Identifier
Mp00024:
Dyck paths
—to 321-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]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[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]=>[1,3,2]=>[1,3,2]=>[.,[[.,.],.]]
[1,1,1,0,0,0]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[1,0,1,0,1,0,1,0]=>[2,1,4,3]=>[2,1,4,3]=>[[.,.],[[.,.],.]]
[1,0,1,0,1,1,0,0]=>[2,4,1,3]=>[4,2,1,3]=>[[[.,.],.],[.,.]]
[1,0,1,1,0,0,1,0]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[1,0,1,1,0,1,0,0]=>[2,3,1,4]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[1,1,0,0,1,0,1,0]=>[3,1,4,2]=>[3,4,1,2]=>[[.,[.,.]],[.,.]]
[1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[1,1,0,1,0,0,1,0]=>[3,1,2,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[1,1,0,1,0,1,0,0]=>[1,3,2,4]=>[1,3,2,4]=>[.,[[.,.],[.,.]]]
[1,1,0,1,1,0,0,0]=>[1,3,4,2]=>[1,4,3,2]=>[.,[[[.,.],.],.]]
[1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[1,1,1,0,0,1,0,0]=>[1,4,2,3]=>[1,4,2,3]=>[.,[[.,.],[.,.]]]
[1,1,1,0,1,0,0,0]=>[1,2,4,3]=>[1,2,4,3]=>[.,[.,[[.,.],.]]]
[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]=>[2,1,4,3,5]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,5]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[1,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,3]=>[2,1,5,4,3]=>[[.,.],[[[.,.],.],.]]
[1,0,1,0,1,1,0,1,0,0]=>[2,4,1,5,3]=>[4,2,5,1,3]=>[[[.,.],[.,.]],[.,.]]
[1,0,1,0,1,1,1,0,0,0]=>[2,4,5,1,3]=>[5,2,1,4,3]=>[[[.,.],.],[[.,.],.]]
[1,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,4]=>[2,1,5,3,4]=>[[.,.],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,4]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]
[1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,4]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,4]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]
[1,0,1,1,0,1,1,0,0,0]=>[2,3,5,1,4]=>[5,2,3,1,4]=>[[[.,.],[.,.]],[.,.]]
[1,0,1,1,1,0,0,0,1,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,0]=>[2,3,1,4,5]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,5]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[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]=>[3,1,4,2,5]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,0,1,0]=>[3,1,4,5,2]=>[3,5,1,4,2]=>[[.,[.,.]],[[.,.],.]]
[1,1,0,0,1,1,0,1,0,0]=>[3,4,1,5,2]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]
[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]=>[3,1,5,2,4]=>[3,5,1,2,4]=>[[.,[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4]=>[5,1,3,2,4]=>[[.,.],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4]=>[3,1,2,5,4]=>[[.,.],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4]=>[1,5,3,2,4]=>[.,[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,0,0,1,0]=>[3,1,2,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,0]=>[1,3,2,4,5]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,0]=>[1,3,4,2,5]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
[1,1,0,1,1,1,0,0,0,0]=>[1,3,4,5,2]=>[1,5,3,4,2]=>[.,[[[.,.],[.,.]],.]]
[1,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3]=>[4,5,2,1,3]=>[[[.,[.,.]],.],[.,.]]
[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]=>[4,1,2,5,3]=>[4,1,5,2,3]=>[[.,.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,3]=>[1,4,5,2,3]=>[.,[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3]=>[1,5,2,4,3]=>[.,[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,0]=>[4,1,2,3,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,0]=>[1,4,2,3,5]=>[1,4,2,3,5]=>[.,[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,0]=>[1,2,4,5,3]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]]
[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]=>[1,5,2,3,4]=>[1,5,2,3,4]=>[.,[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0]=>[1,2,5,3,4]=>[1,2,5,3,4]=>[.,[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,0]=>[1,2,3,5,4]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]
[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]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[[.,.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5]=>[4,2,1,3,6,5]=>[[[.,.],.],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5]=>[2,1,6,4,3,5]=>[[.,.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5]=>[4,2,6,1,3,5]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5]=>[6,2,1,4,3,5]=>[[[.,.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,5,6]=>[4,2,1,3,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>[[.,.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,5,3,6]=>[4,2,5,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,5,1,3,6]=>[5,2,1,4,3,6]=>[[[.,.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>[[.,.],[[[.,.],[.,.]],.]]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,5,6,3]=>[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,5,1,6,3]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,5,6,1,3]=>[6,2,1,4,5,3]=>[[[.,.],.],[[.,[.,.]],.]]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,6,4]=>[2,1,5,6,3,4]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>[5,2,1,6,3,4]=>[[[.,.],.],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,5,6,3,4]=>[2,1,6,3,5,4]=>[[.,.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[2,5,1,6,3,4]=>[5,2,6,3,1,4]=>[[[.,.],[[.,.],.]],[.,.]]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,5,6,1,3,4]=>[6,2,1,3,5,4]=>[[[.,.],.],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,4,6]=>[2,1,5,3,4,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,4,6]=>[5,2,1,3,4,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>[[[.,.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,6]=>[5,2,3,1,4,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>[[.,.],[.,[[[.,.],.],.]]]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,5,1,6,4]=>[5,2,3,6,1,4]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,5,6,1,4]=>[6,2,3,1,5,4]=>[[[.,.],[.,.]],[[.,.],.]]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5]=>[2,1,6,3,4,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5]=>[6,2,1,3,4,5]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5]=>[2,1,3,6,4,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,5]=>[3,2,1,6,4,5]=>[[[.,.],.],[[.,.],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5]=>[6,2,3,1,4,5]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>[[[.,.],.],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>[[[.,.],[.,.]],[[.,.],.]]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,4,6,1,5]=>[6,2,3,4,1,5]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[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]=>[3,1,4,2,6,5]=>[3,4,1,2,6,5]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5]=>[4,1,3,2,6,5]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5]=>[3,6,1,4,2,5]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5]=>[4,6,3,1,2,5]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5]=>[6,1,3,4,2,5]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,5,6]=>[3,4,1,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,5,6]=>[4,1,3,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,5,2,6]=>[3,5,1,4,2,6]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[3,4,1,5,2,6]=>[4,5,3,1,2,6]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[3,4,5,1,2,6]=>[5,1,3,4,2,6]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,5,6,2]=>[3,6,1,4,5,2]=>[[.,[.,.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[3,4,1,5,6,2]=>[4,6,3,1,5,2]=>[[[.,[.,.]],.],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[3,4,5,1,6,2]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[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]=>[3,1,5,2,6,4]=>[3,5,1,6,2,4]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,6,4]=>[5,1,3,6,2,4]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,6,2,4]=>[3,6,1,2,5,4]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,6,2,4]=>[5,6,3,2,1,4]=>[[[[.,[.,.]],.],.],[.,.]]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,6,1,2,4]=>[6,1,3,2,5,4]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,6]=>[3,5,1,2,4,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,6]=>[5,1,3,2,4,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,6]=>[3,1,2,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,6]=>[1,5,3,2,4,6]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,6,4]=>[3,1,2,6,5,4]=>[[.,.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>[.,[[.,.],[[[.,.],.],.]]]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,6,4]=>[1,5,3,6,2,4]=>[.,[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,6,2,4]=>[1,6,3,2,5,4]=>[.,[[[.,.],.],[[.,.],.]]]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>[3,6,1,2,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,5]=>[6,1,3,2,4,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5]=>[3,1,2,6,4,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,5]=>[1,3,2,6,4,5]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,5]=>[1,6,3,2,4,5]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5]=>[3,1,2,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>[.,[[[.,.],.],[[.,.],.]]]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5]=>[1,6,3,4,2,5]=>[.,[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,4,5,6]=>[3,1,2,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>[.,[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>[.,[[[.,.],[.,[.,.]]],.]]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,5,2,6,3]=>[4,5,6,1,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[4,5,1,2,6,3]=>[5,1,6,4,2,3]=>[[.,.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[4,1,5,6,2,3]=>[4,6,2,1,5,3]=>[[[.,[.,.]],.],[[.,.],.]]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[4,5,1,6,2,3]=>[5,6,2,4,1,3]=>[[[.,[.,.]],[.,.]],[.,.]]
[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]=>[4,1,5,2,3,6]=>[4,5,2,1,3,6]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,6]=>[5,1,2,4,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,6]=>[4,1,5,2,3,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,6]=>[1,4,5,2,3,6]=>[.,[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,6]=>[1,5,2,4,3,6]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,5,6,3]=>[4,1,6,2,5,3]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,5,6,3]=>[1,4,6,2,5,3]=>[.,[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,5,2,6,3]=>[1,5,6,4,2,3]=>[.,[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,5,6,2,3]=>[1,6,2,4,5,3]=>[.,[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5]=>[4,6,2,1,3,5]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5]=>[6,1,2,4,3,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5]=>[4,1,6,2,3,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5]=>[1,4,6,2,3,5]=>[.,[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,5]=>[1,6,2,4,3,5]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5]=>[4,1,2,3,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5]=>[1,4,2,3,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[.,[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,4,6,3,5]=>[1,2,6,4,3,5]=>[.,[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,5,6]=>[4,1,2,3,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,5,6]=>[1,4,2,3,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>[.,[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>[.,[.,[[[.,.],[.,.]],.]]]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[5,1,6,2,3,4]=>[5,6,2,3,1,4]=>[[[.,[.,.]],[.,.]],[.,.]]
[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]=>[5,1,2,6,3,4]=>[5,1,6,3,2,4]=>[[.,.],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,6,3,4]=>[1,5,6,3,2,4]=>[.,[[[.,[.,.]],.],[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,6,2,3,4]=>[1,6,2,3,5,4]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,6,4]=>[5,1,2,6,3,4]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,6,4]=>[1,5,2,6,3,4]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,6,4]=>[1,2,5,6,3,4]=>[.,[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,5,6,3,4]=>[1,2,6,3,5,4]=>[.,[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,6]=>[5,1,2,3,4,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,6]=>[1,5,2,3,4,6]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,6]=>[1,2,5,3,4,6]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[.,[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>[.,[.,[.,[[[.,.],.],.]]]]
[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]=>[1,6,2,3,4,5]=>[1,6,2,3,4,5]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5]=>[1,2,6,3,4,5]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5]=>[1,2,3,6,4,5]=>[.,[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]]
[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]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5,7]=>[4,2,1,3,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5,7]=>[2,1,6,4,3,5,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5,7]=>[4,2,6,1,3,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5,7]=>[6,2,1,4,3,5,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,7,5]=>[4,2,1,3,7,6,5]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,6,3,7,5]=>[2,1,6,4,7,3,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5]=>[4,2,6,1,7,3,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,6,1,3,7,5]=>[6,2,1,4,7,3,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,6,7,3,5]=>[2,1,7,4,3,6,5]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,6,7,3,5]=>[4,2,7,1,3,6,5]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,6,1,7,3,5]=>[6,2,7,4,3,1,5]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,6,7,1,3,5]=>[7,2,1,4,3,6,5]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,7,5,6]=>[2,1,4,3,7,5,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,3,7,5,6]=>[4,2,1,3,7,5,6]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,7,3,5,6]=>[2,1,7,4,3,5,6]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,4,1,7,3,5,6]=>[4,2,7,1,3,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,7,1,3,5,6]=>[7,2,1,4,3,5,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,4,1,3,5,7,6]=>[4,2,1,3,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,7,6]=>[4,2,5,1,3,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,5,1,3,7,6]=>[5,2,1,4,3,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,5,7,3,6]=>[2,1,7,4,5,3,6]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,4,1,5,7,3,6]=>[4,2,7,1,5,3,6]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,4,5,1,7,3,6]=>[5,2,7,4,1,3,6]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,5,7,1,3,6]=>[7,2,1,4,5,3,6]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,5,6,7]=>[4,2,1,3,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,4,1,5,3,6,7]=>[4,2,5,1,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,4,5,1,3,6,7]=>[5,2,1,4,3,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,4,1,5,6,3,7]=>[4,2,6,1,5,3,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,4,5,1,6,3,7]=>[5,2,6,4,1,3,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,4,5,6,1,3,7]=>[6,2,1,4,5,3,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,5,6,7,3]=>[2,1,7,4,5,6,3]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1,5,6,7,3]=>[4,2,7,1,5,6,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,5,1,6,7,3]=>[5,2,7,4,1,6,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,5,6,1,7,3]=>[6,2,7,4,5,1,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,5,6,7,1,3]=>[7,2,1,4,5,6,3]=>[[[.,.],.],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,7]=>[2,1,5,6,3,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,5,1,3,6,4,7]=>[5,2,1,6,3,4,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,7]=>[2,1,6,3,5,4,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,5,1,6,3,4,7]=>[5,2,6,3,1,4,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,6,1,3,4,7]=>[6,2,1,3,5,4,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,6,7,4]=>[2,1,5,7,3,6,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,6,7,4]=>[5,2,1,7,3,6,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,5,6,3,7,4]=>[2,1,6,7,5,3,4]=>[[.,.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,5,1,6,3,7,4]=>[5,2,6,7,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,5,6,1,3,7,4]=>[6,2,1,7,5,3,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,6,7,3,4]=>[2,1,7,3,5,6,4]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,5,1,6,7,3,4]=>[5,2,7,3,1,6,4]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,5,6,1,7,3,4]=>[6,2,7,3,5,1,4]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,5,6,7,1,3,4]=>[7,2,1,3,5,6,4]=>[[[.,.],.],[.,[[.,[.,.]],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,6]=>[2,1,5,7,3,4,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,7,4,6]=>[5,2,1,7,3,4,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,5,7,3,4,6]=>[2,1,7,3,5,4,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,5,1,7,3,4,6]=>[5,2,7,3,1,4,6]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,5,7,1,3,4,6]=>[7,2,1,3,5,4,6]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,4,7,6]=>[2,1,5,3,4,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,4,7,6]=>[5,2,1,3,4,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,7,6]=>[5,2,3,1,4,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,3,5,7,4,6]=>[2,1,3,7,5,4,6]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,7,4,6]=>[3,2,1,7,5,4,6]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,1,7,4,6]=>[5,2,3,7,1,4,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,5,7,1,4,6]=>[7,2,3,1,5,4,6]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,7]=>[2,1,5,3,4,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,5,1,3,4,6,7]=>[5,2,1,3,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,1,4,6,7]=>[5,2,3,1,4,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,1,6,4,7]=>[5,2,3,6,1,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,6,1,4,7]=>[6,2,3,1,5,4,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1,5,6,7,4]=>[3,2,1,7,5,6,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,5,1,6,7,4]=>[5,2,3,7,1,6,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,5,6,1,7,4]=>[6,2,3,7,5,1,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,5,6,7,1,4]=>[7,2,3,1,5,6,4]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,6,3,7,4,5]=>[2,1,6,7,4,3,5]=>[[.,.