Identifier
Mp00031:
Dyck paths
—to 312-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]=>[1,2]=>[1,2]=>[.,[.,.]]
[1,1,0,0]=>[2,1]=>[2,1]=>[[.,.],.]
[1,0,1,0,1,0]=>[1,2,3]=>[1,2,3]=>[.,[.,[.,.]]]
[1,0,1,1,0,0]=>[1,3,2]=>[1,3,2]=>[.,[[.,.],.]]
[1,1,0,0,1,0]=>[2,1,3]=>[2,1,3]=>[[.,.],[.,.]]
[1,1,0,1,0,0]=>[2,3,1]=>[3,2,1]=>[[[.,.],.],.]
[1,1,1,0,0,0]=>[3,2,1]=>[3,1,2]=>[[.,.],[.,.]]
[1,0,1,0,1,0,1,0]=>[1,2,3,4]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0]=>[1,2,4,3]=>[1,2,4,3]=>[.,[.,[[.,.],.]]]
[1,0,1,1,0,0,1,0]=>[1,3,2,4]=>[1,3,2,4]=>[.,[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0]=>[1,3,4,2]=>[1,4,3,2]=>[.,[[[.,.],.],.]]
[1,0,1,1,1,0,0,0]=>[1,4,3,2]=>[1,4,2,3]=>[.,[[.,.],[.,.]]]
[1,1,0,0,1,0,1,0]=>[2,1,3,4]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[1,1,0,0,1,1,0,0]=>[2,1,4,3]=>[2,1,4,3]=>[[.,.],[[.,.],.]]
[1,1,0,1,0,0,1,0]=>[2,3,1,4]=>[3,2,1,4]=>[[[.,.],.],[.,.]]
[1,1,0,1,0,1,0,0]=>[2,3,4,1]=>[4,2,3,1]=>[[[.,.],[.,.]],.]
[1,1,0,1,1,0,0,0]=>[2,4,3,1]=>[4,2,1,3]=>[[[.,.],.],[.,.]]
[1,1,1,0,0,0,1,0]=>[3,2,1,4]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[1,1,1,0,0,1,0,0]=>[3,2,4,1]=>[4,3,2,1]=>[[[[.,.],.],.],.]
[1,1,1,0,1,0,0,0]=>[3,4,2,1]=>[4,1,3,2]=>[[.,.],[[.,.],.]]
[1,1,1,1,0,0,0,0]=>[4,3,2,1]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0]=>[1,2,3,5,4]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]
[1,0,1,0,1,1,0,0,1,0]=>[1,2,4,3,5]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]
[1,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,3]=>[1,2,5,4,3]=>[.,[.,[[[.,.],.],.]]]
[1,0,1,0,1,1,1,0,0,0]=>[1,2,5,4,3]=>[1,2,5,3,4]=>[.,[.,[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,0,1,0]=>[1,3,2,4,5]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]
[1,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,5]=>[1,4,3,2,5]=>[.,[[[.,.],.],[.,.]]]
[1,0,1,1,0,1,0,1,0,0]=>[1,3,4,5,2]=>[1,5,3,4,2]=>[.,[[[.,.],[.,.]],.]]
[1,0,1,1,0,1,1,0,0,0]=>[1,3,5,4,2]=>[1,5,3,2,4]=>[.,[[[.,.],.],[.,.]]]
[1,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,5]=>[1,4,2,3,5]=>[.,[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,0]=>[1,4,3,5,2]=>[1,5,4,3,2]=>[.,[[[[.,.],.],.],.]]
[1,0,1,1,1,0,1,0,0,0]=>[1,4,5,3,2]=>[1,5,2,4,3]=>[.,[[.,.],[[.,.],.]]]
[1,0,1,1,1,1,0,0,0,0]=>[1,5,4,3,2]=>[1,5,2,3,4]=>[.,[[.,.],[.,[.,.]]]]
[1,1,0,0,1,0,1,0,1,0]=>[2,1,3,4,5]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,0,0,1,0,1,1,0,0]=>[2,1,3,5,4]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,5]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]
[1,1,0,0,1,1,0,1,0,0]=>[2,1,4,5,3]=>[2,1,5,4,3]=>[[.,.],[[[.,.],.],.]]
[1,1,0,0,1,1,1,0,0,0]=>[2,1,5,4,3]=>[2,1,5,3,4]=>[[.,.],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,0,1,0]=>[2,3,1,4,5]=>[3,2,1,4,5]=>[[[.,.],.],[.,[.,.]]]
[1,1,0,1,0,0,1,1,0,0]=>[2,3,1,5,4]=>[3,2,1,5,4]=>[[[.,.],.],[[.,.],.]]
[1,1,0,1,0,1,0,0,1,0]=>[2,3,4,1,5]=>[4,2,3,1,5]=>[[[.,.],[.,.]],[.,.]]
[1,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,1]=>[5,2,3,4,1]=>[[[.,.],[.,[.,.]]],.]
[1,1,0,1,0,1,1,0,0,0]=>[2,3,5,4,1]=>[5,2,3,1,4]=>[[[.,.],[.,.]],[.,.]]
[1,1,0,1,1,0,0,0,1,0]=>[2,4,3,1,5]=>[4,2,1,3,5]=>[[[.,.],.],[.,[.,.]]]
[1,1,0,1,1,0,0,1,0,0]=>[2,4,3,5,1]=>[5,2,4,3,1]=>[[[.,.],[[.,.],.]],.]
[1,1,0,1,1,0,1,0,0,0]=>[2,4,5,3,1]=>[5,2,1,4,3]=>[[[.,.],.],[[.,.],.]]
[1,1,0,1,1,1,0,0,0,0]=>[2,5,4,3,1]=>[5,2,1,3,4]=>[[[.,.],.],[.,[.,.]]]
[1,1,1,0,0,0,1,0,1,0]=>[3,2,1,4,5]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,1,0,0]=>[3,2,1,5,4]=>[3,1,2,5,4]=>[[.,.],[.,[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,0]=>[3,2,4,1,5]=>[4,3,2,1,5]=>[[[[.,.],.],.],[.,.]]
[1,1,1,0,0,1,0,1,0,0]=>[3,2,4,5,1]=>[5,3,2,4,1]=>[[[[.,.],.],[.,.]],.]
[1,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,1]=>[5,3,2,1,4]=>[[[[.,.],.],.],[.,.]]
[1,1,1,0,1,0,0,0,1,0]=>[3,4,2,1,5]=>[4,1,3,2,5]=>[[.,.],[[.,.],[.,.]]]
[1,1,1,0,1,0,0,1,0,0]=>[3,4,2,5,1]=>[5,4,3,2,1]=>[[[[[.,.],.],.],.],.]
[1,1,1,0,1,0,1,0,0,0]=>[3,4,5,2,1]=>[5,1,3,4,2]=>[[.,.],[[.,[.,.]],.]]
[1,1,1,0,1,1,0,0,0,0]=>[3,5,4,2,1]=>[5,1,3,2,4]=>[[.,.],[[.,.],[.,.]]]
[1,1,1,1,0,0,0,0,1,0]=>[4,3,2,1,5]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,1,1,0,0,0,1,0,0]=>[4,3,2,5,1]=>[5,4,2,3,1]=>[[[[.,.],.],[.,.]],.]
[1,1,1,1,0,0,1,0,0,0]=>[4,3,5,2,1]=>[5,1,4,3,2]=>[[.,.],[[[.,.],.],.]]
[1,1,1,1,0,1,0,0,0,0]=>[4,5,3,2,1]=>[5,1,2,4,3]=>[[.,.],[.,[[.,.],.]]]
