Identifier
Mp00025:
Dyck paths
—to 132-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]=>[2,1]=>[2,1]=>[[.,.],.]
[1,1,0,0]=>[1,2]=>[1,2]=>[.,[.,.]]
[1,0,1,0,1,0]=>[3,2,1]=>[3,2,1]=>[[[.,.],.],.]
[1,0,1,1,0,0]=>[2,3,1]=>[3,1,2]=>[[.,.],[.,.]]
[1,1,0,0,1,0]=>[3,1,2]=>[1,3,2]=>[.,[[.,.],.]]
[1,1,0,1,0,0]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[1,1,1,0,0,0]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[1,0,1,0,1,1,0,0]=>[3,4,2,1]=>[4,3,1,2]=>[[[.,.],.],[.,.]]
[1,0,1,1,0,0,1,0]=>[4,2,3,1]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[1,0,1,1,0,1,0,0]=>[3,2,4,1]=>[4,2,1,3]=>[[[.,.],.],[.,.]]
[1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[1,1,0,0,1,0,1,0]=>[4,3,1,2]=>[1,4,3,2]=>[.,[[[.,.],.],.]]
[1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[1,4,2,3]=>[.,[[.,.],[.,.]]]
[1,1,0,1,0,0,1,0]=>[4,2,1,3]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[1,1,0,1,0,1,0,0]=>[3,2,1,4]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[1,1,0,1,1,0,0,0]=>[2,3,1,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[1,2,4,3]=>[.,[.,[[.,.],.]]]
[1,1,1,0,0,1,0,0]=>[3,1,2,4]=>[1,3,2,4]=>[.,[[.,.],[.,.]]]
[1,1,1,0,1,0,0,0]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[1,0,1,0,1,0,1,1,0,0]=>[4,5,3,2,1]=>[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]]
[1,0,1,0,1,1,0,0,1,0]=>[5,3,4,2,1]=>[5,4,1,3,2]=>[[[.,.],.],[[.,.],.]]
[1,0,1,0,1,1,0,1,0,0]=>[4,3,5,2,1]=>[5,4,2,1,3]=>[[[[.,.],.],.],[.,.]]
[1,0,1,0,1,1,1,0,0,0]=>[3,4,5,2,1]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,0]=>[5,4,2,3,1]=>[5,1,4,3,2]=>[[.,.],[[[.,.],.],.]]
[1,0,1,1,0,0,1,1,0,0]=>[4,5,2,3,1]=>[5,1,4,2,3]=>[[.,.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0,1,0]=>[5,3,2,4,1]=>[5,3,1,4,2]=>[[[.,.],.],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,0]=>[4,3,2,5,1]=>[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]]
[1,0,1,1,0,1,1,0,0,0]=>[3,4,2,5,1]=>[5,3,1,2,4]=>[[[.,.],.],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,0]=>[5,2,3,4,1]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,0]=>[4,2,3,5,1]=>[5,1,3,2,4]=>[[.,.],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,0,0]=>[3,2,4,5,1]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]
[1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,2]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[1,1,0,0,1,0,1,1,0,0]=>[4,5,3,1,2]=>[1,5,4,2,3]=>[.,[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,0,1,0]=>[5,3,4,1,2]=>[1,5,2,4,3]=>[.,[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,0]=>[4,3,5,1,2]=>[1,5,3,2,4]=>[.,[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>[1,5,2,3,4]=>[.,[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,3]=>[4,1,5,3,2]=>[[.,.],[[[.,.],.],.]]
[1,1,0,1,0,0,1,1,0,0]=>[4,5,2,1,3]=>[4,1,5,2,3]=>[[.,.],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,4]=>[4,3,1,5,2]=>[[[.,.],.],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,5]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[1,1,0,1,0,1,1,0,0,0]=>[3,4,2,1,5]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,0]=>[5,2,3,1,4]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,0]=>[4,2,3,1,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0]=>[3,2,4,1,5]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[1,1,0,1,1,1,0,0,0,0]=>[2,3,4,1,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,3]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>[1,2,5,3,4]=>[.,[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,0]=>[5,3,1,2,4]=>[1,4,2,5,3]=>[.,[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,0]=>[4,3,1,2,5]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,1,0,0,0]=>[3,4,1,2,5]=>[1,4,2,3,5]=>[.,[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,0]=>[5,2,1,3,4]=>[3,1,2,5,4]=>[[.,.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0]=>[4,2,1,3,5]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,0,0]=>[3,2,1,4,5]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0]=>[2,3,1,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,0]=>[4,1,2,3,5]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,0]=>[3,1,2,4,5]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,2,1]=>[6,5,4,3,1,2]=>[[[[[.,.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,2,1]=>[6,5,4,1,3,2]=>[[[[.,.],.],.],[[.,.],.]]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,2,1]=>[6,5,4,2,1,3]=>[[[[[.,.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,2,1]=>[6,5,4,1,2,3]=>[[[[.,.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,2,1]=>[6,5,1,4,3,2]=>[[[.,.],.],[[[.,.],.],.]]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,2,1]=>[6,5,1,4,2,3]=>[[[.,.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,2,1]=>[6,5,3,1,4,2]=>[[[[.,.],.],.],[[.,.],.]]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,2,1]=>[6,5,3,2,1,4]=>[[[[[.,.],.],.],.],[.,.]]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,2,1]=>[6,5,3,1,2,4]=>[[[[.,.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,2,1]=>[6,5,1,2,4,3]=>[[[.,.],.],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,2,1]=>[6,5,1,3,2,4]=>[[[.,.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[6,5,2,1,3,4]=>[[[[.,.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,2,1]=>[6,5,1,2,3,4]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,3,1]=>[6,1,5,4,3,2]=>[[.,.],[[[[.,.],.],.],.]]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,3,1]=>[6,1,5,4,2,3]=>[[.,.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,3,1]=>[6,1,5,2,4,3]=>[[.,.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,3,1]=>[6,1,5,3,2,4]=>[[.,.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,3,1]=>[6,1,5,2,3,4]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,4,1]=>[6,4,1,5,3,2]=>[[[.,.],.],[[[.,.],.],.]]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,4,1]=>[6,4,1,5,2,3]=>[[[.,.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,5,1]=>[6,4,3,1,5,2]=>[[[[.,.],.],.],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,1]=>[6,4,3,2,1,5]=>[[[[[.,.],.],.],.],[.,.]]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,1]=>[6,4,3,1,2,5]=>[[[[.,.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,5,1]=>[6,4,1,2,5,3]=>[[[.,.],.],[.,[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,6,1]=>[6,4,1,3,2,5]=>[[[.,.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,6,1]=>[6,4,2,1,3,5]=>[[[[.,.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,6,1]=>[6,4,1,2,3,5]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,4,1]=>[6,1,2,5,4,3]=>[[.,.],[.,[[[.,.],.],.]]]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,4,1]=>[6,1,2,5,3,4]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,5,1]=>[6,1,4,2,5,3]=>[[.,.],[[.,.],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,6,1]=>[6,1,4,3,2,5]=>[[.,.],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,6,1]=>[6,1,4,2,3,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1]=>[6,3,1,2,5,4]=>[[[.,.],.],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[6,3,1,4,2,5]=>[[[.,.],.],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,6,1]=>[6,3,2,1,4,5]=>[[[[.,.],.],.],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,6,1]=>[6,3,1,2,4,5]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,5,1]=>[6,1,2,3,5,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,6,1]=>[6,1,2,4,3,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,6,1]=>[6,1,3,2,4,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,6,1]=>[6,2,1,3,4,5]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[6,1,2,3,4,5]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,2]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,1,2]=>[1,6,5,4,2,3]=>[.,[[[[.,.],.],.],[.,.]]]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,1,2]=>[1,6,5,2,4,3]=>[.,[[[.,.],.],[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,1,2]=>[1,6,5,3,2,4]=>[.,[[[[.,.],.],.],[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,1,2]=>[1,6,5,2,3,4]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,1,2]=>[1,6,2,5,4,3]=>[.,[[.,.],[[[.,.],.],.]]]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,1,2]=>[1,6,2,5,3,4]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,1,2]=>[1,6,4,2,5,3]=>[.,[[[.,.],.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,1,2]=>[1,6,4,3,2,5]=>[.,[[[[.,.],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,1,2]=>[1,6,4,2,3,5]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,1,2]=>[1,6,2,3,5,4]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,1,2]=>[1,6,2,4,3,5]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,1,2]=>[1,6,3,2,4,5]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>[1,6,2,3,4,5]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,3]=>[5,1,6,4,3,2]=>[[.,.],[[[[.,.],.],.],.]]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,1,3]=>[5,1,6,4,2,3]=>[[.,.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,1,3]=>[5,1,6,2,4,3]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,1,3]=>[5,1,6,3,2,4]=>[[.,.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,1,3]=>[5,1,6,2,3,4]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,4]=>[5,4,1,6,3,2]=>[[[.,.],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,1,4]=>[5,4,1,6,2,3]=>[[[.,.],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,5]=>[5,4,3,1,6,2]=>[[[[.,.],.],.],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,1,6]=>[5,4,3,1,2,6]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,1,5]=>[5,4,1,2,6,3]=>[[[.,.],.],[.,[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,1,6]=>[5,4,1,3,2,6]=>[[[.,.],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,1,6]=>[5,4,2,1,3,6]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,1,6]=>[5,4,1,2,3,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,1,4]=>[5,1,2,6,4,3]=>[[.,.],[.,[[[.,.],.],.]]]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,1,4]=>[5,1,2,6,3,4]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,1,5]=>[5,1,4,2,6,3]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,1,6]=>[5,1,4,3,2,6]=>[[.,.],[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,1,6]=>[5,1,4,2,3,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,1,5]=>[5,3,1,2,6,4]=>[[[.,.],.],[.,[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,1,6]=>[5,3,1,4,2,6]=>[[[.,.],.],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,1,6]=>[5,3,2,1,4,6]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,1,6]=>[5,3,1,2,4,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,1,5]=>[5,1,2,3,6,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,1,6]=>[5,1,2,4,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,1,6]=>[5,1,3,2,4,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,1,6]=>[5,2,1,3,4,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6]=>[5,1,2,3,4,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,2,3]=>[1,2,6,5,4,3]=>[.,[.,[[[[.,.],.],.],.]]]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[5,6,4,1,2,3]=>[1,2,6,5,3,4]=>[.,[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,5,1,2,3]=>[1,2,6,3,5,4]=>[.,[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,6,1,2,3]=>[1,2,6,4,3,5]=>[.,[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>[1,2,6,3,4,5]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,2,4]=>[1,5,2,6,4,3]=>[.,[[.,.],[[[.,.],.],.]]]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[5,6,3,1,2,4]=>[1,5,2,6,3,4]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,2,5]=>[1,5,4,2,6,3]=>[.,[[[.,.],.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,2,6]=>[1,5,4,3,2,6]=>[.,[[[[.,.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[4,5,3,1,2,6]=>[1,5,4,2,3,6]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>[1,5,2,3,6,4]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,4,1,2,6]=>[1,5,2,4,3,6]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,5,1,2,6]=>[1,5,3,2,4,6]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6]=>[1,5,2,3,4,6]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,3,4]=>[4,1,2,6,5,3]=>[[.,.],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[5,6,2,1,3,4]=>[4,1,2,6,3,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,3,5]=>[4,1,5,2,6,3]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,3,6]=>[4,1,5,3,2,6]=>[[.,.],[[[.,.],.],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,5,2,1,3,6]=>[4,1,5,2,3,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,4,5]=>[4,3,1,2,6,5]=>[[[.,.],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,4,6]=>[4,3,1,5,2,6]=>[[[.,.],.],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,5,6]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,2,1,5,6]=>[4,3,1,2,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,1,4,5]=>[4,1,2,3,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,3,1,4,6]=>[4,1,2,5,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,3,1,5,6]=>[4,1,3,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,4,1,5,6]=>[4,2,1,3,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6]=>[4,1,2,3,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,2,3,4]=>[1,2,3,6,5,4]=>[.,[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>[1,2,3,6,4,5]=>[.,[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>[1,2,5,3,6,4]=>[.,[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,2,3,6]=>[1,2,5,4,3,6]=>[.,[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,3,6]=>[1,2,5,3,4,6]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,2,4,5]=>[1,4,2,3,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,2,4,6]=>[1,4,2,5,3,6]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,2,5,6]=>[1,4,3,2,5,6]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>[1,4,2,3,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,3,4,5]=>[3,1,2,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,3,4,6]=>[3,1,2,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,3,5,6]=>[3,1,4,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,4,5,6]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,1,4,5,6]=>[3,1,2,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,4,6]=>[1,2,3,5,4,6]=>[.,[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,3,5,6]=>[1,2,4,3,5,6]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,2,4,5,6]=>[1,3,2,4,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,2,1]=>[7,6,5,4,3,1,2]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,2,1]=>[7,6,5,4,1,3,2]=>[[[[[.,.],.],.],.],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,2,1]=>[7,6,5,4,2,1,3]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,2,1]=>[7,6,5,4,1,2,3]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,2,1]=>[7,6,5,1,4,3,2]=>[[[[.,.],.],.],[[[.,.],.],.]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,2,1]=>[7,6,5,1,4,2,3]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,2,1]=>[7,6,5,3,1,4,2]=>[[[[[.,.],.],.],.],[[.,.],.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,2,1]=>[7,6,5,3,2,1,4]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,2,1]=>[7,6,5,3,1,2,4]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,2,1]=>[7,6,5,1,2,4,3]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,2,1]=>[7,6,5,1,3,2,4]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,2,1]=>[7,6,5,2,1,3,4]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[7,6,5,1,2,3,4]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,2,1]=>[7,6,1,5,4,3,2]=>[[[.,.],.],[[[[.,.],.],.],.]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,2,1]=>[7,6,1,5,4,2,3]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,2,1]=>[7,6,1,5,2,4,3]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,2,1]=>[7,6,1,5,3,2,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,2,1]=>[7,6,1,5,2,3,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,2,1]=>[7,6,4,1,5,3,2]=>[[[[.,.],.],.],[[[.,.],.],.]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,2,1]=>[7,6,4,1,5,2,3]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,2,1]=>[7,6,4,3,1,5,2]=>[[[[[.,.],.],.],.],[[.,.],.