Identifier
Mp00025:
Dyck paths
—to 132-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]=>[2,1]=>[2,1]=>[[.,.],.]
[1,1,0,0]=>[1,2]=>[1,2]=>[.,[.,.]]
[1,0,1,0,1,0]=>[3,2,1]=>[2,3,1]=>[[.,[.,.]],.]
[1,0,1,1,0,0]=>[2,3,1]=>[3,2,1]=>[[[.,.],.],.]
[1,1,0,0,1,0]=>[3,1,2]=>[3,1,2]=>[[.,.],[.,.]]
[1,1,0,1,0,0]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[1,1,1,0,0,0]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[1,0,1,0,1,1,0,0]=>[3,4,2,1]=>[2,4,3,1]=>[[.,[[.,.],.]],.]
[1,0,1,1,0,0,1,0]=>[4,2,3,1]=>[3,4,2,1]=>[[[.,[.,.]],.],.]
[1,0,1,1,0,1,0,0]=>[3,2,4,1]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[1,1,0,0,1,0,1,0]=>[4,3,1,2]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[1,1,0,1,0,0,1,0]=>[4,2,1,3]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[1,1,0,1,0,1,0,0]=>[3,2,1,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[1,1,0,1,1,0,0,0]=>[2,3,1,4]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[1,1,1,0,0,1,0,0]=>[3,1,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[1,1,1,0,1,0,0,0]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[1,0,1,0,1,0,1,1,0,0]=>[4,5,3,2,1]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
[1,0,1,0,1,1,0,0,1,0]=>[5,3,4,2,1]=>[2,4,5,3,1]=>[[.,[[.,[.,.]],.]],.]
[1,0,1,0,1,1,0,1,0,0]=>[4,3,5,2,1]=>[2,5,4,3,1]=>[[.,[[[.,.],.],.]],.]
[1,0,1,0,1,1,1,0,0,0]=>[3,4,5,2,1]=>[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.]
[1,0,1,1,0,0,1,0,1,0]=>[5,4,2,3,1]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]
[1,0,1,1,0,0,1,1,0,0]=>[4,5,2,3,1]=>[3,5,2,4,1]=>[[[.,[.,.]],[.,.]],.]
[1,0,1,1,0,1,0,0,1,0]=>[5,3,2,4,1]=>[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.]
[1,0,1,1,0,1,0,1,0,0]=>[4,3,2,5,1]=>[5,3,4,2,1]=>[[[[.,.],[.,.]],.],.]
[1,0,1,1,0,1,1,0,0,0]=>[3,4,2,5,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[1,0,1,1,1,0,0,0,1,0]=>[5,2,3,4,1]=>[4,5,2,3,1]=>[[[.,[.,.]],[.,.]],.]
[1,0,1,1,1,0,0,1,0,0]=>[4,2,3,5,1]=>[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.]
[1,0,1,1,1,0,1,0,0,0]=>[3,2,4,5,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,2]=>[3,1,4,5,2]=>[[.,.],[[.,[.,.]],.]]
[1,1,0,0,1,0,1,1,0,0]=>[4,5,3,1,2]=>[3,1,5,4,2]=>[[.,.],[[[.,.],.],.]]
[1,1,0,0,1,1,0,0,1,0]=>[5,3,4,1,2]=>[4,1,5,3,2]=>[[.,.],[[[.,.],.],.]]
[1,1,0,0,1,1,0,1,0,0]=>[4,3,5,1,2]=>[5,1,4,3,2]=>[[.,.],[[[.,.],.],.]]
[1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>[5,1,3,4,2]=>[[.,.],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,3]=>[2,4,1,5,3]=>[[.,[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0]=>[4,5,2,1,3]=>[2,5,1,4,3]=>[[.,[.,.]],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,4]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,5]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,1,0,0,0]=>[3,4,2,1,5]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[1,1,0,1,1,0,0,0,1,0]=>[5,2,3,1,4]=>[3,5,2,1,4]=>[[[.,[.,.]],.],[.,.]]
[1,1,0,1,1,0,0,1,0,0]=>[4,2,3,1,5]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]]
[1,1,0,1,1,0,1,0,0,0]=>[3,2,4,1,5]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[1,1,0,1,1,1,0,0,0,0]=>[2,3,4,1,5]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[1,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,3]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,0]=>[5,3,1,2,4]=>[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0]=>[4,3,1,2,5]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[1,1,1,0,0,1,1,0,0,0]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,0,1,0]=>[5,2,1,3,4]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0]=>[4,2,1,3,5]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0]=>[3,2,1,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0]=>[2,3,1,4,5]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]=>[2,3,4,5,6,1]=>[[.,[.,[.,[.,[.,.]]]]],.]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,2,1]=>[2,3,4,6,5,1]=>[[.,[.,[.,[[.,.],.]]]],.]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,2,1]=>[2,3,5,6,4,1]=>[[.,[.,[[.,[.,.]],.]]],.]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,2,1]=>[2,3,6,5,4,1]=>[[.,[.,[[[.,.],.],.]]],.]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,2,1]=>[2,3,6,4,5,1]=>[[.,[.,[[.,.],[.,.]]]],.]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,2,1]=>[2,4,5,3,6,1]=>[[.,[[.,[.,.]],[.,.]]],.]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,2,1]=>[2,4,6,3,5,1]=>[[.,[[.,[.,.]],[.,.]]],.]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,2,1]=>[2,5,4,6,3,1]=>[[.,[[[.,.],[.,.]],.]],.]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,2,1]=>[2,6,4,5,3,1]=>[[.,[[[.,.],[.,.]],.]],.]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,2,1]=>[2,6,5,4,3,1]=>[[.,[[[[.,.],.],.],.]],.]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,2,1]=>[2,5,6,3,4,1]=>[[.,[[.,[.,.]],[.,.]]],.]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,2,1]=>[2,6,5,3,4,1]=>[[.,[[[.,.],.],[.,.]]],.]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[2,6,4,3,5,1]=>[[.,[[[.,.],.],[.,.]]],.]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,2,1]=>[2,6,3,4,5,1]=>[[.,[[.,.],[.,[.,.]]]],.]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,3,1]=>[3,4,2,5,6,1]=>[[[.,[.,.]],[.,[.,.]]],.]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,3,1]=>[3,4,2,6,5,1]=>[[[.,[.,.]],[[.,.],.]],.]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,3,1]=>[3,5,2,6,4,1]=>[[[.,[.,.]],[[.,.],.]],.]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,3,1]=>[3,6,2,5,4,1]=>[[[.,[.,.]],[[.,.],.]],.]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,3,1]=>[3,6,2,4,5,1]=>[[[.,[.,.]],[.,[.,.]]],.]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,4,1]=>[4,3,5,2,6,1]=>[[[[.,.],[.,.]],[.,.]],.]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,4,1]=>[4,3,6,2,5,1]=>[[[[.,.],[.,.]],[.,.]],.]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,5,1]=>[5,3,4,6,2,1]=>[[[[.,.],[.,[.,.]]],.],.]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,1]=>[6,3,4,5,2,1]=>[[[[.,.],[.,[.,.]]],.],.]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,1]=>[6,3,5,4,2,1]=>[[[[.,.],[[.,.],.]],.],.]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,5,1]=>[5,4,6,3,2,1]=>[[[[[.,.],[.,.]],.],.],.]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,6,1]=>[6,4,5,3,2,1]=>[[[[[.,.],[.,.]],.],.],.]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,6,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,4,1]=>[4,5,2,3,6,1]=>[[[.,[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,4,1]=>[4,6,2,3,5,1]=>[[[.,[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,5,1]=>[5,4,2,6,3,1]=>[[[[.,.],.],[[.,.],.]],.]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,6,1]=>[6,4,2,5,3,1]=>[[[[.,.],.],[[.,.],.]],.]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,6,1]=>[6,5,2,4,3,1]=>[[[[.,.],.],[[.,.],.]],.]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1]=>[5,3,6,2,4,1]=>[[[[.,.],[.,.]],[.,.]],.]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[6,3,5,2,4,1]=>[[[[.,.],[.,.]],[.,.]],.]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,6,1]=>[6,3,4,2,5,1]=>[[[[.,.],[.,.]],[.,.]],.]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,5,1]=>[5,6,2,3,4,1]=>[[[.,[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,6,1]=>[6,5,2,3,4,1]=>[[[[.,.],.],[.,[.,.]]],.]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,6,1]=>[6,4,2,3,5,1]=>[[[[.,.],.],[.,[.,.]]],.]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],.]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,2]=>[3,1,4,5,6,2]=>[[.,.],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,1,2]=>[3,1,4,6,5,2]=>[[.,.],[[.,[[.,.],.]],.]]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,1,2]=>[3,1,5,6,4,2]=>[[.,.],[[[.,[.,.]],.],.]]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,1,2]=>[3,1,6,5,4,2]=>[[.,.],[[[[.,.],.],.],.]]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,1,2]=>[3,1,6,4,5,2]=>[[.,.],[[[.,.],[.,.]],.]]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,1,2]=>[4,1,5,3,6,2]=>[[.,.],[[[.,.],[.,.]],.]]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,1,2]=>[4,1,6,3,5,2]=>[[.,.],[[[.,.],[.,.]],.]]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,1,2]=>[5,1,4,6,3,2]=>[[.,.],[[[.,[.,.]],.],.]]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,1,2]=>[6,1,4,5,3,2]=>[[.,.],[[[.,[.,.]],.],.]]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,1,2]=>[6,1,5,4,3,2]=>[[.,.],[[[[.,.],.],.],.]]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,1,2]=>[5,1,6,3,4,2]=>[[.,.],[[[.,.],[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,1,2]=>[6,1,5,3,4,2]=>[[.,.],[[[.,.],[.,.]],.]]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,1,2]=>[6,1,4,3,5,2]=>[[.,.],[[[.,.],[.,.]],.]]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>[6,1,3,4,5,2]=>[[.,.],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,3]=>[2,4,1,5,6,3]=>[[.,[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,1,3]=>[2,4,1,6,5,3]=>[[.,[.,.]],[[[.,.],.],.]]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,1,3]=>[2,5,1,6,4,3]=>[[.,[.,.]],[[[.,.],.],.]]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,1,3]=>[2,6,1,5,4,3]=>[[.,[.,.]],[[[.,.],.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,1,3]=>[2,6,1,4,5,3]=>[[.,[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,4]=>[2,3,5,1,6,4]=>[[.,[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,1,4]=>[2,3,6,1,5,4]=>[[.,[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,5]=>[2,3,4,6,1,5]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,6]=>[2,3,4,5,1,6]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,1,6]=>[2,3,5,4,1,6]=>[[.,[.,[[.,.],.]]],[.,.]]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,1,5]=>[2,4,6,3,1,5]=>[[.,[[.,[.,.]],.]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,1,6]=>[2,4,5,3,1,6]=>[[.,[[.,[.,.]],.]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,1,6]=>[2,5,4,3,1,6]=>[[.,[[[.,.],.],.]],[.,.]]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,1,6]=>[2,5,3,4,1,6]=>[[.,[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,1,4]=>[3,5,2,1,6,4]=>[[[.,[.,.]],.],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,1,4]=>[3,6,2,1,5,4]=>[[[.,[.,.]],.],[[.,.],.]]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,1,5]=>[3,4,2,6,1,5]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,1,6]=>[3,4,2,5,1,6]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,1,6]=>[3,5,2,4,1,6]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,1,5]=>[4,3,6,2,1,5]=>[[[[.,.],[.,.]],.],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,1,6]=>[4,3,5,2,1,6]=>[[[[.,.],[.,.]],.],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,1,6]=>[5,3,4,2,1,6]=>[[[[.,.],[.,.]],.],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,1,5]=>[4,6,2,3,1,5]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,1,6]=>[4,5,2,3,1,6]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,1,6]=>[5,4,2,3,1,6]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,1,6]=>[5,3,2,4,1,6]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,2,3]=>[4,1,2,5,6,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[5,6,4,1,2,3]=>[4,1,2,6,5,3]=>[[.,.],[.,[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,5,1,2,3]=>[5,1,2,6,4,3]=>[[.,.],[.,[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,6,1,2,3]=>[6,1,2,5,4,3]=>[[.,.],[.,[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>[6,1,2,4,5,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,2,4]=>[3,1,5,2,6,4]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[5,6,3,1,2,4]=>[3,1,6,2,5,4]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,2,5]=>[3,1,4,6,2,5]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,2,6]=>[3,1,4,5,2,6]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[4,5,3,1,2,6]=>[3,1,5,4,2,6]=>[[.,.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>[4,1,6,3,2,5]=>[[.,.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,4,1,2,6]=>[4,1,5,3,2,6]=>[[.,.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,5,1,2,6]=>[5,1,4,3,2,6]=>[[.,.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6]=>[5,1,3,4,2,6]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,3,4]=>[2,5,1,3,6,4]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[5,6,2,1,3,4]=>[2,6,1,3,5,4]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,3,5]=>[2,4,1,6,3,5]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,3,6]=>[2,4,1,5,3,6]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,5,2,1,3,6]=>[2,5,1,4,3,6]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,4,5]=>[2,3,6,1,4,5]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,4,6]=>[2,3,5,1,4,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,5,6]=>[2,3,4,1,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,2,1,5,6]=>[2,4,3,1,5,6]=>[[.,[[.,.],.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,1,4,5]=>[3,6,2,1,4,5]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,3,1,4,6]=>[3,5,2,1,4,6]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,3,1,5,6]=>[3,4,2,1,5,6]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,4,1,5,6]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,2,3,4]=>[5,1,2,3,6,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>[6,1,2,3,5,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>[4,1,2,6,3,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,2,3,6]=>[4,1,2,5,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,2,4,5]=>[3,1,6,2,4,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,2,4,6]=>[3,1,5,2,4,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,2,5,6]=>[3,1,4,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,3,4,5]=>[2,6,1,3,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,3,4,6]=>[2,5,1,3,4,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,3,5,6]=>[2,4,1,3,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,4,5,6]=>[2,3,1,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>[6,1,2,3,4,5]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1]=>[2,3,4,5,6,7,1]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,2,1]=>[2,3,4,5,7,6,1]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,2,1]=>[2,3,4,6,7,5,1]=>[[.,[.,[.,[[.,[.,.]],.]]]],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,2,1]=>[2,3,4,7,6,5,1]=>[[.,[.,[.,[[[.,.],.],.]]]],.]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,2,1]=>[2,3,4,7,5,6,1]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,2,1]=>[2,3,5,6,4,7,1]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,2,1]=>[2,3,5,7,4,6,1]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,2,1]=>[2,3,6,5,7,4,1]=>[[.,[.,[[[.,.],[.,.]],.]]],.]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,2,1]=>[2,3,7,5,6,4,1]=>[[.,[.,[[[.,.],[.,.]],.]]],.]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,2,1]=>[2,3,7,6,5,4,1]=>[[.,[.,[[[[.,.],.],.],.]]],.]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,2,1]=>[2,3,6,7,4,5,1]=>[[.,[.,[[.,[.,.]],[.,.]]]],.]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,2,1]=>[2,3,7,6,4,5,1]=>[[.,[.,[[[.,.],.],[.,.]]]],.]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,2,1]=>[2,3,7,5,4,6,1]=>[[.,[.,[[[.,.],.],[.,.]]]],.]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[2,3,7,4,5,6,1]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,2,1]=>[2,4,5,3,6,7,1]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,2,1]=>[2,4,5,3,7,6,1]=>[[.,[[.,[.,.]],[[.,.],.]]],.]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,2,1]=>[2,4,6,3,7,5,1]=>[[.,[[.,[.,.]],[[.,.],.]]],.]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,2,1]=>[2,4,7,3,6,5,1]=>[[.,[[.,[.,.]],[[.,.],.]]],.]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,2,1]=>[2,4,7,3,5,6,1]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,2,1]=>[2,5,4,6,3,7,1]=>[[.,[[[.,.],[.,.]],[.,.]]],.]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,2,1]=>[2,5,4,7,3,6,1]=>[[.,[[[.,.],[.,.]],[.,.]]],.]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,2,1]=>[2,6,4,5,7,3,1]=>[[.,[[[.,.],[.,[.,.]]],.]],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,2,1]=>[2,7,4,5,6,3,1]=>[[.,[[[.,.],[.,[.,.]]],.]],.]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,2,1]=>[2,7,4,6,5,3,1]=>[[.,[[[.,.],[[.,.],.]],.]],.]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,2,1]=>[2,6,5,7,4,3,1]=>[[.,[[[[.,.],[.,.]],.],.]],.]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,2,1]=>[2,7,5,6,4,3,1]=>[[.,[[[[.,.],[.,.]],.],.]],.]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[2,7,6,5,4,3,1]=>[[.,[[[[[.,.],.],.],.],.]],.]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,2,1]=>[2,7,6,4,5,3,1]=>[[.,[[[[.,.],.],[.,.]],.]],.]