Identifier
Mp00129:
Dyck paths
—to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶
Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00072: Permutations —binary search tree: left to right⟶ Binary trees
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-3
[1,0]=>[1]=>[1]=>[.,.]
[1,0,1,0]=>[2,1]=>[2,1]=>[[.,.],.]
[1,1,0,0]=>[1,2]=>[1,2]=>[.,[.,.]]
[1,0,1,0,1,0]=>[2,3,1]=>[3,2,1]=>[[[.,.],.],.]
[1,0,1,1,0,0]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[1,1,0,0,1,0]=>[1,3,2]=>[1,3,2]=>[.,[[.,.],.]]
[1,1,0,1,0,0]=>[3,1,2]=>[2,3,1]=>[[.,.],[.,.]]
[1,1,1,0,0,0]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[1,0,1,0,1,0,1,0]=>[2,3,4,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[1,0,1,0,1,1,0,0]=>[2,3,1,4]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[1,0,1,1,0,0,1,0]=>[2,1,4,3]=>[2,1,4,3]=>[[.,.],[[.,.],.]]
[1,0,1,1,0,1,0,0]=>[2,4,1,3]=>[3,2,4,1]=>[[[.,.],.],[.,.]]
[1,0,1,1,1,0,0,0]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[1,1,0,0,1,0,1,0]=>[1,3,4,2]=>[1,4,3,2]=>[.,[[[.,.],.],.]]
[1,1,0,0,1,1,0,0]=>[1,3,2,4]=>[1,3,2,4]=>[.,[[.,.],[.,.]]]
[1,1,0,1,0,0,1,0]=>[3,1,4,2]=>[3,4,1,2]=>[[.,[.,.]],[.,.]]
[1,1,0,1,0,1,0,0]=>[3,4,1,2]=>[2,4,3,1]=>[[.,.],[[.,.],.]]
[1,1,0,1,1,0,0,0]=>[3,1,2,4]=>[2,3,1,4]=>[[.,.],[.,[.,.]]]
[1,1,1,0,0,0,1,0]=>[1,2,4,3]=>[1,2,4,3]=>[.,[.,[[.,.],.]]]
[1,1,1,0,0,1,0,0]=>[1,4,2,3]=>[1,3,4,2]=>[.,[[.,.],[.,.]]]
[1,1,1,0,1,0,0,0]=>[4,1,2,3]=>[2,3,4,1]=>[[.,.],[.,[.,.]]]
[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[1,0,1,0,1,0,1,1,0,0]=>[2,3,4,1,5]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,0]=>[2,3,1,5,4]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]
[1,0,1,0,1,1,0,1,0,0]=>[2,3,5,1,4]=>[4,2,3,5,1]=>[[[.,.],[.,.]],[.,.]]
[1,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,5]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,0]=>[2,1,4,5,3]=>[2,1,5,4,3]=>[[.,.],[[[.,.],.],.]]
[1,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,5]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0,1,0]=>[2,4,1,5,3]=>[4,2,5,1,3]=>[[[.,.],[.,.]],[.,.]]
[1,0,1,1,0,1,0,1,0,0]=>[2,4,5,1,3]=>[3,2,5,4,1]=>[[[.,.],.],[[.,.],.]]
[1,0,1,1,0,1,1,0,0,0]=>[2,4,1,3,5]=>[3,2,4,1,5]=>[[[.,.],.],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,0]=>[2,1,5,3,4]=>[2,1,4,5,3]=>[[.,.],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,0,0]=>[2,5,1,3,4]=>[3,2,4,5,1]=>[[[.,.],.],[.,[.,.]]]
[1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,0]=>[1,3,4,5,2]=>[1,5,3,4,2]=>[.,[[[.,.],[.,.]],.]]
[1,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,0]=>[1,3,5,2,4]=>[1,4,3,5,2]=>[.,[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,1,0,0,0]=>[1,3,2,4,5]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,0]=>[3,1,4,5,2]=>[3,5,1,4,2]=>[[.,[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0]=>[3,1,4,2,5]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,0]=>[3,4,1,5,2]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]
[1,1,0,1,0,1,0,1,0,0]=>[3,4,5,1,2]=>[2,5,3,4,1]=>[[.,.],[[.,[.,.]],.]]
[1,1,0,1,0,1,1,0,0,0]=>[3,4,1,2,5]=>[2,4,3,1,5]=>[[.,.],[[.,.],[.,.]]]
[1,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,4]=>[2,3,1,5,4]=>[[.,.],[.,[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,0]=>[3,1,5,2,4]=>[3,4,1,5,2]=>[[.,[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,0,0]=>[3,5,1,2,4]=>[2,4,3,5,1]=>[[.,.],[[.,.],[.,.]]]
[1,1,0,1,1,1,0,0,0,0]=>[3,1,2,4,5]=>[2,3,1,4,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,0]=>[1,2,4,5,3]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,0]=>[1,4,2,5,3]=>[1,4,5,2,3]=>[.,[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,0,1,0,0]=>[1,4,5,2,3]=>[1,3,5,4,2]=>[.,[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,0]=>[1,4,2,3,5]=>[1,3,4,2,5]=>[.,[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,0]=>[4,1,2,5,3]=>[2,4,5,1,3]=>[[.,.],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,0,0]=>[4,1,5,2,3]=>[4,3,5,1,2]=>[[[.,[.,.]],.],[.,.]]
[1,1,1,0,1,0,1,0,0,0]=>[4,5,1,2,3]=>[2,3,5,4,1]=>[[.,.],[.,[[.,.],.]]]
[1,1,1,0,1,1,0,0,0,0]=>[4,1,2,3,5]=>[2,3,4,1,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0]=>[1,2,3,5,4]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,0]=>[1,2,5,3,4]=>[1,2,4,5,3]=>[.,[.,[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,0]=>[1,5,2,3,4]=>[1,3,4,5,2]=>[.,[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0]=>[5,1,2,3,4]=>[2,3,4,5,1]=>[[.,.],[.,[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>[[[.,.],[.,.]],[[.,.],.]]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,6,1,5]=>[5,2,3,4,6,1]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>[[[.,.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,5,1,6,4]=>[5,2,3,6,1,4]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,5,6,1,4]=>[4,2,3,6,5,1]=>[[[.,.],[.,.]],[[.,.],.]]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,5,1,4,6]=>[4,2,3,5,1,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>[[[.,.],.],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,4,5]=>[3,2,1,5,6,4]=>[[[.,.],.],[[.,.],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,6,1,4,5]=>[4,2,3,5,6,1]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>[[.,.],[[[.,.],[.,.]],.]]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>[[.,.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[[.,.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,6,3,5]=>[2,1,5,4,6,3]=>[[.,.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[2,4,1,5,6,3]=>[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[2,4,1,5,3,6]=>[4,2,5,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[2,4,5,1,6,3]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,1,3]=>[3,2,6,4,5,1]=>[[[.,.],.],[[.,[.,.]],.]]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,5,1,3,6]=>[3,2,5,4,1,6]=>[[[.,.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[2,4,1,3,6,5]=>[3,2,4,1,6,5]=>[[[.,.],.],[.,[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,5]=>[4,2,5,1,6,3]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[2,4,6,1,3,5]=>[3,2,5,4,6,1]=>[[[.,.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,1,3,5,6]=>[3,2,4,1,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>[[.,.],[.,[[[.,.],.],.]]]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,3,6,4]=>[2,1,5,6,3,4]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,6,3,4]=>[2,1,4,6,5,3]=>[[.,.],[[.,.],[[.,.],.]]]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,3,4,6]=>[2,1,4,5,3,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[2,5,1,3,6,4]=>[3,2,5,6,1,4]=>[[[.,.],.],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[2,5,1,6,3,4]=>[5,2,4,6,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[2,5,6,1,3,4]=>[3,2,4,6,5,1]=>[[[.,.],.],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,5,1,3,4,6]=>[3,2,4,5,1,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,3,6,4,5]=>[2,1,3,5,6,4]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,3,4,5]=>[2,1,4,5,6,3]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,6,1,3,4,5]=>[3,2,4,5,6,1]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>[.,[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>[.,[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>[.,[[[.,.],.],[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,4,6,2,5]=>[1,5,3,4,6,2]=>[.,[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>[.,[[.,.],[[[.,.],.],.]]]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,5,2,6,4]=>[1,5,3,6,2,4]=>[.,[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,5,6,2,4]=>[1,4,3,6,5,2]=>[.,[[[.,.],.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,5,2,4,6]=>[1,4,3,5,2,6]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,4,5]=>[1,3,2,5,6,4]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,6,2,4,5]=>[1,4,3,5,6,2]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,4,5,6,2]=>[3,6,1,4,5,2]=>[[.,[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[3,1,4,5,2,6]=>[3,5,1,4,2,6]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5]=>[3,4,1,2,6,5]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[3,1,4,6,2,5]=>[3,5,1,4,6,2]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,1,4,2,5,6]=>[3,4,1,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,1,5,6,2]=>[4,6,3,1,5,2]=>[[[.,[.,.]],.],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,1,5,2,6]=>[4,5,3,1,2,6]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,1,6,2]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,1,2]=>[2,6,3,4,5,1]=>[[.,.],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,6]=>[2,5,3,4,1,6]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,1,2,6,5]=>[2,4,3,1,6,5]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,1,6,2,5]=>[4,5,3,1,6,2]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,6,1,2,5]=>[2,5,3,4,6,1]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>[2,4,3,1,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,2,5,6,4]=>[2,3,1,6,5,4]=>[[.,.],[.,[[[.,.],.],.]]]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,5,4,6]=>[2,3,1,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,5,2,6,4]=>[3,5,1,6,2,4]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[3,1,5,6,2,4]=>[3,4,1,6,5,2]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,4,6]=>[3,4,1,5,2,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[3,5,1,2,6,4]=>[2,5,3,6,1,4]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[3,5,1,6,2,4]=>[5,4,3,6,1,2]=>[[[[.,[.,.]],.],.],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[3,5,6,1,2,4]=>[2,4,3,6,5,1]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[3,5,1,2,4,6]=>[2,4,3,5,1,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,5]=>[2,3,1,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[3,1,2,6,4,5]=>[2,3,1,5,6,4]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,6,2,4,5]=>[3,4,1,5,6,2]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[3,6,1,2,4,5]=>[2,4,3,5,6,1]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[3,1,2,4,5,6]=>[2,3,1,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>[.,[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>[.,[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[.,[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,4,6,3,5]=>[1,2,5,4,6,3]=>[.,[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,2,5,6,3]=>[1,4,6,2,5,3]=>[.,[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2,5,3,6]=>[1,4,5,2,3,6]=>[.,[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,5,2,6,3]=>[1,5,6,4,2,3]=>[.,[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,5,6,2,3]=>[1,3,6,4,5,2]=>[.,[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,6]=>[1,3,5,4,2,6]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,2,3,6,5]=>[1,3,4,2,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,5]=>[1,4,5,2,6,3]=>[.,[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,6,2,3,5]=>[1,3,5,4,6,2]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,2,3,5,6]=>[1,3,4,2,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,2,5,6,3]=>[2,4,6,1,5,3]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,1,2,5,3,6]=>[2,4,5,1,3,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[4,1,5,2,6,3]=>[4,5,6,1,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[4,1,5,6,2,3]=>[4,3,6,1,5,2]=>[[[.,[.,.]],.],[[.,.],.]]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,1,5,2,3,6]=>[4,3,5,1,2,6]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[4,5,1,2,6,3]=>[2,5,6,4,1,3]=>[[.,.],[[[.,.],.],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[4,5,1,6,2,3]=>[5,3,6,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,1,2,3]=>[2,3,6,4,5,1]=>[[.,.],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,1,2,3,6]=>[2,3,5,4,1,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,5]=>[2,3,4,1,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[4,1,2,6,3,5]=>[2,4,5,1,6,3]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[4,1,6,2,3,5]=>[4,3,5,1,6,2]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[4,6,1,2,3,5]=>[2,3,5,4,6,1]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[4,1,2,3,5,6]=>[2,3,4,1,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>[.,[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[.,[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,2,5,3,6,4]=>[1,2,5,6,3,4]=>[.,[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,5,6,3,4]=>[1,2,4,6,5,3]=>[.,[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,5,3,4,6]=>[1,2,4,5,3,6]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,2,3,6,4]=>[1,3,5,6,2,4]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,6,3,4]=>[1,5,4,6,2,3]=>[.,[[[.,[.,.]],.],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,6,2,3,4]=>[1,3,4,6,5,2]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,6,4]=>[2,3,5,6,1,4]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,1,2,6,3,4]=>[2,5,4,6,1,3]=>[[.,.],[[[.,.],.],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[5,1,6,2,3,4]=>[5,3,4,6,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[5,6,1,2,3,4]=>[2,3,4,6,5,1]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[5,1,2,3,4,6]=>[2,3,4,5,1,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,3,6,4,5]=>[1,2,3,5,6,4]=>[.,[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5]=>[1,2,4,5,6,3]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[6,1,2,3,4,5]=>[2,3,4,5,6,1]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,1,7,6]=>[5,2,3,4,1,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,7,1,6]=>[6,2,3,4,5,7,1]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,4,1,6,7,5]=>[4,2,3,1,7,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,4,6,1,7,5]=>[6,2,3,4,7,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,6,7,1,5]=>[5,2,3,4,7,6,1]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,4,6,1,5,7]=>[5,2,3,4,6,1,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,4,1,5,7,6]=>[4,2,3,1,5,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,4,1,7,5,6]=>[4,2,3,1,6,7,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,4,7,1,5,6]=>[5,2,3,4,6,7,1]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,1,5,6,7,4]=>[3,2,1,7,5,6,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,7,4,6]=>[3,2,1,6,5,7,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,5,1,6,7,4]=>[5,2,3,7,1,6,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,3,5,1,6,4,7]=>[5,2,3,6,1,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,5,6,1,7,4]=>[6,2,3,7,5,1,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,1,4]=>[4,2,3,7,5,6,1]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,5,6,1,4,7]=>[4,2,3,6,5,1,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,3,5,1,4,7,6]=>[4,2,3,5,1,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,5,1,7,4,6]=>[5,2,3,6,1,7,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,5,7,1,4,6]=>[4,2,3,6,5,7,1]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,5,1,4,6,7]=>[4,2,3,5,1,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,6,4,7,5]=>[3,2,1,6,7,4,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,7,4,5]=>[3,2,1,5,7,6,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,1,6,4,5,7]=>[3,2,1,5,6,4,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,6,1,4,7,5]=>[4,2,3,6,7,1,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,6,1,7,4,5]=>[6,2,3,5,7,1,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,6,7,1,4,5]=>[4,2,3,5,7,6,1]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,6,1,4,5,7]=>[4,2,3,5,6,1,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,4,7,5,6]=>[3,2,1,4,6,7,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,1,7,4,5,6]=>[3,2,1,5,6,7,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,7,1,4,5,6]=>[4,2,3,5,6,7,1]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,3]=>[2,1,7,4,5,6,3]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,4,5,7,3,6]=>[2,1,6,4,5,7,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,6,3,7,5]=>[2,1,6,4,7,3,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,6,7,3,5]=>[2,1,5,4,7,6,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,3,5,7]=>[2,1,5,4,6,3,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,5,6]=>[2,1,4,3,6,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,4,7,3,5,6]=>[2,1,5,4,6,7,3]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,4,1,5,6,7,3]=>[4,2,7,1,5,6,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,4,1,5,6,3,7]=>[4,2,6,1,5,3,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,4,1,5,3,7,6]=>[4,2,5,1,3,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,4,1,5,7,3,6]=>[4,2,6,1,5,7,3]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,3,6,7]=>[4,2,5,1,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,4,5,1,6,7,3]=>[5,2,7,4,1,6,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,4,5,1,6,3,7]=>[5,2,6,4,1,3,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,4,5,6,1,7,3]=>[6,2,7,4,5,1,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,7,1,3]=>[3,2,7,4,5,6,1]=>[[[.,.],.],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,4,5,6,1,3,7]=>[3,2,6,4,5,1,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,4,5,1,3,7,6]=>[3,2,5,4,1,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,4,5,1,7,3,6]=>[5,2,6,4,1,7,3]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,4,5,7,1,3,6]=>[3,2,6,4,5,7,1]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,4,5,1,3,6,7]=>[3,2,5,4,1,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,1,3,6,7,5]=>[3,2,4,1,7,6,5]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,6,5,7]=>[3,2,4,1,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,1,6,3,7,5]=>[4,2,6,1,7,3,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,1,6,7,3,5]=>[4,2,5,1,7,6,3]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,1,6,3,5,7]=>[4,2,5,1,6,3,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,6,1,3,7,5]=>[3,2,6,4,7,1,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,6,1,7,3,5]=>[6,2,5,4,7,1,3]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,6,7,1,3,5]=>[3,2,5,4,7,6,1]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,1,3,5,7]=>[3,2,5,4,6,1,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,4,1,3,5,7,6]=>[3,2,4,1,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,4,1,3,7,5,6]=>[3,2,4,1,6,7,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,4,1,7,3,5,6]=>[4,2,5,1,6,7,3]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,4,7,1,3,5,6]=>[3,2,5,4,6,7,1]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,4,1,3,5,6,7]=>[3,2,4,1,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,1,3,5,7,4,6]=>[2,1,3,6,5,7,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,5,3,6,7,4]=>[2,1,5,7,3,6,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,3,6,4,7]=>[2,1,5,6,3,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,5,6,3,7,4]=>[2,1,6,7,5,3,4]=>[[.,.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,5,6,7,3,4]=>[2,1,4,7,5,6,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,5,6,3,4,7]=>[2,1,4,6,5,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,5,3,4,7,6]=>[2,1,4,5,3,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,3,7,4,6]=>[2,1,5,6,3,7,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,5,7,3,4,6]=>[2,1,4,6,5,7,3]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,5,3,4,6,7]=>[2,1,4,5,3,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,5,1,3,6,7,4]=>[3,2,5,7,1,6,4]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,5,1,3,6,4,7]=>[3,2,5,6,1,4,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,5,1,6,3,7,4]=>[5,2,6,7,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,5,1,6,7,3,4]=>[5,2,4,7,1,6,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,5,1,6,3,4,7]=>[5,2,4,6,1,3,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,5,6,1,3,7,4]=>[3,2,6,7,5,1,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,5,6,1,7,3,4]=>[6,2,4,7,5,1,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,5,6,7,1,3,4]=>[3,2,4,7,5,6,1]=>[[[.,.],.],[.,[[.,[.,.]],.]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,5,6,1,3,4,7]=>[3,2,4,6,5,1,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,5,1,3,4,7,6]=>[3,2,4,5,1,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,5,1,3,7,4,6]=>[3,2,5,6,1,7,4]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,5,1,7,3,4,6]=>[5,2,4,6,1,7,3]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,5,7,1,3,4,6]=>[3,2,4,6,5,7,1]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,5,1,3,4,6,7]=>[3,2,4,5,1,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,6,4,7,5]=>[2,1,3,6,7,4,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,1,3,6,7,4,5]=>[2,1,3,5,7,6,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,1,3,6,4,5,7]=>[2,1,3,5,6,4,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,6,3,4,7,5]=>[2,1,4,6,7,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,3,7,4,5]=>[2,1,6,5,7,3,4]=>[[.,.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,6,7,3,4,5]=>[2,1,4,5,7,6,3]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,6,3,4,5,7]=>[2,1,4,5,6,3,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,6,1,3,4,7,5]=>[3,2,4,6,7,1,5]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,6,1,3,7,4,5]=>[3,2,6,5,7,1,4]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,6,1,7,3,4,5]=>[6,2,4,5,7,1,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,6,7,1,3,4,5]=>[3,2,4,5,7,6,1]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,6,1,3,4,5,7]=>[3,2,4,5,6,1,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,3,4,7,5,6]=>[2,1,3,4,6,7,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,3,7,4,5,6]=>[2,1,3,5,6,7,4]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,7,3,4,5,6]=>[2,1,4,5,6,7,3]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,7,1,3,4,5,6]=>[3,2,4,5,6,7,1]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,2]=>[1,7,3,4,5,6,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,4,5,7,2,6]=>[1,6,3,4,5,7,2]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]=>[.,[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,3,4,6,2,7,5]=>[1,6,3,4,7,2,5]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,4,6,7,2,5]=>[1,5,3,4,7,6,2]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,4,6,2,5,7]=>[1,5,3,4,6,2,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,4,2,7,5,6]=>[1,4,3,2,6,7,5]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,3,4,7,2,5,6]=>[1,5,3,4,6,7,2]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]=>[.,[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,7,4,6]=>[1,3,2,6,5,7,4]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,5,2,6,7,4]=>[1,5,3,7,2,6,4]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,5,2,6,4,7]=>[1,5,3,6,2,4,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,5,6,2,7,4]=>[1,6,3,7,5,2,4]=>[.,[[[.,.],[[.,.],.]],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,5,6,7,2,4]=>[1,4,3,7,5,6,2]=>[.,[[[.,.],.],[[.,[.,.]],.]