Identifier
Mp00025:
Dyck paths
—to 132-avoiding permutation⟶
Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00016: Binary trees —left-right symmetry⟶ Binary trees
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00016: Binary trees —left-right symmetry⟶ Binary trees
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-2Cc0010;cc-rep-3
[1,0]=>[1]=>[.,.]=>[.,.]
[1,0,1,0]=>[2,1]=>[[.,.],.]=>[.,[.,.]]
[1,1,0,0]=>[1,2]=>[.,[.,.]]=>[[.,.],.]
[1,0,1,0,1,0]=>[3,2,1]=>[[[.,.],.],.]=>[.,[.,[.,.]]]
[1,0,1,1,0,0]=>[2,3,1]=>[[.,[.,.]],.]=>[.,[[.,.],.]]
[1,1,0,0,1,0]=>[3,1,2]=>[[.,.],[.,.]]=>[[.,.],[.,.]]
[1,1,0,1,0,0]=>[2,1,3]=>[[.,.],[.,.]]=>[[.,.],[.,.]]
[1,1,1,0,0,0]=>[1,2,3]=>[.,[.,[.,.]]]=>[[[.,.],.],.]
[1,0,1,0,1,0,1,0]=>[4,3,2,1]=>[[[[.,.],.],.],.]=>[.,[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0]=>[3,4,2,1]=>[[[.,[.,.]],.],.]=>[.,[.,[[.,.],.]]]
[1,0,1,1,0,0,1,0]=>[4,2,3,1]=>[[[.,.],[.,.]],.]=>[.,[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0]=>[3,2,4,1]=>[[[.,.],[.,.]],.]=>[.,[[.,.],[.,.]]]
[1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]=>[.,[[[.,.],.],.]]
[1,1,0,0,1,0,1,0]=>[4,3,1,2]=>[[[.,.],.],[.,.]]=>[[.,.],[.,[.,.]]]
[1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[[.,[.,.]],[.,.]]=>[[.,.],[[.,.],.]]
[1,1,0,1,0,0,1,0]=>[4,2,1,3]=>[[[.,.],.],[.,.]]=>[[.,.],[.,[.,.]]]
[1,1,0,1,0,1,0,0]=>[3,2,1,4]=>[[[.,.],.],[.,.]]=>[[.,.],[.,[.,.]]]
[1,1,0,1,1,0,0,0]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]=>[[.,.],[[.,.],.]]
[1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]=>[[[.,.],.],[.,.]]
[1,1,1,0,0,1,0,0]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]=>[[[.,.],.],[.,.]]
[1,1,1,0,1,0,0,0]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]=>[[[.,.],.],[.,.]]
[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]=>[[[[.,.],.],.],.]
[1,0,1,0,1,0,1,0,1,0]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]=>[.,[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0]=>[4,5,3,2,1]=>[[[[.,[.,.]],.],.],.]=>[.,[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,0]=>[5,3,4,2,1]=>[[[[.,.],[.,.]],.],.]=>[.,[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,1,0,0]=>[4,3,5,2,1]=>[[[[.,.],[.,.]],.],.]=>[.,[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,0]=>[3,4,5,2,1]=>[[[.,[.,[.,.]]],.],.]=>[.,[.,[[[.,.],.],.]]]
[1,0,1,1,0,0,1,0,1,0]=>[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.]=>[.,[[.,.],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0]=>[4,5,2,3,1]=>[[[.,[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,0]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]=>[.,[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,0]=>[4,3,2,5,1]=>[[[[.,.],.],[.,.]],.]=>[.,[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,0]=>[3,4,2,5,1]=>[[[.,[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],.]]]
[1,0,1,1,1,0,0,0,1,0]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,0,1,0,0]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,1,0,0,0]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,.]]]
[1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0]=>[5,4,3,1,2]=>[[[[.,.],.],.],[.,.]]=>[[.,.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,0]=>[5,3,4,1,2]=>[[[.,.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,0,0]=>[4,3,5,1,2]=>[[[.,.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,.]]]
[1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>[[.,[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],.]]
[1,1,0,1,0,0,1,0,1,0]=>[5,4,2,1,3]=>[[[[.,.],.],.],[.,.]]=>[[.,.],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0]=>[4,5,2,1,3]=>[[[.,[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,0]=>[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]]=>[[.,.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]=>[[.,.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0]=>[3,4,2,1,5]=>[[[.,[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],.]]]
[1,1,0,1,1,0,0,0,1,0]=>[5,2,3,1,4]=>[[[.,.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,.]]]
[1,1,0,1,1,0,0,1,0,0]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,.]]]
[1,1,0,1,1,1,0,0,0,0]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],.]]
[1,1,1,0,0,0,1,0,1,0]=>[5,4,1,2,3]=>[[[.,.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>[[.,[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],.]]
[1,1,1,0,0,1,0,0,1,0]=>[5,3,1,2,4]=>[[[.,.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,0]=>[4,3,1,2,5]=>[[[.,.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,0]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],.]]
[1,1,1,0,1,0,0,0,1,0]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],.]]
[1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,.]]
[1,1,1,1,0,0,0,1,0,0]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,.]]
[1,1,1,1,0,0,1,0,0,0]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,.]]
[1,1,1,1,0,1,0,0,0,0]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,.]]
[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,2,1]=>[[[[[.,[.,.]],.],.],.],.]=>[.,[.,[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,2,1]=>[[[[[.,.],[.,.]],.],.],.]=>[.,[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,2,1]=>[[[[[.,.],[.,.]],.],.],.]=>[.,[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,2,1]=>[[[[.,[.,[.,.]]],.],.],.]=>[.,[.,[.,[[[.,.],.],.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,2,1]=>[[[[.,[.,.]],[.,.]],.],.]=>[.,[.,[[.,.],[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,2,1]=>[[[[[.,.],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,2,1]=>[[[[[.,.],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,2,1]=>[[[[.,[.,.]],[.,.]],.],.]=>[.,[.,[[.,.],[[.,.],.]]]]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,2,1]=>[[[[.,.],[.,[.,.]]],.],.]=>[.,[.,[[[.,.],.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,2,1]=>[[[[.,.],[.,[.,.]]],.],.]=>[.,[.,[[[.,.],.],[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[[[[.,.],[.,[.,.]]],.],.]=>[.,[.,[[[.,.],.],[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,2,1]=>[[[.,[.,[.,[.,.]]]],.],.]=>[.,[.,[[[[.,.],.],.],.]]]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,3,1]=>[[[[[.,.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,3,1]=>[[[[.,[.,.]],.],[.,.]],.]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,3,1]=>[[[[.,.],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,3,1]=>[[[.,[.,[.,.]]],[.,.]],.]=>[.,[[.,.],[[[.,.],.],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,4,1]=>[[[[[.,.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,4,1]=>[[[[.,[.,.]],.],[.,.]],.]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,6,1]=>[[[[[.,.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,6,1]=>[[[[.,[.,.]],.],[.,.]],.]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,5,1]=>[[[[.,.],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,6,1]=>[[[[.,.],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,6,1]=>[[[[.,.],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,6,1]=>[[[.,[.,[.,.]]],[.,.]],.]=>[.,[[.,.],[[[.,.],.],.]]]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,4,1]=>[[[[.,.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,4,1]=>[[[.,[.,.]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,5,1]=>[[[[.,.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,6,1]=>[[[[.,.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,6,1]=>[[[.,[.,.]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,6,1]=>[[[[.,.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,6,1]=>[[[[.,.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,6,1]=>[[[.,[.,.]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[.,.],.]]]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,6,1]=>[[[.,.],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,6,1]=>[[[.,.],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,6,1]=>[[[.,.],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[[.,[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[6,5,4,3,1,2]=>[[[[[.,.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[5,6,4,3,1,2]=>[[[[.,[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[6,4,5,3,1,2]=>[[[[.,.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[5,4,6,3,1,2]=>[[[[.,.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,3,1,2]=>[[[.,[.,[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],.],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[6,5,3,4,1,2]=>[[[[.,.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[6,4,3,5,1,2]=>[[[[.,.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[5,4,3,6,1,2]=>[[[[.,.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,3,6,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[6,3,4,5,1,2]=>[[[.,.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[5,3,4,6,1,2]=>[[[.,.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[4,3,5,6,1,2]=>[[[.,.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],.]]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[6,5,4,2,1,3]=>[[[[[.,.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[5,6,4,2,1,3]=>[[[[.,[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[6,4,5,2,1,3]=>[[[[.,.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[5,4,6,2,1,3]=>[[[[.,.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[4,5,6,2,1,3]=>[[[.,[.,[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[6,5,3,2,1,4]=>[[[[[.,.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[5,6,3,2,1,4]=>[[[[.,[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[6,4,3,2,1,5]=>[[[[[.,.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[4,5,3,2,1,6]=>[[[[.,[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[6,3,4,2,1,5]=>[[[[.,.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[5,3,4,2,1,6]=>[[[[.,.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[4,3,5,2,1,6]=>[[[[.,.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,2,1,6]=>[[[.,[.,[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],.],.]]]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[6,5,2,3,1,4]=>[[[[.,.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[5,6,2,3,1,4]=>[[[.,[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[6,4,2,3,1,5]=>[[[[.,.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[5,4,2,3,1,6]=>[[[[.,.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[4,5,2,3,1,6]=>[[[.,[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[6,3,2,4,1,5]=>[[[[.,.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[5,3,2,4,1,6]=>[[[[.,.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[4,3,2,5,1,6]=>[[[[.,.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,2,5,1,6]=>[[[.,[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[6,2,3,4,1,5]=>[[[.,.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,.]]]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[5,2,3,4,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[4,2,3,5,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[3,2,4,5,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,.]]]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6]=>[[.,[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],.]]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[6,5,4,1,2,3]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[5,6,4,1,2,3]=>[[[.,[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[6,4,5,1,2,3]=>[[[.,.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[5,4,6,1,2,3]=>[[[.,.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],.]]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[6,5,3,1,2,4]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[5,6,3,1,2,4]=>[[[.,[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[6,4,3,1,2,5]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[5,4,3,1,2,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[4,5,3,1,2,6]=>[[[.,[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[6,3,4,1,2,5]=>[[[.,.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[5,3,4,1,2,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[4,3,5,1,2,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],.]]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[6,5,2,1,3,4]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[5,6,2,1,3,4]=>[[[.,[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[6,4,2,1,3,5]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[5,4,2,1,3,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,5,2,1,3,6]=>[[[.,[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[6,3,2,1,4,5]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[5,3,2,1,4,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,2,1,5,6]=>[[[.,[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],.]]]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[6,2,3,1,4,5]=>[[[.,.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[5,2,3,1,4,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[4,2,3,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,2,4,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],.]]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[6,5,1,2,3,4]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],.]]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[6,4,1,2,3,5]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[5,4,1,2,3,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,3,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],.]]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[6,3,1,2,4,5]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[5,3,1,2,4,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,1,2,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],.]]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[6,2,1,3,4,5]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,2,1,3,4,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,2,1,3,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,1,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,4,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,3,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,2,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,2,1]=>[[[[[[.,[.,.]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,2,1]=>[[[[[[.,.],[.,.]],.],.],.],.]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,2,1]=>[[[[[[.,.],[.,.]],.],.],.],.]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,2,1]=>[[[[[.,[.,[.,.]]],.],.],.],.]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,2,1]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,2,1]=>[[[[[[.,.],.],[.,.]],.],.],.]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,2,1]=>[[[[[.,[.,.]],[.,.]],.],.],.]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,2,1]=>[[[[[.,.],[.,[.,.]]],.],.],.]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[[[[.,[.,[.,[.,.]]]],.],.],.]=>[.,[.,[.,[[[[.,.],.],.],.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,2,1]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,2,1]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[.,[.,[[.,.],[[[.,.],.],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,2,1]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,2,1]=>[[[[[.,[.,.]],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[[[[[.,.],[.,.]],[.,.]],.],.]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,2,1]=>[[[[.,[.,[.,.]]],[.,.]],.],.]=>[.,[.,[[.,.],[[[.,.],.],.]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[.,[.,[[[.,.],.],[[.,.],.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,2,1]=>[[[[.,[.,.]],[.,[.,.]]],.],.]=>[.,[.,[[[.,.],.],[[.,.],.]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
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[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[.,[.,.]]]]