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,2,1]=>[2,5,6,3,4,7,1]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,2,1]=>[2,5,7,3,4,6,1]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,2,1]=>[2,6,5,3,7,4,1]=>[[.,[[[.,.],.],[[.,.],.]]],.]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,2,1]=>[2,7,5,3,6,4,1]=>[[.,[[[.,.],.],[[.,.],.]]],.]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,2,1]=>[2,7,6,3,5,4,1]=>[[.,[[[.,.],.],[[.,.],.]]],.]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,2,1]=>[2,6,4,7,3,5,1]=>[[.,[[[.,.],[.,.]],[.,.]]],.]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,2,1]=>[2,7,4,6,3,5,1]=>[[.,[[[.,.],[.,.]],[.,.]]],.]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[2,7,4,5,3,6,1]=>[[.,[[[.,.],[.,.]],[.,.]]],.]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,2,1]=>[2,7,5,4,3,6,1]=>[[.,[[[[.,.],.],.],[.,.]]],.]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,2,1]=>[2,6,7,3,4,5,1]=>[[.,[[.,[.,.]],[.,[.,.]]]],.]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,2,1]=>[2,7,6,3,4,5,1]=>[[.,[[[.,.],.],[.,[.,.]]]],.]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,2,1]=>[2,7,5,3,4,6,1]=>[[.,[[[.,.],.],[.,[.,.]]]],.]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,2,1]=>[2,7,4,3,5,6,1]=>[[.,[[[.,.],.],[.,[.,.]]]],.]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,2,1]=>[2,7,3,4,5,6,1]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,3,1]=>[3,4,2,5,6,7,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,3,1]=>[3,4,2,5,7,6,1]=>[[[.,[.,.]],[.,[[.,.],.]]],.]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,3,1]=>[3,4,2,6,7,5,1]=>[[[.,[.,.]],[[.,[.,.]],.]],.]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,3,1]=>[3,4,2,7,6,5,1]=>[[[.,[.,.]],[[[.,.],.],.]],.]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,3,1]=>[3,4,2,7,5,6,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,3,1]=>[3,5,2,6,4,7,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,3,1]=>[3,5,2,7,4,6,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,3,1]=>[3,6,2,5,7,4,1]=>[[[.,[.,.]],[[.,[.,.]],.]],.]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,3,1]=>[3,7,2,5,6,4,1]=>[[[.,[.,.]],[[.,[.,.]],.]],.]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,3,1]=>[3,7,2,6,5,4,1]=>[[[.,[.,.]],[[[.,.],.],.]],.]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,3,1]=>[3,6,2,7,4,5,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,3,1]=>[3,7,2,6,4,5,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,3,1]=>[3,7,2,5,4,6,1]=>[[[.,[.,.]],[[.,.],[.,.]]],.]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,3,1]=>[3,7,2,4,5,6,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,4,1]=>[4,3,5,2,6,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,4,1]=>[4,3,5,2,7,6,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,4,1]=>[4,3,6,2,7,5,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,4,1]=>[4,3,7,2,6,5,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,4,1]=>[4,3,7,2,5,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,5,1]=>[5,3,4,6,2,7,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,5,1]=>[5,3,4,7,2,6,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,6,1]=>[6,3,4,5,7,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,7,1]=>[7,3,4,5,6,2,1]=>[[[[.,.],[.,[.,[.,.]]]],.],.]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,7,1]=>[7,3,4,6,5,2,1]=>[[[[.,.],[.,[[.,.],.]]],.],.]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,6,1]=>[6,3,5,7,4,2,1]=>[[[[.,.],[[.,[.,.]],.]],.],.]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,7,1]=>[7,3,5,6,4,2,1]=>[[[[.,.],[[.,[.,.]],.]],.],.]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,7,1]=>[7,3,6,5,4,2,1]=>[[[[.,.],[[[.,.],.],.]],.],.]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,7,1]=>[7,3,6,4,5,2,1]=>[[[[.,.],[[.,.],[.,.]]],.],.]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,5,1]=>[5,4,6,3,2,7,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,5,1]=>[5,4,7,3,2,6,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,6,1]=>[6,4,5,3,7,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,7,1]=>[7,4,5,3,6,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,7,1]=>[7,4,6,3,5,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,6,1]=>[6,5,4,7,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,7,1]=>[7,5,4,6,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,7,1]=>[7,6,4,5,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,7,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,6,1]=>[6,5,7,3,4,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,7,1]=>[7,5,6,3,4,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,7,1]=>[7,6,5,3,4,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,7,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,7,1]=>[7,6,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,4,1]=>[4,5,2,3,6,7,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,4,1]=>[4,5,2,3,7,6,1]=>[[[.,[.,.]],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,4,1]=>[4,6,2,3,7,5,1]=>[[[.,[.,.]],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,4,1]=>[4,7,2,3,6,5,1]=>[[[.,[.,.]],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,4,1]=>[4,7,2,3,5,6,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,5,1]=>[5,4,2,6,3,7,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,5,1]=>[5,4,2,7,3,6,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,6,1]=>[6,4,2,5,7,3,1]=>[[[[.,.],.],[[.,[.,.]],.]],.]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,7,1]=>[7,4,2,5,6,3,1]=>[[[[.,.],.],[[.,[.,.]],.]],.]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,7,1]=>[7,4,2,6,5,3,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,6,1]=>[6,5,2,7,4,3,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,7,1]=>[7,5,2,6,4,3,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,7,1]=>[7,6,2,5,4,3,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,7,1]=>[7,6,2,4,5,3,1]=>[[[[.,.],.],[[.,[.,.]],.]],.]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,5,1]=>[5,3,6,2,4,7,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,5,1]=>[5,3,7,2,4,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,6,1]=>[6,3,5,2,7,4,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,7,1]=>[7,3,5,2,6,4,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,7,1]=>[7,3,6,2,5,4,1]=>[[[[.,.],[.,.]],[[.,.],.]],.]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,6,1]=>[6,3,4,7,2,5,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,7,1]=>[7,3,4,6,2,5,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,7,1]=>[7,3,4,5,2,6,1]=>[[[[.,.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,7,1]=>[7,3,5,4,2,6,1]=>[[[[.,.],[[.,.],.]],[.,.]],.]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,6,1]=>[6,4,7,3,2,5,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,7,1]=>[7,4,6,3,2,5,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,7,1]=>[7,4,5,3,2,6,1]=>[[[[[.,.],[.,.]],.],[.,.]],.]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,7,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,7,1]=>[7,5,3,4,2,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,5,1]=>[5,6,2,3,4,7,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,5,1]=>[5,7,2,3,4,6,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,6,1]=>[6,5,2,3,7,4,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,7,1]=>[7,5,2,3,6,4,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,7,1]=>[7,6,2,3,5,4,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,6,1]=>[6,4,2,7,3,5,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,7,1]=>[7,4,2,6,3,5,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,7,1]=>[7,4,2,5,3,6,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,7,1]=>[7,5,2,4,3,6,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,6,1]=>[6,3,7,2,4,5,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,7,1]=>[7,3,6,2,4,5,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,7,1]=>[7,3,5,2,4,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,7,1]=>[7,3,4,2,5,6,1]=>[[[[.,.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,7,1]=>[7,4,3,2,5,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,6,1]=>[6,7,2,3,4,5,1]=>[[[.,[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,7,1]=>[7,6,2,3,4,5,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,7,1]=>[7,5,2,3,4,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,7,1]=>[7,4,2,3,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,7,1]=>[7,3,2,4,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1,2]=>[3,1,4,5,6,7,2]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,1,2]=>[3,1,4,5,7,6,2]=>[[.,.],[[.,[.,[[.,.],.]]],.]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,1,2]=>[3,1,4,6,7,5,2]=>[[.,.],[[.,[[.,[.,.]],.]],.]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,1,2]=>[3,1,4,7,6,5,2]=>[[.,.],[[.,[[[.,.],.],.]],.]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,1,2]=>[3,1,4,7,5,6,2]=>[[.,.],[[.,[[.,.],[.,.]]],.]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,1,2]=>[3,1,5,6,4,7,2]=>[[.,.],[[[.,[.,.]],[.,.]],.]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,1,2]=>[3,1,5,7,4,6,2]=>[[.,.],[[[.,[.,.]],[.,.]],.]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,1,2]=>[3,1,6,5,7,4,2]=>[[.,.],[[[[.,.],[.,.]],.],.]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,1,2]=>[3,1,7,5,6,4,2]=>[[.,.],[[[[.,.],[.,.]],.],.]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,1,2]=>[3,1,7,6,5,4,2]=>[[.,.],[[[[[.,.],.],.],.],.]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,1,2]=>[3,1,6,7,4,5,2]=>[[.,.],[[[.,[.,.]],[.,.]],.]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,1,2]=>[3,1,7,6,4,5,2]=>[[.,.],[[[[.,.],.],[.,.]],.]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,1,2]=>[3,1,7,5,4,6,2]=>[[.,.],[[[[.,.],.],[.,.]],.]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,1,2]=>[3,1,7,4,5,6,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,1,2]=>[4,1,5,3,6,7,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,1,2]=>[4,1,5,3,7,6,2]=>[[.,.],[[[.,.],[[.,.],.]],.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,1,2]=>[4,1,6,3,7,5,2]=>[[.,.],[[[.,.],[[.,.],.]],.]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,1,2]=>[4,1,7,3,6,5,2]=>[[.,.],[[[.,.],[[.,.],.]],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,1,2]=>[4,1,7,3,5,6,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,1,2]=>[5,1,4,6,3,7,2]=>[[.,.],[[[.,[.,.]],[.,.]],.]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,1,2]=>[5,1,4,7,3,6,2]=>[[.,.],[[[.,[.,.]],[.,.]],.]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,1,2]=>[6,1,4,5,7,3,2]=>[[.,.],[[[.,[.,[.,.]]],.],.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,1,2]=>[7,1,4,5,6,3,2]=>[[.,.],[[[.,[.,[.,.]]],.],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,1,2]=>[7,1,4,6,5,3,2]=>[[.,.],[[[.,[[.,.],.]],.],.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,1,2]=>[6,1,5,7,4,3,2]=>[[.,.],[[[[.,[.,.]],.],.],.]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,1,2]=>[7,1,5,6,4,3,2]=>[[.,.],[[[[.,[.,.]],.],.],.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,1,2]=>[7,1,6,5,4,3,2]=>[[.,.],[[[[[.,.],.],.],.],.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,1,2]=>[7,1,6,4,5,3,2]=>[[.,.],[[[[.,.],[.,.]],.],.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,1,2]=>[5,1,6,3,4,7,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,1,2]=>[5,1,7,3,4,6,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,1,2]=>[6,1,5,3,7,4,2]=>[[.,.],[[[.,.],[[.,.],.]],.]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,1,2]=>[7,1,5,3,6,4,2]=>[[.,.],[[[.,.],[[.,.],.]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,1,2]=>[7,1,6,3,5,4,2]=>[[.,.],[[[.,.],[[.,.],.]],.]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,1,2]=>[6,1,4,7,3,5,2]=>[[.,.],[[[.,[.,.]],[.,.]],.]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,1,2]=>[7,1,4,6,3,5,2]=>[[.,.],[[[.,[.,.]],[.,.]],.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,1,2]=>[7,1,4,5,3,6,2]=>[[.,.],[[[.,[.,.]],[.,.]],.]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,1,2]=>[7,1,5,4,3,6,2]=>[[.,.],[[[[.,.],.],[.,.]],.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,1,2]=>[6,1,7,3,4,5,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,1,2]=>[7,1,6,3,4,5,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,1,2]=>[7,1,5,3,4,6,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,1,2]=>[7,1,4,3,5,6,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>[7,1,3,4,5,6,2]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,1,3]=>[2,4,1,5,6,7,3]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,1,3]=>[2,4,1,5,7,6,3]=>[[.,[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,1,3]=>[2,4,1,6,7,5,3]=>[[.,[.,.]],[[[.,[.,.]],.],.]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,1,3]=>[2,4,1,7,6,5,3]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,1,3]=>[2,4,1,7,5,6,3]=>[[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,1,3]=>[2,5,1,6,4,7,3]=>[[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,1,3]=>[2,5,1,7,4,6,3]=>[[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,1,3]=>[2,6,1,5,7,4,3]=>[[.,[.,.]],[[[.,[.,.]],.],.]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,1,3]=>[2,7,1,5,6,4,3]=>[[.,[.,.]],[[[.,[.,.]],.],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,1,3]=>[2,7,1,6,5,4,3]=>[[.,[.,.]],[[[[.,.],.],.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,1,3]=>[2,6,1,7,4,5,3]=>[[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,1,3]=>[2,7,1,6,4,5,3]=>[[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,1,3]=>[2,7,1,5,4,6,3]=>[[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,1,3]=>[2,7,1,4,5,6,3]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1,4]=>[2,3,5,1,6,7,4]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,1,4]=>[2,3,5,1,7,6,4]=>[[.,[.,[.,.]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,1,4]=>[2,3,6,1,7,5,4]=>[[.,[.,[.,.]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,1,4]=>[2,3,7,1,6,5,4]=>[[.,[.,[.,.]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,1,4]=>[2,3,7,1,5,6,4]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1,5]=>[2,3,4,6,1,7,5]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,1,5]=>[2,3,4,7,1,6,5]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1,6]=>[2,3,4,5,7,1,6]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,7]=>[2,3,4,5,6,1,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,1,7]=>[2,3,4,6,5,1,7]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,1,6]=>[2,3,5,7,4,1,6]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,1,7]=>[2,3,5,6,4,1,7]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,1,7]=>[2,3,6,5,4,1,7]=>[[.,[.,[[[.,.],.],.]]],[.,.]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,1,7]=>[2,3,6,4,5,1,7]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,1,5]=>[2,4,6,3,1,7,5]=>[[.,[[.,[.,.]],.]],[[.,.],.]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,1,5]=>[2,4,7,3,1,6,5]=>[[.,[[.,[.,.]],.]],[[.,.],.]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,1,6]=>[2,4,5,3,7,1,6]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,1,7]=>[2,4,5,3,6,1,7]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,1,7]=>[2,4,6,3,5,1,7]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,1,6]=>[2,5,4,7,3,1,6]=>[[.,[[[.,.],[.,.]],.]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,1,7]=>[2,5,4,6,3,1,7]=>[[.,[[[.,.],[.,.]],.]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,1,7]=>[2,6,4,5,3,1,7]=>[[.,[[[.,.],[.,.]],.]],[.,.]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,1,7]=>[2,6,5,4,3,1,7]=>[[.,[[[[.,.],.],.],.]],[.,.]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,1,6]=>[2,5,7,3,4,1,6]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,1,7]=>[2,5,6,3,4,1,7]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,1,7]=>[2,6,5,3,4,1,7]=>[[.,[[[.,.],.],[.,.]]],[.,.]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,1,7]=>[2,6,4,3,5,1,7]=>[[.,[[[.,.],.],[.,.]]],[.,.]