Identifier
Mp00101:
Dyck paths
—decomposition reverse⟶
Dyck paths
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Mp00129: Dyck paths —to 321-avoiding permutation (Billey-Jockusch-Stanley)⟶ Permutations
Mp00061: Permutations —to increasing tree⟶ Binary trees
Images
=>
Cc0005;cc-rep-0Cc0005;cc-rep-1Cc0010;cc-rep-3
[1,0]=>[1,0]=>[1]=>[.,.]
[1,0,1,0]=>[1,1,0,0]=>[1,2]=>[.,[.,.]]
[1,1,0,0]=>[1,0,1,0]=>[2,1]=>[[.,.],.]
[1,0,1,0,1,0]=>[1,1,1,0,0,0]=>[1,2,3]=>[.,[.,[.,.]]]
[1,0,1,1,0,0]=>[1,1,0,1,0,0]=>[3,1,2]=>[[.,.],[.,.]]
[1,1,0,0,1,0]=>[1,1,0,0,1,0]=>[1,3,2]=>[.,[[.,.],.]]
[1,1,0,1,0,0]=>[1,0,1,1,0,0]=>[2,1,3]=>[[.,.],[.,.]]
[1,1,1,0,0,0]=>[1,0,1,0,1,0]=>[2,3,1]=>[[.,[.,.]],.]
[1,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0]=>[1,2,3,4]=>[.,[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0]=>[4,1,2,3]=>[[.,.],[.,[.,.]]]
[1,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0]=>[1,4,2,3]=>[.,[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0]=>[3,1,2,4]=>[[.,.],[.,[.,.]]]
[1,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0]=>[3,4,1,2]=>[[.,[.,.]],[.,.]]
[1,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0]=>[1,2,4,3]=>[.,[.,[[.,.],.]]]
[1,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0]=>[3,1,4,2]=>[[.,.],[[.,.],.]]
[1,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0]=>[1,3,2,4]=>[.,[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0]=>[2,1,3,4]=>[[.,.],[.,[.,.]]]
[1,1,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0]=>[2,4,1,3]=>[[.,[.,.]],[.,.]]
[1,1,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,0]=>[1,3,4,2]=>[.,[[.,[.,.]],.]]
[1,1,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,0]=>[2,1,4,3]=>[[.,.],[[.,.],.]]
[1,1,1,0,1,0,0,0]=>[1,0,1,0,1,1,0,0]=>[2,3,1,4]=>[[.,[.,.]],[.,.]]
[1,1,1,1,0,0,0,0]=>[1,0,1,0,1,0,1,0]=>[2,3,4,1]=>[[.,[.,[.,.]]],.]
[1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0]=>[1,2,3,4,5]=>[.,[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,0]=>[5,1,2,3,4]=>[[.,.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0]=>[1,5,2,3,4]=>[.,[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0]=>[4,1,2,3,5]=>[[.,.],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0]=>[4,5,1,2,3]=>[[.,[.,.]],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,0]=>[1,2,5,3,4]=>[.,[.,[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0]=>[4,1,5,2,3]=>[[.,.],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0]=>[1,4,2,3,5]=>[.,[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0]=>[3,1,2,4,5]=>[[.,.],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0]=>[3,5,1,2,4]=>[[.,[.,.]],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0]=>[1,4,5,2,3]=>[.,[[.,[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0]=>[3,1,5,2,4]=>[[.,.],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0]=>[3,4,1,2,5]=>[[.,[.,.]],[.,[.,.]]]
[1,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0]=>[3,4,5,1,2]=>[[.,[.,[.,.]]],[.,.]]
[1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0]=>[1,2,3,5,4]=>[.,[.,[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,0]=>[4,1,2,5,3]=>[[.,.],[.,[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0]=>[1,4,2,5,3]=>[.,[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0]=>[3,1,2,5,4]=>[[.,.],[.,[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0]=>[3,4,1,5,2]=>[[.,[.,.]],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0]=>[1,2,4,3,5]=>[.,[.,[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0]=>[3,1,4,2,5]=>[[.,.],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0]=>[1,3,2,4,5]=>[.,[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0]=>[2,1,3,4,5]=>[[.,.],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0]=>[2,5,1,3,4]=>[[.,[.,.]],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0]=>[1,3,5,2,4]=>[.,[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0]=>[2,1,5,3,4]=>[[.,.],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0]=>[2,4,1,3,5]=>[[.,[.,.]],[.,[.,.]]]
[1,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0]=>[2,4,5,1,3]=>[[.,[.,[.,.]]],[.,.]]
[1,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0]=>[1,2,4,5,3]=>[.,[.,[[.,[.,.]],.]]]
[1,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,0]=>[3,1,4,5,2]=>[[.,.],[[.,[.,.]],.]]
[1,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4]=>[.,[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0]=>[2,1,3,5,4]=>[[.,.],[.,[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0]=>[2,4,1,5,3]=>[[.,[.,.]],[[.,.],.]]
[1,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,5]=>[.,[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,5]=>[[.,.],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0]=>[2,3,1,4,5]=>[[.,[.,.]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0]=>[2,3,5,1,4]=>[[.,[.,[.,.]]],[.,.]]
[1,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0]=>[1,3,4,5,2]=>[.,[[.,[.,[.,.]]],.]]
[1,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0]=>[2,1,4,5,3]=>[[.,.],[[.,[.,.]],.]]
[1,1,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0]=>[2,3,1,5,4]=>[[.,[.,.]],[[.,.],.]]
[1,1,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0]=>[2,3,4,1,5]=>[[.,[.,[.,.]]],[.,.]]
