Identifier
Mp00031:
Dyck paths
—to 312-avoiding permutation⟶
Permutations
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00235: Permutations —descent views to invisible inversion bottoms⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-3
[1,0]=>[1]=>[1]=>[.,.]
[1,0,1,0]=>[1,2]=>[1,2]=>[.,[.,.]]
[1,1,0,0]=>[2,1]=>[2,1]=>[[.,.],.]
[1,0,1,0,1,0]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[1,0,1,1,0,0]=>[1,3,2]=>[1,3,2]=>[.,[[.,.],.]]
[1,1,0,0,1,0]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[1,1,0,1,0,0]=>[2,3,1]=>[3,2,1]=>[[[.,.],.],.]
[1,1,1,0,0,0]=>[3,2,1]=>[2,3,1]=>[[.,[.,.]],.]
[1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[1,2,4,3]=>[.,[.,[[.,.],.]]]
[1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[1,3,2,4]=>[.,[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[1,4,3,2]=>[.,[[[.,.],.],.]]
[1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[1,3,4,2]=>[.,[[.,[.,.]],.]]
[1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[2,1,4,3]=>[[.,.],[[.,.],.]]
[1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[3,2,4,1]=>[[[.,.],[.,.]],.]
[1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[1,1,1,0,1,0,0,0]=>[3,4,2,1]=>[2,4,3,1]=>[[.,[[.,.],.]],.]
[1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]]
[1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[1,2,4,5,3]=>[.,[.,[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[1,5,3,4,2]=>[.,[[[.,.],[.,.]],.]]
[1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[1,4,3,5,2]=>[.,[[[.,.],[.,.]],.]]
[1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[1,0,1,1,1,0,1,0,0,0]=>[1,4,5,3,2]=>[1,3,5,4,2]=>[.,[[.,[[.,.],.]],.]]
[1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[1,3,4,5,2]=>[.,[[.,[.,[.,.]]],.]]
[1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[2,1,5,4,3]=>[[.,.],[[[.,.],.],.]]
[1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[2,1,4,5,3]=>[[.,.],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]
[1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>[3,2,5,4,1]=>[[[.,.],[[.,.],.]],.]
[1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]
[1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[2,3,1,5,4]=>[[.,[.,.]],[[.,.],.]]
[1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]
[1,1,1,0,1,0,0,0,1,0]=>[3,4,2,1,5]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.]
[1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]
[1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[5,3,4,2,1]=>[[[[.,.],[.,.]],.],.]
[1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>[2,5,4,3,1]=>[[.,[[[.,.],.],.]],.]
[1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
[1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[.,[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>[.,[.,[.,[[[.,.],.],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[1,2,3,5,6,4]=>[.,[.,[.,[[.,[.,.]],.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[.,[.,[[.,.],[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>[.,[.,[[[.,.],.],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>[.,[.,[[[.,.],[.,.]],.]]]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[1,2,5,4,6,3]=>[.,[.,[[[.,.],[.,.]],.]]]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[1,2,4,5,3,6]=>[.,[.,[[.,[.,.]],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[1,2,6,5,4,3]=>[.,[.,[[[[.,.],.],.],.]]]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,4,3]=>[1,2,4,6,5,3]=>[.,[.,[[.,[[.,.],.]],.]]]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[1,2,4,5,6,3]=>[.,[.,[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>[.,[[.,.],[[[.,.],.],.]]]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[1,3,2,5,6,4]=>[.,[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>[.,[[[.,.],.],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>[.,[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>[.,[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[1,5,3,4,6,2]=>[.,[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[1,4,3,5,2,6]=>[.,[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[1,6,3,5,4,2]=>[.,[[[.,.],[[.,.],.]],.]]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,4,2]=>[1,4,3,6,5,2]=>[.,[[[.,.],[[.,.],.]],.]]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[1,4,3,5,6,2]=>[.,[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[1,3,4,2,5,6]=>[.,[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[1,3,4,2,6,5]=>[.,[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[1,5,4,3,2,6]=>[.,[[[[.,.],.],.],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[1,6,4,3,5,2]=>[.,[[[[.,.],.],[.,.]],.]]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[1,5,4,3,6,2]=>[.,[[[[.,.],.],[.,.]],.]]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,3,2,6]=>[1,3,5,4,2,6]=>[.,[[.,[[.,.],.]],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,3,6,2]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,3,2]=>[1,3,6,4,5,2]=>[.,[[.,[[.,.],[.,.]]],.]]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,5,3,2]=>[1,3,5,4,6,2]=>[.,[[.,[[.,.],[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[1,3,4,5,2,6]=>[.,[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[1,6,4,5,3,2]=>[.,[[[[.,.],[.,.]],.],.]]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,4,6,3,2]=>[1,3,6,5,4,2]=>[.,[[.,[[[.,.],.],.]],.]]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,4,3,2]=>[1,3,4,6,5,2]=>[.,[[.,[.,[[.,.],.]]],.]]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[1,3,4,5,6,2]=>[.,[[.,[.,[.,[.,.]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>[[.,.],[.,[[[.,.],.],.]]]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[2,1,3,5,6,4]=>[[.,.],[.,[[.,[.,.]],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>[[.,.],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>[[.,.],[[[.,.],[.,.]],.]]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[2,1,5,4,6,3]=>[[.,.],[[[.,.],[.,.]],.]]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[2,1,4,5,3,6]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[2,1,6,5,4,3]=>[[.,.],[[[[.,.],.],.],.]]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,4,3]=>[2,1,4,6,5,3]=>[[.,.],[[.,[[.,.],.]],.]]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[2,1,4,5,6,3]=>[[.,.],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>[[[.,.],.],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>[[[.,.],.],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[3,2,1,5,6,4]=>[[[.,.],.],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>[[[.,.],[.,.]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[5,2,3,4,6,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[4,2,3,5,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[6,2,3,5,4,1]=>[[[.,.],[.,[[.,.],.]]],.]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>[4,2,3,6,5,1]=>[[[.,.],[.,[[.,.],.]]],.]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[4,2,3,5,6,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[3,2,4,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[3,2,4,1,6,5]=>[[[.,.],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[5,2,4,3,1,6]=>[[[.,.],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[6,2,4,3,5,1]=>[[[.,.],[[.,.],[.,.]]],.]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[5,2,4,3,6,1]=>[[[.,.],[[.,.],[.,.]]],.]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,3,1,6]=>[3,2,5,4,1,6]=>[[[.,.],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>[3,2,6,4,5,1]=>[[[.,.],[[.,.],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>[3,2,5,4,6,1]=>[[[.,.],[[.,.],[.,.]]],.]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[3,2,4,5,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[6,2,4,5,3,1]=>[[[.,.],[[.,[.,.]],.]],.]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>[3,2,6,5,4,1]=>[[[.,.],[[[.,.],.],.]],.]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>[3,2,4,6,5,1]=>[[[.,.],[.,[[.,.],.]]],.]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[3,2,4,5,6,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[2,3,1,4,6,5]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[2,3,1,5,4,6]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[2,3,1,6,5,4]=>[[.,[.,.]],[[[.,.],.],.]]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[2,3,1,5,6,4]=>[[.,[.,.]],[[.,[.,.]],.]]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[4,3,2,1,6,5]=>[[[[.,.],.],.],[[.,.],.]]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[5,3,2,4,1,6]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],.]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[5,3,2,4,6,1]=>[[[[.,.],.],[.,[.,.]]],.]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[4,3,2,5,1,6]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>[4,3,2,6,5,1]=>[[[[.,.],.],[[.,.],.]],.]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[4,3,2,5,6,1]=>[[[[.,.],.],[.,[.,.]]],.]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,2,1,5,6]=>[2,4,3,1,5,6]=>[[.,[[.,.],.]],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2,1,6,5]=>[2,4,3,1,6,5]=>[[.,[[.,.],.]],[[.,.],.]]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,2,5,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>[5,4,3,2,6,1]=>[[[[[.,.],.],.],[.,.]],.]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,2,1,6]=>[2,5,3,4,1,6]=>[[.,[[.,.],[.,.]]],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>[2,6,3,4,5,1]=>[[.,[[.,.],[.,[.,.]]]],.]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>[2,5,3,4,6,1]=>[[.,[[.,.],[.,[.,.]]]],.]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,4,2,1,6]=>[2,4,3,5,1,6]=>[[.,[[.,.],[.,.]]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>[6,4,3,5,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>[2,6,3,5,4,1]=>[[.,[[.,.],[[.,.],.]]],.]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>[2,4,3,6,5,1]=>[[.,[[.,.],[[.,.],.]]],.]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]=>[2,4,3,5,6,1]=>[[.,[[.,.],[.,[.,.]]]],.]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[2,3,4,1,6,5]=>[[.,[.,[.,.]]],[[.,.],.]]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[5,3,4,2,1,6]=>[[[[.,.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[6,3,4,2,5,1]=>[[[[.,.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[5,3,4,2,6,1]=>[[[[.,.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,3,5,2,1,6]=>[2,5,4,3,1,6]=>[[.,[[[.,.],.],.]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[2,6,4,3,5,1]=>[[.,[[[.,.],.],[.,.]]],.]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>[2,5,4,3,6,1]=>[[.,[[[.,.],.],[.,.]]],.]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,3,2,1,6]=>[2,3,5,4,1,6]=>[[.,[.,[[.,.],.]]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>[6,3,5,4,2,1]=>[[[[.,.],[[.,.],.]],.],.]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>[2,6,5,4,3,1]=>[[.,[[[[.,.],.],.],.]],.]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>[2,3,6,4,5,1]=>[[.,[.,[[.,.],[.,.]]]],.]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>[2,3,5,4,6,1]=>[[.,[.,[[.,.],[.,.]]]],.]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[6,3,4,5,2,1]=>[[[[.,.],[.,[.,.]]],.],.]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>[2,6,4,5,3,1]=>[[.,[[[.,.],[.,.]],.]],.]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>[2,3,6,5,4,1]=>[[.,[.,[[[.,.],.],.]]],.]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>[2,3,4,6,5,1]=>[[.,[.,[.,[[.,.],.]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[[.,[.,[.,[.,[.,.]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[1,2,3,4,6,7,5]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[1,2,3,6,5,7,4]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[1,2,3,5,6,4,7]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[1,2,3,7,6,5,4]=>[.,[.,[.,[[[[.,.],.],.],.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,5,4]=>[1,2,3,5,7,6,4]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>[1,2,3,5,6,7,4]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>[.,[.,[[.,.],[[[.,.],.],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[1,2,4,3,6,7,5]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>[.,[.,[[[.,.],.],[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[1,2,6,4,5,7,3]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[1,2,5,4,6,3,7]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>[1,2,7,4,6,5,3]=>[.,[.,[[[.,.],[[.,.],.]],.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,5,3]=>[1,2,5,4,7,6,3]=>[.,[.,[[[.,.],[[.,.],.]],.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[1,2,5,4,6,7,3]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[1,2,4,5,3,6,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[1,2,4,5,3,7,6]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[1,2,6,5,4,3,7]=>[.,[.,[[[[.,.],.],.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[1,2,7,5,4,6,3]=>[.,[.,[[[[.,.],.],[.,.]],.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[1,2,6,5,4,7,3]=>[.,[.,[[[[.,.],.],[.,.]],.]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,4,3,7]=>[1,2,4,6,5,3,7]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,4,7,3]=>[1,2,7,6,5,4,3]=>[.,[.,[[[[[.,.],.],.],.],.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,4,3]=>[1,2,4,7,5,6,3]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,6,4,3]=>[1,2,4,6,5,7,3]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[1,2,4,5,6,3,7]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[1,2,7,5,6,4,3]=>[.,[.,[[[[.,.],[.,.]],.],.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,5,7,4,3]=>[1,2,4,7,6,5,3]=>[.,[.,[[.,[[[.,.],.],.]],.]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,5,4,3]=>[1,2,4,5,7,6,3]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[1,2,4,5,6,7,3]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>[.,[[.,.],[.,[[[.,.],.],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[1,3,2,4,6,7,5]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]=>[.,[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[1,3,2,6,5,7,4]=>[.,[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[1,3,2,5,6,4,7]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[1,3,2,7,6,5,4]=>[.,[[.,.],[[[[.,.],.],.],.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,5,4]=>[1,3,2,5,7,6,4]=>[.,[[.,.],[[.,[[.,.],.]],.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[1,3,2,5,6,7,4]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]=>[.,[[[.,.],.],[[[.,.],.],.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[1,4,3,2,6,7,5]=>[.,[[[.,.],.],[[.,[.,.]],.]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[1,7,3,4,5,6,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[1,6,3,4,5,7,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[1,5,3,4,6,2,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[1,7,3,4,6,5,2]=>[.,[[[.,.],[.,[[.,.],.]]],.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,5,2]=>[1,5,3,4,7,6,2]=>[.,[[[.,.],[.,[[.,.],.]]],.]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[1,5,3,4,6,7,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[1,4,3,5,2,6,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[1,4,3,5,2,7,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>[1,6,3,5,4,2,7]=>[.,[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[1,7,3,5,4,6,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[1,6,3,5,4,7,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,4,2,7]=>[1,4,3,6,5,2,7]=>[.,[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,4,7,2]=>[1,7,3,6,5,4,2]=>[.,[[[.,.],[[[.,.],.],.]],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,4,2]=>[1,4,3,7,5,6,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,6,4,2]=>[1,4,3,6,5,7,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[1,4,3,5,6,2,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[1,7,3,5,6,4,2]=>[.,[[[.,.],[[.,[.,.]],.]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,5,7,4,2]=>[1,4,3,7,6,5,2]=>[.,[[[.,.],[[[.,.],.],.]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,5,4,2]=>[1,4,3,5,7,6,2]=>[.,[[[.,.],[.,[[.,.],.]]],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[1,4,3,5,6,7,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[1,3,4,2,5,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[1,3,4,2,5,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[1,3,4,2,6,5,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[1,3,4,2,7,6,5]=>[.,[[.,[.,.]],[[[.,.],.],.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[1,3,4,2,6,7,5]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[1,5,4,3,2,6,7]=>[.,[[[[.,.],.],.],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[1,5,4,3,2,7,6]=>[.,[[[[.,.],.],.],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[1,6,4,3,5,2,7]=>[.,[[[[.,.],.],[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[1,7,4,3,5,6,2]=>[.,[[[[.,.],.],[.,[.,.]]],.]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[1,6,4,3,5,7,2]=>[.,[[[[.,.],.],[.,[.,.]]],.]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[1,5,4,3,6,2,7]=>[.,[[[[.,.],.],[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>[1,7,4,3,6,5,2]=>[.,[[[[.,.],.],[[.,.],.]],.]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,6,7,5,2]=>[1,5,4,3,7,6,2]=>[.,[[[[.,.],.],[[.,.],.]],.]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[1,5,4,3,6,7,2]=>[.,[[[[.,.],.],[.,[.,.]]],.]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,3,2,6,7]=>[1,3,5,4,2,6,7]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,3,2,7,6]=>[1,3,5,4,2,7,6]=>[.,[[.,[[.,.],.]],[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,3,6,2,7]=>[1,6,5,4,3,2,7]=>[.,[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,3,6,7,2]=>[1,7,5,4,3,6,2]=>[.,[[[[[.,.],.],.],[.,.]],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,3,7,6,2]=>[1,6,5,4,3,7,2]=>[.,[[[[[.,.],.],.],[.,.]],.]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,3,2,7]=>[1,3,6,4,5,2,7]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,3,7,2]=>[1,7,6,4,5,3,2]=>[.,[[[[[.,.],.],[.,.]],.],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,3,2]=>[1,3,7,4,5,6,2]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,6,3,2]=>[1,3,6,4,5,7,2]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,5,3,2,7]=>[1,3,5,4,6,2,7]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,5,3,7,2]=>[1,7,5,4,6,3,2]=>[.,[[[[[.,.],.],[.,.]],.],.]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,5,7,3,2]=>[1,3,7,4,6,5,2]=>[.,[[.,[[.,.],[[.,.],.]]],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,5,3,2]=>[1,3,5,4,7,6,2]=>[.,[[.,[[.,.],[[.,.],.]]],.]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,6,5,3,2]=>[1,3,5,4,6,7,2]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[1,3,4,5,2,6,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[1,3,4,5,2,7,6]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[1,6,4,5,3,2,7]=>[.,[[[[.,.],[.,.]],.],[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[1,7,4,5,3,6,2]=>[.,[[[[.,.],[.,.]],[.,.]],.]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[1,6,4,5,3,7,2]=>[.,[[[[.,.],[.,.]],[.,.]],.]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,4,6,3,2,7]=>[1,3,6,5,4,2,7]=>[.,[[.,[[[.,.],.],.]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,4,6,3,7,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,4,6,7,3,2]=>[1,3,7,5,4,6,2]=>[.,[[.,[[[.,.],.],[.,.]]],.]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,4,7,6,3,2]=>[1,3,6,5,4,7,2]=>[.,[[.,[[[.,.],.],[.,.]]],.]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,4,3,2,7]=>[1,3,4,6,5,2,7]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,4,3,7,2]=>[1,7,4,6,5,3,2]=>[.,[[[[.,.],[[.,.],.]],.],.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,4,7,3,2]=>[1,3,7,6,5,4,2]=>[.,[[.,[[[[.,.],.],.],.]],.]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,4,3,2]=>[1,3,4,7,5,6,2]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,6,4,3,2]=>[1,3,4,6,5,7,2]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[1,3,4,5,6,2,7]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[1,7,4,5,6,3,2]=>[.,[[[[.,.],[.,[.,.]]],.],.]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,5,4,7,3,2]=>[1,3,7,5,6,4,2]=>[.,[[.,[[[.,.],[.,.]],.]],.]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,5,7,4,3,2]=>[1,3,4,7,6,5,2]=>[.,[[.,[.,[[[.,.],.],.]]],.]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,5,4,3,2]=>[1,3,4,5,7,6,2]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[1,3,4,5,6,7,2]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[2,1,3,4,6,7,5]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[2,1,3,6,5,7,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[2,1,3,5,6,4,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[2,1,3,7,6,5,4]=>[[.,.],[.,[[[[.,.],.],.],.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,5,4]=>[2,1,3,5,7,6,4]=>[[.,.],[.,[[.,[[.,.],.]],.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[2,1,3,5,6,7,4]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[2,1,4,3,6,7,5]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[2,1,7,4,5,6,3]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[2,1,6,4,5,7,3]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[2,1,5,4,6,3,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>[2,1,7,4,6,5,3]=>[[.,.],[[[.,.],[[.,.],.]],.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,5,3]=>[2,1,5,4,7,6,3]=>[[.,.],[[[.,.],[[.,.],.]],.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[2,1,5,4,6,7,3]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[2,1,4,5,3,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[2,1,4,5,3,7,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>[2,1,6,5,4,3,7]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[2,1,7,5,4,6,3]=>[[.,.],[[[[.,.],.],[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[2,1,6,5,4,7,3]=>[[.,.],[[[[.,.],.],[.,.]],.]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,4,3,7]=>[2,1,4,6,5,3,7]=>[[.,.],[[.,[[.,.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,4,7,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,4,3]=>[2,1,4,7,5,6,3]=>[[.,.],[[.,[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,6,4,3]=>[2,1,4,6,5,7,3]=>[[.,.],[[.,[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[2,1,4,5,6,3,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[2,1,7,5,6,4,3]=>[[.,.],[[[[.,.],[.,.]],.],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,5,7,4,3]=>[2,1,4,7,6,5,3]=>[[.,.],[[.,[[[.,.],.],.]],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,5,4,3]=>[2,1,4,5,7,6,3]=>[[.,.],[[.,[.,[[.,.],.]]],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[2,1,4,5,6,7,3]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[3,2,1,4,6,7,5]=>[[[.,.],.],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[3,2,1,7,5,6,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[3,2,1,6,5,7,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[3,2,1,5,6,4,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,5,4]=>[3,2,1,5,7,6,4]=>[[[.,.],.],[[.,[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[3,2,1,5,6,7,4]=>[[[.,.],.],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[4,2,3,1,5,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[4,2,3,1,7,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[4,2,3,1,6,7,5]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[5,2,3,4,1,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[6,2,3,4,5,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[5,2,3,4,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[7,2,3,4,6,5,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,5,1]=>[5,2,3,4,7,6,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[5,2,3,4,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[4,2,3,5,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[4,2,3,5,1,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[6,2,3,5,4,1,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[7,2,3,5,4,6,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[6,2,3,5,4,7,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,4,1,7]=>[4,2,3,6,5,1,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,4,7,1]=>[7,2,3,6,5,4,1]=>[[[.,.],[.,[[[.,.],.],.]]],.]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,4,1]=>[4,2,3,7,5,6,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,6,4,1]=>[4,2,3,6,5,7,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[4,2,3,5,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[7,2,3,5,6,4,1]=>[[[.,.],[.,[[.,[.,.]],.]]],.]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,5,7,4,1]=>[4,2,3,7,6,5,1]=>[[[.,.],[.,[[[.,.],.],.]]],.]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,5,4,1]=>[4,2,3,5,7,6,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[4,2,3,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>[3,2,4,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[3,2,4,1,5,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[3,2,4,1,6,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[3,2,4,1,7,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[3,2,4,1,6,7,5]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[5,2,4,3,1,6,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[5,2,4,3,1,7,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[6,2,4,3,5,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[7,2,4,3,5,6,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[6,2,4,3,5,7,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[5,2,4,3,6,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[7,2,4,3,6,5,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,6,7,5,1]=>[5,2,4,3,7,6,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[5,2,4,3,6,7,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,3,1,6,7]=>[3,2,5,4,1,6,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,3,1,7,6]=>[3,2,5,4,1,7,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,3,6,1,7]=>[6,2,5,4,3,1,7]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,3,6,7,1]=>[7,2,5,4,3,6,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,3,7,6,1]=>[6,2,5,4,3,7,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,3,1,7]=>[3,2,6,4,5,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,3,7,1]=>[7,2,6,4,5,3,1]=>[[[.,.],[[[.,.],[.,.]],.]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,3,1]=>[3,2,7,4,5,6,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,6,3,1]=>[3,2,6,4,5,7,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,5,3,1,7]=>[3,2,5,4,6,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,5,3,7,1]=>[7,2,5,4,6,3,1]=>[[[.,.],[[[.,.],[.,.]],.]],.]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,5,7,3,1]=>[3,2,7,4,6,5,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,5,3,1]=>[3,2,5,4,7,6,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,6,5,3,1]=>[3,2,5,4,6,7,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[3,2,4,5,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[3,2,4,5,1,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[6,2,4,5,3,1,7]=>[[[.,.],[[.,[.,.]],.]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[7,2,4,5,3,6,1]=>[[[.,.],[[.,[.,.]],[.,.]]],.]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[6,2,4,5,3,7,1]=>[[[.,.],[[.,[.,.]],[.,.]]],.]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,4,6,3,1,7]=>[3,2,6,5,4,1,7]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,4,6,3,7,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,4,6,7,3,1]=>[3,2,7,5,4,6,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,4,7,6,3,1]=>[3,2,6,5,4,7,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,4,3,1,7]=>[3,2,4,6,5,1,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,4,3,7,1]=>[7,2,4,6,5,3,1]=>[[[.,.],[[.,[[.,.],.]],.]],.]