,1]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],.]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,6,5,7,4,8,2]=>[4,8,3,6,2,1,5,7]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,6,5,7,8,4,2]=>[4,8,3,7,2,1,5,6]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,3,6,7,5,4,2,8]=>[4,7,3,6,5,1,2,8]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,6,7,5,8,4,2]=>[4,8,3,7,5,1,2,6]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,6,7,8,5,4,2]=>[4,8,3,7,6,1,2,5]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,6,8,7,5,4,2]=>[5,8,4,7,6,2,3,1]=>[[[[.,[.,.]],[[.,.],.]],[.,.]],.]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,3,7,6,5,4,2,8]=>[5,7,4,6,3,2,1,8]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,7,8,6,5,4,2]=>[5,8,4,7,6,3,1,2]=>[[[[.,[.,.]],[[.,.],.]],.],[.,.]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,8,7,6,5,4,2]=>[6,8,5,7,4,3,2,1]=>[[[[[[.,[.,.]],[.,.]],.],.],.],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,4,3,2,5,6,8,7]=>[4,5,3,2,6,7,8,1]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,4,3,2,6,7,8,5]=>[4,5,3,2,8,1,6,7]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,4,3,2,6,8,7,5]=>[5,6,4,3,8,2,7,1]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,7,6,5,8]=>[5,6,4,3,7,2,1,8]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,3,2,8,7,6,5]=>[6,7,5,4,8,3,2,1]=>[[[[[[.,[.,.]],.],[.,.]],.],.],.]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,4,3,5,2,6,7,8]=>[3,5,2,1,4,6,7,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,8,2]=>[3,8,2,1,4,5,6,7]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,3,5,8,7,6,2]=>[5,8,4,3,6,7,2,1]=>[[[[[.,[.,.]],.],[.,[.,.]]],.],.]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,4,3,6,5,2,7,8]=>[4,6,3,2,5,1,7,8]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,4,3,6,5,7,2,8]=>[4,7,3,2,5,1,6,8]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,8,7,2]=>[5,8,4,3,6,2,7,1]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,3,6,7,5,8,2]=>[4,8,3,2,6,1,5,7]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,3,6,7,8,5,2]=>[4,8,3,2,7,1,5,6]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,3,6,8,7,5,2]=>[5,8,4,3,7,2,6,1]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,3,7,6,8,5,2]=>[5,8,4,3,7,2,1,6]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,3,7,8,6,5,2]=>[5,8,4,3,7,6,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,3,8,7,6,5,2]=>[6,8,5,4,7,3,2,1]=>[[[[[[.,[.,.]],.],[.,.]],.],.],.]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,4,5,3,2,6,7,8]=>[3,5,4,1,2,6,7,8]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,6,3,7,2,8]=>[3,7,5,1,2,4,6,8]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,7,3,2,8]=>[3,7,6,1,2,4,5,8]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,7,3,8,2]=>[3,8,6,1,2,4,5,7]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,8,3,2]=>[3,8,7,1,2,4,5,6]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,4,5,8,7,6,3,2]=>[5,8,7,3,4,6,2,1]=>[[[[.,[[.,.],.]],[.,[.,.]]],.],.]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,4,6,5,8,7,3,2]=>[5,8,7,3,4,2,6,1]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],.]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,4,6,7,5,8,3,2]=>[4,8,7,2,5,1,3,6]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,4,6,7,8,5,3,2]=>[4,8,7,2,6,1,3,5]=>[[[.,[[.,.],.]],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,4,6,8,7,5,3,2]=>[5,8,7,3,6,2,4,1]=>[[[[.,[[.,.],.]],[.,.]],[.,.]],.]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,4,7,6,5,3,2,8]=>[5,7,6,3,4,2,1,8]=>[[[[.,[[.,.],.]],[.,.]],.],[.,.]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,4,8,7,6,5,3,2]=>[6,8,7,4,5,3,2,1]=>[[[[[.,[[.,.],.]],[.,.]],.],.],.]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,5,4,3,2,6,7,8]=>[4,5,3,2,1,6,7,8]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,5,4,3,2,7,6,8]=>[5,6,4,3,2,7,1,8]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,5,4,3,2,7,8,6]=>[5,6,4,3,2,8,1,7]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,5,4,3,2,8,7,6]=>[6,7,5,4,3,8,2,1]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,5,4,3,6,7,2,8]=>[4,7,3,2,1,5,6,8]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,4,3,6,7,8,2]=>[4,8,3,2,1,5,6,7]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,4,3,6,8,7,2]=>[5,8,4,3,2,6,7,1]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,5,4,3,8,7,6,2]=>[6,8,5,4,3,7,2,1]=>[[[[[[.,[.,.]],.],.],[.,.]],.],.]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,5,4,6,3,2,7,8]=>[4,6,5,2,1,3,7,8]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,5,4,6,3,7,2,8]=>[4,7,5,2,1,3,6,8]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,4,6,3,7,8,2]=>[4,8,5,2,1,3,6,7]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,4,6,7,3,8,2]=>[4,8,6,2,1,3,5,7]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,5,4,6,7,8,3,2]=>[4,8,7,2,1,3,5,6]=>[[[.,[[.,.],.]],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,5,4,6,8,7,3,2]=>[5,8,7,3,2,4,6,1]=>[[[[.,[[.,.],.]],.],[.,[.,.]]],.]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,5,4,7,6,3,2,8]=>[5,7,6,3,2,4,1,8]=>[[[[.,[[.,.],.]],.],[.,.]],[.,.]]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,5,4,7,8,6,3,2]=>[5,8,7,3,2,6,1,4]=>[[[[.,[[.,.],.]],.],[.,.]],[.,.]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,5,6,7,4,3,8,2]=>[4,8,6,5,1,2,3,7]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,8,4,3,2]=>[4,8,7,6,1,2,3,5]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,5,7,6,8,4,3,2]=>[5,8,7,6,2,3,1,4]=>[[[.,[[[.,.],.],.]],[.,.]],[.,.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,6,5,4,3,2,7,8]=>[5,6,4,3,2,1,7,8]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,6,5,4,3,2,8,7]=>[6,7,5,4,3,2,8,1]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,6,5,4,3,7,8,2]=>[5,8,4,3,2,1,6,7]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,5,4,3,8,7,2]=>[6,8,5,4,3,2,7,1]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,6,5,4,7,8,3,2]=>[5,8,7,3,2,1,4,6]=>[[[[.,[[.,.],.]],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,6,5,7,4,3,2,8]=>[5,7,6,4,2,1,3,8]=>[[[[.,[[.,.],.]],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,5,7,4,3,8,2]=>[5,8,6,4,2,1,3,7]=>[[[[.,[[.,.],.]],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,6,5,7,8,4,3,2]=>[5,8,7,6,2,1,3,4]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,6,5,8,7,4,3,2]=>[6,8,7,5,3,2,4,1]=>[[[[[.,[[.,.],.]],.],.],[.,.]],.]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,6,7,5,8,4,3,2]=>[5,8,7,6,3,1,2,4]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,6,7,8,5,4,3,2]=>[5,8,7,6,4,1,2,3]=>[[[.,[[[.,.],.],.]],.],[.,[.,.]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,7,6,5,4,3,2,8]=>[6,7,5,4,3,2,1,8]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,7,6,5,4,3,8,2]=>[6,8,5,4,3,2,1,7]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,7,6,5,4,8,3,2]=>[6,8,7,4,3,2,1,5]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,7,6,5,8,4,3,2]=>[6,8,7,5,3,2,1,4]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,7,6,8,5,4,3,2]=>[6,8,7,5,4,2,1,3]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,7,8,6,5,4,3,2]=>[6,8,7,5,4,3,1,2]=>[[[[[.,[[.,.],.]],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8,7,6,5,4,3,2]=>[7,8,6,5,4,3,2,1]=>[[[[[[[.,[.,.]],.],.],.],.],.],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,8,7]=>[3,2,4,5,6,7,8,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,5,7,6,8]=>[3,2,4,5,6,7,1,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,5,7,8,6]=>[3,2,4,5,6,8,1,7]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,5,8,7,6]=>[4,3,5,6,7,8,2,1]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,4,6,5,7,8]=>[3,2,4,5,6,1,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,4,6,7,8,5]=>[3,2,4,5,8,1,6,7]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,4,7,8,6,5]=>[4,3,5,6,8,7,1,2]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,8,7,6,5]=>[5,4,6,7,8,3,2,1]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,3,5,4,6,7,8]=>[3,2,4,5,1,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4,6,8,7]=>[4,3,5,6,2,7,8,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,3,5,4,7,8,6]=>[4,3,5,6,2,8,1,7]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,8,7,6]=>[5,4,6,7,3,8,2,1]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,3,5,6,4,8,7]=>[4,3,5,7,2,6,8,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,8,4]=>[3,2,4,8,1,5,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,8,7,6,5,4]=>[6,5,7,8,4,3,2,1]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,3,5,6,8,7]=>[4,3,5,2,6,7,8,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,4,3,5,7,8,6]=>[4,3,5,2,6,8,1,7]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,5,7,8]=>[4,3,5,2,6,1,7,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>[5,4,6,3,7,2,8,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,3,6,7,5,8]=>[4,3,5,2,7,1,6,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,3,6,7,8,5]=>[4,3,5,2,8,1,6,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