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,6,1,3,7,4,5]=>[6,2,1,7,4,3,5]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,6,7,3,4,5]=>[2,1,7,3,4,6,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,6,1,7,3,4,5]=>[6,2,7,3,4,1,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,6,7,1,3,4,5]=>[7,2,1,3,4,6,5]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,6,3,4,7,5]=>[2,1,6,3,7,4,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,6,1,3,4,7,5]=>[6,2,1,3,7,4,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,3,6,4,7,5]=>[2,1,3,6,7,4,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,7,5]=>[3,2,1,6,7,4,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,6,1,4,7,5]=>[6,2,3,1,7,4,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,3,6,7,4,5]=>[2,1,3,7,4,6,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,1,6,7,4,5]=>[3,2,1,7,4,6,5]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,6,1,7,4,5]=>[6,2,3,7,4,1,5]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,6,7,1,4,5]=>[7,2,3,1,4,6,5]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5,7]=>[2,1,6,3,4,5,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5,7]=>[6,2,1,3,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5,7]=>[2,1,3,6,4,5,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,5,7]=>[3,2,1,6,4,5,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5,7]=>[6,2,3,1,4,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,4,6,1,5,7]=>[6,2,3,4,1,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,4,1,6,7,5]=>[4,2,3,1,7,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,4,6,1,7,5]=>[6,2,3,4,7,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,6,7,1,5]=>[7,2,3,4,1,6,5]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,7,3,4,5,6]=>[2,1,7,3,4,5,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,7,1,3,4,5,6]=>[7,2,1,3,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,7,4,5,6]=>[2,1,3,7,4,5,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,7,4,5,6]=>[3,2,1,7,4,5,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,7,1,4,5,6]=>[7,2,3,1,4,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,3,4,7,5,6]=>[2,1,3,4,7,5,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,4,7,5,6]=>[3,2,1,4,7,5,6]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,4,1,7,5,6]=>[4,2,3,1,7,5,6]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,6]=>[7,2,3,4,1,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,4,1,5,7,6]=>[4,2,3,1,5,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,4,5,1,7,6]=>[5,2,3,4,1,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,6]=>[7,2,3,4,5,1,6]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[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]=>[3,1,4,2,6,5,7]=>[3,4,1,2,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,7]=>[4,1,3,2,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5,7]=>[3,6,1,4,2,5,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5,7]=>[4,6,3,1,2,5,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5,7]=>[6,1,3,4,2,5,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,7,5]=>[3,4,1,2,7,6,5]=>[[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,6,7,5]=>[4,1,3,2,7,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,4,6,2,7,5]=>[3,6,1,4,7,2,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,4,1,6,2,7,5]=>[4,6,3,1,7,2,5]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,4,6,1,2,7,5]=>[6,1,3,4,7,2,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,7,2,5]=>[3,7,1,4,2,6,5]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,4,1,6,7,2,5]=>[4,7,3,1,2,6,5]=>[[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,4,6,1,7,2,5]=>[6,7,3,4,2,1,5]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,6,7,1,2,5]=>[7,1,3,4,2,6,5]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,6]=>[3,4,1,2,7,5,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,7,5,6]=>[4,1,3,2,7,5,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,4,7,2,5,6]=>[3,7,1,4,2,5,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,4,1,7,2,5,6]=>[4,7,3,1,2,5,6]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,4,7,1,2,5,6]=>[7,1,3,4,2,5,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,1,4,2,5,7,6]=>[3,4,1,2,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,4,1,2,5,7,6]=>[4,1,3,2,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,1,4,5,2,7,6]=>[3,5,1,4,2,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,4,1,5,2,7,6]=>[4,5,3,1,2,7,6]=>[[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,7,6]=>[5,1,3,4,2,7,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>[3,7,1,4,5,2,6]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,4,1,5,7,2,6]=>[4,7,3,1,5,2,6]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,4,5,1,7,2,6]=>[5,7,3,4,1,2,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,7,1,2,6]=>[7,1,3,4,5,2,6]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,5,6,7]=>[3,4,1,2,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,5,6,7]=>[4,1,3,2,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,4,5,2,6,7]=>[3,5,1,4,2,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,4,1,5,2,6,7]=>[4,5,3,1,2,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,4,5,1,2,6,7]=>[5,1,3,4,2,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,1,4,5,6,2,7]=>[3,6,1,4,5,2,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,4,1,5,6,2,7]=>[4,6,3,1,5,2,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,4,5,1,6,2,7]=>[5,6,3,4,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,5,6,1,2,7]=>[6,1,3,4,5,2,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,6,7,2]=>[3,7,1,4,5,6,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,4,1,5,6,7,2]=>[4,7,3,1,5,6,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,5,1,6,7,2]=>[5,7,3,4,1,6,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,5,6,1,7,2]=>[6,7,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[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]=>[3,1,5,2,6,4,7]=>[3,5,1,6,2,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,5,1,2,6,4,7]=>[5,1,3,6,2,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,5,6,2,4,7]=>[3,6,1,2,5,4,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,5,1,6,2,4,7]=>[5,6,3,2,1,4,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,5,6,1,2,4,7]=>[6,1,3,2,5,4,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,6,7,4]=>[3,5,1,7,2,6,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,5,1,2,6,7,4]=>[5,1,3,7,2,6,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,5,6,2,7,4]=>[3,6,1,7,5,2,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,5,1,6,2,7,4]=>[5,6,3,7,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,5,6,1,2,7,4]=>[6,1,3,7,5,2,4]=>[[.,.],[[.,[[.,.],.]],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,6,7,2,4]=>[3,7,1,2,5,6,4]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,5,1,6,7,2,4]=>[5,7,3,2,1,6,4]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,5,6,1,7,2,4]=>[6,7,3,2,5,1,4]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,5,6,7,1,2,4]=>[7,1,3,2,5,6,4]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,6]=>[3,5,1,7,2,4,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,7,4,6]=>[5,1,3,7,2,4,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,7,2,4,6]=>[3,7,1,2,5,4,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,7,2,4,6]=>[5,7,3,2,1,4,6]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,7,1,2,4,6]=>[7,1,3,2,5,4,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,7,6]=>[3,5,1,2,4,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,7,6]=>[5,1,3,2,4,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,7,6]=>[3,1,2,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,7,6]=>[1,5,3,2,4,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,7,4,6]=>[3,1,2,7,5,4,6]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,4,6]=>[1,3,2,7,5,4,6]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,7,4,6]=>[1,5,3,7,2,4,6]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,7,2,4,6]=>[1,7,3,2,5,4,6]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,4,6,7]=>[3,5,1,2,4,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,5,1,2,4,6,7]=>[5,1,3,2,4,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,5,4,6,7]=>[3,1,2,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,4,6,7]=>[1,5,3,2,4,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,5,6,4,7]=>[3,1,2,6,5,4,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,2,6,4,7]=>[1,5,3,6,2,4,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,6,2,4,7]=>[1,6,3,2,5,4,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,5,6,7,4]=>[3,1,2,7,5,6,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]=>[.,[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,5,2,6,7,4]=>[1,5,3,7,2,6,4]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,5,6,2,7,4]=>[1,6,3,7,5,2,4]=>[.,[[[.,.],[[.,.],.]],[.,.]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,5,6,7,2,4]=>[1,7,3,2,5,6,4]=>[.,[[[.,.],.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,6,2,7,4,5]=>[3,6,1,7,4,2,5]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,6,1,2,7,4,5]=>[6,1,3,7,4,2,5]=>[[.,.],[[.,[[.,.],.]],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,6,7,2,4,5]=>[3,7,1,2,4,6,5]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,6,1,7,2,4,5]=>[6,7,3,2,4,1,5]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,6,7,1,2,4,5]=>[7,1,3,2,4,6,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,6,2,4,7,5]=>[3,6,1,2,7,4,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,6,1,2,4,7,5]=>[6,1,3,2,7,4,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,2,6,4,7,5]=>[3,1,2,6,7,4,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,6,4,7,5]=>[1,3,2,6,7,4,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,6,2,4,7,5]=>[1,6,3,2,7,4,5]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,6,7,4,5]=>[3,1,2,7,4,6,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,6,7,4,5]=>[1,3,2,7,4,6,5]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,6,2,7,4,5]=>[1,6,3,7,4,2,5]=>[.,[[[.,.],[[.,.],.]],[.,.]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,6,7,2,4,5]=>[1,7,3,2,4,6,5]=>[.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5,7]=>[3,6,1,2,4,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,5,7]=>[6,1,3,2,4,5,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5,7]=>[3,1,2,6,4,5,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,5,7]=>[1,3,2,6,4,5,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,5,7]=>[1,6,3,2,4,5,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5,7]=>[3,1,2,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5,7]=>[1,6,3,4,2,5,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,7,5]=>[3,1,2,4,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>[.,[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]=>[.,[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,4,6,2,7,5]=>[1,6,3,4,7,2,5]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,4,6,7,2,5]=>[1,7,3,4,2,6,5]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,7,2,4,5,6]=>[3,7,1,2,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,7,1,2,4,5,6]=>[7,1,3,2,4,5,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,7,4,5,6]=>[3,1,2,7,4,5,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,7,4,5,6]=>[1,3,2,7,4,5,6]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,7,2,4,5,6]=>[1,7,3,2,4,5,6]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,6]=>[3,1,2,4,7,5,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,4,7,5,6]=>[1,3,2,4,7,5,6]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,4,2,7,5,6]=>[1,4,3,2,7,5,6]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,4,7,2,5,6]=>[1,7,3,4,2,5,6]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,4,5,7,6]=>[3,1,2,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,4,5,7,2,6]=>[1,7,3,4,5,2,6]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7]=>[3,1,2,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,4,5,6,7,2]=>[1,7,3,4,5,6,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,7]=>[4,5,6,1,2,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[4,5,1,2,6,3,7]=>[5,1,6,4,2,3,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,5,6,2,3,7]=>[4,6,2,1,5,3,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[4,5,1,6,2,3,7]=>[5,6,2,4,1,3,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,7]=>[6,1,2,4,5,3,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[4,1,5,2,6,7,3]=>[4,5,7,1,2,6,3]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,5,1,2,6,7,3]=>[5,1,7,4,2,6,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[4,1,5,6,2,7,3]=>[4,6,7,1,5,2,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,5,1,6,2,7,3]=>[5,6,7,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,5,6,1,2,7,3]=>[6,1,7,4,5,2,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,5,6,7,2,3]=>[4,7,2,1,5,6,3]=>[[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,5,1,6,7,2,3]=>[5,7,2,4,1,6,3]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,5,6,1,7,2,3]=>[6,7,2,4,5,1,3]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[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]=>[4,1,5,2,7,3,6]=>[4,5,7,1,2,3,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[4,5,1,2,7,3,6]=>[5,1,7,4,2,3,6]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,5,7,2,3,6]=>[4,7,2,1,5,3,6]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,5,1,7,2,3,6]=>[5,7,2,4,1,3,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,5,7,1,2,3,6]=>[7,1,2,4,5,3,6]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,7,6]=>[4,5,2,1,3,7,6]=>[[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,7,6]=>[5,1,2,4,3,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,7,6]=>[4,1,5,2,3,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,7,6]=>[1,4,5,2,3,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,7,6]=>[1,5,2,4,3,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>[4,1,7,2,5,3,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,2,5,7,3,6]=>[1,4,7,2,5,3,6]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,2,7,3,6]=>[1,5,7,4,2,3,6]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,7,2,3,6]=>[1,7,2,4,5,3,6]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,6,7]=>[4,5,2,1,3,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3,6,7]=>[5,1,2,4,3,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3,6,7]=>[4,1,5,2,3,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3,6,7]=>[1,5,2,4,3,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[4,1,2,5,6,3,7]=>[4,1,6,2,5,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,2,5,6,3,7]=>[1,4,6,2,5,3,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,5,2,6,3,7]=>[1,5,6,4,2,3,7]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,5,6,2,3,7]=>[1,6,2,4,5,3,7]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,7,3]=>[4,1,7,2,5,6,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,5,6,7,3]=>[1,4,7,2,5,6,3]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,5,2,6,7,3]=>[1,5,7,4,2,6,3]=>[.,[[[.,[.,.]],.],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,5,6,2,7,3]=>[1,6,7,4,5,2,3]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,5,6,7,2,3]=>[1,7,2,4,5,6,3]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,5]=>[4,6,7,1,3,2,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,6,1,2,7,3,5]=>[6,1,7,4,3,2,5]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,6,7,2,3,5]=>[4,7,2,1,3,6,5]=>[[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,6,1,7,2,3,5]=>[6,7,2,4,3,1,5]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,6,7,1,2,3,5]=>[7,1,2,4,3,6,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,6,2,3,7,5]=>[4,6,2,1,7,3,5]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,6,1,2,3,7,5]=>[6,1,2,4,7,3,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,6,3,7,5]=>[4,1,6,2,7,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,7,5]=>[1,4,6,2,7,3,5]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,6,2,3,7,5]=>[1,6,2,4,7,3,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,6,7,3,5]=>[4,1,7,2,3,6,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,7,3,5]=>[1,4,7,2,3,6,5]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,4,6,2,7,3,5]=>[1,6,7,4,3,2,5]=>[.,[[[[.,[.,.]],.],.],[.,.