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,2,1]=>[7,6,4,3,2,1,5]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,2,1]=>[7,6,4,3,1,2,5]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,2,1]=>[7,6,4,1,2,5,3]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,2,1]=>[7,6,4,1,3,2,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[7,6,4,2,1,3,5]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,2,1]=>[7,6,4,1,2,3,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,2,1]=>[7,6,1,2,5,4,3]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,2,1]=>[7,6,1,2,5,3,4]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,2,1]=>[7,6,1,4,2,5,3]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,2,1]=>[7,6,1,4,3,2,5]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,2,1]=>[7,6,1,4,2,3,5]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,2,1]=>[7,6,3,1,2,5,4]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,2,1]=>[7,6,3,1,4,2,5]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[7,6,3,2,1,4,5]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,2,1]=>[7,6,3,1,2,4,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,2,1]=>[7,6,1,2,3,5,4]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,2,1]=>[7,6,1,2,4,3,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,2,1]=>[7,6,1,3,2,4,5]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,2,1]=>[7,6,2,1,3,4,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,2,1]=>[7,6,1,2,3,4,5]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,3,1]=>[7,1,6,5,4,3,2]=>[[.,.],[[[[[.,.],.],.],.],.]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,3,1]=>[7,1,6,5,4,2,3]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,3,1]=>[7,1,6,5,2,4,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,3,1]=>[7,1,6,5,3,2,4]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,3,1]=>[7,1,6,5,2,3,4]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,3,1]=>[7,1,6,2,5,4,3]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,3,1]=>[7,1,6,2,5,3,4]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,3,1]=>[7,1,6,4,2,5,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,3,1]=>[7,1,6,4,3,2,5]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,3,1]=>[7,1,6,4,2,3,5]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,3,1]=>[7,1,6,2,3,5,4]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,3,1]=>[7,1,6,2,4,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,3,1]=>[7,1,6,3,2,4,5]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,3,1]=>[7,1,6,2,3,4,5]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,4,1]=>[7,5,1,6,4,3,2]=>[[[.,.],.],[[[[.,.],.],.],.]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,4,1]=>[7,5,1,6,4,2,3]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,4,1]=>[7,5,1,6,2,4,3]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,4,1]=>[7,5,1,6,3,2,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,4,1]=>[7,5,1,6,2,3,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,5,1]=>[7,5,4,1,6,3,2]=>[[[[.,.],.],.],[[[.,.],.],.]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,5,1]=>[7,5,4,1,6,2,3]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,6,1]=>[7,5,4,3,1,6,2]=>[[[[[.,.],.],.],.],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,1]=>[7,5,4,3,2,1,6]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,7,1]=>[7,5,4,3,1,2,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,6,1]=>[7,5,4,1,2,6,3]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,7,1]=>[7,5,4,1,3,2,6]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,7,1]=>[7,5,4,2,1,3,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,7,1]=>[7,5,4,1,2,3,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,5,1]=>[7,5,1,2,6,4,3]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,5,1]=>[7,5,1,2,6,3,4]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,6,1]=>[7,5,1,4,2,6,3]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,7,1]=>[7,5,1,4,3,2,6]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,7,1]=>[7,5,1,4,2,3,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,6,1]=>[7,5,3,1,2,6,4]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>[7,5,3,1,4,2,6]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,7,1]=>[7,5,3,2,1,4,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,7,1]=>[7,5,3,1,2,4,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,6,1]=>[7,5,1,2,3,6,4]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>[7,5,1,2,4,3,6]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,7,1]=>[7,5,1,3,2,4,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,7,1]=>[7,5,2,1,3,4,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,7,1]=>[7,5,1,2,3,4,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,4,1]=>[7,1,2,6,5,4,3]=>[[.,.],[.,[[[[.,.],.],.],.]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,4,1]=>[7,1,2,6,5,3,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,4,1]=>[7,1,2,6,3,5,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,4,1]=>[7,1,2,6,4,3,5]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,4,1]=>[7,1,2,6,3,4,5]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,5,1]=>[7,1,5,2,6,4,3]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,5,1]=>[7,1,5,2,6,3,4]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,6,1]=>[7,1,5,4,2,6,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,7,1]=>[7,1,5,4,3,2,6]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,7,1]=>[7,1,5,4,2,3,6]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,6,1]=>[7,1,5,2,3,6,4]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,7,1]=>[7,1,5,2,4,3,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,7,1]=>[7,1,5,3,2,4,6]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,7,1]=>[7,1,5,2,3,4,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,5,1]=>[7,4,1,2,6,5,3]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,5,1]=>[7,4,1,2,6,3,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,6,1]=>[7,4,1,5,2,6,3]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,7,1]=>[7,4,1,5,3,2,6]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,7,1]=>[7,4,1,5,2,3,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,6,1]=>[7,4,3,1,2,6,5]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>[7,4,3,1,5,2,6]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,7,1]=>[7,4,3,2,1,5,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,7,1]=>[7,4,3,1,2,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,6,1]=>[7,4,1,2,3,6,5]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>[7,4,1,2,5,3,6]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,7,1]=>[7,4,1,3,2,5,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,7,1]=>[7,4,2,1,3,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,7,1]=>[7,4,1,2,3,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,5,1]=>[7,1,2,3,6,5,4]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,5,1]=>[7,1,2,3,6,4,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,6,1]=>[7,1,2,5,3,6,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,7,1]=>[7,1,2,5,4,3,6]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,7,1]=>[7,1,2,5,3,4,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,6,1]=>[7,1,4,2,3,6,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,7,1]=>[7,1,4,2,5,3,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,7,1]=>[7,1,4,3,2,5,6]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,7,1]=>[7,1,4,2,3,5,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,6,1]=>[7,3,1,2,4,6,5]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>[7,3,1,2,5,4,6]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,7,1]=>[7,3,1,4,2,5,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,7,1]=>[7,3,2,1,4,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,7,1]=>[7,3,1,2,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,6,1]=>[7,1,2,3,4,6,5]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>[7,1,2,3,5,4,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,7,1]=>[7,1,2,4,3,5,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,7,1]=>[7,1,3,2,4,5,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,7,1]=>[7,2,1,3,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[7,1,2,3,4,5,6]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,1,2]=>[1,7,6,5,4,2,3]=>[.,[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,1,2]=>[1,7,6,5,2,4,3]=>[.,[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,1,2]=>[1,7,6,5,3,2,4]=>[.,[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,1,2]=>[1,7,6,5,2,3,4]=>[.,[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,1,2]=>[1,7,6,2,5,4,3]=>[.,[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,1,2]=>[1,7,6,2,5,3,4]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,1,2]=>[1,7,6,4,2,5,3]=>[.,[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,1,2]=>[1,7,6,4,3,2,5]=>[.,[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,1,2]=>[1,7,6,4,2,3,5]=>[.,[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,1,2]=>[1,7,6,2,3,5,4]=>[.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,1,2]=>[1,7,6,2,4,3,5]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,1,2]=>[1,7,6,3,2,4,5]=>[.,[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,1,2]=>[1,7,6,2,3,4,5]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,1,2]=>[1,7,2,6,5,4,3]=>[.,[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,1,2]=>[1,7,2,6,5,3,4]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,1,2]=>[1,7,2,6,3,5,4]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,1,2]=>[1,7,2,6,4,3,5]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,1,2]=>[1,7,2,6,3,4,5]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,1,2]=>[1,7,5,2,6,4,3]=>[.,[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,1,2]=>[1,7,5,2,6,3,4]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,1,2]=>[1,7,5,4,2,6,3]=>[.,[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,1,2]=>[1,7,5,4,3,2,6]=>[.,[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,1,2]=>[1,7,5,4,2,3,6]=>[.,[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,1,2]=>[1,7,5,2,3,6,4]=>[.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,1,2]=>[1,7,5,2,4,3,6]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,1,2]=>[1,7,5,3,2,4,6]=>[.,[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,1,2]=>[1,7,5,2,3,4,6]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,1,2]=>[1,7,2,3,6,5,4]=>[.,[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,1,2]=>[1,7,2,3,6,4,5]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,1,2]=>[1,7,2,5,3,6,4]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,1,2]=>[1,7,2,5,4,3,6]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,1,2]=>[1,7,2,5,3,4,6]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,1,2]=>[1,7,4,2,3,6,5]=>[.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,1,2]=>[1,7,4,2,5,3,6]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,1,2]=>[1,7,4,3,2,5,6]=>[.,[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,1,2]=>[1,7,4,2,3,5,6]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,1,2]=>[1,7,2,3,4,6,5]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,1,2]=>[1,7,2,3,5,4,6]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,1,2]=>[1,7,2,4,3,5,6]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,1,2]=>[1,7,3,2,4,5,6]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>[1,7,2,3,4,5,6]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,1,3]=>[6,1,7,5,4,3,2]=>[[.,.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,1,3]=>[6,1,7,5,4,2,3]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,1,3]=>[6,1,7,5,2,4,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,1,3]=>[6,1,7,5,3,2,4]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,1,3]=>[6,1,7,5,2,3,4]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,1,3]=>[6,1,7,2,5,4,3]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,1,3]=>[6,1,7,2,5,3,4]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,1,3]=>[6,1,7,4,2,5,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,1,3]=>[6,1,7,4,3,2,5]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,1,3]=>[6,1,7,4,2,3,5]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,1,3]=>[6,1,7,2,3,5,4]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,1,3]=>[6,1,7,2,4,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,1,3]=>[6,1,7,3,2,4,5]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,1,3]=>[6,1,7,2,3,4,5]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1,4]=>[6,5,1,7,4,3,2]=>[[[.,.],.],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,1,4]=>[6,5,1,7,4,2,3]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,1,4]=>[6,5,1,7,2,4,3]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,1,4]=>[6,5,1,7,3,2,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,1,4]=>[6,5,1,7,2,3,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1,5]=>[6,5,4,1,7,3,2]=>[[[[.,.],.],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,1,5]=>[6,5,4,1,7,2,3]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1,6]=>[6,5,4,3,1,7,2]=>[[[[[.,.],.],.],.],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,1,7]=>[6,5,4,3,1,2,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,1,6]=>[6,5,4,1,2,7,3]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,1,7]=>[6,5,4,1,3,2,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,1,7]=>[6,5,4,2,1,3,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,1,7]=>[6,5,4,1,2,3,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,1,5]=>[6,5,1,2,7,4,3]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,1,5]=>[6,5,1,2,7,3,4]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,1,6]=>[6,5,1,4,2,7,3]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,1,7]=>[6,5,1,4,3,2,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,1,7]=>[6,5,1,4,2,3,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,1,6]=>[6,5,3,1,2,7,4]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,1,7]=>[6,5,3,1,4,2,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,1,7]=>[6,5,3,2,1,4,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,1,7]=>[6,5,3,1,2,4,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,1,6]=>[6,5,1,2,3,7,4]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,1,7]=>[6,5,1,2,4,3,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,1,7]=>[6,5,1,3,2,4,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,1,7]=>[6,5,2,1,3,4,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,1,7]=>[6,5,1,2,3,4,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,1,4]=>[6,1,2,7,5,4,3]=>[[.,.],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,1,4]=>[6,1,2,7,5,3,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,1,4]=>[6,1,2,7,3,5,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,1,4]=>[6,1,2,7,4,3,5]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,1,4]=>[6,1,2,7,3,4,5]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,1,5]=>[6,1,5,2,7,4,3]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,1,5]=>[6,1,5,2,7,3,4]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,1,6]=>[6,1,5,4,2,7,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,1,7]=>[6,1,5,4,3,2,7]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,1,7]=>[6,1,5,4,2,3,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,1,6]=>[6,1,5,2,3,7,4]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,1,7]=>[6,1,5,2,4,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,1,7]=>[6,1,5,3,2,4,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,1,7]=>[6,1,5,2,3,4,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,1,5]=>[6,4,1,2,7,5,3]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,1,5]=>[6,4,1,2,7,3,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,1,6]=>[6,4,1,5,2,7,3]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,1,7]=>[6,4,1,5,3,2,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,1,7]=>[6,4,1,5,2,3,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,1,6]=>[6,4,3,1,2,7,5]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,1,7]=>[6,4,3,1,5,2,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,1,7]=>[6,4,3,2,1,5,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,1,7]=>[6,4,3,1,2,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,1,6]=>[6,4,1,2,3,7,5]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,1,7]=>[6,4,1,2,5,3,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,1,7]=>[6,4,1,3,2,5,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,1,7]=>[6,4,2,1,3,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,1,7]=>[6,4,1,2,3,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,1,5]=>[6,1,2,3,7,5,4]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,1,5]=>[6,1,2,3,7,4,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,1,6]=>[6,1,2,5,3,7,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,1,7]=>[6,1,2,5,4,3,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,1,7]=>[6,1,2,5,3,4,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,1,6]=>[6,1,4,2,3,7,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,1,7]=>[6,1,4,2,5,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,1,7]=>[6,1,4,3,2,5,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,1,7]=>[6,1,4,2,3,5,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,1,6]=>[6,3,1,2,4,7,5]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,1,7]=>[6,3,1,2,5,4,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,1,7]=>[6,3,1,4,2,5,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,1,7]=>[6,3,2,1,4,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,1,7]=>[6,3,1,2,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,1,6]=>[6,1,2,3,4,7,5]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,1,7]=>[6,1,2,3,5,4,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,1,7]=>[6,1,2,4,3,5,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,1,7]=>[6,1,3,2,4,5,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,1,7]=>[6,2,1,3,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>[6,1,2,3,4,5,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,2,3]=>[1,2,7,6,5,4,3]=>[.,[.,[[[[[.,.],.],.],.],.