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,5,6,2,4,7]=>[1,4,3,6,5,2,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,2,4,7,6]=>[1,4,3,5,2,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,2,7,4,6]=>[1,5,3,6,2,7,4]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,7,2,4,6]=>[1,4,3,6,5,7,2]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,5,2,4,6,7]=>[1,4,3,5,2,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>[.,[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,2,6,4,7,5]=>[1,3,2,6,7,4,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,7,4,5]=>[1,3,2,5,7,6,4]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2,6,4,5,7]=>[1,3,2,5,6,4,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,6,2,4,7,5]=>[1,4,3,6,7,2,5]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,6,2,7,4,5]=>[1,6,3,5,7,2,4]=>[.,[[[.,.],[[.,.],.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,6,7,2,4,5]=>[1,4,3,5,7,6,2]=>[.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,3,2,4,7,5,6]=>[1,3,2,4,6,7,5]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,5,6,7,2]=>[3,7,1,4,5,6,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,4,5,6,2,7]=>[3,6,1,4,5,2,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,4,5,2,7,6]=>[3,5,1,4,2,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,4,5,7,2,6]=>[3,6,1,4,5,7,2]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,4,5,2,6,7]=>[3,5,1,4,2,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,7,5]=>[3,4,1,2,7,6,5]=>[[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,4,2,6,5,7]=>[3,4,1,2,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,6,2,7,5]=>[3,6,1,4,7,2,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,4,6,7,2,5]=>[3,5,1,4,7,6,2]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,4,6,2,5,7]=>[3,5,1,4,6,2,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,2,5,7,6]=>[3,4,1,2,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,4,2,7,5,6]=>[3,4,1,2,6,7,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,4,7,2,5,6]=>[3,5,1,4,6,7,2]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,4,2,5,6,7]=>[3,4,1,2,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,4,1,5,6,7,2]=>[4,7,3,1,5,6,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,4,1,5,6,2,7]=>[4,6,3,1,5,2,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,4,1,5,2,7,6]=>[4,5,3,1,2,7,6]=>[[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,4,1,5,7,2,6]=>[4,6,3,1,5,7,2]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,4,1,5,2,6,7]=>[4,5,3,1,2,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,5,1,6,7,2]=>[5,7,3,4,1,6,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,5,1,6,2,7]=>[5,6,3,4,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,1,7,2]=>[6,7,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,1,2]=>[2,7,3,4,5,6,1]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,6,1,2,7]=>[2,6,3,4,5,1,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,5,1,2,7,6]=>[2,5,3,4,1,7,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,5,1,7,2,6]=>[5,6,3,4,1,7,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,5,7,1,2,6]=>[2,6,3,4,5,7,1]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6,7]=>[2,5,3,4,1,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,4,1,2,6,7,5]=>[2,4,3,1,7,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,6,5,7]=>[2,4,3,1,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,4,1,6,2,7,5]=>[4,6,3,1,7,2,5]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[3,4,1,6,7,2,5]=>[4,5,3,1,7,6,2]=>[[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,4,1,6,2,5,7]=>[4,5,3,1,6,2,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,4,6,1,2,7,5]=>[2,6,3,4,7,1,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[3,4,6,1,7,2,5]=>[6,5,3,4,7,1,2]=>[[[[.,[.,.]],[.,.]],.],[.,.]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,4,6,7,1,2,5]=>[2,5,3,4,7,6,1]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,6,1,2,5,7]=>[2,5,3,4,6,1,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,4,1,2,5,7,6]=>[2,4,3,1,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,4,1,2,7,5,6]=>[2,4,3,1,6,7,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[3,4,1,7,2,5,6]=>[4,5,3,1,6,7,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,4,7,1,2,5,6]=>[2,5,3,4,6,7,1]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>[2,4,3,1,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,2,5,6,7,4]=>[2,3,1,7,5,6,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2,5,6,4,7]=>[2,3,1,6,5,4,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,5,4,7,6]=>[2,3,1,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,5,7,4,6]=>[2,3,1,6,5,7,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,2,5,4,6,7]=>[2,3,1,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,5,2,6,7,4]=>[3,5,1,7,2,6,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,5,2,6,4,7]=>[3,5,1,6,2,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,5,6,2,7,4]=>[3,6,1,7,5,2,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,5,6,7,2,4]=>[3,4,1,7,5,6,2]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,5,6,2,4,7]=>[3,4,1,6,5,2,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,5,2,4,7,6]=>[3,4,1,5,2,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,5,2,7,4,6]=>[3,5,1,6,2,7,4]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,1,5,7,2,4,6]=>[3,4,1,6,5,7,2]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,1,5,2,4,6,7]=>[3,4,1,5,2,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,5,1,2,6,7,4]=>[2,5,3,7,1,6,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,5,1,2,6,4,7]=>[2,5,3,6,1,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,5,1,6,2,7,4]=>[5,6,3,7,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,5,1,6,7,2,4]=>[5,4,3,7,1,6,2]=>[[[[.,[.,.]],.],.],[[.,.],.]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[3,5,1,6,2,4,7]=>[5,4,3,6,1,2,7]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,5,6,1,2,7,4]=>[2,6,3,7,5,1,4]=>[[.,.],[[.,[[.,.],.]],[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,5,6,1,7,2,4]=>[6,4,3,7,5,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,5,6,7,1,2,4]=>[2,4,3,7,5,6,1]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,5,6,1,2,4,7]=>[2,4,3,6,5,1,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,1,2,4,7,6]=>[2,4,3,5,1,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,1,2,7,4,6]=>[2,5,3,6,1,7,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,1,7,2,4,6]=>[5,4,3,6,1,7,2]=>[[[[.,[.,.]],.],.],[.,[.,.]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,7,1,2,4,6]=>[2,4,3,6,5,7,1]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,5,1,2,4,6,7]=>[2,4,3,5,1,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,2,4,6,7,5]=>[2,3,1,4,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,1,2,4,6,5,7]=>[2,3,1,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,6,4,7,5]=>[2,3,1,6,7,4,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,1,2,6,7,4,5]=>[2,3,1,5,7,6,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,1,2,6,4,5,7]=>[2,3,1,5,6,4,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,6,2,4,7,5]=>[3,4,1,6,7,2,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,1,6,2,7,4,5]=>[3,6,1,5,7,2,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,1,6,7,2,4,5]=>[3,4,1,5,7,6,2]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,1,6,2,4,5,7]=>[3,4,1,5,6,2,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,6,1,2,4,7,5]=>[2,4,3,6,7,1,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,6,1,2,7,4,5]=>[2,6,3,5,7,1,4]=>[[.,.],[[.,[[.,.],.]],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,6,1,7,2,4,5]=>[6,4,3,5,7,1,2]=>[[[[.,[.,.]],.],[.,.]],[.,.]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,6,7,1,2,4,5]=>[2,4,3,5,7,6,1]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,6,1,2,4,5,7]=>[2,4,3,5,6,1,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,7,6]=>[2,3,1,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,1,2,4,7,5,6]=>[2,3,1,4,6,7,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,1,2,7,4,5,6]=>[2,3,1,5,6,7,4]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,7,2,4,5,6]=>[3,4,1,5,6,7,2]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,7,1,2,4,5,6]=>[2,4,3,5,6,7,1]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>[2,3,1,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>[.,[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,7,3,6]=>[1,2,6,4,5,7,3]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>[.,[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,2,4,6,3,7,5]=>[1,2,6,4,7,3,5]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,2,4,6,7,3,5]=>[1,2,5,4,7,6,3]=>[.,[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,3,5,7]=>[1,2,5,4,6,3,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,2,4,3,7,5,6]=>[1,2,4,3,6,7,5]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,4,2,5,6,7,3]=>[1,4,7,2,5,6,3]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,4,2,5,6,3,7]=>[1,4,6,2,5,3,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,4,2,5,3,7,6]=>[1,4,5,2,3,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,4,2,5,7,3,6]=>[1,4,6,2,5,7,3]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,4,5,2,6,7,3]=>[1,5,7,4,2,6,3]=>[.,[[[.,[.,.]],.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,4,5,2,6,3,7]=>[1,5,6,4,2,3,7]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,4,5,6,2,7,3]=>[1,6,7,4,5,2,3]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,5,6,7,2,3]=>[1,3,7,4,5,6,2]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,6,2,3,7]=>[1,3,6,4,5,2,7]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,4,5,2,3,7,6]=>[1,3,5,4,2,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,5,2,7,3,6]=>[1,5,6,4,2,7,3]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,7,2,3,6]=>[1,3,6,4,5,7,2]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,2,3,6,7]=>[1,3,5,4,2,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,4,2,3,6,7,5]=>[1,3,4,2,7,6,5]=>[.,[[.,.],[.,[[[.,.],.],.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,4,2,3,6,5,7]=>[1,3,4,2,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,4,2,6,3,7,5]=>[1,4,6,2,7,3,5]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,6,7,3,5]=>[1,4,5,2,7,6,3]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,4,6,2,3,7,5]=>[1,3,6,4,7,2,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,6,2,7,3,5]=>[1,6,5,4,7,2,3]=>[.,[[[[.,[.,.]],.],.],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,6,7,2,3,5]=>[1,3,5,4,7,6,2]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,4,2,3,5,7,6]=>[1,3,4,2,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,2,5,6,7,3]=>[2,4,7,1,5,6,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,1,2,5,6,3,7]=>[2,4,6,1,5,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,2,5,3,7,6]=>[2,4,5,1,3,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,1,2,5,7,3,6]=>[2,4,6,1,5,7,3]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,1,2,5,3,6,7]=>[2,4,5,1,3,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,5,2,6,7,3]=>[4,5,7,1,2,6,3]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,1,5,2,6,3,7]=>[4,5,6,1,2,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,5,6,2,7,3]=>[4,6,7,1,5,2,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,1,5,6,7,2,3]=>[4,3,7,1,5,6,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,1,5,6,2,3,7]=>[4,3,6,1,5,2,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,5,2,3,7,6]=>[4,3,5,1,2,7,6]=>[[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[4,1,5,2,7,3,6]=>[4,5,6,1,2,7,3]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,1,5,7,2,3,6]=>[4,3,6,1,5,7,2]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,1,5,2,3,6,7]=>[4,3,5,1,2,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,5,1,2,6,7,3]=>[2,5,7,4,1,6,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,5,1,2,6,3,7]=>[2,5,6,4,1,3,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,5,1,6,2,7,3]=>[5,6,7,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[4,5,1,6,7,2,3]=>[5,3,7,4,1,6,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[4,5,1,6,2,3,7]=>[5,3,6,4,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,5,6,1,2,7,3]=>[2,6,7,4,5,1,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[4,5,6,1,7,2,3]=>[6,3,7,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,7,1,2,3]=>[2,3,7,4,5,6,1]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>[2,3,6,4,5,1,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,5,1,2,3,7,6]=>[2,3,5,4,1,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[4,5,1,2,7,3,6]=>[2,5,6,4,1,7,3]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[4,5,1,7,2,3,6]=>[5,3,6,4,1,7,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,5,7,1,2,3,6]=>[2,3,6,4,5,7,1]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,1,2,3,6,7]=>[2,3,5,4,1,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,1,2,3,6,7,5]=>[2,3,4,1,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,1,2,3,6,5,7]=>[2,3,4,1,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,6,3,7,5]=>[2,4,6,1,7,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[4,1,2,6,7,3,5]=>[2,4,5,1,7,6,3]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,1,2,6,3,5,7]=>[2,4,5,1,6,3,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,6,2,3,7,5]=>[4,3,6,1,7,2,5]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[4,1,6,2,7,3,5]=>[4,6,5,1,7,2,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,1,6,7,2,3,5]=>[4,3,5,1,7,6,2]=>[[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,1,6,2,3,5,7]=>[4,3,5,1,6,2,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,6,1,2,3,7,5]=>[2,3,6,4,7,1,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[4,6,1,2,7,3,5]=>[2,6,5,4,7,1,3]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[4,6,1,7,2,3,5]=>[6,3,5,4,7,1,2]=>[[[.,[.,.]],[[.,.],.]],[.,.]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,6,7,1,2,3,5]=>[2,3,5,4,7,6,1]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,6,1,2,3,5,7]=>[2,3,5,4,6,1,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,7,6]=>[2,3,4,1,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[4,1,2,3,7,5,6]=>[2,3,4,1,6,7,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,7,3,5,6]=>[2,4,5,1,6,7,3]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,1,7,2,3,5,6]=>[4,3,5,1,6,7,2]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,7,1,2,3,5,6]=>[2,3,5,4,6,7,1]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[4,1,2,3,5,6,7]=>[2,3,4,1,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,2,3,5,7,4,6]=>[1,2,3,6,5,7,4]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,2,5,3,6,7,4]=>[1,2,5,7,3,6,4]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,2,5,6,3,7,4]=>[1,2,6,7,5,3,4]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,2,5,6,7,3,4]=>[1,2,4,7,5,6,3]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,2,5,6,3,4,7]=>[1,2,4,6,5,3,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,2,5,3,4,7,6]=>[1,2,4,5,3,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,5,2,3,6,7,4]=>[1,3,5,7,2,6,4]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,7,3,4]=>[1,5,4,7,2,6,3]=>[.,[[[.,[.,.]],.],[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,5,6,2,3,7,4]=>[1,3,6,7,5,2,4]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,6,2,7,3,4]=>[1,6,4,7,5,2,3]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,5,6,7,2,3,4]=>[1,3,4,7,5,6,2]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,1,2,3,6,7,4]=>[2,3,5,7,1,6,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,1,2,3,6,4,7]=>[2,3,5,6,1,4,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,6,3,7,4]=>[2,5,6,7,1,3,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,1,2,6,7,3,4]=>[2,5,4,7,1,6,3]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,1,2,6,3,4,7]=>[2,5,4,6,1,3,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[5,1,6,2,3,7,4]=>[5,3,6,7,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[5,1,6,2,7,3,4]=>[5,6,4,7,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,1,6,7,2,3,4]=>[5,3,4,7,1,6,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[5,1,6,2,3,4,7]=>[5,3,4,6,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[5,6,1,2,3,7,4]=>[2,3,6,7,5,1,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[5,6,1,2,7,3,4]=>[2,6,4,7,5,1,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,6,1,7,2,3,4]=>[6,3,4,7,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,1,2,3,4]=>[2,3,4,7,5,6,1]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,1,2,3,4,7]=>[2,3,4,6,5,1,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,7,6]=>[2,3,4,5,1,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,7,4,6]=>[2,3,5,6,1,7,4]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,1,2,7,3,4,6]=>[2,5,4,6,1,7,3]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[5,1,7,2,3,4,6]=>[5,3,4,6,1,7,2]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[5,7,1,2,3,4,6]=>[2,3,4,6,5,7,1]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[5,1,2,3,4,6,7]=>[2,3,4,5,1,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,2,3,6,7,4,5]=>[1,2,3,5,7,6,4]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,7,5]=>[2,3,4,6,7,1,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,1,2,3,7,4,5]=>[2,3,6,5,7,1,4]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[6,1,2,7,3,4,5]=>[2,6,4,5,7,1,3]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[6,1,7,2,3,4,5]=>[6,3,4,5,7,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[6,7,1,2,3,4,5]=>[2,3,4,5,7,6,1]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[6,1,2,3,4,5,7]=>[2,3,4,5,6,1,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[7,1,2,3,4,5,6]=>[2,3,4,5,6,7,1]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,1]=>[8,2,3,4,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,1,8]=>[7,2,3,4,5,6,1,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,6,1,8,7]=>[6,2,3,4,5,1,8,7]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,6,8,1,7]=>[7,2,3,4,5,6,8,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,6,1,7,8]=>[6,2,3,4,5,1,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,4,5,1,7,8,6]=>[5,2,3,4,1,8,7,6]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,4,5,7,1,8,6]=>[7,2,3,4,5,8,1,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,5,7,8,1,6]=>[6,2,3,4,5,8,7,1]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,4,5,7,1,6,8]=>[6,2,3,4,5,7,1,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,4,5,1,6,8,7]=>[5,2,3,4,1,6,8,7]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,4,5,1,8,6,7]=>[5,2,3,4,1,7,8,6]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,4,5,8,1,6,7]=>[6,2,3,4,5,7,8,1]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,6,7,5,8]=>[4,2,3,1,7,6,5,8]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,8,5,7]=>[4,2,3,1,7,6,8,5]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,6,5,7,8]=>[4,2,3,1,6,5,7,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,4,6,1,7,8,5]=>[6,2,3,4,8,1,7,5]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,4,6,7,1,8,5]=>[7,2,3,4,8,6,1,5]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,4,6,7,8,1,5]=>[5,2,3,4,8,6,7,1]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,7,1,5,8]=>[5,2,3,4,7,6,1,8]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,1,5,8,7]=>[5,2,3,4,6,1,8,7]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,1,8,5,7]=>[6,2,3,4,7,1,8,5]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,4,6,1,5,7,8]=>[5,2,3,4,6,1,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,4,1,5,7,8,6]=>[4,2,3,1,5,8,7,6]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,4,1,5,7,6,8]=>[4,2,3,1,5,7,6,8]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,4,1,7,5,8,6]=>[4,2,3,1,7,8,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,4,1,7,8,5,6]=>[4,2,3,1,6,8,7,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,4,7,1,5,8,6]=>[5,2,3,4,7,8,1,6]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,4,7,1,8,5,6]=>[7,2,3,4,6,8,1,5]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,6,8]=>[5,2,3,4,6,7,1,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,4,1,5,8,6,7]=>[4,2,3,1,5,7,8,6]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,4,1,8,5,6,7]=>[4,2,3,1,6,7,8,5]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,8,1,5,6,7]=>[5,2,3,4,6,7,8,1]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,5,6,7,8,4]=>[3,2,1,8,5,6,7,4]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,5,6,7,4,8]=>[3,2,1,7,5,6,4,8]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,5,6,4,8,7]=>[3,2,1,6,5,4,8,7]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,5,6,8,4,7]=>[3,2,1,7,5,6,8,4]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,5,6,4,7,8]=>[3,2,1,6,5,4,7,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,7,8,4,6]=>[3,2,1,6,5,8,7,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,4,6,8]=>[3,2,1,6,5,7,4,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,5,8,4,6,7]=>[3,2,1,6,5,7,8,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,5,4,6,7,8]=>[3,2,1,5,4,6,7,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,5,1,6,7,8,4]=>[5,2,3,8,1,6,7,4]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,5,1,6,7,4,8]=>[5,2,3,7,1,6,4,8]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,5,1,6,4,8,7]=>[5,2,3,6,1,4,8,7]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,5,1,6,8,4,7]=>[5,2,3,7,1,6,8,4]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,5,1,6,4,7,8]=>[5,2,3,6,1,4,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,5,6,1,7,8,4]=>[6,2,3,8,5,1,7,4]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,5,6,1,7,4,8]=>[6,2,3,7,5,1,4,8]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,5,6,7,1,8,4]=>[7,2,3,8,5,6,1,4]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,8,1,4]=>[4,2,3,8,5,6,7,1]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,5,6,7,1,4,8]=>[4,2,3,7,5,6,1,8]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,8,1,4,7]=>[4,2,3,7,5,6,8,1]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,1,4,7,8,6]=>[4,2,3,5,1,8,7,6]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,7,8,1,4,6]=>[4,2,3,6,5,8,7,1]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,5,1,8,4,6,7]=>[5,2,3,6,1,7,8,4]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,5,1,4,6,7,8]=>[4,2,3,5,1,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,3,1,4,6,7,8,5]=>[3,2,1,4,8,6,7,5]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,3,1,4,6,8,5,7]=>[3,2,1,4,7,6,8,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,3,1,6,4,7,8,5]=>[3,2,1,6,8,4,7,5]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,3,1,6,4,7,5,8]=>[3,2,1,6,7,4,5,8]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,3,1,6,7,4,8,5]=>[3,2,1,7,8,6,4,5]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,6,7,8,4,5]=>[3,2,1,5,8,6,7,4]=>[[[.,.],.],[[.,.],[[.,[.,.]],.]]]