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,4,6,7,2,3,5]=>[1,7,2,4,3,6,5]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5,7]=>[4,6,2,1,3,5,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5,7]=>[6,1,2,4,3,5,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5,7]=>[4,1,6,2,3,5,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5,7]=>[1,4,6,2,3,5,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,5,7]=>[1,6,2,4,3,5,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,7]=>[4,1,2,3,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,7]=>[1,4,2,3,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,2,4,6,3,5,7]=>[1,2,6,4,3,5,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,7,5]=>[4,1,2,3,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,6,7,5]=>[1,4,2,3,7,6,5]=>[.,[[.,.],[.,[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>[.,[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,2,4,6,3,7,5]=>[1,2,6,4,7,3,5]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,6,7,3,5]=>[1,2,7,4,3,6,5]=>[.,[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,1,7,2,3,5,6]=>[4,7,2,1,3,5,6]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,7,1,2,3,5,6]=>[7,1,2,4,3,5,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,7,3,5,6]=>[4,1,7,2,3,5,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,7,3,5,6]=>[1,4,7,2,3,5,6]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,4,7,2,3,5,6]=>[1,7,2,4,3,5,6]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,2,3,7,5,6]=>[4,1,2,3,7,5,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,4,2,3,7,5,6]=>[1,4,2,3,7,5,6]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,2,4,3,7,5,6]=>[1,2,4,3,7,5,6]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,2,4,7,3,5,6]=>[1,2,7,4,3,5,6]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,1,2,3,5,7,6]=>[4,1,2,3,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,4,2,3,5,7,6]=>[1,4,2,3,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>[.,[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,2,4,5,7,3,6]=>[1,2,7,4,5,3,6]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,7]=>[4,1,2,3,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,7]=>[1,4,2,3,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,4]=>[5,6,7,3,1,2,4]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,6,1,2,7,3,4]=>[6,1,7,3,5,2,4]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[5,1,6,7,2,3,4]=>[5,7,2,3,1,6,4]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[5,6,1,7,2,3,4]=>[6,7,2,3,5,1,4]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[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]=>[5,1,6,2,3,7,4]=>[5,6,2,7,1,3,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,6,1,2,3,7,4]=>[6,1,2,7,5,3,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[5,1,2,6,3,7,4]=>[5,1,6,7,2,3,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,6,2,3,7,4]=>[1,6,2,7,5,3,4]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[5,1,2,6,7,3,4]=>[5,1,7,3,2,6,4]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,5,2,6,7,3,4]=>[1,5,7,3,2,6,4]=>[.,[[[.,[.,.]],.],[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,5,6,2,7,3,4]=>[1,6,7,3,5,2,4]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,5,6,7,2,3,4]=>[1,7,2,3,5,6,4]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[5,1,6,2,3,4,7]=>[5,6,2,3,1,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,6,1,2,3,4,7]=>[6,1,2,3,5,4,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,2,6,3,4,7]=>[5,1,6,3,2,4,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,3,4,7]=>[1,5,6,3,2,4,7]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,6,2,3,4,7]=>[1,6,2,3,5,4,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[5,1,2,3,6,4,7]=>[5,1,2,6,3,4,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,2,3,6,4,7]=>[1,5,2,6,3,4,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,2,5,6,3,4,7]=>[1,2,6,3,5,4,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[5,1,2,3,6,7,4]=>[5,1,2,7,3,6,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,6,7,4]=>[1,5,2,7,3,6,4]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,2,5,3,6,7,4]=>[1,2,5,7,3,6,4]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,2,5,6,3,7,4]=>[1,2,6,7,5,3,4]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,2,5,6,7,3,4]=>[1,2,7,3,5,6,4]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,1,7,2,3,4,6]=>[5,7,2,3,1,4,6]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,7,1,2,3,4,6]=>[7,1,2,3,5,4,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,6]=>[5,1,7,3,2,4,6]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,5,2,7,3,4,6]=>[1,5,7,3,2,4,6]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,5,7,2,3,4,6]=>[1,7,2,3,5,4,6]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,7,4,6]=>[5,1,2,7,3,4,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,7,4,6]=>[1,5,2,7,3,4,6]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,7,4,6]=>[1,2,5,7,3,4,6]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6]=>[1,2,7,3,5,4,6]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,7,6]=>[5,1,2,3,4,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,7,6]=>[1,5,2,3,4,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,7,6]=>[1,2,5,3,4,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,7,4,6]=>[1,2,3,7,5,4,6]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,7]=>[5,1,2,3,4,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,6,7]=>[1,5,2,3,4,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,5,3,4,6,7]=>[1,2,5,3,4,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,1,7,2,3,4,5]=>[6,7,2,3,4,1,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[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]=>[6,1,2,7,3,4,5]=>[6,1,7,3,4,2,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,6,2,7,3,4,5]=>[1,6,7,3,4,2,5]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,7,2,3,4,5]=>[1,7,2,3,4,6,5]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,1,2,3,7,4,5]=>[6,1,2,7,4,3,5]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,6,2,3,7,4,5]=>[1,6,2,7,4,3,5]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,6,3,7,4,5]=>[1,2,6,7,4,3,5]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,6,7,3,4,5]=>[1,2,7,3,4,6,5]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,1,2,3,4,7,5]=>[6,1,2,3,7,4,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,3,4,7,5]=>[1,6,2,3,7,4,5]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,6,3,4,7,5]=>[1,2,6,3,7,4,5]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,2,3,6,7,4,5]=>[1,2,3,7,4,6,5]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7]=>[6,1,2,3,4,5,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5,7]=>[1,6,2,3,4,5,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5,7]=>[1,2,6,3,4,5,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5,7]=>[1,2,3,6,4,5,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]
[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]=>[1,7,2,3,4,5,6]=>[1,7,2,3,4,5,6]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,7,3,4,5,6]=>[1,2,7,3,4,5,6]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,3,7,4,5,6]=>[1,2,3,7,4,5,6]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,6]=>[1,2,3,4,7,5,6]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]
[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]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5,8,7]=>[4,2,1,3,6,5,8,7]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5,8,7]=>[2,1,6,4,3,5,8,7]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5,8,7]=>[6,2,1,4,3,5,8,7]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,8,5,7]=>[2,1,4,3,8,6,5,7]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,8,5,7]=>[4,2,1,3,8,6,5,7]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,6,3,8,5,7]=>[4,2,6,1,8,3,5,7]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,6,8,3,5,7]=>[2,1,8,4,3,6,5,7]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,6,8,3,5,7]=>[4,2,8,1,3,6,5,7]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,6,1,8,3,5,7]=>[6,2,8,4,3,1,5,7]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,6,8,1,3,5,7]=>[8,2,1,4,3,6,5,7]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,3,6,5,7,8]=>[4,2,1,3,6,5,7,8]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,6,3,5,7,8]=>[2,1,6,4,3,5,7,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,4,1,6,3,5,7,8]=>[4,2,6,1,3,5,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,6,1,3,5,7,8]=>[6,2,1,4,3,5,7,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5,8]=>[4,2,6,1,7,3,5,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,6,7,1,3,5,8]=>[7,2,1,4,3,6,5,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,6,7,5]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,6,3,7,8,5]=>[2,1,6,4,8,3,7,5]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,4,1,6,3,7,8,5]=>[4,2,6,1,8,3,7,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,4,6,7,3,8,5]=>[2,1,7,4,8,6,3,5]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,4,1,6,7,3,8,5]=>[4,2,7,1,8,6,3,5]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,4,6,1,7,3,8,5]=>[6,2,7,4,8,1,3,5]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,6,1,7,8,3,5]=>[6,2,8,4,3,1,7,5]=>[[[.,.],[[[.,.],.],.]],[[.,.],.]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,6,7,1,8,3,5]=>[7,2,8,4,3,6,1,5]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,7,5,8,6]=>[2,1,4,3,7,8,5,6]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,7,5,8,6]=>[4,2,1,3,7,8,5,6]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,4,7,3,5,8,6]=>[2,1,7,4,3,8,5,6]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,4,1,7,3,5,8,6]=>[4,2,7,1,3,8,5,6]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,7,8,5,6]=>[2,1,4,3,8,5,7,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,7,8,5,6]=>[4,2,1,3,8,5,7,6]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,7,3,8,5,6]=>[2,1,7,4,8,5,3,6]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,4,1,7,3,8,5,6]=>[4,2,7,1,8,5,3,6]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,7,8,3,5,6]=>[2,1,8,4,3,5,7,6]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,7,8,3,5,6]=>[4,2,8,1,3,5,7,6]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,4,7,1,8,3,5,6]=>[7,2,8,4,3,5,1,6]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,7,8,1,3,5,6]=>[8,2,1,4,3,5,7,6]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,4,7,1,3,5,6,8]=>[7,2,1,4,3,5,6,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,7,6,8]=>[4,2,5,1,3,7,6,8]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,4,5,1,7,3,6,8]=>[5,2,7,4,1,3,6,8]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,7,8,6]=>[2,1,4,3,5,8,7,6]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,5,7,8,6]=>[4,2,1,3,5,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,4,5,3,7,8,6]=>[2,1,5,4,3,8,7,6]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,1,5,3,7,8,6]=>[4,2,5,1,3,8,7,6]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,5,1,3,7,8,6]=>[5,2,1,4,3,8,7,6]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,4,5,7,3,8,6]=>[2,1,7,4,5,8,3,6]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,1,5,7,3,8,6]=>[4,2,7,1,5,8,3,6]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,1,7,3,8,6]=>[5,2,7,4,1,8,3,6]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,5,7,1,3,8,6]=>[7,2,1,4,5,8,3,6]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,4,5,7,8,3,6]=>[2,1,8,4,5,3,7,6]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,4,5,1,7,8,3,6]=>[5,2,8,4,1,3,7,6]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,4,5,7,1,8,3,6]=>[7,2,8,4,5,3,1,6]=>[[[.,.],[[[.,.],[.,.]],.]],[.,.]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,4,3,8,5,6,7]=>[2,1,4,3,8,5,6,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,1,3,8,5,6,7]=>[4,2,1,3,8,5,6,7]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,1,8,3,5,6,7]=>[4,2,8,1,3,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,4,3,5,8,6,7]=>[2,1,4,3,5,8,6,7]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,1,3,5,8,6,7]=>[4,2,1,3,5,8,6,7]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,8,6,7]=>[4,2,5,1,3,8,6,7]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,4,5,8,3,6,7]=>[2,1,8,4,5,3,6,7]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,5,8,3,6,7]=>[4,2,8,1,5,3,6,7]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,5,1,8,3,6,7]=>[5,2,8,4,1,3,6,7]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,4,5,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,1,5,3,6,8,7]=>[4,2,5,1,3,6,8,7]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,4,5,6,3,8,7]=>[2,1,6,4,5,3,8,7]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,1,5,6,3,8,7]=>[4,2,6,1,5,3,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,1,6,3,8,7]=>[5,2,6,4,1,3,8,7]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,1,5,6,8,3,7]=>[4,2,8,1,5,6,3,7]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,5,1,6,8,3,7]=>[5,2,8,4,1,6,3,7]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,5,6,1,8,3,7]=>[6,2,8,4,5,1,3,7]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,1,3,5,6,7,8]=>[4,2,1,3,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,4,5,3,6,7,8]=>[2,1,5,4,3,6,7,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,4,1,5,3,6,7,8]=>[4,2,5,1,3,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,4,5,1,3,6,7,8]=>[5,2,1,4,3,6,7,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,4,1,5,6,3,7,8]=>[4,2,6,1,5,3,7,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,4,5,1,6,3,7,8]=>[5,2,6,4,1,3,7,8]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,5,6,1,3,7,8]=>[6,2,1,4,5,3,7,8]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,4,1,5,6,7,3,8]=>[4,2,7,1,5,6,3,8]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,4,5,1,6,7,3,8]=>[5,2,7,4,1,6,3,8]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,4,5,6,1,7,3,8]=>[6,2,7,4,5,1,3,8]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,5,6,7,1,3,8]=>[7,2,1,4,5,6,3,8]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,4,5,6,7,8,3]=>[2,1,8,4,5,6,7,3]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1,5,6,7,8,3]=>[4,2,8,1,5,6,7,3]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,5,1,6,7,8,3]=>[5,2,8,4,1,6,7,3]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,5,6,1,7,8,3]=>[6,2,8,4,5,1,7,3]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,5,6,7,1,8,3]=>[7,2,8,4,5,6,1,3]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,4,5,6,7,8,1,3]=>[8,2,1,4,5,6,7,3]=>[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,8,7]=>[2,1,5,6,3,4,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,5,1,3,6,4,8,7]=>[5,2,1,6,3,4,8,7]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,8,7]=>[2,1,6,3,5,4,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,6,8,4,7]=>[2,1,5,8,3,6,4,7]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,6,8,4,7]=>[5,2,1,8,3,6,4,7]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,5,1,6,3,8,4,7]=>[5,2,6,8,1,3,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,5,6,1,8,3,4,7]=>[6,2,8,3,5,1,4,7]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,5,1,6,3,7,4,8]=>[5,2,6,7,1,3,4,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,5,1,6,7,3,4,8]=>[5,2,7,3,1,6,4,8]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,5,6,1,7,3,4,8]=>[6,2,7,3,5,1,4,8]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,3,6,7,8,4]=>[2,1,5,8,3,6,7,4]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,5,1,3,6,7,8,4]=>[5,2,1,8,3,6,7,4]=>[[[.,.],.],[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,6,3,7,8,4]=>[2,1,6,8,5,3,7,4]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,5,1,6,3,7,8,4]=>[5,2,6,8,1,3,7,4]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,5,6,1,3,7,8,4]=>[6,2,1,8,5,3,7,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,7,3,8,4]=>[2,1,7,8,5,6,3,4]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,5,1,6,7,3,8,4]=>[5,2,7,8,1,6,3,4]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,5,6,1,7,3,8,4]=>[6,2,7,8,5,1,3,4]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,5,6,7,8,3,4]=>[2,1,8,3,5,6,7,4]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,5,1,6,7,8,3,4]=>[5,2,8,3,1,6,7,4]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,5,6,1,7,8,3,4]=>[6,2,8,3,5,1,7,4]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,5,6,7,1,8,3,4]=>[7,2,8,3,5,6,1,4]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5,6,7,8,1,3,4]=>[8,2,1,3,5,6,7,4]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,8,6]=>[2,1,5,7,3,8,4,6]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,5,1,3,7,4,8,6]=>[5,2,1,7,3,8,4,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,5,7,3,4,8,6]=>[2,1,7,3,5,8,4,6]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,5,1,7,3,4,8,6]=>[5,2,7,3,1,8,4,6]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,7,1,3,4,8,6]=>[7,2,1,3,5,8,4,6]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,7,8,4,6]=>[5,2,1,8,3,4,7,6]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,5,7,3,8,4,6]=>[2,1,7,8,5,4,3,6]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,5,1,7,3,8,4,6]=>[5,2,7,8,1,4,3,6]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,7,8,3,4,6]=>[2,1,8,3,5,4,7,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,6,8]=>[2,1,5,7,3,4,6,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,7,4,6,8]=>[5,2,1,7,3,4,6,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,7,4,6,8]=>[3,2,1,7,5,4,6,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,5,1,3,4,7,8,6]=>[5,2,1,3,4,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,3,5,4,7,8,6]=>[2,1,3,5,4,8,7,6]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,3,5,7,4,8,6]=>[2,1,3,7,5,8,4,6]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,1,7,4,8,6]=>[5,2,3,7,1,8,4,6]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,5,7,8,4,6]=>[2,1,3,8,5,4,7,6]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1,5,7,8,4,6]=>[3,2,1,8,5,4,7,6]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,5,7,1,8,4,6]=>[7,2,3,8,5,4,1,6]=>[[[.,.],[.,[[[.,.],.],.]]],[.,.]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,5,7,8,1,4,6]=>[8,2,3,1,5,4,7,6]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,5,3,8,4,6,7]=>[2,1,5,8,3,4,6,7]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,5,1,3,8,4,6,7]=>[5,2,1,8,3,4,6,7]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,8,6,7]=>[5,2,3,1,4,8,6,7]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,3,5,8,4,6,7]=>[2,1,3,8,5,4,6,7]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,1,5,8,4,6,7]=>[3,2,1,8,5,4,6,7]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,5,1,8,4,6,7]=>[5,2,3,8,1,4,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,8,7]=>[2,1,5,3,4,6,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,3,5,6,4,8,7]=>[2,1,3,6,5,4,8,7]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,1,6,4,8,7]=>[5,2,3,6,1,4,8,7]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,5,6,1,4,8,7]=>[6,2,3,1,5,4,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,1,5,6,8,4,7]=>[3,2,1,8,5,6,4,7]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,5,6,8,1,4,7]=>[8,2,3,1,5,6,4,7]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,7,8]=>[2,1,5,3,4,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,1,3,4,6,7,8]=>[5,2,1,3,4,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,5,1,4,6,7,8]=>[5,2,3,1,4,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,5,6,4,7,8]=>[3,2,1,6,5,4,7,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,5,6,1,4,7,8]=>[6,2,3,1,5,4,7,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,5,6,7,4,8]=>[3,2,1,7,5,6,4,8]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,5,1,6,7,4,8]=>[5,2,3,7,1,6,4,8]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,5,6,1,7,4,8]=>[6,2,3,7,5,1,4,8]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,5,6,7,1,4,8]=>[7,2,3,1,5,6,4,8]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,5,6,7,8,4]=>[2,1,3,8,5,6,7,4]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,5,6,7,8,4]=>[3,2,1,8,5,6,7,4]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,5,1,6,7,8,4]=>[5,2,3,8,1,6,7,4]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,5,6,1,7,8,4]=>[6,2,3,8,5,1,7,4]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,5,6,7,1,8,4]=>[7,2,3,8,5,6,1,4]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,5,6,7,8,1,4]=>[8,2,3,1,5,6,7,4]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,6,3,7,4,8,5]=>[2,1,6,7,8,3,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,1,6,7,3,4,8,5]=>[2,1,7,3,8,6,4,5]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[2,6,1,7,3,4,8,5]=>[6,2,7,3,8,1,4,5]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,6,7,1,3,4,8,5]=>[7,2,1,3,8,6,4,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,6,1,3,7,8,4,5]=>[6,2,1,8,4,3,7,5]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