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,4,7,3,1]=>[3,2,7,6,5,4,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,4,3,1]=>[3,2,4,7,5,6,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,6,4,3,1]=>[3,2,4,6,5,7,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[3,2,4,5,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[7,2,4,5,6,3,1]=>[[[.,.],[[.,[.,[.,.]]],.]],.]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,5,4,7,3,1]=>[3,2,7,5,6,4,1]=>[[[.,.],[[[.,.],[.,.]],.]],.]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,5,7,4,3,1]=>[3,2,4,7,6,5,1]=>[[[.,.],[.,[[[.,.],.],.]]],.]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,5,4,3,1]=>[3,2,4,5,7,6,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[3,2,4,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[2,3,1,4,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[2,3,1,4,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[2,3,1,4,7,6,5]=>[[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[2,3,1,4,6,7,5]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[2,3,1,5,4,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[2,3,1,5,4,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[2,3,1,6,5,4,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[2,3,1,7,5,6,4]=>[[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[2,3,1,6,5,7,4]=>[[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[2,3,1,5,6,4,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[2,3,1,7,6,5,4]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,6,7,5,4]=>[2,3,1,5,7,6,4]=>[[.,[.,.]],[[.,[[.,.],.]],.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[2,3,1,5,6,7,4]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[4,3,2,1,5,7,6]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>[4,3,2,1,6,5,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[4,3,2,1,6,7,5]=>[[[[.,.],.],.],[[.,[.,.]],.]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[5,3,2,4,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[5,3,2,4,1,7,6]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[6,3,2,4,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[7,3,2,4,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[6,3,2,4,5,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[5,3,2,4,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[7,3,2,4,6,5,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,6,7,5,1]=>[5,3,2,4,7,6,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[5,3,2,4,6,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[4,3,2,5,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[4,3,2,5,1,7,6]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[6,3,2,5,4,1,7]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[7,3,2,5,4,6,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[6,3,2,5,4,7,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,5,6,4,1,7]=>[4,3,2,6,5,1,7]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,5,6,4,7,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,4,1]=>[4,3,2,7,5,6,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,5,7,6,4,1]=>[4,3,2,6,5,7,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[4,3,2,5,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[7,3,2,5,6,4,1]=>[[[[.,.],.],[[.,[.,.]],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,6,5,7,4,1]=>[4,3,2,7,6,5,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,6,7,5,4,1]=>[4,3,2,5,7,6,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[4,3,2,5,6,7,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7]=>[2,4,3,1,5,6,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,2,1,5,7,6]=>[2,4,3,1,5,7,6]=>[[.,[[.,.],.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,2,1,6,5,7]=>[2,4,3,1,6,5,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,2,1,6,7,5]=>[2,4,3,1,7,6,5]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,2,1,7,6,5]=>[2,4,3,1,6,7,5]=>[[.,[[.,.],.]],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,2,5,1,6,7]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,2,5,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,1,7]=>[6,4,3,2,5,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,1]=>[7,4,3,2,5,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,2,5,7,6,1]=>[6,4,3,2,5,7,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,2,6,5,1,7]=>[5,4,3,2,6,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,2,6,5,7,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,2,6,7,5,1]=>[5,4,3,2,7,6,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,2,7,6,5,1]=>[5,4,3,2,6,7,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,2,1,6,7]=>[2,5,3,4,1,6,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,2,1,7,6]=>[2,5,3,4,1,7,6]=>[[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,2,6,1,7]=>[6,5,3,4,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,2,6,7,1]=>[7,5,3,4,2,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,2,7,6,1]=>[6,5,3,4,2,7,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,2,1,7]=>[2,6,3,4,5,1,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,2,7,1]=>[7,6,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,2,1]=>[2,7,3,4,5,6,1]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,6,2,1]=>[2,6,3,4,5,7,1]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,5,2,1,7]=>[2,5,3,4,6,1,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,5,2,7,1]=>[7,5,3,4,6,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,5,7,2,1]=>[2,7,3,4,6,5,1]=>[[.,[[.,.],[.,[[.,.],.]]]],.]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,5,2,1]=>[2,5,3,4,7,6,1]=>[[.,[[.,.],[.,[[.,.],.]]]],.]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,6,5,2,1]=>[2,5,3,4,6,7,1]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,4,2,1,6,7]=>[2,4,3,5,1,6,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,4,2,1,7,6]=>[2,4,3,5,1,7,6]=>[[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,4,2,6,1,7]=>[6,4,3,5,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,4,2,6,7,1]=>[7,4,3,5,2,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,4,2,7,6,1]=>[6,4,3,5,2,7,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,4,6,2,1,7]=>[2,6,3,5,4,1,7]=>[[.,[[.,.],[[.,.],.]]],[.,.]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,4,6,2,7,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,4,6,7,2,1]=>[2,7,3,5,4,6,1]=>[[.,[[.,.],[[.,.],[.,.]]]],.]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,4,7,6,2,1]=>[2,6,3,5,4,7,1]=>[[.,[[.,.],[[.,.],[.,.]]]],.]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,4,2,1,7]=>[2,4,3,6,5,1,7]=>[[.,[[.,.],[[.,.],.]]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,4,2,7,1]=>[7,4,3,6,5,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,4,7,2,1]=>[2,7,3,6,5,4,1]=>[[.,[[.,.],[[[.,.],.],.]]],.]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,4,2,1]=>[2,4,3,7,5,6,1]=>[[.,[[.,.],[[.,.],[.,.]]]],.]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,6,4,2,1]=>[2,4,3,6,5,7,1]=>[[.,[[.,.],[[.,.],[.,.]]]],.]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,5,4,2,1,7]=>[2,4,3,5,6,1,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,5,4,2,7,1]=>[7,4,3,5,6,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,5,4,7,2,1]=>[2,7,3,5,6,4,1]=>[[.,[[.,.],[[.,[.,.]],.]]],.]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,5,7,4,2,1]=>[2,4,3,7,6,5,1]=>[[.,[[.,.],[[[.,.],.],.]]],.]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,5,4,2,1]=>[2,4,3,5,7,6,1]=>[[.,[[.,.],[.,[[.,.],.]]]],.]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,6,5,4,2,1]=>[2,4,3,5,6,7,1]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[2,3,4,1,5,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[2,3,4,1,6,5,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[2,3,4,1,7,6,5]=>[[.,[.,[.,.]]],[[[.,.],.],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[2,3,4,1,6,7,5]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>[5,3,4,2,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[5,3,4,2,1,7,6]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[6,3,4,2,5,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[7,3,4,2,5,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[6,3,4,2,5,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[5,3,4,2,6,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[7,3,4,2,6,5,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,6,7,5,1]=>[5,3,4,2,7,6,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[5,3,4,2,6,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,3,5,2,1,6,7]=>[2,5,4,3,1,6,7]=>[[.,[[[.,.],.],.]],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,3,5,2,1,7,6]=>[2,5,4,3,1,7,6]=>[[.,[[[.,.],.],.]],[[.,.],.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,3,5,2,6,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,3,5,2,6,7,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,3,5,2,7,6,1]=>[6,5,4,3,2,7,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,3,5,6,2,1,7]=>[2,6,4,3,5,1,7]=>[[.,[[[.,.],.],[.,.]]],[.,.]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,2,7,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,2,1]=>[2,7,4,3,5,6,1]=>[[.,[[[.,.],.],[.,[.,.]]]],.]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,3,5,7,6,2,1]=>[2,6,4,3,5,7,1]=>[[.,[[[.,.],.],[.,[.,.]]]],.]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,3,6,5,2,1,7]=>[2,5,4,3,6,1,7]=>[[.,[[[.,.],.],[.,.]]],[.,.]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,3,6,5,2,7,1]=>[7,5,4,3,6,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,3,6,5,7,2,1]=>[2,7,4,3,6,5,1]=>[[.,[[[.,.],.],[[.,.],.]]],.]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,6,7,5,2,1]=>[2,5,4,3,7,6,1]=>[[.,[[[.,.],.],[[.,.],.]]],.]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3,7,6,5,2,1]=>[2,5,4,3,6,7,1]=>[[.,[[[.,.],.],[.,[.,.]]]],.]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,3,2,1,6,7]=>[2,3,5,4,1,6,7]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,3,2,1,7,6]=>[2,3,5,4,1,7,6]=>[[.,[.,[[.,.],.]]],[[.,.],.]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,3,2,6,1,7]=>[6,3,5,4,2,1,7]=>[[[[.,.],[[.,.],.]],.],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,3,2,6,7,1]=>[7,3,5,4,2,6,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,3,2,7,6,1]=>[6,3,5,4,2,7,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,3,6,2,1,7]=>[2,6,5,4,3,1,7]=>[[.,[[[[.,.],.],.],.]],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,3,6,7,2,1]=>[2,7,5,4,3,6,1]=>[[.,[[[[.,.],.],.],[.,.]]],.]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,3,7,6,2,1]=>[2,6,5,4,3,7,1]=>[[.,[[[[.,.],.],.],[.,.]]],.]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,3,2,1,7]=>[2,3,6,4,5,1,7]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,3,2,7,1]=>[7,3,6,4,5,2,1]=>[[[[.,.],[[.,.],[.,.]]],.],.]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,3,7,2,1]=>[2,7,6,4,5,3,1]=>[[.,[[[[.,.],.],[.,.]],.]],.]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[2,3,7,4,5,6,1]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,6,3,2,1]=>[2,3,6,4,5,7,1]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,5,3,2,1,7]=>[2,3,5,4,6,1,7]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,5,3,2,7,1]=>[7,3,5,4,6,2,1]=>[[[[.,.],[[.,.],[.,.]]],.],.]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,5,3,7,2,1]=>[2,7,5,4,6,3,1]=>[[.,[[[[.,.],.],[.,.]],.]],.]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,5,7,3,2,1]=>[2,3,7,4,6,5,1]=>[[.,[.,[[.,.],[[.,.],.]]]],.]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,5,3,2,1]=>[2,3,5,4,7,6,1]=>[[.,[.,[[.,.],[[.,.],.]]]],.]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,6,5,3,2,1]=>[2,3,5,4,6,7,1]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[2,3,4,5,1,7,6]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[6,3,4,5,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[7,3,4,5,2,6,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[6,3,4,5,2,7,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,4,3,6,2,1,7]=>[2,6,4,5,3,1,7]=>[[.,[[[.,.],[.,.]],.]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,4,3,6,2,7,1]=>[7,6,4,5,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[2,7,4,5,3,6,1]=>[[.,[[[.,.],[.,.]],[.,.]]],.]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,4,3,7,6,2,1]=>[2,6,4,5,3,7,1]=>[[.,[[[.,.],[.,.]],[.,.]]],.]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,4,6,3,2,1,7]=>[2,3,6,5,4,1,7]=>[[.,[.,[[[.,.],.],.]]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,4,6,3,2,7,1]=>[7,3,6,5,4,2,1]=>[[[[.,.],[[[.,.],.],.]],.],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[2,7,6,5,4,3,1]=>[[.,[[[[[.,.],.],.],.],.]],.]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1]=>[2,3,7,5,4,6,1]=>[[.,[.,[[[.,.],.],[.,.]]]],.]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,3,2,1]=>[2,3,6,5,4,7,1]=>[[.,[.,[[[.,.],.],[.,.]]]],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,4,3,2,1,7]=>[2,3,4,6,5,1,7]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,4,3,2,7,1]=>[7,3,4,6,5,2,1]=>[[[[.,.],[.,[[.,.],.]]],.],.]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,4,3,7,2,1]=>[2,7,4,6,5,3,1]=>[[.,[[[.,.],[[.,.],.]],.]],.]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,4,7,3,2,1]=>[2,3,7,6,5,4,1]=>[[.,[.,[[[[.,.],.],.],.]]],.]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,4,3,2,1]=>[2,3,4,7,5,6,1]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,6,4,3,2,1]=>[2,3,4,6,5,7,1]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[7,3,4,5,6,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,5,4,3,7,2,1]=>[2,7,4,5,6,3,1]=>[[.,[[[.,.],[.,[.,.]]],.]],.]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,5,4,7,3,2,1]=>[2,3,7,5,6,4,1]=>[[.,[.,[[[.,.],[.,.]],.]]],.]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,5,7,4,3,2,1]=>[2,3,4,7,6,5,1]=>[[.,[.,[.,[[[.,.],.],.]]]],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,5,4,3,2,1]=>[2,3,4,5,7,6,1]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,8,7,6]=>[1,2,3,4,5,7,8,6]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,4,6,7,5,8]=>[1,2,3,4,7,6,5,8]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,6,7,5]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,4,6,8,7,5]=>[1,2,3,4,7,6,8,5]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,4,7,6,5,8]=>[1,2,3,4,6,7,5,8]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,4,7,6,8,5]=>[1,2,3,4,8,7,6,5]=>[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,4,7,8,6,5]=>[1,2,3,4,6,8,7,5]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,8,7,6,5]=>[1,2,3,4,6,7,8,5]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,7,6]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,8,7,6]=>[1,2,3,5,4,7,8,6]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,3,5,6,4,7,8]=>[1,2,3,6,5,4,7,8]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,3,5,6,4,8,7]=>[1,2,3,6,5,4,8,7]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,3,5,6,7,4,8]=>[1,2,3,7,5,6,4,8]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,5,6,7,4]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,3,5,6,8,7,4]=>[1,2,3,7,5,6,8,4]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,3,5,7,6,4,8]=>[1,2,3,6,5,7,4,8]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,3,5,7,6,8,4]=>[1,2,3,8,5,7,6,4]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,3,5,7,8,6,4]=>[1,2,3,6,5,8,7,4]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3,5,8,7,6,4]=>[1,2,3,6,5,7,8,4]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,3,6,5,4,7,8]=>[1,2,3,5,6,4,7,8]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,3,6,5,4,8,7]=>[1,2,3,5,6,4,8,7]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,3,6,5,7,4,8]=>[1,2,3,7,6,5,4,8]=>[.,[.,[.,[[[[.,.],.],.],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,6,5,7,8,4]=>[1,2,3,8,6,5,7,4]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,3,6,5,8,7,4]=>[1,2,3,7,6,5,8,4]=>[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,3,6,7,5,4,8]=>[1,2,3,5,7,6,4,8]=>[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,3,6,7,5,8,4]=>[1,2,3,8,7,6,5,4]=>[.,[.,[.,[[[[[.,.],.],.],.],.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,3,6,7,8,5,4]=>[1,2,3,5,8,6,7,4]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,3,6,8,7,5,4]=>[1,2,3,5,7,6,8,4]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,3,7,6,5,4,8]=>[1,2,3,5,6,7,4,8]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,3,7,6,5,8,4]=>[1,2,3,8,6,7,5,4]=>[.,[.,[.,[[[[.,.],[.,.]],.],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,3,7,6,8,5,4]=>[1,2,3,5,8,7,6,4]=>[.,[.,[.,[[.,[[[.,.],.],.]],.]]]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,3,7,8,6,5,4]=>[1,2,3,5,6,8,7,4]=>[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,8,7,6,5,4]=>[1,2,3,5,6,7,8,4]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,2,4,3,5,7,8,6]=>[1,2,4,3,5,8,7,6]=>[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,2,4,3,5,8,7,6]=>[1,2,4,3,5,7,8,6]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,6,7,5]=>[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,2,4,3,6,8,7,5]=>[1,2,4,3,7,6,8,5]=>[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,2,4,3,7,6,5,8]=>[1,2,4,3,6,7,5,8]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,2,4,3,7,6,8,5]=>[1,2,4,3,8,7,6,5]=>[.,[.,[[.,.],[[[[.,.],.],.],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,8,7,6,5]=>[1,2,4,3,6,7,8,5]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,2,4,5,3,6,7,8]=>[1,2,5,4,3,6,7,8]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,2,4,5,3,6,8,7]=>[1,2,5,4,3,6,8,7]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,2,4,5,3,7,8,6]=>[1,2,5,4,3,8,7,6]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,2,4,5,3,8,7,6]=>[1,2,5,4,3,7,8,6]=>[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,8,3]=>[1,2,8,4,5,6,7,3]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,6,8,7,3]=>[1,2,7,4,5,6,8,3]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,2,4,5,8,7,6,3]=>[1,2,6,4,5,7,8,3]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,2,4,6,7,5,8,3]=>[1,2,8,4,7,6,5,3]=>[.,[.,[[[.,.],[[[.,.],.],.]],.]]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,2,4,6,8,7,5,3]=>[1,2,5,4,7,6,8,3]=>[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,2,4,7,6,5,3,8]=>[1,2,5,4,6,7,3,8]=>[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,2,4,7,6,5,8,3]=>[1,2,8,4,6,7,5,3]=>[.,[.,[[[.,.],[[.,[.,.]],.]],.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,2,4,7,6,8,5,3]=>[1,2,5,4,8,7,6,3]=>[.,[.,[[[.,.],[[[.,.],.],.]],.]]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,2,4,7,8,6,5,3]=>[1,2,5,4,6,8,7,3]=>[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,4,8,7,6,5,3]=>[1,2,5,4,6,7,8,3]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,5,4,3,6,7,8]=>[1,2,4,5,3,6,7,8]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,5,4,3,7,6,8]=>[1,2,4,5,3,7,6,8]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,5,4,3,7,8,6]=>[1,2,4,5,3,8,7,6]=>[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,5,4,3,8,7,6]=>[1,2,4,5,3,7,8,6]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,2,5,4,6,3,7,8]=>[1,2,6,5,4,3,7,8]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,2,5,4,6,7,3,8]=>[1,2,7,5,4,6,3,8]=>[.,[.,[[[[.,.],.],[.,.]],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,2,5,4,6,7,8,3]=>[1,2,8,5,4,6,7,3]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,2,5,4,6,8,7,3]=>[1,2,7,5,4,6,8,3]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,2,5,4,8,7,6,3]=>[1,2,6,5,4,7,8,3]=>[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,2,5,6,4,3,7,8]=>[1,2,4,6,5,3,7,8]=>[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,2,5,6,4,7,3,8]=>[1,2,7,6,5,4,3,8]=>[.,[.,[[[[[.,.],.],.],.],[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,2,5,6,4,7,8,3]=>[1,2,8,6,5,4,7,3]=>[.,[.,[[[[[.,.],.],.],[.,.]],.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,2,5,6,4,8,7,3]=>[1,2,7,6,5,4,8,3]=>[.,[.,[[[[[.,.],.],.],[.,.]],.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,2,5,6,7,4,8,3]=>[1,2,8,7,5,6,4,3]=>[.,[.,[[[[[.,.],.],[.,.]],.],.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,8,4,3]=>[1,2,4,8,5,6,7,3]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,5,6,8,7,4,3]=>[1,2,4,7,5,6,8,3]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,2,5,7,6,4,3,8]=>[1,2,4,6,5,7,3,8]=>[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,2,5,7,6,4,8,3]=>[1,2,8,6,5,7,4,3]=>[.,[.,[[[[[.,.],.],[.,.]],.],.]]]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,5,7,8,6,4,3]=>[1,2,4,6,5,8,7,3]=>[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,6,5,4,3,7,8]=>[1,2,4,5,6,3,7,8]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,6,5,4,3,8,7]=>[1,2,4,5,6,3,8,7]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,6,5,4,7,8,3]=>[1,2,8,5,6,4,7,3]=>[.,[.,[[[[.,.],[.,.]],[.,.]],.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,2,6,5,7,4,8,3]=>[1,2,8,7,6,5,4,3]=>[.,[.,[[[[[[.,.],.],.],.],.],.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,6,5,7,8,4,3]=>[1,2,4,8,6,5,7,3]=>[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,6,5,8,7,4,3]=>[1,2,4,7,6,5,8,3]=>[.,[.,[[.,[[[.,.],.],[.,.]]],.]]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,6,7,5,8,4,3]=>[1,2,4,8,7,6,5,3]=>[.,[.,[[.,[[[[.,.],.],.],.]],.]]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,6,7,8,5,4,3]=>[1,2,4,5,8,6,7,3]=>[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,7,6,5,4,3,8]=>[1,2,4,5,6,7,3,8]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,7,6,5,4,8,3]=>[1,2,8,5,6,7,4,3]=>[.,[.,[[[[.,.],[.,[.,.]]],.],.]]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,7,6,8,5,4,3]=>[1,2,4,5,8,7,6,3]=>[.,[.,[[.,[.,[[[.,.],.],.]]],.]]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,7,8,6,5,4,3]=>[1,2,4,5,6,8,7,3]=>[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,3]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,5,7,8,6]=>[1,3,2,4,5,8,7,6]=>[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,5,8,7,6]=>[1,3,2,4,5,7,8,6]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,3,2,4,6,7,5,8]=>[1,3,2,4,7,6,5,8]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,2,4,6,8,7,5]=>[1,3,2,4,7,6,8,5]=>[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,7,6,5,8]=>[1,3,2,4,6,7,5,8]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,2,4,7,6,8,5]=>[1,3,2,4,8,7,6,5]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,3,2,4,7,8,6,5]=>[1,3,2,4,6,8,7,5]=>[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,8,7,6,5]=>[1,3,2,4,6,7,8,5]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,7,6]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,8,7,6]=>[1,3,2,5,4,7,8,6]=>[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,2,5,6,4,7,8]=>[1,3,2,6,5,4,7,8]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,2,5,6,4,8,7]=>[1,3,2,6,5,4,8,7]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,2,5,6,8,7,4]=>[1,3,2,7,5,6,8,4]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,2,5,7,6,4,8]=>[1,3,2,6,5,7,4,8]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,6,8,4]=>[1,3,2,8,5,7,6,4]=>[.,[[.,.],[[[.,.],[[.,.],.]],.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,2,5,7,8,6,4]=>[1,3,2,6,5,8,7,4]=>[.,[[.,.],[[[.,.],[[.,.],.]],.]]]
[1,0,1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,2,5,8,7,6,4]=>[1,3,2,6,5,7,8,4]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,2,6,5,4,7,8]=>[1,3,2,5,6,4,7,8]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2,6,5,4,8,7]=>[1,3,2,5,6,4,8,7]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,2,6,5,7,4,8]=>[1,3,2,7,6,5,4,8]=>[.,[[.,.],[[[[.,.],.],.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,5,7,8,4]=>[1,3,2,8,6,5,7,4]=>[.,[[.,.],[[[[.,.],.],[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2,6,5,8,7,4]=>[1,3,2,7,6,5,8,4]=>[.,[[.,.],[[[[.,.],.],[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,2,6,7,5,4,8]=>[1,3,2,5,7,6,4,8]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,2,6,7,5,8,4]=>[1,3,2,8,7,6,5,4]=>[.,[[.,.],[[[[[.,.],.],.],.],.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,7,6,5,4,8]=>[1,3,2,5,6,7,4,8]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,3,2,7,6,5,8,4]=>[1,3,2,8,6,7,5,4]=>[.,[[.,.],[[[[.,.],[.,.]],.],.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,3,2,7,6,8,5,4]=>[1,3,2,5,8,7,6,4]=>[.,[[.,.],[[.,[[[.,.],.],.]],.]]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,3,2,7,8,6,5,4]=>[1,3,2,5,6,8,7,4]=>[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,8,7,6,5,4]=>[1,3,2,5,6,7,8,4]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,4,2,5,6,8,7]=>[1,4,3,2,5,6,8,7]=>[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,4,2,5,7,8,6]=>[1,4,3,2,5,8,7,6]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,4,2,5,8,7,6]=>[1,4,3,2,5,7,8,6]=>[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,4,2,6,7,8,5]=>[1,4,3,2,8,6,7,5]=>[.,[[[.,.],.],[[[.,.],[.,.]],.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,4,2,6,8,7,5]=>[1,4,3,2,7,6,8,5]=>[.,[[[.,.],.],[[[.,.],[.,.]],.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,4,2,7,6,5,8]=>[1,4,3,2,6,7,5,8]=>[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,4,2,7,6,8,5]=>[1,4,3,2,8,7,6,5]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,4,2,7,8,6,5]=>[1,4,3,2,6,8,7,5]=>[.,[[[.,.],.],[[.,[[.,.],.]],.]]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,8,7,6,5]=>[1,4,3,2,6,7,8,5]=>[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,5,2,6,7,8]=>[1,5,3,4,2,6,7,8]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,5,2,7,8,6]=>[1,5,3,4,2,8,7,6]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,5,2,8,7,6]=>[1,5,3,4,2,7,8,6]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,6,2,7,8]=>[1,6,3,4,5,2,7,8]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,7,2,8]=>[1,7,3,4,5,6,2,8]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,2]=>[1,8,3,4,5,6,7,2]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,6,8,7,2]=>[1,7,3,4,5,6,8,2]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,5,7,8,6,2]=>[1,6,3,4,5,8,7,2]=>[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,4,6,5,2,8,7]=>[1,5,3,4,6,2,8,7]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,4,6,7,5,8,2]=>[1,8,3,4,7,6,5,2]=>[.,[[[.,.],[.,[[[.,.],.],.]]],.]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,4,7,6,5,8,2]=>[1,8,3,4,6,7,5,2]=>[.,[[[.,.],[.,[[.,[.,.]],.]]],.]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,8,7,6,5,2]=>[1,5,3,4,6,7,8,2]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,5,4,2,6,7,8]=>[1,4,3,5,2,6,7,8]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,5,4,2,7,6,8]=>[1,4,3,5,2,7,6,8]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,3,5,4,6,2,7,8]=>[1,6,3,5,4,2,7,8]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,3,5,4,6,7,2,8]=>[1,7,3,5,4,6,2,8]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,5,4,6,7,8,2]=>[1,8,3,5,4,6,7,2]=>[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,5,4,7,6,8,2]=>[1,8,3,5,4,7,6,2]=>[.,[[[.,.],[[.,.],[[.,.],.]]],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,5,4,7,8,6,2]=>[1,6,3,5,4,8,7,2]=>[.,[[[.,.],[[.,.],[[.,.],.]]],.]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,3,5,6,4,2,7,8]=>[1,4,3,6,5,2,7,8]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,5,6,4,7,2,8]=>[1,7,3,6,5,4,2,8]=>[.,[[[.,.],[[[.,.],.],.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,5,6,4,7,8,2]=>[1,8,3,6,5,4,7,2]=>[.,[[[.,.],[[[.,.],.],[.,.]]],.]]