[1,1,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,1]=>[[.,[.,[.,[.,.]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,2,3,4,5,6]=>[.,[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0]=>[6,1,2,3,4,5]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,6,2,3,4,5]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0]=>[5,1,2,3,4,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0]=>[5,6,1,2,3,4]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,2,6,3,4,5]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0]=>[5,1,6,2,3,4]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,5,2,3,4,6]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0]=>[4,1,2,3,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0]=>[4,6,1,2,3,5]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,5,6,2,3,4]=>[.,[[.,[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0]=>[4,1,6,2,3,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0]=>[4,5,1,2,3,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,1,2,3]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,2,3,6,4,5]=>[.,[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0]=>[5,1,2,6,3,4]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,5,2,6,3,4]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0]=>[4,1,2,6,3,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0]=>[4,5,1,6,2,3]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,2,5,3,4,6]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0]=>[4,1,5,2,3,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,4,2,3,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0]=>[3,1,2,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0]=>[3,6,1,2,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,4,6,2,3,5]=>[.,[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0]=>[3,1,6,2,4,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0]=>[3,5,1,2,4,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0]=>[3,5,6,1,2,4]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,2,5,6,3,4]=>[.,[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0]=>[4,1,5,6,2,3]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,4,2,6,3,5]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0]=>[3,1,2,6,4,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0]=>[3,5,1,6,2,4]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,4,5,2,3,6]=>[.,[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0]=>[3,1,5,2,4,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,1,2,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,6,1,2,5]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,4,5,6,2,3]=>[.,[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0]=>[3,1,5,6,2,4]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,1,6,2,5]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,1,2,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,1,2]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,2,3,4,6,5]=>[.,[.,[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0]=>[5,1,2,3,6,4]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,5,2,3,6,4]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0]=>[4,1,2,3,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0]=>[4,5,1,2,6,3]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,2,5,3,6,4]=>[.,[.,[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0]=>[4,1,5,2,6,3]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,4,2,3,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0]=>[3,1,2,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0]=>[3,5,1,2,6,4]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,4,5,2,6,3]=>[.,[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0]=>[3,1,5,2,6,4]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,1,2,6,5]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,1,6,2]=>[[.,[.,[.,.]]],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,2,3,5,4,6]=>[.,[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0]=>[4,1,2,5,3,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,4,2,5,3,6]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0]=>[3,1,2,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,1,5,2,6]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,2,4,3,5,6]=>[.,[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0]=>[3,1,4,2,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0]=>[1,3,2,4,5,6]=>[.,[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0]=>[2,1,3,4,5,6]=>[[.,.],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0]=>[2,6,1,3,4,5]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0]=>[1,3,6,2,4,5]=>[.,[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0]=>[2,1,6,3,4,5]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0]=>[2,5,1,3,4,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0]=>[2,5,6,1,3,4]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,2,4,6,3,5]=>[.,[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0]=>[3,1,4,6,2,5]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0]=>[1,3,2,6,4,5]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0]=>[2,1,3,6,4,5]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0]=>[2,5,1,6,3,4]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0]=>[1,3,5,2,4,6]=>[.,[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0]=>[2,1,5,3,4,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0]=>[2,4,1,3,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0]=>[2,4,6,1,3,5]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0]=>[1,3,5,6,2,4]=>[.,[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,5,6,3,4]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0]=>[2,4,1,6,3,5]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0]=>[2,4,5,1,3,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,1,3]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,2,3,5,6,4]=>[.,[.,[.,[[.,[.,.]],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0]=>[4,1,2,5,6,3]=>[[.,.],[.,[[.,[.,.]],.]]]
[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,4,2,5,6,3]=>[.,[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0]=>[3,1,2,5,6,4]=>[[.,.],[.,[[.,[.,.]],.]]]
[1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,1,5,6,2]=>[[.,[.,.]],[[.,[.,.]],.]]
[1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0]=>[1,2,4,3,6,5]=>[.,[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0]=>[3,1,4,2,6,5]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0]=>[1,3,2,4,6,5]=>[.,[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0]=>[2,1,3,4,6,5]=>[[.,.],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0]=>[2,5,1,3,6,4]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0]=>[1,3,5,2,6,4]=>[.,[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0]=>[2,1,5,3,6,4]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0]=>[2,4,1,3,6,5]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0]=>[2,4,5,1,6,3]=>[[.,[.,[.,.]]],[[.,.],.]]
[1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0]=>[1,2,4,5,3,6]=>[.,[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0]=>[3,1,4,5,2,6]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0]=>[1,3,2,5,4,6]=>[.,[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0]=>[2,1,3,5,4,6]=>[[.,.],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0]=>[2,4,1,5,3,6]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0]=>[1,3,4,2,5,6]=>[.,[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0]=>[2,1,4,3,5,6]=>[[.,.],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,1,4,5,6]=>[[.,[.,.]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,6,1,4,5]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0]=>[1,3,4,6,2,5]=>[.,[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0]=>[2,1,4,6,3,5]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,1,6,4,5]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,5,1,4,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,5,6,1,4]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0]=>[1,2,4,5,6,3]=>[.,[.,[[.,[.,[.,.]]],.]]]
[1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0]=>[3,1,4,5,6,2]=>[[.,.],[[.,[.,[.,.]]],.]]
[1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0]=>[1,3,2,5,6,4]=>[.,[[.,.],[[.,[.,.]],.]]]
[1,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0]=>[2,1,3,5,6,4]=>[[.,.],[.,[[.,[.,.]],.]]]
[1,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0]=>[2,4,1,5,6,3]=>[[.,[.,.]],[[.,[.,.]],.]]
[1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0]=>[1,3,4,2,6,5]=>[.,[[.,[.,.]],[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5]=>[[.,.],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,1,4,6,5]=>[[.,[.,.]],[.,[[.,.],.]]]
[1,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,5,1,6,4]=>[[.,[.,[.,.]]],[[.,.],.]]
[1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,2,6]=>[.,[[.,[.,[.,.]]],[.,.]]]
[1,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0]=>[2,1,4,5,3,6]=>[[.,.],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,1,5,4,6]=>[[.,[.,.]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,1,5,6]=>[[.,[.,[.,.]]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,6,1,5]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,2]=>[.,[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0]=>[2,1,4,5,6,3]=>[[.,.],[[.,[.,[.,.]]],.]]