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[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,3,1,2]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,3,1,2]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,3,1,2]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,3,1,2]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,3,1,2]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,3,1,2]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,3,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,3,1,2]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,3,1,2]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,3,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,3,1,2]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,3,1,2]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,3,1,2]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,3,1,2]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[[.,.],[.,[[[[.,.],.],.],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,4,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,4,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,4,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,4,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,4,1,2]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,5,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,6,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,7,1,2]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,7,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,6,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,7,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,7,1,2]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,7,1,2]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,5,1,2]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,6,1,2]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,7,1,2]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,7,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,6,1,2]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,7,1,2]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,7,1,2]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,7,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,6,1,2]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,7,1,2]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,7,1,2]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,7,1,2]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[[.,.],[[[[[.,.],.],.],.],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,2,1,3]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,2,1,3]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,2,1,3]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,2,1,3]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,2,1,3]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,2,1,3]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,2,1,3]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,2,1,3]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,2,1,3]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,2,1,3]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,2,1,3]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,2,1,3]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,2,1,3]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[[.,.],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,2,1,4]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,2,1,4]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,2,1,4]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,2,1,4]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,2,1,4]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,2,1,5]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,2,1,5]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,2,1,6]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,2,1,7]=>[[[[[.,[.,.]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,2,1,6]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,2,1,7]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,2,1,7]=>[[[[[.,.],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,2,1,7]=>[[[[.,[.,[.,.]]],.],.],[.,.]]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,2,1,5]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,2,1,5]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,2,1,6]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,2,1,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,2,1,6]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,2,1,7]=>[[[[.,[.,.]],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,2,1,6]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,2,1,7]=>[[[[.,.],[.,[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,2,1,7]=>[[[.,[.,[.,[.,.]]]],.],[.,.]]=>[[.,.],[.,[[[[.,.],.],.],.]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,3,1,4]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,3,1,4]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,3,1,4]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,3,1,4]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,3,1,4]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,3,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,3,1,5]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,3,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,3,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,3,1,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,3,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,3,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,3,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,3,1,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,4,1,5]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,4,1,5]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,4,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,4,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,4,1,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,5,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,5,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,6,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,6,1,7]=>[[[[.,[.,.]],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,5,1,6]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,5,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,6,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,6,1,7]=>[[[[.,.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,6,1,7]=>[[[.,[.,[.,.]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,4,1,5]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,4,1,5]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,4,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,4,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,4,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,5,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,6,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,5,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,6,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,6,1,7]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,5,1,6]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,5,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]=>[[.,.],[[[[[.,.],.],.],.],.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[7,6,5,4,1,2,3]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[6,7,5,4,1,2,3]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[7,5,6,4,1,2,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[6,5,7,4,1,2,3]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[7,6,4,5,1,2,3]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[6,7,4,5,1,2,3]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[7,5,4,6,1,2,3]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[6,5,4,7,1,2,3]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,4,7,1,2,3]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[7,4,5,6,1,2,3]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[6,4,5,7,1,2,3]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[5,4,6,7,1,2,3]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[[[.,.],.],[[[[.,.],.],.],.]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[7,6,5,3,1,2,4]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[6,7,5,3,1,2,4]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[7,5,6,3,1,2,4]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[6,5,7,3,1,2,4]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,3,1,2,4]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[7,6,4,3,1,2,5]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[6,7,4,3,1,2,5]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[7,5,4,3,1,2,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[6,5,4,3,1,2,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[5,6,4,3,1,2,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[7,4,5,3,1,2,6]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[6,4,5,3,1,2,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[5,4,6,3,1,2,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,5,6,3,1,2,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[7,6,3,4,1,2,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[6,7,3,4,1,2,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[7,5,3,4,1,2,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[6,5,3,4,1,2,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[5,6,3,4,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[7,4,3,5,1,2,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[6,4,3,5,1,2,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[5,4,3,6,1,2,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,5,3,6,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[7,3,4,5,1,2,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[6,3,4,5,1,2,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[5,3,4,6,1,2,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,3,5,6,1,2,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,1,2,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[[[.,.],.],[[[[.,.],.],.],.]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[7,6,5,2,1,3,4]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[6,7,5,2,1,3,4]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[7,5,6,2,1,3,4]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[6,5,7,2,1,3,4]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,7,2,1,3,4]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[7,6,4,2,1,3,5]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[6,7,4,2,1,3,5]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[7,5,4,2,1,3,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[6,5,4,2,1,3,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[5,6,4,2,1,3,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[7,4,5,2,1,3,6]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[6,4,5,2,1,3,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[5,4,6,2,1,3,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,5,6,2,1,3,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[7,6,3,2,1,4,5]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[6,7,3,2,1,4,5]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[7,5,3,2,1,4,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[6,5,3,2,1,4,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[5,6,3,2,1,4,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[7,4,3,2,1,5,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[6,4,3,2,1,5,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,3,2,1,6,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[7,3,4,2,1,5,6]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[6,3,4,2,1,5,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[5,3,4,2,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,3,5,2,1,6,7]=>[[[[.,.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,5,2,1,6,7]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[7,6,2,3,1,4,5]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[6,7,2,3,1,4,5]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[7,5,2,3,1,4,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[6,5,2,3,1,4,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[5,6,2,3,1,4,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[7,4,2,3,1,5,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[6,4,2,3,1,5,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[5,4,2,3,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,5,2,3,1,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[7,3,2,4,1,5,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[6,3,2,4,1,5,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[5,3,2,4,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,3,2,5,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,4,2,5,1,6,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[7,2,3,4,1,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[6,2,3,4,1,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[5,2,3,4,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,2,3,5,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,2,4,5,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,1,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]=>[[[.,.],.],[[[[.,.],.],.],.]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[7,6,5,1,2,3,4]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[6,7,5,1,2,3,4]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[7,5,6,1,2,3,4]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[6,5,7,1,2,3,4]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],.]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[7,6,4,1,2,3,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[6,7,4,1,2,3,5]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[7,5,4,1,2,3,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[6,5,4,1,2,3,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[5,6,4,1,2,3,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[7,4,5,1,2,3,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[6,4,5,1,2,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[5,4,6,1,2,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],.]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[7,6,3,1,2,4,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[6,7,3,1,2,4,5]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[7,5,3,1,2,4,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[6,5,3,1,2,4,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[5,6,3,1,2,4,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[7,4,3,1,2,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[6,4,3,1,2,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[5,4,3,1,2,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,5,3,1,2,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[7,3,4,1,2,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[6,3,4,1,2,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[5,3,4,1,2,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,5,1,2,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,4,5,1,2,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],.]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[7,6,2,1,3,4,5]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[6,7,2,1,3,4,5]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[7,5,2,1,3,4,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[6,5,2,1,3,4,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,6,2,1,3,4,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[7,4,2,1,3,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[6,4,2,1,3,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,4,2,1,3,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,2,1,3,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[7,3,2,1,4,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[6,3,2,1,4,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,3,2,1,4,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[3,4,2,1,5,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[7,2,3,1,4,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[6,2,3,1,4,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,2,3,1,4,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,2,3,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,2,4,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],.]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[7,6,1,2,3,4,5]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[7,5,1,2,3,4,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[6,5,1,2,3,4,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,6,1,2,3,4,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],.]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[7,4,1,2,3,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[6,4,1,2,3,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,1,2,3,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[4,5,1,2,3,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],.]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[7,3,1,2,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[6,3,1,2,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,3,1,2,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,3,1,2,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[7,2,1,3,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,2,1,3,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,2,1,3,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,2,1,3,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,.]]