[1,0,1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,1,6,7,4,5,8]=>[3,2,1,5,7,6,4,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,1,6,4,8,5,7]=>[3,2,1,6,7,4,8,5]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,1,6,8,4,5,7]=>[3,2,1,5,7,6,8,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,1,6,4,5,7,8]=>[3,2,1,5,6,4,7,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,3,6,1,7,4,8,5]=>[6,2,3,7,8,1,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,6,1,7,8,4,5]=>[6,2,3,5,8,1,7,4]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,3,6,7,1,4,8,5]=>[4,2,3,7,8,6,1,5]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,3,6,1,4,5,8,7]=>[4,2,3,5,6,1,8,7]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,6,1,4,5,7,8]=>[4,2,3,5,6,1,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,4,7,8,5,6]=>[3,2,1,4,6,8,7,5]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,3,1,7,4,5,8,6]=>[3,2,1,5,7,8,4,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,7,4,8,5,6]=>[3,2,1,7,6,8,4,5]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,1,7,8,4,5,6]=>[3,2,1,5,6,8,7,4]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,7,8,1,4,5,6]=>[4,2,3,5,6,8,7,1]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,7,1,4,5,6,8]=>[4,2,3,5,6,7,1,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,3,1,4,5,6,8,7]=>[3,2,1,4,5,6,8,7]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,8,6,7]=>[3,2,1,4,5,7,8,6]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,1,4,8,5,6,7]=>[3,2,1,4,6,7,8,5]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,1,8,4,5,6,7]=>[3,2,1,5,6,7,8,4]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,8,1,4,5,6,7]=>[4,2,3,5,6,7,8,1]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,8,3]=>[2,1,8,4,5,6,7,3]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,6,3,8,7]=>[2,1,6,4,5,3,8,7]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,5,3,7,8,6]=>[2,1,5,4,3,8,7,6]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,7,3,8,6]=>[2,1,7,4,5,8,3,6]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,7,8,3,6]=>[2,1,6,4,5,8,7,3]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,5,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,4,5,8,3,6,7]=>[2,1,6,4,5,7,8,3]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,4,5,3,6,7,8]=>[2,1,5,4,3,6,7,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,6,7,5]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,8,5,7]=>[2,1,4,3,7,6,8,5]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,6,3,7,8,5]=>[2,1,6,4,8,3,7,5]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,6,7,3,8,5]=>[2,1,7,4,8,6,3,5]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,6,7,8,3,5]=>[2,1,5,4,8,6,7,3]=>[[.,.],[[[.,.],.],[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,3,5,8,7]=>[2,1,5,4,6,3,8,7]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,3,8,5,7]=>[2,1,6,4,7,3,8,5]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,8,3,5,7]=>[2,1,5,4,7,6,8,3]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,7,8,6]=>[2,1,4,3,5,8,7,6]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,3,7,5,8,6]=>[2,1,4,3,7,8,5,6]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,4,3,7,8,5,6]=>[2,1,4,3,6,8,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,4,7,3,8,5,6]=>[2,1,7,4,6,8,3,5]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,4,7,8,3,5,6]=>[2,1,5,4,6,8,7,3]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,4,7,3,5,6,8]=>[2,1,5,4,6,7,3,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,4,3,5,8,6,7]=>[2,1,4,3,5,7,8,6]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,4,3,8,5,6,7]=>[2,1,4,3,6,7,8,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,4,8,3,5,6,7]=>[2,1,5,4,6,7,8,3]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,4,1,5,6,7,8,3]=>[4,2,8,1,5,6,7,3]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,4,1,5,6,7,3,8]=>[4,2,7,1,5,6,3,8]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,4,1,5,6,8,3,7]=>[4,2,7,1,5,6,8,3]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,4,1,5,6,3,7,8]=>[4,2,6,1,5,3,7,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,5,3,7,6,8]=>[4,2,5,1,3,7,6,8]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,4,1,5,3,6,8,7]=>[4,2,5,1,3,6,8,7]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,5,3,8,6,7]=>[4,2,5,1,3,7,8,6]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,4,1,5,8,3,6,7]=>[4,2,6,1,5,7,8,3]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,1,5,3,6,7,8]=>[4,2,5,1,3,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,4,5,1,6,7,8,3]=>[5,2,8,4,1,6,7,3]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,4,5,1,6,7,3,8]=>[5,2,7,4,1,6,3,8]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,4,5,1,6,3,8,7]=>[5,2,6,4,1,3,8,7]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,4,5,1,6,8,3,7]=>[5,2,7,4,1,6,8,3]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,4,5,1,6,3,7,8]=>[5,2,6,4,1,3,7,8]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,4,5,6,1,7,8,3]=>[6,2,8,4,5,1,7,3]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,4,5,6,1,7,3,8]=>[6,2,7,4,5,1,3,8]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,4,5,6,7,1,8,3]=>[7,2,8,4,5,6,1,3]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,7,8,1,3]=>[3,2,8,4,5,6,7,1]=>[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,4,5,6,7,1,3,8]=>[3,2,7,4,5,6,1,8]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,4,5,6,1,3,8,7]=>[3,2,6,4,5,1,8,7]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,4,5,6,1,8,3,7]=>[6,2,7,4,5,1,8,3]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,4,5,6,1,3,7,8]=>[3,2,6,4,5,1,7,8]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,5,1,3,7,8,6]=>[3,2,5,4,1,8,7,6]=>[[[.,.],.],[[.,.],[[[.,.],.],.]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,5,1,3,7,6,8]=>[3,2,5,4,1,7,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,5,1,7,3,8,6]=>[5,2,7,4,1,8,3,6]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,5,1,7,8,3,6]=>[5,2,6,4,1,8,7,3]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,5,1,7,3,6,8]=>[5,2,6,4,1,7,3,8]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,7,1,3,8,6]=>[3,2,7,4,5,8,1,6]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,7,1,8,3,6]=>[7,2,6,4,5,8,1,3]=>[[[.,.],[[[.,.],[.,.]],.]],[.,.]]
[1,0,1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,4,5,1,8,3,6,7]=>[5,2,6,4,1,7,8,3]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,4,5,1,3,6,7,8]=>[3,2,5,4,1,6,7,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,1,3,6,7,8,5]=>[3,2,4,1,8,6,7,5]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,1,3,6,7,5,8]=>[3,2,4,1,7,6,5,8]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,1,3,6,5,8,7]=>[3,2,4,1,6,5,8,7]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,1,3,6,8,5,7]=>[3,2,4,1,7,6,8,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,1,3,6,5,7,8]=>[3,2,4,1,6,5,7,8]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,1,6,3,7,8,5]=>[4,2,6,1,8,3,7,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,1,6,3,7,5,8]=>[4,2,6,1,7,3,5,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,1,6,7,3,8,5]=>[4,2,7,1,8,6,3,5]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,1,6,7,8,3,5]=>[4,2,5,1,8,6,7,3]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,1,6,3,5,8,7]=>[4,2,5,1,6,3,8,7]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,8,5,7]=>[4,2,6,1,7,3,8,5]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,1,6,8,3,5,7]=>[4,2,5,1,7,6,8,3]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,1,6,3,5,7,8]=>[4,2,5,1,6,3,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,6,1,3,7,8,5]=>[3,2,6,4,8,1,7,5]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,6,1,3,7,5,8]=>[3,2,6,4,7,1,5,8]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,6,1,7,3,8,5]=>[6,2,7,4,8,1,3,5]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,6,7,1,3,8,5]=>[3,2,7,4,8,6,1,5]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,6,7,1,8,3,5]=>[7,2,5,4,8,6,1,3]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,6,7,8,1,3,5]=>[3,2,5,4,8,6,7,1]=>[[[.,.],.],[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,6,7,1,3,5,8]=>[3,2,5,4,7,6,1,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,1,3,5,8,7]=>[3,2,5,4,6,1,8,7]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,1,3,8,5,7]=>[3,2,6,4,7,1,8,5]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,1,8,3,5,7]=>[6,2,5,4,7,1,8,3]=>[[[.,.],[[[.,.],.],.]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,8,1,3,5,7]=>[3,2,5,4,7,6,8,1]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,4,1,3,5,7,8,6]=>[3,2,4,1,5,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,1,3,5,7,6,8]=>[3,2,4,1,5,7,6,8]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,4,1,3,7,5,8,6]=>[3,2,4,1,7,8,5,6]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,4,1,3,7,8,5,6]=>[3,2,4,1,6,8,7,5]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,4,1,3,7,5,6,8]=>[3,2,4,1,6,7,5,8]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,4,1,7,3,5,8,6]=>[4,2,5,1,7,8,3,6]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,4,1,7,3,8,5,6]=>[4,2,7,1,6,8,3,5]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,4,1,7,8,3,5,6]=>[4,2,5,1,6,8,7,3]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,4,7,1,3,5,8,6]=>[3,2,5,4,7,8,1,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,4,7,1,3,8,5,6]=>[3,2,7,4,6,8,1,5]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,4,7,8,1,3,5,6]=>[3,2,5,4,6,8,7,1]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,4,1,3,5,6,8,7]=>[3,2,4,1,5,6,8,7]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1,3,5,8,6,7]=>[3,2,4,1,5,7,8,6]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,1,3,8,5,6,7]=>[3,2,4,1,6,7,8,5]=>[[[.,.],.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,1,8,3,5,6,7]=>[4,2,5,1,6,7,8,3]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,8,1,3,5,6,7]=>[3,2,5,4,6,7,8,1]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,4,1,3,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,5,6,7,8,4]=>[2,1,3,8,5,6,7,4]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,6,4,8,7]=>[2,1,3,6,5,4,8,7]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,7,8,6]=>[2,1,3,5,4,8,7,6]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,7,4,8,6]=>[2,1,3,7,5,8,4,6]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,7,8,4,6]=>[2,1,3,6,5,8,7,4]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4,6,8,7]=>[2,1,3,5,4,6,8,7]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[2,1,3,5,4,8,6,7]=>[2,1,3,5,4,7,8,6]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,6,7,8,4]=>[2,1,5,8,3,6,7,4]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[2,1,5,3,6,4,8,7]=>[2,1,5,6,3,4,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[2,1,5,3,6,8,4,7]=>[2,1,5,7,3,6,8,4]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[2,1,5,3,6,4,7,8]=>[2,1,5,6,3,4,7,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[2,1,5,6,3,7,8,4]=>[2,1,6,8,5,3,7,4]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,1,5,6,7,8,3,4]=>[2,1,4,8,5,6,7,3]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[2,1,5,6,3,4,8,7]=>[2,1,4,6,5,3,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[2,1,5,6,3,4,7,8]=>[2,1,4,6,5,3,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[2,1,5,3,7,4,8,6]=>[2,1,5,7,3,8,4,6]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,1,5,3,7,8,4,6]=>[2,1,5,6,3,8,7,4]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,1,5,3,7,4,6,8]=>[2,1,5,6,3,7,4,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,1,5,7,3,8,4,6]=>[2,1,7,6,5,8,3,4]=>[[.,.],[[[[.,[.,.]],.],.],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,1,5,7,8,3,4,6]=>[2,1,4,6,5,8,7,3]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[2,1,5,3,4,6,8,7]=>[2,1,4,5,3,6,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,1,5,3,8,4,6,7]=>[2,1,5,6,3,7,8,4]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[2,1,5,3,4,6,7,8]=>[2,1,4,5,3,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,5,1,3,6,7,8,4]=>[3,2,5,8,1,6,7,4]=>[[[.,.],.],[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,7,4,8]=>[3,2,5,7,1,6,4,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,5,1,3,6,8,4,7]=>[3,2,5,7,1,6,8,4]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,5,1,3,6,4,7,8]=>[3,2,5,6,1,4,7,8]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[2,5,1,6,3,7,8,4]=>[5,2,6,8,1,3,7,4]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[2,5,1,6,3,7,4,8]=>[5,2,6,7,1,3,4,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,5,1,6,7,3,8,4]=>[5,2,7,8,1,6,3,4]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,5,1,6,7,8,3,4]=>[5,2,4,8,1,6,7,3]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[2,5,1,6,3,4,8,7]=>[5,2,4,6,1,3,8,7]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,5,6,1,3,7,8,4]=>[3,2,6,8,5,1,7,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[2,5,6,1,3,7,4,8]=>[3,2,6,7,5,1,4,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[2,5,6,1,7,3,8,4]=>[6,2,7,8,5,1,3,4]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,5,6,7,1,3,8,4]=>[3,2,7,8,5,6,1,4]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,5,6,7,8,1,3,4]=>[3,2,4,8,5,6,7,1]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,5,6,8,1,3,4,7]=>[3,2,4,7,5,6,8,1]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[2,5,1,3,4,7,8,6]=>[3,2,4,5,1,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[2,5,1,3,7,4,8,6]=>[3,2,5,7,1,8,4,6]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,5,1,3,7,8,4,6]=>[3,2,5,6,1,8,7,4]=>[[[.,.],.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[2,5,1,7,3,4,8,6]=>[5,2,4,7,1,8,3,6]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[2,5,7,1,3,4,8,6]=>[3,2,4,7,5,8,1,6]=>[[[.,.],.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,5,7,1,3,8,4,6]=>[3,2,7,6,5,8,1,4]=>[[[.,.],.],[[[[.,.],.],.],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[2,5,7,8,1,3,4,6]=>[3,2,4,6,5,8,7,1]=>[[[.,.],.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,5,1,3,8,4,6,7]=>[3,2,5,6,1,7,8,4]=>[[[.,.],.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,5,1,3,4,6,7,8]=>[3,2,4,5,1,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,1,3,4,6,7,8,5]=>[2,1,3,4,8,6,7,5]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[2,1,3,6,7,4,8,5]=>[2,1,3,7,8,6,4,5]=>[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,1,3,6,7,8,4,5]=>[2,1,3,5,8,6,7,4]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[2,1,3,6,4,5,8,7]=>[2,1,3,5,6,4,8,7]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,1,3,6,4,8,5,7]=>[2,1,3,6,7,4,8,5]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,7,8,5]=>[2,1,4,6,8,3,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[2,1,6,3,7,4,8,5]=>[2,1,6,7,8,3,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,1,6,3,7,8,4,5]=>[2,1,6,5,8,3,7,4]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,1,6,7,3,4,8,5]=>[2,1,4,7,8,6,3,5]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[2,1,6,7,3,8,4,5]=>[2,1,7,5,8,6,3,4]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,1,6,7,8,3,4,5]=>[2,1,4,5,8,6,7,3]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[2,1,6,3,4,5,8,7]=>[2,1,4,5,6,3,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,1,6,3,4,8,5,7]=>[2,1,4,6,7,3,8,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,1,6,3,8,4,5,7]=>[2,1,6,5,7,3,8,4]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[2,6,1,3,7,4,8,5]=>[3,2,6,7,8,1,4,5]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[2,6,1,3,7,8,4,5]=>[3,2,6,5,8,1,7,4]=>[[[.,.],.],[[[.,.],.],[[.,.],.]]]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[2,6,1,3,7,4,5,8]=>[3,2,6,5,7,1,4,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[2,6,1,7,3,4,8,5]=>[6,2,4,7,8,1,3,5]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[2,6,7,1,3,4,8,5]=>[3,2,4,7,8,6,1,5]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,6,7,1,3,8,4,5]=>[3,2,7,5,8,6,1,4]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[2,6,7,8,1,3,4,5]=>[3,2,4,5,8,6,7,1]=>[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,6,1,3,8,4,5,7]=>[3,2,6,5,7,1,8,4]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,6,1,8,3,4,5,7]=>[6,2,4,5,7,1,8,3]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,6,8,1,3,4,5,7]=>[3,2,4,5,7,6,8,1]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,6,1,3,4,5,7,8]=>[3,2,4,5,6,1,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,1,3,4,5,7,8,6]=>[2,1,3,4,5,8,7,6]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,1,3,4,7,5,8,6]=>[2,1,3,4,7,8,5,6]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[2,1,7,3,4,5,8,6]=>[2,1,4,5,7,8,3,6]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,1,7,3,8,4,5,6]=>[2,1,7,5,6,8,3,4]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,1,7,8,3,4,5,6]=>[2,1,4,5,6,8,7,3]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,1,7,3,4,5,6,8]=>[2,1,4,5,6,7,3,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,7,1,3,4,5,8,6]=>[3,2,4,5,7,8,1,6]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,7,1,8,3,4,5,6]=>[7,2,4,5,6,8,1,3]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,7,8,1,3,4,5,6]=>[3,2,4,5,6,8,7,1]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,7,1,3,4,5,6,8]=>[3,2,4,5,6,7,1,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,1,3,4,5,8,6,7]=>[2,1,3,4,5,7,8,6]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,1,3,4,8,5,6,7]=>[2,1,3,4,6,7,8,5]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,1,3,8,4,5,6,7]=>[2,1,3,5,6,7,8,4]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,1,8,3,4,5,6,7]=>[2,1,4,5,6,7,8,3]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,8,1,3,4,5,6,7]=>[3,2,4,5,6,7,8,1]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,8,2]=>[1,8,3,4,5,6,7,2]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,7,2,8]=>[1,7,3,4,5,6,2,8]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,4,5,6,8,2,7]=>[1,7,3,4,5,6,8,2]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,4,5,6,2,7,8]=>[1,6,3,4,5,2,7,8]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,4,5,2,7,8,6]=>[1,5,3,4,2,8,7,6]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,3,4,5,7,2,8,6]=>[1,7,3,4,5,8,2,6]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,7,8,2,6]=>[1,6,3,4,5,8,7,2]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,4,5,2,8,6,7]=>[1,5,3,4,2,7,8,6]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,4,5,2,6,7,8]=>[1,5,3,4,2,6,7,8]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,6,7,8,5]=>[1,4,3,2,8,6,7,5]=>[.,[[[.,.],.],[[[.,.],[.,.]],.]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,6,2,7,8,5]=>[1,6,3,4,8,2,7,5]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,6,7,2,8,5]=>[1,7,3,4,8,6,2,5]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,6,7,8,2,5]=>[1,5,3,4,8,6,7,2]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,2,5,8,7]=>[1,5,3,4,6,2,8,7]=>[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,4,2,5,7,8,6]=>[1,4,3,2,5,8,7,6]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,4,2,7,5,8,6]=>[1,4,3,2,7,8,5,6]=>[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,4,2,7,8,5,6]=>[1,4,3,2,6,8,7,5]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,4,2,7,5,6,8]=>[1,4,3,2,6,7,5,8]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,4,7,2,5,8,6]=>[1,5,3,4,7,8,2,6]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,4,7,2,5,6,8]=>[1,5,3,4,6,7,2,8]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,4,2,5,6,8,7]=>[1,4,3,2,5,6,8,7]=>[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,3,4,2,5,8,6,7]=>[1,4,3,2,5,7,8,6]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,3,4,2,8,5,6,7]=>[1,4,3,2,6,7,8,5]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,3,4,8,2,5,6,7]=>[1,5,3,4,6,7,8,2]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,5,6,4,8,7]=>[1,3,2,6,5,4,8,7]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,5,6,8,4,7]=>[1,3,2,7,5,6,8,4]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,5,6,4,7,8]=>[1,3,2,6,5,4,7,8]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,7,6]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,7,4,8,6]=>[1,3,2,7,5,8,4,6]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,7,8,4,6]=>[1,3,2,6,5,8,7,4]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,4,6,8]=>[1,3,2,6,5,7,4,8]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,5,4,8,6,7]=>[1,3,2,5,4,7,8,6]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,5,8,4,6,7]=>[1,3,2,6,5,7,8,4]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,5,2,6,7,8,4]=>[1,5,3,8,2,6,7,4]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,5,2,6,7,4,8]=>[1,5,3,7,2,6,4,8]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,5,2,6,4,7,8]=>[1,5,3,6,2,4,7,8]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,5,6,2,7,8,4]=>[1,6,3,8,5,2,7,4]=>[.,[[[.,.],[[.,.],.]],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,5,6,2,7,4,8]=>[1,6,3,7,5,2,4,8]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,5,6,7,2,8,4]=>[1,7,3,8,5,6,2,4]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,5,6,7,8,2,4]=>[1,4,3,8,5,6,7,2]=>[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]