[1,0,1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,5,6,4,8,7,2]=>[1,7,3,6,5,4,8,2]=>[.,[[[.,.],[[[.,.],.],[.,.]]],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,5,6,7,4,8,2]=>[1,8,3,7,5,6,4,2]=>[.,[[[.,.],[[[.,.],[.,.]],.]],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,8,4,2]=>[1,4,3,8,5,6,7,2]=>[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,3,5,7,6,4,2,8]=>[1,4,3,6,5,7,2,8]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,5,7,6,8,4,2]=>[1,4,3,8,5,7,6,2]=>[.,[[[.,.],[[.,.],[[.,.],.]]],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,5,7,8,6,4,2]=>[1,4,3,6,5,8,7,2]=>[.,[[[.,.],[[.,.],[[.,.],.]]],.]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,5,8,7,6,4,2]=>[1,4,3,6,5,7,8,2]=>[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,3,6,5,4,2,7,8]=>[1,4,3,5,6,2,7,8]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,6,5,7,4,8,2]=>[1,8,3,7,6,5,4,2]=>[.,[[[.,.],[[[[.,.],.],.],.]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,6,5,7,8,4,2]=>[1,4,3,8,6,5,7,2]=>[.,[[[.,.],[[[.,.],.],[.,.]]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,3,6,7,5,4,2,8]=>[1,4,3,5,7,6,2,8]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,6,7,5,8,4,2]=>[1,4,3,8,7,6,5,2]=>[.,[[[.,.],[[[[.,.],.],.],.]],.]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,6,7,8,5,4,2]=>[1,4,3,5,8,6,7,2]=>[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,3,7,6,5,4,2,8]=>[1,4,3,5,6,7,2,8]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,7,6,5,8,4,2]=>[1,4,3,8,6,7,5,2]=>[.,[[[.,.],[[[.,.],[.,.]],.]],.]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,8,7,6,5,4,2]=>[1,4,3,5,6,7,8,2]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,4,3,2,5,6,8,7]=>[1,3,4,2,5,6,8,7]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,4,3,2,5,7,6,8]=>[1,3,4,2,5,7,6,8]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,4,3,2,5,8,7,6]=>[1,3,4,2,5,7,8,6]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,4,3,2,6,5,8,7]=>[1,3,4,2,6,5,8,7]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,4,3,2,6,7,8,5]=>[1,3,4,2,8,6,7,5]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,4,3,2,6,8,7,5]=>[1,3,4,2,7,6,8,5]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,7,6,5,8]=>[1,3,4,2,6,7,5,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,4,3,2,7,6,8,5]=>[1,3,4,2,8,7,6,5]=>[.,[[.,[.,.]],[[[[.,.],.],.],.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,4,3,2,7,8,6,5]=>[1,3,4,2,6,8,7,5]=>[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,4,3,2,8,7,6,5]=>[1,3,4,2,6,7,8,5]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,4,3,5,2,6,7,8]=>[1,5,4,3,2,6,7,8]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,4,3,5,2,7,6,8]=>[1,5,4,3,2,7,6,8]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,4,3,5,2,7,8,6]=>[1,5,4,3,2,8,7,6]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,4,3,5,2,8,7,6]=>[1,5,4,3,2,7,8,6]=>[.,[[[[.,.],.],.],[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,4,3,5,6,2,7,8]=>[1,6,4,3,5,2,7,8]=>[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,8,2]=>[1,8,4,3,5,6,7,2]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,3,5,7,6,8,2]=>[1,8,4,3,5,7,6,2]=>[.,[[[[.,.],.],[.,[[.,.],.]]],.]]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,3,5,7,8,6,2]=>[1,6,4,3,5,8,7,2]=>[.,[[[[.,.],.],[.,[[.,.],.]]],.]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,4,3,6,5,2,7,8]=>[1,5,4,3,6,2,7,8]=>[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,3,6,5,7,8,2]=>[1,8,4,3,6,5,7,2]=>[.,[[[[.,.],.],[[.,.],[.,.]]],.]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,8,7,2]=>[1,7,4,3,6,5,8,2]=>[.,[[[[.,.],.],[[.,.],[.,.]]],.]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,4,3,7,6,5,2,8]=>[1,5,4,3,6,7,2,8]=>[.,[[[[.,.],.],[.,[.,.]]],[.,.]]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,3,7,6,8,5,2]=>[1,5,4,3,8,7,6,2]=>[.,[[[[.,.],.],[[[.,.],.],.]],.]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,3,7,8,6,5,2]=>[1,5,4,3,6,8,7,2]=>[.,[[[[.,.],.],[.,[[.,.],.]]],.]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,3,8,7,6,5,2]=>[1,5,4,3,6,7,8,2]=>[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,4,5,3,2,6,8,7]=>[1,3,5,4,2,6,8,7]=>[.,[[.,[[.,.],.]],[.,[[.,.],.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,4,5,3,2,7,6,8]=>[1,3,5,4,2,7,6,8]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,4,5,3,2,8,7,6]=>[1,3,5,4,2,7,8,6]=>[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,4,5,3,6,2,7,8]=>[1,6,5,4,3,2,7,8]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,5,3,6,7,8,2]=>[1,8,5,4,3,6,7,2]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,3,6,8,7,2]=>[1,7,5,4,3,6,8,2]=>[.,[[[[[.,.],.],.],[.,[.,.]]],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,4,5,3,7,8,6,2]=>[1,6,5,4,3,8,7,2]=>[.,[[[[[.,.],.],.],[[.,.],.]],.]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,6,3,2,8,7]=>[1,3,6,4,5,2,8,7]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,6,3,7,2,8]=>[1,7,6,4,5,3,2,8]=>[.,[[[[[.,.],.],[.,.]],.],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,6,3,7,8,2]=>[1,8,6,4,5,3,7,2]=>[.,[[[[[.,.],.],[.,.]],[.,.]],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,7,3,2,8]=>[1,3,7,4,5,6,2,8]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,7,3,8,2]=>[1,8,7,4,5,6,3,2]=>[.,[[[[[.,.],.],[.,[.,.]]],.],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,8,3,2]=>[1,3,8,4,5,6,7,2]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,4,5,7,6,3,8,2]=>[1,8,6,4,5,7,3,2]=>[.,[[[[[.,.],.],[.,[.,.]]],.],.]]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,4,5,8,7,6,3,2]=>[1,3,6,4,5,7,8,2]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,4,6,5,3,7,8,2]=>[1,8,5,4,6,3,7,2]=>[.,[[[[[.,.],.],[.,.]],[.,.]],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,4,6,7,5,3,2,8]=>[1,3,5,4,7,6,2,8]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,4,6,7,5,3,8,2]=>[1,8,5,4,7,6,3,2]=>[.,[[[[[.,.],.],[[.,.],.]],.],.]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,4,6,8,7,5,3,2]=>[1,3,5,4,7,6,8,2]=>[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,4,7,6,5,3,8,2]=>[1,8,5,4,6,7,3,2]=>[.,[[[[[.,.],.],[.,[.,.]]],.],.]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,4,7,6,5,8,3,2]=>[1,3,8,4,6,7,5,2]=>[.,[[.,[[.,.],[[.,[.,.]],.]]],.]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,4,7,6,8,5,3,2]=>[1,3,5,4,8,7,6,2]=>[.,[[.,[[.,.],[[[.,.],.],.]]],.]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,5,4,3,2,6,7,8]=>[1,3,4,5,2,6,7,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,5,4,3,2,7,6,8]=>[1,3,4,5,2,7,6,8]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,5,4,3,2,7,8,6]=>[1,3,4,5,2,8,7,6]=>[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,5,4,3,2,8,7,6]=>[1,3,4,5,2,7,8,6]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,5,4,3,6,2,7,8]=>[1,6,4,5,3,2,7,8]=>[.,[[[[.,.],[.,.]],.],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,4,3,6,7,8,2]=>[1,8,4,5,3,6,7,2]=>[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,4,3,6,8,7,2]=>[1,7,4,5,3,6,8,2]=>[.,[[[[.,.],[.,.]],[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,5,4,3,7,8,6,2]=>[1,6,4,5,3,8,7,2]=>[.,[[[[.,.],[.,.]],[[.,.],.]],.]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,5,4,6,3,2,8,7]=>[1,3,6,5,4,2,8,7]=>[.,[[.,[[[.,.],.],.]],[[.,.],.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,5,4,6,3,7,2,8]=>[1,7,6,5,4,3,2,8]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,4,6,3,7,8,2]=>[1,8,6,5,4,3,7,2]=>[.,[[[[[[.,.],.],.],.],[.,.]],.]]
[1,0,1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,4,6,3,8,7,2]=>[1,7,6,5,4,3,8,2]=>[.,[[[[[[.,.],.],.],.],[.,.]],.]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,4,6,7,3,8,2]=>[1,8,7,5,4,6,3,2]=>[.,[[[[[[.,.],.],.],[.,.]],.],.]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,5,4,6,7,8,3,2]=>[1,3,8,5,4,6,7,2]=>[.,[[.,[[[.,.],.],[.,[.,.]]]],.]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,5,4,7,6,3,2,8]=>[1,3,6,5,4,7,2,8]=>[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,4,7,6,3,8,2]=>[1,8,6,5,4,7,3,2]=>[.,[[[[[[.,.],.],.],[.,.]],.],.]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,5,4,7,6,8,3,2]=>[1,3,8,5,4,7,6,2]=>[.,[[.,[[[.,.],.],[[.,.],.]]],.]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,5,6,4,3,7,2,8]=>[1,7,4,6,5,3,2,8]=>[.,[[[[.,.],[[.,.],.]],.],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,5,6,4,7,3,8,2]=>[1,8,7,6,5,4,3,2]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,5,6,7,4,8,3,2]=>[1,3,8,7,5,6,4,2]=>[.,[[.,[[[[.,.],.],[.,.]],.]],.]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,8,4,3,2]=>[1,3,4,8,5,6,7,2]=>[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,5,7,6,4,3,2,8]=>[1,3,4,6,5,7,2,8]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,5,7,6,4,3,8,2]=>[1,8,4,6,5,7,3,2]=>[.,[[[[.,.],[[.,.],[.,.]]],.],.]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,5,8,7,6,4,3,2]=>[1,3,4,6,5,7,8,2]=>[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,6,5,4,3,2,7,8]=>[1,3,4,5,6,2,7,8]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,6,5,4,3,2,8,7]=>[1,3,4,5,6,2,8,7]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,6,5,4,3,7,8,2]=>[1,8,4,5,6,3,7,2]=>[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,5,4,3,8,7,2]=>[1,7,4,5,6,3,8,2]=>[.,[[[[.,.],[.,[.,.]]],[.,.]],.]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,5,7,4,3,8,2]=>[1,8,4,7,6,5,3,2]=>[.,[[[[.,.],[[[.,.],.],.]],.],.]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,6,5,7,4,8,3,2]=>[1,3,8,7,6,5,4,2]=>[.,[[.,[[[[[.,.],.],.],.],.]],.]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,6,7,5,4,3,2,8]=>[1,3,4,5,7,6,2,8]=>[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,6,7,5,4,8,3,2]=>[1,3,8,5,7,6,4,2]=>[.,[[.,[[[.,.],[[.,.],.]],.]],.]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,6,7,5,8,4,3,2]=>[1,3,4,8,7,6,5,2]=>[.,[[.,[.,[[[[.,.],.],.],.]]],.]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,6,7,8,5,4,3,2]=>[1,3,4,5,8,6,7,2]=>[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,6,8,7,5,4,3,2]=>[1,3,4,5,7,6,8,2]=>[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,7,6,5,4,3,2,8]=>[1,3,4,5,6,7,2,8]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,7,6,5,4,3,8,2]=>[1,8,4,5,6,7,3,2]=>[.,[[[[.,.],[.,[.,[.,.]]]],.],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,7,6,5,4,8,3,2]=>[1,3,8,5,6,7,4,2]=>[.,[[.,[[[.,.],[.,[.,.]]],.]],.]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,7,6,8,5,4,3,2]=>[1,3,4,5,8,7,6,2]=>[.,[[.,[.,[.,[[[.,.],.],.]]]],.]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,7,8,6,5,4,3,2]=>[1,3,4,5,6,8,7,2]=>[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,2]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,5,7,8,6]=>[2,1,3,4,5,8,7,6]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,5,8,7,6]=>[2,1,3,4,5,7,8,6]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,4,6,7,8,5]=>[2,1,3,4,8,6,7,5]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,4,6,8,7,5]=>[2,1,3,4,7,6,8,5]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,4,7,6,8,5]=>[2,1,3,4,8,7,6,5]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,8,7,6,5]=>[2,1,3,4,6,7,8,5]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,3,5,4,7,8,6]=>[2,1,3,5,4,8,7,6]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,8,7,6]=>[2,1,3,5,4,7,8,6]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,3,5,6,4,8,7]=>[2,1,3,6,5,4,8,7]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,8,4]=>[2,1,3,8,5,6,7,4]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,3,5,7,6,8,4]=>[2,1,3,8,5,7,6,4]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,3,5,7,8,6,4]=>[2,1,3,6,5,8,7,4]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,6,5,4,8,7]=>[2,1,3,5,6,4,8,7]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,3,6,5,7,8,4]=>[2,1,3,8,6,5,7,4]=>[[.,.],[.,[[[[.,.],.],[.,.]],.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,3,6,7,5,8,4]=>[2,1,3,8,7,6,5,4]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,3,6,7,8,5,4]=>[2,1,3,5,8,6,7,4]=>[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,3,7,6,5,8,4]=>[2,1,3,8,6,7,5,4]=>[[.,.],[.,[[[[.,.],[.,.]],.],.]]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,8,7,6,5,4]=>[2,1,3,5,6,7,8,4]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,4,3,5,7,8,6]=>[2,1,4,3,5,8,7,6]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,4,3,5,8,7,6]=>[2,1,4,3,5,7,8,6]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,6,7,5]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,3,6,8,7,5]=>[2,1,4,3,7,6,8,5]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,3,7,6,5,8]=>[2,1,4,3,6,7,5,8]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,6,8,5]=>[2,1,4,3,8,7,6,5]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,4,3,7,8,6,5]=>[2,1,4,3,6,8,7,5]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,8,7,6,5]=>[2,1,4,3,6,7,8,5]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,4,5,3,6,7,8]=>[2,1,5,4,3,6,7,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3,7,8,6]=>[2,1,5,4,3,8,7,6]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,6,3,8,7]=>[2,1,6,4,5,3,8,7]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,8,3]=>[2,1,8,4,5,6,7,3]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,1,4,5,7,6,8,3]=>[2,1,8,4,5,7,6,3]=>[[.,.],[[[.,.],[.,[[.,.],.]]],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,1,4,5,7,8,6,3]=>[2,1,6,4,5,8,7,3]=>[[.,.],[[[.,.],[.,[[.,.],.]]],.]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,1,4,5,8,7,6,3]=>[2,1,6,4,5,7,8,3]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,4,6,5,3,8,7]=>[2,1,5,4,6,3,8,7]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,1,4,6,5,7,8,3]=>[2,1,8,4,6,5,7,3]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,1,4,6,5,8,7,3]=>[2,1,7,4,6,5,8,3]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,1,4,6,7,5,8,3]=>[2,1,8,4,7,6,5,3]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,1,4,6,7,8,5,3]=>[2,1,5,4,8,6,7,3]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,1,4,6,8,7,5,3]=>[2,1,5,4,7,6,8,3]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,4,7,6,5,3,8]=>[2,1,5,4,6,7,3,8]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,1,4,7,6,5,8,3]=>[2,1,8,4,6,7,5,3]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,1,4,7,6,8,5,3]=>[2,1,5,4,8,7,6,3]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,1,4,7,8,6,5,3]=>[2,1,5,4,6,8,7,3]=>[[.,.],[[[.,.],[.,[[.,.],.]]],.]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,1,4,8,7,6,5,3]=>[2,1,5,4,6,7,8,3]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,5,4,3,6,7,8]=>[2,1,4,5,3,6,7,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,5,4,3,6,8,7]=>[2,1,4,5,3,6,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,1,5,4,3,7,8,6]=>[2,1,4,5,3,8,7,6]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,4,6,3,8,7]=>[2,1,6,5,4,3,8,7]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,5,4,6,7,8,3]=>[2,1,8,5,4,6,7,3]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,4,7,6,8,3]=>[2,1,8,5,4,7,6,3]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,5,4,7,8,6,3]=>[2,1,6,5,4,8,7,3]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,5,6,4,3,7,8]=>[2,1,4,6,5,3,7,8]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,1,5,6,4,3,8,7]=>[2,1,4,6,5,3,8,7]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,5,6,4,7,3,8]=>[2,1,7,6,5,4,3,8]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,1,5,6,4,7,8,3]=>[2,1,8,6,5,4,7,3]=>[[.,.],[[[[[.,.],.],.],[.,.]],.]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,1,5,6,4,8,7,3]=>[2,1,7,6,5,4,8,3]=>[[.,.],[[[[[.,.],.],.],[.,.]],.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,1,5,6,7,4,8,3]=>[2,1,8,7,5,6,4,3]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,8,4,3]=>[2,1,4,8,5,6,7,3]=>[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,1,5,7,6,4,8,3]=>[2,1,8,6,5,7,4,3]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,1,5,7,6,8,4,3]=>[2,1,4,8,5,7,6,3]=>[[.,.],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,1,5,7,8,6,4,3]=>[2,1,4,6,5,8,7,3]=>[[.,.],[[.,[[.,.],[[.,.],.]]],.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,6,5,4,3,8,7]=>[2,1,4,5,6,3,8,7]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,1,6,5,4,7,8,3]=>[2,1,8,5,6,4,7,3]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,1,6,5,4,8,7,3]=>[2,1,7,5,6,4,8,3]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,5,7,4,8,3]=>[2,1,8,7,6,5,4,3]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,6,5,7,8,4,3]=>[2,1,4,8,6,5,7,3]=>[[.,.],[[.,[[[.,.],.],[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,6,5,8,7,4,3]=>[2,1,4,7,6,5,8,3]=>[[.,.],[[.,[[[.,.],.],[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,1,6,7,5,4,8,3]=>[2,1,8,5,7,6,4,3]=>[[.,.],[[[[.,.],[[.,.],.]],.],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,1,6,7,5,8,4,3]=>[2,1,4,8,7,6,5,3]=>[[.,.],[[.,[[[[.,.],.],.],.]],.]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,1,6,7,8,5,4,3]=>[2,1,4,5,8,6,7,3]=>[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,7,6,5,4,3,8]=>[2,1,4,5,6,7,3,8]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,7,6,5,4,8,3]=>[2,1,8,5,6,7,4,3]=>[[.,.],[[[[.,.],[.,[.,.]]],.],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,7,6,5,8,4,3]=>[2,1,4,8,6,7,5,3]=>[[.,.],[[.,[[[.,.],[.,.]],.]],.]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,7,6,8,5,4,3]=>[2,1,4,5,8,7,6,3]=>[[.,.],[[.,[.,[[[.,.],.],.]]],.]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,7,8,6,5,4,3]=>[2,1,4,5,6,8,7,3]=>[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,8,7,6,5,4,3]=>[2,1,4,5,6,7,8,3]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,6,8,7]=>[3,2,1,4,5,6,8,7]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,5,8,7,6]=>[3,2,1,4,5,7,8,6]=>[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,1,4,6,7,8,5]=>[3,2,1,4,8,6,7,5]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,1,4,6,8,7,5]=>[3,2,1,4,7,6,8,5]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,1,4,7,6,8,5]=>[3,2,1,4,8,7,6,5]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,1,4,7,8,6,5]=>[3,2,1,4,6,8,7,5]=>[[[.,.],.],[.,[[.,[[.,.],.]],.]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,8,7,6,5]=>[3,2,1,4,6,7,8,5]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,1,5,6,4,7,8]=>[3,2,1,6,5,4,7,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,1,5,6,7,4,8]=>[3,2,1,7,5,6,4,8]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,8,4]=>[3,2,1,8,5,6,7,4]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,1,5,6,8,7,4]=>[3,2,1,7,5,6,8,4]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,7,6,8,4]=>[3,2,1,8,5,7,6,4]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,1,5,7,8,6,4]=>[3,2,1,6,5,8,7,4]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,1,5,8,7,6,4]=>[3,2,1,6,5,7,8,4]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,6,5,4,7,8]=>[3,2,1,5,6,4,7,8]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,6,5,7,4,8]=>[3,2,1,7,6,5,4,8]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,5,7,8,4]=>[3,2,1,8,6,5,7,4]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,1,6,5,8,7,4]=>[3,2,1,7,6,5,8,4]=>[[[.,.],.],[[[[.,.],.],[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,1,6,7,5,4,8]=>[3,2,1,5,7,6,4,8]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,6,7,5,8,4]=>[3,2,1,8,7,6,5,4]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,1,6,7,8,5,4]=>[3,2,1,5,8,6,7,4]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,1,6,8,7,5,4]=>[3,2,1,5,7,6,8,4]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,7,6,5,8,4]=>[3,2,1,8,6,7,5,4]=>[[[.,.],.],[[[[.,.],[.,.]],.],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,1,7,6,8,5,4]=>[3,2,1,5,8,7,6,4]=>[[[.,.],.],[[.,[[[.,.],.],.]],.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,1,7,8,6,5,4]=>[3,2,1,5,6,8,7,4]=>[[[.,.],.],[[.,[.,[[.,.],.]]],.]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,8,7,6,5,4]=>[3,2,1,5,6,7,8,4]=>[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,5,7,6,8]=>[4,2,3,1,5,7,6,8]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,4,1,5,7,8,6]=>[4,2,3,1,5,8,7,6]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,8,7,6]=>[4,2,3,1,5,7,8,6]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,4,1,6,5,7,8]=>[4,2,3,1,6,5,7,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,4,1,6,7,5,8]=>[4,2,3,1,7,6,5,8]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,4,1,6,8,7,5]=>[4,2,3,1,7,6,8,5]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,4,1,7,6,8,5]=>[4,2,3,1,8,7,6,5]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,7,8,6,5]=>[4,2,3,1,6,8,7,5]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,8,7,6,5]=>[4,2,3,1,6,7,8,5]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,5,1,6,8,7]=>[5,2,3,4,1,6,8,7]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,5,1,7,8,6]=>[5,2,3,4,1,8,7,6]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,1,8,7,6]=>[5,2,3,4,1,7,8,6]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,6,1,7,8]=>[6,2,3,4,5,1,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,1,8,7]=>[6,2,3,4,5,1,8,7]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,1,8]=>[7,2,3,4,5,6,1,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,1]=>[8,2,3,4,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,8,7,1]=>[7,2,3,4,5,6,8,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,5,7,6,8,1]=>[8,2,3,4,5,7,6,1]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,5,7,8,6,1]=>[6,2,3,4,5,8,7,1]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,5,8,7,6,1]=>[6,2,3,4,5,7,8,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,4,6,5,1,7,8]=>[5,2,3,4,6,1,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,4,6,5,1,8,7]=>[5,2,3,4,6,1,8,7]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,4,6,5,7,1,8]=>[7,2,3,4,6,5,1,8]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,4,6,7,5,1,8]=>[5,2,3,4,7,6,1,8]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,4,6,7,5,8,1]=>[8,2,3,4,7,6,5,1]=>[[[.,.],[.,[.,[[[.,.],.],.]]]],.]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,6,7,8,5,1]=>[5,2,3,4,8,6,7,1]=>[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,4,7,6,5,1,8]=>[5,2,3,4,6,7,1,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,8,7,6,5,1]=>[5,2,3,4,6,7,8,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,5,4,1,6,7,8]=>[4,2,3,5,1,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,5,4,1,7,8,6]=>[4,2,3,5,1,8,7,6]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,3,5,4,6,1,7,8]=>[6,2,3,5,4,1,7,8]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,3,5,4,6,7,1,8]=>[7,2,3,5,4,6,1,8]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,5,4,6,7,8,1]=>[8,2,3,5,4,6,7,1]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,3,5,4,7,6,1,8]=>[6,2,3,5,4,7,1,8]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,5,4,7,6,8,1]=>[8,2,3,5,4,7,6,1]=>[[[.,.],[.,[[.,.],[[.,.],.]]]],.]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,5,4,8,7,6,1]=>[6,2,3,5,4,7,8,1]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,3,5,6,4,7,1,8]=>[7,2,3,6,5,4,1,8]=>[[[.,.],[.,[[[.,.],.],.]]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,5,6,4,7,8,1]=>[8,2,3,6,5,4,7,1]=>[[[.,.],[.,[[[.,.],.],[.,.]]]],.]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,5,6,7,4,8,1]=>[8,2,3,7,5,6,4,1]=>[[[.,.],[.,[[[.,.],[.,.]],.]]],.]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,8,4,1]=>[4,2,3,8,5,6,7,1]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,5,6,8,7,4,1]=>[4,2,3,7,5,6,8,1]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,5,7,6,8,4,1]=>[4,2,3,8,5,7,6,1]=>[[[.,.],[.,[[.,.],[[.,.],.]]]],.]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,5,7,8,6,4,1]=>[4,2,3,6,5,8,7,1]=>[[[.,.],[.,[[.,.],[[.,.],.]]]],.]