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,1,2,3]=>[1,2,7,6,5,3,4]=>[.,[.,[[[[.,.],.],.],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,1,2,3]=>[1,2,7,6,3,5,4]=>[.,[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,1,2,3]=>[1,2,7,6,4,3,5]=>[.,[.,[[[[.,.],.],.],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,1,2,3]=>[1,2,7,6,3,4,5]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,1,2,3]=>[1,2,7,3,6,5,4]=>[.,[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,1,2,3]=>[1,2,7,3,6,4,5]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,1,2,3]=>[1,2,7,5,3,6,4]=>[.,[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,1,2,3]=>[1,2,7,5,4,3,6]=>[.,[.,[[[[.,.],.],.],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,1,2,3]=>[1,2,7,5,3,4,6]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,1,2,3]=>[1,2,7,3,4,6,5]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,1,2,3]=>[1,2,7,3,5,4,6]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,1,2,3]=>[1,2,7,4,3,5,6]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[1,2,7,3,4,5,6]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1,2,4]=>[1,6,2,7,5,4,3]=>[.,[[.,.],[[[[.,.],.],.],.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,1,2,4]=>[1,6,2,7,5,3,4]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,1,2,4]=>[1,6,2,7,3,5,4]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,1,2,4]=>[1,6,2,7,4,3,5]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,1,2,4]=>[1,6,2,7,3,4,5]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1,2,5]=>[1,6,5,2,7,4,3]=>[.,[[[.,.],.],[[[.,.],.],.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,1,2,5]=>[1,6,5,2,7,3,4]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1,2,6]=>[1,6,5,4,2,7,3]=>[.,[[[[.,.],.],.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,2,7]=>[1,6,5,4,3,2,7]=>[.,[[[[[.,.],.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,1,2,7]=>[1,6,5,4,2,3,7]=>[.,[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,1,2,6]=>[1,6,5,2,3,7,4]=>[.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,1,2,7]=>[1,6,5,2,4,3,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,1,2,7]=>[1,6,5,3,2,4,7]=>[.,[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,1,2,7]=>[1,6,5,2,3,4,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,1,2,5]=>[1,6,2,3,7,5,4]=>[.,[[.,.],[.,[[[.,.],.],.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,1,2,5]=>[1,6,2,3,7,4,5]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,1,2,6]=>[1,6,2,5,3,7,4]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,1,2,7]=>[1,6,2,5,4,3,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,1,2,7]=>[1,6,2,5,3,4,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,1,2,6]=>[1,6,4,2,3,7,5]=>[.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,1,2,7]=>[1,6,4,2,5,3,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,1,2,7]=>[1,6,4,3,2,5,7]=>[.,[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,1,2,7]=>[1,6,4,2,3,5,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>[1,6,2,3,4,7,5]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,1,2,7]=>[1,6,2,3,5,4,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,1,2,7]=>[1,6,2,4,3,5,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,1,2,7]=>[1,6,3,2,4,5,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,1,2,7]=>[1,6,2,3,4,5,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,3,4]=>[5,1,2,7,6,4,3]=>[[.,.],[.,[[[[.,.],.],.],.]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,1,3,4]=>[5,1,2,7,6,3,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,1,3,4]=>[5,1,2,7,3,6,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,1,3,4]=>[5,1,2,7,4,3,6]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,1,3,4]=>[5,1,2,7,3,4,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1,3,5]=>[5,1,6,2,7,4,3]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,1,3,5]=>[5,1,6,2,7,3,4]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,3,6]=>[5,1,6,4,2,7,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,3,7]=>[5,1,6,4,3,2,7]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,1,3,7]=>[5,1,6,4,2,3,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,1,3,6]=>[5,1,6,2,3,7,4]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,1,3,7]=>[5,1,6,2,4,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,1,3,7]=>[5,1,6,3,2,4,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,1,3,7]=>[5,1,6,2,3,4,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,4,5]=>[5,4,1,2,7,6,3]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,1,4,5]=>[5,4,1,2,7,3,6]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1,4,6]=>[5,4,1,6,2,7,3]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,4,7]=>[5,4,1,6,3,2,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,1,4,7]=>[5,4,1,6,2,3,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,5,6]=>[5,4,3,1,2,7,6]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,5,7]=>[5,4,3,1,6,2,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,6,7]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,1,6,7]=>[5,4,3,1,2,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,1,5,6]=>[5,4,1,2,3,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,1,5,7]=>[5,4,1,2,6,3,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,1,6,7]=>[5,4,1,3,2,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,1,6,7]=>[5,4,2,1,3,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,1,6,7]=>[5,4,1,2,3,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,1,4,5]=>[5,1,2,3,7,6,4]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,1,4,5]=>[5,1,2,3,7,4,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,1,4,6]=>[5,1,2,6,3,7,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,1,4,7]=>[5,1,2,6,4,3,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,1,4,7]=>[5,1,2,6,3,4,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,1,5,6]=>[5,1,4,2,3,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,1,5,7]=>[5,1,4,2,6,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,1,6,7]=>[5,1,4,3,2,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,1,6,7]=>[5,1,4,2,3,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,1,5,6]=>[5,3,1,2,4,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,1,5,7]=>[5,3,1,2,6,4,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,1,6,7]=>[5,3,1,4,2,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,1,6,7]=>[5,3,2,1,4,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,1,6,7]=>[5,3,1,2,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,1,5,6]=>[5,1,2,3,4,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,1,5,7]=>[5,1,2,3,6,4,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,1,6,7]=>[5,1,2,4,3,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,1,6,7]=>[5,1,3,2,4,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,1,6,7]=>[5,2,1,3,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7]=>[5,1,2,3,4,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,2,3,4]=>[1,2,3,7,6,5,4]=>[.,[.,[.,[[[[.,.],.],.],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,7,5,1,2,3,4]=>[1,2,3,7,6,4,5]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,6,1,2,3,4]=>[1,2,3,7,4,6,5]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,7,1,2,3,4]=>[1,2,3,7,5,4,6]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>[1,2,3,7,4,5,6]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,2,3,5]=>[1,2,6,3,7,5,4]=>[.,[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,7,4,1,2,3,5]=>[1,2,6,3,7,4,5]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,2,3,6]=>[1,2,6,5,3,7,4]=>[.,[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,2,3,7]=>[1,2,6,5,4,3,7]=>[.,[.,[[[[.,.],.],.],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,6,4,1,2,3,7]=>[1,2,6,5,3,4,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,5,1,2,3,6]=>[1,2,6,3,4,7,5]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,5,1,2,3,7]=>[1,2,6,3,5,4,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,6,1,2,3,7]=>[1,2,6,4,3,5,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>[1,2,6,3,4,5,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,2,4,5]=>[1,5,2,3,7,6,4]=>[.,[[.,.],[.,[[[.,.],.],.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,7,3,1,2,4,5]=>[1,5,2,3,7,4,6]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,2,4,6]=>[1,5,2,6,3,7,4]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,2,4,7]=>[1,5,2,6,4,3,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,6,3,1,2,4,7]=>[1,5,2,6,3,4,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,2,5,6]=>[1,5,4,2,3,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,2,5,7]=>[1,5,4,2,6,3,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,2,6,7]=>[1,5,4,3,2,6,7]=>[.,[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,1,2,6,7]=>[1,5,4,2,3,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,4,1,2,5,6]=>[1,5,2,3,4,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,4,1,2,5,7]=>[1,5,2,3,6,4,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,4,1,2,6,7]=>[1,5,2,4,3,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,5,1,2,6,7]=>[1,5,3,2,4,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,4,5,1,2,6,7]=>[1,5,2,3,4,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,3,4,5]=>[4,1,2,3,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,7,2,1,3,4,5]=>[4,1,2,3,7,5,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,3,4,6]=>[4,1,2,6,3,7,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,3,4,7]=>[4,1,2,6,5,3,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,6,2,1,3,4,7]=>[4,1,2,6,3,5,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,3,5,6]=>[4,1,5,2,3,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,3,5,7]=>[4,1,5,2,6,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,3,6,7]=>[4,1,5,3,2,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,2,1,3,6,7]=>[4,1,5,2,3,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,4,5,6]=>[4,3,1,2,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,4,5,7]=>[4,3,1,2,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,4,6,7]=>[4,3,1,5,2,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,5,6,7]=>[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,4,2,1,5,6,7]=>[4,3,1,2,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,3,1,4,5,6]=>[4,1,2,3,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,3,1,4,5,7]=>[4,1,2,3,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,3,1,4,6,7]=>[4,1,2,5,3,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,3,1,5,6,7]=>[4,1,3,2,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,4,1,5,6,7]=>[4,2,1,3,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7]=>[4,1,2,3,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,2,3,4,5]=>[1,2,3,4,7,6,5]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>[1,2,3,4,7,5,6]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,2,3,4,6]=>[1,2,3,6,4,7,5]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,2,3,4,7]=>[1,2,3,6,5,4,7]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,4,7]=>[1,2,3,6,4,5,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,2,3,5,6]=>[1,2,5,3,4,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,2,3,5,7]=>[1,2,5,3,6,4,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,2,3,6,7]=>[1,2,5,4,3,6,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,5,1,2,3,6,7]=>[1,2,5,3,4,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,2,4,5,6]=>[1,4,2,3,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,2,4,5,7]=>[1,4,2,3,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,2,4,6,7]=>[1,4,2,5,3,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,2,5,6,7]=>[1,4,3,2,5,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>[1,4,2,3,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,3,4,5,6]=>[3,1,2,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,3,4,5,7]=>[3,1,2,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,3,4,6,7]=>[3,1,2,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,3,5,6,7]=>[3,1,4,2,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>[1,2,3,4,5,7,6]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,5,7]=>[1,2,3,4,6,5,7]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,4,6,7]=>[1,2,3,5,4,6,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,3,5,6,7]=>[1,2,4,3,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,2,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,2,1]=>[8,7,6,5,4,3,1,2]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,3,2,1]=>[8,7,6,5,4,1,3,2]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,3,2,1]=>[8,7,6,5,4,2,1,3]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,3,2,1]=>[8,7,6,5,4,1,2,3]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,3,2,1]=>[8,7,6,5,1,4,3,2]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,3,2,1]=>[8,7,6,5,1,4,2,3]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,3,2,1]=>[8,7,6,5,3,1,4,2]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,3,2,1]=>[8,7,6,5,3,2,1,4]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,3,2,1]=>[8,7,6,5,3,1,2,4]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,3,2,1]=>[8,7,6,5,1,2,4,3]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,3,2,1]=>[8,7,6,5,1,3,2,4]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,3,2,1]=>[8,7,6,5,2,1,3,4]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,2,1]=>[8,7,6,5,1,2,3,4]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,3,2,1]=>[8,7,6,1,5,4,3,2]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,3,2,1]=>[8,7,6,1,5,4,2,3]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,3,2,1]=>[8,7,6,1,5,2,4,3]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,3,2,1]=>[8,7,6,1,5,3,2,4]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,3,2,1]=>[8,7,6,1,5,2,3,4]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,3,2,1]=>[8,7,6,4,1,5,3,2]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,3,2,1]=>[8,7,6,4,3,1,5,2]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,3,2,1]=>[8,7,6,4,3,2,1,5]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,3,2,1]=>[8,7,6,4,3,1,2,5]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,3,2,1]=>[8,7,6,4,1,2,5,3]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,3,2,1]=>[8,7,6,4,1,3,2,5]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,3,2,1]=>[8,7,6,4,2,1,3,5]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,3,2,1]=>[8,7,6,4,1,2,3,5]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,3,2,1]=>[8,7,6,1,2,5,4,3]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,3,2,1]=>[8,7,6,1,4,2,5,3]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,3,2,1]=>[8,7,6,1,4,3,2,5]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,3,2,1]=>[8,7,6,1,4,2,3,5]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,3,2,1]=>[8,7,6,3,1,4,2,5]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,3,2,1]=>[8,7,6,3,2,1,4,5]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,3,2,1]=>[8,7,6,3,1,2,4,5]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,3,2,1]=>[8,7,6,1,2,3,5,4]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,3,2,1]=>[8,7,6,1,2,4,3,5]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,3,2,1]=>[8,7,6,1,3,2,4,5]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,2,1]=>[8,7,6,2,1,3,4,5]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,2,1]=>[8,7,6,1,2,3,4,5]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,4,2,1]=>[8,7,1,6,5,4,3,2]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,4,2,1]=>[8,7,1,6,5,2,4,3]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,4,2,1]=>[8,7,1,6,5,3,2,4]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,2,1]=>[8,7,1,6,2,5,4,3]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,2,1]=>[8,7,1,6,2