,3,6,8,7,5]=>[5,4,6,3,8,2,7,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,6,8,5]=>[5,4,6,3,8,2,1,7]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,4,3,7,8,6,5]=>[5,4,6,3,8,7,1,2]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>[6,5,7,4,8,3,2,1]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,4,5,3,6,7,8]=>[3,2,5,1,4,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6,8,7]=>[4,3,6,2,5,7,8,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,1,4,5,3,8,7,6]=>[5,4,7,3,6,8,2,1]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,6,3,8,7]=>[4,3,7,2,5,6,8,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,8,3]=>[3,2,8,1,4,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,6,8,7,3]=>[4,3,8,2,5,6,7,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,4,6,5,3,7,8]=>[4,3,6,2,5,1,7,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,4,6,5,3,8,7]=>[5,4,7,3,6,2,8,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,4,6,5,8,7,3]=>[5,4,8,3,6,2,7,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,4,6,7,5,3,8]=>[4,3,7,2,6,1,5,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,4,6,7,5,8,3]=>[4,3,8,2,6,1,5,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,4,6,7,8,5,3]=>[4,3,8,2,7,1,5,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,4,6,8,7,5,3]=>[5,4,8,3,7,2,6,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,4,7,6,5,8,3]=>[5,4,8,3,6,2,1,7]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,4,7,6,8,5,3]=>[5,4,8,3,7,2,1,6]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,4,7,8,6,5,3]=>[5,4,8,3,7,6,1,2]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,5,4,3,6,7,8]=>[4,3,5,2,1,6,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,4,6,3,8,7]=>[5,4,7,3,2,6,8,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,5,4,6,7,3,8]=>[4,3,7,2,1,5,6,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,5,4,6,7,8,3]=>[4,3,8,2,1,5,6,7]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,5,4,6,8,7,3]=>[5,4,8,3,2,6,7,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,4,7,6,8,3]=>[5,4,8,3,2,6,1,7]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,5,4,7,8,6,3]=>[5,4,8,3,2,7,1,6]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,5,4,8,7,6,3]=>[6,5,8,4,3,7,2,1]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,5,6,4,3,7,8]=>[4,3,6,5,1,2,7,8]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,1,5,6,4,3,8,7]=>[5,4,7,6,2,3,8,1]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,1,5,6,4,8,7,3]=>[5,4,8,6,2,3,7,1]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,1,5,6,7,4,8,3]=>[4,3,8,6,1,2,5,7]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,8,4,3]=>[4,3,8,7,1,2,5,6]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,1,5,6,8,7,4,3]=>[5,4,8,7,2,3,6,1]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,1,5,7,6,4,8,3]=>[5,4,8,6,2,3,1,7]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,1,5,7,6,8,4,3]=>[5,4,8,7,2,3,1,6]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,5,7,8,6,4,3]=>[5,4,8,7,2,6,1,3]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,1,5,8,7,6,4,3]=>[6,5,8,7,3,4,2,1]=>[[[[[.,.],[[.,.],.]],[.,.]],.],.]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>[6,5,7,4,3,2,8,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,5,7,4,8,3]=>[5,4,8,6,2,1,3,7]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,6,5,7,8,4,3]=>[5,4,8,7,2,1,3,6]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,6,5,8,7,4,3]=>[6,5,8,7,3,2,4,1]=>[[[[[.,.],[[.,.],.]],.],[.,.]],.]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,6,7,5,4,3,8]=>[5,4,7,6,3,1,2,8]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,6,7,5,4,8,3]=>[5,4,8,6,3,1,2,7]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,6,7,5,8,4,3]=>[5,4,8,7,3,1,2,6]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,6,7,8,5,4,3]=>[5,4,8,7,6,1,2,3]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,1,6,8,7,5,4,3]=>[6,5,8,7,4,2,3,1]=>[[[[[.,.],[[.,.],.]],.],[.,.]],.]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,7,6,5,4,3,8]=>[6,5,7,4,3,2,1,8]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,7,6,5,4,8,3]=>[6,5,8,4,3,2,1,7]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,7,6,5,8,4,3]=>[6,5,8,7,3,2,1,4]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,7,6,8,5,4,3]=>[6,5,8,7,4,2,1,3]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,7,8,6,5,4,3]=>[6,5,8,7,4,3,1,2]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>[7,6,8,5,4,3,2,1]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,6,8,7]=>[4,2,3,5,6,7,8,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,5,7,6,8]=>[4,2,3,5,6,7,1,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>[4,2,3,5,6,8,1,7]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,1,4,6,7,8,5]=>[4,2,3,5,8,1,6,7]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,8,7,6,5]=>[6,4,5,7,8,3,2,1]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,1,5,4,6,7,8]=>[4,2,3,5,1,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,8]=>[5,3,4,6,2,7,1,8]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,8,4]=>[4,2,3,8,1,5,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,1,6,5,4,8,7]=>[6,4,5,7,3,2,8,1]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,1,6,5,8,7,4]=>[6,4,5,8,3,2,7,1]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,6,7,8,5,4]=>[5,3,4,8,7,1,2,6]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,1,7,8,6,5,4]=>[6,4,5,8,7,3,1,2]=>[[[[.,.],[.,[[.,.],.]]],.],[.,.]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,8,7,6,5,4]=>[7,5,6,8,4,3,2,1]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,4,1,5,6,8,7]=>[5,2,3,4,6,7,8,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,5,7,6,8]=>[5,2,3,4,6,7,1,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,4,1,5,7,8,6]=>[5,2,3,4,6,8,1,7]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,8,7,6]=>[6,3,4,5,7,8,2,1]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,4,1,6,5,7,8]=>[5,2,3,4,6,1,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,8,7]=>[6,3,4,5,7,2,8,1]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,4,1,6,7,5,8]=>[5,2,3,4,7,1,6,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>[5,2,3,4,8,1,6,7]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,4,1,6,8,7,5]=>[6,3,4,5,8,2,7,1]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,4,1,7,6,8,5]=>[6,3,4,5,8,2,1,7]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,7,8,6,5]=>[6,3,4,5,8,7,1,2]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,8,7,6,5]=>[7,4,5,6,8,3,2,1]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,5,1,6,8,7]=>[6,2,3,4,5,7,8,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,5,1,7,8,6]=>[6,2,3,4,5,8,1,7]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,1,8,7,6]=>[7,3,4,5,6,8,2,1]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,1,8,7]=>[7,2,3,4,5,6,8,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,8,7,1]=>[8,2,3,4,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,5,7,6,1,8]=>[7,2,3,4,5,6,1,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,5,7,6,8,1]=>[8,2,3,4,5,6,1,7]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,5,7,8,6,1]=>[8,2,3,4,5,7,1,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,8,7,6,1]=>[8,3,4,5,6,7,2,1]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,4,6,5,1,7,8]=>[6,2,3,4,5,1,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,4,6,5,7,1,8]=>[7,2,3,4,5,1,6,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,4,6,5,7,8,1]=>[8,2,3,4,5,1,6,7]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,4,6,7,5,8,1]=>[8,2,3,4,6,1,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,6,7,8,5,1]=>[8,2,3,4,7,1,5,6]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,4,7,6,5,8,1]=>[8,3,4,5,6,2,1,7]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,4,7,6,8,5,1]=>[8,3,4,5,7,2,1,6]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,4,7,8,6,5,1]=>[8,3,4,5,7,6,1,2]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,8,7,6,5,1]=>[8,4,5,6,7,3,2,1]=>[[[[[.,.],[.,[.,[.,.]]]],.],.],.]