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[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,4,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,.]]
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[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,.]]
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[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,6,2,1]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,6,2,1]=>[[[[.,[.,.]],[.,[.,[.,.]]]],.],.]=>[.,[.,[[[[.,.],.],.],[[.,.],.]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,8,2,1]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,6,7,2,1]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,8,2,1]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,7,8,2,1]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,7,2,1]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,8,2,1]=>[[[[[.,.],.],[.,[.,[.,.]]]],.],.]=>[.,[.,[[[[.,.],.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,7,2,1]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[.,[.,[[[[[.,.],.],.],.],[.,.]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,8,2,1]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[.,[.,[[[[[.,.],.],.],.],[.,.]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,8,2,1]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[.,[.,[[[[[.,.],.],.],.],[.,.]]]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,7,8,2,1]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[.,[.,[[[[[.,.],.],.],.],[.,.]]]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,8,2,1]=>[[[[.,.],[.,[.,[.,[.,.]]]]],.],.]=>[.,[.,[[[[[.,.],.],.],.],[.,.]]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,2,1]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.]=>[.,[.,[[[[[[.,.],.],.],.],.],.]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,3,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,2,3,1]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,3,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,2,3,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,2,3,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,2,3,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,2,3,1]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,2,3,1]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,2,3,1]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,2,3,1]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,2,3,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,2,3,1]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,2,3,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,2,3,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,2,3,1]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,2,3,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,2,3,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,2,3,1]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,2,3,1]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[.,[[.,.],[[[[.,.],.],.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,2,3,1]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[.,[[.,.],[[[[[.,.],.],.],.],.]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,4,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,2,4,1]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,2,4,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,2,4,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,2,4,1]=>[[[[[.,[.,[.,.]]],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,4,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,2,4,1]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,2,4,1]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,2,4,1]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,2,5,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,2,5,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,2,6,1]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,7,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,8,1]=>[[[[[[[.,.],.],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,2,8,1]=>[[[[[[.,[.,.]],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,2,8,1]=>[[[[[[.,.],[.,.]],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,2,8,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,2,8,1]=>[[[[[.,[.,.]],[.,.]],.],[.,.]],.]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,3,2,7,1]=>[[[[[[.,.],.],[.,.]],.],[.,.]],.]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,2,8,1]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,3,2,8,1]=>[[[[[.,.],[.,[.,.]]],.],[.,.]],.]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,2,8,1]=>[[[[.,[.,[.,[.,.]]]],.],[.,.]],.]=>[.,[[.,.],[.,[[[[.,.],.],.],.]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,2,5,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,2,5,1]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,2,5,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,4,2,5,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,2,5,1]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,2,6,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,2,6,1]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,2,8,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,2,7,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,2,8,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,2,8,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,2,6,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,2,6,1]=>[[[[[.,[.,.]],.],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,5,2,7,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,5,2,8,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,2,8,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,2,8,1]=>[[[[[[.,.],.],.],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,2,7,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,6,2,8,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[6,4,5,3,7,2,8,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,2,8,1]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,2,8,1]=>[[[[.,[.,[.,.]]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,5,2,7,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,2,8,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,2,8,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,7,2,8,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,2,8,1]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,2,7,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,2,8,1]=>[[[[[.,.],.],[.,[.,.]]],[.,.]],.]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,2,8,1]=>[[[[.,[.,.]],[.,[.,.]]],[.,.]],.]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,2,8,1]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[.,[[.,.],[[[[.,.],.],.],[.,.]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,2,8,1]=>[[[[.,.],[.,[.,[.,.]]]],[.,.]],.]=>[.,[[.,.],[[[[.,.],.],.],[.,.]]]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,2,8,1]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],.]=>[.,[[.,.],[[[[[.,.],.],.],.],.]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,3,4,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,2,3,4,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,3,4,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,3,4,1]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,3,4,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,3,4,1]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,3,4,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,3,4,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,3,4,1]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,3,4,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,3,4,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,3,4,1]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,3,5,1]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,2,3,6,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,3,7,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,3,8,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,2,3,8,1]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,2,3,7,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,2,3,8,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,2,3,8,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,2,3,8,1]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,2,3,8,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,2,3,8,1]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,2,3,8,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,2,3,8,1]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,2,3,8,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,2,3,8,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,3,8,1]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,4,5,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,2,4,5,1]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,2,4,5,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,4,5,1]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,4,6,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,2,4,7,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,2,4,8,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[6,7,5,3,2,4,8,1]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,2,4,8,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,5,6,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,5,6,1]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,5,8,1]=>[[[[[.,[.,.]],.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2,6,7,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,2,6,8,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,7,8,1]=>[[[[[[.,.],.],.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,2,6,7,1]=>[[[[[.,.],[.,.]],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,2,7,8,1]=>[[[[.,[.,[.,.]]],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,5,6,1]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,2,6,7,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,2,7,8,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,2,6,8,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,7,8,1]=>[[[[[.,.],.],[.,.]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,2,6,7,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,2,7,8,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,2,7,8,1]=>[[[[.,.],[.,[.,.]]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,7,8,1]=>[[[.,[.,[.,[.,.]]]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[[[.,.],.],.],.]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,4,5,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,2,3,4,5,1]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,3,4,5,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,2,3,4,5,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,4,5,1]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,4,8,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,2,3,4,8,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,3,4,8,1]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,3,5,6,1]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,5,7,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,5,8,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,2,3,6,7,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[7,5,4,2,3,6,8,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,2,3,7,8,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,2,3,6,8,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[6,4,5,2,3,7,8,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,5,6,2,3,7,8,1]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,4,5,6,1]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,4,5,8,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,4,5,8,1]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,4,6,8,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[6,5,3,2,4,7,8,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[8,4,3,2,5,6,7,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,2,5,6,8,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,7,8,1]=>[[[[[.,.],.],.],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,6,7,8,1]=>[[[[.,[.,.]],.],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,2,5,6,7,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,2,6,7,8,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,6,7,8,1]=>[[[[.,.],[.,.]],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,6,7,8,1]=>[[[.,[.,[.,.]]],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[[[.,.],.],.]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,4,5,6,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,4,5,6,1]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[8,6,2,3,4,5,7,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,5,8,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,4,5,8,1]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,3,4,6,8,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,3,4,7,8,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,3,5,6,7,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,6,7,8,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,6,7,8,1]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,4,5,6,7,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,4,5,6,8,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,6,7,8,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,6,7,8,1]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,6,7,8,1]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],[[.,.],.]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,6,8,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,5,7,8,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,6,7,8,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,6,7,8,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],.],[.,.]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[.,[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,3,1,2]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,3,1,2]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,3,1,2]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,3,1,2]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,3,1,2]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,3,1,2]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,3,1,2]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,3,1,2]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,3,1,2]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,3,1,2]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,3,1,2]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,3,1,2]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,3,1,2]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,3,1,2]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,5,3,1,2]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,3,1,2]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,3,1,2]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,3,1,2]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,3,1,2]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,3,1,2]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,3,1,2]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,3,1,2]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,3,1,2]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,3,1,2]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,3,1,2]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,3,1,2]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[8,5,4,6,7,3,1,2]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,3,1,2]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,3,1,2]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,3,1,2]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,3,1,2]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,4,1,2]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,4,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,4,1,2]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,4,1,2]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,4,1,2]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,4,1,2]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,4,1,2]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,4,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,4,1,2]