Identifier
Mp00024:
Dyck paths
—to 321-avoiding permutation⟶
Permutations
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00086: Permutations —first fundamental transformation⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Images
=>
Cc0005;cc-rep-0Cc0010;cc-rep-3
[1,0]=>[1]=>[1]=>[.,.]
[1,0,1,0]=>[2,1]=>[2,1]=>[[.,.],.]
[1,1,0,0]=>[1,2]=>[1,2]=>[.,[.,.]]
[1,0,1,0,1,0]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[1,0,1,1,0,0]=>[2,3,1]=>[3,2,1]=>[[[.,.],.],.]
[1,1,0,0,1,0]=>[3,1,2]=>[2,3,1]=>[[.,[.,.]],.]
[1,1,0,1,0,0]=>[1,3,2]=>[1,3,2]=>[.,[[.,.],.]]
[1,1,1,0,0,0]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[1,0,1,0,1,0,1,0]=>[2,1,4,3]=>[2,1,4,3]=>[[.,.],[[.,.],.]]
[1,0,1,0,1,1,0,0]=>[2,4,1,3]=>[3,2,4,1]=>[[[.,.],[.,.]],.]
[1,0,1,1,0,0,1,0]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[1,0,1,1,0,1,0,0]=>[2,3,1,4]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[1,0,1,1,1,0,0,0]=>[2,3,4,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[1,1,0,0,1,0,1,0]=>[3,1,4,2]=>[3,4,1,2]=>[[.,[.,.]],[.,.]]
[1,1,0,0,1,1,0,0]=>[3,4,1,2]=>[2,4,3,1]=>[[.,[[.,.],.]],.]
[1,1,0,1,0,0,1,0]=>[3,1,2,4]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[1,1,0,1,0,1,0,0]=>[1,3,2,4]=>[1,3,2,4]=>[.,[[.,.],[.,.]]]
[1,1,0,1,1,0,0,0]=>[1,3,4,2]=>[1,4,3,2]=>[.,[[[.,.],.],.]]
[1,1,1,0,0,0,1,0]=>[4,1,2,3]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[1,1,1,0,0,1,0,0]=>[1,4,2,3]=>[1,3,4,2]=>[.,[[.,[.,.]],.]]
[1,1,1,0,1,0,0,0]=>[1,2,4,3]=>[1,2,4,3]=>[.,[.,[[.,.],.]]]
[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,5]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,5]=>[3,2,4,1,5]=>[[[.,.],[.,.]],[.,.]]
[1,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,3]=>[2,1,5,4,3]=>[[.,.],[[[.,.],.],.]]
[1,0,1,0,1,1,0,1,0,0]=>[2,4,1,5,3]=>[4,2,5,1,3]=>[[[.,.],[.,.]],[.,.]]
[1,0,1,0,1,1,1,0,0,0]=>[2,4,5,1,3]=>[3,2,5,4,1]=>[[[.,.],[[.,.],.]],.]
[1,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,4]=>[2,1,4,5,3]=>[[.,.],[[.,[.,.]],.]]
[1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,4]=>[3,2,4,5,1]=>[[[.,.],[.,[.,.]]],.]
[1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,4]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,4]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]
[1,0,1,1,0,1,1,0,0,0]=>[2,3,5,1,4]=>[4,2,3,5,1]=>[[[.,.],[.,[.,.]]],.]
[1,0,1,1,1,0,0,0,1,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,0]=>[2,3,1,4,5]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[1,0,1,1,1,0,1,0,0,0]=>[2,3,4,1,5]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[1,0,1,1,1,1,0,0,0,0]=>[2,3,4,5,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,5]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,5]=>[2,4,3,1,5]=>[[.,[[.,.],.]],[.,.]]
[1,1,0,0,1,1,0,0,1,0]=>[3,1,4,5,2]=>[3,5,1,4,2]=>[[.,[.,.]],[[.,.],.]]
[1,1,0,0,1,1,0,1,0,0]=>[3,4,1,5,2]=>[4,5,3,1,2]=>[[[.,[.,.]],.],[.,.]]
[1,1,0,0,1,1,1,0,0,0]=>[3,4,5,1,2]=>[2,5,3,4,1]=>[[.,[[.,.],[.,.]]],.]
[1,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4]=>[3,4,1,5,2]=>[[.,[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4]=>[2,4,3,5,1]=>[[.,[[.,.],[.,.]]],.]
[1,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4]=>[2,3,1,5,4]=>[[.,[.,.]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4]=>[1,4,3,5,2]=>[.,[[[.,.],[.,.]],.]]
[1,1,0,1,1,0,0,0,1,0]=>[3,1,2,4,5]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,0,1,0,0]=>[1,3,2,4,5]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,0]=>[1,3,4,2,5]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
[1,1,0,1,1,1,0,0,0,0]=>[1,3,4,5,2]=>[1,5,3,4,2]=>[.,[[[.,.],[.,.]],.]]
[1,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3]=>[4,3,5,1,2]=>[[[.,.],[.,.]],[.,.]]
[1,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3]=>[2,3,5,4,1]=>[[.,[.,[[.,.],.]]],.]
[1,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3]=>[2,4,5,1,3]=>[[.,[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,3]=>[1,4,5,2,3]=>[.,[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3]=>[1,3,5,4,2]=>[.,[[.,[[.,.],.]],.]]
[1,1,1,0,1,0,0,0,1,0]=>[4,1,2,3,5]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[1,1,1,0,1,0,0,1,0,0]=>[1,4,2,3,5]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,1,0,0,0]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,0,0]=>[1,2,4,5,3]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]]
[1,1,1,1,0,0,0,0,1,0]=>[5,1,2,3,4]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,0,1,0,0]=>[1,5,2,3,4]=>[1,3,4,5,2]=>[.,[[.,[.,[.,.]]],.]]
[1,1,1,1,0,0,1,0,0,0]=>[1,2,5,3,4]=>[1,2,4,5,3]=>[.,[.,[[.,[.,.]],.]]]
[1,1,1,1,0,1,0,0,0,0]=>[1,2,3,5,4]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]
[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[[.,.],[[.,.],[[.,.],.]]]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5]=>[3,2,4,1,6,5]=>[[[.,.],[.,.]],[[.,.],.]]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5]=>[2,1,5,4,6,3]=>[[.,.],[[[.,.],[.,.]],.]]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5]=>[4,2,5,1,6,3]=>[[[.,.],[.,.]],[[.,.],.]]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5]=>[3,2,5,4,6,1]=>[[[.,.],[[.,.],[.,.]]],.]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,5,6]=>[3,2,4,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>[[.,.],[[[.,.],.],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,5,3,6]=>[4,2,5,1,3,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,5,1,3,6]=>[3,2,5,4,1,6]=>[[[.,.],[[.,.],.]],[.,.]]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>[[.,.],[[[.,.],[.,.]],.]]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,5,6,3]=>[4,2,6,1,5,3]=>[[[.,.],[.,.]],[[.,.],.]]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,5,1,6,3]=>[5,2,6,4,1,3]=>[[[.,.],[[.,.],.]],[.,.]]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,5,6,1,3]=>[3,2,6,4,5,1]=>[[[.,.],[[.,.],[.,.]]],.]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,6,4]=>[2,1,5,6,3,4]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4]=>[3,2,5,6,1,4]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,5,6,3,4]=>[2,1,4,6,5,3]=>[[.,.],[[.,[[.,.],.]],.]]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[2,5,1,6,3,4]=>[5,2,4,6,1,3]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,5,6,1,3,4]=>[3,2,4,6,5,1]=>[[[.,.],[.,[[.,.],.]]],.]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,4,6]=>[2,1,4,5,3,6]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,4,6]=>[3,2,4,5,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>[[[.,.],.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,6]=>[4,2,3,5,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>[[.,.],[.,[[[.,.],.],.]]]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,5,1,6,4]=>[5,2,3,6,1,4]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,5,6,1,4]=>[4,2,3,6,5,1]=>[[[.,.],[.,[[.,.],.]]],.]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5]=>[2,1,4,5,6,3]=>[[.,.],[[.,[.,[.,.]]],.]]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5]=>[3,2,4,5,6,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5]=>[2,1,3,5,6,4]=>[[.,.],[.,[[.,[.,.]],.]]]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,5]=>[3,2,1,5,6,4]=>[[[.,.],.],[[.,[.,.]],.]]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5]=>[4,2,3,5,6,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>[[[.,.],.],[.,[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>[[[.,.],[.,.]],[[.,.],.]]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,4,6,1,5]=>[5,2,3,4,6,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5]=>[3,4,1,2,6,5]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5]=>[2,4,3,1,6,5]=>[[.,[[.,.],.]],[[.,.],.]]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5]=>[3,5,1,4,6,2]=>[[.,[.,.]],[[.,[.,.]],.]]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5]=>[4,5,3,1,6,2]=>[[[.,[.,.]],.],[[.,.],.]]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5]=>[2,5,3,4,6,1]=>[[.,[[.,.],[.,[.,.]]]],.]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,5,6]=>[3,4,1,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,5,6]=>[2,4,3,1,5,6]=>[[.,[[.,.],.]],[.,[.,.]]]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,5,2,6]=>[3,5,1,4,2,6]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[3,4,1,5,2,6]=>[4,5,3,1,2,6]=>[[[.,[.,.]],.],[.,[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[3,4,5,1,2,6]=>[2,5,3,4,1,6]=>[[.,[[.,.],[.,.]]],[.,.]]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,5,6,2]=>[3,6,1,4,5,2]=>[[.,[.,.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[3,4,1,5,6,2]=>[4,6,3,1,5,2]=>[[[.,[.,.]],.],[[.,.],.]]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[3,4,5,1,6,2]=>[5,6,3,4,1,2]=>[[[.,[.,.]],[.,.]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,5,6,1,2]=>[2,6,3,4,5,1]=>[[.,[[.,.],[.,[.,.]]]],.]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,6,4]=>[3,5,1,6,2,4]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,6,4]=>[2,5,3,6,1,4]=>[[.,[[.,.],[.,.]]],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,6,2,4]=>[3,4,1,6,5,2]=>[[.,[.,.]],[[[.,.],.],.]]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,6,2,4]=>[5,4,3,6,1,2]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,6,1,2,4]=>[2,4,3,6,5,1]=>[[.,[[.,.],[[.,.],.]]],.]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,6]=>[3,4,1,5,2,6]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,6]=>[2,4,3,5,1,6]=>[[.,[[.,.],[.,.]]],[.,.]]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,6]=>[2,3,1,5,4,6]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,6]=>[1,4,3,5,2,6]=>[.,[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,6,4]=>[2,3,1,6,5,4]=>[[.,[.,.]],[[[.,.],.],.]]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>[.,[[.,.],[[[.,.],.],.]]]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,6,4]=>[1,5,3,6,2,4]=>[.,[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,6,2,4]=>[1,4,3,6,5,2]=>[.,[[[.,.],[[.,.],.]],.]]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5]=>[3,4,1,5,6,2]=>[[.,[.,.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,5]=>[2,4,3,5,6,1]=>[[.,[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5]=>[2,3,1,5,6,4]=>[[.,[.,.]],[[.,[.,.]],.]]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,5]=>[1,3,2,5,6,4]=>[.,[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,5]=>[1,4,3,5,6,2]=>[.,[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5]=>[2,3,1,4,6,5]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>[.,[[[.,.],.],[[.,.],.]]]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5]=>[1,5,3,4,6,2]=>[.,[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,4,5,6]=>[2,3,1,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>[.,[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>[.,[[[.,.],[.,[.,.]]],.]]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,5,2,6,3]=>[4,5,6,1,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[4,5,1,2,6,3]=>[2,5,6,4,1,3]=>[[.,[[.,[.,.]],.]],[.,.]]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[4,1,5,6,2,3]=>[4,3,6,1,5,2]=>[[[.,.],[.,.]],[[.,.],.]]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[4,5,1,6,2,3]=>[5,3,6,4,1,2]=>[[[.,.],[[.,.],.]],[.,.]]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3]=>[2,3,6,4,5,1]=>[[.,[.,[[.,.],[.,.]]]],.]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,6]=>[4,3,5,1,2,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,6]=>[2,3,5,4,1,6]=>[[.,[.,[[.,.],.]]],[.,.]]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,6]=>[2,4,5,1,3,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,6]=>[1,4,5,2,3,6]=>[.,[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,6]=>[1,3,5,4,2,6]=>[.,[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,5,6,3]=>[2,4,6,1,5,3]=>[[.,[.,[.,.]]],[[.,.],.]]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,5,6,3]=>[1,4,6,2,5,3]=>[.,[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,5,2,6,3]=>[1,5,6,4,2,3]=>[.,[[[.,[.,.]],.],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,5,6,2,3]=>[1,3,6,4,5,2]=>[.,[[.,[[.,.],[.,.]]],.]]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5]=>[4,3,5,1,6,2]=>[[[.,.],[.,.]],[[.,.],.]]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5]=>[2,3,5,4,6,1]=>[[.,[.,[[.,.],[.,.]]]],.]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5]=>[2,4,5,1,6,3]=>[[.,[.,[.,.]]],[[.,.],.]]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5]=>[1,4,5,2,6,3]=>[.,[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,5]=>[1,3,5,4,6,2]=>[.,[[.,[[.,.],[.,.]]],.]]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5]=>[2,3,4,1,6,5]=>[[.,[.,[.,.]]],[[.,.],.]]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5]=>[1,3,4,2,6,5]=>[.,[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[.,[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,2,4,6,3,5]=>[1,2,5,4,6,3]=>[.,[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,5,6]=>[2,3,4,1,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,5,6]=>[1,3,4,2,5,6]=>[.,[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>[.,[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>[.,[.,[[[.,.],[.,.]],.]]]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[5,1,6,2,3,4]=>[5,3,4,6,1,2]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4]=>[2,3,4,6,5,1]=>[[.,[.,[.,[[.,.],.]]]],.]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[5,1,2,6,3,4]=>[2,5,4,6,1,3]=>[[.,[[.,.],[.,.]]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,6,3,4]=>[1,5,4,6,2,3]=>[.,[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,6,2,3,4]=>[1,3,4,6,5,2]=>[.,[[.,[.,[[.,.],.]]],.]]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,6,4]=>[2,3,5,6,1,4]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,6,4]=>[1,3,5,6,2,4]=>[.,[[.,[.,[.,.]]],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,6,4]=>[1,2,5,6,3,4]=>[.,[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,2,5,6,3,4]=>[1,2,4,6,5,3]=>[.,[.,[[.,[[.,.],.]],.]]]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,6]=>[2,3,4,5,1,6]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,6]=>[1,3,4,5,2,6]=>[.,[[.,[.,[.,.]]],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,6]=>[1,2,4,5,3,6]=>[.,[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[.,[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>[.,[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5]=>[2,3,4,5,6,1]=>[[.,[.,[.,[.,[.,.]]]]],.]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5]=>[1,3,4,5,6,2]=>[.,[[.,[.,[.,[.,.]]]],.]]
[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]=>[1,2,3,6,4,5]=>[1,2,3,5,6,4]=>[.,[.,[.,[[.,[.,.]],.]]]]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5,7]=>[3,2,4,1,6,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5,7]=>[2,1,5,4,6,3,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5,7]=>[4,2,5,1,6,3,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5,7]=>[3,2,5,4,6,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,7,5]=>[3,2,4,1,7,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,6,3,7,5]=>[2,1,6,4,7,3,5]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5]=>[4,2,6,1,7,3,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,6,1,3,7,5]=>[3,2,6,4,7,1,5]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,6,7,3,5]=>[2,1,5,4,7,6,3]=>[[.,.],[[[.,.],[[.,.],.]],.]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,6,7,3,5]=>[4,2,5,1,7,6,3]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,6,1,7,3,5]=>[6,2,5,4,7,1,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,6,7,1,3,5]=>[3,2,5,4,7,6,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,7,5,6]=>[2,1,4,3,6,7,5]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,3,7,5,6]=>[3,2,4,1,6,7,5]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,7,3,5,6]=>[2,1,5,4,6,7,3]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,4,1,7,3,5,6]=>[4,2,5,1,6,7,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,4,7,1,3,5,6]=>[3,2,5,4,6,7,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,4,1,3,5,7,6]=>[3,2,4,1,5,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,7,6]=>[4,2,5,1,3,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,5,1,3,7,6]=>[3,2,5,4,1,7,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,5,7,3,6]=>[2,1,6,4,5,7,3]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,4,1,5,7,3,6]=>[4,2,6,1,5,7,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,4,5,1,7,3,6]=>[5,2,6,4,1,7,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,5,7,1,3,6]=>[3,2,6,4,5,7,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,5,6,7]=>[3,2,4,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,4,1,5,3,6,7]=>[4,2,5,1,3,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,4,5,1,3,6,7]=>[3,2,5,4,1,6,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,4,1,5,6,3,7]=>[4,2,6,1,5,3,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,4,5,1,6,3,7]=>[5,2,6,4,1,3,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,4,5,6,1,3,7]=>[3,2,6,4,5,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,5,6,7,3]=>[2,1,7,4,5,6,3]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1,5,6,7,3]=>[4,2,7,1,5,6,3]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,4,5,1,6,7,3]=>[5,2,7,4,1,6,3]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,5,6,1,7,3]=>[6,2,7,4,5,1,3]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,5,6,7,1,3]=>[3,2,7,4,5,6,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,7]=>[2,1,5,6,3,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,5,1,3,6,4,7]=>[3,2,5,6,1,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,7]=>[2,1,4,6,5,3,7]=>[[.,.],[[.,[[.,.],.]],[.,.]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,5,1,6,3,4,7]=>[5,2,4,6,1,3,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,6,1,3,4,7]=>[3,2,4,6,5,1,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,6,7,4]=>[2,1,5,7,3,6,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,6,7,4]=>[3,2,5,7,1,6,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,5,6,3,7,4]=>[2,1,6,7,5,3,4]=>[[.,.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,5,1,6,3,7,4]=>[5,2,6,7,1,3,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,5,6,1,3,7,4]=>[3,2,6,7,5,1,4]=>[[[.,.],[[.,[.,.]],.]],[.,.]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,6,7,3,4]=>[2,1,4,7,5,6,3]=>[[.,.],[[.,[[.,.],[.,.]]],.]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,5,1,6,7,3,4]=>[5,2,4,7,1,6,3]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,5,6,1,7,3,4]=>[6,2,4,7,5,1,3]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,5,6,7,1,3,4]=>[3,2,4,7,5,6,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,6]=>[2,1,5,6,3,7,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,7,4,6]=>[3,2,5,6,1,7,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,5,7,3,4,6]=>[2,1,4,6,5,7,3]=>[[.,.],[[.,[[.,.],[.,.]]],.]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,5,1,7,3,4,6]=>[5,2,4,6,1,7,3]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,5,7,1,3,4,6]=>[3,2,4,6,5,7,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,1,5,3,4,7,6]=>[2,1,4,5,3,7,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,4,7,6]=>[3,2,4,5,1,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,5,1,4,7,6]=>[4,2,3,5,1,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,1,3,5,7,4,6]=>[2,1,3,6,5,7,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,7,4,6]=>[3,2,1,6,5,7,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,1,7,4,6]=>[5,2,3,6,1,7,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,5,7,1,4,6]=>[4,2,3,6,5,7,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,7]=>[2,1,4,5,3,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,5,1,3,4,6,7]=>[3,2,4,5,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,1,4,6,7]=>[4,2,3,5,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,1,6,4,7]=>[5,2,3,6,1,4,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,6,1,4,7]=>[4,2,3,6,5,1,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1,5,6,7,4]=>[3,2,1,7,5,6,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,5,1,6,7,4]=>[5,2,3,7,1,6,4]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,5,6,1,7,4]=>[6,2,3,7,5,1,4]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,5,6,7,1,4]=>[4,2,3,7,5,6,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,6,3,7,4,5]=>[2,1,6,5,7,3,4]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,6,1,3,7,4,5]=>[3,2,6,5,7,1,4]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,6,7,3,4,5]=>[2,1,4,5,7,6,3]=>[[.,.],[[.,[.,[[.,.],.]]],.]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,6,1,7,3,4,5]=>[6,2,4,5,7,1,3]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,6,7,1,3,4,5]=>[3,2,4,5,7,6,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,6,3,4,7,5]=>[2,1,4,6,7,3,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,6,1,3,4,7,5]=>[3,2,4,6,7,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,3,6,4,7,5]=>[2,1,3,6,7,4,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,7,5]=>[3,2,1,6,7,4,5]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,3,6,1,4,7,5]=>[4,2,3,6,7,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,3,6,7,4,5]=>[2,1,3,5,7,6,4]=>[[.,.],[.,[[.,[[.,.],.]],.]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,1,6,7,4,5]=>[3,2,1,5,7,6,4]=>[[[.,.],.],[[.,[[.,.],.]],.]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,6,1,7,4,5]=>[6,2,3,5,7,1,4]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,3,6,7,1,4,5]=>[4,2,3,5,7,6,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5,7]=>[2,1,4,5,6,3,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,6,1,3,4,5,7]=>[3,2,4,5,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5,7]=>[2,1,3,5,6,4,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,5,7]=>[3,2,1,5,6,4,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5,7]=>[4,2,3,5,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,3,4,6,1,5,7]=>[5,2,3,4,6,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,4,1,6,7,5]=>[4,2,3,1,7,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,3,4,6,1,7,5]=>[6,2,3,4,7,1,5]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,4,6,7,1,5]=>[5,2,3,4,7,6,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,7,3,4,5,6]=>[2,1,4,5,6,7,3]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,7,1,3,4,5,6]=>[3,2,4,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,7,4,5,6]=>[2,1,3,5,6,7,4]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,7,4,5,6]=>[3,2,1,5,6,7,4]=>[[[.,.],.],[[.,[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,7,1,4,5,6]=>[4,2,3,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,3,4,7,5,6]=>[2,1,3,4,6,7,5]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,4,7,5,6]=>[3,2,1,4,6,7,5]=>[[[.,.],.],[.,[[.,[.,.]],.]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,3,4,1,7,5,6]=>[4,2,3,1,6,7,5]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,6]=>[5,2,3,4,6,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,4,1,5,7,6]=>[4,2,3,1,5,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,4,5,1,7,6]=>[5,2,3,4,1,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,3,4,5,7,1,6]=>[6,2,3,4,5,7,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,7]=>[3,4,1,2,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,7]=>[2,4,3,1,6,5,7]=>[[.,[[.,.],.]],[[.,.],[.,.]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5,7]=>[3,5,1,4,6,2,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,4,1,6,2,5,7]=>[4,5,3,1,6,2,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,4,6,1,2,5,7]=>[2,5,3,4,6,1,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,7,5]=>[3,4,1,2,7,6,5]=>[[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,6,7,5]=>[2,4,3,1,7,6,5]=>[[.,[[.,.],.]],[[[.,.],.],.]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,4,6,2,7,5]=>[3,6,1,4,7,2,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[3,4,1,6,2,7,5]=>[4,6,3,1,7,2,5]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[3,4,6,1,2,7,5]=>[2,6,3,4,7,1,5]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,7,2,5]=>[3,5,1,4,7,6,2]=>[[.,[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,4,1,6,7,2,5]=>[4,5,3,1,7,6,2]=>[[[.,[.,.]],.],[[[.,.],.],.]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,4,6,1,7,2,5]=>[6,5,3,4,7,1,2]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,6,7,1,2,5]=>[2,5,3,4,7,6,1]=>[[.,[[.,.],[.,[[.,.],.]]]],.]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,6]=>[3,4,1,2,6,7,5]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,7,5,6]=>[2,4,3,1,6,7,5]=>[[.,[[.,.],.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,4,7,2,5,6]=>[3,5,1,4,6,7,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,4,1,7,2,5,6]=>[4,5,3,1,6,7,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,4,7,1,2,5,6]=>[2,5,3,4,6,7,1]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[3,1,4,2,5,7,6]=>[3,4,1,2,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,4,1,2,5,7,6]=>[2,4,3,1,5,7,6]=>[[.,[[.,.],.]],[.,[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[3,1,4,5,2,7,6]=>[3,5,1,4,2,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,4,1,5,2,7,6]=>[4,5,3,1,2,7,6]=>[[[.,[.,.]],.],[.,[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,7,6]=>[2,5,3,4,1,7,6]=>[[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,4,5,7,2,6]=>[3,6,1,4,5,7,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[3,4,1,5,7,2,6]=>[4,6,3,1,5,7,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,4,5,1,7,2,6]=>[5,6,3,4,1,7,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[3,4,5,7,1,2,6]=>[2,6,3,4,5,7,1]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,5,6,7]=>[3,4,1,2,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,5,6,7]=>[2,4,3,1,5,6,7]=>[[.,[[.,.],.