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,6,5,4,1,7,8]=>[4,2,3,5,6,1,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,6,5,4,1,8,7]=>[4,2,3,5,6,1,8,7]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,6,5,8,7,4,1]=>[4,2,3,7,6,5,8,1]=>[[[.,.],[.,[[[.,.],.],[.,.]]]],.]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,6,7,5,4,8,1]=>[8,2,3,5,7,6,4,1]=>[[[.,.],[.,[[.,[[.,.],.]],.]]],.]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,6,7,5,8,4,1]=>[4,2,3,8,7,6,5,1]=>[[[.,.],[.,[[[[.,.],.],.],.]]],.]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,7,6,5,4,1,8]=>[4,2,3,5,6,7,1,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,7,6,5,4,8,1]=>[8,2,3,5,6,7,4,1]=>[[[.,.],[.,[[.,[.,[.,.]]],.]]],.]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,7,6,8,5,4,1]=>[4,2,3,5,8,7,6,1]=>[[[.,.],[.,[.,[[[.,.],.],.]]]],.]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,7,8,6,5,4,1]=>[4,2,3,5,6,8,7,1]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,8,7,6,5,4,1]=>[4,2,3,5,6,7,8,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,4,3,1,5,6,8,7]=>[3,2,4,1,5,6,8,7]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,4,3,1,5,7,6,8]=>[3,2,4,1,5,7,6,8]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[2,4,3,1,5,7,8,6]=>[3,2,4,1,5,8,7,6]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,4,3,1,5,8,7,6]=>[3,2,4,1,5,7,8,6]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,4,3,1,6,5,7,8]=>[3,2,4,1,6,5,7,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,4,3,1,6,5,8,7]=>[3,2,4,1,6,5,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,4,3,1,6,7,8,5]=>[3,2,4,1,8,6,7,5]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,4,3,1,6,8,7,5]=>[3,2,4,1,7,6,8,5]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,4,3,1,7,6,8,5]=>[3,2,4,1,8,7,6,5]=>[[[.,.],[.,.]],[[[[.,.],.],.],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[2,4,3,1,7,8,6,5]=>[3,2,4,1,6,8,7,5]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,4,3,1,8,7,6,5]=>[3,2,4,1,6,7,8,5]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,4,3,5,1,6,7,8]=>[5,2,4,3,1,6,7,8]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[2,4,3,5,1,6,8,7]=>[5,2,4,3,1,6,8,7]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,4,3,5,1,7,6,8]=>[5,2,4,3,1,7,6,8]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,4,3,5,1,7,8,6]=>[5,2,4,3,1,8,7,6]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[2,4,3,5,6,1,8,7]=>[6,2,4,3,5,1,8,7]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,6,5,1,8,7]=>[5,2,4,3,6,1,8,7]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,6,5,7,1,8]=>[7,2,4,3,6,5,1,8]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,6,5,7,8,1]=>[8,2,4,3,6,5,7,1]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,8,7,1]=>[7,2,4,3,6,5,8,1]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,4,3,6,7,5,8,1]=>[8,2,4,3,7,6,5,1]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,4,3,6,8,7,5,1]=>[5,2,4,3,7,6,8,1]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[2,4,3,7,6,5,1,8]=>[5,2,4,3,6,7,1,8]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,4,3,7,6,5,8,1]=>[8,2,4,3,6,7,5,1]=>[[[.,.],[[.,.],[[.,[.,.]],.]]],.]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,4,3,7,6,8,5,1]=>[5,2,4,3,8,7,6,1]=>[[[.,.],[[.,.],[[[.,.],.],.]]],.]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,4,5,3,1,6,7,8]=>[3,2,5,4,1,6,7,8]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[2,4,5,3,1,6,8,7]=>[3,2,5,4,1,6,8,7]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[2,4,5,3,1,7,6,8]=>[3,2,5,4,1,7,6,8]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,4,5,3,1,7,8,6]=>[3,2,5,4,1,8,7,6]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,4,5,3,1,8,7,6]=>[3,2,5,4,1,7,8,6]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[2,4,5,3,6,1,8,7]=>[6,2,5,4,3,1,8,7]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,4,5,3,6,7,1,8]=>[7,2,5,4,3,6,1,8]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,4,5,3,6,7,8,1]=>[8,2,5,4,3,6,7,1]=>[[[.,.],[[[.,.],.],[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[2,4,5,3,7,6,8,1]=>[8,2,5,4,3,7,6,1]=>[[[.,.],[[[.,.],.],[[.,.],.]]],.]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,4,5,3,8,7,6,1]=>[6,2,5,4,3,7,8,1]=>[[[.,.],[[[.,.],.],[.,[.,.]]]],.]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,6,3,1,7,8]=>[3,2,6,4,5,1,7,8]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,6,3,1,8,7]=>[3,2,6,4,5,1,8,7]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,6,3,7,1,8]=>[7,2,6,4,5,3,1,8]=>[[[.,.],[[[.,.],[.,.]],.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,6,3,7,8,1]=>[8,2,6,4,5,3,7,1]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,6,3,8,7,1]=>[7,2,6,4,5,3,8,1]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,7,3,1,8]=>[3,2,7,4,5,6,1,8]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,7,3,8,1]=>[8,2,7,4,5,6,3,1]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,8,3,1]=>[3,2,8,4,5,6,7,1]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[2,4,5,7,6,3,8,1]=>[8,2,6,4,5,7,3,1]=>[[[.,.],[[[.,.],[.,[.,.]]],.]],.]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,4,6,5,3,1,8,7]=>[3,2,5,4,6,1,8,7]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,4,6,5,3,8,7,1]=>[7,2,5,4,6,3,8,1]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[2,4,6,5,7,3,8,1]=>[8,2,7,4,6,5,3,1]=>[[[.,.],[[[.,.],[[.,.],.]],.]],.]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,4,6,5,7,8,3,1]=>[3,2,8,4,6,5,7,1]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,4,6,5,8,7,3,1]=>[3,2,7,4,6,5,8,1]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[2,4,6,7,5,3,1,8]=>[3,2,5,4,7,6,1,8]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,4,6,7,5,3,8,1]=>[8,2,5,4,7,6,3,1]=>[[[.,.],[[[.,.],[[.,.],.]],.]],.]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,4,6,7,8,5,3,1]=>[3,2,5,4,8,6,7,1]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,4,6,8,7,5,3,1]=>[3,2,5,4,7,6,8,1]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,4,7,8,6,5,3,1]=>[3,2,5,4,6,8,7,1]=>[[[.,.],[[.,.],[.,[[.,.],.]]]],.]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,4,8,7,6,5,3,1]=>[3,2,5,4,6,7,8,1]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,5,4,3,1,6,7,8]=>[3,2,4,5,1,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,5,4,3,1,7,8,6]=>[3,2,4,5,1,8,7,6]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[2,5,4,3,6,1,7,8]=>[6,2,4,5,3,1,7,8]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,5,4,3,6,7,1,8]=>[7,2,4,5,3,6,1,8]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[2,5,4,3,6,8,7,1]=>[7,2,4,5,3,6,8,1]=>[[[.,.],[[.,[.,.]],[.,[.,.]]]],.]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,5,4,3,7,6,8,1]=>[8,2,4,5,3,7,6,1]=>[[[.,.],[[.,[.,.]],[[.,.],.]]],.]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[2,5,4,6,3,1,8,7]=>[3,2,6,5,4,1,8,7]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,5,4,6,3,7,1,8]=>[7,2,6,5,4,3,1,8]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,5,4,6,3,7,8,1]=>[8,2,6,5,4,3,7,1]=>[[[.,.],[[[[.,.],.],.],[.,.]]],.]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,5,4,6,7,3,1,8]=>[3,2,7,5,4,6,1,8]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,5,4,6,7,3,8,1]=>[8,2,7,5,4,6,3,1]=>[[[.,.],[[[[.,.],.],[.,.]],.]],.]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,5,4,6,7,8,3,1]=>[3,2,8,5,4,6,7,1]=>[[[.,.],[[[.,.],.],[.,[.,.]]]],.]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,5,4,7,6,3,1,8]=>[3,2,6,5,4,7,1,8]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,5,4,7,6,3,8,1]=>[8,2,6,5,4,7,3,1]=>[[[.,.],[[[[.,.],.],[.,.]],.]],.]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,5,4,7,6,8,3,1]=>[3,2,8,5,4,7,6,1]=>[[[.,.],[[[.,.],.],[[.,.],.]]],.]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,5,4,7,8,6,3,1]=>[3,2,6,5,4,8,7,1]=>[[[.,.],[[[.,.],.],[[.,.],.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[2,5,6,4,7,3,1,8]=>[3,2,7,6,5,4,1,8]=>[[[.,.],[[[[.,.],.],.],.]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,5,6,4,7,3,8,1]=>[8,2,7,6,5,4,3,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,5,6,4,8,7,3,1]=>[3,2,7,6,5,4,8,1]=>[[[.,.],[[[[.,.],.],.],[.,.]]],.]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,5,6,7,4,3,8,1]=>[8,2,4,7,5,6,3,1]=>[[[.,.],[[.,[[.,.],[.,.]]],.]],.]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,5,6,7,4,8,3,1]=>[3,2,8,7,5,6,4,1]=>[[[.,.],[[[[.,.],.],[.,.]],.]],.]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,8,4,3,1]=>[3,2,4,8,5,6,7,1]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,5,6,8,7,4,3,1]=>[3,2,4,7,5,6,8,1]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,5,7,6,4,8,3,1]=>[3,2,8,6,5,7,4,1]=>[[[.,.],[[[[.,.],.],[.,.]],.]],.]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,5,7,8,6,4,3,1]=>[3,2,4,6,5,8,7,1]=>[[[.,.],[.,[[.,.],[[.,.],.]]]],.]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,6,5,4,7,8,3,1]=>[3,2,8,5,6,4,7,1]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,6,5,4,8,7,3,1]=>[3,2,7,5,6,4,8,1]=>[[[.,.],[[[.,.],[.,.]],[.,.]]],.]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,6,5,7,4,3,8,1]=>[8,2,4,7,6,5,3,1]=>[[[.,.],[[.,[[[.,.],.],.]],.]],.]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,6,5,7,4,8,3,1]=>[3,2,8,7,6,5,4,1]=>[[[.,.],[[[[[.,.],.],.],.],.]],.]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,6,5,8,7,4,3,1]=>[3,2,4,7,6,5,8,1]=>[[[.,.],[.,[[[.,.],.],[.,.]]]],.]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[2,6,7,5,4,8,3,1]=>[3,2,8,5,7,6,4,1]=>[[[.,.],[[[.,.],[[.,.],.]],.]],.]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,6,7,5,8,4,3,1]=>[3,2,4,8,7,6,5,1]=>[[[.,.],[.,[[[[.,.],.],.],.]]],.]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,6,7,8,5,4,3,1]=>[3,2,4,5,8,6,7,1]=>[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,6,8,7,5,4,3,1]=>[3,2,4,5,7,6,8,1]=>[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,7,6,5,4,3,1,8]=>[3,2,4,5,6,7,1,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,7,6,5,4,3,8,1]=>[8,2,4,5,6,7,3,1]=>[[[.,.],[[.,[.,[.,[.,.]]]],.]],.]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,7,6,5,8,4,3,1]=>[3,2,4,8,6,7,5,1]=>[[[.,.],[.,[[[.,.],[.,.]],.]]],.]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,7,8,6,5,4,3,1]=>[3,2,4,5,6,8,7,1]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,8,7,6,5,4,3,1]=>[3,2,4,5,6,7,8,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,6,8,7]=>[2,3,1,4,5,6,8,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,5,7,6,8]=>[2,3,1,4,5,7,6,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,5,8,7,6]=>[2,3,1,4,5,7,8,6]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,2,1,4,6,5,8,7]=>[2,3,1,4,6,5,8,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,2,1,4,6,8,7,5]=>[2,3,1,4,7,6,8,5]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,2,1,4,7,6,5,8]=>[2,3,1,4,6,7,5,8]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,2,1,4,7,6,8,5]=>[2,3,1,4,8,7,6,5]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,2,1,4,8,7,6,5]=>[2,3,1,4,6,7,8,5]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,2,1,5,4,6,7,8]=>[2,3,1,5,4,6,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,7,6,8]=>[2,3,1,5,4,7,6,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,2,1,5,6,4,7,8]=>[2,3,1,6,5,4,7,8]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,2,1,5,6,4,8,7]=>[2,3,1,6,5,4,8,7]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,2,1,5,6,7,4,8]=>[2,3,1,7,5,6,4,8]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,8,4]=>[2,3,1,8,5,6,7,4]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,2,1,5,7,6,4,8]=>[2,3,1,6,5,7,4,8]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,2,1,5,7,8,6,4]=>[2,3,1,6,5,8,7,4]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,2,1,6,5,4,7,8]=>[2,3,1,5,6,4,7,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,2,1,6,5,8,7,4]=>[2,3,1,7,6,5,8,4]=>[[.,[.,.]],[[[[.,.],.],[.,.]],.]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,2,1,6,7,5,8,4]=>[2,3,1,8,7,6,5,4]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,2,1,6,8,7,5,4]=>[2,3,1,5,7,6,8,4]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,2,1,7,6,5,4,8]=>[2,3,1,5,6,7,4,8]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,2,1,7,6,5,8,4]=>[2,3,1,8,6,7,5,4]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,2,1,8,7,6,5,4]=>[2,3,1,5,6,7,8,4]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,2,4,1,5,6,8,7]=>[4,3,2,1,5,6,8,7]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,2,4,1,5,7,6,8]=>[4,3,2,1,5,7,6,8]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,2,4,1,5,7,8,6]=>[4,3,2,1,5,8,7,6]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,2,4,1,5,8,7,6]=>[4,3,2,1,5,7,8,6]=>[[[[.,.],.],.],[.,[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,2,4,1,6,5,7,8]=>[4,3,2,1,6,5,7,8]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,4,1,6,5,8,7]=>[4,3,2,1,6,5,8,7]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,2,4,1,6,7,5,8]=>[4,3,2,1,7,6,5,8]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,2,4,1,6,7,8,5]=>[4,3,2,1,8,6,7,5]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,2,4,1,6,8,7,5]=>[4,3,2,1,7,6,8,5]=>[[[[.,.],.],.],[[[.,.],[.,.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,2,4,1,7,6,5,8]=>[4,3,2,1,6,7,5,8]=>[[[[.,.],.],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,4,1,7,6,8,5]=>[4,3,2,1,8,7,6,5]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,2,4,1,7,8,6,5]=>[4,3,2,1,6,8,7,5]=>[[[[.,.],.],.],[[.,[[.,.],.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,2,4,1,8,7,6,5]=>[4,3,2,1,6,7,8,5]=>[[[[.,.],.],.],[[.,[.,[.,.]]],.]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,5,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,5,1,6,8,7]=>[5,3,2,4,1,6,8,7]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,5,1,7,6,8]=>[5,3,2,4,1,7,6,8]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,5,1,7,8,6]=>[5,3,2,4,1,8,7,6]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,1]=>[8,3,2,4,5,6,7,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,6,8,7,1]=>[7,3,2,4,5,6,8,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,2,4,6,7,5,1,8]=>[5,3,2,4,7,6,1,8]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[3,2,4,6,7,5,8,1]=>[8,3,2,4,7,6,5,1]=>[[[[.,.],.],[.,[[[.,.],.],.]]],.]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,2,4,7,6,5,8,1]=>[8,3,2,4,6,7,5,1]=>[[[[.,.],.],[.,[[.,[.,.]],.]]],.]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,2,4,8,7,6,5,1]=>[5,3,2,4,6,7,8,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,5,4,1,6,7,8]=>[4,3,2,5,1,6,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,5,4,1,7,8,6]=>[4,3,2,5,1,8,7,6]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,5,4,1,8,7,6]=>[4,3,2,5,1,7,8,6]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,5,4,6,1,7,8]=>[6,3,2,5,4,1,7,8]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,5,4,6,1,8,7]=>[6,3,2,5,4,1,8,7]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,5,4,6,7,1,8]=>[7,3,2,5,4,6,1,8]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,7,6,1,8]=>[6,3,2,5,4,7,1,8]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,7,6,8,1]=>[8,3,2,5,4,7,6,1]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,4,7,8,6,1]=>[6,3,2,5,4,8,7,1]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,2,5,6,4,1,8,7]=>[4,3,2,6,5,1,8,7]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,2,5,6,7,4,8,1]=>[8,3,2,7,5,6,4,1]=>[[[[.,.],.],[[[.,.],[.,.]],.]],.]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,8,4,1]=>[4,3,2,8,5,6,7,1]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,2,5,6,8,7,4,1]=>[4,3,2,7,5,6,8,1]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,2,5,7,6,4,8,1]=>[8,3,2,6,5,7,4,1]=>[[[[.,.],.],[[[.,.],[.,.]],.]],.]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,2,5,7,6,8,4,1]=>[4,3,2,8,5,7,6,1]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,5,7,8,6,4,1]=>[4,3,2,6,5,8,7,1]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,2,5,8,7,6,4,1]=>[4,3,2,6,5,7,8,1]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,2,6,5,4,1,8,7]=>[4,3,2,5,6,1,8,7]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,2,6,5,4,8,7,1]=>[7,3,2,5,6,4,8,1]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,6,5,7,4,8,1]=>[8,3,2,7,6,5,4,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,2,6,5,8,7,4,1]=>[4,3,2,7,6,5,8,1]=>[[[[.,.],.],[[[.,.],.],[.,.]]],.]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,2,6,7,5,4,1,8]=>[4,3,2,5,7,6,1,8]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,2,6,7,5,4,8,1]=>[8,3,2,5,7,6,4,1]=>[[[[.,.],.],[[.,[[.,.],.]],.]],.]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,2,6,7,5,8,4,1]=>[4,3,2,8,7,6,5,1]=>[[[[.,.],.],[[[[.,.],.],.],.]],.]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,2,6,8,7,5,4,1]=>[4,3,2,5,7,6,8,1]=>[[[[.,.],.],[.,[[.,.],[.,.]]]],.]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,2,7,6,5,4,1,8]=>[4,3,2,5,6,7,1,8]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,2,7,6,5,4,8,1]=>[8,3,2,5,6,7,4,1]=>[[[[.,.],.],[[.,[.,[.,.]]],.]],.]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,2,7,6,5,8,4,1]=>[4,3,2,8,6,7,5,1]=>[[[[.,.],.],[[[.,.],[.,.]],.]],.]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,2,7,6,8,5,4,1]=>[4,3,2,5,8,7,6,1]=>[[[[.,.],.],[.,[[[.,.],.],.]]],.]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,7,8,6,5,4,1]=>[4,3,2,5,6,8,7,1]=>[[[[.,.],.],[.,[.,[[.,.],.]]]],.]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,2,8,7,6,5,4,1]=>[4,3,2,5,6,7,8,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7,8]=>[2,4,3,1,5,6,7,8]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,4,2,1,5,7,8,6]=>[2,4,3,1,5,8,7,6]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,4,2,1,6,5,7,8]=>[2,4,3,1,6,5,7,8]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,4,2,1,6,5,8,7]=>[2,4,3,1,6,5,8,7]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,4,2,1,6,8,7,5]=>[2,4,3,1,7,6,8,5]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,4,2,1,7,6,8,5]=>[2,4,3,1,8,7,6,5]=>[[.,[[.,.],.]],[[[[.,.],.],.],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,4,2,1,7,8,6,5]=>[2,4,3,1,6,8,7,5]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,4,2,1,8,7,6,5]=>[2,4,3,1,6,7,8,5]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,4,2,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,4,2,5,1,6,8,7]=>[5,4,3,2,1,6,8,7]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,4,2,5,1,7,6,8]=>[5,4,3,2,1,7,6,8]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,4,2,5,1,7,8,6]=>[5,4,3,2,1,8,7,6]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,4,2,5,1,8,7,6]=>[5,4,3,2,1,7,8,6]=>[[[[[.,.],.],.],.],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,4,2,5,6,1,7,8]=>[6,4,3,2,5,1,7,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,4,2,5,6,1,8,7]=>[6,4,3,2,5,1,8,7]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,8,1]=>[8,4,3,2,5,6,7,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,4,2,5,6,8,7,1]=>[7,4,3,2,5,6,8,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,4,2,5,7,6,8,1]=>[8,4,3,2,5,7,6,1]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,4,2,5,7,8,6,1]=>[6,4,3,2,5,8,7,1]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,4,2,6,5,1,7,8]=>[5,4,3,2,6,1,7,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,4,2,6,5,1,8,7]=>[5,4,3,2,6,1,8,7]=>[[[[[.,.],.],.],[.,.]],[[.,.],.]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,4,2,6,5,7,1,8]=>[7,4,3,2,6,5,1,8]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,4,2,6,5,7,8,1]=>[8,4,3,2,6,5,7,1]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,8,7,1]=>[7,4,3,2,6,5,8,1]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,4,2,6,7,5,1,8]=>[5,4,3,2,7,6,1,8]=>[[[[[.,.],.],.],[[.,.],.]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,4,2,6,7,5,8,1]=>[8,4,3,2,7,6,5,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,4,2,6,7,8,5,1]=>[5,4,3,2,8,6,7,1]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,6,8,7,5,1]=>[5,4,3,2,7,6,8,1]=>[[[[[.,.],.],.],[[.,.],[.,.]]],.]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,4,2,7,6,5,1,8]=>[5,4,3,2,6,7,1,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,4,2,7,6,8,5,1]=>[5,4,3,2,8,7,6,1]=>[[[[[.,.],.],.],[[[.,.],.],.]],.]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,4,2,7,8,6,5,1]=>[5,4,3,2,6,8,7,1]=>[[[[[.,.],.],.],[.,[[.,.],.]]],.]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,2,8,7,6,5,1]=>[5,4,3,2,6,7,8,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,5,2,1,6,7,8]=>[2,5,3,4,1,6,7,8]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,5,2,1,7,8,6]=>[2,5,3,4,1,8,7,6]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,5,2,6,1,7,8]=>[6,5,3,4,2,1,7,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,5,2,6,1,8,7]=>[6,5,3,4,2,1,8,7]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,5,2,6,7,1,8]=>[7,5,3,4,2,6,1,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,5,2,6,7,8,1]=>[8,5,3,4,2,6,7,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,5,2,7,6,8,1]=>[8,5,3,4,2,7,6,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,2,8,7,6,1]=>[6,5,3,4,2,7,8,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,6,2,1,7,8]=>[2,6,3,4,5,1,7,8]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,6,2,7,1,8]=>[7,6,3,4,5,2,1,8]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,6,2,7,8,1]=>[8,6,3,4,5,2,7,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,6,2,8,7,1]=>[7,6,3,4,5,2,8,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,7,2,1,8]=>[2,7,3,4,5,6,1,8]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,7,2,8,1]=>[8,7,3,4,5,6,2,1]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,2,1]=>[2,8,3,4,5,6,7,1]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,5,7,6,8,2,1]=>[2,8,3,4,5,7,6,1]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,5,7,8,6,2,1]=>[2,6,3,4,5,8,7,1]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,8,7,6,2,1]=>[2,6,3,4,5,7,8,1]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,4,6,5,7,2,8,1]=>[8,7,3,4,6,5,2,1]=>[[[[[.,.],.],[.,[[.,.],.]]],.],.]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,4,6,7,5,2,8,1]=>[8,5,3,4,7,6,2,1]=>[[[[[.,.],.],[.,[[.,.],.]]],.],.]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,4,6,7,8,5,2,1]=>[2,5,3,4,8,6,7,1]=>[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]