[2,1,6,7,3,8,4,5]=>[2,1,7,8,4,6,3,5]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,6,1,7,3,8,4,5]=>[6,2,7,8,4,1,3,5]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,6,7,8,3,4,5]=>[2,1,8,3,4,6,7,5]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,7,5,8]=>[3,2,1,6,7,4,5,8]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,3,1,6,7,4,5,8]=>[3,2,1,7,4,6,5,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,7,1,4,5,8]=>[7,2,3,1,4,6,5,8]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,7,8,5]=>[2,1,6,3,8,4,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,7,8,5]=>[3,2,1,6,8,4,7,5]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,7,8,5]=>[6,2,3,1,8,4,7,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[2,1,3,6,7,4,8,5]=>[2,1,3,7,8,6,4,5]=>[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,3,1,6,7,4,8,5]=>[3,2,1,7,8,6,4,5]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,3,6,1,7,4,8,5]=>[6,2,3,7,8,1,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[2,3,6,7,1,4,8,5]=>[7,2,3,1,8,6,4,5]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,6,7,8,4,5]=>[2,1,3,8,4,6,7,5]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,3,1,6,7,8,4,5]=>[3,2,1,8,4,6,7,5]=>[[[.,.],.],[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,1,7,8,4,5]=>[6,2,3,8,4,1,7,5]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,1,8,4,5]=>[7,2,3,8,4,6,1,5]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,1,6,3,8,4,5,7]=>[2,1,6,8,4,3,5,7]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,6,1,8,3,4,5,7]=>[6,2,8,3,4,1,5,7]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,6,8,1,3,4,5,7]=>[8,2,1,3,4,6,5,7]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[2,1,6,3,4,8,5,7]=>[2,1,6,3,8,4,5,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[2,6,1,3,4,8,5,7]=>[6,2,1,3,8,4,5,7]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,8,5,7]=>[3,2,1,6,8,4,5,7]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[2,3,1,6,8,4,5,7]=>[3,2,1,8,4,6,5,7]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[2,3,6,1,8,4,5,7]=>[6,2,3,8,4,1,5,7]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[2,3,6,8,1,4,5,7]=>[8,2,3,1,4,6,5,7]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5,8,7]=>[2,1,6,3,4,5,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5,8,7]=>[2,1,3,6,4,5,8,7]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5,8,7]=>[6,2,3,1,4,5,8,7]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,8,5,7]=>[2,1,3,4,8,6,5,7]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,3,4,6,1,8,5,7]=>[6,2,3,4,8,1,5,7]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,6,4,5,7,8]=>[2,1,3,6,4,5,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,6,4,5,7,8]=>[3,2,1,6,4,5,7,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,3,6,1,4,5,7,8]=>[6,2,3,1,4,5,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,7,8]=>[4,2,3,1,6,5,7,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,3,4,1,6,7,5,8]=>[4,2,3,1,7,6,5,8]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,3,4,6,7,1,5,8]=>[7,2,3,4,1,6,5,8]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,6,7,8,5]=>[2,1,3,4,8,6,7,5]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,6,7,8,5]=>[3,2,1,4,8,6,7,5]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[2,3,4,6,1,7,8,5]=>[6,2,3,4,8,1,7,5]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,3,4,6,7,1,8,5]=>[7,2,3,4,8,6,1,5]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,6,7,8,1,5]=>[8,2,3,4,1,6,7,5]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[2,7,1,3,8,4,5,6]=>[7,2,1,8,4,5,3,6]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,7,1,8,3,4,5,6]=>[7,2,8,3,4,5,1,6]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,7,8,1,3,4,5,6]=>[8,2,1,3,4,5,7,6]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[2,1,7,3,4,8,5,6]=>[2,1,7,3,8,5,4,6]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[2,7,1,3,4,8,5,6]=>[7,2,1,3,8,5,4,6]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,3,1,7,4,8,5,6]=>[3,2,1,7,8,5,4,6]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,1,3,7,8,4,5,6]=>[2,1,3,8,4,5,7,6]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,3,1,7,8,4,5,6]=>[3,2,1,8,4,5,7,6]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,3,7,8,1,4,5,6]=>[8,2,3,1,4,5,7,6]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,1,7,3,4,5,8,6]=>[2,1,7,3,4,8,5,6]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[2,7,1,3,4,5,8,6]=>[7,2,1,3,4,8,5,6]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,1,3,7,4,5,8,6]=>[2,1,3,7,4,8,5,6]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,3,1,7,4,5,8,6]=>[3,2,1,7,4,8,5,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,1,3,4,7,5,8,6]=>[2,1,3,4,7,8,5,6]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,7,5,8,6]=>[4,2,3,1,7,8,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,8,6]=>[7,2,3,4,1,8,5,6]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,1,3,4,7,8,5,6]=>[2,1,3,4,8,5,7,6]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,3,1,4,7,8,5,6]=>[3,2,1,4,8,5,7,6]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,3,4,1,7,8,5,6]=>[4,2,3,1,8,5,7,6]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,3,4,7,1,8,5,6]=>[7,2,3,4,8,5,1,6]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[2,3,4,7,8,1,5,6]=>[8,2,3,4,1,5,7,6]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[2,1,7,3,4,5,6,8]=>[2,1,7,3,4,5,6,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[2,7,1,3,4,5,6,8]=>[7,2,1,3,4,5,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,3,1,7,4,5,6,8]=>[3,2,1,7,4,5,6,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[2,3,7,1,4,5,6,8]=>[7,2,3,1,4,5,6,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[2,1,3,4,7,5,6,8]=>[2,1,3,4,7,5,6,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,6,8]=>[7,2,3,4,1,5,6,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,3,4,1,5,7,6,8]=>[4,2,3,1,5,7,6,8]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,6,8]=>[7,2,3,4,5,1,6,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,7,8,6]=>[2,1,3,4,5,8,7,6]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,3,4,1,5,7,8,6]=>[4,2,3,1,5,8,7,6]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,3,4,5,1,7,8,6]=>[5,2,3,4,1,8,7,6]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,3,4,5,7,1,8,6]=>[7,2,3,4,5,8,1,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,7,8,1,6]=>[8,2,3,4,5,1,7,6]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,1,8,3,4,5,6,7]=>[2,1,8,3,4,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,8,1,3,4,5,6,7]=>[8,2,1,3,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,1,3,8,4,5,6,7]=>[2,1,3,8,4,5,6,7]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,3,1,8,4,5,6,7]=>[3,2,1,8,4,5,6,7]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,3,8,1,4,5,6,7]=>[8,2,3,1,4,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[2,1,3,4,8,5,6,7]=>[2,1,3,4,8,5,6,7]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,3,1,4,8,5,6,7]=>[3,2,1,4,8,5,6,7]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,3,4,1,8,5,6,7]=>[4,2,3,1,8,5,6,7]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,3,4,8,1,5,6,7]=>[8,2,3,4,1,5,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[2,1,3,4,5,8,6,7]=>[2,1,3,4,5,8,6,7]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,3,4,1,5,8,6,7]=>[4,2,3,1,5,8,6,7]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,3,4,5,1,8,6,7]=>[5,2,3,4,1,8,6,7]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,3,4,5,8,1,6,7]=>[8,2,3,4,5,1,6,7]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,8,7]=>[3,2,1,4,5,6,8,7]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,8,7]=>[5,2,3,4,1,6,8,7]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,8,7]=>[6,2,3,4,5,1,8,7]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,8,1,7]=>[8,2,3,4,5,6,1,7]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,3,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,7,8]=>[6,2,3,4,5,1,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8]=>[7,2,3,4,5,6,1,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[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]=>[3,1,4,2,6,5,8,7]=>[3,4,1,2,6,5,8,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,8,7]=>[4,1,3,2,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5,8,7]=>[3,6,1,4,2,5,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5,8,7]=>[6,1,3,4,2,5,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,8,5,7]=>[3,4,1,2,8,6,5,7]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,6,8,5,7]=>[4,1,3,2,8,6,5,7]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,8,2,5,7]=>[3,8,1,4,2,6,5,7]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[3,4,1,6,8,2,5,7]=>[4,8,3,1,2,6,5,7]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,6,8,1,2,5,7]=>[8,1,3,4,2,6,5,7]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,7,8]=>[3,4,1,2,6,5,7,8]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[3,4,1,6,2,5,7,8]=>[4,6,3,1,2,5,7,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[3,4,6,1,2,5,7,8]=>[6,1,3,4,2,5,7,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[3,1,4,2,6,7,5,8]=>[3,4,1,2,7,6,5,8]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[3,1,4,6,2,7,5,8]=>[3,6,1,4,7,2,5,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[3,4,1,6,2,7,5,8]=>[4,6,3,1,7,2,5,8]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,4,6,7,2,5,8]=>[3,7,1,4,2,6,5,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[3,4,6,1,7,2,5,8]=>[6,7,3,4,2,1,5,8]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,6,7,8,5]=>[3,4,1,2,8,6,7,5]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,6,7,8,5]=>[4,1,3,2,8,6,7,5]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[3,4,1,6,2,7,8,5]=>[4,6,3,1,8,2,7,5]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[3,4,1,6,7,2,8,5]=>[4,7,3,1,8,6,2,5]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[3,4,6,1,7,2,8,5]=>[6,7,3,4,8,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[3,4,1,6,7,8,2,5]=>[4,8,3,1,2,6,7,5]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,6,1,7,8,2,5]=>[6,8,3,4,2,1,7,5]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,6,7,1,8,2,5]=>[7,8,3,4,2,6,1,5]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,6,7,8,1,2,5]=>[8,1,3,4,2,6,7,5]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,8,6]=>[3,4,1,2,7,8,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,7,5,8,6]=>[4,1,3,2,7,8,5,6]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,7,8,5,6]=>[3,4,1,2,8,5,7,6]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,7,8,5,6]=>[4,1,3,2,8,5,7,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[3,4,1,7,2,8,5,6]=>[4,7,3,1,8,5,2,6]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[3,4,7,1,8,2,5,6]=>[7,8,3,4,2,5,1,6]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,6,8]=>[3,4,1,2,7,5,6,8]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,4,2,5,7,6,8]=>[3,4,1,2,5,7,6,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,1,2,5,7,6,8]=>[4,1,3,2,5,7,6,8]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,4,5,2,7,6,8]=>[3,5,1,4,2,7,6,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,7,6,8]=>[5,1,3,4,2,7,6,8]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,4,5,7,2,6,8]=>[3,7,1,4,5,2,6,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,5,7,8,6]=>[3,4,1,2,5,8,7,6]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,4,5,2,7,8,6]=>[3,5,1,4,2,8,7,6]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[3,4,1,5,2,7,8,6]=>[4,5,3,1,2,8,7,6]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[3,4,1,5,7,8,2,6]=>[4,8,3,1,5,2,7,6]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[3,4,5,7,1,8,2,6]=>[7,8,3,4,5,2,1,6]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,4,2,8,5,6,7]=>[3,4,1,2,8,5,6,7]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[3,4,1,2,8,5,6,7]=>[4,1,3,2,8,5,6,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,4,2,5,8,6,7]=>[3,4,1,2,5,8,6,7]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[3,4,1,5,2,8,6,7]=>[4,5,3,1,2,8,6,7]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,8,6,7]=>[5,1,3,4,2,8,6,7]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[3,4,5,1,8,2,6,7]=>[5,8,3,4,1,2,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,8,1,2,6,7]=>[8,1,3,4,5,2,6,7]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,4,2,5,6,8,7]=>[3,4,1,2,5,6,8,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,1,5,2,6,8,7]=>[4,5,3,1,2,6,8,7]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,1,2,6,8,7]=>[5,1,3,4,2,6,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,4,5,6,2,8,7]=>[3,6,1,4,5,2,8,7]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,1,5,6,2,8,7]=>[4,6,3,1,5,2,8,7]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,1,6,2,8,7]=>[5,6,3,4,1,2,8,7]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[3,1,4,5,6,8,2,7]=>[3,8,1,4,5,6,2,7]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,4,2,5,6,7,8]=>[3,4,1,2,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[3,4,1,2,5,6,7,8]=>[4,1,3,2,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,4,5,2,6,7,8]=>[3,5,1,4,2,6,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[3,4,5,1,2,6,7,8]=>[5,1,3,4,2,6,7,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,4,5,6,2,7,8]=>[3,6,1,4,5,2,7,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,4,1,5,6,2,7,8]=>[4,6,3,1,5,2,7,8]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[3,4,5,1,6,2,7,8]=>[5,6,3,4,1,2,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,5,6,1,2,7,8]=>[6,1,3,4,5,2,7,8]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[3,1,4,5,6,7,2,8]=>[3,7,1,4,5,6,2,8]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[3,4,1,5,6,7,2,8]=>[4,7,3,1,5,6,2,8]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[3,4,5,1,6,7,2,8]=>[5,7,3,4,1,6,2,8]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,4,5,6,1,7,2,8]=>[6,7,3,4,5,1,2,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2,8]=>[7,1,3,4,5,6,2,8]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,2]=>[3,8,1,4,5,6,7,2]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[3,4,1,5,6,7,8,2]=>[4,8,3,1,5,6,7,2]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[3,4,5,1,6,7,8,2]=>[5,8,3,4,1,6,7,2]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,4,5,6,1,7,8,2]=>[6,8,3,4,5,1,7,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,4,5,6,7,1,8,2]=>[7,8,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[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]=>[3,1,5,2,6,4,8,7]=>[3,5,1,6,2,4,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,5,1,2,6,4,8,7]=>[5,1,3,6,2,4,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,5,1,6,2,4,8,7]=>[5,6,3,2,1,4,8,7]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,5,6,1,2,4,8,7]=>[6,1,3,2,5,4,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,6,8,4,7]=>[3,5,1,8,2,6,4,7]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,5,1,2,6,8,4,7]=>[5,1,3,8,2,6,4,7]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,5,6,2,8,4,7]=>[3,6,1,8,5,2,4,7]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,5,6,1,2,8,4,7]=>[6,1,3,8,5,2,4,7]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,5,6,8,2,4,7]=>[3,8,1,2,5,6,4,7]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,5,1,6,8,2,4,7]=>[5,8,3,2,1,6,4,7]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,5,6,1,8,2,4,7]=>[6,8,3,2,5,1,4,7]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,5,6,8,1,2,4,7]=>[8,1,3,2,5,6,4,7]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,7,8]=>[3,5,1,6,2,4,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,5,1,6,2,4,7,8]=>[5,6,3,2,1,4,7,8]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,6,7,4,8]=>[5,1,3,7,2,6,4,8]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,5,1,6,2,7,4,8]=>[5,6,3,7,1,2,4,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,5,6,1,2,7,4,8]=>[6,1,3,7,5,2,4,8]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,5,6,7,2,4,8]=>[3,7,1,2,5,6,4,8]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,5,1,6,7,2,4,8]=>[5,7,3,2,1,6,4,8]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,5,6,7,1,2,4,8]=>[7,1,3,2,5,6,4,8]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,5,6,2,7,8,4]=>[3,6,1,8,5,2,7,4]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,5,1,6,2,7,8,4]=>[5,6,3,8,1,2,7,4]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,5,6,1,2,7,8,4]=>[6,1,3,8,5,2,7,4]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,1,5,6,7,2,8,4]=>[3,7,1,8,5,6,2,4]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,5,1,6,7,2,8,4]=>[5,7,3,8,1,6,2,4]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,5,6,1,7,2,8,4]=>[6,7,3,8,5,1,2,4]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,5,6,7,8,2,4]=>[3,8,1,2,5,6,7,4]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,5,1,6,7,8,2,4]=>[5,8,3,2,1,6,7,4]=>[[[[.,[.,.]],.],.],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,5,6,1,7,8,2,4]=>[6,8,3,2,5,1,7,4]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,5,6,7,1,8,2,4]=>[7,8,3,2,5,6,1,4]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5,6,7,8,1,2,4]=>[8,1,3,2,5,6,7,4]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,8,6]=>[3,5,1,7,2,8,4,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,7,8,4,6]=>[3,5,1,8,2,4,7,6]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,5,1,2,7,8,4,6]=>[5,1,3,8,2,4,7,6]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,5,1,7,2,8,4,6]=>[5,7,3,8,1,4,2,6]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,5,1,7,8,2,4,6]=>[5,8,3,2,1,4,7,6]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,5,7,8,1,2,4,6]=>[8,1,3,2,5,4,7,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,6,8]=>[3,5,1,7,2,4,6,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,7,4,6,8]=>[5,1,3,7,2,4,6,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,7,2,4,6,8]=>[3,7,1,2,5,4,6,8]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,7,2,4,6,8]=>[5,7,3,2,1,4,6,8]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,7,1,2,4,6,8]=>[7,1,3,2,5,4,6,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,7,6,8]=>[3,5,1,2,4,7,6,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,7,6,8]=>[5,1,3,2,4,7,6,8]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,7,6,8]=>[3,1,2,5,4,7,6,8]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,7,6,8]=>[1,5,3,2,4,7,6,8]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,7,4,6,8]=>[3,1,2,7,5,4,6,8]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,4,6,8]=>[1,3,2,7,5,4,6,8]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,7,4,6,8]=>[1,5,3,7,2,4,6,8]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,7,2,4,6,8]=>[1,7,3,2,5,4,6,8]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,4,7,8,6]=>[3,5,1,2,4,8,7,6]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,7,6]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,4,7,8,6]=>[1,5,3,2,4,8,7,6]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,5,7,4,8,6]=>[3,1,2,7,5,8,4,6]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,5,7,4,8,6]=>[1,3,2,7,5,8,4,6]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,2,7,4,8,6]=>[1,5,3,7,2,8,4,6]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,5,7,8,4,6]=>[3,1,2,8,5,4,7,6]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,5,7,8,4,6]=>[1,3,2,8,5,4,7,6]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,5,7,2,8,4,6]=>[1,7,3,8,5,4,2,6]=>[.,[[[.,.],[[[.,.],.],.]],[.,.]]