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,4,5,2,6,7]=>[3,5,1,4,2,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,4,1,5,2,6,7]=>[4,5,3,1,2,6,7]=>[[[.,[.,.]],.],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,4,5,1,2,6,7]=>[2,5,3,4,1,6,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,1,4,5,6,2,7]=>[3,6,1,4,5,2,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,4,1,5,6,2,7]=>[4,6,3,1,5,2,7]=>[[[.,[.,.]],.],[[.,.],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,4,5,1,6,2,7]=>[5,6,3,4,1,2,7]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,4,5,6,1,2,7]=>[2,6,3,4,5,1,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,4,5,6,7,2]=>[3,7,1,4,5,6,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[3,4,1,5,6,7,2]=>[4,7,3,1,5,6,2]=>[[[.,[.,.]],.],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,5,1,6,7,2]=>[5,7,3,4,1,6,2]=>[[[.,[.,.]],[.,.]],[[.,.],.]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[3,4,5,6,1,7,2]=>[6,7,3,4,5,1,2]=>[[[.,[.,.]],[.,[.,.]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2]=>[2,7,3,4,5,6,1]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,7]=>[3,5,1,6,2,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,5,1,2,6,4,7]=>[2,5,3,6,1,4,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,5,6,2,4,7]=>[3,4,1,6,5,2,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,5,1,6,2,4,7]=>[5,4,3,6,1,2,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,5,6,1,2,4,7]=>[2,4,3,6,5,1,7]=>[[.,[[.,.],[[.,.],.]]],[.,.]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,6,7,4]=>[3,5,1,7,2,6,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,5,1,2,6,7,4]=>[2,5,3,7,1,6,4]=>[[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,5,6,2,7,4]=>[3,6,1,7,5,2,4]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,5,1,6,2,7,4]=>[5,6,3,7,1,2,4]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,5,6,1,2,7,4]=>[2,6,3,7,5,1,4]=>[[.,[[.,.],[[.,.],.]]],[.,.]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,6,7,2,4]=>[3,4,1,7,5,6,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,5,1,6,7,2,4]=>[5,4,3,7,1,6,2]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,5,6,1,7,2,4]=>[6,4,3,7,5,1,2]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,5,6,7,1,2,4]=>[2,4,3,7,5,6,1]=>[[.,[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,6]=>[3,5,1,6,2,7,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,7,4,6]=>[2,5,3,6,1,7,4]=>[[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,7,2,4,6]=>[3,4,1,6,5,7,2]=>[[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,5,1,7,2,4,6]=>[5,4,3,6,1,7,2]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,7,1,2,4,6]=>[2,4,3,6,5,7,1]=>[[.,[[.,.],[[.,.],[.,.]]]],.]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,7,6]=>[3,4,1,5,2,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,7,6]=>[2,4,3,5,1,7,6]=>[[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,7,6]=>[2,3,1,5,4,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,7,6]=>[1,4,3,5,2,7,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,7,4,6]=>[2,3,1,6,5,7,4]=>[[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,4,6]=>[1,3,2,6,5,7,4]=>[.,[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,7,4,6]=>[1,5,3,6,2,7,4]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,7,2,4,6]=>[1,4,3,6,5,7,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,4,6,7]=>[3,4,1,5,2,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,5,1,2,4,6,7]=>[2,4,3,5,1,6,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,5,4,6,7]=>[2,3,1,5,4,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,2,4,6,7]=>[1,4,3,5,2,6,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,5,6,4,7]=>[2,3,1,6,5,4,7]=>[[.,[.,.]],[[[.,.],.],[.,.]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,2,6,4,7]=>[1,5,3,6,2,4,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,6,2,4,7]=>[1,4,3,6,5,2,7]=>[.,[[[.,.],[[.,.],.]],[.,.]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,5,6,7,4]=>[2,3,1,7,5,6,4]=>[[.,[.,.]],[[[.,.],[.,.]],.]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]=>[.,[[.,.],[[[.,.],[.,.]],.]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,5,2,6,7,4]=>[1,5,3,7,2,6,4]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,5,6,2,7,4]=>[1,6,3,7,5,2,4]=>[.,[[[.,.],[[.,.],.]],[.,.]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,5,6,7,2,4]=>[1,4,3,7,5,6,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,6,2,7,4,5]=>[3,6,1,5,7,2,4]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,6,1,2,7,4,5]=>[2,6,3,5,7,1,4]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,6,7,2,4,5]=>[3,4,1,5,7,6,2]=>[[.,[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,6,1,7,2,4,5]=>[6,4,3,5,7,1,2]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,6,7,1,2,4,5]=>[2,4,3,5,7,6,1]=>[[.,[[.,.],[.,[[.,.],.]]]],.]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,6,2,4,7,5]=>[3,4,1,6,7,2,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,6,1,2,4,7,5]=>[2,4,3,6,7,1,5]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,2,6,4,7,5]=>[2,3,1,6,7,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,6,4,7,5]=>[1,3,2,6,7,4,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,3,6,2,4,7,5]=>[1,4,3,6,7,2,5]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,6,7,4,5]=>[2,3,1,5,7,6,4]=>[[.,[.,.]],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,6,7,4,5]=>[1,3,2,5,7,6,4]=>[.,[[.,.],[[.,[[.,.],.]],.]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,6,2,7,4,5]=>[1,6,3,5,7,2,4]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,6,7,2,4,5]=>[1,4,3,5,7,6,2]=>[.,[[[.,.],[.,[[.,.],.]]],.]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5,7]=>[3,4,1,5,6,2,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,5,7]=>[2,4,3,5,6,1,7]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,5,7]=>[2,3,1,5,6,4,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,5,7]=>[1,3,2,5,6,4,7]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,3,6,2,4,5,7]=>[1,4,3,5,6,2,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5,7]=>[2,3,1,4,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5,7]=>[1,5,3,4,6,2,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,7,5]=>[2,3,1,4,7,6,5]=>[[.,[.,.]],[.,[[[.,.],.],.]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>[.,[[.,.],[.,[[[.,.],.],.]]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]=>[.,[[[.,.],.],[[[.,.],.],.]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,3,4,6,2,7,5]=>[1,6,3,4,7,2,5]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,3,4,6,7,2,5]=>[1,5,3,4,7,6,2]=>[.,[[[.,.],[.,[[.,.],.]]],.]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,7,2,4,5,6]=>[3,4,1,5,6,7,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,7,1,2,4,5,6]=>[2,4,3,5,6,7,1]=>[[.,[[.,.],[.,[.,[.,.]]]]],.]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,7,4,5,6]=>[2,3,1,5,6,7,4]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,7,4,5,6]=>[1,3,2,5,6,7,4]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,7,2,4,5,6]=>[1,4,3,5,6,7,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,6]=>[2,3,1,4,6,7,5]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,4,7,5,6]=>[1,3,2,4,6,7,5]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,4,2,7,5,6]=>[1,4,3,2,6,7,5]=>[.,[[[.,.],.],[[.,[.,.]],.]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,4,7,2,5,6]=>[1,5,3,4,6,7,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,4,5,7,6]=>[2,3,1,4,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,3,4,5,7,2,6]=>[1,6,3,4,5,7,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7]=>[2,3,1,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,4,5,6,7,2]=>[1,7,3,4,5,6,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,7]=>[4,5,6,1,2,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[4,5,1,2,6,3,7]=>[2,5,6,4,1,3,7]=>[[.,[[.,[.,.]],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[4,1,5,6,2,3,7]=>[4,3,6,1,5,2,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[4,5,1,6,2,3,7]=>[5,3,6,4,1,2,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,7]=>[2,3,6,4,5,1,7]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[4,1,5,2,6,7,3]=>[4,5,7,1,2,6,3]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,5,1,2,6,7,3]=>[2,5,7,4,1,6,3]=>[[.,[[.,[.,.]],.]],[[.,.],.]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[4,1,5,6,2,7,3]=>[4,6,7,1,5,2,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,5,1,6,2,7,3]=>[5,6,7,4,1,2,3]=>[[[.,[.,[.,.]]],.],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[4,5,6,1,2,7,3]=>[2,6,7,4,5,1,3]=>[[.,[[.,[.,.]],[.,.]]],[.,.]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,5,6,7,2,3]=>[4,3,7,1,5,6,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,5,1,6,7,2,3]=>[5,3,7,4,1,6,2]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,5,6,1,7,2,3]=>[6,3,7,4,5,1,2]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,5,6,7,1,2,3]=>[2,3,7,4,5,6,1]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,5,2,7,3,6]=>[4,5,6,1,2,7,3]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[4,5,1,2,7,3,6]=>[2,5,6,4,1,7,3]=>[[.,[[.,[.,.]],.]],[[.,.],.]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[4,1,5,7,2,3,6]=>[4,3,6,1,5,7,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,5,1,7,2,3,6]=>[5,3,6,4,1,7,2]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[4,5,7,1,2,3,6]=>[2,3,6,4,5,7,1]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,7,6]=>[4,3,5,1,2,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[4,5,1,2,3,7,6]=>[2,3,5,4,1,7,6]=>[[.,[.,[[.,.],.]]],[[.,.],.]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,7,6]=>[2,4,5,1,3,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,7,6]=>[1,4,5,2,3,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,7,6]=>[1,3,5,4,2,7,6]=>[.,[[.,[[.,.],.]],[[.,.],.]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6]=>[2,4,6,1,5,7,3]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,2,5,7,3,6]=>[1,4,6,2,5,7,3]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,2,7,3,6]=>[1,5,6,4,2,7,3]=>[.,[[[.,[.,.]],.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,7,2,3,6]=>[1,3,6,4,5,7,2]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,6,7]=>[4,3,5,1,2,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3,6,7]=>[2,3,5,4,1,6,7]=>[[.,[.,[[.,.],.]]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3,6,7]=>[2,4,5,1,3,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,5,3,6,7]=>[1,4,5,2,3,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,5,2,3,6,7]=>[1,3,5,4,2,6,7]=>[.,[[.,[[.,.],.]],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[4,1,2,5,6,3,7]=>[2,4,6,1,5,3,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,2,5,6,3,7]=>[1,4,6,2,5,3,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,5,2,6,3,7]=>[1,5,6,4,2,3,7]=>[.,[[[.,[.,.]],.],[.,[.,.]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,5,6,2,3,7]=>[1,3,6,4,5,2,7]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,7,3]=>[2,4,7,1,5,6,3]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,5,6,7,3]=>[1,4,7,2,5,6,3]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,5,2,6,7,3]=>[1,5,7,4,2,6,3]=>[.,[[[.,[.,.]],.],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,5,6,2,7,3]=>[1,6,7,4,5,2,3]=>[.,[[[.,[.,.]],[.,.]],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,5,6,7,2,3]=>[1,3,7,4,5,6,2]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,5]=>[4,6,5,1,7,2,3]=>[[.,[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,6,1,2,7,3,5]=>[2,6,5,4,7,1,3]=>[[.,[[[.,.],.],[.,.]]],[.,.]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,6,7,2,3,5]=>[4,3,5,1,7,6,2]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,6,1,7,2,3,5]=>[6,3,5,4,7,1,2]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,6,7,1,2,3,5]=>[2,3,5,4,7,6,1]=>[[.,[.,[[.,.],[[.,.],.]]]],.]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,6,2,3,7,5]=>[4,3,6,1,7,2,5]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,6,1,2,3,7,5]=>[2,3,6,4,7,1,5]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,6,3,7,5]=>[2,4,6,1,7,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,7,5]=>[1,4,6,2,7,3,5]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,6,2,3,7,5]=>[1,3,6,4,7,2,5]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,2,6,7,3,5]=>[2,4,5,1,7,6,3]=>[[.,[.,[.,.]]],[[[.,.],.],.]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,7,3,5]=>[1,4,5,2,7,6,3]=>[.,[[.,[.,.]],[[[.,.],.],.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,4,6,2,7,3,5]=>[1,6,5,4,7,2,3]=>[.,[[[[.,.],.],[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,4,6,7,2,3,5]=>[1,3,5,4,7,6,2]=>[.,[[.,[[.,.],[[.,.],.]]],.]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5,7]=>[4,3,5,1,6,2,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,6,1,2,3,5,7]=>[2,3,5,4,6,1,7]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5,7]=>[2,4,5,1,6,3,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5,7]=>[1,4,5,2,6,3,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,5,7]=>[1,3,5,4,6,2,7]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,7]=>[2,3,4,1,6,5,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,7]=>[1,3,4,2,6,5,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,2,4,6,3,5,7]=>[1,2,5,4,6,3,7]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,7,5]=>[2,3,4,1,7,6,5]=>[[.,[.,[.,.]]],[[[.,.],.],.]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,6,7,5]=>[1,3,4,2,7,6,5]=>[.,[[.,[.,.]],[[[.,.],.],.]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>[.,[.,[[.,.],[[[.,.],.],.]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,2,4,6,3,7,5]=>[1,2,6,4,7,3,5]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,6,7,3,5]=>[1,2,5,4,7,6,3]=>[.,[.,[[[.,.],[[.,.],.]],.]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,1,7,2,3,5,6]=>[4,3,5,1,6,7,2]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,7,1,2,3,5,6]=>[2,3,5,4,6,7,1]=>[[.,[.,[[.,.],[.,[.,.]]]]],.]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,7,3,5,6]=>[2,4,5,1,6,7,3]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,7,3,5,6]=>[1,4,5,2,6,7,3]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,4,7,2,3,5,6]=>[1,3,5,4,6,7,2]=>[.,[[.,[[.,.],[.,[.,.]]]],.]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,2,3,7,5,6]=>[2,3,4,1,6,7,5]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,4,2,3,7,5,6]=>[1,3,4,2,6,7,5]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,2,4,3,7,5,6]=>[1,2,4,3,6,7,5]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,2,4,7,3,5,6]=>[1,2,5,4,6,7,3]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,1,2,3,5,7,6]=>[2,3,4,1,5,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,4,2,3,5,7,6]=>[1,3,4,2,5,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>[.,[.,[[[.,.],.],[[.,.],.]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,2,4,5,7,3,6]=>[1,2,6,4,5,7,3]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,7]=>[2,3,4,1,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,7]=>[1,3,4,2,5,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,4]=>[5,6,4,7,1,2,3]=>[[[.,[.,.]],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[5,6,1,2,7,3,4]=>[2,6,4,7,5,1,3]=>[[.,[[.,.],[[.,.],.]]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[5,1,6,7,2,3,4]=>[5,3,4,7,1,6,2]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[5,6,1,7,2,3,4]=>[6,3,4,7,5,1,2]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4]=>[2,3,4,7,5,6,1]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[5,1,6,2,3,7,4]=>[5,3,6,7,1,2,4]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[5,6,1,2,3,7,4]=>[2,3,6,7,5,1,4]=>[[.,[.,[[.,[.,.]],.]]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[5,1,2,6,3,7,4]=>[2,5,6,7,1,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,2,6,3,7,4]=>[1,5,6,7,2,3,4]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,6,2,3,7,4]=>[1,3,6,7,5,2,4]=>[.,[[.,[[.,[.,.]],.]],[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[5,1,2,6,7,3,4]=>[2,5,4,7,1,6,3]=>[[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,5,2,6,7,3,4]=>[1,5,4,7,2,6,3]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,5,6,2,7,3,4]=>[1,6,4,7,5,2,3]=>[.,[[[.,.],[[.,.],.]],[.,.]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,5,6,7,2,3,4]=>[1,3,4,7,5,6,2]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[5,1,6,2,3,4,7]=>[5,3,4,6,1,2,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[5,6,1,2,3,4,7]=>[2,3,4,6,5,1,7]=>[[.,[.,[.,[[.,.],.]]]],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,2,6,3,4,7]=>[2,5,4,6,1,3,7]=>[[.,[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,3,4,7]=>[1,5,4,6,2,3,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,6,2,3,4,7]=>[1,3,4,6,5,2,7]=>[.,[[.,[.,[[.,.],.]]],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[5,1,2,3,6,4,7]=>[2,3,5,6,1,4,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,2,3,6,4,7]=>[1,3,5,6,2,4,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,2,5,3,6,4,7]=>[1,2,5,6,3,4,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,2,5,6,3,4,7]=>[1,2,4,6,5,3,7]=>[.,[.,[[.,[[.,.],.]],[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[5,1,2,3,6,7,4]=>[2,3,5,7,1,6,4]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,6,7,4]=>[1,3,5,7,2,6,4]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,2,5,3,6,7,4]=>[1,2,5,7,3,6,4]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,2,5,6,3,7,4]=>[1,2,6,7,5,3,4]=>[.,[.,[[[.,[.,.]],.],[.,.]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,2,5,6,7,3,4]=>[1,2,4,7,5,6,3]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,1,7,2,3,4,6]=>[5,3,4,6,1,7,2]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,7,1,2,3,4,6]=>[2,3,4,6,5,7,1]=>[[.,[.,[.,[[.,.],[.,.]]]]],.]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,6]=>[2,5,4,6,1,7,3]=>[[.,[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,5,2,7,3,4,6]=>[1,5,4,6,2,7,3]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,5,7,2,3,4,6]=>[1,3,4,6,5,7,2]=>[.,[[.,[.,[[.,.],[.,.]]]],.]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,7,4,6]=>[2,3,5,6,1,7,4]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,7,4,6]=>[1,3,5,6,2,7,4]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,7,4,6]=>[1,2,5,6,3,7,4]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6]=>[1,2,4,6,5,7,3]=>[.,[.,[[.,[[.,.],[.,.]]],.]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,7,6]=>[2,3,4,5,1,7,6]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,7,6]=>[1,3,4,5,2,7,6]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,7,6]=>[1,2,4,5,3,7,6]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,7,4,6]=>[1,2,3,6,5,7,4]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,7]=>[2,3,4,5,1,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,6,7]=>[1,3,4,5,2,6,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,5,3,4,6,7]=>[1,2,4,5,3,6,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[6,1,7,2,3,4,5]=>[6,3,4,5,7,1,2]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5]=>[2,3,4,5,7,6,1]=>[[.,[.,[.,[.,[[.,.],.]]]]],.]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[6,1,2,7,3,4,5]=>[2,6,4,5,7,1,3]=>[[.,[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,6,2,7,3,4,5]=>[1,6,4,5,7,2,3]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,6,7,2,3,4,5]=>[1,3,4,5,7,6,2]=>[.,[[.,[.,[.,[[.,.],.]]]],.]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[6,1,2,3,7,4,5]=>[2,3,6,5,7,1,4]=>[[.,[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,6,2,3,7,4,5]=>[1,3,6,5,7,2,4]=>[.,[[.,[[.,.],[.,.]]],[.,.]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,6,3,7,4,5]=>[1,2,6,5,7,3,4]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,6,7,3,4,5]=>[1,2,4,5,7,6,3]=>[.,[.,[[.,[.,[[.,.],.]]],.]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[6,1,2,3,4,7,5]=>[2,3,4,6,7,1,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,3,4,7,5]=>[1,3,4,6,7,2,5]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,6,3,4,7,5]=>[1,2,4,6,7,3,5]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,2,3,6,4,7,5]=>[1,2,3,6,7,4,5]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,2,3,6,7,4,5]=>[1,2,3,5,7,6,4]=>[.,[.,[.,[[.,[[.,.],.]],.]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7]=>[2,3,4,5,6,1,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5,7]=>[1,3,4,5,6,2,7]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5,7]=>[1,2,4,5,6,3,7]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5,7]=>[1,2,3,5,6,4,7]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6]=>[2,3,4,5,6,7,1]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,7,2,3,4,5,6]=>[1,3,4,5,6,7,2]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,7,3,4,5,6]=>[1,2,4,5,6,7,3]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,3,7,4,5,6]=>[1,2,3,5,6,7,4]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,6]=>[1,2,3,4,6,7,5]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5,8,7]=>[3,2,4,1,6,5,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,4,6,3,5,8,7]=>[2,1,5,4,6,3,8,7]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5,8,7]=>[4,2,5,1,6,3,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5,8,7]=>[3,2,5,4,6,1,8,7]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,8,5,7]=>[2,1,4,3,7,6,8,5]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,8,5,7]=>[3,2,4,1,7,6,8,5]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,4,6,3,8,5,7]=>[2,1,6,4,7,3,8,5]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,6,3,8,5,7]=>[4,2,6,1,7,3,8,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,4,6,1,3,8,5,7]=>[3,2,6,4,7,1,8,5]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,4,6,8,3,5,7]=>[2,1,5,4,7,6,8,3]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,6,8,3,5,7]=>[4,2,5,1,7,6,8,3]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,0,1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,4,6,1,8,3,5,7]=>[6,2,5,4,7,1,8,3]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,4,6,8,1,3,5,7]=>[3,2,5,4,7,6,8,1]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,7,8]=>[2,1,4,3,6,5,7,8]=>[[.,.],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,4,1,3,6,5,7,8]=>[3,2,4,1,6,5,7,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,4,1,6,3,5,7,8]=>[4,2,5,1,6,3,7,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,4,1,3,6,7,5,8]=>[3,2,4,1,7,6,5,8]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5,8]=>[4,2,6,1,7,3,5,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,6,1,3,7,5,8]=>[3,2,6,4,7,1,5,8]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,6,7,1,3,5,8]=>[3,2,5,4,7,6,1,8]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,6,7,8,5]=>[2,1,4,3,8,6,7,5]=>[[.,.],[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,6,7,8,5]=>[3,2,4,1,8,6,7,5]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,4,6,3,7,8,5]=>[2,1,6,4,8,3,7,5]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,4,1,6,3,7,8,5]=>[4,2,6,1,8,3,7,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,4,6,1,3,7,8,5]=>[3,2,6,4,8,1,7,5]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,4,6,7,3,8,5]=>[2,1,7,4,8,6,3,5]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,4,1,6,7,3,8,5]=>[4,2,7,1,8,6,3,5]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,4,6,1,7,3,8,5]=>[6,2,7,4,8,1,3,5]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,4,6,7,1,3,8,5]=>[3,2,7,4,8,6,1,5]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,4,6,7,8,3,5]=>[2,1,5,4,8,6,7,3]=>[[.,.],[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,4,1,6,7,8,3,5]=>[4,2,5,1,8,6,7,3]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,0,1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,4,6,7,1,8,3,5]=>[7,2,5,4,8,6,1,3]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,6,7,8,1,3,5]=>[3,2,5,4,8,6,7,1]=>[[[.,.],[[.,.],[[.,.],[.,.]]]],.]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,7,5,8,6]=>[2,1,4,3,7,8,5,6]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,7,5,8,6]=>[3,2,4,1,7,8,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,4,1,7,3,5,8,6]=>[4,2,5,1,7,8,3,6]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,4,7,1,3,5,8,6]=>[3,2,5,4,7,8,1,6]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,7,8,5,6]=>[2,1,4,3,6,8,7,5]=>[[.,.],[[.,.],[[.,[[.,.],.]],.]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,7,8,5,6]=>[3,2,4,1,6,8,7,5]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,7,3,8,5,6]=>[2,1,7,4,6,8,3,5]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,4,1,7,3,8,5,6]=>[4,2,7,1,6,8,3,5]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,4,7,1,3,8,5,6]=>[3,2,7,4,6,8,1,5]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,7,8,3,5,6]=>[2,1,5,4,6,8,7,3]=>[[.,.],[[[.,.],[.,[[.,.],.]]],.]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,4,1,7,8,3,5,6]=>[4,2,5,1,6,8,7,3]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,0,1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,4,7,8,1,3,5,6]=>[3,2,5,4,6,8,7,1]=>[[[.,.],[[.,.],[.,[[.,.],.]]]],.]
[1,0,1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,4,1,3,7,5,6,8]=>[3,2,4,1,6,7,5,8]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,1,4,7,3,5,6,8]=>[2,1,5,4,6,7,3,8]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,4,1,3,5,7,6,8]=>[3,2,4,1,5,7,6,8]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,7,6,8]=>[4,2,5,1,3,7,6,8]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,4,5,1,3,7,6,8]=>[3,2,5,4,1,7,6,8]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,4,5,1,7,3,6,8]=>[5,2,6,4,1,7,3,8]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,7,8,6]=>[2,1,4,3,5,8,7,6]=>[[.,.],[[.,.],[.,[[[.,.],.],.]]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,5,7,8,6]=>[3,2,4,1,5,8,7,6]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,4,5,3,7,8,6]=>[2,1,5,4,3,8,7,6]=>[[.,.],[[[.,.],.],[[[.,.],.],.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,1,5,3,7,8,6]=>[4,2,5,1,3,8,7,6]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,0,1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,5,1,3,7,8,6]=>[3,2,5,4,1,8,7,6]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,4,5,7,3,8,6]=>[2,1,7,4,5,8,3,6]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,1,5,7,3,8,6]=>[4,2,7,1,5,8,3,6]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,1,7,3,8,6]=>[5,2,7,4,1,8,3,6]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,5,7,1,3,8,6]=>[3,2,7,4,5,8,1,6]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,4,5,7,8,3,6]=>[2,1,6,4,5,8,7,3]=>[[.,.],[[[.,.],[.,[[.,.],.]]],.]]