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,4,1,2]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,4,1,2]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,4,1,2]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,5,1,2]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,6,1,2]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,7,1,2]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,8,1,2]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,8,1,2]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,8,1,2]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,3,6,1,2]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,3,6,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,8,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,8,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,3,8,1,2]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,8,1,2]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,5,1,2]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,5,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,5,1,2]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,4,6,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,8,1,2]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,5,6,1,2]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,5,6,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,5,8,1,2]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,7,1,2]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,8,1,2]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,8,1,2]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,7,8,1,2]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,8,1,2]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,7,8,1,2]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,6,1,2]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,8,1,2]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,6,7,1,2]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,6,8,1,2]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,8,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,7,1,2]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,7,8,1,2]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,8,1,2]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,7,8,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,7,1,2]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,6,8,1,2]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,8,1,2]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,7,8,1,2]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,8,1,2]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,2,1,3]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,2,1,3]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,2,1,3]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,2,1,3]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,4,2,1,3]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,2,1,3]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,2,1,3]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,2,1,3]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,2,1,3]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,2,1,3]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,2,1,3]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,2,1,3]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,5,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,2,1,3]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,2,1,3]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,2,1,3]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,2,1,3]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,2,1,3]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,2,1,3]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,2,1,3]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,2,1,3]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,2,1,3]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,2,1,3]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,2,1,4]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,2,1,4]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,2,1,4]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,2,1,4]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,3,2,1,4]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,2,1,4]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,2,1,4]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,2,1,4]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,3,2,1,4]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,2,1,4]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,2,1,4]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,2,1,4]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,2,1,5]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,3,2,1,5]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,3,2,1,5]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,3,2,1,5]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,2,1,5]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,2,1,6]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,2,1,6]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,2,1,7]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,2,1,8]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,2,1,8]=>[[[[[[.,[.,.]],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,3,2,1,7]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,2,1,8]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,3,2,1,8]=>[[[[[[.,.],[.,.]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,3,2,1,8]=>[[[[[.,[.,[.,.]]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,3,2,1,6]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,3,2,1,6]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,3,2,1,7]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,2,1,8]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,3,2,1,8]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,3,2,1,8]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,3,2,1,8]=>[[[[[[.,.],.],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,3,2,1,8]=>[[[[[.,[.,.]],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,3,2,1,7]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,3,2,1,8]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1,8]=>[[[[[.,.],[.,[.,.]]],.],.],[.,.]]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,2,1,8]=>[[[[.,[.,[.,[.,.]]]],.],.],[.,.]]=>[[.,.],[.,[.,[[[[.,.],.],.],.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,2,1,5]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,2,1,5]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,2,1,5]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,2,1,6]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,4,2,1,7]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,2,1,8]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[6,7,5,3,4,2,1,8]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,2,1,7]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[7,5,6,3,4,2,1,8]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,2,1,8]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,4,2,1,8]=>[[[[.,[.,[.,.]]],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,5,2,1,8]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,5,2,1,8]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,6,2,1,8]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,2,1,8]=>[[[[[[.,.],.],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,7,2,1,8]=>[[[[[.,[.,.]],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,6,2,1,7]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,7,2,1,8]=>[[[[[.,.],[.,.]],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,2,1,6]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,2,1,6]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,5,2,1,8]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,2,1,7]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,7,2,1,8]=>[[[[[.,.],.],[.,[.,.]]],.],[.,.]]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,2,1,7]=>[[[[.,.],[.,[.,[.,.]]]],.],[.,.]]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,2,1,8]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,.]]=>[[.,.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,3,1,4]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,2,3,1,4]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,2,3,1,4]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,3,1,4]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,3,1,4]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,3,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,3,1,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,3,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,3,1,4]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,3,1,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,3,1,4]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,2,3,1,4]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,3,1,4]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,3,1,4]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,3,1,5]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,3,1,5]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,3,1,7]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,3,1,8]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,2,3,1,8]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,2,3,1,7]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,2,3,1,8]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,2,3,1,8]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,2,3,1,6]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,2,3,1,6]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,2,3,1,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,2,3,1,8]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,2,3,1,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,2,3,1,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,2,3,1,8]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,2,3,1,7]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,2,3,1,8]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,3,1,8]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,4,1,5]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,2,4,1,5]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,4,1,5]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,4,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,2,4,1,7]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,2,4,1,8]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,2,4,1,8]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,2,4,1,8]=>[[[[.,[.,[.,.]]],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,5,1,6]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,5,1,6]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,5,1,8]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2,6,1,7]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,2,6,1,8]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,7,1,8]=>[[[[[[.,.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,2,7,1,8]=>[[[[[.,[.,.]],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,2,6,1,8]=>[[[[[.,.],[.,.]],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,2,5,1,6]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,5,1,6]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,2,5,1,8]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[7,5,3,4,2,6,1,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,2,7,1,8]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,2,6,1,7]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,2,6,1,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,2,7,1,8]=>[[[[[.,.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,5,3,6,2,7,1,8]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,2,7,1,8]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[5,3,4,6,2,7,1,8]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,2,7,1,8]=>[[[[.,.],[.,[.,.]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,7,1,8]=>[[[.,[.,[.,[.,.]]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[[.,.],.],.],.]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,4,1,5]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,3,4,1,5]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,2,3,4,1,5]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,4,1,5]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,2,3,4,1,6]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,3,4,1,7]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,4,1,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,2,3,4,1,8]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,3,4,1,7]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,2,3,4,1,8]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,2,3,4,1,8]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,3,4,1,8]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,5,1,7]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,5,1,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[6,7,4,2,3,5,1,8]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,2,3,6,1,7]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[8,4,5,2,3,6,1,7]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,3,7,1,8]=>[[[[.,.],[.,.]],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,4,5,1,7]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,4,5,1,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,4,5,1,8]=>[[[[.,[.,.]],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,2,4,6,1,7]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,4,6,1,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[6,5,3,2,4,7,1,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,7,1,8]=>[[[[[.,.],.],.],[.,[.,.]]],[.,.]]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,4,5,1,6]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,4,5,1,6]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,5,1,8]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,4,5,1,8]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,3,4,6,1,7]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[7,4,2,3,5,6,1,8]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,3,5,7,1,8]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,6,7,1,8]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,4,5,6,1,7]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,6,7,1,8]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,6,7,1,8]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,5,6,1,7]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,6,1,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,6,7,1,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,6,7,1,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,6,7,1,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]=>[[.,.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[[.,.