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,5,7,8,2,4,6]=>[1,8,3,2,5,4,7,6]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,5,2,8,4,6,7]=>[3,5,1,8,2,4,6,7]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,5,1,2,8,4,6,7]=>[5,1,3,8,2,4,6,7]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,5,8,1,2,4,6,7]=>[8,1,3,2,5,4,6,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,8,6,7]=>[3,5,1,2,4,8,6,7]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,8,6,7]=>[5,1,3,2,4,8,6,7]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,8,6,7]=>[1,3,2,5,4,8,6,7]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,8,6,7]=>[1,5,3,2,4,8,6,7]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,5,8,4,6,7]=>[1,3,2,8,5,4,6,7]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,5,2,8,4,6,7]=>[1,5,3,8,2,4,6,7]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,5,8,2,4,6,7]=>[1,8,3,2,5,4,6,7]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,5,2,4,6,8,7]=>[3,5,1,2,4,6,8,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,5,1,2,4,6,8,7]=>[5,1,3,2,4,6,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,2,5,4,6,8,7]=>[3,1,2,5,4,6,8,7]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,5,2,4,6,8,7]=>[1,5,3,2,4,6,8,7]=>[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,2,5,6,4,8,7]=>[1,3,2,6,5,4,8,7]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,5,6,8,4,7]=>[3,1,2,8,5,6,4,7]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,5,6,8,4,7]=>[1,3,2,8,5,6,4,7]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,5,2,6,8,4,7]=>[1,5,3,8,2,6,4,7]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,5,6,2,8,4,7]=>[1,6,3,8,5,2,4,7]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,5,6,8,2,4,7]=>[1,8,3,2,5,6,4,7]=>[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,5,2,4,6,7,8]=>[3,5,1,2,4,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,5,2,4,6,7,8]=>[1,5,3,2,4,6,7,8]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,5,6,4,7,8]=>[1,3,2,6,5,4,7,8]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,5,2,6,4,7,8]=>[1,5,3,6,2,4,7,8]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,5,6,2,4,7,8]=>[1,6,3,2,5,4,7,8]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,5,2,6,7,4,8]=>[1,5,3,7,2,6,4,8]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,5,6,2,7,4,8]=>[1,6,3,7,5,2,4,8]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,5,6,7,2,4,8]=>[1,7,3,2,5,6,4,8]=>[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,5,6,7,8,4]=>[3,1,2,8,5,6,7,4]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,5,2,6,7,8,4]=>[1,5,3,8,2,6,7,4]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,5,6,2,7,8,4]=>[1,6,3,8,5,2,7,4]=>[.,[[[.,.],[[.,.],.]],[[.,.],.]]]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,5,6,7,2,8,4]=>[1,7,3,8,5,6,2,4]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,5,6,7,8,2,4]=>[1,8,3,2,5,6,7,4]=>[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,6,2,7,4,8,5]=>[3,6,1,7,8,2,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,6,1,7,2,4,8,5]=>[6,7,3,2,8,1,4,5]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,6,7,1,2,4,8,5]=>[7,1,3,2,8,6,4,5]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,6,1,2,7,8,4,5]=>[6,1,3,8,4,2,7,5]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,1,6,7,2,8,4,5]=>[3,7,1,8,4,6,2,5]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,6,1,7,2,8,4,5]=>[6,7,3,8,4,1,2,5]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,6,7,1,2,8,4,5]=>[7,1,3,8,4,6,2,5]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,6,1,7,8,2,4,5]=>[6,8,3,2,4,1,7,5]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,6,7,1,8,2,4,5]=>[7,8,3,2,4,6,1,5]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,6,7,8,1,2,4,5]=>[8,1,3,2,4,6,7,5]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,6,1,2,7,4,5,8]=>[6,1,3,7,4,2,5,8]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,6,7,2,4,5,8]=>[3,7,1,2,4,6,5,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,6,4,7,5,8]=>[1,3,2,6,7,4,5,8]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,3,6,2,4,7,5,8]=>[1,6,3,2,7,4,5,8]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,6,7,4,5,8]=>[1,3,2,7,4,6,5,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,3,6,2,7,4,5,8]=>[1,6,3,7,4,2,5,8]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,3,6,7,2,4,5,8]=>[1,7,3,2,4,6,5,8]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,7,8,5]=>[6,1,3,2,8,4,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,7,8,5]=>[3,1,2,6,8,4,7,5]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,7,8,5]=>[1,3,2,6,8,4,7,5]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,7,8,5]=>[1,6,3,2,8,4,7,5]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,6,7,4,8,5]=>[3,1,2,7,8,6,4,5]=>[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,3,6,2,7,4,8,5]=>[1,6,3,7,8,2,4,5]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,6,7,2,4,8,5]=>[1,7,3,2,8,6,4,5]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,6,7,8,4,5]=>[3,1,2,8,4,6,7,5]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,6,7,8,4,5]=>[1,3,2,8,4,6,7,5]=>[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,2,7,8,4,5]=>[1,6,3,8,4,2,7,5]=>[.,[[[.,.],[[.,.],.]],[[.,.],.]]]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,2,8,4,5]=>[1,7,3,8,4,6,2,5]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,6,8,2,4,5,7]=>[3,8,1,2,4,6,5,7]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,6,8,1,2,4,5,7]=>[8,1,3,2,4,6,5,7]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,1,6,2,4,8,5,7]=>[3,6,1,2,8,4,5,7]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,1,2,6,4,8,5,7]=>[3,1,2,6,8,4,5,7]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,6,4,8,5,7]=>[1,3,2,6,8,4,5,7]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,3,6,2,4,8,5,7]=>[1,6,3,2,8,4,5,7]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,6,8,4,5,7]=>[1,3,2,8,4,6,5,7]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,3,6,2,8,4,5,7]=>[1,6,3,8,4,2,5,7]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5,8,7]=>[3,6,1,2,4,5,8,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5,8,7]=>[3,1,2,6,4,5,8,7]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5,8,7]=>[3,1,2,4,6,5,8,7]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5,8,7]=>[1,6,3,4,2,5,8,7]=>[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,8,5,7]=>[3,1,2,4,8,6,5,7]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,4,6,8,5,7]=>[1,3,2,4,8,6,5,7]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,1,6,2,4,5,7,8]=>[3,6,1,2,4,5,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,6,4,5,7,8]=>[1,3,2,6,4,5,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,3,6,2,4,5,7,8]=>[1,6,3,2,4,5,7,8]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,3,4,6,2,5,7,8]=>[1,6,3,4,2,5,7,8]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,3,2,4,6,7,5,8]=>[1,3,2,4,7,6,5,8]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,3,4,6,7,2,5,8]=>[1,7,3,4,2,6,5,8]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,6,7,8,5]=>[3,1,2,4,8,6,7,5]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,3,4,2,6,7,8,5]=>[1,4,3,2,8,6,7,5]=>[.,[[[.,.],.],[[[.,.],[.,.]],.]]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,3,4,6,2,7,8,5]=>[1,6,3,4,8,2,7,5]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,3,4,6,7,2,8,5]=>[1,7,3,4,8,6,2,5]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,3,4,6,7,8,2,5]=>[1,8,3,4,2,6,7,5]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[3,7,1,2,8,4,5,6]=>[7,1,3,8,4,5,2,6]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,1,7,8,2,4,5,6]=>[3,8,1,2,4,5,7,6]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,7,8,1,2,4,5,6]=>[8,1,3,2,4,5,7,6]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[3,7,1,2,4,8,5,6]=>[7,1,3,2,8,5,4,6]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,3,2,7,4,8,5,6]=>[1,3,2,7,8,5,4,6]=>[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,3,7,2,4,8,5,6]=>[1,7,3,2,8,5,4,6]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[3,1,2,7,8,4,5,6]=>[3,1,2,8,4,5,7,6]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,3,2,7,8,4,5,6]=>[1,3,2,8,4,5,7,6]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,3,7,2,8,4,5,6]=>[1,7,3,8,4,5,2,6]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,3,7,8,2,4,5,6]=>[1,8,3,2,4,5,7,6]=>[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[3,1,7,2,4,5,8,6]=>[3,7,1,2,4,8,5,6]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,7,1,2,4,5,8,6]=>[7,1,3,2,4,8,5,6]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,1,2,7,4,5,8,6]=>[3,1,2,7,4,8,5,6]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,3,2,7,4,5,8,6]=>[1,3,2,7,4,8,5,6]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,3,7,2,4,5,8,6]=>[1,7,3,2,4,8,5,6]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,8,6]=>[3,1,2,4,7,8,5,6]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,3,2,4,7,5,8,6]=>[1,3,2,4,7,8,5,6]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,3,4,2,7,5,8,6]=>[1,4,3,2,7,8,5,6]=>[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,3,4,7,2,5,8,6]=>[1,7,3,4,2,8,5,6]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,1,2,4,7,8,5,6]=>[3,1,2,4,8,5,7,6]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,3,2,4,7,8,5,6]=>[1,3,2,4,8,5,7,6]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,3,4,7,2,8,5,6]=>[1,7,3,4,8,5,2,6]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[3,1,7,2,4,5,6,8]=>[3,7,1,2,4,5,6,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,7,1,2,4,5,6,8]=>[7,1,3,2,4,5,6,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,1,2,7,4,5,6,8]=>[3,1,2,7,4,5,6,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,3,2,7,4,5,6,8]=>[1,3,2,7,4,5,6,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,3,7,2,4,5,6,8]=>[1,7,3,2,4,5,6,8]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,6,8]=>[3,1,2,4,7,5,6,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,3,4,7,2,5,6,8]=>[1,7,3,4,2,5,6,8]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[3,1,2,4,5,7,6,8]=>[3,1,2,4,5,7,6,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,7,8,6]=>[1,3,2,4,5,8,7,6]=>[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,3,4,2,5,7,8,6]=>[1,4,3,2,5,8,7,6]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,3,4,5,2,7,8,6]=>[1,5,3,4,2,8,7,6]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,3,4,5,7,2,8,6]=>[1,7,3,4,5,8,2,6]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,3,4,5,7,8,2,6]=>[1,8,3,4,5,2,7,6]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,1,8,2,4,5,6,7]=>[3,8,1,2,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,8,1,2,4,5,6,7]=>[8,1,3,2,4,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,1,2,8,4,5,6,7]=>[3,1,2,8,4,5,6,7]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,3,2,8,4,5,6,7]=>[1,3,2,8,4,5,6,7]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,3,8,2,4,5,6,7]=>[1,8,3,2,4,5,6,7]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[3,1,2,4,8,5,6,7]=>[3,1,2,4,8,5,6,7]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,3,2,4,8,5,6,7]=>[1,3,2,4,8,5,6,7]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,3,4,2,8,5,6,7]=>[1,4,3,2,8,5,6,7]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,3,4,8,2,5,6,7]=>[1,8,3,4,2,5,6,7]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[3,1,2,4,5,8,6,7]=>[3,1,2,4,5,8,6,7]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,3,2,4,5,8,6,7]=>[1,3,2,4,5,8,6,7]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,3,4,2,5,8,6,7]=>[1,4,3,2,5,8,6,7]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,3,4,5,8,2,6,7]=>[1,8,3,4,5,2,6,7]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,8,7]=>[3,1,2,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,3,4,2,5,6,8,7]=>[1,4,3,2,5,6,8,7]=>[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,3,4,5,6,8,2,7]=>[1,8,3,4,5,6,2,7]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7,8]=>[3,1,2,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,3,4,5,2,6,7,8]=>[1,5,3,4,2,6,7,8]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,3,4,5,6,2,7,8]=>[1,6,3,4,5,2,7,8]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,3,4,5,6,7,2,8]=>[1,7,3,4,5,6,2,8]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,4,5,6,7,8,2]=>[1,8,3,4,5,6,7,2]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,8,7]=>[4,5,6,1,2,3,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[4,1,5,6,2,3,8,7]=>[4,6,2,1,5,3,8,7]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[4,5,1,6,2,3,8,7]=>[5,6,2,4,1,3,8,7]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,8,7]=>[6,1,2,4,5,3,8,7]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[4,1,5,2,6,8,3,7]=>[4,5,8,1,2,6,3,7]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[4,5,1,2,6,8,3,7]=>[5,1,8,4,2,6,3,7]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[4,5,1,6,2,8,3,7]=>[5,6,8,4,1,2,3,7]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,6,1,2,8,3,7]=>[6,1,8,4,5,2,3,7]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,5,6,8,2,3,7]=>[4,8,2,1,5,6,3,7]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[4,5,1,6,8,2,3,7]=>[5,8,2,4,1,6,3,7]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[4,5,6,1,8,2,3,7]=>[6,8,2,4,5,1,3,7]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,8,1,2,3,7]=>[8,1,2,4,5,6,3,7]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,7,8]=>[4,5,6,1,2,3,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,5,6,2,3,7,8]=>[4,6,2,1,5,3,7,8]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[4,5,1,6,2,3,7,8]=>[5,6,2,4,1,3,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[4,1,5,2,6,7,3,8]=>[4,5,7,1,2,6,3,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[4,5,1,2,6,7,3,8]=>[5,1,7,4,2,6,3,8]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[4,1,5,6,2,7,3,8]=>[4,6,7,1,5,2,3,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[4,5,1,6,2,7,3,8]=>[5,6,7,4,1,2,3,8]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[4,5,1,6,7,2,3,8]=>[5,7,2,4,1,6,3,8]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3,8]=>[7,1,2,4,5,6,3,8]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,6,7,8,3]=>[4,5,8,1,2,6,7,3]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[4,5,1,6,2,7,8,3]=>[5,6,8,4,1,2,7,3]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,6,1,2,7,8,3]=>[6,1,8,4,5,2,7,3]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[4,1,5,6,7,2,8,3]=>[4,7,8,1,5,6,2,3]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[4,5,1,6,7,2,8,3]=>[5,7,8,4,1,6,2,3]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[4,5,6,1,7,2,8,3]=>[6,7,8,4,5,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[4,1,5,6,7,8,2,3]=>[4,8,2,1,5,6,7,3]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[4,5,1,6,7,8,2,3]=>[5,8,2,4,1,6,7,3]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[4,5,6,1,7,8,2,3]=>[6,8,2,4,5,1,7,3]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,5,6,7,1,8,2,3]=>[7,8,2,4,5,6,1,3]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[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]=>[4,1,5,2,7,3,8,6]=>[4,5,7,1,2,8,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[4,1,5,2,7,8,3,6]=>[4,5,8,1,2,3,7,6]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[4,5,1,2,7,8,3,6]=>[5,1,8,4,2,3,7,6]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[4,1,5,7,2,8,3,6]=>[4,7,8,1,5,3,2,6]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[4,5,1,7,2,8,3,6]=>[5,7,8,4,1,3,2,6]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,7,1,2,8,3,6]=>[7,1,8,4,5,3,2,6]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[4,5,1,7,8,2,3,6]=>[5,8,2,4,1,3,7,6]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,7,8,1,2,3,6]=>[8,1,2,4,5,3,7,6]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[4,5,1,2,7,3,6,8]=>[5,1,7,4,2,3,6,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,7,6,8]=>[4,5,2,1,3,7,6,8]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,7,6,8]=>[4,1,5,2,3,7,6,8]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,7,6,8]=>[1,4,5,2,3,7,6,8]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,7,6,8]=>[1,5,2,4,3,7,6,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,4,2,5,7,3,6,8]=>[1,4,7,2,5,3,6,8]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,2,7,3,6,8]=>[1,5,7,4,2,3,6,8]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,7,2,3,6,8]=>[1,7,2,4,5,3,6,8]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,7,8,6]=>[4,5,2,1,3,8,7,6]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3,7,8,6]=>[4,1,5,2,3,8,7,6]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3,7,8,6]=>[1,5,2,4,3,8,7,6]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,4,2,5,7,3,8,6]=>[1,4,7,2,5,8,3,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,4,5,2,7,3,8,6]=>[1,5,7,4,2,8,3,6]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,4,5,7,2,3,8,6]=>[1,7,2,4,5,8,3,6]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,7,8,3,6]=>[4,1,8,2,5,3,7,6]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,4,5,7,2,8,3,6]=>[1,7,8,4,5,3,2,6]=>[.,[[[[.,[.,.]],[.,.]],.],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,5,2,8,3,6,7]=>[4,5,8,1,2,3,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[4,5,1,2,8,3,6,7]=>[5,1,8,4,2,3,6,7]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[4,5,1,8,2,3,6,7]=>[5,8,2,4,1,3,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,8,1,2,3,6,7]=>[8,1,2,4,5,3,6,7]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,8,6,7]=>[4,1,5,2,3,8,6,7]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,8,6,7]=>[1,4,5,2,3,8,6,7]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,