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,1,7]=>[2,6,3,4,5,1,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,1,4]=>[3,5,2,1,6,7,4]=>[[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,1,4]=>[3,5,2,1,7,6,4]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,1,4]=>[3,6,2,1,7,5,4]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,1,4]=>[3,7,2,1,6,5,4]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,1,4]=>[3,7,2,1,5,6,4]=>[[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,1,5]=>[3,4,2,6,1,7,5]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,1,5]=>[3,4,2,7,1,6,5]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,1,6]=>[3,4,2,5,7,1,6]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,1,7]=>[3,4,2,5,6,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,1,7]=>[3,4,2,6,5,1,7]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,1,6]=>[3,5,2,7,4,1,6]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,1,7]=>[3,5,2,6,4,1,7]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,1,7]=>[3,6,2,5,4,1,7]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,1,7]=>[3,6,2,4,5,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,1,5]=>[4,3,6,2,1,7,5]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,1,5]=>[4,3,7,2,1,6,5]=>[[[[.,.],[.,.]],.],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,1,6]=>[4,3,5,2,7,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,1,7]=>[4,3,5,2,6,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,1,7]=>[4,3,6,2,5,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,1,6]=>[5,3,4,7,2,1,6]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,1,7]=>[5,3,4,6,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,1,7]=>[6,3,4,5,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,1,7]=>[6,3,5,4,2,1,7]=>[[[[.,.],[[.,.],.]],.],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,1,6]=>[5,4,7,3,2,1,6]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,1,7]=>[5,4,6,3,2,1,7]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,1,7]=>[6,4,5,3,2,1,7]=>[[[[[.,.],[.,.]],.],.],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,1,7]=>[6,5,3,4,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,1,5]=>[4,6,2,3,1,7,5]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,1,5]=>[4,7,2,3,1,6,5]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,1,6]=>[4,5,2,3,7,1,6]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,1,7]=>[4,5,2,3,6,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,1,7]=>[4,6,2,3,5,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,1,6]=>[5,4,2,7,3,1,6]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,1,7]=>[5,4,2,6,3,1,7]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,1,7]=>[6,4,2,5,3,1,7]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,1,7]=>[6,5,2,4,3,1,7]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,1,6]=>[5,3,7,2,4,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,1,7]=>[5,3,6,2,4,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,1,7]=>[6,3,5,2,4,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,1,7]=>[6,3,4,2,5,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,1,7]=>[6,4,3,2,5,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,1,6]=>[5,7,2,3,4,1,6]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,1,7]=>[5,6,2,3,4,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,1,7]=>[6,5,2,3,4,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,1,7]=>[6,4,2,3,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,1,7]=>[6,3,2,4,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,2,3]=>[4,1,2,5,6,7,3]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,1,2,3]=>[4,1,2,5,7,6,3]=>[[.,.],[.,[[.,[[.,.],.]],.]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,1,2,3]=>[4,1,2,6,7,5,3]=>[[.,.],[.,[[[.,[.,.]],.],.]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,1,2,3]=>[4,1,2,7,6,5,3]=>[[.,.],[.,[[[[.,.],.],.],.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,1,2,3]=>[4,1,2,7,5,6,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,1,2,3]=>[5,1,2,6,4,7,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,1,2,3]=>[5,1,2,7,4,6,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,1,2,3]=>[6,1,2,5,7,4,3]=>[[.,.],[.,[[[.,[.,.]],.],.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,1,2,3]=>[7,1,2,5,6,4,3]=>[[.,.],[.,[[[.,[.,.]],.],.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,1,2,3]=>[7,1,2,6,5,4,3]=>[[.,.],[.,[[[[.,.],.],.],.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,1,2,3]=>[6,1,2,7,4,5,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,1,2,3]=>[7,1,2,6,4,5,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,1,2,3]=>[7,1,2,5,4,6,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[7,1,2,4,5,6,3]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1,2,4]=>[3,1,5,2,6,7,4]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,1,2,4]=>[3,1,5,2,7,6,4]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,1,2,4]=>[3,1,6,2,7,5,4]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,1,2,4]=>[3,1,7,2,6,5,4]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,1,2,4]=>[3,1,7,2,5,6,4]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1,2,5]=>[3,1,4,6,2,7,5]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,1,2,5]=>[3,1,4,7,2,6,5]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1,2,6]=>[3,1,4,5,7,2,6]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,2,7]=>[3,1,4,5,6,2,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,1,2,7]=>[3,1,4,6,5,2,7]=>[[.,.],[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,1,2,6]=>[3,1,5,7,4,2,6]=>[[.,.],[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,1,2,7]=>[3,1,5,6,4,2,7]=>[[.,.],[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,1,2,7]=>[3,1,6,5,4,2,7]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,1,2,7]=>[3,1,6,4,5,2,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,1,2,5]=>[4,1,6,3,2,7,5]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,1,2,5]=>[4,1,7,3,2,6,5]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,1,2,6]=>[4,1,5,3,7,2,6]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,1,2,7]=>[4,1,5,3,6,2,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,1,2,7]=>[4,1,6,3,5,2,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,1,2,6]=>[5,1,4,7,3,2,6]=>[[.,.],[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,1,2,7]=>[5,1,4,6,3,2,7]=>[[.,.],[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,1,2,7]=>[6,1,4,5,3,2,7]=>[[.,.],[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,1,2,7]=>[6,1,5,4,3,2,7]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>[5,1,7,3,4,2,6]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,1,2,7]=>[5,1,6,3,4,2,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,1,2,7]=>[6,1,5,3,4,2,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,1,2,7]=>[6,1,4,3,5,2,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,1,2,7]=>[6,1,3,4,5,2,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,3,4]=>[2,5,1,3,6,7,4]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,1,3,4]=>[2,5,1,3,7,6,4]=>[[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,1,3,4]=>[2,6,1,3,7,5,4]=>[[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,1,3,4]=>[2,7,1,3,6,5,4]=>[[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,1,3,4]=>[2,7,1,3,5,6,4]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1,3,5]=>[2,4,1,6,3,7,5]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,1,3,5]=>[2,4,1,7,3,6,5]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,3,6]=>[2,4,1,5,7,3,6]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,3,7]=>[2,4,1,5,6,3,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,1,3,7]=>[2,4,1,6,5,3,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,1,3,6]=>[2,5,1,7,4,3,6]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,1,3,7]=>[2,5,1,6,4,3,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,1,3,7]=>[2,6,1,5,4,3,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,1,3,7]=>[2,6,1,4,5,3,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,4,5]=>[2,3,6,1,4,7,5]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,1,4,5]=>[2,3,7,1,4,6,5]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1,4,6]=>[2,3,5,1,7,4,6]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,4,7]=>[2,3,5,1,6,4,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,1,4,7]=>[2,3,6,1,5,4,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,5,6]=>[2,3,4,7,1,5,6]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,5,7]=>[2,3,4,6,1,5,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,6,7]=>[2,3,4,5,1,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,1,6,7]=>[2,3,5,4,1,6,7]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,1,5,6]=>[2,4,7,3,1,5,6]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,1,5,7]=>[2,4,6,3,1,5,7]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,1,6,7]=>[2,4,5,3,1,6,7]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,1,6,7]=>[2,5,4,3,1,6,7]=>[[.,[[[.,.],.],.]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,1,6,7]=>[2,5,3,4,1,6,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,1,4,5]=>[3,6,2,1,4,7,5]=>[[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,1,4,5]=>[3,7,2,1,4,6,5]=>[[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,1,4,6]=>[3,5,2,1,7,4,6]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,1,4,7]=>[3,5,2,1,6,4,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,1,4,7]=>[3,6,2,1,5,4,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,1,5,6]=>[3,4,2,7,1,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,1,5,7]=>[3,4,2,6,1,5,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,1,6,7]=>[3,4,2,5,1,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,1,6,7]=>[3,5,2,4,1,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,1,5,6]=>[4,3,7,2,1,5,6]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,1,5,7]=>[4,3,6,2,1,5,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,1,6,7]=>[4,3,5,2,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,1,6,7]=>[5,3,4,2,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,1,6,7]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,1,5,6]=>[4,7,2,3,1,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,1,5,7]=>[4,6,2,3,1,5,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,1,6,7]=>[4,5,2,3,1,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,1,6,7]=>[5,4,2,3,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,1,6,7]=>[5,3,2,4,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,2,3,4]=>[5,1,2,3,6,7,4]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,7,5,1,2,3,4]=>[5,1,2,3,7,6,4]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,6,1,2,3,4]=>[6,1,2,3,7,5,4]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,7,1,2,3,4]=>[7,1,2,3,6,5,4]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>[7,1,2,3,5,6,4]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,2,3,5]=>[4,1,2,6,3,7,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,7,4,1,2,3,5]=>[4,1,2,7,3,6,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,2,3,6]=>[4,1,2,5,7,3,6]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,2,3,7]=>[4,1,2,5,6,3,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,6,4,1,2,3,7]=>[4,1,2,6,5,3,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,5,1,2,3,6]=>[5,1,2,7,4,3,6]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,5,1,2,3,7]=>[5,1,2,6,4,3,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,6,1,2,3,7]=>[6,1,2,5,4,3,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,2,4,5]=>[3,1,6,2,4,7,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,7,3,1,2,4,5]=>[3,1,7,2,4,6,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,2,4,6]=>[3,1,5,2,7,4,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,2,4,7]=>[3,1,5,2,6,4,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,6,3,1,2,4,7]=>[3,1,6,2,5,4,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,2,5,6]=>[3,1,4,7,2,5,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,2,5,7]=>[3,1,4,6,2,5,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,2,6,7]=>[3,1,4,5,2,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,1,2,6,7]=>[3,1,5,4,2,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,4,1,2,5,6]=>[4,1,7,3,2,5,6]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,4,1,2,5,7]=>[4,1,6,3,2,5,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,4,1,2,6,7]=>[4,1,5,3,2,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,5,1,2,6,7]=>[5,1,4,3,2,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,4,5,1,2,6,7]=>[5,1,3,4,2,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,3,4,5]=>[2,6,1,3,4,7,5]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,7,2,1,3,4,5]=>[2,7,1,3,4,6,5]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,3,4,6]=>[2,5,1,3,7,4,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,3,4,7]=>[2,5,1,3,6,4,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,6,2,1,3,4,7]=>[2,6,1,3,5,4,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,3,5,6]=>[2,4,1,7,3,5,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,3,5,7]=>[2,4,1,6,3,5,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,3,6,7]=>[2,4,1,5,3,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,2,1,3,6,7]=>[2,5,1,4,3,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,4,5,6]=>[2,3,7,1,4,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,4,5,7]=>[2,3,6,1,4,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,4,6,7]=>[2,3,5,1,4,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,5,6,7]=>[2,3,4,1,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,4,2,1,5,6,7]=>[2,4,3,1,5,6,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,3,1,4,5,6]=>[3,7,2,1,4,5,6]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,3,1,4,5,7]=>[3,6,2,1,4,5,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,3,1,4,6,7]=>[3,5,2,1,4,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,3,1,5,6,7]=>[3,4,2,1,5,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,4,1,5,6,7]=>[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,2,3,4,5]=>[6,1,2,3,4,7,5]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>[7,1,2,3,4,6,5]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,2,3,4,6]=>[5,1,2,3,7,4,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,2,3,4,7]=>[5,1,2,3,6,4,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,2,3,5,6]=>[4,1,2,7,3,5,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,2,3,5,7]=>[4,1,2,6,3,5,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,2,3,6,7]=>[4,1,2,5,3,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,2,4,5,6]=>[3,1,7,2,4,5,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,2,4,5,7]=>[3,1,6,2,4,5,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,2,4,6,7]=>[3,1,5,2,4,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,2,5,6,7]=>[3,1,4,2,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,3,4,5,6]=>[2,7,1,3,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,3,4,5,7]=>[2,6,1,3,4,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,3,4,6,7]=>[2,5,1,3,4,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,3,5,6,7]=>[2,4,1,3,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,4,5,6,7]=>[2,3,1,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>[7,1,2,3,4,5,6]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,1]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,2,1]=>[2,3,4,5,6,8,7,1]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,3,2,1]=>[2,3,4,5,7,8,6,1]=>[[.,[.,[.,[.,[[.,[.,.]],.]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,3,2,1]=>[2,3,4,5,8,7,6,1]=>[[.,[.,[.,[.,[[[.,.],.],.]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,3,2,1]=>[2,3,4,5,8,6,7,1]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,3,2,1]=>[2,3,4,6,7,5,8,1]=>[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,3,2,1]=>[2,3,4,6,8,5,7,1]=>[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,3,2,1]=>[2,3,4,7,6,8,5,1]=>[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,3,2,1]=>[2,3,4,8,6,7,5,1]=>[[.,[.,[.,[[[.,.],[.,.]],.]]]],.]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,3,2,1]=>[2,3,4,8,7,6,5,1]=>[[.,[.,[.,[[[[.,.],.],.],.]]]],.]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,3,2,1]=>[2,3,4,7,8,5,6,1]=>[[.,[.,[.,[[.,[.,.]],[.,.]]]]],.]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,3,2,1]=>[2,3,4,8,7,5,6,1]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,3,2,1]=>[2,3,4,8,6,5,7,1]=>[[.,[.,[.,[[[.,.],.],[.,.]]]]],.]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,2,1]=>[2,3,4,8,5,6,7,1]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,1]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,3,2,1]=>[2,3,5,6,4,8,7,1]=>[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,3,2,1]=>[2,3,5,7,4,8,6,1]=>[[.,[.,[[.,[.,.]],[[.,.],.]]]],.]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,3,2,1]=>[2,3,5,8,4,6,7,1]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,6,3,2,1]=>[2,3,6,5,8,4,7,1]=>[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,3,2,1]=>[2,3,7,5,6,8,4,1]=>[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,3,2,1]=>[2,3,8,5,6,7,4,1]=>[[.,[.,[[[.,.],[.,[.,.]]],.]]],.]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,3,2,1]=>[2,3,8,5,7,6,4,1]=>[[.,[.,[[[.,.],[[.,.],.]],.]]],.]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,3,2,1]=>[2,3,8,6,7,5,4,1]=>[[.,[.,[[[[.,.],[.,.]],.],.]]],.]