[1,1,1,1,1,0,0,0,0,0]=>[5,4,3,2,1]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,6,5]=>[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,5,4,6]=>[1,2,3,5,4,6]=>[.,[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,5,6,4]=>[1,2,3,6,5,4]=>[.,[.,[.,[[[.,.],.],.]]]]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,6,5,4]=>[1,2,3,6,4,5]=>[.,[.,[.,[[.,.],[.,.]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,5,6]=>[1,2,4,3,5,6]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5]=>[1,2,4,3,6,5]=>[.,[.,[[.,.],[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,4,5,3,6]=>[1,2,5,4,3,6]=>[.,[.,[[[.,.],.],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,4,5,6,3]=>[1,2,6,4,5,3]=>[.,[.,[[[.,.],[.,.]],.]]]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,5,3]=>[1,2,6,4,3,5]=>[.,[.,[[[.,.],.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,5,4,3,6]=>[1,2,5,3,4,6]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,5,4,6,3]=>[1,2,6,5,4,3]=>[.,[.,[[[[.,.],.],.],.]]]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,5,6,4,3]=>[1,2,6,3,5,4]=>[.,[.,[[.,.],[[.,.],.]]]]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,6,5,4,3]=>[1,2,6,3,4,5]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,4,5,6]=>[1,3,2,4,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,4,6,5]=>[1,3,2,4,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,6]=>[1,3,2,5,4,6]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,6,4]=>[1,3,2,6,5,4]=>[.,[[.,.],[[[.,.],.],.]]]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,6,5,4]=>[1,3,2,6,4,5]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,4,2,5,6]=>[1,4,3,2,5,6]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,4,2,6,5]=>[1,4,3,2,6,5]=>[.,[[[.,.],.],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,2,6]=>[1,5,3,4,2,6]=>[.,[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,2]=>[1,6,3,4,5,2]=>[.,[[[.,.],[.,[.,.]]],.]]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,4,6,5,2]=>[1,6,3,4,2,5]=>[.,[[[.,.],[.,.]],[.,.]]]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,4,2,6]=>[1,5,3,2,4,6]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,4,6,2]=>[1,6,3,5,4,2]=>[.,[[[.,.],[[.,.],.]],.]]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,6,4,2]=>[1,6,3,2,5,4]=>[.,[[[.,.],.],[[.,.],.]]]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,6,5,4,2]=>[1,6,3,2,4,5]=>[.,[[[.,.],.],[.,[.,.]]]]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,4,3,2,5,6]=>[1,4,2,3,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,4,3,2,6,5]=>[1,4,2,3,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,4,3,5,2,6]=>[1,5,4,3,2,6]=>[.,[[[[.,.],.],.],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,4,3,5,6,2]=>[1,6,4,3,5,2]=>[.,[[[[.,.],.],[.,.]],.]]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,4,3,6,5,2]=>[1,6,4,3,2,5]=>[.,[[[[.,.],.],.],[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,4,5,3,2,6]=>[1,5,2,4,3,6]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,4,5,3,6,2]=>[1,6,5,4,3,2]=>[.,[[[[[.,.],.],.],.],.]]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,4,5,6,3,2]=>[1,6,2,4,5,3]=>[.,[[.,.],[[.,[.,.]],.]]]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,4,6,5,3,2]=>[1,6,2,4,3,5]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,5,4,3,2,6]=>[1,5,2,3,4,6]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,5,4,3,6,2]=>[1,6,5,3,4,2]=>[.,[[[[.,.],.],[.,.]],.]]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,5,4,6,3,2]=>[1,6,2,5,4,3]=>[.,[[.,.],[[[.,.],.],.]]]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,5,6,4,3,2]=>[1,6,2,3,5,4]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,6,5,4,3,2]=>[1,6,2,3,4,5]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,6,5]=>[2,1,3,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,3,5,4,6]=>[2,1,3,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,3,5,6,4]=>[2,1,3,6,5,4]=>[[.,.],[.,[[[.,.],.],.]]]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,3,6,5,4]=>[2,1,3,6,4,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,5,6]=>[2,1,4,3,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5]=>[2,1,4,3,6,5]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,5,3,6]=>[2,1,5,4,3,6]=>[[.,.],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,5,6,3]=>[2,1,6,4,5,3]=>[[.,.],[[[.,.],[.,.]],.]]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,5,3]=>[2,1,6,4,3,5]=>[[.,.],[[[.,.],.],[.,.]]]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,5,4,3,6]=>[2,1,5,3,4,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,5,4,6,3]=>[2,1,6,5,4,3]=>[[.,.],[[[[.,.],.],.],.]]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,5,6,4,3]=>[2,1,6,3,5,4]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,6,5,4,3]=>[2,1,6,3,4,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,1,4,5,6]=>[3,2,1,4,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,1,4,6,5]=>[3,2,1,4,6,5]=>[[[.,.],.],[.,[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,6]=>[3,2,1,5,4,6]=>[[[.,.],.],[[.,.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,6,4]=>[3,2,1,6,5,4]=>[[[.,.],.],[[[.,.],.],.]]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,1,6,5,4]=>[3,2,1,6,4,5]=>[[[.,.],.],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,1,5,6]=>[4,2,3,1,5,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,1,6,5]=>[4,2,3,1,6,5]=>[[[.,.],[.,.]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,1,6]=>[5,2,3,4,1,6]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,1]=>[6,2,3,4,5,1]=>[[[.,.],[.,[.,[.,.]]]],.]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,6,5,1]=>[6,2,3,4,1,5]=>[[[.,.],[.,[.,.]]],[.,.]]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,5,4,1,6]=>[5,2,3,1,4,6]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,5,4,6,1]=>[6,2,3,5,4,1]=>[[[.,.],[.,[[.,.],.]]],.]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,5,6,4,1]=>[6,2,3,1,5,4]=>[[[.,.],[.,.]],[[.,.],.]]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,6,5,4,1]=>[6,2,3,1,4,5]=>[[[.,.],[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,3,1,5,6]=>[4,2,1,3,5,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,3,1,6,5]=>[4,2,1,3,6,5]=>[[[.,.],.],[.,[[.,.],.]]]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,3,5,1,6]=>[5,2,4,3,1,6]=>[[[.,.],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,3,5,6,1]=>[6,2,4,3,5,1]=>[[[.,.],[[.,.],[.,.]]],.]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,3,6,5,1]=>[6,2,4,3,1,5]=>[[[.,.],[[.,.],.]],[.,.]]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,5,3,1,6]=>[5,2,1,4,3,6]=>[[[.,.],.],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,5,3,6,1]=>[6,2,5,4,3,1]=>[[[.,.],[[[.,.],.],.]],.]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,5,6,3,1]=>[6,2,1,4,5,3]=>[[[.,.],.],[[.,[.,.]],.]]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,5,3,1]=>[6,2,1,4,3,5]=>[[[.,.],.],[[.,.],[.,.]]]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[2,5,4,3,1,6]=>[5,2,1,3,4,6]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[2,5,4,3,6,1]=>[6,2,5,3,4,1]=>[[[.,.],[[.,.],[.,.]]],.]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[2,5,4,6,3,1]=>[6,2,1,5,4,3]=>[[[.,.],.],[[[.,.],.],.]]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[2,5,6,4,3,1]=>[6,2,1,3,5,4]=>[[[.,.],.],[.,[[.,.],.]]]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[2,6,5,4,3,1]=>[6,2,1,3,4,5]=>[[[.,.