[1,1,0,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,6,2,4,7,8]=>[1,4,3,6,5,2,7,8]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,2,4,7,6,8]=>[1,4,3,5,2,7,6,8]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,2,7,8,4,6]=>[1,5,3,6,2,8,7,4]=>[.,[[[.,.],[.,.]],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,7,4,6,8]=>[1,5,3,6,2,7,4,8]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,7,2,4,8,6]=>[1,4,3,7,5,8,2,6]=>[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,7,2,8,4,6]=>[1,7,3,6,5,8,2,4]=>[.,[[[.,.],[[[.,.],.],.]],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,7,8,2,4,6]=>[1,4,3,6,5,8,7,2]=>[.,[[[.,.],.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,2,4,6,8]=>[1,4,3,6,5,7,2,8]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,5,2,8,4,6,7]=>[1,5,3,6,2,7,8,4]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,5,8,2,4,6,7]=>[1,4,3,6,5,7,8,2]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,5,2,4,6,7,8]=>[1,4,3,5,2,6,7,8]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,3,2,4,6,7,8,5]=>[1,3,2,4,8,6,7,5]=>[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,7,5,8]=>[1,3,2,4,7,6,5,8]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,3,2,4,6,8,5,7]=>[1,3,2,4,7,6,8,5]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,3,2,6,4,7,8,5]=>[1,3,2,6,8,4,7,5]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,3,2,6,4,7,5,8]=>[1,3,2,6,7,4,5,8]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,2,6,7,4,5,8]=>[1,3,2,5,7,6,4,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,6,4,8,5,7]=>[1,3,2,6,7,4,8,5]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,2,6,4,5,7,8]=>[1,3,2,5,6,4,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,3,6,2,7,4,8,5]=>[1,6,3,7,8,2,4,5]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,3,6,7,2,4,8,5]=>[1,4,3,7,8,6,2,5]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,6,7,2,8,4,5]=>[1,7,3,5,8,6,2,4]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,6,7,8,2,4,5]=>[1,4,3,5,8,6,7,2]=>[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]
[1,1,0,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,6,7,2,4,5,8]=>[1,4,3,5,7,6,2,8]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,6,2,4,8,5,7]=>[1,4,3,6,7,2,8,5]=>[.,[[[.,.],.],[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,6,2,8,4,5,7]=>[1,6,3,5,7,2,8,4]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,6,2,4,5,7,8]=>[1,4,3,5,6,2,7,8]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,3,2,4,5,7,8,6]=>[1,3,2,4,5,8,7,6]=>[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,3,2,4,7,5,8,6]=>[1,3,2,4,7,8,5,6]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,4,7,8,5,6]=>[1,3,2,4,6,8,7,5]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,2,4,7,5,6,8]=>[1,3,2,4,6,7,5,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,3,2,7,4,5,8,6]=>[1,3,2,5,7,8,4,6]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,7,4,8,5,6]=>[1,3,2,7,6,8,4,5]=>[.,[[.,.],[[[.,[.,.]],.],[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,2,7,8,4,5,6]=>[1,3,2,5,6,8,7,4]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,2,7,4,5,6,8]=>[1,3,2,5,6,7,4,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,3,7,2,4,5,8,6]=>[1,4,3,5,7,8,2,6]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,3,7,2,4,8,5,6]=>[1,4,3,7,6,8,2,5]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,7,2,8,4,5,6]=>[1,7,3,5,6,8,2,4]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,7,2,4,5,6,8]=>[1,4,3,5,6,7,2,8]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,8,6,7]=>[1,3,2,4,5,7,8,6]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,2,4,8,5,6,7]=>[1,3,2,4,6,7,8,5]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,8,2,4,5,6,7]=>[1,4,3,5,6,7,8,2]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,5,6,7,8,2]=>[3,8,1,4,5,6,7,2]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,4,5,6,7,2,8]=>[3,7,1,4,5,6,2,8]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,4,5,6,2,8,7]=>[3,6,1,4,5,2,8,7]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,1,4,5,6,8,2,7]=>[3,7,1,4,5,6,8,2]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,1,4,5,6,2,7,8]=>[3,6,1,4,5,2,7,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,4,5,2,7,8,6]=>[3,5,1,4,2,8,7,6]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,1,4,5,2,7,6,8]=>[3,5,1,4,2,7,6,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,1,4,5,8,2,6,7]=>[3,6,1,4,5,7,8,2]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,1,4,5,2,6,7,8]=>[3,5,1,4,2,6,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,6,7,8,5]=>[3,4,1,2,8,6,7,5]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,1,4,2,6,7,5,8]=>[3,4,1,2,7,6,5,8]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5,8,7]=>[3,4,1,2,6,5,8,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,1,4,2,6,8,5,7]=>[3,4,1,2,7,6,8,5]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,1,4,2,6,5,7,8]=>[3,4,1,2,6,5,7,8]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,1,4,6,2,7,5,8]=>[3,6,1,4,7,2,5,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,4,6,2,5,8,7]=>[3,5,1,4,6,2,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,1,4,6,2,8,5,7]=>[3,6,1,4,7,2,8,5]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,1,4,6,8,2,5,7]=>[3,5,1,4,7,6,8,2]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,1,4,6,2,5,7,8]=>[3,5,1,4,6,2,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,5,7,8,6]=>[3,4,1,2,5,8,7,6]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,1,4,2,5,7,6,8]=>[3,4,1,2,5,7,6,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,4,2,7,5,8,6]=>[3,4,1,2,7,8,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,1,4,2,7,8,5,6]=>[3,4,1,2,6,8,7,5]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,1,4,2,7,5,6,8]=>[3,4,1,2,6,7,5,8]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,1,4,7,2,8,5,6]=>[3,7,1,4,6,8,2,5]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,1,4,7,2,5,6,8]=>[3,5,1,4,6,7,2,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,2,5,6,8,7]=>[3,4,1,2,5,6,8,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,1,4,2,5,8,6,7]=>[3,4,1,2,5,7,8,6]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,1,4,2,8,5,6,7]=>[3,4,1,2,6,7,8,5]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,1,4,8,2,5,6,7]=>[3,5,1,4,6,7,8,2]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,1,4,2,5,6,7,8]=>[3,4,1,2,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,4,1,5,6,7,8,2]=>[4,8,3,1,5,6,7,2]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,4,1,5,6,7,2,8]=>[4,7,3,1,5,6,2,8]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,4,1,5,6,2,8,7]=>[4,6,3,1,5,2,8,7]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,4,1,5,6,2,7,8]=>[4,6,3,1,5,2,7,8]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,4,1,5,2,7,8,6]=>[4,5,3,1,2,8,7,6]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,4,1,5,7,8,2,6]=>[4,6,3,1,5,8,7,2]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,4,1,5,2,6,8,7]=>[4,5,3,1,2,6,8,7]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,4,5,1,6,7,8,2]=>[5,8,3,4,1,6,7,2]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,4,5,1,6,7,2,8]=>[5,7,3,4,1,6,2,8]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,6,2,7,8]=>[5,6,3,4,1,2,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,5,6,1,7,8,2]=>[6,8,3,4,5,1,7,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,5,6,1,7,2,8]=>[6,7,3,4,5,1,2,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,7,1,8,2]=>[7,8,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,8,1,2]=>[2,8,3,4,5,6,7,1]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,6,7,1,2,8]=>[2,7,3,4,5,6,1,8]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,6,1,2,7,8]=>[2,6,3,4,5,1,7,8]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,4,5,1,2,7,8,6]=>[2,5,3,4,1,8,7,6]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,4,5,1,7,2,8,6]=>[5,7,3,4,1,8,2,6]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,4,5,1,7,2,6,8]=>[5,6,3,4,1,7,2,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,4,5,7,1,2,8,6]=>[2,7,3,4,5,8,1,6]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[3,4,5,7,1,8,2,6]=>[7,6,3,4,5,8,1,2]=>[[[[.,[.,.]],[.,[.,.]]],.],[.,.]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,4,5,7,8,1,2,6]=>[2,6,3,4,5,8,7,1]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[3,4,5,1,8,2,6,7]=>[5,6,3,4,1,7,8,2]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,4,5,8,1,2,6,7]=>[2,6,3,4,5,7,8,1]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,1,2,6,7,8]=>[2,5,3,4,1,6,7,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,4,1,2,6,5,8,7]=>[2,4,3,1,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,4,1,2,6,8,5,7]=>[2,4,3,1,7,6,8,5]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,4,1,2,6,5,7,8]=>[2,4,3,1,6,5,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,4,1,6,2,7,8,5]=>[4,6,3,1,8,2,7,5]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,4,1,6,2,7,5,8]=>[4,6,3,1,7,2,5,8]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,4,1,6,7,2,8,5]=>[4,7,3,1,8,6,2,5]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,4,1,6,7,8,2,5]=>[4,5,3,1,8,6,7,2]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]
[1,1,0,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,4,1,6,7,2,5,8]=>[4,5,3,1,7,6,2,8]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,4,1,6,2,8,5,7]=>[4,6,3,1,7,2,8,5]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,4,1,6,8,2,5,7]=>[4,5,3,1,7,6,8,2]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,6,1,2,7,5,8]=>[2,6,3,4,7,1,5,8]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,6,1,7,2,8,5]=>[6,7,3,4,8,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,6,1,7,8,2,5]=>[6,5,3,4,8,1,7,2]=>[[[[.,[.,.]],[.,.]],.],[[.,.],.]]
[1,1,0,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,6,7,8,1,2,5]=>[2,5,3,4,8,6,7,1]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,0,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,8,1,2,5,7]=>[2,5,3,4,7,6,8,1]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,4,1,2,5,7,8,6]=>[2,4,3,1,5,8,7,6]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,4,1,2,7,5,8,6]=>[2,4,3,1,7,8,5,6]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,4,1,2,7,8,5,6]=>[2,4,3,1,6,8,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,4,1,7,2,5,8,6]=>[4,5,3,1,7,8,2,6]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,4,1,7,2,8,5,6]=>[4,7,3,1,6,8,2,5]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,4,1,7,8,2,5,6]=>[4,5,3,1,6,8,7,2]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,4,7,1,8,2,5,6]=>[7,5,3,4,6,8,1,2]=>[[[[.,[.,.]],[.,.]],[.,.]],[.,.]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,4,7,8,1,2,5,6]=>[2,5,3,4,6,8,7,1]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,7,1,2,5,6,8]=>[2,5,3,4,6,7,1,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,4,1,2,8,5,6,7]=>[2,4,3,1,6,7,8,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,4,1,8,2,5,6,7]=>[4,5,3,1,6,7,8,2]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,4,8,1,2,5,6,7]=>[2,5,3,4,6,7,8,1]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8]=>[2,4,3,1,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,2,5,6,7,8,4]=>[2,3,1,8,5,6,7,4]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,1,2,5,6,7,4,8]=>[2,3,1,7,5,6,4,8]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,1,2,5,6,4,7,8]=>[2,3,1,6,5,4,7,8]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,5,4,7,6,8]=>[2,3,1,5,4,7,6,8]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,1,2,5,7,4,8,6]=>[2,3,1,7,5,8,4,6]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,1,2,5,7,8,4,6]=>[2,3,1,6,5,8,7,4]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,1,2,5,7,4,6,8]=>[2,3,1,6,5,7,4,8]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,1,2,5,4,6,7,8]=>[2,3,1,5,4,6,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,2,6,4,8,7]=>[3,5,1,6,2,4,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,1,5,2,6,8,4,7]=>[3,5,1,7,2,6,8,4]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,1,5,2,6,4,7,8]=>[3,5,1,6,2,4,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,6,2,7,8,4]=>[3,6,1,8,5,2,7,4]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,1,5,6,7,2,8,4]=>[3,7,1,8,5,6,2,4]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,1,5,6,7,8,2,4]=>[3,4,1,8,5,6,7,2]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,1,5,6,7,2,4,8]=>[3,4,1,7,5,6,2,8]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,5,6,2,8,4,7]=>[3,6,1,7,5,2,8,4]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,1,5,6,8,2,4,7]=>[3,4,1,7,5,6,8,2]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,4,7,8,6]=>[3,4,1,5,2,8,7,6]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,1,5,2,4,7,6,8]=>[3,4,1,5,2,7,6,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,5,2,7,4,8,6]=>[3,5,1,7,2,8,4,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,1,5,2,7,8,4,6]=>[3,5,1,6,2,8,7,4]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,7,4,6,8]=>[3,5,1,6,2,7,4,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,5,7,2,4,8,6]=>[3,4,1,7,5,8,2,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,1,5,7,2,8,4,6]=>[3,7,1,6,5,8,2,4]=>[[.,[.,.]],[[[[.,.],.],.],[.,.]]]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,1,5,7,8,2,4,6]=>[3,4,1,6,5,8,7,2]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,1,5,7,2,4,6,8]=>[3,4,1,6,5,7,2,8]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,1,5,2,8,4,6,7]=>[3,5,1,6,2,7,8,4]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,1,5,8,2,4,6,7]=>[3,4,1,6,5,7,8,2]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,1,5,2,4,6,7,8]=>[3,4,1,5,2,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,5,1,2,6,7,8,4]=>[2,5,3,8,1,6,7,4]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,5,1,2,6,7,4,8]=>[2,5,3,7,1,6,4,8]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,5,1,2,6,8,4,7]=>[2,5,3,7,1,6,8,4]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,5,1,2,6,4,7,8]=>[2,5,3,6,1,4,7,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,5,1,6,2,7,8,4]=>[5,6,3,8,1,2,7,4]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,5,1,6,2,7,4,8]=>[5,6,3,7,1,2,4,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,5,1,6,7,2,8,4]=>[5,7,3,8,1,6,2,4]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,5,1,6,7,8,2,4]=>[5,4,3,8,1,6,7,2]=>[[[[.,[.,.]],.],.],[[.,[.,.]],.]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,5,1,6,2,4,8,7]=>[5,4,3,6,1,2,8,7]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,5,1,6,8,2,4,7]=>[5,4,3,7,1,6,8,2]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,5,1,6,2,4,7,8]=>[5,4,3,6,1,2,7,8]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,5,6,1,2,7,8,4]=>[2,6,3,8,5,1,7,4]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,5,6,1,7,2,8,4]=>[6,7,3,8,5,1,2,4]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,5,6,1,7,8,2,4]=>[6,4,3,8,5,1,7,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[1,1,0,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,5,6,1,7,2,4,8]=>[6,4,3,7,5,1,2,8]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,5,6,7,1,2,8,4]=>[2,7,3,8,5,6,1,4]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,5,6,7,8,1,2,4]=>[2,4,3,8,5,6,7,1]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,5,6,1,2,4,8,7]=>[2,4,3,6,5,1,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,5,6,1,2,8,4,7]=>[2,6,3,7,5,1,8,4]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,5,6,1,8,2,4,7]=>[6,4,3,7,5,1,8,2]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,8,1,2,4,7]=>[2,4,3,7,5,6,8,1]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,5,6,1,2,4,7,8]=>[2,4,3,6,5,1,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,1,2,4,7,8,6]=>[2,4,3,5,1,8,7,6]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,1,2,4,7,6,8]=>[2,4,3,5,1,7,6,8]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,1,2,7,4,8,6]=>[2,5,3,7,1,8,4,6]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,1,2,7,8,4,6]=>[2,5,3,6,1,8,7,4]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,1,2,7,4,6,8]=>[2,5,3,6,1,7,4,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,1,7,2,4,8,6]=>[5,4,3,7,1,8,2,6]=>[[[[.,[.,.]],.],.],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,1,7,2,8,4,6]=>[5,7,3,6,1,8,2,4]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,1,7,8,2,4,6]=>[5,4,3,6,1,8,7,2]=>[[[[.,[.,.]],.],.],[.,[[.,.],.]]]