[1,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,1,5,6,4]=>[[.,[.,.]],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,1,6,5]=>[[.,[.,[.,.]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,1,6]=>[[.,[.,[.,[.,.]]]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,1]=>[[.,[.,[.,[.,[.,.]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7]=>[.,[.,[.,[.,[.,[.,[.,.]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[7,1,2,3,4,5,6]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,7,2,3,4,5,6]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[6,1,2,3,4,5,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[6,7,1,2,3,4,5]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,2,7,3,4,5,6]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[6,1,7,2,3,4,5]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,6,2,3,4,5,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[5,1,2,3,4,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[5,7,1,2,3,4,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,6,7,2,3,4,5]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[5,1,7,2,3,4,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[5,6,1,2,3,4,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,1,2,3,4]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,2,3,7,4,5,6]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[6,1,2,7,3,4,5]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,6,2,7,3,4,5]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[5,1,2,7,3,4,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[5,6,1,7,2,3,4]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,2,6,3,4,5,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[5,1,6,2,3,4,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,5,2,3,4,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[4,1,2,3,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[4,7,1,2,3,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,5,7,2,3,4,6]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[4,1,7,2,3,5,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[4,6,1,2,3,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[4,6,7,1,2,3,5]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,2,6,7,3,4,5]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[5,1,6,7,2,3,4]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,5,2,7,3,4,6]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[4,1,2,7,3,5,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[4,6,1,7,2,3,5]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,5,6,2,3,4,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[4,1,6,2,3,5,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[4,5,1,2,3,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[4,5,7,1,2,3,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,5,6,7,2,3,4]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,1,6,7,2,3,5]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[4,5,1,7,2,3,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[4,5,6,1,2,3,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[4,5,6,7,1,2,3]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,2,3,4,7,5,6]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[6,1,2,3,7,4,5]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,6,2,3,7,4,5]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[5,1,2,3,7,4,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[5,6,1,2,7,3,4]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,2,6,3,7,4,5]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[5,1,6,2,7,3,4]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,5,2,3,7,4,6]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[4,1,2,3,7,5,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[4,6,1,2,7,3,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,5,6,2,7,3,4]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[4,1,6,2,7,3,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[4,5,1,2,7,3,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[4,5,6,1,7,2,3]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,2,3,6,4,5,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[5,1,2,6,3,4,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,5,2,6,3,4,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[4,1,2,6,3,5,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[4,5,1,6,2,3,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,2,5,3,4,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[4,1,5,2,3,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,4,2,3,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[3,1,2,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[3,7,1,2,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,4,7,2,3,5,6]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[3,1,7,2,4,5,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[3,6,1,2,4,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[3,6,7,1,2,4,5]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,2,5,7,3,4,6]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[4,1,5,7,2,3,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,4,2,7,3,5,6]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[3,1,2,7,4,5,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[3,6,1,7,2,4,5]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,4,6,2,3,5,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[3,1,6,2,4,5,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[3,5,1,2,4,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[3,5,7,1,2,4,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,4,6,7,2,3,5]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[3,1,6,7,2,4,5]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[3,5,1,7,2,4,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[3,5,6,1,2,4,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[3,5,6,7,1,2,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,2,3,6,7,4,5]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]
[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[5,1,2,6,7,3,4]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,5,2,6,7,3,4]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[4,1,2,6,7,3,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[4,5,1,6,7,2,3]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,2,5,3,7,4,6]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[4,1,5,2,7,3,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,4,2,3,7,5,6]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[3,1,2,4,7,5,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[3,6,1,2,7,4,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,4,6,2,7,3,5]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[3,1,6,2,7,4,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[3,5,1,2,7,4,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[3,5,6,1,7,2,4]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,2,5,6,3,4,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[4,1,5,6,2,3,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,4,2,6,3,5,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[3,1,2,6,4,5,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[3,5,1,6,2,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,4,5,2,3,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[3,1,5,2,4,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[3,4,1,2,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[3,4,7,1,2,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,4,5,7,2,3,6]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[3,1,5,7,2,4,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[3,4,1,7,2,5,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[3,4,6,1,2,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[3,4,6,7,1,2,5]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,2,5,6,7,3,4]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]
[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[4,1,5,6,7,2,3]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,4,2,6,7,3,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,1,2,6,7,4,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[3,5,1,6,7,2,4]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,4,5,2,7,3,6]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[3,1,5,2,7,4,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[3,4,1,2,7,5,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[3,4,6,1,7,2,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,6,2,3,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[3,1,5,6,2,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[3,4,1,6,2,5,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[3,4,5,1,2,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[3,4,5,7,1,2,6]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,4,5,6,7,2,3]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[3,1,5,6,7,2,4]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[3,4,1,6,7,2,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[3,4,5,1,7,2,6]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[3,4,5,6,1,2,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,1,2]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,2,3,4,5,7,6]=>[.,[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[6,1,2,3,4,7,5]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,6,2,3,4,7,5]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[5,1,2,3,4,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[5,6,1,2,3,7,4]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,2,6,3,4,7,5]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[5,1,6,2,3,7,4]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,5,2,3,4,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[4,1,2,3,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[4,6,1,2,3,7,5]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,5,6,2,3,7,4]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[4,1,6,2,3,7,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,5,1,2,3,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[4,5,6,1,2,7,3]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,2,3,6,4,7,5]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[5,1,2,6,3,7,4]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,5,2,6,3,7,4]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[4,1,2,6,3,7,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[4,5,1,6,2,7,3]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,2,5,3,4,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[4,1,5,2,3,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,4,2,3,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[3,1,2,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[3,6,1,2,4,7,5]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,4,6,2,3,7,5]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[3,1,6,2,4,7,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[3,5,1,2,4,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[3,5,6,1,2,7,4]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,2,5,6,3,7,4]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[4,1,5,6,2,7,3]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,4,2,6,3,7,5]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[3,1,2,6,4,7,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[3,5,1,6,2,7,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,4,5,2,3,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[3,1,5,2,4,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[3,4,1,2,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[3,4,6,1,2,7,5]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,4,5,6,2,7,3]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[3,1,5,6,2,7,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[3,4,1,6,2,7,5]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[3,4,5,1,2,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[3,4,5,6,1,7,2]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,2,3,4,6,5,7]=>[.,[.,[.,[.,[[.,.],[.,.]]]]]]
[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[5,1,2,3,6,4,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,5,2,3,6,4,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[4,1,2,3,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[4,5,1,2,6,3,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,2,5,3,6,4,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[4,1,5,2,6,3,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,4,2,3,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[3,1,2,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[3,5,1,2,6,4,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,4,5,2,6,3,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[3,1,5,2,6,4,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[3,4,1,2,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[3,4,5,1,6,2,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,2,3,5,4,6,7]=>[.,[.,[.,[[.,.],[.,[.,.]]]]]]
[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[4,1,2,5,3,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,4,2,5,3,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[3,1,2,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,1,0,0,0]=>[3,4,1,5,2,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,2,4,3,5,6,7]=>[.,[.,[[.,.],[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,1,0,0,0,0]=>[3,1,4,2,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,1,0,0,0,0,0]=>[1,3,2,4,5,6,7]=>[.,[[.,.],[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0]=>[2,1,3,4,5,6,7]=>[[.,.],[.,[.,[.,[.,[.,.]]]]]]