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[3,2,1,4,5,6]=>[3,1,2,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[3,2,1,4,6,5]=>[3,1,2,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[3,2,1,5,4,6]=>[3,1,2,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[3,2,1,5,6,4]=>[3,1,2,6,5,4]=>[[.,.],[.,[[[.,.],.],.]]]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[3,2,1,6,5,4]=>[3,1,2,6,4,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[3,2,4,1,5,6]=>[4,3,2,1,5,6]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[3,2,4,1,6,5]=>[4,3,2,1,6,5]=>[[[[.,.],.],.],[[.,.],.]]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[3,2,4,5,1,6]=>[5,3,2,4,1,6]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,1]=>[6,3,2,4,5,1]=>[[[[.,.],.],[.,[.,.]]],.]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[3,2,4,6,5,1]=>[6,3,2,4,1,5]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[3,2,5,4,1,6]=>[5,3,2,1,4,6]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[3,2,5,4,6,1]=>[6,3,2,5,4,1]=>[[[[.,.],.],[[.,.],.]],.]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[3,2,5,6,4,1]=>[6,3,2,1,5,4]=>[[[[.,.],.],.],[[.,.],.]]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[3,2,6,5,4,1]=>[6,3,2,1,4,5]=>[[[[.,.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[3,4,2,1,5,6]=>[4,1,3,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[3,4,2,1,6,5]=>[4,1,3,2,6,5]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[3,4,2,5,1,6]=>[5,4,3,2,1,6]=>[[[[[.,.],.],.],.],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[3,4,2,5,6,1]=>[6,4,3,2,5,1]=>[[[[[.,.],.],.],[.,.]],.]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[3,4,2,6,5,1]=>[6,4,3,2,1,5]=>[[[[[.,.],.],.],.],[.,.]]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,2,1,6]=>[5,1,3,4,2,6]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,2,6,1]=>[6,5,3,4,2,1]=>[[[[[.,.],.],[.,.]],.],.]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,2,1]=>[6,1,3,4,5,2]=>[[.,.],[[.,[.,[.,.]]],.]]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[3,4,6,5,2,1]=>[6,1,3,4,2,5]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,4,2,1,6]=>[5,1,3,2,4,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,4,2,6,1]=>[6,5,3,2,4,1]=>[[[[[.,.],.],.],[.,.]],.]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,4,6,2,1]=>[6,1,3,5,4,2]=>[[.,.],[[.,[[.,.],.]],.]]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,6,4,2,1]=>[6,1,3,2,5,4]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[3,6,5,4,2,1]=>[6,1,3,2,4,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[4,3,2,1,5,6]=>[4,1,2,3,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[4,3,2,1,6,5]=>[4,1,2,3,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[4,3,2,5,1,6]=>[5,4,2,3,1,6]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[4,3,2,5,6,1]=>[6,4,2,3,5,1]=>[[[[.,.],.],[.,[.,.]]],.]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[4,3,2,6,5,1]=>[6,4,2,3,1,5]=>[[[[.,.],.],[.,.]],[.,.]]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[4,3,5,2,1,6]=>[5,1,4,3,2,6]=>[[.,.],[[[.,.],.],[.,.]]]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[4,3,5,2,6,1]=>[6,5,4,3,2,1]=>[[[[[[.,.],.],.],.],.],.]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[4,3,5,6,2,1]=>[6,1,4,3,5,2]=>[[.,.],[[[.,.],[.,.]],.]]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[4,3,6,5,2,1]=>[6,1,4,3,2,5]=>[[.,.],[[[.,.],.],[.,.]]]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[4,5,3,2,1,6]=>[5,1,2,4,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[4,5,3,2,6,1]=>[6,5,2,4,3,1]=>[[[[.,.],.],[[.,.],.]],.]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[4,5,3,6,2,1]=>[6,1,5,4,3,2]=>[[.,.],[[[[.,.],.],.],.]]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[4,5,6,3,2,1]=>[6,1,2,4,5,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[4,6,5,3,2,1]=>[6,1,2,4,3,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[5,4,3,2,1,6]=>[5,1,2,3,4,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[5,4,3,2,6,1]=>[6,5,2,3,4,1]=>[[[[.,.],.],[.,[.,.]]],.]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[5,4,3,6,2,1]=>[6,1,5,3,4,2]=>[[.,.],[[[.,.],[.,.]],.]]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[5,4,6,3,2,1]=>[6,1,2,5,4,3]=>[[.,.],[.,[[[.,.],.],.]]]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[5,6,4,3,2,1]=>[6,1,2,3,5,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[6,5,4,3,2,1]=>[6,1,2,3,4,5]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,2,3,4,5,7,6]=>[1,2,3,4,5,7,6]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,2,3,4,6,5,7]=>[1,2,3,4,6,5,7]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,2,3,4,6,7,5]=>[1,2,3,4,7,6,5]=>[.,[.,[.,[.,[[[.,.],.],.]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,2,3,4,7,6,5]=>[1,2,3,4,7,5,6]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,2,3,5,4,6,7]=>[1,2,3,5,4,6,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,2,3,5,4,7,6]=>[1,2,3,5,4,7,6]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,2,3,5,6,4,7]=>[1,2,3,6,5,4,7]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,2,3,5,6,7,4]=>[1,2,3,7,5,6,4]=>[.,[.,[.,[[[.,.],[.,.]],.]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,2,3,5,7,6,4]=>[1,2,3,7,5,4,6]=>[.,[.,[.,[[[.,.],.],[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,2,3,6,5,4,7]=>[1,2,3,6,4,5,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,2,3,6,5,7,4]=>[1,2,3,7,6,5,4]=>[.,[.,[.,[[[[.,.],.],.],.]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,2,3,6,7,5,4]=>[1,2,3,7,4,6,5]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,2,3,7,6,5,4]=>[1,2,3,7,4,5,6]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,2,4,3,5,6,7]=>[1,2,4,3,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,2,4,3,5,7,6]=>[1,2,4,3,5,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5,7]=>[1,2,4,3,6,5,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,2,4,3,6,7,5]=>[1,2,4,3,7,6,5]=>[.,[.,[[.,.],[[[.,.],.],.]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,7,6,5]=>[1,2,4,3,7,5,6]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,2,4,5,3,6,7]=>[1,2,5,4,3,6,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,2,4,5,3,7,6]=>[1,2,5,4,3,7,6]=>[.,[.,[[[.,.],.],[[.,.],.]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,2,4,5,6,3,7]=>[1,2,6,4,5,3,7]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,2,4,5,6,7,3]=>[1,2,7,4,5,6,3]=>[.,[.,[[[.,.],[.,[.,.]]],.]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,2,4,5,7,6,3]=>[1,2,7,4,5,3,6]=>[.,[.,[[[.,.],[.,.]],[.,.]]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,2,4,6,5,3,7]=>[1,2,6,4,3,5,7]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,2,4,6,5,7,3]=>[1,2,7,4,6,5,3]=>[.,[.,[[[.,.],[[.,.],.]],.]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,2,4,6,7,5,3]=>[1,2,7,4,3,6,5]=>[.,[.,[[[.,.],.],[[.,.],.]]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,2,4,7,6,5,3]=>[1,2,7,4,3,5,6]=>[.,[.,[[[.,.],.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,2,5,4,3,6,7]=>[1,2,5,3,4,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,2,5,4,3,7,6]=>[1,2,5,3,4,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,2,5,4,6,3,7]=>[1,2,6,5,4,3,7]=>[.,[.,[[[[.,.],.],.],[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,2,5,4,6,7,3]=>[1,2,7,5,4,6,3]=>[.,[.,[[[[.,.],.],[.,.]],.]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,2,5,4,7,6,3]=>[1,2,7,5,4,3,6]=>[.,[.,[[[[.,.],.],.],[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,2,5,6,4,3,7]=>[1,2,6,3,5,4,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,2,5,6,4,7,3]=>[1,2,7,6,5,4,3]=>[.,[.,[[[[[.,.],.],.],.],.]