[1,1,0,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,1,7,2,4,6,8]=>[5,4,3,6,1,7,2,8]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,7,1,2,4,8,6]=>[2,4,3,7,5,8,1,6]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,7,1,2,8,4,6]=>[2,7,3,6,5,8,1,4]=>[[.,.],[[.,[[[.,.],.],.]],[.,.]]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,7,1,8,2,4,6]=>[7,4,3,6,5,8,1,2]=>[[[[.,[.,.]],.],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,7,8,1,2,4,6]=>[2,4,3,6,5,8,7,1]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,1,2,4,6,8]=>[2,4,3,6,5,7,1,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,5,1,2,4,6,8,7]=>[2,4,3,5,1,6,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,5,1,2,4,8,6,7]=>[2,4,3,5,1,7,8,6]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,5,1,8,2,4,6,7]=>[5,4,3,6,1,7,8,2]=>[[[[.,[.,.]],.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,5,8,1,2,4,6,7]=>[2,4,3,6,5,7,8,1]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,5,1,2,4,6,7,8]=>[2,4,3,5,1,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,1,2,4,6,5,8,7]=>[2,3,1,4,6,5,8,7]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[3,1,2,4,6,8,5,7]=>[2,3,1,4,7,6,8,5]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[3,1,2,6,4,7,8,5]=>[2,3,1,6,8,4,7,5]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,1,2,6,7,4,8,5]=>[2,3,1,7,8,6,4,5]=>[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[3,1,2,6,8,4,5,7]=>[2,3,1,5,7,6,8,4]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[3,1,2,6,4,5,7,8]=>[2,3,1,5,6,4,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,1,6,2,4,7,5,8]=>[3,4,1,6,7,2,5,8]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,1,6,2,7,4,8,5]=>[3,6,1,7,8,2,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[3,1,6,7,2,4,5,8]=>[3,4,1,5,7,6,2,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[3,1,6,2,4,5,8,7]=>[3,4,1,5,6,2,8,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[3,1,6,2,4,8,5,7]=>[3,4,1,6,7,2,8,5]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[3,1,6,8,2,4,5,7]=>[3,4,1,5,7,6,8,2]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[3,1,6,2,4,5,7,8]=>[3,4,1,5,6,2,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[3,6,1,2,4,7,8,5]=>[2,4,3,6,8,1,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,6,1,2,4,7,5,8]=>[2,4,3,6,7,1,5,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,6,1,2,7,4,8,5]=>[2,6,3,7,8,1,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[3,6,1,2,7,8,4,5]=>[2,6,3,5,8,1,7,4]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,6,1,7,2,4,8,5]=>[6,4,3,7,8,1,2,5]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[3,6,1,7,2,8,4,5]=>[6,7,3,5,8,1,2,4]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,6,1,7,8,2,4,5]=>[6,4,3,5,8,1,7,2]=>[[[[.,[.,.]],.],[.,.]],[[.,.],.]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[3,6,7,1,2,4,8,5]=>[2,4,3,7,8,6,1,5]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,6,7,1,2,8,4,5]=>[2,7,3,5,8,6,1,4]=>[[.,.],[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[3,6,7,8,1,2,4,5]=>[2,4,3,5,8,6,7,1]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[3,6,1,2,4,5,8,7]=>[2,4,3,5,6,1,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[3,6,1,8,2,4,5,7]=>[6,4,3,5,7,1,8,2]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,6,8,1,2,4,5,7]=>[2,4,3,5,7,6,8,1]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,1,2,4,5,7,6,8]=>[2,3,1,4,5,7,6,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,1,2,4,7,5,8,6]=>[2,3,1,4,7,8,5,6]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[3,1,2,4,7,5,6,8]=>[2,3,1,4,6,7,5,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[3,1,2,7,4,5,8,6]=>[2,3,1,5,7,8,4,6]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[3,1,2,7,4,8,5,6]=>[2,3,1,7,6,8,4,5]=>[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[3,1,2,7,4,5,6,8]=>[2,3,1,5,6,7,4,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[3,1,7,2,4,5,8,6]=>[3,4,1,5,7,8,2,6]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[3,1,7,2,4,8,5,6]=>[3,4,1,7,6,8,2,5]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[3,1,7,2,8,4,5,6]=>[3,7,1,5,6,8,2,4]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[3,1,7,8,2,4,5,6]=>[3,4,1,5,6,8,7,2]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[3,1,7,2,4,5,6,8]=>[3,4,1,5,6,7,2,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[3,7,1,2,4,5,8,6]=>[2,4,3,5,7,8,1,6]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[3,7,8,1,2,4,5,6]=>[2,4,3,5,6,8,7,1]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,7,1,2,4,5,6,8]=>[2,4,3,5,6,7,1,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,8,7]=>[2,3,1,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,1,2,4,5,8,6,7]=>[2,3,1,4,5,7,8,6]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[3,1,2,4,8,5,6,7]=>[2,3,1,4,6,7,8,5]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[3,1,2,8,4,5,6,7]=>[2,3,1,5,6,7,8,4]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,1,8,2,4,5,6,7]=>[3,4,1,5,6,7,8,2]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,8,1,2,4,5,6,7]=>[2,4,3,5,6,7,8,1]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,8,3]=>[1,2,8,4,5,6,7,3]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,6,8,3,7]=>[1,2,7,4,5,6,8,3]=>[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,4,5,6,3,7,8]=>[1,2,6,4,5,3,7,8]=>[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,5,3,7,8,6]=>[1,2,5,4,3,8,7,6]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,7,3,8,6]=>[1,2,7,4,5,8,3,6]=>[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,4,5,3,6,8,7]=>[1,2,5,4,3,6,8,7]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,4,5,3,8,6,7]=>[1,2,5,4,3,7,8,6]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,4,5,8,3,6,7]=>[1,2,6,4,5,7,8,3]=>[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,4,5,3,6,7,8]=>[1,2,5,4,3,6,7,8]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,6,7,5]=>[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,8,5,7]=>[1,2,4,3,7,6,8,5]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,6,3,7,8,5]=>[1,2,6,4,8,3,7,5]=>[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,6,3,7,5,8]=>[1,2,6,4,7,3,5,8]=>[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,6,7,3,8,5]=>[1,2,7,4,8,6,3,5]=>[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,6,7,8,3,5]=>[1,2,5,4,8,6,7,3]=>[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,3,8,5,7]=>[1,2,6,4,7,3,8,5]=>[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,8,3,5,7]=>[1,2,5,4,7,6,8,3]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,4,3,5,7,8,6]=>[1,2,4,3,5,8,7,6]=>[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,4,3,7,5,8,6]=>[1,2,4,3,7,8,5,6]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,4,3,7,8,5,6]=>[1,2,4,3,6,8,7,5]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,4,3,7,5,6,8]=>[1,2,4,3,6,7,5,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,4,7,3,5,8,6]=>[1,2,5,4,7,8,3,6]=>[.,[.,[[[.,.],.],[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,4,7,8,3,5,6]=>[1,2,5,4,6,8,7,3]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,1,1,0,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,4,7,3,5,6,8]=>[1,2,5,4,6,7,3,8]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,4,3,5,8,6,7]=>[1,2,4,3,5,7,8,6]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,6,7,8,5]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,4,8,3,5,6,7]=>[1,2,5,4,6,7,8,3]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,4,2,5,6,7,8,3]=>[1,4,8,2,5,6,7,3]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,4,2,5,6,7,3,8]=>[1,4,7,2,5,6,3,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,4,2,5,6,8,3,7]=>[1,4,7,2,5,6,8,3]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,4,2,5,6,3,7,8]=>[1,4,6,2,5,3,7,8]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,4,2,5,3,7,6,8]=>[1,4,5,2,3,7,6,8]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,4,2,5,7,3,8,6]=>[1,4,7,2,5,8,3,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,4,2,5,3,8,6,7]=>[1,4,5,2,3,7,8,6]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,4,2,5,3,6,7,8]=>[1,4,5,2,3,6,7,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,4,5,2,6,7,8,3]=>[1,5,8,4,2,6,7,3]=>[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,4,5,2,6,7,3,8]=>[1,5,7,4,2,6,3,8]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,4,5,2,6,8,3,7]=>[1,5,7,4,2,6,8,3]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,4,5,2,6,3,7,8]=>[1,5,6,4,2,3,7,8]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,4,5,6,2,7,8,3]=>[1,6,8,4,5,2,7,3]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,4,5,6,2,7,3,8]=>[1,6,7,4,5,2,3,8]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,4,5,6,7,2,8,3]=>[1,7,8,4,5,6,2,3]=>[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,5,6,7,8,2,3]=>[1,3,8,4,5,6,7,2]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,6,7,2,3,8]=>[1,3,7,4,5,6,2,8]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,4,5,6,2,3,8,7]=>[1,3,6,4,5,2,8,7]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,4,5,6,2,8,3,7]=>[1,6,7,4,5,2,8,3]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,6,8,2,3,7]=>[1,3,7,4,5,6,8,2]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,4,5,2,3,7,6,8]=>[1,3,5,4,2,7,6,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,4,5,2,7,3,8,6]=>[1,5,7,4,2,8,3,6]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,4,5,2,7,8,3,6]=>[1,5,6,4,2,8,7,3]=>[.,[[[.,[.,.]],.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,4,5,7,2,3,8,6]=>[1,3,7,4,5,8,2,6]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,4,5,7,8,2,3,6]=>[1,3,6,4,5,8,7,2]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,4,5,7,2,3,6,8]=>[1,3,6,4,5,7,2,8]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,4,5,2,3,8,6,7]=>[1,3,5,4,2,7,8,6]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,4,5,8,2,3,6,7]=>[1,3,6,4,5,7,8,2]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,2,3,6,7,8,5]=>[1,3,4,2,8,6,7,5]=>[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,2,3,6,5,8,7]=>[1,3,4,2,6,5,8,7]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,2,3,6,8,5,7]=>[1,3,4,2,7,6,8,5]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,2,6,3,7,8,5]=>[1,4,6,2,8,3,7,5]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2,6,3,7,5,8]=>[1,4,6,2,7,3,5,8]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,2,6,7,3,8,5]=>[1,4,7,2,8,6,3,5]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,6,7,8,3,5]=>[1,4,5,2,8,6,7,3]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,2,6,3,5,8,7]=>[1,4,5,2,6,3,8,7]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,8,5,7]=>[1,4,6,2,7,3,8,5]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,2,6,3,5,7,8]=>[1,4,5,2,6,3,7,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,6,2,3,7,8,5]=>[1,3,6,4,8,2,7,5]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,6,2,3,7,5,8]=>[1,3,6,4,7,2,5,8]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,6,2,7,3,8,5]=>[1,6,7,4,8,2,3,5]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,6,2,7,8,3,5]=>[1,6,5,4,8,2,7,3]=>[.,[[[[.,[.,.]],.],.],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,7,3,5,8]=>[1,6,5,4,7,2,3,8]=>[.,[[[[.,[.,.]],.],.],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,6,7,2,3,8,5]=>[1,3,7,4,8,6,2,5]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,6,7,2,8,3,5]=>[1,7,5,4,8,6,2,3]=>[.,[[[[.,[.,.]],.],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,6,7,2,3,5,8]=>[1,3,5,4,7,6,2,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,2,3,8,5,7]=>[1,3,6,4,7,2,8,5]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,8,2,3,5,7]=>[1,3,5,4,7,6,8,2]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,4,2,3,5,7,6,8]=>[1,3,4,2,5,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,4,2,3,7,5,8,6]=>[1,3,4,2,7,8,5,6]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,3,7,8,5,6]=>[1,3,4,2,6,8,7,5]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2,3,7,5,6,8]=>[1,3,4,2,6,7,5,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,4,2,7,3,5,8,6]=>[1,4,5,2,7,8,3,6]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,2,7,3,8,5,6]=>[1,4,7,2,6,8,3,5]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,2,7,8,3,5,6]=>[1,4,5,2,6,8,7,3]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,4,2,7,3,5,6,8]=>[1,4,5,2,6,7,3,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,4,7,2,3,5,8,6]=>[1,3,5,4,7,8,2,6]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,7,2,3,8,5,6]=>[1,3,7,4,6,8,2,5]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,4,2,3,5,6,8,7]=>[1,3,4,2,5,6,8,7]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,8,6,7]=>[1,3,4,2,5,7,8,6]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,4,2,3,8,5,6,7]=>[1,3,4,2,6,7,8,5]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,4,2,8,3,5,6,7]=>[1,4,5,2,6,7,8,3]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,2,5,6,7,8,3]=>[2,4,8,1,5,6,7,3]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,2,5,6,3,8,7]=>[2,4,6,1,5,3,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[4,1,2,5,6,8,3,7]=>[2,4,7,1,5,6,8,3]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,1,2,5,6,3,7,8]=>[2,4,6,1,5,3,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0,1,0]=>[4,1,2,5,3,7,8,6]=>[2,4,5,1,3,8,7,6]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,1,2,5,3,7,6,8]=>[2,4,5,1,3,7,6,8]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,1,2,5,7,8,3,6]=>[2,4,6,1,5,8,7,3]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,1,2,5,7,3,6,8]=>[2,4,6,1,5,7,3,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,1,2,5,3,8,6,7]=>[2,4,5,1,3,7,8,6]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,1,2,5,3,6,7,8]=>[2,4,5,1,3,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,5,2,6,7,8,3]=>[4,5,8,1,2,6,7,3]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[4,1,5,2,6,7,3,8]=>[4,5,7,1,2,6,3,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,5,2,6,3,8,7]=>[4,5,6,1,2,3,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,1,5,2,6,8,3,7]=>[4,5,7,1,2,6,8,3]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,1,5,2,6,3,7,8]=>[4,5,6,1,2,3,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[4,1,5,6,2,7,3,8]=>[4,6,7,1,5,2,3,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,5,6,7,2,8,3]=>[4,7,8,1,5,6,2,3]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[4,1,5,6,7,8,2,3]=>[4,3,8,1,5,6,7,2]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,5,6,2,3,8,7]=>[4,3,6,1,5,2,8,7]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[4,1,5,6,8,2,3,7]=>[4,3,7,1,5,6,8,2]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[4,1,5,6,2,3,7,8]=>[4,3,6,1,5,2,7,8]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,7,8,6]=>[4,3,5,1,2,8,7,6]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,1,0,0]=>[4,1,5,2,3,7,6,8]=>[4,3,5,1,2,7,6,8]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,5,2,7,3,8,6]=>[4,5,7,1,2,8,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[4,1,5,2,7,8,3,6]=>[4,5,6,1,2,8,7,3]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[4,1,5,2,7,3,6,8]=>[4,5,6,1,2,7,3,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0,1,0]=>[4,1,5,7,2,3,8,6]=>[4,3,7,1,5,8,2,6]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[4,1,5,7,2,8,3,6]=>[4,7,6,1,5,8,2,3]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[4,1,5,7,8,2,3,6]=>[4,3,6,1,5,8,7,2]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[4,1,5,7,2,3,6,8]=>[4,3,6,1,5,7,2,8]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[4,1,5,2,8,3,6,7]=>[4,5,6,1,2,7,8,3]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[4,1,5,8,2,3,6,7]=>[4,3,6,1,5,7,8,2]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,1,0,0,0,0,0]=>[4,1,5,2,3,6,7,8]=>[4,3,5,1,2,6,7,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,5,1,2,6,7,3,8]=>[2,5,7,4,1,6,3,8]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,5,1,2,6,3,8,7]=>[2,5,6,4,1,3,8,7]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,5,1,2,6,8,3,7]=>[2,5,7,4,1,6,8,3]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,5,1,6,2,7,8,3]=>[5,6,8,4,1,2,7,3]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,5,1,6,2,7,3,8]=>[5,6,7,4,1,2,3,8]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,5,1,6,7,2,8,3]=>[5,7,8,4,1,6,2,3]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,5,1,6,7,8,2,3]=>[5,3,8,4,1,6,7,2]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,5,1,6,7,2,3,8]=>[5,3,7,4,1,6,2,8]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,5,1,6,2,3,8,7]=>[5,3,6,4,1,2,8,7]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,1,0,0]=>[4,5,1,6,2,8,3,7]=>[5,6,7,4,1,2,8,3]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,5,1,6,8,2,3,7]=>[5,3,7,4,1,6,8,2]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,5,1,6,2,3,7,8]=>[5,3,6,4,1,2,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,5,6,1,2,7,8,3]=>[2,6,8,4,5,1,7,3]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,5,6,1,2,7,3,8]=>[2,6,7,4,5,1,3,8]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,5,6,1,7,2,8,3]=>[6,7,8,4,5,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[4,5,6,1,7,8,2,3]=>[6,3,8,4,5,1,7,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[4,5,6,7,1,8,2,3]=>[7,3,8,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,7,8,1,2,3]=>[2,3,8,4,5,6,7,1]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,5,6,1,2,3,8,7]=>[2,3,6,4,5,1,8,7]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[4,5,6,1,2,8,3,7]=>[2,6,7,4,5,1,8,3]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[4,5,6,1,8,2,3,7]=>[6,3,7,4,5,1,8,2]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,5,6,8,1,2,3,7]=>[2,3,7,4,5,6,8,1]=>[[.,.],[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,6,1,2,3,7,8]=>[2,3,6,4,5,1,7,8]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,5,1,2,3,7,8,6]=>[2,3,5,4,1,8,7,6]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,5,1,2,3,7,6,8]=>[2,3,5,4,1,7,6,8]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,5,1,2,7,3,8,6]=>[2,5,7,4,1,8,3,6]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,5,1,2,7,3,6,8]=>[2,5,6,4,1,7,3,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,1,0,0]=>[4,5,1,7,2,8,3,6]=>[5,7,6,4,1,8,2,3]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,5,1,7,8,2,3,6]=>[5,3,6,4,1,8,7,2]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,5,1,7,2,3,6,8]=>[5,3,6,4,1,7,2,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[4,5,7,1,2,8,3,6]=>[2,7,6,4,5,8,1,3]=>[[.,.],[[[[.,.],[.,.]],.],[.,.]]]