[1,1,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,1,0,1,0,0,0,0,0]=>[2,7,1,3,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,1,0,0,0,0]=>[1,3,7,2,4,5,6]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,1,0,0,0,0]=>[2,1,7,3,4,5,6]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,1,0,1,1,0,0,0,0,0]=>[2,6,1,3,4,5,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0]=>[2,6,7,1,3,4,5]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,2,4,7,3,5,6]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,1,0,0,0]=>[3,1,4,7,2,5,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,1,0,0,0]=>[1,3,2,7,4,5,6]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[2,1,3,7,4,5,6]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,1,0,0,0]=>[2,6,1,7,3,4,5]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,3,6,2,4,5,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,1,0,0,0,0]=>[2,1,6,3,4,5,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,1,0,0,0,0,0]=>[2,5,1,3,4,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,1,0,1,0,0,0,0]=>[2,5,7,1,3,4,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,1,0,0,0]=>[1,3,6,7,2,4,5]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,0,0]=>[2,1,6,7,3,4,5]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0]=>[2,5,1,7,3,4,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,1,0,0,0,0]=>[2,5,6,1,3,4,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,1,0,0,0]=>[2,5,6,7,1,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,2,3,5,7,4,6]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[4,1,2,5,7,3,6]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,4,2,5,7,3,6]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,1,0,0]=>[3,1,2,5,7,4,6]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,1,0,0]=>[3,4,1,5,7,2,6]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,2,4,3,7,5,6]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,1,0,0]=>[3,1,4,2,7,5,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,1,0,0]=>[1,3,2,4,7,5,6]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,1,0,0]=>[2,1,3,4,7,5,6]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,0,1,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,1,0,0]=>[2,6,1,3,7,4,5]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,1,0,0]=>[1,3,6,2,7,4,5]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,1,0,0]=>[2,1,6,3,7,4,5]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,1,0,0]=>[2,5,1,3,7,4,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,1,0,0]=>[2,5,6,1,7,3,4]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,2,4,6,3,5,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,1,0,0,0]=>[3,1,4,6,2,5,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,1,0,0,0]=>[1,3,2,6,4,5,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,1,0,0,0]=>[2,1,3,6,4,5,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[2,5,1,6,3,4,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,1,0,0,0,0]=>[1,3,5,2,4,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[2,1,5,3,4,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,1,0,0,0,0,0]=>[2,4,1,3,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,0,1,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,1,0,1,0,0,0,0]=>[2,4,7,1,3,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,1,0,0,0]=>[1,3,5,7,2,4,6]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,0]=>[2,1,5,7,3,4,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,1,0,0,0]=>[2,4,1,7,3,5,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,1,0,0,0,0]=>[2,4,6,1,3,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,1,0,0,0]=>[2,4,6,7,1,3,5]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,2,4,6,7,3,5]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,0,1,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,1,0,0]=>[3,1,4,6,7,2,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[1,3,2,6,7,4,5]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,1,0,0]=>[2,1,3,6,7,4,5]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,1,0,0]=>[2,5,1,6,7,3,4]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,1,0,0]=>[1,3,5,2,7,4,6]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,1,0,0]=>[2,1,5,3,7,4,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0]=>[2,4,1,3,7,5,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,1,0,0]=>[2,4,6,1,7,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,1,0,0,0]=>[1,3,5,6,2,4,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0]=>[2,1,5,6,3,4,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,1,0,0,0]=>[2,4,1,6,3,5,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,0,1,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,1,0,0,0,0]=>[2,4,5,1,3,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,0,1,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,1,0,0,0]=>[2,4,5,7,1,3,6]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,1,0,0]=>[1,3,5,6,7,2,4]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[2,1,5,6,7,3,4]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,0,1,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,1,0,0]=>[2,4,1,6,7,3,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,0,1,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,1,0,0]=>[2,4,5,1,7,3,6]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,0,1,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,1,0,0,0]=>[2,4,5,6,1,3,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0]=>[2,4,5,6,7,1,3]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,2,3,4,6,7,5]=>[.,[.,[.,[.,[[.,[.,.]],.]]]]]
[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[5,1,2,3,6,7,4]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,5,2,3,6,7,4]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[4,1,2,3,6,7,5]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[4,5,1,2,6,7,3]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,2,5,3,6,7,4]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[4,1,5,2,6,7,3]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,4,2,3,6,7,5]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,1,0,0,0,1,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,0,0,0,0,1,0,1,0]=>[3,1,2,4,6,7,5]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,0,0,0,1,1,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,0,1,0,1,0]=>[3,5,1,2,6,7,4]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,4,5,2,6,7,3]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,0,0,0,1,1,1,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,0,1,0,1,0]=>[3,1,5,2,6,7,4]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,1,0,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,0,1,0]=>[3,4,1,2,6,7,5]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,1,0,0,0,1,1,1,1,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,0,1,0,1,0]=>[3,4,5,1,6,7,2]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,2,3,5,4,7,6]=>[.,[.,[.,[[.,.],[[.,.],.]]]]]
[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[4,1,2,5,3,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,1,0,0,1,0]=>[1,4,2,5,3,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,1,2,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,1,0,0,1,0]=>[3,4,1,5,2,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,1,0,0,0,1,0]=>[1,2,4,3,5,7,6]=>[.,[.,[[.,.],[.,[[.,.],.]]]]]
[1,1,1,0,0,1,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,1,0,0,0,1,0]=>[3,1,4,2,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,0]=>[1,3,2,4,5,7,6]=>[.,[[.,.],[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,0,0,0,0,0,1,0]=>[2,1,3,4,5,7,6]=>[[.,.],[.,[.,[.,[[.,.],.]]]]]
[1,1,1,0,0,1,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,1,0,1,0,0,0,0,1,0]=>[2,6,1,3,4,7,5]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,1,0,1,0,0,0,1,0]=>[1,3,6,2,4,7,5]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,0,0,1,0]=>[2,1,6,3,4,7,5]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,1,1,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,0,0,1,0]=>[2,5,1,3,4,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,0,1,0,1,0,0,0,1,0]=>[2,5,6,1,3,7,4]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,1,0,0,1,0]=>[1,2,4,6,3,7,5]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,1,0,0,1,0]=>[3,1,4,6,2,7,5]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,1,0,0,1,0]=>[1,3,2,6,4,7,5]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,1,0,0,1,0]=>[2,1,3,6,4,7,5]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,0,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[2,5,1,6,3,7,4]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,1,0,0,0,1,0]=>[1,3,5,2,4,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,0,0,1,0]=>[2,1,5,3,4,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,0,1,0]=>[2,4,1,3,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,0,1,1,0,0,0,0]=>[1,0,1,1,0,1,1,0,1,0,0,0,1,0]=>[2,4,6,1,3,7,5]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,0]=>[1,3,5,6,2,7,4]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,0,0,1,0]=>[2,1,5,6,3,7,4]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,1,0,0,1,0]=>[2,4,1,6,3,7,5]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,1,0,0,0,1,0]=>[2,4,5,1,3,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,0,0,1,1,1,1,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,0,1,0]=>[2,4,5,6,1,7,3]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,2,3,5,6,4,7]=>[.,[.,[.,[[.,[.,.]],[.,.]]]]]