[1,0,1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,4,5,1,7,8,3,6]=>[5,2,6,4,1,8,7,3]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,0,1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,4,5,7,1,8,3,6]=>[7,2,6,4,5,8,1,3]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,4,3,8,5,6,7]=>[2,1,4,3,6,7,8,5]=>[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,1,3,8,5,6,7]=>[3,2,4,1,6,7,8,5]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,4,8,3,5,6,7]=>[2,1,5,4,6,7,8,3]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,1,8,3,5,6,7]=>[4,2,5,1,6,7,8,3]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,8,1,3,5,6,7]=>[3,2,5,4,6,7,8,1]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,4,3,5,8,6,7]=>[2,1,4,3,5,7,8,6]=>[[.,.],[[.,.],[.,[[.,[.,.]],.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,1,3,5,8,6,7]=>[3,2,4,1,5,7,8,6]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,8,6,7]=>[4,2,5,1,3,7,8,6]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,4,5,8,3,6,7]=>[2,1,6,4,5,7,8,3]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,1,5,8,3,6,7]=>[4,2,6,1,5,7,8,3]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,5,1,8,3,6,7]=>[5,2,6,4,1,7,8,3]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,4,3,5,6,8,7]=>[2,1,4,3,5,6,8,7]=>[[.,.],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,1,3,5,6,8,7]=>[3,2,4,1,5,6,8,7]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,1,4,5,3,6,8,7]=>[2,1,5,4,3,6,8,7]=>[[.,.],[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,1,5,3,6,8,7]=>[4,2,5,1,3,6,8,7]=>[[[.,.],[.,.]],[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,4,5,6,3,8,7]=>[2,1,6,4,5,3,8,7]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,1,5,6,3,8,7]=>[4,2,6,1,5,3,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,1,6,3,8,7]=>[5,2,6,4,1,3,8,7]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,0,1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,6,1,3,8,7]=>[3,2,6,4,5,1,8,7]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,1,5,6,8,3,7]=>[4,2,7,1,5,6,8,3]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,5,1,6,8,3,7]=>[5,2,7,4,1,6,8,3]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,0,1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,5,6,1,8,3,7]=>[6,2,7,4,5,1,8,3]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,4,3,5,6,7,8]=>[2,1,4,3,5,6,7,8]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,4,1,3,5,6,7,8]=>[3,2,4,1,5,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,4,5,3,6,7,8]=>[2,1,5,4,3,6,7,8]=>[[.,.],[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,4,1,5,3,6,7,8]=>[4,2,5,1,3,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,4,5,1,3,6,7,8]=>[3,2,5,4,1,6,7,8]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,4,1,5,6,3,7,8]=>[4,2,6,1,5,3,7,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,4,5,1,6,3,7,8]=>[5,2,6,4,1,3,7,8]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,4,5,6,1,3,7,8]=>[3,2,6,4,5,1,7,8]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,4,1,5,6,7,3,8]=>[4,2,7,1,5,6,3,8]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,4,5,1,6,7,3,8]=>[5,2,7,4,1,6,3,8]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,0,1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,4,5,6,1,7,3,8]=>[6,2,7,4,5,1,3,8]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,4,5,6,7,1,3,8]=>[3,2,7,4,5,6,1,8]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,4,5,6,7,8,3]=>[2,1,8,4,5,6,7,3]=>[[.,.],[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,4,1,5,6,7,8,3]=>[4,2,8,1,5,6,7,3]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,4,5,1,6,7,8,3]=>[5,2,8,4,1,6,7,3]=>[[[.,.],[[.,.],.]],[[.,[.,.]],.]]
[1,0,1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,4,5,6,1,7,8,3]=>[6,2,8,4,5,1,7,3]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,4,5,6,7,1,8,3]=>[7,2,8,4,5,6,1,3]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,4,5,6,7,8,1,3]=>[3,2,8,4,5,6,7,1]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],.]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,8,7]=>[2,1,5,6,3,4,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,8,7]=>[2,1,4,6,5,3,8,7]=>[[.,.],[[.,[[.,.],.]],[[.,.],.]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,5,1,6,3,4,8,7]=>[5,2,4,6,1,3,8,7]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,6,8,4,7]=>[2,1,5,7,3,6,8,4]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,6,8,4,7]=>[3,2,5,7,1,6,8,4]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,5,6,8,1,3,4,7]=>[3,2,4,7,5,6,8,1]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,0,1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,5,1,3,6,4,7,8]=>[3,2,5,6,1,4,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,7,8]=>[2,1,4,6,5,3,7,8]=>[[.,.],[[.,[[.,.],.]],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,5,1,3,6,7,4,8]=>[3,2,5,7,1,6,4,8]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,5,1,6,3,7,4,8]=>[5,2,6,7,1,3,4,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,5,6,1,3,7,4,8]=>[3,2,6,7,5,1,4,8]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,3,6,7,8,4]=>[2,1,5,8,3,6,7,4]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,5,1,3,6,7,8,4]=>[3,2,5,8,1,6,7,4]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,6,3,7,8,4]=>[2,1,6,8,5,3,7,4]=>[[.,.],[[[.,[.,.]],.],[[.,.],.]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,5,1,6,3,7,8,4]=>[5,2,6,8,1,3,7,4]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,5,6,1,3,7,8,4]=>[3,2,6,8,5,1,7,4]=>[[[.,.],[[.,[.,.]],.]],[[.,.],.]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,7,3,8,4]=>[2,1,7,8,5,6,3,4]=>[[.,.],[[[.,[.,.]],[.,.]],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,5,1,6,7,3,8,4]=>[5,2,7,8,1,6,3,4]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,5,6,1,7,3,8,4]=>[6,2,7,8,5,1,3,4]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,5,6,7,1,3,8,4]=>[3,2,7,8,5,6,1,4]=>[[[.,.],[[.,[.,.]],[.,.]]],[.,.]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,5,6,7,8,3,4]=>[2,1,4,8,5,6,7,3]=>[[.,.],[[.,[[.,.],[.,[.,.]]]],.]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,5,1,6,7,8,3,4]=>[5,2,4,8,1,6,7,3]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,5,6,7,8,1,3,4]=>[3,2,4,8,5,6,7,1]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,8,6]=>[2,1,5,7,3,8,4,6]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,5,1,3,7,4,8,6]=>[3,2,5,7,1,8,4,6]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,5,1,7,3,4,8,6]=>[5,2,4,7,1,8,3,6]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,5,7,1,3,4,8,6]=>[3,2,4,7,5,8,1,6]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,5,3,7,8,4,6]=>[2,1,5,6,3,8,7,4]=>[[.,.],[[.,[.,.]],[[[.,.],.],.]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,5,1,3,7,8,4,6]=>[3,2,5,6,1,8,7,4]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,5,7,3,8,4,6]=>[2,1,7,6,5,8,3,4]=>[[.,.],[[[[.,.],.],[.,.]],[.,.]]]
[1,0,1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,5,7,1,3,8,4,6]=>[3,2,7,6,5,8,1,4]=>[[[.,.],[[[.,.],.],[.,.]]],[.,.]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,7,8,3,4,6]=>[2,1,4,6,5,8,7,3]=>[[.,.],[[.,[[.,.],[[.,.],.]]],.]]
[1,0,1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,5,7,8,1,3,4,6]=>[3,2,4,6,5,8,7,1]=>[[[.,.],[.,[[.,.],[[.,.],.]]]],.]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,6,8]=>[2,1,5,6,3,7,4,8]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,7,6,8]=>[3,2,1,5,4,7,6,8]=>[[[.,.],.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,1,5,7,4,6,8]=>[3,2,1,6,5,7,4,8]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,5,1,3,4,7,8,6]=>[3,2,4,5,1,8,7,6]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,1,3,5,4,7,8,6]=>[2,1,3,5,4,8,7,6]=>[[.,.],[.,[[.,.],[[[.,.],.],.]]]]
[1,0,1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,1,4,7,8,6]=>[4,2,3,5,1,8,7,6]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,1,3,5,7,4,8,6]=>[2,1,3,7,5,8,4,6]=>[[.,.],[.,[[[.,.],[.,.]],[.,.]]]]
[1,0,1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,1,7,4,8,6]=>[5,2,3,7,1,8,4,6]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,5,7,8,4,6]=>[2,1,3,6,5,8,7,4]=>[[.,.],[.,[[[.,.],[[.,.],.]],.]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,1,5,7,8,4,6]=>[3,2,1,6,5,8,7,4]=>[[[.,.],.],[[[.,.],[[.,.],.]],.]]
[1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,5,7,8,1,4,6]=>[4,2,3,6,5,8,7,1]=>[[[.,.],[.,[[.,.],[[.,.],.]]]],.]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,5,3,8,4,6,7]=>[2,1,5,6,3,7,8,4]=>[[.,.],[[.,[.,.]],[[.,[.,.]],.]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,5,1,3,8,4,6,7]=>[3,2,5,6,1,7,8,4]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,3,5,4,8,6,7]=>[2,1,3,5,4,7,8,6]=>[[.,.],[.,[[.,.],[[.,[.,.]],.]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,3,1,5,8,4,6,7]=>[3,2,1,6,5,7,8,4]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,3,5,1,8,4,6,7]=>[5,2,3,6,1,7,8,4]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,8,7]=>[2,1,4,5,3,6,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,1,3,5,6,4,8,7]=>[2,1,3,6,5,4,8,7]=>[[.,.],[.,[[[.,.],.],[[.,.],.]]]]
[1,0,1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,3,5,1,6,4,8,7]=>[5,2,3,6,1,4,8,7]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,3,1,5,6,8,4,7]=>[3,2,1,7,5,6,8,4]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,3,5,1,6,8,4,7]=>[5,2,3,7,1,6,8,4]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,3,5,6,8,1,4,7]=>[4,2,3,7,5,6,8,1]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,5,3,4,6,7,8]=>[2,1,4,5,3,6,7,8]=>[[.,.],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,1,3,4,6,7,8]=>[3,2,4,5,1,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,5,4,6,7,8]=>[2,1,3,5,4,6,7,8]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,3,5,1,4,6,7,8]=>[4,2,3,5,1,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,3,1,5,6,4,7,8]=>[3,2,1,6,5,4,7,8]=>[[[.,.],.],[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,5,6,7,4,8]=>[3,2,1,7,5,6,4,8]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,3,5,1,6,7,4,8]=>[5,2,3,7,1,6,4,8]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,3,5,6,1,7,4,8]=>[6,2,3,7,5,1,4,8]=>[[[.,.],[.,[[.,.],.]]],[.,[.,.]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,5,6,7,8,4]=>[2,1,3,8,5,6,7,4]=>[[.,.],[.,[[[.,.],[.,[.,.]]],.]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,5,6,7,8,4]=>[3,2,1,8,5,6,7,4]=>[[[.,.],.],[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,3,5,1,6,7,8,4]=>[5,2,3,8,1,6,7,4]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,3,5,6,1,7,8,4]=>[6,2,3,8,5,1,7,4]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,0,1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,3,5,6,7,1,8,4]=>[7,2,3,8,5,6,1,4]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,0,1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,3,5,6,7,8,1,4]=>[4,2,3,8,5,6,7,1]=>[[[.,.],[.,[[.,.],[.,[.,.]]]]],.]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,6,3,7,4,8,5]=>[2,1,6,7,8,3,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[2,6,1,3,7,4,8,5]=>[3,2,6,7,8,1,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[2,1,6,7,3,4,8,5]=>[2,1,4,7,8,6,3,5]=>[[.,.],[[.,[[.,[.,.]],.]],[.,.]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[2,6,1,7,3,4,8,5]=>[6,2,4,7,8,1,3,5]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[2,6,7,1,3,4,8,5]=>[3,2,4,7,8,6,1,5]=>[[[.,.],[.,[[.,[.,.]],.]]],[.,.]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[2,1,6,3,7,8,4,5]=>[2,1,6,5,8,3,7,4]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[2,6,1,3,7,8,4,5]=>[3,2,6,5,8,1,7,4]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[2,1,6,7,3,8,4,5]=>[2,1,7,5,8,6,3,4]=>[[.,.],[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[2,6,7,1,3,8,4,5]=>[3,2,7,5,8,6,1,4]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[2,1,6,7,8,3,4,5]=>[2,1,4,5,8,6,7,3]=>[[.,.],[[.,[.,[[.,.],[.,.]]]],.]]
[1,0,1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[2,6,7,8,1,3,4,5]=>[3,2,4,5,8,6,7,1]=>[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]
[1,0,1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[2,6,1,3,7,4,5,8]=>[3,2,6,5,7,1,4,8]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,7,5,8]=>[3,2,1,6,7,4,5,8]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[2,3,1,6,7,4,5,8]=>[3,2,1,5,7,6,4,8]=>[[[.,.],.],[[.,[[.,.],.]],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,7,8,5]=>[2,1,4,6,8,3,7,5]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,4,7,8,5]=>[3,2,1,6,8,4,7,5]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[2,1,3,6,7,4,8,5]=>[2,1,3,7,8,6,4,5]=>[[.,.],[.,[[[.,[.,.]],.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,3,1,6,7,4,8,5]=>[3,2,1,7,8,6,4,5]=>[[[.,.],.],[[[.,[.,.]],.],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[2,3,6,1,7,4,8,5]=>[6,2,3,7,8,1,4,5]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[2,1,3,6,7,8,4,5]=>[2,1,3,5,8,6,7,4]=>[[.,.],[.,[[.,[[.,.],[.,.]]],.]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[2,3,1,6,7,8,4,5]=>[3,2,1,5,8,6,7,4]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,1,7,8,4,5]=>[6,2,3,5,8,1,7,4]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[2,1,6,3,8,4,5,7]=>[2,1,6,5,7,3,8,4]=>[[.,.],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[2,6,1,3,8,4,5,7]=>[3,2,6,5,7,1,8,4]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[2,6,1,8,3,4,5,7]=>[6,2,4,5,7,1,8,3]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[2,6,8,1,3,4,5,7]=>[3,2,4,5,7,6,8,1]=>[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[2,1,6,3,4,8,5,7]=>[2,1,4,6,7,3,8,5]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[2,1,3,6,4,8,5,7]=>[2,1,3,6,7,4,8,5]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,8,5,7]=>[3,2,1,6,7,4,8,5]=>[[[.,.],.],[[.,[.,.]],[[.,.],.]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[2,3,1,6,8,4,5,7]=>[3,2,1,5,7,6,8,4]=>[[[.,.],.],[[.,[[.,.],[.,.]]],.]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[2,1,6,3,4,5,8,7]=>[2,1,4,5,6,3,8,7]=>[[.,.],[[.,[.,[.,.]]],[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[2,1,3,6,4,5,8,7]=>[2,1,3,5,6,4,8,7]=>[[.,.],[.,[[.,[.,.]],[[.,.],.]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[2,3,6,1,4,5,8,7]=>[4,2,3,5,6,1,8,7]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[2,1,3,4,6,5,8,7]=>[2,1,3,4,6,5,8,7]=>[[.,.],[.,[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,8,7]=>[4,2,3,1,6,5,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,0,1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[2,3,4,6,1,5,8,7]=>[5,2,3,4,6,1,8,7]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[2,3,1,4,6,8,5,7]=>[3,2,1,4,7,6,8,5]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[2,3,4,1,6,8,5,7]=>[4,2,3,1,7,6,8,5]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,0,1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[2,3,4,6,1,8,5,7]=>[6,2,3,4,7,1,8,5]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[2,6,1,3,4,5,7,8]=>[3,2,4,5,6,1,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[2,3,1,6,4,5,7,8]=>[3,2,1,5,6,4,7,8]=>[[[.,.],.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[2,3,6,1,4,5,7,8]=>[4,2,3,5,6,1,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[2,1,3,4,6,5,7,8]=>[2,1,3,4,6,5,7,8]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[2,3,4,1,6,5,7,8]=>[4,2,3,1,6,5,7,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[2,3,4,6,1,5,7,8]=>[5,2,3,4,6,1,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,6,7,5,8]=>[3,2,1,4,7,6,5,8]=>[[[.,.],.],[.,[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[2,3,4,1,6,7,5,8]=>[4,2,3,1,7,6,5,8]=>[[[.,.],[.,.]],[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[2,3,4,6,7,1,5,8]=>[5,2,3,4,7,6,1,8]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,6,7,8,5]=>[2,1,3,4,8,6,7,5]=>[[.,.],[.,[.,[[[.,.],[.,.]],.]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,6,7,8,5]=>[3,2,1,4,8,6,7,5]=>[[[.,.],.],[.,[[[.,.],[.,.]],.]]]
[1,0,1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[2,3,4,6,1,7,8,5]=>[6,2,3,4,8,1,7,5]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[2,3,4,6,7,1,8,5]=>[7,2,3,4,8,6,1,5]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,0,1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[2,3,4,6,7,8,1,5]=>[5,2,3,4,8,6,7,1]=>[[[.,.],[.,[.,[[.,.],[.,.]]]]],.]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[2,1,7,3,8,4,5,6]=>[2,1,7,5,6,8,3,4]=>[[.,.],[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[2,1,7,8,3,4,5,6]=>[2,1,4,5,6,8,7,3]=>[[.,.],[[.,[.,[.,[[.,.],.]]]],.]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[2,7,1,8,3,4,5,6]=>[7,2,4,5,6,8,1,3]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[2,7,8,1,3,4,5,6]=>[3,2,4,5,6,8,7,1]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,0,1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[2,3,1,7,4,8,5,6]=>[3,2,1,7,6,8,4,5]=>[[[.,.],.],[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[2,3,1,7,8,4,5,6]=>[3,2,1,5,6,8,7,4]=>[[[.,.],.],[[.,[.,[[.,.],.]]],.]]
[1,0,1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[2,3,7,8,1,4,5,6]=>[4,2,3,5,6,8,7,1]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,0,1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[2,7,1,3,4,5,8,6]=>[3,2,4,5,7,8,1,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[2,3,1,7,4,5,8,6]=>[3,2,1,5,7,8,4,6]=>[[[.,.],.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[2,1,3,4,7,5,8,6]=>[2,1,3,4,7,8,5,6]=>[[.,.],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,3,4,1,7,5,8,6]=>[4,2,3,1,7,8,5,6]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,8,6]=>[5,2,3,4,7,8,1,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[2,3,1,4,7,8,5,6]=>[3,2,1,4,6,8,7,5]=>[[[.,.],.],[.,[[.,[[.,.],.]],.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[2,3,4,1,7,8,5,6]=>[4,2,3,1,6,8,7,5]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,0,1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[2,3,4,7,1,8,5,6]=>[7,2,3,4,6,8,1,5]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[2,1,7,3,4,5,6,8]=>[2,1,4,5,6,7,3,8]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[2,7,1,3,4,5,6,8]=>[3,2,4,5,6,7,1,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[2,3,7,1,4,5,6,8]=>[4,2,3,5,6,7,1,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[2,3,4,7,1,5,6,8]=>[5,2,3,4,6,7,1,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[2,1,3,4,5,7,6,8]=>[2,1,3,4,5,7,6,8]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[2,3,1,4,5,7,6,8]=>[3,2,1,4,5,7,6,8]=>[[[.,.],.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[2,3,4,1,5,7,6,8]=>[4,2,3,1,5,7,6,8]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,7,8,6]=>[2,1,3,4,5,8,7,6]=>[[.,.],[.,[.,[.,[[[.,.],.],.]]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[2,3,4,1,5,7,8,6]=>[4,2,3,1,5,8,7,6]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,0,1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[2,3,4,5,1,7,8,6]=>[5,2,3,4,1,8,7,6]=>[[[.,.],[.,[.,.]]],[[[.,.],.],.]]
[1,0,1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[2,3,4,5,7,1,8,6]=>[7,2,3,4,5,8,1,6]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[2,3,4,5,7,8,1,6]=>[6,2,3,4,5,8,7,1]=>[[[.,.],[.,[.,[.,[[.,.],.]]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,1,8,3,4,5,6,7]=>[2,1,4,5,6,7,8,3]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,8,1,3,4,5,6,7]=>[3,2,4,5,6,7,8,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[2,1,3,8,4,5,6,7]=>[2,1,3,5,6,7,8,4]=>[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,3,1,8,4,5,6,7]=>[3,2,1,5,6,7,8,4]=>[[[.,.],.],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[2,3,8,1,4,5,6,7]=>[4,2,3,5,6,7,8,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[2,1,3,4,8,5,6,7]=>[2,1,3,4,6,7,8,5]=>[[.,.],[.,[.,[[.,[.,[.,.]]],.]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[2,3,1,4,8,5,6,7]=>[3,2,1,4,6,7,8,5]=>[[[.,.],.],[.,[[.,[.,[.,.]]],.]]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[2,3,4,1,8,5,6,7]=>[4,2,3,1,6,7,8,5]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,0,1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[2,3,4,8,1,5,6,7]=>[5,2,3,4,6,7,8,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[2,1,3,4,5,8,6,7]=>[2,1,3,4,5,7,8,6]=>[[.,.],[.,[.,[.,[[.,[.,.]],.]]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[2,3,1,4,5,8,6,7]=>[3,2,1,4,5,7,8,6]=>[[[.,.],.],[.,[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[2,3,4,1,5,8,6,7]=>[4,2,3,1,5,7,8,6]=>[[[.,.],[.,.]],[.,[[.,[.,.]],.]]]
[1,0,1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[2,3,4,5,1,8,6,7]=>[5,2,3,4,1,7,8,6]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,0,1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[2,3,4,5,8,1,6,7]=>[6,2,3,4,5,7,8,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,8,7]=>[3,2,1,4,5,6,8,7]=>[[[.,.],.],[.,[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,8,7]=>[5,2,3,4,1,6,8,7]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,0,1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,8,7]=>[6,2,3,4,5,1,8,7]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[2,3,4,5,6,8,1,7]=>[7,2,3,4,5,6,8,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8]=>[2,1,3,4,5,6,7,8]=>[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,7,8]=>[3,2,1,4,5,6,7,8]=>[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[2,3,4,1,5,6,7,8]=>[4,2,3,1,5,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,7,8]=>[5,2,3,4,1,6,7,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,7,8]=>[6,2,3,4,5,1,7,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8]=>[7,2,3,4,5,6,1,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1]=>[8,2,3,4,5,6,7,1]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,8,7]=>[3,4,1,2,6,5,8,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,8,7]=>[2,4,3,1,6,5,8,7]=>[[.,[[.,.],.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[3,1,4,6,2,5,8,7]=>[3,5,1,4,6,2,8,7]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,8,5,7]=>[3,4,1,2,7,6,8,5]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,6,8,5,7]=>[2,4,3,1,7,6,8,5]=>[[.,[[.,.],.]],[[[.,.],[.,.]],.]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,4,6,2,8,5,7]=>[3,6,1,4,7,2,8,5]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[3,4,1,6,2,8,5,7]=>[4,6,3,1,7,2,8,5]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,4,6,8,2,5,7]=>[3,5,1,4,7,6,8,2]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]
[1,1,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[3,4,6,8,1,2,5,7]=>[2,5,3,4,7,6,8,1]=>[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,7,8]=>[3,4,1,2,6,5,7,8]=>[[.,[.,.]],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,7,8]=>[2,4,3,1,6,5,7,8]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[3,1,4,6,2,5,7,8]=>[3,5,1,4,6,2,7,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[3,1,4,2,6,7,5,8]=>[3,4,1,2,7,6,5,8]=>[[.,[.,.]],[.,[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[3,1,4,6,2,7,5,8]=>[3,6,1,4,7,2,5,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[3,4,1,6,2,7,5,8]=>[4,6,3,1,7,2,5,8]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[3,4,6,1,2,7,5,8]=>[2,6,3,4,7,1,5,8]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[3,4,1,6,7,2,5,8]=>[4,5,3,1,7,6,2,8]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,6,7,8,5]=>[3,4,1,2,8,6,7,5]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[3,4,1,6,2,7,8,5]=>[4,6,3,1,8,2,7,5]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[3,4,1,6,7,2,8,5]=>[4,7,3,1,8,6,2,5]=>[[[.,[.,.]],.],[[[.,.],.],[.,.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[3,4,6,1,7,2,8,5]=>[6,7,3,4,8,1,2,5]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[3,4,6,1,7,8,2,5]=>[6,5,3,4,8,1,7,2]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,1,0,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,6,7,8,1,2,5]=>[2,5,3,4,8,6,7,1]=>[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,8,6]=>[3,4,1,2,7,8,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,7,5,8,6]=>[2,4,3,1,7,8,5,6]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[3,4,1,7,2,5,8,6]=>[4,5,3,1,7,8,2,6]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,7,8,5,6]=>[3,4,1,2,6,8,7,5]=>[[.,[.,.]],[.,[[.,[[.,.],.]],.]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,7,8,5,6]=>[2,4,3,1,6,8,7,5]=>[[.,[[.,.],.]],[[.,[[.,.],.]],.]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,7,2,8,5,6]=>[3,7,1,4,6,8,2,5]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[3,4,1,7,2,8,5,6]=>[4,7,3,1,6,8,2,5]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[3,4,1,7,8,2,5,6]=>[4,5,3,1,6,8,7,2]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]
[1,1,0,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[3,4,7,1,8,2,5,6]=>[7,5,3,4,6,8,1,2]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[3,4,7,8,1,2,5,6]=>[2,5,3,4,6,8,7,1]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,6,8]=>[3,4,1,2,6,7,5,8]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,4,7,2,5,6,8]=>[3,5,1,4,6,7,2,8]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,4,2,5,7,6,8]=>[3,4,1,2,5,7,6,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,4,5,2,7,6,8]=>[3,5,1,4,2,7,6,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,5,1,7,2,6,8]=>[5,6,3,4,1,7,2,8]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,4,2,5,7,8,6]=>[3,4,1,2,5,8,7,6]=>[[.,[.,.]],[.,[.,[[[.,.],.],.]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,5,7,8,6]=>[2,4,3,1,5,8,7,6]=>[[.,[[.,.],.]],[.,[[[.,.],.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,4,5,2,7,8,6]=>[3,5,1,4,2,8,7,6]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[3,4,1,5,2,7,8,6]=>[4,5,3,1,2,8,7,6]=>[[[.,[.,.]],.],[.,[[[.,.],.],.]]]