[1,1,1,0,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,6,8,7,5,2,1]=>[2,5,3,4,7,6,8,1]=>[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,4,7,6,5,2,8,1]=>[8,5,3,4,6,7,2,1]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,4,7,8,6,5,2,1]=>[2,5,3,4,6,8,7,1]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,8,7,6,5,2,1]=>[2,5,3,4,6,7,8,1]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,5,4,2,1,6,7,8]=>[2,4,3,5,1,6,7,8]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,5,4,2,1,7,6,8]=>[2,4,3,5,1,7,6,8]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,5,4,2,1,7,8,6]=>[2,4,3,5,1,8,7,6]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,5,4,2,1,8,7,6]=>[2,4,3,5,1,7,8,6]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[3,5,4,2,6,1,8,7]=>[6,4,3,5,2,1,8,7]=>[[[[[.,.],.],[.,.]],.],[[.,.],.]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,5,4,2,6,7,1,8]=>[7,4,3,5,2,6,1,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[3,5,4,2,6,8,7,1]=>[7,4,3,5,2,6,8,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[3,5,4,2,7,6,8,1]=>[8,4,3,5,2,7,6,1]=>[[[[[.,.],.],[.,.]],[[.,.],.]],.]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,5,4,6,2,1,8,7]=>[2,6,3,5,4,1,8,7]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,5,4,6,2,7,1,8]=>[7,6,3,5,4,2,1,8]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[3,5,4,6,2,7,8,1]=>[8,6,3,5,4,2,7,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[3,5,4,6,2,8,7,1]=>[7,6,3,5,4,2,8,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[3,5,4,6,7,2,8,1]=>[8,7,3,5,4,6,2,1]=>[[[[[.,.],.],[[.,.],[.,.]]],.],.]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,5,4,6,8,7,2,1]=>[2,7,3,5,4,6,8,1]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[3,5,4,7,6,2,8,1]=>[8,6,3,5,4,7,2,1]=>[[[[[.,.],.],[[.,.],[.,.]]],.],.]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[3,5,4,7,6,8,2,1]=>[2,8,3,5,4,7,6,1]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,5,4,7,8,6,2,1]=>[2,6,3,5,4,8,7,1]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[3,5,6,4,2,1,7,8]=>[2,4,3,6,5,1,7,8]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,5,6,4,2,1,8,7]=>[2,4,3,6,5,1,8,7]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,5,6,4,2,7,1,8]=>[7,4,3,6,5,2,1,8]=>[[[[[.,.],.],[[.,.],.]],.],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[3,5,6,4,2,8,7,1]=>[7,4,3,6,5,2,8,1]=>[[[[[.,.],.],[[.,.],.]],[.,.]],.]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,5,6,4,7,2,1,8]=>[2,7,3,6,5,4,1,8]=>[[.,[[.,.],[[[.,.],.],.]]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,5,6,4,7,2,8,1]=>[8,7,3,6,5,4,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,5,6,7,4,2,8,1]=>[8,4,3,7,5,6,2,1]=>[[[[[.,.],.],[[.,.],[.,.]]],.],.]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[3,5,6,7,4,8,2,1]=>[2,8,3,7,5,6,4,1]=>[[.,[[.,.],[[[.,.],[.,.]],.]]],.]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,8,4,2,1]=>[2,4,3,8,5,6,7,1]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,5,6,8,7,4,2,1]=>[2,4,3,7,5,6,8,1]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,5,7,6,4,2,1,8]=>[2,4,3,6,5,7,1,8]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,5,7,6,8,4,2,1]=>[2,4,3,8,5,7,6,1]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,5,7,8,6,4,2,1]=>[2,4,3,6,5,8,7,1]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,5,8,7,6,4,2,1]=>[2,4,3,6,5,7,8,1]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,6,5,4,2,1,8,7]=>[2,4,3,5,6,1,8,7]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[3,6,5,4,2,7,8,1]=>[8,4,3,5,6,2,7,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,6,5,4,7,2,8,1]=>[8,7,3,5,6,4,2,1]=>[[[[[.,.],.],[[.,[.,.]],.]],.],.]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,6,5,4,8,7,2,1]=>[2,7,3,5,6,4,8,1]=>[[.,[[.,.],[[.,[.,.]],[.,.]]]],.]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[3,6,5,7,4,2,8,1]=>[8,4,3,7,6,5,2,1]=>[[[[[.,.],.],[[[.,.],.],.]],.],.]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[3,6,5,7,4,8,2,1]=>[2,8,3,7,6,5,4,1]=>[[.,[[.,.],[[[[.,.],.],.],.]]],.]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,6,5,7,8,4,2,1]=>[2,4,3,8,6,5,7,1]=>[[.,[[.,.],[[[.,.],.],[.,.]]]],.]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,6,5,8,7,4,2,1]=>[2,4,3,7,6,5,8,1]=>[[.,[[.,.],[[[.,.],.],[.,.]]]],.]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[3,6,7,5,4,2,8,1]=>[8,4,3,5,7,6,2,1]=>[[[[[.,.],.],[.,[[.,.],.]]],.],.]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[3,6,7,5,4,8,2,1]=>[2,8,3,5,7,6,4,1]=>[[.,[[.,.],[[.,[[.,.],.]],.]]],.]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[3,6,7,5,8,4,2,1]=>[2,4,3,8,7,6,5,1]=>[[.,[[.,.],[[[[.,.],.],.],.]]],.]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,6,7,8,5,4,2,1]=>[2,4,3,5,8,6,7,1]=>[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,7,6,5,4,2,1,8]=>[2,4,3,5,6,7,1,8]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,7,6,5,4,2,8,1]=>[8,4,3,5,6,7,2,1]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,7,6,5,4,8,2,1]=>[2,8,3,5,6,7,4,1]=>[[.,[[.,.],[[.,[.,[.,.]]],.]]],.]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,7,8,6,5,4,2,1]=>[2,4,3,5,6,8,7,1]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,8,7,6,5,4,2,1]=>[2,4,3,5,6,7,8,1]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[4,3,2,1,5,6,8,7]=>[2,3,4,1,5,6,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[4,3,2,1,5,7,6,8]=>[2,3,4,1,5,7,6,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[4,3,2,1,5,7,8,6]=>[2,3,4,1,5,8,7,6]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[4,3,2,1,5,8,7,6]=>[2,3,4,1,5,7,8,6]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[4,3,2,1,6,5,7,8]=>[2,3,4,1,6,5,7,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7]=>[2,3,4,1,6,5,8,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[4,3,2,1,6,7,5,8]=>[2,3,4,1,7,6,5,8]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[4,3,2,1,6,7,8,5]=>[2,3,4,1,8,6,7,5]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[4,3,2,1,6,8,7,5]=>[2,3,4,1,7,6,8,5]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[4,3,2,1,7,6,5,8]=>[2,3,4,1,6,7,5,8]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[4,3,2,1,7,6,8,5]=>[2,3,4,1,8,7,6,5]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[4,3,2,1,7,8,6,5]=>[2,3,4,1,6,8,7,5]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>[2,3,4,1,6,7,8,5]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[4,3,2,5,1,6,7,8]=>[5,3,4,2,1,6,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[4,3,2,5,1,6,8,7]=>[5,3,4,2,1,6,8,7]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,3,2,5,1,7,8,6]=>[5,3,4,2,1,8,7,6]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[4,3,2,5,1,8,7,6]=>[5,3,4,2,1,7,8,6]=>[[[[.,.],[.,.]],.],[[.,[.,.]],.]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[4,3,2,5,6,1,8,7]=>[6,3,4,2,5,1,8,7]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,8,1]=>[8,3,4,2,5,6,7,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[4,3,2,6,5,1,8,7]=>[5,3,4,2,6,1,8,7]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[4,3,2,6,5,7,1,8]=>[7,3,4,2,6,5,1,8]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[4,3,2,6,5,7,8,1]=>[8,3,4,2,6,5,7,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[4,3,2,6,5,8,7,1]=>[7,3,4,2,6,5,8,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[4,3,2,6,7,5,1,8]=>[5,3,4,2,7,6,1,8]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,6,7,8,5,1]=>[5,3,4,2,8,6,7,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[4,3,2,6,8,7,5,1]=>[5,3,4,2,7,6,8,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,3,2,8,7,6,5,1]=>[5,3,4,2,6,7,8,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[4,3,5,2,1,6,7,8]=>[2,5,4,3,1,6,7,8]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[4,3,5,2,1,6,8,7]=>[2,5,4,3,1,6,8,7]=>[[.,[[[.,.],.],.]],[.,[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[4,3,5,2,1,7,8,6]=>[2,5,4,3,1,8,7,6]=>[[.,[[[.,.],.],.]],[[[.,.],.],.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[4,3,5,2,6,1,7,8]=>[6,5,4,3,2,1,7,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,3,5,2,6,1,8,7]=>[6,5,4,3,2,1,8,7]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[4,3,5,2,6,7,1,8]=>[7,5,4,3,2,6,1,8]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[4,3,5,2,6,7,8,1]=>[8,5,4,3,2,6,7,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[4,3,5,2,6,8,7,1]=>[7,5,4,3,2,6,8,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[4,3,5,2,7,6,1,8]=>[6,5,4,3,2,7,1,8]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,3,5,2,7,6,8,1]=>[8,5,4,3,2,7,6,1]=>[[[[[[.,.],.],.],.],[[.,.],.]],.]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[4,3,5,2,8,7,6,1]=>[6,5,4,3,2,7,8,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[4,3,5,6,2,1,8,7]=>[2,6,4,3,5,1,8,7]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[4,3,5,6,2,7,1,8]=>[7,6,4,3,5,2,1,8]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[4,3,5,6,2,7,8,1]=>[8,6,4,3,5,2,7,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,7,2,8,1]=>[8,7,4,3,5,6,2,1]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,8,2,1]=>[2,8,4,3,5,6,7,1]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[4,3,5,6,8,7,2,1]=>[2,7,4,3,5,6,8,1]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[4,3,5,7,6,2,8,1]=>[8,6,4,3,5,7,2,1]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[4,3,5,7,6,8,2,1]=>[2,8,4,3,5,7,6,1]=>[[.,[[[.,.],.],[.,[[.,.],.]]]],.]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,7,8,6,2,1]=>[2,6,4,3,5,8,7,1]=>[[.,[[[.,.],.],[.,[[.,.],.]]]],.]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[4,3,6,5,2,1,8,7]=>[2,5,4,3,6,1,8,7]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[4,3,6,5,2,7,1,8]=>[7,5,4,3,6,2,1,8]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[4,3,6,5,2,8,7,1]=>[7,5,4,3,6,2,8,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,3,6,5,7,2,8,1]=>[8,7,4,3,6,5,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[4,3,6,5,7,8,2,1]=>[2,8,4,3,6,5,7,1]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,8,7,2,1]=>[2,7,4,3,6,5,8,1]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[4,3,6,7,5,2,8,1]=>[8,5,4,3,7,6,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[4,3,6,7,5,8,2,1]=>[2,8,4,3,7,6,5,1]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,6,7,8,5,2,1]=>[2,5,4,3,8,6,7,1]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[4,3,7,6,5,8,2,1]=>[2,8,4,3,6,7,5,1]=>[[.,[[[.,.],.],[[.,[.,.]],.]]],.]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[4,3,7,6,8,5,2,1]=>[2,5,4,3,8,7,6,1]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[4,5,3,2,1,6,7,8]=>[2,3,5,4,1,6,7,8]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[4,5,3,2,1,6,8,7]=>[2,3,5,4,1,6,8,7]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[4,5,3,2,1,7,8,6]=>[2,3,5,4,1,8,7,6]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[4,5,3,2,6,1,8,7]=>[6,3,5,4,2,1,8,7]=>[[[[.,.],[[.,.],.]],.],[[.,.],.]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[4,5,3,2,6,7,1,8]=>[7,3,5,4,2,6,1,8]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[4,5,3,2,6,7,8,1]=>[8,3,5,4,2,6,7,1]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[4,5,3,2,7,6,1,8]=>[6,3,5,4,2,7,1,8]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[4,5,3,2,7,6,8,1]=>[8,3,5,4,2,7,6,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[4,5,3,2,7,8,6,1]=>[6,3,5,4,2,8,7,1]=>[[[[.,.],[[.,.],.]],[[.,.],.]],.]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,3,2,8,7,6,1]=>[6,3,5,4,2,7,8,1]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[4,5,3,6,2,1,8,7]=>[2,6,5,4,3,1,8,7]=>[[.,[[[[.,.],.],.],.]],[[.,.],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[4,5,3,6,2,7,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[4,5,3,6,2,7,8,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[4,5,3,6,2,8,7,1]=>[7,6,5,4,3,2,8,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[4,5,3,6,7,2,8,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[4,5,3,6,7,8,2,1]=>[2,8,5,4,3,6,7,1]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,6,8,7,2,1]=>[2,7,5,4,3,6,8,1]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[4,5,3,7,6,2,8,1]=>[8,6,5,4,3,7,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[4,5,3,7,6,8,2,1]=>[2,8,5,4,3,7,6,1]=>[[.,[[[[.,.],.],.],[[.,.],.]]],.]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[4,5,3,7,8,6,2,1]=>[2,6,5,4,3,8,7,1]=>[[.,[[[[.,.],.],.],[[.,.],.]]],.]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[4,5,3,8,7,6,2,1]=>[2,6,5,4,3,7,8,1]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,6,3,2,1,7,8]=>[2,3,6,4,5,1,7,8]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,6,3,2,1,8,7]=>[2,3,6,4,5,1,8,7]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,6,3,2,7,8,1]=>[8,3,6,4,5,2,7,1]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,6,3,2,8,7,1]=>[7,3,6,4,5,2,8,1]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,6,3,7,2,8,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,6,3,8,7,2,1]=>[2,7,6,4,5,3,8,1]=>[[.,[[[[.,.],.],[.,.]],[.,.]]],.]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,7,3,2,8,1]=>[8,3,7,4,5,6,2,1]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,7,3,8,2,1]=>[2,8,7,4,5,6,3,1]=>[[.,[[[[.,.],.],[.,[.,.]]],.]],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,3,2,1]=>[2,3,8,4,5,6,7,1]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,6,8,7,3,2,1]=>[2,3,7,4,5,6,8,1]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,5,7,8,6,3,2,1]=>[2,3,6,4,5,8,7,1]=>[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[4,5,8,7,6,3,2,1]=>[2,3,6,4,5,7,8,1]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[4,6,5,3,2,8,7,1]=>[7,3,5,4,6,2,8,1]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[4,6,5,3,7,2,8,1]=>[8,7,5,4,6,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[4,6,5,3,8,7,2,1]=>[2,7,5,4,6,3,8,1]=>[[.,[[[[.,.],.],[.,.]],[.,.]]],.]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[4,6,5,7,3,2,8,1]=>[8,3,7,4,6,5,2,1]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[4,6,5,7,3,8,2,1]=>[2,8,7,4,6,5,3,1]=>[[.,[[[[.,.],.],[[.,.],.]],.]],.]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,6,5,8,7,3,2,1]=>[2,3,7,4,6,5,8,1]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[4,6,7,5,3,2,8,1]=>[8,3,5,4,7,6,2,1]=>[[[[.,.],[[.,.],[[.,.],.]]],.],.]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[4,6,7,5,3,8,2,1]=>[2,8,5,4,7,6,3,1]=>[[.,[[[[.,.],.],[[.,.],.]],.]],.]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,6,7,8,5,3,2,1]=>[2,3,5,4,8,6,7,1]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[4,6,8,7,5,3,2,1]=>[2,3,5,4,7,6,8,1]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[4,7,6,5,3,2,1,8]=>[2,3,5,4,6,7,1,8]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[4,7,6,5,3,2,8,1]=>[8,3,5,4,6,7,2,1]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[4,7,6,5,3,8,2,1]=>[2,8,5,4,6,7,3,1]=>[[.,[[[[.,.],.],[.,[.,.]]],.]],.]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[4,7,6,5,8,3,2,1]=>[2,3,8,4,6,7,5,1]=>[[.,[.,[[.,.],[[.,[.,.]],.]]]],.]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[4,8,7,6,5,3,2,1]=>[2,3,5,4,6,7,8,1]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[5,4,3,2,1,6,8,7]=>[2,3,4,5,1,6,8,7]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[5,4,3,2,1,7,6,8]=>[2,3,4,5,1,7,6,8]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[5,4,3,2,1,7,8,6]=>[2,3,4,5,1,8,7,6]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,4,3,2,1,8,7,6]=>[2,3,4,5,1,7,8,6]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[5,4,3,2,6,1,7,8]=>[6,3,4,5,2,1,7,8]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[5,4,3,2,6,1,8,7]=>[6,3,4,5,2,1,8,7]=>[[[[.,.],[.,[.,.]]],.],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,7,8,1]=>[8,3,4,5,2,6,7,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[5,4,3,2,7,6,1,8]=>[6,3,4,5,2,7,1,8]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[5,4,3,2,7,6,8,1]=>[8,3,4,5,2,7,6,1]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[5,4,3,2,7,8,6,1]=>[6,3,4,5,2,8,7,1]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,4,3,2,8,7,6,1]=>[6,3,4,5,2,7,8,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[5,4,3,6,2,1,7,8]=>[2,6,4,5,3,1,7,8]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[5,4,3,6,2,7,1,8]=>[7,6,4,5,3,2,1,8]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[5,4,3,6,2,8,7,1]=>[7,6,4,5,3,2,8,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,8,2,1]=>[2,8,4,5,3,6,7,1]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[5,4,6,3,2,1,7,8]=>[2,3,6,5,4,1,7,8]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[5,4,6,3,2,1,8,7]=>[2,3,6,5,4,1,8,7]=>[[.,[.,[[[.,.],.],.]]],[[.,.],.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[5,4,6,3,2,7,1,8]=>[7,3,6,5,4,2,1,8]=>[[[[.,.],[[[.,.],.],.]],.],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[5,4,6,3,2,8,7,1]=>[7,3,6,5,4,2,8,1]=>[[[[.,.],[[[.,.],.],.]],[.,.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[5,4,6,3,7,2,1,8]=>[2,7,6,5,4,3,1,8]=>[[.,[[[[[.,.],.],.],.],.]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,4,6,3,7,2,8,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[5,4,6,3,8,7,2,1]=>[2,7,6,5,4,3,8,1]=>[[.,[[[[[.,.],.],.],.],[.,.]]],.]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[5,4,6,7,3,2,1,8]=>[2,3,7,5,4,6,1,8]=>[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[5,4,6,7,3,2,8,1]=>[8,3,7,5,4,6,2,1]=>[[[[.,.],[[[.,.],.],[.,.]]],.],.]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[5,4,6,7,3,8,2,1]=>[2,8,7,5,4,6,3,1]=>[[.,[[[[[.,.],.],.],[.,.]],.]],.]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,2,1]=>[2,3,8,5,4,6,7,1]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[5,4,6,8,7,3,2,1]=>[2,3,7,5,4,6,8,1]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[5,4,7,6,3,2,8,1]=>[8,3,6,5,4,7,2,1]=>[[[[.,.],[[[.,.],.],[.,.]]],.],.]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[5,4,8,7,6,3,2,1]=>[2,3,6,5,4,7,8,1]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[5,6,4,3,2,1,7,8]=>[2,3,4,6,5,1,7,8]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[5,6,4,3,7,2,1,8]=>[2,7,4,6,5,3,1,8]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[5,6,4,3,7,2,8,1]=>[8,7,4,6,5,3,2,1]=>[[[[[[.,.],.],[[.,.],.]],.],.],.]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[5,6,4,3,7,8,2,1]=>[2,8,4,6,5,3,7,1]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[5,6,4,3,8,7,2,1]=>[2,7,4,6,5,3,8,1]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[5,6,4,7,3,2,1,8]=>[2,3,7,6,5,4,1,8]=>[[.,[.,[[[[.,.],.],.],.]]],[.,.]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[5,6,4,7,3,2,8,1]=>[8,3,7,6,5,4,2,1]=>[[[[.,.],[[[[.,.],.],.],.]],.],.]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[5,6,4,7,3,8,2,1]=>[2,8,7,6,5,4,3,1]=>[[.,[[[[[[.,.],.],.],.],.],.]],.]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,6,4,7,8,3,2,1]=>[2,3,8,6,5,4,7,1]=>[[.,[.,[[[[.,.],.],.],[.,.]]]],.]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[5,6,4,8,7,3,2,1]=>[2,3,7,6,5,4,8,1]=>[[.,[.,[[[[.,.],.],.],[.,.]]]],.]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,6,7,4,3,2,1,8]=>[2,3,4,7,5,6,1,8]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,4,3,2,1]=>[2,3,4,8,5,6,7,1]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,6,8,7,4,3,2,1]=>[2,3,4,7,5,6,8,1]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[5,7,6,4,3,2,1,8]=>[2,3,4,6,5,7,1,8]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[5,7,6,8,4,3,2,1]=>[2,3,4,8,5,7,6,1]=>[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,7,8,6,4,3,2,1]=>[2,3,4,6,5,8,7,1]=>[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[5,8,7,6,4,3,2,1]=>[2,3,4,6,5,7,8,1]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,5,4,3,2,1,7,8]=>[2,3,4,5,6,1,7,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,5,4,3,2,1,8,7]=>[2,3,4,5,6,1,8,7]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,5,4,3,2,8,7,1]=>[7,3,4,5,6,2,8,1]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[6,5,4,3,7,2,1,8]=>[2,7,4,5,6,3,1,8]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[6,5,4,3,7,2,8,1]=>[8,7,4,5,6,3,2,1]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,2,1]=>[2,8,4,5,6,3,7,1]=>[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[6,5,4,3,8,7,2,1]=>[2,7,4,5,6,3,8,1]=>[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[6,5,4,7,3,2,1,8]=>[2,3,7,5,6,4,1,8]=>[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[6,5,4,7,3,2,8,1]=>[8,3,7,5,6,4,2,1]=>[[[[.,.],[[[.,.],[.,.]],.]],.],.]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[6,5,4,7,3,8,2,1]=>[2,8,7,5,6,4,3,1]=>[[.,[[[[[.,.],.],[.,.]],.],.]],.]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[6,5,4,7,8,3,2,1]=>[2,3,8,5,6,4,7,1]=>[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[6,5,4,8,7,3,2,1]=>[2,3,7,5,6,4,8,1]=>[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[6,5,7,4,3,2,1,8]=>[2,3,4,7,6,5,1,8]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[6,5,7,4,3,2,8,1]=>[8,3,4,7,6,5,2,1]=>[[[[.,.],[.,[[[.,.],.],.]]],.],.]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[6,5,7,4,3,8,2,1]=>[2,8,4,7,6,5,3,1]=>[[.,[[[.,.],[[[.,.],.],.]],.]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[6,5,7,4,8,3,2,1]=>[2,3,8,7,6,5,4,1]=>[[.,[.,[[[[[.,.],.],.],.],.]]],.]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[6,5,7,8,4,3,2,1]=>[2,3,4,8,6,5,7,1]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[6,5,8,7,4,3,2,1]=>[2,3,4,7,6,5,8,1]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[6,7,5,4,3,2,1,8]=>[2,3,4,5,7,6,1,8]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[6,7,5,4,3,2,8,1]=>[8,3,4,5,7,6,2,1]=>[[[[.,.],[.,[.,[[.,.],.]]]],.],.]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[6,7,5,4,8,3,2,1]=>[2,3,8,5,7,6,4,1]=>[[.,[.,[[[.,.],[[.,.],.]],.]]],.]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[6,7,5,8,4,3,2,1]=>[2,3,4,8,7,6,5,1]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],.]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,5,4,3,2,1]=>[2,3,4,5,8,6,7,1]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,8,7,5,4,3,2,1]=>[2,3,4,5,7,6,8,1]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,1,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,6,5,4,3,2,8,1]=>[8,3,4,5,6,7,2,1]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[7,6,5,4,3,8,2,1]=>[2,8,4,5,6,7,3,1]=>[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[7,6,5,4,8,3,2,1]=>[2,3,8,5,6,7,4,1]=>[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[7,6,5,8,4,3,2,1]=>[2,3,4,8,6,7,5,1]=>[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[7,6,8,5,4,3,2,1]=>[2,3,4,5,8,7,6,1]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[7,8,6,5,4,3,2,1]=>[2,3,4,5,6,8,7,1]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,7,6,5,4,3,2,1,9]=>[2,3,4,5,6,7,8,1,9]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,2]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[9,8,7,6,5,4,3,2,1,10]=>[2,3,4,5,6,7,8,9,1,10]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[7,8,6,5,4,3,2,1,9]=>[2,3,4,5,6,8,7,1,9]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,8,9,7,6,5,4,3,2]=>[1,3,4,5,6,7,9,8,2]=>[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,10,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,10,2]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[10,9,8,7,6,5,4,3,2,1,11]=>[2,3,4,5,6,7,8,9,10,1,11]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[8,9,7,6,5,4,3,2,1,10]=>[2,3,4,5,6,7,9,8,1,10]=>[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],[.,.]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[6,8,7,5,4,3,2,1,9]=>[2,3,4,5,7,6,8,1,9]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,7,9,8,6,5,4,3,2]=>[1,3,4,5,6,8,7,9,2]=>[.,[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,9,10,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,10,9,2]=>[.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,11,10,9,8,7,6,5,4,3,2]=>[1,3,4,5,6,7,8,9,10,11,2]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[5,6,7,8,4,3,2,1,9]=>[2,3,4,8,5,6,7,1,9]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],[.,.]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,8,7,6,5,4,3,1,9]=>[3,2,4,5,6,7,8,1,9]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[7,6,5,4,3,2,1,9,8]=>[2,3,4,5,6,7,1,9,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,9,8,7,6,5,4,3]=>[2,1,4,5,6,7,8,9,3]=>[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,9,8,7,6,5,4,2]=>[1,4,3,5,6,7,8,9,2]=>[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[7,6,5,4,3,2,1,8,9]=>[2,3,4,5,6,7,1,8,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,8,7,6,5,4,3,2,9]=>[1,3,4,5,6,7,8,2,9]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,9,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,9,3]=>[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[8,7,6,5,4,3,2,1,10,9]=>[2,3,4,5,6,7,8,1,10,9]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[6,7,5,4,3,2,1,8,9]=>[2,3,4,5,7,6,1,8,9]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,1,10,9,8,7,6,5,4,3]=>[2,1,4,5,6,7,8,9,10,3]=>[[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[8,7,6,5,4,3,2,1,9,10]=>[2,3,4,5,6,7,8,1,9,10]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,9,8,7,6,5,4,3,2,10]=>[1,3,4,5,6,7,8,9,2,10]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,10,9,8,7,6,5,4,3]=>[1,2,4,5,6,7,8,9,10,3]=>[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]
[]=>[]=>[]=>.