[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,1,0,0]=>[4,1,2,5,6,3,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,1,0,0]=>[1,4,2,5,6,3,7]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,1,0,0]=>[3,1,2,5,6,4,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,1,0,0]=>[3,4,1,5,6,2,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,0,0]=>[1,2,4,3,6,5,7]=>[.,[.,[[.,.],[[.,.],[.,.]]]]]
[1,1,1,0,1,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,0]=>[3,1,4,2,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,1,0,0]=>[1,3,2,4,6,5,7]=>[.,[[.,.],[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[2,1,3,4,6,5,7]=>[[.,.],[.,[.,[[.,.],[.,.]]]]]
[1,1,1,0,1,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,1,0,0]=>[2,5,1,3,6,4,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,1,0,0]=>[1,3,5,2,6,4,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,1,0,0]=>[2,1,5,3,6,4,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,1,0,0]=>[2,4,1,3,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[2,4,5,1,6,3,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,1,0,0,0]=>[1,2,4,5,3,6,7]=>[.,[.,[[.,[.,.]],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,1,0,0,0]=>[3,1,4,5,2,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,3,2,5,4,6,7]=>[.,[[.,.],[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,1,0,0,0]=>[2,1,3,5,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,1,0,0,0]=>[2,4,1,5,3,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,1,0,0,0,0]=>[1,3,4,2,5,6,7]=>[.,[[.,[.,.]],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,1,0,0,0,0]=>[2,1,4,3,5,6,7]=>[[.,.],[[.,.],[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[2,3,1,4,5,6,7]=>[[.,[.,.]],[.,[.,[.,[.,.]]]]]
[1,1,1,0,1,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[2,3,7,1,4,5,6]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,1,0,0,0]=>[1,3,4,7,2,5,6]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,1,0,0,0]=>[2,1,4,7,3,5,6]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,1,0,0,0]=>[2,3,1,7,4,5,6]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,1,0,0,0,0]=>[2,3,6,1,4,5,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,1,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,1,0,0,0]=>[2,3,6,7,1,4,5]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,1,0,0]=>[1,2,4,5,7,3,6]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,1,0,0]=>[3,1,4,5,7,2,6]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[1,3,2,5,7,4,6]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,1,0,0]=>[2,1,3,5,7,4,6]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,1,0,0]=>[2,4,1,5,7,3,6]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,1,0,0]=>[1,3,4,2,7,5,6]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,0]=>[2,1,4,3,7,5,6]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,1,0,0]=>[2,3,1,4,7,5,6]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,0,1,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,1,0,0]=>[2,3,6,1,7,4,5]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,1,0,0,0]=>[1,3,4,6,2,5,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,1,0,0,0]=>[2,1,4,6,3,5,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,1,0,0,0]=>[2,3,1,6,4,5,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,0,1,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,1,0,0,0,0]=>[2,3,5,1,4,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,0,1,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,1,0,0,0]=>[2,3,5,7,1,4,6]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,1,0,0]=>[1,3,4,6,7,2,5]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,0,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,1,0,0]=>[2,1,4,6,7,3,5]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[2,3,1,6,7,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,0,1,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,1,0,0]=>[2,3,5,1,7,4,6]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,0,1,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,1,0,0,0]=>[2,3,5,6,1,4,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,0,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,1,0,0]=>[2,3,5,6,7,1,4]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,1,1,1,0,0,0,0,1,0,1,0,1,0]=>[1,2,3,5,6,7,4]=>[.,[.,[.,[[.,[.,[.,.]]],.]]]]
[1,1,1,1,0,0,0,0,1,0,1,1,0,0]=>[1,1,1,0,1,0,0,0,1,0,1,0,1,0]=>[4,1,2,5,6,7,3]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,1,0,0,0,0,1,1,0,0,1,0]=>[1,1,1,0,0,1,0,0,1,0,1,0,1,0]=>[1,4,2,5,6,7,3]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,1,1,0,0,0,0,1,1,0,1,0,0]=>[1,1,0,1,1,0,0,0,1,0,1,0,1,0]=>[3,1,2,5,6,7,4]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,1,0,0,0,0,1,1,1,0,0,0]=>[1,1,0,1,0,1,0,0,1,0,1,0,1,0]=>[3,4,1,5,6,7,2]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,1,0,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,0,1,0]=>[1,2,4,3,6,7,5]=>[.,[.,[[.,.],[[.,[.,.]],.]]]]
[1,1,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,0,1,0]=>[3,1,4,2,6,7,5]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,1,1,0,0,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,0,0,0,1,0,1,0]=>[1,3,2,4,6,7,5]=>[.,[[.,.],[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,0,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,1,3,4,6,7,5]=>[[.,.],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,1,0,0,0,1,0,1,1,0,0,0]=>[1,0,1,1,1,0,1,0,0,0,1,0,1,0]=>[2,5,1,3,6,7,4]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,1,1,0,0,0,1,1,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,0,1,0,1,0]=>[1,3,5,2,6,7,4]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,1,0,0,0,1,1,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,0,1,0,1,0]=>[2,1,5,3,6,7,4]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,1,1,0,0,0,1,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,0,0,0,1,0,1,0]=>[2,4,1,3,6,7,5]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,1,1,0,0,0,1,1,1,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,4,5,1,6,7,3]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,1,0,0,1,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,1,0,0,1,0]=>[1,2,4,5,3,7,6]=>[.,[.,[[.,[.,.]],[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,1,0,0,1,0]=>[3,1,4,5,2,7,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,1,1,0,0,1,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[1,3,2,5,4,7,6]=>[.,[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,1,0,0,1,0]=>[2,1,3,5,4,7,6]=>[[.,.],[.,[[.,.],[[.,.],.]]]]
[1,1,1,1,0,0,1,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,1,0,0,1,0]=>[2,4,1,5,3,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,1,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,1,0,0,0,1,0]=>[1,3,4,2,5,7,6]=>[.,[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,0,1,0]=>[2,1,4,3,5,7,6]=>[[.,.],[[.,.],[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0]=>[2,3,1,4,5,7,6]=>[[.,[.,.]],[.,[.,[[.,.],.]]]]