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,4,1,2,3]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,4,1,2,3]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,4,1,2,3]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,4,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,4,1,2,3]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,4,1,2,3]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,4,1,2,3]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,4,1,2,3]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,4,1,2,3]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,4,1,2,3]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,4,1,2,3]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,4,1,2,3]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,5,1,2,3]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,5,1,2,3]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,5,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,6,1,2,3]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,6,1,2,3]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,8,1,2,3]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,8,1,2,3]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,7,1,2,3]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,8,1,2,3]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,8,1,2,3]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,8,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[8,7,4,5,6,1,2,3]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,6,1,2,3]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,7,1,2,3]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,8,1,2,3]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[6,7,4,5,8,1,2,3]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,8,1,2,3]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[6,5,4,7,8,1,2,3]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,8,1,2,3]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,7,1,2,3]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,8,1,2,3]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[6,4,5,7,8,1,2,3]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,8,1,2,3]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,1,2,3]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,3,1,2,4]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,3,1,2,4]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,3,1,2,4]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,3,1,2,4]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,3,1,2,4]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,3,1,2,4]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,3,1,2,4]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,3,1,2,4]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,3,1,2,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,3,1,2,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,3,1,2,4]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,3,1,2,5]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,3,1,2,5]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,3,1,2,6]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,3,1,2,6]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,3,1,2,7]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,3,1,2,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[6,7,5,4,3,1,2,8]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[7,5,6,4,3,1,2,8]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,3,1,2,7]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,3,1,2,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,3,1,2,8]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,3,1,2,8]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,4,1,2,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,4,1,2,5]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,4,1,2,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,4,1,2,5]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,4,1,2,6]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,4,1,2,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,4,1,2,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,4,1,2,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,1,0,0,0]=>[6,5,7,3,4,1,2,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,6,1,2,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,7,1,2,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,5,1,2,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,5,1,2,6]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,5,1,2,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,6,1,2,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,7,1,2,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,6,1,2,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,6,1,2,7]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,7,1,2,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,7,1,2,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,1,2,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,2,1,3,4]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,2,1,3,4]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,2,1,3,4]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,2,1,3,4]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,2,1,3,4]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,2,1,3,4]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,2,1,3,4]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,2,1,3,4]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,2,1,3,4]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,2,1,3,4]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,2,1,3,4]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,2,1,3,5]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,2,1,3,5]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[8,6,7,4,2,1,3,5]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,2,1,3,5]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,2,1,3,6]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,2,1,3,7]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,2,1,3,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,2,1,3,7]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[6,5,7,4,2,1,3,8]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[7,6,4,5,2,1,3,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[7,5,4,6,2,1,3,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,2,1,3,7]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,2,1,3,8]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,2,1,3,8]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,2,1,4,5]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,2,1,4,5]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,2,1,4,5]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,2,1,4,5]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,2,1,4,5]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,2,1,4,6]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,2,1,4,6]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[8,6,5,3,2,1,4,7]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[7,6,5,3,2,1,4,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,2,1,4,7]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[8,7,4,3,2,1,5,6]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,2,1,5,6]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,2,1,5,7]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,2,1,5,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,1,0,0,0]=>[6,7,4,3,2,1,5,8]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[8,5,4,3,2,1,6,7]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,2,1,6,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,2,1,7,8]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,2,1,7,8]=>[[[[[.,[.,.]],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[8,4,5,3,2,1,6,7]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[7,4,5,3,2,1,6,8]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,2,1,7,8]=>[[[[[.,.],[.,.]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,3,2,1,7,8]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,2,1,5,6]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,2,1,5,6]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,2,1,5,7]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[7,6,3,4,2,1,5,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[6,7,3,4,2,1,5,8]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[6,5,3,4,2,1,7,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,2,1,7,8]=>[[[[.,[.,.]],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[8,4,3,5,2,1,6,7]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[7,4,3,5,2,1,6,8]=>[[[[[.,.],.],[.,.]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,2,1,6,7]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[7,3,4,5,2,1,6,8]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[6,3,4,5,2,1,7,8]=>[[[[.,.],[.,[.,.]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,2,1,7,8]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[[.,.],.],.],.]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,3,1,4,5]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,2,3,1,4,5]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,3,1,4,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,2,3,1,4,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,3,1,4,5]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,3,1,4,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,3,1,4,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,2,3,1,4,8]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,3,1,4,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,2,3,1,4,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,2,3,1,4,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,3,1,4,8]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,3,1,5,6]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,3,1,5,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,3,1,5,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[6,7,4,2,3,1,5,8]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[7,5,4,2,3,1,6,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[8,4,5,2,3,1,6,7]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,3,1,7,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0,1,0]=>[8,7,3,2,4,1,5,6]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,4,1,5,6]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,4,1,5,7]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,4,1,5,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,4,1,6,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,3,2,4,1,7,8]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,5,1,7,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,6,1,7,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,6,1,7,8]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,6,1,7,8]=>[[[[.,.],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,6,1,7,8]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,4,1,5,6]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,4,1,5,6]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[8,6,2,3,4,1,5,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,4,1,5,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,4,1,5,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,3,4,1,6,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,3,4,1,6,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[6,5,2,3,4,1,7,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,6,2,3,4,1,7,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,3,5,1,6,7]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[7,4,2,3,5,1,6,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,6,1,7,8]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,6,1,7,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,5,1,6,7]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,5,1,6,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,4,5,1,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,6,1,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,6,1,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,6,1,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,1,7,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[[[.,.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[8,7,6,5,1,2,3,4]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[7,8,6,5,1,2,3,4]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[8,6,7,5,1,2,3,4]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[7,6,8,5,1,2,3,4]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[6,7,8,5,1,2,3,4]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[8,7,5,6,1,2,3,4]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[7,8,5,6,1,2,3,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[8,6,5,7,1,2,3,4]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[7,6,5,8,1,2,3,4]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[6,7,5,8,1,2,3,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[8,5,6,7,1,2,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[7,5,6,8,1,2,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[6,5,7,8,1,2,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[8,7,6,4,1,2,3,5]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[7,8,6,4,1,2,3,5]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[7,6,8,4,1,2,3,5]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[6,7,8,4,1,2,3,5]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[8,7,5,4,1,2,3,6]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[7,8,5,4,1,2,3,6]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[8,6,5,4,1,2,3,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[7,6,5,4,1,2,3,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[8,5,6,4,1,2,3,7]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[5,6,7,4,1,2,3,8]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[7,8,4,5,1,2,3,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[8,6,4,5,1,2,3,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[5,6,4,7,1,2,3,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,0]=>[8,4,5,6,1,2,3,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[7,4,5,6,1,2,3,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[5,4,6,7,1,2,3,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,1,2,3,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[8,7,6,3,1,2,4,5]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[7,8,6,3,1,2,4,5]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[8,6,7,3,1,2,4,5]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,1,0,0]=>[7,6,8,3,1,2,4,5]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[6,7,8,3,1,2,4,5]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[8,7,5,3,1,2,4,6]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[7,8,5,3,1,2,4,6]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0,1,0]=>[8,5,6,3,1,2,4,7]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[5,6,7,3,1,2,4,8]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[7,8,4,3,1,2,5,6]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[8,6,4,3,1,2,5,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[7,6,4,3,1,2,5,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[7,5,4,3,1,2,6,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[6,5,4,3,1,2,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,1,1,0,0,0,0]=>[5,6,4,3,1,2,7,8]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[5,4,6,3,1,2,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[8,7,3,4,1,2,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[7,8,3,4,1,2,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[8,6,3,4,1,2,5,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[8,5,3,4,1,2,6,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[5,6,3,4,1,2,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[6,4,3,5,1,2,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[5,4,3,6,1,2,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[8,3,4,5,1,2,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[4,3,5,6,1,2,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,1,2,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,2,1,3,4,5]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,2,1,3,4,5]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,2,1,3,4,5]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,2,1,3,4,5]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,2,1,3,4,6]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,2,1,3,4,6]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,2,1,3,4,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,2,1,3,4,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,2,1,3,4,7]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,2,1,3,4,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,2,1,3,4,8]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[8,7,4,2,1,3,5,6]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[7,8,4,2,1,3,5,6]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,2,1,3,5,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[7,6,4,2,1,3,5,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,2,1,3,6,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,2,1,3,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,1,1,0,0,0,0]=>[5,6,4,2,1,3,7,8]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[6,4,5,2,1,3,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[5,4,6,2,1,3,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[4,5,6,2,1,3,7,8]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[8,7,3,2,1,4,5,6]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,2,1,4,5,6]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[8,6,3,2,1,4,5,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[7,6,3,2,1,4,5,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,2,1,4,5,8]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,2,1,4,6,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,2,1,4,6,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[5,6,3,2,1,4,7,8]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[8,4,3,2,1,5,6,7]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,2,1,5,6,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,2,1,5,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,2,1,6,7,8]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,3,2,1,6,7,8]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,2,1,5,6,7]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[6,3,4,2,1,5,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[5,3,4,2,1,6,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,2,1,6,7,8]=>[[[[.,.],[.,.]