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,2,5,6,7,4,3]=>[1,2,7,3,5,6,4]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,2,5,7,6,4,3]=>[1,2,7,3,5,4,6]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,2,6,5,4,3,7]=>[1,2,6,3,4,5,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,2,6,5,4,7,3]=>[1,2,7,6,4,5,3]=>[.,[.,[[[[.,.],.],[.,.]],.]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,2,6,5,7,4,3]=>[1,2,7,3,6,5,4]=>[.,[.,[[.,.],[[[.,.],.],.]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,2,6,7,5,4,3]=>[1,2,7,3,4,6,5]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,2,7,6,5,4,3]=>[1,2,7,3,4,5,6]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,2,4,5,6,7]=>[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,2,4,5,7,6]=>[1,3,2,4,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,6,5,7]=>[1,3,2,4,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,2,4,6,7,5]=>[1,3,2,4,7,6,5]=>[.,[[.,.],[.,[[[.,.],.],.]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,2,4,7,6,5]=>[1,3,2,4,7,5,6]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,4,6,7]=>[1,3,2,5,4,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,7,6]=>[1,3,2,5,4,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,2,5,6,4,7]=>[1,3,2,6,5,4,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,2,5,6,7,4]=>[1,3,2,7,5,6,4]=>[.,[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,2,5,7,6,4]=>[1,3,2,7,5,4,6]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,6,5,4,7]=>[1,3,2,6,4,5,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,5,7,4]=>[1,3,2,7,6,5,4]=>[.,[[.,.],[[[[.,.],.],.],.]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,2,6,7,5,4]=>[1,3,2,7,4,6,5]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,7,6,5,4]=>[1,3,2,7,4,5,6]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,3,4,2,5,6,7]=>[1,4,3,2,5,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5,7,6]=>[1,4,3,2,5,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,3,4,2,6,5,7]=>[1,4,3,2,6,5,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,3,4,2,6,7,5]=>[1,4,3,2,7,6,5]=>[.,[[[.,.],.],[[[.,.],.],.]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,3,4,2,7,6,5]=>[1,4,3,2,7,5,6]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,3,4,5,2,6,7]=>[1,5,3,4,2,6,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,4,5,2,7,6]=>[1,5,3,4,2,7,6]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,3,4,5,6,2,7]=>[1,6,3,4,5,2,7]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,3,4,5,6,7,2]=>[1,7,3,4,5,6,2]=>[.,[[[.,.],[.,[.,[.,.]]]],.]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,3,4,5,7,6,2]=>[1,7,3,4,5,2,6]=>[.,[[[.,.],[.,[.,.]]],[.,.]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,3,4,6,5,2,7]=>[1,6,3,4,2,5,7]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,3,4,6,5,7,2]=>[1,7,3,4,6,5,2]=>[.,[[[.,.],[.,[[.,.],.]]],.]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,3,4,6,7,5,2]=>[1,7,3,4,2,6,5]=>[.,[[[.,.],[.,.]],[[.,.],.]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,3,4,7,6,5,2]=>[1,7,3,4,2,5,6]=>[.,[[[.,.],[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,3,5,4,2,6,7]=>[1,5,3,2,4,6,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,3,5,4,2,7,6]=>[1,5,3,2,4,7,6]=>[.,[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,3,5,4,6,2,7]=>[1,6,3,5,4,2,7]=>[.,[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,3,5,4,6,7,2]=>[1,7,3,5,4,6,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,3,5,4,7,6,2]=>[1,7,3,5,4,2,6]=>[.,[[[.,.],[[.,.],.]],[.,.]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,3,5,6,4,2,7]=>[1,6,3,2,5,4,7]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,3,5,6,4,7,2]=>[1,7,3,6,5,4,2]=>[.,[[[.,.],[[[.,.],.],.]],.]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,3,5,6,7,4,2]=>[1,7,3,2,5,6,4]=>[.,[[[.,.],.],[[.,[.,.]],.]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,3,5,7,6,4,2]=>[1,7,3,2,5,4,6]=>[.,[[[.,.],.],[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,3,6,5,4,2,7]=>[1,6,3,2,4,5,7]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,3,6,5,4,7,2]=>[1,7,3,6,4,5,2]=>[.,[[[.,.],[[.,.],[.,.]]],.]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,3,6,5,7,4,2]=>[1,7,3,2,6,5,4]=>[.,[[[.,.],.],[[[.,.],.],.]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,3,6,7,5,4,2]=>[1,7,3,2,4,6,5]=>[.,[[[.,.],.],[.,[[.,.],.]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,3,7,6,5,4,2]=>[1,7,3,2,4,5,6]=>[.,[[[.,.],.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,4,3,2,5,6,7]=>[1,4,2,3,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,4,3,2,5,7,6]=>[1,4,2,3,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,4,3,2,6,5,7]=>[1,4,2,3,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,4,3,2,6,7,5]=>[1,4,2,3,7,6,5]=>[.,[[.,.],[.,[[[.,.],.],.]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,4,3,2,7,6,5]=>[1,4,2,3,7,5,6]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,3,5,2,6,7]=>[1,5,4,3,2,6,7]=>[.,[[[[.,.],.],.],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,3,5,2,7,6]=>[1,5,4,3,2,7,6]=>[.,[[[[.,.],.],.],[[.,.],.]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,3,5,6,2,7]=>[1,6,4,3,5,2,7]=>[.,[[[[.,.],.],[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,3,5,6,7,2]=>[1,7,4,3,5,6,2]=>[.,[[[[.,.],.],[.,[.,.]]],.]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,3,5,7,6,2]=>[1,7,4,3,5,2,6]=>[.,[[[[.,.],.],[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,3,6,5,2,7]=>[1,6,4,3,2,5,7]=>[.,[[[[.,.],.],.],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,3,6,5,7,2]=>[1,7,4,3,6,5,2]=>[.,[[[[.,.],.],[[.,.],.]],.]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,3,6,7,5,2]=>[1,7,4,3,2,6,5]=>[.,[[[[.,.],.],.],[[.,.],.]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,3,7,6,5,2]=>[1,7,4,3,2,5,6]=>[.,[[[[.,.],.],.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,4,5,3,2,6,7]=>[1,5,2,4,3,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,4,5,3,2,7,6]=>[1,5,2,4,3,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,4,5,3,6,2,7]=>[1,6,5,4,3,2,7]=>[.,[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,4,5,3,6,7,2]=>[1,7,5,4,3,6,2]=>[.,[[[[[.,.],.],.],[.,.]],.]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,4,5,3,7,6,2]=>[1,7,5,4,3,2,6]=>[.,[[[[[.,.],.],.],.],[.,.]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,4,5,6,3,2,7]=>[1,6,2,4,5,3,7]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,4,5,6,3,7,2]=>[1,7,6,4,5,3,2]=>[.,[[[[[.,.],.],[.,.]],.],.]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,4,5,6,7,3,2]=>[1,7,2,4,5,6,3]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,4,5,7,6,3,2]=>[1,7,2,4,5,3,6]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,4,6,5,3,2,7]=>[1,6,2,4,3,5,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,4,6,5,3,7,2]=>[1,7,6,4,3,5,2]=>[.,[[[[[.,.],.],.],[.,.]],.]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,4,6,5,7,3,2]=>[1,7,2,4,6,5,3]=>[.,[[.,.],[[.,[[.,.],.]],.]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,4,6,7,5,3,2]=>[1,7,2,4,3,6,5]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,4,7,6,5,3,2]=>[1,7,2,4,3,5,6]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,5,4,3,2,6,7]=>[1,5,2,3,4,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,5,4,3,2,7,6]=>[1,5,2,3,4,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,5,4,3,6,2,7]=>[1,6,5,3,4,2,7]=>[.,[[[[.,.],.],[.,.]],[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,5,4,3,6,7,2]=>[1,7,5,3,4,6,2]=>[.,[[[[.,.],.],[.,[.,.]]],.]