[1,1,1,1,0,0,1,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[2,3,6,1,4,7,5]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,1,0,0,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,1,0,0,1,0]=>[1,3,4,6,2,7,5]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,1,0,0,1,0]=>[2,1,4,6,3,7,5]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,1,1,0,0,1,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,1,0,0,1,0]=>[2,3,1,6,4,7,5]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,1,0,0,1,1,0,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,1,0,0,0,1,0]=>[2,3,5,1,4,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,1,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0]=>[2,3,5,6,1,7,4]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,0,1,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,1,0,0]=>[1,2,4,5,6,3,7]=>[.,[.,[[.,[.,[.,.]]],[.,.]]]]
[1,1,1,1,0,1,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,1,0,0]=>[3,1,4,5,6,2,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,1,0,1,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,2,5,6,4,7]=>[.,[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,1,0,0]=>[2,1,3,5,6,4,7]=>[[.,.],[.,[[.,[.,.]],[.,.]]]]
[1,1,1,1,0,1,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,1,0,0]=>[2,4,1,5,6,3,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,1,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,1,0,0]=>[1,3,4,2,6,5,7]=>[.,[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0]=>[2,1,4,3,6,5,7]=>[[.,.],[[.,.],[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,1,0,0]=>[2,3,1,4,6,5,7]=>[[.,[.,.]],[.,[[.,.],[.,.]]]]
[1,1,1,1,0,1,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,1,0,0]=>[2,3,5,1,6,4,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,1,0,0,0]=>[1,3,4,5,2,6,7]=>[.,[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,1,0,0,0]=>[2,1,4,5,3,6,7]=>[[.,.],[[.,[.,.]],[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,1,0,0,0]=>[2,3,1,5,4,6,7]=>[[.,[.,.]],[[.,.],[.,[.,.]]]]
[1,1,1,1,0,1,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,1,0,0,0,0]=>[2,3,4,1,5,6,7]=>[[.,[.,[.,.]]],[.,[.,[.,.]]]]
[1,1,1,1,0,1,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,1,0,0,0]=>[2,3,4,7,1,5,6]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,0,1,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,1,0,0]=>[1,3,4,5,7,2,6]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,1,0,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,1,0,0]=>[2,1,4,5,7,3,6]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,1,0,1,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,1,0,0]=>[2,3,1,5,7,4,6]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,1,0,1,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[2,3,4,1,7,5,6]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,0,1,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,1,0,0,0]=>[2,3,4,6,1,5,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,0,1,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,1,0,0]=>[2,3,4,6,7,1,5]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,0,0,0,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,0,1,0,1,0,1,0]=>[1,2,4,5,6,7,3]=>[.,[.,[[.,[.,[.,[.,.]]]],.]]]
[1,1,1,1,1,0,0,0,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,0,1,0,1,0,1,0]=>[3,1,4,5,6,7,2]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,1,0,0,0,0,1,0,0,1,0]=>[1,1,0,0,1,1,0,0,1,0,1,0,1,0]=>[1,3,2,5,6,7,4]=>[.,[[.,.],[[.,[.,[.,.]]],.]]]
[1,1,1,1,1,0,0,0,0,1,0,1,0,0]=>[1,0,1,1,1,0,0,0,1,0,1,0,1,0]=>[2,1,3,5,6,7,4]=>[[.,.],[.,[[.,[.,[.,.]]],.]]]
[1,1,1,1,1,0,0,0,0,1,1,0,0,0]=>[1,0,1,1,0,1,0,0,1,0,1,0,1,0]=>[2,4,1,5,6,7,3]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,1,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,0]=>[1,3,4,2,6,7,5]=>[.,[[.,[.,.]],[[.,[.,.]],.]]]
[1,1,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,0,1,0]=>[2,1,4,3,6,7,5]=>[[.,.],[[.,.],[[.,[.,.]],.]]]
[1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,0,0,0,1,0,1,0]=>[2,3,1,4,6,7,5]=>[[.,[.,.]],[.,[[.,[.,.]],.]]]
[1,1,1,1,1,0,0,0,1,1,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,0,1,0,1,0]=>[2,3,5,1,6,7,4]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,1,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,1,0,0,1,0]=>[1,3,4,5,2,7,6]=>[.,[[.,[.,[.,.]]],[[.,.],.]]]
[1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,1,0,0,1,0]=>[2,1,4,5,3,7,6]=>[[.,.],[[.,[.,.]],[[.,.],.]]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,1,0,0,1,0]=>[2,3,1,5,4,7,6]=>[[.,[.,.]],[[.,.],[[.,.],.]]]
[1,1,1,1,1,0,0,1,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,1,0,0,0,1,0]=>[2,3,4,1,5,7,6]=>[[.,[.,[.,.]]],[.,[[.,.],.]]]
[1,1,1,1,1,0,0,1,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,1,0,0,1,0]=>[2,3,4,6,1,7,5]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,1,0,0]=>[1,3,4,5,6,2,7]=>[.,[[.,[.,[.,[.,.]]]],[.,.]]]
[1,1,1,1,1,0,1,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,1,0,0]=>[2,1,4,5,6,3,7]=>[[.,.],[[.,[.,[.,.]]],[.,.]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[2,3,1,5,6,4,7]=>[[.,[.,.]],[[.,[.,.]],[.,.]]]
[1,1,1,1,1,0,1,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,1,0,0]=>[2,3,4,1,6,5,7]=>[[.,[.,[.,.]]],[[.,.],[.,.]]]
[1,1,1,1,1,0,1,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[2,3,4,5,1,6,7]=>[[.,[.,[.,[.,.]]]],[.,[.,.]]]
[1,1,1,1,1,0,1,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,1,0,0]=>[2,3,4,5,7,1,6]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[1,1,0,0,1,0,1,0,1,0,1,0,1,0]=>[1,3,4,5,6,7,2]=>[.,[[.,[.,[.,[.,[.,.]]]]],.]]
[1,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[1,0,1,1,0,0,1,0,1,0,1,0,1,0]=>[2,1,4,5,6,7,3]=>[[.,.],[[.,[.,[.,[.,.]]]],.]]
[1,1,1,1,1,1,0,0,0,0,1,0,0,0]=>[1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,1,5,6,7,4]=>[[.,[.,.]],[[.,[.,[.,.]]],.]]
[1,1,1,1,1,1,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0]=>[2,3,4,1,6,7,5]=>[[.,[.,[.,.]]],[[.,[.,.]],.]]