[1,0,1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,3,2,1]=>[2,3,8,7,6,5,4,1]=>[[.,[.,[[[[[.,.],.],.],.],.]]],.]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,3,2,1]=>[2,3,6,7,4,5,8,1]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,3,2,1]=>[2,3,6,8,4,5,7,1]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],.]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,7,3,2,1]=>[2,3,7,5,8,4,6,1]=>[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,3,2,1]=>[2,3,8,5,6,4,7,1]=>[[.,[.,[[[.,.],[.,.]],[.,.]]]],.]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,3,2,1]=>[2,3,8,6,5,4,7,1]=>[[.,[.,[[[[.,.],.],.],[.,.]]]],.]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,3,2,1]=>[2,3,8,7,4,5,6,1]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,3,2,1]=>[2,3,8,6,4,5,7,1]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,2,1]=>[2,3,8,5,4,6,7,1]=>[[.,[.,[[[.,.],.],[.,[.,.]]]]],.]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,2,1]=>[2,3,8,4,5,6,7,1]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,4,2,1]=>[2,4,5,3,6,7,8,1]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,4,2,1]=>[2,4,5,3,6,8,7,1]=>[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,4,2,1]=>[2,4,5,3,7,8,6,1]=>[[.,[[.,[.,.]],[[.,[.,.]],.]]],.]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,4,2,1]=>[2,4,5,3,8,7,6,1]=>[[.,[[.,[.,.]],[[[.,.],.],.]]],.]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,4,2,1]=>[2,4,5,3,8,6,7,1]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,2,1]=>[2,4,6,3,7,5,8,1]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,2,1]=>[2,4,6,3,8,5,7,1]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,4,2,1]=>[2,4,8,3,7,6,5,1]=>[[.,[[.,[.,.]],[[[.,.],.],.]]],.]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,4,2,1]=>[2,4,7,3,8,5,6,1]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,4,2,1]=>[2,4,8,3,7,5,6,1]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,4,2,1]=>[2,4,8,3,6,5,7,1]=>[[.,[[.,[.,.]],[[.,.],[.,.]]]],.]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,2,1]=>[2,4,8,3,5,6,7,1]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,5,2,1]=>[2,5,4,8,3,7,6,1]=>[[.,[[[.,.],[.,.]],[[.,.],.]]],.]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,5,2,1]=>[2,5,4,8,3,6,7,1]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,6,2,1]=>[2,6,4,5,7,3,8,1]=>[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,7,2,1]=>[2,7,4,5,6,8,3,1]=>[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,8,2,1]=>[2,8,4,5,6,7,3,1]=>[[.,[[[.,.],[.,[.,[.,.]]]],.]],.]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,3,7,2,1]=>[2,7,4,6,8,5,3,1]=>[[.,[[[.,.],[[.,[.,.]],.]],.]],.]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,8,2,1]=>[2,8,4,7,6,5,3,1]=>[[.,[[[.,.],[[[.,.],.],.]],.]],.]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,3,6,2,1]=>[2,6,5,7,4,3,8,1]=>[[.,[[[[.,.],[.,.]],.],[.,.]]],.]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,8,2,1]=>[2,8,5,7,4,6,3,1]=>[[.,[[[[.,.],[.,.]],[.,.]],.]],.]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,8,2,1]=>[2,8,7,5,6,4,3,1]=>[[.,[[[[[.,.],.],[.,.]],.],.]],.]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,8,2,1]=>[2,8,7,6,5,4,3,1]=>[[.,[[[[[[.,.],.],.],.],.],.]],.]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,3,8,2,1]=>[2,8,7,6,4,5,3,1]=>[[.,[[[[[.,.],.],.],[.,.]],.]],.]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,8,2,1]=>[2,8,7,5,4,6,3,1]=>[[.,[[[[[.,.],.],.],[.,.]],.]],.]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,8,2,1]=>[2,8,7,4,5,6,3,1]=>[[.,[[[[.,.],.],[.,[.,.]]],.]],.]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,5,2,1]=>[2,5,6,3,4,7,8,1]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,5,2,1]=>[2,5,6,3,4,8,7,1]=>[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,5,2,1]=>[2,5,7,3,4,8,6,1]=>[[.,[[.,[.,.]],[.,[[.,.],.]]]],.]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,5,2,1]=>[2,5,8,3,4,6,7,1]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,6,2,1]=>[2,6,5,3,7,4,8,1]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,6,2,1]=>[2,6,5,3,8,4,7,1]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,7,2,1]=>[2,7,6,3,8,5,4,1]=>[[.,[[[.,.],.],[[[.,.],.],.]]],.]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,6,2,1]=>[2,6,4,7,3,5,8,1]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,5,7,2,1]=>[2,7,4,6,3,8,5,1]=>[[.,[[[.,.],[.,.]],[[.,.],.]]],.]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,7,2,1]=>[2,7,4,5,8,3,6,1]=>[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,8,2,1]=>[2,8,4,5,7,3,6,1]=>[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,2,1]=>[2,8,4,5,6,3,7,1]=>[[.,[[[.,.],[.,[.,.]]],[.,.]]],.]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,7,8,2,1]=>[2,8,4,6,5,3,7,1]=>[[.,[[[.,.],[[.,.],.]],[.,.]]],.]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,6,2,1]=>[2,6,8,3,4,5,7,1]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,5,7,2,1]=>[2,7,6,3,4,8,5,1]=>[[.,[[[.,.],.],[.,[[.,.],.]]]],.]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,7,8,2,1]=>[2,8,5,3,6,4,7,1]=>[[.,[[[.,.],.],[[.,.],[.,.]]]],.]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,7,2,1]=>[2,7,4,8,3,5,6,1]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,6,8,2,1]=>[2,8,4,7,3,5,6,1]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,8,2,1]=>[2,8,4,5,3,6,7,1]=>[[.,[[[.,.],[.,.]],[.,[.,.]]]],.]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,8,2,1]=>[2,8,5,4,3,6,7,1]=>[[.,[[[[.,.],.],.],[.,[.,.]]]],.]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,7,2,1]=>[2,7,8,3,4,5,6,1]=>[[.,[[.,[.,.]],[.,[.,[.,.]]]]],.]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,8,2,1]=>[2,8,7,3,4,5,6,1]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,8,2,1]=>[2,8,6,3,4,5,7,1]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,7,8,2,1]=>[2,8,5,3,4,6,7,1]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,8,2,1]=>[2,8,4,3,5,6,7,1]=>[[.,[[[.,.],.],[.,[.,[.,.]]]]],.]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,2,1]=>[2,8,3,4,5,6,7,1]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,3,1]=>[3,4,2,5,6,7,8,1]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,2,3,1]=>[3,4,2,5,6,8,7,1]=>[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,2,3,1]=>[3,4,2,5,7,8,6,1]=>[[[.,[.,.]],[.,[[.,[.,.]],.]]],.]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,3,1]=>[3,4,2,5,8,7,6,1]=>[[[.,[.,.]],[.,[[[.,.],.],.]]],.]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,2,3,1]=>[3,4,2,6,7,5,8,1]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,2,3,1]=>[3,4,2,6,8,5,7,1]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,2,3,1]=>[3,4,2,8,6,7,5,1]=>[[[.,[.,.]],[[[.,.],[.,.]],.]],.]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,2,3,1]=>[3,4,2,8,7,6,5,1]=>[[[.,[.,.]],[[[[.,.],.],.],.]],.]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,2,3,1]=>[3,4,2,8,5,6,7,1]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,2,3,1]=>[3,5,2,6,4,7,8,1]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,2,3,1]=>[3,5,2,6,4,8,7,1]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,2,3,1]=>[3,5,2,7,4,8,6,1]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,2,3,1]=>[3,5,2,8,4,7,6,1]=>[[[.,[.,.]],[[.,.],[[.,.],.]]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,2,3,1]=>[3,5,2,8,4,6,7,1]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,2,3,1]=>[3,6,2,5,7,4,8,1]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,2,3,1]=>[3,7,2,6,8,5,4,1]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,2,3,1]=>[3,8,2,6,7,5,4,1]=>[[[.,[.,.]],[[[.,[.,.]],.],.]],.]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,2,3,1]=>[3,8,2,7,6,5,4,1]=>[[[.,[.,.]],[[[[.,.],.],.],.]],.]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,2,3,1]=>[3,6,2,8,4,5,7,1]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,2,3,1]=>[3,8,2,5,7,4,6,1]=>[[[.,[.,.]],[[.,[.,.]],[.,.]]],.]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,2,3,1]=>[3,7,2,8,4,5,6,1]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,2,3,1]=>[3,8,2,5,4,6,7,1]=>[[[.,[.,.]],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,2,3,1]=>[3,8,2,4,5,6,7,1]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,4,1]=>[4,3,5,2,6,7,8,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,2,4,1]=>[4,3,5,2,8,7,6,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,2,4,1]=>[4,3,5,2,8,6,7,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,2,4,1]=>[4,3,6,2,7,5,8,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,2,4,1]=>[4,3,6,2,8,5,7,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,4,1]=>[4,3,7,2,6,8,5,1]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],.]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,4,1]=>[4,3,8,2,6,7,5,1]=>[[[[.,.],[.,.]],[[.,[.,.]],.]],.]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,2,4,1]=>[4,3,8,2,7,6,5,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,2,4,1]=>[4,3,7,2,8,5,6,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,2,4,1]=>[4,3,8,2,7,5,6,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,2,4,1]=>[4,3,8,2,6,5,7,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,2,4,1]=>[4,3,8,2,5,6,7,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,2,5,1]=>[5,3,4,6,2,8,7,1]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,2,5,1]=>[5,3,4,8,2,7,6,1]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,2,5,1]=>[5,3,4,8,2,6,7,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,2,6,1]=>[6,3,4,5,7,2,8,1]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,2,6,1]=>[6,3,4,5,8,2,7,1]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,7,1]=>[7,3,4,5,6,8,2,1]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,8,1]=>[8,3,4,5,6,7,2,1]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,2,8,1]=>[8,3,4,5,7,6,2,1]=>[[[[.,.],[.,[.,[[.,.],.]]]],.],.]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,2,8,1]=>[8,3,4,7,6,5,2,1]=>[[[[.,.],[.,[[[.,.],.],.]]],.],.]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,2,8,1]=>[8,3,5,6,4,7,2,1]=>[[[[.,.],[[.,[.,.]],[.,.]]],.],.]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,3,2,8,1]=>[8,3,6,5,7,4,2,1]=>[[[[.,.],[[[.,.],[.,.]],.]],.],.]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,2,8,1]=>[8,3,7,5,6,4,2,1]=>[[[[.,.],[[[.,.],[.,.]],.]],.],.]
[1,0,1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,2,8,1]=>[8,3,7,6,5,4,2,1]=>[[[[.,.],[[[[.,.],.],.],.]],.],.]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,8,1]=>[8,3,7,5,4,6,2,1]=>[[[[.,.],[[[.,.],.],[.,.]]],.],.]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,2,8,1]=>[8,3,7,4,5,6,2,1]=>[[[[.,.],[[.,.],[.,[.,.]]]],.],.]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,2,5,1]=>[5,4,6,3,2,8,7,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,2,5,1]=>[5,4,7,3,2,8,6,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,2,5,1]=>[5,4,8,3,2,7,6,1]=>[[[[[.,.],[.,.]],.],[[.,.],.]],.]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,2,5,1]=>[5,4,8,3,2,6,7,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,2,6,1]=>[6,4,5,3,7,2,8,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,2,6,1]=>[6,4,5,3,8,2,7,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,2,7,1]=>[7,4,6,3,8,5,2,1]=>[[[[[.,.],[.,.]],[[.,.],.]],.],.]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,2,8,1]=>[8,4,6,3,7,5,2,1]=>[[[[[.,.],[.,.]],[[.,.],.]],.],.]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,2,8,1]=>[8,4,7,3,6,5,2,1]=>[[[[[.,.],[.,.]],[[.,.],.]],.],.]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,2,6,1]=>[6,5,4,8,3,2,7,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,5,2,7,1]=>[7,5,4,6,3,8,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,5,2,8,1]=>[8,5,4,6,3,7,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,2,7,1]=>[7,6,4,5,8,3,2,1]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,2,8,1]=>[8,6,4,5,7,3,2,1]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,2,8,1]=>[8,7,4,5,6,3,2,1]=>[[[[[[.,.],.],[.,[.,.]]],.],.],.]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,7,2,8,1]=>[8,7,4,6,5,3,2,1]=>[[[[[[.,.],.],[[.,.],.]],.],.],.]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,2,7,1]=>[7,6,5,8,4,3,2,1]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,6,2,8,1]=>[8,6,5,7,4,3,2,1]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,7,2,8,1]=>[8,7,5,6,4,3,2,1]=>[[[[[[[.,.],.],[.,.]],.],.],.],.]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,2,8,1]=>[8,7,6,5,4,3,2,1]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,2,8,1]=>[8,7,6,4,5,3,2,1]=>[[[[[[[.,.],.],.],[.,.]],.],.],.]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,2,6,1]=>[6,5,8,3,4,2,7,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,2,8,1]=>[8,6,5,3,7,4,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,7,2,8,1]=>[8,7,5,3,6,4,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,2,8,1]=>[8,7,6,3,5,4,2,1]=>[[[[[[.,.],.],.],[[.,.],.]],.],.]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,2,8,1]=>[8,7,4,6,3,5,2,1]=>[[[[[[.,.],.],[.,.]],[.,.]],.],.]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,2,8,1]=>[8,7,5,4,3,6,2,1]=>[[[[[[[.,.],.],.],.],[.,.]],.],.]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,2,7,1]=>[7,6,8,3,4,5,2,1]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,2,8,1]=>[8,6,7,3,4,5,2,1]=>[[[[[.,.],[.,.]],[.,[.,.]]],.],.]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,2,8,1]=>[8,7,6,3,4,5,2,1]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,7,2,8,1]=>[8,7,5,3,4,6,2,1]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,2,8,1]=>[8,7,4,3,5,6,2,1]=>[[[[[[.,.],.],.],[.,[.,.]]],.],.]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,2,8,1]=>[8,7,3,4,5,6,2,1]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,3,4,1]=>[4,5,2,3,6,7,8,1]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,3,4,1]=>[4,5,2,3,8,6,7,1]=>[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,3,4,1]=>[4,6,2,3,7,5,8,1]=>[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,3,4,1]=>[4,7,2,3,8,5,6,1]=>[[[.,[.,.]],[.,[[.,.],[.,.]]]],.]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,3,4,1]=>[4,8,2,3,5,6,7,1]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,3,5,1]=>[5,4,2,6,3,7,8,1]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,3,5,1]=>[5,4,2,8,3,6,7,1]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,2,3,6,1]=>[6,4,2,5,8,3,7,1]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,3,8,1]=>[8,4,2,5,6,7,3,1]=>[[[[.,.],.],[[.,[.,[.,.]]],.]],.]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,2,3,8,1]=>[8,4,2,5,7,6,3,1]=>[[[[.,.],.],[[.,[[.,.],.]],.]],.]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,2,3,7,1]=>[7,4,2,6,8,5,3,1]=>[[[[.,.],.],[[[.,[.,.]],.],.]],.]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,2,3,8,1]=>[8,4,2,6,7,5,3,1]=>[[[[.,.],.],[[[.,[.,.]],.],.]],.]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,2,3,8,1]=>[8,5,2,7,4,6,3,1]=>[[[[.,.],.],[[[.,.],[.,.]],.]],.]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,2,3,7,1]=>[7,6,2,5,8,4,3,1]=>[[[[.,.],.],[[[.,[.,.]],.],.]],.]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,2,3,8,1]=>[8,6,2,5,7,4,3,1]=>[[[[.,.],.],[[[.,[.,.]],.],.]],.]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,2,3,8,1]=>[8,7,2,5,6,4,3,1]=>[[[[.,.],.],[[[.,[.,.]],.],.]],.]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,2,3,8,1]=>[8,6,2,7,4,5,3,1]=>[[[[.,.],.],[[[.,.],[.,.]],.]],.]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,2,3,8,1]=>[8,7,2,6,4,5,3,1]=>[[[[.,.],.],[[[.,.],[.,.]],.]],.]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,3,8,1]=>[8,7,2,4,5,6,3,1]=>[[[[.,.],.],[[.,[.,[.,.]]],.]],.]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,4,5,1]=>[5,3,6,2,4,7,8,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,2,4,5,1]=>[5,3,6,2,4,8,7,1]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,2,4,5,1]=>[5,3,7,2,4,8,6,1]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,4,5,1]=>[5,3,8,2,4,6,7,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,2,4,8,1]=>[8,3,7,2,6,5,4,1]=>[[[[.,.],[.,.]],[[[.,.],.],.]],.]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,5,6,1]=>[6,3,4,8,2,5,7,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,5,8,1]=>[8,3,4,7,2,6,5,1]=>[[[[.,.],[.,[.,.]]],[[.,.],.]],.]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2,6,7,1]=>[7,3,4,5,8,2,6,1]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,2,6,7,1]=>[7,3,5,8,4,2,6,1]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,2,6,8,1]=>[8,3,5,7,4,2,6,1]=>[[[[.,.],[[.,[.,.]],.]],[.,.]],.]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,2,7,8,1]=>[8,3,6,4,5,2,7,1]=>[[[[.,.],[[.,.],[.,.]]],[.,.]],.]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,2,5,6,1]=>[6,4,7,3,2,5,8,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,2,6,7,1]=>[7,4,5,3,8,2,6,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,2,6,8,1]=>[8,4,5,3,7,2,6,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,2,7,8,1]=>[8,4,5,3,6,2,7,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,2,7,8,1]=>[8,4,6,3,5,2,7,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,2,6,7,1]=>[7,5,4,8,3,2,6,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,2,7,8,1]=>[8,5,4,6,3,2,7,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,2,7,8,1]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,2,6,7,1]=>[7,5,8,3,4,2,6,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,2,6,8,1]=>[8,5,7,3,4,2,6,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,2,7,8,1]=>[8,5,6,3,4,2,7,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,2,7,8,1]=>[8,6,4,3,5,2,7,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,7,8,1]=>[8,6,3,4,5,2,7,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,3,4,5,1]=>[5,7,2,3,4,8,6,1]=>[[[.,[.,.]],[.,[.,[[.,.],.]]]],.]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,4,5,1]=>[5,8,2,3,4,6,7,1]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,2,3,4,6,1]=>[6,5,2,3,8,4,7,1]=>[[[[.,.],.],[.,[[.,.],[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,4,8,1]=>[8,5,2,3,6,7,4,1]=>[[[[.,.],.],[.,[[.,[.,.]],.]]],.]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,2,3,4,8,1]=>[8,6,2,3,7,5,4,1]=>[[[[.,.],.],[.,[[[.,.],.],.]]],.]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,5,8,1]=>[8,4,2,6,3,7,5,1]=>[[[[.,.],.],[[.,.],[[.,.],.]]],.]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,2,3,6,7,1]=>[7,4,2,5,8,3,6,1]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[7,5,4,2,3,6,8,1]=>[8,4,2,5,7,3,6,1]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,2,3,7,8,1]=>[8,4,2,5,6,3,7,1]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,3,7,8,1]=>[8,6,2,5,4,3,7,1]=>[[[[.,.],.],[[[.,.],.],[.,.]]],.]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,5,6,2,3,7,8,1]=>[8,6,2,4,5,3,7,1]=>[[[[.,.],.],[[.,[.,.]],[.,.]]],.]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,4,5,6,1]=>[6,3,8,2,4,5,7,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,4,5,8,1]=>[8,3,6,2,4,7,5,1]=>[[[[.,.],[.,.]],[.,[[.,.],.]]],.]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,4,6,8,1]=>[8,3,5,2,7,4,6,1]=>[[[[.,.],[.,.]],[[.,.],[.,.]]],.]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,2,5,6,8,1]=>[8,3,4,7,2,5,6,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,7,8,1]=>[8,3,4,5,2,6,7,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,6,7,8,1]=>[8,3,5,4,2,6,7,1]=>[[[[.,.],[[.,.],.]],[.,[.,.]]],.]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,2,5,6,7,1]=>[7,4,8,3,2,5,6,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[7,3,4,2,5,6,8,1]=>[8,4,7,3,2,5,6,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,2,6,7,8,1]=>[8,4,5,3,2,6,7,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,6,7,8,1]=>[8,5,4,3,2,6,7,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,6,7,8,1]=>[8,5,3,4,2,6,7,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,4,5,6,1]=>[6,7,2,3,4,5,8,1]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,3,4,6,7,1]=>[7,5,2,3,8,4,6,1]=>[[[[.,.],.],[.,[[.,.],[.,.]]]],.]