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,5,4,3,7,6,2]=>[1,7,5,3,4,2,6]=>[.,[[[[.,.],.],[.,.]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,4,6,3,2,7]=>[1,6,2,5,4,3,7]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,4,6,3,7,2]=>[1,7,6,5,4,3,2]=>[.,[[[[[[.,.],.],.],.],.],.]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,4,6,7,3,2]=>[1,7,2,5,4,6,3]=>[.,[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,4,7,6,3,2]=>[1,7,2,5,4,3,6]=>[.,[[.,.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,5,6,4,3,2,7]=>[1,6,2,3,5,4,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,5,6,4,3,7,2]=>[1,7,6,3,5,4,2]=>[.,[[[[.,.],.],[[.,.],.]],.]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,5,6,4,7,3,2]=>[1,7,2,6,5,4,3]=>[.,[[.,.],[[[[.,.],.],.],.]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,5,6,7,4,3,2]=>[1,7,2,3,5,6,4]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,5,7,6,4,3,2]=>[1,7,2,3,5,4,6]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,6,5,4,3,2,7]=>[1,6,2,3,4,5,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,6,5,4,3,7,2]=>[1,7,6,3,4,5,2]=>[.,[[[[.,.],.],[.,[.,.]]],.]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,6,5,4,7,3,2]=>[1,7,2,6,4,5,3]=>[.,[[.,.],[[[.,.],[.,.]],.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,5,7,4,3,2]=>[1,7,2,3,6,5,4]=>[.,[[.,.],[.,[[[.,.],.],.]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,6,7,5,4,3,2]=>[1,7,2,3,4,6,5]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,7,6,5,4,3,2]=>[1,7,2,3,4,5,6]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[2,1,3,4,5,6,7]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,7,6]=>[2,1,3,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[2,1,3,4,6,5,7]=>[2,1,3,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,1,3,4,6,7,5]=>[2,1,3,4,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[2,1,3,4,7,6,5]=>[2,1,3,4,7,5,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[2,1,3,5,4,6,7]=>[2,1,3,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[2,1,3,5,4,7,6]=>[2,1,3,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[2,1,3,5,6,4,7]=>[2,1,3,6,5,4,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[2,1,3,5,6,7,4]=>[2,1,3,7,5,6,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[2,1,3,5,7,6,4]=>[2,1,3,7,5,4,6]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[2,1,3,6,5,4,7]=>[2,1,3,6,4,5,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[2,1,3,6,5,7,4]=>[2,1,3,7,6,5,4]=>[[.,.],[.,[[[[.,.],.],.],.]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[2,1,3,6,7,5,4]=>[2,1,3,7,4,6,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[2,1,3,7,6,5,4]=>[2,1,3,7,4,5,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,3,5,6,7]=>[2,1,4,3,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,3,5,7,6]=>[2,1,4,3,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,7]=>[2,1,4,3,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,3,6,7,5]=>[2,1,4,3,7,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,7,6,5]=>[2,1,4,3,7,5,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[2,1,4,5,3,6,7]=>[2,1,5,4,3,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[2,1,4,5,3,7,6]=>[2,1,5,4,3,7,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[2,1,4,5,6,3,7]=>[2,1,6,4,5,3,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[2,1,4,5,6,7,3]=>[2,1,7,4,5,6,3]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[2,1,4,5,7,6,3]=>[2,1,7,4,5,3,6]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[2,1,4,6,5,3,7]=>[2,1,6,4,3,5,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[2,1,4,6,5,7,3]=>[2,1,7,4,6,5,3]=>[[.,.],[[[.,.],[[.,.],.]],.]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[2,1,4,6,7,5,3]=>[2,1,7,4,3,6,5]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[2,1,4,7,6,5,3]=>[2,1,7,4,3,5,6]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,5,4,3,6,7]=>[2,1,5,3,4,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,5,4,3,7,6]=>[2,1,5,3,4,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,4,6,3,7]=>[2,1,6,5,4,3,7]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,4,6,7,3]=>[2,1,7,5,4,6,3]=>[[.,.],[[[[.,.],.],[.,.]],.]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,4,7,6,3]=>[2,1,7,5,4,3,6]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[2,1,5,6,4,3,7]=>[2,1,6,3,5,4,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[2,1,5,6,4,7,3]=>[2,1,7,6,5,4,3]=>[[.,.],[[[[[.,.],.],.],.],.]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[2,1,5,6,7,4,3]=>[2,1,7,3,5,6,4]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[2,1,5,7,6,4,3]=>[2,1,7,3,5,4,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,6,5,4,3,7]=>[2,1,6,3,4,5,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,6,5,4,7,3]=>[2,1,7,6,4,5,3]=>[[.,.],[[[[.,.],.],[.,.]],.]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,5,7,4,3]=>[2,1,7,3,6,5,4]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[2,1,6,7,5,4,3]=>[2,1,7,3,4,6,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,7,6,5,4,3]=>[2,1,7,3,4,5,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[2,3,1,4,5,6,7]=>[3,2,1,4,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[2,3,1,4,5,7,6]=>[3,2,1,4,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[2,3,1,4,6,5,7]=>[3,2,1,4,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,6,7,5]=>[3,2,1,4,7,6,5]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,7,6,5]=>[3,2,1,4,7,5,6]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,4,6,7]=>[3,2,1,5,4,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,7,6]=>[3,2,1,5,4,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[2,3,1,5,6,4,7]=>[3,2,1,6,5,4,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,1,5,6,7,4]=>[3,2,1,7,5,6,4]=>[[[.,.],.],[[[.,.],[.,.]],.]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[2,3,1,5,7,6,4]=>[3,2,1,7,5,4,6]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[2,3,1,6,5,4,7]=>[3,2,1,6,4,5,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,5,7,4]=>[3,2,1,7,6,5,4]=>[[[.,.],.],[[[[.,.],.],.],.]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[2,3,1,6,7,5,4]=>[3,2,1,7,4,6,5]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[2,3,1,7,6,5,4]=>[3,2,1,7,4,5,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,5,6,7]=>[4,2,3,1,5,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[2,3,4,1,5,7,6]=>[4,2,3,1,5,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[2,3,4,1,6,5,7]=>[4,2,3,1,6,5,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[2,3,4,1,6,7,5]=>[4,2,3,1,7,6,5]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[2,3,4,1,7,6,5]=>[4,2,3,1,7,5,6]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,4,5,1,6,7]=>[5,2,3,4,1,6,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[2,3,4,5,1,7,6]=>[5,2,3,4,1,7,6]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,3,4,5,6,1,7]=>[6,2,3,4,5,1,7]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[2,3,4,5,6,7,1]=>[7,2,3,4,5,6,1]=>[[[.,.],[.,[.,[.,[.,.]]]]],.]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[2,3,4,5,7,6,1]=>[7,2,3,4,5,1,6]=>[[[.,.],[.,[.,[.,.]]]],[.,.]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[2,3,4,6,5,1,7]=>[6,2,3,4,1,5,7]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[2,3,4,6,5,7,1]=>[7,2,3,4,6,5,1]=>[[[.,.],[.,[.,[[.,.],.]]]],.]