,5,3,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,4,2,1]=>[8,7,1,6,4,3,2,5]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,4,2,1]=>[8,7,1,6,4,2,3,5]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,4,2,1]=>[8,7,1,6,2,3,5,4]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,2,1]=>[8,7,1,6,2,3,4,5]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,5,2,1]=>[8,7,5,1,6,4,3,2]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,5,2,1]=>[8,7,5,1,6,4,2,3]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,5,2,1]=>[8,7,5,1,6,3,2,4]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,5,2,1]=>[8,7,5,1,6,2,3,4]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,6,2,1]=>[8,7,5,4,1,6,3,2]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,6,2,1]=>[8,7,5,4,1,6,2,3]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,7,2,1]=>[8,7,5,4,3,1,6,2]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,8,2,1]=>[8,7,5,4,3,2,1,6]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,8,2,1]=>[8,7,5,4,3,1,2,6]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,8,2,1]=>[8,7,5,4,1,3,2,6]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,8,2,1]=>[8,7,5,4,1,2,3,6]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,3,6,2,1]=>[8,7,5,1,2,6,4,3]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,3,7,2,1]=>[8,7,5,1,4,2,6,3]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,8,2,1]=>[8,7,5,1,4,3,2,6]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,8,2,1]=>[8,7,5,1,4,2,3,6]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,7,2,1]=>[8,7,5,3,1,2,6,4]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,3,8,2,1]=>[8,7,5,3,1,4,2,6]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,8,2,1]=>[8,7,5,3,2,1,4,6]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,8,2,1]=>[8,7,5,1,2,4,3,6]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,8,2,1]=>[8,7,5,2,1,3,4,6]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,8,2,1]=>[8,7,5,1,2,3,4,6]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,5,2,1]=>[8,7,1,2,6,5,4,3]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,5,2,1]=>[8,7,1,2,6,5,3,4]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,5,2,1]=>[8,7,1,2,6,3,4,5]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,6,2,1]=>[8,7,1,5,2,6,3,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,6,2,1]=>[8,7,4,1,2,6,5,3]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,5,7,2,1]=>[8,7,4,1,5,2,6,3]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,8,2,1]=>[8,7,4,3,1,5,2,6]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,2,1]=>[8,7,4,3,2,1,5,6]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,8,2,1]=>[8,7,4,1,2,3,5,6]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,6,2,1]=>[8,7,1,2,3,6,5,4]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,6,2,1]=>[8,7,1,2,3,6,4,5]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,8,2,1]=>[8,7,1,2,5,4,3,6]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,7,2,1]=>[8,7,3,1,2,4,6,5]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,8,2,1]=>[8,7,3,2,1,4,5,6]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,7,2,1]=>[8,7,1,2,3,4,6,5]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,8,2,1]=>[8,7,1,2,4,3,5,6]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,7,8,2,1]=>[8,7,1,3,2,4,5,6]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,8,2,1]=>[8,7,2,1,3,4,5,6]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,2,1]=>[8,7,1,2,3,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,3,1]=>[8,1,7,6,5,4,3,2]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,2,3,1]=>[8,1,7,6,5,4,2,3]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,2,3,1]=>[8,1,7,6,5,2,4,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,3,1]=>[8,1,7,6,5,3,2,4]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,2,3,1]=>[8,1,7,6,2,5,4,3]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,2,3,1]=>[8,1,7,6,4,2,5,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,2,3,1]=>[8,1,7,6,4,3,2,5]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,2,3,1]=>[8,1,7,6,4,2,3,5]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,2,3,1]=>[8,1,7,6,2,4,3,5]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,2,3,1]=>[8,1,7,6,2,3,4,5]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,2,3,1]=>[8,1,7,2,6,5,4,3]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,2,3,1]=>[8,1,7,2,6,3,5,4]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,2,3,1]=>[8,1,7,2,6,4,3,5]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,2,3,1]=>[8,1,7,2,6,3,4,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,2,3,1]=>[8,1,7,5,4,2,6,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,2,3,1]=>[8,1,7,5,4,3,2,6]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,2,3,1]=>[8,1,7,5,2,4,3,6]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,2,3,1]=>[8,1,7,5,3,2,4,6]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,2,3,1]=>[8,1,7,2,3,6,5,4]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,2,3,1]=>[8,1,7,2,3,6,4,5]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,2,3,1]=>[8,1,7,2,5,3,6,4]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,2,3,1]=>[8,1,7,2,5,4,3,6]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,2,3,1]=>[8,1,7,2,5,3,4,6]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,2,3,1]=>[8,1,7,2,3,4,5,6]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,4,1]=>[8,6,1,7,5,4,3,2]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,2,4,1]=>[8,6,1,7,5,4,2,3]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,2,4,1]=>[8,6,1,7,5,2,4,3]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,2,4,1]=>[8,6,1,7,5,3,2,4]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,2,4,1]=>[8,6,1,7,5,2,3,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,2,4,1]=>[8,6,1,7,2,5,4,3]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,4,1]=>[8,6,1,7,4,2,5,3]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,4,1]=>[8,6,1,7,4,3,2,5]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,2,4,1]=>[8,6,1,7,4,2,3,5]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,2,4,1]=>[8,6,1,7,2,3,5,4]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,2,4,1]=>[8,6,1,7,2,3,4,5]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,2,5,1]=>[8,6,5,1,7,4,3,2]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,2,5,1]=>[8,6,5,1,7,4,2,3]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,3,2,5,1]=>[8,6,5,1,7,2,4,3]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,2,5,1]=>[8,6,5,1,7,3,2,4]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,2,6,1]=>[8,6,5,4,1,7,2,3]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,7,1]=>[8,6,5,4,3,1,7,2]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,8,1]=>[8,6,5,4,3,2,1,7]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,2,8,1]=>[8,6,5,4,3,1,2,7]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,3,2,7,1]=>[8,6,5,4,1,2,7,3]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,2,8,1]=>[8,6,5,4,1,3,2,7]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,2,8,1]=>[8,6,5,4,2,1,3,7]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,2,8,1]=>[8,6,5,4,1,2,3,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,2,8,1]=>[8,6,5,1,4,3,2,7]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,2,7,1]=>[8,6,5,3,1,2,7,4]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,2,8,1]=>[8,6,5,3,2,1,4,7]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,2,8,1]=>[8,6,5,1,2,4,3,7]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,3,2,8,1]=>[8,6,5,1,3,2,4,7]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,2,8,1]=>[8,6,5,1,2,3,4,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,2,5,1]=>[8,6,1,2,7,5,4,3]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,2,5,1]=>[8,6,1,2,7,5,3,4]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,2,5,1]=>[8,6,1,2,7,4,3,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,2,5,1]=>[8,6,1,2,7,3,4,5]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,2,6,1]=>[8,6,1,5,2,7,4,3]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,4,2,7,1]=>[8,6,1,5,4,2,7,3]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,2,8,1]=>[8,6,1,5,4,3,2,7]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,2,8,1]=>[8,6,1,5,2,4,3,7]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,2,8,1]=>[8,6,1,5,3,2,4,7]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,4,2,8,1]=>[8,6,1,5,2,3,4,7]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,2,6,1]=>[8,6,4,1,2,7,5,3]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,2,6,1]=>[8,6,4,1,2,7,3,5]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,5,2,7,1]=>[8,6,4,1,5,2,7,3]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,5,2,8,1]=>[8,6,4,1,5,3,2,7]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,2,8,1]=>[8,6,4,3,2,1,5,7]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,2,7,1]=>[8,6,4,1,2,3,7,5]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,7,2,8,1]=>[8,6,4,1,3,2,5,7]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,2,8,1]=>[8,6,4,2,1,3,5,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,2,8,1]=>[8,6,4,1,2,3,5,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,5,2,7,1]=>[8,6,1,2,5,3,7,4]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,2,8,1]=>[8,6,1,2,5,4,3,7]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,2,8,1]=>[8,6,1,4,2,5,3,7]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,7,2,8,1]=>[8,6,1,4,3,2,5,7]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,2,8,1]=>[8,6,1,4,2,3,5,7]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,2,7,1]=>[8,6,3,1,2,4,7,5]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,2,8,1]=>[8,6,3,1,4,2,5,7]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,2,8,1]=>[8,6,3,2,1,4,5,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,2,7,1]=>[8,6,1,2,3,4,7,5]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,2,8,1]=>[8,6,1,2,3,5,4,7]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,2,8,1]=>[8,6,1,2,4,3,5,7]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,2,8,1]=>[8,6,1,2,3,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,3,4,1]=>[8,1,2,7,6,5,4,3]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,2,3,4,1]=>[8,1,2,7,6,3,5,4]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,3,4,1]=>[8,1,2,7,6,3,4,5]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,3,4,1]=>[8,1,2,7,3,6,5,4]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,3,4,1]=>[8,1,2,7,3,6,4,5]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,3,4,1]=>[8,1,2,7,5,4,3,6]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,3,4,1]=>[8,1,2,7,5,3,4,6]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,3,4,1]=>[8,1,2,7,3,4,6,5]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,3,4,1]=>[8,1,2,7,3,4,5,6]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,2,3,5,1]=>[8,1,6,2,7,3,5,4]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,2,3,5,1]=>[8,1,6,2,7,4,3,5]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,3,5,1]=>[8,1,6,2,7,3,4,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,2,3,6,1]=>[8,1,6,5,2,7,4,3]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,3,8,1]=>[8,1,6,5,4,3,2,7]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,2,3,7,1]=>[8,1,6,5,2,3,7,4]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,2,3,8,1]=>[8,1,6,5,2,3,4,7]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,2,3,7,1]=>[8,1,6,2,5,3,7,4]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,2,3,8,1]=>[8,1,6,2,5,3,4,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,2,3,8,1]=>[8,1,6,4,2,5,3,7]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,2,3,8,1]=>[8,1,6,4,2,3,5,7]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,2,3,8,1]=>[8,1,6,2,3,5,4,7]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,2,3,8,1]=>[8,1,6,2,4,3,5,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,3,8,1]=>[8,1,6,2,3,4,5,7]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,4,5,1]=>[8,5,1,2,7,6,4,3]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,4,5,1]=>[8,5,1,2,7,3,4,6]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,2,4,7,1]=>[8,5,1,6,4,2,7,3]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,2,4,8,1]=>[8,5,1,6,4,3,2,7]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[6,7,5,3,2,4,8,1]=>[8,5,1,6,4,2,3,7]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,2,4,8,1]=>[8,5,1,6,3,2,4,7]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,5,6,1]=>[8,5,4,1,2,7,6,3]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,5,6,1]=>[8,5,4,1,2,7,3,6]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,2,5,7,1]=>[8,5,4,1,6,2,7,3]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,5,8,1]=>[8,5,4,1,6,2,3,7]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,7,8,1]=>[8,5,4,3,2,1,6,7]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,2,6,7,1]=>[8,5,4,1,2,3,7,6]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,7,8,1]=>[8,5,4,2,1,3,6,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,2,7,8,1]=>[8,5,4,1,2,3,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,5,6,1]=>[8,5,1,2,3,7,4,6]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,2,6,7,1]=>[8,5,1,4,2,3,7,6]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,7,8,1]=>[8,5,3,2,1,4,6,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,2,7,8,1]=>[8,5,1,2,4,3,6,7]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,2,7,8,1]=>[8,5,2,1,3,4,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,7,8,1]=>[8,5,1,2,3,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,4,5,1]=>[8,1,2,3,7,6,5,4]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,2,3,4,5,1]=>[8,1,2,3,7,5,4,6]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,4,5,1]=>[8,1,2,3,7,4,5,6]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,4,8,1]=>[8,1,2,6,5,4,3,7]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,3,4,8,1]=>[8,1,2,6,3,4,5,7]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,3,5,6,1]=>[8,1,5,2,3,7,4,6]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,5,7,1]=>[8,1,5,2,6,3,7,4]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,5,8,1]=>[8,1,5,2,6,4,3,7]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[7,5,4,2,3,6,8,1]=>[8,1,5,4,2,6,3,7]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,2,3,7,8,1]=>[8,1,5,4,3,2,6,7]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[5,6,4,2,3,7,8,1]=>[8,1,5,4,2,3,6,7]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,3,7,8,1]=>[8,1,5,3,2,4,6,7]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,5,6,2,3,7,8,1]=>[8,1,5,2,3,4,6,7]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,4,5,6,1]=>[8,4,1,2,3,7,5,6]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,4,5,8,1]=>[8,4,1,2,6,5,3,7]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,4,5,8,1]=>[8,4,1,2,6,3,5,7]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,4,6,8,1]=>[8,4,1,5,2,6,3,7]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[6,5,3,2,4,7,8,1]=>[8,4,1,5,3,2,6,7]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[8,4,3,2,5,6,7,1]=>[8,4,3,1,2,5,7,6]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,2,5,6,8,1]=>[8,4,3,1,2,6,5,7]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,7,8,1]=>[8,4,3,2,1,5,6,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,2,6,7,8,1]=>[8,4,1,3,2,5,6,7]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,6,7,8,1]=>[8,4,2,1,3,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,6,7,8,1]=>[8,4,1,2,3,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,4,5,6,1]=>[8,1,2,3,4,7,6,5]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,4,5,6,1]=>[8,1,2,3,4,7,5,6]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[8,6,2,3,4,5,7,1]=>[8,1,2,3,6,4,7,5]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,5,8,1]=>[8,1,2,3,6,5,4,7]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,4,5,8,1]=>[8,1,2,3,6,4,5,7]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,3,4,6,7,1]=>[8,1,2,5,3,4,7,6]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,3,4,7,8,1]=>[8,1,2,5,4,3,6,7]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,6,2,3,4,7,8,1]=>[8,1,2,5,3,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,3,5,6,7,1]=>[8,1,4,2,3,5,7,6]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[7,4,2,3,5,6,8,1]=>[8,1,4,2,3,6,5,7]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,6,7,8,1]=>[8,1,4,3,2,5,6,7]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,6,7,8,1]=>[8,1,4,2,3,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,4,5,6,7,1]=>[8,3,1,2,4,5,7,6]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,4,5,6,8,1]=>[8,3,1,2,4,6,5,7]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,6,7,8,1]=>[8,3,2,1,4,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,6,7,8,1]=>[8,3,1,2,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,5,6,7,1]=>[8,1,2,3,4,5,7,6]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,6,8,1]=>[8,1,2,3,4,6,5,7]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,5,7,8,1]=>[8,1,2,3,5,4,6,7]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,6,7,8,1]=>[8,1,2,4,3,5,6,7]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,6,7,8,1]=>[8,1,3,2,4,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,1]=>[8,2,1,3,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]=>[8,1,2,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,1,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,1,2]=>[1,8,7,6,5,4,2,3]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,3,1,2]=>[1,8,7,6,5,2,4,3]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,3,1,2]=>[1,8,7,6,5,3,2,4]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,3,1,2]=>[1,8,7,6,5,2,3,4]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,3,1,2]=>[1,8,7,6,2,5,4,3]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,3,1,2]=>[1,8,7,6,4,2,5,3]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,3,1,2]=>[1,8,7,6,4,3,2,5]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,3,1,2]=>[1,8,7,6,4,2,3,5]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,3,1,2]=>[1,8,7,6,2,4,3,5]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,3,1,2]=>[1,8,7,6,3,2,4,5]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,1,2]=>[1,8,7,6,2,3,4,5]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,3,1,2]=>[1,8,7,2,6,5,4,3]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,3,1,2]=>[1,8,7,2,6,5,3,4]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,3,1,2]=>[1,8,7,2,6,3,5,4]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,3,1,2]=>[1,8,7,2,6,3,4,5]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,3,1,2]=>[1,8,7,5,4,3,2,6]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,3,1,2]=>[1,8,7,5,3,2,4,6]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,3,1,2]=>[1,8,7,2,3,6,4,5]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,3,1,2]=>[1,8,7,2,5,4,3,6]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,3,1,2]=>[1,8,7,2,5,3,4,6]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,7,3,1,2]=>[1,8,7,4,2,3,6,5]=>[.,[[[[.,.],.