[1,1,1,0,1,0,1,1,0,1,0,0,1,0,0,0]=>[4,5,7,1,8,2,3,6]=>[7,3,6,4,5,8,1,2]=>[[[.,[.,.]],[[.,[.,.]],.]],[.,.]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,5,7,8,1,2,3,6]=>[2,3,6,4,5,8,7,1]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,5,1,2,3,6,8,7]=>[2,3,5,4,1,6,8,7]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,5,1,2,8,3,6,7]=>[2,5,6,4,1,7,8,3]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,5,8,1,2,3,6,7]=>[2,3,6,4,5,7,8,1]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[4,5,1,2,3,6,7,8]=>[2,3,5,4,1,6,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,2,3,6,7,8,5]=>[2,3,4,1,8,6,7,5]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,1,2,3,6,7,5,8]=>[2,3,4,1,7,6,5,8]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,1,2,3,6,5,8,7]=>[2,3,4,1,6,5,8,7]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,1,2,3,6,8,5,7]=>[2,3,4,1,7,6,8,5]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,1,2,3,6,5,7,8]=>[2,3,4,1,6,5,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,2,6,3,7,8,5]=>[2,4,6,1,8,3,7,5]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,1,2,6,7,3,5,8]=>[2,4,5,1,7,6,3,8]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,1,2,6,3,5,8,7]=>[2,4,5,1,6,3,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,1,2,6,3,8,5,7]=>[2,4,6,1,7,3,8,5]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,1,2,6,3,5,7,8]=>[2,4,5,1,6,3,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,7,8,5]=>[4,3,6,1,8,2,7,5]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,1,6,2,3,7,5,8]=>[4,3,6,1,7,2,5,8]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,6,2,7,3,8,5]=>[4,6,7,1,8,2,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,1,6,2,7,3,5,8]=>[4,6,5,1,7,2,3,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,1,6,7,8,2,3,5]=>[4,3,5,1,8,6,7,2]=>[[[.,[.,.]],.],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,1,6,2,3,5,8,7]=>[4,3,5,1,6,2,8,7]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,1,6,2,3,8,5,7]=>[4,3,6,1,7,2,8,5]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,1,6,8,2,3,5,7]=>[4,3,5,1,7,6,8,2]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,1,6,2,3,5,7,8]=>[4,3,5,1,6,2,7,8]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,6,1,2,3,7,5,8]=>[2,3,6,4,7,1,5,8]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,6,1,2,7,3,8,5]=>[2,6,7,4,8,1,3,5]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,6,1,2,7,8,3,5]=>[2,6,5,4,8,1,7,3]=>[[.,.],[[[[.,.],.],.],[[.,.],.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,6,1,2,7,3,5,8]=>[2,6,5,4,7,1,3,8]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,6,1,7,2,3,8,5]=>[6,3,7,4,8,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,6,1,7,2,8,3,5]=>[6,7,5,4,8,1,2,3]=>[[[[.,[.,[.,.]]],.],.],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,6,1,7,8,2,3,5]=>[6,3,5,4,8,1,7,2]=>[[[.,[.,.]],[[.,.],.]],[[.,.],.]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,6,1,7,2,3,5,8]=>[6,3,5,4,7,1,2,8]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,6,7,1,2,8,3,5]=>[2,7,5,4,8,6,1,3]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,6,7,1,8,2,3,5]=>[7,3,5,4,8,6,1,2]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,6,7,8,1,2,3,5]=>[2,3,5,4,8,6,7,1]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,1,2,8,3,5,7]=>[2,6,5,4,7,1,8,3]=>[[.,.],[[[[.,.],.],.],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,1,8,2,3,5,7]=>[6,3,5,4,7,1,8,2]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,8,1,2,3,5,7]=>[2,3,5,4,7,6,8,1]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,6,1,2,3,5,7,8]=>[2,3,5,4,6,1,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[4,1,2,3,5,7,8,6]=>[2,3,4,1,5,8,7,6]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[4,1,2,3,5,7,6,8]=>[2,3,4,1,5,7,6,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[4,1,2,3,7,5,8,6]=>[2,3,4,1,7,8,5,6]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[4,1,2,3,7,8,5,6]=>[2,3,4,1,6,8,7,5]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,1,0,0,0]=>[4,1,2,3,7,5,6,8]=>[2,3,4,1,6,7,5,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[4,1,2,7,3,5,8,6]=>[2,4,5,1,7,8,3,6]=>[[.,.],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[4,1,2,7,3,8,5,6]=>[2,4,7,1,6,8,3,5]=>[[.,.],[[.,.],[[[.,.],.],[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[4,1,2,7,8,3,5,6]=>[2,4,5,1,6,8,7,3]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[4,1,7,2,3,5,8,6]=>[4,3,5,1,7,8,2,6]=>[[[.,[.,.]],.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[4,1,7,2,3,8,5,6]=>[4,3,7,1,6,8,2,5]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[4,1,7,2,8,3,5,6]=>[4,7,5,1,6,8,2,3]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[4,1,7,8,2,3,5,6]=>[4,3,5,1,6,8,7,2]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[4,7,1,8,2,3,5,6]=>[7,3,5,4,6,8,1,2]=>[[[.,[.,.]],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[4,7,1,2,3,5,6,8]=>[2,3,5,4,6,7,1,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,8,7]=>[2,3,4,1,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[4,1,2,3,5,8,6,7]=>[2,3,4,1,5,7,8,6]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[4,1,2,3,8,5,6,7]=>[2,3,4,1,6,7,8,5]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[4,1,2,8,3,5,6,7]=>[2,4,5,1,6,7,8,3]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,1,0,0,1,0,0,0,0,0]=>[4,1,8,2,3,5,6,7]=>[4,3,5,1,6,7,8,2]=>[[[.,[.,.]],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0]=>[4,8,1,2,3,5,6,7]=>[2,3,5,4,6,7,8,1]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,5,6,7,4]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,6,7,4,8]=>[1,2,3,7,5,6,4,8]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,6,4,8,7]=>[1,2,3,6,5,4,8,7]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,8,4,7]=>[1,2,3,7,5,6,8,4]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[1,2,3,5,6,4,7,8]=>[1,2,3,6,5,4,7,8]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,7,6]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,7,4,8,6]=>[1,2,3,7,5,8,4,6]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,7,8,4,6]=>[1,2,3,6,5,8,7,4]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,4,6,8]=>[1,2,3,6,5,7,4,8]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,7,8,6]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,5,8,4,6,7]=>[1,2,3,6,5,7,8,4]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,2,5,3,6,7,8,4]=>[1,2,5,8,3,6,7,4]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,1,0,0]=>[1,2,5,3,6,7,4,8]=>[1,2,5,7,3,6,4,8]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0,1,0]=>[1,2,5,3,6,4,8,7]=>[1,2,5,6,3,4,8,7]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,1,0,0]=>[1,2,5,3,6,8,4,7]=>[1,2,5,7,3,6,8,4]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[1,2,5,3,6,4,7,8]=>[1,2,5,6,3,4,7,8]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[1,2,5,6,3,7,8,4]=>[1,2,6,8,5,3,7,4]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,1,0,0]=>[1,2,5,6,3,7,4,8]=>[1,2,6,7,5,3,4,8]=>[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0,1,0]=>[1,2,5,6,7,3,8,4]=>[1,2,7,8,5,6,3,4]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,2,5,6,7,8,3,4]=>[1,2,4,8,5,6,7,3]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,2,5,6,3,8,4,7]=>[1,2,6,7,5,3,8,4]=>[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,2,5,6,8,3,4,7]=>[1,2,4,7,5,6,8,3]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,2,5,6,3,4,7,8]=>[1,2,4,6,5,3,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[1,2,5,3,4,7,8,6]=>[1,2,4,5,3,8,7,6]=>[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[1,2,5,3,4,7,6,8]=>[1,2,4,5,3,7,6,8]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[1,2,5,3,7,4,8,6]=>[1,2,5,7,3,8,4,6]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,2,5,3,7,8,4,6]=>[1,2,5,6,3,8,7,4]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,2,5,3,7,4,6,8]=>[1,2,5,6,3,7,4,8]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,2,5,7,3,8,4,6]=>[1,2,7,6,5,8,3,4]=>[.,[.,[[[[.,[.,.]],.],.],[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,2,5,7,8,3,4,6]=>[1,2,4,6,5,8,7,3]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6,8]=>[1,2,4,6,5,7,3,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,2,5,3,4,8,6,7]=>[1,2,4,5,3,7,8,6]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,2,5,3,8,4,6,7]=>[1,2,5,6,3,7,8,4]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,2,5,3,4,6,7,8]=>[1,2,4,5,3,6,7,8]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[1,5,2,3,6,7,8,4]=>[1,3,5,8,2,6,7,4]=>[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,1,0,0]=>[1,5,2,3,6,7,4,8]=>[1,3,5,7,2,6,4,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0,1,0]=>[1,5,2,3,6,4,8,7]=>[1,3,5,6,2,4,8,7]=>[.,[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[1,5,2,3,6,4,7,8]=>[1,3,5,6,2,4,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[1,5,2,6,3,7,8,4]=>[1,5,6,8,2,3,7,4]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,5,2,6,3,7,4,8]=>[1,5,6,7,2,3,4,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[1,5,2,6,7,3,8,4]=>[1,5,7,8,2,6,3,4]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,5,2,6,7,8,3,4]=>[1,5,4,8,2,6,7,3]=>[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,5,2,6,7,3,4,8]=>[1,5,4,7,2,6,3,8]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,5,2,6,3,8,4,7]=>[1,5,6,7,2,3,8,4]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,1,0,0,0]=>[1,5,2,6,8,3,4,7]=>[1,5,4,7,2,6,8,3]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,1,0,0,0,0]=>[1,5,2,6,3,4,7,8]=>[1,5,4,6,2,3,7,8]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0,1,0]=>[1,5,6,2,3,7,8,4]=>[1,3,6,8,5,2,7,4]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,1,0,0]=>[1,5,6,2,3,7,4,8]=>[1,3,6,7,5,2,4,8]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[1,5,6,2,7,3,8,4]=>[1,6,7,8,5,2,3,4]=>[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,1,0,0]=>[1,5,6,2,7,8,3,4]=>[1,6,4,8,5,2,7,3]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]
[1,1,1,1,0,0,1,0,1,0,0,1,1,0,0,0]=>[1,5,6,2,7,3,4,8]=>[1,6,4,7,5,2,3,8]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0,1,0]=>[1,5,6,7,2,3,8,4]=>[1,3,7,8,5,6,2,4]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,5,6,7,2,8,3,4]=>[1,7,4,8,5,6,2,3]=>[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,5,6,7,8,2,3,4]=>[1,3,4,8,5,6,7,2]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,1,0,0]=>[1,5,6,2,3,8,4,7]=>[1,3,6,7,5,2,8,4]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0,1,0]=>[1,5,2,3,4,7,8,6]=>[1,3,4,5,2,8,7,6]=>[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[1,5,2,3,4,7,6,8]=>[1,3,4,5,2,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[1,5,2,3,7,4,8,6]=>[1,3,5,7,2,8,4,6]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,1,0,0,0]=>[1,5,2,3,7,4,6,8]=>[1,3,5,6,2,7,4,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[1,5,2,7,3,4,8,6]=>[1,5,4,7,2,8,3,6]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,7,3,8,4,6]=>[1,5,7,6,2,8,3,4]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,5,2,7,3,4,6,8]=>[1,5,4,6,2,7,3,8]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0,1,0]=>[1,5,7,2,3,4,8,6]=>[1,3,4,7,5,8,2,6]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,5,7,2,3,8,4,6]=>[1,3,7,6,5,8,2,4]=>[.,[[.,.],[[[[.,.],.],.],[.,.]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,5,7,2,8,3,4,6]=>[1,7,4,6,5,8,2,3]=>[.,[[[.,[.,.]],[[.,.],.]],[.,.]]]