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[2,3,4,6,7,5,1]=>[7,2,3,4,1,6,5]=>[[[.,.],[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[2,3,4,7,6,5,1]=>[7,2,3,4,1,5,6]=>[[[.,.],[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[2,3,5,4,1,6,7]=>[5,2,3,1,4,6,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[2,3,5,4,1,7,6]=>[5,2,3,1,4,7,6]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[2,3,5,4,6,1,7]=>[6,2,3,5,4,1,7]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[2,3,5,4,6,7,1]=>[7,2,3,5,4,6,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[2,3,5,4,7,6,1]=>[7,2,3,5,4,1,6]=>[[[.,.],[.,[[.,.],.]]],[.,.]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[2,3,5,6,4,1,7]=>[6,2,3,1,5,4,7]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[2,3,5,6,4,7,1]=>[7,2,3,6,5,4,1]=>[[[.,.],[.,[[[.,.],.],.]]],.]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[2,3,5,6,7,4,1]=>[7,2,3,1,5,6,4]=>[[[.,.],[.,.]],[[.,[.,.]],.]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[2,3,5,7,6,4,1]=>[7,2,3,1,5,4,6]=>[[[.,.],[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[2,3,6,5,4,1,7]=>[6,2,3,1,4,5,7]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[2,3,6,5,4,7,1]=>[7,2,3,6,4,5,1]=>[[[.,.],[.,[[.,.],[.,.]]]],.]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[2,3,6,5,7,4,1]=>[7,2,3,1,6,5,4]=>[[[.,.],[.,.]],[[[.,.],.],.]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[2,3,6,7,5,4,1]=>[7,2,3,1,4,6,5]=>[[[.,.],[.,.]],[.,[[.,.],.]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[2,3,7,6,5,4,1]=>[7,2,3,1,4,5,6]=>[[[.,.],[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[2,4,3,1,5,6,7]=>[4,2,1,3,5,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[2,4,3,1,5,7,6]=>[4,2,1,3,5,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[2,4,3,1,6,5,7]=>[4,2,1,3,6,5,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[2,4,3,1,6,7,5]=>[4,2,1,3,7,6,5]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[2,4,3,1,7,6,5]=>[4,2,1,3,7,5,6]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[2,4,3,5,1,6,7]=>[5,2,4,3,1,6,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[2,4,3,5,1,7,6]=>[5,2,4,3,1,7,6]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[2,4,3,5,6,1,7]=>[6,2,4,3,5,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[2,4,3,5,6,7,1]=>[7,2,4,3,5,6,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[2,4,3,5,7,6,1]=>[7,2,4,3,5,1,6]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[2,4,3,6,5,1,7]=>[6,2,4,3,1,5,7]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[2,4,3,6,5,7,1]=>[7,2,4,3,6,5,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[2,4,3,6,7,5,1]=>[7,2,4,3,1,6,5]=>[[[.,.],[[.,.],.]],[[.,.],.]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[2,4,3,7,6,5,1]=>[7,2,4,3,1,5,6]=>[[[.,.],[[.,.],.]],[.,[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[2,4,5,3,1,6,7]=>[5,2,1,4,3,6,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[2,4,5,3,1,7,6]=>[5,2,1,4,3,7,6]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[2,4,5,3,6,1,7]=>[6,2,5,4,3,1,7]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[2,4,5,3,6,7,1]=>[7,2,5,4,3,6,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[2,4,5,3,7,6,1]=>[7,2,5,4,3,1,6]=>[[[.,.],[[[.,.],.],.]],[.,.]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[2,4,5,6,3,1,7]=>[6,2,1,4,5,3,7]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[2,4,5,6,3,7,1]=>[7,2,6,4,5,3,1]=>[[[.,.],[[[.,.],[.,.]],.]],.]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[2,4,5,6,7,3,1]=>[7,2,1,4,5,6,3]=>[[[.,.],.],[[.,[.,[.,.]]],.]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[2,4,5,7,6,3,1]=>[7,2,1,4,5,3,6]=>[[[.,.],.],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[2,4,6,5,3,1,7]=>[6,2,1,4,3,5,7]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[2,4,6,5,3,7,1]=>[7,2,6,4,3,5,1]=>[[[.,.],[[[.,.],.],[.,.]]],.]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[2,4,6,5,7,3,1]=>[7,2,1,4,6,5,3]=>[[[.,.],.],[[.,[[.,.],.]],.]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[2,4,6,7,5,3,1]=>[7,2,1,4,3,6,5]=>[[[.,.],.],[[.,.],[[.,.],.]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[2,4,7,6,5,3,1]=>[7,2,1,4,3,5,6]=>[[[.,.],.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[2,5,4,3,1,6,7]=>[5,2,1,3,4,6,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[2,5,4,3,1,7,6]=>[5,2,1,3,4,7,6]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,5,4,3,6,1,7]=>[6,2,5,3,4,1,7]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[2,5,4,3,6,7,1]=>[7,2,5,3,4,6,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[2,5,4,3,7,6,1]=>[7,2,5,3,4,1,6]=>[[[.,.],[[.,.],[.,.]]],[.,.]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[2,5,4,6,3,1,7]=>[6,2,1,5,4,3,7]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[2,5,4,6,3,7,1]=>[7,2,6,5,4,3,1]=>[[[.,.],[[[[.,.],.],.],.]],.]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[2,5,4,6,7,3,1]=>[7,2,1,5,4,6,3]=>[[[.,.],.],[[[.,.],[.,.]],.]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[2,5,4,7,6,3,1]=>[7,2,1,5,4,3,6]=>[[[.,.],.],[[[.,.],.],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[2,5,6,4,3,1,7]=>[6,2,1,3,5,4,7]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[2,5,6,4,3,7,1]=>[7,2,6,3,5,4,1]=>[[[.,.],[[.,.],[[.,.],.]]],.]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[2,5,6,4,7,3,1]=>[7,2,1,6,5,4,3]=>[[[.,.],.],[[[[.,.],.],.],.]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[2,5,6,7,4,3,1]=>[7,2,1,3,5,6,4]=>[[[.,.],.],[.,[[.,[.,.]],.]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[2,5,7,6,4,3,1]=>[7,2,1,3,5,4,6]=>[[[.,.],.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[2,6,5,4,3,1,7]=>[6,2,1,3,4,5,7]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[2,6,5,4,3,7,1]=>[7,2,6,3,4,5,1]=>[[[.,.],[[.,.],[.,[.,.]]]],.]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[2,6,5,4,7,3,1]=>[7,2,1,6,4,5,3]=>[[[.,.],.],[[[.,.],[.,.]],.]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[2,6,5,7,4,3,1]=>[7,2,1,3,6,5,4]=>[[[.,.],.],[.,[[[.,.],.],.]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[2,6,7,5,4,3,1]=>[7,2,1,3,4,6,5]=>[[[.,.],.],[.,[.,[[.,.],.]]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[2,7,6,5,4,3,1]=>[7,2,1,3,4,5,6]=>[[[.,.],.],[.,[.,[.,[.,.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[3,2,1,4,5,6,7]=>[3,1,2,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[3,2,1,4,5,7,6]=>[3,1,2,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[3,2,1,4,6,5,7]=>[3,1,2,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[3,2,1,4,6,7,5]=>[3,1,2,4,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,7,6,5]=>[3,1,2,4,7,5,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[3,2,1,5,4,6,7]=>[3,1,2,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[3,2,1,5,4,7,6]=>[3,1,2,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[3,2,1,5,6,4,7]=>[3,1,2,6,5,4,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[3,2,1,5,6,7,4]=>[3,1,2,7,5,6,4]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[3,2,1,5,7,6,4]=>[3,1,2,7,5,4,6]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[3,2,1,6,5,4,7]=>[3,1,2,6,4,5,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[3,2,1,6,5,7,4]=>[3,1,2,7,6,5,4]=>[[.,.],[.,[[[[.,.],.],.],.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[3,2,1,6,7,5,4]=>[3,1,2,7,4,6,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[3,2,1,7,6,5,4]=>[3,1,2,7,4,5,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[3,2,4,1,5,6,7]=>[4,3,2,1,5,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[3,2,4,1,5,7,6]=>[4,3,2,1,5,7,6]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[3,2,4,1,6,5,7]=>[4,3,2,1,6,5,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[3,2,4,1,6,7,5]=>[4,3,2,1,7,6,5]=>[[[[.,.],.],.],[[[.,.],.],.]