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,3,1,2]=>[1,8,7,4,3,2,5,6]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,3,1,2]=>[1,8,7,4,2,3,5,6]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,1,2]=>[1,8,7,3,2,4,5,6]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,1,2]=>[1,8,7,2,3,4,5,6]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,4,1,2]=>[1,8,2,7,6,5,4,3]=>[.,[[.,.],[[[[[.,.],.],.],.],.]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,4,1,2]=>[1,8,2,7,6,4,3,5]=>[.,[[.,.],[[[[.,.],.],.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,4,1,2]=>[1,8,2,7,6,3,4,5]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,1,2]=>[1,8,2,7,3,6,5,4]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,1,2]=>[1,8,2,7,3,6,4,5]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,4,1,2]=>[1,8,2,7,5,3,6,4]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,4,1,2]=>[1,8,2,7,5,4,3,6]=>[.,[[.,.],[[[[.,.],.],.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,4,1,2]=>[1,8,2,7,5,3,4,6]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,4,1,2]=>[1,8,2,7,3,4,6,5]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,4,1,2]=>[1,8,2,7,3,5,4,6]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,4,1,2]=>[1,8,2,7,4,3,5,6]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,1,2]=>[1,8,2,7,3,4,5,6]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,5,1,2]=>[1,8,6,2,7,3,4,5]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,6,1,2]=>[1,8,6,5,2,7,3,4]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,8,1,2]=>[1,8,6,5,4,3,2,7]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,8,1,2]=>[1,8,6,5,3,2,4,7]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,3,6,1,2]=>[1,8,6,2,3,7,4,5]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,8,1,2]=>[1,8,6,2,5,3,4,7]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,8,1,2]=>[1,8,6,4,2,3,5,7]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,3,8,1,2]=>[1,8,6,2,4,3,5,7]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,8,1,2]=>[1,8,6,3,2,4,5,7]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,8,1,2]=>[1,8,6,2,3,4,5,7]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,5,1,2]=>[1,8,2,3,7,6,5,4]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,5,1,2]=>[1,8,2,3,7,6,4,5]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,6,1,2]=>[1,8,2,6,3,7,4,5]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,8,1,2]=>[1,8,2,6,3,5,4,7]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,4,8,1,2]=>[1,8,2,6,3,4,5,7]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,6,1,2]=>[1,8,5,2,3,7,6,4]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,6,1,2]=>[1,8,5,2,3,7,4,6]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,7,1,2]=>[1,8,5,4,2,3,7,6]=>[.,[[[[.,.],.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,8,1,2]=>[1,8,5,4,2,6,3,7]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,1,2]=>[1,8,5,4,3,2,6,7]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,7,8,1,2]=>[1,8,5,4,2,3,6,7]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,8,1,2]=>[1,8,5,3,2,4,6,7]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,6,1,2]=>[1,8,2,3,4,7,6,5]=>[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,6,1,2]=>[1,8,2,3,4,7,5,6]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,8,1,2]=>[1,8,2,3,6,5,4,7]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,6,7,1,2]=>[1,8,2,5,3,4,7,6]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,8,1,2]=>[1,8,2,5,3,6,4,7]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,8,1,2]=>[1,8,2,5,3,4,6,7]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,7,1,2]=>[1,8,4,2,3,5,7,6]=>[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,8,1,2]=>[1,8,4,2,5,3,6,7]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,8,1,2]=>[1,8,4,3,2,5,6,7]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,8,1,2]=>[1,8,4,2,3,5,6,7]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,7,1,2]=>[1,8,2,3,4,5,7,6]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,8,1,2]=>[1,8,2,3,4,6,5,7]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,8,1,2]=>[1,8,2,3,5,4,6,7]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,7,8,1,2]=>[1,8,2,4,3,5,6,7]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,8,1,2]=>[1,8,3,2,4,5,6,7]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2]=>[1,8,2,3,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,1,3]=>[7,1,8,6,5,4,3,2]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,2,1,3]=>[7,1,8,6,5,4,2,3]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,2,1,3]=>[7,1,8,6,5,2,4,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,1,3]=>[7,1,8,6,5,3,2,4]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,2,1,3]=>[7,1,8,6,5,2,3,4]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,2,1,3]=>[7,1,8,6,2,5,4,3]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,2,1,3]=>[7,1,8,6,2,5,3,4]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,2,1,3]=>[7,1,8,6,4,3,2,5]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,2,1,3]=>[7,1,8,6,4,2,3,5]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,2,1,3]=>[7,1,8,6,2,4,3,5]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,2,1,3]=>[7,1,8,6,3,2,4,5]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,2,1,3]=>[7,1,8,6,2,3,4,5]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,2,1,3]=>[7,1,8,2,6,5,4,3]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,2,1,3]=>[7,1,8,2,6,3,5,4]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,2,1,3]=>[7,1,8,2,6,4,3,5]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,2,1,3]=>[7,1,8,5,4,3,2,6]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,2,1,3]=>[7,1,8,5,4,2,3,6]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,2,1,3]=>[7,1,8,5,3,2,4,6]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,2,1,3]=>[7,1,8,5,2,3,4,6]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,2,1,3]=>[7,1,8,2,3,6,5,4]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,2,1,3]=>[7,1,8,2,5,3,6,4]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,2,1,3]=>[7,1,8,2,5,4,3,6]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,2,1,3]=>[7,1,8,4,2,5,3,6]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,2,1,3]=>[7,1,8,2,3,4,5,6]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,1,4]=>[7,6,1,8,5,4,3,2]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,2,1,4]=>[7,6,1,8,5,4,2,3]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,2,1,4]=>[7,6,1,8,5,3,2,4]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,2,1,4]=>[7,6,1,8,5,2,3,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,2,1,4]=>[7,6,1,8,2,5,4,3]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,2,1,4]=>[7,6,1,8,2,5,3,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,1,4]=>[7,6,1,8,4,2,5,3]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,1,4]=>[7,6,1,8,4,3,2,5]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,2,1,4]=>[7,6,1,8,4,2,3,5]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,2,1,4]=>[7,6,1,8,2,3,5,4]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,2,1,4]=>[7,6,1,8,3,2,4,5]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,2,1,4]=>[7,6,1,8,2,3,4,5]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,2,1,5]=>[7,6,5,1,8,4,3,2]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,2,1,5]=>[7,6,5,1,8,4,2,3]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,3,2,1,5]=>[7,6,5,1,8,2,4,3]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,2,1,5]=>[7,6,5,1,8,3,2,4]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,2,1,5]=>[7,6,5,1,8,2,3,4]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,2,1,6]=>[7,6,5,4,1,8,3,2]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,2,1,6]=>[7,6,5,4,1,8,2,3]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,1,7]=>[7,6,5,4,3,1,8,2]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,2,1,8]=>[7,6,5,4,3,1,2,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,3,2,1,7]=>[7,6,5,4,1,2,8,3]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,2,1,8]=>[7,6,5,4,1,3,2,8]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,2,1,8]=>[7,6,5,4,2,1,3,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,2,1,8]=>[7,6,5,4,1,2,3,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,3,2,1,6]=>[7,6,5,1,2,8,4,3]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,3,2,1,6]=>[7,6,5,1,2,8,3,4]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,3,2,1,7]=>[7,6,5,1,4,2,8,3]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,2,1,8]=>[7,6,5,1,4,3,2,8]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,2,1,8]=>[7,6,5,1,4,2,3,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,2,1,7]=>[7,6,5,3,1,2,8,4]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,3,2,1,8]=>[7,6,5,3,1,4,2,8]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,2,1,8]=>[7,6,5,3,2,1,4,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,3,2,1,7]=>[7,6,5,1,2,3,8,4]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,2,1,8]=>[7,6,5,1,2,4,3,8]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1,8]=>[7,6,5,2,1,3,4,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,2,1,8]=>[7,6,5,1,2,3,4,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,2,1,5]=>[7,6,1,2,8,5,4,3]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,4,2,1,7]=>[7,6,1,5,4,2,8,3]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,2,1,7]=>[7,6,1,5,2,3,8,4]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,2,1,8]=>[7,6,1,5,2,4,3,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,5,2,1,7]=>[7,6,4,1,5,2,8,3]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,5,2,1,8]=>[7,6,4,1,5,2,3,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,2,1,8]=>[7,6,4,3,1,5,2,8]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,2,1,8]=>[7,6,4,3,2,1,5,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,7,2,1,8]=>[7,6,4,3,1,2,5,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,2,1,7]=>[7,6,4,1,2,3,8,5]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,2,1,8]=>[7,6,4,2,1,3,5,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,2,1,6]=>[7,6,1,2,3,8,5,4]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,2,1,6]=>[7,6,1,2,3,8,4,5]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,2,1,8]=>[7,6,1,2,5,4,3,8]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,2,1,7]=>[7,6,3,1,2,4,8,5]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,2,1,8]=>[7,6,3,2,1,4,5,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,2,1,7]=>[7,6,1,2,3,4,8,5]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,2,1,8]=>[7,6,1,2,3,4,5,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,3,1,4]=>[7,1,2,8,6,5,4,3]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,3,1,4]=>[7,1,2,8,6,4,3,5]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,3,1,4]=>[7,1,2,8,3,6,5,4]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,3,1,4]=>[7,1,2,8,3,6,4,5]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,3,1,4]=>[7,1,2,8,5,3,4,6]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,2,3,1,4]=>[7,1,2,8,3,5,4,6]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,3,1,4]=>[7,1,2,8,3,4,5,6]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,3,1,5]=>[7,1,6,2,8,5,4,3]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,2,3,1,5]=>[7,1,6,2,8,3,5,4]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,2,3,1,5]=>[7,1,6,2,8,4,3,5]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,3,1,5]=>[7,1,6,2,8,3,4,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,3,1,7]=>[7,1,6,5,4,2,8,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,3,1,8]=>[7,1,6,5,4,3,2,8]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,2,3,1,8]=>[7,1,6,5,4,2,3,8]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,2,3,1,7]=>[7,1,6,5,2,3,8,4]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,2,3,1,8]=>[7,1,6,5,2,4,3,8]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,2,3,1,6]=>[7,1,6,2,3,8,5,4]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,2,3,1,6]=>[7,1,6,2,3,8,4,5]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,2,3,1,7]=>[7,1,6,2,5,3,8,4]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,2,3,1,8]=>[7,1,6,2,5,4,3,8]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,2,3,1,8]=>[7,1,6,2,5,3,4,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,2,3,1,8]=>[7,1,6,4,2,5,3,8]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,2,3,1,8]=>[7,1,6,4,2,3,5,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,3,1,8]=>[7,1,6,2,3,4,5,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,4,1,5]=>[7,5,1,2,8,6,4,3]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,4,1,5]=>[7,5,1,2,8,3,4,6]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,4,1,6]=>[7,5,1,6,2,8,4,3]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,2,4,1,8]=>[7,5,1,6,4,3,2,8]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,2,4,1,8]=>[7,5,1,6,3,2,4,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,5,1,6]=>[7,5,4,1,2,8,3,6]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,2,5,1,7]=>[7,5,4,1,6,2,8,3]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,2,5,1,8]=>[7,5,4,1,6,3,2,8]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,5,1,8]=>[7,5,4,1,6,2,3,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,7,1,8]=>[7,5,4,3,2,1,6,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,2,7,1,8]=>[7,5,4,3,1,2,6,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,2,5,1,6]=>[7,5,1,2,3,8,6,4]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,5,1,6]=>[7,5,1,2,3,8,4,6]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,2,6,1,8]=>[7,5,1,4,2,6,3,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,2,7,1,8]=>[7,5,1,4,2,3,6,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,7,1,8]=>[7,5,3,2,1,4,6,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,2,7,1,8]=>[7,5,3,1,2,4,6,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,2,7,1,8]=>[7,5,1,3,2,4,6,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,7,1,8]=>[7,5,1,2,3,4,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,4,1,5]=>[7,1,2,3,8,6,5,4]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,2,3,4,1,5]=>[7,1,2