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,5,4,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,5,4,1,6,8,7]=>[6,3,4,5,2,7,8,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,3,5,4,1,7,6,8]=>[6,3,4,5,2,7,1,8]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,3,5,4,1,8,7,6]=>[7,4,5,6,3,8,2,1]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,3,5,4,6,7,1,8]=>[7,2,3,4,1,5,6,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,5,4,6,7,8,1]=>[8,2,3,4,1,5,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,5,4,7,8,6,1]=>[8,3,4,5,2,7,1,6]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,5,6,4,7,8,1]=>[8,2,3,5,1,4,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,5,6,7,4,8,1]=>[8,2,3,6,1,4,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,8,4,1]=>[8,2,3,7,1,4,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,5,6,8,7,4,1]=>[8,3,4,7,2,5,6,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,5,7,8,6,4,1]=>[8,3,4,7,2,6,1,5]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,5,8,7,6,4,1]=>[8,4,5,7,3,6,2,1]=>[[[[[.,.],[.,[.,.]]],[.,.]],.],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,6,5,4,1,7,8]=>[6,3,4,5,2,1,7,8]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,6,5,4,1,8,7]=>[7,4,5,6,3,2,8,1]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,6,5,4,7,8,1]=>[8,3,4,5,2,1,6,7]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,6,5,7,4,1,8]=>[7,3,4,6,2,1,5,8]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,6,5,8,7,4,1]=>[8,4,5,7,3,2,6,1]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,6,7,8,5,4,1]=>[8,3,4,7,6,1,2,5]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,7,6,5,4,1,8]=>[7,4,5,6,3,2,1,8]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,7,6,5,4,8,1]=>[8,4,5,6,3,2,1,7]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,8,7,6,5,4,1]=>[8,5,6,7,4,3,2,1]=>[[[[[[.,.],[.,[.,.]]],.],.],.],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,4,3,1,6,5,8,7]=>[6,4,5,3,7,2,8,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,4,3,1,6,8,7,5]=>[6,4,5,3,8,2,7,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,4,3,1,7,6,8,5]=>[6,4,5,3,8,2,1,7]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,4,3,1,7,8,6,5]=>[6,4,5,3,8,7,1,2]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,4,3,1,8,7,6,5]=>[7,5,6,4,8,3,2,1]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,4,3,5,1,6,7,8]=>[5,2,3,1,4,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,7,1,8]=>[7,2,3,1,4,5,6,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,8,1]=>[8,2,3,1,4,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[2,4,3,5,6,8,7,1]=>[8,3,4,2,5,6,7,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,6,5,1,8,7]=>[7,4,5,3,6,2,8,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,8,7,1]=>[8,4,5,3,6,2,7,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,4,3,6,8,7,5,1]=>[8,4,5,3,7,2,6,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,4,3,7,6,5,8,1]=>[8,4,5,3,6,2,1,7]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,4,3,8,7,6,5,1]=>[8,5,6,4,7,3,2,1]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[2,4,5,3,1,6,8,7]=>[6,3,5,2,4,7,8,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,4,5,3,1,7,8,6]=>[6,3,5,2,4,8,1,7]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,4,5,3,6,7,8,1]=>[8,2,4,1,3,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,4,5,3,7,8,6,1]=>[8,3,5,2,4,7,1,6]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,6,3,8,7,1]=>[8,3,6,2,4,5,7,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,6,8,7,3,1]=>[8,3,7,2,4,5,6,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,4,5,7,8,6,3,1]=>[8,3,7,2,4,6,1,5]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[2,4,6,5,3,1,7,8]=>[6,3,5,2,4,1,7,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,4,6,5,3,1,8,7]=>[7,4,6,3,5,2,8,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,4,6,5,3,7,8,1]=>[8,3,5,2,4,1,6,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,4,6,5,3,8,7,1]=>[8,4,6,3,5,2,7,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,4,6,5,7,3,8,1]=>[8,3,6,2,4,1,5,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,4,6,5,7,8,3,1]=>[8,3,7,2,4,1,5,6]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,4,6,5,8,7,3,1]=>[8,4,7,3,5,2,6,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,4,6,7,8,5,3,1]=>[8,3,7,2,6,1,4,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,4,6,8,7,5,3,1]=>[8,4,7,3,6,2,5,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,4,7,6,5,8,3,1]=>[8,4,7,3,5,2,1,6]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,4,7,8,6,5,3,1]=>[8,4,7,3,6,5,1,2]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,4,8,7,6,5,3,1]=>[8,5,7,4,6,3,2,1]=>[[[[[[.,.],[.,.]],[.,.]],.],.],.]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,5,4,3,1,6,7,8]=>[5,3,4,2,1,6,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,5,4,3,1,7,8,6]=>[6,4,5,3,2,8,1,7]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,5,4,3,1,8,7,6]=>[7,5,6,4,3,8,2,1]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,5,4,3,6,7,8,1]=>[8,3,4,2,1,5,6,7]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,5,4,3,6,8,7,1]=>[8,4,5,3,2,6,7,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,5,4,6,3,7,1,8]=>[7,3,5,2,1,4,6,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,5,4,6,3,7,8,1]=>[8,3,5,2,1,4,6,7]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,5,4,6,7,3,1,8]=>[7,3,6,2,1,4,5,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,5,4,6,7,3,8,1]=>[8,3,6,2,1,4,5,7]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,5,4,6,7,8,3,1]=>[8,3,7,2,1,4,5,6]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,5,4,7,6,8,3,1]=>[8,4,7,3,2,5,1,6]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,5,4,7,8,6,3,1]=>[8,4,7,3,2,6,1,5]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,5,4,8,7,6,3,1]=>[8,5,7,4,3,6,2,1]=>[[[[[[.,.],[.,.]],.],[.,.]],.],.]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[2,5,6,4,7,8,3,1]=>[8,3,7,4,1,2,5,6]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,5,6,4,8,7,3,1]=>[8,4,7,5,2,3,6,1]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,5,6,7,4,3,8,1]=>[8,3,6,5,1,2,4,7]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,5,6,7,4,8,3,1]=>[8,3,7,5,1,2,4,6]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,8,4,3,1]=>[8,3,7,6,1,2,4,5]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,6,5,4,3,7,8,1]=>[8,4,5,3,2,1,6,7]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,6,5,4,7,8,3,1]=>[8,4,7,3,2,1,5,6]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,6,5,4,8,7,3,1]=>[8,5,7,4,3,2,6,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,6,5,7,8,4,3,1]=>[8,4,7,6,2,1,3,5]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,6,7,5,8,4,3,1]=>[8,4,7,6,3,1,2,5]=>[[[[.,.],[[.,.],.]],.],[.,[.,.]]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,6,7,8,5,4,3,1]=>[8,4,7,6,5,1,2,3]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,6,8,7,5,4,3,1]=>[8,5,7,6,4,2,3,1]=>[[[[[.,.],[[.,.],.]],.],[.,.]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,7,6,5,4,3,1,8]=>[7,5,6,4,3,2,1,8]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,7,6,5,4,3,8,1]=>[8,5,6,4,3,2,1,7]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,7,6,5,4,8,3,1]=>[8,5,7,4,3,2,1,6]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,7,6,8,5,4,3,1]=>[8,5,7,6,4,2,1,3]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,7,8,6,5,4,3,1]=>[8,5,7,6,4,3,1,2]=>[[[[[.,.],[[.,.],.]],.],.],[.,.]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,8,7,6,5,4,3,1]=>[8,6,7,5,4,3,2,1]=>[[[[[[[.,.],[.,.]],.],.],.],.],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,6,8,7]=>[4,3,2,5,6,7,8,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,5,7,6,8]=>[4,3,2,5,6,7,1,8]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,5,7,8,6]=>[4,3,2,5,6,8,1,7]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,5,8,7,6]=>[5,4,3,6,7,8,2,1]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,2,1,4,7,6,5,8]=>[5,4,3,6,7,2,1,8]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,2,1,4,7,8,6,5]=>[5,4,3,6,8,7,1,2]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,2,1,4,8,7,6,5]=>[6,5,4,7,8,3,2,1]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,2,1,5,4,6,7,8]=>[4,3,2,5,1,6,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,7,6,8]=>[5,4,3,6,2,7,1,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,2,1,5,6,4,7,8]=>[4,3,2,6,1,5,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,2,1,5,6,7,4,8]=>[4,3,2,7,1,5,6,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,8,4]=>[4,3,2,8,1,5,6,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,2,1,5,7,6,4,8]=>[5,4,3,7,2,6,1,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,1,5,7,8,6,4]=>[5,4,3,8,2,7,1,6]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,2,1,5,8,7,6,4]=>[6,5,4,8,3,7,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,2,1,6,5,7,4,8]=>[5,4,3,7,2,1,6,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,2,1,6,5,7,8,4]=>[5,4,3,8,2,1,6,7]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,2,1,6,5,8,7,4]=>[6,5,4,8,3,2,7,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,2,1,6,8,7,5,4]=>[6,5,4,8,7,2,3,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,2,1,7,6,5,4,8]=>[6,5,4,7,3,2,1,8]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,2,1,7,6,5,8,4]=>[6,5,4,8,3,2,1,7]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,2,1,7,6,8,5,4]=>[6,5,4,8,7,2,1,3]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,1,7,8,6,5,4]=>[6,5,4,8,7,3,1,2]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,2,1,8,7,6,5,4]=>[7,6,5,8,4,3,2,1]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,2,4,1,5,6,8,7]=>[5,3,2,4,6,7,8,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,2,4,1,5,7,8,6]=>[5,3,2,4,6,8,1,7]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,4,1,6,5,8,7]=>[6,4,3,5,7,2,8,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,2,4,1,6,7,5,8]=>[5,3,2,4,7,1,6,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