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[3,2,4,1,7,6,5]=>[4,3,2,1,7,5,6]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[3,2,4,5,1,6,7]=>[5,3,2,4,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[3,2,4,5,1,7,6]=>[5,3,2,4,1,7,6]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[3,2,4,5,6,1,7]=>[6,3,2,4,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[3,2,4,5,6,7,1]=>[7,3,2,4,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[3,2,4,5,7,6,1]=>[7,3,2,4,5,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[3,2,4,6,5,1,7]=>[6,3,2,4,1,5,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,2,4,6,5,7,1]=>[7,3,2,4,6,5,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[3,2,4,6,7,5,1]=>[7,3,2,4,1,6,5]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[3,2,4,7,6,5,1]=>[7,3,2,4,1,5,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[3,2,5,4,1,6,7]=>[5,3,2,1,4,6,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[3,2,5,4,1,7,6]=>[5,3,2,1,4,7,6]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[3,2,5,4,6,1,7]=>[6,3,2,5,4,1,7]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[3,2,5,4,6,7,1]=>[7,3,2,5,4,6,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[3,2,5,4,7,6,1]=>[7,3,2,5,4,1,6]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[3,2,5,6,4,1,7]=>[6,3,2,1,5,4,7]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[3,2,5,6,4,7,1]=>[7,3,2,6,5,4,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[3,2,5,6,7,4,1]=>[7,3,2,1,5,6,4]=>[[[[.,.],.],.],[[.,[.,.]],.]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[3,2,5,7,6,4,1]=>[7,3,2,1,5,4,6]=>[[[[.,.],.],.],[[.,.],[.,.]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[3,2,6,5,4,1,7]=>[6,3,2,1,4,5,7]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[3,2,6,5,4,7,1]=>[7,3,2,6,4,5,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[3,2,6,5,7,4,1]=>[7,3,2,1,6,5,4]=>[[[[.,.],.],.],[[[.,.],.],.]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[3,2,6,7,5,4,1]=>[7,3,2,1,4,6,5]=>[[[[.,.],.],.],[.,[[.,.],.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[3,2,7,6,5,4,1]=>[7,3,2,1,4,5,6]=>[[[[.,.],.],.],[.,[.,[.,.]]]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[3,4,2,1,5,6,7]=>[4,1,3,2,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[3,4,2,1,5,7,6]=>[4,1,3,2,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[3,4,2,1,6,5,7]=>[4,1,3,2,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[3,4,2,1,6,7,5]=>[4,1,3,2,7,6,5]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[3,4,2,1,7,6,5]=>[4,1,3,2,7,5,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[3,4,2,5,1,6,7]=>[5,4,3,2,1,6,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[3,4,2,5,1,7,6]=>[5,4,3,2,1,7,6]=>[[[[[.,.],.],.],.],[[.,.],.]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[3,4,2,5,6,1,7]=>[6,4,3,2,5,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[3,4,2,5,6,7,1]=>[7,4,3,2,5,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[3,4,2,5,7,6,1]=>[7,4,3,2,5,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,4,2,6,5,1,7]=>[6,4,3,2,1,5,7]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[3,4,2,6,5,7,1]=>[7,4,3,2,6,5,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[3,4,2,6,7,5,1]=>[7,4,3,2,1,6,5]=>[[[[[.,.],.],.],.],[[.,.],.]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[3,4,2,7,6,5,1]=>[7,4,3,2,1,5,6]=>[[[[[.,.],.],.],.],[.,[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[3,4,5,2,1,6,7]=>[5,1,3,4,2,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[3,4,5,2,1,7,6]=>[5,1,3,4,2,7,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[3,4,5,2,6,1,7]=>[6,5,3,4,2,1,7]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[3,4,5,2,6,7,1]=>[7,5,3,4,2,6,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[3,4,5,2,7,6,1]=>[7,5,3,4,2,1,6]=>[[[[[.,.],.],[.,.]],.],[.,.]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[3,4,5,6,2,1,7]=>[6,1,3,4,5,2,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[3,4,5,6,2,7,1]=>[7,6,3,4,5,2,1]=>[[[[[.,.],.],[.,[.,.]]],.],.]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[3,4,5,6,7,2,1]=>[7,1,3,4,5,6,2]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[3,4,5,7,6,2,1]=>[7,1,3,4,5,2,6]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[3,4,6,5,2,1,7]=>[6,1,3,4,2,5,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[3,4,6,5,2,7,1]=>[7,6,3,4,2,5,1]=>[[[[[.,.],.],[.,.]],[.,.]],.]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[3,4,6,5,7,2,1]=>[7,1,3,4,6,5,2]=>[[.,.],[[.,[.,[[.,.],.]]],.]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[3,4,6,7,5,2,1]=>[7,1,3,4,2,6,5]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[3,4,7,6,5,2,1]=>[7,1,3,4,2,5,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[3,5,4,2,1,6,7]=>[5,1,3,2,4,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[3,5,4,2,1,7,6]=>[5,1,3,2,4,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[3,5,4,2,6,1,7]=>[6,5,3,2,4,1,7]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[3,5,4,2,6,7,1]=>[7,5,3,2,4,6,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[3,5,4,2,7,6,1]=>[7,5,3,2,4,1,6]=>[[[[[.,.],.],.],[.,.]],[.,.]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[3,5,4,6,2,1,7]=>[6,1,3,5,4,2,7]=>[[.,.],[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,4,6,2,7,1]=>[7,6,3,5,4,2,1]=>[[[[[.,.],.],[[.,.],.]],.],.]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[3,5,4,6,7,2,1]=>[7,1,3,5,4,6,2]=>[[.,.],[[.,[[.,.],[.,.]]],.]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[3,5,4,7,6,2,1]=>[7,1,3,5,4,2,6]=>[[.,.],[[.,[[.,.],.]],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[3,5,6,4,2,1,7]=>[6,1,3,2,5,4,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[3,5,6,4,2,7,1]=>[7,6,3,2,5,4,1]=>[[[[[.,.],.],.],[[.,.],.]],.]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[3,5,6,4,7,2,1]=>[7,1,3,6,5,4,2]=>[[.,.],[[.,[[[.,.],.],.]],.]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[3,5,6,7,4,2,1]=>[7,1,3,2,5,6,4]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[3,5,7,6,4,2,1]=>[7,1,3,2,5,4,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[3,6,5,4,2,1,7]=>[6,1,3,2,4,5,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[3,6,5,4,2,7,1]=>[7,6,3,2,4,5,1]=>[[[[[.,.],.],.],[.,[.,.]]],.]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[3,6,5,4,7,2,1]=>[7,1,3,6,4,5,2]=>[[.,.],[[.,[[.,.],[.,.]]],.]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[3,6,5,7,4,2,1]=>[7,1,3,2,6,5,4]=>[[.,.],[[.,.],[[[.,.],.],.]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[3,6,7,5,4,2,1]=>[7,1,3,2,4,6,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[3,7,6,5,4,2,1]=>[7,1,3,2,4,5,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[4,3,2,1,5,6,7]=>[4,1,2,3,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[4,3,2,1,5,7,6]=>[4,1,2,3,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[4,3,2,1,6,5,7]=>[4,1,2,3,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[4,3,2,1,6,7,5]=>[4,1,2,3,7,6,5]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[4,3,2,1,7,6,5]=>[4,1,2,3,7,5,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[4,3,2,5,1,6,7]=>[5,4,2,3,1,6,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[4,3,2,5,1,7,6]=>[5,4,2,3,1,7,6]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[4,3,2,5,6,1,7]=>[6,4,2,3,5,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[4,3,2,5,6,7,1]=>[7,4,2,3,5,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[4,3,2,5,7,6,1]=>[7,4,2,3,5,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[4,3,2,6,5,1,7]=>[6,4,2,3,1,5,7]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[4,3,2,6,5,7,1]=>[7,4,2,3,6,5,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[4,3,2,6,7,5,1]=>[7,4,2,3,1,6,5]=>[[[[.,.],.],[.,.]],[[.,.],.]