,3,8,5,4,6]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,4,1,5]=>[7,1,2,3,8,4,5,6]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,2,3,4,1,6]=>[7,1,2,6,3,8,4,5]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,3,4,1,7]=>[7,1,2,6,5,3,8,4]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,4,1,8]=>[7,1,2,6,5,4,3,8]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,2,3,4,1,8]=>[7,1,2,6,5,3,4,8]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,3,4,1,7]=>[7,1,2,6,3,4,8,5]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,2,3,4,1,8]=>[7,1,2,6,3,5,4,8]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,2,3,4,1,8]=>[7,1,2,6,4,3,5,8]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,3,4,1,8]=>[7,1,2,6,3,4,5,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,5,1,7]=>[7,1,5,2,6,3,8,4]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,5,1,8]=>[7,1,5,2,6,4,3,8]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[6,7,4,2,3,5,1,8]=>[7,1,5,2,6,3,4,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[7,5,4,2,3,6,1,8]=>[7,1,5,4,2,6,3,8]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[8,4,5,2,3,6,1,7]=>[7,1,5,2,3,4,8,6]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,2,3,6,1,8]=>[7,1,5,2,3,6,4,8]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,3,7,1,8]=>[7,1,5,3,2,4,6,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,4,5,1,7]=>[7,4,1,2,6,3,8,5]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,2,4,6,1,7]=>[7,4,1,5,2,3,8,6]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,4,6,1,8]=>[7,4,1,5,2,6,3,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[6,5,3,2,4,7,1,8]=>[7,4,1,5,3,2,6,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,7,1,8]=>[7,4,3,2,1,5,6,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,2,5,6,1,7]=>[7,4,1,2,3,5,8,6]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,6,7,1,8]=>[7,4,1,2,3,5,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,4,5,1,6]=>[7,1,2,3,4,8,6,5]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,4,5,1,6]=>[7,1,2,3,4,8,5,6]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,5,1,8]=>[7,1,2,3,6,5,4,8]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,4,5,1,8]=>[7,1,2,3,6,4,5,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,3,4,6,1,7]=>[7,1,2,5,3,4,8,6]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,6,7,1,8]=>[7,1,4,3,2,5,6,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,6,7,1,8]=>[7,1,4,2,3,5,6,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,4,5,6,1,7]=>[7,3,1,2,4,5,8,6]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[6,3,2,4,5,7,1,8]=>[7,3,1,2,5,4,6,8]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,6,7,1,8]=>[7,3,2,1,4,5,6,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,6,7,1,8]=>[7,3,1,2,4,5,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,5,6,1,7]=>[7,1,2,3,4,5,8,6]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,6,1,8]=>[7,1,2,3,4,6,5,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,5,7,1,8]=>[7,1,2,3,5,4,6,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,6,7,1,8]=>[7,1,2,4,3,5,6,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,6,7,1,8]=>[7,1,3,2,4,5,6,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,6,7,1,8]=>[7,2,1,3,4,5,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8]=>[7,1,2,3,4,5,6,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,1,2,3]=>[1,2,8,7,6,5,4,3]=>[.,[.,[[[[[[.,.],.],.],.],.],.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,1,2,3]=>[1,2,8,7,6,4,3,5]=>[.,[.,[[[[[.,.],.],.],.],[.,.]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,1,2,3]=>[1,2,8,7,6,3,4,5]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,1,2,3]=>[1,2,8,7,5,3,6,4]=>[.,[.,[[[[.,.],.],.],[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,1,2,3]=>[1,2,8,7,5,4,3,6]=>[.,[.,[[[[[.,.],.],.],.],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,1,2,3]=>[1,2,8,7,3,4,6,5]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,1,2,3]=>[1,2,8,7,3,5,4,6]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,1,2,3]=>[1,2,8,7,3,4,5,6]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,1,2,3]=>[1,2,8,3,7,6,5,4]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,1,2,3]=>[1,2,8,3,7,4,6,5]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,1,2,3]=>[1,2,8,3,7,4,5,6]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,1,2,3]=>[1,2,8,6,3,7,5,4]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,6,1,2,3]=>[1,2,8,6,3,7,4,5]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,1,2,3]=>[1,2,8,6,5,4,3,7]=>[.,[.,[[[[[.,.],.],.],.],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,1,2,3]=>[1,2,8,6,3,4,7,5]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,1,2,3]=>[1,2,8,3,4,7,6,5]=>[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,1,2,3]=>[1,2,8,3,6,4,7,5]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,1,2,3]=>[1,2,8,3,6,5,4,7]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,1,2,3]=>[1,2,8,3,6,4,5,7]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,1,2,3]=>[1,2,8,5,3,6,4,7]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,1,2,3]=>[1,2,8,5,4,3,6,7]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,1,2,3]=>[1,2,8,5,3,4,6,7]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,1,2,3]=>[1,2,8,3,4,5,7,6]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,1,2,3]=>[1,2,8,3,4,6,5,7]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,1,2,3]=>[1,2,8,3,5,4,6,7]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,1,2,3]=>[1,2,8,4,3,5,6,7]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,1,2,3]=>[1,2,8,3,4,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,1,2,4]=>[1,7,2,8,6,5,3,4]=>[.,[[.,.],[[[[.,.],.],.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,1,2,4]=>[1,7,2,8,6,3,5,4]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,1,2,4]=>[1,7,2,8,3,6,5,4]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,1,2,4]=>[1,7,2,8,3,6,4,5]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,1,2,4]=>[1,7,2,8,5,3,6,4]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,1,2,4]=>[1,7,2,8,5,4,3,6]=>[.,[[.,.],[[[[.,.],.],.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,1,2,4]=>[1,7,2,8,5,3,4,6]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,1,2,4]=>[1,7,2,8,3,5,4,6]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,1,2,4]=>[1,7,2,8,4,3,5,6]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,1,2,4]=>[1,7,2,8,3,4,5,6]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,1,2,5]=>[1,7,6,2,8,5,4,3]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,1,2,5]=>[1,7,6,2,8,3,4,5]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,1,2,6]=>[1,7,6,5,2,8,4,3]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,1,2,7]=>[1,7,6,5,4,2,8,3]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,1,2,8]=>[1,7,6,5,4,3,2,8]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,1,2,8]=>[1,7,6,5,4,2,3,8]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,1,2,8]=>[1,7,6,5,2,4,3,8]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,3,1,2,7]=>[1,7,6,2,5,3,8,4]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,1,2,8]=>[1,7,6,3,2,4,5,8]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,1,2,8]=>[1,7,6,2,3,4,5,8]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,1,2,5]=>[1,7,2,3,8,6,5,4]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,1,2,5]=>[1,7,2,3,8,6,4,5]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,1,2,5]=>[1,7,2,3,8,4,5,6]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,1,2,6]=>[1,7,2,6,3,8,5,4]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,1,2,6]=>[1,7,2,6,3,8,4,5]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,1,2,8]=>[1,7,2,6,5,4,3,8]=>[.,[[.,.],[[[[.,.],.],.],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,1,2,7]=>[1,7,2,6,3,4,8,5]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,1,2,8]=>[1,7,2,6,3,5,4,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,1,2,8]=>[1,7,2,6,4,3,5,8]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,1,2,8]=>[1,7,5,4,3,2,6,8]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,1,2,7]=>[1,7,5,2,3,4,8,6]=>[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,1,2,6]=>[1,7,2,3,4,8,6,5]=>[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,1,2,6]=>[1,7,2,3,4,8,5,6]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,5,1,2,7]=>[1,7,2,3,6,4,8,5]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,5,1,2,8]=>[1,7,2,3,6,4,5,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,6,1,2,7]=>[1,7,2,5,3,4,8,6]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,1,2,8]=>[1,7,2,5,3,6,4,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,1,2,8]=>[1,7,2,5,3,4,6,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,1,2,7]=>[1,7,4,2,3,5,8,6]=>[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,1,2,8]=>[1,7,4,2,5,3,6,8]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,1,2,7]=>[1,7,2,3,4,5,8,6]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,1,2,8]=>[1,7,2,3,5,4,6,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,1,2,8]=>[1,7,3,2,4,5,6,8]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,1,2,8]=>[1,7,2,3,4,5,6,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,2,1,3,4]=>[6,1,2,8,7,5,3,4]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,1,3,4]=>[6,1,2,8,7,4,3,5]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,1,3,4]=>[6,1,2,8,7,3,4,5]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,1,3,4]=>[6,1,2,8,3,7,4,5]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,1,3,4]=>[6,1,2,8,5,3,7,4]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,1,3,4]=>[6,1,2,8,5,3,4,7]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,1,3,4]=>[6,1,2,8,3,4,7,5]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,1,3,4]=>[6,1,2,8,4,3,5,7]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,1,3,4]=>[6,1,2,8,3,4,5,7]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,1,3,5]=>[6,1,7,2,8,5,4,3]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,2,1,3,5]=>[6,1,7,2,8,3,5,4]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,1,3,5]=>[6,1,7,2,8,3,4,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,2,1,3,6]=>[6,1,7,5,2,8,3,4]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,1,3,7]=>[6,1,7,5,4,2,8,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,2,1,3,8]=>[6,1,7,5,3,2,4,8]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,2,1,3,7]=>[6,1,7,2,5,3,8,4]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,2,1,3,8]=>[6,1,7,4,2,5,3,8]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,2,1,3,7]=>[6,1,7,2,3,4,8,5]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,2,1,3,8]=>[6,1,7,3,2,4,5,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,1,3,8]=>[6,1,7,2,3,4,5,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,1,4,5]=>[6,5,1,2,8,7,4,3]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,2,1,4,5]=>[6,5,1,2,8,7,3,4]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,2,1,4,5]=>[6,5,1,2,8,3,7,4]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,2,1,4,5]=>[6,5,1,2,8,4,3,7]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,1,4,5]=>[6,5,1,2,8,3,4,7]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,1,4,6]=>[6,5,1,7,2,8,4,3]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,2,1,4,6]=>[6,5,1,7,2,8,3,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,2,1,4,7]=>[6,5,1,7,4,2,8,3]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,2,1,4,8]=>[6,5,1,7,4,3,2,8]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,2,1,4,7]=>[6,5,1,7,2,3,8,4]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,1,5,6]=>[6,5,4,1,2,8,3,7]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,2,1,5,7]=>[6,5,4,1,7,2,8,3]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,1,5,8]=>[6,5,4,1,7,2,3,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2,1,6,7]=>[6,5,4,3,1,2,8,7]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,1,7,8]=>[6,5,4,3,2,1,7,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,2,1,7,8]=>[6,5,4,3,1,2,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,1,7,8]=>[6,5,4,2,1,3,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,2,1,7,8]=>[6,5,4,1,2,3,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,1,5,6]=>[6,5,1,2,3,8,4,7]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,2,1,5,7]=>[6,5,1,2,7,3,8,4]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,2,1,7,8]=>[6,5,1,4,3,2,7,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,2,1,6,8]=>[6,5,3,1,2,7,4,8]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,2,1,6,7]=>[6,5,1,2,3,4,8,7]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,2,1,6,8]=>[6,5,1,2,3,7,4,8]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,1,7,8]=>[6,5,1,2,3,4,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,1,4,5]=>[6,1,2,3,8,7,5,4]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,2,3,1,4,5]=>[6,1,2,3,8,7,4,5]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,3,1,4,5]=>[6,1,2,3,8,4,7,5]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,2,3,1,4,5]=>[6,1,2,3,8,5,4,7]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,1,4,5]=>[6,1,2,3,8,4,5,7]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,2,3,1,4,6]=>[6,1,2,7,3,8,5,4]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,3,1,4,7]=>[6,1,2,7,5,3,8,4]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,3,1,4,7]=>[6,1,2,7,3,4,8,5]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,3,1,4,8]=>[6,1,2,7,3,4,5,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,1,5,7]=>[6,1,5,2,7,3,8,4]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[6,7,4,2,3,1,5,8]=>[6,1,5,2,7,3,4,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[7,5,4,2,3,1,6,8]=>[6,1,5,4,2,7,3,8]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[8,7,3,2,4,1,5,6]=>[6,4,1,2,3,8,7,5]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,4,1,5,6]=>[6,4,1,2,3,8,5,7]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,4,1,6,8]=>[6,4,1,5,2,7,3,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,3,2,4,1,7,8]=>[6,4,1,5,2,3,7,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,5,1,7,8]=>[6,4,3,1,5,2,7,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,1,7,8]=>[6,4,3,2,1,5,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,6,1,7,8]=>[6,4,3,1,2,5,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,6,1,7,8]=>[6,4,2,1,3,5,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,6,1,7,8]=>[6,4,1,2,3,5,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,4,1,5,6]=>[6,1,2,3,4,8,7,5]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,4,1,5,6]=>[6,1,2,3,4,8,5,7]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[8,6,2,3,4,1,5,7]=>[6,1,2,3,7,4,8,5]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,1,5,8]=>[6,1,2,3,7,5,4,8]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,4,1,5,8]=>[6,1,2,3,7,4,5,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,6,2,3,4,1,7,8]=>[6,1,2,5,3,4,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,3,5,1,6,7]=>[6,1,4,2,3,5,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,5,1,6,7]=>[6,1,2,3,4,5,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,1,6,8]=>[6,1,2,3,4,7,5,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,5,1,7,8]=>[6,1,2,3,5,4,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,6,1,7,8]=>[6,1,2,4,3,5,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,1,7,8]=>[6,1,2,3,4,5,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,1,2,3,4]=>[1,2,3,8,7,6,5,4]=>[.,[.,[.,[[[[[.,.],.],.],.],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,1,2,3,4]=>[1,2,3,8,7,6,4,5]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,1,2,3,4]=>[1,2,3,8,7,4,6,5]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,1,2,3,4]=>[1,2,3,8,7,5,4,6]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,1,2,3,4]=>[1,2,3,8,7,4,5,6]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,1,2,3,4]=>[1,2,3,8,4,7,6,5]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,1,2,3,4]=>[1,2,3,8,4,7,5,6]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,1,2,3,4]=>[1,2,3,8,6,4,7,5]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,1,2,3,4]=>[1,2,3,8,6,5,4,7]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,1,2,3,4]=>[1,2,3,8,6,4,5,7]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,1,2,3,4]=>[1,2,3,8,4,5,7,6]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,1,2,3,4]=>[1,2,3,8,4,6,5,7]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,1,2,3,4]=>[1,2,3,8,5,4,6,7]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[1,2,3,8,4,5,6,7]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