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,1]=>[9,2,3,4,5,6,7,8,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,7,9,8,1]=>[8,2,3,4,5,6,7,9,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,5,6,8,9,7,1]=>[7,2,3,4,5,6,9,8,1]=>[[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,5,7,8,9,6,1]=>[6,2,3,4,5,9,7,8,1]=>[[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]],.]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,6,7,8,9,5,1]=>[5,2,3,4,9,6,7,8,1]=>[[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]],.]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,8,9,4,1]=>[4,2,3,9,5,6,7,8,1]=>[[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,9,8,7,6,5,4,1]=>[4,2,3,5,6,7,8,9,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,8,9,3,1]=>[3,2,9,4,5,6,7,8,1]=>[[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,9,8,7,6,5,4,3,1]=>[3,2,4,5,6,7,8,9,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,9,1]=>[9,3,2,4,5,6,7,8,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,2,9,8,7,6,5,4,1]=>[4,3,2,5,6,7,8,9,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,8,9,1]=>[9,4,3,2,5,6,7,8,1]=>[[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,9,2,1]=>[2,9,3,4,5,6,7,8,1]=>[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,9,8,7,6,5,4,2,1]=>[2,4,3,5,6,7,8,9,1]=>[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,8,9,1]=>[9,3,4,2,5,6,7,8,1]=>[[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,8,9,2,1]=>[2,9,4,3,5,6,7,8,1]=>[[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,9,3,2,1]=>[2,3,9,4,5,6,7,8,1]=>[[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,7,8,9,1]=>[9,3,4,5,2,6,7,8,1]=>[[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]],.]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,6,7,8,9,3,2,1]=>[2,3,9,5,4,6,7,8,1]=>[[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]],.]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,6,4,7,3,8,2,9,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,9,4,3,2,1]=>[2,3,4,9,5,6,7,8,1]=>[[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[5,9,8,7,6,4,3,2,1]=>[2,3,4,6,5,7,8,9,1]=>[[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,7,8,9,4,3,2,1]=>[2,3,4,9,6,5,7,8,1]=>[[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]],.]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,9,5,4,3,2,1]=>[2,3,4,5,9,6,7,8,1]=>[[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[6,7,9,8,5,4,3,2,1]=>[2,3,4,5,8,6,7,9,1]=>[[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[6,8,7,9,5,4,3,2,1]=>[2,3,4,5,9,6,8,7,1]=>[[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]],.]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[6,9,8,7,5,4,3,2,1]=>[2,3,4,5,7,6,8,9,1]=>[[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[7,6,8,9,5,4,3,2,1]=>[2,3,4,5,9,7,6,8,1]=>[[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]],.]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[7,6,9,8,5,4,3,2,1]=>[2,3,4,5,8,7,6,9,1]=>[[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]],.]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[7,8,6,5,4,3,2,9,1]=>[9,3,4,5,6,8,7,2,1]=>[[[[.,.],[.,[.,[.,[[.,.],.]]]]],.],.]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[7,8,9,6,5,4,3,2,1]=>[2,3,4,5,6,9,7,8,1]=>[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[7,9,8,6,5,4,3,2,1]=>[2,3,4,5,6,8,7,9,1]=>[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,7,6,5,4,3,2,9,1]=>[9,3,4,5,6,7,8,2,1]=>[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[8,7,6,5,4,3,9,2,1]=>[2,9,4,5,6,7,8,3,1]=>[[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[8,7,6,5,4,9,3,2,1]=>[2,3,9,5,6,7,8,4,1]=>[[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[8,7,6,5,9,4,3,2,1]=>[2,3,4,9,6,7,8,5,1]=>[[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[8,7,6,9,5,4,3,2,1]=>[2,3,4,5,9,7,8,6,1]=>[[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]],.]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[8,7,9,6,5,4,3,2,1]=>[2,3,4,5,6,9,8,7,1]=>[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[8,9,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,9,8,1]=>[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,1]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,6,8,9,7]=>[1,2,3,4,5,6,9,8,7]=>[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,5,7,8,9,6]=>[1,2,3,4,5,9,7,8,6]=>[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,9,5]=>[1,2,3,4,9,6,7,8,5]=>[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,9,4]=>[1,2,3,9,5,6,7,8,4]=>[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,8,9,3]=>[1,2,9,4,5,6,7,8,3]=>[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,9,2]=>[1,9,3,4,5,6,7,8,2]=>[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,9,8,7]=>[1,2,3,4,5,6,8,9,7]=>[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,6,7,9,10,8]=>[1,2,3,4,5,6,7,10,9,8]=>[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,4,5,8,7,9,6]=>[1,2,3,4,5,9,8,7,6]=>[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,4,5,6,8,9,10,7]=>[1,2,3,4,5,6,10,8,9,7]=>[.,[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,3,4,7,6,8,9,5]=>[1,2,3,4,9,7,6,8,5]=>[.,[.,[.,[.,[[[[.,.],.],[.,.]],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,3,4,5,7,8,9,10,6]=>[1,2,3,4,5,10,7,8,9,6]=>[.,[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,2,3,6,5,7,8,9,4]=>[1,2,3,9,6,5,7,8,4]=>[.,[.,[.,[[[[.,.],.],[.,[.,.]]],.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,3,4,6,7,8,9,10,5]=>[1,2,3,4,10,6,7,8,9,5]=>[.,[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,2,5,4,6,7,8,9,3]=>[1,2,9,5,4,6,7,8,3]=>[.,[.,[[[[.,.],.],[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,8,9,10,4]=>[1,2,3,10,5,6,7,8,9,4]=>[.,[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,8,9,2]=>[1,9,4,3,5,6,7,8,2]=>[.,[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,8,9,10,3]=>[1,2,10,4,5,6,7,8,9,3]=>[.,[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,3,4,5,6,7,8,9,2]=>[.,[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,10,1]=>[10,2,3,4,5,6,7,8,9,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,7,10,9,8]=>[1,2,3,4,5,6,7,9,10,8]=>[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,5,6,7,8,10,11,9]=>[1,2,3,4,5,6,7,8,11,10,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,4,5,8,9,7,6]=>[1,2,3,4,5,7,9,8,6]=>[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,5,9,8,7,6]=>[1,2,3,4,5,7,8,9,6]=>[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,8,9,10,1]=>[10,3,2,4,5,6,7,8,9,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>[11,2,3,4,5,6,7,8,9,10,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,7,8,11,10,9]=>[1,2,3,4,5,6,7,8,10,11,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,5,6,10,9,8,7]=>[1,2,3,4,5,6,8,9,10,7]=>[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,9,8,7,6,5]=>[1,2,3,4,6,7,8,9,5]=>[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5,10,9,8,7,6]=>[1,2,3,4,5,7,8,9,10,6]=>[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,7,8,3,9,2]=>[1,9,8,4,5,6,7,3,2]=>[.,[[[[[.,.],.],[.,[.,[.,.]]]],.],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,8,9,3,2]=>[1,3,9,4,5,6,7,8,2]=>[.,[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,9,8,7,6,5,4]=>[1,2,3,5,6,7,8,9,4]=>[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,10,9,8,7,6,5]=>[1,2,3,4,6,7,8,9,10,5]=>[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,6,8,7,9]=>[1,2,3,4,5,6,8,7,9]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,5,7,6,9,8]=>[1,2,3,4,5,7,6,9,8]=>[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,8,7,9]=>[1,2,3,4,6,5,8,7,9]=>[.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,9,8]=>[1,2,3,5,4,7,6,9,8]=>[.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]=>[.,[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]=>[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,5,6,9,8,7]=>[1,3,2,4,5,6,8,9,7]=>[.,[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]=>[.,[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7,8,9]=>[1,3,4,2,5,6,7,8,9]=>[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,7,6,5,4,3,2,8,9]=>[1,3,4,5,6,7,2,8,9]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,7,9,8]=>[2,1,3,4,5,6,7,9,8]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,5,6,9,8,7]=>[2,1,3,4,5,6,8,9,7]=>[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7,8,9]=>[2,1,4,3,5,6,7,8,9]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,9,8,7,6,5]=>[2,1,4,3,6,7,8,9,5]=>[[.,.],[[.,.],[[.,[.,[.,[.,.]]]],.]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,8,7,6,5,4,3,9]=>[2,1,4,5,6,7,8,3,9]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8,9]=>[2,3,1,4,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,6,7,9,8]=>[2,3,1,4,5,6,7,9,8]=>[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,5,4,6,7,8,9]=>[2,3,1,5,4,6,7,8,9]=>[[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6,9,8]=>[2,3,1,5,4,7,6,9,8]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,2,1,9,8,7,6,5,4]=>[2,3,1,5,6,7,8,9,4]=>[[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8,9]=>[2,3,4,1,5,6,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[4,3,2,1,6,5,7,8,9]=>[2,3,4,1,6,5,7,8,9]=>[[.,[.,[.,.]]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,8,7,9]=>[2,3,4,1,6,5,8,7,9]=>[[.,[.,[.,.]]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,3,2,1,9,8,7,6,5]=>[2,3,4,1,6,7,8,9,5]=>[[.,[.,[.,.]]],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8,9]=>[2,3,4,5,1,6,7,8,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]=>[5,4,3,2,1,7,6,8,9]=>[2,3,4,5,1,7,6,8,9]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,4,3,2,1,9,8,7,6]=>[2,3,4,5,1,7,8,9,6]=>[[.,[.,[.,[.,.]]]],[[.,[.,[.,.]]],.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[6,5,4,3,2,1,7,8,9]=>[2,3,4,5,6,1,7,8,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[6,5,4,3,2,1,8,7,9]=>[2,3,4,5,6,1,8,7,9]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[6,5,4,3,2,1,9,8,7]=>[2,3,4,5,6,1,8,9,7]=>[[.,[.,[.,[.,[.,.]]]]],[[.,[.,.]],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,6,7,9,8,10]=>[1,2,3,4,5,6,7,9,8,10]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,4,5,6,8,7,10,9]=>[1,2,3,4,5,6,8,7,10,9]=>[.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,3,4,5,7,6,8,9,10]=>[1,2,3,4,5,7,6,8,9,10]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,4,6,7,8,9,10]=>[1,2,3,5,4,6,7,8,9,10]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,9,8,10]=>[1,2,3,5,4,7,6,9,8,10]=>[.,[.,[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,10,9,8,7,6,5,4]=>[1,2,3,5,6,7,8,9,10,4]=>[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7,10,9]=>[1,2,4,3,6,5,8,7,10,9]=>[.,[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,7,6,10,9,8]=>[1,3,2,5,4,7,6,9,10,8]=>[.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,7,8,10,9]=>[2,1,3,4,5,6,7,8,10,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3,10,9,8,7]=>[2,1,4,5,6,3,8,9,10,7]=>[[.,.],[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,8,7,6,5,4,3,10,9]=>[2,1,4,5,6,7,8,3,10,9]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7,8,9,10]=>[2,3,1,4,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,7,6,9,8,10]=>[2,3,1,5,4,7,6,9,8,10]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,2,1,10,9,8,7,6,5,4]=>[2,3,1,5,6,7,8,9,10,4]=>[[.,[.,.]],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7,8,9,10]=>[2,3,4,1,5,6,7,8,9,10]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[4,3,2,1,6,5,8,7,10,9]=>[2,3,4,1,6,5,8,7,10,9]=>[[.,[.,[.,.]]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,6,5,10,9,8,7]=>[2,3,4,1,6,5,8,9,10,7]=>[[.,[.,[.,.]]],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,8,7,6,5,10,9]=>[2,3,4,1,6,7,8,5,10,9]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,3,2,1,10,9,8,7,6,5]=>[2,3,4,1,6,7,8,9,10,5]=>[[.,[.,[.,.]]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1,6,7,8,9,10]=>[2,3,4,5,1,6,7,8,9,10]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[5,4,3,2,1,7,6,9,8,10]=>[2,3,4,5,1,7,6,9,8,10]=>[[.,[.,[.,[.,.]]]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1,10,9,8,7,6]=>[2,3,4,5,1,7,8,9,10,6]=>[[.,[.,[.,[.,.]]]],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1,7,8,9,10]=>[2,3,4,5,6,1,7,8,9,10]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,5,4,3,2,1,10,9,8,7]=>[2,3,4,5,6,1,8,9,10,7]=>[[.,[.,[.,[.,[.,.]]]]],[[.,[.,[.,.]]],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1,8,9,10]=>[2,3,4,5,6,7,1,8,9,10]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[7,6,5,4,3,2,1,9,8,10]=>[2,3,4,5,6,7,1,9,8,10]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,6,5,4,3,2,1,10,9,8]=>[2,3,4,5,6,7,1,9,10,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,[.,.]],.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[10,9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,10,1]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7,8,9]=>[4,2,3,1,5,6,7,8,9]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1,6,7,8,9]=>[5,2,3,4,1,6,7,8,9]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,5,6,1,7,8,9]=>[6,2,3,4,5,1,7,8,9]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,6,7,1,8,9]=>[7,2,3,4,5,6,1,8,9]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,8,1,9]=>[8,2,3,4,5,6,7,1,9]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7,8,9]=>[3,2,4,1,5,6,7,8,9]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,8,9,1,10]=>[9,2,3,4,5,6,7,8,1,10]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[5,6,7,8,10,9,4,3,2,1]=>[2,3,4,9,5,6,7,8,10,1]=>[[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,7,8,10,9,1]=>[9,2,3,4,5,6,7,8,10,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[9,8,10,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,10,9,8,1]=>[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,5,6,8,9,7]=>[1,3,2,4,5,6,9,8,7]=>[.,[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,7,8,2,1,9]=>[2,8,3,4,5,6,7,1,9]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7,8,9]=>[2,4,3,1,5,6,7,8,9]=>[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,10,9,8,7,6,5,4,3,1]=>[3,2,4,5,6,7,8,9,10,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,8,7,6,5,4,3,2,10,1]=>[10,3,4,5,6,7,8,9,2,1]=>[[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[10,9,8,7,6,5,4,3,2,11,1]=>[11,3,4,5,6,7,8,9,10,2,1]=>[[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[8,9,7,6,5,4,3,2,10,1]=>[10,3,4,5,6,7,9,8,2,1]=>[[[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]],.],.]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[9,10,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,10,9,1]=>[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[5,10,9,8,7,6,4,3,2,1]=>[2,3,4,6,5,7,8,9,10,1]=>[[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,8,9,4,3]=>[2,1,4,9,5,6,7,8,3]=>[[.,.],[[.,[[.,.],[.,[.,[.,.]]]]],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,8,9,10,3,1]=>[3,2,10,4,5,6,7,8,9,1]=>[[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[10,11,9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,11,10,1]=>[[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]],.]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,1,9,8,7,6,5,4]=>[3,2,1,5,6,7,8,9,4]=>[[[.,.],.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,6,7,9,8,2]=>[1,8,3,4,5,6,7,9,2]=>[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,6,7,1,9,8]=>[7,2,3,4,5,6,1,9,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,8,9,3]=>[2,1,9,4,5,6,7,8,3]=>[[.,.],[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,5,6,1,9,8,7]=>[6,2,3,4,5,1,8,9,7]=>[[[.,.],[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,8,9,10,3,2,1]=>[2,3,10,4,5,6,7,8,9,1]=>[[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[6,5,4,3,2,1,8,9,7]=>[2,3,4,5,6,1,9,8,7]=>[[.,[.,[.,[.,[.,.]]]]],[[[.,.],.],.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[9,8,7,6,5,4,3,10,2,1]=>[2,10,4,5,6,7,8,9,3,1]=>[[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[9,8,7,6,5,4,10,3,2,1]=>[2,3,10,5,6,7,8,9,4,1]=>[[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[9,8,7,6,5,10,4,3,2,1]=>[2,3,4,10,6,7,8,9,5,1]=>[[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[9,8,7,6,10,5,4,3,2,1]=>[2,3,4,5,10,7,8,9,6,1]=>[[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[9,8,7,10,6,5,4,3,2,1]=>[2,3,4,5,6,10,8,9,7,1]=>[[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,5,7,8,9,10,6,1]=>[6,2,3,4,5,10,7,8,9,1]=>[[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,8,7,9]=>[3,2,4,1,6,5,8,7,9]=>[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,9,8]=>[3,2,1,5,4,7,6,9,8]=>[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,3,1,6,5,8,7,10,9]=>[3,2,4,1,6,5,8,7,10,9]=>[[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,9,8,10]=>[3,2,1,5,4,7,6,9,8,10]=>[[[.,.],.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,5,6,7,9,10,8,1]=>[8,2,3,4,5,6,7,10,9,1]=>[[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,4,5,6,8,9,10,7,1]=>[7,2,3,4,5,6,10,8,9,1]=>[[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,6,7,8,9,10,5,1]=>[5,2,3,4,10,6,7,8,9,1]=>[[[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]],.]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,8,9,10,4,1]=>[4,2,3,10,5,6,7,8,9,1]=>[[[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,8,9,10,2,1]=>[2,10,3,4,5,6,7,8,9,1]=>[[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,6,7,8,9,11,10,1]=>[10,2,3,4,5,6,7,8,9,11,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,3,5,7,9,10,8,6,4,2]=>[1,4,3,6,5,8,7,10,9,2]=>[.,[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,3,6,7,5,9,10,8,4,2]=>[1,4,3,8,7,6,5,10,9,2]=>[.,[[[.,.],[[[[.,.],.],.],[[.,.],.]]],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,5,3,7,9,10,8,6,2]=>[1,6,5,4,3,8,7,10,9,2]=>[.,[[[[[.,.],.],.],[[.,.],[[.,.],.]]],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,4,6,7,5,3,9,10,8,2]=>[1,8,5,4,7,6,3,10,9,2]=>[.,[[[[[.,.],.],[[.,.],.]],[[.,.],.]],.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,5,6,4,7,3,9,10,8,2]=>[1,8,7,6,5,4,3,10,9,2]=>[.,[[[[[[[.,.],.],.],.],.],[[.,.],.]],.]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,4,6,8,9,7,5,3,10,2]=>[1,10,5,4,7,6,9,8,3,2]=>[.,[[[[[.,.],.],[[.,.],[[.,.],.]]],.],.]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,4,7,8,6,9,5,3,10,2]=>[1,10,5,4,9,8,7,6,3,2]=>[.,[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,4,8,9,7,3,10,2]=>[1,10,7,6,5,4,9,8,3,2]=>[.,[[[[[[[.,.],.],.],.],[[.,.],.]],.],.]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,5,7,8,6,4,9,3,10,2]=>[1,10,9,6,5,8,7,4,3,2]=>[.,[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,6,7,5,8,4,9,3,10,2]=>[1,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,1,5,7,9,10,8,6,4]=>[3,2,1,6,5,8,7,10,9,4]=>[[[.,.],.],[[[.,.],[[.,.],[[.,.],.]]],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,3,1,6,7,5,9,10,8,4]=>[3,2,1,8,7,6,5,10,9,4]=>[[[.,.],.],[[[[[.,.],.],.],[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,6,8,9,7,5,10,4]=>[3,2,1,10,7,6,9,8,5,4]=>[[[.,.],.],[[[[[.,.],.],[[.,.],.]],.],.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,3,1,7,8,6,9,5,10,4]=>[3,2,1,10,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1,7,9,10,8,6]=>[3,2,5,4,1,8,7,10,9,6]=>[[[.,.],[[.,.],.]],[[[.,.],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,1,8,9,7,10,6]=>[3,2,5,4,1,10,9,8,7,6]=>[[[.,.],[[.,.],.]],[[[[[.,.],.],.],.],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,4,2,5,1,7,9,10,8,6]=>[5,4,3,2,1,8,7,10,9,6]=>[[[[[.,.],.],.],.],[[[.,.],[[.,.],.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1,8,9,7,10,6]=>[5,4,3,2,1,10,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[2,4,6,7,5,3,1,9,10,8]=>[3,2,5,4,7,6,1,10,9,8]=>[[[.,.],[[.,.],[[.,.],.]]],[[[.,.],.],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[2,5,6,4,7,3,1,9,10,8]=>[3,2,7,6,5,4,1,10,9,8]=>[[[.,.],[[[[.,.],.],.],.]],[[[.,.],.],.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,2,6,7,5,1,9,10,8]=>[5,4,3,2,7,6,1,10,9,8]=>[[[[[.,.],.],.],[[.,.],.]],[[[.,.],.],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[3,5,6,4,2,7,1,9,10,8]=>[7,4,3,6,5,2,1,10,9,8]=>[[[[[.,.],.],[[.,.],.]],.],[[[.,.],.],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,5,3,6,2,7,1,9,10,8]=>[7,6,5,4,3,2,1,10,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,6,4,7,3,8,2,9,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,3,5,7,9,11,12,10,8,6,4,2]=>[1,4,3,6,5,8,7,10,9,12,11,2]=>[.,[[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]]
[1,0,1,1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,3,5,8,9,7,11,12,10,6,4,2]=>[1,4,3,6,5,10,9,8,7,12,11,2]=>[.,[[[.,.],[[.,.],[[[[.,.],.],.],[[.,.],.]]]],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,3,6,7,5,9,11,12,10,8,4,2]=>[1,4,3,8,7,6,5,10,9,12,11,2]=>[.,[[[.,.],[[[[.,.],.],.],[[.,.],[[.,.],.]]]],.]]
[1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,3,6,8,9,7,5,11,12,10,4,2]=>[1,4,3,10,7,6,9,8,5,12,11,2]=>[.,[[[.,.],[[[[.,.],.],[[.,.],.]],[[.,.],.]]],.]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,3,7,8,6,9,5,11,12,10,4,2]=>[1,4,3,10,9,8,7,6,5,12,11,2]=>[.,[[[.,.],[[[[[[.,.],.],.],.],.],[[.,.],.]]],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,4,5,3,7,9,11,12,10,8,6,2]=>[1,6,5,4,3,8,7,10,9,12,11,2]=>[.,[[[[[.,.],.],.],[[.,.],[[.,.],[[.,.],.]]]],.]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,4,5,3,8,9,7,11,12,10,6,2]=>[1,6,5,4,3,10,9,8,7,12,11,2]=>[.,[[[[[.,.],.],.],[[[[.,.],.],.],[[.,.],.]]],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,5,3,9,11,12,10,8,2]=>[1,8,5,4,7,6,3,10,9,12,11,2]=>[.,[[[[[.,.],.],[[.,.],.]],[[.,.],[[.,.],.]]],.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,5,6,4,7,3,9,11,12,10,8,2]=>[1,8,7,6,5,4,3,10,9,12,11,2]=>[.,[[[[[[[.,.],.],.],.],.],[[.,.],[[.,.],.]]],.]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,4,6,8,9,7,5,3,11,12,10,2]=>[1,10,5,4,7,6,9,8,3,12,11,2]=>[.,[[[[[.,.],.],[[.,.],[[.,.],.]]],[[.,.],.]],.]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,4,7,8,6,9,5,3,11,12,10,2]=>[1,10,5,4,9,8,7,6,3,12,11,2]=>[.,[[[[[.,.],.],[[[[.,.],.],.],.]],[[.,.],.]],.]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,5,6,4,8,9,7,3,11,12,10,2]=>[1,10,7,6,5,4,9,8,3,12,11,2]=>[.,[[[[[[[.,.],.],.],.],[[.,.],.]],[[.,.],.]],.]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,5,7,8,6,4,9,3,11,12,10,2]=>[1,10,9,6,5,8,7,4,3,12,11,2]=>[.,[[[[[[[.,.],.],.],[[.,.],.]],.],[[.,.],.]],.]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,6,7,5,8,4,9,3,11,12,10,2]=>[1,10,9,8,7,6,5,4,3,12,11,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]],.]]