,2,4,1,6,8,7,5]=>[6,4,3,5,8,2,7,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,4,1,7,6,8,5]=>[6,4,3,5,8,2,1,7]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,2,4,1,7,8,6,5]=>[6,4,3,5,8,7,1,2]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,2,4,1,8,7,6,5]=>[7,5,4,6,8,3,2,1]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,5,1,6,7,8]=>[5,2,1,3,4,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,7,1,8]=>[7,2,1,3,4,5,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,1]=>[8,2,1,3,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,6,8,7,1]=>[8,3,2,4,5,6,7,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,5,7,6,8,1]=>[8,3,2,4,5,6,1,7]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,5,7,8,6,1]=>[8,3,2,4,5,7,1,6]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,2,4,6,5,8,7,1]=>[8,4,3,5,6,2,7,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,2,4,6,7,5,1,8]=>[7,3,2,4,6,1,5,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,2,4,7,6,5,8,1]=>[8,4,3,5,6,2,1,7]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,5,4,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,5,4,1,7,8,6]=>[6,4,3,5,2,8,1,7]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,5,4,1,8,7,6]=>[7,5,4,6,3,8,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,5,4,6,1,8,7]=>[7,4,3,5,2,6,8,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,7,6,1,8]=>[7,4,3,5,2,6,1,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,7,6,8,1]=>[8,4,3,5,2,6,1,7]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,2,5,6,4,1,8,7]=>[7,4,3,6,2,5,8,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,2,5,6,4,7,8,1]=>[8,3,2,5,1,4,6,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,2,5,6,7,4,1,8]=>[7,3,2,6,1,4,5,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,2,5,6,7,4,8,1]=>[8,3,2,6,1,4,5,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,8,4,1]=>[8,3,2,7,1,4,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,5,7,6,4,8,1]=>[8,4,3,6,2,5,1,7]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,5,7,8,6,4,1]=>[8,4,3,7,2,6,1,5]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,2,6,5,4,7,1,8]=>[7,4,3,5,2,1,6,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,2,6,5,4,8,7,1]=>[8,5,4,6,3,2,7,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,2,6,5,7,4,1,8]=>[7,4,3,6,2,1,5,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,6,5,7,4,8,1]=>[8,4,3,6,2,1,5,7]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,2,6,7,5,4,8,1]=>[8,4,3,6,5,1,2,7]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,2,6,7,5,8,4,1]=>[8,4,3,7,5,1,2,6]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,2,7,6,5,4,1,8]=>[7,5,4,6,3,2,1,8]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,7,8,6,5,4,1]=>[8,5,4,7,6,3,1,2]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,2,8,7,6,5,4,1]=>[8,6,5,7,4,3,2,1]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,4,2,1,5,6,8,7]=>[5,4,2,3,6,7,8,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,4,2,1,5,8,7,6]=>[6,5,3,4,7,8,2,1]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,4,2,1,6,5,8,7]=>[6,5,3,4,7,2,8,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,4,2,1,6,7,8,5]=>[5,4,2,3,8,1,6,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,4,2,1,6,8,7,5]=>[6,5,3,4,8,2,7,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,4,2,1,7,6,8,5]=>[6,5,3,4,8,2,1,7]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,4,2,1,7,8,6,5]=>[6,5,3,4,8,7,1,2]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4,2,1,8,7,6,5]=>[7,6,4,5,8,3,2,1]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,4,2,5,1,6,7,8]=>[5,3,1,2,4,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,4,2,5,1,7,6,8]=>[6,4,2,3,5,7,1,8]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,4,2,5,1,7,8,6]=>[6,4,2,3,5,8,1,7]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,4,2,5,1,8,7,6]=>[7,5,3,4,6,8,2,1]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,7,1,8]=>[7,3,1,2,4,5,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,8,1]=>[8,3,1,2,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,4,2,5,6,8,7,1]=>[8,4,2,3,5,6,7,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,4,2,5,7,6,1,8]=>[7,4,2,3,5,6,1,8]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,4,2,5,7,8,6,1]=>[8,4,2,3,5,7,1,6]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,4,2,5,8,7,6,1]=>[8,5,3,4,6,7,2,1]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,4,2,6,5,1,8,7]=>[7,5,3,4,6,2,8,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,4,2,6,5,7,1,8]=>[7,4,2,3,5,1,6,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,4,2,6,5,7,8,1]=>[8,4,2,3,5,1,6,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,4,2,6,7,5,8,1]=>[8,4,2,3,6,1,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,2,8,7,6,5,1]=>[8,6,4,5,7,3,2,1]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,5,2,1,6,7,8]=>[5,4,1,2,3,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,5,2,1,6,8,7]=>[6,5,2,3,4,7,8,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,5,2,1,7,8,6]=>[6,5,2,3,4,8,1,7]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,5,2,1,8,7,6]=>[7,6,3,4,5,8,2,1]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,5,2,6,1,7,8]=>[6,4,1,2,3,5,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,5,2,6,1,8,7]=>[7,5,2,3,4,6,8,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,5,2,6,7,1,8]=>[7,4,1,2,3,5,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,5,2,6,7,8,1]=>[8,4,1,2,3,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,5,2,7,6,8,1]=>[8,5,2,3,4,6,1,7]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,6,2,1,7,8]=>[6,5,1,2,3,4,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,6,2,1,8,7]=>[7,6,2,3,4,5,8,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,6,2,7,1,8]=>[7,5,1,2,3,4,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,6,2,7,8,1]=>[8,5,1,2,3,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,6,2,8,7,1]=>[8,6,2,3,4,5,7,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,7,2,1,8]=>[7,6,1,2,3,4,5,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,2,8,1]=>[8,6,1,2,3,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,2,1]=>[8,7,1,2,3,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,6,8,7,2,1]=>[8,7,2,3,4,5,6,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,5,7,6,8,2,1]=>[8,7,2,3,4,5,1,6]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,5,7,8,6,2,1]=>[8,7,2,3,4,6,1,5]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,8,7,6,2,1]=>[8,7,3,4,5,6,2,1]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,4,6,5,2,1,8,7]=>[7,6,3,4,5,2,8,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,4,6,5,2,7,1,8]=>[7,5,2,3,4,1,6,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,4,6,5,2,7,8,1]=>[8,5,2,3,4,1,6,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,4,6,5,7,2,8,1]=>[8,6,2,3,4,1,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,4,6,5,7,8,2,1]=>[8,7,2,3,4,1,5,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,4,6,7,5,2,8,1]=>[8,6,2,3,5,1,4,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,4,6,7,8,5,2,1]=>[8,7,2,3,6,1,4,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,4,7,6,5,2,1,8]=>[7,6,3,4,5,2,1,8]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,4,7,6,5,8,2,1]=>[8,7,3,4,5,2,1,6]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,8,7,6,5,2,1]=>[8,7,4,5,6,3,2,1]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,5,4,2,1,6,7,8]=>[5,4,2,3,1,6,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,5,4,2,1,6,8,7]=>[6,5,3,4,2,7,8,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,5,4,2,1,7,8,6]=>[6,5,3,4,2,8,1,7]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,5,4,2,1,8,7,6]=>[7,6,4,5,3,8,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[3,5,4,2,6,7,8,1]=>[8,4,2,3,1,5,6,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,5,4,2,7,6,1,8]=>[7,5,3,4,2,6,1,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,5,4,2,7,8,6,1]=>[8,5,3,4,2,7,1,6]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,5,4,6,2,7,1,8]=>[7,5,2,3,1,4,6,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[3,5,4,6,7,8,2,1]=>[8,7,2,3,1,4,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[3,5,4,7,6,8,2,1]=>[8,7,3,4,2,5,1,6]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,5,6,4,7,2,8,1]=>[8,6,2,4,1,3,5,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,5,6,4,7,8,2,1]=>[8,7,2,4,1,3,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,5,6,7,4,2,8,1]=>[8,6,2,5,1,3,4,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[3,5,6,7,4,8,2,1]=>[8,7,2,5,1,3,4,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,8,4,2,1]=>[8,7,2,6,1,3,4,5]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,5,7,6,4,2,1,8]=>[7,6,3,5,2,4,1,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[3,5,7,6,4,2,8,1]=>[8,6,3,5,2,4,1,7]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[3,5,7,6,4,8,2,1]=>[8,7,3,5,2,4,1,6]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,5,7,6,8,4,2,1]=>[8,7,3,6,2,4,1,5]