[1,1,1,1,1,1,0,0,1,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,1,0,0,1,0]=>[2,3,4,5,1,7,6]=>[[.,[.,[.,[.,.]]]],[[.,.],.]]
[1,1,1,1,1,1,0,1,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,1,0,0]=>[2,3,4,5,6,1,7]=>[[.,[.,[.,[.,[.,.]]]]],[.,.]]
[1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[2,3,4,5,6,7,1]=>[[.,[.,[.,[.,[.,[.,.]]]]]],.]
[1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]=>[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]=>[1,2,3,4,5,6,7,8]=>[.,[.,[.,[.,[.,[.,[.,[.,.]]]]]]]]
[1,0,1,0,1,0,1,0,1,0,1,1,1,0,0,0]=>[1,1,1,1,1,1,0,1,0,1,0,0,0,0,0,0]=>[7,8,1,2,3,4,5,6]=>[[.,[.,.]],[.,[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,0,1,1,1,0,0,1,0,0]=>[1,1,1,1,1,0,1,1,0,0,1,0,0,0,0,0]=>[6,1,8,2,3,4,5,7]=>[[.,.],[[.,.],[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,1,0,0,1,0,1,0,0]=>[1,1,1,1,0,1,1,1,0,0,0,1,0,0,0,0]=>[5,1,2,8,3,4,6,7]=>[[.,.],[.,[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,1,0,1,0,0,0,1,0]=>[1,1,1,1,1,0,0,1,0,1,1,0,0,0,0,0]=>[1,6,7,2,3,4,5,8]=>[.,[[.,[.,.]],[.,[.,[.,[.,.]]]]]]
[1,0,1,0,1,0,1,1,1,1,1,0,0,0,0,0]=>[1,1,1,1,0,1,0,1,0,1,0,1,0,0,0,0]=>[5,6,7,8,1,2,3,4]=>[[.,[.,[.,[.,.]]]],[.,[.,[.,.]]]]
[1,0,1,0,1,1,1,0,0,1,0,1,0,1,0,0]=>[1,1,1,0,1,1,1,1,0,0,0,0,1,0,0,0]=>[4,1,2,3,8,5,6,7]=>[[.,.],[.,[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,0,1,1,1,0,0,1,1,1,0,0,0,0]=>[1,1,1,0,1,1,0,1,0,1,0,0,1,0,0,0]=>[4,6,7,1,8,2,3,5]=>[[.,[.,[.,.]]],[[.,.],[.,[.,.]]]]
[1,0,1,0,1,1,1,0,1,0,0,1,0,0,1,0]=>[1,1,1,1,0,0,1,1,0,0,1,1,0,0,0,0]=>[1,5,2,7,3,4,6,8]=>[.,[[.,.],[[.,.],[.,[.,[.,.]]]]]]
[1,0,1,0,1,1,1,1,1,0,0,0,1,0,0,0]=>[1,1,1,0,1,0,1,1,0,0,1,0,1,0,0,0]=>[4,5,1,7,8,2,3,6]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,0,0,1,1,1,0,1,1,0,0,0,0]=>[1,1,1,0,1,0,1,1,0,1,0,0,0,1,0,0]=>[4,5,7,1,2,8,3,6]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,0,1,1,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,1,0,1,1,1,0,1,0,0,1,0,1,0,0,0]=>[3,6,1,7,8,2,4,5]=>[[.,[.,.]],[[.,[.,.]],[.,[.,.]]]]
[1,0,1,1,1,0,0,1,0,1,0,1,0,1,0,0]=>[1,1,0,1,1,1,1,1,0,0,0,0,0,1,0,0]=>[3,1,2,4,5,8,6,7]=>[[.,.],[.,[.,[.,[[.,.],[.,.]]]]]]
[1,0,1,1,1,0,0,1,0,1,1,1,0,0,0,0]=>[1,1,0,1,1,1,0,1,0,1,0,0,0,1,0,0]=>[3,6,7,1,2,8,4,5]=>[[.,[.,[.,.]]],[.,[[.,.],[.,.]]]]
[1,0,1,1,1,0,0,1,1,1,0,0,1,0,0,0]=>[1,1,0,1,1,0,1,1,0,0,1,0,0,1,0,0]=>[3,5,1,7,2,8,4,6]=>[[.,[.,.]],[[.,.],[[.,.],[.,.]]]]
[1,0,1,1,1,0,1,0,0,1,0,1,0,0,1,0]=>[1,1,1,0,0,1,1,1,0,0,0,1,1,0,0,0]=>[1,4,2,3,7,5,6,8]=>[.,[[.,.],[.,[[.,.],[.,[.,.]]]]]]
[1,0,1,1,1,0,1,0,1,0,0,0,1,0,1,0]=>[1,1,1,1,0,0,0,1,0,1,1,1,0,0,0,0]=>[1,2,5,6,3,4,7,8]=>[.,[.,[[.,[.,.]],[.,[.,[.,.]]]]]]
[1,0,1,1,1,0,1,1,0,0,0,0,1,1,0,0]=>[1,1,1,0,1,0,0,1,0,1,1,0,1,0,0,0]=>[4,1,5,6,8,2,3,7]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,0,1,1,1,1,1,0,0,0,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,1,0,0,0,1,0,1,0,0]=>[3,4,1,2,7,8,5,6]=>[[.,[.,.]],[.,[[.,[.,.]],[.,.]]]]
[1,0,1,1,1,1,1,0,0,1,0,0,0,1,0,0]=>[1,1,0,1,1,0,0,1,0,1,1,0,0,1,0,0]=>[3,1,5,6,2,8,4,7]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,0,1,1,1,1,1,0,1,0,0,0,0,0,1,0]=>[1,1,1,0,0,1,0,1,0,1,0,1,1,0,0,0]=>[1,4,5,6,7,2,3,8]=>[.,[[.,[.,[.,[.,.]]]],[.,[.,.]]]]
[1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]=>[1,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0]=>[3,4,5,6,7,8,1,2]=>[[.,[.,[.,[.,[.,[.,.]]]]]],[.,.]]
[1,1,0,0,1,0,1,1,1,1,0,1,0,0,0,0]=>[1,1,1,0,1,0,1,0,1,1,0,0,0,0,1,0]=>[4,5,6,1,2,3,8,7]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,0,0,1,1,1,0,1,0,0,1,1,0,0,0]=>[1,1,0,1,1,0,1,0,0,1,1,0,0,0,1,0]=>[3,5,1,6,2,4,8,7]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,0,1,0,1,1,1,1,0,0,0,0,1,0,0]=>[1,0,1,1,1,1,0,0,1,0,1,0,1,0,0,0]=>[2,1,6,7,8,3,4,5]=>[[.,.],[[.,[.,[.,.]]],[.,[.,.]]]]