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,2,1,6,7,8]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[[.,.],.],.]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,3,1,4,5,6]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,3,1,4,5,6]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[7,6,2,3,1,4,5,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[6,7,2,3,1,4,5,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0]=>[7,5,2,3,1,4,6,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,3,1,5,6,7]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,3,1,6,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,3,1,6,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,4,1,6,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,5,1,6,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,5,1,6,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],.]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,4,1,5,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,4,1,5,6,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,4,1,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,5,1,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,5,1,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[.,.],.],.],.]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[8,7,6,1,2,3,4,5]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[7,8,6,1,2,3,4,5]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[8,6,7,1,2,3,4,5]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[7,6,8,1,2,3,4,5]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,1,2,3,4,5]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[8,7,5,1,2,3,4,6]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[7,8,5,1,2,3,4,6]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[8,6,5,1,2,3,4,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[7,6,5,1,2,3,4,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[6,7,5,1,2,3,4,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[8,5,6,1,2,3,4,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[7,5,6,1,2,3,4,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[6,5,7,1,2,3,4,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[5,6,7,1,2,3,4,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[8,7,4,1,2,3,5,6]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[8,6,4,1,2,3,5,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[8,5,4,1,2,3,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[6,5,4,1,2,3,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[8,4,5,1,2,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,1,0,0]=>[7,4,5,1,2,3,6,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[4,5,6,1,2,3,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[7,8,3,1,2,4,5,6]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[6,7,3,1,2,4,5,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[8,5,3,1,2,4,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[7,5,3,1,2,4,6,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[7,4,3,1,2,5,6,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,1,0,0,0]=>[6,4,3,1,2,5,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[5,4,3,1,2,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[8,3,4,1,2,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[7,3,4,1,2,5,6,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[4,3,5,1,2,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[3,4,5,1,2,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[8,7,2,1,3,4,5,6]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[7,8,2,1,3,4,5,6]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[8,5,2,1,3,4,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[5,6,2,1,3,4,7,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0,1,0]=>[8,4,2,1,3,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[6,4,2,1,3,5,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[5,4,2,1,3,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[4,5,2,1,3,6,7,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[8,3,2,1,4,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[7,3,2,1,4,5,6,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[5,3,2,1,4,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,3,2,1,5,6,7,8]=>[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[3,4,2,1,5,6,7,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[[.,.],.]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[8,2,3,1,4,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[7,2,3,1,4,5,6,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[6,2,3,1,4,5,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[5,2,3,1,4,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[4,2,3,1,5,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[3,2,4,1,5,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[.,.],.],.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[8,7,1,2,3,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[8,6,1,2,3,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[7,6,1,2,3,4,5,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[6,7,1,2,3,4,5,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[8,5,1,2,3,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[7,5,1,2,3,4,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[6,5,1,2,3,4,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[8,4,1,2,3,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[7,4,1,2,3,5,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[6,4,1,2,3,5,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[5,4,1,2,3,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[4,5,1,2,3,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[8,3,1,2,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[7,3,1,2,4,5,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[6,3,1,2,4,5,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[5,3,1,2,4,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[4,3,1,2,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[8,2,1,3,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[7,2,1,3,4,5,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[5,2,1,3,4,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[4,2,1,3,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[.,.],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,2,3,4,5,6,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[6,1,2,3,4,5,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[5,1,2,3,4,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[4,1,2,3,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[10,1,2,3,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[9,2,1,3,4,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,9,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[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]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]=>[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[11,1,2,3,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,1,3,4,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[9,3,1,2,4,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,1,4,5,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[.,.],[.,.]]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[4,2,3,5,6,7,8,9,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[3,4,2,5,6,7,8,9,1]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[3,2,4,5,6,7,8,9,10,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]
[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]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]=>[.,[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]=>[11,2,1,3,4,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[10,3,1,2,4,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,1,4,5,6,7,8,9]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,1,0]=>[9,4,1,2,3,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,4,1,5,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,5,6,7,8,9,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[4,2,3,5,6,7,8,9,10,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0]=>[11,3,1,2,4,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,1,0]=>[10,4,1,2,3,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,4,1,5,6,7,8,9]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,1,2,5,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,4,5,1,6,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[.,.],.],.],[.,.]]]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[4,5,2,3,6,7,8,9,1]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[4,3,2,5,6,7,8,9,10,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,4,5,1,6,7,8,9]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[9,6,1,2,3,4,5,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,4,5,6,1,7,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[[[.,.],.],[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[6,2,3,4,5,7,8,9,10,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[5,4,2,3,6,7,8,9,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]
[1,0,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[4,5,2,3,6,7,8,9,10,1]=>[[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[.,[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]=>[10,6,1,2,3,4,5,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,4,5,6,1,7,8,9]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[9,7,1,2,3,4,5,6,8]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,4,5,6,7,1,8]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[8,9,1,2,3,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[8,2,3,4,5,6,7,9,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,6,7,8,9,1]=>[[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,1,2]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,2,9,1]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]=>[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,1,0]=>[10,7,1,2,3,4,5,6,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,4,5,6,7,1,8,9]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[9,8,1,2,3,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[9,2,3,4,5,6,7,8,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[.,[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[8,9,2,1,3,4,5,6,7]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[[.,.],.]]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[5,4,3,2,6,7,8,9,10,1]=>[[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[4,3,5,6,7,8,9,1,2]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,2,1]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.]=>[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,4,5,6,7,8,1,9]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[9,10,1,2,3,4,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[9,3,2,4,5,6,7,8,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[9,2,3,4,5,6,7,8,10,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[5,3,4,6,7,8,9,1,2]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,1,2]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[10,9,1,2,3,4,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[10,2,3,4,5,6,7,8,9,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]=>[.,[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,2,3,7,8,9,1]=>[[[[[.,.],.],.],[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[5,6,7,2,3,4,8,9,1]=>[[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],[[[.,.],.],.]]]
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[4,3,5,6,7,8,9,10,1,2]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,2,1]=>[[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.],.]=>[.,[.,[[[[[[[[.,.],.],.],.],.],.],.],.]]]
[]=>[]=>.=>.
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[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[7,2,3,4,5,6,1,8,9]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[[[.,.],.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
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[1,1,1,1,0,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,7,1,2,8,9]=>[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,1,2,8,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]
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[1,1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0,0]=>[7,5,4,3,1,2,6,8,9]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
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[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[8,6,4,2,1,3,5,7,9]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,2,1,6,7,8,9]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
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[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[3,4,2,5,1,6,7,8,9]=>[[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[[.,.],.]]]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[5,2,3,4,1,6,7,8,9]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
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[1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0]=>[4,5,6,1,2,3,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,0]=>[7,5,3,1,2,4,6,8,9]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[5,4,3,1,2,6,7,8,9]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[4,3,5,1,2,6,7,8,9]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,1,2,6,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[4,5,2,1,3,6,7,8,9]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[[.,.],.]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[4,3,2,1,5,6,7,8,9]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[3,4,2,1,5,6,7,8,9]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[[.,.],.]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[8,2,3,1,4,5,6,7,9]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[4,2,3,1,5,6,7,8,9]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[3,2,4,1,5,6,7,8,9]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[7,8,1,2,3,4,5,6,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[8,3,1,2,4,5,6,7,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[5,3,1,2,4,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[4,3,1,2,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[8,2,1,3,4,5,6,7,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1,2,3,4,5,6,7,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[7,1,2,3,4,5,6,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[6,1,2,3,4,5,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[5,1,2,3,4,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]