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,5,7,8,6,4,2,1]=>[8,7,3,6,2,5,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,5,8,7,6,4,2,1]=>[8,7,4,6,3,5,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,6,5,4,2,1,7,8]=>[6,5,3,4,2,1,7,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,6,5,4,2,1,8,7]=>[7,6,4,5,3,2,8,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[3,6,5,4,7,2,1,8]=>[7,6,3,4,2,1,5,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,6,5,4,7,2,8,1]=>[8,6,3,4,2,1,5,7]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[3,6,5,4,7,8,2,1]=>[8,7,3,4,2,1,5,6]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,6,8,7,5,4,2,1]=>[8,7,4,6,5,2,3,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,7,6,5,4,8,2,1]=>[8,7,4,5,3,2,1,6]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,7,6,5,8,4,2,1]=>[8,7,4,6,3,2,1,5]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,7,6,8,5,4,2,1]=>[8,7,4,6,5,2,1,3]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,7,8,6,5,4,2,1]=>[8,7,4,6,5,3,1,2]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,8,7,6,5,4,2,1]=>[8,7,5,6,4,3,2,1]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,3,2,1,5,6,8,7]=>[5,4,3,2,6,7,8,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,3,2,1,5,7,6,8]=>[5,4,3,2,6,7,1,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,3,2,1,5,7,8,6]=>[5,4,3,2,6,8,1,7]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,3,2,1,5,8,7,6]=>[6,5,4,3,7,8,2,1]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,3,2,1,6,5,7,8]=>[5,4,3,2,6,1,7,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7]=>[6,5,4,3,7,2,8,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,3,2,1,6,7,5,8]=>[5,4,3,2,7,1,6,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,3,2,1,6,7,8,5]=>[5,4,3,2,8,1,6,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,3,2,1,6,8,7,5]=>[6,5,4,3,8,2,7,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,2,1,7,6,5,8]=>[6,5,4,3,7,2,1,8]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,3,2,1,7,6,8,5]=>[6,5,4,3,8,2,1,7]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,2,1,7,8,6,5]=>[6,5,4,3,8,7,1,2]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>[7,6,5,4,8,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[4,3,2,5,1,6,7,8]=>[5,3,2,1,4,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,3,2,5,1,8,7,6]=>[7,5,4,3,6,8,2,1]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[4,3,2,5,6,1,8,7]=>[7,4,3,2,5,6,8,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,7,1,8]=>[7,3,2,1,4,5,6,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,8,1]=>[8,3,2,1,4,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[4,3,2,5,6,8,7,1]=>[8,4,3,2,5,6,7,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[4,3,2,5,7,8,6,1]=>[8,4,3,2,5,7,1,6]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[4,3,2,6,5,1,7,8]=>[6,4,3,2,5,1,7,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[4,3,2,6,5,1,8,7]=>[7,5,4,3,6,2,8,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,3,2,6,8,7,5,1]=>[8,5,4,3,7,2,6,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,2,7,8,6,5,1]=>[8,5,4,3,7,6,1,2]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[4,3,5,2,1,6,7,8]=>[5,4,2,1,3,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[4,3,5,2,1,6,8,7]=>[6,5,3,2,4,7,8,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[4,3,5,2,1,8,7,6]=>[7,6,4,3,5,8,2,1]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[4,3,5,2,6,1,7,8]=>[6,4,2,1,3,5,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,3,5,2,6,1,8,7]=>[7,5,3,2,4,6,8,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[4,3,5,2,6,7,8,1]=>[8,4,2,1,3,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[4,3,5,2,7,6,1,8]=>[7,5,3,2,4,6,1,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,3,5,2,7,6,8,1]=>[8,5,3,2,4,6,1,7]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,3,5,2,8,7,6,1]=>[8,6,4,3,5,7,2,1]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[4,3,5,6,2,1,8,7]=>[7,6,3,2,4,5,8,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[4,3,5,6,2,7,8,1]=>[8,5,2,1,3,4,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,8,2,1]=>[8,7,2,1,3,4,5,6]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0,1,0]=>[4,3,5,7,6,2,1,8]=>[7,6,3,2,4,5,1,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,7,8,6,2,1]=>[8,7,3,2,4,6,1,5]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[4,3,6,5,2,1,8,7]=>[7,6,4,3,5,2,8,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[4,3,6,5,2,8,7,1]=>[8,6,4,3,5,2,7,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[4,3,6,5,7,2,1,8]=>[7,6,3,2,4,1,5,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,3,6,5,7,2,8,1]=>[8,6,3,2,4,1,5,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[4,3,6,5,7,8,2,1]=>[8,7,3,2,4,1,5,6]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,8,7,2,1]=>[8,7,4,3,5,2,6,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[4,3,6,7,5,2,8,1]=>[8,6,3,2,5,1,4,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,6,7,8,5,2,1]=>[8,7,3,2,6,1,4,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[4,3,7,6,5,2,1,8]=>[7,6,4,3,5,2,1,8]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,7,8,6,5,2,1]=>[8,7,4,3,6,5,1,2]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[4,3,8,7,6,5,2,1]=>[8,7,5,4,6,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[4,5,3,2,1,6,7,8]=>[5,4,3,1,2,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[4,5,3,2,1,6,8,7]=>[6,5,4,2,3,7,8,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[4,5,3,2,1,8,7,6]=>[7,6,5,3,4,8,2,1]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[4,5,3,2,6,1,7,8]=>[6,4,3,1,2,5,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[4,5,3,2,6,1,8,7]=>[7,5,4,2,3,6,8,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,8,7,1]=>[8,5,4,2,3,6,7,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[4,5,3,6,2,1,8,7]=>[7,6,4,2,3,5,8,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[4,5,3,6,2,7,1,8]=>[7,5,3,1,2,4,6,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[4,5,3,6,2,8,7,1]=>[8,6,4,2,3,5,7,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0,1,0]=>[4,5,3,7,6,2,1,8]=>[7,6,4,2,3,5,1,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[4,5,3,7,6,2,8,1]=>[8,6,4,2,3,5,1,7]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,5,3,7,8,6,2,1]=>[8,7,4,2,3,6,1,5]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,6,3,2,1,7,8]=>[6,5,4,1,2,3,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,6,3,2,1,8,7]=>[7,6,5,2,3,4,8,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,6,3,2,7,8,1]=>[8,5,4,1,2,3,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,6,3,7,2,8,1]=>[8,6,4,1,2,3,5,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,6,3,7,8,2,1]=>[8,7,4,1,2,3,5,6]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,7,3,2,1,8]=>[7,6,5,1,2,3,4,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,7,3,2,8,1]=>[8,6,5,1,2,3,4,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,7,3,8,2,1]=>[8,7,5,1,2,3,4,6]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,3,2,1]=>[8,7,6,1,2,3,4,5]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,6,8,7,3,2,1]=>[8,7,6,2,3,4,5,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[4,5,7,6,3,2,1,8]=>[7,6,5,2,3,4,1,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[4,5,7,6,8,3,2,1]=>[8,7,6,2,3,4,1,5]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,5,8,7,6,3,2,1]=>[8,7,6,3,4,5,2,1]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[4,6,5,3,2,1,8,7]=>[7,6,5,3,4,2,8,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[4,6,5,3,7,2,8,1]=>[8,6,4,2,3,1,5,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[4,6,5,7,3,2,1,8]=>[7,6,5,2,3,1,4,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[4,6,5,7,3,2,8,1]=>[8,6,5,2,3,1,4,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[4,6,5,7,8,3,2,1]=>[8,7,6,2,3,1,4,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,6,5,8,7,3,2,1]=>[8,7,6,3,4,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[4,6,7,5,3,2,8,1]=>[8,6,5,2,4,1,3,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[4,6,7,5,8,3,2,1]=>[8,7,6,2,4,1,3,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,6,7,8,5,3,2,1]=>[8,7,6,2,5,1,3,4]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,6,8,7,5,3,2,1]=>[8,7,6,3,5,2,4,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[4,7,6,5,3,2,1,8]=>[7,6,5,3,4,2,1,8]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[4,7,6,5,3,2,8,1]=>[8,6,5,3,4,2,1,7]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[4,7,6,5,3,8,2,1]=>[8,7,5,3,4,2,1,6]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,7,6,5,8,3,2,1]=>[8,7,6,3,4,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,7,6,8,5,3,2,1]=>[8,7,6,3,5,2,1,4]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[4,7,8,6,5,3,2,1]=>[8,7,6,3,5,4,1,2]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,8,7,6,5,3,2,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,4,3,2,1,6,8,7]=>[6,5,4,3,2,7,8,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,4,3,2,1,7,6,8]=>[6,5,4,