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,3,4,6,8,1]=>[8,5,2,3,7,4,6,1]=>[[[[.,.],.],[.,[[.,.],[.,.]]]],.]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[7,4,2,3,5,6,8,1]=>[8,4,2,7,3,5,6,1]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,6,7,8,1]=>[8,4,2,5,3,6,7,1]=>[[[[.,.],.],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,4,5,6,7,1]=>[7,3,8,2,4,5,6,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,4,5,6,8,1]=>[8,3,7,2,4,5,6,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[6,3,2,4,5,7,8,1]=>[8,3,6,2,4,5,7,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,6,7,8,1]=>[8,3,4,2,5,6,7,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,6,7,8,1]=>[8,4,3,2,5,6,7,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,5,6,7,1]=>[7,8,2,3,4,5,6,1]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,6,8,1]=>[8,7,2,3,4,5,6,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,5,7,8,1]=>[8,6,2,3,4,5,7,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,6,7,8,1]=>[8,4,2,3,5,6,7,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,1]=>[8,3,2,4,5,6,7,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]=>[8,2,3,4,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,1,2]=>[3,1,4,5,6,7,8,2]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,1,2]=>[3,1,4,5,6,8,7,2]=>[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,3,1,2]=>[3,1,4,5,7,8,6,2]=>[[.,.],[[.,[.,[[.,[.,.]],.]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,3,1,2]=>[3,1,4,5,8,6,7,2]=>[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,3,1,2]=>[3,1,4,6,7,5,8,2]=>[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,3,1,2]=>[3,1,4,6,8,5,7,2]=>[[.,.],[[.,[[.,[.,.]],[.,.]]],.]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,3,1,2]=>[3,1,4,7,6,8,5,2]=>[[.,.],[[.,[[[.,.],[.,.]],.]],.]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,3,1,2]=>[3,1,4,8,7,6,5,2]=>[[.,.],[[.,[[[[.,.],.],.],.]],.]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,3,1,2]=>[3,1,4,8,6,5,7,2]=>[[.,.],[[.,[[[.,.],.],[.,.]]],.]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,1,2]=>[3,1,4,8,5,6,7,2]=>[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,3,1,2]=>[3,1,5,6,4,7,8,2]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,3,1,2]=>[3,1,5,6,4,8,7,2]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,3,1,2]=>[3,1,5,7,4,8,6,2]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,3,1,2]=>[3,1,6,5,7,4,8,2]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,3,1,2]=>[3,1,8,6,7,5,4,2]=>[[.,.],[[[[[.,.],[.,.]],.],.],.]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,3,1,2]=>[3,1,8,7,6,5,4,2]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,3,1,2]=>[3,1,6,8,4,5,7,2]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,3,1,2]=>[3,1,7,6,4,8,5,2]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,3,1,2]=>[3,1,8,6,4,7,5,2]=>[[.,.],[[[[.,.],.],[[.,.],.]],.]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,3,1,2]=>[3,1,8,5,7,4,6,2]=>[[.,.],[[[[.,.],[.,.]],[.,.]],.]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,1,2]=>[3,1,8,5,4,6,7,2]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,1,2]=>[3,1,8,4,5,6,7,2]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,4,1,2]=>[4,1,5,3,6,7,8,2]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,4,1,2]=>[4,1,5,3,6,8,7,2]=>[[.,.],[[[.,.],[.,[[.,.],.]]],.]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,4,1,2]=>[4,1,5,3,8,7,6,2]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,4,1,2]=>[4,1,5,3,8,6,7,2]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,1,2]=>[4,1,6,3,7,5,8,2]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,1,2]=>[4,1,6,3,8,5,7,2]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,4,1,2]=>[4,1,7,3,6,8,5,2]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,4,1,2]=>[4,1,8,3,6,7,5,2]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,4,1,2]=>[4,1,7,3,8,5,6,2]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,4,1,2]=>[4,1,8,3,7,5,6,2]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,4,1,2]=>[4,1,8,3,6,5,7,2]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,1,2]=>[4,1,8,3,5,6,7,2]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,5,1,2]=>[5,1,4,8,3,7,6,2]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,6,1,2]=>[6,1,4,5,8,3,7,2]=>[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,7,1,2]=>[7,1,4,5,6,8,3,2]=>[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,8,1,2]=>[8,1,4,5,6,7,3,2]=>[[.,.],[[[.,[.,[.,[.,.]]]],.],.]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,8,1,2]=>[8,1,4,5,7,6,3,2]=>[[.,.],[[[.,[.,[[.,.],.]]],.],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,8,1,2]=>[8,1,4,7,6,5,3,2]=>[[.,.],[[[.,[[[.,.],.],.]],.],.]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,8,1,2]=>[8,1,5,6,4,7,3,2]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,8,1,2]=>[8,1,5,7,4,6,3,2]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,7,1,2]=>[7,1,6,5,8,4,3,2]=>[[.,.],[[[[[.,.],[.,.]],.],.],.]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,8,1,2]=>[8,1,7,5,6,4,3,2]=>[[.,.],[[[[[.,.],[.,.]],.],.],.]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,8,1,2]=>[8,1,7,6,5,4,3,2]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,8,1,2]=>[8,1,6,7,4,5,3,2]=>[[.,.],[[[[.,[.,.]],[.,.]],.],.]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,3,8,1,2]=>[8,1,7,6,4,5,3,2]=>[[.,.],[[[[[.,.],.],[.,.]],.],.]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,5,1,2]=>[5,1,7,3,4,8,6,2]=>[[.,.],[[[.,.],[.,[[.,.],.]]],.]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,5,1,2]=>[5,1,8,3,4,6,7,2]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,6,1,2]=>[6,1,5,3,8,4,7,2]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,8,1,2]=>[8,1,6,3,7,5,4,2]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,8,1,2]=>[8,1,7,3,6,5,4,2]=>[[.,.],[[[.,.],[[[.,.],.],.]],.]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,4,8,1,2]=>[8,1,7,3,5,6,4,2]=>[[.,.],[[[.,.],[[.,[.,.]],.]],.]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,6,1,2]=>[6,1,4,8,3,5,7,2]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,5,7,1,2]=>[7,1,4,6,3,8,5,2]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,5,8,1,2]=>[8,1,4,6,3,7,5,2]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,5,8,1,2]=>[8,1,4,7,3,6,5,2]=>[[.,.],[[[.,[.,.]],[[.,.],.]],.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,8,1,2]=>[8,1,4,5,7,3,6,2]=>[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,1,2]=>[8,1,4,5,6,3,7,2]=>[[.,.],[[[.,[.,[.,.]]],[.,.]],.]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,7,8,1,2]=>[8,1,4,6,5,3,7,2]=>[[.,.],[[[.,[[.,.],.]],[.,.]],.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,6,1,2]=>[6,1,8,3,4,5,7,2]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,6,7,1,2]=>[7,1,5,3,8,4,6,2]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,8,1,2]=>[8,1,5,3,7,4,6,2]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,7,8,1,2]=>[8,1,5,3,6,4,7,2]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,8,1,2]=>[8,1,6,3,5,4,7,2]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,7,1,2]=>[7,1,4,8,3,5,6,2]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,8,1,2]=>[8,1,4,6,3,5,7,2]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,8,1,2]=>[8,1,4,5,3,6,7,2]=>[[.,.],[[[.,[.,.]],[.,[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,8,1,2]=>[8,1,5,4,3,6,7,2]=>[[.,.],[[[[.,.],.],[.,[.,.]]],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,7,1,2]=>[7,1,8,3,4,5,6,2]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,8,1,2]=>[8,1,7,3,4,5,6,2]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,8,1,2]=>[8,1,6,3,4,5,7,2]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,8,1,2]=>[8,1,4,3,5,6,7,2]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2]=>[8,1,3,4,5,6,7,2]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,3]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,1,3]=>[2,4,1,5,8,7,6,3]=>[[.,[.,.]],[[.,[[[.,.],.],.]],.]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,2,1,3]=>[2,4,1,6,7,5,8,3]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,2,1,3]=>[2,4,1,6,8,5,7,3]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,2,1,3]=>[2,4,1,7,6,8,5,3]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,2,1,3]=>[2,4,1,8,6,7,5,3]=>[[.,[.,.]],[[[[.,.],[.,.]],.],.]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,2,1,3]=>[2,4,1,8,7,6,5,3]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,2,1,3]=>[2,4,1,8,5,6,7,3]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,2,1,3]=>[2,5,1,8,4,7,6,3]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,2,1,3]=>[2,5,1,8,4,6,7,3]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,2,1,3]=>[2,6,1,5,7,4,8,3]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,6,2,1,3]=>[2,6,1,5,8,4,7,3]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,7,2,1,3]=>[2,7,1,5,6,8,4,3]=>[[.,[.,.]],[[[.,[.,[.,.]]],.],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,2,1,3]=>[2,8,1,7,6,5,4,3]=>[[.,[.,.]],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,2,1,3]=>[2,6,1,8,4,5,7,3]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,2,1,3]=>[2,8,1,5,6,4,7,3]=>[[.,[.,.]],[[[.,[.,.]],[.,.]],.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,2,1,3]=>[2,8,1,5,4,6,7,3]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,2,1,3]=>[2,8,1,4,5,6,7,3]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,4]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,2,1,4]=>[2,3,6,1,7,5,8,4]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,2,1,4]=>[2,3,6,1,8,5,7,4]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,1,4]=>[2,3,7,1,6,8,5,4]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,1,4]=>[2,3,8,1,6,7,5,4]=>[[.,[.,[.,.]]],[[[.,[.,.]],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,2,1,4]=>[2,3,8,1,7,6,5,4]=>[[.,[.,[.,.]]],[[[[.,.],.],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,2,1,4]=>[2,3,7,1,8,5,6,4]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,2,1,4]=>[2,3,8,1,5,6,7,4]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,2,1,5]=>[2,3,4,6,1,7,8,5]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,2,1,5]=>[2,3,4,6,1,8,7,5]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,2,1,5]=>[2,3,4,8,1,7,6,5]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,2,1,5]=>[2,3,4,8,1,6,7,5]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,2,1,6]=>[2,3,4,5,7,1,8,6]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,2,1,6]=>[2,3,4,5,8,1,7,6]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,1,7]=>[2,3,4,5,6,8,1,7]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,1,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,2,1,8]=>[2,3,4,5,7,6,1,8]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,3,2,1,7]=>[2,3,4,6,8,5,1,7]=>[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,2,1,8]=>[2,3,4,6,7,5,1,8]=>[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,2,1,8]=>[2,3,4,7,6,5,1,8]=>[[.,[.,[.,[[[.,.],.],.]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,2,1,8]=>[2,3,4,7,5,6,1,8]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,2,1,8]=>[2,3,5,6,4,7,1,8]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,2,1,7]=>[2,3,6,5,8,4,1,7]=>[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,3,2,1,8]=>[2,3,6,5,7,4,1,8]=>[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,2,1,8]=>[2,3,7,5,6,4,1,8]=>[[.,[.,[[[.,.],[.,.]],.]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,2,1,8]=>[2,3,7,6,5,4,1,8]=>[[.,[.,[[[[.,.],.],.],.]]],[.,.]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,3,2,1,7]=>[2,3,6,8,4,5,1,7]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1,8]=>[2,3,7,5,4,6,1,8]=>[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,2,1,6]=>[2,4,5,3,7,1,8,6]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,4,2,1,7]=>[2,4,5,3,6,8,1,7]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,2,1,7]=>[2,4,6,3,8,5,1,7]=>[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,2,1,8]=>[2,4,6,3,7,5,1,8]=>[[.,[[.,[.,.]],[[.,.],.]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,4,2,1,8]=>[2,4,7,3,5,6,1,8]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,2,1,6]=>[2,5,4,7,3,1,8,6]=>[[.,[[[.,.],[.,.]],.]],[[.,.],.]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,2,1,6]=>[2,5,4,8,3,1,7,6]=>[[.,[[[.,.],[.,.]],.]],[[.,.],.]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,5,2,1,8]=>[2,5,4,6,3,7,1,8]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,5,2,1,8]=>[2,5,4,7,3,6,1,8]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,2,1,7]=>[2,6,4,5,8,3,1,7]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,2,1,8]=>[2,6,4,5,7,3,1,8]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,2,1,8]=>[2,7,4,5,6,3,1,8]=>[[.,[[[.,.],[.,[.,.]]],.]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,7,2,1,8]=>[2,7,4,6,5,3,1,8]=>[[.,[[[.,.],[[.,.],.]],.]],[.,.]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,2,1,8]=>[2,7,6,5,4,3,1,8]=>[[.,[[[[[.,.],.],.],.],.]],[.,.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,2,1,8]=>[2,5,6,3,4,7,1,8]=>[[.,[[.,[.,.]],[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,7,2,1,8]=>[2,7,5,3,6,4,1,8]=>[[.,[[[.,.],.],[[.,.],.]]],[.,.]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,2,1,8]=>[2,7,6,3,5,4,1,8]=>[[.,[[[.,.],.],[[.,.],.]]],[.,.]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,6,2,1,8]=>[2,6,4,7,3,5,1,8]=>[[.,[[[.,.],[.,.]],[.,.]]],[.,.]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,2,1,8]=>[2,7,3,4,5,6,1,8]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,3,1,4]=>[3,5,2,1,6,7,8,4]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,2,3,1,4]=>[3,5,2,1,6,8,7,4]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,2,3,1,4]=>[3,5,2,1,7,8,6,4]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,3,1,4]=>[3,5,2,1,8,7,6,4]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,3,1,4]=>[3,6,2,1,7,5,8,4]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,3,1,4]=>[3,8,2,1,6,7,5,4]=>[[[.,[.,.]],.],[[[.,[.,.]],.],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,3,1,4]=>[3,8,2,1,7,6,5,4]=>[[[.,[.,.]],.],[[[[.,.],.],.],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,2,3,1,4]=>[3,8,2,1,7,5,6,4]=>[[[.,[.,.]],.],[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,3,1,4]=>[3,8,2,1,5,6,7,4]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,2,3,1,5]=>[3,4,2,8,1,7,6,5]=>[[[.,[.,.]],[.,.]],[[[.,.],.],.]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,3,1,5]=>[3,4,2,8,1,6,7,5]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,3,1,7]=>[3,4,2,5,6,8,1,7]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,3,1,8]=>[3,4,2,5,6,7,1,8]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,2,3,1,8]=>[3,4,2,5,7,6,1,8]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,2,3,1,8]=>[3,4,2,6,7,5,1,8]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,2,3,1,8]=>[3,4,2,7,5,6,1,8]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,2,3,1,6]=>[3,5,2,7,4,1,8,6]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,2,3,1,7]=>[3,5,2,6,4,8,1,7]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,2,3,1,8]=>[3,5,2,6,4,7,1,8]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,2,3,1,8]=>[3,5,2,7,4,6,1,8]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,2,3,1,8]=>[3,7,2,5,6,4,1,8]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,2,3,1,8]=>[3,7,2,6,5,4,1,8]=>[[[.,[.,.]],[[[.,.],.],.]],[.,.]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,2,3,1,7]=>[3,6,2,8,4,5,1,7]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,2,3,1,8]=>[3,7,2,5,4,6,1,8]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,2,4,1,5]=>[4,3,7,2,1,8,6,5]=>[[[[.,.],[.,.]],.],[[[.,.],.],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,4,1,5]=>[4,3,8,2,1,6,7,5]=>[[[[.,.],[.,.]],.],[[.,[.,.]],.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,4,1,6]=>[4,3,5,2,7,1,8,6]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,2,4,1,6]=>[4,3,5,2,8,1,7,6]=>[[[[.,.],[.,.]],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,2,4,1,7]=>[4,3,5,2,6,8,1,7]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,2,4,1,8]=>[4,3,6,2,7,5,1,8]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,2,4,1,8]=>[4,3,7,2,6,5,1,8]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,2,4,1,8]=>[4,3,7,2,5,6,1,8]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,2,5,1,7]=>[5,3,4,6,2,8,1,7]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,2,5,1,8]=>[5,3,4,6,2,7,1,8]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2,6,1,7]=>[6,3,4,5,8,2,1,7]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,2,6,1,7]=>[6,3,5,8,4,2,1,7]=>[[[[.,.],[[.,[.,.]],.]],.],[.,.]]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,7,1,8]=>[7,3,6,5,4,2,1,8]=>[[[[.,.],[[[.,.],.],.]],.],[.,.]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,5,1,6]=>[5,4,8,3,2,1,7,6]=>[[[[[.,.],[.,.]],.],.],[[.,.],.]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,2,6,1,7]=>[6,4,5,3,8,2,1,7]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,2,7,1,8]=>[7,4,6,3,5,2,1,8]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,2,6,1,7]=>[6,5,4,8,3,2,1,7]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,2,6,1,8]=>[6,5,4,7,3,2,1,8]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,2,7,1,8]=>[7,5,4,6,3,2,1,8]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,7,1,8]=>[7,6,4,5,3,2,1,8]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,2,7,1,8]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,2,6,1,7]=>[6,5,8,3,4,2,1,7]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,2,6,1,8]=>[6,5,7,3,4,2,1,8]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,2,7,1,8]=>[7,5,6,3,4,2,1,8]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,2,7,1,8]=>[7,6,5,3,4,2,1,8]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,2,7,1,8]=>[7,6,4,3,5,2,1,8]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,7,1,8]=>[7,6,3,4,5,2,1,8]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,2,3,4,1,6]=>[4,5,2,3,8,1,7,6]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,4,1,8]=>[4,5,2,3,6,7,1,8]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,2,3,4,1,8]=>[4,5,2,3,7,6,1,8]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,2,3,4,1,8]=>[4,6,2,3,7,5,1,8]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,2,3,4,1,8]=>[4,7,2,3,6,5,1,8]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,3,4,1,8]=>[4,7,2,3,5,6,1,8]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,3,5,1,6]=>[5,4,2,8,3,1,7,6]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[7,5,4,2,3,6,1,8]=>[6,4,2,5,7,3,1,8]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,2,3,7,1,8]=>[7,4,2,5,6,3,1,8]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[6,4,5,2,3,7,1,8]=>[7,5,2,6,4,3,1,8]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,3,7,1,8]=>[7,6,2,5,4,3,1,8]=>[[[[.,.],.],[[[.,.],.],.]],[.,.]]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,5,6,2,3,7,1,8]=>[7,6,2,4,5,3,1,8]=>[[[[.,.],.],[[.,[.,.]],.]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,4,5,1,7]=>[5,3,6,2,4,8,1,7]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,4,5,1,8]=>[5,3,7,2,4,6,1,8]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,4,6,1,8]=>[6,3,5,2,7,4,1,8]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[6,5,3,2,4,7,1,8]=>[7,3,5,2,6,4,1,8]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,3,2,4,7,1,8]=>[7,3,6,2,5,4,1,8]=>[[[[.,.],[.,.]],[[.,.],.]],[.,.]]