,1,2,3,5]=>[1,2,7,3,8,6,5,4]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,1,2,3,5]=>[1,2,7,3,8,6,4,5]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,1,2,3,5]=>[1,2,7,3,8,5,4,6]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,1,2,3,5]=>[1,2,7,3,8,4,5,6]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,1,2,3,6]=>[1,2,7,6,3,8,5,4]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,1,2,3,6]=>[1,2,7,6,3,8,4,5]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,1,2,3,7]=>[1,2,7,6,5,3,8,4]=>[.,[.,[[[[.,.],.],.],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,1,2,3,8]=>[1,2,7,6,5,4,3,8]=>[.,[.,[[[[[.,.],.],.],.],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,1,2,3,7]=>[1,2,7,6,3,4,8,5]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,1,2,3,8]=>[1,2,7,6,3,4,5,8]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,1,2,3,6]=>[1,2,7,3,4,8,6,5]=>[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,1,2,3,6]=>[1,2,7,3,4,8,5,6]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,1,2,3,7]=>[1,2,7,3,6,4,8,5]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,1,2,3,8]=>[1,2,7,5,3,6,4,8]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,1,2,3,8]=>[1,2,7,5,3,4,6,8]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,1,2,3,7]=>[1,2,7,3,4,5,8,6]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,1,2,3,8]=>[1,2,7,3,4,6,5,8]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,1,2,3,8]=>[1,2,7,4,3,5,6,8]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,1,2,3,8]=>[1,2,7,3,4,5,6,8]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,1,2,4,5]=>[1,6,2,3,8,7,4,5]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,1,2,4,5]=>[1,6,2,3,8,5,4,7]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,1,2,4,5]=>[1,6,2,3,8,4,5,7]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,1,2,4,6]=>[1,6,2,7,3,8,5,4]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,1,2,4,6]=>[1,6,2,7,3,8,4,5]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,1,2,4,7]=>[1,6,2,7,3,4,8,5]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,1,2,4,8]=>[1,6,2,7,3,5,4,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,1,2,4,8]=>[1,6,2,7,3,4,5,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,1,2,5,6]=>[1,6,5,2,3,8,4,7]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,1,2,5,7]=>[1,6,5,2,7,3,8,4]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,1,2,5,8]=>[1,6,5,2,7,4,3,8]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,1,2,7,8]=>[1,6,5,4,3,2,7,8]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,1,2,7,8]=>[1,6,5,3,2,4,7,8]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,1,2,5,6]=>[1,6,2,3,4,8,7,5]=>[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,1,2,5,6]=>[1,6,2,3,4,8,5,7]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,1,2,5,7]=>[1,6,2,3,7,4,8,5]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,1,2,5,8]=>[1,6,2,3,7,4,5,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,1,2,6,7]=>[1,6,2,5,3,4,8,7]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,1,2,6,8]=>[1,6,2,5,3,7,4,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,1,2,7,8]=>[1,6,2,5,3,4,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,1,2,7,8]=>[1,6,4,2,5,3,7,8]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,1,2,7,8]=>[1,6,4,3,2,5,7,8]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,1,2,6,7]=>[1,6,2,3,4,5,8,7]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,1,2,7,8]=>[1,6,2,3,4,5,7,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,1,3,4,5]=>[5,1,2,3,8,7,6,4]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,2,1,3,4,5]=>[5,1,2,3,8,7,4,6]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,1,3,4,5]=>[5,1,2,3,8,4,7,6]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,1,3,4,5]=>[5,1,2,3,8,4,6,7]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,2,1,3,4,6]=>[5,1,2,7,3,8,6,4]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,2,1,3,4,6]=>[5,1,2,7,3,8,4,6]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,2,1,3,4,8]=>[5,1,2,7,6,3,4,8]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,1,3,4,7]=>[5,1,2,7,3,4,8,6]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,2,1,3,4,8]=>[5,1,2,7,3,6,4,8]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,1,3,4,8]=>[5,1,2,7,3,4,6,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,1,3,5,6]=>[5,1,6,2,3,8,4,7]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,1,3,5,7]=>[5,1,6,2,7,3,8,4]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,1,3,5,8]=>[5,1,6,2,7,4,3,8]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,2,1,3,7,8]=>[5,1,6,4,3,2,7,8]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[5,6,4,2,1,3,7,8]=>[5,1,6,4,2,3,7,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,2,1,3,6,8]=>[5,1,6,2,3,7,4,8]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[6,4,5,2,1,3,7,8]=>[5,1,6,2,4,3,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,1,3,7,8]=>[5,1,6,3,2,4,7,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[4,5,6,2,1,3,7,8]=>[5,1,6,2,3,4,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[8,7,3,2,1,4,5,6]=>[5,4,1,2,3,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,1,4,5,6]=>[5,4,1,2,3,8,6,7]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,1,4,5,7]=>[5,4,1,2,7,3,8,6]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,1,4,5,8]=>[5,4,1,2,7,6,3,8]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,2,1,4,6,7]=>[5,4,1,6,2,3,8,7]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,1,4,6,8]=>[5,4,1,6,2,7,3,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[6,5,3,2,1,4,7,8]=>[5,4,1,6,3,2,7,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,2,1,5,6,8]=>[5,4,3,1,2,7,6,8]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,1,5,7,8]=>[5,4,3,1,6,2,7,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,1,6,7,8]=>[5,4,3,1,2,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,1,6,7,8]=>[5,4,2,1,3,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,1,6,7,8]=>[5,4,1,2,3,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,1,4,5,6]=>[5,1,2,3,4,8,7,6]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,1,4,5,6]=>[5,1,2,3,4,8,6,7]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,1,4,5,8]=>[5,1,2,3,7,6,4,8]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,3,1,4,6,8]=>[5,1,2,6,3,7,4,8]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,1,6,7,8]=>[5,1,4,3,2,6,7,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,1,6,7,8]=>[5,1,4,2,3,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,1,6,7,8]=>[5,3,1,4,2,6,7,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,1,6,7,8]=>[5,3,2,1,4,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,1,6,7,8]=>[5,3,1,2,4,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,1,5,6,7]=>[5,1,2,3,4,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,1,6,7,8]=>[5,1,2,4,3,6,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,1,6,7,8]=>[5,2,1,3,4,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>[5,1,2,3,4,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,1,2,3,4,5]=>[1,2,3,4,8,7,6,5]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,1,2,3,4,5]=>[1,2,3,4,8,7,5,6]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,1,2,3,4,5]=>[1,2,3,4,8,5,7,6]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,1,2,3,4,5]=>[1,2,3,4,8,6,5,7]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,1,2,3,4,5]=>[1,2,3,4,8,5,6,7]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,1,2,3,4,6]=>[1,2,3,7,4,8,6,5]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,1,2,3,4,6]=>[1,2,3,7,4,8,5,6]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,1,2,3,4,7]=>[1,2,3,7,6,4,8,5]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,1,2,3,4,8]=>[1,2,3,7,6,5,4,8]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,1,2,3,4,8]=>[1,2,3,7,6,4,5,8]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,1,2,3,4,7]=>[1,2,3,7,4,5,8,6]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,1,2,3,4,8]=>[1,2,3,7,4,6,5,8]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,1,2,3,4,8]=>[1,2,3,7,5,4,6,8]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,1,2,3,4,8]=>[1,2,3,7,4,5,6,8]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[8,7,4,1,2,3,5,6]=>[1,2,6,3,4,8,7,5]=>[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,1,2,3,5,6]=>[1,2,6,3,4,8,5,7]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,1,2,3,5,7]=>[1,2,6,3,7,4,8,5]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,1,2,3,7,8]=>[1,2,6,5,4,3,7,8]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[8,4,5,1,2,3,6,7]=>[1,2,6,3,4,5,8,7]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,1,2,3,6,8]=>[1,2,6,3,4,7,5,8]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[4,5,6,1,2,3,7,8]=>[1,2,6,3,4,5,7,8]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,1,2,4,5,6]=>[1,5,2,3,4,8,6,7]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,1,2,4,5,8]=>[1,5,2,3,7,4,6,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,1,2,4,6,7]=>[1,5,2,6,3,4,8,7]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,1,2,4,6,8]=>[1,5,2,6,3,7,4,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,1,2,5,6,8]=>[1,5,4,2,3,7,6,8]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,1,2,5,7,8]=>[1,5,4,2,6,3,7,8]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,1,2,6,7,8]=>[1,5,4,3,2,6,7,8]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,1,2,5,6,7]=>[1,5,2,3,4,6,8,7]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[7,3,4,1,2,5,6,8]=>[1,5,2,3,4,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,1,2,6,7,8]=>[1,5,2,4,3,6,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,1,2,6,7,8]=>[1,5,2,3,4,6,7,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,1,3,4,5,6]=>[4,1,2,3,5,8,7,6]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,1,3,4,5,6]=>[4,1,2,3,5,8,6,7]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,1,3,4,6,7]=>[4,1,2,6,3,5,8,7]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,1,3,5,7,8]=>[4,1,5,2,6,3,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,1,4,5,6,8]=>[4,3,1,2,5,7,6,8]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[6,3,2,1,4,5,7,8]=>[4,3,1,2,6,5,7,8]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,1,5,6,7,8]=>[4,3,1,2,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,1,4,5,6,7]=>[4,1,2,3,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,1,4,5,6,8]=>[4,1,2,3,5,7,6,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,1,4,5,7,8]=>[4,1,2,3,6,5,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,1,4,6,7,8]=>[4,1,2,5,3,6,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,1,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,1,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[8,7,1,2,3,4,5,6]=>[1,2,3,4,5,8,7,6]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,6]=>[1,2,3,4,5,8,6,7]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[8,6,1,2,3,4,5,7]=>[1,2,3,4,7,5,8,6]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[7,6,1,2,3,4,5,8]=>[1,2,3,4,7,6,5,8]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,7,1,2,3,4,5,8]=>[1,2,3,4,7,5,6,8]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[8,5,1,2,3,4,6,7]=>[1,2,3,6,4,5,8,7]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[7,5,1,2,3,4,6,8]=>[1,2,3,6,4,7,5,8]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,5,1,2,3,4,7,8]=>[1,2,3,6,5,4,7,8]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[5,6,1,2,3,4,7,8]=>[1,2,3,6,4,5,7,8]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[8,4,1,2,3,5,6,7]=>[1,2,5,3,4,6,8,7]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[7,4,1,2,3,5,6,8]=>[1,2,5,3,4,7,6,8]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[6,4,1,2,3,5,7,8]=>[1,2,5,3,6,4,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[5,4,1,2,3,6,7,8]=>[1,2,5,4,3,6,7,8]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[4,5,1,2,3,6,7,8]=>[1,2,5,3,4,6,7,8]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[8,3,1,2,4,5,6,7]=>[1,4,2,3,5,6,8,7]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[7,3,1,2,4,5,6,8]=>[1,4,2,3,5,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[6,3,1,2,4,5,7,8]=>[1,4,2,3,6,5,7,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[5,3,1,2,4,6,7,8]=>[1,4,2,5,3,6,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[4,3,1,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[8,2,1,3,4,5,6,7]=>[3,1,2,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[7,2,1,3,4,5,6,8]=>[3,1,2,4,5,7,6,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[4,2,1,3,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,8,7]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,2,3,4,5,6,8]=>[1,2,3,4,5,7,6,8]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,2,3,4,5,7,8]=>[1,2,3,4,6,5,7,8]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,2,3,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,2,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,9,8]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1]=>[9,1,2,3,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[10,1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,10,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[9,2,1,3,4,5,6,7,8]=>[3,1,2,4,5,6,7,9,8]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,9,1]=>[9,2,1,3,4,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,1]=>[10,1,2,3,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[11,1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[4,2,3,5,6,7,8,9,1]=>[9,1,3,2,4,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[3,4,2,5,6,7,8,9,1]=>[9,3,1,2,4,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,9,10,1]=>[10,2,1,3,4,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>[11,1,2,3,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,2,6,7,8,9,1]=>[9,4,1,2,3,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[3,4,2,5,6,7,8,9,10,1]=>[10,3,1,2,4,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,9,10,11,1]=>[11,2,1,3,4,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,2,6,7,8,9,10,1]=>[10,4,1,2,3,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[3,4,2,5,6,7,8,9,10,11,1]=>[11,3,1,2,4,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[9,6,1,2,3,4,5,7,8]=>[1,2,3,4,7,5,6,9,8]=>[.,[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,4,5,6,1,7,8]=>[7,1,2,3,4,5,6,9,8]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[6,2,3,4,5,7,8,9,10,1]=>[10,1,2,3,5,4,6,7,8,9]=>[[.,.],[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,2,8,9,1]=>[9,6,1,2,3,4,5,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,4,5,2,6,7,8,9,10,11,1]=>[11,4,1,2,3,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[9,7,1,2,3,4,5,6,8]=>[1,2,3,4,5,8,6,9,7]=>[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,4,5,6,7,1,8]=>[8,1,2,3,4,5,6,9,7]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[8,9,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,9,7,8]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[8,2,3,4,5,6,7,9,1]=>[9,1,2,3,4,5,7,6,8]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,1,2]=>[1,9,2,3,4,5,6,7,8]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,2,9,1]=>[9,7,1,2,3,4,5,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,2,8,9,10,1]=>[10,6,1,2,3,4,5,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,4,5,6,7,1,8,9]=>[8,1,2,3,4,5,6,7,10,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[9,8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,9,8,7]=>[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,4,5,6,7,8,1]=>[9,1,2,3,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[4,3,5,6,7,8,9,1,2]=>[1,9,3,2,4,5,6,7,8]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,2,1]=>[9,8,1,2,3,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,2,9,10,1]=>[10,7,1,2,3,4,5,6,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,2,8,9,10,11,1]=>[11,6,1,2,3,4,5,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,4,5,6,7,8,1,9]=>[9,1,2,3,4,5,6,7,10,8]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[9,10,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,10,8,9]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,1,2]=>[1,10,2,3,4,5,6,7,8,9]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,2,9,10,11,1]=>[11,7,1,2,3,4,5,6,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[10,9,1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,10,9,8]=>[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,4,5,6,7,8,9,1]=>[10,1,2,3,4,5,6,7,9,8]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,2,1]=>[10,9,1,2,3,4,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[]=>[]=>[]=>.