[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]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,3,2,1]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,7,9,6,5,4,3,2,1]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[8,7,6,9,5,4,3,2,1]=>[[[[[[[[.,.],.],[.,.]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,9,4,3,2,1]=>[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,9,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,9,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,3,2,9,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,10,8,7,6,5,4,3,2,1]=>[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[7,8,9,6,5,4,3,2,1]=>[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[9,8,10,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[8,6,7,9,5,4,3,2,1]=>[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[9,8,7,10,6,5,4,3,2,1]=>[[[[[[[[[.,.],.],[.,.]],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[8,7,5,6,9,4,3,2,1]=>[[[[[[[.,.],.],[.,[.,.]]],.],.],.],.]=>[.,[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,10,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[8,7,6,4,5,9,3,2,1]=>[[[[[[[.,.],.],.],[.,[.,.]]],.],.],.]=>[.,[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,10,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,3,4,9,2,1]=>[[[[[[[.,.],.],.],.],[.,[.,.]]],.],.]=>[.,[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,10,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[8,7,6,5,4,2,3,9,1]=>[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,10,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,2,10,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,10,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[10,11,9,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,[.,.]],.],.],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[8,9,10,7,6,5,4,3,2,1]=>[[[[[[[[.,[.,[.,.]]],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[10,9,11,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,5,4,3,2,1]=>[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,3,1,2,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,9,8,7,6,5,4,3,2,11,1]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[10,9,8,7,6,5,4,3,2,1,11]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,6,5,4,3,2,1]=>[[[[[[[.,[.,[.,[.,.]]]],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[[[[.,.],.],.],.]]]]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[8,7,5,4,3,6,9,2,1]=>[[[[[[[.,.],.],.],.],[.,[.,.]]],.],.]=>[.,[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,4,2,1,3,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,4,3,2,1]=>[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.]=>[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,5,3,2,1,4,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,5,4,3,2,1]=>[[[[[[.,[.,[.,[.,[.,.]]]]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[[[[.,.],.],.],.],.]]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[8,6,5,4,3,2,7,9,1]=>[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,4,3,2,1,5,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,3,2,8,9,1]=>[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[9,8,7,5,4,3,2,1,6,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,3,2,1]=>[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.]=>[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[6,5,4,3,2,7,8,9,1]=>[[[[[[.,.],.],.],.],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[9,8,6,5,4,3,2,1,7,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,10,4,3,2,1]=>[[[[[.,[.,[.,[.,[.,[.,.]]]]]],.],.],.],.]=>[.,[.,[.,[.,[[[[[[.,.],.],.],.],.],.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,1,2,3,4,5,10]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,6,5,4,3,2,9,10,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[9,7,6,5,4,3,2,1,8,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[9,7,8,6,5,4,3,2,1]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[8,9,6,7,5,4,3,2,1]=>[[[[[[[.,[.,.]],[.,.]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[9,6,7,8,5,4,3,2,1]=>[[[[[[[.,.],[.,[.,.]]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,6,4,3,2,1]=>[[[[[[[[.,.],.],.],[.,.]],.],.],.],.]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,5,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[9,8,7,4,5,6,3,2,1]=>[[[[[[[.,.],.],.],[.,[.,.]]],.],.],.]=>[.,[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,4,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,5,6,7,8,2,1]=>[[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.],.]=>[.,[.,[[[[[[.,.],.],.],.],.],[.,.]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,2,3,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,2,3,1]=>[[[[[[[.,[.,.]],.],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,5,2,3,1]=>[[[[[[[.,.],.],.],.],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,2,3,1]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]],.]=>[.,[[.,.],[[[[[[.,.],.],.],.],.],.]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,2,3,4,1]=>[[[[[[[.,.],.],.],.],.],[.,[.,.]]],.]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[9,8,2,3,4,5,6,7,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],.],[.,[.,.]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[8,9,2,3,4,5,6,7,1]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],.]=>[.,[[[[[[.,.],.],.],.],.],[[.,.],.]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,3,1,2]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,3,1,2]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[9,7,8,6,5,4,3,1,2]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,3,1,2]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]]=>[[.,.],[.,[[[[[[.,.],.],.],.],.],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,4,1,2]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,6,3,4,1,2]=>[[[[[[.,.],.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[9,7,8,5,6,3,4,1,2]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[9,8,3,4,5,6,7,1,2]=>[[[[.,.],.],[.,[.,[.,[.,.]]]]],[.,.]]=>[[.,.],[[[[[.,.],.],.],.],[.,[.,.]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,5,6,7,8,1,2]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]=>[[.,.],[[[[[[.,.],.],.],.],.],[.,.]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,1,2,3]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,5,1,2,3]=>[[[[[[.,.],.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[8,9,6,7,4,5,1,2,3]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[9,8,7,4,5,6,1,2,3]=>[[[[[.,.],.],.],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[7,8,9,4,5,6,1,2,3]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,1,2,3]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]=>[[[.,.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,1,2,3,4]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,6,1,2,3,4]=>[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[9,7,8,5,6,1,2,3,4]=>[[[[.,.],[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[9,8,5,6,7,1,2,3,4]=>[[[[.,.],.],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[8,9,5,6,7,1,2,3,4]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[9,5,6,7,8,1,2,3,4]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[.,.],.],.],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,1,2,3,4]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,1,2,3,4,5]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,1,0,0,0]=>[7,8,9,6,1,2,3,4,5]=>[[[.,[.,[.,.]]],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[[[.,.],.],.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0,1,0]=>[9,8,6,7,1,2,3,4,5]=>[[[[.,.],.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[9,6,7,8,1,2,3,4,5]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,1,2,3,4,5]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[9,8,7,1,2,3,4,5,6]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[9,7,8,1,2,3,4,5,6]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,8,9,1,2,3,4,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[10,8,9,7,6,5,4,3,2,1]=>[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[10,9,8,6,7,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,5,6,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,7,8,9,10,3,2,1]=>[[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.],.],.]=>[.,[.,[.,[[[[[[[.,.],.],.],.],.],.],.]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,2,3,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[10,8,9,6,7,4,5,2,3,1]=>[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,4,5,6,2,3,1]=>[[[[.,[.,[.,[.,.]]]],[.,[.,.]]],[.,.]],.]=>[.,[[.,.],[[[.,.],.],[[[[.,.],.],.],.]]]]
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,7,8,9,10,2,3,1]=>[[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]],.]=>[.,[[.,.],[[[[[[[.,.],.],.],.],.],.],.]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[8,9,10,5,6,7,2,3,4,1]=>[[[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]],.]=>[.,[[[.,.],.],[[[.,.],.],[[[.,.],.],.]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[10,9,2,3,4,5,6,7,8,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,3,1,2]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[9,10,8,7,6,5,4,3,1,2]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,3,4,1,2]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,5,6,3,4,1,2]=>[[[[[[[.,.],.],.],.],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[10,9,7,8,5,6,3,4,1,2]=>[[[[[[.,.],.],[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,5,6,3,4,1,2]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[10,3,4,5,6,7,8,9,1,2]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,1,2,3]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,4,5,1,2,3]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[10,8,9,6,7,4,5,1,2,3]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,4,5,6,1,2,3]=>[[[[.,[.,.]],[.,.]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,7,8,9,10,1,2,3]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,1,2,3,4]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[9,10,7,8,5,6,1,2,3,4]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[8,9,10,5,6,7,1,2,3,4]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[10,9,5,6,7,8,1,2,3,4]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[9,10,5,6,7,8,1,2,3,4]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,10,1,2,3,4]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,1,2,3,4,5]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[10,8,9,6,7,1,2,3,4,5]=>[[[[.,.],[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[10,6,7,8,9,1,2,3,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[[.,.],.],.],[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,1,2,3,4,5,6]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,1,0]=>[10,7,8,9,1,2,3,4,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,1,2,3,4,5,6]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[10,9,8,1,2,3,4,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[10,8,9,1,2,3,4,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[8,9,10,1,2,3,4,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,4,2,1,3]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,2,1,4]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,3,2,1,5]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,4,3,2,1,6]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[9,8,6,5,4,3,2,1,7]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,2,1,8]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,4,2,1,3]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,2,3,1,4]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,5,3,2,1,4]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,3,4,2,1,5]=>[[[[[[[.,.],.],.],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,6,4,3,2,1,5]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[9,8,7,4,5,3,2,1,6]=>[[[[[[[.,.],.],.],[.,.]],.],.],[.,.]]=>[[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[10,9,8,7,5,4,3,2,1,6]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[10,9,8,6,5,4,3,2,1,7]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[9,6,7,5,4,3,2,1,8]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[10,9,7,6,5,4,3,2,1,8]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,5,4,3,2,1,9]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,4,3,1,2,7,8,9,10]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[7,6,5,4,3,1,2,8,9,10]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[11,10,9,8,7,6,5,4,3,1,2]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,7,9,6,5,4,3,1,2]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[8,9,7,6,5,4,3,2,1,10]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9,10,11]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[3,4,2,1,5,6,7,8,9,10]=>[[[.,[.,.]],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,[[.,.],.]]]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[4,3,1,2,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9,10,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[9,8,10,7,6,5,4,3,1,2]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,7,9,6,5,4,2,1,3]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[8,7,9,6,5,4,2,3,1]=>[[[[[[[.,.],[.,.]],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,5,4,2,1,3]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[9,6,5,4,3,2,1,7,8]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[9,8,5,4,3,2,1,6,7]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0,1,0]=>[9,8,7,4,3,2,1,5,6]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,3,2,1,4,5]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,2,1,3,4]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1,10]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[9,1,2,3,4,5,6,7,8,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[10,1,2,3,4,5,6,7,8,9,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[9,2,1,3,4,5,6,7,8,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[9,8,6,1,2,3,4,5,7]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,1,2,3,4,6]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,1,2,3,5]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,1,2,4]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9,10]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9,10]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,1,7,8,9,10]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8,9,10]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1,9,10]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[9,6,5,4,3,2,7,1,8]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,6,5,4,3,2,9,1,10]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,2,1,3]=>[[[.,[.,[.,[.,[.,[.,.]]]]]],.],[.,.]]=>[[.,.],[.,[[[[[[.,.],.],.],.],.],.]]]
[1,1,1,0,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,2,1,3,4]=>[[[.,[.,[.,[.,[.,.]]]]],.],[.,[.,.]]]=>[[[.,.],.],[.,[[[[[.,.],.],.],.],.]]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,2,1,3,4,5]=>[[[.,[.,[.,[.,.]]]],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[[[[.,.],.],.],.]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,1,0,0,0]=>[7,8,9,2,1,3,4,5,6]=>[[[.,[.,[.,.]]],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[[[.,.],.],.]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,3,2,5,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,3,5,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[10,9,7,6,8,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,9,5,4,3,2,1]=>[[[[[[[[[.,.],.],.],[.,.]],.],.],.],.],.]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[8,9,7,6,4,3,2,1,5]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,4,3,5,1,2]=>[[[[[[[.,.],.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,4,3,2,5,1,10]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],[.,.]]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[9,8,7,6,4,3,5,2,1,10]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],[.,.]]=>[[.,.],[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,4,3,2,7,8,9,10,1]=>[[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]],.]=>[.,[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[7,6,5,4,2,3,8,9,1]=>[[[[[[.,.],.],.],.],[.,[.,[.,.]]]],.]=>[.,[[[[.,.],.],.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,1,2,8]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[8,9,6,5,4,3,2,1,7]=>[[[[[[[.,[.,.]],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[7,8,9,5,4,3,2,1,6]=>[[[[[[.,[.,[.,.]]],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[7,8,9,6,5,4,3,2,1,10]=>[[[[[[[.,[.,[.,.]]],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,4,3,2,1,5]=>[[[[[.,[.,[.,[.,.]]]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[[[.,.],.],.],.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[7,6,5,4,3,2,1,8,9,10]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,3,9,1,2]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[[[.,.],.],.],.],.]]]