[1,1,1,1,0,0,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,2,3,4,6,8]=>[1,3,4,6,5,7,2,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,8,6,7]=>[1,3,4,5,2,7,8,6]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,5,2,3,8,4,6,7]=>[1,3,5,6,2,7,8,4]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,5,8,2,3,4,6,7]=>[1,3,4,6,5,7,8,2]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,2,3,6,7,8,4]=>[2,3,5,8,1,6,7,4]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0,1,0]=>[5,1,2,3,6,4,8,7]=>[2,3,5,6,1,4,8,7]=>[[.,.],[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,1,2,3,6,4,7,8]=>[2,3,5,6,1,4,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0,1,0]=>[5,1,2,6,3,7,8,4]=>[2,5,6,8,1,3,7,4]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0,1,0]=>[5,1,2,6,7,3,8,4]=>[2,5,7,8,1,6,3,4]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0,1,0]=>[5,1,2,6,3,4,8,7]=>[2,5,4,6,1,3,8,7]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,1,0,0]=>[5,1,2,6,3,8,4,7]=>[2,5,6,7,1,3,8,4]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,1,1,1,0,0,0,0]=>[5,1,2,6,3,4,7,8]=>[2,5,4,6,1,3,7,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0,1,0]=>[5,1,6,2,3,7,8,4]=>[5,3,6,8,1,2,7,4]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[5,1,6,2,3,7,4,8]=>[5,3,6,7,1,2,4,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,6,2,7,3,8,4]=>[5,6,7,8,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[5,1,6,2,7,8,3,4]=>[5,6,4,8,1,2,7,3]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[5,1,6,2,7,3,4,8]=>[5,6,4,7,1,2,3,8]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0,1,0]=>[5,1,6,7,2,3,8,4]=>[5,3,7,8,1,6,2,4]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[5,1,6,7,2,8,3,4]=>[5,7,4,8,1,6,2,3]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[5,1,6,7,8,2,3,4]=>[5,3,4,8,1,6,7,2]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,1,0,0]=>[5,1,6,2,3,8,4,7]=>[5,3,6,7,1,2,8,4]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[5,1,6,2,8,3,4,7]=>[5,6,4,7,1,2,8,3]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0,1,0]=>[5,6,1,2,3,7,8,4]=>[2,3,6,8,5,1,7,4]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[5,6,1,2,7,3,8,4]=>[2,6,7,8,5,1,3,4]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[5,6,1,2,7,8,3,4]=>[2,6,4,8,5,1,7,3]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[5,6,1,7,2,3,8,4]=>[6,3,7,8,5,1,2,4]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[5,6,1,7,2,8,3,4]=>[6,7,4,8,5,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[5,6,1,7,8,2,3,4]=>[6,3,4,8,5,1,7,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[5,6,7,1,2,3,8,4]=>[2,3,7,8,5,6,1,4]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[5,6,7,1,2,8,3,4]=>[2,7,4,8,5,6,1,3]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[5,6,7,1,8,2,3,4]=>[7,3,4,8,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[2,3,4,8,5,6,7,1]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,7,1,2,3,4,8]=>[2,3,4,7,5,6,1,8]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[5,6,1,2,3,8,4,7]=>[2,3,6,7,5,1,8,4]=>[[.,.],[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[5,6,8,1,2,3,4,7]=>[2,3,4,7,5,6,8,1]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[5,6,1,2,3,4,7,8]=>[2,3,4,6,5,1,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0,1,0]=>[5,1,2,3,4,7,8,6]=>[2,3,4,5,1,8,7,6]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[5,1,2,3,4,7,6,8]=>[2,3,4,5,1,7,6,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[5,1,2,3,7,4,8,6]=>[2,3,5,7,1,8,4,6]=>[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[5,1,2,3,7,4,6,8]=>[2,3,5,6,1,7,4,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,2,7,3,4,8,6]=>[2,5,4,7,1,8,3,6]=>[[.,.],[[[.,.],.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,1,1,0,0,0,0]=>[5,1,2,7,3,4,6,8]=>[2,5,4,6,1,7,3,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[5,1,7,2,8,3,4,6]=>[5,7,4,6,1,8,2,3]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[5,7,1,2,3,4,8,6]=>[2,3,4,7,5,8,1,6]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,1,0,0]=>[5,7,1,2,3,8,4,6]=>[2,3,7,6,5,8,1,4]=>[[.,.],[.,[[[[.,.],.],.],[.,.]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,1,0,0,0]=>[5,7,1,2,8,3,4,6]=>[2,7,4,6,5,8,1,3]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[5,7,8,1,2,3,4,6]=>[2,3,4,6,5,8,7,1]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,1,2,3,4,6,8]=>[2,3,4,6,5,7,1,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,8,7]=>[2,3,4,5,1,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[5,1,2,3,4,8,6,7]=>[2,3,4,5,1,7,8,6]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[5,1,2,3,8,4,6,7]=>[2,3,5,6,1,7,8,4]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,1,2,8,3,4,6,7]=>[2,5,4,6,1,7,8,3]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[5,8,1,2,3,4,6,7]=>[2,3,4,6,5,7,8,1]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[5,1,2,3,4,6,7,8]=>[2,3,4,5,1,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,6,7,5]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,1,0,0]=>[1,2,3,4,6,7,5,8]=>[1,2,3,4,7,6,5,8]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[1,2,3,4,6,8,5,7]=>[1,2,3,4,7,6,8,5]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0]=>[1,2,3,6,4,7,8,5]=>[1,2,3,6,8,4,7,5]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[1,2,3,6,4,7,5,8]=>[1,2,3,6,7,4,5,8]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[1,2,3,6,7,4,8,5]=>[1,2,3,7,8,6,4,5]=>[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,2,3,6,7,8,4,5]=>[1,2,3,5,8,6,7,4]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,2,3,6,7,4,5,8]=>[1,2,3,5,7,6,4,8]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0,1,0]=>[1,2,3,6,4,5,8,7]=>[1,2,3,5,6,4,8,7]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,1,0,0]=>[1,2,3,6,4,8,5,7]=>[1,2,3,6,7,4,8,5]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,1,0,1,0,0,0]=>[1,2,3,6,8,4,5,7]=>[1,2,3,5,7,6,8,4]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,2,3,6,4,5,7,8]=>[1,2,3,5,6,4,7,8]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0,1,0]=>[1,2,6,3,4,7,8,5]=>[1,2,4,6,8,3,7,5]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0,1,0]=>[1,2,6,3,7,4,8,5]=>[1,2,6,7,8,3,4,5]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,2,6,3,7,8,4,5]=>[1,2,6,5,8,3,7,4]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[1,2,6,7,3,4,8,5]=>[1,2,4,7,8,6,3,5]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,2,6,7,3,8,4,5]=>[1,2,7,5,8,6,3,4]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,2,6,7,8,3,4,5]=>[1,2,4,5,8,6,7,3]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0,1,0]=>[1,2,6,3,4,5,8,7]=>[1,2,4,5,6,3,8,7]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,2,6,3,8,4,5,7]=>[1,2,6,5,7,3,8,4]=>[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,2,6,3,4,5,7,8]=>[1,2,4,5,6,3,7,8]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[1,6,2,3,4,7,5,8]=>[1,3,4,6,7,2,5,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[1,6,2,3,7,4,8,5]=>[1,3,6,7,8,2,4,5]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,6,2,3,7,4,5,8]=>[1,3,6,5,7,2,4,8]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0,1,0]=>[1,6,2,7,3,4,8,5]=>[1,6,4,7,8,2,3,5]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,6,2,7,3,8,4,5]=>[1,6,7,5,8,2,3,4]=>[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,1,1,0,0,0,0]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,6,7,2,3,8,4,5]=>[1,3,7,5,8,6,2,4]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,6,7,8,2,3,4,5]=>[1,3,4,5,8,6,7,2]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,6,7,2,3,4,5,8]=>[1,3,4,5,7,6,2,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[1,6,2,3,4,5,8,7]=>[1,3,4,5,6,2,8,7]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,8,5,7]=>[1,3,4,6,7,2,8,5]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[6,1,2,3,4,7,8,5]=>[2,3,4,6,8,1,7,5]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,1,2,3,4,7,5,8]=>[2,3,4,6,7,1,5,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[6,1,2,3,7,4,8,5]=>[2,3,6,7,8,1,4,5]=>[[.,.],[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,1,0,0]=>[6,1,2,7,3,8,4,5]=>[2,6,7,5,8,1,3,4]=>[[.,.],[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[6,1,2,7,8,3,4,5]=>[2,6,4,5,8,1,7,3]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,1,1,0,1,0,0,0,1,1,0,0,0,0]=>[6,1,2,7,3,4,5,8]=>[2,6,4,5,7,1,3,8]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,0]=>[6,1,7,2,8,3,4,5]=>[6,7,4,5,8,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[6,1,7,8,2,3,4,5]=>[6,3,4,5,8,1,7,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[6,1,7,2,3,4,5,8]=>[6,3,4,5,7,1,2,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[6,7,1,2,3,4,8,5]=>[2,3,4,7,8,6,1,5]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[6,7,1,2,3,8,4,5]=>[2,3,7,5,8,6,1,4]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[6,7,1,8,2,3,4,5]=>[7,3,4,5,8,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,7,8,1,2,3,4,5]=>[2,3,4,5,8,6,7,1]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[6,7,1,2,3,4,5,8]=>[2,3,4,5,7,6,1,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,8,7]=>[2,3,4,5,6,1,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[6,1,2,8,3,4,5,7]=>[2,6,4,5,7,1,8,3]=>[[.,.],[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[6,1,8,2,3,4,5,7]=>[6,3,4,5,7,1,8,2]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[6,8,1,2,3,4,5,7]=>[2,3,4,5,7,6,8,1]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[6,1,2,3,4,5,7,8]=>[2,3,4,5,6,1,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[1,2,3,4,7,5,8,6]=>[1,2,3,4,7,8,5,6]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,2,3,4,7,8,5,6]=>[1,2,3,4,6,8,7,5]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,6,7,5,8]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[1,2,3,7,4,5,8,6]=>[1,2,3,5,7,8,4,6]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,2,3,7,4,8,5,6]=>[1,2,3,7,6,8,4,5]=>[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,2,3,7,8,4,5,6]=>[1,2,3,5,6,8,7,4]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[1,2,7,3,4,5,8,6]=>[1,2,4,5,7,8,3,6]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,2,7,3,4,8,5,6]=>[1,2,4,7,6,8,3,5]=>[.,[.,[[.,.],[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,2,7,3,8,4,5,6]=>[1,2,7,5,6,8,3,4]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,2,7,8,3,4,5,6]=>[1,2,4,5,6,8,7,3]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[1,7,2,3,4,5,8,6]=>[1,3,4,5,7,8,2,6]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,8,6]=>[2,3,4,5,7,8,1,6]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[7,1,2,3,4,8,5,6]=>[2,3,4,7,6,8,1,5]=>[[.,.],[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[7,1,2,3,8,4,5,6]=>[2,3,7,5,6,8,1,4]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[7,1,2,8,3,4,5,6]=>[2,7,4,5,6,8,1,3]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[7,1,8,2,3,4,5,6]=>[7,3,4,5,6,8,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[7,8,1,2,3,4,5,6]=>[2,3,4,5,6,8,7,1]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[7,1,2,3,4,5,6,8]=>[2,3,4,5,6,7,1,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,2,3,8,4,5,6,7]=>[1,2,3,5,6,7,8,4]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[8,1,2,3,4,5,6,7]=>[2,3,4,5,6,7,8,1]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,9,7]=>[2,3,4,5,6,8,9,1,7]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,9,1,3,4,5,6,7,8]=>[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]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,10,8]=>[2,3,4,5,6,7,9,10,1,8]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[1,8,2,3,4,5,6,9,7]=>[1,3,4,5,6,8,9,2,7]=>[.,[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,9,8]=>[2,3,4,5,6,7,1,9,8]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2,1,9,3,4,5,6,7,8]=>[2,1,4,5,6,7,8,9,3]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,8,1,3,4,5,6,7,9]=>[3,2,4,5,6,7,8,1,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,10,1,3,4,5,6,7,8,9]=>[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]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]=>[10,1,2,3,4,5,6,7,8,11,9]=>[2,3,4,5,6,7,8,10,11,1,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7,10,9]=>[2,3,4,5,6,7,8,1,10,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[2,1,10,3,4,5,6,7,8,9]=>[2,1,4,5,6,7,8,9,10,3]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[2,11,1,3,4,5,6,7,8,9,10]=>[3,2,4,5,6,7,8,9,10,11,1]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,8,11,10]=>[2,3,4,5,6,7,8,9,1,11,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[1,7,2,3,4,5,6,9,8]=>[1,3,4,5,6,7,2,9,8]=>[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[2,1,8,3,4,5,6,7,9]=>[2,1,4,5,6,7,8,3,9]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[2,9,10,1,3,4,5,6,7,8]=>[3,2,4,5,6,7,8,10,9,1]=>[[[.,.],.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,1,0]=>[1,2,3,4,5,8,6,9,7]=>[1,2,3,4,5,8,9,6,7]=>[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7,9,8]=>[2,3,1,4,5,6,7,9,8]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,6,8,7,9]=>[1,2,3,4,5,6,8,7,9]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[2,1,3,4,5,6,9,7,8]=>[2,1,3,4,5,6,8,9,7]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,4,1,3,5,6,7,8,9]=>[3,2,4,1,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,5,6,8,9,7]=>[1,2,3,4,5,6,9,8,7]=>[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0,1,0]=>[7,1,2,3,4,8,5,9,6]=>[2,3,4,7,8,9,1,5,6]=>[[.,.],[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,9,8]=>[2,1,3,4,5,6,7,9,8]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,3,9,2,4,5,6,7,8]=>[1,4,3,5,6,7,8,9,2]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,1,0]=>[1,2,3,4,5,6,9,7,10,8]=>[1,2,3,4,5,6,9,10,7,8]=>[.,[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,6,7,9,8,10]=>[1,2,3,4,5,6,7,9,8,10]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,1,0]=>[7,1,2,3,4,5,8,9,6]=>[2,3,4,5,7,9,1,8,6]=>[[.,.],[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[2,1,3,4,5,6,7,10,8,9]=>[2,1,3,4,5,6,7,9,10,8]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,1,2,3,4,5,8,7,9]=>[2,3,4,5,6,1,8,7,9]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,3,9,1,4,5,6,7,8]=>[4,2,3,5,6,7,8,9,1]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,3,2,4,5,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,4,1,3,5,6,7,8,9,10]=>[3,2,4,1,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,5,6,7,9,10,8]=>[1,2,3,4,5,6,7,10,9,8]=>[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0,1,0]=>[8,1,2,3,4,5,9,6,10,7]=>[2,3,4,5,8,9,10,1,6,7]=>[[.,.],[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8,10,9]=>[2,1,3,4,5,6,7,8,10,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,1,0]=>[6,1,2,3,4,5,8,9,7]=>[2,3,4,5,6,1,9,8,7]=>[[.,.],[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,0,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,3,1,9,4,5,6,7,8]=>[3,2,1,5,6,7,8,9,4]=>[[[.,.],.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[]=>[]=>[]=>.
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,8,9,1,2]=>[2,9,3,4,5,6,7,8,1]=>[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,6,7,8,1,2,9]=>[2,8,3,4,5,6,7,1,9]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8,9]=>[2,4,3,1,5,6,7,8,9]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[3,1,2,4,5,6,9,7,8]=>[2,3,1,4,5,6,8,9,7]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[3,1,2,9,4,5,6,7,8]=>[2,3,1,5,6,7,8,9,4]=>[[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,1,9,2,4,5,6,7,8]=>[3,4,1,5,6,7,8,9,2]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,9,1,2,4,5,6,7,8]=>[2,4,3,5,6,7,8,9,1]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9]=>[2,3,1,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,5,6,7,8,9,2,3]=>[1,3,9,4,5,6,7,8,2]=>[.,[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,4,2,3,5,6,7,8,9]=>[1,3,4,2,5,6,7,8,9]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,7,8,9,1,2,3]=>[2,3,9,4,5,6,7,8,1]=>[[.,.],[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,1,2,3,7,8,9]=>[2,3,6,4,5,1,7,8,9]=>[[.,.],[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,1,2,3,6,7,8,9]=>[2,3,5,4,1,6,7,8,9]=>[[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[4,1,2,3,9,5,6,7,8]=>[2,3,4,1,6,7,8,9,5]=>[[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8,9]=>[2,3,4,1,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,5,2,3,4,6,7,8,9]=>[1,3,4,5,2,6,7,8,9]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,8,9,1,2,3,4]=>[2,3,4,9,5,6,7,8,1]=>[[.,.],[.,[.,[[.,[.,[.,[.,.]]]],.]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,7,8,1,2,3,4,9]=>[2,3,4,8,5,6,7,1,9]=>[[.,.],[.,[.,[[.,[.,[.,.]]],[.,.]]]]]
[1,1,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[5,6,1,2,3,4,7,8,9]=>[2,3,4,6,5,1,7,8,9]=>[[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[5,1,2,3,4,9,6,7,8]=>[2,3,4,5,1,7,8,9,6]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,0,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[5,9,1,2,3,4,6,7,8]=>[2,3,4,6,5,7,8,9,1]=>[[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[5,1,2,3,4,6,7,8,9]=>[2,3,4,5,1,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,2,6,3,4,5,7,8,9]=>[1,2,4,5,6,3,7,8,9]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,7,8,9,1,2,3,4,5]=>[2,3,4,5,9,6,7,8,1]=>[[.,.],[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0,0]=>[6,7,9,1,2,3,4,5,8]=>[2,3,4,5,8,6,7,9,1]=>[[.,.],[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0,0]=>[6,8,1,2,3,4,5,7,9]=>[2,3,4,5,7,6,8,1,9]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0,0]=>[6,1,2,3,4,5,9,7,8]=>[2,3,4,5,6,1,8,9,7]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0,0]=>[6,9,1,2,3,4,5,7,8]=>[2,3,4,5,7,6,8,9,1]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[6,1,2,3,4,5,7,8,9]=>[2,3,4,5,6,1,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0,0]=>[1,7,9,2,3,4,5,6,8]=>[1,3,4,5,6,8,7,9,2]=>[.,[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0,0]=>[1,7,2,3,4,5,6,8,9]=>[1,3,4,5,6,7,2,8,9]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0,0]=>[7,1,8,2,3,4,5,6,9]=>[7,3,4,5,6,8,1,2,9]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[7,8,9,1,2,3,4,5,6]=>[2,3,4,5,6,9,7,8,1]=>[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[7,8,1,2,3,4,5,6,9]=>[2,3,4,5,6,8,7,1,9]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[7,1,2,3,4,5,9,6,8]=>[2,3,4,5,7,8,1,9,6]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[7,9,1,2,3,4,5,6,8]=>[2,3,4,5,6,8,7,9,1]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[7,1,2,3,4,5,6,8,9]=>[2,3,4,5,6,7,1,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[1,2,3,4,5,8,9,6,7]=>[1,2,3,4,5,7,9,8,6]=>[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[1,2,3,4,5,8,6,7,9]=>[1,2,3,4,5,7,8,6,9]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0,0]=>[1,2,3,4,8,9,5,6,7]=>[1,2,3,4,6,7,9,8,5]=>[.,[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0,0]=>[1,2,3,8,4,5,6,7,9]=>[1,2,3,5,6,7,8,4,9]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0,0]=>[1,8,2,9,3,4,5,6,7]=>[1,8,4,5,6,7,9,2,3]=>[.,[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,8,9,2,3,4,5,6,7]=>[1,3,4,5,6,7,9,8,2]=>[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,8,2,3,4,5,6,7,9]=>[1,3,4,5,6,7,8,2,9]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[8,1,2,3,9,4,5,6,7]=>[2,3,8,5,6,7,9,1,4]=>[[.,.],[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[8,9,1,2,3,4,5,6,7]=>[2,3,4,5,6,7,9,8,1]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[8,1,2,3,4,5,6,7,9]=>[2,3,4,5,6,7,8,1,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,2,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,8,9,7]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,2,3,4,5,9,6,7,8]=>[1,2,3,4,5,7,8,9,6]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,2,3,4,9,5,6,7,8]=>[1,2,3,4,6,7,8,9,5]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,2,3,9,4,5,6,7,8]=>[1,2,3,5,6,7,8,9,4]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,2,9,3,4,5,6,7,8]=>[1,2,4,5,6,7,8,9,3]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,9,2,3,4,5,6,7,8]=>[1,3,4,5,6,7,8,9,2]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[9,1,2,3,4,5,6,7,8]=>[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]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,9,1]=>[9,2,3,4,5,6,7,8,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,8,1,9]=>[8,2,3,4,5,6,7,1,9]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,6,7,9,1,8]=>[8,2,3,4,5,6,7,9,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,5,6,8,9,1,7]=>[7,2,3,4,5,6,9,8,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,7,8,9,1,6]=>[6,2,3,4,5,9,7,8,1]=>[[[.,.],[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,6,7,8,9,1,5]=>[5,2,3,4,9,6,7,8,1]=>[[[.,.],[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,8,9,1,4]=>[4,2,3,9,5,6,7,8,1]=>[[[.,.],[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,7,8,9,1,3]=>[3,2,9,4,5,6,7,8,1]=>[[[.,.],.