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[4,3,2,7,6,5,1]=>[7,4,2,3,1,5,6]=>[[[[.,.],.],[.,.]],[.,[.,.]]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[4,3,5,2,1,6,7]=>[5,1,4,3,2,6,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[4,3,5,2,1,7,6]=>[5,1,4,3,2,7,6]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[4,3,5,2,6,1,7]=>[6,5,4,3,2,1,7]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[4,3,5,2,6,7,1]=>[7,5,4,3,2,6,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[4,3,5,2,7,6,1]=>[7,5,4,3,2,1,6]=>[[[[[[.,.],.],.],.],.],[.,.]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[4,3,5,6,2,1,7]=>[6,1,4,3,5,2,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[4,3,5,6,2,7,1]=>[7,6,4,3,5,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[4,3,5,6,7,2,1]=>[7,1,4,3,5,6,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[4,3,5,7,6,2,1]=>[7,1,4,3,5,2,6]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[4,3,6,5,2,1,7]=>[6,1,4,3,2,5,7]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[4,3,6,5,2,7,1]=>[7,6,4,3,2,5,1]=>[[[[[[.,.],.],.],.],[.,.]],.]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[4,3,6,5,7,2,1]=>[7,1,4,3,6,5,2]=>[[.,.],[[[.,.],[[.,.],.]],.]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[4,3,6,7,5,2,1]=>[7,1,4,3,2,6,5]=>[[.,.],[[[.,.],.],[[.,.],.]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[4,3,7,6,5,2,1]=>[7,1,4,3,2,5,6]=>[[.,.],[[[.,.],.],[.,[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[4,5,3,2,1,6,7]=>[5,1,2,4,3,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[4,5,3,2,1,7,6]=>[5,1,2,4,3,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[4,5,3,2,6,1,7]=>[6,5,2,4,3,1,7]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[4,5,3,2,6,7,1]=>[7,5,2,4,3,6,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[4,5,3,2,7,6,1]=>[7,5,2,4,3,1,6]=>[[[[.,.],.],[[.,.],.]],[.,.]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[4,5,3,6,2,1,7]=>[6,1,5,4,3,2,7]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[4,5,3,6,2,7,1]=>[7,6,5,4,3,2,1]=>[[[[[[[.,.],.],.],.],.],.],.]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[4,5,3,6,7,2,1]=>[7,1,5,4,3,6,2]=>[[.,.],[[[[.,.],.],[.,.]],.]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[4,5,3,7,6,2,1]=>[7,1,5,4,3,2,6]=>[[.,.],[[[[.,.],.],.],[.,.]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[4,5,6,3,2,1,7]=>[6,1,2,4,5,3,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[4,5,6,3,2,7,1]=>[7,6,2,4,5,3,1]=>[[[[.,.],.],[[.,[.,.]],.]],.]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,5,6,3,7,2,1]=>[7,1,6,4,5,3,2]=>[[.,.],[[[[.,.],[.,.]],.],.]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[4,5,6,7,3,2,1]=>[7,1,2,4,5,6,3]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[4,5,7,6,3,2,1]=>[7,1,2,4,5,3,6]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[4,6,5,3,2,1,7]=>[6,1,2,4,3,5,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[4,6,5,3,2,7,1]=>[7,6,2,4,3,5,1]=>[[[[.,.],.],[[.,.],[.,.]]],.]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[4,6,5,3,7,2,1]=>[7,1,6,4,3,5,2]=>[[.,.],[[[[.,.],.],[.,.]],.]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[4,6,5,7,3,2,1]=>[7,1,2,4,6,5,3]=>[[.,.],[.,[[.,[[.,.],.]],.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[4,6,7,5,3,2,1]=>[7,1,2,4,3,6,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[4,7,6,5,3,2,1]=>[7,1,2,4,3,5,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[5,4,3,2,1,6,7]=>[5,1,2,3,4,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[5,4,3,2,1,7,6]=>[5,1,2,3,4,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[5,4,3,2,6,1,7]=>[6,5,2,3,4,1,7]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[5,4,3,2,6,7,1]=>[7,5,2,3,4,6,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[5,4,3,2,7,6,1]=>[7,5,2,3,4,1,6]=>[[[[.,.],.],[.,[.,.]]],[.,.]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[5,4,3,6,2,1,7]=>[6,1,5,3,4,2,7]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[5,4,3,6,2,7,1]=>[7,6,5,3,4,2,1]=>[[[[[[.,.],.],.],[.,.]],.],.]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[5,4,3,6,7,2,1]=>[7,1,5,3,4,6,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[5,4,3,7,6,2,1]=>[7,1,5,3,4,2,6]=>[[.,.],[[[.,.],[.,.]],[.,.]]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[5,4,6,3,2,1,7]=>[6,1,2,5,4,3,7]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[5,4,6,3,2,7,1]=>[7,6,2,5,4,3,1]=>[[[[.,.],.],[[[.,.],.],.]],.]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[5,4,6,3,7,2,1]=>[7,1,6,5,4,3,2]=>[[.,.],[[[[[.,.],.],.],.],.]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[5,4,6,7,3,2,1]=>[7,1,2,5,4,6,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[5,4,7,6,3,2,1]=>[7,1,2,5,4,3,6]=>[[.,.],[.,[[[.,.],.],[.,.]]]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[5,6,4,3,2,1,7]=>[6,1,2,3,5,4,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[5,6,4,3,2,7,1]=>[7,6,2,3,5,4,1]=>[[[[.,.],.],[.,[[.,.],.]]],.]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[5,6,4,3,7,2,1]=>[7,1,6,3,5,4,2]=>[[.,.],[[[.,.],[[.,.],.]],.]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[5,6,4,7,3,2,1]=>[7,1,2,6,5,4,3]=>[[.,.],[.,[[[[.,.],.],.],.]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[5,6,7,4,3,2,1]=>[7,1,2,3,5,6,4]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[5,7,6,4,3,2,1]=>[7,1,2,3,5,4,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[6,5,4,3,2,1,7]=>[6,1,2,3,4,5,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[6,5,4,3,2,7,1]=>[7,6,2,3,4,5,1]=>[[[[.,.],.],[.,[.,[.,.]]]],.]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[6,5,4,3,7,2,1]=>[7,1,6,3,4,5,2]=>[[.,.],[[[.,.],[.,[.,.]]],.]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[6,5,4,7,3,2,1]=>[7,1,2,6,4,5,3]=>[[.,.],[.,[[[.,.],[.,.]],.]]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[6,5,7,4,3,2,1]=>[7,1,2,3,6,5,4]=>[[.,.],[.,[.,[[[.,.],.],.]]]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[6,7,5,4,3,2,1]=>[7,1,2,3,4,6,5]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[7,6,5,4,3,2,1]=>[7,1,2,3,4,5,6]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,2,3,4,5,6,7,8]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,5,7,8]=>[1,2,4,3,6,5,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,2,4,5,7,6,8]=>[1,3,2,4,5,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,4,2,6,7,5,8]=>[1,4,3,2,7,6,5,8]=>[.,[[[.,.],.],[[[.,.],.],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,4,3,2,7,6,5,8]=>[1,4,2,3,7,5,6,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,1,3,4,5,6,8,7]=>[2,1,3,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,8,7]=>[2,1,4,3,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,1,4,5,7,8,6]=>[3,2,1,4,5,8,7,6]=>[[[.,.],.],[.,[.,[[[.,.],.],.]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[2,3,4,1,6,7,8,5]=>[4,2,3,1,8,6,7,5]=>[[[.,.],[.,.]],[[[.,.],[.,.]],.]]
[1,1,1,0,0,0,1,0,1,0,1,1,1,0,0,0]=>[3,2,1,4,5,8,7,6]=>[3,1,2,4,5,8,6,7]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,1,0,0,0,0,1,1,1,1,0,0,0,0]=>[4,3,2,1,8,7,6,5]=>[4,1,2,3,8,5,6,7]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
Map
to 312-avoiding permutation
Description
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.
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