[1,1,0,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,6,7,1,8]=>[7,3,5,4,2,6,1,8]=>[[[[.,.],[[.,.],.]],[.,.]],[.,.]]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,2,6,7,1,8]=>[7,4,5,3,2,6,1,8]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,6,7,1,8]=>[7,5,4,3,2,6,1,8]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,6,7,1,8]=>[7,5,3,4,2,6,1,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,3,4,6,1,8]=>[6,5,2,3,7,4,1,8]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,6,2,3,4,7,1,8]=>[7,6,2,3,5,4,1,8]=>[[[[.,.],.],[.,[[.,.],.]]],[.,.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,3,5,6,1,7]=>[6,4,2,8,3,5,1,7]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[7,4,2,3,5,6,1,8]=>[6,4,2,7,3,5,1,8]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,3,5,7,1,8]=>[7,4,2,6,3,5,1,8]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,6,7,1,8]=>[7,4,2,5,3,6,1,8]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,4,5,6,1,7]=>[6,3,8,2,4,5,1,7]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,6,7,1,8]=>[7,3,5,2,4,6,1,8]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,6,1,8]=>[6,7,2,3,4,5,1,8]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,5,7,1,8]=>[7,6,2,3,4,5,1,8]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,6,7,1,8]=>[7,4,2,3,5,6,1,8]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8]=>[7,2,3,4,5,6,1,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,1,2,3]=>[4,1,2,5,6,7,8,3]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,1,2,3]=>[4,1,2,5,6,8,7,3]=>[[.,.],[.,[[.,[.,[[.,.],.]]],.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,1,2,3]=>[4,1,2,5,8,6,7,3]=>[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,1,2,3]=>[4,1,2,6,8,5,7,3]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,1,2,3]=>[4,1,2,8,7,6,5,3]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,1,2,3]=>[4,1,2,7,8,5,6,3]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,1,2,3]=>[4,1,2,8,7,5,6,3]=>[[.,.],[.,[[[[.,.],.],[.,.]],.]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,1,2,3]=>[4,1,2,8,5,6,7,3]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,1,2,3]=>[5,1,2,6,4,8,7,3]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,6,1,2,3]=>[6,1,2,5,8,4,7,3]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,1,2,3]=>[8,1,2,5,6,7,4,3]=>[[.,.],[.,[[[.,[.,[.,.]]],.],.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,1,2,3]=>[7,1,2,6,8,5,4,3]=>[[.,.],[.,[[[[.,[.,.]],.],.],.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,1,2,3]=>[8,1,2,6,7,5,4,3]=>[[.,.],[.,[[[[.,[.,.]],.],.],.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,1,2,3]=>[8,1,2,7,6,5,4,3]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,1,2,3]=>[6,1,2,7,4,5,8,3]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,1,2,3]=>[6,1,2,8,4,5,7,3]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,1,2,3]=>[8,1,2,6,4,7,5,3]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,1,2,3]=>[8,1,2,7,4,6,5,3]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,7,1,2,3]=>[7,1,2,5,8,4,6,3]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,1,2,3]=>[8,1,2,5,7,4,6,3]=>[[.,.],[.,[[[.,[.,.]],[.,.]],.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,1,2,3]=>[7,1,2,8,4,5,6,3]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,1,2,3]=>[8,1,2,7,4,5,6,3]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,1,2,3]=>[8,1,2,6,4,5,7,3]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,1,2,3]=>[8,1,2,4,5,6,7,3]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,1,2,4]=>[3,1,5,2,6,7,8,4]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,1,2,4]=>[3,1,5,2,8,7,6,4]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,1,2,4]=>[3,1,5,2,8,6,7,4]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,1,2,4]=>[3,1,6,2,7,5,8,4]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,1,2,4]=>[3,1,6,2,8,5,7,4]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,1,2,4]=>[3,1,8,2,6,7,5,4]=>[[.,.],[[.,.],[[[.,[.,.]],.],.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,1,2,4]=>[3,1,8,2,7,6,5,4]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,1,2,4]=>[3,1,7,2,8,5,6,4]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,1,2,4]=>[3,1,8,2,7,5,6,4]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,1,2,4]=>[3,1,8,2,6,5,7,4]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,1,2,4]=>[3,1,8,2,5,6,7,4]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,1,2,5]=>[3,1,4,6,2,7,8,5]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,1,2,5]=>[3,1,4,6,2,8,7,5]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,1,2,5]=>[3,1,4,8,2,6,7,5]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,1,2,6]=>[3,1,4,5,7,2,8,6]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,1,2,7]=>[3,1,4,5,6,8,2,7]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,1,2,8]=>[3,1,4,5,6,7,2,8]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,1,2,8]=>[3,1,4,7,5,6,2,8]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,1,2,5]=>[4,1,6,3,2,7,8,5]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,1,2,5]=>[4,1,7,3,2,8,6,5]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,1,2,5]=>[4,1,8,3,2,7,6,5]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,1,2,5]=>[4,1,8,3,2,6,7,5]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,1,2,6]=>[4,1,5,3,7,2,8,6]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,1,2,6]=>[4,1,5,3,8,2,7,6]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,4,1,2,7]=>[4,1,5,3,6,8,2,7]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,1,2,7]=>[4,1,6,3,8,5,2,7]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,1,2,8]=>[4,1,6,3,7,5,2,8]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,1,2,6]=>[5,1,4,7,3,2,8,6]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,1,2,6]=>[5,1,4,8,3,2,7,6]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,5,1,2,8]=>[5,1,4,7,3,6,2,8]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,1,2,7]=>[6,1,4,5,8,3,2,7]=>[[.,.],[[[.,[.,[.,.]]],.],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,7,1,2,8]=>[7,1,4,6,5,3,2,8]=>[[.,.],[[[.,[[.,.],.]],.],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,6,1,2,8]=>[6,1,5,7,4,3,2,8]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,7,1,2,8]=>[7,1,5,6,4,3,2,8]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,1,2,8]=>[7,1,6,5,4,3,2,8]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,1,2,6]=>[5,1,7,3,4,2,8,6]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,1,2,6]=>[5,1,8,3,4,2,7,6]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,5,1,2,7]=>[5,1,6,3,4,8,2,7]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,7,1,2,8]=>[7,1,5,3,6,4,2,8]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,1,2,8]=>[7,1,6,3,5,4,2,8]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,1,2,7]=>[6,1,8,3,4,5,2,7]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,1,2,8]=>[7,1,3,4,5,6,2,8]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,1,3,4]=>[2,5,1,3,6,7,8,4]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,2,1,3,4]=>[2,5,1,3,6,8,7,4]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,2,1,3,4]=>[2,5,1,3,7,8,6,4]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,1,3,4]=>[2,5,1,3,8,6,7,4]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,1,3,4]=>[2,6,1,3,8,5,7,4]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,1,3,4]=>[2,7,1,3,6,8,5,4]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,1,3,4]=>[2,8,1,3,6,7,5,4]=>[[.,[.,.]],[.,[[[.,[.,.]],.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,1,3,4]=>[2,8,1,3,7,6,5,4]=>[[.,[.,.]],[.,[[[[.,.],.],.],.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,2,1,3,4]=>[2,8,1,3,7,5,6,4]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,1,3,4]=>[2,8,1,3,6,5,7,4]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,1,3,4]=>[2,8,1,3,5,6,7,4]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,1,3,5]=>[2,4,1,6,3,7,8,5]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,2,1,3,5]=>[2,4,1,7,3,8,6,5]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,2,1,3,6]=>[2,4,1,5,7,3,8,6]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,2,1,3,6]=>[2,4,1,5,8,3,7,6]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,1,3,7]=>[2,4,1,5,6,8,3,7]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,1,3,8]=>[2,4,1,5,6,7,3,8]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,2,1,3,7]=>[2,4,1,6,8,5,3,7]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,2,1,3,8]=>[2,4,1,7,5,6,3,8]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,2,1,3,6]=>[2,5,1,8,4,3,7,6]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,2,1,3,8]=>[2,5,1,6,4,7,3,8]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,2,1,3,8]=>[2,7,1,5,6,4,3,8]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,1,4,5]=>[2,3,6,1,4,7,8,5]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,2,1,4,5]=>[2,3,6,1,4,8,7,5]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,2,1,4,5]=>[2,3,7,1,4,8,6,5]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,1,4,5]=>[2,3,8,1,4,6,7,5]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,1,4,6]=>[2,3,5,1,7,4,8,6]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,2,1,4,6]=>[2,3,5,1,8,4,7,6]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,2,1,4,7]=>[2,3,5,1,6,8,4,7]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[6,7,5,3,2,1,4,8]=>[2,3,5,1,7,6,4,8]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,2,1,4,7]=>[2,3,6,1,8,5,4,7]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,2,1,4,8]=>[2,3,6,1,7,5,4,8]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,2,1,4,8]=>[2,3,7,1,5,6,4,8]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,1,5,6]=>[2,3,4,7,1,5,8,6]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,1,5,6]=>[2,3,4,8,1,5,7,6]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,2,1,5,7]=>[2,3,4,6,1,8,5,7]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,2,1,5,8]=>[2,3,4,6,1,7,5,8]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,1,5,8]=>[2,3,4,7,1,6,5,8]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2,1,6,7]=>[2,3,4,5,8,1,6,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,2,1,6,8]=>[2,3,4,5,7,1,6,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,1,7,8]=>[2,3,4,5,6,1,7,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,2,1,7,8]=>[2,3,4,6,5,1,7,8]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,2,1,7,8]=>[2,3,5,6,4,1,7,8]=>[[.,[.,[[.,[.,.]],.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,1,7,8]=>[2,3,6,5,4,1,7,8]=>[[.,[.,[[[.,.],.],.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,2,1,7,8]=>[2,3,6,4,5,1,7,8]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,2,1,5,6]=>[2,4,7,3,1,5,8,6]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,1,5,6]=>[2,4,8,3,1,5,7,6]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,2,1,5,7]=>[2,4,6,3,1,8,5,7]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,2,1,6,7]=>[2,5,4,8,3,1,6,7]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,1,7,8]=>[2,6,4,5,3,1,7,8]=>[[.,[[[.,.],[.,.]],.]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,2,1,6,7]=>[2,5,8,3,4,1,6,7]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,2,1,6,8]=>[2,5,7,3,4,1,6,8]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,2,1,7,8]=>[2,6,5,3,4,1,7,8]=>[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,1,7,8]=>[2,6,3,4,5,1,7,8]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,1,4,5]=>[3,6,2,1,4,7,8,5]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,2,3,1,4,5]=>[3,6,2,1,4,8,7,5]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,3,1,4,5]=>[3,7,2,1,4,8,6,5]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,2,3,1,4,6]=>[3,5,2,1,7,4,8,6]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,3,1,4,7]=>[3,5,2,1,6,8,4,7]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,3,1,4,7]=>[3,6,2,1,8,5,4,7]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,2,3,1,4,8]=>[3,6,2,1,7,5,4,8]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,3,1,4,8]=>[3,7,2,1,5,6,4,8]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,1,5,8]=>[3,4,2,6,1,7,5,8]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,2,3,1,7,8]=>[3,4,2,5,6,1,7,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,2,3,1,6,8]=>[3,5,2,7,4,1,6,8]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,3,1,7,8]=>[3,6,2,5,4,1,7,8]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,4,1,5,6]=>[4,3,8,2,1,5,7,6]=>[[[[.,.],[.,.]],.],[.,[[.,.],.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,4,1,5,7]=>[4,3,6,2,1,8,5,7]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,4,1,5,8]=>[4,3,7,2,1,6,5,8]=>[[[[.,.],[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,2,4,1,6,7]=>[4,3,5,2,8,1,6,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,4,1,6,8]=>[4,3,5,2,7,1,6,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[6,5,3,2,4,1,7,8]=>[4,3,5,2,6,1,7,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,3,2,4,1,7,8]=>[4,3,6,2,5,1,7,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,1,7,8]=>[6,3,4,5,2,1,7,8]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[6,3,4,2,5,1,7,8]=>[5,4,6,3,2,1,7,8]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,6,1,7,8]=>[6,5,4,3,2,1,7,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,6,1,7,8]=>[6,5,3,4,2,1,7,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,4,1,5,6]=>[4,8,2,3,1,5,7,6]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,3,4,1,6,7]=>[4,5,2,3,8,1,6,7]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,3,4,1,6,8]=>[4,5,2,3,7,1,6,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,3,5,1,6,7]=>[5,4,2,8,3,1,6,7]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,3,5,1,7,8]=>[5,4,2,6,3,1,7,8]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,6,1,7,8]=>[6,4,2,5,3,1,7,8]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,4,5,1,6,7]=>[5,3,8,2,4,1,6,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,4,5,1,6,8]=>[5,3,7,2,4,1,6,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[6,3,2,4,5,1,7,8]=>[5,3,6,2,4,1,7,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,6,1,7,8]=>[6,3,5,2,4,1,7,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,6,1,7,8]=>[6,4,3,2,5,1,7,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,5,1,6,7]=>[5,8,2,3,4,1,6,7]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,1,6,8]=>[5,7,2,3,4,1,6,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,5,1,7,8]=>[5,6,2,3,4,1,7,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,6,1,7,8]=>[6,5,2,3,4,1,7,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,1,7,8]=>[6,2,3,4,5,1,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,4]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,1,2,3,4]=>[5,1,2,3,6,8,7,4]=>[[.,.],[.,[.,[[.,[[.,.],.]],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,1,2,3,4]=>[5,1,2,3,7,8,6,4]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,1,2,3,4]=>[5,1,2,3,8,7,6,4]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,1,2,3,4]=>[5,1,2,3,8,6,7,4]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,1,2,3,4]=>[6,1,2,3,7,5,8,4]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,1,2,3,4]=>[6,1,2,3,8,5,7,4]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,1,2,3,4]=>[7,1,2,3,6,8,5,4]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,1,2,3,4]=>[8,1,2,3,6,7,5,4]=>[[.,.],[.,[.,[[[.,[.,.]],.],.]