[1,1,1,0,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[5,6,7,4,8,9,1,2,3]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[6,5,7,8,9,1,2,3,4]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[.,.],.],.],[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[8,7,9,1,2,3,4,5,6]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[.,.],[.,.]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[8,1,2,3,4,5,6,7,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[7,6,8,9,1,2,3,4,5]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[.,.],.],[.,.]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[7,1,2,3,4,5,6,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[6,1,2,3,4,5,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[5,4,6,7,8,9,1,2,3]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[[[.,.],.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[5,1,2,3,4,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[9,8,7,5,6,4,3,2,1,10]=>[[[[[[[[.,.],.],.],[.,.]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[9,7,8,5,4,3,2,1,6]=>[[[[[[[.,.],[.,.]],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[9,6,7,4,5,2,3,1,8]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[9,10,6,7,4,5,2,3,1,8]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[8,7,6,5,4,3,2,1,9,10]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[1,1,1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,1,2,3,7,8,9,10]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[[[.,.],.],.]]
[1,1,1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,1,2,3,4,9,10]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,1,2,3,4,5,10]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[[[.,.],.],.],.]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[6,5,7,4,8,3,9,2,10,1]=>[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[10,8,6,4,2,1,3,5,7,9]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[7,6,8,5,9,4,10,3,11,2,12,1]=>[[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]]
[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]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]=>[[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],.],.]
[1,1,0,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,11,1,2]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]=>[[.,.],[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[10,7,6,5,4,3,2,1,8,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[9,5,4,3,2,1,6,7,8]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0,0]=>[3,2,4,1,5,6,7,8,9,10]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[[.,.],[.,.]]]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,1,11]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]=>[[.,.],[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,11,1,2,3,4,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[[.,.],.]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,5,4,3,2,1,7,8,9,10]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[9,8,7,6,5,3,2,4,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[3,2,1,4,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[11,9,10,8,7,6,5,4,3,2,1]=>[[[[[[[[[[.,.],[.,.]],.],.],.],.],.],.],.],.]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,5,4,3,9,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[5,4,3,2,1,6,7,8,9,10]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[4,3,2,1,5,6,7,8,9,10]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]=>[[[[[[[.,.],.],.],.],.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[11,2,3,4,5,6,7,8,9,1,10]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[11,9,8,7,6,5,4,3,2,1,10]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,2,8,1]=>[[[[[[[[.,.],.],.],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,3,2,1,4]=>[[[[.,[.,[.,[.,[.,.]]]]],.],.],[.,.]]=>[[.,.],[.,[.,[[[[[.,.],.],.],.],.]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[8,9,1,2,3,4,5,6,7,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]=>[[[[[[[[.,.],.],.],.],.],.],.],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,1,2,3,4,10]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[[[[.,.],.],.],.],.]]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,1,2,10]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]=>[[[.,.],.],[[[[[[[.,.],.],.],.],.],.],.]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,4,3,2,1,5,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[9,10,7,6,5,4,3,2,1,8]=>[[[[[[[[.,[.,.]],.],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0,1,0]=>[9,8,6,5,1,2,3,4,7]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[8,7,9,5,6,3,4,1,2]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]=>[11,10,1,2,3,4,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]=>[[[[[[[[[.,.],.],.],.],.],.],.],.],[.,[.,.]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0,1,0]=>[9,8,4,1,2,3,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[9,8,7,5,4,6,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[10,9,8,6,5,7,4,3,2,1]=>[[[[[[[[[.,.],.],.],.],[.,.]],.],.],.],.]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,5,4,3,2,9,1]=>[[[[[[[[[.,.],.],.],.],.],.],.],[.,.]],.]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[9,8,6,5,4,3,7,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[10,9,7,6,5,4,8,3,2,1]=>[[[[[[[[[.,.],.],.],.],.],[.,.]],.],.],.]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[9,8,6,5,4,7,3,2,1]=>[[[[[[[[.,.],.],.],.],[.,.]],.],.],.]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[10,9,7,6,5,4,3,8,2,1]=>[[[[[[[[[.,.],.],.],.],.],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[8,9,10,4,5,6,1,2,3,7]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[8,9,5,6,3,4,1,2,7]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[10,7,8,5,6,3,4,1,2,9]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,5,4,3,1,2,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[9,7,6,5,4,3,8,2,1]=>[[[[[[[[.,.],.],.],.],.],[.,.]],.],.]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[9,8,5,4,6,7,3,2,1]=>[[[[[[[.,.],.],.],[.,[.,.]]],.],.],.]=>[.,[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[7,8,9,2,3,4,1,5,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[9,3,4,5,6,7,1,2,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]=>[[[.,.],.],[[[[[.,.],.],.],.],[.,.]]]
[1,1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2,9,10]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[9,8,10,6,7,4,5,2,3,1]=>[[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,.]],.]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[5,4,6,3,7,2,8,1,9,10]=>[[[[[.,.],[.,.]],[.,.]],[.,.]],[.,[.,.]]]=>[[[.,.],.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[10,7,8,6,5,4,3,2,1,9]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,0,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,2,3,1,4]=>[[[.,[.,[.,[.,[.,.]]]]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[[[[.,.],.],.],.],.]]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[9,4,3,5,6,7,8,2,1]=>[[[[[.,.],.],[.,[.,[.,[.,.]]]]],.],.]=>[.,[.,[[[[[.,.],.],.],.],[.,[.,.]]]]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[9,2,3,4,5,6,7,8,1,10]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]=>[[.,.],[[[[[[[.,.],.],.],.],.],.],[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0]=>[9,7,5,3,1,2,4,6,8,10]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[11,12,9,10,7,8,5,6,3,4,1,2]=>[[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[10,8,9,6,5,4,3,2,1,7]=>[[[[[[[[.,.],[.,.]],.],.],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[8,9,5,6,4,3,2,1,7]=>[[[[[[.,[.,.]],[.,.]],.],.],.],[.,.]]=>[[.,.],[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[7,8,5,6,3,4,1,2,9,10]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[11,12,1,2,3,4,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]=>[[[[[[[[[[.,.],.],.],.],.],.],.],.],.],[[.,.],.]]
[1,0,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,11,2,1]=>[[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.],.]=>[.,[.,[[[[[[[[[.,.],.],.],.],.],.],.],.],.]]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[11,3,4,5,6,7,8,9,10,1,2]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]=>[[.,.],[[[[[[[[.,.],.],.],.],.],.],.],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[9,7,8,4,3,2,1,5,6]=>[[[[[[.,.],[.,.]],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[10,3,2,4,5,6,7,8,9,1]=>[[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]=>[.,[[[[[[[.,.],.],.],.],.],.],[.,[.,.]]]]
[1,1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[3,4,2,5,1,6,7,8,9,10]=>[[[.,[.,.]],[.,.]],[.,[.,[.,[.,[.,.]]]]]]=>[[[[[[.,.],.],.],.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[5,6,4,7,3,8,2,9,1,10]=>[[[[[.,[.,.]],[.,.]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[7,8,9,4,5,6,1,2,3,10]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[[.,.],.],[[[.,.],.],.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[10,8,7,6,5,4,2,1,3,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[9,7,5,3,1,2,4,6,8]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[10,8,6,5,4,3,2,1,7,9]=>[[[[[[[[.,.],.],.],.],.],.],.],[.,[.,.]]]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[6,4,5,7,3,8,2,9,1,10]=>[[[[[.,.],[.,[.,.]]],[.,.]],[.,.]],[.,.]]=>[[.,.],[[.,.],[[.,.],[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[9,7,5,2,3,1,4,6,8]=>[[[[[.,.],.],.],[.,.]],[.,[.,[.,.]]]]=>[[[[.,.],.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,1,0,0,1,0,0]=>[9,7,5,2,3,1,4,6,8,10]=>[[[[[.,.],.],.],[.,.]],[.,[.,[.,[.,.]]]]]=>[[[[[.,.],.],.],.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[7,8,9,3,4,5,1,2,6]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]=>[[[.,.],.],[[[.,.],.],[[[.,.],.],.]]]
Map
to 132-avoiding permutation
Description
Sends a Dyck path to a 132-avoiding permutation.
This bijection is defined in [1, Section 2].
This bijection is defined in [1, Section 2].
Map
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.
Map
left-right symmetry
Description
Return the left-right symmetrized tree of a binary tree.
searching the database
Sorry, this map was not found in the database.