[1,1,0,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[3,4,5,1,2,7,8,6]=>[2,5,3,4,1,8,7,6]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]
[1,1,0,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,5,7,1,2,8,6]=>[2,7,3,4,5,8,1,6]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[3,4,1,5,7,8,2,6]=>[4,6,3,1,5,8,7,2]=>[[[.,[.,.]],.],[[.,[[.,.],.]],.]]
[1,1,0,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[3,4,5,7,1,8,2,6]=>[7,6,3,4,5,8,1,2]=>[[[[.,.],.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,5,7,8,1,2,6]=>[2,6,3,4,5,8,7,1]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,4,2,8,5,6,7]=>[3,4,1,2,6,7,8,5]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[3,4,1,2,8,5,6,7]=>[2,4,3,1,6,7,8,5]=>[[.,[[.,.],.]],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,4,8,2,5,6,7]=>[3,5,1,4,6,7,8,2]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[3,4,1,8,2,5,6,7]=>[4,5,3,1,6,7,8,2]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[3,4,8,1,2,5,6,7]=>[2,5,3,4,6,7,8,1]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,4,2,5,8,6,7]=>[3,4,1,2,5,7,8,6]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,4,5,8,2,6,7]=>[3,6,1,4,5,7,8,2]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[3,4,5,1,8,2,6,7]=>[5,6,3,4,1,7,8,2]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[3,4,5,8,1,2,6,7]=>[2,6,3,4,5,7,8,1]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[3,1,4,2,5,6,8,7]=>[3,4,1,2,5,6,8,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,1,5,2,6,8,7]=>[4,5,3,1,2,6,8,7]=>[[[.,[.,.]],.],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[3,1,4,5,6,2,8,7]=>[3,6,1,4,5,2,8,7]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,1,5,6,2,8,7]=>[4,6,3,1,5,2,8,7]=>[[[.,[.,.]],.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,1,6,2,8,7]=>[5,6,3,4,1,2,8,7]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[3,1,4,5,6,8,2,7]=>[3,7,1,4,5,6,8,2]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,4,2,5,6,7,8]=>[3,4,1,2,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[3,4,1,2,5,6,7,8]=>[2,4,3,1,5,6,7,8]=>[[.,[[.,.],.]],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,4,5,2,6,7,8]=>[3,5,1,4,2,6,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[3,4,5,1,2,6,7,8]=>[2,5,3,4,1,6,7,8]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,4,5,6,2,7,8]=>[3,6,1,4,5,2,7,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[3,4,1,5,6,2,7,8]=>[4,6,3,1,5,2,7,8]=>[[[.,[.,.]],.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[3,4,5,1,6,2,7,8]=>[5,6,3,4,1,2,7,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[3,4,5,6,1,2,7,8]=>[2,6,3,4,5,1,7,8]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[3,1,4,5,6,7,2,8]=>[3,7,1,4,5,6,2,8]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[3,4,1,5,6,7,2,8]=>[4,7,3,1,5,6,2,8]=>[[[.,[.,.]],.],[[.,[.,.]],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[3,4,5,1,6,7,2,8]=>[5,7,3,4,1,6,2,8]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[3,4,5,6,1,7,2,8]=>[6,7,3,4,5,1,2,8]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,0,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[3,4,5,6,7,1,2,8]=>[2,7,3,4,5,6,1,8]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,2]=>[3,8,1,4,5,6,7,2]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[3,4,1,5,6,7,8,2]=>[4,8,3,1,5,6,7,2]=>[[[.,[.,.]],.],[[.,[.,[.,.]]],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[3,4,5,1,6,7,8,2]=>[5,8,3,4,1,6,7,2]=>[[[.,[.,.]],[.,.]],[[.,[.,.]],.]]
[1,1,0,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[3,4,5,6,1,7,8,2]=>[6,8,3,4,5,1,7,2]=>[[[.,[.,.]],[.,[.,.]]],[[.,.],.]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[3,4,5,6,7,1,8,2]=>[7,8,3,4,5,6,1,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2]=>[2,8,3,4,5,6,7,1]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,8,7]=>[3,5,1,6,2,4,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[3,5,1,6,2,4,8,7]=>[5,4,3,6,1,2,8,7]=>[[[[.,.],.],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,5,6,1,2,4,8,7]=>[2,4,3,6,5,1,8,7]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,6,8,4,7]=>[3,5,1,7,2,6,8,4]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[3,5,1,2,6,8,4,7]=>[2,5,3,7,1,6,8,4]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[3,1,5,6,2,8,4,7]=>[3,6,1,7,5,2,8,4]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[3,1,5,6,8,2,4,7]=>[3,4,1,7,5,6,8,2]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[3,5,1,6,8,2,4,7]=>[5,4,3,7,1,6,8,2]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[3,5,6,1,8,2,4,7]=>[6,4,3,7,5,1,8,2]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[3,5,6,8,1,2,4,7]=>[2,4,3,7,5,6,8,1]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,7,8]=>[3,5,1,6,2,4,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,5,1,6,2,4,7,8]=>[5,4,3,6,1,2,7,8]=>[[[[.,.],.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[3,5,6,1,2,4,7,8]=>[2,4,3,6,5,1,7,8]=>[[.,[[.,.],[[.,.],.]]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,6,7,4,8]=>[2,5,3,7,1,6,4,8]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[3,5,1,6,2,7,4,8]=>[5,6,3,7,1,2,4,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[3,1,5,6,7,2,4,8]=>[3,4,1,7,5,6,2,8]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[3,5,6,1,7,2,4,8]=>[6,4,3,7,5,1,2,8]=>[[[[.,.],.],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,5,1,2,6,7,8,4]=>[2,5,3,8,1,6,7,4]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[3,1,5,6,2,7,8,4]=>[3,6,1,8,5,2,7,4]=>[[.,[.,.]],[[[.,.],.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[3,5,1,6,2,7,8,4]=>[5,6,3,8,1,2,7,4]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[3,5,6,1,2,7,8,4]=>[2,6,3,8,5,1,7,4]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[3,1,5,6,7,2,8,4]=>[3,7,1,8,5,6,2,4]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[3,5,1,6,7,2,8,4]=>[5,7,3,8,1,6,2,4]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[3,5,6,1,7,2,8,4]=>[6,7,3,8,5,1,2,4]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[3,5,6,7,1,2,8,4]=>[2,7,3,8,5,6,1,4]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[3,1,5,6,7,8,2,4]=>[3,4,1,8,5,6,7,2]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[3,5,6,1,7,8,2,4]=>[6,4,3,8,5,1,7,2]=>[[[[.,.],.],[[.,.],.]],[[.,.],.]]
[1,1,0,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[3,5,6,7,8,1,2,4]=>[2,4,3,8,5,6,7,1]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,8,6]=>[3,5,1,7,2,8,4,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,5,7,2,4,8,6]=>[3,4,1,7,5,8,2,6]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,5,1,7,2,4,8,6]=>[5,4,3,7,1,8,2,6]=>[[[[.,.],.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,5,7,1,2,4,8,6]=>[2,4,3,7,5,8,1,6]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,5,2,7,8,4,6]=>[3,5,1,6,2,8,7,4]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,5,1,2,7,8,4,6]=>[2,5,3,6,1,8,7,4]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,5,7,2,8,4,6]=>[3,7,1,6,5,8,2,4]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,5,1,7,2,8,4,6]=>[5,7,3,6,1,8,2,4]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,5,7,1,2,8,4,6]=>[2,7,3,6,5,8,1,4]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,5,7,8,2,4,6]=>[3,4,1,6,5,8,7,2]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,5,1,7,8,2,4,6]=>[5,4,3,6,1,8,7,2]=>[[[[.,.],.],[.,.]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,5,7,1,8,2,4,6]=>[7,4,3,6,5,8,1,2]=>[[[[.,.],.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,5,7,8,1,2,4,6]=>[2,4,3,6,5,8,7,1]=>[[.,[[.,.],[[.,.],[[.,.],.]]]],.]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,6,8]=>[3,5,1,6,2,7,4,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,5,1,2,7,4,6,8]=>[2,5,3,6,1,7,4,8]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,5,7,2,4,6,8]=>[3,4,1,6,5,7,2,8]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,5,7,1,2,4,6,8]=>[2,4,3,6,5,7,1,8]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,7,6,8]=>[3,4,1,5,2,7,6,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,7,6,8]=>[2,4,3,5,1,7,6,8]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,7,6,8]=>[2,3,1,5,4,7,6,8]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6,8]=>[1,3,2,5,4,7,6,8]=>[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,5,2,4,7,6,8]=>[1,4,3,5,2,7,6,8]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,7,4,6,8]=>[2,3,1,6,5,7,4,8]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,5,7,4,6,8]=>[1,3,2,6,5,7,4,8]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,5,2,7,4,6,8]=>[1,5,3,6,2,7,4,8]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,5,7,2,4,6,8]=>[1,4,3,6,5,7,2,8]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,5,2,4,7,8,6]=>[3,4,1,5,2,8,7,6]=>[[.,[.,.]],[[.,.],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,5,1,2,4,7,8,6]=>[2,4,3,5,1,8,7,6]=>[[.,[[.,.],[.,.]]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,5,4,7,8,6]=>[1,3,2,5,4,8,7,6]=>[.,[[.,.],[[.,.],[[[.,.],.],.]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,5,7,4,8,6]=>[2,3,1,7,5,8,4,6]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,2,5,7,4,8,6]=>[1,3,2,7,5,8,4,6]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,2,7,4,8,6]=>[1,5,3,7,2,8,4,6]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,2,4,8,6]=>[1,4,3,7,5,8,2,6]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,5,7,8,4,6]=>[2,3,1,6,5,8,7,4]=>[[.,[.,.]],[[[.,.],[[.,.],.]],.]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,2,5,7,8,4,6]=>[1,3,2,6,5,8,7,4]=>[.,[[.,.],[[[.,.],[[.,.],.]],.]]]
[1,1,0,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,5,2,7,8,4,6]=>[1,5,3,6,2,8,7,4]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]
[1,1,0,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,5,7,2,8,4,6]=>[1,7,3,6,5,8,2,4]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,5,7,8,2,4,6]=>[1,4,3,6,5,8,7,2]=>[.,[[[.,.],[[.,.],[[.,.],.]]],.]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,5,2,8,4,6,7]=>[3,5,1,6,2,7,8,4]=>[[.,[.,.]],[[.,.],[[.,[.,.]],.]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,5,8,2,4,6,7]=>[3,4,1,6,5,7,8,2]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,5,1,8,2,4,6,7]=>[5,4,3,6,1,7,8,2]=>[[[[.,.],.],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,5,8,1,2,4,6,7]=>[2,4,3,6,5,7,8,1]=>[[.,[[.,.],[[.,.],[.,[.,.]]]]],.]
[1,1,0,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,5,1,2,4,8,6,7]=>[2,4,3,5,1,7,8,6]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,8,6,7]=>[1,3,2,5,4,7,8,6]=>[.,[[.,.],[[.,.],[[.,[.,.]],.]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,3,2,5,8,4,6,7]=>[1,3,2,6,5,7,8,4]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]
[1,1,0,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,3,5,2,8,4,6,7]=>[1,5,3,6,2,7,8,4]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,1,0,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,3,5,8,2,4,6,7]=>[1,4,3,6,5,7,8,2]=>[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,3,2,5,6,4,8,7]=>[1,3,2,6,5,4,8,7]=>[.,[[.,.],[[[.,.],.],[[.,.],.]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,5,6,8,4,7]=>[1,3,2,7,5,6,8,4]=>[.,[[.,.],[[[.,.],[.,[.,.]]],.]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,5,2,4,6,7,8]=>[3,4,1,5,2,6,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,5,1,2,4,6,7,8]=>[2,4,3,5,1,6,7,8]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,5,4,6,7,8]=>[2,3,1,5,4,6,7,8]=>[[.,[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,5,4,6,7,8]=>[1,3,2,5,4,6,7,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,3,5,2,4,6,7,8]=>[1,4,3,5,2,6,7,8]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,2,5,6,4,7,8]=>[2,3,1,6,5,4,7,8]=>[[.,[.,.]],[[[.,.],.],[.,[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,5,6,4,7,8]=>[1,3,2,6,5,4,7,8]=>[.,[[.,.],[[[.,.],.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,3,5,2,6,4,7,8]=>[1,5,3,6,2,4,7,8]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,3,5,6,2,4,7,8]=>[1,4,3,6,5,2,7,8]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,1,2,5,6,7,4,8]=>[2,3,1,7,5,6,4,8]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,3,5,2,6,7,4,8]=>[1,5,3,7,2,6,4,8]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,3,5,6,2,7,4,8]=>[1,6,3,7,5,2,4,8]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,5,6,7,8,4]=>[2,3,1,8,5,6,7,4]=>[[.,[.,.]],[[[.,.],[.,[.,.]]],.]]
[1,1,0,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,3,5,2,6,7,8,4]=>[1,5,3,8,2,6,7,4]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,1,0,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,3,5,6,2,7,8,4]=>[1,6,3,8,5,2,7,4]=>[.,[[[.,.],[[.,.],.]],[[.,.],.]]]
[1,1,0,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,3,5,6,7,2,8,4]=>[1,7,3,8,5,6,2,4]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,5,6,7,8,2,4]=>[1,4,3,8,5,6,7,2]=>[.,[[[.,.],[[.,.],[.,[.,.]]]],.]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,1,6,2,7,4,8,5]=>[3,6,1,7,8,2,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,6,1,2,7,4,8,5]=>[2,6,3,7,8,1,4,5]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,6,1,7,2,4,8,5]=>[6,4,3,7,8,1,2,5]=>[[[[.,.],.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,6,7,1,2,4,8,5]=>[2,4,3,7,8,6,1,5]=>[[.,[[.,.],[[.,[.,.]],.]]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,6,1,2,7,8,4,5]=>[2,6,3,5,8,1,7,4]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,6,1,7,2,8,4,5]=>[6,7,3,5,8,1,2,4]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,6,7,1,2,8,4,5]=>[2,7,3,5,8,6,1,4]=>[[.,[[.,.],[.,[[.,.],.]]]],[.,.]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,6,1,7,8,2,4,5]=>[6,4,3,5,8,1,7,2]=>[[[[.,.],.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,6,7,8,1,2,4,5]=>[2,4,3,5,8,6,7,1]=>[[.,[[.,.],[.,[[.,.],[.,.]]]]],.]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,1,6,7,2,4,5,8]=>[3,4,1,5,7,6,2,8]=>[[.,[.,.]],[[.,[[.,.],.]],[.,.]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,1,6,2,4,7,5,8]=>[3,4,1,6,7,2,5,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,6,1,2,4,7,5,8]=>[2,4,3,6,7,1,5,8]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,6,4,7,5,8]=>[1,3,2,6,7,4,5,8]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,3,2,6,7,4,5,8]=>[1,3,2,5,7,6,4,8]=>[.,[[.,.],[[.,[[.,.],.]],[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,3,6,7,2,4,5,8]=>[1,4,3,5,7,6,2,8]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,7,8,5]=>[2,4,3,6,8,1,7,5]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,1,2,6,4,7,8,5]=>[2,3,1,6,8,4,7,5]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,4,7,8,5]=>[1,3,2,6,8,4,7,5]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,1,2,6,7,4,8,5]=>[2,3,1,7,8,6,4,5]=>[[.,[.,.]],[[[.,[.,.]],.],[.,.]]]
[1,1,0,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,3,6,2,7,4,8,5]=>[1,6,3,7,8,2,4,5]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,3,6,7,2,4,8,5]=>[1,4,3,7,8,6,2,5]=>[.,[[[.,.],[[.,[.,.]],.]],[.,.]]]
[1,1,0,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,2,8,4,5]=>[1,7,3,5,8,6,2,4]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,1,0,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,3,6,7,8,2,4,5]=>[1,4,3,5,8,6,7,2]=>[.,[[[.,.],[.,[[.,.],[.,.]]]],.]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,1,6,8,2,4,5,7]=>[3,4,1,5,7,6,8,2]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,1,6,2,4,8,5,7]=>[3,4,1,6,7,2,8,5]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,6,4,8,5,7]=>[1,3,2,6,7,4,8,5]=>[.,[[.,.],[[.,[.,.]],[[.,.],.]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,3,6,2,4,8,5,7]=>[1,4,3,6,7,2,8,5]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,1,2,6,8,4,5,7]=>[2,3,1,5,7,6,8,4]=>[[.,[.,.]],[[.,[[.,.],[.,.]]],.]]
[1,1,0,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,3,6,2,8,4,5,7]=>[1,6,3,5,7,2,8,4]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,1,6,2,4,5,8,7]=>[3,4,1,5,6,2,8,7]=>[[.,[.,.]],[[.,[.,.]],[[.,.],.]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,6,1,2,4,5,8,7]=>[2,4,3,5,6,1,8,7]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5,8,7]=>[2,3,1,4,6,5,8,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,3,2,4,6,5,8,7]=>[1,3,2,4,6,5,8,7]=>[.,[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,3,4,6,2,5,8,7]=>[1,5,3,4,6,2,8,7]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,8,5,7]=>[2,3,1,4,7,6,8,5]=>[[.,[.,.]],[.,[[[.,.],[.,.]],.]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,3,2,4,6,8,5,7]=>[1,3,2,4,7,6,8,5]=>[.,[[.,.],[.,[[[.,.],[.,.]],.]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,1,6,2,4,5,7,8]=>[3,4,1,5,6,2,7,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,6,4,5,7,8]=>[2,3,1,5,6,4,7,8]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,3,2,6,4,5,7,8]=>[1,3,2,5,6,4,7,8]=>[.,[[.,.],[[.,[.,.]],[.,[.,.]]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,3,6,2,4,5,7,8]=>[1,4,3,5,6,2,7,8]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,3,2,4,6,5,7,8]=>[1,3,2,4,6,5,7,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,3,2,4,6,7,5,8]=>[1,3,2,4,7,6,5,8]=>[.,[[.,.],[.,[[[.,.],.],[.,.]]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,3,4,2,6,7,8,5]=>[1,4,3,2,8,6,7,5]=>[.,[[[.,.],.],[[[.,.],[.,.]],.]]]
[1,1,0,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,3,4,6,2,7,8,5]=>[1,6,3,4,8,2,7,5]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,0,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,3,4,6,7,2,8,5]=>[1,7,3,4,8,6,2,5]=>[.,[[[.,.],[.,[[.,.],.]]],[.,.]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[3,1,7,2,8,4,5,6]=>[3,7,1,5,6,8,2,4]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[3,1,7,8,2,4,5,6]=>[3,4,1,5,6,8,7,2]=>[[.,[.,.]],[[.,[.,[[.,.],.]]],.]]
[1,1,0,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[3,7,8,1,2,4,5,6]=>[2,4,3,5,6,8,7,1]=>[[.,[[.,.],[.,[.,[[.,.],.]]]]],.]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[3,1,7,2,4,8,5,6]=>[3,4,1,7,6,8,2,5]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[3,1,2,7,4,8,5,6]=>[2,3,1,7,6,8,4,5]=>[[.,[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,3,2,7,4,8,5,6]=>[1,3,2,7,6,8,4,5]=>[.,[[.,.],[[[.,.],[.,.]],[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,3,7,2,4,8,5,6]=>[1,4,3,7,6,8,2,5]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,3,2,7,8,4,5,6]=>[1,3,2,5,6,8,7,4]=>[.,[[.,.],[[.,[.,[[.,.],.]]],.]]]
[1,1,0,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,3,7,2,8,4,5,6]=>[1,7,3,5,6,8,2,4]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[3,1,7,2,4,5,8,6]=>[3,4,1,5,7,8,2,6]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[3,7,1,2,4,5,8,6]=>[2,4,3,5,7,8,1,6]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[3,1,2,7,4,5,8,6]=>[2,3,1,5,7,8,4,6]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,3,2,7,4,5,8,6]=>[1,3,2,5,7,8,4,6]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,3,7,2,4,5,8,6]=>[1,4,3,5,7,8,2,6]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,8,6]=>[2,3,1,4,7,8,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,3,2,4,7,5,8,6]=>[1,3,2,4,7,8,5,6]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,3,4,2,7,5,8,6]=>[1,4,3,2,7,8,5,6]=>[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,3,4,7,2,5,8,6]=>[1,5,3,4,7,8,2,6]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,3,2,4,7,8,5,6]=>[1,3,2,4,6,8,7,5]=>[.,[[.,.],[.,[[.,[[.,.],.]],.]]]]
[1,1,0,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,3,4,2,7,8,5,6]=>[1,4,3,2,6,8,7,5]=>[.,[[[.,.],.],[[.,[[.,.],.]],.]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[3,1,7,2,4,5,6,8]=>[3,4,1,5,6,7,2,8]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[3,7,1,2,4,5,6,8]=>[2,4,3,5,6,7,1,8]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[3,1,2,7,4,5,6,8]=>[2,3,1,5,6,7,4,8]=>[[.,[.,.]],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,3,2,7,4,5,6,8]=>[1,3,2,5,6,7,4,8]=>[.,[[.,.],[[.,[.,[.,.]]],[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,3,7,2,4,5,6,8]=>[1,4,3,5,6,7,2,8]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[3,1,2,4,7,5,6,8]=>[2,3,1,4,6,7,5,8]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,3,2,4,7,5,6,8]=>[1,3,2,4,6,7,5,8]=>[.,[[.,.],[.,[[.,[.,.]],[.,.]]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,3,4,2,7,5,6,8]=>[1,4,3,2,6,7,5,8]=>[.,[[[.,.],.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,3,4,7,2,5,6,8]=>[1,5,3,4,6,7,2,8]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[3,1,2,4,5,7,6,8]=>[2,3,1,4,5,7,6,8]=>[[.,[.,.]],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,3,4,2,5,7,6,8]=>[1,4,3,2,5,7,6,8]=>[.,[[[.,.],.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,7,8,6]=>[1,3,2,4,5,8,7,6]=>[.,[[.,.],[.,[.,[[[.,.],.],.]]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,3,4,2,5,7,8,6]=>[1,4,3,2,5,8,7,6]=>[.,[[[.,.],.],[.,[[[.,.],.],.]]]]
[1,1,0,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,3,4,5,2,7,8,6]=>[1,5,3,4,2,8,7,6]=>[.,[[[.,.],[.,.]],[[[.,.],.],.]]]