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,1,2,3,4]=>[8,1,2,3,7,6,5,4]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,1,2,3,4]=>[7,1,2,3,8,5,6,4]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,1,2,3,4]=>[8,1,2,3,7,5,6,4]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,1,2,3,4]=>[8,1,2,3,6,5,7,4]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[8,1,2,3,5,6,7,4]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,1,2,3,5]=>[4,1,2,6,3,7,8,5]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,1,2,3,5]=>[4,1,2,6,3,8,7,5]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,1,2,3,5]=>[4,1,2,7,3,8,6,5]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,1,2,3,5]=>[4,1,2,8,3,6,7,5]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,1,2,3,6]=>[4,1,2,5,7,3,8,6]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,1,2,3,6]=>[4,1,2,5,8,3,7,6]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,1,2,3,7]=>[4,1,2,5,6,8,3,7]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,1,2,3,8]=>[4,1,2,5,6,7,3,8]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,1,2,3,8]=>[4,1,2,5,7,6,3,8]=>[[.,.],[.,[[.,[[.,.],.]],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,1,2,3,7]=>[4,1,2,6,8,5,3,7]=>[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,1,2,3,8]=>[4,1,2,6,7,5,3,8]=>[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,1,2,3,8]=>[4,1,2,7,5,6,3,8]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,1,2,3,6]=>[5,1,2,8,4,3,7,6]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,1,2,3,7]=>[5,1,2,6,4,8,3,7]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,1,2,3,8]=>[7,1,2,6,5,4,3,8]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,1,2,3,8]=>[7,1,2,6,4,5,3,8]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,1,2,3,8]=>[7,1,2,5,4,6,3,8]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,1,2,3,8]=>[7,1,2,4,5,6,3,8]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,1,2,4,5]=>[3,1,6,2,4,7,8,5]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,1,2,4,5]=>[3,1,6,2,4,8,7,5]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,1,2,4,5]=>[3,1,8,2,4,7,6,5]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,1,2,4,6]=>[3,1,5,2,7,4,8,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,1,2,4,6]=>[3,1,5,2,8,4,7,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,1,2,4,7]=>[3,1,5,2,6,8,4,7]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,1,2,4,8]=>[3,1,7,2,5,6,4,8]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,1,2,5,6]=>[3,1,4,7,2,5,8,6]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,1,2,5,6]=>[3,1,4,8,2,5,7,6]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,1,2,5,7]=>[3,1,4,6,2,8,5,7]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,1,2,6,7]=>[3,1,4,5,8,2,6,7]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,1,2,7,8]=>[3,1,4,6,5,2,7,8]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,1,2,7,8]=>[3,1,5,6,4,2,7,8]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,1,2,7,8]=>[3,1,6,5,4,2,7,8]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,1,2,5,6]=>[4,1,7,3,2,5,8,6]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,1,2,5,8]=>[4,1,6,3,2,7,5,8]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,1,2,5,8]=>[4,1,7,3,2,6,5,8]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,1,2,6,7]=>[4,1,5,3,8,2,6,7]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,1,2,7,8]=>[4,1,6,3,5,2,7,8]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,1,2,6,7]=>[5,1,4,8,3,2,6,7]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,1,2,7,8]=>[6,1,4,5,3,2,7,8]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,1,2,7,8]=>[5,1,6,3,4,2,7,8]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,1,2,7,8]=>[6,1,3,4,5,2,7,8]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,1,3,4,5]=>[2,6,1,3,4,7,8,5]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,1,3,4,5]=>[2,7,1,3,4,8,6,5]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,1,3,4,5]=>[2,8,1,3,4,6,7,5]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,2,1,3,4,6]=>[2,5,1,3,7,4,8,6]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,2,1,3,4,6]=>[2,5,1,3,8,4,7,6]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,1,3,4,7]=>[2,5,1,3,6,8,4,7]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,2,1,3,4,8]=>[2,5,1,3,7,6,4,8]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,1,3,4,7]=>[2,6,1,3,8,5,4,7]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,2,1,3,4,8]=>[2,6,1,3,7,5,4,8]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,1,3,4,8]=>[2,7,1,3,5,6,4,8]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[8,7,4,2,1,3,5,6]=>[2,4,1,7,3,5,8,6]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,1,3,5,6]=>[2,4,1,8,3,5,7,6]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,1,3,5,7]=>[2,4,1,6,3,8,5,7]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,1,3,5,8]=>[2,4,1,6,3,7,5,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,2,1,3,6,7]=>[2,4,1,5,8,3,6,7]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,2,1,3,7,8]=>[2,4,1,5,6,3,7,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[5,6,4,2,1,3,7,8]=>[2,4,1,6,5,3,7,8]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,2,1,3,6,8]=>[2,5,1,7,4,3,6,8]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[6,4,5,2,1,3,7,8]=>[2,5,1,6,4,3,7,8]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,1,3,7,8]=>[2,6,1,5,4,3,7,8]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[4,5,6,2,1,3,7,8]=>[2,6,1,4,5,3,7,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[8,7,3,2,1,4,5,6]=>[2,3,7,1,4,5,8,6]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,1,4,5,6]=>[2,3,8,1,4,5,7,6]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,1,4,5,7]=>[2,3,6,1,4,8,5,7]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,2,1,4,6,7]=>[2,3,5,1,8,4,6,7]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,3,2,1,4,7,8]=>[2,3,6,1,5,4,7,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[8,4,3,2,1,5,6,7]=>[2,3,4,8,1,5,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,2,1,5,6,8]=>[2,3,4,7,1,5,6,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,1,5,7,8]=>[2,3,4,6,1,5,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,6,7,8]=>[2,3,4,5,1,6,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,1,6,7,8]=>[2,3,5,4,1,6,7,8]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,2,1,5,6,7]=>[2,4,8,3,1,5,6,7]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,2,1,6,7,8]=>[2,4,5,3,1,6,7,8]=>[[.,[[.,[.,.]],.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,1,6,7,8]=>[2,5,4,3,1,6,7,8]=>[[.,[[[.,.],.],.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,1,6,7,8]=>[2,5,3,4,1,6,7,8]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,1,4,5,6]=>[3,7,2,1,4,5,8,6]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,1,4,5,6]=>[3,8,2,1,4,5,7,6]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[8,6,2,3,1,4,5,7]=>[3,6,2,1,4,8,5,7]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,1,4,5,8]=>[3,6,2,1,4,7,5,8]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,3,1,4,6,8]=>[3,5,2,1,7,4,6,8]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,3,1,4,7,8]=>[3,5,2,1,6,4,7,8]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[5,6,2,3,1,4,7,8]=>[3,6,2,1,5,4,7,8]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,3,1,5,6,7]=>[3,4,2,8,1,5,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[7,4,2,3,1,5,6,8]=>[3,4,2,7,1,5,6,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,1,6,7,8]=>[3,4,2,5,1,6,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,1,6,7,8]=>[3,5,2,4,1,6,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,4,1,5,6,7]=>[4,3,8,2,1,5,6,7]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,4,1,5,6,8]=>[4,3,7,2,1,5,6,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,1,6,7,8]=>[4,3,5,2,1,6,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,1,6,7,8]=>[5,3,4,2,1,6,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,1,6,7,8]=>[5,4,3,2,1,6,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,1,5,6,7]=>[4,8,2,3,1,5,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,1,5,7,8]=>[4,6,2,3,1,5,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,1,6,7,8]=>[4,5,2,3,1,6,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,1,6,7,8]=>[5,4,2,3,1,6,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,1,6,7,8]=>[5,3,2,4,1,6,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,1,2,3,4,5]=>[6,1,2,3,4,7,8,5]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,1,2,3,4,5]=>[6,1,2,3,4,8,7,5]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,1,2,3,4,5]=>[7,1,2,3,4,8,6,5]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,1,2,3,4,5]=>[8,1,2,3,4,7,6,5]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,1,2,3,4,5]=>[8,1,2,3,4,6,7,5]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,1,2,3,4,6]=>[5,1,2,3,7,4,8,6]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,1,2,3,4,6]=>[5,1,2,3,8,4,7,6]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,1,2,3,4,7]=>[5,1,2,3,6,8,4,7]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,1,2,3,4,8]=>[5,1,2,3,6,7,4,8]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,1,2,3,4,8]=>[5,1,2,3,7,6,4,8]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,1,2,3,4,7]=>[6,1,2,3,8,5,4,7]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,1,2,3,4,8]=>[6,1,2,3,7,5,4,8]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,1,2,3,4,8]=>[7,1,2,3,6,5,4,8]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,1,2,3,4,8]=>[7,1,2,3,5,6,4,8]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[8,7,4,1,2,3,5,6]=>[4,1,2,7,3,5,8,6]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,1,2,3,5,7]=>[4,1,2,6,3,8,5,7]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,1,2,3,5,8]=>[4,1,2,6,3,7,5,8]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,1,2,3,6,7]=>[4,1,2,5,8,3,6,7]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[7,5,4,1,2,3,6,8]=>[4,1,2,5,7,3,6,8]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,1,2,3,7,8]=>[4,1,2,5,6,3,7,8]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[5,6,4,1,2,3,7,8]=>[4,1,2,6,5,3,7,8]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,1,2,4,5,6]=>[3,1,8,2,4,5,7,6]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,1,2,4,5,8]=>[3,1,6,2,4,7,5,8]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,1,2,4,6,7]=>[3,1,5,2,8,4,6,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,1,2,4,6,8]=>[3,1,5,2,7,4,6,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[5,6,3,1,2,4,7,8]=>[3,1,6,2,5,4,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[8,4,3,1,2,5,6,7]=>[3,1,4,8,2,5,6,7]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,1,2,6,7,8]=>[3,1,4,5,2,6,7,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,1,2,5,6,7]=>[4,1,8,3,2,5,6,7]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[6,3,4,1,2,5,7,8]=>[4,1,6,3,2,5,7,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,1,2,6,7,8]=>[5,1,4,3,2,6,7,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,1,2,6,7,8]=>[5,1,3,4,2,6,7,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,1,3,4,5,6]=>[2,7,1,3,4,5,8,6]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,1,3,4,5,6]=>[2,8,1,3,4,5,7,6]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,1,3,4,6,7]=>[2,5,1,3,8,4,6,7]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,1,3,4,7,8]=>[2,5,1,3,6,4,7,8]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[5,6,2,1,3,4,7,8]=>[2,6,1,3,5,4,7,8]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,1,3,5,6,7]=>[2,4,1,8,3,5,6,7]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,1,3,5,7,8]=>[2,4,1,6,3,5,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,1,3,6,7,8]=>[2,4,1,5,3,6,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,1,3,6,7,8]=>[2,5,1,4,3,6,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,1,4,5,6,7]=>[2,3,8,1,4,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,1,4,5,6,8]=>[2,3,7,1,4,5,6,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[6,3,2,1,4,5,7,8]=>[2,3,6,1,4,5,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,1,4,6,7,8]=>[2,3,5,1,4,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,1,5,6,7,8]=>[2,4,3,1,5,6,7,8]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,1,4,5,6,7]=>[3,8,2,1,4,5,6,7]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,1,4,6,7,8]=>[3,5,2,1,4,6,7,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,1,5,6,7,8]=>[3,4,2,1,5,6,7,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,1,5,6,7,8]=>[4,3,2,1,5,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[8,7,1,2,3,4,5,6]=>[7,1,2,3,4,5,8,6]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,6]=>[8,1,2,3,4,5,7,6]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[8,6,1,2,3,4,5,7]=>[6,1,2,3,4,8,5,7]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[7,6,1,2,3,4,5,8]=>[6,1,2,3,4,7,5,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,7,1,2,3,4,5,8]=>[7,1,2,3,4,6,5,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[8,5,1,2,3,4,6,7]=>[5,1,2,3,8,4,6,7]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,5,1,2,3,4,7,8]=>[5,1,2,3,6,4,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[5,6,1,2,3,4,7,8]=>[6,1,2,3,5,4,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[8,4,1,2,3,5,6,7]=>[4,1,2,8,3,5,6,7]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[7,4,1,2,3,5,6,8]=>[4,1,2,7,3,5,6,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[5,4,1,2,3,6,7,8]=>[4,1,2,5,3,6,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[4,5,1,2,3,6,7,8]=>[5,1,2,4,3,6,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[8,3,1,2,4,5,6,7]=>[3,1,8,2,4,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[7,3,1,2,4,5,6,8]=>[3,1,7,2,4,5,6,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[4,3,1,2,5,6,7,8]=>[3,1,4,2,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[8,2,1,3,4,5,6,7]=>[2,8,1,3,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[7,2,1,3,4,5,6,8]=>[2,7,1,3,4,5,6,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[6,2,1,3,4,5,7,8]=>[2,6,1,3,4,5,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[5,2,1,3,4,6,7,8]=>[2,5,1,3,4,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[4,2,1,3,5,6,7,8]=>[2,4,1,3,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,6,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,2,3,4,5,7,8]=>[6,1,2,3,4,5,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,2,3,4,6,7,8]=>[5,1,2,3,4,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,2,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,8]=>[9,1,2,3,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1]=>[9,2,3,4,5,6,7,8,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[10,1,2,3,4,5,6,7,8,9]=>[10,1,2,3,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[9,2,1,3,4,5,6,7,8]=>[2,9,1,3,4,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,9,1]=>[9,3,2,4,5,6,7,8,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,1]=>[10,2,3,4,5,6,7,8,9,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[11,1,2,3,4,5,6,7,8,9,10]=>[11,1,2,3,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,1,3,4,5,6,7,8,9]=>[2,10,1,3,4,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[9,3,1,2,4,5,6,7,8]=>[3,1,9,2,4,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[3,4,2,5,6,7,8,9,1]=>[9,4,3,2,5,6,7,8,1]=>[[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,9,10,1]=>[10,3,2,4,5,6,7,8,9,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>[11,2,3,4,5,6,7,8,9,10,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]=>[12,1,2,3,4,5,6,7,8,9,10,11]=>[12,1,2,3,4,5,6,7,8,9,10,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]=>[11,2,1,3,4,5,6,7,8,9,10]=>[2,11,1,3,4,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[9,3,2,1,4,5,6,7,8]=>[2,3,9,1,4,5,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,5,6,7,8,9,1]=>[9,3,4,2,5,6,7,8,1]=>[[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[12,2,1,3,4,5,6,7,8,9,10,11]=>[2,12,1,3,4,5,6,7,8,9,10,11]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]=>[10,4,1,2,3,5,6,7,8,9]=>[4,1,2,10,3,5,6,7,8,9]=>[[.,.],[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[10,3,2,1,4,5,6,7,8,9]=>[2,3,10,1,4,5,6,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[9,6,1,2,3,4,5,7,8]=>[6,1,2,3,4,9,5,7,8]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,1,0]=>[9,4,3,1,2,5,6,7,8]=>[3,1,4,9,2,5,6,7,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[9,7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,9,6,8]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[9,4,3,2,1,5,6,7,8]=>[2,3,4,9,1,5,6,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[8,9,1,2,3,4,5,6,7]=>[9,1,2,3,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[8,2,3,4,5,6,7,9,1]=>[9,8,2,3,4,5,6,7,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,6,7,8,9,1]=>[9,3,4,5,2,6,7,8,1]=>[[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]],.]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,1,2]=>[9,1,3,4,5,6,7,8,2]=>[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[10,4,3,2,1,5,6,7,8,9]=>[2,3,4,10,1,5,6,7,8,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[9,8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,9,7]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,4,5,6,7,8,1]=>[8,9,2,3,4,5,6,7,1]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,2,1]=>[2,9,3,4,5,6,7,8,1]=>[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[9,10,1,2,3,4,5,6,7,8]=>[10,1,2,3,4,5,6,7,9,8]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[9,8,2,1,3,4,5,6,7]=>[2,8,1,3,4,5,6,9,7]=>[[.,[.,.]],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[9,2,3,4,5,6,7,8,10,1]=>[10,9,2,3,4,5,6,7,8,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[4,3,5,6,7,8,9,2,1]=>[2,9,4,3,5,6,7,8,1]=>[[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]],.]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,1,2]=>[10,1,3,4,5,6,7,8,9,2]=>[[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[10,9,1,2,3,4,5,6,7,8]=>[9,1,2,3,4,5,6,7,10,8]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,2,1]=>[2,10,3,4,5,6,7,8,9,1]=>[[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[]=>[]=>[]=>.