3,2,7,1,8]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,4,3,2,1,7,8,6]=>[6,5,4,3,2,8,1,7]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,4,3,2,1,8,7,6]=>[7,6,5,4,3,8,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,4,3,2,6,1,7,8]=>[6,4,3,2,1,5,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[5,4,3,2,6,1,8,7]=>[7,5,4,3,2,6,8,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[5,4,3,2,6,7,1,8]=>[7,4,3,2,1,5,6,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,7,8,1]=>[8,4,3,2,1,5,6,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[5,4,3,2,6,8,7,1]=>[8,5,4,3,2,6,7,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[5,4,3,2,7,6,1,8]=>[7,5,4,3,2,6,1,8]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[5,4,3,2,7,6,8,1]=>[8,5,4,3,2,6,1,7]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,3,2,7,8,6,1]=>[8,5,4,3,2,7,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,4,3,2,8,7,6,1]=>[8,6,5,4,3,7,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[5,4,3,6,2,7,1,8]=>[7,5,3,2,1,4,6,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[5,4,3,6,2,7,8,1]=>[8,5,3,2,1,4,6,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[5,4,3,6,7,2,1,8]=>[7,6,3,2,1,4,5,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[5,4,3,6,7,2,8,1]=>[8,6,3,2,1,4,5,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,8,2,1]=>[8,7,3,2,1,4,5,6]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[5,4,3,6,8,7,2,1]=>[8,7,4,3,2,5,6,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[5,4,3,7,8,6,2,1]=>[8,7,4,3,2,6,1,5]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[5,4,3,8,7,6,2,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[5,4,6,3,2,1,7,8]=>[6,5,4,2,1,3,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[5,4,6,3,2,1,8,7]=>[7,6,5,3,2,4,8,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[5,4,6,3,2,7,8,1]=>[8,5,4,2,1,3,6,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,4,6,3,2,8,7,1]=>[8,6,5,3,2,4,7,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[5,4,6,3,7,2,1,8]=>[7,6,4,2,1,3,5,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,4,6,3,7,2,8,1]=>[8,6,4,2,1,3,5,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[5,4,6,7,3,2,1,8]=>[7,6,5,2,1,3,4,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,4,6,7,3,8,2,1]=>[8,7,5,2,1,3,4,6]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,2,1]=>[8,7,6,2,1,3,4,5]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[5,4,7,6,3,2,1,8]=>[7,6,5,3,2,4,1,8]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[5,4,7,6,3,8,2,1]=>[8,7,5,3,2,4,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,4,7,6,8,3,2,1]=>[8,7,6,3,2,4,1,5]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[5,4,7,8,6,3,2,1]=>[8,7,6,3,2,5,1,4]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[5,6,4,3,2,1,7,8]=>[6,5,4,3,1,2,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[5,6,4,3,2,1,8,7]=>[7,6,5,4,2,3,8,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[5,6,4,3,2,7,1,8]=>[7,5,4,3,1,2,6,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[5,6,4,3,7,2,1,8]=>[7,6,4,3,1,2,5,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[5,6,4,3,8,7,2,1]=>[8,7,5,4,2,3,6,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,6,4,7,8,3,2,1]=>[8,7,6,3,1,2,4,5]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,6,7,4,3,2,1,8]=>[7,6,5,4,1,2,3,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[5,6,7,4,3,2,8,1]=>[8,6,5,4,1,2,3,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[5,6,7,4,3,8,2,1]=>[8,7,5,4,1,2,3,6]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,6,7,4,8,3,2,1]=>[8,7,6,4,1,2,3,5]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,4,3,2,1]=>[8,7,6,5,1,2,3,4]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,6,8,7,4,3,2,1]=>[8,7,6,5,2,3,4,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[5,7,6,4,3,2,1,8]=>[7,6,5,4,2,3,1,8]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[5,7,6,4,3,2,8,1]=>[8,6,5,4,2,3,1,7]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,7,6,4,8,3,2,1]=>[8,7,6,4,2,3,1,5]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[5,7,6,8,4,3,2,1]=>[8,7,6,5,2,3,1,4]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,7,8,6,4,3,2,1]=>[8,7,6,5,2,4,1,3]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,8,7,6,4,3,2,1]=>[8,7,6,5,3,4,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,5,4,3,2,1,8,7]=>[7,6,5,4,3,2,8,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[6,5,4,3,2,7,1,8]=>[7,5,4,3,2,1,6,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[6,5,4,3,2,7,8,1]=>[8,5,4,3,2,1,6,7]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,5,4,3,2,8,7,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[6,5,4,3,7,2,1,8]=>[7,6,4,3,2,1,5,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,2,1]=>[8,7,4,3,2,1,5,6]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[6,5,4,7,3,2,1,8]=>[7,6,5,3,2,1,4,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[6,5,4,7,8,3,2,1]=>[8,7,6,3,2,1,4,5]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[6,5,4,8,7,3,2,1]=>[8,7,6,4,3,2,5,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[6,5,7,4,3,2,1,8]=>[7,6,5,4,2,1,3,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[6,5,7,4,8,3,2,1]=>[8,7,6,4,2,1,3,5]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[6,5,7,8,4,3,2,1]=>[8,7,6,5,2,1,3,4]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[6,5,8,7,4,3,2,1]=>[8,7,6,5,3,2,4,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[6,7,5,4,3,2,1,8]=>[7,6,5,4,3,1,2,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[6,7,5,4,3,8,2,1]=>[8,7,5,4,3,1,2,6]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[6,7,5,4,8,3,2,1]=>[8,7,6,4,3,1,2,5]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[6,7,5,8,4,3,2,1]=>[8,7,6,5,3,1,2,4]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,5,4,3,2,1]=>[8,7,6,5,4,1,2,3]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,8,7,5,4,3,2,1]=>[8,7,6,5,4,2,3,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,1,2]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[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]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,9,8,7,6,5,4,3,2]=>[8,9,7,6,5,4,3,2,1]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[7,8,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,1,2,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,10,9,8,7,6,5,4,3,2]=>[9,10,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[8,9,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,1,2,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[7,6,8,5,4,3,2,1,9]=>[8,7,6,5,4,2,1,3,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[6,8,7,5,4,3,2,1,9]=>[8,7,6,5,4,2,3,1,9]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,11,10,9,8,7,6,5,4,3,2]=>[10,11,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[8,7,9,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,2,1,3,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[7,6,5,8,4,3,2,1,9]=>[8,7,6,5,3,2,1,4,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[6,7,8,5,4,3,2,1,9]=>[8,7,6,5,4,1,2,3,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]=>[8,7,6,9,5,4,3,2,1,10]=>[9,8,7,6,5,3,2,1,4,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[4,8,7,6,5,3,2,1,9]=>[8,7,6,4,5,3,2,1,9]=>[[[[[[[.,.],.],.],[.,.]],.],.],[.,.]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[5,9,8,7,6,4,3,2,1,10]=>[9,8,7,6,4,5,3,2,1,10]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[7,6,5,4,3,8,2,1,9]=>[8,7,5,4,3,2,1,6,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]=>[8,7,6,5,4,9,3,2,1,10]=>[9,8,7,5,4,3,2,1,6,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[7,6,5,4,3,2,8,1,9]=>[8,6,5,4,3,2,1,7,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,8,7,6,5,4,3,1,9]=>[8,6,7,5,4,3,2,1,9]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,6,5,4,3,2,1,9,8]=>[8,7,6,5,4,3,2,9,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,9,8,7,6,5,4,3]=>[8,7,9,6,5,4,3,2,1]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]=>[8,7,6,5,4,3,9,2,1,10]=>[9,8,6,5,4,3,2,1,7,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,8,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,8,7,6,5,4,3,2,9]=>[7,8,6,5,4,3,2,1,9]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[6,7,5,4,3,2,1,9,8]=>[8,7,6,5,4,2,3,9,1]=>[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,9,8,7,6,5,4,3]=>[7,8,9,6,5,4,3,2,1]=>[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]=>[8,7,6,5,4,3,2,9,1,10]=>[9,7,6,5,4,3,2,1,8,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,7,6,5,4,3,2,1,10,9]=>[9,8,7,6,5,4,3,2,10,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,1,10,9,8,7,6,5,4,3]=>[9,8,10,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[8,7,6,5,4,3,2,1,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,9,8,7,6,5,4,3,2,10]=>[8,9,7,6,5,4,3,2,1,10]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,10,9,8,7,6,5,4,3]=>[8,9,10,7,6,5,4,3,2,1]=>[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]
[]=>[]=>[]=>.