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[7,8,6,5,4,3,2,1,9]=>[8,7,6,5,4,3,1,2,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[7,6,8,5,4,3,2,1,9]=>[8,7,6,5,4,2,1,3,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[6,7,8,5,4,3,2,1,9]=>[8,7,6,5,4,1,2,3,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[7,6,5,8,4,3,2,1,9]=>[8,7,6,5,3,2,1,4,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,8,2,1,9]=>[8,7,5,4,3,2,1,6,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,2,8,1,9]=>[8,6,5,4,3,2,1,7,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[5,4,6,3,7,2,8,1,9]=>[8,6,4,2,1,3,5,7,9]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[8,2,3,4,5,6,7,1,9]=>[8,1,2,3,4,5,7,6,9]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,1,9]=>[8,2,1,3,4,5,6,7,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1,9]=>[8,1,2,3,4,5,6,7,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,1,2,9]=>[1,8,7,6,5,4,3,2,9]=>[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2,9]=>[1,8,2,3,4,5,6,7,9]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,2,1,8,9]=>[7,6,5,4,3,2,1,8,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,4,3,2,7,1,8,9]=>[7,5,4,3,1,2,6,8,9]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8,9]=>[7,1,2,3,4,5,6,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,1,2,8,9]=>[1,7,2,3,4,5,6,8,9]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,1,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,4,3,2,1,7,8,9]=>[6,5,4,3,1,2,7,8,9]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,1,7,8,9]=>[6,1,2,3,4,5,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[8,6,4,2,1,3,5,7,9]=>[5,1,6,2,7,3,8,4,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[4,5,3,2,1,6,7,8,9]=>[5,4,3,1,2,6,7,8,9]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[3,4,2,5,1,6,7,8,9]=>[5,3,1,2,4,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9]=>[5,1,2,3,4,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[3,4,2,1,5,6,7,8,9]=>[4,3,1,2,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[8,2,3,1,4,5,6,7,9]=>[4,1,2,3,5,6,8,7,9]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9]=>[4,1,2,3,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8,9]=>[1,4,2,3,5,6,7,8,9]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9]=>[3,1,2,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1,2,3,4,5,6,7,9]=>[1,2,3,4,5,6,8,7,9]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[7,1,2,3,4,5,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[6,1,2,3,4,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[5,1,2,3,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,3,2,1]=>[9,8,7,6,5,4,3,1,2]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,7,9,6,5,4,3,2,1]=>[9,8,7,6,5,4,2,1,3]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[8,7,6,9,5,4,3,2,1]=>[9,8,7,6,5,3,2,1,4]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,9,4,3,2,1]=>[9,8,7,6,4,3,2,1,5]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,9,3,2,1]=>[9,8,7,5,4,3,2,1,6]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,9,2,1]=>[9,8,6,5,4,3,2,1,7]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,9,1]=>[9,7,6,5,4,3,2,1,8]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,10,8,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,3,1,2]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[7,8,9,6,5,4,3,2,1]=>[9,8,7,6,5,4,1,2,3]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[9,8,10,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,2,1,3]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[9,8,7,10,6,5,4,3,2,1]=>[10,9,8,7,6,5,3,2,1,4]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,10,5,4,3,2,1]=>[10,9,8,7,6,4,3,2,1,5]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,10,4,3,2,1]=>[10,9,8,7,5,4,3,2,1,6]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,10,3,2,1]=>[10,9,8,6,5,4,3,2,1,7]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,10,2,1]=>[10,9,7,6,5,4,3,2,1,8]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,2,1,9]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,10,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[10,11,9,8,7,6,5,4,3,2,1]=>[11,10,9,8,7,6,5,4,3,1,2]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[8,9,10,7,6,5,4,3,2,1]=>[10,9,8,7,6,5,4,1,2,3]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[7,6,8,9,5,4,3,2,1]=>[9,8,7,6,5,2,1,3,4]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,5,4,3,2,1]=>[9,8,7,6,5,1,2,3,4]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,1,2,10]=>[1,9,8,7,6,5,4,3,2,10]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,9,8,7,6,5,4,3,2,11,1]=>[11,9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,9,8,7,6,5,4,3,2,1,11]=>[10,9,8,7,6,5,4,3,2,1,11]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,6,5,4,3,2,1]=>[10,9,8,7,6,5,1,2,3,4]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,4,3,2,1]=>[9,8,7,6,1,2,3,4,5]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,5,4,3,2,1]=>[10,9,8,7,6,1,2,3,4,5]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,2,8,9,1]=>[9,6,5,4,3,2,1,7,8]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,3,2,1]=>[9,8,7,1,2,3,4,5,6]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,7,8,9,1]=>[9,5,4,3,2,1,6,7,8]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,10,4,3,2,1]=>[10,9,8,7,1,2,3,4,5,6]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,6,5,4,3,2,9,10,1]=>[10,7,6,5,4,3,2,1,8,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[9,7,8,6,5,4,3,2,1]=>[9,8,7,6,5,4,1,3,2]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,2,3,1]=>[9,1,8,7,6,5,4,3,2]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[8,9,6,7,4,5,2,3,1]=>[9,1,8,2,7,3,6,4,5]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,2,3,1]=>[9,1,8,2,3,4,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,2,3,4,1]=>[9,1,2,8,3,4,5,6,7]=>[[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[9,8,2,3,4,5,6,7,1]=>[9,1,2,3,4,5,8,7,6]=>[[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[8,9,2,3,4,5,6,7,1]=>[9,1,2,3,4,5,8,6,7]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,3,1,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,3,1,2]=>[1,9,8,7,6,5,4,2,3]=>[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[9,7,8,6,5,4,3,1,2]=>[1,9,8,7,6,5,2,4,3]=>[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,4,1,2]=>[1,9,2,8,7,6,5,4,3]=>[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[9,8,3,4,5,6,7,1,2]=>[1,9,2,3,4,5,8,7,6]=>[.,[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,5,6,7,8,1,2]=>[1,9,2,3,4,5,6,8,7]=>[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,1,2,3]=>[1,2,9,8,7,6,5,4,3]=>[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,1,2,3]=>[1,2,9,3,4,5,6,7,8]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,1,2,3,4]=>[1,2,3,9,8,7,6,5,4]=>[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,1,2,3,4]=>[1,2,3,9,4,5,6,7,8]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,1,2,3,4,5]=>[1,2,3,4,9,8,7,6,5]=>[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[9,6,7,8,1,2,3,4,5]=>[1,2,3,4,9,5,6,8,7]=>[.,[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,1,2,3,4,5]=>[1,2,3,4,9,5,6,7,8]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[9,8,7,1,2,3,4,5,6]=>[1,2,3,4,5,9,8,7,6]=>[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[9,7,8,1,2,3,4,5,6]=>[1,2,3,4,5,9,6,8,7]=>[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,8,9,1,2,3,4,5,6]=>[1,2,3,4,5,9,6,7,8]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,7,8,9,10,3,2,1]=>[10,9,8,1,2,3,4,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,2,3,1]=>[10,1,9,8,7,6,5,4,3,2]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[10,8,9,6,7,4,5,2,3,1]=>[10,1,9,2,8,3,7,4,6,5]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,10,2,3,4,1]=>[10,1,2,9,3,4,5,6,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,2,3,4,5,1]=>[10,1,2,3,9,4,5,6,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[10,9,2,3,4,5,6,7,8,1]=>[10,1,2,3,4,5,6,9,8,7]=>[[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,3,1,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,10,8,7,6,5,4,3,1,2]=>[1,10,9,8,7,6,5,4,2,3]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[10,3,4,5,6,7,8,9,1,2]=>[1,10,2,3,4,5,6,7,9,8]=>[.,[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,1,2,3]=>[1,2,10,9,8,7,6,5,4,3]=>[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,7,8,9,10,1,2,3]=>[1,2,10,3,4,5,6,7,8,9]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,1,2,3,4]=>[1,2,3,10,9,8,7,6,5,4]=>[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,10,1,2,3,4]=>[1,2,3,10,4,5,6,7,8,9]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,1,2,3,4,5]=>[1,2,3,4,10,9,8,7,6,5]=>[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[10,6,7,8,9,1,2,3,4,5]=>[1,2,3,4,10,5,6,7,9,8]=>[.,[.,[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,1,2,3,4,5]=>[1,2,3,4,10,5,6,7,8,9]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,1,2,3,4,5,6]=>[1,2,3,4,5,10,9,8,7,6]=>[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[10,7,8,9,1,2,3,4,5,6]=>[1,2,3,4,5,10,6,7,9,8]=>[.,[.,[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,1,2,3,4,5,6]=>[1,2,3,4,5,10,6,7,8,9]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[10,9,8,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,10,9,8,7]=>[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[8,9,10,1,2,3,4,5,6,7]=>[1,2,3,4,5,6,10,7,8,9]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,2,1,3]=>[8,1,9,7,6,5,4,3,2]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,2,1,8]=>[8,7,6,5,4,3,1,9,2]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,2,1,3]=>[9,1,10,8,7,6,5,4,3,2]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,2,3,1,4]=>[8,1,2,9,7,6,5,4,3]=>[[.,.],[.,[[[[[[.,.],.],.],.],.],.]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,3,4,2,1,5]=>[8,7,1,2,9,6,5,4,3]=>[[[.,.],.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,5,4,3,2,1,9]=>[9,8,7,6,5,4,3,1,10,2]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,6,4,3,2,1,7,8,9,10]=>[6,5,4,3,1,2,7,8,9,10]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[6,7,5,4,3,2,1,8,9,10,11]=>[7,6,5,4,3,1,2,8,9,10,11]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[6,7,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,1,2,8,9,10]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,10,9,8,7,6,5,4,3,1,2]=>[1,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,7,9,6,5,4,3,1,2]=>[1,9,8,7,6,5,3,2,4]=>[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[8,9,7,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,3,1,2,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9,10]=>[3,1,2,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[9,8,10,7,6,5,4,3,1,2]=>[1,10,9,8,7,6,5,3,2,4]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[9,6,5,4,3,2,1,7,8]=>[7,6,5,4,3,1,2,9,8]=>[[[[[[.,.],.],.],.],.],[.,[[.,.],.]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1,10]=>[9,1,2,3,4,5,6,7,8,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,1,2,3,4,5,6,7,8,10]=>[1,2,3,4,5,6,7,9,8,10]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[10,1,2,3,4,5,6,7,8,9,11]=>[1,2,3,4,5,6,7,8,10,9,11]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9,10]=>[4,1,2,3,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9,10]=>[5,1,2,3,4,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,1,7,8,9,10]=>[6,1,2,3,4,5,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8,9,10]=>[7,1,2,3,4,5,6,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1,9,10]=>[8,1,2,3,4,5,6,7,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,6,5,4,3,2,9,1,10]=>[9,7,6,5,4,3,2,1,8,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,2,1,3]=>[8,1,9,2,3,4,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[7,8,9,2,1,3,4,5,6]=>[5,1,2,3,4,9,6,7,8]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[7,8,6,5,4,3,2,9,1]=>[9,7,6,5,4,3,1,2,8]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,9,1,2]=>[1,9,7,6,5,4,3,2,8]=>[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[7,6,5,4,3,2,1,8,9,10]=>[7,6,5,4,3,2,1,8,9,10]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[8,9,2,3,4,5,1,6,7]=>[7,1,2,3,4,5,9,6,8]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[7,8,9,2,3,1,4,5,6]=>[6,1,2,3,4,9,5,7,8]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[6,5,7,8,9,1,2,3,4]=>[1,2,3,9,5,4,6,7,8]=>[.,[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[8,7,9,1,2,3,4,5,6]=>[1,2,3,4,5,9,7,6,8]=>[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[8,1,2,3,4,5,6,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[7,6,8,9,1,2,3,4,5]=>[1,2,3,4,9,6,5,7,8]=>[.,[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[7,1,2,3,4,5,6,8,9,10]=>[1,2,3,4,5,7,6,8,9,10]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[6,1,2,3,4,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[5,4,6,7,8,9,1,2,3]=>[1,2,9,4,3,5,6,7,8]=>[.,[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[5,1,2,3,4,6,7,8,9,10]=>[1,2,3,5,4,6,7,8,9,10]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[8,7,9,6,5,4,3,2,1,10]=>[9,8,7,6,5,4,2,1,3,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[8,7,6,9,5,4,3,2,1,10]=>[9,8,7,6,5,3,2,1,4,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,6,5,4,9,3,2,1,10]=>[9,8,7,5,4,3,2,1,6,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,6,5,4,3,9,2,1,10]=>[9,8,6,5,4,3,2,1,7,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,6,5,4,3,2,1,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[6,5,7,4,8,3,9,2,10,1]=>[10,8,6,4,2,1,3,5,7,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[10,8,6,4,2,1,3,5,7,9]=>[6,1,7,2,8,3,9,4,10,5]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>[12,10,8,6,4,2,1,3,5,7,9,11]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,11,1,2]=>[1,11,2,3,4,5,6,7,8,9,10]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[10,7,6,5,4,3,2,1,8,9]=>[8,7,6,5,4,3,1,2,10,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[[.,.],.]]]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,1,11]=>[10,1,2,3,4,5,6,7,8,9,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,11,1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,11,9,10]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,4,3,2,1,7,8,9,10]=>[6,5,4,3,2,1,7,8,9,10]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[5,4,3,2,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[4,3,2,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[11,2,3,4,5,6,7,8,9,1,10]=>[10,1,2,3,4,5,6,7,8,11,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[11,9,8,7,6,5,4,3,2,1,10]=>[10,9,8,7,6,5,4,3,1,11,2]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,3,2,1,4]=>[8,7,1,9,2,3,4,5,6]=>[[[.,.],.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,1,2,10]=>[1,9,2,3,4,5,6,7,8,10]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]=>[11,10,1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,11,10,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,4,6,3,2,1]=>[9,8,7,5,1,6,4,3,2]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[7,8,2,3,4,5,6,9,1]=>[9,1,2,3,4,7,5,6,8]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,5,6,7,2,1,8]=>[8,7,1,2,3,4,5,9,6]=>[[[.,.],.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,5,6,7,1,2,8]=>[1,8,2,3,4,5,6,9,7]=>[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,2,3,4,1,5]=>[8,1,2,3,9,4,5,6,7]=>[[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[8,9,7,6,5,4,3,2,10,1]=>[10,8,7,6,5,4,3,1,2,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[5,6,4,7,3,8,2,9,1]=>[9,7,5,3,1,2,4,6,8]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,2,3,1,4]=>[8,1,2,9,3,4,5,6,7]=>[[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[9,2,3,4,5,6,7,8,1,10]=>[9,1,2,3,4,5,6,8,7,10]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[11,12,1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,12,10,11]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,11,2,1]=>[11,10,1,2,3,4,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[11,3,4,5,6,7,8,9,10,1,2]=>[1,11,2,3,4,5,6,7,8,10,9]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[7,8,9,2,3,4,5,1,6]=>[8,1,2,3,4,9,5,6,7]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,0,1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,2,11,1]=>[11,9,1,2,3,4,5,6,7,8,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[5,6,4,7,3,8,2,9,1,10]=>[9,7,5,3,1,2,4,6,8,10]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[9,7,5,3,1,2,4,6,8]=>[1,6,2,7,3,8,4,9,5]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[12,10,9,8,7,6,5,4,3,2,1,11]=>[11,10,9,8,7,6,5,4,3,1,12,2]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[[.,.],.]]
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
Map
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.