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,1,9]=>[2,3,4,5,6,7,8,1,9]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[7,8,6,5,4,3,2,1,9]=>[2,3,4,5,6,8,7,1,9]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,4,3,2,1,9]=>[2,3,4,8,5,6,7,1,9]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[8,7,6,4,5,3,2,1,9]=>[2,3,5,6,4,7,8,1,9]=>[[.,[.,[[.,[.,.]],[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[8,7,5,4,6,3,2,1,9]=>[2,3,6,5,7,4,8,1,9]=>[[.,[.,[[[.,.],[.,.]],[.,.]]]],[.,.]]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,2,1,9]=>[2,8,3,4,5,6,7,1,9]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[5,4,6,3,7,2,8,1,9]=>[8,7,6,5,4,3,2,1,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1,9]=>[8,2,3,4,5,6,7,1,9]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,1,2,9]=>[3,1,4,5,6,7,8,2,9]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[8,6,5,4,3,2,1,7,9]=>[2,3,4,5,6,8,1,7,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,2,1,8,9]=>[2,3,4,5,6,7,1,8,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[6,7,5,4,3,2,1,8,9]=>[2,3,4,5,7,6,1,8,9]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,[.,.]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8,9]=>[7,2,3,4,5,6,1,8,9]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[7,5,4,3,2,1,6,8,9]=>[2,3,4,5,7,1,6,8,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,1,7,8,9]=>[2,3,4,5,6,1,7,8,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,4,3,2,1,7,8,9]=>[2,3,4,6,5,1,7,8,9]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[4,3,5,2,6,1,7,8,9]=>[6,5,4,3,2,1,7,8,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,1,7,8,9]=>[6,2,3,4,5,1,7,8,9]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[8,6,4,2,1,3,5,7,9]=>[2,4,1,6,3,8,5,7,9]=>[[.,[.,.]],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0,0]=>[7,6,4,2,1,3,5,8,9]=>[2,4,1,6,3,7,5,8,9]=>[[.,[.,.]],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0,0]=>[6,4,3,2,1,5,7,8,9]=>[2,3,4,6,1,5,7,8,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,1,6,7,8,9]=>[2,3,4,5,1,6,7,8,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[4,5,3,2,1,6,7,8,9]=>[2,3,5,4,1,6,7,8,9]=>[[.,[.,[[.,.],.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[3,4,2,5,1,6,7,8,9]=>[5,4,3,2,1,6,7,8,9]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9]=>[5,2,3,4,1,6,7,8,9]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0]=>[5,4,2,1,3,6,7,8,9]=>[2,4,1,5,3,6,7,8,9]=>[[.,[.,.]],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[5,3,2,1,4,6,7,8,9]=>[2,3,5,1,4,6,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1,5,6,7,8,9]=>[2,3,4,1,5,6,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[3,4,2,1,5,6,7,8,9]=>[2,4,3,1,5,6,7,8,9]=>[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[4,2,3,1,5,6,7,8,9]=>[3,4,2,1,5,6,7,8,9]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,4,1,5,6,7,8,9]=>[4,3,2,1,5,6,7,8,9]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9]=>[4,2,3,1,5,6,7,8,9]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[8,7,1,2,3,4,5,6,9]=>[7,1,2,3,4,5,8,6,9]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[7,8,1,2,3,4,5,6,9]=>[8,1,2,3,4,5,7,6,9]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0,0]=>[5,4,1,2,3,6,7,8,9]=>[4,1,2,5,3,6,7,8,9]=>[[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[4,3,1,2,5,6,7,8,9]=>[3,1,4,2,5,6,7,8,9]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[8,2,1,3,4,5,6,7,9]=>[2,8,1,3,4,5,6,7,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[4,2,1,3,5,6,7,8,9]=>[2,4,1,3,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8,9]=>[2,3,1,4,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1,2,3,4,5,6,7,9]=>[8,1,2,3,4,5,6,7,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[7,1,2,3,4,5,6,8,9]=>[7,1,2,3,4,5,6,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[6,1,2,3,4,5,7,8,9]=>[6,1,2,3,4,5,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[5,1,2,3,4,6,7,8,9]=>[5,1,2,3,4,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8,9]=>[4,1,2,3,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9]=>[3,1,2,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,1]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,9,8,1]=>[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,7,9,6,5,4,3,2,1]=>[2,3,4,5,6,9,8,7,1]=>[[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[8,7,6,9,5,4,3,2,1]=>[2,3,4,5,9,7,8,6,1]=>[[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,9,4,3,2,1]=>[2,3,4,9,6,7,8,5,1]=>[[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]],.]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,9,3,2,1]=>[2,3,9,5,6,7,8,4,1]=>[[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,9,2,1]=>[2,9,4,5,6,7,8,3,1]=>[[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,9,1]=>[9,3,4,5,6,7,8,2,1]=>[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,10,1]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,10,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,10,9,1]=>[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[7,8,9,6,5,4,3,2,1]=>[2,3,4,5,6,9,7,8,1]=>[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[9,8,10,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,10,9,8,1]=>[[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[9,8,7,10,6,5,4,3,2,1]=>[2,3,4,5,6,10,8,9,7,1]=>[[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,10,5,4,3,2,1]=>[2,3,4,5,10,7,8,9,6,1]=>[[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]],.]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,10,4,3,2,1]=>[2,3,4,10,6,7,8,9,5,1]=>[[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]],.]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,10,3,2,1]=>[2,3,10,5,6,7,8,9,4,1]=>[[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]],.]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,10,2,1]=>[2,10,4,5,6,7,8,9,3,1]=>[[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,2,10,1]=>[10,3,4,5,6,7,8,9,2,1]=>[[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,2,1,10]=>[2,3,4,5,6,7,8,9,1,10]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,10,9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,10,11,1]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[10,11,9,8,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,8,9,11,10,1]=>[[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[8,9,10,7,6,5,4,3,2,1]=>[2,3,4,5,6,7,10,8,9,1]=>[[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[7,6,8,9,5,4,3,2,1]=>[2,3,4,5,9,7,6,8,1]=>[[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,5,4,3,2,1]=>[2,3,4,5,9,6,7,8,1]=>[[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,9,8,7,6,5,4,3,2,11,1]=>[11,3,4,5,6,7,8,9,10,2,1]=>[[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,9,8,7,6,5,4,3,2,1,11]=>[2,3,4,5,6,7,8,9,10,1,11]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,6,5,4,3,2,1]=>[2,3,4,5,6,10,7,8,9,1]=>[[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[6,5,7,8,9,4,3,2,1]=>[2,3,4,9,6,5,7,8,1]=>[[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]],.]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,4,3,2,1]=>[2,3,4,9,5,6,7,8,1]=>[[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,5,4,3,2,1]=>[2,3,4,5,10,6,7,8,9,1]=>[[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]],.]
[1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[5,4,6,7,8,9,3,2,1]=>[2,3,9,5,4,6,7,8,1]=>[[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,3,2,1]=>[2,3,9,4,5,6,7,8,1]=>[[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,10,4,3,2,1]=>[2,3,4,10,5,6,7,8,9,1]=>[[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[9,7,8,6,5,4,3,2,1]=>[2,3,4,5,6,8,9,7,1]=>[[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[8,9,6,7,5,4,3,2,1]=>[2,3,4,5,7,9,6,8,1]=>[[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]],.]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[7,8,9,5,6,4,3,2,1]=>[2,3,4,6,9,5,7,8,1]=>[[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,5,3,2,1]=>[2,3,5,6,4,7,8,9,1]=>[[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,4,5,3,2,1]=>[2,3,5,9,4,6,7,8,1]=>[[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,3,4,2,1]=>[2,4,9,3,5,6,7,8,1]=>[[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,2,3,1]=>[3,4,2,5,6,7,8,9,1]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,2,3,1]=>[3,9,2,4,5,6,7,8,1]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,2,3,4,1]=>[4,5,2,3,6,7,8,9,1]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,3,1,2]=>[3,1,4,5,6,7,8,9,2]=>[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,1,2,3]=>[4,1,2,5,6,7,8,9,3]=>[[.,.],[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,9,4]=>[[.,.],[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,1,2,3,4,5]=>[6,1,2,3,4,7,8,9,5]=>[[.,.],[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[9,8,7,1,2,3,4,5,6]=>[7,1,2,3,4,5,8,9,6]=>[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,8,9,1,2,3,4,5,6]=>[9,1,2,3,4,5,7,8,6]=>[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,7,8,9,10,3,2,1]=>[2,3,10,4,5,6,7,8,9,1]=>[[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[10,8,9,6,7,4,5,2,3,1]=>[3,5,2,7,4,9,6,10,8,1]=>[[[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,3,1,2]=>[3,1,4,5,6,7,8,9,10,2]=>[[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,1,2,3]=>[4,1,2,5,6,7,8,9,10,3]=>[[.,.],[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,1,2,3,4]=>[5,1,2,3,6,7,8,9,10,4]=>[[.,.],[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,1,2,3,4,5]=>[6,1,2,3,4,7,8,9,10,5]=>[[.,.],[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,1,2,3,4,5]=>[10,1,2,3,4,6,7,8,9,5]=>[[.,.],[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,1,2,3,4,5,6]=>[7,1,2,3,4,5,8,9,10,6]=>[[.,.],[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[10,9,8,1,2,3,4,5,6,7]=>[8,1,2,3,4,5,6,9,10,7]=>[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,9,3]=>[[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,9,4]=>[[.,[.,[.,.]]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,3,2,1,5]=>[2,3,4,6,1,7,8,9,5]=>[[.,[.,[.,[.,.]]]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,4,3,2,1,6]=>[2,3,4,5,7,1,8,9,6]=>[[.,[.,[.,[.,[.,.]]]]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[9,8,6,5,4,3,2,1,7]=>[2,3,4,5,6,8,1,9,7]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,9,1,8]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,2,1,3]=>[2,4,1,5,6,7,8,9,10,3]=>[[.,[.,.]],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,3,2,1,4]=>[2,3,5,1,6,7,8,9,10,4]=>[[.,[.,[.,.]]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,4,3,2,1,5]=>[2,3,4,6,1,7,8,9,10,5]=>[[.,[.,[.,[.,.]]]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,5,4,3,2,1,6]=>[2,3,4,5,7,1,8,9,10,6]=>[[.,[.,[.,[.,[.,.]]]]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[10,9,8,6,5,4,3,2,1,7]=>[2,3,4,5,6,8,1,9,10,7]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[10,9,7,6,5,4,3,2,1,8]=>[2,3,4,5,6,7,9,1,10,8]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,5,4,3,2,1,9]=>[2,3,4,5,6,7,8,10,1,9]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,10,9,8,7,6,5,4,3,1,2]=>[3,1,4,5,6,7,8,9,10,11,2]=>[[.,.],[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[8,9,7,6,5,4,3,2,1,10]=>[2,3,4,5,6,7,9,8,1,10]=>[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9,10]=>[3,1,2,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[3,4,2,1,5,6,7,8,9,10]=>[2,4,3,1,5,6,7,8,9,10]=>[[.,[[.,.],.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[4,3,1,2,5,6,7,8,9,10]=>[3,1,4,2,5,6,7,8,9,10]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9,10,11]=>[3,1,2,4,5,6,7,8,9,10,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[9,6,5,4,3,2,1,7,8]=>[2,3,4,5,6,9,1,7,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[9,8,5,4,3,2,1,6,7]=>[2,3,4,5,8,1,6,9,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,2,1,3,4]=>[2,5,1,3,6,7,8,9,4]=>[[.,[.,.]],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1,10]=>[9,2,3,4,5,6,7,8,1,10]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,1,2,3,4,5,6,7,8,10]=>[9,1,2,3,4,5,6,7,8,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[10,1,2,3,4,5,6,7,8,9,11]=>[10,1,2,3,4,5,6,7,8,9,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[9,8,6,1,2,3,4,5,7]=>[6,1,2,3,4,8,5,9,7]=>[[.,.],[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,9,5,4,3,2,1]=>[2,3,4,5,9,7,8,10,6,1]=>[[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]],.]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,1,2,8]=>[3,1,4,5,6,7,9,2,8]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[7,8,6,5,4,3,2,9,1]=>[9,3,4,5,6,8,7,2,1]=>[[[[.,.],[.,[.,[.,[[.,.],.]]]]],.],.]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[7,6,5,4,3,2,1,8,9,10]=>[2,3,4,5,6,7,1,8,9,10]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[8,7,9,1,2,3,4,5,6]=>[9,1,2,3,4,5,8,7,6]=>[[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[8,1,2,3,4,5,6,7,9,10]=>[8,1,2,3,4,5,6,7,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[7,1,2,3,4,5,6,8,9,10]=>[7,1,2,3,4,5,6,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[6,1,2,3,4,5,7,8,9,10]=>[6,1,2,3,4,5,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[5,1,2,3,4,6,7,8,9,10]=>[5,1,2,3,4,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8,9,10]=>[4,1,2,3,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[9,8,7,5,6,4,3,2,1,10]=>[2,3,4,6,7,5,8,9,1,10]=>[[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,6,5,4,3,2,1,9,10]=>[2,3,4,5,6,7,8,1,9,10]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[6,5,7,4,8,3,9,2,10,1]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,0,1,1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[7,6,8,4,3,5,9,2,10,1]=>[10,9,4,8,3,7,6,5,2,1]=>[[[[[[.,.],.],[.,.]],[[[.,.],.],.]],.],.]
[1,1,0,1,0,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[7,6,8,5,9,4,10,2,1,3]=>[2,10,1,9,8,7,6,5,4,3]=>[[.,[.,.]],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[10,8,6,4,2,1,3,5,7,9]=>[2,4,1,6,3,8,5,10,7,9]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>[12,11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,11,1,2]=>[11,1,3,4,5,6,7,8,9,10,2]=>[[.,.],[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[10,7,6,5,4,3,2,1,8,9]=>[2,3,4,5,6,7,10,1,8,9]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[9,5,4,3,2,1,6,7,8]=>[2,3,4,5,9,1,6,7,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[10,5,4,3,2,1,6,7,8,9]=>[2,3,4,5,10,1,6,7,8,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[10,6,5,4,3,2,1,7,8,9]=>[2,3,4,5,6,10,1,7,8,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[3,2,4,1,5,6,7,8,9,10]=>[4,3,2,1,5,6,7,8,9,10]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,4,3,2,1,7,8,9,10]=>[2,3,4,5,6,1,7,8,9,10]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[4,2,1,3,5,6,7,8,9,10]=>[2,4,1,3,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]=>[9,8,7,2,1,3,4,5,6]=>[2,7,1,3,4,5,8,9,6]=>[[.,[.,.]],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8,9,10]=>[2,3,1,4,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,5,4,3,9,2,1]=>[2,9,4,5,6,7,8,10,3,1]=>[[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]],.]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[5,4,3,2,1,6,7,8,9,10]=>[2,3,4,5,1,6,7,8,9,10]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[4,3,2,1,5,6,7,8,9,10]=>[2,3,4,1,5,6,7,8,9,10]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[10,2,3,4,5,6,7,8,9,11,1]=>[11,10,2,3,4,5,6,7,8,9,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[11,9,8,7,6,5,4,3,2,1,10]=>[2,3,4,5,6,7,8,9,11,1,10]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,2,8,1]=>[8,3,4,5,6,7,9,2,1]=>[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[8,9,1,2,3,4,5,6,7,10]=>[9,1,2,3,4,5,6,8,7,10]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,2,1,3,4]=>[2,5,1,3,6,7,8,9,10,4]=>[[.,[.,.]],[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]=>[11,10,1,2,3,4,5,6,7,8,9]=>[10,1,2,3,4,5,6,7,8,11,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0]=>[9,8,4,1,2,3,5,6,7]=>[4,1,2,8,3,5,6,9,7]=>[[.,.],[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,5,4,3,1,2,9]=>[3,1,4,5,6,7,8,10,2,9]=>[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,8,2,1]=>[2,8,4,5,6,7,9,3,1]=>[[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]],.]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0]=>[10,9,2,1,3,4,5,6,7,8]=>[2,9,1,3,4,5,6,7,10,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0,0,0]=>[5,4,2,1,3,6,7,8,9,10]=>[2,4,1,5,3,6,7,8,9,10]=>[[.,[.,.]],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,5,6,7,1,2,8]=>[7,1,9,3,4,5,6,2,8]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[8,9,7,6,5,4,3,2,10,1]=>[10,3,4,5,6,7,9,8,2,1]=>[[[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]],.],.]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[5,6,4,7,3,8,2,9,1]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[1,1,0,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[6,7,5,8,4,9,3,10,1,2]=>[10,1,9,8,7,6,5,4,3,2]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,4,6,3,7,2,8,1,9,10]=>[8,7,6,5,4,3,2,1,9,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,2,3,1,4]=>[3,9,2,1,5,6,7,8,4]=>[[[.,[.,.]],.],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[9,6,5,4,3,1,2,7,8]=>[3,1,4,5,6,9,2,7,8]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[9,7,5,3,1,2,4,6,8,10]=>[3,1,5,2,7,4,9,6,8,10]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9,10,11,12]=>[3,1,2,4,5,6,7,8,9,10,11,12]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[7,5,6,4,8,3,9,2,10,1]=>[10,9,8,6,7,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,1,0,0]=>[9,8,10,1,2,3,4,5,6,7]=>[10,1,2,3,4,5,6,9,8,7]=>[[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[3,4,2,5,1,6,7,8,9,10]=>[5,4,3,2,1,6,7,8,9,10]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[5,6,4,7,3,8,2,9,1,10]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,7,5,8,4,9,3,10,2,11,1,12]=>[11,10,9,8,7,6,5,4,3,2,1,12]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,5,4,2,1,3,9]=>[2,4,1,5,6,7,8,10,3,9]=>[[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[12,10,11,8,9,6,7,4,5,2,3,1]=>[3,5,2,7,4,9,6,11,8,12,10,1]=>[[[.,[.,.]],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[9,7,5,3,1,2,4,6,8]=>[3,1,5,2,7,4,9,6,8]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[9,8,6,4,2,1,3,5,7]=>[2,4,1,6,3,8,5,9,7]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[6,4,5,7,3,8,2,9,1]=>[9,8,7,6,4,5,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[6,4,5,7,3,8,2,9,1,10]=>[9,8,7,6,4,5,3,2,1,10]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[12,11,10,9,8,7,6,5,4,3,1,2]=>[3,1,4,5,6,7,8,9,10,11,12,2]=>[[.,.],[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[10,5,6,4,7,3,8,2,9,1]=>[9,8,7,6,10,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[12,10,9,8,7,6,5,4,3,2,1,11]=>[2,3,4,5,6,7,8,9,10,12,1,11]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],[.,.]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,1,0,0]=>[9,8,6,4,2,1,3,5,7,10]=>[2,4,1,6,3,8,5,9,7,10]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
Map
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.