[1,1,0,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,3,4,5,7,2,8,6]=>[1,7,3,4,5,8,2,6]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,3,4,5,7,8,2,6]=>[1,6,3,4,5,8,7,2]=>[.,[[[.,.],[.,[.,[[.,.],.]]]],.]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,1,8,2,4,5,6,7]=>[3,4,1,5,6,7,8,2]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,8,1,2,4,5,6,7]=>[2,4,3,5,6,7,8,1]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[3,1,2,8,4,5,6,7]=>[2,3,1,5,6,7,8,4]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,3,2,8,4,5,6,7]=>[1,3,2,5,6,7,8,4]=>[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]
[1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,3,8,2,4,5,6,7]=>[1,4,3,5,6,7,8,2]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[3,1,2,4,8,5,6,7]=>[2,3,1,4,6,7,8,5]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,3,2,4,8,5,6,7]=>[1,3,2,4,6,7,8,5]=>[.,[[.,.],[.,[[.,[.,[.,.]]],.]]]]
[1,1,0,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,3,4,2,8,5,6,7]=>[1,4,3,2,6,7,8,5]=>[.,[[[.,.],.],[[.,[.,[.,.]]],.]]]
[1,1,0,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,3,4,8,2,5,6,7]=>[1,5,3,4,6,7,8,2]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[3,1,2,4,5,8,6,7]=>[2,3,1,4,5,7,8,6]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,3,2,4,5,8,6,7]=>[1,3,2,4,5,7,8,6]=>[.,[[.,.],[.,[.,[[.,[.,.]],.]]]]]
[1,1,0,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,3,4,2,5,8,6,7]=>[1,4,3,2,5,7,8,6]=>[.,[[[.,.],.],[.,[[.,[.,.]],.]]]]
[1,1,0,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,3,4,5,2,8,6,7]=>[1,5,3,4,2,7,8,6]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,8,7]=>[2,3,1,4,5,6,8,7]=>[[.,[.,.]],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,8,7]=>[1,3,2,4,5,6,8,7]=>[.,[[.,.],[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,3,4,2,5,6,8,7]=>[1,4,3,2,5,6,8,7]=>[.,[[[.,.],.],[.,[.,[[.,.],.]]]]]
[1,1,0,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,3,4,5,6,8,2,7]=>[1,7,3,4,5,6,8,2]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7,8]=>[2,3,1,4,5,6,7,8]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7,8]=>[1,3,2,4,5,6,7,8]=>[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,3,4,2,5,6,7,8]=>[1,4,3,2,5,6,7,8]=>[.,[[[.,.],.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,3,4,5,2,6,7,8]=>[1,5,3,4,2,6,7,8]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,3,4,5,6,2,7,8]=>[1,6,3,4,5,2,7,8]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,3,4,5,6,7,2,8]=>[1,7,3,4,5,6,2,8]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,3,4,5,6,7,8,2]=>[1,8,3,4,5,6,7,2]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,8,7]=>[4,5,6,1,2,3,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,1,0,0]=>[4,5,1,2,6,3,8,7]=>[2,5,6,4,1,3,8,7]=>[[.,[[.,[.,.]],.]],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0,1,0]=>[4,1,5,6,2,3,8,7]=>[4,3,6,1,5,2,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,1,0,0]=>[4,5,1,6,2,3,8,7]=>[5,3,6,4,1,2,8,7]=>[[[.,.],[[.,.],.]],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,8,7]=>[2,3,6,4,5,1,8,7]=>[[.,[.,[[.,.],[.,.]]]],[[.,.],.]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0,1,0]=>[4,1,5,2,6,8,3,7]=>[4,5,7,1,2,6,8,3]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,1,0,0]=>[4,5,1,2,6,8,3,7]=>[2,5,7,4,1,6,8,3]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,1,0,0]=>[4,5,1,6,2,8,3,7]=>[5,6,7,4,1,2,8,3]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,0,1,1,0,1,1,0,0,0]=>[4,5,6,1,2,8,3,7]=>[2,6,7,4,5,1,8,3]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0,1,0]=>[4,1,5,6,8,2,3,7]=>[4,3,7,1,5,6,8,2]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,0,0,0,1,0,1,1,1,0,1,0,0,0]=>[4,5,6,1,8,2,3,7]=>[6,3,7,4,5,1,8,2]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[4,5,6,8,1,2,3,7]=>[2,3,7,4,5,6,8,1]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,7,8]=>[4,5,6,1,2,3,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,0]=>[4,1,5,6,2,3,7,8]=>[4,3,6,1,5,2,7,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,1,0,0]=>[4,5,1,6,2,3,7,8]=>[5,3,6,4,1,2,7,8]=>[[[.,.],[[.,.],.]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,7,8]=>[2,3,6,4,5,1,7,8]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0,1,0]=>[4,1,5,2,6,7,3,8]=>[4,5,7,1,2,6,3,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,1,0,0]=>[4,5,1,2,6,7,3,8]=>[2,5,7,4,1,6,3,8]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0,1,0]=>[4,1,5,6,2,7,3,8]=>[4,6,7,1,5,2,3,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,1,0,0]=>[4,5,1,6,2,7,3,8]=>[5,6,7,4,1,2,3,8]=>[[[.,[.,[.,.]]],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,1,0,0,0]=>[4,5,6,1,2,7,3,8]=>[2,6,7,4,5,1,3,8]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,1,0,0]=>[4,5,1,6,7,2,3,8]=>[5,3,7,4,1,6,2,8]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,6,7,8,3]=>[4,5,8,1,2,6,7,3]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,1,0,0]=>[4,5,1,6,2,7,8,3]=>[5,6,8,4,1,2,7,3]=>[[[.,[.,[.,.]]],.],[.,[[.,.],.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,1,0,0,0]=>[4,5,6,1,2,7,8,3]=>[2,6,8,4,5,1,7,3]=>[[.,[[.,[.,.]],[.,.]]],[[.,.],.]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0,1,0]=>[4,1,5,6,7,2,8,3]=>[4,7,8,1,5,6,2,3]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,1,0,0]=>[4,5,1,6,7,2,8,3]=>[5,7,8,4,1,6,2,3]=>[[[.,[.,[.,.]]],.],[[.,.],[.,.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,1,0,0,0]=>[4,5,6,1,7,2,8,3]=>[6,7,8,4,5,1,2,3]=>[[[.,[.,[.,.]]],[.,.]],[.,[.,.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,0]=>[4,1,5,6,7,8,2,3]=>[4,3,8,1,5,6,7,2]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,0,0,0,1,1,1,1,0,0,1,0,0,0]=>[4,5,6,1,7,8,2,3]=>[6,3,8,4,5,1,7,2]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,0,0,0]=>[4,5,6,7,1,8,2,3]=>[7,3,8,4,5,6,1,2]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[4,5,6,7,8,1,2,3]=>[2,3,8,4,5,6,7,1]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,7,3,8,6]=>[4,5,7,1,2,8,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0]=>[4,5,1,2,7,3,8,6]=>[2,5,7,4,1,8,3,6]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0,1,0]=>[4,1,5,7,2,3,8,6]=>[4,3,7,1,5,8,2,6]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0,1,0]=>[4,1,5,2,7,8,3,6]=>[4,5,6,1,2,8,7,3]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0,1,0]=>[4,1,5,7,2,8,3,6]=>[4,7,6,1,5,8,2,3]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,1,0,0,0]=>[4,5,7,1,2,8,3,6]=>[2,7,6,4,5,8,1,3]=>[[.,[[[.,.],.],[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0,1,0]=>[4,1,5,7,8,2,3,6]=>[4,3,6,1,5,8,7,2]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,1,0,0]=>[4,5,1,7,8,2,3,6]=>[5,3,6,4,1,8,7,2]=>[[[.,.],[[.,.],.]],[[[.,.],.],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[4,5,7,1,8,2,3,6]=>[7,3,6,4,5,8,1,2]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,0,0,1,0,0,1,1,1,1,0,0,0,0]=>[4,5,7,8,1,2,3,6]=>[2,3,6,4,5,8,7,1]=>[[.,[.,[[.,.],[.,[[.,.],.]]]]],.]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0,1,0]=>[4,1,5,2,7,3,6,8]=>[4,5,6,1,2,7,3,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,1,0,0]=>[4,5,1,2,7,3,6,8]=>[2,5,6,4,1,7,3,8]=>[[.,[[.,[.,.]],.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0,1,0]=>[4,1,5,7,2,3,6,8]=>[4,3,6,1,5,7,2,8]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,1,0,0]=>[4,5,1,7,2,3,6,8]=>[5,3,6,4,1,7,2,8]=>[[[.,.],[[.,.],.]],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0,1,0]=>[4,1,5,2,3,7,6,8]=>[4,3,5,1,2,7,6,8]=>[[[.,.],[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,7,6,8]=>[2,4,5,1,3,7,6,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,7,6,8]=>[1,4,5,2,3,7,6,8]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,7,6,8]=>[1,3,5,4,2,7,6,8]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,5,7,3,6,8]=>[2,4,6,1,5,7,3,8]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0,1,0]=>[4,1,5,2,3,7,8,6]=>[4,3,5,1,2,8,7,6]=>[[[.,.],[.,.]],[.,[[[.,.],.],.]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,1,0,0]=>[4,5,1,2,3,7,8,6]=>[2,3,5,4,1,8,7,6]=>[[.,[.,[[.,.],.]]],[[[.,.],.],.]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0,1,0]=>[4,1,2,5,3,7,8,6]=>[2,4,5,1,3,8,7,6]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,4,2,5,7,3,8,6]=>[1,4,7,2,5,8,3,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,4,5,2,7,3,8,6]=>[1,5,7,4,2,8,3,6]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,4,5,7,2,3,8,6]=>[1,3,7,4,5,8,2,6]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0,1,0]=>[4,1,2,5,7,8,3,6]=>[2,4,6,1,5,8,7,3]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,4,5,2,7,8,3,6]=>[1,5,6,4,2,8,7,3]=>[.,[[[.,[.,.]],.],[[[.,.],.],.]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,5,2,8,3,6,7]=>[4,5,6,1,2,7,8,3]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,1,0,0]=>[4,5,1,2,8,3,6,7]=>[2,5,6,4,1,7,8,3]=>[[.,[[.,[.,.]],.]],[[.,[.,.]],.]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0,1,0]=>[4,1,5,8,2,3,6,7]=>[4,3,6,1,5,7,8,2]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,0,0,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,8,1,2,3,6,7]=>[2,3,6,4,5,7,8,1]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,5,3,8,6,7]=>[2,4,5,1,3,7,8,6]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,8,6,7]=>[1,4,5,2,3,7,8,6]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,8,6,7]=>[1,3,5,4,2,7,8,6]=>[.,[[.,[[.,.],.]],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,5,8,2,3,6,7]=>[1,3,6,4,5,7,8,2]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,1,0,0]=>[4,5,1,2,3,6,8,7]=>[2,3,5,4,1,6,8,7]=>[[.,[.,[[.,.],.]]],[.,[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,5,6,3,8,7]=>[2,4,6,1,5,3,8,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,6,2,3,8,7]=>[1,3,6,4,5,2,8,7]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,5,6,8,3,7]=>[2,4,7,1,5,6,8,3]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,5,6,8,3,7]=>[1,4,7,2,5,6,8,3]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,5,2,6,8,3,7]=>[1,5,7,4,2,6,8,3]=>[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,5,6,2,8,3,7]=>[1,6,7,4,5,2,8,3]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,5,6,8,2,3,7]=>[1,3,7,4,5,6,8,2]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0,1,0]=>[4,1,5,2,3,6,7,8]=>[4,3,5,1,2,6,7,8]=>[[[.,.],[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,1,0,0]=>[4,5,1,2,3,6,7,8]=>[2,3,5,4,1,6,7,8]=>[[.,[.,[[.,.],.]]],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,5,3,6,7,8]=>[2,4,5,1,3,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,5,3,6,7,8]=>[1,4,5,2,3,6,7,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0,1,0]=>[4,1,2,5,6,3,7,8]=>[2,4,6,1,5,3,7,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,4,2,5,6,3,7,8]=>[1,4,6,2,5,3,7,8]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,4,5,2,6,3,7,8]=>[1,5,6,4,2,3,7,8]=>[.,[[[.,[.,.]],.],[.,[.,[.,.]]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,4,2,5,6,7,3,8]=>[1,4,7,2,5,6,3,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,4,5,2,6,7,3,8]=>[1,5,7,4,2,6,3,8]=>[.,[[[.,[.,.]],.],[[.,.],[.,.]]]]
[1,1,1,0,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,4,5,6,2,7,3,8]=>[1,6,7,4,5,2,3,8]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,0,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,4,5,6,7,2,3,8]=>[1,3,7,4,5,6,2,8]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,5,6,7,8,3]=>[2,4,8,1,5,6,7,3]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,5,6,7,8,3]=>[1,4,8,2,5,6,7,3]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,4,5,2,6,7,8,3]=>[1,5,8,4,2,6,7,3]=>[.,[[[.,[.,.]],.],[[.,[.,.]],.]]]
[1,1,1,0,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,4,5,6,2,7,8,3]=>[1,6,8,4,5,2,7,3]=>[.,[[[.,[.,.]],[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,4,5,6,7,2,8,3]=>[1,7,8,4,5,6,2,3]=>[.,[[[.,[.,.]],[.,[.,.]]],[.,.]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,4,5,6,7,8,2,3]=>[1,3,8,4,5,6,7,2]=>[.,[[.,[[.,.],[.,[.,[.,.]]]]],.]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,8,5]=>[4,6,7,1,8,2,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,1,0,0]=>[4,6,1,2,7,3,8,5]=>[2,6,7,4,8,1,3,5]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,1,0,0]=>[4,6,1,7,2,3,8,5]=>[6,3,7,4,8,1,2,5]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,1,0,0]=>[4,6,1,2,7,8,3,5]=>[2,6,5,4,8,1,7,3]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,1,0,0]=>[4,6,1,7,2,8,3,5]=>[6,7,5,4,8,1,2,3]=>[[[[.,[.,.]],.],[.,.]],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0,1,0]=>[4,1,6,7,8,2,3,5]=>[4,3,5,1,8,6,7,2]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,1,0,0]=>[4,6,1,7,8,2,3,5]=>[6,3,5,4,8,1,7,2]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,0,1,0,0,0,1,1,1,0,1,0,0,0]=>[4,6,7,1,8,2,3,5]=>[7,3,5,4,8,6,1,2]=>[[[.,.],[[.,.],[[.,.],.]]],[.,.]]
[1,1,1,0,1,0,0,0,1,1,1,1,0,0,0,0]=>[4,6,7,8,1,2,3,5]=>[2,3,5,4,8,6,7,1]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,5,8]=>[4,6,5,1,7,2,3,8]=>[[.,[[.,.],.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,1,0,0]=>[4,6,1,2,7,3,5,8]=>[2,6,5,4,7,1,3,8]=>[[.,[[[.,.],.],[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,1,0,0]=>[4,6,1,7,2,3,5,8]=>[6,3,5,4,7,1,2,8]=>[[[.,.],[[.,.],[.,.]]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0,1,0]=>[4,1,6,2,3,7,5,8]=>[4,3,6,1,7,2,5,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,1,0,0]=>[4,6,1,2,3,7,5,8]=>[2,3,6,4,7,1,5,8]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,7,5,8]=>[1,4,6,2,7,3,5,8]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,4,6,2,3,7,5,8]=>[1,3,6,4,7,2,5,8]=>[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0,1,0]=>[4,1,2,6,7,3,5,8]=>[2,4,5,1,7,6,3,8]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,6,2,7,3,5,8]=>[1,6,5,4,7,2,3,8]=>[.,[[[[.,.],.],[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,6,7,2,3,5,8]=>[1,3,5,4,7,6,2,8]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,7,8,5]=>[4,3,6,1,8,2,7,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,7,8,5]=>[2,4,6,1,8,3,7,5]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,7,8,5]=>[1,4,6,2,8,3,7,5]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,6,2,3,7,8,5]=>[1,3,6,4,8,2,7,5]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,2,6,7,3,8,5]=>[1,4,7,2,8,6,3,5]=>[.,[[.,[.,.]],[[[.,.],.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,6,2,7,3,8,5]=>[1,6,7,4,8,2,3,5]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,6,7,2,3,8,5]=>[1,3,7,4,8,6,2,5]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,6,7,8,3,5]=>[1,4,5,2,8,6,7,3]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]
[1,1,1,0,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,6,2,7,8,3,5]=>[1,6,5,4,8,2,7,3]=>[.,[[[[.,.],.],[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,6,7,2,8,3,5]=>[1,7,5,4,8,6,2,3]=>[.,[[[[.,.],.],[[.,.],.]],[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,6,1,2,8,3,5,7]=>[2,6,5,4,7,1,8,3]=>[[.,[[[.,.],.],[.,.]]],[[.,.],.]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,6,8,2,3,5,7]=>[4,3,5,1,7,6,8,2]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,6,1,8,2,3,5,7]=>[6,3,5,4,7,1,8,2]=>[[[.,.],[[.,.],[.,.]]],[[.,.],.]]
[1,1,1,0,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,6,8,1,2,3,5,7]=>[2,3,5,4,7,6,8,1]=>[[.,[.,[[.,.],[[.,.],[.,.]]]]],.]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,6,2,3,8,5,7]=>[4,3,6,1,7,2,8,5]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,2,6,3,8,5,7]=>[2,4,6,1,7,3,8,5]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,4,2,6,3,8,5,7]=>[1,4,6,2,7,3,8,5]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,4,6,2,3,8,5,7]=>[1,3,6,4,7,2,8,5]=>[.,[[.,[[.,.],[.,.]]],[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,4,6,8,2,3,5,7]=>[1,3,5,4,7,6,8,2]=>[.,[[.,[[.,.],[[.,.],[.,.]]]],.]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,1,6,2,3,5,8,7]=>[4,3,5,1,6,2,8,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,1,2,6,3,5,8,7]=>[2,4,5,1,6,3,8,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,4,2,6,3,5,8,7]=>[1,4,5,2,6,3,8,7]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,8,7]=>[2,3,4,1,6,5,8,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,8,7]=>[1,3,4,2,6,5,8,7]=>[.,[[.,[.,.]],[[.,.],[[.,.],.]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,8,7]=>[1,2,4,3,6,5,8,7]=>[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,8,5,7]=>[2,3,4,1,7,6,8,5]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,6,8,5,7]=>[1,3,4,2,7,6,8,5]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]
[1,1,1,0,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,2,4,3,6,8,5,7]=>[1,2,4,3,7,6,8,5]=>[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]
[1,1,1,0,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,2,4,6,3,8,5,7]=>[1,2,6,4,7,3,8,5]=>[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]
[1,1,1,0,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,2,4,6,8,3,5,7]=>[1,2,5,4,7,6,8,3]=>[.,[.,[[[.,.],[[.,.],[.,.]]],.]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,1,6,2,3,5,7,8]=>[4,3,5,1,6,2,7,8]=>[[[.,.],[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,6,3,5,7,8]=>[2,4,5,1,6,3,7,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,4,2,6,3,5,7,8]=>[1,4,5,2,6,3,7,8]=>[.,[[.,[.,.]],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,7,8]=>[2,3,4,1,6,5,7,8]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,1,2,3,6,7,5,8]=>[2,3,4,1,7,6,5,8]=>[[.,[.,[.,.]]],[[[.,.],.],[.,.]]]
[1,1,1,0,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,2,4,6,3,7,5,8]=>[1,2,6,4,7,3,5,8]=>[.,[.,[[[.,.],[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,6,7,8,5]=>[2,3,4,1,8,6,7,5]=>[[.,[.,[.,.]]],[[[.,.],[.,.]],.]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,4,2,3,6,7,8,5]=>[1,3,4,2,8,6,7,5]=>[.,[[.,[.,.]],[[[.,.],[.,.]],.]]]
[1,1,1,0,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,2,4,3,6,7,8,5]=>[1,2,4,3,8,6,7,5]=>[.,[.,[[.,.],[[[.,.],[.,.]],.]]]]
[1,1,1,0,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,2,4,6,3,7,8,5]=>[1,2,6,4,8,3,7,5]=>[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]
[1,1,1,0,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,2,4,6,7,3,8,5]=>[1,2,7,4,8,6,3,5]=>[.,[.,[[[.,.],[[.,.],.]],[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,1,7,2,8,3,5,6]=>[4,7,5,1,6,8,2,3]=>[[.,[[.,.],.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,1,7,8,2,3,5,6]=>[4,3,5,1,6,8,7,2]=>[[[.,.],[.,.]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,7,1,8,2,3,5,6]=>[7,3,5,4,6,8,1,2]=>[[[.,.],[[.,.],[.,[.,.]]]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,1,7,2,3,8,5,6]=>[4,3,7,1,6,8,2,5]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,1,2,7,3,8,5,6]=>[2,4,7,1,6,8,3,5]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,4,2,7,3,8,5,6]=>[1,4,7,2,6,8,3,5]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,4,7,2,3,8,5,6]=>[1,3,7,4,6,8,2,5]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,1,2,7,8,3,5,6]=>[2,4,5,1,6,8,7,3]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,4,2,7,8,3,5,6]=>[1,4,5,2,6,8,7,3]=>[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,1,7,2,3,5,8,6]=>[4,3,5,1,7,8,2,6]=>[[[.,.],[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,1,2,7,3,5,8,6]=>[2,4,5,1,7,8,3,6]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,4,2,7,3,5,8,6]=>[1,4,5,2,7,8,3,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,4,7,2,3,5,8,6]=>[1,3,5,4,7,8,2,6]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,7,5,8,6]=>[2,3,4,1,7,8,5,6]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,7,5,8,6]=>[1,3,4,2,7,8,5,6]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,7,5,8,6]=>[1,2,4,3,7,8,5,6]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,1,1,0,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,2,4,7,3,5,8,6]=>[1,2,5,4,7,8,3,6]=>[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,7,8,5,6]=>[2,3,4,1,6,8,7,5]=>[[.,[.,[.,.]]],[[.,[[.,.],.]],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,4,2,3,7,8,5,6]=>[1,3,4,2,6,8,7,5]=>[.,[[.,[.,.]],[[.,[[.,.],.]],.]]]
[1,1,1,0,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,2,4,7,8,3,5,6]=>[1,2,5,4,6,8,7,3]=>[.,[.,[[[.,.],[.,[[.,.],.]]],.]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,7,1,2,3,5,6,8]=>[2,3,5,4,6,7,1,8]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,4,2,7,3,5,6,8]=>[1,4,5,2,6,7,3,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,1,2,3,7,5,6,8]=>[2,3,4,1,6,7,5,8]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,4,2,3,7,5,6,8]=>[1,3,4,2,6,7,5,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,2,4,3,7,5,6,8]=>[1,2,4,3,6,7,5,8]=>[.,[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,1,1,0,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,2,4,7,3,5,6,8]=>[1,2,5,4,6,7,3,8]=>[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,1,2,3,5,7,6,8]=>[2,3,4,1,5,7,6,8]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,4,2,3,5,7,6,8]=>[1,3,4,2,5,7,6,8]=>[.,[[.,[.,.]],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,2,4,3,5,7,6,8]=>[1,2,4,3,5,7,6,8]=>[.,[.,[[.,.],[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,7,8,6]=>[2,3,4,1,5,8,7,6]=>[[.,[.,[.,.]]],[.,[[[.,.],.],.]]]
[1,1,1,0,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,4,3,5,7,8,6]=>[1,2,4,3,5,8,7,6]=>[.,[.,[[.,.],[.,[[[.,.],.],.]]]]]
[1,1,1,0,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,2,4,5,3,7,8,6]=>[1,2,5,4,3,8,7,6]=>[.,[.,[[[.,.],.],[[[.,.],.],.]]]]
[1,1,1,0,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,4,5,7,3,8,6]=>[1,2,7,4,5,8,3,6]=>[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0,1,0]=>[4,1,8,2,3,5,6,7]=>[4,3,5,1,6,7,8,2]=>[[[.,.],[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,1,0,0]=>[4,8,1,2,3,5,6,7]=>[2,3,5,4,6,7,8,1]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0,1,0]=>[4,1,2,8,3,5,6,7]=>[2,4,5,1,6,7,8,3]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,4,2,8,3,5,6,7]=>[1,4,5,2,6,7,8,3]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0,1,0]=>[4,1,2,3,8,5,6,7]=>[2,3,4,1,6,7,8,5]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,4,2,3,8,5,6,7]=>[1,3,4,2,6,7,8,5]=>[.,[[.,[.,.]],[[.,[.,[.,.]]],.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,4,3,8,5,6,7]=>[1,2,4,3,6,7,8,5]=>[.,[.,[[.,.],[[.,[.,[.,.]]],.]]]]