[1,1,0,1,1,1,0,0,1,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,1,0,1,0,0,1,0,0]=>[2,1,5,7,3,8,4,6]=>[[.,.],[[.,[.,.]],[[.,.],[.,.]]]]
[1,1,1,0,0,1,0,0,1,1,1,0,1,0,0,0]=>[1,1,0,1,0,1,1,0,0,0,1,1,0,0,1,0]=>[3,4,1,2,6,5,8,7]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,0,1,0,1,0,1,0,1,0,0]=>[1,0,1,1,1,1,1,1,0,0,0,0,0,0,1,0]=>[2,1,3,4,5,6,8,7]=>[[.,.],[.,[.,[.,[.,[[.,.],.]]]]]]
[1,1,1,0,0,1,0,1,0,1,1,1,0,0,0,0]=>[1,0,1,1,1,1,0,1,0,1,0,0,0,0,1,0]=>[2,6,7,1,3,4,8,5]=>[[.,[.,[.,.]]],[.,[.,[[.,.],.]]]]
[1,1,1,0,0,1,0,1,1,1,0,0,1,0,0,0]=>[1,0,1,1,1,0,1,1,0,0,1,0,0,0,1,0]=>[2,5,1,7,3,4,8,6]=>[[.,[.,.]],[[.,.],[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0]=>[1,0,1,1,0,1,1,1,0,0,0,1,0,0,1,0]=>[2,4,1,3,7,5,8,6]=>[[.,[.,.]],[.,[[.,.],[[.,.],.]]]]
[1,1,1,0,0,1,1,1,0,1,0,0,0,1,0,0]=>[1,0,1,1,1,0,0,1,0,1,1,0,0,0,1,0]=>[2,1,5,6,3,4,8,7]=>[[.,.],[[.,[.,.]],[.,[[.,.],.]]]]
[1,1,1,0,0,1,1,1,1,1,0,0,0,0,0,0]=>[1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0]=>[2,4,5,6,7,1,8,3]=>[[.,[.,[.,[.,[.,.]]]]],[[.,.],.]]
[1,1,1,0,1,0,0,1,0,1,0,1,0,0,1,0]=>[1,1,0,0,1,1,1,1,0,0,0,0,1,1,0,0]=>[1,3,2,4,5,7,6,8]=>[.,[[.,.],[.,[.,[[.,.],[.,.]]]]]]
[1,1,1,0,1,0,0,1,1,1,0,0,0,0,1,0]=>[1,1,0,0,1,1,0,1,0,1,0,0,1,1,0,0]=>[1,3,5,6,2,7,4,8]=>[.,[[.,[.,[.,.]]],[[.,.],[.,.]]]]
[1,1,1,0,1,0,1,0,0,1,0,0,1,0,1,0]=>[1,1,1,0,0,0,1,1,0,0,1,1,1,0,0,0]=>[1,2,4,3,6,5,7,8]=>[.,[.,[[.,.],[[.,.],[.,[.,.]]]]]]
[1,1,1,0,1,1,0,0,0,1,0,0,1,1,0,0]=>[1,1,0,1,0,0,1,1,0,0,1,1,0,1,0,0]=>[3,1,4,2,6,8,5,7]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,0,1,1,1,0,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,1,0,0,1,0,1,0,0]=>[2,1,4,3,7,8,5,6]=>[[.,.],[[.,.],[[.,[.,.]],[.,.]]]]
[1,1,1,1,1,0,0,0,1,0,1,0,1,0,0,0]=>[1,0,1,0,1,1,1,1,0,0,0,0,1,0,1,0]=>[2,3,1,4,5,7,8,6]=>[[.,[.,.]],[.,[.,[[.,[.,.]],.]]]]
[1,1,1,1,1,0,0,0,1,1,1,0,0,0,0,0]=>[1,0,1,0,1,1,0,1,0,1,0,0,1,0,1,0]=>[2,3,5,6,1,7,8,4]=>[[.,[.,[.,[.,.]]]],[[.,[.,.]],.]]
[1,1,1,1,1,0,0,1,0,0,1,0,0,1,0,0]=>[1,0,1,1,0,0,1,1,0,0,1,1,0,0,1,0]=>[2,1,4,3,6,5,8,7]=>[[.,.],[[.,.],[[.,.],[[.,.],.]]]]
[1,1,1,1,1,0,1,0,0,0,1,0,0,0,1,0]=>[1,1,0,0,1,0,1,1,0,0,1,0,1,1,0,0]=>[1,3,4,2,6,7,5,8]=>[.,[[.,[.,.]],[[.,[.,.]],[.,.]]]]
[1,1,1,1,1,1,1,0,0,0,0,1,0,0,0,0]=>[1,0,1,0,1,0,1,1,0,0,1,0,1,0,1,0]=>[2,3,4,1,6,7,8,5]=>[[.,[.,[.,.]]],[[.,[.,[.,.]]],.]]
Map
decomposition reverse
Description
This map is recursively defined as follows.
The unique empty path of semilength $0$ is sent to itself.
Let $D$ be a Dyck path of semilength $n > 0$ and decompose it into $1 D_1 0 D_2$ with Dyck paths $D_1, D_2$ of respective semilengths $n_1$ and $n_2$ such that $n_1$ is minimal. One then has $n_1+n_2 = n-1$.
Now let $\tilde D_1$ and $\tilde D_2$ be the recursively defined respective images of $D_1$ and $D_2$ under this map. The image of $D$ is then defined as $1 \tilde D_2 0 \tilde D_1$.
The unique empty path of semilength $0$ is sent to itself.
Let $D$ be a Dyck path of semilength $n > 0$ and decompose it into $1 D_1 0 D_2$ with Dyck paths $D_1, D_2$ of respective semilengths $n_1$ and $n_2$ such that $n_1$ is minimal. One then has $n_1+n_2 = n-1$.
Now let $\tilde D_1$ and $\tilde D_2$ be the recursively defined respective images of $D_1$ and $D_2$ under this map. The image of $D$ is then defined as $1 \tilde D_2 0 \tilde D_1$.
Map
to 321-avoiding permutation (Billey-Jockusch-Stanley)
Description
The Billey-Jockusch-Stanley bijection to 321-avoiding permutations.
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
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