8,6,7]=>[1,5,2,4,3,8,6,7]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,5,2,8,3,6,7]=>[1,5,8,4,2,3,6,7]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[4,5,1,2,3,6,8,7]=>[5,1,2,4,3,6,8,7]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,5,6,3,8,7]=>[4,1,6,2,5,3,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,5,6,8,3,7]=>[1,4,8,2,5,6,3,7]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,5,2,6,8,3,7]=>[1,5,8,4,2,6,3,7]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,5,6,2,8,3,7]=>[1,6,8,4,5,2,3,7]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,5,2,3,6,7,8]=>[4,5,2,1,3,6,7,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[4,5,1,2,3,6,7,8]=>[5,1,2,4,3,6,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,5,3,6,7,8]=>[4,1,5,2,3,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,5,3,6,7,8]=>[1,4,5,2,3,6,7,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,5,2,3,6,7,8]=>[1,5,2,4,3,6,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,2,5,6,3,7,8]=>[1,4,6,2,5,3,7,8]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,5,2,6,3,7,8]=>[1,5,6,4,2,3,7,8]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,5,6,2,3,7,8]=>[1,6,2,4,5,3,7,8]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,2,5,6,7,3,8]=>[1,4,7,2,5,6,3,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,4,5,2,6,7,3,8]=>[1,5,7,4,2,6,3,8]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,4,5,6,2,7,3,8]=>[1,6,7,4,5,2,3,8]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,5,6,7,2,3,8]=>[1,7,2,4,5,6,3,8]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,5,6,7,8,3]=>[4,1,8,2,5,6,7,3]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,5,6,7,8,3]=>[1,4,8,2,5,6,7,3]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,4,5,2,6,7,8,3]=>[1,5,8,4,2,6,7,3]=>[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,4,5,6,2,7,8,3]=>[1,6,8,4,5,2,7,3]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,4,5,6,7,2,8,3]=>[1,7,8,4,5,6,2,3]=>[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,4,5,6,7,8,2,3]=>[1,8,2,4,5,6,7,3]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,8,5]=>[4,6,7,1,8,2,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[4,6,1,2,7,3,8,5]=>[6,1,7,4,8,2,3,5]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[4,1,6,7,2,8,3,5]=>[4,7,8,1,3,6,2,5]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,6,1,7,2,8,3,5]=>[6,7,8,4,3,1,2,5]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,6,7,1,2,8,3,5]=>[7,1,8,4,3,6,2,5]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,6,7,8,2,3,5]=>[4,8,2,1,3,6,7,5]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,6,7,1,8,2,3,5]=>[7,8,2,4,3,6,1,5]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,5,8]=>[4,6,7,1,3,2,5,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,6,7,2,3,5,8]=>[4,7,2,1,3,6,5,8]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,6,1,7,2,3,5,8]=>[6,7,2,4,3,1,5,8]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,6,2,3,7,5,8]=>[4,6,2,1,7,3,5,8]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[4,6,1,2,3,7,5,8]=>[6,1,2,4,7,3,5,8]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,2,6,3,7,5,8]=>[4,1,6,2,7,3,5,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,7,5,8]=>[1,4,6,2,7,3,5,8]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,4,6,2,3,7,5,8]=>[1,6,2,4,7,3,5,8]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,6,7,3,5,8]=>[4,1,7,2,3,6,5,8]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,2,6,7,3,5,8]=>[1,4,7,2,3,6,5,8]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,6,2,7,3,5,8]=>[1,6,7,4,3,2,5,8]=>[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,6,7,2,3,5,8]=>[1,7,2,4,3,6,5,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,7,8,5]=>[4,6,2,1,8,3,7,5]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,7,8,5]=>[6,1,2,4,8,3,7,5]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,7,8,5]=>[4,1,6,2,8,3,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,7,8,5]=>[1,4,6,2,8,3,7,5]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,7,8,5]=>[1,6,2,4,8,3,7,5]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,2,6,7,3,8,5]=>[1,4,7,2,8,6,3,5]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,6,2,7,3,8,5]=>[1,6,7,4,8,2,3,5]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,6,7,2,3,8,5]=>[1,7,2,4,8,6,3,5]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,6,7,8,3,5]=>[1,4,8,2,3,6,7,5]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,6,2,7,8,3,5]=>[1,6,8,4,3,2,7,5]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,6,7,2,8,3,5]=>[1,7,8,4,3,6,2,5]=>[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,6,1,2,8,3,5,7]=>[6,1,8,4,3,2,5,7]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,6,8,2,3,5,7]=>[4,8,2,1,3,6,5,7]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,6,1,8,2,3,5,7]=>[6,8,2,4,3,1,5,7]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,6,8,1,2,3,5,7]=>[8,1,2,4,3,6,5,7]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,6,1,2,3,8,5,7]=>[6,1,2,4,8,3,5,7]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,6,3,8,5,7]=>[4,1,6,2,8,3,5,7]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,8,5,7]=>[1,4,6,2,8,3,5,7]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,6,2,3,8,5,7]=>[1,6,2,4,8,3,5,7]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,6,8,3,5,7]=>[4,1,8,2,3,6,5,7]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,8,3,5,7]=>[1,4,8,2,3,6,5,7]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,4,6,2,8,3,5,7]=>[1,6,8,4,3,2,5,7]=>[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,4,6,8,2,3,5,7]=>[1,8,2,4,3,6,5,7]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5,8,7]=>[4,6,2,1,3,5,8,7]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5,8,7]=>[6,1,2,4,3,5,8,7]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5,8,7]=>[4,1,6,2,3,5,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5,8,7]=>[1,4,6,2,3,5,8,7]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,5,8,7]=>[1,6,2,4,3,5,8,7]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,8,7]=>[4,1,2,3,6,5,8,7]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,8,7]=>[1,4,2,3,6,5,8,7]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,8,5,7]=>[4,1,2,3,8,6,5,7]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,6,8,5,7]=>[1,4,2,3,8,6,5,7]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,6,8,3,5,7]=>[1,2,8,4,3,6,5,7]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,1,6,2,3,5,7,8]=>[4,6,2,1,3,5,7,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,6,1,2,3,5,7,8]=>[6,1,2,4,3,5,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,6,3,5,7,8]=>[4,1,6,2,3,5,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,6,3,5,7,8]=>[1,4,6,2,3,5,7,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,4,6,2,3,5,7,8]=>[1,6,2,4,3,5,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,7,8]=>[4,1,2,3,6,5,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,7,8]=>[1,4,2,3,6,5,7,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,2,4,6,3,5,7,8]=>[1,2,6,4,3,5,7,8]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,1,2,3,6,7,5,8]=>[4,1,2,3,7,6,5,8]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,2,4,6,3,7,5,8]=>[1,2,6,4,7,3,5,8]=>[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,6,7,8,5]=>[4,1,2,3,8,6,7,5]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,6,7,5]=>[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,2,4,6,3,7,8,5]=>[1,2,6,4,8,3,7,5]=>[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,6,7,3,8,5]=>[1,2,7,4,8,6,3,5]=>[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,6,7,8,3,5]=>[1,2,8,4,3,6,7,5]=>[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,7,1,2,8,3,5,6]=>[7,1,8,4,3,5,2,6]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,1,7,8,2,3,5,6]=>[4,8,2,1,3,5,7,6]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,7,1,8,2,3,5,6]=>[7,8,2,4,3,5,1,6]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,7,8,1,2,3,5,6]=>[8,1,2,4,3,5,7,6]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,7,2,3,8,5,6]=>[4,7,2,1,8,5,3,6]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,2,7,3,8,5,6]=>[4,1,7,2,8,5,3,6]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,4,2,7,3,8,5,6]=>[1,4,7,2,8,5,3,6]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,1,2,7,8,3,5,6]=>[4,1,8,2,3,5,7,6]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,4,2,7,8,3,5,6]=>[1,4,8,2,3,5,7,6]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,4,7,2,8,3,5,6]=>[1,7,8,4,3,5,2,6]=>[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,2,7,3,5,8,6]=>[4,1,7,2,3,8,5,6]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,4,2,7,3,5,8,6]=>[1,4,7,2,3,8,5,6]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,4,7,2,3,5,8,6]=>[1,7,2,4,3,8,5,6]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,7,5,8,6]=>[4,1,2,3,7,8,5,6]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,7,5,8,6]=>[1,4,2,3,7,8,5,6]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,7,5,8,6]=>[1,2,4,3,7,8,5,6]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,7,8,5,6]=>[4,1,2,3,8,5,7,6]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,7,8,5,6]=>[1,4,2,3,8,5,7,6]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,7,8,5,6]=>[1,2,4,3,8,5,7,6]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,2,4,7,3,8,5,6]=>[1,2,7,4,8,5,3,6]=>[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,2,4,7,8,3,5,6]=>[1,2,8,4,3,5,7,6]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,7,1,2,3,5,6,8]=>[7,1,2,4,3,5,6,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,1,2,7,3,5,6,8]=>[4,1,7,2,3,5,6,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,4,2,7,3,5,6,8]=>[1,4,7,2,3,5,6,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,4,7,2,3,5,6,8]=>[1,7,2,4,3,5,6,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,2,3,7,5,6,8]=>[4,1,2,3,7,5,6,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,4,2,3,7,5,6,8]=>[1,4,2,3,7,5,6,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,2,4,3,7,5,6,8]=>[1,2,4,3,7,5,6,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,2,4,7,3,5,6,8]=>[1,2,7,4,3,5,6,8]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,2,3,5,7,6,8]=>[4,1,2,3,5,7,6,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,4,2,3,5,7,6,8]=>[1,4,2,3,5,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,7,8,6]=>[4,1,2,3,5,8,7,6]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,7,8,6]=>[1,4,2,3,5,8,7,6]=>[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,4,3,5,7,8,6]=>[1,2,4,3,5,8,7,6]=>[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,2,4,5,3,7,8,6]=>[1,2,5,4,3,8,7,6]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,4,5,7,3,8,6]=>[1,2,7,4,5,8,3,6]=>[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,2,4,5,7,8,3,6]=>[1,2,8,4,5,3,7,6]=>[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[4,1,8,2,3,5,6,7]=>[4,8,2,1,3,5,6,7]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[4,8,1,2,3,5,6,7]=>[8,1,2,4,3,5,6,7]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[4,1,2,8,3,5,6,7]=>[4,1,8,2,3,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,4,2,8,3,5,6,7]=>[1,4,8,2,3,5,6,7]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,4,8,2,3,5,6,7]=>[1,8,2,4,3,5,6,7]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[4,1,2,3,8,5,6,7]=>[4,1,2,3,8,5,6,7]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,4,2,3,8,5,6,7]=>[1,4,2,3,8,5,6,7]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,8,5,6,7]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,4,8,3,5,6,7]=>[1,2,8,4,3,5,6,7]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[4,1,2,3,5,8,6,7]=>[4,1,2,3,5,8,6,7]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,4,2,3,5,8,6,7]=>[1,4,2,3,5,8,6,7]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,4,3,5,8,6,7]=>[1,2,4,3,5,8,6,7]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,2,4,5,3,8,6,7]=>[1,2,5,4,3,8,6,7]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,8,7]=>[4,1,2,3,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,8,7]=>[1,4,2,3,5,6,8,7]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,2,4,5,3,6,8,7]=>[1,2,5,4,3,6,8,7]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,2,4,5,6,8,3,7]=>[1,2,8,4,5,6,3,7]=>[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,7,8]=>[4,1,2,3,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,7,8]=>[1,4,2,3,5,6,7,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,4,5,3,6,7,8]=>[1,2,5,4,3,6,7,8]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,5,6,7,8,3]=>[1,2,8,4,5,6,7,3]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,8,4]=>[5,6,7,8,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[5,6,1,2,7,3,8,4]=>[6,1,7,8,5,2,3,4]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[5,1,6,7,2,3,8,4]=>[5,7,2,8,1,6,3,4]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[5,6,1,7,2,3,8,4]=>[6,7,2,8,5,1,3,4]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,8,4]=>[7,1,2,8,5,6,3,4]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[5,1,6,2,7,8,3,4]=>[5,6,8,3,1,2,7,4]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[5,6,1,2,7,8,3,4]=>[6,1,8,3,5,2,7,4]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[5,1,6,7,2,8,3,4]=>[5,7,8,3,1,6,2,4]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[5,6,1,7,2,8,3,4]=>[6,7,8,3,5,1,2,4]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,7,1,2,8,3,4]=>[7,1,8,3,5,6,2,4]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[5,1,6,7,8,2,3,4]=>[5,8,2,3,1,6,7,4]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[5,6,1,7,8,2,3,4]=>[6,8,2,3,5,1,7,4]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,6,7,1,8,2,3,4]=>[7,8,2,3,5,6,1,4]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[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]=>[5,1,6,2,7,3,4,8]=>[5,6,7,3,1,2,4,8]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4,8]=>[7,1,2,3,5,6,4,8]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[5,1,6,2,3,7,4,8]=>[5,6,2,7,1,3,4,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,5,2,6,3,7,4,8]=>[1,5,6,7,2,3,4,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,5,6,2,3,7,4,8]=>[1,6,2,7,5,3,4,8]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,5,2,6,7,3,4,8]=>[1,5,7,3,2,6,4,8]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[5,1,6,2,3,7,8,4]=>[5,6,2,8,1,3,7,4]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[5,6,1,2,3,7,8,4]=>[6,1,2,8,5,3,7,4]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,5,2,6,3,7,8,4]=>[1,5,6,8,2,3,7,4]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,5,6,2,3,7,8,4]=>[1,6,2,8,5,3,7,4]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,5,2,6,7,3,8,4]=>[1,5,7,8,2,6,3,4]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,5,6,2,7,3,8,4]=>[1,6,7,8,5,2,3,4]=>[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,5,6,7,2,3,8,4]=>[1,7,2,8,5,6,3,4]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[5,1,2,6,7,8,3,4]=>[5,1,8,3,2,6,7,4]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,5,2,6,7,8,3,4]=>[1,5,8,3,2,6,7,4]=>[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,5,6,2,7,8,3,4]=>[1,6,8,3,5,2,7,4]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,5,6,7,2,8,3,4]=>[1,7,8,3,5,6,2,4]=>[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,5,6,7,8,2,3,4]=>[1,8,2,3,5,6,7,4]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[5,1,6,8,2,3,4,7]=>[5,8,2,3,1,6,4,7]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[5,6,1,8,2,3,4,7]=>[6,8,2,3,5,1,4,7]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,8,1,2,3,4,7]=>[8,1,2,3,5,6,4,7]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[5,1,6,2,3,8,4,7]=>[5,6,2,8,1,3,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[5,6,1,2,3,8,4,7]=>[6,1,2,8,5,3,4,7]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,5,2,6,3,8,4,7]=>[1,5,6,8,2,3,4,7]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,5,6,2,3,8,4,7]=>[1,6,2,8,5,3,4,7]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[5,1,2,6,8,3,4,7]=>[5,1,8,3,2,6,4,7]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,5,6,2,8,3,4,7]=>[1,6,8,3,5,2,4,7]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,5,6,8,2,3,4,7]=>[1,8,2,3,5,6,4,7]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[5,1,2,6,3,4,8,7]=>[5,1,6,3,2,4,8,7]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[5,1,2,3,6,4,8,7]=>[5,1,2,6,3,4,8,7]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,5,2,3,6,4,8,7]=>[1,5,2,6,3,4,8,7]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,5,3,6,4,8,7]=>[1,2,5,6,3,4,8,7]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,6,8,4,7]=>[1,5,2,8,3,6,4,7]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,2,5,3,6,8,4,7]=>[1,2,5,8,3,6,4,7]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,2,5,6,3,8,4,7]=>[1,2,6,8,5,3,4,7]=>[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,2,5,6,8,3,4,7]=>[1,2,8,3,5,6,4,7]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4,7,8]=>[6,1,2,3,5,4,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[5,1,2,6,3,4,7,8]=>[5,1,6,3,2,4,7,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,6,3,4,7,8]=>[1,5,6,3,2,4,7,8]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,6,4,7,8]=>[5,1,2,6,3,4,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,6,4,7,8]=>[1,5,2,6,3,4,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,6,4,7,8]=>[1,2,5,6,3,4,7,8]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,2,5,6,3,4,7,8]=>[1,2,6,3,5,4,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,6,7,4,8]=>[5,1,2,7,3,6,4,8]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,6,7,4,8]=>[1,5,2,7,3,6,4,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,6,7,4,8]=>[1,2,5,7,3,6,4,8]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,2,5,6,3,7,4,8]=>[1,2,6,7,5,3,4,8]=>[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,6,7,8,4]=>[5,1,2,8,3,6,7,4]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,2,5,3,6,7,8,4]=>[1,2,5,8,3,6,7,4]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,2,5,6,3,7,8,4]=>[1,2,6,8,5,3,7,4]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,2,5,6,7,3,8,4]=>[1,2,7,8,5,6,3,4]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,2,5,6,7,8,3,4]=>[1,2,8,3,5,6,7,4]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,7,2,8,3,4,6]=>[5,7,8,3,1,4,2,6]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[5,7,1,2,8,3,4,6]=>[7,1,8,3,5,4,2,6]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,1,0,0]=>[5,7,1,8,2,3,4,6]=>[7,8,2,3,5,4,1,6]=>[[[.,[.,.]],[.,[[.,.],.]]],[.,.]