[1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,4,8,3,5,6,7]=>[1,2,5,4,6,7,8,3]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0,1,0]=>[4,1,2,3,5,8,6,7]=>[2,3,4,1,5,7,8,6]=>[[.,[.,[.,.]]],[.,[[.,[.,.]],.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,4,2,3,5,8,6,7]=>[1,3,4,2,5,7,8,6]=>[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]
[1,1,1,0,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,4,3,5,8,6,7]=>[1,2,4,3,5,7,8,6]=>[.,[.,[[.,.],[.,[[.,[.,.]],.]]]]]
[1,1,1,0,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,2,4,5,3,8,6,7]=>[1,2,5,4,3,7,8,6]=>[.,[.,[[[.,.],.],[[.,[.,.]],.]]]]
[1,1,1,0,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,2,4,5,8,3,6,7]=>[1,2,6,4,5,7,8,3]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,8,7]=>[2,3,4,1,5,6,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,8,7]=>[1,3,4,2,5,6,8,7]=>[.,[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,1,1,0,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,8,7]=>[1,2,4,3,5,6,8,7]=>[.,[.,[[.,.],[.,[.,[[.,.],.]]]]]]
[1,1,1,0,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,2,4,5,3,6,8,7]=>[1,2,5,4,3,6,8,7]=>[.,[.,[[[.,.],.],[.,[[.,.],.]]]]]
[1,1,1,0,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,2,4,5,6,8,3,7]=>[1,2,7,4,5,6,8,3]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,7,8]=>[2,3,4,1,5,6,7,8]=>[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,7,8]=>[1,3,4,2,5,6,7,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,7,8]=>[1,2,4,3,5,6,7,8]=>[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,4,5,3,6,7,8]=>[1,2,5,4,3,6,7,8]=>[.,[.,[[[.,.],.],[.,[.,[.,.]]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,4,5,6,7,8,3]=>[1,2,8,4,5,6,7,3]=>[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,8,4]=>[5,6,7,8,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,0,0]=>[5,6,1,2,7,3,8,4]=>[2,6,7,8,5,1,3,4]=>[[.,[[.,[.,[.,.]]],.]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0,1,0]=>[5,1,6,7,2,3,8,4]=>[5,3,7,8,1,6,2,4]=>[[[.,.],[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,1,0,0]=>[5,6,1,7,2,3,8,4]=>[6,3,7,8,5,1,2,4]=>[[[.,.],[[.,[.,.]],.]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,8,4]=>[2,3,7,8,5,6,1,4]=>[[.,[.,[[.,[.,.]],[.,.]]]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0,1,0]=>[5,1,6,2,7,8,3,4]=>[5,6,4,8,1,2,7,3]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,0,0]=>[5,6,1,2,7,8,3,4]=>[2,6,4,8,5,1,7,3]=>[[.,[[.,.],[[.,.],.]]],[[.,.],.]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0,1,0]=>[5,1,6,7,2,8,3,4]=>[5,7,4,8,1,6,2,3]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,1,0,0]=>[5,6,1,7,2,8,3,4]=>[6,7,4,8,5,1,2,3]=>[[[.,[.,.]],[[.,.],.]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,1,0,0,0]=>[5,6,7,1,2,8,3,4]=>[2,7,4,8,5,6,1,3]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0,1,0]=>[5,1,6,7,8,2,3,4]=>[5,3,4,8,1,6,7,2]=>[[[.,.],[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,1,0,0]=>[5,6,1,7,8,2,3,4]=>[6,3,4,8,5,1,7,2]=>[[[.,.],[.,[[.,.],.]]],[[.,.],.]]
[1,1,1,1,0,0,0,0,1,1,1,0,1,0,0,0]=>[5,6,7,1,8,2,3,4]=>[7,3,4,8,5,6,1,2]=>[[[.,.],[.,[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[2,3,4,8,5,6,7,1]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,4,8]=>[5,6,4,7,1,2,3,8]=>[[[.,[.,.]],[.,.]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,1,0,0,0]=>[5,6,7,1,2,3,4,8]=>[2,3,4,7,5,6,1,8]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0,1,0]=>[5,1,6,2,3,7,4,8]=>[5,3,6,7,1,2,4,8]=>[[[.,.],[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,5,2,6,3,7,4,8]=>[1,5,6,7,2,3,4,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,1,0,0,0]=>[1,5,6,2,3,7,4,8]=>[1,3,6,7,5,2,4,8]=>[.,[[.,[[.,[.,.]],.]],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,1,0,0]=>[1,5,2,6,7,3,4,8]=>[1,5,4,7,2,6,3,8]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,1,0,0,0]=>[1,5,6,2,7,3,4,8]=>[1,6,4,7,5,2,3,8]=>[.,[[[.,.],[[.,.],.]],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0,1,0]=>[5,1,6,2,3,7,8,4]=>[5,3,6,8,1,2,7,4]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,1,0,0]=>[5,6,1,2,3,7,8,4]=>[2,3,6,8,5,1,7,4]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0,1,0]=>[5,1,2,6,3,7,8,4]=>[2,5,6,8,1,3,7,4]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,1,0,0]=>[1,5,2,6,3,7,8,4]=>[1,5,6,8,2,3,7,4]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,1,1,0,0,1,1,0,0,0]=>[1,5,6,2,3,7,8,4]=>[1,3,6,8,5,2,7,4]=>[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0,1,0]=>[5,1,2,6,7,3,8,4]=>[2,5,7,8,1,6,3,4]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,1,0,0]=>[1,5,2,6,7,3,8,4]=>[1,5,7,8,2,6,3,4]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,1,0,1,0,0,0]=>[1,5,6,2,7,3,8,4]=>[1,6,7,8,5,2,3,4]=>[.,[[[.,[.,[.,.]]],.],[.,[.,.]]]]
[1,1,1,1,0,0,0,1,1,0,1,1,0,0,0,0]=>[1,5,6,7,2,3,8,4]=>[1,3,7,8,5,6,2,4]=>[.,[[.,[[.,[.,.]],[.,.]]],[.,.]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,1,0,0]=>[1,5,2,6,7,8,3,4]=>[1,5,4,8,2,6,7,3]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,1,1,1,0,0,0,1,1,1,0,0,1,0,0,0]=>[1,5,6,2,7,8,3,4]=>[1,6,4,8,5,2,7,3]=>[.,[[[.,.],[[.,.],.]],[[.,.],.]]]
[1,1,1,1,0,0,0,1,1,1,0,1,0,0,0,0]=>[1,5,6,7,2,8,3,4]=>[1,7,4,8,5,6,2,3]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,1,1,0,0,0,1,1,1,1,0,0,0,0,0]=>[1,5,6,7,8,2,3,4]=>[1,3,4,8,5,6,7,2]=>[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0,1,0]=>[5,1,6,2,8,3,4,7]=>[5,6,4,7,1,2,8,3]=>[[[.,[.,.]],[.,.]],[.,[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,0,1,1,1,0,0,0]=>[5,6,8,1,2,3,4,7]=>[2,3,4,7,5,6,8,1]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0,1,0]=>[5,1,6,2,3,8,4,7]=>[5,3,6,7,1,2,8,4]=>[[[.,.],[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,1,0,0]=>[5,6,1,2,3,8,4,7]=>[2,3,6,7,5,1,8,4]=>[[.,[.,[[.,[.,.]],.]]],[[.,.],.]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0,1,0]=>[5,1,2,6,3,8,4,7]=>[2,5,6,7,1,3,8,4]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,1,0,0]=>[1,5,2,6,3,8,4,7]=>[1,5,6,7,2,3,8,4]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,1,0,0,0]=>[1,5,6,2,3,8,4,7]=>[1,3,6,7,5,2,8,4]=>[.,[[.,[[.,[.,.]],.]],[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,1,0,0]=>[1,5,2,6,8,3,4,7]=>[1,5,4,7,2,6,8,3]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0,1,0]=>[5,1,2,6,3,4,8,7]=>[2,5,4,6,1,3,8,7]=>[[.,[[.,.],[.,.]]],[.,[[.,.],.]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,1,0,0]=>[1,5,2,3,6,4,8,7]=>[1,3,5,6,2,4,8,7]=>[.,[[.,[.,[.,.]]],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,5,3,6,4,8,7]=>[1,2,5,6,3,4,8,7]=>[.,[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,1,0,0,0]=>[1,2,5,3,6,8,4,7]=>[1,2,5,7,3,6,8,4]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,1,1,1,0,0,1,0,1,1,0,1,0,0,0,0]=>[1,2,5,6,3,8,4,7]=>[1,2,6,7,5,3,8,4]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]
[1,1,1,1,0,0,1,0,1,1,1,0,0,0,0,0]=>[1,2,5,6,8,3,4,7]=>[1,2,4,7,5,6,8,3]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,1,0,0]=>[5,6,1,2,3,4,7,8]=>[2,3,4,6,5,1,7,8]=>[[.,[.,[.,[[.,.],.]]]],[.,[.,.]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0,1,0]=>[5,1,2,6,3,4,7,8]=>[2,5,4,6,1,3,7,8]=>[[.,[[.,.],[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,1,0,0]=>[1,5,2,6,3,4,7,8]=>[1,5,4,6,2,3,7,8]=>[.,[[[.,.],[.,.]],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,6,4,7,8]=>[2,3,5,6,1,4,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,6,4,7,8]=>[1,3,5,6,2,4,7,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,6,4,7,8]=>[1,2,5,6,3,4,7,8]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,2,5,6,3,4,7,8]=>[1,2,4,6,5,3,7,8]=>[.,[.,[[.,[[.,.],.]],[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,6,7,4,8]=>[1,3,5,7,2,6,4,8]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,0,0,1,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,6,7,4,8]=>[1,2,5,7,3,6,4,8]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,0,0,1,1,0,1,0,1,0,0,0,0]=>[1,2,5,6,3,7,4,8]=>[1,2,6,7,5,3,4,8]=>[.,[.,[[[.,[.,.]],.],[.,[.,.]]]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,6,7,8,4]=>[2,3,5,8,1,6,7,4]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,6,7,8,4]=>[1,3,5,8,2,6,7,4]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]
[1,1,1,1,0,0,1,1,1,0,0,0,1,0,0,0]=>[1,2,5,3,6,7,8,4]=>[1,2,5,8,3,6,7,4]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,1,1,1,0,0,1,1,1,0,0,1,0,0,0,0]=>[1,2,5,6,3,7,8,4]=>[1,2,6,8,5,3,7,4]=>[.,[.,[[[.,[.,.]],.],[[.,.],.]]]]
[1,1,1,1,0,0,1,1,1,0,1,0,0,0,0,0]=>[1,2,5,6,7,3,8,4]=>[1,2,7,8,5,6,3,4]=>[.,[.,[[[.,[.,.]],[.,.]],[.,.]]]]
[1,1,1,1,0,0,1,1,1,1,0,0,0,0,0,0]=>[1,2,5,6,7,8,3,4]=>[1,2,4,8,5,6,7,3]=>[.,[.,[[.,[[.,.],[.,[.,.]]]],.]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0,1,0]=>[5,1,7,2,8,3,4,6]=>[5,7,4,6,1,8,2,3]=>[[[.,[.,.]],[.,.]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,1,0,0]=>[5,7,1,2,8,3,4,6]=>[2,7,4,6,5,8,1,3]=>[[.,[[.,.],[[.,.],[.,.]]]],[.,.]]
[1,1,1,1,0,1,0,0,0,0,1,1,1,0,0,0]=>[5,7,8,1,2,3,4,6]=>[2,3,4,6,5,8,7,1]=>[[.,[.,[.,[[.,.],[[.,.],.]]]]],.]
[1,1,1,1,0,1,0,0,0,1,0,0,1,1,0,0]=>[5,7,1,2,3,8,4,6]=>[2,3,7,6,5,8,1,4]=>[[.,[.,[[[.,.],.],[.,.]]]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,1,0,0]=>[1,5,2,7,3,8,4,6]=>[1,5,7,6,2,8,3,4]=>[.,[[.,[[.,.],.]],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,1,0,0,0]=>[1,5,7,2,3,8,4,6]=>[1,3,7,6,5,8,2,4]=>[.,[[.,[[[.,.],.],[.,.]]],[.,.]]]
[1,1,1,1,0,1,0,0,0,1,1,0,1,0,0,0]=>[1,5,7,2,8,3,4,6]=>[1,7,4,6,5,8,2,3]=>[.,[[[.,.],[[.,.],[.,.]]],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,1,0,0]=>[5,7,1,2,3,4,8,6]=>[2,3,4,7,5,8,1,6]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,8,6]=>[2,5,4,7,1,8,3,6]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,7,3,4,8,6]=>[1,5,4,7,2,8,3,6]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,7,2,3,4,8,6]=>[1,3,4,7,5,8,2,6]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,2,3,7,4,8,6]=>[1,3,5,7,2,8,4,6]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,1,0,0,0]=>[1,2,5,3,7,4,8,6]=>[1,2,5,7,3,8,4,6]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,1,0,0,0]=>[1,2,5,3,7,8,4,6]=>[1,2,5,6,3,8,7,4]=>[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]
[1,1,1,1,0,1,0,0,1,1,0,1,0,0,0,0]=>[1,2,5,7,3,8,4,6]=>[1,2,7,6,5,8,3,4]=>[.,[.,[[[[.,.],.],[.,.]],[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,1,0,0,0,0,0]=>[1,2,5,7,8,3,4,6]=>[1,2,4,6,5,8,7,3]=>[.,[.,[[.,[[.,.],[[.,.],.]]],.]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,1,0,0]=>[5,7,1,2,3,4,6,8]=>[2,3,4,6,5,7,1,8]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,7,3,4,6,8]=>[2,5,4,6,1,7,3,8]=>[[.,[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,1,0,0]=>[1,5,2,7,3,4,6,8]=>[1,5,4,6,2,7,3,8]=>[.,[[[.,.],[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,1,0,0,0]=>[1,5,7,2,3,4,6,8]=>[1,3,4,6,5,7,2,8]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0,1,0]=>[5,1,2,3,7,4,6,8]=>[2,3,5,6,1,7,4,8]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,1,0,0]=>[1,5,2,3,7,4,6,8]=>[1,3,5,6,2,7,4,8]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,1,0,0,0]=>[1,2,5,3,7,4,6,8]=>[1,2,5,6,3,7,4,8]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,1,0,0,1,1,0,0,0,0]=>[1,2,5,7,3,4,6,8]=>[1,2,4,6,5,7,3,8]=>[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,7,6,8]=>[2,3,4,5,1,7,6,8]=>[[.,[.,[.,[.,.]]]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,7,6,8]=>[1,3,4,5,2,7,6,8]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,7,6,8]=>[1,2,4,5,3,7,6,8]=>[.,[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,7,6,8]=>[1,2,3,5,4,7,6,8]=>[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,1,0,1,0,1,0,1,1,0,0,0,0,0]=>[1,2,3,5,7,4,6,8]=>[1,2,3,6,5,7,4,8]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,7,8,6]=>[2,3,4,5,1,8,7,6]=>[[.,[.,[.,[.,.]]]],[[[.,.],.],.]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,1,0,0]=>[1,5,2,3,4,7,8,6]=>[1,3,4,5,2,8,7,6]=>[.,[[.,[.,[.,.]]],[[[.,.],.],.]]]
[1,1,1,1,0,1,0,1,1,0,0,0,1,0,0,0]=>[1,2,5,3,4,7,8,6]=>[1,2,4,5,3,8,7,6]=>[.,[.,[[.,[.,.]],[[[.,.],.],.]]]]
[1,1,1,1,0,1,0,1,1,0,0,1,0,0,0,0]=>[1,2,3,5,4,7,8,6]=>[1,2,3,5,4,8,7,6]=>[.,[.,[.,[[.,.],[[[.,.],.],.]]]]]
[1,1,1,1,0,1,0,1,1,0,1,0,0,0,0,0]=>[1,2,3,5,7,4,8,6]=>[1,2,3,7,5,8,4,6]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,1,1,1,0,1,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,5,7,8,4,6]=>[1,2,3,6,5,8,7,4]=>[.,[.,[.,[[[.,.],[[.,.],.]],.]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,1,0,0]=>[5,8,1,2,3,4,6,7]=>[2,3,4,6,5,7,8,1]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],.]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0,1,0]=>[5,1,2,8,3,4,6,7]=>[2,5,4,6,1,7,8,3]=>[[.,[[.,.],[.,.]]],[[.,[.,.]],.]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,1,0,0]=>[1,5,2,8,3,4,6,7]=>[1,5,4,6,2,7,8,3]=>[.,[[[.,.],[.,.]],[[.,[.,.]],.]]]
[1,1,1,1,0,1,1,0,0,0,0,1,1,0,0,0]=>[1,5,8,2,3,4,6,7]=>[1,3,4,6,5,7,8,2]=>[.,[[.,[.,[[.,.],[.,[.,.]]]]],.]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0,1,0]=>[5,1,2,3,8,4,6,7]=>[2,3,5,6,1,7,8,4]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,1,1,0,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,5,3,8,4,6,7]=>[1,2,5,6,3,7,8,4]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,8,6,7]=>[2,3,4,5,1,7,8,6]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,1,0,0]=>[1,5,2,3,4,8,6,7]=>[1,3,4,5,2,7,8,6]=>[.,[[.,[.,[.,.]]],[[.,[.,.]],.]]]
[1,1,1,1,0,1,1,0,0,1,0,0,1,0,0,0]=>[1,2,5,3,4,8,6,7]=>[1,2,4,5,3,7,8,6]=>[.,[.,[[.,[.,.]],[[.,[.,.]],.]]]]
[1,1,1,1,0,1,1,0,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,8,6,7]=>[1,2,3,5,4,7,8,6]=>[.,[.,[.,[[.,.],[[.,[.,.]],.]]]]]
[1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0]=>[1,2,3,5,8,4,6,7]=>[1,2,3,6,5,7,8,4]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,8,7]=>[2,3,4,5,1,6,8,7]=>[[.,[.,[.,[.,.]]]],[.,[[.,.],.]]]
[1,1,1,1,0,1,1,0,1,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,8,7]=>[1,2,3,5,4,6,8,7]=>[.,[.,[.,[[.,.],[.,[[.,.],.]]]]]]
[1,1,1,1,0,1,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,5,6,4,8,7]=>[1,2,3,6,5,4,8,7]=>[.,[.,[.,[[[.,.],.],[[.,.],.]]]]]
[1,1,1,1,0,1,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,5,6,8,4,7]=>[1,2,3,7,5,6,8,4]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,7,8]=>[2,3,4,5,1,6,7,8]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0]=>[1,5,2,3,4,6,7,8]=>[1,3,4,5,2,6,7,8]=>[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,5,3,4,6,7,8]=>[1,2,4,5,3,6,7,8]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,7,8]=>[1,2,3,5,4,6,7,8]=>[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,1,1,0,0,1,0,0,0,0,0]=>[1,2,3,5,6,4,7,8]=>[1,2,3,6,5,4,7,8]=>[.,[.,[.,[[[.,.],.],[.,[.,.]]]]]]
[1,1,1,1,0,1,1,1,0,1,0,0,0,0,0,0]=>[1,2,3,5,6,7,4,8]=>[1,2,3,7,5,6,4,8]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,5,6,7,8,4]=>[1,2,3,8,5,6,7,4]=>[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[6,1,7,2,8,3,4,5]=>[6,7,4,5,8,1,2,3]=>[[[.,[.,.]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0,1,0]=>[6,1,7,8,2,3,4,5]=>[6,3,4,5,8,1,7,2]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,1,0,0]=>[6,7,1,8,2,3,4,5]=>[7,3,4,5,8,6,1,2]=>[[[.,.],[.,[.,[[.,.],.]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,0,0,0]=>[6,7,8,1,2,3,4,5]=>[2,3,4,5,8,6,7,1]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]
[1,1,1,1,1,0,0,0,0,1,0,0,1,1,0,0]=>[6,7,1,2,3,8,4,5]=>[2,3,7,5,8,6,1,4]=>[[.,[.,[[.,.],[[.,.],.]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0,1,0]=>[6,1,2,7,3,8,4,5]=>[2,6,7,5,8,1,3,4]=>[[.,[[.,[.,.]],[.,.]]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,0]=>[1,6,2,7,3,8,4,5]=>[1,6,7,5,8,2,3,4]=>[.,[[[.,[.,.]],[.,.]],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,1,0,0,0]=>[1,6,7,2,3,8,4,5]=>[1,3,7,5,8,6,2,4]=>[.,[[.,[[.,.],[[.,.],.]]],[.,.]]]
[1,1,1,1,1,0,0,0,0,1,1,1,0,0,0,0]=>[1,6,7,8,2,3,4,5]=>[1,3,4,5,8,6,7,2]=>[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,8,5]=>[2,3,4,7,8,6,1,5]=>[[.,[.,[.,[[.,[.,.]],.]]]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,1,0,0]=>[1,6,2,7,3,4,8,5]=>[1,6,4,7,8,2,3,5]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0,1,0]=>[6,1,2,3,7,4,8,5]=>[2,3,6,7,8,1,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,1,0,0]=>[1,6,2,3,7,4,8,5]=>[1,3,6,7,8,2,4,5]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,2,6,3,7,4,8,5]=>[1,2,6,7,8,3,4,5]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,1,0,1,1,0,0,0,0]=>[1,2,6,7,3,4,8,5]=>[1,2,4,7,8,6,3,5]=>[.,[.,[[.,[[.,[.,.]],.]],[.,.]]]]
[1,1,1,1,1,0,0,0,1,1,0,0,1,0,0,0]=>[1,2,6,3,7,8,4,5]=>[1,2,6,5,8,3,7,4]=>[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,2,6,7,8,3,4,5]=>[1,2,4,5,8,6,7,3]=>[.,[.,[[.,[.,[[.,.],[.,.]]]],.]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0,1,0]=>[6,1,7,2,3,4,5,8]=>[6,3,4,5,7,1,2,8]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,0,0]=>[6,7,1,2,3,4,5,8]=>[2,3,4,5,7,6,1,8]=>[[.,[.,[.,[.,[[.,.],.]]]]],[.,.]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0,1,0]=>[6,1,2,7,3,4,5,8]=>[2,6,4,5,7,1,3,8]=>[[.,[[.,.],[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,1,0,0]=>[1,6,2,7,3,4,5,8]=>[1,6,4,5,7,2,3,8]=>[.,[[[.,.],[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,1,0,0,0]=>[1,6,7,2,3,4,5,8]=>[1,3,4,5,7,6,2,8]=>[.,[[.,[.,[.,[[.,.],.]]]],[.,.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,6,2,3,7,4,5,8]=>[1,3,6,5,7,2,4,8]=>[.,[[.,[[.,.],[.,.]]],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0,1,0]=>[6,1,2,3,4,7,5,8]=>[2,3,4,6,7,1,5,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,1,0,0]=>[1,6,2,3,4,7,5,8]=>[1,3,4,6,7,2,5,8]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,6,4,7,5,8]=>[1,2,3,6,7,4,5,8]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,2,3,6,7,4,5,8]=>[1,2,3,5,7,6,4,8]=>[.,[.,[.,[[.,[[.,.],.]],[.,.]]]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,7,8,5]=>[2,3,4,6,8,1,7,5]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,1,1,1,0,0,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,7,8,5]=>[1,2,4,6,8,3,7,5]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]
[1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,7,8,5]=>[1,2,3,6,8,4,7,5]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,1,1,1,1,0,0,1,1,0,1,0,0,0,0,0]=>[1,2,3,6,7,4,8,5]=>[1,2,3,7,8,6,4,5]=>[.,[.,[.,[[[.,[.,.]],.],[.,.]]]]]
[1,1,1,1,1,0,0,1,1,1,0,0,0,0,0,0]=>[1,2,3,6,7,8,4,5]=>[1,2,3,5,8,6,7,4]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[6,1,8,2,3,4,5,7]=>[6,3,4,5,7,1,8,2]=>[[[.,.],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[6,8,1,2,3,4,5,7]=>[2,3,4,5,7,6,8,1]=>[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0,1,0]=>[6,1,2,8,3,4,5,7]=>[2,6,4,5,7,1,8,3]=>[[.,[[.,.],[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,1,0,0]=>[1,6,2,8,3,4,5,7]=>[1,6,4,5,7,2,8,3]=>[.,[[[.,.],[.,[.,.]]],[[.,.],.]]]
[1,1,1,1,1,0,1,0,0,0,0,1,1,0,0,0]=>[1,6,8,2,3,4,5,7]=>[1,3,4,5,7,6,8,2]=>[.,[[.,[.,[.,[[.,.],[.,.]]]]],.]]