[1,0,1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,4,6,8,10,11,9,7,5,3,12,2]=>[1,12,5,4,7,6,9,8,11,10,3,2]=>[.,[[[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]],.],.]]
[1,0,1,1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,0,0]=>[1,4,6,9,10,8,11,7,5,3,12,2]=>[1,12,5,4,7,6,11,10,9,8,3,2]=>[.,[[[[[.,.],.],[[.,.],[[[[.,.],.],.],.]]],.],.]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,4,7,8,6,10,11,9,5,3,12,2]=>[1,12,5,4,9,8,7,6,11,10,3,2]=>[.,[[[[[.,.],.],[[[[.,.],.],.],[[.,.],.]]],.],.]]
[1,0,1,1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,4,7,9,10,8,6,11,5,3,12,2]=>[1,12,5,4,11,8,7,10,9,6,3,2]=>[.,[[[[[.,.],.],[[[[.,.],.],[[.,.],.]],.]],.],.]]
[1,0,1,1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,0,0]=>[1,4,8,9,7,10,6,11,5,3,12,2]=>[1,12,5,4,11,10,9,8,7,6,3,2]=>[.,[[[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.],.]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,5,6,4,8,10,11,9,7,3,12,2]=>[1,12,7,6,5,4,9,8,11,10,3,2]=>[.,[[[[[[[.,.],.],.],.],[[.,.],[[.,.],.]]],.],.]]
[1,0,1,1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,5,6,4,9,10,8,11,7,3,12,2]=>[1,12,7,6,5,4,11,10,9,8,3,2]=>[.,[[[[[[[.,.],.],.],.],[[[[.,.],.],.],.]],.],.]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,5,7,8,6,4,10,11,9,3,12,2]=>[1,12,9,6,5,8,7,4,11,10,3,2]=>[.,[[[[[[[.,.],.],.],[[.,.],.]],[[.,.],.]],.],.]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,6,7,5,8,4,10,11,9,3,12,2]=>[1,12,9,8,7,6,5,4,11,10,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.],.]]
[1,0,1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,0,0]=>[1,5,7,9,10,8,6,4,11,3,12,2]=>[1,12,11,6,5,8,7,10,9,4,3,2]=>[.,[[[[[[[.,.],.],.],[[.,.],[[.,.],.]]],.],.],.]]
[1,0,1,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,0,0]=>[1,5,8,9,7,10,6,4,11,3,12,2]=>[1,12,11,6,5,10,9,8,7,4,3,2]=>[.,[[[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],.],.]]
[1,0,1,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,6,7,5,9,10,8,4,11,3,12,2]=>[1,12,11,8,7,6,5,10,9,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.]]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[1,6,8,9,7,5,10,4,11,3,12,2]=>[1,12,11,10,7,6,9,8,5,4,3,2]=>[.,[[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.],.]]
[1,0,1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,7,8,6,9,5,10,4,11,3,12,2]=>[1,12,11,10,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,3,1,5,7,9,11,12,10,8,6,4]=>[3,2,1,6,5,8,7,10,9,12,11,4]=>[[[.,.],.],[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[2,3,1,5,8,9,7,11,12,10,6,4]=>[3,2,1,6,5,10,9,8,7,12,11,4]=>[[[.,.],.],[[[.,.],[[[[.,.],.],.],[[.,.],.]]],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,1,6,7,5,9,11,12,10,8,4]=>[3,2,1,8,7,6,5,10,9,12,11,4]=>[[[.,.],.],[[[[[.,.],.],.],[[.,.],[[.,.],.]]],.]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[2,3,1,6,8,9,7,5,11,12,10,4]=>[3,2,1,10,7,6,9,8,5,12,11,4]=>[[[.,.],.],[[[[[.,.],.],[[.,.],.]],[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[2,3,1,7,8,6,9,5,11,12,10,4]=>[3,2,1,10,9,8,7,6,5,12,11,4]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[2,3,1,6,8,10,11,9,7,5,12,4]=>[3,2,1,12,7,6,9,8,11,10,5,4]=>[[[.,.],.],[[[[[.,.],.],[[.,.],[[.,.],.]]],.],.]]
[1,1,0,1,0,0,1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[2,3,1,6,9,10,8,11,7,5,12,4]=>[3,2,1,12,7,6,11,10,9,8,5,4]=>[[[.,.],.],[[[[[.,.],.],[[[[.,.],.],.],.]],.],.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,7,8,6,10,11,9,5,12,4]=>[3,2,1,12,9,8,7,6,11,10,5,4]=>[[[.,.],.],[[[[[[[.,.],.],.],.],[[.,.],.]],.],.]]
[1,1,0,1,0,0,1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[2,3,1,7,9,10,8,6,11,5,12,4]=>[3,2,1,12,11,8,7,10,9,6,5,4]=>[[[.,.],.],[[[[[[[.,.],.],.],[[.,.],.]],.],.],.]]
[1,1,0,1,0,0,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,3,1,8,9,7,10,6,11,5,12,4]=>[3,2,1,12,11,10,9,8,7,6,5,4]=>[[[.,.],.],[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,5,3,1,7,9,11,12,10,8,6]=>[3,2,5,4,1,8,7,10,9,12,11,6]=>[[[.,.],[[.,.],.]],[[[.,.],[[.,.],[[.,.],.]]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,4,5,3,1,8,9,7,11,12,10,6]=>[3,2,5,4,1,10,9,8,7,12,11,6]=>[[[.,.],[[.,.],.]],[[[[[.,.],.],.],[[.,.],.]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,4,5,3,1,8,10,11,9,7,12,6]=>[3,2,5,4,1,12,9,8,11,10,7,6]=>[[[.,.],[[.,.],.]],[[[[[.,.],.],[[.,.],.]],.],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[2,4,5,3,1,9,10,8,11,7,12,6]=>[3,2,5,4,1,12,11,10,9,8,7,6]=>[[[.,.],[[.,.],.]],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,4,2,5,1,7,9,11,12,10,8,6]=>[5,4,3,2,1,8,7,10,9,12,11,6]=>[[[[[.,.],.],.],.],[[[.,.],[[.,.],[[.,.],.]]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,2,5,1,8,9,7,11,12,10,6]=>[5,4,3,2,1,10,9,8,7,12,11,6]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],[[.,.],.]],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,4,2,5,1,8,10,11,9,7,12,6]=>[5,4,3,2,1,12,9,8,11,10,7,6]=>[[[[[.,.],.],.],.],[[[[[.,.],.],[[.,.],.]],.],.]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,4,2,5,1,9,10,8,11,7,12,6]=>[5,4,3,2,1,12,11,10,9,8,7,6]=>[[[[[.,.],.],.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,4,6,7,5,3,1,9,11,12,10,8]=>[3,2,5,4,7,6,1,10,9,12,11,8]=>[[[.,.],[[.,.],[[.,.],.]]],[[[.,.],[[.,.],.]],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,4,6,7,5,3,1,10,11,9,12,8]=>[3,2,5,4,7,6,1,12,11,10,9,8]=>[[[.,.],[[.,.],[[.,.],.]]],[[[[[.,.],.],.],.],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,5,6,4,7,3,1,9,11,12,10,8]=>[3,2,7,6,5,4,1,10,9,12,11,8]=>[[[.,.],[[[[.,.],.],.],.]],[[[.,.],[[.,.],.]],.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,5,6,4,7,3,1,10,11,9,12,8]=>[3,2,7,6,5,4,1,12,11,10,9,8]=>[[[.,.],[[[[.,.],.],.],.]],[[[[[.,.],.],.],.],.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,4,2,6,7,5,1,9,11,12,10,8]=>[5,4,3,2,7,6,1,10,9,12,11,8]=>[[[[[.,.],.],.],[[.,.],.]],[[[.,.],[[.,.],.]],.]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,4,2,6,7,5,1,10,11,9,12,8]=>[5,4,3,2,7,6,1,12,11,10,9,8]=>[[[[[.,.],.],.],[[.,.],.]],[[[[[.,.],.],.],.],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,5,6,4,2,7,1,9,11,12,10,8]=>[7,4,3,6,5,2,1,10,9,12,11,8]=>[[[[[.,.],.],[[.,.],.]],.],[[[.,.],[[.,.],.]],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,5,6,4,2,7,1,10,11,9,12,8]=>[7,4,3,6,5,2,1,12,11,10,9,8]=>[[[[[.,.],.],[[.,.],.]],.],[[[[[.,.],.],.],.],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[4,5,3,6,2,7,1,9,11,12,10,8]=>[7,6,5,4,3,2,1,10,9,12,11,8]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],[[.,.],.]],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1,10,11,9,12,8]=>[7,6,5,4,3,2,1,12,11,10,9,8]=>[[[[[[[.,.],.],.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,1,1,0,1,0,0]=>[2,4,6,8,9,7,5,3,1,11,12,10]=>[3,2,5,4,7,6,9,8,1,12,11,10]=>[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],[[[.,.],.],.]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0,1,1,0,1,0,0]=>[2,4,7,8,6,9,5,3,1,11,12,10]=>[3,2,5,4,9,8,7,6,1,12,11,10]=>[[[.,.],[[.,.],[[[[.,.],.],.],.]]],[[[.,.],.],.]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[2,5,6,4,8,9,7,3,1,11,12,10]=>[3,2,7,6,5,4,9,8,1,12,11,10]=>[[[.,.],[[[[.,.],.],.],[[.,.],.]]],[[[.,.],.],.]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0,1,1,0,1,0,0]=>[2,5,7,8,6,4,9,3,1,11,12,10]=>[3,2,9,6,5,8,7,4,1,12,11,10]=>[[[.,.],[[[[.,.],.],[[.,.],.]],.]],[[[.,.],.],.]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[2,6,7,5,8,4,9,3,1,11,12,10]=>[3,2,9,8,7,6,5,4,1,12,11,10]=>[[[.,.],[[[[[[.,.],.],.],.],.],.]],[[[.,.],.],.]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[3,4,2,6,8,9,7,5,1,11,12,10]=>[5,4,3,2,7,6,9,8,1,12,11,10]=>[[[[[.,.],.],.],[[.,.],[[.,.],.]]],[[[.,.],.],.]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,2,7,8,6,9,5,1,11,12,10]=>[5,4,3,2,9,8,7,6,1,12,11,10]=>[[[[[.,.],.],.],[[[[.,.],.],.],.]],[[[.,.],.],.]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,5,6,4,2,8,9,7,1,11,12,10]=>[7,4,3,6,5,2,9,8,1,12,11,10]=>[[[[[.,.],.],[[.,.],.]],[[.,.],.]],[[[.,.],.],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,5,3,6,2,8,9,7,1,11,12,10]=>[7,6,5,4,3,2,9,8,1,12,11,10]=>[[[[[[[.,.],.],.],.],.],[[.,.],.]],[[[.,.],.],.]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0,0,1,1,0,1,0,0]=>[3,5,7,8,6,4,2,9,1,11,12,10]=>[9,4,3,6,5,8,7,2,1,12,11,10]=>[[[[[.,.],.],[[.,.],[[.,.],.]]],.],[[[.,.],.],.]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[3,6,7,5,8,4,2,9,1,11,12,10]=>[9,4,3,8,7,6,5,2,1,12,11,10]=>[[[[[.,.],.],[[[[.,.],.],.],.]],.],[[[.,.],.],.]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[4,5,3,7,8,6,2,9,1,11,12,10]=>[9,6,5,4,3,8,7,2,1,12,11,10]=>[[[[[[[.,.],.],.],.],[[.,.],.]],.],[[[.,.],.],.]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,6,7,5,3,8,2,9,1,11,12,10]=>[9,8,5,4,7,6,3,2,1,12,11,10]=>[[[[[[[.,.],.],.],[[.,.],.]],.],.],[[[.,.],.],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[5,6,4,7,3,8,2,9,1,11,12,10]=>[9,8,7,6,5,4,3,2,1,12,11,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[[[.,.],.],.]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[11,10,9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,10,11,1]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
[1,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,9,10,8,7,6,5,4,3,1]=>[3,2,4,5,6,7,8,10,9,1]=>[[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,11,10,9,8,7,6,5,4,3,1]=>[3,2,4,5,6,7,8,9,10,11,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,0,1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,9,8,7,6,5,3]=>[1,2,5,4,6,7,8,9,3]=>[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,9,8,7,6,4]=>[1,2,3,6,5,7,8,9,4]=>[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,3,4,6,9,8,7,5]=>[1,2,3,4,7,6,8,9,5]=>[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,4,5,7,9,8,6]=>[1,2,3,4,5,8,7,9,6]=>[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[9,8,7,6,5,4,3,2,1,11,10]=>[2,3,4,5,6,7,8,9,1,11,10]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,8,9,10,4,3,2,1]=>[2,3,4,10,5,6,7,8,9,1]=>[[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]=>[5,6,4,3,2,1,7,8,9]=>[2,3,4,6,5,1,7,8,9]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[4,5,3,2,1,6,7,8,9]=>[2,3,5,4,1,6,7,8,9]=>[[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7,8,9]=>[1,4,3,2,5,6,7,8,9]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[8,9,10,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,10,8,9,1]=>[[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,5,6,7,8,10,9,11]=>[1,2,3,4,5,6,7,8,10,9,11]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,4,2,5,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[6,7,8,9,10,5,4,3,2,1]=>[2,3,4,5,10,6,7,8,9,1]=>[[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[7,8,9,10,6,5,4,3,2,1]=>[2,3,4,5,6,10,7,8,9,1]=>[[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]],.]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,2,10,9,8,7,6,5,4,1]=>[4,3,2,5,6,7,8,9,10,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7,8,9,10]=>[2,4,3,1,5,6,7,8,9,10]=>[[.,[[.,.],.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,11,10]=>[1,3,2,5,4,7,6,9,8,11,10]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,2,1,6,5,8,7,10,9]=>[2,4,3,1,6,5,8,7,10,9]=>[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,4,1,6,5,8,7,10,9]=>[4,3,2,1,6,5,8,7,10,9]=>[[[[.,.],.],.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,5,4,6,1,8,7,10,9]=>[6,3,2,5,4,1,8,7,10,9]=>[[[[.,.],.],[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,5,4,7,6,8,1,10,9]=>[8,3,2,5,4,7,6,1,10,9]=>[[[[.,.],.],[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,7,6,9,8,10,1]=>[10,3,2,5,4,7,6,9,8,1]=>[[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,6,5,9,8,10,7]=>[2,1,4,3,6,5,10,9,8,7]=>[[.,.],[[.,.],[[.,.],[[[[.,.],.],.],.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,4,3,7,6,9,8,10,5]=>[2,1,4,3,10,7,6,9,8,5]=>[[.,.],[[.,.],[[[[.,.],.],[[.,.],.]],.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,4,7,6,9,8,10,3]=>[2,1,10,5,4,7,6,9,8,3]=>[[.,.],[[[[.,.],.],[[.,.],[[.,.],.]]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,4,7,6,9,10,8]=>[1,3,2,5,4,7,6,10,9,8]=>[.,[[.,.],[[.,.],[[.,.],[[[.,.],.],.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7,8,9,10]=>[3,2,4,1,5,6,7,8,9,10]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,3,5,7,9,8,6,4,2]=>[1,4,3,6,5,8,7,9,2]=>[.,[[[.,.],[[.,.],[[.,.],[.,.]]]],.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,3,5,2,6,1,8,7,10,9]=>[6,5,4,3,2,1,8,7,10,9]=>[[[[[[.,.],.],.],.],.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,5,4,6,3,8,7,10,9]=>[2,1,6,5,4,3,8,7,10,9]=>[[.,.],[[[[.,.],.],.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[2,1,6,5,7,4,8,3,10,9]=>[2,1,8,7,6,5,4,3,10,9]=>[[.,.],[[[[[[.,.],.],.],.],.],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[3,2,6,5,7,4,8,1,10,9]=>[8,3,2,7,6,5,4,1,10,9]=>[[[[.,.],.],[[[[.,.],.],.],.]],[[.,.],.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,3,6,5,7,2,8,1,10,9]=>[8,7,4,3,6,5,2,1,10,9]=>[[[[[[.,.],.],.],[[.,.],.]],.],[[.,.],.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[5,4,6,3,7,2,8,1,10,9]=>[8,7,6,5,4,3,2,1,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,4,3,7,6,8,5,10,9]=>[2,1,4,3,8,7,6,5,10,9]=>[[.,.],[[.,.],[[[[.,.],.],.],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,7,6,8,5,10,9]=>[4,3,2,1,8,7,6,5,10,9]=>[[[[.,.],.],.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[4,3,5,2,7,6,8,1,10,9]=>[8,5,4,3,2,7,6,1,10,9]=>[[[[[[.,.],.],.],.],[[.,.],.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,4,7,6,8,3,10,9]=>[2,1,8,5,4,7,6,3,10,9]=>[[.,.],[[[[.,.],.],[[.,.],.]],[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,4,3,8,7,9,6,10,5]=>[2,1,4,3,10,9,8,7,6,5]=>[[.,.],[[.,.],[[[[[[.,.],.],.],.],.],.]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,4,1,8,7,9,6,10,5]=>[4,3,2,1,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,8,7,9,6,10,1]=>[10,5,4,3,2,9,8,7,6,1]=>[[[[[[.,.],.],.],.],[[[[.,.],.],.],.]],.]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,5,4,8,7,9,6,10,3]=>[2,1,10,5,4,9,8,7,6,3]=>[[.,.],[[[[.,.],.],[[[[.,.],.],.],.]],.]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,5,4,8,7,9,6,10,1]=>[10,3,2,5,4,9,8,7,6,1]=>[[[[.,.],.],[[.,.],[[[[.,.],.],.],.]]],.]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,3,6,5,8,7,9,2,10,1]=>[10,9,4,3,6,5,8,7,2,1]=>[[[[[[.,.],.],.],[[.,.],[[.,.],.]]],.],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[5,4,6,3,8,7,9,2,10,1]=>[10,9,6,5,4,3,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[4,3,7,6,8,5,9,2,10,1]=>[10,9,4,3,8,7,6,5,2,1]=>[[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],.]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,4,7,6,8,3,9,2,10,1]=>[10,9,8,5,4,7,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,5,8,7,9,4,10,3]=>[2,1,10,9,6,5,8,7,4,3]=>[[.,.],[[[[[[.,.],.],.],[[.,.],.]],.],.]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,6,5,8,7,9,4,10,1]=>[10,3,2,9,6,5,8,7,4,1]=>[[[[.,.],.],[[[[.,.],.],[[.,.],.]],.]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,5,7,4,8,3,9,2,10,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,1,7,6,8,5,9,4,10,3]=>[2,1,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[3,2,7,6,8,5,9,4,10,1]=>[10,3,2,9,8,7,6,5,4,1]=>[[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,4,1,6,5,9,8,10,7]=>[4,3,2,1,6,5,10,9,8,7]=>[[[[.,.],.],.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[4,3,5,2,6,1,9,8,10,7]=>[6,5,4,3,2,1,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3,9,8,10,7]=>[2,1,6,5,4,3,10,9,8,7]=>[[.,.],[[[[.,.],.],.],[[[[.,.],.],.],.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,5,4,6,1,9,8,10,7]=>[6,3,2,5,4,1,10,9,8,7]=>[[[[.,.],.],[[.,.],.]],[[[[.,.],.],.],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[2,1,6,5,7,4,9,8,10,3]=>[2,1,10,7,6,5,4,9,8,3]=>[[.,.],[[[[[[.,.],.],.],.],[[.,.],.]],.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[3,2,6,5,7,4,9,8,10,1]=>[10,3,2,7,6,5,4,9,8,1]=>[[[[.,.],.],[[[[.,.],.],.],[[.,.],.]]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,3,6,5,7,2,9,8,10,1]=>[10,7,4,3,6,5,2,9,8,1]=>[[[[[[.,.],.],.],[[.,.],.]],[[.,.],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[5,4,6,3,7,2,9,8,10,1]=>[10,7,6,5,4,3,2,9,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,4,1,7,6,9,8,10,5]=>[4,3,2,1,10,7,6,9,8,5]=>[[[[.,.],.],.],[[[[.,.],.],[[.,.],.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[4,3,5,2,7,6,9,8,10,1]=>[10,5,4,3,2,7,6,9,8,1]=>[[[[[[.,.],.],.],.],[[.,.],[[.,.],.]]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,4,1,6,5,8,7,10,9,12,11]=>[4,3,2,1,6,5,8,7,10,9,12,11]=>[[[[.,.],.],.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[4,3,5,2,6,1,8,7,10,9,12,11]=>[6,5,4,3,2,1,8,7,10,9,12,11]=>[[[[[[.,.],.],.],.],.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,5,4,6,3,8,7,10,9,12,11]=>[2,1,6,5,4,3,8,7,10,9,12,11]=>[[.,.],[[[[.,.],.],.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,5,4,6,1,8,7,10,9,12,11]=>[6,3,2,5,4,1,8,7,10,9,12,11]=>[[[[.,.],.],[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,6,5,7,4,8,3,10,9,12,11]=>[2,1,8,7,6,5,4,3,10,9,12,11]=>[[.,.],[[[[[[.,.],.],.],.],.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,6,5,7,4,8,1,10,9,12,11]=>[8,3,2,7,6,5,4,1,10,9,12,11]=>[[[[.,.],.],[[[[.,.],.],.],.]],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,3,6,5,7,2,8,1,10,9,12,11]=>[8,7,4,3,6,5,2,1,10,9,12,11]=>[[[[[[.,.],.],.],[[.,.],.]],.],[[.,.],[[.,.],.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[5,4,6,3,7,2,8,1,10,9,12,11]=>[8,7,6,5,4,3,2,1,10,9,12,11]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,7,6,8,5,10,9,12,11]=>[2,1,4,3,8,7,6,5,10,9,12,11]=>[[.,.],[[.,.],[[[[.,.],.],.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,4,1,7,6,8,5,10,9,12,11]=>[4,3,2,1,8,7,6,5,10,9,12,11]=>[[[[.,.],.],.],[[[[.,.],.],.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,3,5,2,7,6,8,1,10,9,12,11]=>[8,5,4,3,2,7,6,1,10,9,12,11]=>[[[[[[.,.],.],.],.],[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,5,4,7,6,8,3,10,9,12,11]=>[2,1,8,5,4,7,6,3,10,9,12,11]=>[[.,.],[[[[.,.],.],[[.,.],.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,2,5,4,7,6,8,1,10,9,12,11]=>[8,3,2,5,4,7,6,1,10,9,12,11]=>[[[[.,.],.],[[.,.],[[.,.],.]]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[2,1,4,3,8,7,9,6,10,5,12,11]=>[2,1,4,3,10,9,8,7,6,5,12,11]=>[[.,.],[[.,.],[[[[[[.,.],.],.],.],.],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,8,7,9,6,10,5,12,11]=>[4,3,2,1,10,9,8,7,6,5,12,11]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,3,5,2,8,7,9,6,10,1,12,11]=>[10,5,4,3,2,9,8,7,6,1,12,11]=>[[[[[[.,.],.],.],.],[[[[.,.],.],.],.]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,4,8,7,9,6,10,3,12,11]=>[2,1,10,5,4,9,8,7,6,3,12,11]=>[[.,.],[[[[.,.],.],[[[[.,.],.],.],.]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[3,2,5,4,8,7,9,6,10,1,12,11]=>[10,3,2,5,4,9,8,7,6,1,12,11]=>[[[[.,.],.],[[.,.],[[[[.,.],.],.],.]]],[[.,.],.]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,3,6,5,8,7,9,2,10,1,12,11]=>[10,9,4,3,6,5,8,7,2,1,12,11]=>[[[[[[.,.],.],.],[[.,.],[[.,.],.]]],.],[[.,.],.]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[5,4,6,3,8,7,9,2,10,1,12,11]=>[10,9,6,5,4,3,8,7,2,1,12,11]=>[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],[[.,.],.]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[4,3,7,6,8,5,9,2,10,1,12,11]=>[10,9,4,3,8,7,6,5,2,1,12,11]=>[[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],[[.,.],.]