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,7,9,8,1]=>[9,2,3,4,5,6,7,8,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,5,6,8,7,9,1]=>[9,2,3,4,5,6,7,1,8]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,6,9,8,7,1]=>[9,3,4,5,6,7,8,2,1]=>[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,4,5,7,6,8,9,1]=>[9,2,3,4,5,6,1,7,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,4,5,8,7,6,9,1]=>[9,3,4,5,6,7,2,1,8]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,4,6,5,7,8,9,1]=>[9,2,3,4,5,1,6,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,9,8,7,6,5,4,1]=>[9,6,7,8,5,4,3,2,1]=>[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,8,9,1]=>[9,2,3,1,4,5,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[2,8,7,6,5,4,3,9,1]=>[9,6,7,5,4,3,2,1,8]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,9,8,7,6,5,4,3,1]=>[9,7,8,6,5,4,3,2,1]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,9,1]=>[9,2,1,3,4,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,8,9,1]=>[9,3,1,2,4,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,2,6,7,8,9,1]=>[9,4,1,2,3,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,6,7,2,8,9,1]=>[9,6,1,2,3,4,5,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,8,2,9,1]=>[9,7,1,2,3,4,5,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,9,2,1]=>[9,8,1,2,3,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[3,8,7,6,5,4,9,2,1]=>[9,8,5,6,4,3,2,1,7]=>[[[[[[[.,.],.],[.,.]],.],.],.],[.,.]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[4,5,6,3,7,8,9,2,1]=>[9,8,4,1,2,3,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,9,3,2,1]=>[9,8,7,1,2,3,4,5,6]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[4,8,7,6,5,9,3,2,1]=>[9,8,7,4,5,3,2,1,6]=>[[[[[[[.,.],.],.],[.,.]],.],.],[.,.]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[4,9,8,7,6,5,3,2,1]=>[9,8,7,5,6,4,3,2,1]=>[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,6,4,7,3,8,2,9,1]=>[9,7,5,3,1,2,4,6,8]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,9,4,3,2,1]=>[9,8,7,6,1,2,3,4,5]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[5,8,7,6,9,4,3,2,1]=>[9,8,7,6,3,4,2,1,5]=>[[[[[[[.,.],.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[5,9,8,7,6,4,3,2,1]=>[9,8,7,6,4,5,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,8,9,1]=>[9,5,4,3,2,1,6,7,8]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,9,5,4,3,2,1]=>[9,8,7,6,5,1,2,3,4]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[6,7,9,8,5,4,3,2,1]=>[9,8,7,6,5,2,3,4,1]=>[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[6,8,7,9,5,4,3,2,1]=>[9,8,7,6,5,2,3,1,4]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[6,9,8,7,5,4,3,2,1]=>[9,8,7,6,5,3,4,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[7,6,5,4,3,2,8,9,1]=>[9,6,5,4,3,2,1,7,8]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[7,6,5,4,3,2,9,8,1]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[7,6,8,9,5,4,3,2,1]=>[9,8,7,6,5,2,1,3,4]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[7,6,9,8,5,4,3,2,1]=>[9,8,7,6,5,3,2,4,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[7,8,6,5,4,3,2,9,1]=>[9,7,6,5,4,3,1,2,8]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[7,8,9,6,5,4,3,2,1]=>[9,8,7,6,5,4,1,2,3]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[7,9,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,2,3,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,7,6,5,4,3,2,9,1]=>[9,7,6,5,4,3,2,1,8]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[8,7,6,5,4,3,9,2,1]=>[9,8,6,5,4,3,2,1,7]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[8,7,6,5,4,9,3,2,1]=>[9,8,7,5,4,3,2,1,6]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[8,7,6,5,9,4,3,2,1]=>[9,8,7,6,4,3,2,1,5]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[8,7,6,9,5,4,3,2,1]=>[9,8,7,6,5,3,2,1,4]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[8,7,9,6,5,4,3,2,1]=>[9,8,7,6,5,4,2,1,3]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[8,9,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,1,2]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,9,8]=>[2,3,4,5,6,7,8,9,1]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,6,8,9,7]=>[2,3,4,5,6,7,9,1,8]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,5,7,8,9,6]=>[2,3,4,5,6,9,1,7,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,9,5]=>[2,3,4,5,9,1,6,7,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,9,4]=>[2,3,4,9,1,5,6,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,8,9,3]=>[2,3,9,1,4,5,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,9,2]=>[2,9,1,3,4,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,8,10,9]=>[2,3,4,5,6,7,8,9,10,1]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,9,8,7]=>[3,4,5,6,7,8,9,2,1]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,6,7,9,10,8]=>[2,3,4,5,6,7,8,10,1,9]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,5,6,8,9,10,7]=>[2,3,4,5,6,7,10,1,8,9]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,4,5,7,8,9,10,6]=>[2,3,4,5,6,10,1,7,8,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,9,10,5]=>[2,3,4,5,10,1,6,7,8,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,9,10,4]=>[2,3,4,10,1,5,6,7,8,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,8,9,10,3]=>[2,3,10,1,4,5,6,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,9,10,2]=>[2,10,1,3,4,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,8,9,11,10]=>[2,3,4,5,6,7,8,9,10,11,1]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,7,10,9,8]=>[3,4,5,6,7,8,9,10,2,1]=>[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,6,7,8,10,11,9]=>[2,3,4,5,6,7,8,9,11,1,10]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,5,9,8,7,6]=>[4,5,6,7,8,9,3,2,1]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,9,10,1]=>[10,2,1,3,4,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,9,10,11,2]=>[2,11,1,3,4,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>[11,1,2,3,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,7,8,11,10,9]=>[3,4,5,6,7,8,9,10,11,2,1]=>[[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,5,6,10,9,8,7]=>[4,5,6,7,8,9,10,3,2,1]=>[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,8,9,10,1]=>[10,3,1,2,4,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,9,10,11,1]=>[11,2,1,3,4,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,9,10,11,12,2]=>[2,12,1,3,4,5,6,7,8,9,10,11]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,9,8,7,6,5]=>[5,6,7,8,9,4,3,2,1]=>[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,2,6,7,8,9,10,1]=>[10,4,1,2,3,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,8,9,10,11,1]=>[11,3,1,2,4,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5,10,9,8,7,6]=>[5,6,7,8,9,10,4,3,2,1]=>[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,2,6,7,8,9,10,11,1]=>[11,4,1,2,3,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,2,8,9,10,1]=>[10,6,1,2,3,4,5,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,9,8,7,6,5,4]=>[6,7,8,9,5,4,3,2,1]=>[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,6,7,8,2,9,10,1]=>[10,7,1,2,3,4,5,6,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,10,9,8,7,6,5]=>[6,7,8,9,10,5,4,3,2,1]=>[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,2,8,9,10,11,1]=>[11,6,1,2,3,4,5,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,8,2,9,10,11,1]=>[11,7,1,2,3,4,5,6,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,6,8,7,9]=>[2,3,4,5,6,7,8,1,9]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,5,7,6,8,9]=>[2,3,4,5,6,7,1,8,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,5,7,6,9,8]=>[3,4,5,6,7,8,2,9,1]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,4,6,5,7,8,9]=>[2,3,4,5,6,1,7,8,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8,9]=>[2,3,4,5,1,6,7,8,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8,9]=>[2,3,4,1,5,6,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7,9]=>[4,5,6,3,7,2,8,1,9]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],[.,.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8,9]=>[2,3,1,4,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,6,7,9,8]=>[3,4,2,5,6,7,8,9,1]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,7,8,9]=>[3,4,2,5,1,6,7,8,9]=>[[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8]=>[5,6,4,7,3,8,2,9,1]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7,8,9]=>[3,4,2,1,5,6,7,8,9]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,7,9,8]=>[3,2,4,5,6,7,8,9,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,5,6,8,7,9]=>[3,2,4,5,6,7,8,1,9]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8,9]=>[3,2,4,1,5,6,7,8,9]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,9]=>[5,4,6,3,7,2,8,1,9]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,8,7,6,5,4,3,9]=>[7,6,8,5,4,3,2,1,9]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,5,4,6,7,8,9]=>[4,3,2,5,1,6,7,8,9]=>[[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,2,1,9,8,7,6,5,4]=>[8,7,6,9,5,4,3,2,1]=>[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[4,3,2,1,6,5,7,8,9]=>[5,4,3,2,6,1,7,8,9]=>[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,3,2,1,9,8,7,6,5]=>[8,7,6,5,9,4,3,2,1]=>[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]=>[5,4,3,2,1,7,6,8,9]=>[6,5,4,3,2,7,1,8,9]=>[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,4,3,2,1,9,8,7,6]=>[8,7,6,5,4,9,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[6,5,4,3,2,1,8,7,9]=>[7,6,5,4,3,2,8,1,9]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[6,5,4,3,2,1,9,8,7]=>[8,7,6,5,4,3,9,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,6,7,9,8,10]=>[2,3,4,5,6,7,8,9,1,10]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,5,6,8,7,9,10]=>[2,3,4,5,6,7,8,1,9,10]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,4,5,7,6,8,9,10]=>[2,3,4,5,6,7,1,8,9,10]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,6,5,7,8,9,10]=>[2,3,4,5,6,1,7,8,9,10]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8,9,10]=>[2,3,4,5,1,6,7,8,9,10]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,10,9,8,7,6,5,4]=>[7,8,9,10,6,5,4,3,2,1]=>[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8,9,10]=>[2,3,4,1,5,6,7,8,9,10]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8,9,10]=>[2,3,1,4,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8,10]=>[5,6,4,7,3,8,2,9,1,10]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,7,8,10,9]=>[3,2,4,5,6,7,8,9,10,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