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,7,8,1,2,3,4,6]=>[8,1,2,3,5,4,7,6]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[5,1,7,2,3,8,4,6]=>[5,7,2,8,1,4,3,6]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[5,1,2,7,3,8,4,6]=>[5,1,7,8,2,4,3,6]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,2,7,3,8,4,6]=>[1,5,7,8,2,4,3,6]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,7,2,3,8,4,6]=>[1,7,2,8,5,4,3,6]=>[.,[[.,.],[[[[.,.],.],.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[5,1,2,7,8,3,4,6]=>[5,1,8,3,2,4,7,6]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[1,5,2,7,8,3,4,6]=>[1,5,8,3,2,4,7,6]=>[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,5,7,2,8,3,4,6]=>[1,7,8,3,5,4,2,6]=>[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[5,7,1,2,3,4,8,6]=>[7,1,2,3,5,8,4,6]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,8,6]=>[5,1,7,3,2,8,4,6]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,7,3,4,8,6]=>[1,5,7,3,2,8,4,6]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,7,2,3,4,8,6]=>[1,7,2,3,5,8,4,6]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[5,1,2,3,7,4,8,6]=>[5,1,2,7,3,8,4,6]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,2,3,7,4,8,6]=>[1,5,2,7,3,8,4,6]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,2,5,3,7,4,8,6]=>[1,2,5,7,3,8,4,6]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,8,6]=>[1,2,7,3,5,8,4,6]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,7,8,4,6]=>[1,5,2,8,3,4,7,6]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,2,5,3,7,8,4,6]=>[1,2,5,8,3,4,7,6]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,2,5,7,3,8,4,6]=>[1,2,7,8,5,4,3,6]=>[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,2,5,7,8,3,4,6]=>[1,2,8,3,5,4,7,6]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[5,7,1,2,3,4,6,8]=>[7,1,2,3,5,4,6,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,6,8]=>[5,1,7,3,2,4,6,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,5,2,7,3,4,6,8]=>[1,5,7,3,2,4,6,8]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,5,7,2,3,4,6,8]=>[1,7,2,3,5,4,6,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,7,4,6,8]=>[5,1,2,7,3,4,6,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,7,4,6,8]=>[1,5,2,7,3,4,6,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,7,4,6,8]=>[1,2,5,7,3,4,6,8]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6,8]=>[1,2,7,3,5,4,6,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,7,6,8]=>[1,5,2,3,4,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,7,6,8]=>[1,2,5,3,4,7,6,8]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,7,4,6,8]=>[1,2,3,7,5,4,6,8]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,7,8,6]=>[5,1,2,3,4,8,7,6]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,7,8,6]=>[1,5,2,3,4,8,7,6]=>[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,5,3,4,7,8,6]=>[1,2,5,3,4,8,7,6]=>[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,7,6]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,3,5,7,4,8,6]=>[1,2,3,7,5,8,4,6]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,7,8,4,6]=>[1,2,3,8,5,4,7,6]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[5,1,8,2,3,4,6,7]=>[5,8,2,3,1,4,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[5,8,1,2,3,4,6,7]=>[8,1,2,3,5,4,6,7]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[5,1,2,8,3,4,6,7]=>[5,1,8,3,2,4,6,7]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,5,2,8,3,4,6,7]=>[1,5,8,3,2,4,6,7]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,5,8,2,3,4,6,7]=>[1,8,2,3,5,4,6,7]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,2,3,8,4,6,7]=>[5,1,2,8,3,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[1,5,2,3,8,4,6,7]=>[1,5,2,8,3,4,6,7]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,5,3,8,4,6,7]=>[1,2,5,8,3,4,6,7]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,5,8,3,4,6,7]=>[1,2,8,3,5,4,6,7]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,8,6,7]=>[5,1,2,3,4,8,6,7]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,8,6,7]=>[1,5,2,3,4,8,6,7]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,8,6,7]=>[1,2,5,3,4,8,6,7]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,8,6,7]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,2,3,5,8,4,6,7]=>[1,2,3,8,5,4,6,7]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,8,7]=>[5,1,2,3,4,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,6,8,7]=>[1,5,2,3,4,6,8,7]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[1,2,5,3,4,6,8,7]=>[1,2,5,3,4,6,8,7]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,5,6,4,8,7]=>[1,2,3,6,5,4,8,7]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,5,6,8,4,7]=>[1,2,3,8,5,6,4,7]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,7,8]=>[5,1,2,3,4,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,5,2,3,4,6,7,8]=>[1,5,2,3,4,6,7,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,5,3,4,6,7,8]=>[1,2,5,3,4,6,7,8]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,2,3,5,6,4,7,8]=>[1,2,3,6,5,4,7,8]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,2,3,5,6,7,4,8]=>[1,2,3,7,5,6,4,8]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,5,6,7,4]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[6,1,7,2,8,3,4,5]=>[6,7,8,3,4,1,2,5]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[6,7,1,2,8,3,4,5]=>[7,1,8,3,4,6,2,5]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[6,1,7,8,2,3,4,5]=>[6,8,2,3,4,1,7,5]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,7,1,8,2,3,4,5]=>[7,8,2,3,4,6,1,5]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[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]=>[6,1,7,2,3,8,4,5]=>[6,7,2,8,4,1,3,5]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[6,1,2,7,3,8,4,5]=>[6,1,7,8,4,2,3,5]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,6,2,7,3,8,4,5]=>[1,6,7,8,4,2,3,5]=>[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,6,7,2,3,8,4,5]=>[1,7,2,8,4,6,3,5]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[6,1,2,7,8,3,4,5]=>[6,1,8,3,4,2,7,5]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,6,2,7,8,3,4,5]=>[1,6,8,3,4,2,7,5]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,6,7,8,2,3,4,5]=>[1,8,2,3,4,6,7,5]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[6,1,7,2,3,4,8,5]=>[6,7,2,3,8,1,4,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[6,1,2,7,3,4,8,5]=>[6,1,7,3,8,2,4,5]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,1,0,0,0]=>[1,6,7,2,3,4,8,5]=>[1,7,2,3,8,6,4,5]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[6,1,2,3,7,4,8,5]=>[6,1,2,7,8,3,4,5]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,6,2,3,7,4,8,5]=>[1,6,2,7,8,3,4,5]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,2,6,3,7,4,8,5]=>[1,2,6,7,8,3,4,5]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,2,6,7,3,4,8,5]=>[1,2,7,3,8,6,4,5]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[6,1,2,3,7,8,4,5]=>[6,1,2,8,4,3,7,5]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[1,6,2,3,7,8,4,5]=>[1,6,2,8,4,3,7,5]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,2,6,3,7,8,4,5]=>[1,2,6,8,4,3,7,5]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]
[1,1,1,1,1,0,0,0,1,1,0,1,0,0,0,0]=>[1,2,6,7,3,8,4,5]=>[1,2,7,8,4,6,3,5]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,2,6,7,8,3,4,5]=>[1,2,8,3,4,6,7,5]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[6,1,7,2,3,4,5,8]=>[6,7,2,3,4,1,5,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5,8]=>[7,1,2,3,4,6,5,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[6,1,2,7,3,4,5,8]=>[6,1,7,3,4,2,5,8]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,6,2,7,3,4,5,8]=>[1,6,7,3,4,2,5,8]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,6,7,2,3,4,5,8]=>[1,7,2,3,4,6,5,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,1,0,0,0]=>[1,2,6,3,7,4,5,8]=>[1,2,6,7,4,3,5,8]=>[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,2,6,7,3,4,5,8]=>[1,2,7,3,4,6,5,8]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[6,1,2,3,4,7,5,8]=>[6,1,2,3,7,4,5,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,6,2,3,4,7,5,8]=>[1,6,2,3,7,4,5,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[1,2,6,3,4,7,5,8]=>[1,2,6,3,7,4,5,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,6,4,7,5,8]=>[1,2,3,6,7,4,5,8]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,2,3,6,7,4,5,8]=>[1,2,3,7,4,6,5,8]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,7,8,5]=>[6,1,2,3,8,4,7,5]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,7,8,5]=>[1,2,6,3,8,4,7,5]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,7,8,5]=>[1,2,3,6,8,4,7,5]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,2,3,6,7,4,8,5]=>[1,2,3,7,8,6,4,5]=>[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,6,7,8,4,5]=>[1,2,3,8,4,6,7,5]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[6,1,8,2,3,4,5,7]=>[6,8,2,3,4,1,5,7]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,8,1,2,3,4,5,7]=>[8,1,2,3,4,6,5,7]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[6,1,2,8,3,4,5,7]=>[6,1,8,3,4,2,5,7]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,6,2,8,3,4,5,7]=>[1,6,8,3,4,2,5,7]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,6,8,2,3,4,5,7]=>[1,8,2,3,4,6,5,7]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[6,1,2,3,8,4,5,7]=>[6,1,2,8,4,3,5,7]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[1,6,2,3,8,4,5,7]=>[1,6,2,8,4,3,5,7]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,2,6,3,8,4,5,7]=>[1,2,6,8,4,3,5,7]=>[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[1,2,6,8,3,4,5,7]=>[1,2,8,3,4,6,5,7]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[6,1,2,3,4,8,5,7]=>[6,1,2,3,8,4,5,7]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,3,4,8,5,7]=>[1,6,2,3,8,4,5,7]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[1,2,6,3,4,8,5,7]=>[1,2,6,3,8,4,5,7]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,2,3,6,4,8,5,7]=>[1,2,3,6,8,4,5,7]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,2,3,6,8,4,5,7]=>[1,2,3,8,4,6,5,7]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,8,7]=>[6,1,2,3,4,5,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5,8,7]=>[1,6,2,3,4,5,8,7]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5,8,7]=>[1,2,6,3,4,5,8,7]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5,8,7]=>[1,2,3,6,4,5,8,7]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,6,8,5,7]=>[1,2,3,4,8,6,5,7]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7,8]=>[6,1,2,3,4,5,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,6,2,3,4,5,7,8]=>[1,6,2,3,4,5,7,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,2,6,3,4,5,7,8]=>[1,2,6,3,4,5,7,8]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,2,3,6,4,5,7,8]=>[1,2,3,6,4,5,7,8]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,6,7,5,8]=>[1,2,3,4,7,6,5,8]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,6,7,5]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,1,8,2,3,4,5,6]=>[7,8,2,3,4,5,1,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[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]=>[7,1,2,8,3,4,5,6]=>[7,1,8,3,4,5,2,6]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,7,2,8,3,4,5,6]=>[1,7,8,3,4,5,2,6]=>[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,7,8,2,3,4,5,6]=>[1,8,2,3,4,5,7,6]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,1,2,3,8,4,5,6]=>[7,1,2,8,4,5,3,6]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,7,2,3,8,4,5,6]=>[1,7,2,8,4,5,3,6]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,2,7,3,8,4,5,6]=>[1,2,7,8,4,5,3,6]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,2,7,8,3,4,5,6]=>[1,2,8,3,4,5,7,6]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,1,2,3,4,8,5,6]=>[7,1,2,3,8,5,4,6]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,7,2,3,4,8,5,6]=>[1,7,2,3,8,5,4,6]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,2,7,3,4,8,5,6]=>[1,2,7,3,8,5,4,6]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,2,3,7,4,8,5,6]=>[1,2,3,7,8,5,4,6]=>[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,2,3,7,8,4,5,6]=>[1,2,3,8,4,5,7,6]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,8,6]=>[7,1,2,3,4,8,5,6]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,7,2,3,4,5,8,6]=>[1,7,2,3,4,8,5,6]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,2,7,3,4,5,8,6]=>[1,2,7,3,4,8,5,6]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,2,3,7,4,5,8,6]=>[1,2,3,7,4,8,5,6]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,8,6]=>[1,2,3,4,7,8,5,6]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,7,8,5,6]=>[1,2,3,4,8,5,7,6]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,8]=>[7,1,2,3,4,5,6,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,7,2,3,4,5,6,8]=>[1,7,2,3,4,5,6,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,2,7,3,4,5,6,8]=>[1,2,7,3,4,5,6,8]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,2,3,7,4,5,6,8]=>[1,2,3,7,4,5,6,8]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,7,5,6,8]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[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]=>[1,8,2,3,4,5,6,7]=>[1,8,2,3,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,2,8,3,4,5,6,7]=>[1,2,8,3,4,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,2,3,8,4,5,6,7]=>[1,2,3,8,4,5,6,7]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,8,5,6,7]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,8,6,7]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[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]=>[8,1,2,3,4,5,6,7,9]=>[8,1,2,3,4,5,6,7,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1,9]=>[8,2,3,4,5,6,7,1,9]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[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]=>[9,1,2,3,4,5,6,7,8,10]=>[9,1,2,3,4,5,6,7,8,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,9,7]=>[8,1,2,3,4,5,9,6,7]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,8,9]=>[7,1,2,3,4,5,6,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8,9]=>[7,2,3,4,5,6,1,8,9]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,9,1,8]=>[9,2,3,4,5,6,7,1,8]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1,10]=>[9,2,3,4,5,6,7,8,1,10]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[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]=>[10,1,2,3,4,5,6,7,8,9,11]=>[10,1,2,3,4,5,6,7,8,9,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,10,8]=>[9,1,2,3,4,5,6,10,7,8]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7,9,10]=>[8,1,2,3,4,5,6,7,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,9,8]=>[7,1,2,3,4,5,6,9,8]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7,8,9]=>[6,1,2,3,4,5,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,7,8,9]=>[6,2,3,4,5,1,7,8,9]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,9,8]=>[7,2,3,4,5,6,1,9,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,10,1,9]=>[10,2,3,4,5,6,7,8,1,9]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0]=>[10,1,2,3,4,5,6,7,8,11,9]=>[10,1,2,3,4,5,6,7,11,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7,10,9]=>[8,1,2,3,4,5,6,7,10,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,8,9,10]=>[7,1,2,3,4,5,6,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,8,9,6]=>[7,1,2,3,4,9,5,8,6]=>[[.,.],[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,7,8,9]=>[5,1,2,3,4,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,7,8,9]=>[5,2,3,4,1,6,7,8,9]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,9,1,7,8]=>[9,2,3,4,5,6,1,7,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,3,4,5,6,8,1,9,7]=>[8,2,3,4,5,6,9,1,7]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,11,1,10]=>[11,2,3,4,5,6,7,8,9,1,10]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7,8,9,10]=>[6,1,2,3,4,5,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[8,1,2,3,9,4,5,6,7]=>[8,1,2,9,4,5,6,3,7]=>[[.,.],[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,9,7,8]=>[6,1,2,3,4,5,9,7,8]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,8,9,7]=>[6,1,2,3,4,5,9,8,7]=>[[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,7,8,9]=>[4,1,2,3,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[2,3,4,1,5,6,7,8,9]=>[4,2,3,1,5,6,7,8,9]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,10,1,8,9]=>[10,2,3,4,5,6,7,1,8,9]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>[9,2,3,4,5,6,7,10,1,8]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]=>[9,1,2,3,4,10,5,6,7,8]=>[9,1,2,3,10,5,6,7,4,8]=>[[.,.],[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,7,8,9,10]=>[5,1,2,3,4,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7,8,9]=>[3,1,2,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[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]=>[2,3,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[2,3,4,5,9,1,6,7,8]=>[9,2,3,4,5,1,6,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,1,2]=>[9,1,3,4,5,6,7,8,2]=>[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,7,8,9,10]=>[4,1,2,3,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[8,1,9,2,3,4,5,6,7]=>[8,9,2,3,4,5,6,1,7]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,9,6,7,8]=>[5,1,2,3,4,9,6,7,8]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[7,9,1,2,3,4,5,6,8]=>[9,1,2,3,4,5,7,6,8]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,10,1,7,8,9]=>[10,2,3,4,5,6,1,7,8,9]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,9,2]=>[8,9,3,4,5,6,7,1,2]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7,8,9,10]=>[3,1,2,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[9,10,1,2,3,4,5,6,7,8]=>[10,1,2,3,4,5,6,7,9,8]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,8,7,9]=>[4,1,2,3,5,6,8,7,9]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,9,8]=>[2,1,3,4,5,6,7,9,8]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,6,9]=>[8,1,2,3,4,5,7,6,9]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,4,5,6,7,1,8,9,2]=>[7,9,3,4,5,6,1,8,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,4,5,6,7,8,1,9,3]=>[8,2,9,4,5,6,7,1,3]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],[.,.]]
[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]=>[9,1,10,2,3,4,5,6,7,8]=>[9,10,2,3,4,5,6,7,1,8]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[4,1,2,3,9,5,6,7,8]=>[4,1,2,3,9,5,6,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,9,7,8]=>[2,1,3,4,5,6,9,7,8]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[5,9,1,2,3,4,6,7,8]=>[9,1,2,3,5,4,6,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,1,10,2]=>[9,10,3,4,5,6,7,8,1,2]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[]=>[]=>[]=>.