[1,1,1,1,1,0,1,0,0,0,1,0,1,0,0,0]=>[1,2,6,3,8,4,5,7]=>[1,2,6,5,7,3,8,4]=>[.,[.,[[[.,.],[.,.]],[[.,.],.]]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,3,4,8,5,7]=>[1,3,4,6,7,2,8,5]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]
[1,1,1,1,1,0,1,0,0,1,0,1,0,0,0,0]=>[1,2,3,6,4,8,5,7]=>[1,2,3,6,7,4,8,5]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,0,1,1,0,0,0,0,0]=>[1,2,3,6,8,4,5,7]=>[1,2,3,5,7,6,8,4]=>[.,[.,[.,[[.,[[.,.],[.,.]]],.]]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,8,7]=>[2,3,4,5,6,1,8,7]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,1,0,0]=>[1,6,2,3,4,5,8,7]=>[1,3,4,5,6,2,8,7]=>[.,[[.,[.,[.,[.,.]]]],[[.,.],.]]]
[1,1,1,1,1,0,1,0,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5,8,7]=>[1,2,4,5,6,3,8,7]=>[.,[.,[[.,[.,[.,.]]],[[.,.],.]]]]
[1,1,1,1,1,0,1,0,1,0,0,1,0,0,0,0]=>[1,2,3,6,4,5,8,7]=>[1,2,3,5,6,4,8,7]=>[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,8,7]=>[1,2,3,4,6,5,8,7]=>[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,6,8,5,7]=>[1,2,3,4,7,6,8,5]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7,8]=>[2,3,4,5,6,1,7,8]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,1,0,0]=>[1,6,2,3,4,5,7,8]=>[1,3,4,5,6,2,7,8]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,1,0,0,0]=>[1,2,6,3,4,5,7,8]=>[1,2,4,5,6,3,7,8]=>[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,1,1,1,1,0,1,1,0,0,0,1,0,0,0,0]=>[1,2,3,6,4,5,7,8]=>[1,2,3,5,6,4,7,8]=>[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8]=>[1,2,3,4,6,5,7,8]=>[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]
[1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,6,7,5,8]=>[1,2,3,4,7,6,5,8]=>[.,[.,[.,[.,[[[.,.],.],[.,.]]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,6,7,8,5]=>[1,2,3,4,8,6,7,5]=>[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[7,1,8,2,3,4,5,6]=>[7,3,4,5,6,8,1,2]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,6]=>[2,3,4,5,6,8,7,1]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[7,1,2,8,3,4,5,6]=>[2,7,4,5,6,8,1,3]=>[[.,[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[1,7,2,8,3,4,5,6]=>[1,7,4,5,6,8,2,3]=>[.,[[[.,.],[.,[.,[.,.]]]],[.,.]]]
[1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,7,8,2,3,4,5,6]=>[1,3,4,5,6,8,7,2]=>[.,[[.,[.,[.,[.,[[.,.],.]]]]],.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[7,1,2,3,8,4,5,6]=>[2,3,7,5,6,8,1,4]=>[[.,[.,[[.,.],[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0]=>[1,7,2,3,8,4,5,6]=>[1,3,7,5,6,8,2,4]=>[.,[[.,[[.,.],[.,[.,.]]]],[.,.]]]
[1,1,1,1,1,1,0,0,0,0,1,0,1,0,0,0]=>[1,2,7,3,8,4,5,6]=>[1,2,7,5,6,8,3,4]=>[.,[.,[[[.,.],[.,[.,.]]],[.,.]]]]
[1,1,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,2,7,8,3,4,5,6]=>[1,2,4,5,6,8,7,3]=>[.,[.,[[.,[.,[.,[[.,.],.]]]],.]]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[7,1,2,3,4,8,5,6]=>[2,3,4,7,6,8,1,5]=>[[.,[.,[.,[[.,.],[.,.]]]]],[.,.]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,1,0,0]=>[1,7,2,3,4,8,5,6]=>[1,3,4,7,6,8,2,5]=>[.,[[.,[.,[[.,.],[.,.]]]],[.,.]]]
[1,1,1,1,1,1,0,0,0,1,0,0,1,0,0,0]=>[1,2,7,3,4,8,5,6]=>[1,2,4,7,6,8,3,5]=>[.,[.,[[.,[[.,.],[.,.]]],[.,.]]]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,0,0,0]=>[1,2,3,7,4,8,5,6]=>[1,2,3,7,6,8,4,5]=>[.,[.,[.,[[[.,.],[.,.]],[.,.]]]]]
[1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,2,3,7,8,4,5,6]=>[1,2,3,5,6,8,7,4]=>[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,8,6]=>[2,3,4,5,7,8,1,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,1,0,0]=>[1,7,2,3,4,5,8,6]=>[1,3,4,5,7,8,2,6]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,1,1,1,0,0,1,0,0,0,1,0,0,0]=>[1,2,7,3,4,5,8,6]=>[1,2,4,5,7,8,3,6]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]
[1,1,1,1,1,1,0,0,1,0,0,1,0,0,0,0]=>[1,2,3,7,4,5,8,6]=>[1,2,3,5,7,8,4,6]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,8,6]=>[1,2,3,4,7,8,5,6]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,7,8,5,6]=>[1,2,3,4,6,8,7,5]=>[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,8]=>[2,3,4,5,6,7,1,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,7,2,3,4,5,6,8]=>[1,3,4,5,6,7,2,8]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0]=>[1,2,7,3,4,5,6,8]=>[1,2,4,5,6,7,3,8]=>[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]
[1,1,1,1,1,1,0,1,0,0,0,1,0,0,0,0]=>[1,2,3,7,4,5,6,8]=>[1,2,3,5,6,7,4,8]=>[.,[.,[.,[[.,[.,[.,.]]],[.,.]]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,6,8]=>[1,2,3,4,6,7,5,8]=>[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,7,6,8]=>[1,2,3,4,5,7,6,8]=>[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,7,8,6]=>[1,2,3,4,5,8,7,6]=>[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7]=>[2,3,4,5,6,7,8,1]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,8,2,3,4,5,6,7]=>[1,3,4,5,6,7,8,2]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,2,8,3,4,5,6,7]=>[1,2,4,5,6,7,8,3]=>[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]
[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]=>[1,2,3,4,8,5,6,7]=>[1,2,3,4,6,7,8,5]=>[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,8,6,7]=>[1,2,3,4,5,7,8,6]=>[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,8,7]=>[1,2,3,4,5,6,8,7]=>[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,8]=>[2,3,4,5,6,7,8,9,1]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1]=>[9,2,3,4,5,6,7,8,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[10,1,2,3,4,5,6,7,8,9]=>[2,3,4,5,6,7,8,9,10,1]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7,9]=>[2,3,4,5,6,7,8,1,9]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,1,9]=>[8,2,3,4,5,6,7,1,9]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,1]=>[10,2,3,4,5,6,7,8,9,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0]=>[11,1,2,3,4,5,6,7,8,9,10]=>[2,3,4,5,6,7,8,9,10,11,1]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,8,10]=>[2,3,4,5,6,7,8,9,1,10]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,9,7]=>[2,3,4,5,6,8,9,1,7]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,8,9]=>[2,3,4,5,6,7,1,8,9]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,8,9]=>[7,2,3,4,5,6,1,8,9]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,9,1,8]=>[8,2,3,4,5,6,7,9,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,1,10]=>[9,2,3,4,5,6,7,8,1,10]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,10,11,1]=>[11,2,3,4,5,6,7,8,9,10,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,0,1,0]=>[12,1,2,3,4,5,6,7,8,9,10,11]=>[2,3,4,5,6,7,8,9,10,11,12,1]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,1,0]=>[10,1,2,3,4,5,6,7,8,9,11]=>[2,3,4,5,6,7,8,9,10,1,11]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,10,8]=>[2,3,4,5,6,7,9,10,1,8]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7,9,10]=>[2,3,4,5,6,7,8,1,9,10]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,[.,.]]]
[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,9,8]=>[2,3,4,5,6,7,1,9,8]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7,8,9]=>[2,3,4,5,6,1,7,8,9]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,7,8,9]=>[6,2,3,4,5,1,7,8,9]=>[[[.,.],[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[2,3,4,5,6,7,1,9,8]=>[7,2,3,4,5,6,1,9,8]=>[[[.,.],[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,0,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,8,9,1,7]=>[7,2,3,4,5,6,9,8,1]=>[[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]],.]
[1,0,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,10,1,9]=>[9,2,3,4,5,6,7,8,10,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,1,0]=>[10,1,2,3,4,5,6,7,8,11,9]=>[2,3,4,5,6,7,8,10,11,1,9]=>[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],[.,.]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,7,10,9]=>[2,3,4,5,6,7,8,1,10,9]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,6,8,9,10]=>[2,3,4,5,6,7,1,8,9,10]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,[.,[.,.]]]]
[1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,9,6,8]=>[2,3,4,5,7,8,1,9,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,1,0]=>[7,1,2,3,4,5,8,9,6]=>[2,3,4,5,7,9,1,8,6]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[[.,.],.]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,7,8,9]=>[2,3,4,5,1,6,7,8,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[2,3,4,5,1,6,7,8,9]=>[5,2,3,4,1,6,7,8,9]=>[[[.,.],[.,[.,.]]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0]=>[2,3,4,5,6,8,1,9,7]=>[8,2,3,4,5,6,9,1,7]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,5,7,8,9,1,6]=>[6,2,3,4,5,9,7,8,1]=>[[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]],.]
[1,0,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,9,10,1,8]=>[8,2,3,4,5,6,7,10,9,1]=>[[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]
[1,0,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,8,9,11,1,10]=>[10,2,3,4,5,6,7,8,9,11,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,1,0]=>[9,1,2,3,4,5,6,7,8,11,10]=>[2,3,4,5,6,7,8,9,1,11,10]=>[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],[[.,.],.]]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,1,0]=>[8,1,2,3,4,5,6,10,7,9]=>[2,3,4,5,6,8,9,1,10,7]=>[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[[.,.],.]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,7,8,9,10]=>[2,3,4,5,6,1,7,8,9,10]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,1,0]=>[8,1,2,3,9,4,5,6,7]=>[2,3,8,5,6,7,9,1,4]=>[[.,[.,[[.,.],[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,9,7,8]=>[2,3,4,5,6,1,8,9,7]=>[[.,[.,[.,[.,[.,.]]]]],[[.,[.,.]],.]]
[1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,8,9,7]=>[2,3,4,5,6,1,9,8,7]=>[[.,[.,[.,[.,[.,.]]]]],[[[.,.],.],.]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,7,8,9]=>[2,3,4,1,5,6,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[2,3,4,1,5,6,7,8,9]=>[4,2,3,1,5,6,7,8,9]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0]=>[2,3,4,5,6,1,9,7,8]=>[6,2,3,4,5,1,8,9,7]=>[[[.,.],[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,0,1,1,1,1,1,1,0,1,1,0,1,0,0,0,0,0,0,0]=>[2,3,4,5,6,7,9,1,10,8]=>[9,2,3,4,5,6,7,10,1,8]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,4,6,7,8,9,1,5]=>[5,2,3,4,9,6,7,8,1]=>[[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]],.]
[1,0,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,6,8,9,10,1,7]=>[7,2,3,4,5,6,10,8,9,1]=>[[[.,.],[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0,1,0]=>[9,1,2,3,4,10,5,6,7,8]=>[2,3,4,9,6,7,8,10,1,5]=>[[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]],[.,.]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[5,1,2,3,4,6,7,8,9,10]=>[2,3,4,5,1,6,7,8,9,10]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,8,7,9]=>[2,3,4,5,6,1,8,7,9]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],[.,.]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7,8,9]=>[2,3,1,4,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[8,9,1,2,3,4,5,6,7]=>[2,3,4,5,6,7,9,8,1]=>[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,7,8,9]=>[3,2,1,4,5,6,7,8,9]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,1,2]=>[2,9,3,4,5,6,7,8,1]=>[[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]
[1,0,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,3,5,6,7,8,9,1,4]=>[4,2,3,9,5,6,7,8,1]=>[[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,5,7,8,9,10,1,6]=>[6,2,3,4,5,10,7,8,9,1]=>[[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[4,1,2,3,5,6,7,8,9,10]=>[2,3,4,1,5,6,7,8,9,10]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,1,0]=>[5,1,2,3,4,9,6,7,8]=>[2,3,4,5,1,7,8,9,6]=>[[.,[.,[.,[.,.]]]],[[.,[.,[.,.]]],.]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8,9]=>[2,1,3,4,5,6,7,8,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,1,0,0]=>[7,9,1,2,3,4,5,6,8]=>[2,3,4,5,6,8,7,9,1]=>[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]
[1,1,0,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,9,2]=>[8,9,3,4,5,6,7,1,2]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],[.,.]]
[1,0,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[2,4,5,6,7,8,9,1,3]=>[3,2,9,4,5,6,7,8,1]=>[[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]],.]
[1,0,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,4,6,7,8,9,10,1,5]=>[5,2,3,4,10,6,7,8,9,1]=>[[[.,.],[.,[.,[[.,.],[.,[.,[.,.]]]]]]],.]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7,8,9,10]=>[2,3,1,4,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[9,10,1,2,3,4,5,6,7,8]=>[2,3,4,5,6,7,8,10,9,1]=>[[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]],.]
[1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,9,8]=>[2,1,3,4,5,6,7,9,8]=>[[.,.],[.,[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[2,3,1,4,5,6,7,8,9,10]=>[3,2,1,4,5,6,7,8,9,10]=>[[[.,.],.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,1,0,0]=>[7,8,1,2,3,4,5,6,9]=>[2,3,4,5,6,8,7,1,9]=>[[.,[.,[.,[.,[.,[[.,.],.]]]]]],[.,.]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,1,0,0]=>[6,9,1,2,3,4,5,7,8]=>[2,3,4,5,7,6,8,9,1]=>[[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]
[1,1,0,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[3,4,5,6,7,1,8,9,2]=>[7,9,3,4,5,6,1,8,2]=>[[[.,[.,.]],[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,2,9]=>[2,8,3,4,5,6,7,1,9]=>[[.,[[.,.],[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[2,4,5,6,7,8,1,9,3]=>[8,2,9,4,5,6,7,1,3]=>[[[.,.],[[.,.],[.,[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,10,1,2]=>[2,10,3,4,5,6,7,8,9,1]=>[[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,0,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,3,5,6,7,8,9,10,1,4]=>[4,2,3,10,5,6,7,8,9,1]=>[[[.,.],[.,[[.,.],[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,1,0]=>[9,1,10,2,3,4,5,6,7,8]=>[9,3,4,5,6,7,8,10,1,2]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8,9,10]=>[2,1,3,4,5,6,7,8,9,10]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,1,0]=>[7,1,8,2,3,4,5,6,9]=>[7,3,4,5,6,8,1,2,9]=>[[[.,.],[.,[.,[.,[.,.]]]]],[.,[.,.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,1,0]=>[4,1,2,3,9,5,6,7,8]=>[2,3,4,1,6,7,8,9,5]=>[[.,[.,[.,.]]],[[.,[.,[.,[.,.]]]],.]]
[1,0,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,9,7,8]=>[2,1,3,4,5,6,8,9,7]=>[[.,.],[.,[.,[.,[.,[[.,[.,.]],.]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[5,9,1,2,3,4,6,7,8]=>[2,3,4,6,5,7,8,9,1]=>[[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]],.]
[1,1,0,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[3,4,5,6,7,8,9,1,10,2]=>[9,10,3,4,5,6,7,8,1,2]=>[[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[2,4,5,6,7,8,9,10,1,3]=>[3,2,10,4,5,6,7,8,9,1]=>[[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]],.]
[]=>[]=>[]=>.
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6,9,8]=>[1,3,2,5,4,7,6,9,8]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,5,7,9,2,4,6,8]=>[1,4,3,6,5,8,7,9,2]=>[.,[[[.,.],[[.,.],[[.,.],[.,.]]]],.]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[1,3,9,2,4,5,6,7,8]=>[1,4,3,5,6,7,8,9,2]=>[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7,9,8]=>[1,3,2,4,5,6,7,9,8]=>[.,[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]]
[1,1,0,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0]=>[1,3,4,5,6,7,9,2,8]=>[1,8,3,4,5,6,7,9,2]=>[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7,8,9]=>[1,3,2,4,5,6,7,8,9]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,3,4,2,5,6,7,8,9]=>[1,4,3,2,5,6,7,8,9]=>[.,[[[.,.],.],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,3,4,5,6,7,8,9,2]=>[1,9,3,4,5,6,7,8,2]=>[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,4,2,5,3,7,6,9,8]=>[1,4,5,2,3,7,6,9,8]=>[.,[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,4,2,5,6,7,8,9,3]=>[1,4,9,2,5,6,7,8,3]=>[.,[[.,[.,.]],[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,4,5,6,7,8,9,2,3]=>[1,3,9,4,5,6,7,8,2]=>[.,[[.,[[.,.],[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,8,7,9]=>[1,3,4,2,6,5,8,7,9]=>[.,[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,8,7,9]=>[1,2,4,3,6,5,8,7,9]=>[.,[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,1,1,0,0,0,0]=>[1,2,4,9,3,5,6,7,8]=>[1,2,5,4,6,7,8,9,3]=>[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,7,8,9]=>[1,3,4,2,5,6,7,8,9]=>[.,[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,7,8,9]=>[1,2,4,3,5,6,7,8,9]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,4,5,6,7,8,9,3]=>[1,2,9,4,5,6,7,8,3]=>[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,7,6,9,8]=>[1,2,3,5,4,7,6,9,8]=>[.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,1,0,1,1,1,0,0,0,1,1,0,0,0,0,0]=>[1,2,3,5,9,4,6,7,8]=>[1,2,3,6,5,7,8,9,4]=>[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0]=>[1,5,2,3,4,6,7,8,9]=>[1,3,4,5,2,6,7,8,9]=>[.,[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,7,8,9]=>[1,2,3,5,4,6,7,8,9]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,5,6,7,8,9,4]=>[1,2,3,9,5,6,7,8,4]=>[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,0]=>[1,6,2,7,3,8,4,9,5]=>[1,6,7,8,9,2,3,4,5]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,8,7,9]=>[1,2,3,4,6,5,8,7,9]=>[.,[.,[.,[.,[[.,.],[[.,.],[.,.]]]]]]]
[1,1,1,1,1,0,1,1,0,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,6,9,5,7,8]=>[1,2,3,4,7,6,8,9,5]=>[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,0,0,1,0,0,0]=>[1,2,6,3,4,5,7,8,9]=>[1,2,4,5,6,3,7,8,9]=>[.,[.,[[.,[.,[.,.]]],[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9]=>[1,2,3,4,6,5,7,8,9]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,6,7,8,9,5]=>[1,2,3,4,9,6,7,8,5]=>[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]
[1,1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,7,4,8,5,9,6]=>[1,2,3,7,8,9,4,5,6]=>[.,[.,[.,[[.,[.,[.,.]]],[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,8,6,9]=>[1,2,3,4,7,8,5,6,9]=>[.,[.,[.,[.,[[.,[.,.]],[.,[.,.]]]]]]]
[1,1,1,1,1,1,0,0,1,1,0,0,1,0,0,0,0,0]=>[1,2,3,4,7,5,8,9,6]=>[1,2,3,4,7,9,5,8,6]=>[.,[.,[.,[.,[[.,[.,.]],[[.,.],.]]]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0,0]=>[1,7,9,2,3,4,5,6,8]=>[1,3,4,5,6,8,7,9,2]=>[.,[[.,[.,[.,[.,[[.,.],[.,.]]]]]],.]]
[1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,7,6,9,8]=>[1,2,3,4,5,7,6,9,8]=>[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]
[1,1,1,1,1,1,0,1,0,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,7,9,6,8]=>[1,2,3,4,5,8,7,9,6]=>[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]
[1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0,0]=>[1,7,2,3,4,5,6,8,9]=>[1,3,4,5,6,7,2,8,9]=>[.,[[.,[.,[.,[.,[.,.]]]]],[.,[.,.]]]]
[1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,7,6,8,9]=>[1,2,3,4,5,7,6,8,9]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,7,8,9,6]=>[1,2,3,4,5,9,7,8,6]=>[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0,0]=>[1,8,2,9,3,4,5,6,7]=>[1,8,4,5,6,7,9,2,3]=>[.,[[[.,.],[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0,0]=>[1,8,9,2,3,4,5,6,7]=>[1,3,4,5,6,7,9,8,2]=>[.,[[.,[.,[.,[.,[.,[[.,.],.]]]]]],.]]
[1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0]=>[1,2,3,4,8,9,5,6,7]=>[1,2,3,4,6,7,9,8,5]=>[.,[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]]
[1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0,0]=>[1,8,2,3,4,5,6,9,7]=>[1,3,4,5,6,8,9,2,7]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,8,6,9,7]=>[1,2,3,4,5,8,9,6,7]=>[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,8,9,6,7]=>[1,2,3,4,5,7,9,8,6]=>[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0,0]=>[1,8,2,3,4,5,6,7,9]=>[1,3,4,5,6,7,8,2,9]=>[.,[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]]
[1,1,1,1,1,1,1,0,1,0,0,0,0,1,0,0,0,0]=>[1,2,3,8,4,5,6,7,9]=>[1,2,3,5,6,7,8,4,9]=>[.,[.,[.,[[.,[.,[.,[.,.]]]],[.,.]]]]]