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[5,4,7,6,8,3,9,2,10,1,12,11]=>[10,9,8,5,4,7,6,3,2,1,12,11]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[2,1,6,5,8,7,9,4,10,3,12,11]=>[2,1,10,9,6,5,8,7,4,3,12,11]=>[[.,.],[[[[[[.,.],.],.],[[.,.],.]],.],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[3,2,6,5,8,7,9,4,10,1,12,11]=>[10,3,2,9,6,5,8,7,4,1,12,11]=>[[[[.,.],.],[[[[.,.],.],[[.,.],.]],.]],[[.,.],.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[6,5,7,4,8,3,9,2,10,1,12,11]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[[.,.],.]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[2,1,7,6,8,5,9,4,10,3,12,11]=>[2,1,10,9,8,7,6,5,4,3,12,11]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[3,2,7,6,8,5,9,4,10,1,12,11]=>[10,3,2,9,8,7,6,5,4,1,12,11]=>[[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],[[.,.],.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,9,8,10,7,12,11]=>[2,1,4,3,6,5,10,9,8,7,12,11]=>[[.,.],[[.,.],[[.,.],[[[[.,.],.],.],[[.,.],.]]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5,9,8,10,7,12,11]=>[4,3,2,1,6,5,10,9,8,7,12,11]=>[[[[.,.],.],.],[[.,.],[[[[.,.],.],.],[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[4,3,5,2,6,1,9,8,10,7,12,11]=>[6,5,4,3,2,1,10,9,8,7,12,11]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,4,6,3,9,8,10,7,12,11]=>[2,1,6,5,4,3,10,9,8,7,12,11]=>[[.,.],[[[[.,.],.],.],[[[[.,.],.],.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,5,4,6,1,9,8,10,7,12,11]=>[6,3,2,5,4,1,10,9,8,7,12,11]=>[[[[.,.],.],[[.,.],.]],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,6,5,7,4,9,8,10,3,12,11]=>[2,1,10,7,6,5,4,9,8,3,12,11]=>[[.,.],[[[[[[.,.],.],.],.],[[.,.],.]],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,6,5,7,4,9,8,10,1,12,11]=>[10,3,2,7,6,5,4,9,8,1,12,11]=>[[[[.,.],.],[[[[.,.],.],.],[[.,.],.]]],[[.,.],.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[4,3,6,5,7,2,9,8,10,1,12,11]=>[10,7,4,3,6,5,2,9,8,1,12,11]=>[[[[[[.,.],.],.],[[.,.],.]],[[.,.],.]],[[.,.],.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[5,4,6,3,7,2,9,8,10,1,12,11]=>[10,7,6,5,4,3,2,9,8,1,12,11]=>[[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],[[.,.],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,4,3,7,6,9,8,10,5,12,11]=>[2,1,4,3,10,7,6,9,8,5,12,11]=>[[.,.],[[.,.],[[[[.,.],.],[[.,.],.]],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,7,6,9,8,10,5,12,11]=>[4,3,2,1,10,7,6,9,8,5,12,11]=>[[[[.,.],.],.],[[[[.,.],.],[[.,.],.]],[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[4,3,5,2,7,6,9,8,10,1,12,11]=>[10,5,4,3,2,7,6,9,8,1,12,11]=>[[[[[[.,.],.],.],.],[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,4,7,6,9,8,10,3,12,11]=>[2,1,10,5,4,7,6,9,8,3,12,11]=>[[.,.],[[[[.,.],.],[[.,.],[[.,.],.]]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,5,4,7,6,9,8,10,1,12,11]=>[10,3,2,5,4,7,6,9,8,1,12,11]=>[[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]],[[.,.],.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,4,3,6,5,10,9,11,8,12,7]=>[2,1,4,3,6,5,12,11,10,9,8,7]=>[[.,.],[[.,.],[[.,.],[[[[[[.,.],.],.],.],.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,4,1,6,5,10,9,11,8,12,7]=>[4,3,2,1,6,5,12,11,10,9,8,7]=>[[[[.,.],.],.],[[.,.],[[[[[[.,.],.],.],.],.],.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1,10,9,11,8,12,7]=>[6,5,4,3,2,1,12,11,10,9,8,7]=>[[[[[[.,.],.],.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,5,4,6,3,10,9,11,8,12,7]=>[2,1,6,5,4,3,12,11,10,9,8,7]=>[[.,.],[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,5,4,6,1,10,9,11,8,12,7]=>[6,3,2,5,4,1,12,11,10,9,8,7]=>[[[[.,.],.],[[.,.],.]],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,5,7,4,10,9,11,8,12,3]=>[2,1,12,7,6,5,4,11,10,9,8,3]=>[[.,.],[[[[[[.,.],.],.],.],[[[[.,.],.],.],.]],.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,6,5,7,4,10,9,11,8,12,1]=>[12,3,2,7,6,5,4,11,10,9,8,1]=>[[[[.,.],.],[[[[.,.],.],.],[[[[.,.],.],.],.]]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,6,5,7,2,10,9,11,8,12,1]=>[12,7,4,3,6,5,2,11,10,9,8,1]=>[[[[[[.,.],.],.],[[.,.],.]],[[[[.,.],.],.],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[5,4,6,3,7,2,10,9,11,8,12,1]=>[12,7,6,5,4,3,2,11,10,9,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[[[[.,.],.],.],.]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,4,3,7,6,10,9,11,8,12,5]=>[2,1,4,3,12,7,6,11,10,9,8,5]=>[[.,.],[[.,.],[[[[.,.],.],[[[[.,.],.],.],.]],.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,4,1,7,6,10,9,11,8,12,5]=>[4,3,2,1,12,7,6,11,10,9,8,5]=>[[[[.,.],.],.],[[[[.,.],.],[[[[.,.],.],.],.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,7,6,10,9,11,8,12,1]=>[12,5,4,3,2,7,6,11,10,9,8,1]=>[[[[[[.,.],.],.],.],[[.,.],[[[[.,.],.],.],.]]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,5,4,7,6,10,9,11,8,12,3]=>[2,1,12,5,4,7,6,11,10,9,8,3]=>[[.,.],[[[[.,.],.],[[.,.],[[[[.,.],.],.],.]]],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,2,5,4,7,6,10,9,11,8,12,1]=>[12,3,2,5,4,7,6,11,10,9,8,1]=>[[[[.,.],.],[[.,.],[[.,.],[[[[.,.],.],.],.]]]],.]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,5,8,7,10,9,11,4,12,3]=>[2,1,12,11,6,5,8,7,10,9,4,3]=>[[.,.],[[[[[[.,.],.],.],[[.,.],[[.,.],.]]],.],.]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,6,5,8,7,10,9,11,4,12,1]=>[12,3,2,11,6,5,8,7,10,9,4,1]=>[[[[.,.],.],[[[[.,.],.],[[.,.],[[.,.],.]]],.]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[6,5,7,4,8,3,10,9,11,2,12,1]=>[12,11,8,7,6,5,4,3,10,9,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]],.],.]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[2,1,7,6,8,5,10,9,11,4,12,3]=>[2,1,12,11,8,7,6,5,10,9,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,7,6,8,5,10,9,11,4,12,1]=>[12,3,2,11,8,7,6,5,10,9,4,1]=>[[[[.,.],.],[[[[[[.,.],.],.],.],[[.,.],.]],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,1,6,5,9,8,10,7,11,4,12,3]=>[2,1,12,11,6,5,10,9,8,7,4,3]=>[[.,.],[[[[[[.,.],.],.],[[[[.,.],.],.],.]],.],.]]
[1,1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[3,2,6,5,9,8,10,7,11,4,12,1]=>[12,3,2,11,6,5,10,9,8,7,4,1]=>[[[[.,.],.],[[[[.,.],.],[[[[.,.],.],.],.]],.]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,5,7,4,9,8,10,3,11,2,12,1]=>[12,11,10,7,6,5,4,9,8,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.],.],.]
[1,1,0,0,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,1,7,6,9,8,10,5,11,4,12,3]=>[2,1,12,11,10,7,6,9,8,5,4,3]=>[[.,.],[[[[[[[[.,.],.],.],.],[[.,.],.]],.],.],.]]
[1,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[3,2,7,6,9,8,10,5,11,4,12,1]=>[12,3,2,11,10,7,6,9,8,5,4,1]=>[[[[.,.],.],[[[[[[.,.],.],.],[[.,.],.]],.],.]],.]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,3,6,5,8,7,10,9,11,2,12,1]=>[12,11,4,3,6,5,8,7,10,9,2,1]=>[[[[[[.,.],.],.],[[.,.],[[.,.],[[.,.],.]]]],.],.]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,3,7,6,8,5,10,9,11,2,12,1]=>[12,11,4,3,8,7,6,5,10,9,2,1]=>[[[[[[.,.],.],.],[[[[.,.],.],.],[[.,.],.]]],.],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[5,4,6,3,8,7,10,9,11,2,12,1]=>[12,11,6,5,4,3,8,7,10,9,2,1]=>[[[[[[[[.,.],.],.],.],.],[[.,.],[[.,.],.]]],.],.]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[5,4,7,6,8,3,10,9,11,2,12,1]=>[12,11,8,5,4,7,6,3,10,9,2,1]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],[[.,.],.]],.],.]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[6,5,8,7,9,4,10,3,11,2,12,1]=>[12,11,10,9,6,5,8,7,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],[[.,.],.]],.],.],.],.]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[1,1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[4,3,6,5,9,8,10,7,11,2,12,1]=>[12,11,4,3,6,5,10,9,8,7,2,1]=>[[[[[[.,.],.],.],[[.,.],[[[[.,.],.],.],.]]],.],.]
[1,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[4,3,7,6,9,8,10,5,11,2,12,1]=>[12,11,4,3,10,7,6,9,8,5,2,1]=>[[[[[[.,.],.],.],[[[[.,.],.],[[.,.],.]],.]],.],.]
[1,1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,4,6,3,9,8,10,7,11,2,12,1]=>[12,11,6,5,4,3,10,9,8,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]],.],.]
[1,1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,4,7,6,9,8,10,3,11,2,12,1]=>[12,11,10,5,4,7,6,9,8,3,2,1]=>[[[[[[[[.,.],.],.],.],[[.,.],[[.,.],.]]],.],.],.]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[2,1,4,3,8,7,10,9,11,6,12,5]=>[2,1,4,3,12,11,8,7,10,9,6,5]=>[[.,.],[[.,.],[[[[[[.,.],.],.],[[.,.],.]],.],.]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,4,1,8,7,10,9,11,6,12,5]=>[4,3,2,1,12,11,8,7,10,9,6,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],[[.,.],.]],.],.]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,8,7,10,9,11,6,12,1]=>[12,5,4,3,2,11,8,7,10,9,6,1]=>[[[[[[.,.],.],.],.],[[[[.,.],.],[[.,.],.]],.]],.]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[2,1,5,4,8,7,10,9,11,6,12,3]=>[2,1,12,5,4,11,8,7,10,9,6,3]=>[[.,.],[[[[.,.],.],[[[[.,.],.],[[.,.],.]],.]],.]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[3,2,5,4,8,7,10,9,11,6,12,1]=>[12,3,2,5,4,11,8,7,10,9,6,1]=>[[[[.,.],.],[[.,.],[[[[.,.],.],[[.,.],.]],.]]],.]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,1,8,7,9,6,10,5,11,4,12,3]=>[2,1,12,11,10,9,8,7,6,5,4,3]=>[[.,.],[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[1,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[3,2,8,7,9,6,10,5,11,4,12,1]=>[12,3,2,11,10,9,8,7,6,5,4,1]=>[[[[.,.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]],.]
[1,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[4,3,8,7,9,6,10,5,11,2,12,1]=>[12,11,4,3,10,9,8,7,6,5,2,1]=>[[[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]],.],.]
[1,1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[5,4,8,7,9,6,10,3,11,2,12,1]=>[12,11,10,5,4,9,8,7,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[[[[.,.],.],.],.]],.],.],.]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,1,4,3,9,8,10,7,11,6,12,5]=>[2,1,4,3,12,11,10,9,8,7,6,5]=>[[.,.],[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]]
[1,1,1,0,0,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[3,2,4,1,9,8,10,7,11,6,12,5]=>[4,3,2,1,12,11,10,9,8,7,6,5]=>[[[[.,.],.],.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,9,8,10,7,11,6,12,1]=>[12,5,4,3,2,11,10,9,8,7,6,1]=>[[[[[[.,.],.],.],.],[[[[[[.,.],.],.],.],.],.]],.]
[1,1,0,0,1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[2,1,5,4,9,8,10,7,11,6,12,3]=>[2,1,12,5,4,11,10,9,8,7,6,3]=>[[.,.],[[[[.,.],.],[[[[[[.,.],.],.],.],.],.]],.]]
[1,1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[3,2,5,4,9,8,10,7,11,6,12,1]=>[12,3,2,5,4,11,10,9,8,7,6,1]=>[[[[.,.],.],[[.,.],[[[[[[.,.],.],.],.],.],.]]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,6,5,8,7,11,10,12,9]=>[2,1,4,3,6,5,8,7,12,11,10,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[[[[.,.],.],.],.]]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,4,1,6,5,8,7,11,10,12,9]=>[4,3,2,1,6,5,8,7,12,11,10,9]=>[[[[.,.],.],.],[[.,.],[[.,.],[[[[.,.],.],.],.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[4,3,5,2,6,1,8,7,11,10,12,9]=>[6,5,4,3,2,1,8,7,12,11,10,9]=>[[[[[[.,.],.],.],.],.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3,8,7,11,10,12,9]=>[2,1,6,5,4,3,8,7,12,11,10,9]=>[[.,.],[[[[.,.],.],.],[[.,.],[[[[.,.],.],.],.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,5,4,6,1,8,7,11,10,12,9]=>[6,3,2,5,4,1,8,7,12,11,10,9]=>[[[[.,.],.],[[.,.],.]],[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,6,5,7,4,8,3,11,10,12,9]=>[2,1,8,7,6,5,4,3,12,11,10,9]=>[[.,.],[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,6,5,7,4,8,1,11,10,12,9]=>[8,3,2,7,6,5,4,1,12,11,10,9]=>[[[[.,.],.],[[[[.,.],.],.],.]],[[[[.,.],.],.],.]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[4,3,6,5,7,2,8,1,11,10,12,9]=>[8,7,4,3,6,5,2,1,12,11,10,9]=>[[[[[[.,.],.],.],[[.,.],.]],.],[[[[.,.],.],.],.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[5,4,6,3,7,2,8,1,11,10,12,9]=>[8,7,6,5,4,3,2,1,12,11,10,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[[[[.,.],.],.],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,6,8,5,11,10,12,9]=>[2,1,4,3,8,7,6,5,12,11,10,9]=>[[.,.],[[.,.],[[[[.,.],.],.],[[[[.,.],.],.],.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,4,1,7,6,8,5,11,10,12,9]=>[4,3,2,1,8,7,6,5,12,11,10,9]=>[[[[.,.],.],.],[[[[.,.],.],.],[[[[.,.],.],.],.]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[4,3,5,2,7,6,8,1,11,10,12,9]=>[8,5,4,3,2,7,6,1,12,11,10,9]=>[[[[[[.,.],.],.],.],[[.,.],.]],[[[[.,.],.],.],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,7,6,8,3,11,10,12,9]=>[2,1,8,5,4,7,6,3,12,11,10,9]=>[[.,.],[[[[.,.],.],[[.,.],.]],[[[[.,.],.],.],.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,2,5,4,7,6,8,1,11,10,12,9]=>[8,3,2,5,4,7,6,1,12,11,10,9]=>[[[[.,.],.],[[.,.],[[.,.],.]]],[[[[.,.],.],.],.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[2,1,4,3,8,7,9,6,11,10,12,5]=>[2,1,4,3,12,9,8,7,6,11,10,5]=>[[.,.],[[.,.],[[[[[[.,.],.],.],.],[[.,.],.]],.]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[3,2,4,1,8,7,9,6,11,10,12,5]=>[4,3,2,1,12,9,8,7,6,11,10,5]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],[[.,.],.]],.]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,3,5,2,8,7,9,6,11,10,12,1]=>[12,5,4,3,2,9,8,7,6,11,10,1]=>[[[[[[.,.],.],.],.],[[[[.,.],.],.],[[.,.],.]]],.]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,4,8,7,9,6,11,10,12,3]=>[2,1,12,5,4,9,8,7,6,11,10,3]=>[[.,.],[[[[.,.],.],[[[[.,.],.],.],[[.,.],.]]],.]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,8,7,9,6,11,10,12,1]=>[12,3,2,5,4,9,8,7,6,11,10,1]=>[[[[.,.],.],[[.,.],[[[[.,.],.],.],[[.,.],.]]]],.]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,3,6,5,8,7,9,2,11,10,12,1]=>[12,9,4,3,6,5,8,7,2,11,10,1]=>[[[[[[.,.],.],.],[[.,.],[[.,.],.]]],[[.,.],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[5,4,6,3,8,7,9,2,11,10,12,1]=>[12,9,6,5,4,3,8,7,2,11,10,1]=>[[[[[[[[.,.],.],.],.],.],[[.,.],.]],[[.,.],.]],.]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[4,3,7,6,8,5,9,2,11,10,12,1]=>[12,9,4,3,8,7,6,5,2,11,10,1]=>[[[[[[.,.],.],.],[[[[.,.],.],.],.]],[[.,.],.]],.]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[5,4,7,6,8,3,9,2,11,10,12,1]=>[12,9,8,5,4,7,6,3,2,11,10,1]=>[[[[[[[[.,.],.],.],.],[[.,.],.]],.],[[.,.],.]],.]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[2,1,6,5,8,7,9,4,11,10,12,3]=>[2,1,12,9,6,5,8,7,4,11,10,3]=>[[.,.],[[[[[[.,.],.],.],[[.,.],.]],[[.,.],.]],.]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[3,2,6,5,8,7,9,4,11,10,12,1]=>[12,3,2,9,6,5,8,7,4,11,10,1]=>[[[[.,.],.],[[[[.,.],.],[[.,.],.]],[[.,.],.]]],.]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[6,5,7,4,8,3,9,2,11,10,12,1]=>[12,9,8,7,6,5,4,3,2,11,10,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]],.]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[2,1,7,6,8,5,9,4,11,10,12,3]=>[2,1,12,9,8,7,6,5,4,11,10,3]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],[[.,.],.]],.]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[3,2,7,6,8,5,9,4,11,10,12,1]=>[12,3,2,9,8,7,6,5,4,11,10,1]=>[[[[.,.],.],[[[[[[.,.],.],.],.],.],[[.,.],.]]],.]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,4,3,6,5,9,8,11,10,12,7]=>[2,1,4,3,6,5,12,9,8,11,10,7]=>[[.,.],[[.,.],[[.,.],[[[[.,.],.],[[.,.],.]],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,4,1,6,5,9,8,11,10,12,7]=>[4,3,2,1,6,5,12,9,8,11,10,7]=>[[[[.,.],.],.],[[.,.],[[[[.,.],.],[[.,.],.]],.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[4,3,5,2,6,1,9,8,11,10,12,7]=>[6,5,4,3,2,1,12,9,8,11,10,7]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],[[.,.],.]],.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,4,6,3,9,8,11,10,12,7]=>[2,1,6,5,4,3,12,9,8,11,10,7]=>[[.,.],[[[[.,.],.],.],[[[[.,.],.],[[.,.],.]],.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1,9,8,11,10,12,7]=>[6,3,2,5,4,1,12,9,8,11,10,7]=>[[[[.,.],.],[[.,.],.]],[[[[.,.],.],[[.,.],.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,6,5,7,4,9,8,11,10,12,3]=>[2,1,12,7,6,5,4,9,8,11,10,3]=>[[.,.],[[[[[[.,.],.],.],.],[[.,.],[[.,.],.]]],.]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,6,5,7,4,9,8,11,10,12,1]=>[12,3,2,7,6,5,4,9,8,11,10,1]=>[[[[.,.],.],[[[[.,.],.],.],[[.,.],[[.,.],.]]]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[4,3,6,5,7,2,9,8,11,10,12,1]=>[12,7,4,3,6,5,2,9,8,11,10,1]=>[[[[[[.,.],.],.],[[.,.],.]],[[.,.],[[.,.],.]]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[5,4,6,3,7,2,9,8,11,10,12,1]=>[12,7,6,5,4,3,2,9,8,11,10,1]=>[[[[[[[[.,.],.],.],.],.],.],[[.,.],[[.,.],.]]],.]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,4,3,7,6,9,8,11,10,12,5]=>[2,1,4,3,12,7,6,9,8,11,10,5]=>[[.,.],[[.,.],[[[[.,.],.],[[.,.],[[.,.],.]]],.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,4,1,7,6,9,8,11,10,12,5]=>[4,3,2,1,12,7,6,9,8,11,10,5]=>[[[[.,.],.],.],[[[[.,.],.],[[.,.],[[.,.],.]]],.]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[4,3,5,2,7,6,9,8,11,10,12,1]=>[12,5,4,3,2,7,6,9,8,11,10,1]=>[[[[[[.,.],.],.],.],[[.,.],[[.,.],[[.,.],.]]]],.]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,4,7,6,9,8,11,10,12,3]=>[2,1,12,5,4,7,6,9,8,11,10,3]=>[[.,.],[[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]],.]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,7,6,9,8,11,10,12,1]=>[12,3,2,5,4,7,6,9,8,11,10,1]=>[[[[.,.],.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,9,8,7,6,5,4,3,2,1,12,11]=>[2,3,4,5,6,7,8,9,10,1,12,11]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,6,5,3,8,7,10,9]=>[2,1,5,4,6,3,8,7,10,9]=>[[.,.],[[[.,.],[.,.]],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,1,4,3,6,8,7,5,10,9]=>[2,1,4,3,7,6,8,5,10,9]=>[[.,.],[[.,.],[[[.,.],[.,.]],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,3,6,5,8,10,9,7]=>[2,1,4,3,6,5,9,8,10,7]=>[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,4,6,3,7,2,8,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,6,5,7,4,8,3,9,2]=>[1,9,8,7,6,5,4,3,2]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,0,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,1,7,8,9,10,6,5,4,3]=>[2,1,4,5,6,10,7,8,9,3]=>[[.,.],[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[3,4,2,1,6,5,9,10,8,7]=>[2,4,3,1,6,5,8,10,9,7]=>[[.,[[.,.],.]],[[.,.],[[.,[[.,.],.]],.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0,0]=>[5,6,4,7,3,8,2,10,9,1]=>[9,8,7,6,5,4,3,2,10,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[4,5,3,6,2,7,1,8,9]=>[7,6,5,4,3,2,1,8,9]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[5,7,6,4,8,3,9,2,10,1]=>[10,9,8,6,5,7,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]
Map
to 312-avoiding permutation
Description
Map
descent views to invisible inversion bottoms
Description
Return a permutation whose multiset of invisible inversion bottoms is the multiset of descent views of the given permutation.
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
An invisible inversion of a permutation $\sigma$ is a pair $i < j$ such that $i < \sigma(j) < \sigma(i)$. The element $\sigma(j)$ is then an invisible inversion bottom.
A descent view in a permutation $\pi$ is an element $\pi(j)$ such that $\pi(i+1) < \pi(j) < \pi(i)$, and additionally the smallest element in the decreasing run containing $\pi(i)$ is smaller than the smallest element in the decreasing run containing $\pi(j)$.
This map is a bijection $\chi:\mathfrak S_n \to \mathfrak S_n$, such that
- the multiset of descent views in $\pi$ is the multiset of invisible inversion bottoms in $\chi(\pi)$,
- the set of left-to-right maxima of $\pi$ is the set of maximal elements in the cycles of $\chi(\pi)$,
- the set of global ascent of $\pi$ is the set of global ascent of $\chi(\pi)$,
- the set of maximal elements in the decreasing runs of $\pi$ is the set of weak deficiency positions of $\chi(\pi)$, and
- the set of minimal elements in the decreasing runs of $\pi$ is the set of weak deficiency values of $\chi(\pi)$.
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.