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,7,6,9,8]=>[1,5,3,2,4,7,6,9,8]=>[.,[[[.,.],.],[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,3,9,2,4,5,6,7,8]=>[1,9,3,2,4,5,6,7,8]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]=>[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,3,4,2,5,6,7,8,9]=>[1,4,3,2,5,6,7,8,9]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,3,4,5,6,7,8,9,2]=>[1,9,3,4,5,6,7,8,2]=>[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,7,6,9,8]=>[1,4,5,2,3,7,6,9,8]=>[.,[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,4,2,5,6,7,8,9,3]=>[1,4,9,2,5,6,7,8,3]=>[.,[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,8,7,9]=>[1,4,2,3,6,5,8,7,9]=>[.,[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]=>[.,[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,2,4,9,3,5,6,7,8]=>[1,2,9,4,3,5,6,7,8]=>[.,[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,7,8,9]=>[1,4,2,3,5,6,7,8,9]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,4,5,6,7,8,9,3]=>[1,2,9,4,5,6,7,8,3]=>[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,7,6,9,8]=>[1,2,3,5,4,7,6,9,8]=>[.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,2,3,5,9,4,6,7,8]=>[1,2,3,9,5,4,6,7,8]=>[.,[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,5,6,7,8,9,4]=>[1,2,3,9,5,6,7,8,4]=>[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,6,2,7,3,8,4,9,5]=>[1,6,7,8,9,2,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,8,7,9]=>[1,2,3,4,6,5,8,7,9]=>[.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,6,8,5,7,9]=>[1,2,3,4,8,6,5,7,9]=>[.,[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,6,9,5,7,8]=>[1,2,3,4,9,6,5,7,8]=>[.,[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,6,7,8,9,5]=>[1,2,3,4,9,6,7,8,5]=>[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,7,4,8,5,9,6]=>[1,2,3,7,8,9,4,5,6]=>[.,[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,8,6,9]=>[1,2,3,4,7,8,5,6,9]=>[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,8,9,6]=>[1,2,3,4,7,9,5,8,6]=>[.,[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]=>[1,7,9,2,3,4,5,6,8]=>[1,9,2,3,4,5,7,6,8]=>[.,[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0,0]=>[1,7,2,3,4,5,6,9,8]=>[1,7,2,3,4,5,6,9,8]=>[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,6,9,8]=>[1,2,3,4,7,5,6,9,8]=>[.,[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,7,6,9,8]=>[1,2,3,4,5,7,6,9,8]=>[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,7,9,6,8]=>[1,2,3,4,5,9,7,6,8]=>[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[1,7,2,3,4,5,6,8,9]=>[1,7,2,3,4,5,6,8,9]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,7,8,9,6]=>[1,2,3,4,5,9,7,8,6]=>[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[1,8,9,2,3,4,5,6,7]=>[1,9,2,3,4,5,6,8,7]=>[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,8,9,5,6,7]=>[1,2,3,4,9,5,6,8,7]=>[.,[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[1,8,2,3,4,5,6,9,7]=>[1,8,2,3,4,5,9,6,7]=>[.,[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0,0]=>[1,2,3,8,4,5,6,9,7]=>[1,2,3,8,4,5,9,6,7]=>[.,[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,8,5,6,9,7]=>[1,2,3,4,8,5,9,6,7]=>[.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,8,6,9,7]=>[1,2,3,4,5,8,9,6,7]=>[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,8,9,6,7]=>[1,2,3,4,5,9,6,8,7]=>[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,8,2,3,4,5,6,7,9]=>[1,8,2,3,4,5,6,7,9]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,8,7,9]=>[1,2,3,4,5,6,8,7,9]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,8,9,7]=>[1,2,3,4,5,6,9,8,7]=>[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,9,2,3,4,5,6,7,8]=>[1,9,2,3,4,5,6,7,8]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,2,9,3,4,5,6,7,8]=>[1,2,9,3,4,5,6,7,8]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,2,3,9,4,5,6,7,8]=>[1,2,3,9,4,5,6,7,8]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,2,3,4,9,5,6,7,8]=>[1,2,3,4,9,5,6,7,8]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,9,6,7,8]=>[1,2,3,4,5,9,6,7,8]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,9,7,8]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[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]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>[4,2,6,1,8,3,9,5,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5,9,8]=>[4,2,6,1,7,3,5,9,8]=>[[[.,.],[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,7,6,9,8]=>[4,2,5,1,3,7,6,9,8]=>[[[.,.],[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,7,6,9,8]=>[3,2,1,5,4,7,6,9,8]=>[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5,8,9]=>[4,2,6,1,7,3,5,8,9]=>[[[.,.],[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,6,3,8,5,9,7,10]=>[4,2,6,1,8,3,9,5,7,10]=>[[[.,.],[.,.]],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,8,6,9,7]=>[4,2,5,1,3,8,9,6,7]=>[[[.,.],[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5,9,8,10]=>[4,2,6,1,7,3,5,9,8,10]=>[[[.,.],[.,.]],[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,7,5,9,8]=>[3,2,1,6,7,4,5,9,8]=>[[[.,.],.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,7,6,9,8,10]=>[4,2,5,1,3,7,6,9,8,10]=>[[[.,.],[.,.]],[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,7,6,9,8,10]=>[3,2,1,5,4,7,6,9,8,10]=>[[[.,.],.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,6,8,1,3,5,7,9]=>[8,2,1,4,3,6,5,7,9]=>[[[.,.],.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6,9,8,11,10]=>[1,3,2,5,4,7,6,9,8,11,10]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,4,1,5,3,6,7,8,9]=>[4,2,5,1,3,6,7,8,9]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,8,7,10,9]=>[1,4,2,3,6,5,8,7,10,9]=>[.,[[.,.],[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,9,7,8]=>[2,1,4,3,6,5,9,7,8]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,1,4,3,5,6,7,8,9]=>[2,1,4,3,5,6,7,8,9]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,4,5,6,7,8,9,3]=>[2,1,9,4,5,6,7,8,3]=>[[.,.],[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[2,1,9,3,4,5,6,7,8]=>[2,1,9,3,4,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,9,1,3,4,5,6,7,8]=>[9,2,1,3,4,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,8,7,9]=>[3,4,1,2,6,5,8,7,9]=>[[.,[.,.]],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,8,9,2,5,6,7]=>[3,9,1,4,2,5,6,8,7]=>[[.,[.,.]],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,1,4,2,5,6,7,8,9]=>[3,4,1,2,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,9,2]=>[3,9,1,4,5,6,7,8,2]=>[[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,7,8,9]=>[4,5,6,1,2,3,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,8,4,9]=>[5,6,7,8,1,2,3,4,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[7,1,8,2,9,3,4,5,6]=>[7,8,9,3,4,5,1,2,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]
[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]=>[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,9,7,10,8]=>[2,1,4,3,6,5,9,10,7,8]=>[[.,.],[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,9,10,7,8]=>[2,1,4,3,6,5,10,7,9,8]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,10,7,8,9]=>[2,1,4,3,6,5,10,7,8,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,7,5,8,6,10,9]=>[2,1,4,3,7,8,5,6,10,9]=>[[.,.],[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,8,5,9,6,10,7]=>[2,1,4,3,8,9,10,5,6,7]=>[[.,.],[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[2,1,4,3,10,5,6,7,8,9]=>[2,1,4,3,10,5,6,7,8,9]=>[[.,.],[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,8,7,10,9]=>[2,1,5,6,3,4,8,7,10,9]=>[[.,.],[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,8,7,10,9]=>[2,1,6,3,5,4,8,7,10,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,9,7,10,8]=>[2,1,5,6,3,4,9,10,7,8]=>[[.,.],[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,9,10,7,8]=>[2,1,6,3,5,4,10,7,9,8]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,6,3,7,4,8,5,10,9]=>[2,1,6,7,8,3,4,5,10,9]=>[[.,.],[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,7,3,8,4,9,5,10,6]=>[2,1,7,8,9,10,3,4,5,6]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[2,1,10,3,4,5,6,7,8,9]=>[2,1,10,3,4,5,6,7,8,9]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,10,1,3,4,5,6,7,8,9]=>[10,2,1,3,4,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,8,7,10,9]=>[3,4,1,2,6,5,8,7,10,9]=>[[.,[.,.]],[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,8,7,10,9]=>[4,1,3,2,6,5,8,7,10,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,9,7,10,8]=>[3,4,1,2,6,5,9,10,7,8]=>[[.,[.,.]],[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,8,6,10,9]=>[3,4,1,2,7,8,5,6,10,9]=>[[.,[.,.]],[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,7,8,5,6,10,9]=>[4,1,3,2,8,5,7,6,10,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,8,5,9,6,10,7]=>[3,4,1,2,8,9,10,5,6,7]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,8,9,10,5,6,7]=>[4,1,3,2,10,5,6,8,9,7]=>[[.,.],[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[3,1,4,2,5,6,7,8,9,10]=>[3,4,1,2,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,9,10,2]=>[3,10,1,4,5,6,7,8,9,2]=>[[.,[.,.]],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,8,7,10,9]=>[4,5,6,1,2,3,8,7,10,9]=>[[.,[.,[.,.]]],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,9,7,10,8]=>[4,5,6,1,2,3,9,10,7,8]=>[[.,[.,[.,.]]],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,9,10,7,8]=>[6,1,2,4,5,3,10,7,9,8]=>[[.,.],[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,8,4,10,9]=>[5,6,7,8,1,2,3,4,10,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4,10,9]=>[8,1,2,3,5,6,7,4,10,9]=>[[.,.],[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[6,1,7,2,8,3,9,4,10,5]=>[6,7,8,9,10,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[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]=>[[.,.],[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[8,1,9,2,10,3,4,5,6,7]=>[8,9,10,3,4,5,6,1,2,7]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],[.,[.,.]]]
[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]=>[3,1,5,2,6,4,8,7,9]=>[3,5,1,6,2,4,8,7,9]=>[[.,[.,.]],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,7,6,9,8]=>[3,5,1,2,4,7,6,9,8]=>[[.,[.,.]],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,7,6,9,8]=>[3,1,2,5,4,7,6,9,8]=>[[.,.],[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,8,7,10,9]=>[3,5,1,6,2,4,8,7,10,9]=>[[.,[.,.]],[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,8,6,10,9]=>[3,5,1,7,2,8,4,6,10,9]=>[[.,[.,.]],[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,9,6,10,8]=>[3,5,1,7,2,9,4,10,6,8]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,7,4,6,9,8]=>[3,1,2,7,5,4,6,9,8]=>[[.,.],[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,7,6,9,8,10]=>[3,1,2,5,4,7,6,9,8,10]=>[[.,.],[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,9,10,8]=>[1,2,3,4,5,6,7,10,9,8]=>[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,10,8,9]=>[1,2,3,4,5,6,7,10,8,9]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,10,11,9]=>[1,2,3,4,5,6,7,8,11,10,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,9,7,10,8]=>[1,2,3,4,5,6,9,10,7,8]=>[.,[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,11,9,10]=>[1,2,3,4,5,6,7,8,11,9,10]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,8,7,9]=>[4,1,2,3,6,5,8,7,9]=>[[.,.],[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,3,4,5,6,7,8,9,2]=>[.,[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,10,2,3,4,5,6,7,8,9]=>[1,10,2,3,4,5,6,7,8,9]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,11,2,3,4,5,6,7,8,9,10]=>[1,11,2,3,4,5,6,7,8,9,10]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[1,9,2,3,4,5,6,7,8,10]=>[1,9,2,3,4,5,6,7,8,10]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,9,4,8]=>[5,6,7,9,1,2,3,4,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,8,9,10,7]=>[1,2,3,4,5,6,10,8,9,7]=>[.,[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,7,8,9,10,6]=>[1,2,3,4,5,10,7,8,9,6]=>[.,[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,6,7,8,9,10,5]=>[1,2,3,4,10,6,7,8,9,5]=>[.,[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,5,6,7,8,9,10,4]=>[1,2,3,10,5,6,7,8,9,4]=>[.,[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,4,5,6,7,8,9,10,3]=>[1,2,10,4,5,6,7,8,9,3]=>[.,[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5,8,7,9]=>[3,1,2,4,6,5,8,7,9]=>[[.,.],[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6,10,8,9]=>[1,3,2,5,4,7,6,10,8,9]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,7,6,9,8,10]=>[1,2,3,5,4,7,6,9,8,10]=>[.,[.,[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[1,2,10,3,4,5,6,7,8,9]=>[1,2,10,3,4,5,6,7,8,9]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[1,2,3,10,4,5,6,7,8,9]=>[1,2,3,10,4,5,6,7,8,9]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[1,2,3,4,10,5,6,7,8,9]=>[1,2,3,4,10,5,6,7,8,9]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,10,6,7,8,9]=>[1,2,3,4,5,10,6,7,8,9]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,10,7,8,9]=>[1,2,3,4,5,6,10,7,8,9]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,7,5,9,6,10,8]=>[2,1,4,3,7,9,5,10,6,8]=>[[.,.],[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,9,6,10,8]=>[2,1,5,7,3,9,4,10,6,8]=>[[.,.],[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6,9,10,8]=>[1,3,2,5,4,7,6,10,9,8]=>[.,[[.,.],[[.,.],[[.,.],[[[.,.],.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,8,7,10,9]=>[1,2,4,3,6,5,8,7,10,9]=>[.,[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,9,10,6,7,8]=>[1,2,3,4,5,10,6,7,9,8]=>[.,[.,[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]]]
[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]=>[4,1,2,3,6,5,8,7,10,9]=>[4,1,2,3,6,5,8,7,10,9]=>[[.,.],[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,8,7,10,9]=>[6,1,2,3,4,5,8,7,10,9]=>[[.,.],[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,8,7,10,9]=>[1,2,3,4,6,5,8,7,10,9]=>[.,[.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,1,8,2,9,3]=>[7,8,9,4,5,6,1,2,3]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,6,1,7,3,8,4,9,5]=>[6,2,7,8,9,1,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,4,5,6,7,8,9,1,10,3]=>[9,2,10,4,5,6,7,8,1,3]=>[[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,9,8,10]=>[1,2,3,4,5,6,7,9,8,10]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,10,9,11]=>[1,2,3,4,5,6,7,8,10,9,11]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,8,7,10,9]=>[1,2,3,4,5,6,8,7,10,9]=>[.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7,8,9,10,11]=>[3,1,2,4,5,6,7,8,9,10,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,2,9]=>[3,8,1,4,5,6,7,2,9]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[1,9,10,2,3,4,5,6,7,8]=>[1,10,2,3,4,5,6,7,9,8]=>[.,[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,7,8,9,10]=>[1,2,3,5,4,6,7,8,9,10]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,9,6,7,10,8]=>[1,2,3,4,5,9,6,10,7,8]=>[.,[.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,6,2,8,3,9,5,10,7]=>[4,6,8,1,9,2,10,3,5,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,8,5,10,9]=>[4,6,7,1,8,2,3,5,10,9]=>[[.,[.,[.,.]]],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,8,6,10,9]=>[2,1,5,7,3,8,4,6,10,9]=>[[.,.],[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,9,6,10,8]=>[3,4,1,2,7,9,5,10,6,8]=>[[.,[.,.]],[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[2,3,9,1,4,5,6,7,8]=>[9,2,3,1,4,5,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0,0]=>[2,3,4,10,1,5,6,7,8,9]=>[10,2,3,4,1,5,6,7,8,9]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,6,2,7,4,8,5,10,9]=>[3,6,1,7,8,2,4,5,10,9]=>[[.,[.,.]],[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,7,3,8,6,10,9]=>[4,5,7,1,2,8,3,6,10,9]=>[[.,[.,[.,.]]],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,2,6,3,8,5,9,7]=>[4,1,6,2,8,3,9,5,7]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[2,8,1,3,4,5,6,7,9]=>[8,2,1,3,4,5,6,7,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[2,1,8,3,4,5,6,7,9]=>[2,1,8,3,4,5,6,7,9]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[2,9,1,3,4,5,6,7,8,10]=>[9,2,1,3,4,5,6,7,8,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,8,7,10,9,12,11]=>[4,5,6,1,2,3,8,7,10,9,12,11]=>[[.,[.,[.,.]]],[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,7,8,5,6,11,12,9,10]=>[4,1,3,2,8,5,7,6,12,9,11,10]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,12,10,11]=>[1,2,3,4,5,6,7,8,9,12,10,11]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,7,6,8,9,10]=>[1,2,3,4,5,7,6,8,9,10]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,9,10,11,2]=>[3,11,1,4,5,6,7,8,9,10,2]=>[[.,[.,.]],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,8,7,10,9,12,11]=>[2,1,5,6,3,4,8,7,10,9,12,11]=>[[.,.],[[.,[.,.]],[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8,10,9]=>[2,1,3,4,5,6,7,8,10,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,8,7,10,9,12,11]=>[3,5,1,6,2,4,8,7,10,9,12,11]=>[[.,[.,.]],[[.,.],[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[3,1,2,9,4,5,6,7,8]=>[3,1,2,9,4,5,6,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[2,11,1,3,4,5,6,7,8,9,10]=>[11,2,1,3,4,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,9,10,2]=>[8,10,3,4,5,6,7,1,9,2]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,8,7,10,9,12,11]=>[3,4,1,2,6,5,8,7,10,9,12,11]=>[[.,[.,.]],[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,7,2,8,3,9,5,10,6]=>[4,7,8,1,9,10,2,3,5,6]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
Map
to 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
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.