[1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,8,6,7,9]=>[1,2,3,4,5,7,8,6,9]=>[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,8,7,9]=>[1,2,3,4,5,6,8,7,9]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,8,9,7]=>[1,2,3,4,5,6,9,8,7]=>[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,9,2,3,4,5,6,7,8]=>[1,3,4,5,6,7,8,9,2]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,2,9,3,4,5,6,7,8]=>[1,2,4,5,6,7,8,9,3]=>[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,2,3,9,4,5,6,7,8]=>[1,2,3,5,6,7,8,9,4]=>[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]
[1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,2,3,4,9,5,6,7,8]=>[1,2,3,4,6,7,8,9,5]=>[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,9,6,7,8]=>[1,2,3,4,5,7,8,9,6]=>[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,9,7,8]=>[1,2,3,4,5,6,8,9,7]=>[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,9,8]=>[1,2,3,4,5,6,7,9,8]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9]=>[1,2,3,4,5,6,7,8,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,8,7,9]=>[2,1,4,3,6,5,8,7,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5,8,7,9]=>[3,2,4,1,6,5,8,7,9]=>[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5,8,7,9]=>[4,2,5,1,6,3,8,7,9]=>[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,6,3,8,5,7,9]=>[4,2,6,1,7,3,8,5,9]=>[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,1,6,3,8,5,9,7]=>[4,2,6,1,8,3,9,5,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5,9,8]=>[4,2,6,1,7,3,5,9,8]=>[[[.,.],[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,7,6,9,8]=>[4,2,5,1,3,7,6,9,8]=>[[[.,.],[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,7,6,9,8]=>[3,2,1,5,4,7,6,9,8]=>[[[.,.],.],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,8,7,10,9]=>[2,1,4,3,6,5,8,7,10,9]=>[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,4,1,3,6,5,8,7,10,9]=>[3,2,4,1,6,5,8,7,10,9]=>[[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,4,6,1,3,5,8,7,9]=>[3,2,5,4,6,1,8,7,9]=>[[[.,.],[[.,.],[.,.]]],[[.,.],[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,4,1,6,3,5,8,7,10,9]=>[4,2,5,1,6,3,8,7,10,9]=>[[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,4,1,6,8,3,5,7,9]=>[4,2,5,1,7,6,8,3,9]=>[[[.,.],[.,.]],[[[.,.],[.,.]],[.,.]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,4,1,6,3,8,5,7,10,9]=>[4,2,6,1,7,3,8,5,10,9]=>[[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,4,1,6,3,8,9,5,7]=>[4,2,6,1,7,3,9,8,5]=>[[[.,.],[.,.]],[[.,.],[[[.,.],.],.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,1,6,3,8,5,10,7,9]=>[4,2,6,1,8,3,9,5,10,7]=>[[[.,.],[.,.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5,8,9]=>[4,2,6,1,7,3,5,8,9]=>[[[.,.],[.,.]],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,6,3,8,5,9,7,10]=>[4,2,6,1,8,3,9,5,7,10]=>[[[.,.],[.,.]],[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,8,6,9,7]=>[4,2,5,1,3,8,9,6,7]=>[[[.,.],[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,6,3,7,5,9,8,10]=>[4,2,6,1,7,3,5,9,8,10]=>[[[.,.],[.,.]],[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,6,4,7,5,9,8]=>[3,2,1,6,7,4,5,9,8]=>[[[.,.],.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,1,5,3,7,6,9,8,10]=>[4,2,5,1,3,7,6,9,8,10]=>[[[.,.],[.,.]],[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,1,5,4,7,6,9,8,10]=>[3,2,1,5,4,7,6,9,8,10]=>[[[.,.],.],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6,9,8,10]=>[1,3,2,5,4,7,6,9,8,10]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6,9,8,11,10]=>[1,3,2,5,4,7,6,9,8,11,10]=>[.,[[.,.],[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[2,4,1,5,3,6,7,8,9]=>[4,2,5,1,3,6,7,8,9]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,4,6,8,10,1,3,5,7,9]=>[3,2,5,4,7,6,9,8,10,1]=>[[[.,.],[[.,.],[[.,.],[[.,.],[.,.]]]]],.]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,0,1,0,0]=>[2,3,1,9,4,5,6,7,8]=>[3,2,1,5,6,7,8,9,4]=>[[[.,.],.],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,4,2,3,6,5,8,7,10,9]=>[1,3,4,2,6,5,8,7,10,9]=>[.,[[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[2,1,4,3,5,6,7,8,9]=>[2,1,4,3,5,6,7,8,9]=>[[.,.],[[.,.],[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[2,4,1,3,5,6,7,8,9]=>[3,2,4,1,5,6,7,8,9]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,4,5,6,7,8,9,3]=>[2,1,9,4,5,6,7,8,3]=>[[.,.],[[[.,.],[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,5,6,7,8,9,3,4]=>[2,1,4,9,5,6,7,8,3]=>[[.,.],[[.,[[.,.],[.,[.,[.,.]]]]],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[2,1,9,3,4,5,6,7,8]=>[2,1,4,5,6,7,8,9,3]=>[[.,.],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,9,1,3,4,5,6,7,8]=>[3,2,4,5,6,7,8,9,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,8,7,9]=>[3,4,1,2,6,5,8,7,9]=>[[.,[.,.]],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,8,9,2,5,6,7]=>[3,5,1,4,6,7,9,8,2]=>[[.,[.,.]],[[.,[.,[.,[[.,.],.]]]],.]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[3,1,4,2,5,6,7,8,9]=>[3,4,1,2,5,6,7,8,9]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[3,4,1,2,5,6,7,8,9]=>[2,4,3,1,5,6,7,8,9]=>[[.,[[.,.],.]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,9,2]=>[3,9,1,4,5,6,7,8,2]=>[[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,7,8,9]=>[4,5,6,1,2,3,7,8,9]=>[[.,[.,[.,.]]],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,7,8,9]=>[2,3,6,4,5,1,7,8,9]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[4,5,6,7,8,9,1,2,3]=>[2,3,9,4,5,6,7,8,1]=>[[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,8,4,9]=>[5,6,7,8,1,2,3,4,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4,9]=>[2,3,4,8,5,6,7,1,9]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],[.,.]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[5,6,7,8,9,1,2,3,4]=>[2,3,4,9,5,6,7,8,1]=>[[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]],.]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[6,7,8,9,1,2,3,4,5]=>[2,3,4,5,9,6,7,8,1]=>[[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,0,0,0]=>[7,8,9,1,2,3,4,5,6]=>[2,3,4,5,6,9,7,8,1]=>[[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,4,1,3,6,8,5,7,10,9]=>[3,2,4,1,7,6,8,5,10,9]=>[[[.,.],[.,.]],[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,8,10,7,9]=>[2,1,4,3,6,5,9,8,10,7]=>[[.,.],[[.,.],[[.,.],[[[.,.],[.,.]],.]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,9,7,10,8]=>[2,1,4,3,6,5,9,10,7,8]=>[[.,.],[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,9,10,7,8]=>[2,1,4,3,6,5,8,10,9,7]=>[[.,.],[[.,.],[[.,.],[[.,[[.,.],.]],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,6,5,10,7,8,9]=>[2,1,4,3,6,5,8,9,10,7]=>[[.,.],[[.,.],[[.,.],[[.,[.,[.,.]]],.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,7,5,8,6,10,9]=>[2,1,4,3,7,8,5,6,10,9]=>[[.,.],[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,8,5,9,6,10,7]=>[2,1,4,3,8,9,10,5,6,7]=>[[.,.],[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0]=>[2,1,4,3,10,5,6,7,8,9]=>[2,1,4,3,6,7,8,9,10,5]=>[[.,.],[[.,.],[[.,[.,[.,[.,[.,.]]]]],.]]]
[1,0,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[2,4,1,3,5,6,7,8,9,10]=>[3,2,4,1,5,6,7,8,9,10]=>[[[.,.],[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,8,7,10,9]=>[2,1,5,6,3,4,8,7,10,9]=>[[.,.],[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,8,7,10,9]=>[2,1,4,6,5,3,8,7,10,9]=>[[.,.],[[.,[[.,.],.]],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,9,7,10,8]=>[2,1,5,6,3,4,9,10,7,8]=>[[.,.],[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,5,6,3,4,9,10,7,8]=>[2,1,4,6,5,3,8,10,9,7]=>[[.,.],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,6,3,7,4,8,5,10,9]=>[2,1,6,7,8,3,4,5,10,9]=>[[.,.],[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,7,3,8,4,9,5,10,6]=>[2,1,7,8,9,10,3,4,5,6]=>[[.,.],[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,7,8,9,10,1,3,4,5,6]=>[3,2,4,5,6,10,7,8,9,1]=>[[[.,.],[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,1,0]=>[2,1,10,3,4,5,6,7,8,9]=>[2,1,4,5,6,7,8,9,10,3]=>[[.,.],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0]=>[2,10,1,3,4,5,6,7,8,9]=>[3,2,4,5,6,7,8,9,10,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,8,7,10,9]=>[3,4,1,2,6,5,8,7,10,9]=>[[.,[.,.]],[.,[[.,.],[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[3,4,1,2,6,5,8,7,10,9]=>[2,4,3,1,6,5,8,7,10,9]=>[[.,[[.,.],.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[3,4,6,8,10,1,2,5,7,9]=>[2,5,3,4,7,6,9,8,10,1]=>[[.,[[.,.],[.,[[.,.],[[.,.],[.,.]]]]]],.]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,9,7,10,8]=>[3,4,1,2,6,5,9,10,7,8]=>[[.,[.,.]],[.,[[.,.],[[.,[.,.]],[.,.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,8,6,10,9]=>[3,4,1,2,7,8,5,6,10,9]=>[[.,[.,.]],[.,[[.,[.,.]],[.,[[.,.],.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,7,8,5,6,10,9]=>[2,4,3,1,6,8,7,5,10,9]=>[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,8,5,9,6,10,7]=>[3,4,1,2,8,9,10,5,6,7]=>[[.,[.,.]],[.,[[.,[.,[.,.]]],[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,8,9,10,5,6,7]=>[2,4,3,1,6,7,10,8,9,5]=>[[.,[[.,.],.]],[[.,[.,[[.,.],[.,.]]]],.]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,1,0]=>[3,1,4,2,5,6,7,8,9,10]=>[3,4,1,2,5,6,7,8,9,10]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,0,0,1,1,1,1,1,1,0,0,0,0,0,0,1,1,0,0]=>[3,4,1,2,5,6,7,8,9,10]=>[2,4,3,1,5,6,7,8,9,10]=>[[.,[[.,.],.]],[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,9,10,2]=>[3,10,1,4,5,6,7,8,9,2]=>[[.,[.,.]],[[.,[.,[.,[.,[.,[.,.]]]]]],.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,8,7,10,9]=>[4,5,6,1,2,3,8,7,10,9]=>[[.,[.,[.,.]]],[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,9,7,10,8]=>[4,5,6,1,2,3,9,10,7,8]=>[[.,[.,[.,.]]],[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,9,10,7,8]=>[2,3,6,4,5,1,8,10,9,7]=>[[.,[.,[[.,.],[.,.]]]],[[.,[[.,.],.]],.]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,5,6,1,2,3,7,8,9,10]=>[2,3,6,4,5,1,7,8,9,10]=>[[.,[.,[[.,.],[.,.]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[4,5,6,7,8,9,10,1,2,3]=>[2,3,10,4,5,6,7,8,9,1]=>[[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[5,1,6,2,7,3,8,4,10,9]=>[5,6,7,8,1,2,3,4,10,9]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4,10,9]=>[2,3,4,8,5,6,7,1,10,9]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],[[.,.],.]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[5,6,7,8,1,2,3,4,9,10]=>[2,3,4,8,5,6,7,1,9,10]=>[[.,[.,[.,[[.,.],[.,[.,.]]]]]],[.,[.,.]]]
[1,1,1,1,0,0,0,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[5,6,7,8,9,10,1,2,3,4]=>[2,3,4,10,5,6,7,8,9,1]=>[[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[6,1,7,2,8,3,9,4,10,5]=>[6,7,8,9,10,1,2,3,4,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,1,1,1,0,0,0,0,0]=>[6,7,8,9,10,1,2,3,4,5]=>[2,3,4,5,10,6,7,8,9,1]=>[[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0]=>[7,8,9,10,1,2,3,4,5,6]=>[2,3,4,5,6,10,7,8,9,1]=>[[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,1,0,0,0]=>[8,9,10,1,2,3,4,5,6,7]=>[2,3,4,5,6,7,10,8,9,1]=>[[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]],.]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,10]=>[1,2,3,4,5,6,7,8,9,10]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,8,7,9]=>[3,5,1,6,2,4,8,7,9]=>[[.,[.,.]],[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,1,5,2,4,7,6,9,8]=>[3,4,1,5,2,7,6,9,8]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,7,6,9,8]=>[2,3,1,5,4,7,6,9,8]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,8,7,10,9]=>[3,5,1,6,2,4,8,7,10,9]=>[[.,[.,.]],[[.,.],[.,[[.,.],[[.,.],.]]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,8,6,10,9]=>[3,5,1,7,2,8,4,6,10,9]=>[[.,[.,.]],[[.,.],[[.,.],[.,[[.,.],.]]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,7,4,9,6,10,8]=>[3,5,1,7,2,9,4,10,6,8]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,1,2,5,4,7,6,9,8,10]=>[2,3,1,5,4,7,6,9,8,10]=>[[.,[.,.]],[[.,.],[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,9,10,8]=>[1,2,3,4,5,6,7,10,9,8]=>[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,10,8,9]=>[1,2,3,4,5,6,7,9,10,8]=>[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,10,11,9]=>[1,2,3,4,5,6,7,8,11,10,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[[[.,.],.],.]]]]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,9,7,10,8]=>[1,2,3,4,5,6,9,10,7,8]=>[.,[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]]
[1,1,1,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,11,9,10]=>[1,2,3,4,5,6,7,8,10,11,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,[.,.]],.]]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,8,7,9]=>[2,3,4,1,6,5,8,7,9]=>[[.,[.,[.,.]]],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,3,4,5,6,7,8,9,10,2]=>[1,10,3,4,5,6,7,8,9,2]=>[.,[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0,0]=>[1,10,2,3,4,5,6,7,8,9]=>[1,3,4,5,6,7,8,9,10,2]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]],.]]
[1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,11,2,3,4,5,6,7,8,9,10]=>[1,3,4,5,6,7,8,9,10,11,2]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]]
[1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0,0]=>[1,9,2,3,4,5,6,7,8,10]=>[1,3,4,5,6,7,8,9,2,10]=>[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],[.,.]]]
[1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,10,9]=>[1,2,3,4,5,6,7,8,10,9]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,8,9,10,7]=>[1,2,3,4,5,6,10,8,9,7]=>[.,[.,[.,[.,[.,[.,[[[.,.],[.,.]],.]]]]]]]
[1,1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,7,8,9,10,6]=>[1,2,3,4,5,10,7,8,9,6]=>[.,[.,[.,[.,[.,[[[.,.],[.,[.,.]]],.]]]]]]
[1,1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,6,7,8,9,10,5]=>[1,2,3,4,10,6,7,8,9,5]=>[.,[.,[.,[.,[[[.,.],[.,[.,[.,.]]]],.]]]]]
[1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,5,6,7,8,9,10,4]=>[1,2,3,10,5,6,7,8,9,4]=>[.,[.,[.,[[[.,.],[.,[.,[.,[.,.]]]]],.]]]]
[1,1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]=>[1,2,4,5,6,7,8,9,10,3]=>[1,2,10,4,5,6,7,8,9,3]=>[.,[.,[[[.,.],[.,[.,[.,[.,[.,.]]]]]],.]]]
[1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,1,2,4,6,5,8,7,9]=>[2,3,1,4,6,5,8,7,9]=>[[.,[.,.]],[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,9,11,10]=>[1,2,3,4,5,6,7,8,9,11,10]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6,10,8,9]=>[1,3,2,5,4,7,6,9,10,8]=>[.,[[.,.],[[.,.],[[.,.],[[.,[.,.]],.]]]]]
[1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,7,6,9,8,10]=>[1,2,3,5,4,7,6,9,8,10]=>[.,[.,[.,[[.,.],[[.,.],[[.,.],[.,.]]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0,0]=>[1,2,10,3,4,5,6,7,8,9]=>[1,2,4,5,6,7,8,9,10,3]=>[.,[.,[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0,0]=>[1,2,3,10,4,5,6,7,8,9]=>[1,2,3,5,6,7,8,9,10,4]=>[.,[.,[.,[[.,[.,[.,[.,[.,[.,.]]]]]],.]]]]
[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]=>[.,[.,[.,[.,[[.,[.,[.,[.,[.,.]]]]],.]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,10,6,7,8,9]=>[1,2,3,4,5,7,8,9,10,6]=>[.,[.,[.,[.,[.,[[.,[.,[.,[.,.]]]],.]]]]]]
[1,1,1,1,1,1,1,1,1,0,0,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,10,7,8,9]=>[1,2,3,4,5,6,8,9,10,7]=>[.,[.,[.,[.,[.,[.,[[.,[.,[.,.]]],.]]]]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,4,3,7,5,9,6,10,8]=>[2,1,4,3,7,9,5,10,6,8]=>[[.,.],[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,9,6,10,8]=>[2,1,5,7,3,9,4,10,6,8]=>[[.,.],[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,3,2,5,4,7,6,9,10,8]=>[1,3,2,5,4,7,6,10,9,8]=>[.,[[.,.],[[.,.],[[.,.],[[[.,.],.],.]]]]]
[1,1,0,1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,3,5,7,9,10,2,4,6,8]=>[1,4,3,6,5,8,7,10,9,2]=>[.,[[[.,.],[[.,.],[[.,.],[[.,.],.]]]],.]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,2,4,3,6,5,8,7,10,9]=>[1,2,4,3,6,5,8,7,10,9]=>[.,[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,1,1,1,1,1,0,0,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,9,10,7,8]=>[1,2,3,4,5,6,8,10,9,7]=>[.,[.,[.,[.,[.,[.,[[.,[[.,.],.]],.]]]]]]]
[1,1,1,1,1,1,1,1,0,0,0,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,9,10,6,7,8]=>[1,2,3,4,5,7,8,10,9,6]=>[.,[.,[.,[.,[.,[[.,[.,[[.,.],.]]],.]]]]]]
[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]=>[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,1,2,3,6,5,8,7,10,9]=>[2,3,4,1,6,5,8,7,10,9]=>[[.,[.,[.,.]]],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,5,8,7,10,9]=>[2,3,4,5,6,1,8,7,10,9]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],[[.,.],.]]]
[1,1,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0,1,0,0]=>[1,12,2,3,4,5,6,7,8,9,10,11]=>[1,3,4,5,6,7,8,9,10,11,12,2]=>[.,[[.,[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]],.]]
[1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,1,0,0]=>[10,11,1,2,3,4,5,6,7,8,9]=>[2,3,4,5,6,7,8,9,11,10,1]=>[[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]],.]
[1,1,1,1,1,0,1,0,1,0,1,0,1,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,8,7,10,9]=>[1,2,3,4,6,5,8,7,10,9]=>[.,[.,[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]]
[1,1,1,0,0,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,1,8,2,9,3]=>[7,8,9,4,5,6,1,2,3]=>[[[.,[.,[.,.]]],[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,1,1,1,1,0,1,0,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,9,7,8,10]=>[1,2,3,4,5,6,8,9,7,10]=>[.,[.,[.,[.,[.,[.,[[.,[.,.]],[.,.]]]]]]]]
[1,0,1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0]=>[2,4,5,6,7,8,9,1,10,3]=>[9,2,10,4,5,6,7,8,1,3]=>[[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,9,8,10]=>[1,2,3,4,5,6,7,9,8,10]=>[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]
[1,1,1,1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8,10,9,11]=>[1,2,3,4,5,6,7,8,10,9,11]=>[.,[.,[.,[.,[.,[.,[.,[.,[[.,.],[.,.]]]]]]]]]]
[1,1,1,1,1,1,1,0,1,0,1,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,8,7,10,9]=>[1,2,3,4,5,6,8,7,10,9]=>[.,[.,[.,[.,[.,[.,[[.,.],[[.,.],.]]]]]]]]
[1,1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[3,1,2,4,5,6,7,8,9,10,11]=>[2,3,1,4,5,6,7,8,9,10,11]=>[[.,[.,.]],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,2,9]=>[3,8,1,4,5,6,7,2,9]=>[[.,[.,.]],[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,1,0,0,0]=>[1,9,10,2,3,4,5,6,7,8]=>[1,3,4,5,6,7,8,10,9,2]=>[.,[[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]],.]]
[1,1,1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,0,0]=>[1,2,3,5,4,6,7,8,9,10]=>[1,2,3,5,4,6,7,8,9,10]=>[.,[.,[.,[[.,.],[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,2,6,3,4,5,7,8,9,10]=>[1,2,4,5,6,3,7,8,9,10]=>[.,[.,[[.,[.,[.,.]]],[.,[.,[.,[.,.]]]]]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,6,2,8,3,9,5,10,7]=>[4,6,8,1,9,2,10,3,5,7]=>[[.,[.,[.,.]]],[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,6,2,7,3,8,5,10,9]=>[4,6,7,1,8,2,3,5,10,9]=>[[.,[.,[.,.]]],[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,7,4,8,6,10,9]=>[2,1,5,7,3,8,4,6,10,9]=>[[.,.],[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,1,1,0,0,0]=>[6,7,9,1,2,3,4,5,8]=>[2,3,4,5,8,6,7,9,1]=>[[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]],.]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,7,5,9,6,10,8]=>[3,4,1,2,7,9,5,10,6,8]=>[[.,[.,.]],[.,[[.,[.,.]],[[.,.],[.,.]]]]]
[1,0,1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8,9,10,11]=>[2,1,3,4,5,6,7,8,9,10,11]=>[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,1,1,0,0,0]=>[2,3,9,1,4,5,6,7,8]=>[4,2,3,5,6,7,8,9,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]],.]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,6,2,7,4,8,5,10,9]=>[3,6,1,7,8,2,4,5,10,9]=>[[.,[.,.]],[[.,[.,.]],[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,7,3,8,6,10,9]=>[4,5,7,1,2,8,3,6,10,9]=>[[.,[.,[.,.]]],[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,1,0,0]=>[2,8,1,3,4,5,6,7,9]=>[3,2,4,5,6,7,8,1,9]=>[[[.,.],[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0,1,0]=>[2,1,8,3,4,5,6,7,9]=>[2,1,4,5,6,7,8,3,9]=>[[.,.],[[.,[.,[.,[.,[.,.]]]]],[.,.]]]
[1,1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,3,2,4,5,6,7,8,9,10]=>[1,3,2,4,5,6,7,8,9,10]=>[.,[[.,.],[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,5,2,6,3,8,7,10,9,12,11]=>[4,5,6,1,2,3,8,7,10,9,12,11]=>[[.,[.,[.,.]]],[.,[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[3,4,1,2,7,8,5,6,11,12,9,10]=>[2,4,3,1,6,8,7,5,10,12,11,9]=>[[.,[[.,.],.]],[[.,[[.,.],.]],[[.,[[.,.],.]],.]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0,0]=>[1,4,2,3,5,6,7,8,9,10]=>[1,3,4,2,5,6,7,8,9,10]=>[.,[[.,[.,.]],[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,1,1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,8,7,9,10]=>[1,2,3,4,5,6,8,7,9,10]=>[.,[.,[.,[.,[.,[.,[[.,.],[.,[.,.]]]]]]]]]
[1,1,1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0,0,0]=>[1,2,3,4,5,7,6,8,9,10]=>[1,2,3,4,5,7,6,8,9,10]=>[.,[.,[.,[.,[.,[[.,.],[.,[.,[.,.]]]]]]]]]
[1,1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0,0,0]=>[1,2,3,4,6,5,7,8,9,10]=>[1,2,3,4,6,5,7,8,9,10]=>[.,[.,[.,[.,[[.,.],[.,[.,[.,[.,.]]]]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]=>[3,1,4,5,6,7,8,9,10,11,2]=>[3,11,1,4,5,6,7,8,9,10,2]=>[[.,[.,.]],[[.,[.,[.,[.,[.,[.,[.,.]]]]]]],.]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,5,3,6,4,8,7,10,9,12,11]=>[2,1,5,6,3,4,8,7,10,9,12,11]=>[[.,.],[[.,[.,.]],[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[1,0,1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,7,8,10,9]=>[2,1,3,4,5,6,7,8,10,9]=>[[.,.],[.,[.,[.,[.,[.,[.,[[.,.],.]]]]]]]]
[1,1,1,0,1,1,1,0,1,1,1,0,0,1,0,0,0,1,0,0,0,1,0,0]=>[1,4,2,3,5,8,6,7,9,12,10,11]=>[1,3,4,2,5,7,8,6,9,11,12,10]=>[.,[[.,[.,.]],[.,[[.,[.,.]],[.,[[.,[.,.]],.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,5,2,6,4,8,7,10,9,12,11]=>[3,5,1,6,2,4,8,7,10,9,12,11]=>[[.,[.,.]],[[.,.],[.,[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0,1,0]=>[3,1,2,9,4,5,6,7,8]=>[2,3,1,5,6,7,8,9,4]=>[[.,[.,.]],[[.,[.,[.,[.,[.,.]]]]],.]]
[1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,1,0,0]=>[2,11,1,3,4,5,6,7,8,9,10]=>[3,2,4,5,6,7,8,9,10,11,1]=>[[[.,.],[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]],.]
[1,1,0,1,1,0,1,1,1,1,1,0,0,0,0,1,0,0,1,0,0,1,0,0]=>[1,3,2,4,6,5,7,12,8,9,10,11]=>[1,3,2,4,6,5,7,9,10,11,12,8]=>[.,[[.,.],[.,[[.,.],[.,[[.,[.,[.,[.,.]]]],.]]]]]]
[1,1,0,0,1,1,1,1,1,1,1,0,0,1,0,0,0,0,0,0]=>[3,4,5,6,7,8,1,9,10,2]=>[8,10,3,4,5,6,7,1,9,2]=>[[[.,[.,.]],[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,1,1,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0,0]=>[1,2,3,5,4,10,6,7,8,9]=>[1,2,3,5,4,7,8,9,10,6]=>[.,[.,[.,[[.,.],[[.,[.,[.,[.,.]]]],.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[3,1,4,2,6,5,8,7,10,9,12,11]=>[3,4,1,2,6,5,8,7,10,9,12,11]=>[[.,[.,.]],[.,[[.,.],[[.,.],[[.,.],[[.,.],.]]]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0,1,0,1,0,1,0]=>[4,1,7,2,8,3,9,5,10,6]=>[4,7,8,1,9,10,2,3,5,6]=>[[.,[.,[.,.]]],[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0,0,0]=>[1,2,4,3,5,6,7,8,9,10]=>[1,2,4,3,5,6,7,8,9,10]=>[.,[.,[[.,.],[.,[.,[.,[.,[.,[.,.]]]]]]]]]
Map
to 321-avoiding permutation
Description
Sends a Dyck path to a 321-avoiding permutation.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
This bijection defined in [3, pp. 60] and in [2, Section 3.1].
It is shown in [1] that it sends the number of centered tunnels to the number of fixed points, the number of right tunnels to the number of exceedences, and the semilength plus the height of the middle point to 2 times the length of the longest increasing subsequence.
Map
first fundamental transformation
Description
Return the permutation whose cycles are the subsequences between successive left to right maxima.
Map
to increasing tree
Description
Sends a permutation to its associated increasing tree.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
This tree is recursively obtained by sending the unique permutation of length $0$ to the empty tree, and sending a permutation $\sigma$ of length $n \geq 1$ to a root node with two subtrees $L$ and $R$ by splitting $\sigma$ at the index $\sigma^{-1}(1)$, normalizing both sides again to permutations and sending the permutations on the left and on the right of $\sigma^{-1}(1)$ to the trees $L$ and $R$, respectively.
searching the database
Sorry, this map was not found in the database.