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,9,10,1]=>[10,2,3,4,5,6,7,8,9,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,7,8,9,1,10]=>[9,2,3,4,5,6,7,8,1,10]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,6,7,1,8,9]=>[7,2,3,4,5,6,1,8,9]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,6,7,8,10,1,9]=>[9,2,3,4,5,6,7,8,10,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,4,5,6,1,9,7,8]=>[6,2,3,4,5,1,8,9,7]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,9,10,1,8]=>[8,2,3,4,5,6,7,10,9,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,4,5,1,8,9,6,7]=>[5,2,3,4,1,7,9,8,6]=>[[[.,.],[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,8,9,10,1,7]=>[7,2,3,4,5,6,10,8,9,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],[[.,[.,.]],.]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,4,1,7,8,9,5,6]=>[4,2,3,1,6,9,7,8,5]=>[[[.,.],[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,7,8,9,10,1,6]=>[6,2,3,4,5,10,7,8,9,1]=>[[[.,.],[.,[.,[.,.]]]],[[.,[.,[.,.]]],.]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,6,7,8,9,4,5]=>[3,2,1,5,9,6,7,8,4]=>[[[.,.],.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,6,7,8,9,10,1,5]=>[5,2,3,4,10,6,7,8,9,1]=>[[[.,.],[.,[.,.]]],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,1,5,6,7,8,9,3,4]=>[2,1,4,9,5,6,7,8,3]=>[[.,.],[[.,.],[[.,[.,[.,[.,.]]]],.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,8,9,10,1,4]=>[4,2,3,10,5,6,7,8,9,1]=>[[[.,.],[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,7,8,9,10,1,3]=>[3,2,10,4,5,6,7,8,9,1]=>[[[.,.],.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,8,9,10,1,2]=>[2,10,3,4,5,6,7,8,9,1]=>[[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>[11,2,3,4,5,6,7,8,9,10,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,6,7,8,9,11,1,10]=>[10,2,3,4,5,6,7,8,9,11,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,6,1,7,8,9]=>[6,2,3,4,5,1,7,8,9]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,1,6,7,8,9]=>[5,2,3,4,1,6,7,8,9]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,1,5,6,7,8,9]=>[4,2,3,1,5,6,7,8,9]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,4,5,10,1,6,7,8,9]=>[6,2,3,4,5,7,8,9,10,1]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[4,5,6,1,2,3,9,10,7,8]=>[2,3,6,4,5,1,8,10,9,7]=>[[.,.],[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,6,7,1,9,8]=>[7,2,3,4,5,6,1,9,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6,9,8]=>[3,2,1,5,4,7,6,9,8]=>[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,5,4,6,7,8,9]=>[3,2,1,5,4,6,7,8,9]=>[[[.,.],.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,8,9,3]=>[2,1,9,4,5,6,7,8,3]=>[[.,.],[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,6,5,7,8,9]=>[2,1,4,3,6,5,7,8,9]=>[[.,.],[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9]=>[2,1,4,3,5,6,7,8,9]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,1,3,4,5,6,8,7,9]=>[2,1,3,4,5,6,8,7,9]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,8,9,2]=>[1,9,3,4,5,6,7,8,2]=>[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,4,2,5,6,7,8,9]=>[1,4,3,2,5,6,7,8,9]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,5,4,6,7,8,9]=>[1,3,2,5,4,6,7,8,9]=>[.,[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,3,2,4,5,6,8,9,7]=>[1,3,2,4,5,6,9,8,7]=>[.,[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]=>[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,8,9,3]=>[1,2,9,4,5,6,7,8,3]=>[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]=>[.,[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,8,9,4]=>[1,2,3,9,5,6,7,8,4]=>[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6,9,8]=>[1,2,3,5,4,7,6,9,8]=>[.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,6,7,8,9,5]=>[1,2,3,4,9,6,7,8,5]=>[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,4,5,7,8,9,6]=>[1,2,3,4,5,9,7,8,6]=>[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,4,5,7,6,9,8]=>[1,2,3,4,5,7,6,9,8]=>[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6,9,8,10]=>[3,2,1,5,4,7,6,9,8,10]=>[[[.,.],.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,6,5,8,7,9,10]=>[2,1,4,3,6,5,8,7,9,10]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]]
[1,0,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,1,4,3,5,6,7,8,9,10]=>[2,1,4,3,5,6,7,8,9,10]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,3,4,5,6,7,8,9,2]=>[.,[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,7,6,9,10,8]=>[1,3,2,5,4,7,6,10,9,8]=>[.,[[.,.],[[.,.],[[.,.],[[[.,.],.],.]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,8,9,10,3]=>[1,2,10,4,5,6,7,8,9,3]=>[.,[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,8,7,10,9]=>[1,2,4,3,6,5,8,7,10,9]=>[.,[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,8,9,10,4]=>[1,2,3,10,5,6,7,8,9,4]=>[.,[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6,9,8,10]=>[1,2,3,5,4,7,6,9,8,10]=>[.,[.,[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,4,6,7,8,9,10]=>[1,2,3,5,4,6,7,8,9,10]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,6,7,8,9,10,5]=>[1,2,3,4,10,6,7,8,9,5]=>[.,[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,8,7,10,9]=>[1,2,3,4,6,5,8,7,10,9]=>[.,[.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,7,8,9,10,6]=>[1,2,3,4,5,10,7,8,9,6]=>[.,[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,3,4,5,7,6,8,9,10]=>[1,2,3,4,5,7,6,8,9,10]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,8,9,10,7]=>[1,2,3,4,5,6,10,8,9,7]=>[.,[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,4,5,6,8,7,10,9]=>[1,2,3,4,5,6,8,7,10,9]=>[.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,5,6,7,8,9,2]=>[3,9,1,4,5,6,7,8,2]=>[[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,4,5,6,1,7,8,9,2]=>[6,9,3,4,5,1,7,8,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,5,6,7,1,8,9,2]=>[7,9,3,4,5,6,1,8,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,7,8,1,9,2]=>[8,9,3,4,5,6,7,1,2]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,5,6,7,8,9,10,2]=>[3,10,1,4,5,6,7,8,9,2]=>[[.,[.,.]],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,5,6,7,8,1,9,10,2]=>[8,10,3,4,5,6,7,1,9,2]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,7,8,9,1,10,2]=>[9,10,3,4,5,6,7,8,1,2]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,4,5,6,7,9,2,8]=>[1,8,3,4,5,6,7,9,2]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[9,1,2,3,4,5,6,7,8,10]=>[2,3,4,5,6,7,8,9,1,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,10,2,3,4,5,6,7,8,9]=>[1,3,4,5,6,7,8,9,10,2]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[10,1,2,3,4,5,6,7,8,9,11]=>[2,3,4,5,6,7,8,9,10,1,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0,0]=>[8,9,1,2,3,4,5,6,7,10]=>[2,3,4,5,6,7,9,8,1,10]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[1,9,10,2,3,4,5,6,7,8]=>[1,3,4,5,6,7,8,10,9,2]=>[.,[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[1,11,2,3,4,5,6,7,8,9,10]=>[1,3,4,5,6,7,8,9,10,11,2]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,1,4,5,6,7,8,2,9]=>[3,8,1,4,5,6,7,2,9]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9,10]=>[2,3,1,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,2,3,4,5,6,7,10,8,9]=>[1,2,3,4,5,6,7,9,10,8]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,2,3,4,5,6,7,8,11,9,10]=>[1,2,3,4,5,6,7,8,10,11,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0,1,0]=>[1,2,3,4,7,5,8,9,6]=>[1,2,3,4,7,9,5,8,6]=>[.,[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0,1,0,1,0]=>[1,2,3,6,4,7,8,9,5]=>[1,2,3,6,9,4,7,8,5]=>[.,[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,2,5,3,6,7,8,9,4]=>[1,2,5,9,3,6,7,8,4]=>[.,[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,4,2,5,6,7,8,9,3]=>[1,4,9,2,5,6,7,8,3]=>[.,[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[10,1,2,3,4,5,6,7,8,9]=>[2,3,4,5,6,7,8,9,10,1]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[8,1,2,3,4,5,6,7,9,10]=>[2,3,4,5,6,7,8,1,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[7,1,2,3,4,5,6,8,9,10]=>[2,3,4,5,6,7,1,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[6,1,2,3,4,5,7,8,9,10]=>[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]=>[5,1,2,3,4,6,7,8,9,10]=>[2,3,4,5,1,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[4,1,2,3,5,6,7,8,9,10]=>[2,3,4,1,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[11,1,2,3,4,5,6,7,8,9,10]=>[2,3,4,5,6,7,8,9,10,11,1]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,4,2,5,6,7,8,9]=>[3,4,1,2,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,7,8,9,10,1,3,4,5,6]=>[3,2,4,5,6,10,7,8,9,1]=>[[[.,.],.],[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,1,6,2,7,8,9]=>[5,6,3,4,1,2,7,8,9]=>[[[.,[.,.]],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,1,4,8,9,2,5,6,7]=>[3,5,1,4,6,7,9,8,2]=>[[.,[.,.]],[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,8,9,10,1,2,3,4]=>[2,3,4,10,5,6,7,8,9,1]=>[[.,.],[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[5,1,2,3,4,7,6,8,9]=>[2,3,4,5,1,7,6,8,9]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,3,5,9,4,6,7,8]=>[1,2,3,6,5,7,8,9,4]=>[.,[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,1,0,0]=>[1,2,3,4,5,7,9,6,8]=>[1,2,3,4,5,8,7,9,6]=>[.,[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[1,2,3,4,5,6,10,7,8,9]=>[1,2,3,4,5,6,8,9,10,7]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,1,0,0,0]=>[1,2,3,4,6,9,5,7,8]=>[1,2,3,4,7,6,8,9,5]=>[.,[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[1,2,3,4,5,10,6,7,8,9]=>[1,2,3,4,5,7,8,9,10,6]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,0]=>[1,2,3,4,10,5,6,7,8,9]=>[1,2,3,4,6,7,8,9,10,5]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,0,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,9,3,5,6,7,8]=>[1,2,5,4,6,7,8,9,3]=>[.,[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[1,2,3,10,4,5,6,7,8,9]=>[1,2,3,5,6,7,8,9,10,4]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,2,10,3,4,5,6,7,8,9]=>[1,2,4,5,6,7,8,9,10,3]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,1,0,0]=>[1,2,3,4,7,5,8,6,9]=>[1,2,3,4,7,8,5,6,9]=>[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,2,5,4,7,6,9,8]=>[2,3,1,5,4,7,6,9,8]=>[[.,.],[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,5,2,4,7,6,9,8]=>[3,4,1,5,2,7,6,9,8]=>[[.,[.,.]],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,5,2,6,4,8,7,9]=>[3,5,1,6,2,4,8,7,9]=>[[.,[.,.]],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,4,2,6,5,8,7,9]=>[3,4,1,2,6,5,8,7,9]=>[[.,[.,.]],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,2,5,4,7,6,9,8,10]=>[2,3,1,5,4,7,6,9,8,10]=>[[.,.],[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5,8,7,10,9]=>[3,4,1,2,6,5,8,7,10,9]=>[[.,[.,.]],[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,1,2,5,6,7,8,9,10]=>[2,4,3,1,5,6,7,8,9,10]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,7,8,9,10,1,2,3]=>[2,3,10,4,5,6,7,8,9,1]=>[[.,.],[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[1,9,2,3,4,5,6,7,8,10]=>[1,3,4,5,6,7,8,9,2,10]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,8,4,5,6,7,9,10]=>[1,2,3,5,6,7,8,4,9,10]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,4,6,8,10,1,3,5,7,9]=>[3,2,5,4,7,6,9,8,10,1]=>[[[.,.],.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[6,1,7,2,8,3,9,4,10,5]=>[6,7,8,9,10,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,4,6,8,10,12,1,3,5,7,9,11]=>[3,2,5,4,7,6,9,8,11,10,12,1]=>[[[.,.],.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[7,1,8,2,9,3,10,4,11,5,12,6]=>[7,8,9,10,11,12,1,2,3,4,5,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10,11]=>[1,2,3,4,5,6,7,8,9,10,11]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[3,1,2,4,5,6,7,8,9,10,11]=>[2,3,1,4,5,6,7,8,9,10,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0,0]=>[8,1,2,3,4,5,6,10,7,9]=>[2,3,4,5,6,8,9,1,10,7]=>[[.,.],[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[3,1,10,2,4,5,6,7,8,9]=>[3,4,1,5,6,7,8,9,10,2]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,5,6,7,8,9,10,11,2]=>[3,11,1,4,5,6,7,8,9,10,2]=>[[.,[.,.]],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,5,6,7,8,10,9,11]=>[1,2,3,4,5,6,7,8,10,9,11]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[6,7,8,9,10,1,2,3,4,5]=>[2,3,4,5,10,6,7,8,9,1]=>[[.,.],[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[9,1,10,2,3,4,5,6,7,8]=>[9,3,4,5,6,7,8,10,1,2]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[3,7,8,9,10,1,2,4,5,6]=>[2,4,3,5,6,10,7,8,9,1]=>[[.,.],[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,3,10,1,4,5,6,7,8,9]=>[4,2,3,5,6,7,8,9,10,1]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0,1,0]=>[6,1,2,3,4,7,8,9,5]=>[2,3,4,6,9,1,7,8,5]=>[[.,.],[.,[.,[[.,.],[[.,[.,.]],.]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0,0]=>[1,2,3,4,5,8,6,7,9,10]=>[1,2,3,4,5,7,8,6,9,10]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,1,1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[5,10,1,2,3,4,6,7,8,9]=>[2,3,4,6,5,7,8,9,10,1]=>[[.,.],[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[9,10,1,2,3,4,5,6,7,8]=>[2,3,4,5,6,7,8,10,9,1]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]=>[10,11,1,2,3,4,5,6,7,8,9]=>[2,3,4,5,6,7,8,9,11,10,1]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,4,5,6,8,1,9,7]=>[8,2,3,4,5,6,9,1,7]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,9,1,10,8]=>[9,2,3,4,5,6,7,10,1,8]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[7,8,9,10,1,2,3,4,5,6]=>[2,3,4,5,6,10,7,8,9,1]=>[[.,.],[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[8,9,10,1,2,3,4,5,6,7]=>[2,3,4,5,6,7,10,8,9,1]=>[[.,.],[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,7,8,9,10,1,11,2]=>[10,11,3,4,5,6,7,8,9,1,2]=>[[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[4,1,2,3,6,5,8,7,9]=>[2,3,4,1,6,5,8,7,9]=>[[.,.],[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,4,5,6,7,8,1,9,3]=>[8,2,9,4,5,6,7,1,3]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,1,2,3,4,9,10]=>[2,3,4,8,5,6,7,1,9,10]=>[[.,.],[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]]
[1,1,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,1,2,3,7,8,9,10]=>[2,3,6,4,5,1,7,8,9,10]=>[[.,.],[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[1,2,3,4,5,6,9,7,8,10]=>[1,2,3,4,5,6,8,9,7,10]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,4,2,3,5,6,7,8,9,10]=>[1,3,4,2,5,6,7,8,9,10]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[3,1,2,10,4,5,6,7,8,9]=>[2,3,1,5,6,7,8,9,10,4]=>[[.,.],[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[5,1,2,3,4,10,6,7,8,9]=>[2,3,4,5,1,7,8,9,10,6]=>[[.,.],[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[5,7,8,9,10,1,2,3,4,6]=>[2,3,4,6,5,10,7,8,9,1]=>[[.,.],[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]]
[1,1,1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,7,8,9,10,1,2,3,5,6]=>[2,3,5,4,6,10,7,8,9,1]=>[[.,.],[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,4,5,6,7,8,10,1,11,9]=>[10,2,3,4,5,6,7,8,11,1,9]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[5,6,7,8,10,1,2,3,4,9]=>[2,3,4,9,5,6,7,8,10,1]=>[[.,.],[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,5,6,7,8,10,11,9]=>[1,2,3,4,5,6,7,8,11,10,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,4,5,6,7,8,9,1,10,3]=>[9,2,10,4,5,6,7,8,1,3]=>[[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,4,2,5,3,7,6,9,8]=>[1,4,5,2,3,7,6,9,8]=>[.,[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,4,2,3,6,5,8,7,9]=>[1,3,4,2,6,5,8,7,9]=>[.,[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,4,2,3,6,5,8,7,10,9]=>[1,3,4,2,6,5,8,7,10,9]=>[.,[[.,.],[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,5,8,7,9]=>[3,2,4,1,6,5,8,7,9]=>[[[.,.],.],[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0,0]=>[2,1,7,8,9,10,3,4,5,6]=>[2,1,4,5,6,10,7,8,9,3]=>[[.,.],[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[3,4,1,2,8,9,10,5,6,7]=>[2,4,3,1,6,7,10,8,9,5]=>[[.,.],[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[5,6,7,8,1,2,3,4,10,9]=>[2,3,4,8,5,6,7,1,10,9]=>[[.,.],[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,5,6,7,1,8,2,9,3]=>[7,8,9,4,5,6,1,2,3]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,1,0]=>[8,1,2,3,4,5,6,9,10,7]=>[2,3,4,5,6,8,10,1,9,7]=>[[.,.],[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0,0]=>[1,2,3,4,5,6,9,10,7,8]=>[1,2,3,4,5,6,8,10,9,7]=>[.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,5,4,7,6,10,8,9]=>[1,3,2,5,4,7,6,9,10,8]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,8,5,10,7,9]=>[4,2,6,1,8,3,9,5,10,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[3,4,6,8,10,1,2,5,7,9]=>[2,5,3,4,7,6,9,8,10,1]=>[[.,.],[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[1,6,2,7,3,8,4,9,5,10]=>[1,6,7,8,9,2,3,4,5,10]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,5,4,7,6,9,8,12,10,11]=>[1,3,2,5,4,7,6,9,8,11,12,10]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,12,2,3,4,5,6,7,8,9,10,11]=>[1,3,4,5,6,7,8,9,10,11,12,2]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0,0]=>[12,1,2,3,4,5,6,7,8,9,10,11]=>[2,3,4,5,6,7,8,9,10,11,12,1]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,5,3,7,6,9,8,10]=>[4,2,5,1,3,7,6,9,8,10]=>[[[.,.],[.,.]],[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0,1,0]=>[2,1,5,6,3,4,9,10,7,8,12,11]=>[2,1,4,6,5,3,8,10,9,7,12,11]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[2,4,1,6,3,8,5,7,9]=>[4,2,6,1,7,3,8,5,9]=>[[[.,.],[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0,0]=>[4,5,6,9,10,1,2,3,7,8]=>[2,3,7,4,5,6,8,10,9,1]=>[[.,.],[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]]
[1,1,1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[4,5,8,9,10,1,2,3,6,7]=>[2,3,6,4,5,7,10,8,9,1]=>[[.,.],[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,6,3,5,8,7,9]=>[4,2,5,1,6,3,8,7,9]=>[[[.,.],[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,5,3,7,6,9,8]=>[4,2,5,1,3,7,6,9,8]=>[[[.,.],[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,4,1,3,6,5,8,7,10,9]=>[3,2,4,1,6,5,8,7,10,9]=>[[[.,.],.],[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[2,1,4,3,6,5,8,7,10,9,12,11]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,0,1,1,1,1,0,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[2,6,8,9,10,1,3,4,5,7]=>[3,2,4,5,7,6,10,8,9,1]=>[[[.,.],.],[.,[.,[[.,.],[[.,[.,.]],.]]]]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[2,8,9,10,11,12,1,3,4,5,6,7]=>[3,2,4,5,6,7,12,8,9,10,11,1]=>[[[.,.],.],[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0,1,0]=>[1,6,2,7,3,8,4,9,5]=>[1,6,7,8,9,2,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[5,1,6,2,7,3,8,4,9]=>[5,6,7,8,1,2,3,4,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,7,8,9,10,11,1,12,2]=>[11,12,3,4,5,6,7,8,9,10,1,2]=>[[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
Map
first fundamental transformation
Description
Return the permutation whose cycles are the subsequences between successive left to right maxima.
Map
binary search tree: left to right
Description
Return the shape of the binary search tree of the permutation as a non labelled binary tree.
searching the database
Sorry, this map was not found in the database.