8,9,10]=>[3,2,4,1,5,6,7,8,9,10]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,10,9]=>[6,5,7,4,8,3,9,2,10,1]=>[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,2,1,10,9,8,7,6,5,4]=>[9,8,7,10,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,3,2,1,10,9,8,7,6,5]=>[9,8,7,6,10,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1,10,9,8,7,6]=>[9,8,7,6,5,10,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,5,4,3,2,1,10,9,8,7]=>[9,8,7,6,5,4,10,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[7,6,5,4,3,2,1,9,8,10]=>[8,7,6,5,4,3,2,9,1,10]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,6,5,4,3,2,1,10,9,8]=>[9,8,7,6,5,4,3,10,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8,9]=>[3,1,2,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8,9]=>[4,1,2,3,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8,9]=>[5,1,2,3,4,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,6,1,7,8,9]=>[6,1,2,3,4,5,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,6,7,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8,9,10]=>[3,1,2,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7,8,9]=>[4,2,3,1,5,6,7,8,9]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8,9,10]=>[4,1,2,3,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,3,5,4,1,6,7,8,9]=>[5,2,3,4,1,6,7,8,9]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8,9,10]=>[5,1,2,3,4,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,4,6,5,1,7,8,9]=>[6,2,3,4,5,1,7,8,9]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,1,7,8,9,10]=>[6,1,2,3,4,5,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,4,5,7,6,1,8,9]=>[7,2,3,4,5,6,1,8,9]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,1,8,9,10]=>[7,1,2,3,4,5,6,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,5,6,8,7,1,9]=>[8,2,3,4,5,6,7,1,9]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,6,7,8,1,9,10]=>[8,1,2,3,4,5,6,7,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,5,6,8,9,7]=>[3,2,4,5,6,7,9,1,8]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,7,8,10,9,1]=>[10,2,3,4,5,6,7,8,9,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[8,10,9,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,2,3,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[9,8,10,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,2,1,3]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,6,8,9,7]=>[4,2,3,5,6,7,9,1,8]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,6,7,9,8]=>[4,2,3,5,6,7,8,9,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7,8,9]=>[4,3,1,2,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,10,9,8,7,6,5,4,3,1]=>[10,8,9,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,8,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,2,1,9]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[10,9,8,7,6,5,4,3,2,11,1]=>[11,9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[8,9,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,1,2,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[9,10,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,1,2]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[5,10,9,8,7,6,4,3,2,1]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[4,10,9,8,7,6,5,3,2,1]=>[10,9,8,6,7,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[10,11,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,1,2]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,1,9,8,7,6,5,4]=>[8,6,7,9,5,4,3,2,1]=>[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,2,1,9,8,7,6,5]=>[8,7,5,6,9,4,3,2,1]=>[[[[[[[.,.],.],[.,[.,.]]],.],.],.],.]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,3,2,1,9,8,7,6]=>[8,7,6,4,5,9,3,2,1]=>[[[[[[[.,.],.],.],[.,[.,.]]],.],.],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,6,4,3,2,1,9,8,7]=>[8,7,6,5,3,4,9,2,1]=>[[[[[[[.,.],.],.],.],[.,[.,.]]],.],.]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,3,6,7,8,9]=>[2,3,5,1,4,6,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,3,6,7,8,9]=>[3,2,5,1,4,6,7,8,9]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,6,5,7,8,9,10,1]=>[10,2,3,4,5,1,6,7,8,9]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,7,8,1,9]=>[8,2,1,3,4,5,6,7,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,6,7,9,8,2]=>[3,9,2,4,5,6,7,8,1]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,7,1,9,8]=>[8,2,3,4,5,6,7,9,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,8,9,3]=>[3,2,9,1,4,5,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,1,9,8,7]=>[8,3,4,5,6,7,9,2,1]=>[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,6,7,10,9,8,1]=>[10,3,4,5,6,7,8,9,2,1]=>[[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,9,10,3,2,1]=>[10,9,8,1,2,3,4,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[6,5,4,3,2,1,8,9,7]=>[7,6,5,4,3,2,9,1,8]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[9,8,7,6,5,4,3,10,2,1]=>[10,9,7,6,5,4,3,2,1,8]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[9,8,7,6,5,4,10,3,2,1]=>[10,9,8,6,5,4,3,2,1,7]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[9,8,7,6,5,10,4,3,2,1]=>[10,9,8,7,5,4,3,2,1,6]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[9,8,7,6,10,5,4,3,2,1]=>[10,9,8,7,6,4,3,2,1,5]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[9,8,7,10,6,5,4,3,2,1]=>[10,9,8,7,6,5,3,2,1,4]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,4,5,7,6,8,9,10,1]=>[10,2,3,4,5,6,1,7,8,9]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,9,8,10]=>[6,4,5,7,3,8,2,9,1,10]=>[[[[[.,.],[.,[.,.]]],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,9,10,2,1]=>[10,9,1,2,3,4,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,7,8,9,11,10,1]=>[11,2,3,4,5,6,7,8,9,10,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,9,10,11,2,1]=>[11,10,1,2,3,4,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,10,9,8,7,2,1]=>[10,9,7,6,5,4,8,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,3,5,7,9,10,8,6,4,2]=>[5,10,4,9,3,8,2,7,1,6]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,6,4,7,3,8,2,9,1,10]=>[9,7,5,3,1,2,4,6,8,10]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,1,11,10,9,8,7,6,5,4,3]=>[10,9,11,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,11,10,9,8,7,6,5,4,3,1]=>[11,9,10,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,4,5,7,9,8,6]=>[3,4,5,6,7,9,2,8,1]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[9,8,7,6,5,4,3,2,1,11,10]=>[10,9,8,7,6,5,4,3,2,11,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,9,10,4,3,2,1]=>[10,9,8,7,1,2,3,4,5,6]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,6,4,3,2,1,7,8,9]=>[6,5,4,3,1,2,7,8,9]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,5,3,2,1,6,7,8,9]=>[5,4,3,1,2,6,7,8,9]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7,8,9]=>[2,4,1,3,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,8,9,4]=>[4,2,3,9,1,5,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[8,9,10,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,1,2,3]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,6,7,8,10,9,11]=>[2,3,4,5,6,7,8,9,10,1,11]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,4,5,7,8,6,9]=>[2,3,4,5,6,8,1,7,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,4,2,5,1,6,7,8,9]=>[5,3,1,2,4,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,9,10,5,4,3,2,1]=>[10,9,8,7,6,1,2,3,4,5]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[7,8,9,10,6,5,4,3,2,1]=>[10,9,8,7,6,5,1,2,3,4]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,8,9,10,1,11]=>[10,1,2,3,4,5,6,7,8,9,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,7,8,2,9]=>[2,8,1,3,4,5,6,7,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[8,7,6,5,4,3,2,10,9,1]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,1,10,9]=>[9,2,3,4,5,6,7,8,10,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,5,6,1,8,9,7]=>[7,2,3,4,5,6,9,1,8]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,6,4,3,2,1,7,8,9,10]=>[6,5,4,3,1,2,7,8,9,10]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,6,4,3,2,7,1,8,9]=>[7,5,4,3,1,2,6,8,9]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[6,7,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,1,2,8,9,10]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[6,7,5,4,3,2,1,8,9,10,11]=>[7,6,5,4,3,1,2,8,9,10,11]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,8,9,10,2,11,1]=>[11,9,1,2,3,4,5,6,7,8,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7,8,9,10]=>[2,4,1,3,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,9,5]=>[5,2,3,4,9,1,6,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,2,1,7,8,9,6]=>[6,5,4,3,2,9,1,7,8]=>[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,2,8,7,6,5,4,1,9]=>[8,6,5,7,4,3,2,1,9]=>[[[[[[[.,.],.],[.,.]],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,9,10,1]=>[10,7,6,5,4,3,2,1,8,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,4,7,6,9,10,8]=>[5,6,4,7,3,8,2,10,1,9]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,5,6,7,9,8,1,10]=>[9,2,3,4,5,6,7,8,1,10]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,5,7,4,8,3,9,2,10,1]=>[10,8,6,4,2,1,3,5,7,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>[[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>[12,10,8,6,4,2,1,3,5,7,9,11]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,7,8,9,1,11,10]=>[10,2,3,4,5,6,7,8,9,11,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,5,1,7,8,9,6]=>[6,2,3,4,5,9,1,7,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,6,7,8,10,9,1]=>[10,3,2,4,5,6,7,8,9,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0]=>[7,6,5,4,3,2,1,9,10,8]=>[8,7,6,5,4,3,2,10,1,9]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,8,9,10,7]=>[7,6,5,4,3,2,10,1,8,9]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,3,6,5,8,10,9,7]=>[6,5,7,4,8,3,10,2,9,1]=>[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,8,7,9]=>[4,6,3,5,7,2,8,1,9]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,4,6,3,7,2,8,1,9]=>[8,6,4,2,1,3,5,7,9]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[4,5,3,6,2,7,1,8,9]=>[7,5,3,1,2,4,6,8,9]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
Map
to 312-avoiding permutation
Description
Map
major-index to inversion-number bijection
Description
Return the permutation whose Lehmer code equals the major code of the preimage.
This map sends the major index to the number of inversions.
This map sends the major index to the number of inversions.
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.